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This is PART 31: Centers X(60001) - X(62000)

PART 1: Introduction and Centers X(1) - X(1000) PART 2: Centers X(1001) - X(3000) PART 3: Centers X(3001) - X(5000)
PART 4: Centers X(5001) - X(7000) PART 5: Centers X(7001) - X(10000) PART 6: Centers X(10001) - X(12000)
PART 7: Centers X(12001) - X(14000) PART 8: Centers X(14001) - X(16000) PART 9: Centers X(16001) - X(18000)
PART 10: Centers X(18001) - X(20000) PART 11: Centers X(20001) - X(22000) PART 12: Centers X(22001) - X(24000)
PART 13: Centers X(24001) - X(26000) PART 14: Centers X(26001) - X(28000) PART 15: Centers X(28001) - X(30000)
PART 16: Centers X(30001) - X(32000) PART 17: Centers X(32001) - X(34000) PART 18: Centers X(34001) - X(36000)
PART 19: Centers X(36001) - X(38000) PART 20: Centers X(38001) - X(40000) PART 21: Centers X(40001) - X(42000)
PART 22: Centers X(42001) - X(44000) PART 23: Centers X(44001) - X(46000) PART 24: Centers X(46001) - X(48000)
PART 25: Centers X(48001) - X(50000) PART 26: Centers X(50001) - X(52000) PART 27: Centers X(52001) - X(54000)
PART 28: Centers X(54001) - X(56000) PART 29: Centers X(56001) - X(58000) PART 30: Centers X(58001) - X(60000)
PART 31: Centers X(60001) - X(62000) PART 32: Centers X(62001) - X(64000) PART 33: Centers X(64001) - X(66000)
PART 34: Centers X(66001) - X(68000) PART 35: Centers X(68001) - X(70000) PART 36: Centers X(70001) - X(72000)

X(60001) = X(2)X(1897)∩X(33)X(650)

Barycentrics    a^2*(a - b - c)*(a^2 + b^2 - c^2)*(a*b - b^2 + a*c - c^2)*(a^2 - b^2 + c^2)*(a^3 - a^2*b - a*b^2 + b^3 + a*c^2 + b*c^2 - 2*c^3)*(a^3 + a*b^2 - 2*b^3 - a^2*c + b^2*c - a*c^2 + c^3) : :

X(60001) lies on the cubic K555 and these lines: {2, 1897}, {25, 40116}, {33, 650}, {103, 1473}, {607, 2115}, {677, 1993}, {949, 2338}, {1252, 1260}, {19354, 40141}, {42071, 52213}, {56640, 59195}, {57518, 57928}

X(60001) = X(i)-isoconjugate of X(j) for these (i,j): {77, 56639}, {905, 56786}, {1456, 31637}, {1462, 26006}, {1814, 43035}, {7177, 56900}, {23696, 23973}, {36146, 39470}
X(60001) = X(i)-Dao conjugate of X(j) for these (i,j): {926, 47422}, {39014, 39470}, {45250, 348}
X(60001) = cevapoint of X(926) and X(47422)
X(60001) = barycentric product X(i)*X(j) for these {i,j}: {1861, 2338}, {2340, 52781}, {3693, 36122}, {7046, 52213}, {7071, 56668}, {15742, 56787}, {40116, 50333}
X(60001) = barycentric quotient X(i)/X(j) for these {i,j}: {607, 56639}, {926, 39470}, {2338, 31637}, {2340, 26006}, {2356, 43035}, {7071, 56900}, {8750, 56786}, {36122, 34018}, {37908, 14953}, {39014, 47422}, {40116, 927}, {42071, 39063}, {52213, 7056}, {56787, 1565}

X(60002) = X(2)X(112)∩X(6)X(41511)

Barycentrics    a^2*(a^4 - b^4 + b^2*c^2 - c^4)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 + 2*a^2*b^2*c^2 - a^2*c^4 - b^2*c^4)*(a^6 - a^2*b^4 - a^4*c^2 + 2*a^2*b^2*c^2 - b^4*c^2 - a^2*c^4 + c^6) : :

X(60002) lies on the cubics K283 and K555 and these lines: {2, 112}, {6, 41511}, {22, 250}, {25, 10423}, {251, 4580}, {1177, 5012}, {1993, 36823}, {1995, 10422}, {9979, 46340}, {37804, 52630}, {40856, 57496}, {57486, 57490}

X(60002) = isotomic conjugate of X(57476)
X(60002) = polar conjugate of X(39269)
X(60002) = X(i)-isoconjugate of X(j) for these (i,j): {31, 57476}, {48, 39269}, {67, 18669}, {858, 2157}, {3455, 20884}
X(60002) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 57476}, {187, 5181}, {1249, 39269}, {5099, 47138}, {40583, 858}
X(60002) = cevapoint of X(i) and X(j) for these (i,j): {23, 36415}, {6593, 10317}
X(60002) = trilinear pole of line {9517, 18374}
X(60002) = barycentric product X(i)*X(j) for these {i,j}: {23, 2373}, {316, 1177}, {7664, 10422}, {18374, 46140}, {18876, 37765}, {37801, 52513}, {51823, 57481}
X(60002) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 57476}, {4, 39269}, {23, 858}, {316, 1236}, {1177, 67}, {2373, 18019}, {2492, 47138}, {6593, 5181}, {8744, 5523}, {10317, 14961}, {10422, 10415}, {10423, 935}, {10510, 19510}, {12824, 12827}, {14246, 59422}, {16568, 20884}, {18374, 2393}, {18876, 34897}, {37801, 52512}, {40949, 15116}, {42659, 42665}, {51823, 57496}, {52142, 57485}
X(60002) = {X(2),X(51823)}-harmonic conjugate of X(2373)

X(60003) = X(11)X(244)∩X(100)X(6555)

Barycentrics    (3*a - b - c)*(b - c)^2*(3*a^3 - a^2*b - 3*a*b^2 + b^3 - a^2*c - 2*a*b*c + 3*b^2*c - 3*a*c^2 + 3*b*c^2 + c^3) : :

X(60003) lies on the Mandart circle and these lines: {11, 244}, {100, 6555}, {952, 52116}, {3738, 52117}, {3887, 52115}, {14872, 52111}, {15313, 58893}

X(60003) = X(189)-Ceva conjugate of X(4521)
X(60003) = barycentric product X(4534)*X(53997)

X(60004) = X(11)X(522)∩X(513)X(52117)

Barycentrics    (a - b - c)*(2*a - b - c)*(b - c)^2*(2*a^5 - a^4*b - 4*a^3*b^2 + 2*a^2*b^3 + 2*a*b^4 - b^5 - a^4*c + 4*a^3*b*c + 2*a^2*b^2*c - 4*a*b^3*c - b^4*c - 4*a^3*c^2 + 2*a^2*b*c^2 + 2*b^3*c^2 + 2*a^2*c^3 - 4*a*b*c^3 + 2*b^2*c^3 + 2*a*c^4 - b*c^4 - c^5) : :

X(60004) lies on the Mandart circle and these lines: {11, 522}, {513, 52117}, {515, 52116}, {1319, 56939}, {3319, 37738}, {4953, 33646}, {18339, 37001}

X(60004) = reflection of X(1319) in X(56939)
X(60004) = X(189)-Ceva conjugate of X(1639)

X(60005) = X(1)X(5)∩X(100)X(280)

Barycentrics    (2*a^4 - a^3*b - a^2*b^2 + a*b^3 - b^4 - a^3*c + 2*a^2*b*c - a*b^2*c - a^2*c^2 - a*b*c^2 + 2*b^2*c^2 + a*c^3 - c^4)*(2*a^6 - a^5*b - 3*a^4*b^2 + 2*a^3*b^3 - a*b^5 + b^6 - a^5*c - 2*a^4*b*c + 6*a^3*b^2*c - 5*a*b^4*c + 2*b^5*c - 3*a^4*c^2 + 6*a^3*b*c^2 - 8*a^2*b^2*c^2 + 6*a*b^3*c^2 - b^4*c^2 + 2*a^3*c^3 + 6*a*b^2*c^3 - 4*b^3*c^3 - 5*a*b*c^4 - b^2*c^4 - a*c^5 + 2*b*c^5 + c^6) : :

X(60005) lies on the Mandart circle and these lines: {1, 5}, {100, 280}, {900, 52116}, {1145, 52114}, {1364, 14872}, {2800, 40953}, {2801, 52115}, {5687, 49207}

X(60006) = X(11)X(65)∩X(109)X(1433)

Barycentrics    a^2*(a^5*b - a^4*b^2 - 2*a^3*b^3 + 2*a^2*b^4 + a*b^5 - b^6 + a^5*c + 2*a^3*b^2*c - 3*a*b^4*c - a^4*c^2 + 2*a^3*b*c^2 - 4*a^2*b^2*c^2 + 2*a*b^3*c^2 + b^4*c^2 - 2*a^3*c^3 + 2*a*b^2*c^3 + 2*a^2*c^4 - 3*a*b*c^4 + b^2*c^4 + a*c^5 - c^6)*(a^7*b - a^6*b^2 - 3*a^5*b^3 + 3*a^4*b^4 + 3*a^3*b^5 - 3*a^2*b^6 - a*b^7 + b^8 + a^7*c - a^5*b^2*c + 2*a^4*b^3*c - a^3*b^4*c - 4*a^2*b^5*c + a*b^6*c + 2*b^7*c - a^6*c^2 - a^5*b*c^2 + 6*a^4*b^2*c^2 - 6*a^3*b^3*c^2 - a^2*b^4*c^2 + 7*a*b^5*c^2 - 4*b^6*c^2 - 3*a^5*c^3 + 2*a^4*b*c^3 - 6*a^3*b^2*c^3 + 16*a^2*b^3*c^3 - 7*a*b^4*c^3 - 2*b^5*c^3 + 3*a^4*c^4 - a^3*b*c^4 - a^2*b^2*c^4 - 7*a*b^3*c^4 + 6*b^4*c^4 + 3*a^3*c^5 - 4*a^2*b*c^5 + 7*a*b^2*c^5 - 2*b^3*c^5 - 3*a^2*c^6 + a*b*c^6 - 4*b^2*c^6 - a*c^7 + 2*b*c^7 + c^8) : :

X(60006) lies on the Mandart circle and these lines: {11, 65}, {109, 1433}, {1158, 1364}, {2807, 52115}, {2818, 52117}, {3738, 52116}, {6001, 52114}, {13528, 52113}, {14872, 52112}

X(60006) = reflection of X(1364) in X(1158)

X(60007) = X(3)X(324)∩X(5)X(577)

Barycentrics    (a^8 - 3*a^6*b^2 + 4*a^4*b^4 - 3*a^2*b^6 + b^8 - 3*a^6*c^2 + 3*a^4*b^2*c^2 + 3*a^2*b^4*c^2 - 3*b^6*c^2 + 3*a^4*c^4 + a^2*b^2*c^4 + 3*b^4*c^4 - a^2*c^6 - b^2*c^6)*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6 - 3*a^6*c^2 + 3*a^4*b^2*c^2 + a^2*b^4*c^2 - b^6*c^2 + 4*a^4*c^4 + 3*a^2*b^2*c^4 + 3*b^4*c^4 - 3*a^2*c^6 - 3*b^2*c^6 + c^8) : :

X(60007) lies on these lines: {2, 19210}, {3, 324}, {4, 31610}, {5, 577}, {95, 18027}, {140, 343}, {549, 13157}, {1179, 3135}, {1232, 3964}, {5449, 58417}, {6924, 22341}, {7514, 16391}, {15760, 44405}, {19176, 26876}, {19179, 46760}, {23195, 34449}, {40800, 43998}

X(60007) = isogonal conjugate of X(3567)
X(60007) = isotomic conjugate of the complement of X(43980)
X(60007) = X(1)-isoconjugate of X(3567)
X(60007) = X(3)-Dao conjugate of X(3567)
X(60007) = cevapoint of X(i) and X(j) for these (i,j): {2, 43980}, {3, 1656}
X(60007) = trilinear pole of line {6368, 32320}
X(60007) = barycentric quotient X(6)/X(3567)

X(60008) = X(4)X(47055)∩X(30)X(146)

Barycentrics    a^16 - 8*a^14*b^2 + 26*a^12*b^4 - 44*a^10*b^6 + 40*a^8*b^8 - 16*a^6*b^10 - 2*a^4*b^12 + 4*a^2*b^14 - b^16 - 8*a^14*c^2 + 2*a^12*b^2*c^2 + 6*a^10*b^4*c^2 + 34*a^8*b^6*c^2 - 46*a^6*b^8*c^2 + 12*a^4*b^10*c^2 - 8*a^2*b^12*c^2 + 8*b^14*c^2 + 26*a^12*c^4 + 6*a^10*b^2*c^4 - 99*a^8*b^4*c^4 + 56*a^6*b^6*c^4 + 39*a^4*b^8*c^4 - 28*b^12*c^4 - 44*a^10*c^6 + 34*a^8*b^2*c^6 + 56*a^6*b^4*c^6 - 98*a^4*b^6*c^6 + 4*a^2*b^8*c^6 + 56*b^10*c^6 + 40*a^8*c^8 - 46*a^6*b^2*c^8 + 39*a^4*b^4*c^8 + 4*a^2*b^6*c^8 - 70*b^8*c^8 - 16*a^6*c^10 + 12*a^4*b^2*c^10 + 56*b^6*c^10 - 2*a^4*c^12 - 8*a^2*b^2*c^12 - 28*b^4*c^12 + 4*a^2*c^14 + 8*b^2*c^14 - c^16 : :
X(60008) = 2 X[399] - 3 X[1138], 5 X[399] - 6 X[18285], 3 X[1138] - 4 X[11749], 5 X[1138] - 4 X[18285], 5 X[11749] - 3 X[18285], 3 X[376] - 2 X[52056], 3 X[476] - 4 X[55319], 5 X[631] - 6 X[14851], 2 X[1553] - 3 X[34312], 5 X[15081] - 4 X[18319], 3 X[17511] - 2 X[34150], 4 X[34150] - 3 X[34193], 3 X[36172] - 4 X[52219]

X(60008) lies on the curve Q070 and these lines: {4, 47055}, {20, 31990}, {30, 146}, {376, 52056}, {476, 55319}, {631, 14851}, {1553, 34312}, {1657, 3471}, {3146, 3470}, {3448, 16168}, {15081, 18319}, {17511, 34150}, {36172, 52219}

X(60008) = reflection of X(i) in X(j) for these {i,j}: {146, 14731}, {399, 11749}, {12383, 38581}, {34193, 17511}
X(60008) = {X(399),X(11749)}-harmonic conjugate of X(1138)

X(60009) = X(4)X(47055)∩X(30)X(146)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(b^2 - c^2)*(Sqrt[3]*(a^2 - b^2 - c^2) + 2*S) : :

X(60009) lies on these lines: {520, 647}, {523, 14447}, {525, 44712}, {526, 6138}, {924, 55223}, {4558, 38414}, {5995, 53187}, {6111, 6783}, {6137, 8675}, {14380, 36297}, {35909, 36296}, {41997, 53576}

X(60009) = reflection of X(6138) in X(57123)
X(60009) = isogonal conjugate of X(36309)
X(60009) = isotomic conjugate of the polar conjugate of X(6138)
X(60009) = isogonal conjugate of the polar conjugate of X(23871)
X(60009) = X(i)-Ceva conjugate of X(j) for these (i,j): {17403, 46113}, {23871, 6138}, {38413, 3}, {50465, 16186}, {52203, 125}
X(60009) = X(i)-isoconjugate of X(j) for these (i,j): {1, 36309}, {14, 162}, {15, 36129}, {19, 23896}, {92, 5994}, {158, 38413}, {301, 32676}, {470, 32678}, {648, 2154}, {662, 8738}, {811, 3458}, {823, 36297}, {2151, 46456}, {8739, 32680}, {24019, 40710}, {36306, 51806}, {36311, 56829}
X(60009) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 36309}, {6, 23896}, {122, 44703}, {125, 14}, {1084, 8738}, {1147, 38413}, {2972, 44714}, {15526, 301}, {15610, 472}, {17423, 3458}, {17433, 6117}, {18334, 470}, {22391, 5994}, {30472, 6331}, {35071, 40710}, {35444, 14618}, {38994, 4}, {40578, 46456}, {40581, 648}, {43962, 264}, {47899, 2052}, {55066, 2154}
X(60009) = crossdifference of every pair of points on line {4, 14}
X(60009) = X(i)-line conjugate of X(j) for these (i,j): {6783, 6111}, {14380, 36297}
X(60009) = barycentric product X(i)*X(j) for these {i,j}: {3, 23871}, {13, 8552}, {16, 525}, {69, 6138}, {125, 17403}, {299, 647}, {471, 520}, {523, 44719}, {526, 40709}, {850, 46113}, {895, 9205}, {2152, 14208}, {3265, 8740}, {3267, 34395}, {3268, 36296}, {3457, 45792}, {4558, 30468}, {5664, 39377}, {14380, 41888}, {14590, 41997}, {15412, 44712}, {16186, 23895}, {20578, 52437}, {23283, 44718}, {23286, 33530}, {23870, 50465}, {38413, 43962}, {40710, 57123}, {44689, 51664}
X(60009) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 23896}, {6, 36309}, {13, 46456}, {16, 648}, {184, 5994}, {299, 6331}, {471, 6528}, {512, 8738}, {520, 40710}, {525, 301}, {526, 470}, {577, 38413}, {647, 14}, {810, 2154}, {2081, 6117}, {2152, 162}, {2153, 36129}, {3049, 3458}, {6138, 4}, {6587, 44703}, {8552, 298}, {8611, 44691}, {8740, 107}, {9205, 44146}, {9409, 36298}, {10097, 36310}, {11081, 36306}, {14270, 8739}, {14380, 36311}, {14908, 9207}, {16186, 23870}, {17403, 18020}, {17434, 44714}, {20578, 6344}, {20975, 20579}, {22115, 17402}, {23286, 51268}, {23871, 264}, {30468, 14618}, {34395, 112}, {36296, 476}, {36297, 36840}, {38413, 57580}, {38414, 39295}, {39201, 36297}, {39377, 39290}, {40709, 35139}, {41997, 14592}, {44712, 14570}, {44719, 99}, {46113, 110}, {50465, 23895}, {52342, 44427}, {52743, 6110}, {55221, 46926}, {57123, 471}

X(60010) = X(520)X(647)∩X(523)X(14336)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(b^2 - c^2)*(Sqrt[3]*(a^2 - b^2 - c^2) - 2*S) : :

X(60010) lies on these lines: {520, 647}, {523, 14446}, {525, 44711}, {526, 6137}, {924, 55221}, {4558, 38413}, {5994, 53187}, {6110, 6782}, {6138, 8675}, {14380, 36296}, {35909, 36297}, {41998, 53576}

X(60010) = reflection of X(6137) in X(57122)
X(60010) = isogonal conjugate of X(36306)
X(60010) = isotomic conjugate of the polar conjugate of X(6137)
X(60010) = isogonal conjugate of the polar conjugate of X(23870)
X(60010) = X(i)-Ceva conjugate of X(j) for these (i,j): {17402, 46112}, {23870, 6137}, {38414, 3}, {50466, 16186}, {52204, 125}
X(60010) = X(i)-isoconjugate of X(j) for these (i,j): {1, 36306}, {13, 162}, {16, 36129}, {19, 23895}, {92, 5995}, {158, 38414}, {300, 32676}, {471, 32678}, {648, 2153}, {662, 8737}, {811, 3457}, {823, 36296}, {2152, 46456}, {8740, 32680}, {24019, 40709}, {36308, 56829}, {36309, 51805}
X(60010) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 36306}, {6, 23895}, {122, 44702}, {125, 13}, {1084, 8737}, {1147, 38414}, {2972, 44713}, {15526, 300}, {15609, 473}, {17423, 3457}, {17433, 6116}, {18334, 471}, {22391, 5995}, {30471, 6331}, {35071, 40709}, {35443, 14618}, {38993, 4}, {40579, 46456}, {40580, 648}, {43961, 264}, {47898, 2052}, {55066, 2153}
X(60010) = crossdifference of every pair of points on line {4, 13}
X(60010) = X(i)-line conjugate of X(j) for these (i,j): {6782, 6110}, {14380, 36296}
X(60010) = barycentric product X(i)*X(j) for these {i,j}: {3, 23870}, {14, 8552}, {15, 525}, {69, 6137}, {125, 17402}, {298, 647}, {470, 520}, {523, 44718}, {526, 40710}, {850, 46112}, {895, 9204}, {2151, 14208}, {3265, 8739}, {3267, 34394}, {3268, 36297}, {3458, 45792}, {4558, 30465}, {5664, 39378}, {14380, 41887}, {14590, 41998}, {15412, 44711}, {16186, 23896}, {20579, 52437}, {23284, 44719}, {23286, 33529}, {23871, 50466}, {38414, 43961}, {40709, 57122}, {44688, 51664}
X(60010) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 23895}, {6, 36306}, {14, 46456}, {15, 648}, {184, 5995}, {298, 6331}, {470, 6528}, {512, 8737}, {520, 40709}, {525, 300}, {526, 471}, {577, 38414}, {647, 13}, {810, 2153}, {2081, 6116}, {2151, 162}, {2154, 36129}, {3049, 3457}, {6137, 4}, {6587, 44702}, {8552, 299}, {8611, 44690}, {8739, 107}, {9204, 44146}, {9409, 36299}, {10097, 36307}, {11086, 36309}, {14270, 8740}, {14380, 36308}, {14908, 9206}, {16186, 23871}, {17402, 18020}, {17434, 44713}, {20579, 6344}, {20975, 20578}, {22115, 17403}, {23286, 51275}, {23870, 264}, {30465, 14618}, {34394, 112}, {36296, 36839}, {36297, 476}, {38413, 39295}, {38414, 57579}, {39201, 36296}, {39378, 39290}, {40710, 35139}, {41998, 14592}, {44711, 14570}, {44718, 99}, {46112, 110}, {50466, 23896}, {52343, 44427}, {52743, 6111}, {55223, 46925}, {57122, 470}

X(60011) = X(3)X(5995)∩X(15)X(112)

Barycentrics    a^2/(Sqrt[3]*(2*a^6 - a^4*b^2 - b^6 - a^4*c^2 + b^4*c^2 + b^2*c^4 - c^6) + 2*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*S) : :

X(60011) lies on the circumcircle and these lines: {3, 5995}, {4, 46650}, {15, 112}, {16, 2715}, {98, 23871}, {99, 5473}, {107, 470}, {110, 14538}, {476, 36186}, {511, 5994}, {691, 14539}, {1350, 9202}, {5618, 6771}, {9203, 18860}, {10409, 14540}, {14541, 36515}, {16806, 36755}, {18863, 36514}, {36759, 59136}, {38613, 47036}, {41406, 58963}

X(60011) = reflection of X(i) in X(j) for these {i,j}: {4, 46650}, {5995, 3}
X(60011) = isogonal conjugate of X(41022)
X(60011) = isogonal conjugate of the anticomplement of X(41022)
X(60011) = isogonal conjugate of the complement of X(41022)
X(60011) = Thomson-isogonal conjugate of X(23870)
X(60011) = Collings transform of X(46650)
X(60011) = X(1)-isoconjugate of X(41022)
X(60011) = X(3)-Dao conjugate of X(41022)
X(60011) = barycentric quotient X(6)/X(41022)

X(60012) = X(3)X(5994)∩X(16)X(112)

Barycentrics    a^2/(Sqrt[3]*(2*a^6 - a^4*b^2 - b^6 - a^4*c^2 + b^4*c^2 + b^2*c^4 - c^6) - 2*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*S) : :

X(60012) lies on the circumcircle and these lines: {3, 5994}, {4, 46651}, {15, 2715}, {16, 112}, {98, 23870}, {99, 5474}, {107, 471}, {110, 14539}, {476, 36185}, {511, 5995}, {691, 14538}, {1350, 9203}, {5619, 6774}, {9202, 18860}, {10410, 14541}, {14540, 36514}, {16807, 36756}, {18864, 36515}, {36760, 59136}, {38613, 47035}, {41407, 58963}

X(60012) lies on the circumcircle and these lines: reflection of X(i) in X(j) for these {i,j}: {4, 46651}, {5994, 3}
X(60012) = isogonal conjugate of X(41023)
X(60012) = isogonal conjugate of the anticomplement of X(41023)
X(60012) = isogonal conjugate of the complement of X(41023)
X(60012) = Thomson-isogonalconjugate of X(23871)
X(60012) = Collings transform of X(46651)
X(60012) = X(1)-isoconjugate of X(41023)
X(60012) = X(3)-Dao conjugate of X(41023)
X(60012) = barycentric quotient X(6)/X(41023)

X(60013) = X(99)X(323)∩X(186)X(648)

Barycentrics    (2*a^6*b^2 - 4*a^4*b^4 + 2*a^2*b^6 - a^6*c^2 - b^6*c^2 + 2*a^4*c^4 + 2*b^4*c^4 - a^2*c^6 - b^2*c^6)*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6 - 2*a^6*c^2 + b^6*c^2 + 4*a^4*c^4 - 2*b^4*c^4 - 2*a^2*c^6 + b^2*c^6) : :
X(60013) = 7 X[2] - 8 X[40485], 4 X[18334] - X[35139], 7 X[18334] - 4 X[40485], 7 X[35139] - 16 X[40485]

X(60013) lies on the Steiner circumellipse and these lines: {2, 18334}, {15, 23896}, {16, 23895}, {99, 323}, {186, 648}, {524, 53192}, {668, 42701}, {670, 7799}, {671, 9213}, {892, 7771}, {2966, 7757}, {3431, 54959}, {6528, 14165}, {7811, 18829}, {14616, 14838}, {15412, 46138}, {16077, 57487}, {16577, 35174}, {37802, 46134}, {41143, 53230}, {51224, 57268}

X(60013) = reflection of X(i) in X(j) for these {i,j}: {2, 18334}, {35139, 2}
X(60013) = isogonal conjugate of X(3016)
X(60013) = isotomic conjugate of the isogonal conjugate of X(32730)
X(60013) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3016}, {2624, 56398}
X(60013) = X(3)-Dao conjugate of X(3016)
X(60013) = trilinear pole of line {2, 526}
X(60013) = barycentric product X(i)*X(j) for these {i,j}: {76, 32730}, {1494, 52763}
X(60013) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 3016}, {94, 52983}, {476, 56398}, {32730, 6}, {32731, 14560}, {36143, 32678}, {52763, 30}

X(60014) = X(6)X(64)∩X(99)X(284)

Barycentrics    (a^3*b - 2*a^2*b^2 + a*b^3 - a^3*c - b^3*c + a^2*c^2 + b^2*c^2)*(a^3*b - a^2*b^2 - a^3*c + 2*a^2*c^2 - b^2*c^2 - a*c^3 + b*c^3) : :

X(60014) lies on the Steiner circumellipse and these lines: {6, 664}, {9, 668}, {19, 18026}, {55, 190}, {57, 4569}, {99, 284}, {333, 670}, {335, 51995}, {385, 17963}, {648, 2299}, {666, 2195}, {673, 46135}, {909, 54953}, {1024, 2481}, {1121, 23351}, {1174, 6606}, {1436, 53642}, {1945, 53211}, {2161, 35174}, {2258, 32038}, {2259, 54952}, {2291, 35157}, {2316, 4555}, {2319, 18830}, {2339, 54982}, {2364, 4597}, {2432, 34393}, {3451, 6613}, {4562, 7077}, {4572, 38991}, {6169, 14727}, {6528, 8748}, {6540, 33635}, {9443, 35167}, {10025, 53208}, {11051, 53640}, {17346, 53648}, {18829, 40882}, {20935, 54987}, {32041, 50127}, {34820, 53658}, {35171, 37686}, {36799, 54985}, {46132, 52652}, {54967, 56243}

X(60014) = isotomic conjugate of X(46180)
X(60014) = isotomic conjugate of the anticomplement of X(46180)
X(60014) = isotomic conjugate of the complement of X(46180)
X(60014) = isotomic conjugate of the isogonal conjugate of X(59020)
X(60014) = X(31)-isoconjugate of X(46180)
X(60014) = X(2)-Dao conjugate of X(46180)
X(60014) = cevapoint of X(2) and X(46180)
X(60014) = trilinear pole of line {2, 663}
X(60014) = barycentric product X(i)*X(j) for these {i,j}: {9, 34084}, {76, 59020}, {85, 30627}
X(60014) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 46180}, {30627, 9}, {34084, 85}, {59020, 6}

X(60015) = X(6)X(23896)∩X(16)X(99)

Barycentrics    (Sqrt[3]*c^2*(a^4 + b^4 - a^2*c^2 - b^2*c^2) - 2*(2*a^2*b^2 - a^2*c^2 - b^2*c^2)*S)*(Sqrt[3]*b^2*(a^4 - a^2*b^2 - b^2*c^2 + c^4) + 2*(a^2*b^2 - 2*a^2*c^2 + b^2*c^2)*S) : :

X(60015) lies on the Steiner circumellipse and these lines: {6, 23896}, {13, 35139}, {16, 99}, {298, 18829}, {299, 670}, {385, 11081}, {523, 46303}, {530, 16248}, {648, 8740}, {3441, 12188}, {8604, 32037}, {16460, 25152}, {32036, 51890}, {37786, 53199}

X(60015) = trilinear pole of line {2, 6138}

X(60016) = X(6)X(23895)∩X(15)X(99)

Barycentrics    (Sqrt[3]*c^2*(a^4 + b^4 - a^2*c^2 - b^2*c^2) + 2*(2*a^2*b^2 - a^2*c^2 - b^2*c^2)*S)*(Sqrt[3]*b^2*(a^4 - a^2*b^2 - b^2*c^2 + c^4) - 2*(a^2*b^2 - 2*a^2*c^2 + b^2*c^2)*S) : :

X(60016) lies on the Steiner circumellipse and these lines: {6, 23895}, {14, 35139}, {15, 99}, {298, 670}, {299, 18829}, {385, 11086}, {523, 46303}, {531, 16247}, {648, 8739}, {3440, 12188}, {8603, 32036}, {16459, 25162}, {32037, 51891}, {37785, 53199}

X(60016) = trilinear pole of line {2, 6137}

X(60017) = X(1)X(5894)∩X(33)X(57)

Barycentrics    a*(a^10 - 2*a^9*b + a^8*b^2 - 2*a^6*b^4 + 4*a^5*b^5 - 2*a^4*b^6 + a^2*b^8 - 2*a*b^9 + b^10 - 2*a^9*c - a^8*b*c + 3*a^7*b^2*c + 3*a^6*b^3*c + 3*a^5*b^4*c - 3*a^4*b^5*c - 7*a^3*b^6*c + a^2*b^7*c + 3*a*b^8*c + a^8*c^2 + 3*a^7*b*c^2 - 6*a^6*b^2*c^2 - 7*a^5*b^3*c^2 + 6*a^4*b^4*c^2 + 5*a^3*b^5*c^2 + 2*a^2*b^6*c^2 - a*b^7*c^2 - 3*b^8*c^2 + 3*a^6*b*c^3 - 7*a^5*b^2*c^3 - 2*a^4*b^3*c^3 + 2*a^3*b^4*c^3 - a^2*b^5*c^3 + 5*a*b^6*c^3 - 2*a^6*c^4 + 3*a^5*b*c^4 + 6*a^4*b^2*c^4 + 2*a^3*b^3*c^4 - 6*a^2*b^4*c^4 - 5*a*b^5*c^4 + 2*b^6*c^4 + 4*a^5*c^5 - 3*a^4*b*c^5 + 5*a^3*b^2*c^5 - a^2*b^3*c^5 - 5*a*b^4*c^5 - 2*a^4*c^6 - 7*a^3*b*c^6 + 2*a^2*b^2*c^6 + 5*a*b^3*c^6 + 2*b^4*c^6 + a^2*b*c^7 - a*b^2*c^7 + a^2*c^8 + 3*a*b*c^8 - 3*b^2*c^8 - 2*a*c^9 + c^10) : :

X(60017) lies on the excentral-hexyl ellipse and these lines: {1, 5894}, {3, 25087}, {33, 57}, {84, 294}, {109, 7070}, {223, 1040}, {910, 3220}, {918, 58035}, {991, 20277}, {1394, 2124}, {1541, 51400}, {1721, 41010}, {1750, 5400}, {1754, 1768}, {2254, 58037}, {2814, 16528}, {4319, 53547}, {34498, 41403}

X(60017) = reflection of X(58038) in X(3)
X(60017) = X(3100)-Ceva conjugate of X(1)

X(60018) = X(1)X(43724)∩X(46)X(80)

Barycentrics    a*(a^11*b - 5*a^9*b^3 + 10*a^7*b^5 - 10*a^5*b^7 + 5*a^3*b^9 - a*b^11 + a^11*c - 8*a^10*b*c + 6*a^9*b^2*c + 15*a^8*b^3*c - 22*a^7*b^4*c + 20*a^5*b^6*c - 10*a^4*b^7*c - 3*a^3*b^8*c - 2*a*b^10*c + 3*b^11*c + 6*a^9*b*c^2 - 18*a^8*b^2*c^2 + 8*a^7*b^3*c^2 + 24*a^6*b^4*c^2 - 28*a^5*b^5*c^2 + 4*a^4*b^6*c^2 + 8*a^3*b^7*c^2 - 8*a^2*b^8*c^2 + 6*a*b^9*c^2 - 2*b^10*c^2 - 5*a^9*c^3 + 15*a^8*b*c^3 + 8*a^7*b^2*c^3 - 48*a^6*b^3*c^3 + 18*a^5*b^4*c^3 + 26*a^4*b^5*c^3 - 24*a^3*b^6*c^3 + 16*a^2*b^7*c^3 + 3*a*b^8*c^3 - 9*b^9*c^3 - 22*a^7*b*c^4 + 24*a^6*b^2*c^4 + 18*a^5*b^3*c^4 - 40*a^4*b^4*c^4 + 14*a^3*b^5*c^4 + 8*a^2*b^6*c^4 - 10*a*b^7*c^4 + 8*b^8*c^4 + 10*a^7*c^5 - 28*a^5*b^2*c^5 + 26*a^4*b^3*c^5 + 14*a^3*b^4*c^5 - 32*a^2*b^5*c^5 + 4*a*b^6*c^5 + 6*b^7*c^5 + 20*a^5*b*c^6 + 4*a^4*b^2*c^6 - 24*a^3*b^3*c^6 + 8*a^2*b^4*c^6 + 4*a*b^5*c^6 - 12*b^6*c^6 - 10*a^5*c^7 - 10*a^4*b*c^7 + 8*a^3*b^2*c^7 + 16*a^2*b^3*c^7 - 10*a*b^4*c^7 + 6*b^5*c^7 - 3*a^3*b*c^8 - 8*a^2*b^2*c^8 + 3*a*b^3*c^8 + 8*b^4*c^8 + 5*a^3*c^9 + 6*a*b^2*c^9 - 9*b^3*c^9 - 2*a*b*c^10 - 2*b^2*c^10 - a*c^11 + 3*b*c^11) : :

X(60018) lies on the excentral-hexyl ellipse and these lines: {1, 43724}, {4, 33811}, {9, 40616}, {40, 50899}, {46, 80}, {579, 5822}, {1012, 10606}, {1020, 38554}, {1394, 1745}, {1716, 58034}, {1724, 3149}, {2817, 24031}, {3182, 10361}, {3738, 6326}, {5587, 21228}, {5720, 56885}, {7971, 52129}

X(60019) = X(1)X(30263)∩X(84)X(412)

Barycentrics    a*(a^13*b^2 + a^12*b^3 - 5*a^11*b^4 - 5*a^10*b^5 + 10*a^9*b^6 + 10*a^8*b^7 - 10*a^7*b^8 - 10*a^6*b^9 + 5*a^5*b^10 + 5*a^4*b^11 - a^3*b^12 - a^2*b^13 - a^13*b*c - 3*a^12*b^2*c + 6*a^11*b^3*c + 13*a^10*b^4*c - 13*a^9*b^5*c - 22*a^8*b^6*c + 12*a^7*b^7*c + 18*a^6*b^8*c - 3*a^5*b^9*c - 7*a^4*b^10*c - 2*a^3*b^11*c + a^2*b^12*c + a*b^13*c + a^13*c^2 - 3*a^12*b*c^2 - a^11*b^2*c^2 - 5*a^10*b^3*c^2 + a^9*b^4*c^2 + 27*a^8*b^5*c^2 - 6*a^7*b^6*c^2 - 22*a^6*b^7*c^2 + 7*a^5*b^8*c^2 - a^4*b^9*c^2 - a^3*b^10*c^2 + 3*a^2*b^11*c^2 - a*b^12*c^2 + b^13*c^2 + a^12*c^3 + 6*a^11*b*c^3 - 5*a^10*b^2*c^3 - 15*a^8*b^4*c^3 - 4*a^7*b^5*c^3 + 34*a^6*b^6*c^3 - 16*a^5*b^7*c^3 - 9*a^4*b^8*c^3 + 14*a^3*b^9*c^3 - 5*a^2*b^10*c^3 - b^12*c^3 - 5*a^11*c^4 + 13*a^10*b*c^4 + a^9*b^2*c^4 - 15*a^8*b^3*c^4 + 16*a^7*b^4*c^4 - 20*a^6*b^5*c^4 - 12*a^5*b^6*c^4 + 28*a^4*b^7*c^4 - 3*a^3*b^8*c^4 - a^2*b^9*c^4 + 3*a*b^10*c^4 - 5*b^11*c^4 - 5*a^10*c^5 - 13*a^9*b*c^5 + 27*a^8*b^2*c^5 - 4*a^7*b^3*c^5 - 20*a^6*b^4*c^5 + 38*a^5*b^5*c^5 - 16*a^4*b^6*c^5 - 12*a^3*b^7*c^5 + 9*a^2*b^8*c^5 - 9*a*b^9*c^5 + 5*b^10*c^5 + 10*a^9*c^6 - 22*a^8*b*c^6 - 6*a^7*b^2*c^6 + 34*a^6*b^3*c^6 - 12*a^5*b^4*c^6 - 16*a^4*b^5*c^6 + 10*a^3*b^6*c^6 - 6*a^2*b^7*c^6 - 2*a*b^8*c^6 + 10*b^9*c^6 + 10*a^8*c^7 + 12*a^7*b*c^7 - 22*a^6*b^2*c^7 - 16*a^5*b^3*c^7 + 28*a^4*b^4*c^7 - 12*a^3*b^5*c^7 - 6*a^2*b^6*c^7 + 16*a*b^7*c^7 - 10*b^8*c^7 - 10*a^7*c^8 + 18*a^6*b*c^8 + 7*a^5*b^2*c^8 - 9*a^4*b^3*c^8 - 3*a^3*b^4*c^8 + 9*a^2*b^5*c^8 - 2*a*b^6*c^8 - 10*b^7*c^8 - 10*a^6*c^9 - 3*a^5*b*c^9 - a^4*b^2*c^9 + 14*a^3*b^3*c^9 - a^2*b^4*c^9 - 9*a*b^5*c^9 + 10*b^6*c^9 + 5*a^5*c^10 - 7*a^4*b*c^10 - a^3*b^2*c^10 - 5*a^2*b^3*c^10 + 3*a*b^4*c^10 + 5*b^5*c^10 + 5*a^4*c^11 - 2*a^3*b*c^11 + 3*a^2*b^2*c^11 - 5*b^4*c^11 - a^3*c^12 + a^2*b*c^12 - a*b^2*c^12 - b^3*c^12 - a^2*c^13 + a*b*c^13 + b^2*c^13) : :

X(60019) lies on the excentral-hexyl ellipse and these lines: {1, 30263}, {84, 412}, {1715, 1768}, {1765, 58038}, {2270, 58036}, {5400, 15803}, {8677, 33810}, {21228, 52027}

X(60019) = X(10538)-Ceva conjugate of X(1)

X(60020) = X(1)X(36127)∩X(19)X(102)

Barycentrics    a*(a^14*b - 3*a^13*b^2 - 2*a^12*b^3 + 14*a^11*b^4 - 5*a^10*b^5 - 25*a^9*b^6 + 20*a^8*b^7 + 20*a^7*b^8 - 25*a^6*b^9 - 5*a^5*b^10 + 14*a^4*b^11 - 2*a^3*b^12 - 3*a^2*b^13 + a*b^14 + a^14*c - 2*a^13*b*c + 3*a^12*b^2*c - 4*a^11*b^3*c - 15*a^10*b^4*c + 34*a^9*b^5*c + 11*a^8*b^6*c - 56*a^7*b^7*c + 11*a^6*b^8*c + 34*a^5*b^9*c - 15*a^4*b^10*c - 4*a^3*b^11*c + 3*a^2*b^12*c - 2*a*b^13*c + b^14*c - 3*a^13*c^2 + 3*a^12*b*c^2 - 8*a^11*b^2*c^2 + 16*a^10*b^3*c^2 + 5*a^9*b^4*c^2 - 61*a^8*b^5*c^2 + 56*a^7*b^6*c^2 + 56*a^6*b^7*c^2 - 73*a^5*b^8*c^2 - 7*a^4*b^9*c^2 + 16*a^3*b^10*c^2 - 8*a^2*b^11*c^2 + 7*a*b^12*c^2 + b^13*c^2 - 2*a^12*c^3 - 4*a^11*b*c^3 + 16*a^10*b^2*c^3 - 28*a^9*b^3*c^3 + 30*a^8*b^4*c^3 + 40*a^7*b^5*c^3 - 96*a^6*b^6*c^3 + 24*a^5*b^7*c^3 + 42*a^4*b^8*c^3 - 36*a^3*b^9*c^3 + 16*a^2*b^10*c^3 + 4*a*b^11*c^3 - 6*b^12*c^3 + 14*a^11*c^4 - 15*a^10*b*c^4 + 5*a^9*b^2*c^4 + 30*a^8*b^3*c^4 - 120*a^7*b^4*c^4 + 54*a^6*b^5*c^4 + 78*a^5*b^6*c^4 - 80*a^4*b^7*c^4 + 50*a^3*b^8*c^4 + 17*a^2*b^9*c^4 - 27*a*b^10*c^4 - 6*b^11*c^4 - 5*a^10*c^5 + 34*a^9*b*c^5 - 61*a^8*b^2*c^5 + 40*a^7*b^3*c^5 + 54*a^6*b^4*c^5 - 116*a^5*b^5*c^5 + 46*a^4*b^6*c^5 + 40*a^3*b^7*c^5 - 49*a^2*b^8*c^5 + 2*a*b^9*c^5 + 15*b^10*c^5 - 25*a^9*c^6 + 11*a^8*b*c^6 + 56*a^7*b^2*c^6 - 96*a^6*b^3*c^6 + 78*a^5*b^4*c^6 + 46*a^4*b^5*c^6 - 128*a^3*b^6*c^6 + 24*a^2*b^7*c^6 + 19*a*b^8*c^6 + 15*b^9*c^6 + 20*a^8*c^7 - 56*a^7*b*c^7 + 56*a^6*b^2*c^7 + 24*a^5*b^3*c^7 - 80*a^4*b^4*c^7 + 40*a^3*b^5*c^7 + 24*a^2*b^6*c^7 - 8*a*b^7*c^7 - 20*b^8*c^7 + 20*a^7*c^8 + 11*a^6*b*c^8 - 73*a^5*b^2*c^8 + 42*a^4*b^3*c^8 + 50*a^3*b^4*c^8 - 49*a^2*b^5*c^8 + 19*a*b^6*c^8 - 20*b^7*c^8 - 25*a^6*c^9 + 34*a^5*b*c^9 - 7*a^4*b^2*c^9 - 36*a^3*b^3*c^9 + 17*a^2*b^4*c^9 + 2*a*b^5*c^9 + 15*b^6*c^9 - 5*a^5*c^10 - 15*a^4*b*c^10 + 16*a^3*b^2*c^10 + 16*a^2*b^3*c^10 - 27*a*b^4*c^10 + 15*b^5*c^10 + 14*a^4*c^11 - 4*a^3*b*c^11 - 8*a^2*b^2*c^11 + 4*a*b^3*c^11 - 6*b^4*c^11 - 2*a^3*c^12 + 3*a^2*b*c^12 + 7*a*b^2*c^12 - 6*b^3*c^12 - 3*a^2*c^13 - 2*a*b*c^13 + b^2*c^13 + a*c^14 + b*c^14) : :

X(60020) lies on the excentral-hexyl ellipse and these lines: {1, 36127}, {19, 102}, {64, 1715}, {108, 1490}, {207, 6261}, {920, 1768}, {1532, 1549}, {1713, 5120}, {1714, 5400}, {2804, 6326}, {33781, 58034}, {34050, 51660}

X(60021) = X(8)X(42701)∩X(21)X(323)

Barycentrics    a*(a^5*b + a^4*b^2 - 2*a^3*b^3 - 2*a^2*b^4 + a*b^5 + b^6 + 2*a^5*c + a^4*b*c - a^3*b^2*c - 2*a^2*b^3*c - a*b^4*c + b^5*c - 2*a^3*b*c^2 - 2*a^2*b^2*c^2 - 2*a*b^3*c^2 - 2*b^4*c^2 - 4*a^3*c^3 - 2*a^2*b*c^3 - a*b^2*c^3 - 2*b^3*c^3 + a*b*c^4 + b^2*c^4 + 2*a*c^5 + b*c^5)*(2*a^5*b - 4*a^3*b^3 + 2*a*b^5 + a^5*c + a^4*b*c - 2*a^3*b^2*c - 2*a^2*b^3*c + a*b^4*c + b^5*c + a^4*c^2 - a^3*b*c^2 - 2*a^2*b^2*c^2 - a*b^3*c^2 + b^4*c^2 - 2*a^3*c^3 - 2*a^2*b*c^3 - 2*a*b^2*c^3 - 2*b^3*c^3 - 2*a^2*c^4 - a*b*c^4 - 2*b^2*c^4 + a*c^5 + b*c^5 + c^6) : :

X(60021) lies on the Feuerbach circumhypbora and these lines: {8, 42701}, {21, 323}, {79, 18593}, {80, 16577}, {186, 1030}, {314, 7799}, {451, 1896}, {581, 3467}, {5561, 45924}, {40214, 52380}

X(60021) = isogonal conjugate of X(45923)
X(60021) = X(1)-isoconjugate of X(45923)
X(60021) = X(3)-Dao conjugate of X(45923)
X(60021) = trilinear pole of line {526, 650}
X(60021) = barycentric quotient X(6)/X(45923)

X(60022) = X(15)X(38413)∩X(110)X(186)

Barycentrics    a^2*(a^8 - a^4*b^4 - 2*a^2*b^6 + 2*b^8 - 4*a^6*c^2 + 4*a^2*b^4*c^2 - 2*b^6*c^2 + 6*a^4*c^4 - b^4*c^4 - 4*a^2*c^6 + c^8)*(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8 - a^4*c^4 + 4*a^2*b^2*c^4 - b^4*c^4 - 2*a^2*c^6 - 2*b^2*c^6 + 2*c^8) : :

X(60022) lies on the MacBeath circumconic and these lines: {15, 38413}, {16, 38414}, {110, 186}, {249, 34834}, {323, 4558}, {338, 40427}, {394, 43755}, {525, 2986}, {648, 3580}, {842, 35189}, {895, 8675}, {1138, 34312}, {1304, 10689}, {1332, 42701}, {1993, 44769}, {4563, 7799}, {5663, 15396}, {6515, 48373}, {10419, 50464}, {11064, 37802}, {14355, 33927}, {14919, 52584}, {17708, 37645}

X(60022) = isogonal conjugate of X(3018)
X(60022) = isogonal conjugate of the complement of X(35520)
X(60022) = isotomic conjugate of the polar conjugate of X(32710)
X(60022) = X(15396)-anticomplementary conjugate of X(4329)
X(60022) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3018}, {19, 17702}, {661, 7471}, {2173, 34150}, {25641, 36151}, {32678, 55130}
X(60022) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 3018}, {6, 17702}, {18334, 55130}, {36830, 7471}, {36896, 34150}
X(60022) = cevapoint of X(6) and X(5663)
X(60022) = trilinear pole of line {3, 526}
X(60022) = barycentric product X(i)*X(j) for these {i,j}: {69, 32710}, {99, 15453}, {1494, 15469}, {3268, 35189}, {15396, 35520}, {32711, 45792}, {35139, 53234}
X(60022) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 17702}, {6, 3018}, {74, 34150}, {110, 7471}, {477, 58086}, {526, 55130}, {2986, 52498}, {5663, 25641}, {14385, 15468}, {15396, 477}, {15453, 523}, {15469, 30}, {32710, 4}, {35189, 476}, {36116, 36129}, {51349, 14254}, {53234, 526}

X(60023) = X(3)X(38414)∩X(15)X(110)

Barycentrics    a^2*(3*(a^2 + b^2 - c^2)*(-a^2 + b^2 + c^2)*(-a^4 - a^2*b^2 + 2*b^4 + 2*a^2*c^2 - b^2*c^2 - c^4) + Sqrt[3]*(-2*a^2 + 4*b^2 - 2*c^2)*(a^2 + b^2 - c^2)*(-a^2 + b^2 + c^2)*S)*(3*(a^2 - b^2 + c^2)*(-a^2 + b^2 + c^2)*(-a^4 + 2*a^2*b^2 - b^4 - a^2*c^2 - b^2*c^2 + 2*c^4) + Sqrt[3]*(a^2 - b^2 + c^2)*(-a^2 + b^2 + c^2)*(-2*a^2 - 2*b^2 + 4*c^2)*S) : :

X(60023) lies on the MacBeath circumconic and these lines: {3, 38414}, {15, 110}, {17, 36316}, {125, 10217}, {470, 648}, {3292, 38413}, {4558, 44718}

X(60023) = isogonal conjugate of X(23712)
X(60023) = isotomic conjugate of the polar conjugate of X(2378)
X(60023) = isogonal conjugate of the polar conjugate of X(43091)
X(60023) = X(43091)-Ceva conjugate of X(2378)
X(60023) = X(i)-isoconjugate of X(j) for these (i,j): {1, 23712}, {19, 530}, {162, 9200}
X(60023) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 23712}, {6, 530}, {125, 9200}
X(60023) = barycentric product X(i)*X(j) for these {i,j}: {3, 43091}, {69, 2378}, {36316, 44718}, {40709, 47072}
X(60023) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 530}, {6, 23712}, {647, 9200}, {895, 52748}, {2378, 4}, {36296, 11537}, {36297, 18776}, {43091, 264}, {47072, 470}

X(60024) = X(3)X(38413)∩X(16)X(110)

Barycentrics    a^2*(3*(a^2 + b^2 - c^2)*(-a^2 + b^2 + c^2)*(-a^4 - a^2*b^2 + 2*b^4 + 2*a^2*c^2 - b^2*c^2 - c^4) - Sqrt[3]*(-2*a^2 + 4*b^2 - 2*c^2)*(a^2 + b^2 - c^2)*(-a^2 + b^2 + c^2)*S)*(3*(a^2 - b^2 + c^2)*(-a^2 + b^2 + c^2)*(-a^4 + 2*a^2*b^2 - b^4 - a^2*c^2 - b^2*c^2 + 2*c^4) - Sqrt[3]*(a^2 - b^2 + c^2)*(-a^2 + b^2 + c^2)*(-2*a^2 - 2*b^2 + 4*c^2)*S) : :

X(60024) lies on the MacBeath circumconic and these lines: {3, 38413}, {16, 110}, {18, 36317}, {125, 10218}, {471, 648}, {3292, 38414}, {4558, 44719}

X(60024) = isogonal conjugate of X(23713)
X(60024) = isotomic conjugate of the polar conjugate of X(2379)
X(60024) = isogonal conjugate of the polar conjugate of X(43092)
X(60024) = X(43092)-Ceva conjugate of X(2379)
X(60024) = X(i)-isoconjugate of X(j) for these (i,j): {1, 23713}, {19, 531}, {162, 9201}
X(60024) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 23713}, {6, 531}, {125, 9201}
X(60024) = barycentric product X(i)*X(j) for these {i,j}: {3, 43092}, {69, 2379}, {36317, 44719}, {40710, 47073}
X(60024) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 531}, {6, 23713}, {647, 9201}, {895, 52749}, {2379, 4}, {36296, 18777}, {36297, 11549}, {43092, 264}, {47073, 471}

X(60025) = X(6)X(1813)∩X(9)X(1332)

Barycentrics    a^2*(a^4 - a^3*b - a^2*b^2 - a*b^3 + 2*b^4 + a^2*b*c + 2*a*b^2*c - b^3*c - 2*a^2*c^2 + a*b*c^2 - b^2*c^2 - b*c^3 + c^4)*(a^4 - 2*a^2*b^2 + b^4 - a^3*c + a^2*b*c + a*b^2*c - b^3*c - a^2*c^2 + 2*a*b*c^2 - b^2*c^2 - a*c^3 - b*c^3 + 2*c^4) : :

X(60025) lies on the MacBeath circumconic and these lines: {6, 1813}, {9, 1332}, {19, 651}, {55, 1331}, {110, 2299}, {193, 44765}, {284, 4558}, {333, 4563}, {648, 8748}, {895, 2773}, {1024, 1814}, {1351, 42071}, {5905, 43190}, {7008, 13138}, {8602, 56544}, {13427, 55397}, {13456, 55398}, {23351, 53295}

X(60025) = reflection of X(1813) in X(6)
X(60025) = isogonal conjugate of the complement of X(33864)
X(60025) = X(i)-isoconjugate of X(j) for these (i,j): {281, 51661}, {661, 7462}
X(60025) = X(36830)-Dao conjugate of X(7462)
X(60025) = cevapoint of X(6) and X(8679)
X(60025) = trilinear pole of line {3, 663}
X(60025) = barycentric quotient X(i)/X(j) for these {i,j}: {110, 7462}, {603, 51661}, {8679, 53839}

X(60026) = X(1)X(4559)∩X(43)X(1699)

Barycentrics    a*(a^8*b^2 - 2*a^7*b^3 - a^6*b^4 + 4*a^5*b^5 - a^4*b^6 - 2*a^3*b^7 + a^2*b^8 + 2*a^8*b*c - 6*a^7*b^2*c + 2*a^6*b^3*c + 6*a^5*b^4*c - 2*a^4*b^5*c - 2*a^3*b^6*c - 2*a^2*b^7*c + 2*a*b^8*c + a^8*c^2 - 6*a^7*b*c^2 + 2*a^6*b^2*c^2 + 2*a^5*b^3*c^2 - 2*a^4*b^4*c^2 - 2*a^3*b^5*c^2 + 6*a^2*b^6*c^2 - 2*a*b^7*c^2 + b^8*c^2 - 2*a^7*c^3 + 2*a^6*b*c^3 + 2*a^5*b^2*c^3 - 6*a^4*b^3*c^3 + 6*a^3*b^4*c^3 - 2*a^2*b^5*c^3 + 2*a*b^6*c^3 - 2*b^7*c^3 - a^6*c^4 + 6*a^5*b*c^4 - 2*a^4*b^2*c^4 + 6*a^3*b^3*c^4 - 6*a^2*b^4*c^4 - 2*a*b^5*c^4 - b^6*c^4 + 4*a^5*c^5 - 2*a^4*b*c^5 - 2*a^3*b^2*c^5 - 2*a^2*b^3*c^5 - 2*a*b^4*c^5 + 4*b^5*c^5 - a^4*c^6 - 2*a^3*b*c^6 + 6*a^2*b^2*c^6 + 2*a*b^3*c^6 - b^4*c^6 - 2*a^3*c^7 - 2*a^2*b*c^7 - 2*a*b^2*c^7 - 2*b^3*c^7 + a^2*c^8 + 2*a*b*c^8 + b^2*c^8) : :

X(60026) lies on the Kiepert circumhyperbola of the excentral triangle, the excentral-hexyl ellipse, and these lines: {1, 4559}, {43, 1699}, {165, 3185}, {846, 1768}, {1764, 53280}, {2939, 58038}, {53343, 58035}

X(60027) = X(1)X(3659)∩X(40)X(167)

Barycentrics    a*(3*a^3 + 5*a^2*b - 3*a*b^2 - 5*b^3 + 5*a^2*c - 10*a*b*c + 5*b^2*c - 3*a*c^2 + 5*b*c^2 - 5*c^3 - 2*(a^3 + a^2*b - a*b^2 - b^3 + a^2*c - 2*a*b*c + 5*b^2*c - a*c^2 + 5*b*c^2 - c^3)*Sin[A/2] - 2*(a - b - c)*(a^2 + 2*a*b + b^2 + 2*a*c - 2*b*c + c^2)*Sin[B/2] - 2*(a - b - c)*(a^2 + 2*a*b + b^2 + 2*a*c - 2*b*c + c^2)*Sin[C/2]) : :
X(60027) = 3 X[165] - 2 X[7597], 5 X[1698] - 4 X[45304]

X(60027) lies on the Kiepert circumhyperbola of the excentral triangle, the Bevan circle, and these lines: {1, 3659}, {40, 167}, {57, 10506}, {165, 7597}, {166, 55168}, {168, 504}, {1697, 10501}, {1698, 45304}, {3339, 12814}, {9805, 12523}

X(60027) = reflection of X(1) in X(3659)

X(60028) = X(2)X(6)∩X(20)X(217)

Barycentrics    a^2*b^2*c^2*(b^2-c^2)^2+2*a^8*(b^2+c^2)-a^6*(4*b^4+3*b^2*c^2+4*c^4)+2*a^4*(b^6+c^6) : :

Let A1 be the intersection of the perpendicular bisector of BC and line AX(57507) and similarly define B1 and C1. Then A1, B1, and C1 are collinear on a line with tripole X(60028). (Ivan Pavlov, 02-Nov-2023)

X(60028) lies on these lines: {2, 6}, {4, 1625}, {20, 217}, {32, 34148}, {39, 5889}, {51, 15355}, {52, 39575}, {54, 10316}, {110, 10311}, {112, 13352}, {182, 5481}, {184, 10313}, {216, 2979}, {232, 3060}, {382, 41367}, {418, 11402}, {511, 22240}, {576, 52128}, {577, 5012}, {631, 41334}, {1147, 10312}, {1351, 45141}, {1511, 41414}, {1914, 9637}, {1971, 9544}, {3087, 30506}, {3095, 9475}, {3146, 32445}, {3284, 11422}, {3331, 3543}, {3524, 50678}, {5158, 23061}, {5475, 50435}, {5562, 26216}, {5890, 14961}, {6638, 38292}, {7592, 23115}, {7772, 15801}, {8743, 36747}, {8779, 34986}, {9545, 14585}, {9605, 12160}, {10298, 54082}, {10574, 22401}, {10733, 46301}, {10986, 51393}, {11610, 58064}, {11672, 37465}, {12161, 22120}, {13509, 18445}, {14912, 14965}, {15087, 22121}, {15305, 33843}, {15340, 31723}, {17578, 38297}, {23128, 56292}, {26714, 58851}, {35360, 47739}, {37184, 43718}, {51335, 56920}, {52672, 53174}

X(60028) = X(i)-Ceva conjugate of X(j) for these {i, j}: {42330, 3}, {44144, 37184}
X(60028) = pole of line {525, 35474} with respect to the MacBeath circumconic
X(60028) = pole of line {6, 14767} with respect to the Stammler hyperbola
X(60028) = pole of line {525, 35474} with respect to the dual conic of nine-point circle
X(60028) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(35098)}}, {{A, B, C, X(183), X(5481)}}, {{A, B, C, X(385), X(55999)}}, {{A, B, C, X(3289), X(57507)}}, {{A, B, C, X(5304), X(42346)}}, {{A, B, C, X(40799), X(59208)}}, {{A, B, C, X(41894), X(56290)}}
X(60028) = barycentric product X(i)*X(j) for these (i, j): {44144, 57507}
X(60028) = barycentric quotient X(i)/X(j) for these (i, j): {57507, 43718}
X(60028) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 3051, 5304}, {6, 40805, 59208}, {1994, 52058, 6}, {3289, 59208, 40805}, {40805, 59208, 2}

X(60029) = X(4)X(30200)∩X(21)X(523)

Barycentrics    (b - c)*(a^5 - a^4*b - a*b^4 + b^5 - a^3*b*c - a*b^3*c - 2*a^3*c^2 + a^2*b*c^2 + a*b^2*c^2 - 2*b^3*c^2 + 2*a*b*c^3 + a*c^4 + b*c^4)*(a^5 - 2*a^3*b^2 + a*b^4 - a^4*c - a^3*b*c + a^2*b^2*c + 2*a*b^3*c + b^4*c + a*b^2*c^2 - a*b*c^3 - 2*b^2*c^3 - a*c^4 + c^5) : :

X(60029) lies on the Feuerbach circumhyperbola, the X-parabola (see X(12065), and these lines: {4, 30200}, {8, 4036}, {9, 4024}, {21, 523}, {79, 6003}, {314, 850}, {513, 10266}, {522, 6597}, {900, 6595}, {1172, 2501}, {2320, 17166}, {3139, 12079}, {3738, 6599}, {5466, 53353}, {6598, 35057}, {7253, 14777}, {8674, 11604}, {10279, 44409}, {43746, 47203}

X(60029) = X(4575)-isoconjugate of X(37982)
X(60029) = X(136)-Dao conjugate of X(37982)
X(60029) = cevapoint of X(i) and X(j) for these (i,j): {512, 47227}, {523, 8674}
X(60029) = trilinear pole of line {115, 650}
X(60029) = barycentric quotient X(2501)/X(37982)

X(60030) = X(1)X(57243)∩X(21)X(525)

Barycentrics    (b - c)*(a^7 - a^6*b - a^5*b^2 + a^4*b^3 + a^3*b^4 - a^2*b^5 - a*b^6 + b^7 - a^5*b*c + 2*a^3*b^3*c - a*b^5*c - a^5*c^2 + a^3*b^2*c^2 + a^2*b^3*c^2 - b^5*c^2 - a^3*b*c^3 - a*b^3*c^3 - a^3*c^4 - b^3*c^4 + 2*a*b*c^5 + a*c^6 + b*c^6)*(a^7 - a^5*b^2 - a^3*b^4 + a*b^6 - a^6*c - a^5*b*c - a^3*b^3*c + 2*a*b^5*c + b^6*c - a^5*c^2 + a^3*b^2*c^2 + a^4*c^3 + 2*a^3*b*c^3 + a^2*b^2*c^3 - a*b^3*c^3 - b^4*c^3 + a^3*c^4 - a^2*c^5 - a*b*c^5 - b^2*c^5 - a*c^6 + c^7) : :

X(60030) lies on the Feuerbach circumhyperbola, the orthic-asymptotic hyperbola, and these lines: {1, 57243}, {9, 4064}, {21, 525}, {314, 3267}, {523, 1172}, {1896, 14618}, {2806, 11604}, {5489, 21789}, {6003, 15314}, {8674, 43735}

X(60030) = cevapoint of X(i) and X(j) for these (i,j): {523, 47203}, {647, 2878}
X(60030) = trilinear pole of line {125, 650}

X(60031) = X(21)X(512)∩X(314)X(523)

Barycentrics    a*(b - c)*(a^2*b^3 + a*b^4 + a^4*c - a^2*b^2*c + b^4*c - a^3*c^2 - 2*a^2*b*c^2 - a*b^2*c^2 + b^3*c^2 - a^2*c^3 + a*c^4)*(a^4*b - a^3*b^2 - a^2*b^3 + a*b^4 - 2*a^2*b^2*c - a^2*b*c^2 - a*b^2*c^2 + a^2*c^3 + b^2*c^3 + a*c^4 + b*c^4) : :

X(60031) lies on the Feuerbach circumhyperbola, the Lemoine-asymptotic hyperbola, and these lines: {8, 4705}, {9, 4079}, {21, 512}, {79, 6002}, {256, 6003}, {314, 523}, {1172, 2489}, {1896, 58757}, {2787, 11604}, {3140, 51441}, {3907, 6598}, {8674, 11609}, {10266, 29150}

X(60031) = trilinear pole of line {650, 3124}

X(60032) = X(5)X(86)∩X(27)X(53)

Barycentrics    (a^4 + a^3*b + a*b^3 + b^4 + a^3*c + a^2*b*c + a*b^2*c + b^3*c - 2*a^2*c^2 - a*b*c^2 - 2*b^2*c^2 - a*c^3 - b*c^3 + c^4)*(a^4 + a^3*b - 2*a^2*b^2 - a*b^3 + b^4 + a^3*c + a^2*b*c - a*b^2*c - b^3*c + a*b*c^2 - 2*b^2*c^2 + a*c^3 + b*c^3 + c^4) : :

X(60032) lies on the circumconics {{A,B,C,X(2),X(7)}} and {{A,B,C,X(4),X(5)}}, and on these lines: {2, 17221}, {5, 86}, {27, 53}, {75, 29477}, {310, 311}, {1246, 5292}, {6650, 16560}, {7543, 13450}, {17500, 52394}, {27427, 27447}, {27473, 27483}, {37759, 39700}, {39704, 41004}

X(60032) = isotomic conjugate of the anticomplement of X(45939)
X(60032) = trilinear pole of line {514, 12077}

X(60033) = X(5)X(58)∩X(6)X(21011)

Barycentrics    (a^5 + b^5 + a^3*b*c - a^2*b^2*c + a*b^3*c - 2*a^3*c^2 - a^2*b*c^2 - a*b^2*c^2 - 2*b^3*c^2 - a*b*c^3 + a*c^4 + b*c^4)*(a^5 - 2*a^3*b^2 + a*b^4 + a^3*b*c - a^2*b^2*c - a*b^3*c + b^4*c - a^2*b*c^2 - a*b^2*c^2 + a*b*c^3 - 2*b^2*c^3 + c^5) : :

X(60033) lies on the circumconics {{A,B,C,X(1),X(6)}} and {{A,B,C,X(4),X(5)}}, and on these lines: {5, 58}, {6, 21011}, {53, 1474}, {86, 311}, {1329, 36052}, {2163, 9612}, {2983, 17369}, {5331, 11103}, {8747, 13450}, {37259, 52150}

X(60033) = X(9562)-isoconjugate of X(54121)
X(60033) = trilinear pole of line {649, 12077}

X(60034) = X(4)X(18831)∩X(5)X(99)

Barycentrics    (a^6 - a^4*b^2 - a^2*b^4 + b^6 - 3*a^4*c^2 - 3*b^4*c^2 + 4*a^2*c^4 + 4*b^2*c^4 - 2*c^6)*(a^6 - 3*a^4*b^2 + 4*a^2*b^4 - 2*b^6 - a^4*c^2 + 4*b^4*c^2 - a^2*c^4 - 3*b^2*c^4 + c^6) : :

X(60034) lies on the circumconic {{A,B,C,X(4),X(5)}}, the Steiner circumellipse, and these lines: {4, 18831}, {5, 99}, {53, 648}, {76, 25043}, {95, 38394}, {190, 21011}, {302, 32037}, {303, 32036}, {311, 670}, {316, 1263}, {671, 24978}, {1487, 31617}, {2966, 40853}, {4577, 17500}, {6528, 13450}, {10412, 46138}, {27364, 35136}, {46134, 56272}, {53199, 56434}

X(60034) = isotomic conjugate of X(5965)
X(60034) = antitomic conjugate of X(2)
X(60034) = isotomic conjugate of the anticomplement of X(5965)
X(60034) = isotomic conjugate of the complement of X(5965)
X(60034) = isotomic conjugate of the isogonal conjugate of X(5966)
X(60034) = X(31)-isoconjugate of X(5965)
X(60034) = X(2)-Dao conjugate of X(5965)
X(60034) = cevapoint of X(2) and X(5965)
X(60034) = trilinear pole of line {2, 12077}
X(60034) = barycentric product X(76)*X(5966)
X(60034) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 5965}, {5966, 6}, {58962, 32737}

X(60035) = X(3)X(53577)∩X(4)X(110)

Barycentrics    (a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - 2*a^4*c^2 + 2*a^2*b^2*c^2 - 2*b^4*c^2 + a^2*c^4 + b^2*c^4)*(a^6 - 2*a^4*b^2 + a^2*b^4 - a^4*c^2 + 2*a^2*b^2*c^2 + b^4*c^2 - a^2*c^4 - 2*b^2*c^4 + c^6) : :

X(60035) lies on the circumconic {{A,B,C,X(4),X(5)}}, the Johnson circumconic, and these lines: {3, 53577}, {4, 110}, {5, 23181}, {30, 39986}, {52, 13450}, {53, 1625}, {68, 56684}, {94, 12219}, {115, 577}, {265, 526}, {311, 5891}, {317, 6528}, {327, 11185}, {338, 12358}, {381, 3613}, {382, 17703}, {1141, 3153}, {1624, 36160}, {2797, 6321}, {2980, 31723}, {3091, 16837}, {3574, 40449}, {5562, 56272}, {5961, 30512}, {7574, 51456}, {8797, 18537}, {9826, 36789}, {9927, 58084}, {10419, 14989}, {11591, 25043}, {13556, 21731}, {14790, 50529}, {14918, 36831}, {15470, 36184}, {15619, 31724}, {18403, 39371}, {18404, 22261}, {18420, 51389}, {18569, 34449}, {21649, 58261}, {23306, 35235}, {33581, 38956}, {36053, 52383}, {36853, 38897}, {37230, 51870}, {41078, 44715}, {45938, 53419}, {46723, 59428}

X(60035) = reflection of X(i) in X(j) for these {i,j}: {3, 53577}, {23181, 5}
X(60035) = X(40427)-anticomplementary conjugate of X(4329)
X(60035) = X(i)-Ceva conjugate of X(j) for these (i,j): {10420, 15328}, {12028, 15454}
X(60035) = X(i)-isoconjugate of X(j) for these (i,j): {54, 1725}, {275, 2315}, {403, 2169}, {2148, 3580}, {2167, 3003}, {2190, 13754}, {2616, 15329}, {36134, 55121}
X(60035) = X(i)-Dao conjugate of X(j) for these (i,j): {5, 13754}, {137, 55121}, {216, 3580}, {14363, 403}, {15450, 686}, {18402, 1986}, {39019, 6334}, {40588, 3003}, {52869, 113}
X(60035) = cevapoint of X(i) and X(j) for these (i,j): {5, 1154}, {51, 52945}, {526, 53577}, {14391, 41221}, {55073, 55132}
X(60035) = trilinear pole of line {216, 12077}
X(60035) = barycentric product X(i)*X(j) for these {i,j}: {5, 2986}, {51, 40832}, {53, 57829}, {99, 35361}, {311, 14910}, {324, 5504}, {343, 1300}, {687, 6368}, {1154, 40427}, {10420, 18314}, {12028, 14918}, {12077, 18878}, {14213, 36053}, {14570, 15328}, {15421, 35360}, {15451, 57932}, {23290, 43755}, {40423, 52945}, {52505, 56272}
X(60035) = barycentric quotient X(i)/X(j) for these {i,j}: {5, 3580}, {51, 3003}, {53, 403}, {216, 13754}, {324, 44138}, {687, 18831}, {1154, 34834}, {1300, 275}, {1625, 15329}, {1953, 1725}, {2986, 95}, {3199, 44084}, {5504, 97}, {6368, 6334}, {10420, 18315}, {11062, 1986}, {12077, 55121}, {14576, 52000}, {14910, 54}, {15328, 15412}, {15451, 686}, {15454, 43768}, {18180, 18609}, {32708, 933}, {35360, 16237}, {35361, 523}, {36053, 2167}, {40427, 46138}, {40832, 34384}, {41536, 16172}, {51363, 53568}, {51513, 47236}, {52945, 113}, {55219, 21731}, {56272, 52504}, {57829, 34386}, {58942, 4993}
X(60035) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 12319, 39118}, {1300, 2986, 5504}, {1300, 5504, 15454}, {2986, 58942, 15454}, {5504, 58942, 1300}, {38936, 59288, 15454}, {58731, 58924, 15454}

X(60036) = X(5)X(525)∩X(53)X(523)

Barycentrics    (b^2 - c^2)*(a^4*b^4 - 2*a^2*b^6 + b^8 + a^6*c^2 + a^2*b^4*c^2 - 2*b^6*c^2 - 2*a^4*c^4 + b^4*c^4 + a^2*c^6)*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + a^4*c^4 + a^2*b^2*c^4 + b^4*c^4 - 2*a^2*c^6 - 2*b^2*c^6 + c^8) : :

X(60036) lies on the circumconic {{A,B,C,X(4),X(5)}}, the orthic-asymptotic hyperbola, and these lines: {4, 15412}, {5, 525}, {53, 523}, {311, 3267}, {526, 52177}, {879, 1987}, {935, 47214}, {1141, 1298}, {1510, 2980}, {1972, 14977}, {2797, 6321}, {2966, 4230}, {4064, 21011}, {4580, 17035}, {5489, 13450}, {14380, 15459}, {21449, 23286}, {27352, 59744}, {39180, 39286}, {43462, 50460}

X(60036) = X(53205)-Ceva conjugate of X(1987)
X(60036) = X(i)-isoconjugate of X(j) for these (i,j): {110, 1955}, {163, 401}, {662, 1971}, {1101, 6130}, {2313, 18315}, {4575, 41204}, {4592, 58311}, {23997, 32545}, {32428, 36134}, {36084, 52128}
X(60036) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 401}, {136, 41204}, {137, 32428}, {244, 1955}, {523, 6130}, {1084, 1971}, {5139, 58311}, {36901, 44137}, {38987, 52128}
X(60036) = cevapoint of X(i) and X(j) for these (i,j): {523, 45259}, {868, 5489}, {3569, 15451}
X(60036) = trilinear pole of line {125, 12077}
X(60036) = crossdifference of every pair of points on line {129, 1971}
X(60036) = barycentric product X(i)*X(j) for these {i,j}: {125, 53205}, {339, 53708}, {523, 1972}, {850, 1987}, {1298, 18314}, {1577, 1956}, {14618, 14941}, {18027, 53175}, {32542, 56981}, {35442, 41210}, {40804, 43665}, {43673, 51960}
X(60036) = barycentric quotient X(i)/X(j) for these {i,j}: {115, 6130}, {512, 1971}, {523, 401}, {661, 1955}, {850, 44137}, {1298, 18315}, {1956, 662}, {1972, 99}, {1987, 110}, {2395, 32545}, {2489, 58311}, {2501, 41204}, {3569, 52128}, {12077, 32428}, {14618, 16089}, {14941, 4558}, {32542, 56980}, {40804, 2421}, {45259, 39081}, {51960, 34211}, {52177, 32661}, {53175, 577}, {53205, 18020}, {53708, 250}, {57500, 14966}

X(60037) = X(5)X(512)∩X(311)X(523)

Barycentrics    (b^2 - c^2)*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6 - a^6*c^2 + 2*a^4*b^2*c^2 - 4*a^2*b^4*c^2 + b^6*c^2 + 2*a^4*c^4 + 2*a^2*b^2*c^4 - 2*b^4*c^4 - a^2*c^6 + b^2*c^6)*(-(a^6*b^2) + 2*a^4*b^4 - a^2*b^6 + a^6*c^2 + 2*a^4*b^2*c^2 + 2*a^2*b^4*c^2 + b^6*c^2 - 2*a^4*c^4 - 4*a^2*b^2*c^4 - 2*b^4*c^4 + a^2*c^6 + b^2*c^6) : :

X(60037) lies on the circumconic {{A,B,C,X(4),X(5)}}, the Lemoinec-asymptotic hyperbola, and these lines: {4, 58756}, {5, 512}, {53, 2489}, {311, 523}, {1510, 3613}, {4079, 21011}, {13450, 58757}, {17500, 18105}, {35364, 53331}, {36300, 58869}, {36301, 58870}

X(60037) = X(1101)-isoconjugate of X(53567)
X(60037) = X(523)-Dao conjugate of X(53567)
X(60037) = trilinear pole of line {3124, 12077}
X(60037) = barycentric quotient X(115)/X(53567)

X(60038) = X(2)X(332)∩X(37)X(78)

Barycentrics    a^2*(a^3 - a^2*b - a*b^2 + b^3 - a^2*c - 2*a*b*c - b^2*c - 3*a*c^2 - 3*b*c^2 - c^3)*(a^3 - a^2*b - 3*a*b^2 - b^3 - a^2*c - 2*a*b*c - 3*b^2*c - a*c^2 - b*c^2 + c^3) : :

X(60038) lies on the circumconics {{A,B,C,X(1),X(3)}} and {{A,B,C,X(4),X(5)}}, and on these lines: {1, 1880}, {2, 332}, {3, 1400}, {6, 283}, {25, 284}, {29, 393}, {37, 78}, {42, 219}, {77, 940}, {81, 57744}, {941, 2271}, {967, 5019}, {1433, 46012}, {2278, 46010}, {2350, 5120}, {2359, 37538}, {4258, 53088}, {4273, 45129}, {5105, 39951}, {5110, 37282}, {5736, 31637}, {5747, 57527}, {5783, 16344}, {8882, 35196}, {10570, 40942}, {14553, 37250}, {16372, 45966}, {23696, 55261}, {36744, 46018}, {37628, 55259}, {41489, 52158}

X(60038) = isogonal conjugate of X(5712)
X(60038) = isogonal conjugate of the anticomplement of X(5737)
X(60038) = isogonal conjugate of the complement of X(14552)
X(60038) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5712}, {2, 54421}, {28, 8896}, {63, 37384}, {65, 37265}, {225, 23602}
X(60038) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 5712}, {3162, 37384}, {32664, 54421}, {40591, 8896}, {40602, 37265}
X(60038) = cevapoint of X(6) and X(37504)
X(60038) = trilinear pole of line {512, 652}
X(60038) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 5712}, {25, 37384}, {31, 54421}, {71, 8896}, {284, 37265}, {2193, 23602}

X(60039) = X(2)X(47421)∩X(6)X(23181)

Barycentrics    a^2*(-(a^4*b^4) + 2*a^2*b^6 - b^8 + a^6*c^2 - a^2*b^4*c^2 + 2*b^6*c^2 - 2*a^4*c^4 - b^4*c^4 + a^2*c^6)*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6 - a^4*c^4 - a^2*b^2*c^4 - b^4*c^4 + 2*a^2*c^6 + 2*b^2*c^6 - c^8) : :

X(60039) lies on the circumconic {{A,B,C,X(2),X(6)}}, the Johnson circumconic, and these lines: {2, 47421}, {6, 23181}, {25, 1625}, {110, 8882}, {111, 45938}, {393, 35360}, {418, 41271}, {467, 6528}, {686, 2395}, {2165, 3124}, {2433, 44715}, {3289, 14910}, {3580, 16081}, {8749, 36831}, {14389, 42300}, {37644, 40815}, {39024, 41891}

X(60039) = isogonal conjugate of X(44375)
X(60039) = isogonal conjugate of the anticomplement of X(44388)
X(60039) = isogonal conjugate of the complement of X(44363)
X(60039) = polar conjugate of the isotomic conjugate of X(57679)
X(60039) = X(i)-isoconjugate of X(j) for these (i,j): {1, 44375}, {63, 421}, {75, 58312}, {92, 51458}
X(60039) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 44375}, {206, 58312}, {3162, 421}, {22391, 51458}
X(60039) = cevapoint of X(6) and X(54082)
X(60039) = trilinear pole of line {216, 512}
X(60039) = barycentric product X(i)*X(j) for these {i,j}: {4, 57679}, {25, 57846}
X(60039) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 44375}, {25, 421}, {32, 58312}, {184, 51458}, {57679, 69}, {57846, 305}

X(60040) = X(6)X(525)∩X(25)X(523)

Barycentrics    (b^2 - c^2)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 + 2*a^2*b^2*c^2 - a^2*c^4 - b^2*c^4)*(-a^6 + a^2*b^4 + a^4*c^2 - 2*a^2*b^2*c^2 + b^4*c^2 + a^2*c^4 - c^6) : :

X(60040) lies on the circumconic {{A,B,C,X(2),X(6)}}, the orthic-asymptotic hyperbola, and these lines: {2, 2485}, {6, 525}, {25, 523}, {42, 4064}, {111, 2373}, {251, 4580}, {263, 8675}, {393, 14618}, {694, 9035}, {804, 16098}, {879, 1177}, {935, 10423}, {1169, 15420}, {1383, 31296}, {1400, 57243}, {1989, 14592}, {2165, 18312}, {2394, 8749}, {2489, 13854}, {2492, 8791}, {2799, 14910}, {2966, 16237}, {3003, 53173}, {3143, 9178}, {3228, 46140}, {6130, 46316}, {6587, 18310}, {8770, 47125}, {8882, 15412}, {14948, 56685}, {23878, 34288}, {33631, 39183}, {35522, 40347}, {37128, 37220}, {40144, 57071}, {40570, 56320}, {41489, 58759}, {41511, 53374}, {41941, 50944}, {41942, 50945}, {46245, 52486}

X(60040) = isotomic conjugate of the anticomplement of X(52628)
X(60040) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {10422, 21294}, {36095, 34518}, {36142, 2892}
X(60040) = X(i)-isoconjugate of X(j) for these (i,j): {63, 46592}, {110, 18669}, {162, 14961}, {163, 858}, {662, 2393}, {692, 17172}, {1101, 47138}, {1576, 20884}, {4575, 5523}, {4592, 14580}, {5181, 36142}, {23889, 57485}, {23997, 52672}, {24039, 51962}, {36085, 47426}
X(60040) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 858}, {125, 14961}, {136, 5523}, {244, 18669}, {523, 47138}, {1084, 2393}, {1086, 17172}, {3162, 46592}, {4858, 20884}, {4988, 21109}, {5139, 14580}, {17416, 19510}, {23992, 5181}, {36901, 1236}, {38988, 47426}, {39021, 12827}, {48317, 1560}, {55065, 21017}
X(60040) = cevapoint of X(i) and X(j) for these (i,j): {523, 2492}, {524, 34990}, {647, 690}, {1084, 33919}, {1648, 5489}
X(60040) = trilinear pole of line {125, 512}
X(60040) = crossdifference of every pair of points on line {2393, 14961}
X(60040) = barycentric product X(i)*X(j) for these {i,j}: {339, 10423}, {512, 46140}, {523, 2373}, {661, 37220}, {850, 1177}, {879, 52486}, {10097, 58078}, {10422, 35522}, {14618, 18876}, {14977, 51823}, {20902, 36095}, {36823, 43665}, {36884, 52076}, {46165, 58784}
X(60040) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 46592}, {115, 47138}, {351, 47426}, {512, 2393}, {514, 17172}, {523, 858}, {647, 14961}, {661, 18669}, {690, 5181}, {850, 1236}, {1177, 110}, {1577, 20884}, {2373, 99}, {2395, 52672}, {2489, 14580}, {2501, 5523}, {3120, 21109}, {3906, 19510}, {4024, 21017}, {5466, 59422}, {9178, 57485}, {10422, 691}, {10423, 250}, {14273, 1560}, {18876, 4558}, {20975, 42665}, {36823, 2421}, {37220, 799}, {46140, 670}, {46165, 4576}, {51823, 4235}, {52486, 877}, {52513, 4611}, {55121, 12827}, {56685, 53367}

X(60041) = X(1)X(273)∩X(3)X(7)

Barycentrics    (a + b - c)*(a - b + c)*(a^3 - a^2*b - a*b^2 + b^3 - 2*a*b*c - a*c^2 - b*c^2)*(a^3 - a*b^2 - a^2*c - 2*a*b*c - b^2*c - a*c^2 + c^3) : :

X(60041) lies on the circumconics {{A,B,C,X(1),X(3)}} and {{A,B,C,X(2),X(7)}}, and these lines: {1, 273}, {2, 219}, {3, 7}, {21, 52673}, {27, 226}, {29, 57809}, {48, 37389}, {57, 7573}, {75, 78}, {77, 1088}, {86, 283}, {92, 55107}, {102, 58993}, {272, 1175}, {282, 40447}, {310, 332}, {335, 41246}, {411, 17220}, {497, 3477}, {651, 46882}, {653, 2294}, {673, 2259}, {675, 15439}, {903, 54952}, {947, 21620}, {1014, 39734}, {1036, 3485}, {1037, 3475}, {1057, 5603}, {1069, 5738}, {1210, 24202}, {1246, 5132}, {1433, 1440}, {1441, 34772}, {1442, 1446}, {1445, 25523}, {1659, 5414}, {1794, 13329}, {1795, 3664}, {1807, 7269}, {2066, 13390}, {2338, 40942}, {3466, 36118}, {4373, 27815}, {5226, 7522}, {5543, 5936}, {5714, 7534}, {5932, 36620}, {6828, 21270}, {6986, 46887}, {7015, 7249}, {8545, 15656}, {11374, 53821}, {13407, 52185}, {16099, 41003}, {17394, 40702}, {20028, 27653}, {20289, 52269}, {21453, 47487}, {22464, 40442}, {24310, 44733}, {24929, 30266}, {27383, 58002}, {27385, 40424}, {54392, 58001}, {56047, 56559}

X(60041) = isogonal conjugate of X(14547)
X(60041) = isotomic conjugate of X(6734)
X(60041) = isotomic conjugate of the anticomplement of X(13411)
X(60041) = isotomic conjugate of the complement of X(34772)
X(60041) = isotomic conjugate of the polar conjugate of X(40573)
X(60041) = X(i)-isoconjugate of X(j) for these (i,j): {1, 14547}, {3, 1859}, {4, 23207}, {6, 40937}, {8, 40956}, {9, 2260}, {21, 40952}, {31, 6734}, {33, 4303}, {37, 46882}, {41, 5249}, {42, 54356}, {55, 942}, {58, 40967}, {65, 8021}, {71, 46884}, {212, 1838}, {219, 1841}, {281, 14597}, {284, 2294}, {333, 40978}, {442, 2194}, {500, 7073}, {521, 53323}, {607, 18607}, {651, 33525}, {943, 37993}, {1172, 18591}, {1402, 51978}, {1783, 52306}, {1844, 8606}, {1865, 2193}, {2150, 21675}, {2299, 56839}, {2318, 46883}, {2361, 45926}, {3694, 46890}, {3939, 50354}, {4183, 39791}, {6186, 31938}, {41509, 46887}
X(60041) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 6734}, {3, 14547}, {9, 40937}, {10, 40967}, {223, 942}, {226, 56839}, {478, 2260}, {1214, 442}, {2982, 2949}, {3160, 5249}, {36033, 23207}, {36103, 1859}, {38991, 33525}, {39006, 52306}, {40589, 46882}, {40590, 2294}, {40592, 54356}, {40602, 8021}, {40605, 51978}, {40611, 40952}, {40617, 50354}, {40622, 23752}, {40837, 1838}, {47345, 1865}, {56325, 21675}, {59608, 55010}
X(60041) = cevapoint of X(i) and X(j) for these (i,j): {1, 226}, {2, 34772}, {7, 1442}, {57, 73}, {943, 2982}
X(60041) = trilinear pole of line {514, 652}
X(60041) = barycentric product X(i)*X(j) for these {i,j}: {7, 40435}, {57, 40422}, {69, 40573}, {75, 2982}, {77, 40447}, {85, 943}, {226, 40412}, {307, 40395}, {331, 1794}, {333, 52560}, {349, 1175}, {514, 54952}, {664, 56320}, {2003, 57885}, {2259, 6063}, {3261, 15439}, {4391, 36048}, {6332, 58993}, {7282, 57860}, {15467, 40572}, {17095, 57710}, {32651, 35519}
X(60041) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40937}, {2, 6734}, {6, 14547}, {7, 5249}, {12, 21675}, {19, 1859}, {28, 46884}, {34, 1841}, {37, 40967}, {48, 23207}, {56, 2260}, {57, 942}, {58, 46882}, {65, 2294}, {73, 18591}, {77, 18607}, {81, 54356}, {222, 4303}, {225, 1865}, {226, 442}, {278, 1838}, {284, 8021}, {333, 51978}, {349, 1234}, {603, 14597}, {604, 40956}, {663, 33525}, {943, 9}, {1175, 284}, {1214, 56839}, {1396, 46883}, {1400, 40952}, {1402, 40978}, {1442, 16585}, {1459, 52306}, {1708, 14054}, {1794, 219}, {2003, 500}, {2006, 45926}, {2259, 55}, {2260, 37993}, {2982, 1}, {3219, 31938}, {3668, 55010}, {3669, 50354}, {4654, 3824}, {7178, 23752}, {7282, 445}, {14775, 3064}, {15439, 101}, {32651, 109}, {32674, 53323}, {36048, 651}, {37755, 41393}, {37797, 41557}, {40395, 29}, {40412, 333}, {40422, 312}, {40435, 8}, {40447, 318}, {40570, 2299}, {40572, 3190}, {40573, 4}, {41342, 45038}, {41572, 41571}, {52373, 39791}, {52560, 226}, {54952, 190}, {56320, 522}, {57691, 8606}, {57710, 7110}, {58993, 653}

X(60042) = X(2)X(4024)∩X(27)X(2501)

Barycentrics    (b - c)*(a^3 + b^3 + a^2*c + b^2*c - a*c^2 - b*c^2 - 2*c^3)*(-a^3 - a^2*b + a*b^2 + 2*b^3 + b^2*c - b*c^2 - c^3) : :

X(60042) lies on the circumconic {{A,B,C,X(2),X(7)}}, the X-parabola (see X(12065), and these lines: {2, 4024}, {27, 2501}, {75, 4036}, {86, 523}, {310, 850}, {514, 59267}, {675, 28482}, {903, 35162}, {2786, 6650}, {4467, 10278}, {5466, 53333}, {7192, 8029}, {52394, 58784}

X(60042) = X(i)-isoconjugate of X(j) for these (i,j): {162, 20754}, {163, 10026}, {662, 20666}, {692, 17770}, {4556, 20685}
X(60042) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 10026}, {125, 20754}, {1084, 20666}, {1086, 17770}, {35080, 51578}, {41180, 35114}
X(60042) = cevapoint of X(523) and X(2786)
X(60042) = trilinear pole of line {115, 514}
X(60042) = crossdifference of every pair of points on line {20666, 20754}
X(60042) = barycentric product X(i)*X(j) for these {i,j}: {514, 35162}, {3261, 28482}
X(60042) = barycentric quotient X(i)/X(j) for these {i,j}: {512, 20666}, {514, 17770}, {523, 10026}, {647, 20754}, {2786, 51578}, {4608, 31064}, {4705, 20685}, {28482, 101}, {35162, 190}

X(60043) = X(1)X(4024)∩X(2)X(4036)

Barycentrics    (b - c)*(a^4 + b^4 + a^3*c + b^3*c - a^2*c^2 - b^2*c^2 - a*c^3 - b*c^3)*(-a^4 - a^3*b + a^2*b^2 + a*b^3 + b^3*c + b^2*c^2 - b*c^3 - c^4) : :

X(60043) lies on the circumconic {{A,B,C,X(1),X(2)}}, the X-parabola (see X(12065), and these lines: {1, 4024}, {2, 4036}, {28, 2501}, {81, 523}, {105, 53686}, {274, 850}, {513, 59265}, {1432, 27469}, {2787, 17946}, {3733, 8029}, {15328, 57682}, {52376, 58784}

X(60043) = X(i)-isoconjugate of X(j) for these (i,j): {163, 44396}, {424, 4575}, {662, 5164}
X(60043) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 44396}, {136, 424}, {1084, 5164}
X(60043) = cevapoint of X(523) and X(2787)
X(60043) = trilinear pole of line {115, 513}
X(60043) = barycentric product X(i)*X(j) for these {i,j}: {693, 53686}, {2501, 57849}, {14618, 57682}
X(60043) = barycentric quotient X(i)/X(j) for these {i,j}: {512, 5164}, {523, 44396}, {2501, 424}, {53686, 100}, {57682, 4558}, {57849, 4563}

X(60044) = X(1)X(4064)∩X(28)X(523)

Barycentrics    (b - c)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 + a^5*c - a^3*b^2*c - a^2*b^3*c + b^5*c + 2*a^2*b^2*c^2 + a^2*b*c^3 + a*b^2*c^3 - a^2*c^4 - b^2*c^4 - a*c^5 - b*c^5)*(-a^6 - a^5*b + a^2*b^4 + a*b^5 - a^2*b^3*c + b^5*c + a^4*c^2 + a^3*b*c^2 - 2*a^2*b^2*c^2 - a*b^3*c^2 + b^4*c^2 + a^2*b*c^3 + a^2*c^4 - b*c^5 - c^6) : :

X(60044) lies on the circumconic {{A,B,C,X(1),X(2)}}, the the orthic-asymptotic hyperbola, and these lines: {1, 4064}, {28, 523}, {57, 21192}, {81, 525}, {105, 43659}, {274, 3267}, {879, 43700}, {2787, 16100}, {3140, 51258}, {4560, 40143}, {4580, 52376}

X(60044) = nine-point-circle-of-orthic-triangle-inverse of X(7374)}
X(60044) = X(163)-isoconjugate of X(30447)
X(60044) = X(115)-Dao conjugate of X(30447)
X(60044) = cevapoint of X(i) and X(j) for these (i,j): {523, 47227}, {647, 8674}
X(60044) = trilinear pole of line {125, 513}
X(60044) = barycentric product X(i)*X(j) for these {i,j}: {693, 43659}, {850, 43700}
X(60044) = barycentric quotient X(i)/X(j) for these {i,j}: {523, 30447}, {43659, 100}, {43700, 110}

X(60045) = X(1)X(4079)∩X(2)X(4705)

Barycentrics    a*(b - c)*(-(a*b^3) + a^3*c + a^2*b*c - 2*a*b^2*c - b^3*c + a*b*c^2 + a*c^3)*(a^3*b + a*b^3 + a^2*b*c + a*b^2*c - 2*a*b*c^2 - a*c^3 - b*c^3) : :

X(60045) lies on the circumconic {{A,B,C,X(1),X(2)}}, the Lemoine-asymptotic hyperbola, and these lines: {1, 4079}, {2, 4705}, {28, 2489}, {81, 512}, {105, 2375}, {274, 523}, {2787, 39925}, {4160, 30571}, {9178, 53271}, {18105, 52376}, {28840, 34914}

X(60045) = X(i)-isoconjugate of X(j) for these (i,j): {101, 8682}, {110, 57040}
X(60045) = X(i)-Dao conjugate of X(j) for these (i,j): {244, 57040}, {1015, 8682}
X(60045) = trilinear pole of line {513, 3124}
X(60045) = barycentric product X(693)*X(2375)
X(60045) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 8682}, {661, 57040}, {2375, 100}

X(60046) = X(1)X(18026)∩X(3)X(664)

Barycentrics    (a^5*b - 2*a^3*b^3 + a*b^5 - a^5*c + a^3*b^2*c + a^2*b^3*c - b^5*c + a^4*c^2 - a^3*b*c^2 - a*b^3*c^2 + b^4*c^2 + a^3*c^3 + b^3*c^3 - a^2*c^4 - b^2*c^4)*(a^5*b - a^4*b^2 - a^3*b^3 + a^2*b^4 - a^5*c + a^3*b^2*c - a^3*b*c^2 + b^4*c^2 + 2*a^3*c^3 - a^2*b*c^3 + a*b^2*c^3 - b^3*c^3 - b^2*c^4 - a*c^5 + b*c^5) : :

X(60046) lies on the circumconic {{A,B,C,X(1),X(3)}}, the Steiner circumellipse, and these lines: {1, 18026}, {3, 664}, {29, 6528}, {77, 4569}, {78, 668}, {99, 283}, {190, 219}, {284, 648}, {296, 53211}, {332, 670}, {401, 53206}, {1433, 53642}, {1794, 54952}, {1795, 54953}, {1807, 35174}, {2359, 6648}, {2481, 23696}, {4562, 40863}, {6606, 47487}, {17973, 35154}, {18816, 37628}, {18831, 35196}, {31637, 46135}, {33296, 54951}, {38983, 46404}, {44331, 53205}, {52158, 53639}

X(60046) = isogonal conjugate of X(45932)
X(60046) = antitomic conjugate of X(2)
X(60046) = isotomic conjugate of the isogonal conjugate of X(59016)
X(60046) = X(1)-isoconjugate of X(45932)
X(60046) = X(3)-Dao conjugate of X(45932)
X(60046) = trilinear pole of line {2, 652}
X(60046) = barycentric product X(76)*X(59016)
X(60046) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 45932}, {59016, 6}

X(60047) = X(1)X(651)∩X(3)X(1813)

Barycentrics    a^2*(a^2 - 2*a*b + b^2 + a*c + b*c - 2*c^2)*(a^2 - b^2 - c^2)*(a^2 + a*b - 2*b^2 - 2*a*c + b*c + c^2) : :

X(60047) lies on the circumconic {{A,B,C,X(1),X(3)}}, the MacBeath circumconic, and these lines: {1, 651}, {3, 1813}, {29, 648}, {77, 7004}, {78, 1332}, {102, 14733}, {110, 284}, {145, 10570}, {155, 38248}, {219, 1331}, {282, 1998}, {283, 4558}, {332, 4563}, {663, 10764}, {677, 2323}, {938, 54972}, {947, 34486}, {949, 18889}, {1036, 34068}, {1037, 14935}, {1069, 3561}, {1071, 7100}, {1449, 56225}, {1461, 38668}, {1797, 53550}, {1814, 23696}, {1936, 23707}, {2990, 35348}, {3292, 17973}, {3478, 37516}, {3746, 52185}, {4318, 10703}, {5942, 43190}, {7982, 56148}, {8759, 23893}, {13136, 51565}, {18315, 35196}, {23351, 53295}, {46639, 52158}, {52746, 55996}, {53334, 57457}

X(60047) = isogonal conjugate of X(23710)
X(60047) = isotomic conjugate of the polar conjugate of X(2291)
X(60047) = isogonal conjugate of the polar conjugate of X(1121)
X(60047) = X(1121)-Ceva conjugate of X(2291)
X(60047) = X(i)-isoconjugate of X(j) for these (i,j): {1, 23710}, {4, 1155}, {6, 37805}, {19, 527}, {25, 30806}, {33, 1323}, {34, 6745}, {55, 38461}, {65, 52891}, {92, 1055}, {108, 6366}, {162, 30574}, {196, 56763}, {278, 6603}, {281, 6610}, {393, 6510}, {607, 37780}, {915, 12831}, {1638, 1783}, {1897, 14413}, {3064, 23890}, {6139, 18026}, {6174, 36125}, {7128, 33573}, {14392, 36118}, {14414, 36127}, {18344, 56543}, {23346, 44426}, {35293, 36124}, {36121, 51408}
X(60047) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 23710}, {6, 527}, {9, 37805}, {125, 30574}, {223, 38461}, {6505, 30806}, {11517, 6745}, {22391, 1055}, {34467, 14413}, {36033, 1155}, {38983, 6366}, {39006, 1638}, {40602, 52891}
X(60047) = trilinear pole of line {3, 652}
X(60047) = barycentric product X(i)*X(j) for these {i,j}: {3, 1121}, {63, 1156}, {69, 2291}, {77, 41798}, {78, 34056}, {304, 34068}, {348, 4845}, {521, 37139}, {652, 35157}, {1332, 35348}, {1797, 52746}, {6332, 14733}, {6516, 23893}, {7182, 18889}, {35518, 36141}
X(60047) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 37805}, {3, 527}, {6, 23710}, {48, 1155}, {57, 38461}, {63, 30806}, {77, 37780}, {184, 1055}, {212, 6603}, {219, 6745}, {222, 1323}, {255, 6510}, {284, 52891}, {603, 6610}, {647, 30574}, {652, 6366}, {895, 52764}, {1121, 264}, {1156, 92}, {1459, 1638}, {1797, 36887}, {1813, 56543}, {2188, 56763}, {2252, 12831}, {2291, 4}, {3270, 33573}, {3955, 6647}, {4845, 281}, {7193, 24685}, {8677, 42762}, {14733, 653}, {18889, 33}, {20752, 35293}, {22086, 30573}, {22356, 6174}, {22383, 14413}, {23351, 3064}, {23893, 44426}, {32660, 23346}, {32728, 32674}, {34056, 273}, {34068, 19}, {35157, 46404}, {35348, 17924}, {36054, 14414}, {36059, 23890}, {36141, 108}, {37139, 18026}, {41798, 318}, {52746, 46109}

X(60048) = X(283)X(512)∩X(284)X(523)

Barycentrics    (b - c)*(-a^2 + b^2 + c^2)*(a^6 - a^5*b - a*b^5 + b^6 - a^4*b*c - a*b^4*c - 2*a^4*c^2 + a^3*b*c^2 + a*b^3*c^2 - 2*b^4*c^2 + a^2*b*c^3 + a*b^2*c^3 + a^2*c^4 + b^2*c^4)*(a^6 - 2*a^4*b^2 + a^2*b^4 - a^5*c - a^4*b*c + a^3*b^2*c + a^2*b^3*c + a*b^3*c^2 + b^4*c^2 + a*b^2*c^3 - a*b*c^4 - 2*b^2*c^4 - a*c^5 + c^6) : :

X(60048) lies on the circumconic {{A,B,C,X(1),X(3)}}, the orthic-asymptotic hyperbola, and these lines: {3, 57243}, {29, 14618}, {219, 4064}, {283, 525}, {284, 523}, {332, 3267}, {2394, 53334}, {2785, 40081}, {7015, 30212}, {15412, 35196}, {52158, 58759}

X(60048) = trilinear pole of line {125, 652}

X(60049) = X(1)X(1332)∩X(6)X(1331)

Barycentrics    a^2*(a^3 - a*b^2 + 2*b^3 - a^2*c - b^2*c - a*c^2 + c^3)*(a^3 - a^2*b - a*b^2 + b^3 - a*c^2 - b*c^2 + 2*c^3) : :

X(60049) lies on the circumconic {{A,B,C,X(1),X(6)}}, the MacBeath circumconic, and these lines: {1, 1332}, {6, 1331}, {34, 651}, {56, 1813}, {58, 4558}, {86, 4563}, {106, 29241}, {110, 1474}, {193, 43190}, {287, 32029}, {320, 56783}, {518, 1411}, {648, 8747}, {674, 15397}, {895, 2774}, {998, 3751}, {1027, 1814}, {1438, 2323}, {1797, 23345}, {1815, 2424}, {2191, 3315}, {2412, 23887}, {2989, 53352}, {3226, 54979}, {3445, 12595}, {4587, 24483}, {7129, 13138}, {8540, 9432}, {12649, 44765}, {13136, 36123}

X(60049) = reflection of X(1331) in X(6)
X(60049) = isogonal conjugate of X(3011)
X(60049) = isogonal conjugate of the anticomplement of X(50752)
X(60049) = isogonal conjugate of the complement of X(3006)
X(60049) = isotomic conjugate of the polar conjugate of X(9085)
X(60049) = X(15397)-anticomplementary conjugate of X(4329)
X(60049) = X(29241)-Ceva conjugate of X(35365)
X(60049) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3011}, {19, 9028}, {100, 29240}, {661, 4237}, {910, 53133}, {1783, 2504}, {1824, 51607}, {2224, 5513}
X(60049) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 3011}, {6, 9028}, {8054, 29240}, {36830, 4237}, {39006, 2504}
X(60049) = cevapoint of X(6) and X(674)
X(60049) = trilinear pole of line {3, 649}
X(60049) = barycentric product X(i)*X(j) for these {i,j}: {69, 9085}, {190, 35365}, {514, 29241}, {649, 54979}, {3006, 15397}
X(60049) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 9028}, {6, 3011}, {103, 53133}, {110, 4237}, {649, 29240}, {674, 5513}, {1459, 2504}, {1790, 51607}, {9085, 4}, {15397, 675}, {29241, 190}, {35365, 514}, {54979, 1978}

X(60050) = X(1)X(4705)∩X(58)X(512)

Barycentrics    a^2*(b - c)*(a^3 + b^3 + a^2*c + b^2*c - a*c^2 - b*c^2 - 2*c^3)*(a^3 + a^2*b - a*b^2 - 2*b^3 - b^2*c + b*c^2 + c^3) : :

X(60050) lies on the circumconic {{A,B,C,X(1),X(6)}}, the Lemoine-asymptotic hyperbola, and these lines: {1, 4705}, {6, 4079}, {58, 512}, {86, 523}, {106, 28482}, {1474, 2489}, {3226, 35162}, {3733, 22260}, {5029, 17962}, {8747, 58757}, {9013, 34916}, {9178, 53315}, {9277, 38469}, {35364, 53301}, {50344, 52558}

X(60050) = X(i)-isoconjugate of X(j) for these (i,j): {100, 17770}, {662, 10026}, {799, 20666}, {811, 20754}, {4610, 20685}, {31064, 35342}, {37135, 51578}
X(60050) = X(i)-Dao conjugate of X(j) for these (i,j): {1084, 10026}, {8054, 17770}, {17423, 20754}, {38996, 20666}
X(60050) = cevapoint of X(512) and X(5029)
X(60050) = trilinear pole of line {649, 3124}
X(60050) = crossdifference of every pair of points on line {10026, 17770}
X(60050) = barycentric product X(i)*X(j) for these {i,j}: {514, 28482}, {649, 35162}
X(60050) = barycentric quotient X(i)/X(j) for these {i,j}: {512, 10026}, {649, 17770}, {669, 20666}, {3049, 20754}, {5029, 51578}, {28482, 190}, {35162, 1978}, {50344, 31064}, {50487, 20685}

X(60051) = TRILINEAR POLE OF LINE X(3)X(13)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 - 3*a^4*b^2*c^2 - 2*a^2*b^4*c^2 + 4*b^6*c^2 - 2*a^2*b^2*c^4 - 6*b^4*c^4 + 2*a^2*c^6 + 4*b^2*c^6 - c^8 - 2*Sqrt[3]*a^2*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)*S) : :

X(60051) lies on the MacBeath circumconic, the Simmons circumconic that has perspector X(13), and these lines: {13, 11600}, {17, 36316}, {110, 36306}, {476, 16806}, {895, 11139}, {930, 5995}, {1625, 55251}, {4558, 23895}, {4563, 55220}, {8172, 11586}, {11087, 18777}, {11537, 40667}, {14919, 36308}, {36300, 51270}, {36839, 38414}, {46925, 57647}

X(60051) = X(i)-isoconjugate of X(j) for these (i,j): {526, 3376}, {661, 11146}, {1510, 3384}, {1577, 11137}, {2151, 23872}, {2624, 16771}, {11141, 32679}, {23284, 35199}
X(60051) = X(i)-Dao conjugate of X(j) for these (i,j): {36830, 11146}, {40578, 23872}
X(60051) = cevapoint of X(i) and X(j) for these (i,j): {523, 11542}, {525, 44383}, {23283, 36208}, {36304, 55199}
X(60051) = trilinear pole of line {3, 13}
X(60051) = barycentric product X(i)*X(j) for these {i,j}: {13, 32036}, {17, 23895}, {99, 11139}, {300, 16806}, {476, 19779}, {930, 16770}, {3375, 32680}, {3457, 55220}, {5995, 34389}, {11142, 46139}, {35139, 51890}, {36306, 40712}
X(60051) = barycentric quotient X(i)/X(j) for these {i,j}: {13, 23872}, {17, 23870}, {110, 11146}, {476, 16771}, {930, 19778}, {1576, 11137}, {3375, 32679}, {3457, 55221}, {5618, 11581}, {5995, 61}, {8603, 57122}, {11083, 57142}, {11087, 23284}, {11134, 44809}, {11139, 523}, {11142, X(60051) = 1510}, {14560, 11141}, {15475, 43968}, {16770, 41298}, {16806, 15}, {19779, 3268}, {21461, 6137}, {23895, 302}, {32036, 298}, {32678, 3376}, {32737, 51891}, {35330, 52971}, {35331, 40695}, {36148, 3384}, {36304, 35443}, {36306, 473}, {36839, 8838}, {38414, 52348}, {51890, 526}, {52930, 11127}, {55199, 30465}

X(60052) = TRILINEAR POLE OF LINE X(3)X(14)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 - 3*a^4*b^2*c^2 - 2*a^2*b^4*c^2 + 4*b^6*c^2 - 2*a^2*b^2*c^4 - 6*b^4*c^4 + 2*a^2*c^6 + 4*b^2*c^6 - c^8 + 2*Sqrt[3]*a^2*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)*S) : :

X(60052) lies on the MacBeath circumconic, the Simmons circumconic that has perspector X(14), and these lines: {14, 11601}, {18, 36317}, {110, 36309}, {476, 16807}, {895, 11138}, {930, 5994}, {1625, 55251}, {4558, 23896}, {4563, 55222}, {8173, 15743}, {11082, 18776}, {11549, 40668}, {14919, 36311}, {36301, 51277}, {36840, 38413}, {46926, 57647}

X(60052) = X(i)-isoconjugate of X(j) for these (i,j): {526, 3383}, {661, 11145}, {1510, 3375}, {1577, 11134}, {2152, 23873}, {2624, 16770}, {11142, 32679}, {23283, 35198}
X(60052) = X(i)-Dao conjugate of X(j) for these (i,j): {36830, 11145}, {40579, 23873}
X(60052) = cevapoint of X(i) and X(j) for these (i,j): {523, 11543}, {525, 44382}, {23284, 36209}, {36305, 55201}
X(60052) = trilinear pole of line {3, 14}
X(60052) = barycentric product X(i)*X(j) for these {i,j}: {14, 32037}, {18, 23896}, {99, 11138}, {301, 16807}, {476, 19778}, {930, 16771}, {3384, 32680}, {3458, 55222}, {5994, 34390}, {11141, 46139}, {35139, 51891}, {36309, 40711}
X(60052) = barycentric quotient X(i)/X(j) for these {i,j}: {14, 23873}, {18, 23871}, {110, 11145}, {476, 16770}, {930, 19779}, {1576, 11134}, {3384, 32679}, {3458, 55223}, {5619, 11582}, {5994, 62}, {8604, 57123}, {11082, 23283}, {11088, 57143}, {11137, 44809}, {11138, 523}, {11141, 1510}, {14560, 11142}, {15475, 43967}, {16771, 41298}, {16807, 16}, {19778, 3268}, {21462, 6138}, {23896, 303}, {32037, 299}, {32678, 3383}, {32737, 51890}, {35329, 52972}, {35332, 40696}, {36148, 3375}, {36305, 35444}, {36309, 472}, {36840, 8836}, {38413, 52349}, {51891, 526}, {52929, 11126}, {55201, 30468}

X(60053) = TRILINEAR POLE OF LINE X(3)X(125)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^2 - b^2 - c^2)*(a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^2 - b^2 + a*c + c^2) : :

X(60053) lies on the MacBeath circumconic, the orthic-asymptotic hyperbola, and these lines: {6, 43084}, {68, 53168}, {69, 56399}, {74, 51456}, {94, 323}, {99, 54959}, {110, 476}, {155, 58725}, {193, 56403}, {249, 14570}, {265, 895}, {287, 328}, {394, 57482}, {511, 53768}, {524, 1989}, {525, 4558}, {648, 14618}, {651, 32680}, {687, 44427}, {879, 43083}, {935, 58979}, {1141, 41205}, {1331, 4064}, {1352, 14356}, {1503, 53771}, {1813, 57243}, {1992, 56395}, {1993, 57486}, {2394, 2407}, {2421, 17708}, {2990, 37783}, {3267, 4563}, {3580, 16310}, {3629, 56404}, {5654, 39170}, {6193, 53169}, {6368, 39193}, {9214, 54554}, {10412, 44768}, {11060, 41617}, {11064, 11079}, {12028, 13754}, {14254, 15068}, {14582, 14977}, {14591, 16237}, {15421, 43755}, {15455, 26696}, {16167, 35189}, {18576, 58885}, {20573, 44137}, {30529, 37779}, {37784, 56006}, {41597, 58925}, {43187, 55226}, {46639, 58759}

X(60053) = reflection of X(i) in X(j) for these {i,j}: {74, 51456}, {265, 51847}, {3580, 16310}, {39193, 47390}, {53768, 56397}
X(60053) = isogonal conjugate of X(47230)
X(60053) = isotomic conjugate of X(44427)
X(60053) = isotomic conjugate of the anticomplement of X(6334)
X(60053) = isotomic conjugate of the isogonal conjugate of X(32662)
X(60053) = isotomic conjugate of the polar conjugate of X(476)
X(60053) = isogonal conjugate of the polar conjugate of X(35139)
X(35139)-Ceva conjugate of X(476)
X(60053) = X(i)-isoconjugate of X(j) for these (i,j): {1, 47230}, {4, 2624}, {19, 526}, {25, 32679}, {31, 44427}, {50, 24006}, {92, 14270}, {162, 2088}, {163, 35235}, {186, 661}, {340, 798}, {512, 52414}, {654, 1825}, {656, 52418}, {810, 14165}, {1096, 8552}, {1109, 14591}, {1577, 34397}, {1835, 9404}, {1870, 55210}, {1973, 3268}, {2081, 2190}, {2245, 54244}, {2315, 14222}, {2433, 35201}, {2436, 36063}, {2501, 6149}, {2616, 11062}, {2623, 51801}, {2643, 14590}, {3258, 36131}, {3708, 53176}, {4242, 20982}, {4707, 14975}, {5962, 55216}, {6198, 21828}, {14838, 44113}, {16186, 24019}, {16577, 58313}, {18334, 36129}, {21741, 44428}, {36119, 52743}, {36128, 44814}, {41502, 51663}, {52413, 57099}, {52416, 55250}, {56792, 56829}
X(60053) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 44427}, {3, 47230}, {5, 2081}, {6, 526}, {115, 35235}, {125, 2088}, {577, 44808}, {1511, 52743}, {6337, 3268}, {6338, 45792}, {6503, 8552}, {6505, 32679}, {14993, 2501}, {15295, 2489}, {22391, 14270}, {31998, 340}, {35071, 16186}, {36033, 2624}, {36830, 186}, {38999, 47414}, {39008, 3258}, {39021, 16221}, {39054, 52414}, {39062, 14165}, {39170, 1637}, {40596, 52418}, {52032, 41078}, {52881, 45808}, {56399, 55121}
X(60053) = cevapoint of X(i) and X(j) for these (i,j): {6, 55121}, {265, 14582}, {394, 41077}, {523, 16310}, {525, 11064}, {647, 13754}, {1989, 43088}, {2407, 14570}, {9033, 56399}, {43083, 50433}
X(60053) = trilinear pole of line {3, 125}
X(60053) = barycentric product X(i)*X(j) for these {i,j}: {3, 35139}, {63, 32680}, {69, 476}, {75, 36061}, {76, 32662}, {94, 4558}, {99, 265}, {110, 328}, {249, 14592}, {300, 38413}, {301, 38414}, {304, 32678}, {305, 14560}, {326, 36129}, {339, 58979}, {394, 46456}, {525, 39295}, {670, 52153}, {1789, 35174}, {1799, 46155}, {1989, 4563}, {2166, 4592}, {4590, 14582}, {5961, 46134}, {6331, 50433}, {6742, 57985}, {11060, 52608}, {11064, 39290}, {14356, 17932}, {14559, 30786}, {15475, 47389}, {16077, 51254}, {18020, 43083}, {18878, 39170}, {20573, 32661}, {23181, 46138}, {23588, 45792}, {23895, 40710}, {23896, 40709}, {37638, 54959}, {41512, 57829}, {43088, 57763}, {43755, 57486}, {44769, 57482}, {47318, 52381}, {52431, 55209}
X(60053) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 44427}, {3, 526}, {6, 47230}, {48, 2624}, {49, 44809}, {63, 32679}, {69, 3268}, {94, 14618}, {99, 340}, {110, 186}, {112, 52418}, {155, 44816}, {184, 14270}, {216, 2081}, {249, 14590}, {250, 53176}, {265, 523}, {328, 850}, {343, 41078}, {394, 8552}, {476, 4}, {477, 53158}, {520, 16186}, {523, 35235}, {647, 2088}, {648, 14165}, {662, 52414}, {759, 54244}, {895, 9213}, {925, 5962}, {930, 562}, {1147, 44808}, {1300, 14222}, {1332, 42701}, {1576, 34397}, {1625, 11062}, {1636, 47414}, {1789, 3738}, {1793, 35057}, {1807, 57099}, {1989, 2501}, {2166, 24006}, {2222, 1825}, {2407, 14920}, {2420, 39176}, {2437, 47228}, {2617, 51801}, {3284, 52743}, {3292, 44814}, {3615, 44428}, {3926, 45792}, {4558, 323}, {4563, 7799}, {4575, 6149}, {5504, 15470}, {5627, 18808}, {5961, 924}, {5994, 8739}, {5995, 8740}, {6390, 45808}, {6742, 860}, {7100, 53527}, {8606, 53562}, {9033, 3258}, {10217, 23283}, {10218, 23284}, {10412, 2970}, {10420, 38936}, {11060, 2489}, {11064, 5664}, {11077, 2623}, {11079, 2433}, {12028, 15328}, {13486, 1870}, {14356, 16230}, {14380, 56792}, {14559, 468}, {14560, 25}, {14570, 14918}, {14582, 115}, {14591, 36423}, {14592, 338}, {14595, 15475}, {15329, 1986}, {15395, 1304}, {15475, 8754}, {17702, 55130}, {18384, 58757}, {18883, 57065}, {23181, 1154}, {23357, 14591}, {23895, 471}, {23896, 470}, {23968, 6103}, {26700, 1835}, {31676, 20188}, {32661, 50}, {32662, 6}, {32663, 2436}, {32678, 19}, {32680, 92}, {32710, 58072}, {35139, 264}, {35189, 32710}, {36047, 36130}, {36061, 1}, {36129, 158}, {36296, 6138}, {36297, 6137}, {38413, 15}, {38414, 16}, {39170, 55121}, {39290, 16080}, {39295, 648}, {40709, 23871}, {40710, 23870}, {41392, 1990}, {41512, 403}, {43083, 125}, {43088, 136}, {43754, 14355}, {43965, 6143}, {44769, 57487}, {45792, 23965}, {46155, 427}, {46456, 2052}, {46969, 58727}, {47053, 2914}, {47318, 52412}, {47390, 52603}, {50433, 647}, {50461, 8562}, {50463, 23286}, {50464, 14380}, {50465, 57123}, {50466, 57122}, {51254, 9033}, {52153, 512}, {52351, 7265}, {52381, 4707}, {52388, 6370}, {52390, 51663}, {52431, 55210}, {52603, 3043}, {53169, 55136}, {54959, 43530}, {55121, 16221}, {56395, 14273}, {56399, 1637}, {56403, 47236}, {57482, 41079}, {57736, 2605}, {57985, 4467}, {58979, 250}, {59209, 14446}, {59210, 14447}
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2407, 2410, 39295}, {14559, 46155, 14560}, {14560, 46155, 476}, {23895, 23896, 476}, {39290, 39295, 2410}

X(60054) = TRILINEAR POLE OF LINE X(3)X(3124)

Barycentrics    a^2*(a^2 - b^2)*(a^2 - c^2)*(a^4 - 3*a^2*b^2 + 4*b^4 - 3*b^2*c^2 + c^4)*(a^4 + b^4 - 3*a^2*c^2 - 3*b^2*c^2 + 4*c^4) : :

X(60054) lies on the MacBeath circumconic, the Lemoine-asymptotic hyperbola, and these lines: {110, 2489}, {287, 51441}, {512, 4558}, {523, 4563}, {648, 58757}, {895, 1570}, {1331, 4079}, {1332, 4705}, {2422, 43754}, {2987, 8681}, {3564, 41909}, {18315, 58756}, {32127, 56007}, {44767, 53351}

X(60054) = isogonal conjugate of X(45687)
X(60054) = isogonal conjugate of the anticomplement of X(45688)
X(60054) = isotomic conjugate of the anticomplement of X(2510)
X(60054) = X(i)-isoconjugate of X(j) for these (i,j): {1, 45687}, {661, 35297}
X(60054) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 45687}, {36830, 35297}
X(60054) = cevapoint of X(i) and X(j) for these (i,j): {6, 2872}, {523, 45921}
X(60054) = trilinear pole of line {3, 3124}
X(60054) = barycentric product X(99)*X(14498)
X(60054) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 45687}, {110, 35297}, {14498, 523}

X(60055) = TRILINEAR POLE OF LINE X(1)X(115)

Barycentrics    (a - b)*(a - c)*(a^4 + a^3*b + a^2*b^2 + a*b^3 + b^4 - 2*a^2*c^2 - 2*a*b*c^2 - 2*b^2*c^2 + c^4)*(a^4 - 2*a^2*b^2 + b^4 + a^3*c - 2*a*b^2*c + a^2*c^2 - 2*b^2*c^2 + a*c^3 + c^4) : :

X(60055) lies on the Mandart circumellipse, the X-parabola (see X(12065), and these lines: {100, 4024}, {110, 12072}, {162, 2501}, {190, 4036}, {249, 12071}, {523, 662}, {799, 850}, {2349, 12079}, {2395, 36084}, {2580, 39241}, {2581, 39240}, {4599, 58784}, {5466, 36085}, {6083, 14734}, {9218, 12069}, {10412, 32680}, {37212, 39185}

X(60055) = cevapoint of X(523) and X(17768)
X(60055) = trilinear pole of line {1, 115}
X(60055) = barycentric product X(75)*X(59088)
X(60055) = barycentric quotient X(59088)/X(1)

X(60056) = TRILINEAR POLE OF LINE X(1)X(125)

Barycentrics    (a - b)*(a - c)*(a^6 + a^5*b + a*b^5 + b^6 - a^4*c^2 - a^3*b*c^2 + a^2*b^2*c^2 - a*b^3*c^2 - b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 + a^5*c - a^3*b^2*c + a^2*b^2*c^2 - b^4*c^2 - a*b^2*c^3 - b^2*c^4 + a*c^5 + c^6) : :

X(60056) lies on the Mandart circumellipse, the orthic-asymptotic hyperbola, and these lines: {100, 4064}, {162, 523}, {525, 662}, {651, 57243}, {799, 3267}, {823, 14618}, {879, 36084}, {897, 51258}, {4580, 4599}, {14592, 32680}, {14977, 36085}

X(60056) = trilinear pole of line {1, 125}

X(60057) = TRILINEAR POLE OF LINE X(1)X(3124)

Barycentrics    a*(a - b)*(a - c)*(-b^4 + a^3*c - 2*a*b^2*c + a^2*c^2 + a*c^3)*(a^3*b + a^2*b^2 + a*b^3 - 2*a*b*c^2 - c^4) : :

X(60057) lies on the Mandart circumellipse, the Lemoine-asymptotic hyperbola, and these lines: {100, 4079}, {162, 2489}, {190, 4705}, {512, 662}, {523, 799}, {823, 58757}, {882, 37134}, {1821, 51441}, {2422, 36084}, {4599, 18105}, {9178, 36085}, {15475, 32680}, {37204, 52618}

X(60057) = trilinear pole of line {1, 3124}

X(60058) = X(44)X(14425)∩X(65)X(6789)

Barycentrics    (2*a - b - c)*(a + b - c)*(a - b + c)*(a^3 - 2*a^2*b - 2*a^2*c + 5*a*b*c - b^2*c - b*c^2) : :
X(60058) = 3 X[1319] - 2 X[39752]

X(60058) lies on these lines: {44, 14425}, {65, 6789}, {214, 519}, {899, 43924}, {1155, 3667}, {1447, 3263}, {1737, 22102}, {1788, 6790}, {2222, 39445}, {5433, 23869}, {5844, 24216}, {6079, 8686}, {6788, 24914}, {7180, 9360}, {15325, 53618}

X(60058) = reflection of X(i) in X(j) for these {i,j}: {14027, 3911}, {53618, 15325}
X(60058) = barycentric product X(3911)*X(9458)
X(60058) = barycentric quotient X(9458)/X(4997)

X(60059) = X(59)X(518)∩X(65)X(1083)

Barycentrics    a*(a + b - c)*(a - b + c)*(2*a^4 - 5*a^3*b + 5*a^2*b^2 - 3*a*b^3 + b^4 - 5*a^3*c + 8*a^2*b*c - 4*a*b^2*c + 5*a^2*c^2 - 4*a*b*c^2 + 2*b^2*c^2 - 3*a*c^3 + c^4) : :

X(60059) lies on these lines: {44, 3669}, {46, 14661}, {59, 518}, {65, 1083}, {241, 5526}, {514, 2348}, {1155, 3309}, {1429, 5525}, {1708, 56528}, {3911, 36954}, {6603, 45234}, {6706, 9318}, {18343, 24914}, {24798, 27006}

X(60060) = X(11)X(516)∩X(105)X(927)

Barycentrics    (a + b - c)*(a - b + c)*(2*a^6 - 3*a^5*b + 2*a^4*b^2 - 3*a^3*b^3 + 2*a^2*b^4 - 3*a^5*c + 2*a^4*b*c + 2*a^3*b^2*c - a^2*b^3*c + a*b^4*c - b^5*c + 2*a^4*c^2 + 2*a^3*b*c^2 - 2*a^2*b^2*c^2 - a*b^3*c^2 - 3*a^3*c^3 - a^2*b*c^3 - a*b^2*c^3 + 2*b^3*c^3 + 2*a^2*c^4 + a*b*c^4 - b*c^5) : :
X(60060) = X[3322] + 2 X[3911], 3 X[7677] - X[14189]

X(60060) lies on these lines: {11, 516}, {105, 927}, {108, 242}, {514, 1319}, {515, 5532}, {676, 1279}, {1284, 4077}, {1360, 3323}, {1362, 51435}, {1421, 5018}, {1456, 3676}, {1458, 4724}, {2222, 14204}, {2223, 52480}, {2348, 3234}, {3057, 31852}, {3685, 4998}, {5144, 5427}, {6610, 28209}, {9436, 17768}, {15251, 53617}, {15253, 37897}, {34805, 43065}, {40554, 51400}, {44675, 55370}

X(60060) = reflection of X(55370) in X(44675)

X(60061) = X(100)X(518)∩X(516)X(3021)

Barycentrics    a*(2*a^7 - 5*a^6*b + 6*a^5*b^2 - 5*a^4*b^3 - 2*a^3*b^4 + 9*a^2*b^5 - 6*a*b^6 + b^7 - 5*a^6*c + 6*a^5*b*c - 2*a^4*b^2*c + a^3*b^3*c - 8*a^2*b^4*c + 9*a*b^5*c - b^6*c + 6*a^5*c^2 - 2*a^4*b*c^2 + 6*a^3*b^2*c^2 - a^2*b^3*c^2 - 14*a*b^4*c^2 + b^5*c^2 - 5*a^4*c^3 + a^3*b*c^3 - a^2*b^2*c^3 + 22*a*b^3*c^3 - b^4*c^3 - 2*a^3*c^4 - 8*a^2*b*c^4 - 14*a*b^2*c^4 - b^3*c^4 + 9*a^2*c^5 + 9*a*b*c^5 + b^2*c^5 - 6*a*c^6 - b*c^6 + c^7) : :

X(60061) lies on these lines: {100, 518}, {516, 3021}, {1083, 37605}, {1319, 3309}, {5160, 59812}, {14201, 34855}, {14661, 37618}, {39754, 41339}

X(60062) = X(11)X(515)∩X(30)X(1785)

Barycentrics    2*a^9 - 3*a^8*b - a^7*b^2 + 4*a^6*b^3 - 4*a^5*b^4 + a^4*b^5 + 3*a^3*b^6 - 2*a^2*b^7 - 3*a^8*c + 8*a^7*b*c - 5*a^6*b^2*c - 4*a^5*b^3*c + 10*a^4*b^4*c - 8*a^3*b^5*c - a^2*b^6*c + 4*a*b^7*c - b^8*c - a^7*c^2 - 5*a^6*b*c^2 + 16*a^5*b^2*c^2 - 11*a^4*b^3*c^2 - 7*a^3*b^4*c^2 + 15*a^2*b^5*c^2 - 8*a*b^6*c^2 + b^7*c^2 + 4*a^6*c^3 - 4*a^5*b*c^3 - 11*a^4*b^2*c^3 + 24*a^3*b^3*c^3 - 12*a^2*b^4*c^3 - 4*a*b^5*c^3 + 3*b^6*c^3 - 4*a^5*c^4 + 10*a^4*b*c^4 - 7*a^3*b^2*c^4 - 12*a^2*b^3*c^4 + 16*a*b^4*c^4 - 3*b^5*c^4 + a^4*c^5 - 8*a^3*b*c^5 + 15*a^2*b^2*c^5 - 4*a*b^3*c^5 - 3*b^4*c^5 + 3*a^3*c^6 - a^2*b*c^6 - 8*a*b^2*c^6 + 3*b^3*c^6 - 2*a^2*c^7 + 4*a*b*c^7 + b^2*c^7 - b*c^8 : :
X(60062) = X[10538] - 3 X[13587]

X(60062) lies on these lines: {11, 515}, {30, 1785}, {36, 56423}, {65, 31866}, {108, 2734}, {243, 24032}, {516, 3326}, {522, 1155}, {851, 24006}, {1324, 14667}, {1459, 2635}, {1846, 38554}, {1861, 40558}, {2222, 14204}, {2718, 53610}, {7354, 51889}, {9393, 52306}, {10538, 13587}, {18339, 24914}, {36975, 56825}

X(60062) = midpoint of X(i) and X(j) for these {i,j}: {6905, 45766}, {36975, 56825}

X(60063) = X(542)X(38679)∩X(690)X(691)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^16 - 3*a^14*b^2 + 3*a^12*b^4 + 5*a^10*b^6 - 10*a^8*b^8 - a^6*b^10 + 7*a^4*b^12 - a^2*b^14 - b^16 - 3*a^14*c^2 + 9*a^12*b^2*c^2 - 15*a^10*b^4*c^2 - 5*a^8*b^6*c^2 + 39*a^6*b^8*c^2 - 48*a^4*b^10*c^2 + 16*a^2*b^12*c^2 + 3*a^12*c^4 - 15*a^10*b^2*c^4 + 45*a^8*b^4*c^4 - 41*a^6*b^6*c^4 + 81*a^4*b^8*c^4 - 36*a^2*b^10*c^4 + 4*b^12*c^4 + 5*a^10*c^6 - 5*a^8*b^2*c^6 - 41*a^6*b^4*c^6 - 79*a^4*b^6*c^6 + 21*a^2*b^8*c^6 - 10*a^8*c^8 + 39*a^6*b^2*c^8 + 81*a^4*b^4*c^8 + 21*a^2*b^6*c^8 - 6*b^8*c^8 - a^6*c^10 - 48*a^4*b^2*c^10 - 36*a^2*b^4*c^10 + 7*a^4*c^12 + 16*a^2*b^2*c^12 + 4*b^4*c^12 - a^2*c^14 - c^16) : :

X(60063) lies on the curve Q000aH3 and these lines: {542, 38679}, {690, 691}, {895, 54246}, {4558, 39138}, {14830, 22265}, {17708, 59775}, {53605, 53793}

X(60063) = reflection of X(20404) in X(691)

X(60064) = X(1)X(4076)∩X(106)X(519)

Barycentrics    a^7 - 3*a^6*b + 10*a^4*b^3 + 3*a^3*b^4 - 3*a^2*b^5 - 3*a^6*c + 18*a^5*b*c - 30*a^4*b^2*c - 36*a^3*b^3*c + 15*a^2*b^4*c - 30*a^4*b*c^2 + 131*a^3*b^2*c^2 - 45*a^2*b^3*c^2 + 9*a*b^4*c^2 - b^5*c^2 + 10*a^4*c^3 - 36*a^3*b*c^3 - 45*a^2*b^2*c^3 + 18*a*b^3*c^3 - 3*b^4*c^3 + 3*a^3*c^4 + 15*a^2*b*c^4 + 9*a*b^2*c^4 - 3*b^3*c^4 - 3*a^2*c^5 - b^2*c^5 : :

X(60064) lies on the curve Q000aH3 and these lines: {1, 4076}, {2, 14507}, {106, 519}, {3189, 21306}, {3667, 38671}, {5516, 21290}, {44873, 53790}, {53799, 58371}

X(60064) = reflection of X(i) in X(j) for these {i,j}: {6079, 106}, {21290, 5516}
X(60064) = anticomplement of X(14507)

X(60065) = X(2)X(14505)∩X(101)X(514)

Barycentrics    (a - b)*(a - c)*(a^6 - a^5*b - 2*a^3*b^3 + 3*a^2*b^4 - a*b^5 - a^5*c + a^4*b*c + 2*a^3*b^2*c - 4*a^2*b^3*c + 3*a*b^4*c - b^5*c + 2*a^3*b*c^2 + 2*a^2*b^2*c^2 - 2*a*b^3*c^2 + 4*b^4*c^2 - 2*a^3*c^3 - 4*a^2*b*c^3 - 2*a*b^2*c^3 - 6*b^3*c^3 + 3*a^2*c^4 + 3*a*b*c^4 + 4*b^2*c^4 - a*c^5 - b*c^5) : :
X(60065) = 3 X[2] - 4 X[55316]

X(60065) lies on the curve Q000aH3 and these lines: {2, 14505}, {59, 56322}, {101, 514}, {150, 1566}, {218, 56379}, {516, 38666}, {2724, 2808}, {14732, 20096}, {14887, 50351}, {18328, 59362}

X(60065) = midpoint of X(14732) and X(20096)
X(60065) = reflection of X(i) in X(j) for these {i,j}: {150, 1566}, {927, 101}, {14505, 55316}, {14512, 2724}
X(60065) = anticomplement of X(14505)
X(60065) = {X(14505),X(55316)}-harmonic conjugate of X(2)

X(60066) = X(2)X(45772)∩X(4)X(542)

Barycentrics    7*a^12 - 16*a^10*b^2 + 8*a^8*b^4 + 5*a^6*b^6 - 10*a^4*b^8 + 11*a^2*b^10 - 5*b^12 - 16*a^10*c^2 + 42*a^8*b^2*c^2 - 31*a^6*b^4*c^2 + 26*a^4*b^6*c^2 - 30*a^2*b^8*c^2 + 17*b^10*c^2 + 8*a^8*c^4 - 31*a^6*b^2*c^4 - 9*a^4*b^4*c^4 + 17*a^2*b^6*c^4 - 22*b^8*c^4 + 5*a^6*c^6 + 26*a^4*b^2*c^6 + 17*a^2*b^4*c^6 + 20*b^6*c^6 - 10*a^4*c^8 - 30*a^2*b^2*c^8 - 22*b^4*c^8 + 11*a^2*c^10 + 17*b^2*c^10 - 5*c^12 : :
X(60066) = 3 X[9166] - X[45774]

X(60066) lies on these lines: {2, 45772}, {4, 542}, {1551, 22329}, {2793, 3543}, {6792, 58856}, {8593, 54395}, {9166, 45774}

X(60066) = reflection of X(i) in X(j) for these {i,j}: {45772, 2}, {48983, 9880}
X(60066) = {X(51482),X(51483)}-harmonic conjugate of X(9144)

X(60067) = X(2)X(98)∩X(4)X(42810)

Barycentrics    a^2*(11*b^2*c^2 + 8*a^2*(a^2 - b^2 - c^2) - 3*b^2*c^2*J^2) + 2*Sqrt[-((a^2 - b^2 - c^2)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^2 + b^2 + c^2))]*S : :

X(60067) lies on the Jerabek circumhyperbola of the anticomplementary triangle, the Hatzipolakis-Suppa ellipse (see X(46440)), and these lines: {2, 98}, {4, 42810}, {69, 5003}, {1503, 5002}, {3564, 5000}, {5001, 18440}, {12383, 40894}, {15069, 41199}, {34240, 44780}

X(60067) = reflection of X(i) in X(j) for these {i,j}: {3448, 32619}, {5002, 41198}
X(60067) = anticomplement of X(32618)
X(60067) = anticomplement of the isogonal conjugate of X(5000)
X(60067) = anticomplement of the isotomic conjugate of X(44780)
X(60067) = anticomplementary isogonal conjugate of X(5002)
X(60067) = psi-transform of X(47613)
X(60067) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1, 5002}, {92, 44780}, {5000, 8}, {8767, 34239}, {41196, 6360}, {41198, 4329}, {44778, 192}, {44780, 6327}
X(60067) = X(i)-Ceva conjugate of X(j) for these (i,j): {34240, 5003}, {44780, 2}
{X(1352),X(32619)}-harmonic conjugate of X(2)

X(60068) = X(2)X(98)∩X(4)X(42809)

Barycentrics    a^2*(11*b^2*c^2 + 8*a^2*(a^2 - b^2 - c^2) - 3*b^2*c^2*J^2) - 2*Sqrt[-((a^2 - b^2 - c^2)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^2 + b^2 + c^2))]*S : :

X(60068) lies on the Jerabek circumhyperbola of the anticomplementary triangle, the Hatzipolakis-Suppa ellipse (see X(46440)), and these lines: {2, 98}, {4, 42809}, {69, 5002}, {1503, 5003}, {3564, 5001}, {5000, 18440}, {12383, 40895}, {15069, 41198}, {34239, 44781}

X(60068) = reflection of X(i) in X(j) for these {i,j}: {3448, 32618}, {5003, 41199}
X(60068) = anticomplement of X(32619)
X(60068) = anticomplement of the isogonal conjugate of X(5001)
X(60068) = anticomplement of the isotomic conjugate of X(44781)
X(60068) = anticomplementary isogonal conjugate of X(5003)
X(60068) = psi-transform of X(47612)
X(60068) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1, 5003}, {92, 44781}, {5001, 8}, {8767, 34240}, {41197, 6360}, {41199, 4329}, {44779, 192}, {44781, 6327}
X(60068) = X(i)-Ceva conjugate of X(j) for these (i,j): {34239, 5002}, {44781, 2}
X(60068) = {X(1352),X(32618)}-harmonic conjugate of X(2)

X(60069) = X(2)X(14)∩X(17)X(39)

Barycentrics    Sqrt[3]*(a^2*b^4 - b^6 + 4*a^2*b^2*c^2 + b^4*c^2 + a^2*c^4 + b^2*c^4 - c^6) - (-4*a^4 + 8*a^2*b^2 - 2*b^4 + 8*a^2*c^2 + 4*b^2*c^2 - 2*c^4)*S : :

X(60069) lies on these lines: {2, 14}, {5, 23004}, {6, 16529}, {13, 8724}, {16, 5613}, {17, 39}, {18, 5471}, {62, 6783}, {99, 624}, {115, 16966}, {140, 53442}, {395, 22997}, {542, 16242}, {547, 53447}, {636, 7836}, {2782, 46054}, {3107, 33390}, {3132, 8175}, {5092, 21157}, {5116, 11646}, {5469, 36764}, {5470, 6775}, {5474, 19107}, {5479, 42918}, {5872, 10104}, {6672, 6782}, {6773, 42089}, {6774, 6777}, {7799, 21360}, {8290, 8292}, {9113, 16961}, {9116, 9886}, {9750, 43460}, {10616, 41754}, {10645, 22512}, {10646, 41023}, {11289, 52642}, {11308, 54298}, {11481, 48656}, {11603, 13188}, {13102, 42095}, {14144, 31704}, {16002, 42580}, {16268, 41746}, {16963, 51203}, {18582, 46854}, {19106, 22797}, {22510, 23302}, {22998, 45880}, {30471, 41094}, {33389, 41021}, {34755, 47864}, {36252, 42488}, {36962, 42100}, {36968, 41043}, {37824, 52643}, {42111, 59396}, {42489, 53464}, {42914, 59402}, {43028, 59384}, {48657, 54490}, {51013, 51207}

X(60069) = reflection of X(14) in X(37835)
X(60069) = circumcircle-of-outer-Napoleon-triangle-inverse of X(6780)
X(60069) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14, 5464, 6780}, {15, 6114, 14}, {16, 5613, 6778}, {18, 25236, 5471}, {617, 18581, 47860}, {619, 5978, 5464}, {619, 6114, 15}, {5464, 22490, 12154}, {6775, 37832, 5470}, {6777, 33416, 6774}, {9886, 50858, 9116}, {11646, 15561, 36766}, {18581, 47860, 14}

X(60070) = CIRCUMCIRCLE-INVERSE OF X(11600)

Barycentrics    Sin[A]*Cos[3*A - Pi/6]*Sec[2*A - Pi/6] : :

X(60070) lies on these lines: {3, 11600}, {14, 36248}, {17, 38944}, {2070, 15743}, {6105, 11087}, {7502, 40104}, {8172, 34009}, {8603, 50469}, {37848, 52203}

X(60070) = circumcircle-inverse of X(11600)

X(60071) = X(2)X(2245)∩X(10)X(908)

Barycentrics    (a*b*(a+b)+(a^2+b^2)*c-c^3)*(-b^3+a*c^2+b*c^2+a^2*(b+c)) : :

X(60071) lies on the Kiepert hyperbola and on these lines: {1, 60089}, {2, 2245}, {3, 5397}, {4, 5396}, {5, 60112}, {6, 24624}, {10, 908}, {21, 43531}, {30, 54679}, {76, 3936}, {81, 10478}, {94, 8818}, {98, 26282}, {192, 4080}, {226, 17080}, {262, 8229}, {321, 3262}, {381, 54528}, {411, 54972}, {469, 40149}, {661, 60074}, {671, 31179}, {1446, 33949}, {1751, 32911}, {1916, 31120}, {2171, 60091}, {2292, 60116}, {3240, 13576}, {3452, 60243}, {3485, 60086}, {3835, 4049}, {4052, 42044}, {4295, 26028}, {4358, 18055}, {4383, 57721}, {4389, 30588}, {4648, 60169}, {5057, 5143}, {5226, 60188}, {5233, 60097}, {5249, 56226}, {5278, 60235}, {5327, 60080}, {5712, 60156}, {5718, 46487}, {5739, 60206}, {5741, 34258}, {6539, 31056}, {6824, 60164}, {6825, 60154}, {6828, 57719}, {6837, 60157}, {6838, 60158}, {6841, 57720}, {6852, 60173}, {6871, 43533}, {6872, 60077}, {6985, 56845}, {7377, 54739}, {10883, 43672}, {11111, 54624}, {11114, 60078}, {11813, 25378}, {14009, 60110}, {14534, 19684}, {14554, 37651}, {16705, 58012}, {17056, 57722}, {17234, 39994}, {17577, 60079}, {18134, 40013}, {18139, 40012}, {18316, 56402}, {18393, 56419}, {22000, 56214}, {24457, 35353}, {24597, 55962}, {26758, 27797}, {27131, 60203}, {29643, 43534}, {30566, 30830}, {30828, 60242}, {30834, 60251}, {30937, 60134}, {30964, 31006}, {32782, 60084}, {33133, 60088}, {35466, 60247}, {36002, 56144}, {37330, 60108}, {37633, 60085}, {37635, 60258}, {37662, 60087}, {37680, 60075}, {52212, 57645}, {52255, 60227}, {52269, 54516}

X(60071) = isogonal conjugate of X(2278)
X(60071) = isotomic conjugate of X(1150)
X(60071) = trilinear pole of line {10015, 11809}
X(60071) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 2278}, {6, 993}, {31, 1150}, {48, 5136}, {101, 55969}, {604, 49492}, {692, 48321}, {5546, 51659}, {14299, 32641}
X(60071) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 1150}, {3, 2278}, {9, 993}, {1015, 55969}, {1086, 48321}, {1249, 5136}, {3161, 49492}
X(60071) = X(i)-cross conjugate of X(j) for these {i, j}: {4424, 75}, {4957, 514}, {5718, 2}, {18118, 38340}, {39542, 7}, {45095, 58026}, {46487, 24624}, {49277, 190}
X(60071) = pole of line {5718, 46487} with respect to the Kiepert hyperbola
X(60071) = pole of line {4791, 23809} with respect to the Steiner inellipse
X(60071) = pole of line {1150, 2278} with respect to the Wallace hyperbola
X(60071) = pole of line {994, 4850} with respect to the dual conic of Yff parabola
X(60071) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(5692)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(5396)}}, {{A, B, C, X(6), X(661)}}, {{A, B, C, X(7), X(264)}}, {{A, B, C, X(21), X(312)}}, {{A, B, C, X(27), X(2476)}}, {{A, B, C, X(57), X(5903)}}, {{A, B, C, X(79), X(2006)}}, {{A, B, C, X(81), X(92)}}, {{A, B, C, X(85), X(88)}}, {{A, B, C, X(86), X(57948)}}, {{A, B, C, X(89), X(514)}}, {{A, B, C, X(90), X(25430)}}, {{A, B, C, X(192), X(3835)}}, {{A, B, C, X(239), X(29643)}}, {{A, B, C, X(278), X(12047)}}, {{A, B, C, X(306), X(19767)}}, {{A, B, C, X(313), X(58010)}}, {{A, B, C, X(325), X(26282)}}, {{A, B, C, X(334), X(56166)}}, {{A, B, C, X(335), X(32931)}}, {{A, B, C, X(379), X(37371)}}, {{A, B, C, X(381), X(56402)}}, {{A, B, C, X(385), X(31120)}}, {{A, B, C, X(445), X(6985)}}, {{A, B, C, X(458), X(8229)}}, {{A, B, C, X(524), X(31179)}}, {{A, B, C, X(561), X(40418)}}, {{A, B, C, X(673), X(33108)}}, {{A, B, C, X(739), X(2186)}}, {{A, B, C, X(857), X(1013)}}, {{A, B, C, X(901), X(46405)}}, {{A, B, C, X(940), X(5741)}}, {{A, B, C, X(941), X(1826)}}, {{A, B, C, X(1150), X(5718)}}, {{A, B, C, X(1156), X(27475)}}, {{A, B, C, X(1168), X(20924)}}, {{A, B, C, X(1211), X(19684)}}, {{A, B, C, X(1246), X(1441)}}, {{A, B, C, X(1389), X(2990)}}, {{A, B, C, X(1434), X(6336)}}, {{A, B, C, X(1491), X(40109)}}, {{A, B, C, X(1848), X(16705)}}, {{A, B, C, X(2238), X(31006)}}, {{A, B, C, X(2254), X(45885)}}, {{A, B, C, X(2296), X(7018)}}, {{A, B, C, X(2320), X(25094)}}, {{A, B, C, X(3218), X(34535)}}, {{A, B, C, X(3240), X(3912)}}, {{A, B, C, X(3948), X(30964)}}, {{A, B, C, X(4383), X(18139)}}, {{A, B, C, X(4389), X(4945)}}, {{A, B, C, X(4654), X(27131)}}, {{A, B, C, X(4671), X(42285)}}, {{A, B, C, X(4728), X(24457)}}, {{A, B, C, X(4997), X(28659)}}, {{A, B, C, X(5136), X(46487)}}, {{A, B, C, X(5143), X(7146)}}, {{A, B, C, X(5219), X(5561)}}, {{A, B, C, X(5226), X(5249)}}, {{A, B, C, X(5233), X(37633)}}, {{A, B, C, X(5278), X(17056)}}, {{A, B, C, X(5312), X(32858)}}, {{A, B, C, X(5712), X(5739)}}, {{A, B, C, X(6063), X(8049)}}, {{A, B, C, X(6650), X(25385)}}, {{A, B, C, X(6828), X(37279)}}, {{A, B, C, X(6841), X(57531)}}, {{A, B, C, X(6856), X(6994)}}, {{A, B, C, X(6871), X(7490)}}, {{A, B, C, X(7017), X(46880)}}, {{A, B, C, X(7357), X(40419)}}, {{A, B, C, X(7466), X(37445)}}, {{A, B, C, X(9258), X(57397)}}, {{A, B, C, X(9328), X(25417)}}, {{A, B, C, X(10478), X(56827)}}, {{A, B, C, X(10570), X(52500)}}, {{A, B, C, X(10883), X(26003)}}, {{A, B, C, X(11341), X(37330)}}, {{A, B, C, X(11681), X(37203)}}, {{A, B, C, X(14017), X(27052)}}, {{A, B, C, X(14260), X(40215)}}, {{A, B, C, X(14377), X(21907)}}, {{A, B, C, X(14584), X(51583)}}, {{A, B, C, X(14621), X(25760)}}, {{A, B, C, X(17234), X(37680)}}, {{A, B, C, X(17740), X(26587)}}, {{A, B, C, X(18123), X(57876)}}, {{A, B, C, X(18134), X(32911)}}, {{A, B, C, X(18743), X(42044)}}, {{A, B, C, X(19701), X(41809)}}, {{A, B, C, X(19717), X(31037)}}, {{A, B, C, X(19740), X(27081)}}, {{A, B, C, X(20028), X(58008)}}, {{A, B, C, X(20332), X(45965)}}, {{A, B, C, X(20569), X(39705)}}, {{A, B, C, X(20570), X(56048)}}, {{A, B, C, X(21241), X(21417)}}, {{A, B, C, X(21251), X(21428)}}, {{A, B, C, X(22030), X(39974)}}, {{A, B, C, X(22294), X(30575)}}, {{A, B, C, X(22307), X(53114)}}, {{A, B, C, X(24597), X(30828)}}, {{A, B, C, X(26738), X(30608)}}, {{A, B, C, X(26758), X(26860)}}, {{A, B, C, X(27064), X(36503)}}, {{A, B, C, X(27789), X(56027)}}, {{A, B, C, X(29572), X(49988)}}, {{A, B, C, X(30635), X(39712)}}, {{A, B, C, X(30710), X(39700)}}, {{A, B, C, X(30830), X(48080)}}, {{A, B, C, X(30834), X(35466)}}, {{A, B, C, X(31014), X(52891)}}, {{A, B, C, X(32011), X(57947)}}, {{A, B, C, X(32023), X(39734)}}, {{A, B, C, X(34860), X(55953)}}, {{A, B, C, X(34919), X(56075)}}, {{A, B, C, X(36002), X(37448)}}, {{A, B, C, X(37142), X(39971)}}, {{A, B, C, X(37389), X(52255)}}, {{A, B, C, X(37635), X(37656)}}, {{A, B, C, X(39741), X(40216)}}, {{A, B, C, X(42467), X(56041)}}, {{A, B, C, X(50040), X(55036)}}, {{A, B, C, X(55010), X(56845)}}, {{A, B, C, X(55985), X(56231)}}, {{A, B, C, X(56354), X(57661)}}
X(60071) = barycentric product X(i)*X(j) for these (i, j): {1, 58026}, {75, 994}, {45095, 86}, {46018, 76}
X(60071) = barycentric quotient X(i)/X(j) for these (i, j): {1, 993}, {2, 1150}, {4, 5136}, {6, 2278}, {8, 49492}, {513, 55969}, {514, 48321}, {994, 1}, {1769, 14299}, {4017, 51659}, {45095, 10}, {46018, 6}, {58026, 75}

X(60072) = X(2)X(12191)∩X(99)X(262)

Barycentrics    ((a^2-b^2)^2*(a^2+b^2)-2*(a^4+a^2*b^2+b^4)*c^2+3*(a^2+b^2)*c^4)*(a^6+3*b^4*c^2-2*b^2*c^4+c^6-a^4*(2*b^2+c^2)+a^2*(b-c)*(b+c)*(3*b^2+c^2)) : :

X(60072) lies on the Kiepert hyperbola and on these lines: {2, 12191}, {4, 12177}, {30, 54675}, {76, 10754}, {98, 316}, {99, 262}, {115, 54122}, {384, 15483}, {542, 54678}, {598, 5182}, {671, 41146}, {1078, 7607}, {1691, 54839}, {3399, 50640}, {5025, 60128}, {5034, 54753}, {5207, 9302}, {5466, 53331}, {5503, 7799}, {7608, 7769}, {7612, 12176}, {7763, 60234}, {7809, 54731}, {7812, 54752}, {7827, 54915}, {7883, 54816}, {7937, 60248}, {9166, 11167}, {10352, 60190}, {10484, 19911}, {11161, 54840}, {11172, 16041}, {11361, 54487}, {11676, 54978}, {12203, 60117}, {13885, 60274}, {13938, 60275}, {14033, 60268}, {14041, 43535}, {14061, 60101}, {14458, 52034}, {14494, 46236}, {18906, 60126}, {19120, 53418}, {23334, 58765}, {32458, 60232}, {39099, 39266}, {44132, 46105}, {52088, 54716}

X(60072) = reflection of X(i) in X(j) for these {i,j}: {54122, 115}, {99, 51580}
X(60072) = isogonal conjugate of X(2021)
X(60072) = isotomic conjugate of X(15993)
X(60072) = trilinear pole of line {183, 9832}
X(60072) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 2021}, {31, 15993}, {9417, 51259}
X(60072) = X(i)-vertex conjugate of X(j) for these {i, j}: {32, 54839}, {42346, 57729}
X(60072) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 15993}, {3, 2021}, {39058, 51259}
X(60072) = X(i)-cross conjugate of X(j) for these {i, j}: {44380, 2}, {59775, 99}
X(60072) = pole of line {44380, 60072} with respect to the Kiepert hyperbola
X(60072) = pole of line {2021, 15993} with respect to the Wallace hyperbola
X(60072) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(99), X(43187)}}, {{A, B, C, X(182), X(30541)}}, {{A, B, C, X(265), X(6393)}}, {{A, B, C, X(287), X(12177)}}, {{A, B, C, X(290), X(4590)}}, {{A, B, C, X(297), X(15980)}}, {{A, B, C, X(316), X(20573)}}, {{A, B, C, X(458), X(35930)}}, {{A, B, C, X(524), X(41146)}}, {{A, B, C, X(729), X(10630)}}, {{A, B, C, X(733), X(8753)}}, {{A, B, C, X(737), X(57728)}}, {{A, B, C, X(2698), X(2987)}}, {{A, B, C, X(3114), X(43664)}}, {{A, B, C, X(3224), X(6464)}}, {{A, B, C, X(3225), X(39652)}}, {{A, B, C, X(3228), X(9154)}}, {{A, B, C, X(3455), X(10014)}}, {{A, B, C, X(3978), X(16069)}}, {{A, B, C, X(5182), X(39446)}}, {{A, B, C, X(5641), X(18023)}}, {{A, B, C, X(6531), X(14970)}}, {{A, B, C, X(15993), X(44380)}}, {{A, B, C, X(18896), X(35142)}}, {{A, B, C, X(20027), X(50640)}}, {{A, B, C, X(34386), X(43714)}}, {{A, B, C, X(35146), X(41909)}}, {{A, B, C, X(39927), X(47646)}}, {{A, B, C, X(40832), X(57541)}}, {{A, B, C, X(42299), X(57943)}}, {{A, B, C, X(46310), X(54998)}}, {{A, B, C, X(52239), X(54413)}}, {{A, B, C, X(53765), X(57799)}}, {{A, B, C, X(56979), X(57452)}}
X(60072) = barycentric quotient X(i)/X(j) for these (i, j): {2, 15993}, {6, 2021}, {290, 51259}, {53775, 3148}

X(60073) = X(4)X(6036)∩X(115)X(439)

Barycentrics    (3*a^4-2*a^2*b^2+3*b^4-3*(a^2+b^2)*c^2+2*c^4)*(3*a^4+2*b^4-3*b^2*c^2+3*c^4-a^2*(3*b^2+2*c^2)) : :
X(60073) = -8*X[35021]+3*X[60322]

X(60073) lies on the Kiepert hyperbola and on these lines: {2, 39764}, {4, 6036}, {5, 54873}, {6, 60178}, {30, 54767}, {76, 33233}, {83, 33249}, {98, 10011}, {99, 2996}, {114, 7612}, {115, 439}, {147, 43537}, {230, 8781}, {325, 56064}, {542, 60185}, {620, 32824}, {671, 35297}, {2023, 60095}, {3054, 60101}, {3618, 10155}, {3815, 60198}, {5395, 32988}, {5461, 60113}, {5466, 45687}, {5485, 41134}, {5490, 8997}, {5491, 13989}, {5976, 60180}, {5984, 60336}, {6054, 60175}, {6055, 60150}, {6721, 53103}, {6722, 18845}, {7608, 7792}, {7806, 60233}, {9166, 35927}, {9478, 60132}, {10159, 58446}, {10302, 15597}, {10352, 60128}, {10723, 39663}, {11174, 11669}, {14971, 54476}, {16984, 60098}, {17004, 43529}, {17006, 42006}, {23053, 60143}, {23234, 54644}, {32458, 60262}, {33235, 44531}, {33250, 53106}, {35005, 36849}, {35021, 60322}, {37688, 60213}, {41139, 60103}, {53033, 60285}

X(60073) = reflection of X(i) in X(j) for these {i,j}: {38259, 115}, {99, 51579}
X(60073) = isogonal conjugate of X(1570)
X(60073) = isotomic conjugate of X(44377)
X(60073) = trilinear pole of line {193, 36181}
X(60073) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 1570}, {31, 44377}
X(60073) = X(i)-vertex conjugate of X(j) for these {i, j}: {25, 8781}, {671, 39644}, {41533, 60280}
X(60073) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 44377}, {3, 1570}
X(60073) = X(i)-cross conjugate of X(j) for these {i, j}: {44381, 2}, {55122, 99}
X(60073) = pole of line {44381, 60073} with respect to the Kiepert hyperbola
X(60073) = pole of line {1570, 44377} with respect to the Wallace hyperbola
X(60073) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(37637)}}, {{A, B, C, X(25), X(33233)}}, {{A, B, C, X(67), X(40511)}}, {{A, B, C, X(99), X(30610)}}, {{A, B, C, X(114), X(297)}}, {{A, B, C, X(193), X(36611)}}, {{A, B, C, X(230), X(6531)}}, {{A, B, C, X(249), X(3563)}}, {{A, B, C, X(287), X(6036)}}, {{A, B, C, X(427), X(33249)}}, {{A, B, C, X(439), X(38282)}}, {{A, B, C, X(468), X(35297)}}, {{A, B, C, X(524), X(44401)}}, {{A, B, C, X(597), X(15597)}}, {{A, B, C, X(1297), X(32901)}}, {{A, B, C, X(1494), X(40429)}}, {{A, B, C, X(1799), X(7857)}}, {{A, B, C, X(1989), X(36953)}}, {{A, B, C, X(2165), X(40405)}}, {{A, B, C, X(2987), X(43662)}}, {{A, B, C, X(3054), X(3815)}}, {{A, B, C, X(3228), X(42349)}}, {{A, B, C, X(3329), X(17006)}}, {{A, B, C, X(4590), X(17983)}}, {{A, B, C, X(5976), X(47646)}}, {{A, B, C, X(6330), X(57553)}}, {{A, B, C, X(6353), X(32989)}}, {{A, B, C, X(7792), X(37688)}}, {{A, B, C, X(7806), X(17004)}}, {{A, B, C, X(8770), X(39644)}}, {{A, B, C, X(8889), X(32988)}}, {{A, B, C, X(9516), X(52154)}}, {{A, B, C, X(14061), X(30786)}}, {{A, B, C, X(14659), X(57260)}}, {{A, B, C, X(14734), X(17708)}}, {{A, B, C, X(21448), X(41533)}}, {{A, B, C, X(22110), X(41139)}}, {{A, B, C, X(33235), X(37453)}}, {{A, B, C, X(33250), X(52297)}}, {{A, B, C, X(34208), X(56360)}}, {{A, B, C, X(34473), X(57799)}}, {{A, B, C, X(35140), X(40428)}}, {{A, B, C, X(35927), X(52290)}}, {{A, B, C, X(38749), X(51454)}}, {{A, B, C, X(39968), X(43664)}}, {{A, B, C, X(40120), X(44145)}}, {{A, B, C, X(40410), X(40416)}}, {{A, B, C, X(41134), X(52141)}}, {{A, B, C, X(42332), X(52395)}}, {{A, B, C, X(44377), X(44381)}}, {{A, B, C, X(44558), X(45838)}}, {{A, B, C, X(52250), X(52299)}}
X(60073) = barycentric quotient X(i)/X(j) for these (i, j): {2, 44377}, {6, 1570}

X(60074) = X(2)X(1577)∩X(10)X(522)

Barycentrics    b*(b-c)*c*(a^2-a*b+b^2-c^2)*(a^2-b^2-a*c+c^2) : :

X(60074) lies on the Kiepert hyperbola and on these lines: {2, 1577}, {4, 6003}, {5, 56283}, {10, 522}, {11, 52303}, {30, 54842}, {76, 18160}, {80, 885}, {83, 18070}, {98, 759}, {226, 514}, {275, 57215}, {321, 4391}, {495, 523}, {513, 60089}, {525, 43683}, {655, 24029}, {656, 60112}, {661, 60071}, {666, 35174}, {671, 14616}, {693, 30588}, {812, 2161}, {929, 2222}, {1022, 46781}, {1026, 51562}, {1446, 23100}, {2006, 2401}, {2051, 4129}, {2166, 35347}, {2254, 56419}, {2614, 6757}, {2618, 3737}, {2627, 17104}, {2785, 11599}, {2786, 11608}, {3762, 4080}, {4369, 60085}, {4581, 60086}, {4582, 24004}, {4585, 47318}, {4823, 56226}, {6002, 13478}, {6980, 39212}, {7178, 43682}, {7192, 60258}, {7489, 21789}, {8808, 21188}, {10015, 60091}, {11247, 15313}, {14208, 60242}, {14223, 17886}, {14554, 59737}, {14837, 60249}, {15065, 18003}, {15309, 60156}, {17924, 40149}, {20566, 60288}, {23105, 50574}, {23226, 54969}, {23875, 43675}, {24035, 53811}, {28292, 54668}, {28840, 60083}, {29013, 60088}, {29066, 40718}, {32671, 60179}, {32680, 37140}, {34079, 60134}, {36035, 54528}, {36815, 43671}, {37009, 56950}, {43672, 45926}, {45664, 50104}, {46160, 60111}, {46384, 57645}, {47947, 60139}, {48003, 56320}, {48612, 60170}, {50453, 60245}, {50457, 57722}, {56322, 60229}, {58361, 60097}

X(60074) = midpoint of X(i) and X(j) for these {i,j}: {3762, 36038}
X(60074) = isogonal conjugate of X(1983)
X(60074) = isotomic conjugate of X(4585)
X(60074) = trilinear pole of line {11, 1090}
X(60074) = perspector of circumconic {{A, B, C, X(14616), X(18359)}}
X(60074) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 1983}, {31, 4585}, {36, 101}, {48, 4242}, {50, 6742}, {59, 654}, {100, 7113}, {109, 2323}, {110, 2245}, {163, 758}, {190, 52434}, {214, 32665}, {215, 655}, {249, 42666}, {320, 32739}, {644, 52440}, {651, 2361}, {662, 3724}, {664, 52426}, {692, 3218}, {765, 21758}, {825, 3792}, {860, 32661}, {901, 17455}, {906, 1870}, {1023, 16944}, {1101, 2610}, {1110, 3960}, {1252, 53314}, {1262, 53285}, {1331, 52413}, {1415, 4511}, {1461, 58328}, {1464, 5546}, {1576, 3936}, {1783, 52407}, {1813, 52427}, {1918, 55237}, {2149, 3738}, {2222, 34544}, {4282, 4551}, {4453, 23990}, {4558, 44113}, {4564, 8648}, {4570, 21828}, {4736, 32671}, {4867, 34073}, {4881, 34080}, {4996, 32675}, {5081, 32660}, {6370, 23357}, {6739, 32640}, {8750, 22128}, {8818, 52603}, {14591, 52388}, {17923, 32656}, {23344, 40215}, {26744, 34921}, {27950, 34067}, {32641, 34586}, {32719, 51583}, {35069, 36069}, {38353, 59103}, {44717, 58313}, {51562, 52059}, {52377, 57174}, {52378, 53562}
X(60074) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 4585}, {3, 1983}, {11, 2323}, {115, 758}, {244, 2245}, {513, 21758}, {514, 3960}, {523, 2610}, {650, 3738}, {661, 53314}, {1015, 36}, {1084, 3724}, {1086, 3218}, {1146, 4511}, {1249, 4242}, {1577, 3904}, {4858, 3936}, {4988, 53527}, {5190, 1870}, {5520, 40584}, {5521, 52413}, {6544, 53535}, {6615, 654}, {8054, 7113}, {8287, 323}, {14838, 32679}, {15898, 101}, {26932, 22128}, {34021, 55237}, {35076, 4973}, {35090, 35204}, {35092, 214}, {35119, 27950}, {35128, 4996}, {35508, 58328}, {36901, 35550}, {36909, 644}, {38979, 17455}, {38982, 35069}, {38984, 34544}, {38991, 2361}, {39006, 52407}, {39025, 52426}, {40615, 1443}, {40619, 320}, {40621, 4881}, {40622, 18593}, {40624, 32851}, {46398, 16586}, {50330, 21828}, {53167, 4880}, {55053, 52434}, {55065, 4053}, {56416, 1023}
X(60074) = X(i)-Ceva conjugate of X(j) for these {i, j}: {655, 60091}, {32680, 24624}, {35174, 80}, {36804, 18359}, {57645, 11}
X(60074) = X(i)-cross conjugate of X(j) for these {i, j}: {11, 57645}, {867, 264}, {900, 693}, {1146, 40437}, {2600, 3737}, {2610, 523}, {10015, 514}, {36035, 4077}, {45147, 7372}, {45260, 54121}, {46384, 11}
X(60074) = pole of line {515, 2245} with respect to the excircles-radical circle
X(60074) = pole of line {22464, 30384} with respect to the incircle
X(60074) = pole of line {3724, 44425} with respect to the orthoptic circle of the Steiner inellipse
X(60074) = pole of line {758, 1870} with respect to the polar circle
X(60074) = pole of line {2245, 6905} with respect to the excentral-hexyl ellipse
X(60074) = pole of line {80, 758} with respect to the Steiner circumellipse
X(60074) = pole of line {758, 908} with respect to the Steiner inellipse
X(60074) = pole of line {1983, 4585} with respect to the Wallace hyperbola
X(60074) = pole of line {1725, 2310} with respect to the Suppa-Cucoanes circle
X(60074) = pole of line {4358, 17895} with respect to the dual conic of circumcircle
X(60074) = pole of line {18359, 32849} with respect to the dual conic of incircle
X(60074) = pole of line {27781, 49274} with respect to the dual conic of Feuerbach hyperbola
X(60074) = pole of line {2610, 4707} with respect to the dual conic of Stammler hyperbola
X(60074) = pole of line {2610, 21828} with respect to the dual conic of Wallace hyperbola
X(60074) = pole of line {4858, 32851} with respect to the dual conic of Suppa-Cucoanes circle
X(60074) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(24433)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(278), X(51889)}}, {{A, B, C, X(297), X(7427)}}, {{A, B, C, X(335), X(5376)}}, {{A, B, C, X(513), X(23876)}}, {{A, B, C, X(514), X(522)}}, {{A, B, C, X(525), X(6003)}}, {{A, B, C, X(693), X(4791)}}, {{A, B, C, X(812), X(23887)}}, {{A, B, C, X(824), X(29066)}}, {{A, B, C, X(900), X(23598)}}, {{A, B, C, X(918), X(1026)}}, {{A, B, C, X(1022), X(1086)}}, {{A, B, C, X(1024), X(8735)}}, {{A, B, C, X(1146), X(23893)}}, {{A, B, C, X(1577), X(2627)}}, {{A, B, C, X(2006), X(52212)}}, {{A, B, C, X(2399), X(43728)}}, {{A, B, C, X(2614), X(7178)}}, {{A, B, C, X(2785), X(2786)}}, {{A, B, C, X(3125), X(3572)}}, {{A, B, C, X(3762), X(24004)}}, {{A, B, C, X(3960), X(10015)}}, {{A, B, C, X(4369), X(50453)}}, {{A, B, C, X(4585), X(4707)}}, {{A, B, C, X(6548), X(21198)}}, {{A, B, C, X(14628), X(18359)}}, {{A, B, C, X(14837), X(21188)}}, {{A, B, C, X(15313), X(23875)}}, {{A, B, C, X(17435), X(34905)}}, {{A, B, C, X(18003), X(27853)}}, {{A, B, C, X(20316), X(23685)}}, {{A, B, C, X(23100), X(40166)}}, {{A, B, C, X(46384), X(52303)}}, {{A, B, C, X(46782), X(52626)}}, {{A, B, C, X(52222), X(53560)}}
X(60074) = barycentric product X(i)*X(j) for these (i, j): {11, 35174}, {274, 55238}, {319, 43082}, {328, 54244}, {338, 37140}, {693, 80}, {759, 850}, {1086, 36804}, {1111, 51562}, {1411, 35519}, {1577, 24624}, {1807, 46107}, {2006, 4391}, {2161, 3261}, {2166, 4467}, {2170, 46405}, {2222, 34387}, {2610, 57555}, {2611, 35139}, {2618, 39277}, {3676, 52409}, {3738, 57645}, {4077, 6740}, {4560, 60091}, {4858, 655}, {10412, 56934}, {14616, 523}, {14838, 94}, {15065, 7192}, {16732, 47318}, {17886, 476}, {17924, 52351}, {18155, 52383}, {18160, 1989}, {18359, 514}, {18815, 522}, {18817, 23226}, {20566, 513}, {20948, 34079}, {23962, 32671}, {23994, 36069}, {24002, 36910}, {24006, 57985}, {32680, 8287}, {34535, 3904}, {34857, 52619}, {36038, 40437}, {40495, 6187}, {44426, 52392}, {46160, 52618}, {46384, 57568}, {51975, 6548}, {52356, 7}, {52371, 52621}, {57788, 900}, {57789, 8648}
X(60074) = barycentric quotient X(i)/X(j) for these (i, j): {2, 4585}, {4, 4242}, {6, 1983}, {11, 3738}, {80, 100}, {94, 15455}, {115, 2610}, {244, 53314}, {274, 55237}, {512, 3724}, {513, 36}, {514, 3218}, {522, 4511}, {523, 758}, {649, 7113}, {650, 2323}, {654, 34544}, {655, 4564}, {661, 2245}, {663, 2361}, {667, 52434}, {693, 320}, {759, 110}, {812, 27950}, {850, 35550}, {900, 214}, {905, 22128}, {1015, 21758}, {1022, 40215}, {1086, 3960}, {1109, 6370}, {1111, 4453}, {1168, 901}, {1365, 51663}, {1411, 109}, {1459, 52407}, {1491, 3792}, {1577, 3936}, {1635, 17455}, {1647, 53535}, {1769, 34586}, {1807, 1331}, {2006, 651}, {2161, 101}, {2166, 6742}, {2170, 654}, {2222, 59}, {2310, 53285}, {2341, 5546}, {2605, 6149}, {2610, 35069}, {2611, 526}, {2643, 42666}, {3063, 52426}, {3120, 53527}, {3125, 21828}, {3261, 20924}, {3271, 8648}, {3667, 4881}, {3675, 53555}, {3676, 1443}, {3738, 4996}, {3762, 51583}, {3900, 58328}, {3937, 22379}, {4017, 1464}, {4024, 4053}, {4077, 41804}, {4120, 40988}, {4391, 32851}, {4516, 53562}, {4777, 4867}, {4791, 27757}, {4802, 4880}, {4858, 3904}, {4957, 23884}, {4977, 4973}, {6003, 27086}, {6187, 692}, {6370, 4736}, {6545, 53546}, {6548, 52553}, {6591, 52413}, {6740, 643}, {7178, 18593}, {7252, 4282}, {7265, 42701}, {7649, 1870}, {8287, 32679}, {8648, 215}, {8674, 35204}, {10015, 16586}, {10412, 6757}, {14584, 23703}, {14616, 99}, {14838, 323}, {15065, 3952}, {16732, 4707}, {17104, 52603}, {17886, 3268}, {17924, 17923}, {18160, 7799}, {18344, 52427}, {18359, 190}, {18815, 664}, {20566, 668}, {20982, 2624}, {21132, 53525}, {21180, 52368}, {21758, 52059}, {23226, 22115}, {23345, 16944}, {24002, 17078}, {24006, 860}, {24624, 662}, {30572, 53537}, {32671, 23357}, {32675, 2149}, {34079, 163}, {34172, 36167}, {34535, 655}, {34857, 4557}, {35174, 4998}, {36035, 6739}, {36069, 1101}, {36804, 1016}, {36815, 3573}, {36910, 644}, {37140, 249}, {38938, 13589}, {39534, 1845}, {40172, 23344}, {40437, 36037}, {40495, 40075}, {42759, 42768}, {43082, 79}, {43728, 56757}, {43924, 52440}, {44426, 5081}, {46160, 1634}, {46384, 35128}, {47227, 40584}, {47318, 4567}, {51562, 765}, {51663, 3028}, {51834, 57600}, {51975, 17780}, {52212, 24029}, {52351, 1332}, {52356, 8}, {52371, 3939}, {52380, 4636}, {52383, 4551}, {52391, 23067}, {52392, 6516}, {52409, 3699}, {52431, 906}, {53522, 11700}, {54244, 186}, {55126, 11570}, {55238, 37}, {56405, 57119}, {56426, 35281}, {56934, 10411}, {57645, 35174}, {57736, 4575}, {57788, 4555}, {57985, 4592}, {59837, 6126}, {60091, 4552}
X(60074) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3762, 36038, 23884}

X(60075) = X(2)X(4251)∩X(10)X(1001)

Barycentrics    (a^2+b*(b-c)-a*(b+c))*(a^2+c*(-b+c)-a*(b+c)) : :

X(60075) lies on the Kiepert hyperbola and on these lines: {2, 4251}, {3, 43672}, {4, 13329}, {5, 56144}, {6, 17758}, {9, 60265}, {10, 1001}, {30, 54687}, {41, 55161}, {76, 17277}, {83, 17352}, {98, 24880}, {106, 24737}, {169, 1445}, {218, 226}, {220, 17761}, {262, 17749}, {275, 37448}, {277, 24797}, {321, 3294}, {333, 40012}, {376, 54712}, {381, 54517}, {386, 60108}, {405, 60227}, {496, 58458}, {497, 10482}, {499, 6710}, {631, 45097}, {657, 23100}, {672, 14377}, {673, 3730}, {949, 34847}, {966, 18840}, {1150, 39994}, {1210, 58442}, {1434, 4253}, {1479, 13576}, {1714, 60152}, {1722, 60321}, {1746, 60167}, {1751, 30810}, {2051, 37679}, {2052, 26003}, {2348, 24774}, {2886, 58456}, {3216, 45964}, {3545, 54690}, {3589, 5138}, {3618, 58012}, {3678, 16825}, {3813, 40534}, {3841, 40718}, {4080, 31018}, {4208, 60077}, {4209, 5030}, {4444, 14838}, {4847, 50715}, {5022, 57521}, {5129, 43533}, {5224, 10159}, {5233, 60251}, {5278, 40013}, {5292, 60165}, {5358, 57720}, {5737, 21529}, {7719, 40149}, {7808, 60109}, {16549, 24596}, {16609, 43682}, {16611, 60245}, {16850, 60110}, {17307, 60278}, {17308, 60203}, {17348, 34790}, {17349, 60236}, {17381, 32014}, {17528, 60078}, {17745, 30949}, {18483, 48944}, {19732, 60084}, {19868, 56993}, {21373, 26563}, {24588, 56507}, {24597, 60169}, {25651, 57710}, {26244, 60099}, {27299, 60230}, {29604, 60243}, {31144, 60277}, {31191, 56226}, {31638, 56667}, {32911, 57722}, {34016, 40017}, {35466, 60085}, {36728, 54586}, {36731, 60172}, {37407, 60157}, {37427, 54726}, {37428, 54516}, {37680, 60071}, {37681, 57826}, {37686, 40031}, {37687, 60087}, {38938, 54528}, {41785, 56746}, {47352, 55949}, {50736, 54623}, {53391, 54739}

X(60075) = isogonal conjugate of X(4253)
X(60075) = isotomic conjugate of X(17234)
X(60075) = trilinear pole of line {4724, 5160}
X(60075) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 4253}, {2, 3941}, {6, 3873}, {31, 17234}, {32, 33933}, {55, 17092}, {56, 25082}, {58, 3970}, {81, 22277}, {692, 47676}, {934, 52594}, {1014, 40599}, {2149, 17059}, {3052, 27827}
X(60075) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 25082}, {2, 17234}, {3, 4253}, {9, 3873}, {10, 3970}, {223, 17092}, {650, 17059}, {1015, 4905}, {1086, 47676}, {6376, 33933}, {14714, 52594}, {24151, 27827}, {32664, 3941}, {40586, 22277}
X(60075) = X(i)-cross conjugate of X(j) for these {i, j}: {1334, 1}, {3058, 7}, {4382, 190}, {4904, 514}, {17337, 2}, {20507, 666}
X(60075) = pole of line {17337, 60075} with respect to the Kiepert hyperbola
X(60075) = pole of line {4468, 21185} with respect to the Steiner inellipse
X(60075) = pole of line {4253, 17234} with respect to the Wallace hyperbola
X(60075) = pole of line {55, 17278} with respect to the dual conic of Yff parabola
X(60075) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(673)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(13329)}}, {{A, B, C, X(5), X(37448)}}, {{A, B, C, X(6), X(3294)}}, {{A, B, C, X(7), X(6666)}}, {{A, B, C, X(8), X(277)}}, {{A, B, C, X(9), X(218)}}, {{A, B, C, X(11), X(23100)}}, {{A, B, C, X(25), X(17681)}}, {{A, B, C, X(27), X(11108)}}, {{A, B, C, X(37), X(16783)}}, {{A, B, C, X(55), X(2141)}}, {{A, B, C, X(57), X(1126)}}, {{A, B, C, X(58), X(37502)}}, {{A, B, C, X(69), X(37650)}}, {{A, B, C, X(75), X(17279)}}, {{A, B, C, X(79), X(27475)}}, {{A, B, C, X(80), X(85)}}, {{A, B, C, X(86), X(17259)}}, {{A, B, C, X(88), X(25439)}}, {{A, B, C, X(90), X(7131)}}, {{A, B, C, X(101), X(2053)}}, {{A, B, C, X(106), X(3500)}}, {{A, B, C, X(141), X(17352)}}, {{A, B, C, X(169), X(5452)}}, {{A, B, C, X(238), X(56542)}}, {{A, B, C, X(239), X(16825)}}, {{A, B, C, X(274), X(996)}}, {{A, B, C, X(279), X(1000)}}, {{A, B, C, X(312), X(24789)}}, {{A, B, C, X(330), X(1016)}}, {{A, B, C, X(333), X(979)}}, {{A, B, C, X(335), X(32019)}}, {{A, B, C, X(386), X(5138)}}, {{A, B, C, X(391), X(37681)}}, {{A, B, C, X(405), X(37389)}}, {{A, B, C, X(427), X(33838)}}, {{A, B, C, X(458), X(21554)}}, {{A, B, C, X(469), X(8728)}}, {{A, B, C, X(497), X(4847)}}, {{A, B, C, X(596), X(30701)}}, {{A, B, C, X(672), X(3730)}}, {{A, B, C, X(759), X(7132)}}, {{A, B, C, X(943), X(1170)}}, {{A, B, C, X(966), X(3618)}}, {{A, B, C, X(983), X(40398)}}, {{A, B, C, X(1019), X(3445)}}, {{A, B, C, X(1121), X(43731)}}, {{A, B, C, X(1150), X(37680)}}, {{A, B, C, X(1213), X(17381)}}, {{A, B, C, X(1220), X(56051)}}, {{A, B, C, X(1223), X(3062)}}, {{A, B, C, X(1247), X(52652)}}, {{A, B, C, X(1268), X(17293)}}, {{A, B, C, X(1334), X(4253)}}, {{A, B, C, X(1479), X(5236)}}, {{A, B, C, X(1509), X(32013)}}, {{A, B, C, X(1577), X(41501)}}, {{A, B, C, X(1698), X(17308)}}, {{A, B, C, X(1722), X(11679)}}, {{A, B, C, X(1847), X(2006)}}, {{A, B, C, X(1855), X(56746)}}, {{A, B, C, X(2161), X(7096)}}, {{A, B, C, X(2218), X(2224)}}, {{A, B, C, X(2333), X(2350)}}, {{A, B, C, X(2334), X(39950)}}, {{A, B, C, X(2339), X(39947)}}, {{A, B, C, X(2478), X(37382)}}, {{A, B, C, X(2481), X(55967)}}, {{A, B, C, X(3227), X(56353)}}, {{A, B, C, X(3296), X(38059)}}, {{A, B, C, X(3467), X(55965)}}, {{A, B, C, X(3589), X(5224)}}, {{A, B, C, X(3617), X(31191)}}, {{A, B, C, X(3668), X(57858)}}, {{A, B, C, X(3678), X(14838)}}, {{A, B, C, X(3741), X(27299)}}, {{A, B, C, X(3841), X(16603)}}, {{A, B, C, X(3911), X(31018)}}, {{A, B, C, X(4095), X(4369)}}, {{A, B, C, X(4097), X(39956)}}, {{A, B, C, X(4564), X(15446)}}, {{A, B, C, X(4846), X(56382)}}, {{A, B, C, X(4998), X(56163)}}, {{A, B, C, X(5084), X(37102)}}, {{A, B, C, X(5125), X(30810)}}, {{A, B, C, X(5129), X(7490)}}, {{A, B, C, X(5192), X(31925)}}, {{A, B, C, X(5233), X(35466)}}, {{A, B, C, X(5278), X(32911)}}, {{A, B, C, X(5559), X(9311)}}, {{A, B, C, X(5560), X(32015)}}, {{A, B, C, X(6601), X(24181)}}, {{A, B, C, X(7162), X(39273)}}, {{A, B, C, X(7163), X(40076)}}, {{A, B, C, X(7319), X(56054)}}, {{A, B, C, X(7320), X(9328)}}, {{A, B, C, X(7346), X(9361)}}, {{A, B, C, X(7658), X(8074)}}, {{A, B, C, X(7875), X(31090)}}, {{A, B, C, X(9780), X(29604)}}, {{A, B, C, X(10405), X(43734)}}, {{A, B, C, X(11174), X(26244)}}, {{A, B, C, X(14621), X(32009)}}, {{A, B, C, X(14829), X(37679)}}, {{A, B, C, X(16815), X(36480)}}, {{A, B, C, X(16816), X(50023)}}, {{A, B, C, X(17234), X(17337)}}, {{A, B, C, X(17307), X(47355)}}, {{A, B, C, X(17682), X(28044)}}, {{A, B, C, X(20569), X(54120)}}, {{A, B, C, X(21446), X(38271)}}, {{A, B, C, X(21453), X(30494)}}, {{A, B, C, X(23493), X(54413)}}, {{A, B, C, X(24388), X(55076)}}, {{A, B, C, X(25007), X(26364)}}, {{A, B, C, X(25425), X(40408)}}, {{A, B, C, X(27789), X(52393)}}, {{A, B, C, X(30107), X(31330)}}, {{A, B, C, X(30710), X(55988)}}, {{A, B, C, X(31144), X(47352)}}, {{A, B, C, X(32635), X(43760)}}, {{A, B, C, X(33938), X(33945)}}, {{A, B, C, X(34234), X(39963)}}, {{A, B, C, X(34860), X(34892)}}, {{A, B, C, X(34918), X(55984)}}, {{A, B, C, X(36796), X(56146)}}, {{A, B, C, X(37388), X(50399)}}, {{A, B, C, X(37673), X(37686)}}, {{A, B, C, X(38009), X(56218)}}, {{A, B, C, X(38250), X(59457)}}, {{A, B, C, X(39697), X(54123)}}, {{A, B, C, X(39717), X(55970)}}, {{A, B, C, X(39748), X(39981)}}, {{A, B, C, X(40415), X(56212)}}, {{A, B, C, X(40434), X(43758)}}, {{A, B, C, X(42030), X(42304)}}, {{A, B, C, X(42290), X(57705)}}, {{A, B, C, X(42310), X(55941)}}, {{A, B, C, X(44040), X(58004)}}, {{A, B, C, X(46797), X(57506)}}, {{A, B, C, X(48074), X(56155)}}, {{A, B, C, X(51284), X(54390)}}, {{A, B, C, X(55918), X(55986)}}
X(60075) = barycentric quotient X(i)/X(j) for these (i, j): {1, 3873}, {2, 17234}, {6, 4253}, {9, 25082}, {11, 17059}, {31, 3941}, {37, 3970}, {42, 22277}, {57, 17092}, {75, 33933}, {513, 4905}, {514, 47676}, {657, 52594}, {1334, 40599}, {8056, 27827}, {21044, 21946}, {21132, 23761}

X(60076) = X(2)X(1014)∩X(10)X(57)

Barycentrics    (a+b-c)*(a-b+c)*(a^2+2*a*b+(b+c)^2)*(a^2+2*a*c+(b+c)^2) : :

X(60076) lies on the Kiepert hyperbola and on these lines: {2, 1014}, {3, 60158}, {4, 940}, {5, 60157}, {6, 60107}, {7, 321}, {10, 57}, {30, 54688}, {69, 34258}, {76, 18141}, {81, 60155}, {85, 60197}, {98, 59069}, {226, 269}, {333, 32022}, {376, 54758}, {377, 37655}, {381, 54726}, {459, 37276}, {479, 1446}, {497, 4349}, {553, 60267}, {631, 60154}, {948, 36907}, {980, 3597}, {1029, 7381}, {1056, 3666}, {1058, 37595}, {1119, 40149}, {1213, 57663}, {1214, 60321}, {1462, 6817}, {1751, 37642}, {1764, 6916}, {2051, 5712}, {2478, 60077}, {2551, 53004}, {3090, 60164}, {3424, 26118}, {3545, 54757}, {3911, 60243}, {3945, 45100}, {4052, 4654}, {4059, 40154}, {4080, 56049}, {5067, 60173}, {5071, 54727}, {5084, 43531}, {5219, 56226}, {5226, 30588}, {5228, 56172}, {5323, 37037}, {5397, 6947}, {5435, 60203}, {5718, 45098}, {5739, 60097}, {5746, 17811}, {5747, 56216}, {6539, 19825}, {6821, 37676}, {6833, 60166}, {6834, 60174}, {6854, 60112}, {6864, 57719}, {6865, 54972}, {6896, 57720}, {6899, 57710}, {6949, 60162}, {6952, 60159}, {7146, 43677}, {7247, 8817}, {7382, 14996}, {7386, 60152}, {7392, 60153}, {11001, 54947}, {14021, 60229}, {14257, 55110}, {14829, 60206}, {15682, 54789}, {17300, 60261}, {18134, 60254}, {18139, 60242}, {24597, 57721}, {25934, 60237}, {31643, 60264}, {36728, 54880}, {37185, 60170}, {37456, 60147}, {37631, 54689}, {37633, 60156}, {37646, 55962}, {37666, 60092}, {37683, 60149}, {37684, 54119}, {41245, 56460}, {49744, 54721}

X(60076) = isogonal conjugate of X(4254)
X(60076) = isotomic conjugate of X(14555)
X(60076) = trilinear pole of line {3669, 523}
X(60076) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 4254}, {6, 5250}, {9, 16466}, {31, 14555}, {41, 17321}, {48, 4194}, {55, 5256}, {219, 7713}, {284, 3931}, {607, 54404}, {643, 50492}, {2193, 39579}, {5546, 50332}
X(60076) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 14555}, {3, 4254}, {9, 5250}, {223, 5256}, {478, 16466}, {1249, 4194}, {3160, 17321}, {40590, 3931}, {40615, 47995}, {40622, 48402}, {47345, 39579}, {55060, 50492}
X(60076) = X(i)-cross conjugate of X(j) for these {i, j}: {10404, 7}, {37674, 2}
X(60076) = pole of line {37674, 60076} with respect to the Kiepert hyperbola
X(60076) = pole of line {4254, 14555} with respect to the Wallace hyperbola
X(60076) = pole of line {3333, 14551} with respect to the dual conic of Yff parabola
X(60076) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(189)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(36746)}}, {{A, B, C, X(6), X(5120)}}, {{A, B, C, X(7), X(57)}}, {{A, B, C, X(8), X(17022)}}, {{A, B, C, X(20), X(37276)}}, {{A, B, C, X(27), X(277)}}, {{A, B, C, X(37), X(56208)}}, {{A, B, C, X(56), X(46331)}}, {{A, B, C, X(65), X(57663)}}, {{A, B, C, X(69), X(940)}}, {{A, B, C, X(79), X(8056)}}, {{A, B, C, X(81), X(3296)}}, {{A, B, C, X(85), X(278)}}, {{A, B, C, X(88), X(43733)}}, {{A, B, C, X(89), X(5551)}}, {{A, B, C, X(92), X(3421)}}, {{A, B, C, X(196), X(14257)}}, {{A, B, C, X(222), X(34400)}}, {{A, B, C, X(241), X(37543)}}, {{A, B, C, X(279), X(4298)}}, {{A, B, C, X(281), X(34404)}}, {{A, B, C, X(333), X(4648)}}, {{A, B, C, X(377), X(7490)}}, {{A, B, C, X(445), X(6899)}}, {{A, B, C, X(451), X(7381)}}, {{A, B, C, X(469), X(5084)}}, {{A, B, C, X(552), X(36623)}}, {{A, B, C, X(553), X(21454)}}, {{A, B, C, X(673), X(26040)}}, {{A, B, C, X(951), X(57418)}}, {{A, B, C, X(967), X(51223)}}, {{A, B, C, X(1000), X(1255)}}, {{A, B, C, X(1073), X(43724)}}, {{A, B, C, X(1246), X(39981)}}, {{A, B, C, X(1389), X(56354)}}, {{A, B, C, X(1407), X(20615)}}, {{A, B, C, X(1412), X(56155)}}, {{A, B, C, X(1422), X(7091)}}, {{A, B, C, X(1434), X(42304)}}, {{A, B, C, X(1788), X(40420)}}, {{A, B, C, X(1824), X(21448)}}, {{A, B, C, X(2006), X(9578)}}, {{A, B, C, X(2298), X(7097)}}, {{A, B, C, X(2339), X(34919)}}, {{A, B, C, X(2982), X(7131)}}, {{A, B, C, X(2985), X(54123)}}, {{A, B, C, X(3577), X(56230)}}, {{A, B, C, X(3668), X(57866)}}, {{A, B, C, X(3911), X(34529)}}, {{A, B, C, X(3945), X(37655)}}, {{A, B, C, X(4032), X(8033)}}, {{A, B, C, X(4059), X(6604)}}, {{A, B, C, X(4340), X(56382)}}, {{A, B, C, X(4349), X(10004)}}, {{A, B, C, X(4359), X(19825)}}, {{A, B, C, X(4373), X(30101)}}, {{A, B, C, X(4654), X(5435)}}, {{A, B, C, X(4869), X(37666)}}, {{A, B, C, X(5219), X(5226)}}, {{A, B, C, X(5372), X(37635)}}, {{A, B, C, X(5556), X(39963)}}, {{A, B, C, X(5557), X(39980)}}, {{A, B, C, X(5558), X(39948)}}, {{A, B, C, X(5712), X(14829)}}, {{A, B, C, X(5739), X(37633)}}, {{A, B, C, X(6557), X(30513)}}, {{A, B, C, X(6817), X(15149)}}, {{A, B, C, X(6819), X(6834)}}, {{A, B, C, X(6820), X(6833)}}, {{A, B, C, X(6857), X(37181)}}, {{A, B, C, X(6864), X(37279)}}, {{A, B, C, X(6896), X(57531)}}, {{A, B, C, X(6952), X(37192)}}, {{A, B, C, X(6994), X(17582)}}, {{A, B, C, X(7003), X(56225)}}, {{A, B, C, X(7195), X(7247)}}, {{A, B, C, X(7382), X(52252)}}, {{A, B, C, X(7498), X(37185)}}, {{A, B, C, X(8044), X(57858)}}, {{A, B, C, X(8605), X(11051)}}, {{A, B, C, X(8818), X(21694)}}, {{A, B, C, X(10305), X(42467)}}, {{A, B, C, X(11578), X(41798)}}, {{A, B, C, X(12436), X(14377)}}, {{A, B, C, X(13577), X(39734)}}, {{A, B, C, X(14497), X(56352)}}, {{A, B, C, X(14555), X(37674)}}, {{A, B, C, X(14996), X(32863)}}, {{A, B, C, X(15998), X(30711)}}, {{A, B, C, X(17097), X(56231)}}, {{A, B, C, X(17300), X(37683)}}, {{A, B, C, X(17316), X(39594)}}, {{A, B, C, X(17778), X(37684)}}, {{A, B, C, X(18134), X(37642)}}, {{A, B, C, X(18139), X(24597)}}, {{A, B, C, X(18490), X(25417)}}, {{A, B, C, X(18928), X(25934)}}, {{A, B, C, X(21739), X(27789)}}, {{A, B, C, X(24298), X(43757)}}, {{A, B, C, X(26118), X(52283)}}, {{A, B, C, X(27818), X(52374)}}, {{A, B, C, X(30701), X(56046)}}, {{A, B, C, X(30710), X(56044)}}, {{A, B, C, X(30828), X(37646)}}, {{A, B, C, X(30962), X(37676)}}, {{A, B, C, X(36603), X(43732)}}, {{A, B, C, X(37092), X(37392)}}, {{A, B, C, X(37394), X(37445)}}, {{A, B, C, X(39703), X(54120)}}, {{A, B, C, X(39947), X(55938)}}, {{A, B, C, X(40434), X(43734)}}, {{A, B, C, X(40435), X(56217)}}, {{A, B, C, X(43740), X(56201)}}, {{A, B, C, X(50442), X(54451)}}, {{A, B, C, X(56367), X(57918)}}
X(60076) = barycentric product X(i)*X(j) for these (i, j): {59069, 850}, {59760, 7}
X(60076) = barycentric quotient X(i)/X(j) for these (i, j): {1, 5250}, {2, 14555}, {4, 4194}, {6, 4254}, {7, 17321}, {34, 7713}, {56, 16466}, {57, 5256}, {65, 3931}, {77, 54404}, {225, 39579}, {3676, 47995}, {4017, 50332}, {7178, 48402}, {7180, 50492}, {59069, 110}, {59760, 8}

X(60077) = X(1)X(4052)∩X(10)X(391)

Barycentrics    (3*a^2+2*a*(b+c)-(b-3*c)*(b+c))*(3*a^2+2*a*(b+c)+(3*b-c)*(b+c)) : :

X(60077) lies on the Kiepert hyperbola and on these lines: {1, 4052}, {2, 4252}, {3, 45098}, {6, 43533}, {8, 60267}, {10, 391}, {20, 2051}, {30, 54689}, {76, 3945}, {86, 57826}, {98, 7407}, {145, 321}, {193, 56210}, {226, 452}, {262, 7390}, {346, 5717}, {377, 60107}, {381, 54587}, {387, 60079}, {459, 11109}, {475, 60246}, {938, 4747}, {1446, 38298}, {1751, 5177}, {2047, 3317}, {2475, 60155}, {2476, 55962}, {2478, 60076}, {2996, 17379}, {3091, 13478}, {3146, 45100}, {3543, 19766}, {3618, 37161}, {3624, 56226}, {3742, 56155}, {3753, 57705}, {3812, 9309}, {3832, 60167}, {3839, 60172}, {4190, 60087}, {4195, 60254}, {4208, 60075}, {4678, 6539}, {4835, 60245}, {4869, 13740}, {5046, 60156}, {5129, 17758}, {5342, 40149}, {5698, 60321}, {6361, 54933}, {6871, 24624}, {6872, 60071}, {6904, 14554}, {6919, 60085}, {6998, 14494}, {7380, 7612}, {7410, 10155}, {10449, 60276}, {11319, 60242}, {16062, 18841}, {17300, 60285}, {17555, 56346}, {17677, 18842}, {19684, 60170}, {19877, 60243}, {20052, 27797}, {25441, 54553}, {25650, 51675}, {26051, 32022}, {26131, 56987}, {34258, 45784}, {36721, 54690}, {36722, 54712}, {37144, 43543}, {37145, 43542}, {37146, 43446}, {37147, 43447}, {37150, 54786}, {37162, 60169}, {37655, 60084}, {37666, 60206}, {46932, 60203}, {49743, 60143}, {50736, 60094}, {51171, 60149}, {52245, 56161}, {54367, 54624}

X(60077) = isogonal conjugate of X(4255)
X(60077) = isotomic conjugate of X(5232)
X(60077) = trilinear pole of line {2527, 4394}
X(60077) = pole of line {4255, 5232} with respect to the Wallace hyperbola
X(60077) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(145)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(1042)}}, {{A, B, C, X(7), X(1219)}}, {{A, B, C, X(8), X(86)}}, {{A, B, C, X(9), X(5436)}}, {{A, B, C, X(20), X(11109)}}, {{A, B, C, X(29), X(346)}}, {{A, B, C, X(34), X(2298)}}, {{A, B, C, X(65), X(39956)}}, {{A, B, C, X(75), X(5556)}}, {{A, B, C, X(79), X(4373)}}, {{A, B, C, X(81), X(937)}}, {{A, B, C, X(85), X(39716)}}, {{A, B, C, X(87), X(959)}}, {{A, B, C, X(105), X(989)}}, {{A, B, C, X(193), X(17379)}}, {{A, B, C, X(263), X(23493)}}, {{A, B, C, X(274), X(55937)}}, {{A, B, C, X(279), X(4307)}}, {{A, B, C, X(287), X(8813)}}, {{A, B, C, X(297), X(7407)}}, {{A, B, C, X(318), X(58001)}}, {{A, B, C, X(341), X(56074)}}, {{A, B, C, X(377), X(4200)}}, {{A, B, C, X(390), X(27523)}}, {{A, B, C, X(405), X(7518)}}, {{A, B, C, X(406), X(5046)}}, {{A, B, C, X(458), X(7390)}}, {{A, B, C, X(461), X(4082)}}, {{A, B, C, X(474), X(3753)}}, {{A, B, C, X(475), X(2475)}}, {{A, B, C, X(551), X(20052)}}, {{A, B, C, X(596), X(36606)}}, {{A, B, C, X(860), X(6871)}}, {{A, B, C, X(941), X(57666)}}, {{A, B, C, X(943), X(55989)}}, {{A, B, C, X(957), X(39949)}}, {{A, B, C, X(964), X(4198)}}, {{A, B, C, X(979), X(1002)}}, {{A, B, C, X(996), X(3296)}}, {{A, B, C, X(1065), X(10309)}}, {{A, B, C, X(1222), X(5558)}}, {{A, B, C, X(1224), X(5561)}}, {{A, B, C, X(1257), X(2297)}}, {{A, B, C, X(1376), X(3812)}}, {{A, B, C, X(1509), X(56043)}}, {{A, B, C, X(1698), X(46932)}}, {{A, B, C, X(1706), X(5437)}}, {{A, B, C, X(1842), X(54389)}}, {{A, B, C, X(2049), X(6994)}}, {{A, B, C, X(2296), X(56164)}}, {{A, B, C, X(2478), X(4194)}}, {{A, B, C, X(3091), X(17555)}}, {{A, B, C, X(3241), X(20057)}}, {{A, B, C, X(3527), X(57662)}}, {{A, B, C, X(3615), X(6556)}}, {{A, B, C, X(3617), X(3624)}}, {{A, B, C, X(3618), X(4869)}}, {{A, B, C, X(3621), X(3636)}}, {{A, B, C, X(3622), X(3632)}}, {{A, B, C, X(3701), X(57877)}}, {{A, B, C, X(3742), X(3913)}}, {{A, B, C, X(4185), X(50408)}}, {{A, B, C, X(4196), X(26051)}}, {{A, B, C, X(4646), X(37674)}}, {{A, B, C, X(4648), X(37681)}}, {{A, B, C, X(4668), X(46934)}}, {{A, B, C, X(4866), X(56088)}}, {{A, B, C, X(5125), X(5177)}}, {{A, B, C, X(5129), X(14004)}}, {{A, B, C, X(5136), X(6872)}}, {{A, B, C, X(5187), X(11105)}}, {{A, B, C, X(5439), X(5687)}}, {{A, B, C, X(5551), X(39697)}}, {{A, B, C, X(5698), X(54396)}}, {{A, B, C, X(5712), X(37666)}}, {{A, B, C, X(5717), X(36419)}}, {{A, B, C, X(5836), X(25524)}}, {{A, B, C, X(6601), X(51723)}}, {{A, B, C, X(6995), X(13740)}}, {{A, B, C, X(7319), X(28626)}}, {{A, B, C, X(7378), X(16062)}}, {{A, B, C, X(7380), X(37174)}}, {{A, B, C, X(8747), X(56047)}}, {{A, B, C, X(9780), X(19877)}}, {{A, B, C, X(10013), X(46187)}}, {{A, B, C, X(10449), X(29822)}}, {{A, B, C, X(10570), X(34919)}}, {{A, B, C, X(13736), X(57527)}}, {{A, B, C, X(14552), X(19684)}}, {{A, B, C, X(17122), X(24440)}}, {{A, B, C, X(17300), X(51171)}}, {{A, B, C, X(17677), X(52284)}}, {{A, B, C, X(17697), X(28076)}}, {{A, B, C, X(19741), X(31303)}}, {{A, B, C, X(20053), X(38314)}}, {{A, B, C, X(20090), X(37677)}}, {{A, B, C, X(25417), X(40406)}}, {{A, B, C, X(30711), X(37870)}}, {{A, B, C, X(34434), X(55919)}}, {{A, B, C, X(37161), X(57534)}}, {{A, B, C, X(38247), X(59267)}}, {{A, B, C, X(38306), X(57724)}}, {{A, B, C, X(39748), X(39975)}}, {{A, B, C, X(40430), X(56203)}}, {{A, B, C, X(41439), X(45989)}}, {{A, B, C, X(42285), X(43734)}}, {{A, B, C, X(42287), X(56382)}}, {{A, B, C, X(49745), X(52382)}}, {{A, B, C, X(52344), X(58028)}}, {{A, B, C, X(54125), X(57866)}}, {{A, B, C, X(56146), X(56200)}}
X(60077) = barycentric quotient X(i)/X(j) for these (i, j): {2, 5232}, {6, 4255}

X(60078) = X(1)X(4080)∩X(10)X(44)

Barycentrics    (2*a^2+a*(b+c)-(b-2*c)*(b+c))*(2*a^2+a*(b+c)+(2*b-c)*(b+c)) : :

X(60078) lies on the Kiepert hyperbola and on these lines: {1, 4080}, {2, 4257}, {6, 60079}, {8, 27797}, {10, 44}, {17, 37145}, {18, 37144}, {30, 2051}, {51, 3919}, {76, 17378}, {83, 17677}, {226, 535}, {321, 519}, {376, 45098}, {381, 13478}, {513, 4049}, {516, 54933}, {524, 60276}, {540, 60084}, {597, 60094}, {671, 46922}, {730, 34475}, {1125, 14020}, {1751, 17532}, {1877, 40149}, {2047, 10194}, {2476, 60247}, {2478, 60169}, {2718, 19634}, {2796, 11611}, {2901, 50123}, {3017, 54119}, {3454, 51672}, {3543, 45100}, {3679, 6539}, {3754, 57666}, {3828, 5294}, {3830, 54586}, {3839, 60167}, {3845, 60172}, {4052, 51071}, {4065, 43677}, {4084, 50601}, {4217, 60242}, {4658, 43676}, {4669, 60267}, {4795, 5722}, {4868, 39974}, {5046, 60258}, {5480, 38309}, {5717, 56282}, {6175, 57721}, {6998, 7608}, {7380, 7607}, {7390, 53099}, {7407, 43537}, {7410, 53098}, {10159, 13740}, {10187, 37146}, {10188, 37147}, {10197, 60188}, {10302, 17297}, {11109, 16080}, {11112, 14554}, {11114, 60071}, {11608, 50889}, {11645, 54701}, {13576, 50287}, {13735, 60251}, {14584, 60091}, {15682, 54689}, {16062, 43527}, {16394, 27739}, {17182, 57722}, {17499, 50074}, {17528, 60075}, {17555, 43530}, {17556, 60085}, {17577, 24624}, {17579, 60087}, {17758, 49738}, {19722, 54928}, {19738, 54744}, {19862, 51679}, {19883, 56226}, {20615, 58565}, {25496, 48808}, {26098, 48833}, {28845, 54668}, {32431, 54677}, {33682, 60089}, {33688, 56161}, {36721, 56144}, {36722, 43672}, {36872, 50301}, {37654, 54786}, {40012, 48868}, {40013, 49744}, {41099, 54587}, {43531, 54367}, {48817, 60254}, {48855, 60257}, {48870, 60206}, {48888, 60112}, {50171, 60097}, {50300, 60135}, {50736, 60092}, {53620, 56209}, {56969, 60109}

X(60078) = isogonal conjugate of X(4256)
X(60078) = isotomic conjugate of X(17271)
X(60078) = trilinear pole of line {1635, 4809}
X(60078) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 4256}, {31, 17271}, {692, 47894}
X(60078) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 17271}, {3, 4256}, {1086, 47894}
X(60078) = X(i)-cross conjugate of X(j) for these {i, j}: {52246, 60079}
X(60078) = pole of line {52246, 60078} with respect to the Kiepert hyperbola
X(60078) = pole of line {4256, 17271} with respect to the Wallace hyperbola
X(60078) = pole of line {17382, 29833} with respect to the dual conic of Yff parabola
X(60078) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(44)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(4257)}}, {{A, B, C, X(7), X(996)}}, {{A, B, C, X(8), X(551)}}, {{A, B, C, X(12), X(21689)}}, {{A, B, C, X(27), X(37150)}}, {{A, B, C, X(29), X(11113)}}, {{A, B, C, X(30), X(11109)}}, {{A, B, C, X(34), X(54336)}}, {{A, B, C, X(58), X(4274)}}, {{A, B, C, X(65), X(39748)}}, {{A, B, C, X(75), X(5561)}}, {{A, B, C, X(79), X(596)}}, {{A, B, C, X(80), X(86)}}, {{A, B, C, X(87), X(994)}}, {{A, B, C, X(100), X(5883)}}, {{A, B, C, X(145), X(51071)}}, {{A, B, C, X(257), X(35170)}}, {{A, B, C, X(291), X(31161)}}, {{A, B, C, X(381), X(17555)}}, {{A, B, C, X(404), X(3754)}}, {{A, B, C, X(427), X(17677)}}, {{A, B, C, X(428), X(13740)}}, {{A, B, C, X(469), X(54367)}}, {{A, B, C, X(502), X(34920)}}, {{A, B, C, X(514), X(752)}}, {{A, B, C, X(522), X(535)}}, {{A, B, C, X(524), X(46922)}}, {{A, B, C, X(527), X(29066)}}, {{A, B, C, X(553), X(26223)}}, {{A, B, C, X(597), X(17297)}}, {{A, B, C, X(673), X(49725)}}, {{A, B, C, X(730), X(4785)}}, {{A, B, C, X(860), X(17577)}}, {{A, B, C, X(937), X(39980)}}, {{A, B, C, X(943), X(55992)}}, {{A, B, C, X(1000), X(30712)}}, {{A, B, C, X(1065), X(46435)}}, {{A, B, C, X(1121), X(34914)}}, {{A, B, C, X(1125), X(3679)}}, {{A, B, C, X(1210), X(45701)}}, {{A, B, C, X(1219), X(43733)}}, {{A, B, C, X(1222), X(5557)}}, {{A, B, C, X(1224), X(55955)}}, {{A, B, C, X(1509), X(35168)}}, {{A, B, C, X(1698), X(3828)}}, {{A, B, C, X(1883), X(17678)}}, {{A, B, C, X(1884), X(13735)}}, {{A, B, C, X(2297), X(56136)}}, {{A, B, C, X(2298), X(36125)}}, {{A, B, C, X(2787), X(2796)}}, {{A, B, C, X(3017), X(3178)}}, {{A, B, C, X(3227), X(4672)}}, {{A, B, C, X(3241), X(3244)}}, {{A, B, C, X(3255), X(51565)}}, {{A, B, C, X(3296), X(56145)}}, {{A, B, C, X(3306), X(54286)}}, {{A, B, C, X(3467), X(40430)}}, {{A, B, C, X(3613), X(45095)}}, {{A, B, C, X(3615), X(11813)}}, {{A, B, C, X(3616), X(4669)}}, {{A, B, C, X(3617), X(19883)}}, {{A, B, C, X(3622), X(34641)}}, {{A, B, C, X(3624), X(4745)}}, {{A, B, C, X(3625), X(38314)}}, {{A, B, C, X(3626), X(25055)}}, {{A, B, C, X(3632), X(51103)}}, {{A, B, C, X(3634), X(19875)}}, {{A, B, C, X(3636), X(4677)}}, {{A, B, C, X(3911), X(40426)}}, {{A, B, C, X(3912), X(50287)}}, {{A, B, C, X(4013), X(8818)}}, {{A, B, C, X(4214), X(48816)}}, {{A, B, C, X(4234), X(37226)}}, {{A, B, C, X(4654), X(5294)}}, {{A, B, C, X(4668), X(51108)}}, {{A, B, C, X(4674), X(39798)}}, {{A, B, C, X(4701), X(51105)}}, {{A, B, C, X(4746), X(51110)}}, {{A, B, C, X(4868), X(37633)}}, {{A, B, C, X(5064), X(16062)}}, {{A, B, C, X(5125), X(17532)}}, {{A, B, C, X(5136), X(11114)}}, {{A, B, C, X(5550), X(38098)}}, {{A, B, C, X(5551), X(6553)}}, {{A, B, C, X(5556), X(36588)}}, {{A, B, C, X(5559), X(24857)}}, {{A, B, C, X(5665), X(56220)}}, {{A, B, C, X(6630), X(59267)}}, {{A, B, C, X(6734), X(10197)}}, {{A, B, C, X(6735), X(10199)}}, {{A, B, C, X(6998), X(52281)}}, {{A, B, C, X(7380), X(52282)}}, {{A, B, C, X(9328), X(56042)}}, {{A, B, C, X(10056), X(10916)}}, {{A, B, C, X(10072), X(10915)}}, {{A, B, C, X(10266), X(56143)}}, {{A, B, C, X(11019), X(34619)}}, {{A, B, C, X(11105), X(37375)}}, {{A, B, C, X(11239), X(49627)}}, {{A, B, C, X(11240), X(49626)}}, {{A, B, C, X(11604), X(55076)}}, {{A, B, C, X(12572), X(39585)}}, {{A, B, C, X(14377), X(56044)}}, {{A, B, C, X(15065), X(57830)}}, {{A, B, C, X(15173), X(40436)}}, {{A, B, C, X(16825), X(50291)}}, {{A, B, C, X(17132), X(28475)}}, {{A, B, C, X(17277), X(49738)}}, {{A, B, C, X(17379), X(50074)}}, {{A, B, C, X(17537), X(37168)}}, {{A, B, C, X(19862), X(53620)}}, {{A, B, C, X(19868), X(48851)}}, {{A, B, C, X(19878), X(51066)}}, {{A, B, C, X(20052), X(51106)}}, {{A, B, C, X(20053), X(51104)}}, {{A, B, C, X(20057), X(51096)}}, {{A, B, C, X(23493), X(27375)}}, {{A, B, C, X(26003), X(36722)}}, {{A, B, C, X(27475), X(36954)}}, {{A, B, C, X(28580), X(29148)}}, {{A, B, C, X(28599), X(52569)}}, {{A, B, C, X(29574), X(49488)}}, {{A, B, C, X(31397), X(45700)}}, {{A, B, C, X(34434), X(39949)}}, {{A, B, C, X(34860), X(43732)}}, {{A, B, C, X(34918), X(36596)}}, {{A, B, C, X(35633), X(42042)}}, {{A, B, C, X(36480), X(50305)}}, {{A, B, C, X(36721), X(37448)}}, {{A, B, C, X(36916), X(56146)}}, {{A, B, C, X(37869), X(42030)}}, {{A, B, C, X(39712), X(43097)}}, {{A, B, C, X(39724), X(54974)}}, {{A, B, C, X(39948), X(57748)}}, {{A, B, C, X(39957), X(47947)}}, {{A, B, C, X(39977), X(56149)}}, {{A, B, C, X(42471), X(48866)}}, {{A, B, C, X(45989), X(56032)}}, {{A, B, C, X(48814), X(57527)}}, {{A, B, C, X(50023), X(50286)}}, {{A, B, C, X(50736), X(57534)}}, {{A, B, C, X(52518), X(57662)}}, {{A, B, C, X(52759), X(56395)}}, {{A, B, C, X(55090), X(56046)}}
X(60078) = barycentric quotient X(i)/X(j) for these (i, j): {2, 17271}, {6, 4256}, {514, 47894}

X(60079) = X(2)X(4256)∩X(10)X(45)

Barycentrics    (a^2-a*(b+c)+(b-2*c)*(b+c))*(a^2-a*(b+c)-(2*b-c)*(b+c)) : :

X(60079) lies on the Kiepert hyperbola and on these lines: {1, 30588}, {2, 4256}, {4, 37654}, {6, 60078}, {8, 4080}, {10, 45}, {17, 37144}, {18, 37145}, {21, 60247}, {30, 13478}, {76, 17271}, {226, 519}, {321, 3679}, {377, 60169}, {381, 2051}, {387, 60077}, {522, 4049}, {524, 60083}, {528, 60135}, {540, 60156}, {543, 47039}, {551, 3772}, {671, 17346}, {740, 60116}, {752, 60089}, {966, 54786}, {996, 33136}, {1714, 4217}, {1724, 17537}, {1751, 11113}, {1834, 5114}, {1992, 54770}, {2047, 10195}, {2475, 60258}, {2551, 56172}, {2796, 11608}, {3017, 14534}, {3454, 60242}, {3543, 60167}, {3545, 45098}, {3578, 54775}, {3617, 27797}, {3634, 51599}, {3711, 4013}, {3741, 48808}, {3828, 32777}, {3830, 60172}, {3839, 45100}, {3845, 54586}, {4052, 4669}, {4745, 60267}, {5292, 51668}, {5295, 56282}, {5587, 54933}, {6175, 57722}, {6539, 53620}, {6998, 7607}, {7380, 7608}, {7390, 43537}, {7407, 53099}, {7410, 60123}, {8808, 52121}, {10159, 16062}, {10187, 37147}, {10188, 37146}, {10449, 60236}, {11109, 43530}, {11111, 55962}, {11112, 60085}, {11114, 24624}, {11236, 40515}, {11611, 50086}, {13740, 43527}, {14554, 17556}, {15682, 54587}, {16080, 17555}, {17251, 60276}, {17313, 17528}, {17330, 52246}, {17577, 60071}, {17678, 19792}, {17679, 39994}, {18513, 32864}, {19723, 54676}, {19875, 60203}, {20083, 51672}, {21283, 24222}, {28849, 54668}, {29066, 35353}, {32431, 54510}, {33137, 48833}, {33937, 60197}, {34258, 48852}, {34619, 60229}, {36721, 43672}, {36722, 56144}, {36944, 45700}, {37156, 60225}, {37375, 60087}, {37660, 48836}, {37715, 49725}, {38462, 40149}, {40718, 50287}, {41099, 54689}, {45701, 60188}, {48814, 60235}, {48839, 54119}, {48850, 60261}, {48867, 60082}, {49729, 60206}, {50056, 60084}, {50226, 58012}, {50736, 57826}, {51975, 60091}, {56969, 60090}

X(60079) = reflection of X(i) in X(j) for these {i,j}: {47040, 2}
X(60079) = isogonal conjugate of X(4257)
X(60079) = isotomic conjugate of X(17378)
X(60079) = trilinear pole of line {1639, 4893}
X(60079) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 4257}, {31, 17378}, {692, 47755}, {27754, 28607}
X(60079) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 17378}, {3, 4257}, {1086, 47755}, {36911, 27754}
X(60079) = X(i)-cross conjugate of X(j) for these {i, j}: {17330, 2}, {52246, 60078}
X(60079) = pole of line {17330, 52246} with respect to the Kiepert hyperbola
X(60079) = pole of line {4257, 17378} with respect to the Wallace hyperbola
X(60079) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(45)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(4256)}}, {{A, B, C, X(7), X(42285)}}, {{A, B, C, X(8), X(519)}}, {{A, B, C, X(9), X(56104)}}, {{A, B, C, X(12), X(21690)}}, {{A, B, C, X(25), X(17677)}}, {{A, B, C, X(27), X(54367)}}, {{A, B, C, X(29), X(17532)}}, {{A, B, C, X(30), X(17555)}}, {{A, B, C, X(65), X(39974)}}, {{A, B, C, X(69), X(37654)}}, {{A, B, C, X(75), X(80)}}, {{A, B, C, X(79), X(31359)}}, {{A, B, C, X(86), X(5561)}}, {{A, B, C, X(106), X(3551)}}, {{A, B, C, X(145), X(4669)}}, {{A, B, C, X(256), X(994)}}, {{A, B, C, X(257), X(14377)}}, {{A, B, C, X(264), X(15065)}}, {{A, B, C, X(274), X(35170)}}, {{A, B, C, X(318), X(3419)}}, {{A, B, C, X(330), X(35168)}}, {{A, B, C, X(341), X(4863)}}, {{A, B, C, X(381), X(11109)}}, {{A, B, C, X(386), X(5114)}}, {{A, B, C, X(407), X(48814)}}, {{A, B, C, X(428), X(16062)}}, {{A, B, C, X(461), X(50736)}}, {{A, B, C, X(469), X(37150)}}, {{A, B, C, X(514), X(28580)}}, {{A, B, C, X(524), X(17346)}}, {{A, B, C, X(528), X(23887)}}, {{A, B, C, X(536), X(29066)}}, {{A, B, C, X(537), X(3887)}}, {{A, B, C, X(551), X(3617)}}, {{A, B, C, X(572), X(9567)}}, {{A, B, C, X(673), X(48829)}}, {{A, B, C, X(752), X(23876)}}, {{A, B, C, X(758), X(51290)}}, {{A, B, C, X(860), X(11114)}}, {{A, B, C, X(937), X(36603)}}, {{A, B, C, X(941), X(53114)}}, {{A, B, C, X(983), X(56149)}}, {{A, B, C, X(998), X(8769)}}, {{A, B, C, X(1000), X(4373)}}, {{A, B, C, X(1016), X(27494)}}, {{A, B, C, X(1089), X(24006)}}, {{A, B, C, X(1120), X(39710)}}, {{A, B, C, X(1121), X(5695)}}, {{A, B, C, X(1125), X(53620)}}, {{A, B, C, X(1126), X(28509)}}, {{A, B, C, X(1219), X(43734)}}, {{A, B, C, X(1220), X(5560)}}, {{A, B, C, X(1222), X(11058)}}, {{A, B, C, X(1224), X(17501)}}, {{A, B, C, X(1257), X(55992)}}, {{A, B, C, X(1698), X(19875)}}, {{A, B, C, X(1894), X(37038)}}, {{A, B, C, X(1904), X(48816)}}, {{A, B, C, X(2785), X(2796)}}, {{A, B, C, X(2901), X(5295)}}, {{A, B, C, X(3017), X(20653)}}, {{A, B, C, X(3175), X(19792)}}, {{A, B, C, X(3241), X(3626)}}, {{A, B, C, X(3467), X(40436)}}, {{A, B, C, X(3616), X(4745)}}, {{A, B, C, X(3621), X(34641)}}, {{A, B, C, X(3622), X(38098)}}, {{A, B, C, X(3624), X(51066)}}, {{A, B, C, X(3625), X(31145)}}, {{A, B, C, X(3632), X(4677)}}, {{A, B, C, X(3636), X(51068)}}, {{A, B, C, X(3661), X(50287)}}, {{A, B, C, X(3680), X(36596)}}, {{A, B, C, X(3772), X(42034)}}, {{A, B, C, X(3828), X(9780)}}, {{A, B, C, X(4084), X(4189)}}, {{A, B, C, X(4102), X(45032)}}, {{A, B, C, X(4186), X(17678)}}, {{A, B, C, X(4385), X(5101)}}, {{A, B, C, X(4668), X(51093)}}, {{A, B, C, X(4685), X(10449)}}, {{A, B, C, X(4847), X(34619)}}, {{A, B, C, X(4866), X(41711)}}, {{A, B, C, X(5064), X(13740)}}, {{A, B, C, X(5125), X(11113)}}, {{A, B, C, X(5136), X(17577)}}, {{A, B, C, X(5556), X(43972)}}, {{A, B, C, X(5557), X(24857)}}, {{A, B, C, X(6553), X(7317)}}, {{A, B, C, X(6556), X(15998)}}, {{A, B, C, X(6734), X(45701)}}, {{A, B, C, X(6735), X(45700)}}, {{A, B, C, X(6736), X(34625)}}, {{A, B, C, X(6757), X(36934)}}, {{A, B, C, X(6998), X(52282)}}, {{A, B, C, X(7319), X(51782)}}, {{A, B, C, X(7380), X(52281)}}, {{A, B, C, X(7518), X(50741)}}, {{A, B, C, X(7576), X(37156)}}, {{A, B, C, X(10570), X(52344)}}, {{A, B, C, X(11105), X(17579)}}, {{A, B, C, X(13606), X(39702)}}, {{A, B, C, X(14004), X(17528)}}, {{A, B, C, X(14942), X(31140)}}, {{A, B, C, X(15173), X(40430)}}, {{A, B, C, X(15232), X(34265)}}, {{A, B, C, X(15315), X(34434)}}, {{A, B, C, X(17132), X(28292)}}, {{A, B, C, X(17251), X(46922)}}, {{A, B, C, X(17277), X(17313)}}, {{A, B, C, X(17330), X(17378)}}, {{A, B, C, X(17461), X(54310)}}, {{A, B, C, X(17743), X(32018)}}, {{A, B, C, X(18490), X(36606)}}, {{A, B, C, X(19877), X(51069)}}, {{A, B, C, X(20057), X(51070)}}, {{A, B, C, X(22334), X(57662)}}, {{A, B, C, X(23604), X(34288)}}, {{A, B, C, X(26003), X(36721)}}, {{A, B, C, X(29615), X(49488)}}, {{A, B, C, X(30513), X(55076)}}, {{A, B, C, X(32635), X(56137)}}, {{A, B, C, X(32777), X(42029)}}, {{A, B, C, X(34892), X(55954)}}, {{A, B, C, X(36038), X(56416)}}, {{A, B, C, X(36722), X(37448)}}, {{A, B, C, X(36924), X(58254)}}, {{A, B, C, X(36954), X(39749)}}, {{A, B, C, X(37390), X(50056)}}, {{A, B, C, X(38271), X(55993)}}, {{A, B, C, X(39742), X(41434)}}, {{A, B, C, X(39748), X(39960)}}, {{A, B, C, X(39798), X(56159)}}, {{A, B, C, X(39959), X(55931)}}, {{A, B, C, X(39980), X(57748)}}, {{A, B, C, X(39981), X(47947)}}, {{A, B, C, X(39982), X(56174)}}, {{A, B, C, X(39983), X(56134)}}, {{A, B, C, X(40014), X(42326)}}, {{A, B, C, X(40509), X(42318)}}, {{A, B, C, X(41506), X(48863)}}, {{A, B, C, X(43093), X(44176)}}, {{A, B, C, X(48852), X(59305)}}, {{A, B, C, X(49772), X(50316)}}, {{A, B, C, X(52654), X(55926)}}, {{A, B, C, X(52755), X(52902)}}, {{A, B, C, X(55953), X(56138)}}
X(60079) = barycentric quotient X(i)/X(j) for these (i, j): {2, 17378}, {6, 4257}, {514, 47755}, {3679, 27754}

X(60080) = X(10)X(41)∩X(21)X(76)

Barycentrics    (a^4-b^2*c^2+c^4-a^2*b*(b+c)-a*b*c*(b+c))*(b^4+(a+c)*(a^3-(a^2+a*b+b^2)*c)) : :

X(60080) lies on the Kiepert hyperbola and on these lines: {2, 2194}, {3, 54739}, {4, 2204}, {6, 45964}, {10, 41}, {21, 76}, {25, 40149}, {30, 54691}, {31, 226}, {55, 321}, {56, 1446}, {83, 2476}, {262, 33854}, {381, 54630}, {598, 17577}, {671, 11114}, {904, 3924}, {1036, 60197}, {1447, 3415}, {1751, 37330}, {1754, 2051}, {1916, 5985}, {2053, 60244}, {2208, 8808}, {2996, 6872}, {4049, 47800}, {4080, 5698}, {5276, 60108}, {5282, 43534}, {5327, 60071}, {5395, 6871}, {5397, 7380}, {5485, 11111}, {6186, 43682}, {6187, 60091}, {6856, 18841}, {6857, 18840}, {6912, 54821}, {6998, 60112}, {7474, 57722}, {7735, 60152}, {8229, 13478}, {12514, 56282}, {16996, 43688}, {17758, 37522}, {30768, 60243}, {34068, 36007}, {37284, 60265}, {40824, 45962}, {50739, 60143}, {52269, 54729}

X(60080) = isogonal conjugate of X(4259)
X(60080) = trilinear pole of line {3063, 523}
X(60080) = X(i)-vertex conjugate of X(j) for these {i, j}: {3415, 56358}
X(60080) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(675)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(5135)}}, {{A, B, C, X(8), X(3011)}}, {{A, B, C, X(19), X(272)}}, {{A, B, C, X(21), X(25)}}, {{A, B, C, X(27), X(37149)}}, {{A, B, C, X(37), X(2980)}}, {{A, B, C, X(66), X(1441)}}, {{A, B, C, X(85), X(37208)}}, {{A, B, C, X(90), X(1311)}}, {{A, B, C, X(95), X(39956)}}, {{A, B, C, X(183), X(33854)}}, {{A, B, C, X(251), X(1175)}}, {{A, B, C, X(261), X(9309)}}, {{A, B, C, X(305), X(18123)}}, {{A, B, C, X(333), X(36124)}}, {{A, B, C, X(385), X(16998)}}, {{A, B, C, X(393), X(57818)}}, {{A, B, C, X(405), X(7466)}}, {{A, B, C, X(427), X(2476)}}, {{A, B, C, X(468), X(11114)}}, {{A, B, C, X(596), X(43948)}}, {{A, B, C, X(917), X(56139)}}, {{A, B, C, X(941), X(32085)}}, {{A, B, C, X(976), X(3757)}}, {{A, B, C, X(1002), X(40419)}}, {{A, B, C, X(1013), X(4223)}}, {{A, B, C, X(1156), X(5695)}}, {{A, B, C, X(1218), X(40416)}}, {{A, B, C, X(1390), X(9103)}}, {{A, B, C, X(1447), X(5282)}}, {{A, B, C, X(1754), X(37558)}}, {{A, B, C, X(1799), X(34259)}}, {{A, B, C, X(2165), X(57830)}}, {{A, B, C, X(2346), X(45129)}}, {{A, B, C, X(2726), X(55918)}}, {{A, B, C, X(3560), X(35973)}}, {{A, B, C, X(3924), X(7081)}}, {{A, B, C, X(4220), X(54343)}}, {{A, B, C, X(4232), X(11111)}}, {{A, B, C, X(4233), X(37284)}}, {{A, B, C, X(4518), X(33127)}}, {{A, B, C, X(5094), X(17577)}}, {{A, B, C, X(5125), X(37330)}}, {{A, B, C, X(5276), X(16992)}}, {{A, B, C, X(5698), X(8756)}}, {{A, B, C, X(5711), X(37543)}}, {{A, B, C, X(5985), X(40820)}}, {{A, B, C, X(6353), X(6872)}}, {{A, B, C, X(6828), X(25985)}}, {{A, B, C, X(6856), X(7378)}}, {{A, B, C, X(6857), X(6995)}}, {{A, B, C, X(6871), X(8889)}}, {{A, B, C, X(6932), X(26020)}}, {{A, B, C, X(7735), X(45962)}}, {{A, B, C, X(7766), X(16996)}}, {{A, B, C, X(8229), X(17555)}}, {{A, B, C, X(9108), X(56027)}}, {{A, B, C, X(9307), X(54454)}}, {{A, B, C, X(9780), X(30768)}}, {{A, B, C, X(14017), X(37325)}}, {{A, B, C, X(14947), X(19628)}}, {{A, B, C, X(16020), X(49991)}}, {{A, B, C, X(16048), X(35993)}}, {{A, B, C, X(16997), X(17000)}}, {{A, B, C, X(17003), X(31090)}}, {{A, B, C, X(19846), X(29679)}}, {{A, B, C, X(30542), X(39960)}}, {{A, B, C, X(36007), X(52891)}}, {{A, B, C, X(38557), X(52145)}}, {{A, B, C, X(39732), X(57726)}}, {{A, B, C, X(39748), X(56195)}}, {{A, B, C, X(39798), X(45838)}}, {{A, B, C, X(39945), X(56254)}}, {{A, B, C, X(39974), X(45819)}}, {{A, B, C, X(39975), X(45857)}}, {{A, B, C, X(47209), X(47210)}}, {{A, B, C, X(50739), X(52301)}}

X(60081) = X(2)X(5138)∩X(76)X(405)

Barycentrics    (a^4+b^4-2*a*b*(a+b)*c-(a+b)^2*c^2)*(a^4-b^2*c^2+c^4-2*a*b*c*(b+c)-a^2*b*(b+2*c)) : :

X(60081) lies on the Kiepert hyperbola and on these lines: {2, 5138}, {6, 60108}, {9, 43534}, {10, 3684}, {30, 54692}, {58, 17758}, {76, 405}, {83, 442}, {226, 238}, {242, 40149}, {261, 40017}, {275, 25985}, {321, 1621}, {381, 54729}, {427, 40395}, {452, 2996}, {572, 43672}, {598, 17532}, {671, 11113}, {1006, 54739}, {1446, 1447}, {1916, 17000}, {2051, 7413}, {3737, 4444}, {5177, 5395}, {5985, 11606}, {6913, 54821}, {6998, 57719}, {7380, 54972}, {7735, 60165}, {10477, 16998}, {16817, 60197}, {16845, 18840}, {18786, 60245}, {18842, 50741}, {19309, 58011}, {24624, 37330}, {26052, 60155}, {33854, 45964}, {34258, 37502}, {36815, 60091}, {37325, 43675}

X(60081) = isogonal conjugate of X(4260)
X(60081) = isotomic conjugate of X(37664)
X(60081) = trilinear pole of line {4435, 21007}
X(60081) = pole of line {4260, 37664} with respect to the Wallace hyperbola
X(60081) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3757)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(5), X(25985)}}, {{A, B, C, X(6), X(5138)}}, {{A, B, C, X(9), X(87)}}, {{A, B, C, X(25), X(213)}}, {{A, B, C, X(28), X(47511)}}, {{A, B, C, X(37), X(32085)}}, {{A, B, C, X(58), X(105)}}, {{A, B, C, X(66), X(57831)}}, {{A, B, C, X(72), X(1799)}}, {{A, B, C, X(95), X(39798)}}, {{A, B, C, X(272), X(2298)}}, {{A, B, C, X(291), X(40419)}}, {{A, B, C, X(385), X(17000)}}, {{A, B, C, X(393), X(57858)}}, {{A, B, C, X(427), X(442)}}, {{A, B, C, X(452), X(6353)}}, {{A, B, C, X(468), X(11113)}}, {{A, B, C, X(475), X(26052)}}, {{A, B, C, X(513), X(57881)}}, {{A, B, C, X(572), X(5481)}}, {{A, B, C, X(612), X(16817)}}, {{A, B, C, X(675), X(1390)}}, {{A, B, C, X(860), X(37330)}}, {{A, B, C, X(941), X(57408)}}, {{A, B, C, X(1016), X(56138)}}, {{A, B, C, X(1220), X(40415)}}, {{A, B, C, X(2165), X(57877)}}, {{A, B, C, X(2724), X(56139)}}, {{A, B, C, X(2862), X(56153)}}, {{A, B, C, X(2980), X(39983)}}, {{A, B, C, X(3961), X(16823)}}, {{A, B, C, X(4183), X(4223)}}, {{A, B, C, X(4518), X(6598)}}, {{A, B, C, X(4998), X(52654)}}, {{A, B, C, X(5019), X(37502)}}, {{A, B, C, X(5094), X(17532)}}, {{A, B, C, X(5177), X(8889)}}, {{A, B, C, X(5665), X(56358)}}, {{A, B, C, X(6907), X(26020)}}, {{A, B, C, X(6920), X(35973)}}, {{A, B, C, X(6995), X(16845)}}, {{A, B, C, X(6998), X(37279)}}, {{A, B, C, X(7413), X(11109)}}, {{A, B, C, X(9106), X(36602)}}, {{A, B, C, X(9307), X(57818)}}, {{A, B, C, X(10482), X(15344)}}, {{A, B, C, X(11169), X(39982)}}, {{A, B, C, X(11323), X(19309)}}, {{A, B, C, X(16774), X(57866)}}, {{A, B, C, X(26227), X(30117)}}, {{A, B, C, X(30733), X(37325)}}, {{A, B, C, X(33854), X(37670)}}, {{A, B, C, X(36124), X(40435)}}, {{A, B, C, X(37060), X(37377)}}, {{A, B, C, X(37315), X(37321)}}, {{A, B, C, X(37362), X(47510)}}, {{A, B, C, X(39956), X(45857)}}, {{A, B, C, X(40405), X(54117)}}, {{A, B, C, X(50741), X(52284)}}

X(60082) = X(6)X(321)∩X(10)X(31)

Barycentrics    (a^3+a^2*(b+c)+a*b*(b+c)+b^2*(b+c))*(a^3+a^2*(b+c)+a*c*(b+c)+c^2*(b+c)) : :

X(60082) lies on the Kiepert hyperbola and on these lines: {1, 56282}, {2, 1333}, {4, 2203}, {6, 321}, {10, 31}, {30, 54693}, {76, 81}, {83, 18096}, {86, 57722}, {98, 59112}, {226, 604}, {262, 4220}, {379, 36907}, {381, 54533}, {608, 40149}, {739, 839}, {894, 56342}, {940, 40013}, {1150, 60084}, {1407, 1446}, {1911, 5311}, {2051, 19645}, {2052, 5317}, {2162, 19734}, {2221, 4359}, {2298, 60264}, {2345, 6539}, {3589, 50320}, {3597, 37399}, {3618, 60155}, {3969, 48863}, {4052, 19738}, {4080, 9456}, {4261, 17587}, {4383, 60097}, {5051, 43531}, {5712, 60242}, {5716, 11319}, {7549, 13599}, {10159, 33172}, {11320, 28606}, {11611, 17961}, {13576, 51743}, {14484, 50698}, {16783, 40515}, {17379, 60257}, {17863, 43675}, {18825, 57979}, {19701, 28607}, {19728, 24589}, {19730, 36619}, {19731, 39964}, {19732, 34819}, {23349, 35353}, {24597, 60206}, {26540, 60241}, {27064, 56003}, {28776, 60188}, {29647, 40718}, {32911, 34258}, {33113, 50412}, {34475, 40735}, {36794, 40395}, {37633, 40012}, {37652, 56210}, {37674, 39994}, {37685, 44140}, {41806, 60247}, {43685, 51333}, {47511, 60108}, {48867, 60079}, {50115, 60267}, {53417, 54744}, {54933, 56960}, {57656, 60265}

X(60082) = isogonal conjugate of X(4261)
X(60082) = isotomic conjugate of X(32782)
X(60082) = trilinear pole of line {667, 51635}
X(60082) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 4261}, {31, 32782}, {48, 5142}, {58, 56541}, {190, 838}, {2206, 56564}
X(60082) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 32782}, {3, 4261}, {10, 56541}, {1249, 5142}, {40603, 56564}, {55053, 838}
X(60082) = pole of line {839, 36080} with respect to the Hutson-Moses hyperbola
X(60082) = pole of line {4261, 32782} with respect to the Wallace hyperbola
X(60082) = pole of line {32774, 37522} with respect to the dual conic of Yff parabola
X(60082) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1724)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(31)}}, {{A, B, C, X(7), X(5294)}}, {{A, B, C, X(8), X(46103)}}, {{A, B, C, X(25), X(18098)}}, {{A, B, C, X(27), X(964)}}, {{A, B, C, X(57), X(5264)}}, {{A, B, C, X(79), X(39700)}}, {{A, B, C, X(85), X(5300)}}, {{A, B, C, X(86), X(2997)}}, {{A, B, C, X(92), X(5016)}}, {{A, B, C, X(189), X(39716)}}, {{A, B, C, X(239), X(5311)}}, {{A, B, C, X(251), X(981)}}, {{A, B, C, X(256), X(28606)}}, {{A, B, C, X(264), X(21287)}}, {{A, B, C, X(330), X(52393)}}, {{A, B, C, X(333), X(19684)}}, {{A, B, C, X(335), X(26061)}}, {{A, B, C, X(427), X(33736)}}, {{A, B, C, X(458), X(4220)}}, {{A, B, C, X(469), X(5051)}}, {{A, B, C, X(513), X(9022)}}, {{A, B, C, X(518), X(51743)}}, {{A, B, C, X(870), X(52394)}}, {{A, B, C, X(873), X(55970)}}, {{A, B, C, X(940), X(32911)}}, {{A, B, C, X(996), X(35058)}}, {{A, B, C, X(1016), X(27789)}}, {{A, B, C, X(1255), X(17743)}}, {{A, B, C, X(1509), X(2985)}}, {{A, B, C, X(1839), X(2345)}}, {{A, B, C, X(1877), X(4358)}}, {{A, B, C, X(2185), X(44687)}}, {{A, B, C, X(2287), X(19716)}}, {{A, B, C, X(2296), X(40415)}}, {{A, B, C, X(2339), X(19607)}}, {{A, B, C, X(2982), X(39945)}}, {{A, B, C, X(3112), X(56065)}}, {{A, B, C, X(3306), X(28997)}}, {{A, B, C, X(3589), X(33172)}}, {{A, B, C, X(3613), X(18096)}}, {{A, B, C, X(3661), X(29647)}}, {{A, B, C, X(4206), X(19281)}}, {{A, B, C, X(4383), X(37633)}}, {{A, B, C, X(4680), X(30690)}}, {{A, B, C, X(4812), X(33157)}}, {{A, B, C, X(4921), X(19722)}}, {{A, B, C, X(5235), X(19701)}}, {{A, B, C, X(5249), X(28776)}}, {{A, B, C, X(5333), X(19732)}}, {{A, B, C, X(5712), X(24597)}}, {{A, B, C, X(5967), X(52757)}}, {{A, B, C, X(6994), X(37037)}}, {{A, B, C, X(7357), X(39712)}}, {{A, B, C, X(7377), X(24989)}}, {{A, B, C, X(8025), X(19742)}}, {{A, B, C, X(8044), X(58010)}}, {{A, B, C, X(11109), X(19645)}}, {{A, B, C, X(11319), X(59186)}}, {{A, B, C, X(11341), X(47511)}}, {{A, B, C, X(14377), X(39747)}}, {{A, B, C, X(15474), X(56044)}}, {{A, B, C, X(16552), X(16783)}}, {{A, B, C, X(16704), X(19717)}}, {{A, B, C, X(17379), X(37652)}}, {{A, B, C, X(17776), X(17863)}}, {{A, B, C, X(19723), X(42025)}}, {{A, B, C, X(19734), X(27644)}}, {{A, B, C, X(19738), X(41629)}}, {{A, B, C, X(21454), X(50115)}}, {{A, B, C, X(23292), X(26540)}}, {{A, B, C, X(25430), X(55990)}}, {{A, B, C, X(27064), X(36570)}}, {{A, B, C, X(30834), X(41806)}}, {{A, B, C, X(31229), X(41878)}}, {{A, B, C, X(37634), X(37651)}}, {{A, B, C, X(37674), X(37680)}}, {{A, B, C, X(39948), X(46638)}}, {{A, B, C, X(39952), X(40409)}}, {{A, B, C, X(40399), X(57662)}}, {{A, B, C, X(40420), X(40426)}}, {{A, B, C, X(40434), X(55988)}}, {{A, B, C, X(40446), X(56224)}}, {{A, B, C, X(45998), X(56960)}}, {{A, B, C, X(50698), X(52288)}}, {{A, B, C, X(52395), X(58020)}}, {{A, B, C, X(54378), X(54379)}}, {{A, B, C, X(56037), X(56353)}}, {{A, B, C, X(56219), X(57666)}}
X(60082) = barycentric product X(i)*X(j) for these (i, j): {513, 839}, {54336, 75}, {57979, 667}, {59112, 850}
X(60082) = barycentric quotient X(i)/X(j) for these (i, j): {2, 32782}, {4, 5142}, {6, 4261}, {37, 56541}, {321, 56564}, {667, 838}, {839, 668}, {54336, 1}, {57979, 6386}, {59112, 110}

X(60083) = X(2)X(5030)∩X(10)X(527)

Barycentrics    (a^2-2*b^2+b*c+c^2+a*(b+c))*(a^2+a*(b+c)+(b-c)*(b+2*c)) : :

X(60083) lies on the Kiepert hyperbola and on these lines: {2, 5030}, {4, 4658}, {6, 60094}, {7, 10708}, {10, 527}, {30, 56144}, {63, 60203}, {76, 17297}, {81, 54735}, {226, 1323}, {321, 3761}, {381, 43672}, {515, 54668}, {524, 60079}, {535, 40718}, {543, 47040}, {544, 1478}, {553, 60249}, {598, 46922}, {599, 60276}, {671, 17378}, {758, 59261}, {940, 54768}, {1330, 43533}, {1751, 45930}, {2051, 36731}, {3545, 45097}, {3830, 54517}, {3845, 54687}, {4049, 28846}, {4080, 4510}, {4648, 54831}, {4654, 38461}, {5290, 60321}, {5714, 42050}, {5905, 6539}, {7245, 43534}, {7607, 21554}, {8680, 60116}, {10159, 33838}, {11611, 49518}, {13478, 36728}, {15682, 54690}, {16080, 37448}, {16831, 30588}, {17532, 60227}, {17681, 43527}, {17732, 60229}, {24624, 51311}, {26003, 43530}, {28840, 60074}, {29069, 54933}, {29148, 35353}, {32594, 57719}, {34475, 46180}, {37427, 60158}, {37428, 54972}, {37631, 54928}, {41099, 54712}, {42028, 54549}, {42045, 54744}, {45924, 54900}

X(60083) = reflection of X(i) in X(j) for these {i,j}: {47039, 2}
X(60083) = isogonal conjugate of X(4262)
X(60083) = isotomic conjugate of X(17346)
X(60083) = trilinear pole of line {1638, 4379}
X(60083) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 4262}, {31, 17346}, {692, 27486}, {32739, 50450}
X(60083) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 17346}, {3, 4262}, {1086, 27486}, {40619, 50450}
X(60083) = X(i)-cross conjugate of X(j) for these {i, j}: {17392, 2}, {33866, 14377}
X(60083) = pole of line {17392, 60083} with respect to the Kiepert hyperbola
X(60083) = pole of line {4262, 17346} with respect to the Wallace hyperbola
X(60083) = pole of line {4860, 17301} with respect to the dual conic of Yff parabola
X(60083) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1121)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(5030)}}, {{A, B, C, X(7), X(514)}}, {{A, B, C, X(27), X(17528)}}, {{A, B, C, X(30), X(37448)}}, {{A, B, C, X(57), X(31164)}}, {{A, B, C, X(63), X(3927)}}, {{A, B, C, X(68), X(5733)}}, {{A, B, C, X(79), X(85)}}, {{A, B, C, X(80), X(27475)}}, {{A, B, C, X(86), X(17251)}}, {{A, B, C, X(189), X(55090)}}, {{A, B, C, X(277), X(5556)}}, {{A, B, C, X(279), X(30424)}}, {{A, B, C, X(335), X(996)}}, {{A, B, C, X(381), X(26003)}}, {{A, B, C, X(428), X(33838)}}, {{A, B, C, X(519), X(17316)}}, {{A, B, C, X(524), X(17378)}}, {{A, B, C, X(535), X(824)}}, {{A, B, C, X(536), X(29148)}}, {{A, B, C, X(544), X(918)}}, {{A, B, C, X(553), X(5905)}}, {{A, B, C, X(596), X(56044)}}, {{A, B, C, X(599), X(46922)}}, {{A, B, C, X(673), X(5561)}}, {{A, B, C, X(758), X(28840)}}, {{A, B, C, X(870), X(903)}}, {{A, B, C, X(1224), X(40023)}}, {{A, B, C, X(1434), X(43732)}}, {{A, B, C, X(1478), X(5236)}}, {{A, B, C, X(1577), X(8818)}}, {{A, B, C, X(1847), X(52374)}}, {{A, B, C, X(1855), X(17732)}}, {{A, B, C, X(3227), X(32935)}}, {{A, B, C, X(3241), X(49765)}}, {{A, B, C, X(3254), X(55984)}}, {{A, B, C, X(3296), X(10405)}}, {{A, B, C, X(3661), X(48822)}}, {{A, B, C, X(3679), X(16831)}}, {{A, B, C, X(3912), X(50282)}}, {{A, B, C, X(4102), X(4866)}}, {{A, B, C, X(4391), X(5074)}}, {{A, B, C, X(4643), X(18032)}}, {{A, B, C, X(4674), X(39981)}}, {{A, B, C, X(4785), X(46180)}}, {{A, B, C, X(4791), X(32631)}}, {{A, B, C, X(5064), X(17681)}}, {{A, B, C, X(5290), X(5307)}}, {{A, B, C, X(5551), X(56043)}}, {{A, B, C, X(5557), X(9311)}}, {{A, B, C, X(5558), X(9328)}}, {{A, B, C, X(5560), X(32008)}}, {{A, B, C, X(5665), X(44178)}}, {{A, B, C, X(6173), X(8545)}}, {{A, B, C, X(6650), X(20569)}}, {{A, B, C, X(7131), X(17098)}}, {{A, B, C, X(7319), X(56217)}}, {{A, B, C, X(7490), X(50736)}}, {{A, B, C, X(9309), X(48587)}}, {{A, B, C, X(11109), X(36731)}}, {{A, B, C, X(13476), X(47915)}}, {{A, B, C, X(14621), X(20568)}}, {{A, B, C, X(17346), X(17392)}}, {{A, B, C, X(17532), X(37389)}}, {{A, B, C, X(17555), X(36728)}}, {{A, B, C, X(18490), X(50834)}}, {{A, B, C, X(21554), X(52282)}}, {{A, B, C, X(24692), X(54974)}}, {{A, B, C, X(25430), X(55931)}}, {{A, B, C, X(29573), X(49495)}}, {{A, B, C, X(30712), X(44572)}}, {{A, B, C, X(33696), X(56060)}}, {{A, B, C, X(39980), X(41790)}}, {{A, B, C, X(41439), X(48074)}}, {{A, B, C, X(51100), X(55937)}}, {{A, B, C, X(54120), X(56145)}}, {{A, B, C, X(55926), X(56165)}}
X(60083) = barycentric quotient X(i)/X(j) for these (i, j): {2, 17346}, {6, 4262}, {514, 27486}, {693, 50450}

X(60084) = X(2)X(5105)∩X(4)X(1764)

Barycentrics    (a^2*(b+c)+b*(b+c)^2+a*(2*b^2+b*c+c^2))*(a^2*(b+c)+c*(b+c)^2+a*(b^2+b*c+2*c^2)) : :

X(60084) lies on the Kiepert hyperbola and on these lines: {2, 5105}, {4, 1764}, {10, 3666}, {30, 54694}, {57, 52357}, {75, 60264}, {76, 16739}, {83, 333}, {141, 226}, {274, 58025}, {321, 4357}, {381, 54721}, {536, 60267}, {540, 60078}, {757, 14534}, {940, 43531}, {966, 60107}, {1150, 60082}, {1211, 2051}, {1751, 5737}, {3661, 60230}, {3741, 5847}, {4080, 27184}, {4260, 53663}, {4778, 35353}, {5224, 34258}, {5232, 45100}, {5235, 57721}, {5743, 14554}, {5745, 60088}, {6539, 17147}, {8582, 53004}, {11679, 56328}, {13478, 16435}, {13576, 31330}, {17238, 60261}, {17811, 56216}, {18139, 30588}, {18141, 58012}, {18143, 40012}, {19732, 60075}, {19804, 60288}, {20883, 40149}, {20913, 60244}, {29593, 56197}, {29611, 60229}, {31008, 40024}, {31993, 56214}, {32777, 60135}, {32782, 60071}, {33172, 57722}, {36951, 43534}, {37655, 60077}, {41809, 60097}, {50056, 60079}

X(60084) = isogonal conjugate of X(4264)
X(60084) = trilinear pole of line {14288, 48131}
X(60084) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 4264}, {6, 57280}, {48, 37390}, {1333, 26115}, {2150, 10408}, {20986, 34262}
X(60084) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 4264}, {9, 57280}, {37, 26115}, {1249, 37390}, {56325, 10408}
X(60084) = pole of line {2517, 14349} with respect to the Steiner inellipse
X(60084) = pole of line {14349, 28478} with respect to the dual conic of Bevan circle
X(60084) = pole of line {19863, 31993} with respect to the dual conic of Yff parabola
X(60084) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(56944)}}, {{A, B, C, X(6), X(5105)}}, {{A, B, C, X(9), X(34404)}}, {{A, B, C, X(27), X(13728)}}, {{A, B, C, X(57), X(75)}}, {{A, B, C, X(80), X(56224)}}, {{A, B, C, X(81), X(596)}}, {{A, B, C, X(92), X(57725)}}, {{A, B, C, X(141), X(333)}}, {{A, B, C, X(189), X(59760)}}, {{A, B, C, X(257), X(30710)}}, {{A, B, C, X(306), X(10479)}}, {{A, B, C, X(310), X(39712)}}, {{A, B, C, X(312), X(44417)}}, {{A, B, C, X(334), X(56052)}}, {{A, B, C, X(335), X(37870)}}, {{A, B, C, X(517), X(56230)}}, {{A, B, C, X(522), X(2339)}}, {{A, B, C, X(536), X(4706)}}, {{A, B, C, X(824), X(5847)}}, {{A, B, C, X(940), X(5224)}}, {{A, B, C, X(966), X(18141)}}, {{A, B, C, X(996), X(2994)}}, {{A, B, C, X(1150), X(32782)}}, {{A, B, C, X(1211), X(6358)}}, {{A, B, C, X(1214), X(1764)}}, {{A, B, C, X(1221), X(27483)}}, {{A, B, C, X(1255), X(42285)}}, {{A, B, C, X(1412), X(45989)}}, {{A, B, C, X(2221), X(15315)}}, {{A, B, C, X(2985), X(39722)}}, {{A, B, C, X(3008), X(29679)}}, {{A, B, C, X(3661), X(3741)}}, {{A, B, C, X(3668), X(58010)}}, {{A, B, C, X(3676), X(57923)}}, {{A, B, C, X(3687), X(28659)}}, {{A, B, C, X(3840), X(29593)}}, {{A, B, C, X(3911), X(27184)}}, {{A, B, C, X(3912), X(31330)}}, {{A, B, C, X(4359), X(17147)}}, {{A, B, C, X(4417), X(37660)}}, {{A, B, C, X(4847), X(29611)}}, {{A, B, C, X(5232), X(35510)}}, {{A, B, C, X(5235), X(18139)}}, {{A, B, C, X(5278), X(33172)}}, {{A, B, C, X(5737), X(18134)}}, {{A, B, C, X(5936), X(58008)}}, {{A, B, C, X(8056), X(39708)}}, {{A, B, C, X(8580), X(26001)}}, {{A, B, C, X(10571), X(53995)}}, {{A, B, C, X(16435), X(17555)}}, {{A, B, C, X(17234), X(19732)}}, {{A, B, C, X(17238), X(37683)}}, {{A, B, C, X(17284), X(25006)}}, {{A, B, C, X(17292), X(29673)}}, {{A, B, C, X(18136), X(39798)}}, {{A, B, C, X(18140), X(56326)}}, {{A, B, C, X(18229), X(24987)}}, {{A, B, C, X(18359), X(56058)}}, {{A, B, C, X(20913), X(31008)}}, {{A, B, C, X(24603), X(26037)}}, {{A, B, C, X(25417), X(39697)}}, {{A, B, C, X(25430), X(31359)}}, {{A, B, C, X(29591), X(29655)}}, {{A, B, C, X(29596), X(33117)}}, {{A, B, C, X(29604), X(29667)}}, {{A, B, C, X(30832), X(37646)}}, {{A, B, C, X(30966), X(37676)}}, {{A, B, C, X(34860), X(39948)}}, {{A, B, C, X(36807), X(56228)}}, {{A, B, C, X(37633), X(41809)}}, {{A, B, C, X(39700), X(55090)}}, {{A, B, C, X(39711), X(39980)}}, {{A, B, C, X(39717), X(40033)}}, {{A, B, C, X(40023), X(44733)}}, {{A, B, C, X(50605), X(56810)}}, {{A, B, C, X(52782), X(56047)}}
X(60084) = barycentric product X(i)*X(j) for these (i, j): {312, 46331}, {34278, 57905}
X(60084) = barycentric quotient X(i)/X(j) for these (i, j): {1, 57280}, {4, 37390}, {6, 4264}, {10, 26115}, {12, 10408}, {2051, 34262}, {34278, 572}, {46331, 57}

X(60085) = X(2)X(1412)∩X(10)X(56)

Barycentrics    (a+b-c)*(a-b+c)*(a^2+a*(-b+c)+b*(b+c))*(a^2+a*(b-c)+c*(b+c)) : :

X(60085) lies on the Kiepert hyperbola and on these lines: {1, 54933}, {2, 1412}, {4, 37469}, {6, 14554}, {7, 4080}, {10, 56}, {30, 54696}, {57, 321}, {76, 1434}, {81, 60087}, {98, 59124}, {226, 1407}, {381, 54511}, {553, 4052}, {738, 1446}, {940, 2051}, {1150, 60097}, {1416, 11269}, {1435, 40149}, {1477, 9059}, {1751, 37646}, {3676, 4049}, {4032, 60091}, {4187, 43531}, {4369, 60074}, {5061, 40718}, {5219, 30588}, {5397, 6963}, {5435, 6539}, {5711, 12053}, {5712, 45098}, {6612, 8808}, {6904, 43533}, {6918, 57719}, {6919, 60077}, {6922, 54972}, {6926, 60158}, {6946, 60112}, {6964, 60157}, {6967, 60154}, {6983, 60164}, {6996, 54821}, {7146, 11611}, {7153, 60244}, {11112, 60079}, {13478, 37634}, {14829, 34258}, {16080, 24884}, {16878, 32918}, {17107, 60265}, {17234, 60251}, {17556, 60078}, {18141, 60254}, {18593, 60245}, {31231, 60203}, {34050, 36907}, {35466, 60075}, {37240, 60227}, {37374, 56144}, {37430, 54698}, {37558, 60321}, {37633, 60071}, {37642, 60107}, {41245, 60288}, {43043, 60135}, {57663, 60267}, {58027, 60264}

X(60085) = isogonal conjugate of X(4266)
X(60085) = isotomic conjugate of X(5233)
X(60085) = trilinear pole of line {7286, 30725}
X(60085) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 4266}, {6, 3877}, {9, 995}, {31, 5233}, {41, 4389}, {55, 4850}, {281, 23206}, {284, 4424}, {644, 9002}, {2175, 33934}, {2194, 26580}, {2320, 20973}, {2364, 17461}, {3694, 4247}, {3939, 48335}, {5546, 48350}
X(60085) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 5233}, {3, 4266}, {9, 3877}, {223, 4850}, {478, 995}, {1214, 26580}, {3160, 4389}, {40590, 4424}, {40593, 33934}, {40615, 44435}, {40617, 48335}, {40622, 50453}
X(60085) = X(i)-cross conjugate of X(j) for these {i, j}: {5434, 7}, {40401, 996}
X(60085) = pole of line {4266, 5233} with respect to the Wallace hyperbola
X(60085) = pole of line {999, 17720} with respect to the dual conic of Yff parabola
X(60085) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(956)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(37469)}}, {{A, B, C, X(6), X(5053)}}, {{A, B, C, X(7), X(3676)}}, {{A, B, C, X(27), X(474)}}, {{A, B, C, X(56), X(57)}}, {{A, B, C, X(81), X(8666)}}, {{A, B, C, X(85), X(2006)}}, {{A, B, C, X(86), X(37660)}}, {{A, B, C, X(88), X(14377)}}, {{A, B, C, X(89), X(4817)}}, {{A, B, C, X(189), X(56218)}}, {{A, B, C, X(278), X(10106)}}, {{A, B, C, X(279), X(4315)}}, {{A, B, C, X(312), X(34918)}}, {{A, B, C, X(333), X(3680)}}, {{A, B, C, X(469), X(4187)}}, {{A, B, C, X(553), X(5435)}}, {{A, B, C, X(664), X(7223)}}, {{A, B, C, X(673), X(4413)}}, {{A, B, C, X(940), X(14829)}}, {{A, B, C, X(996), X(40426)}}, {{A, B, C, X(1150), X(37633)}}, {{A, B, C, X(1214), X(37522)}}, {{A, B, C, X(1222), X(55952)}}, {{A, B, C, X(1389), X(56234)}}, {{A, B, C, X(1476), X(34051)}}, {{A, B, C, X(2319), X(38825)}}, {{A, B, C, X(2985), X(39703)}}, {{A, B, C, X(3254), X(4675)}}, {{A, B, C, X(3306), X(7284)}}, {{A, B, C, X(3476), X(17079)}}, {{A, B, C, X(3912), X(11269)}}, {{A, B, C, X(4032), X(4369)}}, {{A, B, C, X(4417), X(37634)}}, {{A, B, C, X(4654), X(31231)}}, {{A, B, C, X(5061), X(7146)}}, {{A, B, C, X(5556), X(44848)}}, {{A, B, C, X(5559), X(55956)}}, {{A, B, C, X(6904), X(7490)}}, {{A, B, C, X(6918), X(37279)}}, {{A, B, C, X(7224), X(32023)}}, {{A, B, C, X(7377), X(26020)}}, {{A, B, C, X(8044), X(57877)}}, {{A, B, C, X(10570), X(36795)}}, {{A, B, C, X(11347), X(37278)}}, {{A, B, C, X(15314), X(58001)}}, {{A, B, C, X(16577), X(34016)}}, {{A, B, C, X(17234), X(35466)}}, {{A, B, C, X(17743), X(36805)}}, {{A, B, C, X(18134), X(37646)}}, {{A, B, C, X(18141), X(37642)}}, {{A, B, C, X(18785), X(21448)}}, {{A, B, C, X(21446), X(43762)}}, {{A, B, C, X(24297), X(40434)}}, {{A, B, C, X(24914), X(44733)}}, {{A, B, C, X(26745), X(52393)}}, {{A, B, C, X(30101), X(39695)}}, {{A, B, C, X(32008), X(43759)}}, {{A, B, C, X(32016), X(55970)}}, {{A, B, C, X(32017), X(56046)}}, {{A, B, C, X(34523), X(34527)}}, {{A, B, C, X(37092), X(37245)}}, {{A, B, C, X(37240), X(37389)}}, {{A, B, C, X(37374), X(37448)}}, {{A, B, C, X(37432), X(37445)}}, {{A, B, C, X(39270), X(52212)}}, {{A, B, C, X(39698), X(56145)}}, {{A, B, C, X(40027), X(40415)}}, {{A, B, C, X(40218), X(56642)}}, {{A, B, C, X(42304), X(52374)}}, {{A, B, C, X(42318), X(46916)}}, {{A, B, C, X(56208), X(56255)}}, {{A, B, C, X(56358), X(57785)}}
X(60085) = barycentric product X(i)*X(j) for these (i, j): {7, 996}, {56, 58027}, {226, 55942}, {3676, 9059}, {40401, 85}, {40426, 5219}, {59124, 850}
X(60085) = barycentric quotient X(i)/X(j) for these (i, j): {1, 3877}, {2, 5233}, {6, 4266}, {7, 4389}, {56, 995}, {57, 4850}, {65, 4424}, {85, 33934}, {226, 26580}, {603, 23206}, {996, 8}, {1405, 20973}, {1434, 16712}, {2099, 17461}, {3669, 48335}, {3676, 44435}, {4017, 48350}, {7178, 50453}, {9059, 3699}, {30725, 23888}, {32686, 5548}, {40401, 9}, {40426, 30608}, {43052, 21130}, {43924, 9002}, {55942, 333}, {58027, 3596}, {59124, 110}

X(60086) = X(2)X(12)∩X(7)X(76)

Barycentrics    (a+b-c)*(a-b+c)*(b+c)*(a^2+a*c+b*(b+c))*(a^2+a*b+c*(b+c)) : :

X(60086) lies on the Kiepert hyperbola and on these lines: {1, 2051}, {2, 12}, {3, 40455}, {4, 608}, {7, 76}, {8, 181}, {10, 1400}, {30, 54697}, {35, 54699}, {37, 60321}, {42, 37865}, {57, 52357}, {65, 321}, {98, 8687}, {171, 15971}, {226, 1042}, {377, 60206}, {495, 13731}, {497, 45100}, {671, 6648}, {859, 40453}, {942, 54739}, {964, 1460}, {1056, 45098}, {1058, 54689}, {1118, 2052}, {1193, 4551}, {1254, 4032}, {1284, 60230}, {1402, 26115}, {1426, 1867}, {1441, 60197}, {1478, 13478}, {1479, 54586}, {1751, 5230}, {1788, 19822}, {1834, 13576}, {1916, 30669}, {2171, 43677}, {2197, 3597}, {2359, 54972}, {2363, 24624}, {2475, 54119}, {2550, 43533}, {2594, 3476}, {3144, 60246}, {3295, 54728}, {3339, 60276}, {3485, 60071}, {3585, 60172}, {3649, 4080}, {3671, 4052}, {3812, 24993}, {3831, 4298}, {3931, 54933}, {3947, 56226}, {4334, 5290}, {4552, 11611}, {4581, 60074}, {4848, 60267}, {5061, 5080}, {5229, 60167}, {5252, 60097}, {5587, 57719}, {5818, 60112}, {6539, 40663}, {7184, 60320}, {7248, 10404}, {7276, 15556}, {7354, 50702}, {8707, 60251}, {9553, 10480}, {9578, 31339}, {10401, 20245}, {10944, 20040}, {15888, 21321}, {18178, 20028}, {18990, 19513}, {19925, 43672}, {30941, 40827}, {37191, 60156}, {37225, 60188}, {40012, 56155}, {40024, 56928}, {43534, 45208}, {52245, 56901}, {52367, 54686}, {56191, 56214}

X(60086) = isogonal conjugate of X(4267)
X(60086) = trilinear pole of line {7180, 523}
X(60086) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 4267}, {6, 17185}, {9, 40153}, {21, 1193}, {27, 22074}, {29, 22345}, {41, 16705}, {55, 54308}, {56, 46877}, {57, 46889}, {58, 960}, {60, 2292}, {81, 2269}, {86, 20967}, {110, 17420}, {163, 3910}, {261, 3725}, {270, 22076}, {283, 1829}, {284, 3666}, {333, 2300}, {593, 21033}, {643, 6371}, {662, 52326}, {757, 40966}, {849, 3704}, {1172, 22097}, {1178, 18235}, {1211, 2150}, {1333, 3687}, {1412, 3965}, {1437, 46878}, {1444, 40976}, {1682, 2363}, {1812, 2354}, {1848, 2193}, {2092, 2185}, {2175, 16739}, {2194, 4357}, {2328, 24471}, {3737, 53280}, {3882, 7252}, {4636, 50330}, {5546, 48131}, {7257, 57157}, {20911, 57657}, {46879, 53083}
X(60086) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 46877}, {3, 4267}, {9, 17185}, {10, 960}, {37, 3687}, {115, 3910}, {223, 54308}, {244, 17420}, {478, 40153}, {960, 1682}, {1084, 52326}, {1214, 4357}, {3160, 16705}, {4075, 3704}, {5452, 46889}, {6741, 57158}, {36908, 24471}, {40586, 2269}, {40590, 3666}, {40593, 16739}, {40599, 3965}, {40600, 20967}, {40607, 40966}, {40611, 1193}, {40622, 3004}, {47345, 1848}, {55060, 6371}, {56325, 1211}, {59608, 3674}
X(60086) = X(i)-Ceva conjugate of X(j) for these {i, j}: {36098, 4581}
X(60086) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {43070, 5484}
X(60086) = X(i)-cross conjugate of X(j) for these {i, j}: {37, 30710}, {65, 961}, {513, 4551}, {2533, 4566}, {57185, 4552}
X(60086) = pole of line {1682, 4267} with respect to the Stammler hyperbola
X(60086) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2975)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(54300)}}, {{A, B, C, X(7), X(56)}}, {{A, B, C, X(8), X(37)}}, {{A, B, C, X(12), X(8736)}}, {{A, B, C, X(42), X(56164)}}, {{A, B, C, X(79), X(4674)}}, {{A, B, C, X(80), X(5260)}}, {{A, B, C, X(85), X(18097)}}, {{A, B, C, X(189), X(56219)}}, {{A, B, C, X(225), X(388)}}, {{A, B, C, X(281), X(27410)}}, {{A, B, C, X(377), X(37384)}}, {{A, B, C, X(406), X(37191)}}, {{A, B, C, X(502), X(15065)}}, {{A, B, C, X(513), X(1193)}}, {{A, B, C, X(523), X(529)}}, {{A, B, C, X(525), X(29207)}}, {{A, B, C, X(951), X(57417)}}, {{A, B, C, X(961), X(31643)}}, {{A, B, C, X(989), X(18098)}}, {{A, B, C, X(996), X(42471)}}, {{A, B, C, X(1000), X(56221)}}, {{A, B, C, X(1214), X(5711)}}, {{A, B, C, X(1219), X(42027)}}, {{A, B, C, X(1220), X(14624)}}, {{A, B, C, X(1222), X(41683)}}, {{A, B, C, X(1245), X(9309)}}, {{A, B, C, X(1254), X(7211)}}, {{A, B, C, X(1284), X(45208)}}, {{A, B, C, X(1329), X(8818)}}, {{A, B, C, X(1334), X(59269)}}, {{A, B, C, X(1478), X(56827)}}, {{A, B, C, X(1791), X(2298)}}, {{A, B, C, X(1826), X(2551)}}, {{A, B, C, X(1869), X(2550)}}, {{A, B, C, X(2171), X(43074)}}, {{A, B, C, X(2294), X(37225)}}, {{A, B, C, X(2363), X(4581)}}, {{A, B, C, X(2475), X(3144)}}, {{A, B, C, X(2533), X(4645)}}, {{A, B, C, X(3296), X(53114)}}, {{A, B, C, X(3436), X(21074)}}, {{A, B, C, X(3577), X(56259)}}, {{A, B, C, X(3600), X(3668)}}, {{A, B, C, X(3649), X(5298)}}, {{A, B, C, X(3671), X(4848)}}, {{A, B, C, X(3695), X(37715)}}, {{A, B, C, X(3753), X(12709)}}, {{A, B, C, X(4032), X(6645)}}, {{A, B, C, X(4036), X(5080)}}, {{A, B, C, X(4267), X(52087)}}, {{A, B, C, X(4307), X(56382)}}, {{A, B, C, X(4391), X(46878)}}, {{A, B, C, X(4866), X(56255)}}, {{A, B, C, X(4999), X(11604)}}, {{A, B, C, X(5061), X(52567)}}, {{A, B, C, X(5230), X(57808)}}, {{A, B, C, X(5434), X(52382)}}, {{A, B, C, X(5484), X(34920)}}, {{A, B, C, X(5555), X(7288)}}, {{A, B, C, X(5556), X(15320)}}, {{A, B, C, X(5558), X(11194)}}, {{A, B, C, X(5560), X(56132)}}, {{A, B, C, X(5561), X(56135)}}, {{A, B, C, X(6757), X(20060)}}, {{A, B, C, X(7178), X(43053)}}, {{A, B, C, X(7319), X(41506)}}, {{A, B, C, X(10408), X(52357)}}, {{A, B, C, X(11109), X(51558)}}, {{A, B, C, X(11681), X(45095)}}, {{A, B, C, X(18082), X(58019)}}, {{A, B, C, X(19874), X(31339)}}, {{A, B, C, X(25430), X(45032)}}, {{A, B, C, X(25466), X(41501)}}, {{A, B, C, X(27809), X(54120)}}, {{A, B, C, X(29471), X(39735)}}, {{A, B, C, X(30478), X(43740)}}, {{A, B, C, X(30479), X(37868)}}, {{A, B, C, X(31356), X(41446)}}, {{A, B, C, X(31359), X(55035)}}, {{A, B, C, X(40504), X(45988)}}, {{A, B, C, X(43731), X(56215)}}, {{A, B, C, X(46187), X(52555)}}, {{A, B, C, X(52560), X(57283)}}
X(60086) = barycentric product X(i)*X(j) for these (i, j): {12, 14534}, {56, 60264}, {181, 40827}, {321, 961}, {523, 6648}, {850, 8687}, {1169, 34388}, {1220, 226}, {1240, 1400}, {1441, 2298}, {1577, 36098}, {1791, 40149}, {2359, 57809}, {2363, 6358}, {4552, 4581}, {4554, 57162}, {4605, 57161}, {7178, 8707}, {14624, 7}, {30710, 65}, {31643, 37}, {36147, 4077}, {57853, 8736}
X(60086) = barycentric quotient X(i)/X(j) for these (i, j): {1, 17185}, {6, 4267}, {7, 16705}, {9, 46877}, {10, 3687}, {12, 1211}, {37, 960}, {42, 2269}, {55, 46889}, {56, 40153}, {57, 54308}, {65, 3666}, {73, 22097}, {85, 16739}, {181, 2092}, {210, 3965}, {213, 20967}, {225, 1848}, {226, 4357}, {228, 22074}, {512, 52326}, {523, 3910}, {594, 3704}, {661, 17420}, {756, 21033}, {961, 81}, {1169, 60}, {1220, 333}, {1240, 28660}, {1400, 1193}, {1402, 2300}, {1409, 22345}, {1427, 24471}, {1441, 20911}, {1500, 40966}, {1791, 1812}, {1826, 46878}, {1880, 1829}, {2092, 1682}, {2171, 2292}, {2197, 22076}, {2295, 18235}, {2298, 21}, {2333, 40976}, {2359, 283}, {2363, 2185}, {3668, 3674}, {3700, 57158}, {4017, 48131}, {4032, 59509}, {4077, 4509}, {4551, 3882}, {4552, 53332}, {4559, 53280}, {4581, 4560}, {6354, 41003}, {6358, 18697}, {6648, 99}, {7178, 3004}, {7180, 6371}, {7211, 27697}, {8687, 110}, {8707, 645}, {8736, 429}, {14534, 261}, {14624, 8}, {15232, 19608}, {17757, 51407}, {30710, 314}, {31643, 274}, {32736, 5546}, {34388, 1228}, {36098, 662}, {36147, 643}, {40149, 54314}, {40827, 18021}, {51421, 51414}, {52139, 46879}, {52928, 4565}, {57162, 650}, {57185, 50330}, {57652, 2354}, {60245, 59191}, {60264, 3596}

X(60087) = X(2)X(4271)∩X(10)X(3877)

Barycentrics    (a*b*(a+b)+(a-b)^2*c-c^3)*(-b^3+b*c^2+a*c*(-2*b+c)+a^2*(b+c)) : :

X(60087) lies on the Kiepert hyperbola and on these lines: {2, 4271}, {10, 3877}, {76, 5741}, {81, 60085}, {226, 4850}, {321, 5233}, {381, 54698}, {404, 43531}, {908, 4052}, {1751, 37680}, {2051, 37651}, {2594, 3476}, {3210, 4080}, {3452, 60267}, {3936, 40012}, {3969, 60264}, {4190, 60077}, {4383, 24624}, {4398, 31053}, {4417, 40013}, {4642, 18393}, {5187, 43533}, {5313, 60089}, {5397, 6911}, {5712, 60169}, {5718, 57722}, {6882, 60112}, {6890, 60157}, {6891, 60164}, {6915, 54972}, {6943, 57719}, {6944, 60154}, {6953, 60158}, {13478, 32911}, {14534, 40214}, {17579, 60078}, {18134, 39994}, {18600, 57826}, {27162, 58012}, {27186, 30588}, {28452, 54679}, {29849, 43534}, {37356, 57720}, {37375, 60079}, {37662, 60071}, {37679, 57721}, {37687, 60075}

X(60087) = isogonal conjugate of X(4268)
X(60087) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 4268}, {6, 8666}
X(60087) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 4268}, {9, 8666}
X(60087) = X(i)-cross conjugate of X(j) for these {i, j}: {3987, 75}, {22791, 7}, {37663, 2}
X(60087) = pole of line {37663, 60087} with respect to the Kiepert hyperbola
X(60087) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(4271)}}, {{A, B, C, X(27), X(4193)}}, {{A, B, C, X(57), X(5697)}}, {{A, B, C, X(75), X(56058)}}, {{A, B, C, X(81), X(312)}}, {{A, B, C, X(85), X(39962)}}, {{A, B, C, X(88), X(92)}}, {{A, B, C, X(189), X(908)}}, {{A, B, C, X(239), X(29849)}}, {{A, B, C, X(278), X(30384)}}, {{A, B, C, X(404), X(469)}}, {{A, B, C, X(514), X(26745)}}, {{A, B, C, X(561), X(32011)}}, {{A, B, C, X(661), X(39966)}}, {{A, B, C, X(673), X(11680)}}, {{A, B, C, X(693), X(39741)}}, {{A, B, C, X(857), X(35994)}}, {{A, B, C, X(1150), X(37662)}}, {{A, B, C, X(1246), X(57830)}}, {{A, B, C, X(1255), X(1476)}}, {{A, B, C, X(1826), X(39956)}}, {{A, B, C, X(1848), X(3476)}}, {{A, B, C, X(2006), X(7741)}}, {{A, B, C, X(2339), X(56100)}}, {{A, B, C, X(2594), X(3969)}}, {{A, B, C, X(3210), X(4358)}}, {{A, B, C, X(3452), X(18600)}}, {{A, B, C, X(3596), X(20028)}}, {{A, B, C, X(3936), X(4383)}}, {{A, B, C, X(4384), X(29664)}}, {{A, B, C, X(4398), X(39707)}}, {{A, B, C, X(4417), X(32911)}}, {{A, B, C, X(4998), X(7357)}}, {{A, B, C, X(5187), X(7490)}}, {{A, B, C, X(5219), X(27186)}}, {{A, B, C, X(5278), X(5718)}}, {{A, B, C, X(5313), X(33077)}}, {{A, B, C, X(5560), X(31053)}}, {{A, B, C, X(5743), X(19684)}}, {{A, B, C, X(5748), X(30379)}}, {{A, B, C, X(6557), X(41012)}}, {{A, B, C, X(6943), X(37279)}}, {{A, B, C, X(7018), X(56166)}}, {{A, B, C, X(7284), X(25430)}}, {{A, B, C, X(7377), X(35973)}}, {{A, B, C, X(8049), X(32023)}}, {{A, B, C, X(8056), X(30690)}}, {{A, B, C, X(14621), X(25960)}}, {{A, B, C, X(14829), X(37651)}}, {{A, B, C, X(15474), X(50442)}}, {{A, B, C, X(17234), X(37687)}}, {{A, B, C, X(17381), X(31247)}}, {{A, B, C, X(18134), X(37680)}}, {{A, B, C, X(18139), X(37679)}}, {{A, B, C, X(18743), X(50106)}}, {{A, B, C, X(27789), X(55090)}}, {{A, B, C, X(30566), X(52206)}}, {{A, B, C, X(32017), X(39700)}}, {{A, B, C, X(34523), X(39698)}}, {{A, B, C, X(34991), X(56230)}}, {{A, B, C, X(37356), X(57531)}}, {{A, B, C, X(40418), X(57948)}}, {{A, B, C, X(42467), X(56352)}}, {{A, B, C, X(55936), X(56231)}}, {{A, B, C, X(56086), X(56089)}}
X(60087) = barycentric quotient X(i)/X(j) for these (i, j): {1, 8666}, {6, 4268}

X(60088) = X(2)X(48)∩X(4)X(31)

Barycentrics    (b+c)*(a^4+a^3*b+a*b^3+b^4-(a^2+a*b+b^2)*c^2)*(a^4-a^2*b^2+a^3*c-b^2*c^2+c^4+a*(-(b^2*c)+c^3)) : :

X(60088) lies on the Kiepert hyperbola and on these lines: {2, 48}, {4, 31}, {10, 228}, {19, 2052}, {63, 76}, {71, 321}, {83, 18083}, {98, 15440}, {226, 1409}, {275, 2148}, {459, 2155}, {464, 60206}, {515, 57719}, {612, 60108}, {671, 36060}, {758, 56282}, {1011, 60110}, {1400, 40149}, {1446, 52373}, {1820, 5392}, {1821, 60199}, {2051, 40940}, {2156, 43678}, {2157, 46105}, {2159, 16080}, {2215, 5307}, {2578, 2592}, {2579, 2593}, {3136, 40718}, {3142, 56227}, {3151, 54119}, {3597, 54418}, {3822, 37056}, {4362, 26893}, {5271, 34258}, {5745, 60084}, {5905, 60257}, {8680, 43675}, {9288, 37892}, {13726, 54331}, {14547, 45964}, {17758, 40687}, {17784, 43533}, {22001, 43683}, {22321, 43534}, {25453, 60109}, {26872, 60254}, {28274, 54739}, {29013, 60074}, {29043, 56144}, {33133, 60071}, {37759, 60261}, {56803, 60264}

X(60088) = isogonal conjugate of X(4269)
X(60088) = trilinear pole of line {810, 523}
X(60088) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 4269}, {2, 4215}, {81, 26893}, {284, 37591}
X(60088) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 4269}, {32664, 4215}, {40586, 26893}, {40590, 37591}
X(60088) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(19), X(31)}}, {{A, B, C, X(27), X(65)}}, {{A, B, C, X(37), X(19810)}}, {{A, B, C, X(57), X(56195)}}, {{A, B, C, X(72), X(40573)}}, {{A, B, C, X(92), X(15232)}}, {{A, B, C, X(158), X(40161)}}, {{A, B, C, X(225), X(306)}}, {{A, B, C, X(278), X(38955)}}, {{A, B, C, X(333), X(18097)}}, {{A, B, C, X(464), X(8896)}}, {{A, B, C, X(469), X(37056)}}, {{A, B, C, X(512), X(46179)}}, {{A, B, C, X(758), X(29013)}}, {{A, B, C, X(1193), X(56803)}}, {{A, B, C, X(1214), X(3072)}}, {{A, B, C, X(1427), X(34234)}}, {{A, B, C, X(1441), X(7224)}}, {{A, B, C, X(1826), X(26063)}}, {{A, B, C, X(1903), X(40444)}}, {{A, B, C, X(2982), X(56254)}}, {{A, B, C, X(3136), X(31909)}}, {{A, B, C, X(3144), X(3151)}}, {{A, B, C, X(3668), X(13577)}}, {{A, B, C, X(3694), X(8748)}}, {{A, B, C, X(4362), X(41233)}}, {{A, B, C, X(5271), X(5307)}}, {{A, B, C, X(7363), X(18083)}}, {{A, B, C, X(8680), X(15313)}}, {{A, B, C, X(9028), X(56728)}}, {{A, B, C, X(15320), X(25523)}}, {{A, B, C, X(16583), X(18084)}}, {{A, B, C, X(17751), X(40940)}}, {{A, B, C, X(17902), X(21072)}}, {{A, B, C, X(21935), X(52369)}}, {{A, B, C, X(22321), X(27943)}}, {{A, B, C, X(26222), X(56196)}}, {{A, B, C, X(37203), X(43703)}}, {{A, B, C, X(37652), X(38262)}}, {{A, B, C, X(37887), X(56133)}}, {{A, B, C, X(39944), X(43739)}}, {{A, B, C, X(42467), X(55416)}}
X(60088) = barycentric product X(i)*X(j) for these (i, j): {15440, 850}
X(60088) = barycentric quotient X(i)/X(j) for these (i, j): {6, 4269}, {31, 4215}, {42, 26893}, {65, 37591}, {15440, 110}

X(60089) = X(2)X(36)∩X(79)X(94)

Barycentrics    (b+c)*(a^3+a^2*b+a*b^2+b^3+a*b*c-(a+b)*c^2)*(a^3+a^2*c-b^2*c+c^3+a*(-b^2+b*c+c^2)) : :

X(60089) lies on the Kiepert hyperbola and on these lines: {1, 60071}, {2, 36}, {4, 29046}, {10, 2245}, {30, 54699}, {37, 60116}, {58, 3585}, {65, 60091}, {76, 320}, {79, 94}, {98, 29044}, {226, 1464}, {321, 758}, {513, 60074}, {515, 2051}, {527, 60276}, {572, 5397}, {752, 60079}, {1835, 40149}, {2550, 54786}, {2801, 54739}, {2901, 43677}, {3583, 54648}, {3597, 50037}, {3724, 45095}, {3743, 60321}, {4444, 29148}, {4868, 54933}, {4886, 34258}, {5229, 55962}, {5313, 60087}, {5587, 60112}, {6539, 54288}, {9655, 15654}, {10791, 60109}, {10895, 19762}, {12115, 45098}, {14554, 45885}, {18406, 54528}, {18492, 57720}, {18513, 54735}, {19925, 57719}, {28845, 56144}, {33682, 60078}, {37865, 59304}, {40013, 49999}

X(60089) = isogonal conjugate of X(4276)
X(60089) = trilinear pole of line {21828, 523}
X(60089) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 4276}, {58, 5692}, {163, 23876}, {1333, 33077}
X(60089) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 4276}, {10, 5692}, {37, 33077}, {115, 23876}
X(60089) = X(i)-cross conjugate of X(j) for these {i, j}: {37715, 10}
X(60089) = pole of line {37715, 60089} with respect to the Kiepert hyperbola
X(60089) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(993)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(38955)}}, {{A, B, C, X(8), X(56221)}}, {{A, B, C, X(12), X(3822)}}, {{A, B, C, X(36), X(58)}}, {{A, B, C, X(37), X(80)}}, {{A, B, C, X(72), X(40442)}}, {{A, B, C, X(87), X(4674)}}, {{A, B, C, X(225), X(1478)}}, {{A, B, C, X(261), X(11604)}}, {{A, B, C, X(502), X(5080)}}, {{A, B, C, X(523), X(535)}}, {{A, B, C, X(525), X(29046)}}, {{A, B, C, X(572), X(5396)}}, {{A, B, C, X(661), X(40109)}}, {{A, B, C, X(740), X(29148)}}, {{A, B, C, X(994), X(1400)}}, {{A, B, C, X(996), X(42027)}}, {{A, B, C, X(1426), X(4911)}}, {{A, B, C, X(1441), X(5620)}}, {{A, B, C, X(1826), X(15065)}}, {{A, B, C, X(2321), X(30513)}}, {{A, B, C, X(3293), X(49999)}}, {{A, B, C, X(3649), X(54288)}}, {{A, B, C, X(3668), X(4293)}}, {{A, B, C, X(3714), X(3743)}}, {{A, B, C, X(3814), X(21019)}}, {{A, B, C, X(5556), X(56173)}}, {{A, B, C, X(5557), X(31503)}}, {{A, B, C, X(5560), X(41506)}}, {{A, B, C, X(5665), X(56195)}}, {{A, B, C, X(7951), X(8818)}}, {{A, B, C, X(8680), X(29066)}}, {{A, B, C, X(16606), X(55926)}}, {{A, B, C, X(17097), X(56254)}}, {{A, B, C, X(17501), X(56132)}}, {{A, B, C, X(18097), X(24630)}}, {{A, B, C, X(21894), X(45885)}}, {{A, B, C, X(35576), X(43732)}}, {{A, B, C, X(42285), X(55035)}}, {{A, B, C, X(48826), X(56281)}}, {{A, B, C, X(55931), X(56255)}}
X(60089) = barycentric product X(i)*X(j) for these (i, j): {29044, 850}
X(60089) = barycentric quotient X(i)/X(j) for these (i, j): {6, 4276}, {10, 33077}, {37, 5692}, {523, 23876}, {29044, 110}

X(60090) = X(10)X(39)∩X(58)X(83)

Barycentrics    (a*b^2*(b+c)+b^2*c*(b+c)+a^2*(b^2+c^2))*(a*c^2*(b+c)+b*c^2*(b+c)+a^2*(b^2+c^2)) : :

X(60090) lies on the Kiepert hyperbola and on these lines: {1, 60230}, {2, 5145}, {5, 60320}, {6, 33688}, {8, 56197}, {10, 39}, {30, 54701}, {38, 321}, {58, 83}, {76, 16887}, {87, 26963}, {98, 572}, {194, 10479}, {226, 1401}, {262, 48888}, {310, 40016}, {511, 2051}, {513, 24688}, {538, 60276}, {594, 20671}, {993, 19263}, {1009, 28386}, {3097, 6539}, {3771, 60188}, {3831, 60244}, {3923, 56556}, {3934, 17758}, {4080, 30942}, {4201, 60149}, {4660, 13576}, {4871, 30588}, {12263, 40515}, {13478, 19540}, {13632, 54834}, {14058, 36907}, {17398, 21257}, {18152, 31630}, {18982, 52357}, {21238, 39798}, {23660, 24512}, {30966, 40024}, {31276, 60236}, {32010, 34020}, {32022, 56737}, {43534, 52656}, {56969, 60079}, {58656, 59666}

X(60090) = isogonal conjugate of X(4279)
X(60090) = isotomic conjugate of X(37678)
X(60090) = trilinear pole of line {21123, 523}
X(60090) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 4279}, {31, 37678}, {5384, 38995}
X(60090) = pole of line {4279, 33688} with respect to the Wallace hyperbola
X(60090) = pole of line {20913, 21264} with respect to the dual conic of Yff parabola
X(60090) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1107)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(5145)}}, {{A, B, C, X(8), X(3840)}}, {{A, B, C, X(27), X(37148)}}, {{A, B, C, X(37), X(40010)}}, {{A, B, C, X(38), X(39)}}, {{A, B, C, X(42), X(27375)}}, {{A, B, C, X(43), X(3831)}}, {{A, B, C, X(75), X(87)}}, {{A, B, C, X(79), X(40418)}}, {{A, B, C, X(141), X(37686)}}, {{A, B, C, X(257), X(32020)}}, {{A, B, C, X(261), X(43749)}}, {{A, B, C, X(313), X(3613)}}, {{A, B, C, X(444), X(52256)}}, {{A, B, C, X(511), X(572)}}, {{A, B, C, X(514), X(730)}}, {{A, B, C, X(519), X(30942)}}, {{A, B, C, X(751), X(56128)}}, {{A, B, C, X(752), X(30519)}}, {{A, B, C, X(871), X(984)}}, {{A, B, C, X(996), X(56164)}}, {{A, B, C, X(997), X(26013)}}, {{A, B, C, X(1002), X(39697)}}, {{A, B, C, X(1089), X(21685)}}, {{A, B, C, X(1125), X(31330)}}, {{A, B, C, X(1224), X(56052)}}, {{A, B, C, X(1573), X(30571)}}, {{A, B, C, X(1861), X(4660)}}, {{A, B, C, X(1920), X(39933)}}, {{A, B, C, X(2239), X(50454)}}, {{A, B, C, X(2296), X(43972)}}, {{A, B, C, X(3626), X(30957)}}, {{A, B, C, X(3634), X(26037)}}, {{A, B, C, X(3679), X(4871)}}, {{A, B, C, X(3771), X(6734)}}, {{A, B, C, X(3864), X(24512)}}, {{A, B, C, X(3865), X(28386)}}, {{A, B, C, X(3923), X(52652)}}, {{A, B, C, X(3934), X(18152)}}, {{A, B, C, X(4196), X(56737)}}, {{A, B, C, X(4201), X(4212)}}, {{A, B, C, X(4492), X(58027)}}, {{A, B, C, X(4518), X(30982)}}, {{A, B, C, X(4817), X(39713)}}, {{A, B, C, X(6383), X(56332)}}, {{A, B, C, X(6386), X(24688)}}, {{A, B, C, X(10453), X(50608)}}, {{A, B, C, X(10479), X(43223)}}, {{A, B, C, X(10916), X(33171)}}, {{A, B, C, X(11109), X(37365)}}, {{A, B, C, X(12782), X(20888)}}, {{A, B, C, X(14621), X(33682)}}, {{A, B, C, X(16606), X(18148)}}, {{A, B, C, X(17038), X(58019)}}, {{A, B, C, X(17042), X(39966)}}, {{A, B, C, X(17555), X(19540)}}, {{A, B, C, X(18793), X(57666)}}, {{A, B, C, X(24880), X(27701)}}, {{A, B, C, X(26015), X(50311)}}, {{A, B, C, X(29066), X(46180)}}, {{A, B, C, X(29637), X(29673)}}, {{A, B, C, X(31359), X(40027)}}, {{A, B, C, X(36602), X(39711)}}, {{A, B, C, X(36862), X(39949)}}, {{A, B, C, X(39708), X(56212)}}, {{A, B, C, X(39974), X(41683)}}, {{A, B, C, X(39982), X(56125)}}, {{A, B, C, X(40085), X(45108)}}, {{A, B, C, X(40738), X(57944)}}, {{A, B, C, X(45782), X(45785)}}, {{A, B, C, X(46952), X(57825)}}, {{A, B, C, X(52547), X(56333)}}

X(60091) = X(2)X(2006)∩X(4)X(80)

Barycentrics    b*(a+b-c)*c*(a-b+c)*(b+c)*(a^2-a*b+b^2-c^2)*(a^2-b^2-a*c+c^2) : :

X(60091) lies on the Kiepert hyperbola and on these lines: {1, 5397}, {2, 2006}, {4, 80}, {5, 51879}, {7, 60258}, {10, 15065}, {12, 60116}, {65, 60089}, {91, 96}, {92, 275}, {98, 2222}, {201, 18395}, {226, 4605}, {655, 16548}, {671, 35174}, {1029, 41910}, {1087, 37732}, {1109, 4551}, {1411, 30147}, {1441, 30588}, {1751, 2161}, {1807, 54972}, {2003, 24149}, {2051, 52212}, {2166, 35320}, {2171, 60071}, {2341, 40395}, {2594, 6757}, {2595, 17104}, {2599, 7741}, {2606, 2621}, {2915, 43680}, {3911, 24209}, {4032, 60085}, {4559, 56415}, {4957, 52659}, {6187, 60080}, {6354, 43682}, {6648, 14534}, {7578, 21741}, {10015, 60074}, {13576, 34857}, {13582, 17484}, {14204, 23067}, {14584, 60078}, {16609, 60135}, {17906, 18679}, {20566, 34258}, {22342, 54969}, {26942, 43683}, {32675, 60134}, {36804, 60251}, {36815, 60081}, {40017, 46405}, {41563, 55944}, {43533, 52409}, {45926, 56327}, {51975, 60079}, {52371, 56144}, {52392, 60156}, {53391, 57721}, {56417, 60154}, {57807, 60242}

X(60091) = isogonal conjugate of X(4282)
X(60091) = trilinear pole of line {12, 2599}
X(60091) = perspector of circumconic {{A, B, C, X(35174), X(57645)}}
X(60091) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 4282}, {21, 7113}, {36, 284}, {48, 17515}, {50, 3615}, {58, 2323}, {60, 2245}, {81, 2361}, {86, 52426}, {110, 654}, {163, 3738}, {215, 24624}, {283, 52413}, {320, 57657}, {333, 52434}, {643, 21758}, {662, 8648}, {758, 2150}, {759, 34544}, {1172, 52407}, {1333, 4511}, {1412, 58328}, {1464, 7054}, {1576, 3904}, {1790, 52427}, {1870, 2193}, {1983, 3737}, {2185, 3724}, {2194, 3218}, {2206, 32851}, {2287, 52440}, {2299, 22128}, {2600, 36134}, {4556, 53562}, {4558, 58313}, {4565, 53285}, {4636, 21828}, {4996, 34079}, {5546, 53314}, {6369, 14586}, {6740, 52059}, {32661, 44428}, {35192, 56844}
X(60091) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 4282}, {10, 2323}, {37, 4511}, {115, 3738}, {137, 2600}, {226, 22128}, {244, 654}, {1084, 8648}, {1214, 3218}, {1249, 17515}, {4858, 3904}, {4988, 53525}, {15898, 284}, {16591, 27950}, {34586, 34544}, {35069, 4996}, {36909, 2287}, {40586, 2361}, {40590, 36}, {40599, 58328}, {40600, 52426}, {40603, 32851}, {40611, 7113}, {40622, 3960}, {47345, 1870}, {52659, 17191}, {55060, 21758}, {55064, 53285}, {56325, 758}, {59608, 1443}
X(60091) = X(i)-Ceva conjugate of X(j) for these {i, j}: {655, 60074}, {18815, 52383}, {34535, 14628}, {57645, 12}
X(60091) = X(i)-cross conjugate of X(j) for these {i, j}: {12, 57645}, {2245, 6757}, {2610, 4551}, {21933, 40437}, {40663, 1441}, {45260, 693}
X(60091) = pole of line {2600, 3738} with respect to the polar circle
X(60091) = pole of line {4282, 34544} with respect to the Stammler hyperbola
X(60091) = pole of line {3738, 8068} with respect to the Steiner inellipse
X(60091) = pole of line {1737, 52383} with respect to the dual conic of Yff parabola
X(60091) = pole of line {35128, 53046} with respect to the dual conic of Wallace hyperbola
X(60091) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(57), X(1866)}}, {{A, B, C, X(72), X(18397)}}, {{A, B, C, X(80), X(52351)}}, {{A, B, C, X(91), X(92)}}, {{A, B, C, X(306), X(10573)}}, {{A, B, C, X(525), X(2800)}}, {{A, B, C, X(655), X(4552)}}, {{A, B, C, X(1214), X(5903)}}, {{A, B, C, X(1825), X(6354)}}, {{A, B, C, X(1826), X(54283)}}, {{A, B, C, X(1830), X(16578)}}, {{A, B, C, X(2006), X(52383)}}, {{A, B, C, X(2501), X(18785)}}, {{A, B, C, X(2603), X(35320)}}, {{A, B, C, X(3466), X(4674)}}, {{A, B, C, X(4858), X(16732)}}, {{A, B, C, X(6358), X(56285)}}, {{A, B, C, X(7017), X(10570)}}, {{A, B, C, X(7178), X(43048)}}, {{A, B, C, X(15065), X(18359)}}, {{A, B, C, X(15556), X(26942)}}, {{A, B, C, X(21907), X(24145)}}, {{A, B, C, X(30147), X(56810)}}, {{A, B, C, X(34857), X(55238)}}, {{A, B, C, X(36913), X(40663)}}, {{A, B, C, X(39770), X(56320)}}, {{A, B, C, X(56908), X(56926)}}
X(60091) = barycentric product X(i)*X(j) for these (i, j): {10, 18815}, {12, 14616}, {264, 52391}, {1411, 313}, {1441, 80}, {1446, 36910}, {1577, 655}, {1807, 57809}, {1825, 328}, {2006, 321}, {2161, 349}, {2166, 40999}, {2222, 850}, {2599, 46138}, {3668, 52409}, {3724, 57789}, {4077, 51562}, {4552, 60074}, {4554, 55238}, {4566, 52356}, {14628, 4080}, {15065, 7}, {16577, 94}, {18359, 226}, {18817, 22342}, {20566, 65}, {20573, 21741}, {20948, 32675}, {21207, 52377}, {24624, 6358}, {34388, 759}, {34535, 3936}, {34857, 6063}, {35174, 523}, {36804, 7178}, {40149, 52351}, {40663, 57788}, {41013, 52392}, {41226, 43682}, {46405, 661}, {52383, 75}, {52431, 52575}, {56285, 57985}, {57645, 758}
X(60091) = barycentric quotient X(i)/X(j) for these (i, j): {4, 17515}, {6, 4282}, {10, 4511}, {12, 758}, {37, 2323}, {42, 2361}, {65, 36}, {73, 52407}, {80, 21}, {181, 3724}, {210, 58328}, {213, 52426}, {225, 1870}, {226, 3218}, {265, 1789}, {321, 32851}, {349, 20924}, {512, 8648}, {523, 3738}, {655, 662}, {661, 654}, {758, 4996}, {759, 60}, {1042, 52440}, {1214, 22128}, {1254, 1464}, {1400, 7113}, {1402, 52434}, {1411, 58}, {1441, 320}, {1446, 17078}, {1577, 3904}, {1807, 283}, {1824, 52427}, {1825, 186}, {1880, 52413}, {2006, 81}, {2161, 284}, {2166, 3615}, {2171, 2245}, {2222, 110}, {2245, 34544}, {2341, 7054}, {2594, 6149}, {2599, 1154}, {2618, 6369}, {3120, 53525}, {3649, 4973}, {3668, 1443}, {3724, 215}, {3911, 17191}, {4017, 53314}, {4041, 53285}, {4077, 4453}, {4552, 4585}, {4554, 55237}, {4559, 1983}, {4705, 53562}, {4848, 4881}, {6187, 2194}, {6354, 18593}, {6358, 3936}, {6740, 1098}, {7178, 3960}, {7180, 21758}, {12077, 2600}, {14584, 52680}, {14616, 261}, {14628, 16704}, {15065, 8}, {15556, 27086}, {16577, 323}, {16609, 27950}, {18359, 333}, {18815, 86}, {20566, 314}, {21741, 50}, {21828, 57174}, {21864, 26744}, {22342, 22115}, {24006, 44428}, {24624, 2185}, {30572, 53535}, {32675, 163}, {34079, 2150}, {34242, 4225}, {34300, 15777}, {34388, 35550}, {34535, 24624}, {34857, 55}, {35174, 99}, {36078, 36134}, {36804, 645}, {36910, 2287}, {38955, 56757}, {40149, 17923}, {40663, 214}, {41013, 5081}, {41226, 56440}, {45926, 54356}, {46405, 799}, {47318, 4612}, {51421, 11700}, {51562, 643}, {52351, 1812}, {52356, 7253}, {52371, 2328}, {52377, 4570}, {52382, 56844}, {52383, 1}, {52391, 3}, {52392, 1444}, {52409, 1043}, {52431, 2193}, {53545, 53546}, {53551, 53555}, {55195, 46384}, {55197, 2610}, {55238, 650}, {56285, 860}, {56417, 3193}, {56422, 35193}, {57185, 21828}, {57645, 14616}, {60074, 4560}
X(60091) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2006, 18359, 14628}, {18359, 18815, 2006}

X(60092) = X(2)X(4258)∩X(10)X(390)

Barycentrics    (3*a^2-2*a*(b+c)+(b-c)*(3*b+c))*(3*a^2-2*a*(b+c)-(b-c)*(b+3*c)) : :

X(60092) lies on the Kiepert hyperbola and on these lines: {2, 4258}, {3, 45097}, {4, 37681}, {6, 57826}, {10, 390}, {20, 43672}, {30, 54712}, {76, 391}, {193, 60236}, {226, 5222}, {321, 30854}, {381, 54690}, {452, 60227}, {459, 26003}, {1334, 60267}, {1446, 5819}, {1654, 60285}, {2996, 17349}, {3091, 56144}, {3543, 54687}, {3618, 37161}, {3839, 54517}, {3945, 17758}, {4052, 16833}, {4080, 20111}, {4208, 43531}, {4383, 45100}, {5225, 13576}, {5232, 17681}, {6625, 51171}, {9312, 44559}, {14494, 21554}, {14552, 40013}, {17277, 43533}, {17528, 54624}, {18841, 33838}, {29598, 56226}, {32911, 60170}, {36728, 54689}, {36731, 54587}, {37108, 60157}, {37407, 60164}, {37423, 57719}, {37427, 54757}, {37428, 54787}, {37448, 56346}, {37655, 40012}, {37666, 60076}, {50736, 60078}

X(60092) = isogonal conjugate of X(5022)
X(60092) = isotomic conjugate of X(4869)
X(60092) = trilinear pole of line {8653, 523}
X(60092) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 5022}, {31, 4869}, {48, 57534}
X(60092) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 4869}, {3, 5022}, {1249, 57534}
X(60092) = X(i)-cross conjugate of X(j) for these {i, j}: {9580, 7}, {21872, 1}, {37650, 2}
X(60092) = pole of line {37650, 60092} with respect to the Kiepert hyperbola
X(60092) = pole of line {4869, 5022} with respect to the Wallace hyperbola
X(60092) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(55937)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(391)}}, {{A, B, C, X(7), X(18230)}}, {{A, B, C, X(8), X(279)}}, {{A, B, C, X(9), X(1170)}}, {{A, B, C, X(20), X(26003)}}, {{A, B, C, X(27), X(5129)}}, {{A, B, C, X(57), X(4866)}}, {{A, B, C, X(69), X(37681)}}, {{A, B, C, X(79), X(56217)}}, {{A, B, C, X(80), X(277)}}, {{A, B, C, X(81), X(7160)}}, {{A, B, C, X(85), X(7319)}}, {{A, B, C, X(88), X(41790)}}, {{A, B, C, X(90), X(55986)}}, {{A, B, C, X(104), X(56355)}}, {{A, B, C, X(145), X(3227)}}, {{A, B, C, X(193), X(17349)}}, {{A, B, C, X(278), X(56086)}}, {{A, B, C, X(294), X(5819)}}, {{A, B, C, X(312), X(1847)}}, {{A, B, C, X(333), X(44794)}}, {{A, B, C, X(452), X(37389)}}, {{A, B, C, X(469), X(4208)}}, {{A, B, C, X(514), X(36605)}}, {{A, B, C, X(903), X(56081)}}, {{A, B, C, X(1000), X(9328)}}, {{A, B, C, X(1016), X(6553)}}, {{A, B, C, X(1121), X(27818)}}, {{A, B, C, X(1156), X(7131)}}, {{A, B, C, X(1219), X(17743)}}, {{A, B, C, X(1246), X(3945)}}, {{A, B, C, X(1432), X(41446)}}, {{A, B, C, X(1434), X(7320)}}, {{A, B, C, X(1654), X(51171)}}, {{A, B, C, X(2006), X(56075)}}, {{A, B, C, X(2316), X(56005)}}, {{A, B, C, X(2478), X(37102)}}, {{A, B, C, X(3008), X(35158)}}, {{A, B, C, X(3091), X(37448)}}, {{A, B, C, X(3617), X(29598)}}, {{A, B, C, X(3618), X(5232)}}, {{A, B, C, X(3680), X(34056)}}, {{A, B, C, X(4209), X(28120)}}, {{A, B, C, X(4373), X(30701)}}, {{A, B, C, X(4383), X(37655)}}, {{A, B, C, X(4384), X(39587)}}, {{A, B, C, X(4869), X(37650)}}, {{A, B, C, X(5022), X(21872)}}, {{A, B, C, X(5046), X(37382)}}, {{A, B, C, X(5225), X(5236)}}, {{A, B, C, X(5556), X(27475)}}, {{A, B, C, X(5560), X(42326)}}, {{A, B, C, X(6650), X(54123)}}, {{A, B, C, X(6994), X(11108)}}, {{A, B, C, X(6995), X(17681)}}, {{A, B, C, X(7261), X(56264)}}, {{A, B, C, X(7378), X(33838)}}, {{A, B, C, X(8813), X(15740)}}, {{A, B, C, X(9309), X(39970)}}, {{A, B, C, X(14018), X(31049)}}, {{A, B, C, X(14552), X(32911)}}, {{A, B, C, X(14555), X(37666)}}, {{A, B, C, X(18097), X(56157)}}, {{A, B, C, X(21446), X(33576)}}, {{A, B, C, X(21454), X(39948)}}, {{A, B, C, X(30494), X(42310)}}, {{A, B, C, X(30712), X(32009)}}, {{A, B, C, X(31359), X(39716)}}, {{A, B, C, X(31371), X(56382)}}, {{A, B, C, X(32635), X(39273)}}, {{A, B, C, X(34018), X(56088)}}, {{A, B, C, X(34234), X(55030)}}, {{A, B, C, X(34529), X(43740)}}, {{A, B, C, X(34578), X(43731)}}, {{A, B, C, X(36101), X(38271)}}, {{A, B, C, X(37279), X(37423)}}, {{A, B, C, X(39797), X(57705)}}, {{A, B, C, X(40403), X(55989)}}, {{A, B, C, X(42290), X(57666)}}
X(60092) = barycentric quotient X(i)/X(j) for these (i, j): {2, 4869}, {4, 57534}, {6, 5022}

X(60093) = X(2)X(1692)∩X(4)X(3972)

Barycentrics    (2*(a^4+b^4)-(a^2+b^2)*c^2+c^4)*(2*a^4-a^2*b^2+b^4-b^2*c^2+2*c^4) : :

X(60093) lies on the Kiepert hyperbola and on these lines: {2, 1692}, {4, 3972}, {5, 60117}, {6, 8781}, {30, 54713}, {76, 230}, {83, 7887}, {98, 18440}, {183, 60213}, {262, 7792}, {381, 54659}, {385, 43529}, {597, 60211}, {598, 33228}, {671, 1003}, {1352, 7612}, {1916, 7806}, {2489, 60338}, {2996, 3767}, {3054, 60248}, {3314, 60231}, {3329, 60233}, {3399, 7786}, {3407, 16984}, {3589, 60096}, {3618, 14494}, {3815, 60178}, {5304, 60262}, {5395, 5475}, {5476, 60127}, {5485, 14568}, {6036, 54978}, {6055, 55009}, {6680, 60151}, {7608, 11174}, {7610, 10302}, {7735, 40824}, {7790, 54996}, {7795, 60285}, {7832, 18840}, {7875, 60098}, {7930, 10159}, {8176, 54639}, {9756, 14061}, {10000, 46318}, {10033, 54481}, {11168, 60277}, {14492, 50963}, {15819, 60126}, {16989, 60234}, {17004, 42006}, {17008, 60232}, {18841, 32955}, {18845, 32980}, {19687, 53105}, {22486, 60095}, {22515, 60189}, {23055, 33231}, {31489, 60198}, {32981, 38259}, {37637, 60101}, {37688, 60099}, {37689, 60201}, {39563, 41895}, {44401, 60220}, {51023, 60150}, {53475, 60218}, {59373, 60240}

X(60093) = isogonal conjugate of X(5028)
X(60093) = isotomic conjugate of X(7778)
X(60093) = trilinear pole of line {32220, 39904}
X(60093) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 5028}, {31, 7778}, {48, 57533}
X(60093) = X(i)-vertex conjugate of X(j) for these {i, j}: {25, 76}, {2353, 60218}
X(60093) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 7778}, {3, 5028}, {1249, 57533}
X(60093) = pole of line {5028, 7778} with respect to the Wallace hyperbola
X(60093) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(13335)}}, {{A, B, C, X(6), X(230)}}, {{A, B, C, X(25), X(7807)}}, {{A, B, C, X(111), X(7835)}}, {{A, B, C, X(183), X(7792)}}, {{A, B, C, X(249), X(3425)}}, {{A, B, C, X(251), X(7857)}}, {{A, B, C, X(264), X(40416)}}, {{A, B, C, X(297), X(37071)}}, {{A, B, C, X(305), X(7828)}}, {{A, B, C, X(385), X(7806)}}, {{A, B, C, X(393), X(40405)}}, {{A, B, C, X(427), X(7887)}}, {{A, B, C, X(458), X(56370)}}, {{A, B, C, X(468), X(1003)}}, {{A, B, C, X(597), X(7610)}}, {{A, B, C, X(737), X(46316)}}, {{A, B, C, X(755), X(21448)}}, {{A, B, C, X(761), X(39954)}}, {{A, B, C, X(1016), X(57727)}}, {{A, B, C, X(1352), X(56892)}}, {{A, B, C, X(1509), X(57726)}}, {{A, B, C, X(1989), X(9516)}}, {{A, B, C, X(2165), X(56067)}}, {{A, B, C, X(2353), X(7789)}}, {{A, B, C, X(2366), X(10603)}}, {{A, B, C, X(2367), X(3972)}}, {{A, B, C, X(2697), X(18880)}}, {{A, B, C, X(2710), X(40801)}}, {{A, B, C, X(3054), X(31489)}}, {{A, B, C, X(3314), X(16984)}}, {{A, B, C, X(3329), X(17004)}}, {{A, B, C, X(3589), X(15271)}}, {{A, B, C, X(3618), X(34229)}}, {{A, B, C, X(3767), X(56891)}}, {{A, B, C, X(3815), X(37637)}}, {{A, B, C, X(4232), X(33191)}}, {{A, B, C, X(5094), X(33228)}}, {{A, B, C, X(5152), X(52145)}}, {{A, B, C, X(5304), X(37689)}}, {{A, B, C, X(5976), X(32544)}}, {{A, B, C, X(6353), X(30558)}}, {{A, B, C, X(6677), X(37199)}}, {{A, B, C, X(6995), X(33189)}}, {{A, B, C, X(7378), X(32955)}}, {{A, B, C, X(7832), X(40022)}}, {{A, B, C, X(7930), X(39998)}}, {{A, B, C, X(7942), X(8024)}}, {{A, B, C, X(8889), X(32972)}}, {{A, B, C, X(9289), X(51454)}}, {{A, B, C, X(9307), X(35511)}}, {{A, B, C, X(11059), X(14568)}}, {{A, B, C, X(11168), X(47352)}}, {{A, B, C, X(11174), X(37688)}}, {{A, B, C, X(11184), X(44401)}}, {{A, B, C, X(11284), X(35920)}}, {{A, B, C, X(14356), X(18440)}}, {{A, B, C, X(14617), X(42535)}}, {{A, B, C, X(15464), X(44571)}}, {{A, B, C, X(15597), X(42849)}}, {{A, B, C, X(16774), X(56334)}}, {{A, B, C, X(16989), X(17008)}}, {{A, B, C, X(17040), X(56360)}}, {{A, B, C, X(17984), X(51510)}}, {{A, B, C, X(18575), X(40511)}}, {{A, B, C, X(19687), X(37453)}}, {{A, B, C, X(30542), X(42286)}}, {{A, B, C, X(31360), X(45838)}}, {{A, B, C, X(32085), X(42407)}}, {{A, B, C, X(32980), X(52299)}}, {{A, B, C, X(32981), X(38282)}}, {{A, B, C, X(33231), X(52301)}}, {{A, B, C, X(34154), X(55075)}}, {{A, B, C, X(34288), X(41909)}}, {{A, B, C, X(35568), X(44182)}}, {{A, B, C, X(35940), X(40132)}}, {{A, B, C, X(37876), X(57644)}}, {{A, B, C, X(40413), X(54958)}}, {{A, B, C, X(44557), X(47643)}}, {{A, B, C, X(45819), X(52669)}}, {{A, B, C, X(46235), X(57504)}}, {{A, B, C, X(47200), X(47206)}}, {{A, B, C, X(57822), X(57926)}}
X(60093) = barycentric quotient X(i)/X(j) for these (i, j): {2, 7778}, {4, 57533}, {6, 5028}

X(60094) = X(2)X(4262)∩X(10)X(528)

Barycentrics    (2*a^2-a*(b+c)+(b-c)*(2*b+c))*(2*a^2-a*(b+c)-(b-c)*(b+2*c)) : :

X(60094) lies on the Kiepert hyperbola and on these lines: {2, 4262}, {6, 60083}, {10, 528}, {30, 43672}, {76, 17346}, {226, 544}, {239, 4080}, {321, 4115}, {376, 45097}, {381, 56144}, {519, 43534}, {597, 60078}, {662, 32014}, {673, 10708}, {812, 4049}, {1018, 6539}, {2051, 36728}, {3583, 13576}, {3830, 54687}, {3845, 54517}, {4134, 14839}, {5011, 37787}, {5485, 37654}, {7608, 21554}, {10159, 17681}, {10302, 17271}, {11113, 60227}, {13478, 36731}, {15682, 54712}, {16080, 26003}, {17023, 30588}, {17034, 50133}, {17197, 17392}, {17330, 60276}, {17528, 43531}, {24712, 34578}, {32911, 54648}, {33838, 43527}, {37427, 60157}, {37428, 57719}, {37448, 43530}, {37681, 54622}, {41099, 54690}, {45926, 54842}, {48841, 60108}, {50736, 60077}, {54770, 59373}

X(60094) = reflection of X(i) in X(j) for these {i,j}: {55162, 2}
X(60094) = isogonal conjugate of X(5030)
X(60094) = isotomic conjugate of X(17297)
X(60094) = trilinear pole of line {1962, 4448}
X(60094) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 5030}, {31, 17297}, {692, 48571}
X(60094) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 17297}, {3, 5030}, {1086, 48571}
X(60094) = pole of line {5030, 17297} with respect to the Wallace hyperbola
X(60094) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(15254)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(4262)}}, {{A, B, C, X(8), X(14377)}}, {{A, B, C, X(30), X(26003)}}, {{A, B, C, X(57), X(55931)}}, {{A, B, C, X(59), X(40076)}}, {{A, B, C, X(75), X(17359)}}, {{A, B, C, X(79), X(32008)}}, {{A, B, C, X(80), X(514)}}, {{A, B, C, X(85), X(5560)}}, {{A, B, C, X(86), X(49731)}}, {{A, B, C, X(106), X(48074)}}, {{A, B, C, X(239), X(519)}}, {{A, B, C, X(277), X(7319)}}, {{A, B, C, X(279), X(43734)}}, {{A, B, C, X(312), X(50103)}}, {{A, B, C, X(335), X(32012)}}, {{A, B, C, X(381), X(37448)}}, {{A, B, C, X(428), X(17681)}}, {{A, B, C, X(469), X(17528)}}, {{A, B, C, X(516), X(55000)}}, {{A, B, C, X(522), X(544)}}, {{A, B, C, X(527), X(1156)}}, {{A, B, C, X(553), X(27065)}}, {{A, B, C, X(596), X(17743)}}, {{A, B, C, X(597), X(17271)}}, {{A, B, C, X(662), X(1018)}}, {{A, B, C, X(903), X(4422)}}, {{A, B, C, X(996), X(39721)}}, {{A, B, C, X(1000), X(55937)}}, {{A, B, C, X(1016), X(6650)}}, {{A, B, C, X(1334), X(4251)}}, {{A, B, C, X(1434), X(5559)}}, {{A, B, C, X(1992), X(37654)}}, {{A, B, C, X(2006), X(12019)}}, {{A, B, C, X(2161), X(2224)}}, {{A, B, C, X(2339), X(4866)}}, {{A, B, C, X(2796), X(40459)}}, {{A, B, C, X(3065), X(4564)}}, {{A, B, C, X(3521), X(56382)}}, {{A, B, C, X(3570), X(4169)}}, {{A, B, C, X(3583), X(5236)}}, {{A, B, C, X(3679), X(17023)}}, {{A, B, C, X(3828), X(29610)}}, {{A, B, C, X(3911), X(43757)}}, {{A, B, C, X(4384), X(50291)}}, {{A, B, C, X(4674), X(39979)}}, {{A, B, C, X(4685), X(17034)}}, {{A, B, C, X(4745), X(29614)}}, {{A, B, C, X(4785), X(14839)}}, {{A, B, C, X(5064), X(33838)}}, {{A, B, C, X(5556), X(56217)}}, {{A, B, C, X(5561), X(27475)}}, {{A, B, C, X(5620), X(31010)}}, {{A, B, C, X(7131), X(36599)}}, {{A, B, C, X(7160), X(39948)}}, {{A, B, C, X(7261), X(18821)}}, {{A, B, C, X(7317), X(56043)}}, {{A, B, C, X(9311), X(43731)}}, {{A, B, C, X(11109), X(36728)}}, {{A, B, C, X(11113), X(37389)}}, {{A, B, C, X(14621), X(42285)}}, {{A, B, C, X(15171), X(52374)}}, {{A, B, C, X(15320), X(17277)}}, {{A, B, C, X(16833), X(49476)}}, {{A, B, C, X(17132), X(28521)}}, {{A, B, C, X(17197), X(17761)}}, {{A, B, C, X(17281), X(30892)}}, {{A, B, C, X(17330), X(46922)}}, {{A, B, C, X(17349), X(50133)}}, {{A, B, C, X(17501), X(42326)}}, {{A, B, C, X(17555), X(36731)}}, {{A, B, C, X(18097), X(56132)}}, {{A, B, C, X(18359), X(43758)}}, {{A, B, C, X(19821), X(35652)}}, {{A, B, C, X(20568), X(40509)}}, {{A, B, C, X(21554), X(52281)}}, {{A, B, C, X(24297), X(34056)}}, {{A, B, C, X(24298), X(34529)}}, {{A, B, C, X(29617), X(49477)}}, {{A, B, C, X(32009), X(43972)}}, {{A, B, C, X(32015), X(33696)}}, {{A, B, C, X(32847), X(41140)}}, {{A, B, C, X(36603), X(41790)}}, {{A, B, C, X(36871), X(49484)}}, {{A, B, C, X(37279), X(37428)}}, {{A, B, C, X(38271), X(44178)}}, {{A, B, C, X(39704), X(39717)}}, {{A, B, C, X(39797), X(57666)}}, {{A, B, C, X(39950), X(46187)}}, {{A, B, C, X(39971), X(53114)}}, {{A, B, C, X(39974), X(40747)}}, {{A, B, C, X(40435), X(55090)}}
X(60094) = barycentric quotient X(i)/X(j) for these (i, j): {2, 17297}, {6, 5030}, {514, 48571}

X(60095) = X(4)X(7757)∩X(83)X(1003)

Barycentrics    (4*a^2*b^2+(a^2+b^2)*c^2-3*c^4)*(-3*b^4+b^2*c^2+a^2*(b^2+4*c^2)) : :

X(60095) lies on the Kiepert hyperbola and on these lines: {4, 7757}, {6, 33692}, {30, 60117}, {39, 5395}, {76, 33228}, {83, 1003}, {98, 1351}, {115, 54750}, {194, 38259}, {262, 38136}, {325, 60180}, {511, 7612}, {524, 60218}, {538, 2996}, {543, 54872}, {598, 9300}, {599, 60217}, {671, 9766}, {1916, 9764}, {1992, 60150}, {2023, 60073}, {2549, 54753}, {2782, 60189}, {3094, 60096}, {3406, 5171}, {3407, 5034}, {3566, 60106}, {3830, 54659}, {3845, 54713}, {5969, 8781}, {5976, 56064}, {7607, 33706}, {7608, 37071}, {7786, 18841}, {7788, 60181}, {7807, 43527}, {7837, 43535}, {7840, 60214}, {7887, 10159}, {8556, 60101}, {9466, 32972}, {11147, 54616}, {11163, 14492}, {11167, 37671}, {11257, 54873}, {13468, 60220}, {14458, 41624}, {14711, 60200}, {14881, 54846}, {19099, 54628}, {19100, 54627}, {19687, 53102}, {22329, 60175}, {22486, 60093}, {22712, 53104}, {32447, 54868}, {32451, 60280}, {32973, 44562}, {32980, 43681}, {32981, 60145}, {33456, 54653}, {33457, 54652}, {34087, 57518}, {44434, 60336}, {50571, 60238}, {51373, 60262}, {55122, 60226}

X(60095) = reflection of X(i) in X(j) for these {i,j}: {54750, 115}
X(60095) = isogonal conjugate of X(5033)
X(60095) = isotomic conjugate of X(8667)
X(60095) = pole of line {5033, 8667} with respect to the Wallace hyperbola
X(60095) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(21399)}}, {{A, B, C, X(39), X(5013)}}, {{A, B, C, X(264), X(3228)}}, {{A, B, C, X(305), X(7757)}}, {{A, B, C, X(325), X(14614)}}, {{A, B, C, X(427), X(1003)}}, {{A, B, C, X(428), X(7887)}}, {{A, B, C, X(511), X(1351)}}, {{A, B, C, X(524), X(9766)}}, {{A, B, C, X(538), X(3566)}}, {{A, B, C, X(599), X(9300)}}, {{A, B, C, X(3094), X(5034)}}, {{A, B, C, X(3095), X(5171)}}, {{A, B, C, X(3266), X(11055)}}, {{A, B, C, X(3613), X(9462)}}, {{A, B, C, X(3815), X(8556)}}, {{A, B, C, X(3978), X(9764)}}, {{A, B, C, X(5064), X(7807)}}, {{A, B, C, X(5969), X(47734)}}, {{A, B, C, X(6664), X(45090)}}, {{A, B, C, X(7378), X(33191)}}, {{A, B, C, X(7409), X(33231)}}, {{A, B, C, X(7714), X(32972)}}, {{A, B, C, X(7788), X(41624)}}, {{A, B, C, X(7837), X(7840)}}, {{A, B, C, X(8801), X(40405)}}, {{A, B, C, X(11163), X(37671)}}, {{A, B, C, X(11184), X(13468)}}, {{A, B, C, X(18361), X(36882)}}, {{A, B, C, X(18575), X(25322)}}, {{A, B, C, X(18880), X(45096)}}, {{A, B, C, X(30541), X(39951)}}, {{A, B, C, X(31152), X(35920)}}, {{A, B, C, X(31360), X(45108)}}, {{A, B, C, X(37071), X(52281)}}, {{A, B, C, X(41530), X(53200)}}, {{A, B, C, X(42313), X(44422)}}, {{A, B, C, X(43098), X(57822)}}, {{A, B, C, X(45819), X(56057)}}, {{A, B, C, X(48913), X(51541)}}, {{A, B, C, X(52282), X(56370)}}

X(60096) = X(2)X(3787)∩X(4)X(7786)

Barycentrics    (4*a^2*b^2+3*(a^2+b^2)*c^2-c^4)*(-b^4+3*b^2*c^2+a^2*(3*b^2+4*c^2)) : :

X(60096) lies on the Kiepert hyperbola and on these lines: {2, 3787}, {4, 7786}, {6, 60101}, {30, 54714}, {39, 2996}, {76, 3815}, {83, 3053}, {98, 5050}, {114, 43532}, {183, 60187}, {194, 43681}, {230, 60248}, {262, 21850}, {325, 60099}, {381, 54718}, {511, 14494}, {538, 60200}, {597, 60220}, {598, 8356}, {671, 2023}, {1007, 18840}, {1506, 60151}, {2021, 54753}, {3055, 60178}, {3094, 60095}, {3329, 60128}, {3407, 5033}, {3589, 60093}, {3618, 7612}, {3934, 32825}, {3972, 11170}, {5395, 6683}, {5485, 7757}, {5490, 13983}, {5491, 8992}, {5503, 5976}, {6194, 60333}, {7607, 7792}, {7608, 22712}, {7736, 60212}, {7777, 42006}, {7778, 10159}, {7790, 60115}, {7857, 43527}, {7875, 60104}, {7884, 9302}, {8182, 54639}, {8781, 31489}, {10007, 54905}, {10155, 15819}, {10302, 11184}, {11055, 60216}, {11171, 54869}, {11179, 60150}, {14485, 54993}, {17005, 43529}, {18842, 51224}, {18845, 33023}, {19695, 53107}, {22110, 60277}, {22486, 60211}, {24256, 60202}, {32451, 60217}, {32991, 38259}, {33234, 53109}, {33272, 53101}, {33706, 54645}, {40016, 57518}, {40108, 54868}, {41895, 44562}, {44422, 54523}, {46236, 54822}, {47352, 60103}, {51373, 60201}

X(60096) = isogonal conjugate of X(5034)
X(60096) = isotomic conjugate of X(15271)
X(60096) = X(i)-vertex conjugate of X(j) for these {i, j}: {25, 60248}
X(60096) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 15271}, {3, 5034}
X(60096) = pole of line {15491, 60096} with respect to the Kiepert hyperbola
X(60096) = pole of line {5034, 15271} with respect to the Wallace hyperbola
X(60096) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(13334)}}, {{A, B, C, X(6), X(3815)}}, {{A, B, C, X(25), X(32992)}}, {{A, B, C, X(39), X(3053)}}, {{A, B, C, X(141), X(45090)}}, {{A, B, C, X(230), X(31489)}}, {{A, B, C, X(264), X(39968)}}, {{A, B, C, X(305), X(7786)}}, {{A, B, C, X(325), X(11174)}}, {{A, B, C, X(427), X(11285)}}, {{A, B, C, X(458), X(37451)}}, {{A, B, C, X(468), X(44543)}}, {{A, B, C, X(511), X(5050)}}, {{A, B, C, X(524), X(42849)}}, {{A, B, C, X(597), X(11184)}}, {{A, B, C, X(1007), X(3618)}}, {{A, B, C, X(1016), X(57726)}}, {{A, B, C, X(1509), X(57727)}}, {{A, B, C, X(3055), X(37637)}}, {{A, B, C, X(3094), X(5033)}}, {{A, B, C, X(3329), X(7777)}}, {{A, B, C, X(3563), X(30535)}}, {{A, B, C, X(3589), X(7778)}}, {{A, B, C, X(3613), X(31360)}}, {{A, B, C, X(5094), X(8356)}}, {{A, B, C, X(6353), X(32987)}}, {{A, B, C, X(6664), X(24861)}}, {{A, B, C, X(7757), X(11059)}}, {{A, B, C, X(7771), X(23297)}}, {{A, B, C, X(7806), X(17005)}}, {{A, B, C, X(7857), X(39668)}}, {{A, B, C, X(7875), X(7925)}}, {{A, B, C, X(8770), X(27375)}}, {{A, B, C, X(8889), X(32990)}}, {{A, B, C, X(9516), X(30537)}}, {{A, B, C, X(14356), X(46235)}}, {{A, B, C, X(15271), X(15491)}}, {{A, B, C, X(17381), X(30761)}}, {{A, B, C, X(17980), X(44557)}}, {{A, B, C, X(18575), X(42286)}}, {{A, B, C, X(19695), X(52298)}}, {{A, B, C, X(22110), X(47352)}}, {{A, B, C, X(30499), X(40802)}}, {{A, B, C, X(32991), X(38282)}}, {{A, B, C, X(33023), X(52299)}}, {{A, B, C, X(34816), X(45108)}}, {{A, B, C, X(39951), X(56004)}}, {{A, B, C, X(40405), X(46952)}}

X(60097) = X(2)X(4277)∩X(10)X(3702)

Barycentrics    b*c*(c*(b+c)+a*(3*b+c))*(b*(b+c)+a*(b+3*c)) : :

X(60097) lies on the Kiepert hyperbola and on these lines: {2, 4277}, {4, 34466}, {5, 54933}, {10, 3702}, {69, 60169}, {75, 4080}, {83, 37680}, {141, 39994}, {226, 4359}, {312, 6539}, {321, 3264}, {594, 36791}, {693, 4049}, {899, 40718}, {908, 40515}, {1150, 60085}, {1211, 40013}, {1491, 35353}, {3216, 16454}, {3661, 60288}, {3687, 56214}, {3936, 17758}, {3948, 60276}, {4052, 4980}, {4383, 60082}, {4384, 60135}, {4417, 57722}, {4671, 27797}, {4679, 13576}, {5233, 60071}, {5252, 60086}, {5278, 13478}, {5718, 24589}, {5739, 60076}, {14534, 32911}, {14555, 60156}, {16729, 17330}, {17077, 46480}, {17277, 24624}, {19804, 26738}, {20108, 50634}, {32014, 52379}, {32782, 40012}, {37656, 60258}, {41809, 60084}, {50171, 60078}, {58361, 60074}

X(60097) = isogonal conjugate of X(5035)
X(60097) = isotomic conjugate of X(37633)
X(60097) = trilinear pole of line {3762, 4985}
X(60097) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 5035}, {31, 37633}, {692, 48320}, {1333, 56191}, {2206, 31025}, {32739, 47780}, {34073, 57052}
X(60097) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 37633}, {3, 5035}, {37, 56191}, {1086, 48320}, {40603, 31025}, {40619, 47780}
X(60097) = X(i)-cross conjugate of X(j) for these {i, j}: {4714, 75}, {5241, 2}, {17530, 264}, {21027, 40216}
X(60097) = pole of line {5241, 60097} with respect to the Kiepert hyperbola
X(60097) = pole of line {5035, 37633} with respect to the Wallace hyperbola
X(60097) = pole of line {4424, 24589} with respect to the dual conic of Yff parabola
X(60097) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(4277)}}, {{A, B, C, X(75), X(693)}}, {{A, B, C, X(80), X(55942)}}, {{A, B, C, X(81), X(5743)}}, {{A, B, C, X(88), X(257)}}, {{A, B, C, X(141), X(37680)}}, {{A, B, C, X(274), X(18359)}}, {{A, B, C, X(312), X(3702)}}, {{A, B, C, X(333), X(5741)}}, {{A, B, C, X(334), X(56169)}}, {{A, B, C, X(335), X(4665)}}, {{A, B, C, X(469), X(16454)}}, {{A, B, C, X(514), X(39706)}}, {{A, B, C, X(561), X(56212)}}, {{A, B, C, X(594), X(661)}}, {{A, B, C, X(596), X(39698)}}, {{A, B, C, X(899), X(1491)}}, {{A, B, C, X(908), X(17077)}}, {{A, B, C, X(1150), X(5233)}}, {{A, B, C, X(1211), X(32911)}}, {{A, B, C, X(2350), X(52651)}}, {{A, B, C, X(2997), X(58017)}}, {{A, B, C, X(3006), X(4384)}}, {{A, B, C, X(3008), X(31079)}}, {{A, B, C, X(3216), X(40603)}}, {{A, B, C, X(3613), X(46772)}}, {{A, B, C, X(3679), X(21130)}}, {{A, B, C, X(3701), X(34265)}}, {{A, B, C, X(3936), X(17277)}}, {{A, B, C, X(4383), X(32782)}}, {{A, B, C, X(4391), X(30608)}}, {{A, B, C, X(4417), X(5278)}}, {{A, B, C, X(4671), X(4793)}}, {{A, B, C, X(4776), X(52043)}}, {{A, B, C, X(4945), X(16724)}}, {{A, B, C, X(4980), X(18743)}}, {{A, B, C, X(5235), X(5718)}}, {{A, B, C, X(5241), X(37633)}}, {{A, B, C, X(5252), X(17743)}}, {{A, B, C, X(5559), X(46638)}}, {{A, B, C, X(5739), X(14555)}}, {{A, B, C, X(7017), X(56201)}}, {{A, B, C, X(7018), X(40216)}}, {{A, B, C, X(16729), X(51975)}}, {{A, B, C, X(17308), X(26251)}}, {{A, B, C, X(17740), X(26591)}}, {{A, B, C, X(25322), X(39957)}}, {{A, B, C, X(25430), X(39700)}}, {{A, B, C, X(26005), X(37659)}}, {{A, B, C, X(29576), X(30970)}}, {{A, B, C, X(30711), X(59761)}}, {{A, B, C, X(32018), X(36805)}}, {{A, B, C, X(33172), X(37679)}}, {{A, B, C, X(36795), X(52344)}}, {{A, B, C, X(37651), X(37660)}}, {{A, B, C, X(39711), X(55952)}}, {{A, B, C, X(39963), X(57725)}}, {{A, B, C, X(39979), X(42286)}}, {{A, B, C, X(39983), X(56123)}}, {{A, B, C, X(40826), X(58020)}}
X(60097) = barycentric product X(i)*X(j) for these (i, j): {4391, 46480}, {39974, 76}, {42285, 75}
X(60097) = barycentric quotient X(i)/X(j) for these (i, j): {2, 37633}, {6, 5035}, {10, 56191}, {321, 31025}, {514, 48320}, {693, 47780}, {3261, 4828}, {4777, 57052}, {39974, 6}, {42285, 1}, {46480, 651}

X(60098) = X(39)X(671)∩X(83)X(187)

Barycentrics    (3*a^2*b^2+2*(a^2+b^2)*c^2-c^4)*(-b^4+2*b^2*c^2+a^2*(2*b^2+3*c^2)) : :

X(60098) lies on the Kiepert hyperbola and on these lines: {2, 13330}, {3, 11170}, {4, 11171}, {5, 43532}, {6, 33689}, {30, 54715}, {39, 671}, {76, 1506}, {83, 187}, {98, 575}, {194, 5485}, {262, 52996}, {325, 42006}, {381, 54903}, {384, 15483}, {385, 60101}, {511, 7608}, {538, 60216}, {597, 8587}, {598, 7747}, {631, 22679}, {1007, 60232}, {1153, 60238}, {1916, 3815}, {2023, 11606}, {2996, 32962}, {3005, 5466}, {3091, 54488}, {3094, 60177}, {3095, 60126}, {3266, 40016}, {3314, 60099}, {3406, 11842}, {3407, 11174}, {3589, 43528}, {3934, 10302}, {5052, 17006}, {5395, 32965}, {5976, 35005}, {6194, 10155}, {6680, 43527}, {7607, 7806}, {7612, 16989}, {7736, 54122}, {7746, 54816}, {7757, 60228}, {7769, 54841}, {7774, 60212}, {7787, 60148}, {7792, 60104}, {7797, 9302}, {7803, 54752}, {7808, 34885}, {7827, 54840}, {7828, 54749}, {7864, 60115}, {7875, 60093}, {7925, 60213}, {7931, 10159}, {8597, 44562}, {8781, 17005}, {8859, 44500}, {9698, 32476}, {10484, 44453}, {10485, 60184}, {10583, 18841}, {11059, 40162}, {11257, 54869}, {11602, 22692}, {11603, 22691}, {11669, 22712}, {13334, 54868}, {14881, 54724}, {15819, 53108}, {16922, 46305}, {16984, 60073}, {17004, 60248}, {18840, 32975}, {18842, 33215}, {18843, 33226}, {18844, 33247}, {18845, 32997}, {20081, 60200}, {20105, 43681}, {22486, 42011}, {26235, 31630}, {31276, 60143}, {31489, 60233}, {32450, 43676}, {32995, 38259}, {33192, 53101}, {33256, 53109}, {37345, 55009}, {42849, 54487}, {43537, 51171}, {44377, 60231}, {44422, 60192}, {44434, 60333}, {51373, 60202}, {54805, 57633}

X(60098) = isogonal conjugate of X(5038)
X(60098) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 5038}, {8786, 33689}
X(60098) = pole of line {5038, 33689} with respect to the Wallace hyperbola
X(60098) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(11171)}}, {{A, B, C, X(6), X(7777)}}, {{A, B, C, X(25), X(16921)}}, {{A, B, C, X(39), X(187)}}, {{A, B, C, X(95), X(1031)}}, {{A, B, C, X(111), X(13410)}}, {{A, B, C, X(182), X(52996)}}, {{A, B, C, X(194), X(11059)}}, {{A, B, C, X(230), X(17005)}}, {{A, B, C, X(251), X(1506)}}, {{A, B, C, X(308), X(25322)}}, {{A, B, C, X(325), X(3329)}}, {{A, B, C, X(385), X(3815)}}, {{A, B, C, X(427), X(7824)}}, {{A, B, C, X(468), X(33013)}}, {{A, B, C, X(511), X(575)}}, {{A, B, C, X(1007), X(16989)}}, {{A, B, C, X(1502), X(45090)}}, {{A, B, C, X(2963), X(52395)}}, {{A, B, C, X(2987), X(30499)}}, {{A, B, C, X(3055), X(17006)}}, {{A, B, C, X(3094), X(39560)}}, {{A, B, C, X(3095), X(11842)}}, {{A, B, C, X(3108), X(7764)}}, {{A, B, C, X(3314), X(11174)}}, {{A, B, C, X(3589), X(7931)}}, {{A, B, C, X(3613), X(9229)}}, {{A, B, C, X(3934), X(26235)}}, {{A, B, C, X(4518), X(40738)}}, {{A, B, C, X(4590), X(30537)}}, {{A, B, C, X(5094), X(7833)}}, {{A, B, C, X(5970), X(8601)}}, {{A, B, C, X(6353), X(32962)}}, {{A, B, C, X(6680), X(39668)}}, {{A, B, C, X(6683), X(8024)}}, {{A, B, C, X(6995), X(32975)}}, {{A, B, C, X(7378), X(32978)}}, {{A, B, C, X(7736), X(7774)}}, {{A, B, C, X(7778), X(7875)}}, {{A, B, C, X(7786), X(9464)}}, {{A, B, C, X(7792), X(7925)}}, {{A, B, C, X(7906), X(39951)}}, {{A, B, C, X(8597), X(52293)}}, {{A, B, C, X(8786), X(8787)}}, {{A, B, C, X(8889), X(32965)}}, {{A, B, C, X(10007), X(17949)}}, {{A, B, C, X(10485), X(44453)}}, {{A, B, C, X(11169), X(35511)}}, {{A, B, C, X(15464), X(57926)}}, {{A, B, C, X(16984), X(44377)}}, {{A, B, C, X(17000), X(37661)}}, {{A, B, C, X(17004), X(31489)}}, {{A, B, C, X(18372), X(57903)}}, {{A, B, C, X(31239), X(39998)}}, {{A, B, C, X(32995), X(38282)}}, {{A, B, C, X(32997), X(52299)}}, {{A, B, C, X(33215), X(52284)}}, {{A, B, C, X(38262), X(56067)}}, {{A, B, C, X(40511), X(44571)}}
X(60098) = barycentric quotient X(i)/X(j) for these (i, j): {6, 5038}, {8859, 33689}

X(60099) = X(4)X(3934)∩X(83)X(183)

Barycentrics    (2*a^2*b^2+3*(a^2+b^2)*c^2+c^4)*(b^4+3*b^2*c^2+a^2*(3*b^2+2*c^2)) : :

X(60099) lies on the Kiepert hyperbola and on these lines: {2, 11175}, {4, 3934}, {30, 54716}, {39, 18840}, {76, 8362}, {83, 183}, {98, 5026}, {141, 262}, {194, 60285}, {226, 30869}, {230, 60215}, {305, 31630}, {325, 60096}, {385, 60129}, {511, 14484}, {538, 60143}, {598, 7811}, {599, 54509}, {671, 5976}, {1916, 16986}, {2023, 5503}, {2052, 42394}, {2996, 31276}, {3094, 60180}, {3314, 60098}, {3407, 41412}, {3424, 15819}, {3619, 40824}, {3763, 60213}, {5395, 20065}, {5485, 9466}, {6194, 43951}, {6683, 60183}, {7607, 58446}, {7608, 7778}, {7697, 60115}, {7735, 18841}, {7757, 10302}, {7786, 10159}, {7792, 43527}, {7865, 54904}, {7868, 8781}, {7870, 54816}, {7931, 60233}, {7937, 9478}, {8357, 53105}, {8782, 60271}, {10033, 54566}, {10155, 37690}, {11055, 60286}, {11669, 44377}, {14492, 24256}, {16990, 60190}, {17004, 43528}, {18842, 42850}, {21356, 60268}, {22329, 60239}, {22486, 54487}, {26244, 60075}, {33025, 38259}, {33210, 41895}, {37637, 60186}, {37688, 60093}, {38744, 60140}, {40016, 40022}, {40332, 54773}, {44422, 54521}, {51373, 60212}

X(60099) = isogonal conjugate of X(5039)
X(60099) = isotomic conjugate of X(11174)
X(60099) = X(i)-vertex conjugate of X(j) for these {i, j}: {25, 60215}
X(60099) = pole of line {5039, 11174} with respect to the Wallace hyperbola
X(60099) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(5188)}}, {{A, B, C, X(25), X(39)}}, {{A, B, C, X(141), X(183)}}, {{A, B, C, X(230), X(7868)}}, {{A, B, C, X(297), X(51373)}}, {{A, B, C, X(305), X(3934)}}, {{A, B, C, X(308), X(9307)}}, {{A, B, C, X(325), X(15271)}}, {{A, B, C, X(385), X(16986)}}, {{A, B, C, X(468), X(11287)}}, {{A, B, C, X(511), X(5085)}}, {{A, B, C, X(733), X(44557)}}, {{A, B, C, X(1799), X(7800)}}, {{A, B, C, X(3094), X(41412)}}, {{A, B, C, X(3613), X(24861)}}, {{A, B, C, X(3619), X(7735)}}, {{A, B, C, X(3763), X(7792)}}, {{A, B, C, X(4518), X(30869)}}, {{A, B, C, X(5026), X(5976)}}, {{A, B, C, X(6179), X(47847)}}, {{A, B, C, X(6292), X(41650)}}, {{A, B, C, X(6353), X(33202)}}, {{A, B, C, X(7757), X(26235)}}, {{A, B, C, X(7761), X(51454)}}, {{A, B, C, X(7778), X(37688)}}, {{A, B, C, X(7786), X(39998)}}, {{A, B, C, X(7811), X(10130)}}, {{A, B, C, X(7875), X(16988)}}, {{A, B, C, X(7931), X(17004)}}, {{A, B, C, X(8357), X(37453)}}, {{A, B, C, X(8770), X(17042)}}, {{A, B, C, X(9229), X(56067)}}, {{A, B, C, X(9462), X(42286)}}, {{A, B, C, X(9466), X(11059)}}, {{A, B, C, X(9516), X(57822)}}, {{A, B, C, X(14486), X(30499)}}, {{A, B, C, X(15048), X(21448)}}, {{A, B, C, X(17234), X(26244)}}, {{A, B, C, X(17980), X(30495)}}, {{A, B, C, X(21356), X(42850)}}, {{A, B, C, X(21358), X(22329)}}, {{A, B, C, X(22712), X(42313)}}, {{A, B, C, X(26243), X(33172)}}, {{A, B, C, X(27375), X(39951)}}, {{A, B, C, X(29011), X(30541)}}, {{A, B, C, X(31276), X(57518)}}, {{A, B, C, X(33025), X(38282)}}, {{A, B, C, X(33210), X(52290)}}, {{A, B, C, X(39749), X(57726)}}
X(60099) = barycentric product X(i)*X(j) for these (i, j): {11175, 76}
X(60099) = barycentric quotient X(i)/X(j) for these (i, j): {2, 11174}, {6, 5039}, {11175, 6}

X(60100) = X(2)X(7826)∩X(3)X(14488)

Barycentrics    (3*(a^2+b^2)+2*c^2)*(3*a^2+2*b^2+3*c^2) : :

X(60100) lies on the Kiepert hyperbola and on these lines: {2, 7826}, {3, 14488}, {4, 17508}, {5, 60132}, {6, 60278}, {30, 54717}, {76, 47355}, {83, 51126}, {98, 3628}, {140, 60142}, {141, 56059}, {262, 3526}, {316, 60146}, {321, 29630}, {547, 54934}, {548, 54890}, {549, 14492}, {597, 60279}, {598, 7911}, {631, 52519}, {632, 54920}, {671, 7859}, {1078, 60129}, {1656, 53100}, {1916, 6683}, {3090, 54845}, {3096, 18841}, {3407, 14065}, {3424, 7486}, {3533, 60330}, {3534, 54582}, {3589, 10159}, {3618, 60183}, {5055, 7943}, {5066, 54477}, {5067, 60322}, {5070, 60335}, {5072, 60326}, {5286, 60200}, {5485, 7803}, {6539, 29590}, {6656, 53109}, {6704, 11606}, {7375, 60305}, {7376, 60306}, {7388, 12818}, {7389, 12819}, {7607, 55860}, {7608, 55859}, {7745, 60282}, {7760, 18840}, {7768, 60182}, {7769, 60202}, {7770, 53105}, {7784, 60283}, {7786, 60180}, {7790, 38259}, {7812, 54616}, {7822, 54748}, {7827, 60216}, {7828, 60181}, {7834, 60214}, {7841, 54494}, {7846, 60190}, {7850, 43527}, {7852, 43535}, {7883, 60239}, {7886, 38223}, {7889, 43459}, {7899, 60215}, {7942, 60218}, {8370, 33698}, {10302, 48310}, {10303, 14484}, {10304, 54520}, {11289, 43547}, {11290, 43546}, {11303, 12821}, {11304, 12820}, {11540, 54734}, {12150, 55755}, {14036, 54540}, {14046, 54539}, {15022, 60147}, {15709, 60127}, {15717, 43951}, {16045, 60219}, {16896, 32450}, {16987, 31239}, {18842, 32006}, {18843, 32956}, {32829, 60201}, {32838, 60259}, {32884, 60262}, {32992, 60280}, {33699, 54813}, {37453, 60141}, {39784, 40344}, {41134, 60271}, {43688, 55767}, {46219, 60332}, {47352, 60131}, {47598, 60192}, {50693, 54706}, {55856, 60334}

X(60100) = isogonal conjugate of X(5041)
X(60100) = isotomic conjugate of X(34573)
X(60100) = trilinear pole of line {20063, 31299}
X(60100) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 5041}, {31, 34573}, {48, 52285}
X(60100) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 34573}, {3, 5041}, {1249, 52285}
X(60100) = X(i)-cross conjugate of X(j) for these {i, j}: {7927, 99}, {31065, 4577}, {51127, 2}
X(60100) = pole of line {51127, 60100} with respect to the Kiepert hyperbola
X(60100) = pole of line {5041, 34573} with respect to the Wallace hyperbola
X(60100) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(29630)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(17508)}}, {{A, B, C, X(6), X(47355)}}, {{A, B, C, X(39), X(729)}}, {{A, B, C, X(95), X(14387)}}, {{A, B, C, X(111), X(57421)}}, {{A, B, C, X(141), X(51126)}}, {{A, B, C, X(287), X(34483)}}, {{A, B, C, X(297), X(3628)}}, {{A, B, C, X(327), X(57927)}}, {{A, B, C, X(419), X(14043)}}, {{A, B, C, X(458), X(3526)}}, {{A, B, C, X(549), X(52289)}}, {{A, B, C, X(597), X(48310)}}, {{A, B, C, X(694), X(55075)}}, {{A, B, C, X(996), X(39730)}}, {{A, B, C, X(1016), X(13606)}}, {{A, B, C, X(1125), X(29590)}}, {{A, B, C, X(3225), X(39968)}}, {{A, B, C, X(3266), X(7859)}}, {{A, B, C, X(3329), X(16987)}}, {{A, B, C, X(3589), X(25322)}}, {{A, B, C, X(3978), X(6683)}}, {{A, B, C, X(5055), X(11331)}}, {{A, B, C, X(5117), X(14065)}}, {{A, B, C, X(6292), X(17949)}}, {{A, B, C, X(6704), X(40850)}}, {{A, B, C, X(7486), X(52283)}}, {{A, B, C, X(7770), X(37453)}}, {{A, B, C, X(7803), X(11059)}}, {{A, B, C, X(7826), X(13622)}}, {{A, B, C, X(7877), X(40826)}}, {{A, B, C, X(7917), X(35140)}}, {{A, B, C, X(8601), X(41440)}}, {{A, B, C, X(10014), X(52660)}}, {{A, B, C, X(10303), X(52288)}}, {{A, B, C, X(13623), X(48892)}}, {{A, B, C, X(14377), X(39729)}}, {{A, B, C, X(17042), X(54413)}}, {{A, B, C, X(17337), X(17398)}}, {{A, B, C, X(17352), X(17381)}}, {{A, B, C, X(18023), X(32027)}}, {{A, B, C, X(19829), X(30829)}}, {{A, B, C, X(20251), X(56004)}}, {{A, B, C, X(30541), X(43691)}}, {{A, B, C, X(32009), X(35172)}}, {{A, B, C, X(32015), X(35158)}}, {{A, B, C, X(34573), X(51127)}}, {{A, B, C, X(35146), X(42349)}}, {{A, B, C, X(39397), X(46284)}}, {{A, B, C, X(39979), X(40408)}}, {{A, B, C, X(52281), X(55859)}}, {{A, B, C, X(52282), X(55860)}}
X(60100) = barycentric product X(i)*X(j) for these (i, j): {34572, 76}
X(60100) = barycentric quotient X(i)/X(j) for these (i, j): {2, 34573}, {4, 52285}, {6, 5041}, {34572, 6}

X(60101) = X(2)X(5034)∩X(4)X(1078)

Barycentrics    ((a^2-b^2)^2-3*(a^2+b^2)*c^2)*(a^4-3*b^2*c^2+c^4-a^2*(3*b^2+2*c^2)) : :

X(60101) lies on the Kiepert hyperbola and on these lines: {2, 5034}, {4, 1078}, {6, 60096}, {30, 54718}, {32, 5395}, {69, 14494}, {76, 5013}, {83, 230}, {94, 26235}, {98, 35705}, {99, 15819}, {141, 8781}, {182, 7612}, {183, 262}, {316, 14485}, {325, 7608}, {381, 54714}, {385, 60098}, {598, 7610}, {599, 60211}, {671, 8356}, {1007, 10155}, {1691, 54906}, {1799, 30505}, {2080, 54868}, {2549, 2996}, {2986, 11056}, {3054, 60073}, {3314, 60233}, {3407, 17004}, {3926, 55797}, {3934, 60151}, {4027, 60136}, {5182, 15597}, {5392, 40022}, {5485, 52691}, {5939, 9751}, {6055, 9302}, {6393, 60202}, {7615, 32885}, {7763, 18840}, {7769, 10159}, {7771, 9756}, {7778, 60178}, {7787, 32897}, {7788, 54645}, {7793, 18845}, {7799, 10302}, {7806, 60129}, {7808, 32867}, {7809, 54724}, {7811, 54826}, {8556, 60095}, {9466, 54750}, {9752, 53127}, {9877, 43535}, {10104, 60117}, {10352, 17006}, {10753, 54978}, {11059, 59763}, {11140, 39998}, {11185, 54488}, {12150, 18842}, {13468, 54905}, {14061, 60072}, {15589, 53099}, {16986, 43529}, {16990, 60234}, {17008, 60190}, {19695, 53106}, {20423, 60127}, {21356, 60240}, {22329, 54509}, {31168, 54822}, {32458, 35005}, {32815, 52770}, {32833, 60143}, {32834, 43681}, {33023, 38259}, {33234, 53105}, {34803, 53098}, {37637, 60093}, {37647, 53108}, {37668, 60333}, {37671, 50985}, {37804, 60225}, {42006, 51373}, {43459, 58849}, {44377, 60198}, {46951, 60200}

X(60101) = reflection of X(i) in X(j) for these {i,j}: {99, 39100}
X(60101) = inverse of X(15819) in Wallace hyperbola
X(60101) = isogonal conjugate of X(5052)
X(60101) = isotomic conjugate of X(3815)
X(60101) = trilinear pole of line {39099, 523}
X(60101) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 5052}, {31, 3815}, {1918, 16740}, {1973, 48876}, {3402, 15819}
X(60101) = X(i)-vertex conjugate of X(j) for these {i, j}: {25, 83}, {32, 54906}, {3407, 42288}
X(60101) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 3815}, {3, 5052}, {6337, 48876}, {34021, 16740}, {51580, 15819}
X(60101) = X(i)-cross conjugate of X(j) for these {i, j}: {23878, 99}, {58446, 2}
X(60101) = pole of line {58446, 60101} with respect to the Kiepert hyperbola
X(60101) = pole of line {3815, 5052} with respect to the Wallace hyperbola
X(60101) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(5171)}}, {{A, B, C, X(6), X(5034)}}, {{A, B, C, X(25), X(11285)}}, {{A, B, C, X(32), X(5013)}}, {{A, B, C, X(69), X(34229)}}, {{A, B, C, X(95), X(308)}}, {{A, B, C, X(111), X(42288)}}, {{A, B, C, X(141), X(230)}}, {{A, B, C, X(182), X(1351)}}, {{A, B, C, X(183), X(3114)}}, {{A, B, C, X(249), X(5481)}}, {{A, B, C, X(276), X(31622)}}, {{A, B, C, X(297), X(37451)}}, {{A, B, C, X(305), X(32832)}}, {{A, B, C, X(325), X(37688)}}, {{A, B, C, X(427), X(32992)}}, {{A, B, C, X(468), X(8356)}}, {{A, B, C, X(524), X(11168)}}, {{A, B, C, X(599), X(7610)}}, {{A, B, C, X(729), X(21448)}}, {{A, B, C, X(1016), X(52133)}}, {{A, B, C, X(1078), X(1799)}}, {{A, B, C, X(1494), X(40826)}}, {{A, B, C, X(1502), X(40410)}}, {{A, B, C, X(1509), X(56358)}}, {{A, B, C, X(1989), X(42286)}}, {{A, B, C, X(2165), X(31360)}}, {{A, B, C, X(2373), X(57899)}}, {{A, B, C, X(2770), X(10130)}}, {{A, B, C, X(2998), X(45857)}}, {{A, B, C, X(3054), X(44377)}}, {{A, B, C, X(3228), X(11169)}}, {{A, B, C, X(3314), X(17004)}}, {{A, B, C, X(3620), X(57857)}}, {{A, B, C, X(5094), X(44543)}}, {{A, B, C, X(5970), X(51450)}}, {{A, B, C, X(6353), X(32990)}}, {{A, B, C, X(6393), X(48906)}}, {{A, B, C, X(6464), X(10014)}}, {{A, B, C, X(7763), X(40022)}}, {{A, B, C, X(7769), X(39998)}}, {{A, B, C, X(7778), X(37637)}}, {{A, B, C, X(7799), X(26235)}}, {{A, B, C, X(7806), X(16986)}}, {{A, B, C, X(7925), X(17006)}}, {{A, B, C, X(8556), X(8667)}}, {{A, B, C, X(8840), X(51373)}}, {{A, B, C, X(8889), X(32987)}}, {{A, B, C, X(9462), X(41909)}}, {{A, B, C, X(9516), X(30542)}}, {{A, B, C, X(14659), X(34238)}}, {{A, B, C, X(14665), X(39954)}}, {{A, B, C, X(15597), X(22110)}}, {{A, B, C, X(15819), X(23878)}}, {{A, B, C, X(16990), X(17008)}}, {{A, B, C, X(18023), X(55958)}}, {{A, B, C, X(19695), X(52297)}}, {{A, B, C, X(21356), X(23055)}}, {{A, B, C, X(25322), X(30537)}}, {{A, B, C, X(30541), X(40801)}}, {{A, B, C, X(31625), X(57881)}}, {{A, B, C, X(32020), X(40419)}}, {{A, B, C, X(32085), X(39968)}}, {{A, B, C, X(32152), X(51454)}}, {{A, B, C, X(32828), X(57518)}}, {{A, B, C, X(32991), X(52299)}}, {{A, B, C, X(33023), X(38282)}}, {{A, B, C, X(33234), X(37453)}}, {{A, B, C, X(33272), X(52290)}}, {{A, B, C, X(34816), X(45838)}}, {{A, B, C, X(52141), X(52691)}}, {{A, B, C, X(55967), X(57535)}}, {{A, B, C, X(57540), X(57569)}}
X(60101) = barycentric product X(i)*X(j) for these (i, j): {30535, 76}
X(60101) = barycentric quotient X(i)/X(j) for these (i, j): {2, 3815}, {6, 5052}, {69, 48876}, {183, 15819}, {274, 16740}, {30535, 6}
X(60101) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {15819, 46318, 99}

X(60102) = X(2)X(12007)∩X(5)X(18843)

Barycentrics    (7*a^4-6*a^2*b^2+7*b^4-10*(a^2+b^2)*c^2+3*c^4)*(7*a^4+3*b^4-10*b^2*c^2+7*c^4-2*a^2*(5*b^2+3*c^2)) : :

X(60102) lies on the Kiepert hyperbola and on these lines: {2, 12007}, {3, 55816}, {5, 18843}, {6, 60333}, {20, 53105}, {30, 54720}, {76, 10303}, {83, 7486}, {114, 10153}, {147, 60103}, {183, 60262}, {193, 60233}, {230, 14484}, {262, 37689}, {459, 37453}, {549, 5485}, {671, 10304}, {1513, 54845}, {2996, 15717}, {3091, 53109}, {3523, 43676}, {3526, 18840}, {3534, 32532}, {3543, 33698}, {3628, 18841}, {3839, 54494}, {4052, 50829}, {5055, 18842}, {5056, 53102}, {5066, 60281}, {5072, 18844}, {5304, 14494}, {5395, 15022}, {5503, 6036}, {5984, 8587}, {6776, 60175}, {6811, 60305}, {6813, 60306}, {7000, 12819}, {7374, 12818}, {7608, 37665}, {7735, 53099}, {8781, 15589}, {9740, 50985}, {9744, 54644}, {9752, 54890}, {9753, 60329}, {9754, 60323}, {9756, 60327}, {13860, 52519}, {15640, 17503}, {15683, 41895}, {15698, 54637}, {15709, 60143}, {17008, 60260}, {21845, 31683}, {21846, 31684}, {26288, 60224}, {26289, 60223}, {33699, 54647}, {34229, 60201}, {37637, 43537}, {37667, 60234}, {37688, 60259}, {38227, 60326}, {38259, 50693}, {43560, 48477}, {43561, 48476}, {49140, 53106}, {53015, 60324}, {55864, 60210}, {58883, 60322}

X(60102) = isogonal conjugate of X(5102)
X(60102) = X(i)-vertex conjugate of X(j) for these {i, j}: {25, 14484}, {1383, 14486}, {3425, 54845}
X(60102) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(55711)}}, {{A, B, C, X(20), X(37453)}}, {{A, B, C, X(25), X(10303)}}, {{A, B, C, X(66), X(46217)}}, {{A, B, C, X(95), X(44556)}}, {{A, B, C, X(183), X(37689)}}, {{A, B, C, X(193), X(17004)}}, {{A, B, C, X(230), X(15589)}}, {{A, B, C, X(253), X(45838)}}, {{A, B, C, X(254), X(53963)}}, {{A, B, C, X(393), X(12007)}}, {{A, B, C, X(427), X(7486)}}, {{A, B, C, X(468), X(10304)}}, {{A, B, C, X(549), X(4232)}}, {{A, B, C, X(1297), X(21448)}}, {{A, B, C, X(1383), X(43662)}}, {{A, B, C, X(2165), X(13622)}}, {{A, B, C, X(2963), X(34285)}}, {{A, B, C, X(3431), X(5966)}}, {{A, B, C, X(3526), X(6995)}}, {{A, B, C, X(3534), X(53857)}}, {{A, B, C, X(3563), X(40103)}}, {{A, B, C, X(3628), X(7378)}}, {{A, B, C, X(5055), X(52284)}}, {{A, B, C, X(5056), X(38433)}}, {{A, B, C, X(5304), X(34229)}}, {{A, B, C, X(5481), X(8770)}}, {{A, B, C, X(6353), X(15717)}}, {{A, B, C, X(8889), X(15022)}}, {{A, B, C, X(9740), X(23055)}}, {{A, B, C, X(11169), X(36948)}}, {{A, B, C, X(13606), X(57727)}}, {{A, B, C, X(13854), X(43834)}}, {{A, B, C, X(14486), X(39389)}}, {{A, B, C, X(14489), X(29180)}}, {{A, B, C, X(15321), X(46223)}}, {{A, B, C, X(15464), X(52188)}}, {{A, B, C, X(15640), X(52292)}}, {{A, B, C, X(15683), X(52290)}}, {{A, B, C, X(15709), X(52301)}}, {{A, B, C, X(17008), X(37667)}}, {{A, B, C, X(17040), X(46208)}}, {{A, B, C, X(37665), X(37688)}}, {{A, B, C, X(38282), X(50693)}}, {{A, B, C, X(40801), X(44763)}}, {{A, B, C, X(44658), X(52187)}}, {{A, B, C, X(45819), X(46952)}}, {{A, B, C, X(49140), X(52297)}}

X(60103) = X(2)X(5477)∩X(4)X(6055)

Barycentrics    (5*a^4-2*a^2*b^2+5*b^4-5*(a^2+b^2)*c^2+2*c^4)*(5*a^4+2*b^4-5*b^2*c^2+5*c^4-a^2*(5*b^2+2*c^2)) : :
X(60103) = 2*X[14830]+X[54659]

X(60103) lies on the Kiepert hyperbola and on these lines: {2, 5477}, {4, 6055}, {6, 60211}, {30, 60189}, {76, 7610}, {99, 5485}, {114, 53103}, {115, 41895}, {147, 60102}, {230, 671}, {262, 14848}, {385, 42010}, {485, 13681}, {486, 13801}, {524, 8781}, {542, 7612}, {543, 2996}, {598, 14061}, {1916, 8859}, {1992, 60240}, {2482, 60200}, {2794, 54894}, {3566, 9180}, {3849, 54872}, {5182, 15597}, {5215, 54750}, {5395, 14971}, {5461, 53101}, {5466, 9123}, {5503, 22329}, {5984, 54921}, {6036, 14494}, {6054, 7607}, {6722, 54639}, {7792, 54509}, {7806, 54487}, {8593, 37637}, {8860, 11167}, {9112, 55951}, {9113, 55950}, {9167, 60285}, {9740, 60262}, {9756, 54568}, {9771, 60198}, {9830, 60218}, {9877, 54122}, {10302, 11168}, {10723, 60176}, {11161, 44401}, {11163, 42011}, {11170, 12150}, {11172, 45018}, {11177, 43537}, {11184, 60178}, {12042, 54713}, {13468, 60202}, {13908, 33342}, {13968, 33343}, {14273, 60338}, {14830, 54659}, {15271, 60277}, {18800, 23053}, {19661, 38224}, {23234, 53104}, {30786, 54607}, {34229, 60143}, {35021, 54845}, {38259, 41135}, {41133, 54103}, {41139, 60073}, {42035, 52022}, {42036, 52021}, {43681, 52695}, {44534, 60280}, {47352, 60096}, {49102, 54869}, {54723, 58849}, {54916, 55164}, {55801, 60126}

X(60103) = reflection of X(i) in X(j) for these {i,j}: {41895, 115}, {99, 11147}
X(60103) = isogonal conjugate of X(5107)
X(60103) = isotomic conjugate of X(22110)
X(60103) = trilinear pole of line {1992, 38381}
X(60103) = X(i)-vertex conjugate of X(j) for these {i, j}: {25, 671}, {39644, 60280}
X(60103) = X(i)-cross conjugate of X(j) for these {i, j}: {2793, 99}, {11161, 671}, {39905, 648}, {44401, 2}
X(60103) = pole of line {11161, 44401} with respect to the Kiepert hyperbola
X(60103) = pole of line {5107, 22110} with respect to the Wallace hyperbola
X(60103) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(7610)}}, {{A, B, C, X(25), X(57729)}}, {{A, B, C, X(99), X(52141)}}, {{A, B, C, X(111), X(249)}}, {{A, B, C, X(230), X(524)}}, {{A, B, C, X(287), X(6055)}}, {{A, B, C, X(385), X(8859)}}, {{A, B, C, X(468), X(8598)}}, {{A, B, C, X(543), X(3566)}}, {{A, B, C, X(597), X(11168)}}, {{A, B, C, X(729), X(46316)}}, {{A, B, C, X(842), X(32901)}}, {{A, B, C, X(1494), X(40428)}}, {{A, B, C, X(1976), X(14659)}}, {{A, B, C, X(1992), X(23055)}}, {{A, B, C, X(2770), X(10554)}}, {{A, B, C, X(3054), X(9771)}}, {{A, B, C, X(3455), X(8770)}}, {{A, B, C, X(3815), X(15597)}}, {{A, B, C, X(4590), X(18818)}}, {{A, B, C, X(5306), X(13468)}}, {{A, B, C, X(6094), X(9164)}}, {{A, B, C, X(6323), X(21448)}}, {{A, B, C, X(6353), X(35287)}}, {{A, B, C, X(8860), X(11163)}}, {{A, B, C, X(9084), X(9123)}}, {{A, B, C, X(9166), X(30786)}}, {{A, B, C, X(9740), X(37689)}}, {{A, B, C, X(11161), X(34246)}}, {{A, B, C, X(11184), X(37637)}}, {{A, B, C, X(14061), X(42008)}}, {{A, B, C, X(14388), X(14565)}}, {{A, B, C, X(14848), X(56401)}}, {{A, B, C, X(15271), X(47352)}}, {{A, B, C, X(17983), X(18823)}}, {{A, B, C, X(22110), X(44401)}}, {{A, B, C, X(23582), X(57561)}}, {{A, B, C, X(30541), X(54172)}}, {{A, B, C, X(32697), X(35191)}}, {{A, B, C, X(34898), X(36953)}}, {{A, B, C, X(36616), X(39644)}}, {{A, B, C, X(41139), X(44377)}}, {{A, B, C, X(41357), X(47200)}}, {{A, B, C, X(43664), X(57895)}}

X(60104) = X(2)X(12829)∩X(76)X(620)

Barycentrics    (2*a^4-a^2*b^2+2*b^4-2*(a^2+b^2)*c^2+c^4)*(2*a^4+b^4-2*b^2*c^2+2*c^4-a^2*(2*b^2+c^2)) : :

X(60104) lies on the Kiepert hyperbola and on these lines: {2, 12829}, {4, 12042}, {6, 60233}, {30, 54723}, {76, 620}, {83, 7603}, {99, 43676}, {114, 7607}, {115, 33257}, {141, 60231}, {147, 7612}, {148, 60219}, {183, 43529}, {230, 1916}, {262, 6036}, {385, 8781}, {542, 60175}, {598, 14971}, {671, 13586}, {2023, 60177}, {2459, 60269}, {2460, 60270}, {2996, 20094}, {3329, 7608}, {3399, 42788}, {3406, 38743}, {4027, 37637}, {5058, 60194}, {5062, 60196}, {5395, 32963}, {5461, 54494}, {5466, 11176}, {5485, 33216}, {5503, 8859}, {5976, 43688}, {5984, 43537}, {5989, 60214}, {6054, 54644}, {6055, 14458}, {6671, 43538}, {6672, 43539}, {6721, 11668}, {6722, 53102}, {7735, 60234}, {7777, 60178}, {7787, 34127}, {7792, 60098}, {7797, 38739}, {7864, 38737}, {7874, 10159}, {7875, 60096}, {7880, 10302}, {7925, 56064}, {7945, 18840}, {8289, 54122}, {8290, 60181}, {8587, 44401}, {9166, 33698}, {9478, 54539}, {10352, 17006}, {11177, 60185}, {11599, 28550}, {11606, 44534}, {14061, 39590}, {14231, 43120}, {14245, 43121}, {14494, 16989}, {15300, 60228}, {17005, 60198}, {17008, 40824}, {18841, 32976}, {19696, 53106}, {22329, 42010}, {33193, 41895}, {33244, 38259}, {34229, 60232}, {35005, 36859}, {35021, 53100}, {37459, 43532}, {37667, 60262}, {37688, 42006}, {37689, 60260}, {38230, 60176}, {40108, 60126}, {43150, 53104}, {44531, 54540}, {51171, 60333}, {52886, 60250}, {54805, 55007}

X(60104) = reflection of X(i) in X(j) for these {i,j}: {53105, 115}, {99, 51581}
X(60104) = isogonal conjugate of X(5111)
X(60104) = isotomic conjugate of X(7925)
X(60104) = trilinear pole of line {3629, 18873}
X(60104) = X(i)-vertex conjugate of X(j) for these {i, j}: {25, 1916}, {11606, 39644}, {41533, 43535}
X(60104) = pole of line {5111, 7925} with respect to the Wallace hyperbola
X(60104) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(17004)}}, {{A, B, C, X(25), X(7907)}}, {{A, B, C, X(67), X(40429)}}, {{A, B, C, X(111), X(620)}}, {{A, B, C, X(114), X(46807)}}, {{A, B, C, X(141), X(16984)}}, {{A, B, C, X(183), X(7806)}}, {{A, B, C, X(193), X(46208)}}, {{A, B, C, X(230), X(385)}}, {{A, B, C, X(249), X(5966)}}, {{A, B, C, X(251), X(5058)}}, {{A, B, C, X(427), X(32967)}}, {{A, B, C, X(468), X(11176)}}, {{A, B, C, X(523), X(57926)}}, {{A, B, C, X(699), X(1569)}}, {{A, B, C, X(733), X(46316)}}, {{A, B, C, X(1031), X(40410)}}, {{A, B, C, X(1297), X(14565)}}, {{A, B, C, X(1691), X(46314)}}, {{A, B, C, X(1972), X(57562)}}, {{A, B, C, X(1989), X(4590)}}, {{A, B, C, X(2459), X(2460)}}, {{A, B, C, X(2786), X(28550)}}, {{A, B, C, X(2963), X(40416)}}, {{A, B, C, X(2966), X(14734)}}, {{A, B, C, X(3054), X(17005)}}, {{A, B, C, X(3228), X(36953)}}, {{A, B, C, X(3329), X(37688)}}, {{A, B, C, X(3455), X(7863)}}, {{A, B, C, X(3815), X(17006)}}, {{A, B, C, X(4232), X(33216)}}, {{A, B, C, X(5481), X(43120)}}, {{A, B, C, X(5970), X(17980)}}, {{A, B, C, X(6036), X(46806)}}, {{A, B, C, X(6353), X(32964)}}, {{A, B, C, X(6995), X(32977)}}, {{A, B, C, X(7378), X(32976)}}, {{A, B, C, X(7603), X(23297)}}, {{A, B, C, X(7735), X(17008)}}, {{A, B, C, X(7777), X(37637)}}, {{A, B, C, X(7874), X(39998)}}, {{A, B, C, X(7875), X(15271)}}, {{A, B, C, X(7880), X(26235)}}, {{A, B, C, X(7886), X(8024)}}, {{A, B, C, X(7891), X(8770)}}, {{A, B, C, X(7945), X(40022)}}, {{A, B, C, X(8859), X(22329)}}, {{A, B, C, X(8889), X(32963)}}, {{A, B, C, X(9164), X(18818)}}, {{A, B, C, X(9229), X(45838)}}, {{A, B, C, X(9477), X(40428)}}, {{A, B, C, X(11060), X(14658)}}, {{A, B, C, X(12042), X(57799)}}, {{A, B, C, X(14971), X(42008)}}, {{A, B, C, X(16989), X(34229)}}, {{A, B, C, X(17983), X(35511)}}, {{A, B, C, X(18023), X(40511)}}, {{A, B, C, X(19696), X(52297)}}, {{A, B, C, X(30610), X(53874)}}, {{A, B, C, X(33193), X(52290)}}, {{A, B, C, X(33244), X(38282)}}, {{A, B, C, X(33257), X(37453)}}, {{A, B, C, X(34238), X(46322)}}, {{A, B, C, X(34816), X(57943)}}, {{A, B, C, X(36864), X(36897)}}, {{A, B, C, X(36955), X(43663)}}, {{A, B, C, X(37667), X(37689)}}, {{A, B, C, X(38741), X(51454)}}, {{A, B, C, X(39968), X(44571)}}, {{A, B, C, X(40826), X(52154)}}, {{A, B, C, X(42332), X(45108)}}, {{A, B, C, X(43098), X(56057)}}, {{A, B, C, X(43188), X(53603)}}, {{A, B, C, X(51316), X(56360)}}, {{A, B, C, X(52141), X(52695)}}, {{A, B, C, X(55999), X(57729)}}
X(60104) = barycentric product X(i)*X(j) for these (i, j): {18873, 290}
X(60104) = barycentric quotient X(i)/X(j) for these (i, j): {2, 7925}, {6, 5111}, {18873, 511}

X(60105) = X(2)X(2076)∩X(6)X(11606)

Barycentrics    (a^4+3*a^2*b^2+b^4+(a^2+b^2)*c^2-c^4)*(a^4-b^4+b^2*c^2+c^4+a^2*(b^2+3*c^2)) : :

X(60105) lies on the Kiepert hyperbola and on these lines: {2, 2076}, {4, 44090}, {6, 11606}, {30, 54724}, {76, 5475}, {83, 4045}, {98, 19130}, {262, 40236}, {381, 9302}, {626, 10159}, {671, 7753}, {1916, 35705}, {2996, 33018}, {3399, 14881}, {3406, 10796}, {3407, 53504}, {3543, 54826}, {3839, 54678}, {3972, 33021}, {5149, 19686}, {5395, 33019}, {5476, 14458}, {5485, 33016}, {6033, 22681}, {6034, 43535}, {7533, 60111}, {7736, 60177}, {7745, 39089}, {7766, 54122}, {7774, 43688}, {7777, 35005}, {7791, 18841}, {7806, 60136}, {7809, 10302}, {7889, 43459}, {7897, 60232}, {7944, 56059}, {8176, 60131}, {9866, 24256}, {10997, 53484}, {11361, 54822}, {14494, 37182}, {14930, 38259}, {16924, 18840}, {16989, 60184}, {18842, 33017}, {18843, 33279}, {19689, 34885}, {32968, 60183}, {32983, 60143}, {32986, 54616}, {37187, 60137}, {37242, 60148}, {37348, 44434}, {37349, 55028}, {40246, 54804}, {42535, 60128}, {54901, 59373}

X(60105) = isogonal conjugate of X(5116)
X(60105) = trilinear pole of line {5113, 32218}
X(60105) = pole of line {3329, 60105} with respect to the Kiepert hyperbola
X(60105) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(1031)}}, {{A, B, C, X(25), X(16044)}}, {{A, B, C, X(32), X(46313)}}, {{A, B, C, X(80), X(40738)}}, {{A, B, C, X(251), X(7785)}}, {{A, B, C, X(427), X(6655)}}, {{A, B, C, X(428), X(33020)}}, {{A, B, C, X(458), X(40236)}}, {{A, B, C, X(626), X(59180)}}, {{A, B, C, X(694), X(51450)}}, {{A, B, C, X(695), X(3108)}}, {{A, B, C, X(699), X(8601)}}, {{A, B, C, X(733), X(27375)}}, {{A, B, C, X(1383), X(5475)}}, {{A, B, C, X(2998), X(43726)}}, {{A, B, C, X(3228), X(22336)}}, {{A, B, C, X(3521), X(57799)}}, {{A, B, C, X(3613), X(5103)}}, {{A, B, C, X(3832), X(37187)}}, {{A, B, C, X(4045), X(31125)}}, {{A, B, C, X(4232), X(33016)}}, {{A, B, C, X(5064), X(33021)}}, {{A, B, C, X(5169), X(40889)}}, {{A, B, C, X(5481), X(54998)}}, {{A, B, C, X(6353), X(33018)}}, {{A, B, C, X(6664), X(40425)}}, {{A, B, C, X(6995), X(16924)}}, {{A, B, C, X(7378), X(7791)}}, {{A, B, C, X(7391), X(37337)}}, {{A, B, C, X(7408), X(32968)}}, {{A, B, C, X(7409), X(16043)}}, {{A, B, C, X(7533), X(46511)}}, {{A, B, C, X(7753), X(52898)}}, {{A, B, C, X(7759), X(34154)}}, {{A, B, C, X(7766), X(7774)}}, {{A, B, C, X(7855), X(9515)}}, {{A, B, C, X(7897), X(16989)}}, {{A, B, C, X(8024), X(46225)}}, {{A, B, C, X(8878), X(46227)}}, {{A, B, C, X(8889), X(33019)}}, {{A, B, C, X(13377), X(46275)}}, {{A, B, C, X(14356), X(19130)}}, {{A, B, C, X(14608), X(31068)}}, {{A, B, C, X(14930), X(20080)}}, {{A, B, C, X(15321), X(39968)}}, {{A, B, C, X(23297), X(33666)}}, {{A, B, C, X(24256), X(59249)}}, {{A, B, C, X(30496), X(39951)}}, {{A, B, C, X(30535), X(43702)}}, {{A, B, C, X(30537), X(57926)}}, {{A, B, C, X(32983), X(52301)}}, {{A, B, C, X(33017), X(52284)}}, {{A, B, C, X(35705), X(57452)}}, {{A, B, C, X(36953), X(40416)}}, {{A, B, C, X(37841), X(43950)}}, {{A, B, C, X(40826), X(45819)}}, {{A, B, C, X(42286), X(43098)}}, {{A, B, C, X(44144), X(48901)}}, {{A, B, C, X(51510), X(54129)}}, {{A, B, C, X(54120), X(55940)}}

X(60106) = X(2)X(512)∩X(4)X(2489)

Barycentrics    (b-c)*(b+c)*(-2*a^2*b^2+(a^2+b^2)*c^2)*(b^2*c^2+a^2*(b^2-2*c^2)) : :
X(60106) = -5*X[7786]+2*X[14824], -2*X[9489]+3*X[15724]

X(60106) lies on the Kiepert hyperbola and on these lines: {2, 512}, {4, 2489}, {10, 4079}, {13, 11618}, {14, 11617}, {17, 58869}, {18, 58870}, {30, 54725}, {76, 523}, {83, 18105}, {94, 15475}, {98, 729}, {115, 62155}, {262, 1499}, {275, 58756}, {321, 4705}, {381, 54902}, {485, 58825}, {486, 58827}, {511, 54811}, {524, 54603}, {525, 62109}, {542, 54881}, {598, 25423}, {669, 3972}, {671, 804}, {688, 54621}, {690, 882}, {691, 9150}, {876, 40017}, {881, 886}, {887, 11176}, {1503, 54600}, {2052, 58757}, {2793, 43532}, {2794, 54631}, {3143, 43665}, {3399, 32473}, {3566, 62024}, {3667, 62249}, {3849, 54607}, {3906, 43688}, {4785, 55949}, {5475, 44445}, {5485, 23878}, {5503, 59775}, {7786, 14824}, {8704, 62055}, {8781, 35364}, {9009, 22486}, {9147, 46156}, {9148, 34087}, {9489, 15724}, {9830, 54602}, {11645, 54651}, {12073, 42006}, {14398, 54541}, {14431, 43685}, {14458, 30217}, {14560, 32717}, {16080, 47206}, {24624, 37132}, {27550, 43539}, {27551, 43538}, {28470, 62101}, {32014, 50344}, {32696, 62108}, {40016, 52618}, {40162, 57082}, {41880, 57575}, {41881, 57576}, {54750, 55122} X(60106) lies on the Kiepert hyperbola and on these lines: {2, 512}, {4, 2489}, {10, 4079}, {13, 11618}, {14, 11617}, {17, 58869}, {18, 58870}, {30, 54725}, {76, 523}, {83, 18105}, {94, 15475}, {98, 729}, {115, 62155}, {262, 1499}, {275, 58756}, {321, 4705}, {381, 54902}, {485, 58825}, {486, 58827}, {511, 54811}, {524, 54603}, {525, 62109}, {542, 54881}, {598, 25423}, {669, 3972}, {671, 804}, {688, 54621}, {690, 882}, {691, 9150}, {876, 40017}, {881, 886}, {887, 11176}, {1503, 54600}, {2052, 58757}, {2793, 43532}, {2794, 54631}, {3143, 43665}, {3399, 32473}, {3566, 62024}, {3667, 62249}, {3849, 54607}, {3906, 43688}, {4785, 55949}, {5475, 44445}, {5485, 23878}, {5503, 59775}, {7786, 14824}, {8704, 62055}, {8781, 35364}, {9009, 22486}, {9147, 46156}, {9148, 34087}, {9489, 15724}, {9830, 54602}, {11645, 54651}, {12073, 42006}, {14398, 54541}, {14431, 43685}, {14458, 30217}, {14560, 32717}, {16080, 47206}, {24624, 37132}, {27550, 43539}, {27551, 43538}, {28470, 62101}, {32014, 50344}, {32696, 62108}, {40016, 52618}, {40162, 57082}, {41880, 57575}, {41881, 57576}, {54750, 55122}

X(60106) = reflection of X(i) in X(j) for these {i,j}: {62155, 115}, {887, 11176}
X(60106) = isogonal conjugate of X(5118)
X(60106) = isotomic conjugate of X(23342)
X(60106) = trilinear pole of line {3124, 523}
X(60106) = perspector of circumconic {{A, B, C, X(3228), X(34087)}}
X(60106) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 5118}, {31, 23342}, {110, 2234}, {163, 538}, {662, 3231}, {799, 33875}, {887, 24037}, {888, 24041}, {1101, 9148}, {4556, 52893}, {4592, 46522}, {4599, 52961}, {6786, 36084}, {14609, 23889}, {23997, 36822}, {30938, 32739}, {36133, 52067}, {36142, 45672}, {52894, 52935}
X(60106) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 54600}
X(60106) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 23342}, {3, 5118}, {115, 538}, {244, 2234}, {512, 887}, {523, 9148}, {1084, 3231}, {3005, 888}, {3124, 52961}, {5139, 46522}, {23992, 45672}, {36901, 30736}, {38987, 6786}, {38996, 33875}, {39010, 52067}, {40619, 30938}
X(60106) = X(i)-Ceva conjugate of X(j) for these {i, j}: {9150, 3228}, {57993, 34087}
X(60106) = X(i)-cross conjugate of X(j) for these {i, j}: {9148, 523}, {33228, 42345}, {52625, 76}
X(60106) = pole of line {5118, 7757} with respect to the 1st Brocard circle
X(60106) = pole of line {7757, 11634} with respect to the 2nd Brocard circle
X(60106) = pole of line {3228, 5201} with respect to the circumcircle
X(60106) = pole of line {76, 23342} with respect to the orthocentroidal circle
X(60106) = pole of line {511, 3124} with respect to the orthoptic circle of the Steiner inellipse
X(60106) = pole of line {538, 46522} with respect to the polar circle
X(60106) = pole of line {52625, 60106} with respect to the Kiepert hyperbola
X(60106) = pole of line {5118, 38366} with respect to the Stammler hyperbola
X(60106) = pole of line {538, 59765} with respect to the Steiner inellipse
X(60106) = pole of line {5118, 23342} with respect to the Wallace hyperbola
X(60106) = pole of line {30736, 34087} with respect to the dual conic of Brocard inellipse
X(60106) = pole of line {888, 6786} with respect to the dual conic of Wallace hyperbola
X(60106) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(3111)}}, {{A, B, C, X(25), X(36165)}}, {{A, B, C, X(99), X(2395)}}, {{A, B, C, X(115), X(11182)}}, {{A, B, C, X(264), X(6787)}}, {{A, B, C, X(290), X(47044)}}, {{A, B, C, X(305), X(14700)}}, {{A, B, C, X(325), X(14898)}}, {{A, B, C, X(512), X(523)}}, {{A, B, C, X(525), X(32472)}}, {{A, B, C, X(690), X(804)}}, {{A, B, C, X(729), X(52765)}}, {{A, B, C, X(843), X(46142)}}, {{A, B, C, X(850), X(5996)}}, {{A, B, C, X(881), X(23099)}}, {{A, B, C, X(1499), X(23878)}}, {{A, B, C, X(1637), X(47206)}}, {{A, B, C, X(3124), X(52721)}}, {{A, B, C, X(3143), X(4230)}}, {{A, B, C, X(3228), X(14608)}}, {{A, B, C, X(3906), X(25423)}}, {{A, B, C, X(4108), X(8599)}}, {{A, B, C, X(9148), X(52625)}}, {{A, B, C, X(9293), X(45693)}}, {{A, B, C, X(9513), X(14948)}}, {{A, B, C, X(10630), X(36897)}}, {{A, B, C, X(12065), X(52475)}}, {{A, B, C, X(14356), X(43917)}}, {{A, B, C, X(15421), X(21732)}}, {{A, B, C, X(34246), X(34290)}}, {{A, B, C, X(39680), X(56748)}}, {{A, B, C, X(52145), X(53604)}}, {{A, B, C, X(53221), X(53919)}}, {{A, B, C, X(56957), X(57583)}}
X(60106) = barycentric product X(i)*X(j) for these (i, j): {115, 9150}, {729, 850}, {1084, 57993}, {1109, 36133}, {1577, 37132}, {2394, 52752}, {3124, 886}, {3228, 523}, {14608, 5466}, {32717, 338}, {34087, 512}, {35366, 83}, {41309, 52632}, {43665, 52765}, {46156, 52618}, {52762, 9180}, {57459, 62109}, {57540, 9148}
X(60106) = barycentric quotient X(i)/X(j) for these (i, j): {2, 23342}, {6, 5118}, {115, 9148}, {512, 3231}, {523, 538}, {661, 2234}, {669, 33875}, {690, 45672}, {693, 30938}, {729, 110}, {850, 30736}, {886, 34537}, {888, 52067}, {1084, 887}, {2395, 36822}, {2489, 46522}, {3005, 52961}, {3124, 888}, {3228, 99}, {3569, 6786}, {4079, 52894}, {4705, 52893}, {5466, 52756}, {9148, 35073}, {9150, 4590}, {9178, 14609}, {14608, 5468}, {22260, 52625}, {23099, 1645}, {32717, 249}, {34087, 670}, {35366, 141}, {36133, 24041}, {37132, 662}, {41309, 5467}, {46156, 1634}, {51510, 17941}, {52752, 2407}, {52762, 9182}, {52765, 2421}, {57459, 14614}, {57540, 9150}, {57993, 44168}

X(60107) = X(2)X(4254)∩X(10)X(497)

Barycentrics    ((a-b)*(a+b)^2+(a^2-4*a*b-b^2)*c+(a+b)*c^2+c^3)*(a^3+a^2*(b+c)+(b-c)*(b+c)^2+a*(b^2-4*b*c-c^2)) : :

X(60107) lies on the Kiepert hyperbola and on these lines: {2, 4254}, {3, 60157}, {4, 4383}, {5, 60158}, {6, 60076}, {10, 497}, {30, 54726}, {69, 40012}, {76, 14555}, {81, 60169}, {226, 2999}, {321, 18228}, {376, 54757}, {377, 60077}, {381, 54688}, {443, 43531}, {459, 26005}, {631, 60164}, {966, 60084}, {1029, 7382}, {1058, 44307}, {1211, 18840}, {1446, 5813}, {1751, 37650}, {2270, 8808}, {2478, 43533}, {2895, 40021}, {3090, 60154}, {3524, 54727}, {3525, 60173}, {3545, 54758}, {3618, 14534}, {4052, 31142}, {4080, 19789}, {4423, 19866}, {5233, 60254}, {5397, 6854}, {5712, 17758}, {5739, 40013}, {5741, 60242}, {5802, 17825}, {6818, 13576}, {6822, 56161}, {6833, 60174}, {6834, 60166}, {6864, 54972}, {6865, 21363}, {6896, 57710}, {6899, 57720}, {6947, 60112}, {6949, 60159}, {6952, 60162}, {7381, 55027}, {7386, 60153}, {7392, 60152}, {14484, 26118}, {17277, 60206}, {32911, 60156}, {36731, 54880}, {37185, 60168}, {37276, 56346}, {37456, 43951}, {37642, 60085}, {37663, 45098}, {37680, 60155}, {37681, 60167}, {41099, 54789}, {41106, 54947}, {41867, 56226}

X(60107) = isogonal conjugate of X(5120)
X(60107) = isotomic conjugate of X(18141)
X(60107) = trilinear pole of line {47921, 523}
X(60107) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 5120}, {31, 18141}, {48, 4200}
X(60107) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 18141}, {3, 5120}, {1249, 4200}
X(60107) = X(i)-cross conjugate of X(j) for these {i, j}: {12701, 7}, {21871, 1}, {37679, 2}
X(60107) = pole of line {37679, 60107} with respect to the Kiepert hyperbola
X(60107) = pole of line {5120, 18141} with respect to the Wallace hyperbola
X(60107) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(31435)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(36745)}}, {{A, B, C, X(6), X(210)}}, {{A, B, C, X(7), X(4328)}}, {{A, B, C, X(8), X(57)}}, {{A, B, C, X(19), X(56207)}}, {{A, B, C, X(21), X(56231)}}, {{A, B, C, X(27), X(5084)}}, {{A, B, C, X(63), X(55964)}}, {{A, B, C, X(69), X(4383)}}, {{A, B, C, X(80), X(189)}}, {{A, B, C, X(81), X(1000)}}, {{A, B, C, X(84), X(56230)}}, {{A, B, C, X(88), X(2994)}}, {{A, B, C, X(89), X(7317)}}, {{A, B, C, X(90), X(55987)}}, {{A, B, C, X(92), X(277)}}, {{A, B, C, X(104), X(56354)}}, {{A, B, C, X(196), X(21370)}}, {{A, B, C, X(223), X(2270)}}, {{A, B, C, X(278), X(312)}}, {{A, B, C, X(279), X(12575)}}, {{A, B, C, X(294), X(5813)}}, {{A, B, C, X(329), X(38271)}}, {{A, B, C, X(443), X(469)}}, {{A, B, C, X(445), X(6896)}}, {{A, B, C, X(451), X(7382)}}, {{A, B, C, X(521), X(55112)}}, {{A, B, C, X(941), X(56255)}}, {{A, B, C, X(957), X(2221)}}, {{A, B, C, X(967), X(57705)}}, {{A, B, C, X(1016), X(39696)}}, {{A, B, C, X(1119), X(2997)}}, {{A, B, C, X(1121), X(42304)}}, {{A, B, C, X(1211), X(3618)}}, {{A, B, C, X(1214), X(15740)}}, {{A, B, C, X(1246), X(57858)}}, {{A, B, C, X(1255), X(3296)}}, {{A, B, C, X(1258), X(34260)}}, {{A, B, C, X(1422), X(3680)}}, {{A, B, C, X(1427), X(41506)}}, {{A, B, C, X(1465), X(15509)}}, {{A, B, C, X(1824), X(39951)}}, {{A, B, C, X(2006), X(6557)}}, {{A, B, C, X(2316), X(57418)}}, {{A, B, C, X(2321), X(52223)}}, {{A, B, C, X(2339), X(2982)}}, {{A, B, C, X(2478), X(7490)}}, {{A, B, C, X(2481), X(40154)}}, {{A, B, C, X(2895), X(14997)}}, {{A, B, C, X(3091), X(37276)}}, {{A, B, C, X(3227), X(42360)}}, {{A, B, C, X(4102), X(9311)}}, {{A, B, C, X(4209), X(28137)}}, {{A, B, C, X(4358), X(19789)}}, {{A, B, C, X(4423), X(34585)}}, {{A, B, C, X(4848), X(37655)}}, {{A, B, C, X(4997), X(54361)}}, {{A, B, C, X(5120), X(21871)}}, {{A, B, C, X(5226), X(41867)}}, {{A, B, C, X(5233), X(37642)}}, {{A, B, C, X(5435), X(31142)}}, {{A, B, C, X(5559), X(39980)}}, {{A, B, C, X(5712), X(17277)}}, {{A, B, C, X(5739), X(32911)}}, {{A, B, C, X(5741), X(24597)}}, {{A, B, C, X(6598), X(56199)}}, {{A, B, C, X(6605), X(11578)}}, {{A, B, C, X(6650), X(39703)}}, {{A, B, C, X(6818), X(15149)}}, {{A, B, C, X(6819), X(6833)}}, {{A, B, C, X(6820), X(6834)}}, {{A, B, C, X(6856), X(37181)}}, {{A, B, C, X(6865), X(37279)}}, {{A, B, C, X(6899), X(57531)}}, {{A, B, C, X(6949), X(37192)}}, {{A, B, C, X(6994), X(17559)}}, {{A, B, C, X(7003), X(39943)}}, {{A, B, C, X(7224), X(56163)}}, {{A, B, C, X(7261), X(8817)}}, {{A, B, C, X(7319), X(39963)}}, {{A, B, C, X(7320), X(39948)}}, {{A, B, C, X(7381), X(52252)}}, {{A, B, C, X(8814), X(57818)}}, {{A, B, C, X(10305), X(56234)}}, {{A, B, C, X(10429), X(57661)}}, {{A, B, C, X(11604), X(38255)}}, {{A, B, C, X(14497), X(56041)}}, {{A, B, C, X(15314), X(58002)}}, {{A, B, C, X(15474), X(18359)}}, {{A, B, C, X(18134), X(37650)}}, {{A, B, C, X(18141), X(37679)}}, {{A, B, C, X(18490), X(27789)}}, {{A, B, C, X(26005), X(37669)}}, {{A, B, C, X(26118), X(52288)}}, {{A, B, C, X(30479), X(43071)}}, {{A, B, C, X(30513), X(56201)}}, {{A, B, C, X(30701), X(55988)}}, {{A, B, C, X(30710), X(39721)}}, {{A, B, C, X(30711), X(44794)}}, {{A, B, C, X(32008), X(44733)}}, {{A, B, C, X(34051), X(56089)}}, {{A, B, C, X(34234), X(34546)}}, {{A, B, C, X(34259), X(45127)}}, {{A, B, C, X(36100), X(39947)}}, {{A, B, C, X(36603), X(43731)}}, {{A, B, C, X(37086), X(37394)}}, {{A, B, C, X(37887), X(50442)}}, {{A, B, C, X(39797), X(57744)}}, {{A, B, C, X(40397), X(43742)}}, {{A, B, C, X(40399), X(42467)}}, {{A, B, C, X(40434), X(43733)}}, {{A, B, C, X(43745), X(52374)}}, {{A, B, C, X(46108), X(51400)}}, {{A, B, C, X(56224), X(59760)}}, {{A, B, C, X(57663), X(57666)}}
X(60107) = barycentric quotient X(i)/X(j) for these (i, j): {2, 18141}, {4, 4200}, {6, 5120}

X(60108) = X(2)X(3786)∩X(4)X(5283)

Barycentrics    (2*a^2*b^2+2*a*b*(a+b)*c+(a+b)^2*c^2-c^4)*(-b^4+b^2*c^2+2*a*b*c*(b+c)+a^2*(b^2+2*b*c+2*c^2)) : :

X(60108) lies on the Kiepert hyperbola and on these lines: {2, 3786}, {4, 5283}, {6, 60081}, {9, 40718}, {25, 40395}, {30, 54729}, {76, 442}, {83, 405}, {98, 5275}, {181, 60188}, {226, 984}, {262, 37661}, {321, 3790}, {381, 54692}, {386, 60075}, {452, 5395}, {573, 56144}, {598, 11113}, {612, 60088}, {671, 17532}, {991, 7413}, {1446, 7179}, {1655, 2996}, {2052, 25985}, {2092, 56161}, {3487, 56542}, {4253, 43531}, {5276, 60080}, {5485, 50741}, {5542, 56226}, {5988, 11608}, {6829, 54739}, {6907, 54821}, {6998, 54972}, {7380, 57719}, {9534, 32022}, {10445, 54668}, {14534, 37507}, {16845, 18841}, {16999, 60128}, {26052, 60156}, {30116, 60135}, {37330, 60071}, {42758, 47975}, {43684, 57518}, {47511, 60082}, {48841, 60094}

X(60108) = isogonal conjugate of X(5138)
X(60108) = isotomic conjugate of X(16992)
X(60108) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 5138}, {6, 54419}, {31, 16992}, {48, 11341}
X(60108) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 16992}, {3, 5138}, {9, 54419}, {1249, 11341}
X(60108) = pole of line {5138, 16992} with respect to the Wallace hyperbola
X(60108) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(5208)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(25985)}}, {{A, B, C, X(6), X(4260)}}, {{A, B, C, X(7), X(9108)}}, {{A, B, C, X(9), X(984)}}, {{A, B, C, X(12), X(52651)}}, {{A, B, C, X(25), X(181)}}, {{A, B, C, X(37), X(264)}}, {{A, B, C, X(65), X(35612)}}, {{A, B, C, X(66), X(40412)}}, {{A, B, C, X(72), X(305)}}, {{A, B, C, X(105), X(994)}}, {{A, B, C, X(183), X(37661)}}, {{A, B, C, X(256), X(58008)}}, {{A, B, C, X(325), X(5275)}}, {{A, B, C, X(386), X(3108)}}, {{A, B, C, X(405), X(427)}}, {{A, B, C, X(406), X(26052)}}, {{A, B, C, X(452), X(8889)}}, {{A, B, C, X(468), X(17532)}}, {{A, B, C, X(573), X(991)}}, {{A, B, C, X(941), X(1441)}}, {{A, B, C, X(943), X(1390)}}, {{A, B, C, X(1002), X(40216)}}, {{A, B, C, X(1362), X(3126)}}, {{A, B, C, X(1655), X(57518)}}, {{A, B, C, X(2092), X(37507)}}, {{A, B, C, X(2726), X(57726)}}, {{A, B, C, X(3006), X(30116)}}, {{A, B, C, X(3263), X(47975)}}, {{A, B, C, X(3613), X(39983)}}, {{A, B, C, X(3920), X(30172)}}, {{A, B, C, X(4232), X(50741)}}, {{A, B, C, X(4492), X(58007)}}, {{A, B, C, X(5094), X(11113)}}, {{A, B, C, X(5136), X(37330)}}, {{A, B, C, X(5142), X(47511)}}, {{A, B, C, X(5177), X(6353)}}, {{A, B, C, X(5665), X(7249)}}, {{A, B, C, X(6598), X(33111)}}, {{A, B, C, X(6913), X(26020)}}, {{A, B, C, X(6937), X(35973)}}, {{A, B, C, X(7018), X(31359)}}, {{A, B, C, X(7378), X(16845)}}, {{A, B, C, X(7380), X(37279)}}, {{A, B, C, X(7413), X(17555)}}, {{A, B, C, X(7777), X(16999)}}, {{A, B, C, X(8770), X(43074)}}, {{A, B, C, X(8801), X(57858)}}, {{A, B, C, X(16601), X(56542)}}, {{A, B, C, X(16830), X(32778)}}, {{A, B, C, X(17040), X(57866)}}, {{A, B, C, X(19858), X(29667)}}, {{A, B, C, X(20565), X(39737)}}, {{A, B, C, X(30571), X(32023)}}, {{A, B, C, X(37224), X(37362)}}, {{A, B, C, X(39951), X(57689)}}
X(60108) = barycentric product X(i)*X(j) for these (i, j): {45966, 76}
X(60108) = barycentric quotient X(i)/X(j) for these (i, j): {1, 54419}, {2, 16992}, {4, 11341}, {6, 5138}, {45966, 6}

X(60109) = X(2)X(4279)∩X(43)X(321)

Barycentrics    (a^3*(b+c)+a*b^2*(b+c)+b^2*c*(b+c)+a^2*(b^2+b*c+c^2))*(a^3*(b+c)+a*c^2*(b+c)+b*c^2*(b+c)+a^2*(b^2+b*c+c^2)) : :

X(60109) lies on the Kiepert hyperbola and on these lines: {1, 60244}, {2, 4279}, {3, 60320}, {4, 54388}, {6, 33688}, {10, 2176}, {32, 37148}, {43, 321}, {76, 386}, {86, 40031}, {182, 13478}, {226, 1403}, {262, 573}, {381, 54701}, {893, 3923}, {1078, 32014}, {1125, 22520}, {1916, 3029}, {2051, 19540}, {2162, 33682}, {2238, 60110}, {3993, 39967}, {4201, 6625}, {4660, 40718}, {6539, 59296}, {7793, 25526}, {7808, 60075}, {9534, 56210}, {10789, 32772}, {10791, 60089}, {17379, 51449}, {25453, 60088}, {29825, 30588}, {30116, 60288}, {37632, 40017}, {41269, 43534}, {48813, 54770}, {56197, 59299}, {56737, 58012}, {56969, 60078}, {59312, 60203}

X(60109) = isogonal conjugate of X(5145)
X(60109) = trilinear pole of line {20979, 523}
X(60109) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(43)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(54388)}}, {{A, B, C, X(6), X(4279)}}, {{A, B, C, X(8), X(6685)}}, {{A, B, C, X(32), X(42)}}, {{A, B, C, X(58), X(3223)}}, {{A, B, C, X(79), X(6384)}}, {{A, B, C, X(81), X(56138)}}, {{A, B, C, X(86), X(3551)}}, {{A, B, C, X(87), X(45988)}}, {{A, B, C, X(182), X(573)}}, {{A, B, C, X(192), X(33682)}}, {{A, B, C, X(291), X(994)}}, {{A, B, C, X(350), X(41269)}}, {{A, B, C, X(444), X(1008)}}, {{A, B, C, X(469), X(37148)}}, {{A, B, C, X(594), X(5224)}}, {{A, B, C, X(596), X(39741)}}, {{A, B, C, X(731), X(17961)}}, {{A, B, C, X(870), X(1929)}}, {{A, B, C, X(894), X(3923)}}, {{A, B, C, X(899), X(30116)}}, {{A, B, C, X(941), X(56196)}}, {{A, B, C, X(985), X(3112)}}, {{A, B, C, X(1002), X(56145)}}, {{A, B, C, X(1220), X(32011)}}, {{A, B, C, X(1224), X(56212)}}, {{A, B, C, X(1246), X(42027)}}, {{A, B, C, X(1897), X(30554)}}, {{A, B, C, X(2238), X(37632)}}, {{A, B, C, X(2296), X(30571)}}, {{A, B, C, X(2350), X(10014)}}, {{A, B, C, X(2998), X(40409)}}, {{A, B, C, X(3596), X(3821)}}, {{A, B, C, X(3679), X(29825)}}, {{A, B, C, X(3993), X(17379)}}, {{A, B, C, X(4201), X(4213)}}, {{A, B, C, X(4207), X(56737)}}, {{A, B, C, X(5212), X(48830)}}, {{A, B, C, X(5530), X(33137)}}, {{A, B, C, X(6048), X(26102)}}, {{A, B, C, X(9534), X(43223)}}, {{A, B, C, X(11109), X(19540)}}, {{A, B, C, X(13610), X(58021)}}, {{A, B, C, X(14621), X(32020)}}, {{A, B, C, X(15320), X(57824)}}, {{A, B, C, X(17555), X(37365)}}, {{A, B, C, X(17982), X(39724)}}, {{A, B, C, X(19684), X(56213)}}, {{A, B, C, X(19858), X(26037)}}, {{A, B, C, X(24349), X(49482)}}, {{A, B, C, X(24996), X(26364)}}, {{A, B, C, X(25610), X(40027)}}, {{A, B, C, X(29633), X(32778)}}, {{A, B, C, X(29850), X(30172)}}, {{A, B, C, X(39708), X(56052)}}, {{A, B, C, X(39748), X(39966)}}, {{A, B, C, X(39961), X(42346)}}, {{A, B, C, X(40748), X(55975)}}, {{A, B, C, X(56165), X(56224)}}

X(60110) = X(2)X(3736)∩X(10)X(2276)

Barycentrics    (b^2*c*(b+c)+a*b*(b+c)^2+a^2*(b^2+b*c+c^2))*(b*c^2*(b+c)+a*c*(b+c)^2+a^2*(b^2+b*c+c^2)) : :

X(60110) lies on the Kiepert hyperbola and on these lines: {2, 3736}, {6, 40718}, {8, 60230}, {10, 2276}, {76, 10471}, {83, 1008}, {226, 1469}, {321, 984}, {381, 54563}, {966, 56161}, {1011, 60088}, {1446, 7204}, {1655, 56210}, {1751, 4199}, {2051, 48888}, {2238, 60109}, {3407, 38813}, {3617, 56197}, {3840, 56226}, {3862, 43534}, {3954, 56282}, {4080, 17794}, {4192, 13478}, {5046, 13584}, {5224, 40024}, {8299, 48863}, {13576, 50295}, {13725, 32022}, {14009, 60071}, {16850, 60075}, {17277, 56167}, {17758, 30945}, {24512, 43531}, {26037, 60203}, {26117, 60149}, {30588, 30942}, {30962, 58012}, {30965, 57722}, {37193, 60155}, {40515, 56542}, {43096, 56660}, {45305, 54668}, {45782, 60244}, {45787, 50290}, {52245, 56901}, {59171, 60245}

X(60110) = isogonal conjugate of X(5156)
X(60110) = isotomic conjugate of X(37632)
X(60110) = trilinear pole of line {3250, 17458}
X(60110) = pole of line {5156, 37632} with respect to the Wallace hyperbola
X(60110) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(310)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(75)}}, {{A, B, C, X(8), X(3741)}}, {{A, B, C, X(9), X(10477)}}, {{A, B, C, X(25), X(52256)}}, {{A, B, C, X(37), X(57824)}}, {{A, B, C, X(42), X(10479)}}, {{A, B, C, X(79), X(2296)}}, {{A, B, C, X(274), X(55940)}}, {{A, B, C, X(427), X(1008)}}, {{A, B, C, X(475), X(37193)}}, {{A, B, C, X(594), X(3613)}}, {{A, B, C, X(596), X(1002)}}, {{A, B, C, X(740), X(58020)}}, {{A, B, C, X(941), X(42027)}}, {{A, B, C, X(966), X(30962)}}, {{A, B, C, X(985), X(32010)}}, {{A, B, C, X(1011), X(26893)}}, {{A, B, C, X(1220), X(56052)}}, {{A, B, C, X(1245), X(2350)}}, {{A, B, C, X(1502), X(3773)}}, {{A, B, C, X(1698), X(26037)}}, {{A, B, C, X(1724), X(3954)}}, {{A, B, C, X(1861), X(50295)}}, {{A, B, C, X(3223), X(32925)}}, {{A, B, C, X(3617), X(3840)}}, {{A, B, C, X(3661), X(18895)}}, {{A, B, C, X(3679), X(30942)}}, {{A, B, C, X(3783), X(18891)}}, {{A, B, C, X(4192), X(17555)}}, {{A, B, C, X(4196), X(13725)}}, {{A, B, C, X(4199), X(5125)}}, {{A, B, C, X(4212), X(26117)}}, {{A, B, C, X(4651), X(50605)}}, {{A, B, C, X(4871), X(53620)}}, {{A, B, C, X(5136), X(14009)}}, {{A, B, C, X(5224), X(24512)}}, {{A, B, C, X(5235), X(31006)}}, {{A, B, C, X(5278), X(30965)}}, {{A, B, C, X(6384), X(30571)}}, {{A, B, C, X(16552), X(56542)}}, {{A, B, C, X(16606), X(34265)}}, {{A, B, C, X(17277), X(30945)}}, {{A, B, C, X(18031), X(57725)}}, {{A, B, C, X(18793), X(56162)}}, {{A, B, C, X(24880), X(27700)}}, {{A, B, C, X(25446), X(27701)}}, {{A, B, C, X(26015), X(48802)}}, {{A, B, C, X(29637), X(33117)}}, {{A, B, C, X(30479), X(49511)}}, {{A, B, C, X(30710), X(56138)}}, {{A, B, C, X(30953), X(52133)}}, {{A, B, C, X(32783), X(36568)}}, {{A, B, C, X(39798), X(46772)}}, {{A, B, C, X(39967), X(56131)}}, {{A, B, C, X(39974), X(56125)}}, {{A, B, C, X(39983), X(40010)}}, {{A, B, C, X(41446), X(42285)}}, {{A, B, C, X(56164), X(59760)}}

X(60111) = X(2)X(1634)∩X(83)X(110)

Barycentrics    (a^2*b^2*(a^2+b^2)+(a^2-b^2)^2*c^2-(a^2+b^2)*c^4)*(-(b^4*c^2)+b^2*c^4+a^4*(b^2+c^2)+a^2*(-b^4-2*b^2*c^2+c^4)) : :

X(60111) lies on the Kiepert hyperbola and on these lines: {2, 1634}, {3, 54843}, {4, 9463}, {5, 54529}, {10, 46148}, {30, 54733}, {76, 4576}, {83, 110}, {94, 46155}, {226, 46153}, {237, 54547}, {262, 9465}, {321, 4553}, {542, 54902}, {670, 40016}, {671, 14957}, {694, 13309}, {1613, 55028}, {1916, 46161}, {2052, 46151}, {2394, 46147}, {2592, 46167}, {2593, 46166}, {3051, 30505}, {4049, 46150}, {4080, 46162}, {4444, 46159}, {5189, 11606}, {5466, 46154}, {5485, 37190}, {7533, 60105}, {7768, 55034}, {9147, 46156}, {11188, 34289}, {11632, 54881}, {11646, 44445}, {13576, 46163}, {14223, 46157}, {16063, 54122}, {20021, 43665}, {22735, 46040}, {31078, 42006}, {34087, 46303}, {40149, 46152}, {43673, 46164}, {46160, 60074}, {46165, 53345}, {46336, 60212}

X(60111) = isogonal conjugate of X(5201)
X(60111) = anticomplement of X(38998)
X(60111) = trilinear pole of line {39, 36157}
X(60111) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 5201}, {48, 46511}, {37132, 38998}
X(60111) = X(i)-vertex conjugate of X(j) for these {i, j}: {3455, 60226}
X(60111) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 5201}, {1249, 46511}, {38998, 38998}
X(60111) = pole of line {3231, 60111} with respect to the Kiepert hyperbola
X(60111) = pole of line {5201, 38998} with respect to the Wallace hyperbola
X(60111) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(67), X(110)}}, {{A, B, C, X(69), X(9463)}}, {{A, B, C, X(111), X(290)}}, {{A, B, C, X(251), X(34384)}}, {{A, B, C, X(263), X(5486)}}, {{A, B, C, X(327), X(45096)}}, {{A, B, C, X(420), X(5189)}}, {{A, B, C, X(468), X(14957)}}, {{A, B, C, X(879), X(52153)}}, {{A, B, C, X(1383), X(19222)}}, {{A, B, C, X(3051), X(3203)}}, {{A, B, C, X(3225), X(38278)}}, {{A, B, C, X(3228), X(9147)}}, {{A, B, C, X(3231), X(38998)}}, {{A, B, C, X(4232), X(37190)}}, {{A, B, C, X(7668), X(8901)}}, {{A, B, C, X(8770), X(44176)}}, {{A, B, C, X(9076), X(18020)}}, {{A, B, C, X(9141), X(46302)}}, {{A, B, C, X(9465), X(20023)}}, {{A, B, C, X(11175), X(38005)}}, {{A, B, C, X(11188), X(44134)}}, {{A, B, C, X(13485), X(43696)}}, {{A, B, C, X(13574), X(41520)}}, {{A, B, C, X(14970), X(34537)}}, {{A, B, C, X(15328), X(15364)}}, {{A, B, C, X(17983), X(18024)}}, {{A, B, C, X(18019), X(31065)}}, {{A, B, C, X(18384), X(46316)}}, {{A, B, C, X(18896), X(31125)}}, {{A, B, C, X(20022), X(53365)}}, {{A, B, C, X(39389), X(42299)}}, {{A, B, C, X(42021), X(42065)}}, {{A, B, C, X(43731), X(56357)}}, {{A, B, C, X(43732), X(56329)}}
X(60111) = barycentric product X(i)*X(j) for these (i, j): {141, 39427}
X(60111) = barycentric quotient X(i)/X(j) for these (i, j): {4, 46511}, {6, 5201}, {3231, 38998}, {39427, 83}

X(60112) = X(2)X(5396)∩X(4)X(2245)

Barycentrics    (a*(a-b)^2*b*(a+b)+(a^4+b^4)*c-a*b*(a+b)*c^2-2*(a^2+b^2)*c^3+c^5)*(-(a^3*c^2)+a^4*(b+c)+b*(b^2-c^2)^2-a^2*(2*b^3+b^2*c+c^3)+a*(-(b^2*c^2)+c^4)) : :

X(60112) lies on the Kiepert hyperbola and on these lines: {2, 5396}, {3, 24624}, {4, 2245}, {5, 60071}, {6, 5397}, {20, 55944}, {30, 54735}, {94, 52388}, {98, 5767}, {140, 60247}, {201, 18395}, {226, 1737}, {275, 5136}, {381, 54648}, {387, 60154}, {631, 55962}, {656, 60074}, {860, 2052}, {1006, 1751}, {1029, 6839}, {2051, 6830}, {2294, 60116}, {3597, 5797}, {5587, 60089}, {5657, 13576}, {5706, 57710}, {5818, 60086}, {6826, 60156}, {6827, 60155}, {6840, 55027}, {6843, 60170}, {6844, 45100}, {6854, 60076}, {6879, 45098}, {6881, 57722}, {6882, 60087}, {6883, 57721}, {6905, 13478}, {6946, 60085}, {6947, 60107}, {6963, 14554}, {6987, 60168}, {6998, 60080}, {7380, 45964}, {14266, 45885}, {18391, 60188}, {28459, 54929}, {48888, 60078}, {50701, 60167}

X(60112) = isogonal conjugate of X(5398)
X(60112) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 5398}, {3, 54368}
X(60112) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 5398}, {36103, 54368}
X(60112) = X(i)-cross conjugate of X(j) for these {i, j}: {5721, 4}
X(60112) = pole of line {5721, 60112} with respect to the Kiepert hyperbola
X(60112) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(5902)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(201)}}, {{A, B, C, X(5), X(5136)}}, {{A, B, C, X(6), X(5396)}}, {{A, B, C, X(7), X(11551)}}, {{A, B, C, X(8), X(847)}}, {{A, B, C, X(9), X(18397)}}, {{A, B, C, X(21), X(91)}}, {{A, B, C, X(29), X(6829)}}, {{A, B, C, X(37), X(1243)}}, {{A, B, C, X(65), X(50317)}}, {{A, B, C, X(68), X(57985)}}, {{A, B, C, X(75), X(104)}}, {{A, B, C, X(80), X(7110)}}, {{A, B, C, X(84), X(39708)}}, {{A, B, C, X(90), X(52344)}}, {{A, B, C, X(158), X(943)}}, {{A, B, C, X(225), X(51223)}}, {{A, B, C, X(264), X(38955)}}, {{A, B, C, X(318), X(52663)}}, {{A, B, C, X(405), X(37381)}}, {{A, B, C, X(406), X(6826)}}, {{A, B, C, X(451), X(6839)}}, {{A, B, C, X(475), X(6827)}}, {{A, B, C, X(522), X(55918)}}, {{A, B, C, X(947), X(29306)}}, {{A, B, C, X(997), X(25005)}}, {{A, B, C, X(1000), X(55076)}}, {{A, B, C, X(1006), X(5125)}}, {{A, B, C, X(1061), X(39943)}}, {{A, B, C, X(1065), X(1268)}}, {{A, B, C, X(1389), X(31359)}}, {{A, B, C, X(1577), X(57820)}}, {{A, B, C, X(1861), X(5657)}}, {{A, B, C, X(2166), X(15175)}}, {{A, B, C, X(2294), X(39983)}}, {{A, B, C, X(2962), X(4511)}}, {{A, B, C, X(3427), X(5936)}}, {{A, B, C, X(3467), X(56280)}}, {{A, B, C, X(4194), X(6854)}}, {{A, B, C, X(4200), X(6947)}}, {{A, B, C, X(4231), X(16062)}}, {{A, B, C, X(5767), X(6530)}}, {{A, B, C, X(5818), X(46878)}}, {{A, B, C, X(6734), X(18391)}}, {{A, B, C, X(6830), X(11109)}}, {{A, B, C, X(6840), X(52252)}}, {{A, B, C, X(6843), X(7498)}}, {{A, B, C, X(6877), X(7518)}}, {{A, B, C, X(6889), X(37189)}}, {{A, B, C, X(6905), X(17555)}}, {{A, B, C, X(6911), X(11105)}}, {{A, B, C, X(10175), X(43734)}}, {{A, B, C, X(10308), X(57723)}}, {{A, B, C, X(10623), X(29084)}}, {{A, B, C, X(14497), X(42285)}}, {{A, B, C, X(19605), X(55931)}}, {{A, B, C, X(24880), X(34243)}}, {{A, B, C, X(28626), X(38306)}}, {{A, B, C, X(34860), X(37518)}}, {{A, B, C, X(43659), X(55994)}}, {{A, B, C, X(45885), X(46393)}}, {{A, B, C, X(55091), X(56027)}}
X(60112) = barycentric quotient X(i)/X(j) for these (i, j): {6, 5398}, {19, 54368}

X(60113) = X(2)X(44541)∩X(4)X(51173)

Barycentrics    (11*(a^2+b^2)-13*c^2)*(11*a^2-13*b^2+11*c^2) : :

X(60113) lies on the Kiepert hyperbola and on these lines: {2, 44541}, {4, 51173}, {6, 54476}, {20, 60123}, {30, 53103}, {98, 50687}, {381, 10155}, {597, 60145}, {1992, 38259}, {3091, 53098}, {3146, 7607}, {3522, 10185}, {3543, 7612}, {3830, 60185}, {3832, 7608}, {3839, 14494}, {3845, 54523}, {5059, 53859}, {5068, 60144}, {5461, 60073}, {5485, 20080}, {5503, 8596}, {7408, 60124}, {7620, 60216}, {7762, 60219}, {7841, 60183}, {8352, 60143}, {8591, 8781}, {8796, 42391}, {10159, 32982}, {11160, 43681}, {11303, 43445}, {11304, 43444}, {11317, 54616}, {12101, 54612}, {14068, 43528}, {15683, 53104}, {15687, 60322}, {17578, 43537}, {19569, 60218}, {32898, 60198}, {32979, 43527}, {32996, 43529}, {34621, 60160}, {38253, 52282}, {41895, 51170}, {43448, 45103}, {46034, 54568}, {50688, 60337}, {50689, 53099}, {52281, 60137}, {53101, 53419}, {53418, 54642}, {54097, 60285}

X(60113) = isogonal conjugate of X(5585)
X(60113) = pole of line {5032, 60113} with respect to the Kiepert hyperbola
X(60113) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(249), X(11736)}}, {{A, B, C, X(297), X(50687)}}, {{A, B, C, X(428), X(32982)}}, {{A, B, C, X(1992), X(20080)}}, {{A, B, C, X(2987), X(14490)}}, {{A, B, C, X(3087), X(42391)}}, {{A, B, C, X(3146), X(52282)}}, {{A, B, C, X(3426), X(11741)}}, {{A, B, C, X(3543), X(37174)}}, {{A, B, C, X(3832), X(52281)}}, {{A, B, C, X(3926), X(17505)}}, {{A, B, C, X(5064), X(32979)}}, {{A, B, C, X(5203), X(51541)}}, {{A, B, C, X(7408), X(7841)}}, {{A, B, C, X(7409), X(8370)}}, {{A, B, C, X(7714), X(54097)}}, {{A, B, C, X(8352), X(52301)}}, {{A, B, C, X(8591), X(52450)}}, {{A, B, C, X(11160), X(51170)}}, {{A, B, C, X(13603), X(21399)}}, {{A, B, C, X(14487), X(30541)}}, {{A, B, C, X(17501), X(54123)}}, {{A, B, C, X(21765), X(36882)}}, {{A, B, C, X(22334), X(56362)}}, {{A, B, C, X(32533), X(56339)}}, {{A, B, C, X(43699), X(56267)}}, {{A, B, C, X(44541), X(52187)}}, {{A, B, C, X(46851), X(56004)}}, {{A, B, C, X(55999), X(57715)}}

X(60114) = X(2)X(3964)∩X(4)X(394)

Barycentrics    ((a^2-b^2)^3+(-a^4+6*a^2*b^2+3*b^4)*c^2-(a^2+3*b^2)*c^4+c^6)*(a^6+(b^2-c^2)^3-a^4*(b^2+3*c^2)+a^2*(-b^4+6*b^2*c^2+3*c^4)) : :

X(60114) lies on the Kiepert hyperbola and on these lines: {2, 3964}, {3, 60166}, {4, 394}, {5, 60174}, {10, 10629}, {30, 54844}, {69, 2052}, {76, 4176}, {83, 11427}, {98, 7386}, {141, 60221}, {226, 53996}, {262, 7392}, {275, 6819}, {343, 459}, {377, 60158}, {443, 60154}, {485, 6805}, {486, 6806}, {524, 54771}, {631, 60159}, {1032, 59424}, {1370, 3424}, {1992, 54926}, {2478, 60157}, {3090, 60162}, {3316, 3539}, {3317, 3540}, {3524, 54498}, {3525, 60160}, {3543, 54886}, {5067, 60163}, {5084, 60164}, {5189, 60324}, {6504, 15066}, {6515, 34289}, {6803, 13599}, {6804, 40448}, {6815, 31363}, {6997, 14484}, {7381, 60167}, {7382, 45100}, {7391, 60147}, {7394, 43951}, {7533, 60328}, {7841, 54779}, {8796, 37192}, {10996, 13380}, {11001, 54942}, {11064, 56346}, {11433, 37874}, {14458, 44442}, {15702, 54500}, {16063, 47586}, {17559, 60173}, {18841, 37649}, {33190, 54558}, {37276, 60246}, {37349, 54706}, {37636, 60256}, {37638, 38253}, {37645, 40393}, {37672, 54797}, {40112, 54792}, {40149, 52385}, {43537, 46336}, {51833, 52582}, {52032, 60130}, {52283, 52583}, {52713, 60266}, {53021, 56296}, {55869, 60249}

X(60114) = isogonal conjugate of X(8573)
X(60114) = isotomic conjugate of X(11433)
X(60114) = trilinear pole of line {21668, 47090}
X(60114) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 8573}, {19, 1181}, {31, 11433}, {48, 3089}, {1973, 40680}, {4575, 13400}
X(60114) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 11433}, {3, 8573}, {6, 1181}, {136, 13400}, {1249, 3089}, {6337, 40680}
X(60114) = pole of line {17811, 60114} with respect to the Kiepert hyperbola
X(60114) = pole of line {1181, 8573} with respect to the Stammler hyperbola
X(60114) = pole of line {8573, 11433} with respect to the Wallace hyperbola
X(60114) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(6820)}}, {{A, B, C, X(5), X(6819)}}, {{A, B, C, X(8), X(54451)}}, {{A, B, C, X(20), X(47633)}}, {{A, B, C, X(63), X(34401)}}, {{A, B, C, X(68), X(1073)}}, {{A, B, C, X(69), X(394)}}, {{A, B, C, X(80), X(56230)}}, {{A, B, C, X(97), X(56004)}}, {{A, B, C, X(141), X(11427)}}, {{A, B, C, X(189), X(43740)}}, {{A, B, C, X(249), X(56338)}}, {{A, B, C, X(278), X(10629)}}, {{A, B, C, X(287), X(14826)}}, {{A, B, C, X(297), X(7386)}}, {{A, B, C, X(305), X(55972)}}, {{A, B, C, X(343), X(37669)}}, {{A, B, C, X(458), X(7392)}}, {{A, B, C, X(631), X(37192)}}, {{A, B, C, X(1000), X(56352)}}, {{A, B, C, X(1275), X(30679)}}, {{A, B, C, X(1370), X(52283)}}, {{A, B, C, X(1502), X(53481)}}, {{A, B, C, X(2475), X(37276)}}, {{A, B, C, X(2987), X(17040)}}, {{A, B, C, X(2994), X(6601)}}, {{A, B, C, X(3296), X(56041)}}, {{A, B, C, X(3431), X(56002)}}, {{A, B, C, X(3519), X(36609)}}, {{A, B, C, X(3619), X(37649)}}, {{A, B, C, X(5905), X(55869)}}, {{A, B, C, X(6340), X(18022)}}, {{A, B, C, X(6464), X(45011)}}, {{A, B, C, X(6515), X(15066)}}, {{A, B, C, X(6524), X(8770)}}, {{A, B, C, X(6804), X(52280)}}, {{A, B, C, X(6821), X(54372)}}, {{A, B, C, X(6997), X(52288)}}, {{A, B, C, X(7058), X(30680)}}, {{A, B, C, X(8797), X(57909)}}, {{A, B, C, X(9292), X(10318)}}, {{A, B, C, X(10603), X(57908)}}, {{A, B, C, X(10984), X(45186)}}, {{A, B, C, X(11064), X(37878)}}, {{A, B, C, X(11185), X(52713)}}, {{A, B, C, X(11270), X(56361)}}, {{A, B, C, X(11331), X(44442)}}, {{A, B, C, X(11433), X(14457)}}, {{A, B, C, X(14361), X(57483)}}, {{A, B, C, X(14593), X(21448)}}, {{A, B, C, X(15474), X(55110)}}, {{A, B, C, X(15998), X(56355)}}, {{A, B, C, X(30541), X(31626)}}, {{A, B, C, X(32319), X(40799)}}, {{A, B, C, X(34403), X(52350)}}, {{A, B, C, X(36948), X(39287)}}, {{A, B, C, X(37187), X(37190)}}, {{A, B, C, X(37636), X(37645)}}, {{A, B, C, X(37643), X(53415)}}, {{A, B, C, X(40384), X(54453)}}, {{A, B, C, X(40405), X(56267)}}, {{A, B, C, X(41081), X(52392)}}, {{A, B, C, X(41890), X(56364)}}, {{A, B, C, X(42352), X(42484)}}, {{A, B, C, X(43981), X(56067)}}, {{A, B, C, X(55020), X(55412)}}, {{A, B, C, X(55021), X(55411)}}, {{A, B, C, X(56204), X(56234)}}, {{A, B, C, X(57874), X(57906)}}
X(60114) = barycentric product X(i)*X(j) for these (i, j): {1217, 69}, {1502, 46680}, {4143, 59086}, {27356, 95}
X(60114) = barycentric quotient X(i)/X(j) for these (i, j): {2, 11433}, {3, 1181}, {4, 3089}, {6, 8573}, {69, 40680}, {1217, 4}, {2501, 13400}, {3546, 18910}, {14489, 45099}, {27356, 5}, {36747, 52014}, {46680, 32}, {59086, 6529}

X(60115) = X(2)X(9743)∩X(6)X(14485)

Barycentrics    (4*a^2*b^2*(a^2+b^2)+(5*a^4+2*a^2*b^2+5*b^4)*c^2-6*(a^2+b^2)*c^4+c^6)*(b^6-6*b^4*c^2+5*b^2*c^4+a^4*(5*b^2+4*c^2)+a^2*(-6*b^4+2*b^2*c^2+4*c^4)) : :

X(60115) lies on the Kiepert hyperbola and on these lines: {2, 9743}, {3, 60187}, {4, 44500}, {6, 14485}, {30, 11167}, {39, 53099}, {76, 51438}, {83, 53093}, {98, 1384}, {262, 15048}, {381, 54509}, {511, 5485}, {598, 1503}, {671, 54131}, {1499, 43665}, {2394, 8704}, {2782, 5503}, {2793, 46040}, {2794, 43535}, {3424, 7737}, {3906, 43673}, {5480, 54814}, {6194, 60259}, {6248, 18840}, {7608, 11257}, {7694, 60190}, {7697, 60099}, {7709, 14494}, {7771, 9756}, {7790, 60096}, {7864, 60098}, {11172, 51224}, {11179, 18842}, {11185, 22676}, {14484, 22682}, {14639, 54675}, {32515, 60180}, {36990, 60140}, {39266, 40824}, {43537, 52854}, {45103, 53017}, {48663, 60213}, {53016, 60147}, {58782, 60199}

X(60115) = isogonal conjugate of X(8722)
X(60115) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 598}
X(60115) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(44500)}}, {{A, B, C, X(6), X(21163)}}, {{A, B, C, X(25), X(53774)}}, {{A, B, C, X(30), X(8704)}}, {{A, B, C, X(39), X(52518)}}, {{A, B, C, X(64), X(27375)}}, {{A, B, C, X(263), X(34099)}}, {{A, B, C, X(393), X(46034)}}, {{A, B, C, X(511), X(843)}}, {{A, B, C, X(516), X(28565)}}, {{A, B, C, X(726), X(28296)}}, {{A, B, C, X(1503), X(3906)}}, {{A, B, C, X(2710), X(14906)}}, {{A, B, C, X(2782), X(2793)}}, {{A, B, C, X(3531), X(30499)}}, {{A, B, C, X(7737), X(45031)}}, {{A, B, C, X(22334), X(40322)}}, {{A, B, C, X(32472), X(32515)}}, {{A, B, C, X(34130), X(41443)}}, {{A, B, C, X(39266), X(43976)}}, {{A, B, C, X(44557), X(54998)}}, {{A, B, C, X(52477), X(54131)}}

X(60116) = X(2)X(758)∩X(4)X(3743)

Barycentrics    (b+c)*(2*a*b*(a+b)+(a^2+a*b+b^2)*c-c^3)*(-b^3+b*c^2+a^2*(b+2*c)+a*c*(b+2*c)) : :

X(60116) lies on the Kiepert hyperbola and on these lines: {1, 24624}, {2, 758}, {4, 3743}, {10, 4053}, {12, 60091}, {37, 60089}, {40, 57710}, {76, 35550}, {94, 6757}, {98, 44430}, {321, 3822}, {495, 523}, {515, 60172}, {516, 54526}, {517, 54699}, {527, 55949}, {551, 54553}, {671, 4664}, {740, 60079}, {912, 54700}, {993, 14534}, {1029, 1478}, {1962, 48841}, {2051, 45944}, {2292, 60071}, {2294, 60112}, {2650, 60247}, {2784, 54491}, {2792, 55003}, {2801, 54497}, {3724, 15175}, {4672, 43531}, {4736, 31019}, {4868, 13576}, {5587, 54528}, {5711, 43680}, {8680, 60083}, {11374, 59282}, {13478, 50317}, {25080, 60156}, {29046, 54533}, {29069, 54563}, {30447, 43682}, {32014, 41847}, {37346, 43683}, {40395, 54368}, {54288, 60203}, {54335, 60235}, {55944, 58380}

X(60116) = isogonal conjugate of X(9275)
X(60116) = trilinear pole of line {2610, 523}
X(60116) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 9275}, {58, 5251}, {110, 50349}
X(60116) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 9275}, {10, 5251}, {244, 50349}
X(60116) = X(i)-cross conjugate of X(j) for these {i, j}: {7951, 6757}
X(60116) = pole of line {2610, 6003} with respect to the orthoptic circle of the Steiner inellipse
X(60116) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(12)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(5620)}}, {{A, B, C, X(8), X(502)}}, {{A, B, C, X(37), X(5692)}}, {{A, B, C, X(63), X(3695)}}, {{A, B, C, X(65), X(3822)}}, {{A, B, C, X(79), X(26725)}}, {{A, B, C, X(80), X(8818)}}, {{A, B, C, X(442), X(5665)}}, {{A, B, C, X(495), X(4551)}}, {{A, B, C, X(596), X(39769)}}, {{A, B, C, X(993), X(2292)}}, {{A, B, C, X(994), X(2171)}}, {{A, B, C, X(996), X(34895)}}, {{A, B, C, X(1089), X(31359)}}, {{A, B, C, X(1125), X(55089)}}, {{A, B, C, X(1441), X(53114)}}, {{A, B, C, X(1577), X(27475)}}, {{A, B, C, X(2294), X(54368)}}, {{A, B, C, X(2594), X(37719)}}, {{A, B, C, X(3467), X(10176)}}, {{A, B, C, X(3649), X(43732)}}, {{A, B, C, X(3678), X(7162)}}, {{A, B, C, X(3701), X(56203)}}, {{A, B, C, X(3833), X(56135)}}, {{A, B, C, X(3932), X(4868)}}, {{A, B, C, X(3992), X(36872)}}, {{A, B, C, X(4013), X(42285)}}, {{A, B, C, X(4120), X(51975)}}, {{A, B, C, X(4647), X(41847)}}, {{A, B, C, X(4664), X(42713)}}, {{A, B, C, X(4674), X(5883)}}, {{A, B, C, X(4705), X(59272)}}, {{A, B, C, X(5219), X(37715)}}, {{A, B, C, X(5557), X(52382)}}, {{A, B, C, X(11107), X(30447)}}, {{A, B, C, X(11116), X(37982)}}, {{A, B, C, X(12514), X(25080)}}, {{A, B, C, X(13739), X(37346)}}, {{A, B, C, X(21051), X(40780)}}, {{A, B, C, X(21674), X(54335)}}, {{A, B, C, X(27690), X(50757)}}, {{A, B, C, X(37701), X(52383)}}, {{A, B, C, X(41013), X(56221)}}, {{A, B, C, X(52388), X(52392)}}
X(60116) = barycentric product X(i)*X(j) for these (i, j): {59034, 850}
X(60116) = barycentric quotient X(i)/X(j) for these (i, j): {6, 9275}, {37, 5251}, {661, 50349}, {59034, 110}

X(60117) = X(3)X(8781)∩X(4)X(1692)

Barycentrics    (2*(a^6+b^6)-(3*a^4+4*a^2*b^2+3*b^4)*c^2+2*(a^2+b^2)*c^4-c^6)*(2*a^6-3*a^4*b^2-b^6+2*b^4*c^2-3*b^2*c^4+2*c^6+2*a^2*(b^4-2*b^2*c^2)) : :

X(60117) lies on the Kiepert hyperbola and on these lines: {2, 13335}, {3, 8781}, {4, 1692}, {5, 60093}, {20, 60260}, {30, 60095}, {76, 3564}, {98, 13881}, {262, 7745}, {275, 57533}, {381, 54906}, {460, 2052}, {512, 60338}, {542, 54750}, {671, 39646}, {1916, 11257}, {2548, 14494}, {2794, 54978}, {2996, 6776}, {3407, 10358}, {3543, 54889}, {3849, 60240}, {5395, 14561}, {5490, 12256}, {5491, 12257}, {5503, 9774}, {6249, 54539}, {6337, 9744}, {7612, 7694}, {7752, 60178}, {7784, 56064}, {7836, 9742}, {8370, 54751}, {10104, 60101}, {11645, 41895}, {12203, 60072}, {12252, 54822}, {14265, 60199}, {14537, 60127}, {19102, 45107}, {19105, 45106}, {23700, 47736}, {33971, 54703}, {34507, 60285}, {35830, 60270}, {35831, 60269}, {36990, 54858}, {44518, 60189}, {53017, 54873}

X(60117) = isogonal conjugate of X(9737)
X(60117) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(460)}}, {{A, B, C, X(5), X(57533)}}, {{A, B, C, X(6), X(13335)}}, {{A, B, C, X(32), X(46320)}}, {{A, B, C, X(54), X(44557)}}, {{A, B, C, X(68), X(57872)}}, {{A, B, C, X(69), X(39647)}}, {{A, B, C, X(182), X(695)}}, {{A, B, C, X(264), X(54393)}}, {{A, B, C, X(511), X(3224)}}, {{A, B, C, X(804), X(23698)}}, {{A, B, C, X(847), X(52618)}}, {{A, B, C, X(1093), X(39645)}}, {{A, B, C, X(1799), X(14593)}}, {{A, B, C, X(2165), X(35142)}}, {{A, B, C, X(2207), X(3425)}}, {{A, B, C, X(3527), X(43950)}}, {{A, B, C, X(6337), X(6776)}}, {{A, B, C, X(6530), X(57504)}}, {{A, B, C, X(6531), X(9307)}}, {{A, B, C, X(7745), X(33971)}}, {{A, B, C, X(8601), X(43702)}}, {{A, B, C, X(9289), X(47388)}}, {{A, B, C, X(11257), X(14382)}}, {{A, B, C, X(12203), X(51259)}}, {{A, B, C, X(14052), X(21448)}}, {{A, B, C, X(18321), X(52728)}}, {{A, B, C, X(18384), X(40102)}}, {{A, B, C, X(28470), X(28526)}}, {{A, B, C, X(39646), X(52145)}}, {{A, B, C, X(42377), X(51316)}}, {{A, B, C, X(44175), X(47847)}}

X(60118) = X(2)X(53097)∩X(3)X(54616)

Barycentrics    (a^4+14*a^2*b^2+b^4+6*(a^2+b^2)*c^2-7*c^4)*(a^4-7*b^4+6*b^2*c^2+c^4+2*a^2*(3*b^2+7*c^2)) : :

X(60118) lies on the Kiepert hyperbola and on these lines: {2, 53097}, {3, 54616}, {5, 60143}, {6, 47586}, {20, 18842}, {30, 60284}, {39, 54814}, {76, 5068}, {83, 3522}, {275, 52301}, {381, 54637}, {383, 33604}, {427, 54710}, {459, 52284}, {468, 60137}, {598, 3146}, {671, 3832}, {1080, 33605}, {1513, 54523}, {1656, 60183}, {2996, 3854}, {3091, 5485}, {3424, 8550}, {3523, 18841}, {3543, 60281}, {3815, 60331}, {3839, 32532}, {4052, 30308}, {4232, 56346}, {5056, 18840}, {5059, 5395}, {5094, 38253}, {5304, 60336}, {5480, 53099}, {6504, 7533}, {6658, 54833}, {6776, 54857}, {6811, 54597}, {6813, 43536}, {6847, 54719}, {6848, 54695}, {6995, 54531}, {7000, 14241}, {7374, 14226}, {7378, 54867}, {7390, 54624}, {7391, 54797}, {7394, 54785}, {7407, 54786}, {7408, 60120}, {7409, 39284}, {7500, 54772}, {7519, 54792}, {7607, 14853}, {7735, 54921}, {7736, 43951}, {9300, 54815}, {9744, 54890}, {9748, 53104}, {9753, 11668}, {9993, 54920}, {10302, 15022}, {10513, 60259}, {13860, 60185}, {14068, 54872}, {15683, 60282}, {15717, 60239}, {17578, 53101}, {18843, 49135}, {18844, 50691}, {18845, 50690}, {31099, 54771}, {32979, 54916}, {32980, 54751}, {32982, 54915}, {33019, 54753}, {33290, 60151}, {37349, 54761}, {37434, 54755}, {37456, 54759}, {37463, 43555}, {37464, 43554}, {37665, 60147}, {41895, 50689}, {45103, 50687}, {50693, 54639}, {53023, 60328}

X(60118) = isogonal conjugate of X(10541)
X(60118) = X(i)-vertex conjugate of X(j) for these {i, j}: {3425, 54523}
X(60118) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(5), X(52301)}}, {{A, B, C, X(6), X(53097)}}, {{A, B, C, X(20), X(52284)}}, {{A, B, C, X(25), X(5068)}}, {{A, B, C, X(64), X(39389)}}, {{A, B, C, X(67), X(46952)}}, {{A, B, C, X(111), X(52518)}}, {{A, B, C, X(140), X(7409)}}, {{A, B, C, X(393), X(22336)}}, {{A, B, C, X(427), X(3522)}}, {{A, B, C, X(468), X(3832)}}, {{A, B, C, X(1297), X(43908)}}, {{A, B, C, X(1383), X(3527)}}, {{A, B, C, X(1656), X(7408)}}, {{A, B, C, X(3088), X(16063)}}, {{A, B, C, X(3091), X(4232)}}, {{A, B, C, X(3108), X(14528)}}, {{A, B, C, X(3146), X(5094)}}, {{A, B, C, X(3425), X(57730)}}, {{A, B, C, X(3523), X(7378)}}, {{A, B, C, X(3531), X(40103)}}, {{A, B, C, X(3532), X(39951)}}, {{A, B, C, X(3541), X(5189)}}, {{A, B, C, X(3542), X(7533)}}, {{A, B, C, X(3613), X(38005)}}, {{A, B, C, X(3839), X(53857)}}, {{A, B, C, X(3854), X(6353)}}, {{A, B, C, X(4518), X(5558)}}, {{A, B, C, X(5056), X(6995)}}, {{A, B, C, X(5059), X(8889)}}, {{A, B, C, X(5169), X(37460)}}, {{A, B, C, X(5481), X(43719)}}, {{A, B, C, X(5486), X(8801)}}, {{A, B, C, X(7249), X(7320)}}, {{A, B, C, X(8550), X(10002)}}, {{A, B, C, X(8797), X(46208)}}, {{A, B, C, X(10301), X(15022)}}, {{A, B, C, X(10415), X(14542)}}, {{A, B, C, X(10513), X(37665)}}, {{A, B, C, X(13574), X(18855)}}, {{A, B, C, X(14930), X(37668)}}, {{A, B, C, X(15464), X(34285)}}, {{A, B, C, X(17040), X(52443)}}, {{A, B, C, X(18575), X(52187)}}, {{A, B, C, X(30786), X(31371)}}, {{A, B, C, X(31857), X(35485)}}, {{A, B, C, X(39955), X(40801)}}, {{A, B, C, X(41896), X(45011)}}, {{A, B, C, X(43726), X(51316)}}, {{A, B, C, X(43731), X(57726)}}, {{A, B, C, X(43732), X(57727)}}, {{A, B, C, X(50687), X(52293)}}, {{A, B, C, X(50689), X(52290)}}, {{A, B, C, X(50690), X(52299)}}

X(60119) = X(2)X(74)∩X(13)X(1525)

Barycentrics    ((a^2-b^2)^2+(a^2+b^2)*c^2-2*c^4)*(a^4+4*a^2*b^2+b^4-2*(a^2+b^2)*c^2+c^4)*(a^4-2*b^4+b^2*c^2+c^4+a^2*(b^2-2*c^2))*(a^4-2*a^2*(b^2-2*c^2)+(b^2-c^2)^2) : :

X(60119) lies on the Kiepert hyperbola and on these lines: {2, 74}, {4, 6128}, {13, 1525}, {14, 1524}, {30, 2986}, {76, 1494}, {94, 5627}, {96, 2883}, {98, 32111}, {275, 10152}, {378, 22455}, {381, 34289}, {403, 16080}, {542, 54925}, {671, 9139}, {801, 44458}, {1513, 60317}, {1514, 51544}, {1552, 60133}, {1555, 48451}, {2071, 56063}, {2394, 55121}, {2433, 19912}, {2996, 56686}, {3830, 54913}, {3845, 54864}, {5306, 40354}, {5485, 36875}, {5622, 32738}, {6504, 59497}, {6623, 56270}, {7578, 37077}, {10257, 16243}, {10722, 54738}, {11456, 60122}, {12079, 47332}, {12112, 18316}, {13582, 52403}, {14989, 55957}, {15395, 39295}, {15682, 54784}, {15760, 60225}, {18781, 54837}, {24624, 36083}, {35908, 60266}, {36890, 40824}, {37118, 60138}, {39874, 54667}, {39985, 52933}, {40355, 51548}, {41099, 54771}, {41889, 54556}, {43678, 52646}, {44440, 60255}, {46105, 52493}, {46147, 59763}, {46808, 60256}, {52165, 54943}, {54803, 56966}

X(60119) = isogonal conjugate of X(10564)
X(60119) = trilinear pole of line {2433, 34288}
X(60119) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 10564}, {163, 46229}, {2173, 15066}, {5063, 14206}, {9406, 32833}, {46234, 52438}
X(60119) = X(i)-vertex conjugate of X(j) for these {i, j}: {186, 1494}, {250, 48362}, {3425, 60317}, {10419, 14910}, {18316, 22455}
X(60119) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 10564}, {115, 46229}, {9410, 32833}, {36896, 15066}
X(60119) = X(i)-cross conjugate of X(j) for these {i, j}: {381, 5627}, {1514, 4}, {51544, 16080}
X(60119) = pole of line {1514, 51544} with respect to the Kiepert hyperbola
X(60119) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(18361)}}, {{A, B, C, X(6), X(37470)}}, {{A, B, C, X(20), X(36612)}}, {{A, B, C, X(30), X(113)}}, {{A, B, C, X(64), X(11058)}}, {{A, B, C, X(74), X(1494)}}, {{A, B, C, X(146), X(1138)}}, {{A, B, C, X(235), X(44458)}}, {{A, B, C, X(265), X(6128)}}, {{A, B, C, X(376), X(6623)}}, {{A, B, C, X(378), X(381)}}, {{A, B, C, X(477), X(10706)}}, {{A, B, C, X(523), X(541)}}, {{A, B, C, X(841), X(45019)}}, {{A, B, C, X(847), X(43695)}}, {{A, B, C, X(1141), X(57747)}}, {{A, B, C, X(1177), X(32710)}}, {{A, B, C, X(1179), X(3521)}}, {{A, B, C, X(1513), X(37855)}}, {{A, B, C, X(2980), X(18550)}}, {{A, B, C, X(3531), X(15364)}}, {{A, B, C, X(3845), X(37118)}}, {{A, B, C, X(4846), X(34288)}}, {{A, B, C, X(6526), X(46199)}}, {{A, B, C, X(6530), X(32111)}}, {{A, B, C, X(7576), X(15760)}}, {{A, B, C, X(7577), X(37077)}}, {{A, B, C, X(10295), X(47332)}}, {{A, B, C, X(10420), X(32711)}}, {{A, B, C, X(11070), X(34334)}}, {{A, B, C, X(13381), X(22466)}}, {{A, B, C, X(13452), X(15319)}}, {{A, B, C, X(14264), X(40352)}}, {{A, B, C, X(14457), X(46412)}}, {{A, B, C, X(14860), X(16835)}}, {{A, B, C, X(15328), X(47050)}}, {{A, B, C, X(15459), X(30247)}}, {{A, B, C, X(16075), X(52661)}}, {{A, B, C, X(16081), X(53201)}}, {{A, B, C, X(18808), X(52488)}}, {{A, B, C, X(34150), X(52475)}}, {{A, B, C, X(35512), X(36889)}}, {{A, B, C, X(37943), X(52403)}}, {{A, B, C, X(37984), X(54995)}}, {{A, B, C, X(45179), X(52069)}}, {{A, B, C, X(46426), X(48362)}}, {{A, B, C, X(52447), X(53832)}}, {{A, B, C, X(55978), X(57852)}}
X(60119) = barycentric product X(i)*X(j) for these (i, j): {1302, 2394}, {1494, 34288}, {1577, 36083}, {16080, 4846}, {32681, 850}, {34289, 74}, {36889, 40385}, {40387, 60256}, {41079, 52933}, {57819, 8749}
X(60119) = barycentric quotient X(i)/X(j) for these (i, j): {6, 10564}, {74, 15066}, {523, 46229}, {1302, 2407}, {1494, 32833}, {2394, 30474}, {2433, 8675}, {4846, 11064}, {8749, 378}, {16080, 44134}, {32681, 110}, {32738, 2420}, {34288, 30}, {34289, 3260}, {36083, 662}, {40352, 5063}, {40354, 44080}, {40385, 376}, {40387, 37645}, {51544, 4550}, {52933, 44769}, {56925, 51389}

X(60120) = X(17)X(472)∩X(18)X(473)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(2*(a^2-b^2)^2-3*(a^2+b^2)*c^2+c^4)*(2*a^4+b^4-3*b^2*c^2+2*c^4-a^2*(3*b^2+4*c^2)) : :

X(60120) lies on the Kiepert hyperbola and on these lines: {2, 10985}, {3, 60171}, {4, 11423}, {6, 39284}, {17, 472}, {18, 473}, {25, 7608}, {30, 13599}, {76, 52281}, {83, 52282}, {98, 5064}, {107, 58878}, {262, 428}, {264, 11140}, {297, 43527}, {381, 40448}, {394, 54911}, {427, 7607}, {458, 10159}, {468, 60144}, {470, 10187}, {471, 10188}, {524, 54636}, {597, 54798}, {671, 39849}, {1585, 10194}, {1586, 10195}, {1992, 54930}, {1994, 54801}, {2052, 6748}, {3087, 8796}, {3535, 43565}, {3536, 43564}, {3543, 31363}, {3590, 55569}, {3591, 55573}, {3830, 60121}, {3845, 60122}, {5094, 10185}, {5392, 41628}, {6353, 53098}, {6995, 53099}, {7378, 43537}, {7408, 60118}, {7409, 47586}, {7576, 57718}, {7714, 14494}, {8352, 54682}, {8889, 60123}, {9221, 18559}, {10301, 60332}, {11317, 54898}, {11331, 60182}, {11427, 54531}, {11433, 54710}, {11547, 60161}, {12101, 54585}, {14129, 54914}, {14165, 56346}, {15682, 54763}, {15809, 60124}, {37672, 54922}, {39286, 57489}, {41099, 54660}, {43530, 52280}, {44128, 60221}, {52253, 60225}, {52284, 53859}, {52285, 53100}, {54797, 59373}

X(60120) = isogonal conjugate of X(10979)
X(60120) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 10979}, {48, 1656}, {63, 15004}
X(60120) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 10979}, {1249, 1656}, {3162, 15004}
X(60120) = X(i)-cross conjugate of X(j) for these {i, j}: {47122, 107}, {52295, 264}
X(60120) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(288)}}, {{A, B, C, X(6), X(6748)}}, {{A, B, C, X(25), X(10985)}}, {{A, B, C, X(51), X(1988)}}, {{A, B, C, X(53), X(52154)}}, {{A, B, C, X(97), X(1173)}}, {{A, B, C, X(264), X(472)}}, {{A, B, C, X(287), X(43726)}}, {{A, B, C, X(297), X(5064)}}, {{A, B, C, X(324), X(36809)}}, {{A, B, C, X(381), X(52280)}}, {{A, B, C, X(394), X(52518)}}, {{A, B, C, X(427), X(52282)}}, {{A, B, C, X(428), X(458)}}, {{A, B, C, X(1172), X(55992)}}, {{A, B, C, X(1614), X(9781)}}, {{A, B, C, X(1993), X(41628)}}, {{A, B, C, X(3087), X(52188)}}, {{A, B, C, X(3527), X(56347)}}, {{A, B, C, X(3531), X(36609)}}, {{A, B, C, X(4994), X(16837)}}, {{A, B, C, X(7576), X(52253)}}, {{A, B, C, X(7745), X(57688)}}, {{A, B, C, X(7841), X(15809)}}, {{A, B, C, X(8439), X(13157)}}, {{A, B, C, X(8601), X(10318)}}, {{A, B, C, X(8794), X(16263)}}, {{A, B, C, X(8795), X(57822)}}, {{A, B, C, X(13472), X(56338)}}, {{A, B, C, X(15318), X(54449)}}, {{A, B, C, X(15321), X(42313)}}, {{A, B, C, X(16835), X(31626)}}, {{A, B, C, X(23964), X(57253)}}, {{A, B, C, X(32085), X(42298)}}, {{A, B, C, X(34288), X(40402)}}, {{A, B, C, X(34412), X(44176)}}, {{A, B, C, X(34572), X(57409)}}, {{A, B, C, X(36121), X(56037)}}, {{A, B, C, X(36421), X(36916)}}, {{A, B, C, X(36910), X(53817)}}, {{A, B, C, X(39849), X(56395)}}, {{A, B, C, X(40384), X(44549)}}, {{A, B, C, X(40711), X(41898)}}, {{A, B, C, X(40712), X(41897)}}, {{A, B, C, X(46848), X(55982)}}, {{A, B, C, X(54124), X(57852)}}
X(60120) = barycentric product X(i)*X(j) for these (i, j): {2052, 56338}, {13472, 264}
X(60120) = barycentric quotient X(i)/X(j) for these (i, j): {4, 1656}, {6, 10979}, {25, 15004}, {8884, 4994}, {13472, 3}, {56338, 394}

X(60121) = X(2)X(1568)∩X(30)X(275)

Barycentrics    (a^8-a^6*(b^2-2*c^2)-(b^2-c^2)^3*(2*b^2+c^2)+a^2*(b^2-c^2)^2*(5*b^2+2*c^2)+a^4*(-3*b^4+b^2*c^2-6*c^4))*(a^8+a^6*(2*b^2-c^2)+(b^2-c^2)^3*(b^2+2*c^2)+a^2*(b^2-c^2)^2*(2*b^2+5*c^2)+a^4*(-6*b^4+b^2*c^2-3*c^4)) : :

X(60121) lies on the Kiepert hyperbola and on these lines: {2, 1568}, {3, 43530}, {4, 5158}, {5, 16080}, {6, 60122}, {20, 60193}, {30, 275}, {83, 34664}, {94, 18478}, {140, 60138}, {376, 56346}, {381, 2052}, {459, 3545}, {1181, 46729}, {1498, 46727}, {1514, 54658}, {2394, 6368}, {2986, 38323}, {3091, 56270}, {3424, 5656}, {3524, 60137}, {3543, 60161}, {3830, 60120}, {3839, 8796}, {3845, 39284}, {5071, 38253}, {6809, 10194}, {6810, 10195}, {7395, 43527}, {7399, 10159}, {9300, 54709}, {10706, 54547}, {12101, 54791}, {12112, 54486}, {12233, 40448}, {13160, 60225}, {13582, 34007}, {13860, 60124}, {15032, 18316}, {15682, 54531}, {16072, 37874}, {16654, 60132}, {22467, 56063}, {40393, 52069}, {41099, 54867}, {41106, 54710}, {45089, 45300}

X(60121) = isogonal conjugate of X(11430)
X(60121) = trilinear pole of line {14391, 523}
X(60121) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(381)}}, {{A, B, C, X(5), X(30)}}, {{A, B, C, X(6), X(11438)}}, {{A, B, C, X(20), X(3545)}}, {{A, B, C, X(54), X(5627)}}, {{A, B, C, X(68), X(46412)}}, {{A, B, C, X(74), X(41891)}}, {{A, B, C, X(93), X(1138)}}, {{A, B, C, X(95), X(265)}}, {{A, B, C, X(140), X(3845)}}, {{A, B, C, X(264), X(1294)}}, {{A, B, C, X(276), X(53201)}}, {{A, B, C, X(323), X(15032)}}, {{A, B, C, X(376), X(3091)}}, {{A, B, C, X(382), X(5055)}}, {{A, B, C, X(403), X(38323)}}, {{A, B, C, X(427), X(34664)}}, {{A, B, C, X(428), X(7399)}}, {{A, B, C, X(525), X(42330)}}, {{A, B, C, X(546), X(549)}}, {{A, B, C, X(547), X(3627)}}, {{A, B, C, X(548), X(38071)}}, {{A, B, C, X(550), X(5066)}}, {{A, B, C, X(631), X(3839)}}, {{A, B, C, X(632), X(14893)}}, {{A, B, C, X(1006), X(52269)}}, {{A, B, C, X(1012), X(17556)}}, {{A, B, C, X(1093), X(14542)}}, {{A, B, C, X(1173), X(15053)}}, {{A, B, C, X(1176), X(18401)}}, {{A, B, C, X(1217), X(31371)}}, {{A, B, C, X(1513), X(8370)}}, {{A, B, C, X(1532), X(11112)}}, {{A, B, C, X(1593), X(16072)}}, {{A, B, C, X(1594), X(52069)}}, {{A, B, C, X(1656), X(3830)}}, {{A, B, C, X(1657), X(19709)}}, {{A, B, C, X(1989), X(8884)}}, {{A, B, C, X(2050), X(54367)}}, {{A, B, C, X(2165), X(16263)}}, {{A, B, C, X(3090), X(3543)}}, {{A, B, C, X(3146), X(5071)}}, {{A, B, C, X(3149), X(17532)}}, {{A, B, C, X(3163), X(47304)}}, {{A, B, C, X(3459), X(18363)}}, {{A, B, C, X(3522), X(41106)}}, {{A, B, C, X(3523), X(41099)}}, {{A, B, C, X(3524), X(3832)}}, {{A, B, C, X(3526), X(14269)}}, {{A, B, C, X(3530), X(23046)}}, {{A, B, C, X(3532), X(11058)}}, {{A, B, C, X(3534), X(3851)}}, {{A, B, C, X(3544), X(15683)}}, {{A, B, C, X(3613), X(11744)}}, {{A, B, C, X(3628), X(15687)}}, {{A, B, C, X(3843), X(5054)}}, {{A, B, C, X(3853), X(15699)}}, {{A, B, C, X(3854), X(19708)}}, {{A, B, C, X(3855), X(10304)}}, {{A, B, C, X(3856), X(17504)}}, {{A, B, C, X(3857), X(34200)}}, {{A, B, C, X(3858), X(12100)}}, {{A, B, C, X(3859), X(45759)}}, {{A, B, C, X(3860), X(15712)}}, {{A, B, C, X(3861), X(11539)}}, {{A, B, C, X(5025), X(55008)}}, {{A, B, C, X(5056), X(15682)}}, {{A, B, C, X(5064), X(7395)}}, {{A, B, C, X(5067), X(50687)}}, {{A, B, C, X(5068), X(11001)}}, {{A, B, C, X(5070), X(38335)}}, {{A, B, C, X(5072), X(15681)}}, {{A, B, C, X(5076), X(15703)}}, {{A, B, C, X(5079), X(15684)}}, {{A, B, C, X(5481), X(55978)}}, {{A, B, C, X(5656), X(10002)}}, {{A, B, C, X(6145), X(51032)}}, {{A, B, C, X(6526), X(52187)}}, {{A, B, C, X(6662), X(14861)}}, {{A, B, C, X(6830), X(11114)}}, {{A, B, C, X(6831), X(11113)}}, {{A, B, C, X(6841), X(28459)}}, {{A, B, C, X(6842), X(28452)}}, {{A, B, C, X(6844), X(11111)}}, {{A, B, C, X(6905), X(17577)}}, {{A, B, C, X(6906), X(37375)}}, {{A, B, C, X(6941), X(17579)}}, {{A, B, C, X(6945), X(37430)}}, {{A, B, C, X(7387), X(56965)}}, {{A, B, C, X(7392), X(34621)}}, {{A, B, C, X(7507), X(54994)}}, {{A, B, C, X(7540), X(37347)}}, {{A, B, C, X(7565), X(35921)}}, {{A, B, C, X(7576), X(13160)}}, {{A, B, C, X(7841), X(13860)}}, {{A, B, C, X(8226), X(37428)}}, {{A, B, C, X(8439), X(36412)}}, {{A, B, C, X(8797), X(18850)}}, {{A, B, C, X(8801), X(35512)}}, {{A, B, C, X(9307), X(52487)}}, {{A, B, C, X(10019), X(44268)}}, {{A, B, C, X(10024), X(38321)}}, {{A, B, C, X(10296), X(49674)}}, {{A, B, C, X(10297), X(44218)}}, {{A, B, C, X(11361), X(37446)}}, {{A, B, C, X(11479), X(34609)}}, {{A, B, C, X(11676), X(33013)}}, {{A, B, C, X(11737), X(15704)}}, {{A, B, C, X(12101), X(55856)}}, {{A, B, C, X(12811), X(15686)}}, {{A, B, C, X(12812), X(35404)}}, {{A, B, C, X(13623), X(57897)}}, {{A, B, C, X(13732), X(36583)}}, {{A, B, C, X(14041), X(37334)}}, {{A, B, C, X(14254), X(16075)}}, {{A, B, C, X(14483), X(41890)}}, {{A, B, C, X(14491), X(41894)}}, {{A, B, C, X(14528), X(18361)}}, {{A, B, C, X(14787), X(31723)}}, {{A, B, C, X(14788), X(34603)}}, {{A, B, C, X(14863), X(52441)}}, {{A, B, C, X(14891), X(41991)}}, {{A, B, C, X(14938), X(31846)}}, {{A, B, C, X(15078), X(35488)}}, {{A, B, C, X(15318), X(15740)}}, {{A, B, C, X(15321), X(38305)}}, {{A, B, C, X(15702), X(50689)}}, {{A, B, C, X(15980), X(37345)}}, {{A, B, C, X(16251), X(18852)}}, {{A, B, C, X(17505), X(22268)}}, {{A, B, C, X(17528), X(19541)}}, {{A, B, C, X(17530), X(37468)}}, {{A, B, C, X(18434), X(45838)}}, {{A, B, C, X(18550), X(18586)}}, {{A, B, C, X(18851), X(31361)}}, {{A, B, C, X(19646), X(50415)}}, {{A, B, C, X(21400), X(57895)}}, {{A, B, C, X(22261), X(52154)}}, {{A, B, C, X(22270), X(32533)}}, {{A, B, C, X(22466), X(30537)}}, {{A, B, C, X(31724), X(48411)}}, {{A, B, C, X(32085), X(43917)}}, {{A, B, C, X(33699), X(35018)}}, {{A, B, C, X(34007), X(37943)}}, {{A, B, C, X(34613), X(37990)}}, {{A, B, C, X(35403), X(55857)}}, {{A, B, C, X(35732), X(36436)}}, {{A, B, C, X(36439), X(42280)}}, {{A, B, C, X(36445), X(52402)}}, {{A, B, C, X(36454), X(42282)}}, {{A, B, C, X(36457), X(42281)}}, {{A, B, C, X(36463), X(52401)}}, {{A, B, C, X(36477), X(36729)}}, {{A, B, C, X(36530), X(36730)}}, {{A, B, C, X(36948), X(43699)}}, {{A, B, C, X(37984), X(44273)}}, {{A, B, C, X(38322), X(46029)}}, {{A, B, C, X(41981), X(41990)}}, {{A, B, C, X(41988), X(41992)}}, {{A, B, C, X(44157), X(48911)}}, {{A, B, C, X(44275), X(50008)}}, {{A, B, C, X(45011), X(52188)}}, {{A, B, C, X(50700), X(50741)}}

X(60122) = X(2)X(11430)∩X(4)X(3284)

Barycentrics    (2*a^8+a^2*(b^2-2*c^2)*(b^2-c^2)^2-(b^2-c^2)^3*(b^2+2*c^2)-a^6*(5*b^2+2*c^2)+a^4*(3*b^4+5*b^2*c^2))*(2*a^8-a^2*(b^2-c^2)^2*(2*b^2-c^2)+(b^2-c^2)^3*(2*b^2+c^2)-a^6*(2*b^2+5*c^2)+a^4*(5*b^2*c^2+3*c^4)) : :

X(60122) lies on the Kiepert hyperbola and on these lines: {2, 11430}, {3, 16080}, {4, 3284}, {5, 43530}, {6, 60121}, {20, 56270}, {30, 2052}, {76, 34664}, {94, 51254}, {98, 18396}, {262, 16657}, {275, 381}, {376, 459}, {520, 2394}, {801, 16072}, {1513, 60124}, {1514, 54820}, {1656, 60138}, {2797, 14223}, {3091, 60193}, {3524, 38253}, {3543, 8796}, {3545, 56346}, {3830, 39284}, {3839, 60161}, {3845, 60120}, {5071, 60137}, {5392, 52069}, {6146, 13380}, {6809, 10195}, {6810, 10194}, {7395, 10159}, {7399, 43527}, {7503, 60225}, {11001, 54710}, {11456, 60119}, {12022, 60130}, {12241, 13599}, {14249, 47304}, {15682, 54867}, {18945, 60166}, {34007, 60191}, {34289, 38323}, {34725, 54703}, {36413, 54923}, {37892, 55008}, {39874, 54604}, {41099, 54531}, {41362, 46727}, {41372, 51937}, {54994, 60241}

X(60122) = isogonal conjugate of X(11438)
X(60122) = trilinear pole of line {1636, 523}
X(60122) = X(i)-vertex conjugate of X(j) for these {i, j}: {3425, 60124}, {9307, 18532}
X(60122) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(30)}}, {{A, B, C, X(5), X(381)}}, {{A, B, C, X(6), X(11430)}}, {{A, B, C, X(20), X(376)}}, {{A, B, C, X(24), X(52069)}}, {{A, B, C, X(25), X(34664)}}, {{A, B, C, X(54), X(34570)}}, {{A, B, C, X(68), X(1105)}}, {{A, B, C, X(69), X(1294)}}, {{A, B, C, X(74), X(41890)}}, {{A, B, C, X(95), X(4846)}}, {{A, B, C, X(110), X(11459)}}, {{A, B, C, X(140), X(3830)}}, {{A, B, C, X(156), X(11591)}}, {{A, B, C, X(235), X(16072)}}, {{A, B, C, X(253), X(18852)}}, {{A, B, C, X(264), X(265)}}, {{A, B, C, X(378), X(38323)}}, {{A, B, C, X(382), X(549)}}, {{A, B, C, X(384), X(55008)}}, {{A, B, C, X(428), X(7395)}}, {{A, B, C, X(477), X(46259)}}, {{A, B, C, X(542), X(2797)}}, {{A, B, C, X(546), X(5055)}}, {{A, B, C, X(547), X(3843)}}, {{A, B, C, X(548), X(15681)}}, {{A, B, C, X(550), X(3534)}}, {{A, B, C, X(631), X(3543)}}, {{A, B, C, X(632), X(38335)}}, {{A, B, C, X(847), X(5627)}}, {{A, B, C, X(1012), X(11112)}}, {{A, B, C, X(1093), X(1989)}}, {{A, B, C, X(1138), X(45736)}}, {{A, B, C, X(1217), X(15077)}}, {{A, B, C, X(1297), X(55978)}}, {{A, B, C, X(1300), X(9307)}}, {{A, B, C, X(1503), X(41372)}}, {{A, B, C, X(1513), X(7841)}}, {{A, B, C, X(1532), X(17556)}}, {{A, B, C, X(1614), X(11444)}}, {{A, B, C, X(1656), X(3845)}}, {{A, B, C, X(1657), X(8703)}}, {{A, B, C, X(1658), X(18564)}}, {{A, B, C, X(2041), X(36437)}}, {{A, B, C, X(2042), X(36455)}}, {{A, B, C, X(2050), X(37150)}}, {{A, B, C, X(3090), X(3839)}}, {{A, B, C, X(3091), X(3545)}}, {{A, B, C, X(3146), X(3524)}}, {{A, B, C, X(3149), X(11113)}}, {{A, B, C, X(3153), X(7552)}}, {{A, B, C, X(3344), X(33702)}}, {{A, B, C, X(3346), X(18851)}}, {{A, B, C, X(3431), X(41894)}}, {{A, B, C, X(3519), X(18317)}}, {{A, B, C, X(3522), X(11001)}}, {{A, B, C, X(3523), X(15682)}}, {{A, B, C, X(3525), X(50687)}}, {{A, B, C, X(3526), X(15687)}}, {{A, B, C, X(3528), X(15683)}}, {{A, B, C, X(3529), X(10304)}}, {{A, B, C, X(3530), X(15684)}}, {{A, B, C, X(3532), X(48911)}}, {{A, B, C, X(3560), X(28452)}}, {{A, B, C, X(3613), X(18434)}}, {{A, B, C, X(3627), X(5054)}}, {{A, B, C, X(3628), X(14269)}}, {{A, B, C, X(3832), X(5071)}}, {{A, B, C, X(3851), X(5066)}}, {{A, B, C, X(3853), X(15694)}}, {{A, B, C, X(3861), X(15703)}}, {{A, B, C, X(5056), X(41099)}}, {{A, B, C, X(5059), X(19708)}}, {{A, B, C, X(5064), X(7399)}}, {{A, B, C, X(5068), X(41106)}}, {{A, B, C, X(5070), X(14893)}}, {{A, B, C, X(5072), X(38071)}}, {{A, B, C, X(5073), X(12100)}}, {{A, B, C, X(5076), X(11539)}}, {{A, B, C, X(5079), X(23046)}}, {{A, B, C, X(6175), X(6845)}}, {{A, B, C, X(6530), X(18396)}}, {{A, B, C, X(6639), X(18568)}}, {{A, B, C, X(6676), X(34725)}}, {{A, B, C, X(6761), X(14249)}}, {{A, B, C, X(6823), X(34609)}}, {{A, B, C, X(6829), X(52269)}}, {{A, B, C, X(6830), X(17577)}}, {{A, B, C, X(6831), X(17532)}}, {{A, B, C, X(6905), X(11114)}}, {{A, B, C, X(6906), X(17579)}}, {{A, B, C, X(6909), X(37430)}}, {{A, B, C, X(6941), X(37375)}}, {{A, B, C, X(6985), X(28459)}}, {{A, B, C, X(7386), X(34621)}}, {{A, B, C, X(7400), X(44442)}}, {{A, B, C, X(7403), X(56965)}}, {{A, B, C, X(7485), X(34613)}}, {{A, B, C, X(7503), X(7576)}}, {{A, B, C, X(7509), X(34603)}}, {{A, B, C, X(7514), X(7540)}}, {{A, B, C, X(7526), X(38321)}}, {{A, B, C, X(7574), X(44262)}}, {{A, B, C, X(7580), X(37428)}}, {{A, B, C, X(7667), X(11414)}}, {{A, B, C, X(7833), X(11676)}}, {{A, B, C, X(7999), X(52525)}}, {{A, B, C, X(8370), X(13860)}}, {{A, B, C, X(8727), X(17528)}}, {{A, B, C, X(8797), X(43699)}}, {{A, B, C, X(8884), X(14457)}}, {{A, B, C, X(9289), X(53201)}}, {{A, B, C, X(9909), X(12362)}}, {{A, B, C, X(10201), X(18404)}}, {{A, B, C, X(10299), X(15640)}}, {{A, B, C, X(10323), X(52397)}}, {{A, B, C, X(10691), X(39568)}}, {{A, B, C, X(11111), X(50701)}}, {{A, B, C, X(11361), X(37334)}}, {{A, B, C, X(11413), X(44458)}}, {{A, B, C, X(11454), X(15035)}}, {{A, B, C, X(11456), X(15066)}}, {{A, B, C, X(11541), X(15705)}}, {{A, B, C, X(11744), X(45838)}}, {{A, B, C, X(11818), X(14787)}}, {{A, B, C, X(12101), X(46219)}}, {{A, B, C, X(12103), X(15689)}}, {{A, B, C, X(12225), X(44837)}}, {{A, B, C, X(12241), X(41365)}}, {{A, B, C, X(12605), X(14070)}}, {{A, B, C, X(13632), X(36685)}}, {{A, B, C, X(13732), X(36512)}}, {{A, B, C, X(14041), X(37446)}}, {{A, B, C, X(14118), X(18559)}}, {{A, B, C, X(14483), X(41891)}}, {{A, B, C, X(14860), X(32533)}}, {{A, B, C, X(14891), X(49134)}}, {{A, B, C, X(14938), X(17505)}}, {{A, B, C, X(15078), X(18560)}}, {{A, B, C, X(15331), X(18561)}}, {{A, B, C, X(15454), X(16075)}}, {{A, B, C, X(15619), X(52518)}}, {{A, B, C, X(15685), X(33923)}}, {{A, B, C, X(15686), X(15696)}}, {{A, B, C, X(15688), X(15704)}}, {{A, B, C, X(15692), X(33703)}}, {{A, B, C, X(15698), X(49135)}}, {{A, B, C, X(15702), X(17578)}}, {{A, B, C, X(15709), X(50688)}}, {{A, B, C, X(15710), X(49140)}}, {{A, B, C, X(15711), X(49133)}}, {{A, B, C, X(15715), X(50692)}}, {{A, B, C, X(15719), X(50691)}}, {{A, B, C, X(15720), X(33699)}}, {{A, B, C, X(15740), X(18846)}}, {{A, B, C, X(15749), X(18855)}}, {{A, B, C, X(15759), X(49139)}}, {{A, B, C, X(15765), X(18587)}}, {{A, B, C, X(16239), X(35403)}}, {{A, B, C, X(16251), X(18847)}}, {{A, B, C, X(16370), X(37468)}}, {{A, B, C, X(16418), X(20420)}}, {{A, B, C, X(16657), X(33971)}}, {{A, B, C, X(16835), X(45301)}}, {{A, B, C, X(17504), X(49136)}}, {{A, B, C, X(17800), X(34200)}}, {{A, B, C, X(18324), X(18563)}}, {{A, B, C, X(18401), X(34801)}}, {{A, B, C, X(18550), X(46452)}}, {{A, B, C, X(18585), X(18586)}}, {{A, B, C, X(22270), X(57895)}}, {{A, B, C, X(23582), X(42313)}}, {{A, B, C, X(31829), X(54992)}}, {{A, B, C, X(32085), X(45088)}}, {{A, B, C, X(32418), X(52552)}}, {{A, B, C, X(34285), X(35512)}}, {{A, B, C, X(34297), X(56399)}}, {{A, B, C, X(34622), X(44241)}}, {{A, B, C, X(35401), X(45760)}}, {{A, B, C, X(35732), X(36445)}}, {{A, B, C, X(35912), X(47111)}}, {{A, B, C, X(35930), X(37345)}}, {{A, B, C, X(36436), X(52402)}}, {{A, B, C, X(36454), X(52401)}}, {{A, B, C, X(36463), X(42282)}}, {{A, B, C, X(36477), X(36730)}}, {{A, B, C, X(36530), X(36729)}}, {{A, B, C, X(37022), X(37429)}}, {{A, B, C, X(37196), X(44285)}}, {{A, B, C, X(37447), X(44217)}}, {{A, B, C, X(38305), X(45090)}}, {{A, B, C, X(43891), X(59278)}}, {{A, B, C, X(45011), X(52187)}}, {{A, B, C, X(45759), X(49137)}}, {{A, B, C, X(51519), X(52073)}}, {{A, B, C, X(52392), X(56261)}}, {{A, B, C, X(57747), X(57819)}}

X(60123) = X(2)X(52719)∩X(4)X(3054)

Barycentrics    (7*a^4-10*a^2*b^2+7*b^4-12*(a^2+b^2)*c^2+5*c^4)*(7*a^4+5*b^4-12*b^2*c^2+7*c^4-2*a^2*(6*b^2+5*c^2)) : :

X(60123) lies on the Kiepert hyperbola and on these lines: {2, 52719}, {3, 41895}, {4, 3054}, {5, 53101}, {6, 53098}, {20, 60113}, {22, 54781}, {25, 54893}, {30, 54896}, {69, 60198}, {76, 3533}, {140, 2996}, {230, 10155}, {376, 17503}, {381, 54642}, {383, 54580}, {427, 54892}, {468, 8796}, {598, 3090}, {631, 671}, {1080, 54581}, {1370, 54762}, {1513, 54519}, {1656, 5395}, {2052, 52290}, {3091, 54476}, {3147, 54685}, {3523, 38259}, {3524, 32532}, {3525, 5485}, {3526, 60200}, {3528, 54720}, {3529, 33698}, {3545, 45103}, {3628, 54639}, {3855, 54494}, {5056, 18845}, {5067, 18842}, {5071, 60281}, {5094, 60161}, {5466, 47122}, {6036, 60280}, {6353, 39284}, {6776, 60337}, {6811, 43566}, {6813, 43567}, {6833, 54780}, {6879, 54630}, {6880, 54691}, {6927, 54692}, {6949, 54755}, {6952, 54754}, {6956, 54729}, {6977, 54799}, {6997, 54765}, {7000, 54543}, {7374, 54542}, {7380, 54623}, {7383, 54779}, {7386, 54761}, {7391, 54601}, {7392, 54764}, {7410, 60079}, {7493, 54927}, {7494, 54666}, {7558, 54777}, {7607, 14912}, {7608, 33550}, {7612, 8550}, {7735, 11669}, {7736, 53108}, {7749, 54868}, {8889, 60120}, {9744, 60335}, {9754, 54890}, {10299, 53105}, {11001, 54647}, {13579, 46336}, {13585, 16063}, {13860, 54520}, {14064, 54872}, {14458, 58883}, {14494, 37637}, {15597, 60240}, {15682, 54478}, {15702, 54637}, {15709, 60228}, {16045, 54915}, {16051, 54913}, {17006, 60234}, {21735, 53106}, {23053, 60211}, {32956, 54916}, {32968, 54753}, {32969, 54833}, {32977, 54750}, {33189, 54751}, {33703, 54493}, {34229, 60178}, {37446, 54565}, {37463, 43540}, {37464, 43541}, {38227, 60329}, {38282, 54867}, {39874, 47586}, {40132, 54864}, {41139, 54616}, {41400, 54482}, {43461, 60334}, {46219, 60285}, {46935, 60145}, {52292, 56270}, {52293, 60193}, {52299, 54531}, {54889, 56370}

X(60123) = isogonal conjugate of X(11482)
X(60123) = X(i)-vertex conjugate of X(j) for these {i, j}: {25, 10155}, {3425, 54519}
X(60123) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(5210)}}, {{A, B, C, X(6), X(53092)}}, {{A, B, C, X(25), X(3533)}}, {{A, B, C, X(54), X(21448)}}, {{A, B, C, X(67), X(8797)}}, {{A, B, C, X(69), X(3054)}}, {{A, B, C, X(70), X(3090)}}, {{A, B, C, X(95), X(46217)}}, {{A, B, C, X(111), X(13472)}}, {{A, B, C, X(140), X(6353)}}, {{A, B, C, X(252), X(18854)}}, {{A, B, C, X(376), X(52292)}}, {{A, B, C, X(468), X(631)}}, {{A, B, C, X(524), X(23054)}}, {{A, B, C, X(1656), X(8889)}}, {{A, B, C, X(2165), X(15464)}}, {{A, B, C, X(2963), X(5486)}}, {{A, B, C, X(3147), X(7495)}}, {{A, B, C, X(3459), X(55029)}}, {{A, B, C, X(3519), X(6340)}}, {{A, B, C, X(3523), X(38282)}}, {{A, B, C, X(3524), X(53857)}}, {{A, B, C, X(3525), X(4232)}}, {{A, B, C, X(3532), X(14489)}}, {{A, B, C, X(3545), X(52293)}}, {{A, B, C, X(3563), X(14528)}}, {{A, B, C, X(5056), X(52299)}}, {{A, B, C, X(5067), X(52284)}}, {{A, B, C, X(7494), X(10018)}}, {{A, B, C, X(7505), X(46336)}}, {{A, B, C, X(7610), X(23053)}}, {{A, B, C, X(7714), X(46219)}}, {{A, B, C, X(8770), X(43908)}}, {{A, B, C, X(8801), X(57927)}}, {{A, B, C, X(10299), X(37453)}}, {{A, B, C, X(10603), X(18853)}}, {{A, B, C, X(14940), X(16063)}}, {{A, B, C, X(15597), X(23055)}}, {{A, B, C, X(16774), X(40410)}}, {{A, B, C, X(16835), X(54172)}}, {{A, B, C, X(17006), X(17008)}}, {{A, B, C, X(17040), X(17983)}}, {{A, B, C, X(21735), X(52297)}}, {{A, B, C, X(22268), X(40347)}}, {{A, B, C, X(30542), X(36889)}}, {{A, B, C, X(34229), X(37637)}}, {{A, B, C, X(36611), X(45857)}}, {{A, B, C, X(37118), X(40132)}}, {{A, B, C, X(37518), X(39954)}}, {{A, B, C, X(39951), X(43662)}}, {{A, B, C, X(40118), X(46081)}}, {{A, B, C, X(41522), X(46412)}}, {{A, B, C, X(42021), X(44535)}}, {{A, B, C, X(43726), X(52717)}}, {{A, B, C, X(44556), X(44658)}}, {{A, B, C, X(45838), X(46223)}}

X(60124) = X(25)X(671)∩X(76)X(468)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(2*(a^4-a^2*b^2+b^4)+(a^2+b^2)*c^2-c^4)*(2*a^4-b^4+b^2*c^2+2*c^4+a^2*(b^2-2*c^2)) : :

X(60124) lies on these lines: {2, 44102}, {3, 54898}, {5, 54682}, {22, 54871}, {23, 54680}, {24, 54513}, {25, 671}, {30, 54897}, {76, 468}, {83, 5094}, {250, 52940}, {297, 54916}, {427, 598}, {428, 17503}, {458, 54915}, {1513, 60122}, {1594, 54730}, {1995, 54796}, {2489, 5466}, {2996, 4232}, {3089, 54779}, {3542, 54558}, {4231, 54691}, {5020, 54836}, {5064, 45103}, {5133, 54684}, {5169, 54683}, {5395, 52284}, {5485, 6353}, {5999, 54828}, {6995, 41895}, {7378, 53101}, {7408, 60113}, {7409, 54476}, {7714, 32532}, {8889, 18842}, {10159, 52292}, {10301, 53105}, {10302, 37453}, {13860, 60121}, {13862, 54551}, {14223, 47206}, {15809, 60120}, {18559, 54483}, {18840, 52290}, {37362, 54729}, {38259, 52301}, {38282, 60143}, {43527, 52293}, {52285, 54494}, {52297, 60277}, {52298, 60238}, {52299, 54616}, {53857, 60285}, {54660, 58883}

X(60124) = isogonal conjugate of X(11511)
X(60124) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 11511}, {48, 7841}
X(60124) = X(i)-vertex conjugate of X(j) for these {i, j}: {3425, 60122}
X(60124) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 11511}, {1249, 7841}
X(60124) = X(i)-cross conjugate of X(j) for these {i, j}: {14277, 935}
X(60124) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(250)}}, {{A, B, C, X(66), X(30786)}}, {{A, B, C, X(67), X(305)}}, {{A, B, C, X(111), X(57388)}}, {{A, B, C, X(264), X(8791)}}, {{A, B, C, X(393), X(2374)}}, {{A, B, C, X(427), X(5094)}}, {{A, B, C, X(428), X(52292)}}, {{A, B, C, X(842), X(18532)}}, {{A, B, C, X(1656), X(15809)}}, {{A, B, C, X(1799), X(5486)}}, {{A, B, C, X(1990), X(52752)}}, {{A, B, C, X(2373), X(9307)}}, {{A, B, C, X(2980), X(40347)}}, {{A, B, C, X(4232), X(6353)}}, {{A, B, C, X(5064), X(52293)}}, {{A, B, C, X(6103), X(47206)}}, {{A, B, C, X(6995), X(52290)}}, {{A, B, C, X(7714), X(53857)}}, {{A, B, C, X(8889), X(52284)}}, {{A, B, C, X(9876), X(14357)}}, {{A, B, C, X(10301), X(37453)}}, {{A, B, C, X(10415), X(18018)}}, {{A, B, C, X(13854), X(17983)}}, {{A, B, C, X(19577), X(57518)}}, {{A, B, C, X(38282), X(52301)}}, {{A, B, C, X(47259), X(57485)}}
X(60124) = barycentric quotient X(i)/X(j) for these (i, j): {4, 7841}, {6, 11511}

X(60125) = X(2)X(1974)∩X(25)X(76)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4+b^4+(a^2+b^2)*c^2)*(a^4+a^2*b^2+b^2*c^2+c^4) : :

X(60125) lies on the Kiepert hyperbola and on these lines: {2, 1974}, {4, 36417}, {6, 60141}, {25, 76}, {30, 54898}, {83, 427}, {112, 59188}, {275, 15809}, {381, 54682}, {428, 671}, {468, 10159}, {598, 5064}, {1513, 40448}, {1799, 27369}, {2052, 52439}, {2374, 35567}, {2996, 6995}, {3830, 54897}, {4231, 54739}, {4232, 60285}, {5094, 43527}, {5395, 7378}, {5485, 7714}, {5986, 11606}, {6353, 18840}, {7408, 38259}, {7409, 18845}, {7576, 54513}, {8889, 18841}, {10301, 43676}, {13599, 13860}, {15652, 60266}, {32085, 40016}, {34603, 54871}, {37453, 60278}, {38282, 60183}, {43681, 52301}, {52281, 54915}, {52282, 54916}, {52285, 53109}, {52293, 60182}, {52297, 56059}

X(60125) = isogonal conjugate of X(11574)
X(60125) = isotomic conjugate of X(45201)
X(60125) = trilinear pole of line {37912, 523}
X(60125) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 11574}, {3, 17446}, {6, 45220}, {31, 45201}, {48, 6656}, {63, 1194}, {71, 16735}, {82, 22424}, {1176, 21336}, {2514, 4592}, {4575, 47126}, {10547, 21424}, {23642, 34055}
X(60125) = X(i)-vertex conjugate of X(j) for these {i, j}: {1799, 60125}, {3425, 40448}
X(60125) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 45201}, {3, 11574}, {9, 45220}, {136, 47126}, {141, 22424}, {1249, 6656}, {3162, 1194}, {5139, 2514}, {36103, 17446}, {40938, 21248}
X(60125) = X(i)-cross conjugate of X(j) for these {i, j}: {18105, 112}, {23285, 1289}
X(60125) = pole of line {2514, 47126} with respect to the polar circle
X(60125) = pole of line {11574, 22424} with respect to the Stammler hyperbola
X(60125) = pole of line {11574, 45201} with respect to the Wallace hyperbola
X(60125) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(5), X(15809)}}, {{A, B, C, X(6), X(1799)}}, {{A, B, C, X(25), X(1974)}}, {{A, B, C, X(32), X(9917)}}, {{A, B, C, X(66), X(305)}}, {{A, B, C, X(67), X(57852)}}, {{A, B, C, X(95), X(39951)}}, {{A, B, C, X(251), X(2373)}}, {{A, B, C, X(264), X(13854)}}, {{A, B, C, X(393), X(47847)}}, {{A, B, C, X(427), X(8791)}}, {{A, B, C, X(428), X(468)}}, {{A, B, C, X(1039), X(52133)}}, {{A, B, C, X(1041), X(56358)}}, {{A, B, C, X(1179), X(3563)}}, {{A, B, C, X(1294), X(34427)}}, {{A, B, C, X(1513), X(52280)}}, {{A, B, C, X(2857), X(57409)}}, {{A, B, C, X(2862), X(57386)}}, {{A, B, C, X(2980), X(8770)}}, {{A, B, C, X(3108), X(9076)}}, {{A, B, C, X(4232), X(7714)}}, {{A, B, C, X(5064), X(5094)}}, {{A, B, C, X(6325), X(34572)}}, {{A, B, C, X(6353), X(6995)}}, {{A, B, C, X(6531), X(46104)}}, {{A, B, C, X(7378), X(8889)}}, {{A, B, C, X(7408), X(38282)}}, {{A, B, C, X(7409), X(52299)}}, {{A, B, C, X(8840), X(34854)}}, {{A, B, C, X(8884), X(40801)}}, {{A, B, C, X(9307), X(13575)}}, {{A, B, C, X(11380), X(12143)}}, {{A, B, C, X(14489), X(34449)}}, {{A, B, C, X(15321), X(30786)}}, {{A, B, C, X(15652), X(19136)}}, {{A, B, C, X(18018), X(39436)}}, {{A, B, C, X(18019), X(41513)}}, {{A, B, C, X(18105), X(59188)}}, {{A, B, C, X(25985), X(37362)}}, {{A, B, C, X(29180), X(45302)}}, {{A, B, C, X(51862), X(58306)}}
X(60125) = barycentric product X(i)*X(j) for these (i, j): {1241, 25}, {2489, 35567}
X(60125) = barycentric quotient X(i)/X(j) for these (i, j): {1, 45220}, {2, 45201}, {4, 6656}, {6, 11574}, {19, 17446}, {25, 1194}, {28, 16735}, {39, 22424}, {427, 21248}, {1241, 305}, {1843, 23642}, {2489, 2514}, {2501, 47126}, {17442, 21336}, {20883, 21424}, {35567, 52608}

X(60126) = X(2)X(8179)∩X(83)X(576)

Barycentrics    (a^2*b^2*(a^2+b^2)-(a^4-5*a^2*b^2+b^4)*c^2+3*(a^2+b^2)*c^4-2*c^6)*(2*b^6-3*b^4*c^2+b^2*c^4+a^4*(b-c)*(b+c)-a^2*(3*b^4+5*b^2*c^2+c^4)) : :

X(60126) lies on the Kiepert hyperbola and on these lines: {2, 8179}, {3, 60184}, {4, 44453}, {5, 60177}, {6, 60148}, {13, 44464}, {14, 44460}, {30, 54901}, {39, 7607}, {76, 11261}, {83, 576}, {98, 574}, {194, 49793}, {262, 7603}, {381, 54737}, {511, 598}, {538, 11167}, {671, 11178}, {698, 5485}, {1503, 54614}, {1916, 7697}, {2080, 3407}, {2782, 32480}, {2794, 54481}, {3090, 60234}, {3094, 43532}, {3095, 60098}, {3406, 5038}, {3525, 60263}, {3906, 43665}, {5503, 7617}, {6248, 53105}, {7757, 60220}, {8586, 11170}, {8587, 11171}, {8704, 60106}, {10290, 24206}, {10335, 54122}, {11257, 53100}, {11606, 37242}, {12243, 54840}, {14488, 22682}, {14651, 54731}, {14853, 54724}, {15819, 60093}, {18906, 60072}, {20423, 54804}, {31276, 43529}, {32149, 43527}, {37348, 44434}, {40108, 60104}, {43528, 49111}, {55801, 60103}

X(60126) = isogonal conjugate of X(11842)
X(60126) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 54614}
X(60126) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(44453)}}, {{A, B, C, X(6), X(32447)}}, {{A, B, C, X(39), X(576)}}, {{A, B, C, X(54), X(17042)}}, {{A, B, C, X(263), X(11261)}}, {{A, B, C, X(290), X(18575)}}, {{A, B, C, X(327), X(523)}}, {{A, B, C, X(420), X(37242)}}, {{A, B, C, X(511), X(574)}}, {{A, B, C, X(538), X(8704)}}, {{A, B, C, X(698), X(1499)}}, {{A, B, C, X(726), X(28565)}}, {{A, B, C, X(1235), X(12251)}}, {{A, B, C, X(2080), X(3094)}}, {{A, B, C, X(2698), X(30495)}}, {{A, B, C, X(3095), X(5038)}}, {{A, B, C, X(3613), X(57908)}}, {{A, B, C, X(5117), X(35925)}}, {{A, B, C, X(5967), X(11178)}}, {{A, B, C, X(8586), X(11171)}}, {{A, B, C, X(11166), X(14491)}}, {{A, B, C, X(33565), X(59264)}}, {{A, B, C, X(41517), X(54999)}}, {{A, B, C, X(44658), X(54124)}}
X(60126) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {574, 32469, 7709}

X(60127) = X(4)X(9300)∩X(83)X(376)

Barycentrics    (a^4+10*a^2*b^2+b^4+4*(a^2+b^2)*c^2-5*c^4)*(a^4-5*b^4+4*b^2*c^2+c^4+2*a^2*(2*b^2+5*c^2)) : :

X(60127) lies on the Kiepert hyperbola and on these lines: {2, 21850}, {3, 55780}, {4, 9300}, {5, 60285}, {6, 60150}, {20, 60145}, {25, 60193}, {30, 5395}, {69, 60217}, {76, 3545}, {83, 376}, {275, 7714}, {381, 2996}, {383, 22235}, {427, 56270}, {428, 60161}, {542, 60280}, {598, 15682}, {631, 43527}, {671, 41099}, {1080, 22237}, {1503, 60325}, {1513, 53099}, {1992, 60218}, {2549, 54714}, {3090, 10159}, {3091, 43681}, {3424, 14912}, {3524, 18841}, {3529, 53102}, {3533, 60182}, {3534, 54639}, {3543, 18845}, {3590, 6813}, {3591, 6811}, {3815, 54523}, {3830, 53101}, {3839, 38259}, {3845, 41895}, {3855, 43676}, {5064, 8796}, {5066, 60200}, {5071, 18840}, {5306, 60185}, {5475, 54713}, {5476, 60093}, {5480, 14494}, {5485, 9766}, {6353, 43530}, {6776, 54845}, {6997, 60255}, {7000, 60291}, {7374, 60292}, {7391, 60191}, {7394, 13582}, {7608, 58883}, {7612, 14853}, {7709, 54814}, {7710, 54890}, {7735, 60175}, {7736, 14492}, {7739, 54858}, {7753, 54846}, {7774, 60214}, {7837, 54122}, {8889, 16080}, {9744, 14488}, {9753, 53104}, {9770, 60180}, {9993, 60192}, {11001, 18842}, {11172, 14614}, {11648, 54718}, {12101, 54642}, {13860, 43537}, {14458, 39874}, {14482, 54716}, {14537, 60117}, {15698, 60239}, {15709, 60100}, {15719, 60238}, {16041, 60151}, {19130, 60202}, {19708, 54616}, {20423, 60101}, {22806, 60208}, {22807, 60207}, {33703, 60146}, {34608, 40393}, {37665, 54519}, {37671, 60212}, {43460, 54582}, {43461, 54920}, {45109, 60271}, {52290, 60138}, {52519, 53023}, {53015, 60323}, {54906, 59373}

X(60127) = isogonal conjugate of X(12017)
X(60127) = trilinear pole of line {47447, 523}
X(60127) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 60325}, {3425, 53099}
X(60127) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(5), X(7714)}}, {{A, B, C, X(6), X(33878)}}, {{A, B, C, X(25), X(3545)}}, {{A, B, C, X(30), X(8889)}}, {{A, B, C, X(66), X(30537)}}, {{A, B, C, X(69), X(9300)}}, {{A, B, C, X(74), X(39951)}}, {{A, B, C, X(251), X(14491)}}, {{A, B, C, X(263), X(44422)}}, {{A, B, C, X(264), X(52187)}}, {{A, B, C, X(376), X(427)}}, {{A, B, C, X(381), X(6353)}}, {{A, B, C, X(393), X(55958)}}, {{A, B, C, X(428), X(3090)}}, {{A, B, C, X(468), X(41099)}}, {{A, B, C, X(631), X(5064)}}, {{A, B, C, X(842), X(39955)}}, {{A, B, C, X(1000), X(7249)}}, {{A, B, C, X(1138), X(39978)}}, {{A, B, C, X(1173), X(18854)}}, {{A, B, C, X(1297), X(13472)}}, {{A, B, C, X(1494), X(8801)}}, {{A, B, C, X(1594), X(34608)}}, {{A, B, C, X(1989), X(8797)}}, {{A, B, C, X(1992), X(9766)}}, {{A, B, C, X(3108), X(3431)}}, {{A, B, C, X(3296), X(4518)}}, {{A, B, C, X(3425), X(34572)}}, {{A, B, C, X(3524), X(7378)}}, {{A, B, C, X(3527), X(3563)}}, {{A, B, C, X(3531), X(8770)}}, {{A, B, C, X(3541), X(44442)}}, {{A, B, C, X(3543), X(52299)}}, {{A, B, C, X(3613), X(21850)}}, {{A, B, C, X(3839), X(38282)}}, {{A, B, C, X(3845), X(52290)}}, {{A, B, C, X(4232), X(41106)}}, {{A, B, C, X(4846), X(6340)}}, {{A, B, C, X(5071), X(6995)}}, {{A, B, C, X(5094), X(15682)}}, {{A, B, C, X(5481), X(13452)}}, {{A, B, C, X(5486), X(11058)}}, {{A, B, C, X(5627), X(47582)}}, {{A, B, C, X(7394), X(37943)}}, {{A, B, C, X(7409), X(15702)}}, {{A, B, C, X(7736), X(37671)}}, {{A, B, C, X(7774), X(7837)}}, {{A, B, C, X(9607), X(15740)}}, {{A, B, C, X(9770), X(14614)}}, {{A, B, C, X(10002), X(14912)}}, {{A, B, C, X(11001), X(52284)}}, {{A, B, C, X(11738), X(39389)}}, {{A, B, C, X(14487), X(21448)}}, {{A, B, C, X(14489), X(36616)}}, {{A, B, C, X(15321), X(36948)}}, {{A, B, C, X(15709), X(52285)}}, {{A, B, C, X(16615), X(39954)}}, {{A, B, C, X(16774), X(46952)}}, {{A, B, C, X(18575), X(38005)}}, {{A, B, C, X(18852), X(20480)}}, {{A, B, C, X(31105), X(35473)}}, {{A, B, C, X(36611), X(57408)}}, {{A, B, C, X(36875), X(47734)}}, {{A, B, C, X(38305), X(43699)}}, {{A, B, C, X(42299), X(42377)}}, {{A, B, C, X(43733), X(57727)}}, {{A, B, C, X(43734), X(57726)}}, {{A, B, C, X(45819), X(46204)}}, {{A, B, C, X(52487), X(55023)}}

X(60128) = X(2)X(2056)∩X(4)X(2080)

Barycentrics    (a^4-a^2*b^2+b^4-2*(a^2+b^2)*c^2)*(a^4-2*b^2*c^2+c^4-a^2*(2*b^2+c^2)) : :

X(60128) lies on the Kiepert hyperbola and on these lines: {2, 2056}, {3, 43532}, {4, 2080}, {5, 11170}, {6, 33689}, {20, 54488}, {30, 54903}, {32, 598}, {69, 60234}, {76, 574}, {83, 7746}, {98, 17004}, {141, 43529}, {148, 7616}, {182, 7607}, {183, 1916}, {193, 53099}, {194, 49793}, {230, 3407}, {262, 385}, {325, 60233}, {381, 54715}, {524, 10484}, {599, 42010}, {626, 54841}, {671, 1078}, {1691, 60184}, {1975, 54750}, {2896, 54822}, {2996, 32965}, {3314, 8781}, {3329, 60096}, {3398, 60148}, {3399, 7754}, {3620, 60262}, {3788, 10159}, {4027, 37637}, {5025, 60072}, {5171, 54869}, {5182, 10153}, {5395, 32962}, {5466, 31296}, {5485, 32480}, {6055, 54731}, {7608, 7777}, {7610, 43535}, {7735, 60190}, {7749, 10131}, {7774, 14494}, {7785, 54724}, {7787, 18842}, {7792, 60129}, {7801, 10302}, {7808, 60239}, {7812, 54804}, {7823, 14485}, {7836, 18840}, {7837, 60192}, {7840, 60211}, {7868, 60231}, {7870, 60277}, {7925, 60178}, {7940, 60278}, {8586, 60177}, {8587, 8860}, {8597, 17503}, {9302, 14880}, {10130, 40016}, {10349, 18841}, {10352, 60073}, {11669, 17005}, {12110, 54868}, {12150, 60282}, {13085, 17129}, {13468, 54540}, {13881, 54872}, {14484, 37667}, {15271, 42006}, {15589, 60260}, {16055, 57813}, {16984, 60215}, {16986, 60213}, {16990, 40824}, {16997, 45964}, {16999, 60108}, {17128, 54751}, {18845, 32995}, {19911, 33274}, {20065, 54826}, {22329, 54487}, {30505, 52898}, {32997, 38259}, {33192, 41895}, {33226, 60219}, {33256, 53105}, {34229, 54122}, {34506, 54840}, {36864, 54978}, {38732, 39652}, {39141, 60263}, {42535, 60105}, {53263, 60226}

X(60128) = isogonal conjugate of X(13330)
X(60128) = isotomic conjugate of X(7777)
X(60128) = trilinear pole of line {15826, 523}
X(60128) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 13330}, {31, 7777}, {75, 41278}
X(60128) = X(i)-vertex conjugate of X(j) for these {i, j}: {25, 3407}, {32, 60184}, {42288, 54906}
X(60128) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 7777}, {3, 13330}, {206, 41278}
X(60128) = pole of line {37688, 60128} with respect to the Kiepert hyperbola
X(60128) = pole of line {13330, 41278} with respect to the Stammler hyperbola
X(60128) = pole of line {7777, 13330} with respect to the Wallace hyperbola
X(60128) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(2080)}}, {{A, B, C, X(6), X(5038)}}, {{A, B, C, X(25), X(7824)}}, {{A, B, C, X(32), X(111)}}, {{A, B, C, X(67), X(40826)}}, {{A, B, C, X(69), X(17008)}}, {{A, B, C, X(95), X(2998)}}, {{A, B, C, X(141), X(7806)}}, {{A, B, C, X(182), X(576)}}, {{A, B, C, X(183), X(385)}}, {{A, B, C, X(192), X(261)}}, {{A, B, C, X(230), X(3314)}}, {{A, B, C, X(251), X(7815)}}, {{A, B, C, X(308), X(9516)}}, {{A, B, C, X(325), X(17004)}}, {{A, B, C, X(330), X(4998)}}, {{A, B, C, X(427), X(16921)}}, {{A, B, C, X(468), X(7833)}}, {{A, B, C, X(599), X(8859)}}, {{A, B, C, X(694), X(46320)}}, {{A, B, C, X(695), X(46316)}}, {{A, B, C, X(699), X(7781)}}, {{A, B, C, X(729), X(40103)}}, {{A, B, C, X(733), X(2056)}}, {{A, B, C, X(880), X(9062)}}, {{A, B, C, X(1078), X(31296)}}, {{A, B, C, X(1383), X(42346)}}, {{A, B, C, X(1502), X(2963)}}, {{A, B, C, X(1691), X(44453)}}, {{A, B, C, X(1799), X(7793)}}, {{A, B, C, X(2165), X(9229)}}, {{A, B, C, X(2373), X(54114)}}, {{A, B, C, X(2623), X(3224)}}, {{A, B, C, X(2698), X(14565)}}, {{A, B, C, X(2980), X(39968)}}, {{A, B, C, X(3094), X(46314)}}, {{A, B, C, X(3329), X(15271)}}, {{A, B, C, X(3398), X(32447)}}, {{A, B, C, X(3620), X(37689)}}, {{A, B, C, X(3788), X(39998)}}, {{A, B, C, X(4232), X(33215)}}, {{A, B, C, X(4590), X(9462)}}, {{A, B, C, X(5094), X(33013)}}, {{A, B, C, X(5486), X(9227)}}, {{A, B, C, X(6353), X(32965)}}, {{A, B, C, X(6464), X(31617)}}, {{A, B, C, X(6664), X(53864)}}, {{A, B, C, X(6995), X(32978)}}, {{A, B, C, X(7378), X(32975)}}, {{A, B, C, X(7610), X(7840)}}, {{A, B, C, X(7617), X(42008)}}, {{A, B, C, X(7735), X(16990)}}, {{A, B, C, X(7746), X(8024)}}, {{A, B, C, X(7774), X(34229)}}, {{A, B, C, X(7777), X(37688)}}, {{A, B, C, X(7792), X(16986)}}, {{A, B, C, X(7801), X(26235)}}, {{A, B, C, X(7836), X(40022)}}, {{A, B, C, X(7868), X(16984)}}, {{A, B, C, X(7925), X(37637)}}, {{A, B, C, X(8586), X(39560)}}, {{A, B, C, X(8597), X(52292)}}, {{A, B, C, X(8889), X(32962)}}, {{A, B, C, X(9076), X(31622)}}, {{A, B, C, X(9289), X(14712)}}, {{A, B, C, X(9483), X(59249)}}, {{A, B, C, X(10014), X(30498)}}, {{A, B, C, X(10104), X(57799)}}, {{A, B, C, X(14357), X(51541)}}, {{A, B, C, X(14383), X(46806)}}, {{A, B, C, X(15464), X(25322)}}, {{A, B, C, X(15589), X(37667)}}, {{A, B, C, X(16992), X(16999)}}, {{A, B, C, X(16997), X(37670)}}, {{A, B, C, X(18019), X(44185)}}, {{A, B, C, X(18575), X(43098)}}, {{A, B, C, X(23297), X(27366)}}, {{A, B, C, X(24861), X(40425)}}, {{A, B, C, X(32480), X(52141)}}, {{A, B, C, X(32995), X(52299)}}, {{A, B, C, X(32997), X(38282)}}, {{A, B, C, X(33192), X(52290)}}, {{A, B, C, X(33256), X(37453)}}, {{A, B, C, X(34816), X(40416)}}, {{A, B, C, X(35511), X(57822)}}, {{A, B, C, X(38262), X(45857)}}, {{A, B, C, X(40429), X(44558)}}, {{A, B, C, X(40738), X(56042)}}, {{A, B, C, X(42354), X(57541)}}, {{A, B, C, X(43658), X(57899)}}, {{A, B, C, X(44531), X(50731)}}, {{A, B, C, X(46786), X(51474)}}, {{A, B, C, X(52133), X(56353)}}
X(60128) = barycentric quotient X(i)/X(j) for these (i, j): {2, 7777}, {6, 13330}, {32, 41278}

X(60129) = X(2)X(12212)∩X(4)X(12054)

Barycentrics    (a^4+3*a^2*b^2+b^4+2*(a^2+b^2)*c^2)*(a^4+2*b^2*c^2+c^4+a^2*(2*b^2+3*c^2)) : :

X(60129) lies on the Kiepert hyperbola and on these lines: {2, 12212}, {4, 12054}, {6, 33686}, {30, 54904}, {32, 43527}, {76, 3329}, {83, 7761}, {98, 7875}, {114, 54731}, {147, 9302}, {182, 14458}, {262, 3098}, {381, 54566}, {385, 60099}, {598, 7924}, {671, 10352}, {1078, 60100}, {1916, 11174}, {2996, 33269}, {3314, 10159}, {3399, 48673}, {3406, 10345}, {3407, 3589}, {3618, 54122}, {3815, 43529}, {4027, 43535}, {5039, 16988}, {7607, 16984}, {7736, 60232}, {7774, 18840}, {7777, 60213}, {7787, 18841}, {7792, 60128}, {7806, 60101}, {7814, 60278}, {7840, 60277}, {9300, 54748}, {10334, 60214}, {10353, 11606}, {10796, 54724}, {12150, 60238}, {14492, 48901}, {16987, 60215}, {16989, 60212}, {17004, 60187}, {33278, 53101}, {37665, 60285}, {38744, 55009}, {39668, 40016}, {42010, 42849}, {44000, 54539}, {51171, 60259}

X(60129) = isogonal conjugate of X(13331)
X(60129) = isotomic conjugate of X(16986)
X(60129) = trilinear pole of line {14318, 50546}
X(60129) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 13331}, {31, 16986}
X(60129) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 16986}, {3, 13331}
X(60129) = pole of line {13331, 16986} with respect to the Wallace hyperbola
X(60129) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(12054)}}, {{A, B, C, X(6), X(733)}}, {{A, B, C, X(32), X(3108)}}, {{A, B, C, X(39), X(41756)}}, {{A, B, C, X(182), X(1297)}}, {{A, B, C, X(251), X(7808)}}, {{A, B, C, X(308), X(45819)}}, {{A, B, C, X(325), X(7875)}}, {{A, B, C, X(385), X(9154)}}, {{A, B, C, X(427), X(7876)}}, {{A, B, C, X(458), X(37455)}}, {{A, B, C, X(592), X(3425)}}, {{A, B, C, X(699), X(7798)}}, {{A, B, C, X(1031), X(31360)}}, {{A, B, C, X(1239), X(31622)}}, {{A, B, C, X(3224), X(7839)}}, {{A, B, C, X(3314), X(3589)}}, {{A, B, C, X(3398), X(48673)}}, {{A, B, C, X(3618), X(7774)}}, {{A, B, C, X(3815), X(7806)}}, {{A, B, C, X(5094), X(7924)}}, {{A, B, C, X(5967), X(10352)}}, {{A, B, C, X(6353), X(33269)}}, {{A, B, C, X(7736), X(16989)}}, {{A, B, C, X(7761), X(23297)}}, {{A, B, C, X(7777), X(7792)}}, {{A, B, C, X(7823), X(9484)}}, {{A, B, C, X(7840), X(47352)}}, {{A, B, C, X(7868), X(16987)}}, {{A, B, C, X(8290), X(36820)}}, {{A, B, C, X(8859), X(42849)}}, {{A, B, C, X(9990), X(33665)}}, {{A, B, C, X(10345), X(45093)}}, {{A, B, C, X(17381), X(31090)}}, {{A, B, C, X(17743), X(40738)}}, {{A, B, C, X(30542), X(40416)}}, {{A, B, C, X(34816), X(52395)}}, {{A, B, C, X(37665), X(51171)}}, {{A, B, C, X(37876), X(40102)}}, {{A, B, C, X(38317), X(46807)}}, {{A, B, C, X(39955), X(42288)}}
X(60129) = barycentric quotient X(i)/X(j) for these (i, j): {2, 16986}, {6, 13331}

X(60130) = X(2)X(5654)∩X(3)X(2986)

Barycentrics    (2*a^2*b^2*(a^2-b^2)^2+(a^2+b^2)*(a^4+b^4)*c^2-3*(a^2+b^2)^2*c^4+3*(a^2+b^2)*c^6-c^8)*(-(b^2*(b^2-c^2)^3)+a^6*(b^2+2*c^2)+a^4*(-3*b^4+b^2*c^2-4*c^4)+a^2*(3*b^6-6*b^4*c^2+b^2*c^4+2*c^6)) : :

X(60130) lies on the Kiepert hyperbola and on these lines: {2, 5654}, {3, 2986}, {4, 3003}, {5, 34289}, {30, 54913}, {94, 39170}, {96, 1181}, {98, 11456}, {275, 378}, {376, 54784}, {381, 54864}, {403, 2052}, {671, 47383}, {925, 46260}, {3545, 54771}, {5392, 15760}, {6241, 43766}, {6623, 8796}, {7527, 7578}, {7592, 40448}, {9818, 40393}, {12022, 60122}, {12233, 57718}, {13579, 44440}, {13585, 52403}, {14264, 16080}, {14458, 16658}, {14912, 54660}, {15032, 54969}, {16654, 54909}, {16659, 46727}, {18405, 54573}, {34224, 46729}, {37077, 54663}, {37118, 43530}, {44218, 54803}, {44458, 54496}, {52032, 60114}, {53023, 54736}

X(60130) = isogonal conjugate of X(13352)
X(60130) = trilinear pole of line {686, 523}
X(60130) = pole of line {686, 924} with respect to the orthoptic circle of the Steiner inellipse
X(60130) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(403)}}, {{A, B, C, X(5), X(64)}}, {{A, B, C, X(6), X(9730)}}, {{A, B, C, X(24), X(15760)}}, {{A, B, C, X(30), X(52154)}}, {{A, B, C, X(54), X(1093)}}, {{A, B, C, X(66), X(45138)}}, {{A, B, C, X(68), X(57829)}}, {{A, B, C, X(69), X(52487)}}, {{A, B, C, X(70), X(14860)}}, {{A, B, C, X(74), X(264)}}, {{A, B, C, X(93), X(11270)}}, {{A, B, C, X(113), X(52552)}}, {{A, B, C, X(254), X(15740)}}, {{A, B, C, X(265), X(45838)}}, {{A, B, C, X(305), X(55978)}}, {{A, B, C, X(381), X(37118)}}, {{A, B, C, X(631), X(6623)}}, {{A, B, C, X(647), X(16311)}}, {{A, B, C, X(1141), X(16263)}}, {{A, B, C, X(1173), X(15045)}}, {{A, B, C, X(1176), X(1299)}}, {{A, B, C, X(1179), X(14542)}}, {{A, B, C, X(1181), X(52032)}}, {{A, B, C, X(1300), X(2165)}}, {{A, B, C, X(1485), X(2383)}}, {{A, B, C, X(1487), X(13489)}}, {{A, B, C, X(1594), X(9818)}}, {{A, B, C, X(1637), X(47208)}}, {{A, B, C, X(2071), X(16868)}}, {{A, B, C, X(2963), X(11744)}}, {{A, B, C, X(3426), X(3613)}}, {{A, B, C, X(3431), X(6344)}}, {{A, B, C, X(3459), X(50480)}}, {{A, B, C, X(3519), X(44157)}}, {{A, B, C, X(3521), X(22261)}}, {{A, B, C, X(3527), X(5892)}}, {{A, B, C, X(3531), X(45108)}}, {{A, B, C, X(3532), X(6662)}}, {{A, B, C, X(3541), X(18537)}}, {{A, B, C, X(5486), X(46412)}}, {{A, B, C, X(5627), X(57822)}}, {{A, B, C, X(6530), X(11456)}}, {{A, B, C, X(7503), X(45179)}}, {{A, B, C, X(7505), X(44440)}}, {{A, B, C, X(7527), X(7577)}}, {{A, B, C, X(7547), X(52262)}}, {{A, B, C, X(7592), X(19170)}}, {{A, B, C, X(8797), X(35512)}}, {{A, B, C, X(9209), X(39263)}}, {{A, B, C, X(10257), X(35488)}}, {{A, B, C, X(13472), X(15424)}}, {{A, B, C, X(13481), X(43713)}}, {{A, B, C, X(14457), X(22270)}}, {{A, B, C, X(14490), X(45090)}}, {{A, B, C, X(14528), X(45195)}}, {{A, B, C, X(14618), X(42313)}}, {{A, B, C, X(14940), X(52403)}}, {{A, B, C, X(15014), X(37446)}}, {{A, B, C, X(15412), X(42298)}}, {{A, B, C, X(16220), X(40879)}}, {{A, B, C, X(16835), X(16837)}}, {{A, B, C, X(18848), X(57747)}}, {{A, B, C, X(18880), X(57899)}}, {{A, B, C, X(20563), X(34801)}}, {{A, B, C, X(30474), X(58081)}}, {{A, B, C, X(32111), X(41372)}}, {{A, B, C, X(35490), X(44911)}}, {{A, B, C, X(37778), X(47383)}}, {{A, B, C, X(37984), X(49672)}}, {{A, B, C, X(40441), X(59281)}}, {{A, B, C, X(45301), X(57387)}}, {{A, B, C, X(52441), X(57640)}}

X(60131) = X(2)X(55764)∩X(3)X(55740)

Barycentrics    (4*a^2+7*b^2+4*c^2)*(4*(a^2+b^2)+7*c^2) : :

X(60131) lies on the Kiepert hyperbola and on these lines: {2, 55764}, {3, 55740}, {4, 55631}, {30, 54917}, {83, 21358}, {98, 15694}, {141, 60239}, {262, 15699}, {316, 60281}, {524, 43527}, {598, 20582}, {599, 60238}, {620, 43535}, {671, 3763}, {1153, 60184}, {1916, 14971}, {3096, 53107}, {3424, 15708}, {3619, 18842}, {5466, 7950}, {7607, 16239}, {7608, 55857}, {7784, 53109}, {7794, 55771}, {7799, 60259}, {7827, 60285}, {7850, 54639}, {7868, 54509}, {7883, 60146}, {7937, 17503}, {8176, 60105}, {11165, 60181}, {11606, 47005}, {11737, 14488}, {12100, 14458}, {12812, 60329}, {14869, 53100}, {14890, 60323}, {15685, 54477}, {15686, 60326}, {15688, 60132}, {15697, 54519}, {15810, 54901}, {16509, 60180}, {18841, 21356}, {18845, 23334}, {33288, 54540}, {34573, 60277}, {41134, 60280}, {47352, 60100}, {51143, 60287}, {54539, 55164}

X(60131) = isogonal conjugate of X(14075)
X(60131) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55631)}}, {{A, B, C, X(141), X(21358)}}, {{A, B, C, X(297), X(15694)}}, {{A, B, C, X(458), X(15699)}}, {{A, B, C, X(524), X(3763)}}, {{A, B, C, X(599), X(20582)}}, {{A, B, C, X(3619), X(21356)}}, {{A, B, C, X(11331), X(12100)}}, {{A, B, C, X(15708), X(52283)}}, {{A, B, C, X(16239), X(52282)}}, {{A, B, C, X(34573), X(47352)}}, {{A, B, C, X(34816), X(35146)}}, {{A, B, C, X(51143), X(51186)}}, {{A, B, C, X(52281), X(55857)}}, {{A, B, C, X(56067), X(57539)}}

X(60132) = X(2)X(6030)∩X(4)X(5355)

Barycentrics    (3*a^4+4*a^2*b^2+3*b^4-(a^2+b^2)*c^2-2*c^4)*(3*a^4-2*b^4-b^2*c^2+3*c^4-a^2*(b^2-4*c^2)) : :
X(60132) = -5*X[83]+8*X[546], -2*X[550]+5*X[6287], 5*X[2896]+X[49135], -7*X[3528]+10*X[6292], -8*X[3530]+5*X[8725], -11*X[3855]+5*X[12252], -13*X[5079]+10*X[49112], -2*X[15681]+5*X[31168], -22*X[15720]+25*X[31268]

X(60132) lies on the Kiepert hyperbola and on these lines: {2, 6030}, {3, 55743}, {4, 5355}, {5, 60100}, {6, 14488}, {30, 10302}, {76, 382}, {83, 546}, {230, 60334}, {262, 36990}, {275, 52285}, {381, 60239}, {383, 43545}, {542, 60271}, {550, 6287}, {598, 14269}, {671, 15687}, {732, 60180}, {754, 5485}, {1080, 43544}, {1503, 14492}, {1513, 53104}, {1916, 41622}, {2394, 12073}, {2794, 9302}, {2896, 49135}, {2996, 50688}, {3424, 9993}, {3528, 6292}, {3529, 3734}, {3530, 8725}, {3543, 60200}, {3627, 60250}, {3830, 60228}, {3839, 54639}, {3845, 60282}, {3851, 7919}, {3855, 12252}, {4052, 17766}, {5079, 49112}, {5306, 54934}, {5395, 6249}, {5480, 54890}, {5999, 60231}, {6054, 42010}, {6194, 48884}, {6776, 43951}, {6811, 43558}, {6813, 43559}, {7000, 60294}, {7374, 60293}, {7607, 9756}, {7608, 43460}, {7710, 14494}, {7735, 60322}, {7736, 60330}, {8781, 35705}, {9478, 60073}, {9744, 53099}, {9748, 60147}, {9752, 43537}, {9753, 60150}, {9754, 53103}, {9755, 14458}, {10155, 43461}, {10301, 16080}, {10722, 43532}, {11669, 13860}, {12022, 54736}, {12156, 17503}, {13111, 53105}, {14042, 60151}, {14639, 55009}, {14853, 54520}, {14931, 35005}, {15681, 31168}, {15688, 60131}, {15720, 31268}, {16654, 60121}, {18405, 54550}, {20088, 38259}, {34200, 60279}, {35018, 60182}, {35021, 60136}, {37463, 43443}, {37464, 43442}, {37900, 60225}, {38071, 60238}, {38227, 54644}, {43676, 50251}, {53015, 60185}, {53017, 54714}, {53023, 54582}

X(60132) = isogonal conjugate of X(14810)
X(60132) = trilinear pole of line {47453, 523}
X(60132) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 14810}, {38, 56916}
X(60132) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 14492}, {25, 60334}, {3108, 57713}, {3425, 53104}
X(60132) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(5), X(52285)}}, {{A, B, C, X(6), X(17508)}}, {{A, B, C, X(25), X(382)}}, {{A, B, C, X(30), X(10301)}}, {{A, B, C, X(54), X(29316)}}, {{A, B, C, X(64), X(14495)}}, {{A, B, C, X(66), X(21765)}}, {{A, B, C, X(69), X(33750)}}, {{A, B, C, X(251), X(6030)}}, {{A, B, C, X(265), X(5355)}}, {{A, B, C, X(305), X(32533)}}, {{A, B, C, X(427), X(546)}}, {{A, B, C, X(428), X(550)}}, {{A, B, C, X(468), X(15687)}}, {{A, B, C, X(512), X(42288)}}, {{A, B, C, X(523), X(15321)}}, {{A, B, C, X(732), X(32472)}}, {{A, B, C, X(754), X(1499)}}, {{A, B, C, X(842), X(13603)}}, {{A, B, C, X(1173), X(29180)}}, {{A, B, C, X(1297), X(57715)}}, {{A, B, C, X(1390), X(14496)}}, {{A, B, C, X(1494), X(45819)}}, {{A, B, C, X(1503), X(16264)}}, {{A, B, C, X(1799), X(3521)}}, {{A, B, C, X(2980), X(18575)}}, {{A, B, C, X(3244), X(20056)}}, {{A, B, C, X(3425), X(3426)}}, {{A, B, C, X(3456), X(48674)}}, {{A, B, C, X(3528), X(7408)}}, {{A, B, C, X(3529), X(6995)}}, {{A, B, C, X(3544), X(7409)}}, {{A, B, C, X(3563), X(46848)}}, {{A, B, C, X(3626), X(29838)}}, {{A, B, C, X(3629), X(50251)}}, {{A, B, C, X(3667), X(17766)}}, {{A, B, C, X(3851), X(5064)}}, {{A, B, C, X(3855), X(7378)}}, {{A, B, C, X(4518), X(17501)}}, {{A, B, C, X(5094), X(14269)}}, {{A, B, C, X(5481), X(14483)}}, {{A, B, C, X(5560), X(56358)}}, {{A, B, C, X(5561), X(52133)}}, {{A, B, C, X(5627), X(53955)}}, {{A, B, C, X(5966), X(46851)}}, {{A, B, C, X(6353), X(50688)}}, {{A, B, C, X(7576), X(37900)}}, {{A, B, C, X(7714), X(49135)}}, {{A, B, C, X(9751), X(42299)}}, {{A, B, C, X(9993), X(45031)}}, {{A, B, C, X(10308), X(53899)}}, {{A, B, C, X(11169), X(22336)}}, {{A, B, C, X(11270), X(39955)}}, {{A, B, C, X(11645), X(31950)}}, {{A, B, C, X(11815), X(54036)}}, {{A, B, C, X(12173), X(20850)}}, {{A, B, C, X(14486), X(22334)}}, {{A, B, C, X(14490), X(40801)}}, {{A, B, C, X(15319), X(34168)}}, {{A, B, C, X(33971), X(36990)}}, {{A, B, C, X(34174), X(35705)}}, {{A, B, C, X(34572), X(57713)}}, {{A, B, C, X(35482), X(37349)}}, {{A, B, C, X(38005), X(57822)}}, {{A, B, C, X(43726), X(45857)}}
X(60132) = barycentric quotient X(i)/X(j) for these (i, j): {6, 14810}, {251, 56916}

X(60133) = X(2)X(112)∩X(4)X(1177)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^6-a^4*b^2+b^6-b^2*c^4-a^2*(b^2-c^2)^2)*(a^6-a^4*c^2-b^4*c^2+c^6-a^2*(b^2-c^2)^2) : :

X(60133) lies on the Kiepert hyperbola and on these lines: {2, 112}, {4, 1177}, {6, 60266}, {10, 8750}, {30, 54919}, {53, 54685}, {76, 648}, {98, 403}, {107, 20410}, {226, 32674}, {262, 378}, {297, 2986}, {321, 1783}, {338, 2207}, {458, 34289}, {468, 10422}, {598, 36794}, {671, 5523}, {1249, 5485}, {1446, 32714}, {1552, 60119}, {1916, 15014}, {2052, 6529}, {2394, 8749}, {2996, 41361}, {3424, 6623}, {4049, 8752}, {5392, 56296}, {5466, 8753}, {6504, 54395}, {6531, 43665}, {7608, 37118}, {8370, 54796}, {8744, 37778}, {8781, 32697}, {14223, 57065}, {15262, 55973}, {16080, 32695}, {18840, 46165}, {24624, 36095}, {30247, 47426}, {30505, 32581}, {31636, 60179}, {35940, 60260}, {36099, 37220}, {37784, 44146}, {40393, 53489}, {40866, 54925}, {41204, 43532}, {41366, 43676}, {43673, 43717}, {43681, 56865}, {44458, 54709}, {46741, 54777}, {51358, 58268}, {51968, 52288}, {52281, 54864}, {52282, 54913}, {52403, 54705}, {52415, 54554}, {53784, 60262}

X(60133) = isogonal conjugate of X(14961)
X(60133) = trilinear pole of line {25, 51823}
X(60133) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 14961}, {3, 18669}, {48, 858}, {63, 2393}, {184, 20884}, {228, 17172}, {255, 5523}, {326, 14580}, {662, 42665}, {906, 21109}, {1236, 9247}, {1437, 21017}, {4575, 47138}, {5181, 36060}, {14210, 34158}, {24018, 46592}
X(60133) = X(i)-vertex conjugate of X(j) for these {i, j}: {287, 57655}, {14908, 60133}
X(60133) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 14961}, {136, 47138}, {1084, 42665}, {1249, 858}, {1560, 5181}, {3162, 2393}, {5190, 21109}, {6523, 5523}, {14091, 41603}, {15259, 14580}, {15477, 34158}, {36103, 18669}
X(60133) = X(i)-cross conjugate of X(j) for these {i, j}: {6, 10422}, {1177, 2373}, {2492, 107}, {8791, 17983}, {10097, 935}, {15128, 30786}, {32740, 2374}, {37981, 264}, {44823, 22456}, {47298, 34208}
X(60133) = pole of line {5181, 21109} with respect to the polar circle
X(60133) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(14908)}}, {{A, B, C, X(25), X(52905)}}, {{A, B, C, X(66), X(23327)}}, {{A, B, C, X(67), X(15118)}}, {{A, B, C, X(74), X(287)}}, {{A, B, C, X(112), X(648)}}, {{A, B, C, X(127), X(338)}}, {{A, B, C, X(249), X(38534)}}, {{A, B, C, X(265), X(44549)}}, {{A, B, C, X(290), X(57829)}}, {{A, B, C, X(297), X(403)}}, {{A, B, C, X(378), X(458)}}, {{A, B, C, X(393), X(41370)}}, {{A, B, C, X(419), X(15014)}}, {{A, B, C, X(468), X(37855)}}, {{A, B, C, X(523), X(34579)}}, {{A, B, C, X(525), X(11744)}}, {{A, B, C, X(729), X(57655)}}, {{A, B, C, X(1061), X(14621)}}, {{A, B, C, X(1063), X(17743)}}, {{A, B, C, X(1172), X(5547)}}, {{A, B, C, X(1177), X(18876)}}, {{A, B, C, X(1294), X(15412)}}, {{A, B, C, X(1300), X(16081)}}, {{A, B, C, X(1560), X(5523)}}, {{A, B, C, X(1974), X(36879)}}, {{A, B, C, X(1976), X(15388)}}, {{A, B, C, X(2207), X(8743)}}, {{A, B, C, X(2373), X(46140)}}, {{A, B, C, X(2492), X(20410)}}, {{A, B, C, X(6330), X(14618)}}, {{A, B, C, X(6623), X(52283)}}, {{A, B, C, X(8744), X(36415)}}, {{A, B, C, X(9154), X(57732)}}, {{A, B, C, X(10293), X(34897)}}, {{A, B, C, X(10419), X(34536)}}, {{A, B, C, X(11270), X(34386)}}, {{A, B, C, X(13219), X(35140)}}, {{A, B, C, X(13854), X(51260)}}, {{A, B, C, X(14248), X(56015)}}, {{A, B, C, X(14376), X(43695)}}, {{A, B, C, X(15471), X(34581)}}, {{A, B, C, X(16230), X(47151)}}, {{A, B, C, X(17983), X(37765)}}, {{A, B, C, X(18817), X(35142)}}, {{A, B, C, X(18850), X(42373)}}, {{A, B, C, X(22466), X(36952)}}, {{A, B, C, X(32113), X(47455)}}, {{A, B, C, X(32581), X(36794)}}, {{A, B, C, X(34168), X(53769)}}, {{A, B, C, X(34207), X(40404)}}, {{A, B, C, X(35512), X(42287)}}, {{A, B, C, X(37118), X(52281)}}, {{A, B, C, X(39645), X(58757)}}, {{A, B, C, X(41237), X(45179)}}, {{A, B, C, X(43660), X(54973)}}, {{A, B, C, X(43917), X(46115)}}, {{A, B, C, X(47277), X(47459)}}, {{A, B, C, X(47279), X(47456)}}, {{A, B, C, X(47280), X(47458)}}, {{A, B, C, X(47388), X(54962)}}, {{A, B, C, X(47449), X(47454)}}, {{A, B, C, X(47450), X(47453)}}, {{A, B, C, X(47460), X(47464)}}, {{A, B, C, X(47461), X(47463)}}, {{A, B, C, X(51228), X(52661)}}, {{A, B, C, X(51823), X(58078)}}, {{A, B, C, X(52415), X(57065)}}, {{A, B, C, X(54124), X(57819)}}
X(60133) = barycentric product X(i)*X(j) for these (i, j): {19, 37220}, {25, 46140}, {111, 58078}, {1177, 264}, {1577, 36095}, {2373, 4}, {2374, 56685}, {10422, 44146}, {10423, 850}, {16081, 36823}, {18876, 2052}, {32085, 46165}, {37778, 41511}, {43678, 52513}, {51823, 671}, {52486, 98}
X(60133) = barycentric quotient X(i)/X(j) for these (i, j): {4, 858}, {6, 14961}, {19, 18669}, {25, 2393}, {27, 17172}, {92, 20884}, {235, 41603}, {264, 1236}, {393, 5523}, {403, 12827}, {468, 5181}, {512, 42665}, {895, 51253}, {1177, 3}, {1826, 21017}, {2207, 14580}, {2373, 69}, {2374, 56579}, {2501, 47138}, {5094, 19510}, {6531, 52672}, {7649, 21109}, {8753, 57485}, {10422, 895}, {10423, 110}, {17983, 59422}, {18876, 394}, {32713, 46592}, {32740, 34158}, {36095, 662}, {36823, 36212}, {37197, 15126}, {37220, 304}, {37981, 15116}, {43678, 52512}, {44102, 47426}, {46105, 57476}, {46140, 305}, {46165, 3933}, {51823, 524}, {52486, 325}, {52513, 20806}, {58078, 3266}
X(60133) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {468, 10422, 10424}

X(60134) = X(2)X(163)∩X(10)X(692)

Barycentrics    (a+b)*(a+c)*(a^4-a^3*b+a^2*b^2-a*b^3+b^4-(a^2-a*b+b^2)*c^2)*(a^4-a^3*c-b^2*c^2+c^4+a*(b-c)*c*(b+c)+a^2*(-b^2+c^2)) : :

X(60134) lies on the Kiepert hyperbola and on these lines: {2, 163}, {4, 30902}, {10, 692}, {76, 662}, {83, 34072}, {94, 32678}, {101, 321}, {226, 1415}, {671, 36142}, {923, 5466}, {1446, 1461}, {1910, 43665}, {2052, 24019}, {2159, 2394}, {2576, 2593}, {2577, 2592}, {4049, 9456}, {4052, 34080}, {4080, 14953}, {4444, 18268}, {4593, 40016}, {5011, 11611}, {5392, 36145}, {11140, 36148}, {13576, 32666}, {16080, 36131}, {17197, 36907}, {24580, 60242}, {24624, 32671}, {30588, 34073}, {30937, 60071}, {32674, 40149}, {32675, 60091}, {34067, 43534}, {34069, 40718}, {34071, 60244}, {34074, 60267}, {34075, 60288}, {34079, 60074}, {34087, 36133}, {34289, 36149}, {36141, 45748}, {36147, 60264}, {52012, 56282}

X(60134) = isogonal conjugate of X(14963)
X(60134) = trilinear pole of line {31, 523}
X(60134) = X(i)-cross conjugate of X(j) for these {i, j}: {46533, 514}
X(60134) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(30882)}}, {{A, B, C, X(28), X(36022)}}, {{A, B, C, X(69), X(30902)}}, {{A, B, C, X(81), X(30905)}}, {{A, B, C, X(86), X(30906)}}, {{A, B, C, X(101), X(163)}}, {{A, B, C, X(514), X(37202)}}, {{A, B, C, X(1150), X(30937)}}, {{A, B, C, X(1821), X(2372)}}, {{A, B, C, X(2989), X(45136)}}, {{A, B, C, X(3453), X(7132)}}, {{A, B, C, X(7139), X(40145)}}, {{A, B, C, X(7332), X(21253)}}, {{A, B, C, X(9075), X(43093)}}, {{A, B, C, X(14953), X(37168)}}, {{A, B, C, X(16099), X(42555)}}
X(60134) = barycentric product X(i)*X(j) for these (i, j): {37219, 6}
X(60134) = barycentric quotient X(i)/X(j) for these (i, j): {6, 14963}, {37219, 76}

X(60135) = X(2)X(101)∩X(4)X(595)

Barycentrics    (b+c)*(a^3+b^3-(a^2+b^2)*c)*(a^3-a^2*b+c^2*(-b+c)) : :

X(60135) lies on the Kiepert hyperbola and on these lines: {1, 45964}, {2, 101}, {4, 595}, {10, 4557}, {63, 40013}, {76, 190}, {83, 4628}, {98, 17734}, {226, 3997}, {262, 995}, {292, 3960}, {321, 1018}, {515, 43672}, {528, 60079}, {671, 5134}, {758, 43534}, {812, 2161}, {993, 19263}, {1020, 1446}, {1751, 4548}, {1916, 40859}, {2051, 3772}, {2996, 17732}, {3008, 14554}, {3419, 60227}, {3822, 40718}, {4384, 60097}, {4584, 40017}, {4629, 32014}, {4675, 17750}, {5485, 41325}, {7680, 56144}, {8299, 48863}, {13478, 32653}, {16600, 60245}, {16609, 60091}, {17281, 60276}, {18101, 30505}, {22001, 43675}, {24076, 56282}, {24593, 39994}, {24624, 36087}, {25466, 36949}, {29069, 54739}, {30116, 60108}, {32777, 60084}, {39993, 52941}, {41320, 43678}, {41326, 43676}, {43043, 60085}, {43681, 56744}, {46105, 56747}, {50300, 60078}

X(60135) = isogonal conjugate of X(14964)
X(60135) = trilinear pole of line {42, 47403}
X(60135) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 14964}, {21, 43039}, {58, 57015}, {81, 674}, {86, 2225}, {163, 23887}, {274, 8618}, {333, 51657}, {905, 4249}, {1333, 3006}, {3733, 42723}
X(60135) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 14964}, {10, 57015}, {37, 3006}, {115, 23887}, {40586, 674}, {40600, 2225}, {40611, 43039}
X(60135) = pole of line {3011, 53312} with respect to the dual conic of Yff parabola
X(60135) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(18097)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(37), X(16788)}}, {{A, B, C, X(57), X(56246)}}, {{A, B, C, X(63), X(595)}}, {{A, B, C, X(65), X(14377)}}, {{A, B, C, X(85), X(56133)}}, {{A, B, C, X(101), X(190)}}, {{A, B, C, X(116), X(21045)}}, {{A, B, C, X(150), X(21091)}}, {{A, B, C, X(277), X(56173)}}, {{A, B, C, X(514), X(5773)}}, {{A, B, C, X(523), X(544)}}, {{A, B, C, X(673), X(4674)}}, {{A, B, C, X(675), X(43093)}}, {{A, B, C, X(758), X(812)}}, {{A, B, C, X(759), X(1821)}}, {{A, B, C, X(1016), X(27809)}}, {{A, B, C, X(1577), X(52383)}}, {{A, B, C, X(1826), X(56746)}}, {{A, B, C, X(2224), X(37130)}}, {{A, B, C, X(2333), X(3730)}}, {{A, B, C, X(3822), X(16603)}}, {{A, B, C, X(3887), X(8680)}}, {{A, B, C, X(3997), X(40779)}}, {{A, B, C, X(4039), X(40859)}}, {{A, B, C, X(4062), X(37854)}}, {{A, B, C, X(4095), X(16600)}}, {{A, B, C, X(4384), X(56191)}}, {{A, B, C, X(4456), X(4548)}}, {{A, B, C, X(15320), X(55161)}}, {{A, B, C, X(17743), X(56186)}}, {{A, B, C, X(17761), X(24237)}}, {{A, B, C, X(18101), X(27010)}}, {{A, B, C, X(29511), X(49997)}}, {{A, B, C, X(30575), X(43757)}}, {{A, B, C, X(30701), X(42471)}}, {{A, B, C, X(34892), X(41683)}}, {{A, B, C, X(37908), X(46497)}}, {{A, B, C, X(43043), X(50453)}}, {{A, B, C, X(44178), X(56195)}}, {{A, B, C, X(46018), X(57660)}}, {{A, B, C, X(55240), X(56853)}}, {{A, B, C, X(56127), X(56132)}}
X(60135) = barycentric product X(i)*X(j) for these (i, j): {10, 675}, {37, 37130}, {42, 43093}, {1577, 36087}, {2224, 321}, {18082, 46158}, {21207, 52941}, {32682, 850}
X(60135) = barycentric quotient X(i)/X(j) for these (i, j): {6, 14964}, {10, 3006}, {37, 57015}, {42, 674}, {213, 2225}, {523, 23887}, {675, 86}, {1018, 42723}, {1400, 43039}, {1402, 51657}, {1918, 8618}, {2224, 81}, {8750, 4249}, {32682, 110}, {36087, 662}, {37130, 274}, {43093, 310}, {46158, 16887}, {52941, 4570}

X(60136) = X(2)X(12830)∩X(4)X(38229)

Barycentrics    (3*a^4-a^2*b^2+3*b^4-3*(a^2+b^2)*c^2+c^4)*(3*a^4+b^4-3*b^2*c^2+3*c^4-a^2*(3*b^2+c^2)) : :

X(60136) lies on the Kiepert hyperbola and on these lines: {2, 12830}, {4, 38229}, {17, 32553}, {18, 32552}, {76, 33259}, {83, 6722}, {99, 51585}, {114, 53104}, {115, 53106}, {147, 7607}, {148, 60209}, {230, 11606}, {385, 35005}, {542, 54644}, {671, 33265}, {2996, 33014}, {4027, 60101}, {5395, 33011}, {5984, 7612}, {6036, 7608}, {6055, 14492}, {7735, 60177}, {7766, 60234}, {7779, 8781}, {7806, 60105}, {8782, 60180}, {8859, 60271}, {9115, 40706}, {9117, 40707}, {9166, 54646}, {9167, 10302}, {9478, 59266}, {10352, 60187}, {11177, 60175}, {11602, 39555}, {11603, 39554}, {14061, 60146}, {17008, 43688}, {18840, 33000}, {18841, 32998}, {33254, 60219}, {35021, 60132}, {36521, 60216}, {41151, 54813}, {42010, 44367}, {43535, 44534}

X(60136) = reflection of X(i) in X(j) for these {i,j}: {53106, 115}, {99, 51585}
X(60136) = isogonal conjugate of X(15514)
X(60136) = trilinear pole of line {32455, 523}
X(60136) = X(i)-vertex conjugate of X(j) for these {i, j}: {25, 11606}, {39644, 43535}
X(60136) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(33259)}}, {{A, B, C, X(111), X(41533)}}, {{A, B, C, X(230), X(7779)}}, {{A, B, C, X(468), X(33265)}}, {{A, B, C, X(699), X(46316)}}, {{A, B, C, X(1031), X(2963)}}, {{A, B, C, X(1691), X(46306)}}, {{A, B, C, X(1989), X(35511)}}, {{A, B, C, X(3455), X(56362)}}, {{A, B, C, X(5966), X(39554)}}, {{A, B, C, X(6353), X(33014)}}, {{A, B, C, X(6722), X(31125)}}, {{A, B, C, X(6995), X(33000)}}, {{A, B, C, X(7378), X(32998)}}, {{A, B, C, X(7766), X(17008)}}, {{A, B, C, X(8859), X(44367)}}, {{A, B, C, X(8889), X(33011)}}, {{A, B, C, X(14565), X(29011)}}, {{A, B, C, X(25322), X(42349)}}, {{A, B, C, X(34214), X(46314)}}, {{A, B, C, X(36948), X(43664)}}, {{A, B, C, X(40511), X(43098)}}, {{A, B, C, X(52395), X(53864)}}

X(60137) = X(2)X(38292)∩X(4)X(10192)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(5*(a^2-b^2)^2-2*(a^2+b^2)*c^2-3*c^4)*(5*a^4-3*b^4-2*b^2*c^2+5*c^4-2*a^2*(b^2+5*c^2)) : :

X(60137) lies on the Kiepert hyperbola and on these lines: {2, 38292}, {4, 10192}, {6, 38253}, {25, 43951}, {30, 54923}, {98, 52299}, {262, 38282}, {297, 18845}, {381, 54552}, {427, 60147}, {451, 60157}, {458, 38259}, {459, 23292}, {468, 60118}, {470, 43557}, {471, 43556}, {472, 43552}, {473, 43553}, {631, 31363}, {1131, 3536}, {1132, 3535}, {1249, 54710}, {1585, 43561}, {1586, 43560}, {2052, 33630}, {2996, 52288}, {3424, 8889}, {3524, 60121}, {3525, 13599}, {4232, 60328}, {5064, 54815}, {5067, 40448}, {5071, 60122}, {5094, 47586}, {5395, 52283}, {6143, 60159}, {6353, 14484}, {6819, 13579}, {6995, 54706}, {6997, 54705}, {7378, 60327}, {7490, 45100}, {7505, 60174}, {7714, 54520}, {11001, 54585}, {11064, 60221}, {11331, 60145}, {11427, 16080}, {11538, 37192}, {14039, 54828}, {14940, 60162}, {15702, 54763}, {18840, 53415}, {19708, 54838}, {33230, 54682}, {33285, 54551}, {37119, 60166}, {37187, 60105}, {37276, 60155}, {37453, 60331}, {37645, 42410}, {37669, 60241}, {41106, 54512}, {43681, 52289}, {52252, 60158}, {52281, 60113}, {52282, 54476}, {52284, 60324}, {52290, 53099}, {52298, 54921}, {56270, 56296}, {59767, 60237}

X(60137) = isogonal conjugate of X(15851)
X(60137) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 15851}, {48, 3832}
X(60137) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 15851}, {1249, 3832}
X(60137) = X(i)-cross conjugate of X(j) for these {i, j}: {40065, 4}
X(60137) = pole of line {40065, 60137} with respect to the Kiepert hyperbola
X(60137) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(33630)}}, {{A, B, C, X(53), X(46223)}}, {{A, B, C, X(54), X(1073)}}, {{A, B, C, X(264), X(3535)}}, {{A, B, C, X(297), X(52299)}}, {{A, B, C, X(394), X(3431)}}, {{A, B, C, X(458), X(38282)}}, {{A, B, C, X(475), X(37276)}}, {{A, B, C, X(1061), X(56230)}}, {{A, B, C, X(1173), X(56345)}}, {{A, B, C, X(1249), X(40170)}}, {{A, B, C, X(3108), X(56363)}}, {{A, B, C, X(3618), X(53415)}}, {{A, B, C, X(5067), X(52280)}}, {{A, B, C, X(6143), X(37192)}}, {{A, B, C, X(6353), X(52288)}}, {{A, B, C, X(6819), X(7505)}}, {{A, B, C, X(6820), X(37119)}}, {{A, B, C, X(8056), X(40396)}}, {{A, B, C, X(8797), X(53506)}}, {{A, B, C, X(8889), X(52283)}}, {{A, B, C, X(10192), X(17040)}}, {{A, B, C, X(11064), X(11427)}}, {{A, B, C, X(14376), X(23292)}}, {{A, B, C, X(14528), X(36609)}}, {{A, B, C, X(15466), X(33702)}}, {{A, B, C, X(20421), X(31626)}}, {{A, B, C, X(25430), X(40397)}}, {{A, B, C, X(34208), X(42330)}}, {{A, B, C, X(36617), X(43718)}}, {{A, B, C, X(38264), X(42300)}}, {{A, B, C, X(39389), X(56364)}}, {{A, B, C, X(40410), X(56340)}}
X(60137) = barycentric quotient X(i)/X(j) for these (i, j): {4, 3832}, {6, 15851}

X(60138) = X(3)X(54585)∩X(4)X(10182)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(5*(a^2-b^2)^2-(a^2+b^2)*c^2-4*c^4)*(5*a^4-4*b^4-b^2*c^2+5*c^4-a^2*(b^2+10*c^2)) : :

X(60138) lies on the Kiepert hyperbola and on these lines: {3, 54585}, {4, 10182}, {5, 54512}, {25, 54582}, {30, 54924}, {98, 52293}, {140, 60121}, {186, 54809}, {262, 52292}, {297, 45103}, {419, 54583}, {427, 54477}, {428, 54813}, {458, 17503}, {468, 14492}, {470, 12817}, {471, 12816}, {472, 54480}, {473, 54479}, {475, 54789}, {598, 11331}, {631, 54838}, {671, 52289}, {1585, 43563}, {1586, 43562}, {1594, 54879}, {1656, 60122}, {3090, 54667}, {3516, 54820}, {3522, 54923}, {3533, 54763}, {3535, 60308}, {3536, 60307}, {4232, 54520}, {5068, 54552}, {5094, 14458}, {5117, 54584}, {7770, 54897}, {7892, 54828}, {7901, 54551}, {10301, 54717}, {13599, 46219}, {14484, 53857}, {14920, 18366}, {14940, 54827}, {15000, 54808}, {31916, 54701}, {32532, 52288}, {37118, 60119}, {37119, 54942}, {37125, 54733}, {37162, 54932}, {37174, 54642}, {37453, 54643}, {37648, 46206}, {38282, 54707}, {40448, 55856}, {43462, 60193}, {52252, 54947}, {52280, 54791}, {52281, 54478}, {52283, 60281}, {52284, 54519}, {52290, 60127}, {52297, 54734}, {52298, 54851}, {52299, 54612}, {54598, 55569}, {54599, 55573}

X(60138) = isogonal conjugate of X(15860)
X(60138) = trilinear pole of line {523, 56369}
X(60138) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 15860}, {48, 3845}
X(60138) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 15860}, {1249, 3845}
X(60138) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(54), X(40384)}}, {{A, B, C, X(297), X(52293)}}, {{A, B, C, X(458), X(52292)}}, {{A, B, C, X(468), X(52289)}}, {{A, B, C, X(1990), X(30537)}}, {{A, B, C, X(5094), X(11331)}}, {{A, B, C, X(10293), X(53024)}}, {{A, B, C, X(14919), X(57713)}}, {{A, B, C, X(23964), X(39389)}}, {{A, B, C, X(52280), X(55856)}}, {{A, B, C, X(52288), X(53857)}}
X(60138) = barycentric quotient X(i)/X(j) for these (i, j): {4, 3845}, {6, 15860}

X(60139) = X(2)X(8818)∩X(10)X(79)

Barycentrics    (a+2*b+c)*(a+b+2*c)*(a^2+a*b+b^2-c^2)*(a^2-b^2+a*c+c^2) : :

X(60139) lies on these lines: {2, 8818}, {4, 56402}, {6, 54929}, {10, 79}, {30, 57710}, {81, 60172}, {226, 1255}, {265, 54528}, {321, 4102}, {381, 57720}, {445, 16080}, {553, 38340}, {598, 19738}, {671, 42045}, {1029, 40438}, {1126, 3585}, {1171, 1989}, {1268, 2160}, {1770, 33670}, {3615, 43531}, {3681, 59261}, {4654, 43682}, {5047, 52375}, {5325, 7110}, {5397, 28459}, {6539, 17484}, {6742, 11599}, {10385, 41504}, {11076, 17011}, {13407, 50148}, {15455, 39994}, {17378, 54775}, {26734, 56947}, {31143, 60267}, {31144, 43261}, {31164, 43683}, {42044, 43677}, {43530, 57531}, {47947, 60074}, {52381, 56226}

X(60139) = isogonal conjugate of X(17454)
X(60139) = isotomic conjugate of X(3578)
X(60139) = trilinear pole of line {24920, 41800}
X(60139) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 17454}, {6, 3647}, {31, 3578}, {35, 1100}, {42, 17190}, {1125, 2174}, {1213, 17104}, {1399, 3686}, {1839, 52408}, {1962, 40214}, {2003, 3683}, {2308, 3219}, {2605, 35342}, {3649, 35192}, {4001, 14975}, {6198, 22054}, {14838, 35327}, {20970, 56934}, {23201, 52412}, {32636, 52405}, {35057, 36075}
X(60139) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 3578}, {3, 17454}, {9, 3647}, {8818, 3650}, {40592, 17190}, {56847, 1213}
X(60139) = X(i)-cross conjugate of X(j) for these {i, j}: {1, 1268}, {514, 38340}, {11544, 7}, {37631, 2}, {55236, 6742}
X(60139) = pole of line {37631, 60139} with respect to the Kiepert hyperbola
X(60139) = pole of line {3578, 17190} with respect to the Wallace hyperbola
X(60139) = pole of line {50148, 57419} with respect to the dual conic of Yff parabola
X(60139) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3219)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(1494)}}, {{A, B, C, X(27), X(6175)}}, {{A, B, C, X(30), X(445)}}, {{A, B, C, X(74), X(40214)}}, {{A, B, C, X(79), X(30690)}}, {{A, B, C, X(81), X(2349)}}, {{A, B, C, X(265), X(56402)}}, {{A, B, C, X(290), X(47647)}}, {{A, B, C, X(381), X(57531)}}, {{A, B, C, X(514), X(553)}}, {{A, B, C, X(524), X(42045)}}, {{A, B, C, X(599), X(19738)}}, {{A, B, C, X(1171), X(47947)}}, {{A, B, C, X(1255), X(4102)}}, {{A, B, C, X(1268), X(43260)}}, {{A, B, C, X(1989), X(8818)}}, {{A, B, C, X(2308), X(4813)}}, {{A, B, C, X(2346), X(56037)}}, {{A, B, C, X(3228), X(32938)}}, {{A, B, C, X(3578), X(3649)}}, {{A, B, C, X(3782), X(5434)}}, {{A, B, C, X(4067), X(37685)}}, {{A, B, C, X(4683), X(43098)}}, {{A, B, C, X(4980), X(28604)}}, {{A, B, C, X(5556), X(15474)}}, {{A, B, C, X(6740), X(42033)}}, {{A, B, C, X(10404), X(50068)}}, {{A, B, C, X(11544), X(56846)}}, {{A, B, C, X(17098), X(55985)}}, {{A, B, C, X(17501), X(56228)}}, {{A, B, C, X(21739), X(55090)}}, {{A, B, C, X(26743), X(37222)}}, {{A, B, C, X(26751), X(39704)}}, {{A, B, C, X(31143), X(42028)}}, {{A, B, C, X(35162), X(40439)}}, {{A, B, C, X(40164), X(46277)}}, {{A, B, C, X(41816), X(42025)}}, {{A, B, C, X(43733), X(56050)}}
X(60139) = barycentric product X(i)*X(j) for these (i, j): {1126, 20565}, {1255, 30690}, {1268, 79}, {2160, 32018}, {4102, 52374}, {4608, 6742}, {4632, 55236}, {15455, 47947}, {32014, 8818}, {40438, 6757}, {52393, 6539}, {55209, 58294}, {57419, 75}
X(60139) = barycentric quotient X(i)/X(j) for these (i, j): {1, 3647}, {2, 3578}, {6, 17454}, {79, 1125}, {81, 17190}, {1126, 35}, {1171, 40214}, {1255, 3219}, {1268, 319}, {2160, 1100}, {4102, 42033}, {4608, 4467}, {4632, 55235}, {6186, 2308}, {6538, 7206}, {6539, 3969}, {6742, 4427}, {6757, 4647}, {7073, 3683}, {7100, 3916}, {7110, 3686}, {8818, 1213}, {20565, 1269}, {28615, 2174}, {30690, 4359}, {31010, 7265}, {32014, 34016}, {32018, 33939}, {32635, 4420}, {33635, 52405}, {40438, 56934}, {47947, 14838}, {50344, 2605}, {52344, 3702}, {52372, 32636}, {52374, 553}, {52381, 4001}, {52382, 3649}, {52388, 41014}, {52393, 8025}, {52569, 6533}, {55236, 4988}, {56402, 15670}, {56844, 4973}, {56847, 3650}, {57419, 1}, {58294, 55210}

X(60140) = X(2)X(2794)∩X(30)X(5503)

Barycentrics    (3*a^6+a^4*b^2+a^2*b^4+3*b^6-4*(a^4+a^2*b^2+b^4)*c^2+3*(a^2+b^2)*c^4-2*c^6)*(3*a^6-2*b^6+3*b^4*c^2-4*b^2*c^4+3*c^6+a^4*(-4*b^2+c^2)+a^2*(3*b^4-4*b^2*c^2+c^4)) : :
X(60140) = -3*X[9166]+2*X[53015], -4*X[9756]+5*X[14061]

X(60140) lies on the Kiepert hyperbola and on these lines: {2, 2794}, {5, 60186}, {20, 60262}, {30, 5503}, {76, 15069}, {98, 39663}, {99, 7710}, {115, 3424}, {147, 60201}, {262, 10722}, {316, 8781}, {516, 34899}, {523, 52459}, {542, 5485}, {598, 38072}, {671, 1503}, {690, 43673}, {1499, 14223}, {1916, 10723}, {2394, 2793}, {2548, 53099}, {2782, 60180}, {2784, 4052}, {2996, 38664}, {5466, 39904}, {6033, 60213}, {7612, 9862}, {7891, 43529}, {9166, 53015}, {9756, 14061}, {9880, 32532}, {10153, 14830}, {10991, 43537}, {11623, 47586}, {12243, 54637}, {14458, 14639}, {14484, 39838}, {14485, 53418}, {14561, 18842}, {14651, 60150}, {15428, 23698}, {19055, 45107}, {19056, 45106}, {20774, 60266}, {22505, 60215}, {22521, 54747}, {29012, 54822}, {32472, 46040}, {36990, 60115}, {38741, 56064}, {38744, 60099}, {38745, 53033}, {41022, 42036}, {41023, 42035}, {41895, 46034}, {44145, 46105}, {45031, 60179}, {53419, 54475}

X(60140) = reflection of X(i) in X(j) for these {i,j}: {22664, 7694}, {3424, 115}, {99, 7710}
X(60140) = isogonal conjugate of X(18860)
X(60140) = trilinear pole of line {7735, 523}
X(60140) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 671}, {32901, 54998}
X(60140) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(57729)}}, {{A, B, C, X(30), X(2793)}}, {{A, B, C, X(64), X(3455)}}, {{A, B, C, X(74), X(2065)}}, {{A, B, C, X(99), X(685)}}, {{A, B, C, X(115), X(45031)}}, {{A, B, C, X(290), X(34473)}}, {{A, B, C, X(316), X(1300)}}, {{A, B, C, X(460), X(54996)}}, {{A, B, C, X(511), X(729)}}, {{A, B, C, X(512), X(43702)}}, {{A, B, C, X(516), X(2789)}}, {{A, B, C, X(523), X(2794)}}, {{A, B, C, X(542), X(1499)}}, {{A, B, C, X(690), X(1503)}}, {{A, B, C, X(1093), X(57771)}}, {{A, B, C, X(1177), X(14649)}}, {{A, B, C, X(1297), X(8753)}}, {{A, B, C, X(1494), X(9154)}}, {{A, B, C, X(1976), X(2710)}}, {{A, B, C, X(2207), X(39644)}}, {{A, B, C, X(2373), X(8599)}}, {{A, B, C, X(2782), X(32472)}}, {{A, B, C, X(2783), X(28475)}}, {{A, B, C, X(2784), X(3667)}}, {{A, B, C, X(2792), X(28292)}}, {{A, B, C, X(2796), X(28296)}}, {{A, B, C, X(3426), X(6323)}}, {{A, B, C, X(5641), X(17983)}}, {{A, B, C, X(6524), X(34412)}}, {{A, B, C, X(9084), X(9141)}}, {{A, B, C, X(10723), X(47736)}}, {{A, B, C, X(11060), X(34130)}}, {{A, B, C, X(14248), X(41533)}}, {{A, B, C, X(15384), X(38699)}}, {{A, B, C, X(15484), X(56401)}}, {{A, B, C, X(18878), X(52035)}}, {{A, B, C, X(23700), X(32901)}}, {{A, B, C, X(28294), X(53792)}}, {{A, B, C, X(32695), X(53883)}}, {{A, B, C, X(38072), X(46731)}}, {{A, B, C, X(42299), X(43664)}}, {{A, B, C, X(43291), X(43917)}}
X(60140) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2794, 7694, 22664}

X(60141) = X(2)X(1843)∩X(25)X(83)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(2*a^2*b^2+(a^2+b^2)*c^2+c^4)*(b^2*(b^2+c^2)+a^2*(b^2+2*c^2)) : :

X(60141) lies on the Kiepert hyperbola and on these lines: {2, 1843}, {4, 1194}, {6, 60125}, {25, 83}, {30, 54682}, {76, 427}, {98, 1184}, {264, 40016}, {325, 40831}, {381, 54898}, {428, 598}, {468, 43527}, {671, 5064}, {1513, 13599}, {2052, 15809}, {2996, 7378}, {3845, 54897}, {5094, 10159}, {5359, 16277}, {5395, 6995}, {6353, 18841}, {7408, 18845}, {7409, 38259}, {7576, 54730}, {7714, 18842}, {8889, 8891}, {10301, 53102}, {13860, 40448}, {31133, 54796}, {34603, 54684}, {34609, 54836}, {37453, 60100}, {40162, 56920}, {52281, 54916}, {52282, 54915}, {52284, 60285}, {52285, 53105}, {52292, 60182}, {52298, 56059}, {52299, 60183}, {52301, 60145}

X(60141) = isogonal conjugate of X(19126)
X(60141) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 19126}, {48, 7770}, {4575, 47128}
X(60141) = X(i)-vertex conjugate of X(j) for these {i, j}: {3425, 13599}
X(60141) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 19126}, {136, 47128}, {1249, 7770}, {40938, 8891}
X(60141) = X(i)-cross conjugate of X(j) for these {i, j}: {3867, 4}, {40022, 47847}
X(60141) = pole of line {3867, 60141} with respect to the Kiepert hyperbola
X(60141) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(15809)}}, {{A, B, C, X(6), X(305)}}, {{A, B, C, X(25), X(264)}}, {{A, B, C, X(66), X(1799)}}, {{A, B, C, X(105), X(45104)}}, {{A, B, C, X(251), X(9307)}}, {{A, B, C, X(325), X(1184)}}, {{A, B, C, X(428), X(5094)}}, {{A, B, C, X(468), X(5064)}}, {{A, B, C, X(858), X(46426)}}, {{A, B, C, X(1039), X(4518)}}, {{A, B, C, X(1041), X(7249)}}, {{A, B, C, X(1093), X(14486)}}, {{A, B, C, X(2374), X(8801)}}, {{A, B, C, X(3108), X(57388)}}, {{A, B, C, X(3425), X(15318)}}, {{A, B, C, X(3613), X(8770)}}, {{A, B, C, X(3867), X(8891)}}, {{A, B, C, X(5359), X(8743)}}, {{A, B, C, X(5486), X(57852)}}, {{A, B, C, X(6353), X(7378)}}, {{A, B, C, X(6995), X(8889)}}, {{A, B, C, X(7408), X(52299)}}, {{A, B, C, X(7409), X(38282)}}, {{A, B, C, X(7714), X(52284)}}, {{A, B, C, X(8793), X(58075)}}, {{A, B, C, X(8890), X(56067)}}, {{A, B, C, X(9918), X(14378)}}, {{A, B, C, X(13854), X(32085)}}, {{A, B, C, X(13860), X(52280)}}, {{A, B, C, X(16837), X(43662)}}, {{A, B, C, X(18019), X(39955)}}, {{A, B, C, X(18575), X(36616)}}, {{A, B, C, X(30786), X(43726)}}, {{A, B, C, X(31360), X(37876)}}, {{A, B, C, X(37453), X(52285)}}, {{A, B, C, X(51843), X(56920)}}
X(60141) = barycentric product X(i)*X(j) for these (i, j): {25, 59758}, {31360, 4}, {37876, 427}
X(60141) = barycentric quotient X(i)/X(j) for these (i, j): {4, 7770}, {6, 19126}, {427, 8891}, {2501, 47128}, {31360, 69}, {37876, 1799}, {59758, 305}

X(60142) = X(5)X(10302)∩X(83)X(550)

Barycentrics    (a^4+8*a^2*b^2+b^4+3*(a^2+b^2)*c^2-4*c^4)*(a^4-4*b^4+3*b^2*c^2+c^4+a^2*(3*b^2+8*c^2)) : :

X(60142) lies on the Kiepert hyperbola and on these lines: {2, 44300}, {3, 55778}, {5, 10302}, {6, 53100}, {20, 54639}, {30, 60282}, {76, 3851}, {83, 550}, {140, 60100}, {275, 10301}, {381, 60228}, {382, 598}, {383, 33607}, {546, 671}, {1080, 33606}, {1513, 60192}, {1656, 60278}, {2996, 13571}, {3091, 60200}, {3528, 54616}, {3529, 18842}, {3530, 60238}, {3544, 7794}, {3815, 54920}, {3850, 60250}, {3855, 5485}, {5079, 60277}, {5395, 49135}, {5480, 7608}, {6054, 60271}, {6776, 60324}, {6811, 43569}, {6813, 43568}, {7000, 60299}, {7374, 60300}, {7736, 52519}, {7867, 60183}, {7912, 60285}, {8550, 54857}, {9300, 54717}, {9744, 43951}, {9753, 53103}, {9993, 14494}, {10159, 35018}, {10185, 38227}, {10299, 18841}, {11257, 54814}, {12110, 60148}, {13860, 60175}, {14042, 54872}, {14045, 60151}, {14269, 17503}, {14853, 43537}, {15681, 60283}, {15687, 45103}, {15688, 60287}, {15720, 43527}, {23234, 42010}, {32467, 54566}, {33229, 54915}, {33279, 54753}, {33280, 54833}, {37463, 43545}, {37464, 43544}, {37900, 40393}, {38071, 60216}, {39284, 52285}, {43460, 54890}, {43461, 53099}, {46517, 54926}, {49139, 53102}, {50688, 53101}, {53023, 60329}

X(60142) = isogonal conjugate of X(20190)
X(60142) = trilinear pole of line {47448, 523}
X(60142) = X(i)-vertex conjugate of X(j) for these {i, j}: {3425, 60192}
X(60142) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(5), X(10301)}}, {{A, B, C, X(6), X(52987)}}, {{A, B, C, X(25), X(3851)}}, {{A, B, C, X(54), X(14388)}}, {{A, B, C, X(67), X(45108)}}, {{A, B, C, X(140), X(52285)}}, {{A, B, C, X(264), X(38005)}}, {{A, B, C, X(382), X(5094)}}, {{A, B, C, X(427), X(550)}}, {{A, B, C, X(428), X(35018)}}, {{A, B, C, X(468), X(546)}}, {{A, B, C, X(842), X(1173)}}, {{A, B, C, X(1297), X(14863)}}, {{A, B, C, X(1594), X(37900)}}, {{A, B, C, X(1885), X(47629)}}, {{A, B, C, X(3108), X(29011)}}, {{A, B, C, X(3521), X(30786)}}, {{A, B, C, X(3529), X(52284)}}, {{A, B, C, X(3544), X(52301)}}, {{A, B, C, X(3613), X(17983)}}, {{A, B, C, X(3855), X(4232)}}, {{A, B, C, X(4518), X(5557)}}, {{A, B, C, X(5064), X(15720)}}, {{A, B, C, X(5189), X(35482)}}, {{A, B, C, X(5486), X(57823)}}, {{A, B, C, X(5559), X(7249)}}, {{A, B, C, X(7378), X(10299)}}, {{A, B, C, X(7775), X(22100)}}, {{A, B, C, X(8889), X(49135)}}, {{A, B, C, X(14269), X(52292)}}, {{A, B, C, X(14357), X(52090)}}, {{A, B, C, X(14483), X(43656)}}, {{A, B, C, X(14860), X(52192)}}, {{A, B, C, X(15321), X(15464)}}, {{A, B, C, X(15687), X(52293)}}, {{A, B, C, X(16835), X(39389)}}, {{A, B, C, X(26861), X(57852)}}, {{A, B, C, X(31856), X(44438)}}, {{A, B, C, X(32085), X(45090)}}, {{A, B, C, X(39951), X(43719)}}, {{A, B, C, X(43917), X(44300)}}, {{A, B, C, X(45819), X(55958)}}, {{A, B, C, X(52141), X(53144)}}, {{A, B, C, X(53890), X(57715)}}

X(60143) = X(2)X(14482)∩X(4)X(599)

Barycentrics    (a^2+7*b^2+c^2)*(a^2+b^2+7*c^2) : :
X(60143) = -3*X[3545]+2*X[14484]

X(60143) lies on the Kiepert hyperbola and on these lines: {2, 14482}, {3, 47586}, {4, 599}, {5, 60118}, {6, 54616}, {20, 60324}, {30, 46944}, {69, 598}, {76, 33230}, {83, 1992}, {98, 2482}, {141, 5485}, {193, 54639}, {262, 5071}, {298, 54617}, {299, 54618}, {315, 53107}, {316, 54494}, {325, 60268}, {343, 54771}, {376, 3424}, {381, 43951}, {511, 54814}, {524, 18842}, {538, 60099}, {542, 54800}, {549, 60336}, {597, 18841}, {631, 43537}, {671, 19662}, {1916, 33285}, {2394, 18310}, {2996, 33190}, {3090, 53099}, {3091, 60328}, {3096, 60250}, {3407, 14039}, {3525, 7607}, {3528, 53100}, {3533, 53859}, {3543, 60327}, {3544, 7794}, {3545, 14484}, {3590, 7376}, {3591, 7375}, {3618, 60238}, {3619, 10302}, {3620, 41895}, {3631, 23334}, {3830, 54815}, {3839, 54706}, {4648, 55949}, {5054, 54921}, {5055, 60331}, {5067, 7608}, {5286, 60183}, {5395, 7762}, {5461, 5503}, {5590, 60223}, {5591, 60224}, {6656, 43681}, {7388, 60292}, {7389, 60291}, {7612, 11168}, {7620, 32532}, {7770, 60145}, {7778, 60240}, {7790, 60216}, {7795, 60186}, {7799, 60248}, {7803, 56059}, {7810, 17538}, {7812, 60146}, {7818, 54890}, {7827, 60278}, {7840, 60190}, {7841, 38259}, {7854, 11541}, {7883, 53106}, {8352, 60113}, {8370, 18845}, {8556, 60185}, {8591, 16990}, {8596, 11606}, {8860, 60263}, {9741, 11167}, {9770, 54509}, {10153, 22247}, {10511, 34897}, {10521, 50118}, {11001, 14458}, {11054, 60277}, {11172, 32817}, {11185, 17503}, {11303, 43556}, {11304, 43557}, {11317, 54476}, {13637, 60204}, {13757, 60205}, {14069, 43528}, {14488, 31173}, {14492, 41106}, {14494, 22110}, {15533, 60284}, {15682, 54519}, {15698, 54866}, {15709, 60102}, {15715, 60322}, {17130, 49138}, {17297, 54770}, {17392, 54624}, {18840, 20582}, {19569, 54539}, {19708, 60150}, {19826, 56209}, {22165, 60281}, {23053, 60073}, {23055, 33231}, {29627, 30588}, {31143, 60155}, {31144, 32022}, {31162, 54668}, {31276, 60098}, {32808, 54626}, {32809, 54625}, {32810, 54503}, {32811, 54507}, {32832, 60198}, {32833, 60101}, {32834, 60262}, {32836, 60212}, {32869, 60259}, {32874, 33196}, {32951, 43529}, {32956, 60285}, {32983, 60105}, {32984, 60177}, {32985, 60184}, {33223, 43688}, {33232, 43676}, {33780, 60197}, {34229, 60103}, {34505, 60219}, {34511, 55794}, {37636, 54778}, {37690, 42011}, {38282, 60124}, {40824, 46951}, {41099, 54520}, {43448, 50993}, {43665, 52629}, {45103, 50990}, {47286, 60200}, {49743, 60077}, {50739, 60080}, {50992, 60282}, {51142, 54647}, {51189, 53418}, {51481, 59763}, {52283, 56270}, {52288, 60193}, {59373, 60239}

X(60143) = reflection of X(i) in X(j) for these {i,j}: {14482, 2}
X(60143) = isogonal conjugate of X(21309)
X(60143) = isotomic conjugate of X(59373)
X(60143) = anticomplement of X(51588)
X(60143) = trilinear pole of line {47311, 48545}
X(60143) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 21309}, {31, 59373}, {48, 52301}
X(60143) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 59373}, {3, 21309}, {1249, 52301}, {51588, 51588}
X(60143) = pole of line {21358, 60143} with respect to the Kiepert hyperbola
X(60143) = pole of line {21309, 44839} with respect to the Wallace hyperbola
X(60143) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(53097)}}, {{A, B, C, X(25), X(33230)}}, {{A, B, C, X(69), X(599)}}, {{A, B, C, X(141), X(1992)}}, {{A, B, C, X(263), X(41440)}}, {{A, B, C, X(264), X(54171)}}, {{A, B, C, X(277), X(40023)}}, {{A, B, C, X(297), X(3524)}}, {{A, B, C, X(325), X(42850)}}, {{A, B, C, X(327), X(36889)}}, {{A, B, C, X(335), X(18490)}}, {{A, B, C, X(376), X(52283)}}, {{A, B, C, X(419), X(33285)}}, {{A, B, C, X(420), X(32986)}}, {{A, B, C, X(458), X(5071)}}, {{A, B, C, X(524), X(21356)}}, {{A, B, C, X(538), X(41520)}}, {{A, B, C, X(596), X(56335)}}, {{A, B, C, X(597), X(3619)}}, {{A, B, C, X(1000), X(34892)}}, {{A, B, C, X(1007), X(11168)}}, {{A, B, C, X(1073), X(55978)}}, {{A, B, C, X(2482), X(36890)}}, {{A, B, C, X(3296), X(34914)}}, {{A, B, C, X(3431), X(40802)}}, {{A, B, C, X(3525), X(52282)}}, {{A, B, C, X(3545), X(52288)}}, {{A, B, C, X(3618), X(20582)}}, {{A, B, C, X(3620), X(11160)}}, {{A, B, C, X(3679), X(29627)}}, {{A, B, C, X(4385), X(33780)}}, {{A, B, C, X(4648), X(31144)}}, {{A, B, C, X(4846), X(51024)}}, {{A, B, C, X(5067), X(52281)}}, {{A, B, C, X(5117), X(14039)}}, {{A, B, C, X(5641), X(9164)}}, {{A, B, C, X(5967), X(19662)}}, {{A, B, C, X(6330), X(18852)}}, {{A, B, C, X(6353), X(33190)}}, {{A, B, C, X(7317), X(30701)}}, {{A, B, C, X(7714), X(32956)}}, {{A, B, C, X(7778), X(23055)}}, {{A, B, C, X(7840), X(16990)}}, {{A, B, C, X(7841), X(38282)}}, {{A, B, C, X(8370), X(52299)}}, {{A, B, C, X(8753), X(21448)}}, {{A, B, C, X(8797), X(57908)}}, {{A, B, C, X(8860), X(37690)}}, {{A, B, C, X(9141), X(14364)}}, {{A, B, C, X(9214), X(18310)}}, {{A, B, C, X(9462), X(19222)}}, {{A, B, C, X(9466), X(20023)}}, {{A, B, C, X(11001), X(11331)}}, {{A, B, C, X(14482), X(52187)}}, {{A, B, C, X(15533), X(50994)}}, {{A, B, C, X(15702), X(37174)}}, {{A, B, C, X(18854), X(52581)}}, {{A, B, C, X(20421), X(30541)}}, {{A, B, C, X(21358), X(38005)}}, {{A, B, C, X(22110), X(34229)}}, {{A, B, C, X(22165), X(50990)}}, {{A, B, C, X(23053), X(44377)}}, {{A, B, C, X(27818), X(39711)}}, {{A, B, C, X(31926), X(50727)}}, {{A, B, C, X(33231), X(57533)}}, {{A, B, C, X(34403), X(36952)}}, {{A, B, C, X(34578), X(36588)}}, {{A, B, C, X(39708), X(56054)}}, {{A, B, C, X(40014), X(59760)}}, {{A, B, C, X(40028), X(55955)}}, {{A, B, C, X(40814), X(46951)}}, {{A, B, C, X(41106), X(52289)}}, {{A, B, C, X(42287), X(47354)}}, {{A, B, C, X(42313), X(50967)}}, {{A, B, C, X(44146), X(52713)}}, {{A, B, C, X(50991), X(50992)}}, {{A, B, C, X(55972), X(57822)}}
X(60143) = barycentric product X(i)*X(j) for these (i, j): {58090, 850}
X(60143) = barycentric quotient X(i)/X(j) for these (i, j): {2, 59373}, {4, 52301}, {6, 21309}, {7736, 44839}, {21358, 51588}, {58090, 110}

X(60144) = X(2)X(22330)∩X(4)X(8589)

Barycentrics    (4*a^4-10*a^2*b^2+4*b^4-9*(a^2+b^2)*c^2+5*c^4)*(4*a^4+5*b^4-9*b^2*c^2+4*c^4-a^2*(9*b^2+10*c^2)) : :

X(60144) lies on the Kiepert hyperbola and on these lines: {2, 22330}, {3, 45103}, {4, 8589}, {5, 17503}, {6, 10185}, {20, 54642}, {25, 54791}, {76, 55856}, {83, 46219}, {140, 598}, {275, 52292}, {381, 54478}, {383, 54480}, {468, 60120}, {550, 54494}, {631, 60281}, {632, 60283}, {671, 1656}, {1080, 54479}, {1513, 54582}, {1657, 54646}, {2052, 52293}, {2996, 46935}, {3055, 7607}, {3090, 32532}, {3091, 54896}, {3522, 54476}, {3523, 53101}, {3525, 60284}, {3526, 60282}, {3533, 18842}, {3545, 54647}, {3628, 60228}, {3815, 11668}, {3850, 54493}, {3851, 33698}, {4232, 54892}, {5056, 41895}, {5067, 54637}, {5068, 60113}, {5070, 60216}, {5094, 39284}, {6811, 43563}, {6813, 43562}, {7000, 54598}, {7374, 54599}, {7399, 54897}, {7533, 54601}, {7570, 54801}, {7892, 54872}, {9744, 60322}, {9753, 60331}, {10302, 55860}, {12816, 37464}, {12817, 37463}, {13860, 54477}, {14789, 54483}, {15712, 53107}, {15720, 53109}, {16063, 54765}, {16239, 60287}, {31489, 53104}, {35018, 53105}, {37334, 54584}, {37446, 54583}, {37647, 60248}, {38227, 53099}, {43460, 60325}, {43461, 53100}, {46336, 54764}, {48154, 60286}, {52284, 54893}, {52290, 54531}, {52296, 54685}, {52300, 54663}, {53857, 60161}, {55859, 60239}

X(60144) = isogonal conjugate of X(22234)
X(60144) = X(i)-vertex conjugate of X(j) for these {i, j}: {3425, 54582}
X(60144) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(8589)}}, {{A, B, C, X(5), X(52292)}}, {{A, B, C, X(6), X(22330)}}, {{A, B, C, X(25), X(55856)}}, {{A, B, C, X(111), X(57730)}}, {{A, B, C, X(140), X(5094)}}, {{A, B, C, X(264), X(15464)}}, {{A, B, C, X(427), X(46219)}}, {{A, B, C, X(468), X(1656)}}, {{A, B, C, X(842), X(14528)}}, {{A, B, C, X(3090), X(53857)}}, {{A, B, C, X(3533), X(52284)}}, {{A, B, C, X(5056), X(52290)}}, {{A, B, C, X(5486), X(40410)}}, {{A, B, C, X(5966), X(39951)}}, {{A, B, C, X(6353), X(46935)}}, {{A, B, C, X(7495), X(52296)}}, {{A, B, C, X(10301), X(55860)}}, {{A, B, C, X(13472), X(43656)}}, {{A, B, C, X(15712), X(52298)}}, {{A, B, C, X(17983), X(57927)}}, {{A, B, C, X(30786), X(42021)}}, {{A, B, C, X(31489), X(37647)}}, {{A, B, C, X(31846), X(46081)}}, {{A, B, C, X(32085), X(46223)}}, {{A, B, C, X(34567), X(39389)}}, {{A, B, C, X(35018), X(37453)}}, {{A, B, C, X(44658), X(55958)}}, {{A, B, C, X(46217), X(57408)}}, {{A, B, C, X(51524), X(52145)}}

X(60145) = X(2)X(22331)∩X(3)X(54523)

Barycentrics    (7*(a^2+b^2)-c^2)*(7*a^2-b^2+7*c^2) : :

X(60145) lies on the Kiepert hyperbola and on these lines: {2, 22331}, {3, 54523}, {4, 51732}, {5, 60185}, {6, 43681}, {20, 60127}, {30, 54707}, {76, 51170}, {98, 5068}, {140, 10155}, {262, 3522}, {315, 56059}, {381, 54612}, {458, 54710}, {597, 60113}, {598, 32982}, {671, 32979}, {1656, 53103}, {1916, 14031}, {3091, 60150}, {3146, 14492}, {3407, 33290}, {3424, 3854}, {3523, 14494}, {3618, 18845}, {3832, 14458}, {3851, 60322}, {5056, 7612}, {5059, 14484}, {5286, 60209}, {5485, 32971}, {5503, 33201}, {6392, 60250}, {6656, 54616}, {7388, 43536}, {7389, 54597}, {7406, 54689}, {7533, 40178}, {7762, 18840}, {7768, 60277}, {7770, 60143}, {7787, 32897}, {7803, 53107}, {7812, 60279}, {7841, 60284}, {7878, 60228}, {8370, 54637}, {10358, 54858}, {11172, 32962}, {11289, 43555}, {11290, 43554}, {11303, 33605}, {11304, 33604}, {11331, 60137}, {14037, 40824}, {14068, 54540}, {14930, 43688}, {15022, 60175}, {15683, 54643}, {15717, 60192}, {16925, 60240}, {17578, 54520}, {18841, 53489}, {18842, 32974}, {20080, 60285}, {21734, 54522}, {25555, 54873}, {32879, 60201}, {32883, 60248}, {32965, 60268}, {32980, 54906}, {32981, 60095}, {32991, 60218}, {32995, 43535}, {32996, 54539}, {32997, 54487}, {33020, 60212}, {33023, 54905}, {33025, 54773}, {34007, 54640}, {36670, 54885}, {37162, 60165}, {37174, 54531}, {38253, 52289}, {38259, 51171}, {43951, 50690}, {46935, 60123}, {49135, 52519}, {50687, 54582}, {50689, 54519}, {50693, 54521}, {52301, 60141}, {53101, 54097}

X(60145) = isogonal conjugate of X(22332)
X(60145) = trilinear pole of line {47630, 523}
X(60145) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55705)}}, {{A, B, C, X(6), X(22331)}}, {{A, B, C, X(89), X(989)}}, {{A, B, C, X(297), X(5068)}}, {{A, B, C, X(419), X(14031)}}, {{A, B, C, X(458), X(3522)}}, {{A, B, C, X(468), X(32979)}}, {{A, B, C, X(2207), X(39955)}}, {{A, B, C, X(3108), X(14248)}}, {{A, B, C, X(3146), X(52289)}}, {{A, B, C, X(3832), X(11331)}}, {{A, B, C, X(3854), X(52283)}}, {{A, B, C, X(3926), X(14861)}}, {{A, B, C, X(4232), X(32971)}}, {{A, B, C, X(5056), X(37174)}}, {{A, B, C, X(5059), X(52288)}}, {{A, B, C, X(5094), X(32982)}}, {{A, B, C, X(5117), X(33290)}}, {{A, B, C, X(5557), X(54123)}}, {{A, B, C, X(5558), X(17743)}}, {{A, B, C, X(6339), X(38005)}}, {{A, B, C, X(6620), X(14037)}}, {{A, B, C, X(7320), X(14621)}}, {{A, B, C, X(7766), X(14930)}}, {{A, B, C, X(7770), X(52301)}}, {{A, B, C, X(8601), X(11175)}}, {{A, B, C, X(14528), X(30535)}}, {{A, B, C, X(17040), X(20080)}}, {{A, B, C, X(23297), X(47730)}}, {{A, B, C, X(30701), X(43732)}}, {{A, B, C, X(32533), X(53024)}}, {{A, B, C, X(32974), X(52284)}}, {{A, B, C, X(34567), X(55999)}}, {{A, B, C, X(41366), X(41370)}}, {{A, B, C, X(42021), X(51732)}}, {{A, B, C, X(47735), X(52224)}}, {{A, B, C, X(56004), X(57730)}}

X(60146) = X(2)X(55817)∩X(3)X(54645)

Barycentrics    (5*(a^2+b^2)-2*c^2)*(5*a^2-2*b^2+5*c^2) : :

X(60146) lies on the Kiepert hyperbola and on these lines: {2, 55817}, {3, 54645}, {4, 55710}, {5, 54644}, {6, 60209}, {20, 54522}, {30, 54734}, {76, 6144}, {98, 3850}, {140, 53108}, {262, 1657}, {316, 60100}, {381, 54851}, {546, 54934}, {548, 60192}, {550, 54920}, {1656, 11668}, {3627, 14492}, {3843, 14458}, {3851, 60335}, {5068, 54921}, {5072, 60175}, {5485, 7760}, {6656, 60238}, {7608, 15712}, {7745, 10159}, {7768, 10302}, {7770, 60277}, {7790, 18845}, {7803, 18843}, {7812, 60143}, {7827, 33698}, {7841, 60283}, {7860, 60278}, {7878, 17503}, {7883, 60131}, {7911, 43527}, {8370, 60216}, {10484, 33268}, {11289, 43549}, {11290, 43548}, {11303, 54594}, {11304, 54593}, {14040, 43529}, {14044, 54539}, {14061, 60136}, {14066, 54540}, {14484, 50691}, {14494, 21735}, {14893, 54477}, {15684, 54643}, {17538, 54523}, {18840, 32027}, {19695, 54905}, {23046, 54608}, {32455, 60250}, {32875, 60201}, {32889, 60262}, {33247, 60268}, {33267, 44562}, {33286, 43528}, {33703, 60127}, {35005, 52886}, {38335, 54582}, {49140, 54521}, {53109, 53489}

X(60146) = isogonal conjugate of X(31652)
X(60146) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55710)}}, {{A, B, C, X(6), X(6144)}}, {{A, B, C, X(249), X(34567)}}, {{A, B, C, X(287), X(14861)}}, {{A, B, C, X(458), X(1657)}}, {{A, B, C, X(1016), X(5557)}}, {{A, B, C, X(1509), X(5559)}}, {{A, B, C, X(3627), X(52289)}}, {{A, B, C, X(3843), X(11331)}}, {{A, B, C, X(8601), X(42346)}}, {{A, B, C, X(8753), X(57421)}}, {{A, B, C, X(14528), X(20251)}}, {{A, B, C, X(14621), X(43731)}}, {{A, B, C, X(15712), X(52281)}}, {{A, B, C, X(17505), X(53024)}}, {{A, B, C, X(17743), X(43732)}}, {{A, B, C, X(17983), X(52395)}}, {{A, B, C, X(32901), X(57713)}}, {{A, B, C, X(35140), X(57896)}}, {{A, B, C, X(38005), X(40405)}}, {{A, B, C, X(50691), X(52288)}}

X(60147) = X(2)X(14927)∩X(3)X(55741)

Barycentrics    (5*a^4+6*a^2*b^2+5*b^4-2*(a^2+b^2)*c^2-3*c^4)*(5*a^4-3*b^4-2*b^2*c^2+5*c^4-2*a^2*(b^2-3*c^2)) : :
X(60147) = -5*X[3091]+4*X[14535], -3*X[3839]+2*X[18842]

X(60147) lies on these lines: {2, 14927}, {3, 55741}, {4, 43136}, {6, 43951}, {20, 18840}, {25, 38253}, {30, 46944}, {76, 3146}, {83, 3832}, {115, 54800}, {147, 5503}, {226, 4344}, {230, 54921}, {275, 7409}, {381, 54616}, {383, 43555}, {427, 60137}, {428, 54710}, {459, 6995}, {671, 5984}, {1080, 43554}, {1370, 60237}, {1503, 14484}, {1513, 53103}, {2052, 7408}, {2996, 7823}, {3091, 14535}, {3316, 7374}, {3317, 7000}, {3522, 10159}, {3543, 5485}, {3830, 54637}, {3839, 18842}, {3845, 60284}, {4052, 50865}, {5059, 17128}, {5068, 43527}, {5395, 50689}, {5480, 54520}, {5921, 60180}, {6776, 14492}, {6811, 34089}, {6813, 34091}, {7378, 56346}, {7391, 60114}, {7500, 60221}, {7519, 60256}, {7710, 60333}, {7735, 47586}, {7736, 60331}, {7766, 38259}, {9740, 51022}, {9744, 60192}, {9748, 60132}, {9752, 60335}, {9753, 53100}, {9755, 60325}, {9770, 51025}, {9993, 54857}, {10155, 13860}, {10302, 15683}, {10513, 60201}, {11167, 51216}, {11669, 43460}, {14068, 60151}, {14488, 14853}, {15022, 60100}, {15705, 60279}, {15717, 60278}, {16080, 52301}, {16621, 31363}, {16656, 40190}, {20080, 43688}, {36997, 43676}, {37456, 60076}, {37463, 43445}, {37464, 43444}, {37665, 60118}, {37689, 60336}, {39874, 52519}, {40236, 60212}, {43537, 53015}, {43681, 50690}, {49745, 57826}, {50688, 60219}, {53016, 60115}, {53023, 54706}

X(60147) = reflection of X(i) in X(j) for these {i,j}: {54800, 115}
X(60147) = isogonal conjugate of X(31884)
X(60147) = isotomic conjugate of X(10513)
X(60147) = trilinear pole of line {47454, 50642}
X(60147) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 31884}, {31, 10513}
X(60147) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 14484}, {25, 54921}, {3425, 53103}
X(60147) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 10513}, {3, 31884}
X(60147) = pole of line {5304, 60147} with respect to the Kiepert hyperbola
X(60147) = pole of line {10513, 31884} with respect to the Wallace hyperbola
X(60147) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(7408)}}, {{A, B, C, X(5), X(7409)}}, {{A, B, C, X(6), X(29180)}}, {{A, B, C, X(7), X(4344)}}, {{A, B, C, X(20), X(6995)}}, {{A, B, C, X(25), X(3146)}}, {{A, B, C, X(30), X(13574)}}, {{A, B, C, X(64), X(251)}}, {{A, B, C, X(66), X(35510)}}, {{A, B, C, X(67), X(21765)}}, {{A, B, C, X(74), X(14495)}}, {{A, B, C, X(105), X(3062)}}, {{A, B, C, X(111), X(14490)}}, {{A, B, C, X(253), X(14927)}}, {{A, B, C, X(264), X(46208)}}, {{A, B, C, X(305), X(15749)}}, {{A, B, C, X(346), X(15314)}}, {{A, B, C, X(393), X(13481)}}, {{A, B, C, X(427), X(3832)}}, {{A, B, C, X(428), X(3522)}}, {{A, B, C, X(468), X(50687)}}, {{A, B, C, X(1297), X(1383)}}, {{A, B, C, X(1799), X(31371)}}, {{A, B, C, X(2697), X(44836)}}, {{A, B, C, X(2770), X(15448)}}, {{A, B, C, X(2980), X(8801)}}, {{A, B, C, X(3088), X(7394)}}, {{A, B, C, X(3089), X(7391)}}, {{A, B, C, X(3091), X(7378)}}, {{A, B, C, X(3108), X(52518)}}, {{A, B, C, X(3346), X(41513)}}, {{A, B, C, X(3425), X(16835)}}, {{A, B, C, X(3431), X(29316)}}, {{A, B, C, X(3527), X(5481)}}, {{A, B, C, X(3541), X(37349)}}, {{A, B, C, X(3543), X(4232)}}, {{A, B, C, X(3563), X(13603)}}, {{A, B, C, X(3839), X(52284)}}, {{A, B, C, X(4194), X(37456)}}, {{A, B, C, X(4198), X(50698)}}, {{A, B, C, X(5059), X(7714)}}, {{A, B, C, X(5064), X(5068)}}, {{A, B, C, X(5304), X(10513)}}, {{A, B, C, X(5556), X(52133)}}, {{A, B, C, X(5560), X(57727)}}, {{A, B, C, X(5561), X(57726)}}, {{A, B, C, X(5967), X(5984)}}, {{A, B, C, X(6325), X(11744)}}, {{A, B, C, X(6340), X(18296)}}, {{A, B, C, X(6353), X(17578)}}, {{A, B, C, X(6623), X(31099)}}, {{A, B, C, X(6776), X(16264)}}, {{A, B, C, X(6994), X(7390)}}, {{A, B, C, X(7319), X(56358)}}, {{A, B, C, X(7487), X(7500)}}, {{A, B, C, X(7519), X(18533)}}, {{A, B, C, X(7766), X(20080)}}, {{A, B, C, X(8889), X(50689)}}, {{A, B, C, X(9083), X(39732)}}, {{A, B, C, X(9105), X(10429)}}, {{A, B, C, X(9154), X(9473)}}, {{A, B, C, X(9307), X(52443)}}, {{A, B, C, X(10301), X(15683)}}, {{A, B, C, X(10309), X(39728)}}, {{A, B, C, X(10405), X(36124)}}, {{A, B, C, X(11738), X(29011)}}, {{A, B, C, X(14489), X(40103)}}, {{A, B, C, X(14491), X(53890)}}, {{A, B, C, X(14528), X(34572)}}, {{A, B, C, X(14906), X(57260)}}, {{A, B, C, X(14930), X(15589)}}, {{A, B, C, X(15022), X(52285)}}, {{A, B, C, X(16263), X(41896)}}, {{A, B, C, X(16774), X(45833)}}, {{A, B, C, X(18846), X(32826)}}, {{A, B, C, X(20062), X(37122)}}, {{A, B, C, X(22336), X(52188)}}, {{A, B, C, X(30542), X(46952)}}, {{A, B, C, X(33893), X(40174)}}, {{A, B, C, X(34285), X(43726)}}, {{A, B, C, X(38449), X(40815)}}, {{A, B, C, X(39457), X(52392)}}, {{A, B, C, X(40102), X(43695)}}, {{A, B, C, X(42008), X(46731)}}, {{A, B, C, X(43660), X(54459)}}, {{A, B, C, X(45090), X(46217)}}
X(60147) = barycentric quotient X(i)/X(j) for these (i, j): {2, 10513}, {6, 31884}

X(60148) = X(2)X(11842)∩X(76)X(575)

Barycentrics    (2*a^6+b^4*c^2-3*b^2*c^4+2*c^6-a^4*(3*b^2+c^2)+a^2*(b^4-7*b^2*c^2-c^4))*(2*a^6+2*b^6-3*b^4*c^2+b^2*c^4-a^4*(b^2+3*c^2)+a^2*(-b^4-7*b^2*c^2+c^4)) : :

X(60148) lies on the Kiepert hyperbola and on these lines: {2, 11842}, {3, 60177}, {4, 39560}, {5, 60184}, {6, 60126}, {30, 54737}, {32, 7608}, {76, 575}, {182, 671}, {187, 262}, {381, 54901}, {598, 8590}, {631, 60234}, {1078, 60198}, {1153, 42011}, {1352, 54749}, {1691, 11170}, {1916, 8350}, {2080, 10484}, {3288, 5466}, {3398, 60128}, {3399, 13330}, {5033, 54868}, {5067, 60263}, {5503, 7622}, {6776, 9302}, {7787, 60098}, {7808, 60186}, {8587, 22566}, {9180, 15925}, {9744, 54731}, {10290, 31958}, {10302, 51140}, {10358, 53109}, {10485, 43532}, {10796, 54487}, {11179, 54840}, {11606, 37348}, {12110, 60142}, {12203, 53106}, {14494, 46453}, {15702, 60240}, {18842, 42421}, {32519, 43688}, {33190, 54833}, {37242, 60105}, {39141, 54750}, {43535, 49102}

X(60148) = isogonal conjugate of X(32447)
X(60148) = X(i)-vertex conjugate of X(j) for these {i, j}: {32, 11170}
X(60148) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(39560)}}, {{A, B, C, X(6), X(11842)}}, {{A, B, C, X(32), X(575)}}, {{A, B, C, X(54), X(3224)}}, {{A, B, C, X(182), X(187)}}, {{A, B, C, X(290), X(30542)}}, {{A, B, C, X(419), X(35925)}}, {{A, B, C, X(420), X(37348)}}, {{A, B, C, X(574), X(8590)}}, {{A, B, C, X(1691), X(11171)}}, {{A, B, C, X(2080), X(10485)}}, {{A, B, C, X(3398), X(13330)}}, {{A, B, C, X(3425), X(51450)}}, {{A, B, C, X(5468), X(6233)}}, {{A, B, C, X(6531), X(11169)}}, {{A, B, C, X(8753), X(47643)}}, {{A, B, C, X(9154), X(19222)}}, {{A, B, C, X(14382), X(33813)}}, {{A, B, C, X(30499), X(46123)}}, {{A, B, C, X(35473), X(46512)}}, {{A, B, C, X(36615), X(43908)}}, {{A, B, C, X(39287), X(40102)}}, {{A, B, C, X(53864), X(57908)}}

X(60149) = X(2)X(18755)∩X(10)X(3685)

Barycentrics    (a^2+b^2-b*c-c^2-a*(b+c))*(a^2-b^2-b*c+c^2-a*(b+c)) : :

X(60149) lies on the Kiepert hyperbola and on these lines: {2, 18755}, {4, 14024}, {6, 6625}, {8, 43534}, {10, 3685}, {30, 54740}, {69, 60236}, {76, 1654}, {98, 7385}, {148, 16552}, {192, 26036}, {193, 57826}, {226, 239}, {262, 7379}, {275, 54372}, {321, 3975}, {381, 54657}, {391, 2996}, {966, 56210}, {1029, 19742}, {1446, 10030}, {1714, 7787}, {2051, 7384}, {2238, 16044}, {2271, 33045}, {2478, 56161}, {2896, 29433}, {3496, 11608}, {3543, 54532}, {3545, 54885}, {3839, 54862}, {4051, 6630}, {4052, 50095}, {4080, 17152}, {4201, 60090}, {4444, 4560}, {5046, 13576}, {5232, 60285}, {5278, 54119}, {5395, 37681}, {5739, 60257}, {6999, 13478}, {7745, 20142}, {14555, 60261}, {16704, 60258}, {16910, 40030}, {17023, 56226}, {17034, 17300}, {17238, 18840}, {17277, 17685}, {17379, 33028}, {17493, 60245}, {17565, 37686}, {17680, 40017}, {17743, 32865}, {17778, 57722}, {18088, 33110}, {20088, 33295}, {20180, 25466}, {26051, 43531}, {26117, 60110}, {29610, 60243}, {29673, 39722}, {30588, 33129}, {32022, 33029}, {33031, 54770}, {33157, 60203}, {33822, 37650}, {36662, 45098}, {36706, 45097}, {37652, 60156}, {37653, 40013}, {37683, 60076}, {37684, 60169}, {41232, 56214}, {50014, 54120}, {50133, 54831}, {51171, 60077}

X(60149) = isogonal conjugate of X(33863)
X(60149) = isotomic conjugate of X(17300)
X(60149) = trilinear pole of line {3716, 47100}
X(60149) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 33863}, {6, 32913}, {31, 17300}, {32, 33943}, {48, 4212}, {1333, 29653}
X(60149) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 17300}, {3, 33863}, {9, 32913}, {37, 29653}, {1249, 4212}, {6376, 33943}
X(60149) = X(i)-cross conjugate of X(j) for these {i, j}: {17277, 2}, {17685, 6625}, {33095, 7}
X(60149) = pole of line {17277, 17685} with respect to the Kiepert hyperbola
X(60149) = pole of line {21118, 48082} with respect to the Steiner circumellipse
X(60149) = pole of line {17300, 17695} with respect to the Wallace hyperbola
X(60149) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6650)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(37510)}}, {{A, B, C, X(5), X(54372)}}, {{A, B, C, X(6), X(1654)}}, {{A, B, C, X(7), X(17260)}}, {{A, B, C, X(8), X(239)}}, {{A, B, C, X(65), X(39971)}}, {{A, B, C, X(69), X(17349)}}, {{A, B, C, X(75), X(1031)}}, {{A, B, C, X(79), X(32009)}}, {{A, B, C, X(80), X(274)}}, {{A, B, C, X(81), X(43073)}}, {{A, B, C, X(145), X(50095)}}, {{A, B, C, X(193), X(391)}}, {{A, B, C, X(251), X(2333)}}, {{A, B, C, X(256), X(1258)}}, {{A, B, C, X(257), X(673)}}, {{A, B, C, X(291), X(56011)}}, {{A, B, C, X(297), X(7385)}}, {{A, B, C, X(335), X(32008)}}, {{A, B, C, X(385), X(4095)}}, {{A, B, C, X(458), X(7379)}}, {{A, B, C, X(469), X(26051)}}, {{A, B, C, X(594), X(52395)}}, {{A, B, C, X(596), X(1016)}}, {{A, B, C, X(862), X(17680)}}, {{A, B, C, X(941), X(40747)}}, {{A, B, C, X(966), X(17379)}}, {{A, B, C, X(1000), X(38247)}}, {{A, B, C, X(1220), X(27483)}}, {{A, B, C, X(1509), X(42285)}}, {{A, B, C, X(1824), X(56229)}}, {{A, B, C, X(2238), X(7148)}}, {{A, B, C, X(2895), X(19742)}}, {{A, B, C, X(2991), X(32635)}}, {{A, B, C, X(3227), X(5559)}}, {{A, B, C, X(3296), X(39720)}}, {{A, B, C, X(3467), X(4567)}}, {{A, B, C, X(3613), X(23901)}}, {{A, B, C, X(3617), X(17023)}}, {{A, B, C, X(3618), X(17238)}}, {{A, B, C, X(3620), X(37681)}}, {{A, B, C, X(4196), X(33029)}}, {{A, B, C, X(4207), X(33028)}}, {{A, B, C, X(4212), X(17685)}}, {{A, B, C, X(4213), X(33030)}}, {{A, B, C, X(4373), X(25101)}}, {{A, B, C, X(4651), X(17034)}}, {{A, B, C, X(4671), X(33129)}}, {{A, B, C, X(5046), X(15149)}}, {{A, B, C, X(5232), X(51171)}}, {{A, B, C, X(5278), X(17778)}}, {{A, B, C, X(5560), X(56051)}}, {{A, B, C, X(5739), X(37652)}}, {{A, B, C, X(6598), X(36796)}}, {{A, B, C, X(6601), X(20257)}}, {{A, B, C, X(6999), X(17555)}}, {{A, B, C, X(7319), X(39736)}}, {{A, B, C, X(7384), X(11109)}}, {{A, B, C, X(8601), X(23493)}}, {{A, B, C, X(9361), X(52176)}}, {{A, B, C, X(9510), X(39748)}}, {{A, B, C, X(9534), X(41233)}}, {{A, B, C, X(9780), X(29610)}}, {{A, B, C, X(14555), X(37683)}}, {{A, B, C, X(14621), X(31359)}}, {{A, B, C, X(16704), X(37656)}}, {{A, B, C, X(16816), X(32847)}}, {{A, B, C, X(17232), X(37650)}}, {{A, B, C, X(17277), X(17300)}}, {{A, B, C, X(18097), X(56122)}}, {{A, B, C, X(18299), X(57815)}}, {{A, B, C, X(18359), X(44129)}}, {{A, B, C, X(19684), X(26044)}}, {{A, B, C, X(19732), X(26109)}}, {{A, B, C, X(19787), X(41839)}}, {{A, B, C, X(20568), X(42326)}}, {{A, B, C, X(21739), X(39706)}}, {{A, B, C, X(27447), X(43749)}}, {{A, B, C, X(27494), X(30701)}}, {{A, B, C, X(28605), X(33157)}}, {{A, B, C, X(29591), X(36478)}}, {{A, B, C, X(29593), X(29633)}}, {{A, B, C, X(29614), X(53620)}}, {{A, B, C, X(30133), X(33090)}}, {{A, B, C, X(32012), X(32018)}}, {{A, B, C, X(32911), X(37653)}}, {{A, B, C, X(33937), X(33941)}}, {{A, B, C, X(34434), X(40432)}}, {{A, B, C, X(34860), X(55954)}}, {{A, B, C, X(36871), X(43731)}}, {{A, B, C, X(37128), X(57666)}}, {{A, B, C, X(37654), X(50074)}}, {{A, B, C, X(39700), X(56184)}}, {{A, B, C, X(39740), X(43734)}}, {{A, B, C, X(39952), X(57705)}}, {{A, B, C, X(39979), X(56174)}}, {{A, B, C, X(40028), X(55967)}}, {{A, B, C, X(46872), X(56043)}}, {{A, B, C, X(56132), X(56186)}}
X(60149) = barycentric quotient X(i)/X(j) for these (i, j): {1, 32913}, {2, 17300}, {4, 4212}, {6, 33863}, {10, 29653}, {75, 33943}, {17349, 17695}
X(60149) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 33030, 6625}

X(60150) = X(2)X(8780)∩X(4)X(5306)

Barycentrics    (5*a^4+2*a^2*b^2+5*b^4-4*(a^2+b^2)*c^2-c^4)*(5*a^4-4*a^2*b^2-b^4+2*(a^2-2*b^2)*c^2+5*c^4) : :
X(60150) = -2*X[3830]+3*X[41895]

X(60150) lies on the Kiepert hyperbola and on these lines: {2, 8780}, {3, 55729}, {4, 5306}, {6, 60127}, {20, 43681}, {25, 56270}, {30, 2996}, {32, 54858}, {69, 60202}, {76, 376}, {83, 3545}, {115, 54659}, {230, 60185}, {262, 14912}, {381, 5395}, {383, 22237}, {427, 60193}, {428, 8796}, {485, 13674}, {486, 13794}, {542, 8781}, {597, 33692}, {598, 41099}, {631, 10159}, {671, 9862}, {1080, 22235}, {1285, 54856}, {1327, 13832}, {1328, 13831}, {1370, 60255}, {1503, 7612}, {1513, 43537}, {1916, 11177}, {1992, 60095}, {2052, 7714}, {2394, 3566}, {2794, 60189}, {3090, 43527}, {3091, 60145}, {3399, 40923}, {3524, 7789}, {3529, 43676}, {3534, 60200}, {3543, 38259}, {3590, 6811}, {3591, 6813}, {3767, 54846}, {3830, 41895}, {3839, 18845}, {3845, 53101}, {3855, 53102}, {4049, 28529}, {5064, 60161}, {5066, 54639}, {5071, 18841}, {5304, 54520}, {5392, 34608}, {5485, 8667}, {5984, 35005}, {6054, 56064}, {6055, 60073}, {6353, 16080}, {6504, 44442}, {6776, 14494}, {7000, 60292}, {7374, 60291}, {7391, 13582}, {7394, 60191}, {7494, 60225}, {7607, 58883}, {7710, 53104}, {7735, 14458}, {7736, 60192}, {7737, 54718}, {7788, 40824}, {8550, 60330}, {8889, 43530}, {9300, 54523}, {9302, 46453}, {9744, 11669}, {9752, 60322}, {9753, 60132}, {9755, 43951}, {9756, 10155}, {9993, 54477}, {10033, 54773}, {10302, 11147}, {10722, 54767}, {11167, 55177}, {11179, 60096}, {11456, 54763}, {11645, 60218}, {11648, 59363}, {12101, 54896}, {13691, 54628}, {13810, 54627}, {13860, 53099}, {14033, 60151}, {14223, 55122}, {14537, 54714}, {14651, 60140}, {14830, 54750}, {14853, 52519}, {15702, 60183}, {15709, 60278}, {15710, 60210}, {15719, 60277}, {16990, 54748}, {18842, 41106}, {19708, 60143}, {26118, 60258}, {32874, 44251}, {33456, 60207}, {33457, 60208}, {33703, 60209}, {34609, 43670}, {36990, 54845}, {37665, 54522}, {37689, 54866}, {38227, 60335}, {41400, 43532}, {43460, 60175}, {45101, 49260}, {45102, 49263}, {46264, 60217}, {46333, 60250}, {49361, 54626}, {49364, 54625}, {50974, 60260}, {51023, 60093}, {54905, 59373}

X(60150) = reflection of X(i) in X(j) for these {i,j}: {54659, 115}
X(60150) = isogonal conjugate of X(33878)
X(60150) = trilinear pole of line {47459, 523}
X(60150) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 7612}, {25, 60185}, {468, 46423}, {3425, 43537}, {3431, 54172}, {10623, 39954}, {11270, 40801}, {20421, 21448}
X(60150) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(7714)}}, {{A, B, C, X(6), X(12017)}}, {{A, B, C, X(24), X(34608)}}, {{A, B, C, X(25), X(74)}}, {{A, B, C, X(30), X(3566)}}, {{A, B, C, X(54), X(14486)}}, {{A, B, C, X(64), X(3563)}}, {{A, B, C, X(66), X(1989)}}, {{A, B, C, X(67), X(44556)}}, {{A, B, C, X(69), X(2980)}}, {{A, B, C, X(95), X(52188)}}, {{A, B, C, X(111), X(11738)}}, {{A, B, C, X(251), X(3431)}}, {{A, B, C, X(253), X(36611)}}, {{A, B, C, X(265), X(6340)}}, {{A, B, C, X(381), X(8889)}}, {{A, B, C, X(393), X(1494)}}, {{A, B, C, X(427), X(3545)}}, {{A, B, C, X(428), X(631)}}, {{A, B, C, X(468), X(15682)}}, {{A, B, C, X(519), X(28529)}}, {{A, B, C, X(523), X(46204)}}, {{A, B, C, X(542), X(36875)}}, {{A, B, C, X(1000), X(56358)}}, {{A, B, C, X(1138), X(2697)}}, {{A, B, C, X(1141), X(18852)}}, {{A, B, C, X(1297), X(13452)}}, {{A, B, C, X(1300), X(55023)}}, {{A, B, C, X(1383), X(20421)}}, {{A, B, C, X(1799), X(45138)}}, {{A, B, C, X(1992), X(8667)}}, {{A, B, C, X(2165), X(18358)}}, {{A, B, C, X(3090), X(5064)}}, {{A, B, C, X(3108), X(14491)}}, {{A, B, C, X(3147), X(34603)}}, {{A, B, C, X(3296), X(52133)}}, {{A, B, C, X(3425), X(11270)}}, {{A, B, C, X(3426), X(8770)}}, {{A, B, C, X(3524), X(6995)}}, {{A, B, C, X(3542), X(44442)}}, {{A, B, C, X(3543), X(38282)}}, {{A, B, C, X(3830), X(52290)}}, {{A, B, C, X(3839), X(52299)}}, {{A, B, C, X(4231), X(11111)}}, {{A, B, C, X(4232), X(11001)}}, {{A, B, C, X(5071), X(7378)}}, {{A, B, C, X(5094), X(41099)}}, {{A, B, C, X(5481), X(13472)}}, {{A, B, C, X(5627), X(13854)}}, {{A, B, C, X(5641), X(42377)}}, {{A, B, C, X(6344), X(18018)}}, {{A, B, C, X(6622), X(34609)}}, {{A, B, C, X(7391), X(37943)}}, {{A, B, C, X(7408), X(15702)}}, {{A, B, C, X(7493), X(18559)}}, {{A, B, C, X(7494), X(7576)}}, {{A, B, C, X(7735), X(7788)}}, {{A, B, C, X(8791), X(43949)}}, {{A, B, C, X(8797), X(15321)}}, {{A, B, C, X(8801), X(55958)}}, {{A, B, C, X(9093), X(39732)}}, {{A, B, C, X(9862), X(36890)}}, {{A, B, C, X(10301), X(15698)}}, {{A, B, C, X(10308), X(39954)}}, {{A, B, C, X(10422), X(46423)}}, {{A, B, C, X(10603), X(18847)}}, {{A, B, C, X(11147), X(13608)}}, {{A, B, C, X(11177), X(40820)}}, {{A, B, C, X(13139), X(39978)}}, {{A, B, C, X(13574), X(53955)}}, {{A, B, C, X(13603), X(21448)}}, {{A, B, C, X(14483), X(39951)}}, {{A, B, C, X(14489), X(22334)}}, {{A, B, C, X(14912), X(33971)}}, {{A, B, C, X(15619), X(31371)}}, {{A, B, C, X(15749), X(17703)}}, {{A, B, C, X(16835), X(18851)}}, {{A, B, C, X(17040), X(32085)}}, {{A, B, C, X(18850), X(40413)}}, {{A, B, C, X(19708), X(52301)}}, {{A, B, C, X(22336), X(44658)}}, {{A, B, C, X(26255), X(35481)}}, {{A, B, C, X(30537), X(36948)}}, {{A, B, C, X(30542), X(38005)}}, {{A, B, C, X(32319), X(43952)}}, {{A, B, C, X(34168), X(59278)}}, {{A, B, C, X(34223), X(38443)}}, {{A, B, C, X(37362), X(50741)}}, {{A, B, C, X(40119), X(46429)}}, {{A, B, C, X(41106), X(52284)}}, {{A, B, C, X(43733), X(57726)}}, {{A, B, C, X(43734), X(57727)}}

X(60151) = X(83)X(1692)∩X(98)X(384)

Barycentrics    (a^2*b^2*(a^2+b^2)+(2*a^4+a^2*b^2+2*b^4)*c^2-(a^2+b^2)*c^4+c^6)*(b^6-b^4*c^2+2*b^2*c^4+a^4*(2*b^2+c^2)+a^2*(-b^4+b^2*c^2+c^4)) : :

X(60151) lies on the Kiepert hyperbola and on these lines: {5, 54978}, {30, 54747}, {39, 8781}, {83, 1692}, {98, 384}, {194, 40824}, {262, 5025}, {297, 37892}, {538, 60202}, {1506, 60096}, {1916, 5254}, {2996, 18906}, {3399, 6656}, {3406, 7770}, {3424, 14035}, {3934, 60101}, {6680, 60093}, {6683, 60198}, {7607, 7892}, {7608, 7901}, {7612, 7697}, {7786, 60178}, {7827, 54841}, {8352, 54583}, {8370, 55009}, {9466, 60217}, {10155, 32951}, {11272, 14064}, {11317, 54584}, {11361, 14458}, {11668, 14067}, {11669, 14065}, {14030, 54851}, {14031, 47586}, {14032, 60323}, {14033, 60150}, {14034, 53100}, {14036, 60175}, {14037, 43537}, {14038, 60335}, {14039, 60185}, {14041, 14492}, {14042, 60132}, {14043, 53104}, {14044, 54890}, {14045, 60142}, {14046, 60192}, {14047, 53108}, {14062, 14488}, {14063, 14484}, {14066, 60326}, {14068, 60147}, {14069, 53103}, {16041, 60127}, {20081, 60201}, {22486, 54713}, {31276, 60212}, {32821, 43529}, {32996, 43951}, {33013, 54675}, {33283, 53099}, {33284, 54920}, {33285, 54523}, {33287, 60331}, {33290, 60118}, {33291, 54734}, {34505, 60214}, {40016, 51481}, {40162, 40814}

X(60151) = isogonal conjugate of X(34870)
X(60151) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(39), X(1692)}}, {{A, B, C, X(194), X(40814)}}, {{A, B, C, X(290), X(9229)}}, {{A, B, C, X(297), X(384)}}, {{A, B, C, X(458), X(5025)}}, {{A, B, C, X(511), X(13335)}}, {{A, B, C, X(695), X(34238)}}, {{A, B, C, X(732), X(9484)}}, {{A, B, C, X(1235), X(39266)}}, {{A, B, C, X(2987), X(27375)}}, {{A, B, C, X(3094), X(30496)}}, {{A, B, C, X(5254), X(14603)}}, {{A, B, C, X(6248), X(44132)}}, {{A, B, C, X(7892), X(52282)}}, {{A, B, C, X(7901), X(52281)}}, {{A, B, C, X(8601), X(41517)}}, {{A, B, C, X(11331), X(11361)}}, {{A, B, C, X(14001), X(37174)}}, {{A, B, C, X(14035), X(52283)}}, {{A, B, C, X(14041), X(52289)}}, {{A, B, C, X(14063), X(52288)}}, {{A, B, C, X(14498), X(41440)}}, {{A, B, C, X(18906), X(47733)}}, {{A, B, C, X(36790), X(51249)}}, {{A, B, C, X(40815), X(42486)}}, {{A, B, C, X(42313), X(43714)}}, {{A, B, C, X(56247), X(57924)}}, {{A, B, C, X(56332), X(57922)}}

X(60152) = X(2)X(5800)∩X(4)X(5276)

Barycentrics    (a^4+b^4-c^4+2*a^2*b*(b+c)+2*a*b*c*(b+c))*(a^4-b^4+c^4+2*a^2*c*(b+c)+2*a*b*c*(b+c)) : :

X(60152) lies on the Kiepert hyperbola and on these lines: {1, 36907}, {2, 5800}, {4, 5276}, {6, 60153}, {8, 60197}, {10, 17742}, {30, 54754}, {76, 377}, {83, 2478}, {226, 612}, {321, 2550}, {376, 54695}, {381, 54755}, {388, 1446}, {406, 52583}, {443, 18840}, {1029, 7391}, {1370, 60156}, {1714, 60075}, {2303, 36851}, {2475, 2996}, {3543, 54780}, {3545, 54719}, {4049, 20516}, {4080, 20344}, {5046, 5395}, {5084, 18841}, {6353, 60246}, {6826, 54739}, {6925, 54821}, {6997, 60155}, {6998, 60154}, {7102, 40149}, {7380, 60164}, {7386, 60076}, {7390, 60158}, {7392, 60107}, {7394, 55027}, {7407, 60157}, {7735, 60080}, {10159, 37462}, {11606, 16995}, {13478, 26118}, {13577, 24476}, {16063, 60258}, {16997, 54122}, {17582, 60183}, {26032, 60257}, {37456, 60167}, {37675, 60165}, {44442, 54760}, {46336, 60169}

X(60152) = isogonal conjugate of X(36740)
X(60152) = isotomic conjugate of X(45962)
X(60152) = trilinear pole of line {2509, 50539}
X(60152) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 36740}, {31, 45962}, {63, 45786}
X(60152) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 45962}, {3, 36740}, {3162, 45786}
X(60152) = pole of line {5275, 60152} with respect to the Kiepert hyperbola
X(60152) = pole of line {36740, 45962} with respect to the Wallace hyperbola
X(60152) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(7219)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(36741)}}, {{A, B, C, X(7), X(19)}}, {{A, B, C, X(8), X(33)}}, {{A, B, C, X(12), X(13854)}}, {{A, B, C, X(25), X(65)}}, {{A, B, C, X(29), X(26052)}}, {{A, B, C, X(37), X(66)}}, {{A, B, C, X(69), X(941)}}, {{A, B, C, X(79), X(39732)}}, {{A, B, C, X(85), X(36124)}}, {{A, B, C, X(251), X(51223)}}, {{A, B, C, X(256), X(8048)}}, {{A, B, C, X(281), X(50861)}}, {{A, B, C, X(393), X(1441)}}, {{A, B, C, X(406), X(1370)}}, {{A, B, C, X(427), X(2478)}}, {{A, B, C, X(428), X(37462)}}, {{A, B, C, X(443), X(6995)}}, {{A, B, C, X(451), X(7391)}}, {{A, B, C, X(475), X(6997)}}, {{A, B, C, X(955), X(43079)}}, {{A, B, C, X(957), X(28479)}}, {{A, B, C, X(959), X(3415)}}, {{A, B, C, X(994), X(28476)}}, {{A, B, C, X(1002), X(8817)}}, {{A, B, C, X(1220), X(57925)}}, {{A, B, C, X(1243), X(14486)}}, {{A, B, C, X(1311), X(57726)}}, {{A, B, C, X(1486), X(24476)}}, {{A, B, C, X(2475), X(6353)}}, {{A, B, C, X(3108), X(57705)}}, {{A, B, C, X(3296), X(39723)}}, {{A, B, C, X(4194), X(7386)}}, {{A, B, C, X(4200), X(7392)}}, {{A, B, C, X(4518), X(30513)}}, {{A, B, C, X(5046), X(8889)}}, {{A, B, C, X(5084), X(7378)}}, {{A, B, C, X(5177), X(37394)}}, {{A, B, C, X(5230), X(29641)}}, {{A, B, C, X(5275), X(45962)}}, {{A, B, C, X(5486), X(39974)}}, {{A, B, C, X(5555), X(7249)}}, {{A, B, C, X(6836), X(25985)}}, {{A, B, C, X(6850), X(35973)}}, {{A, B, C, X(6957), X(26020)}}, {{A, B, C, X(7394), X(52252)}}, {{A, B, C, X(7408), X(17582)}}, {{A, B, C, X(7409), X(17559)}}, {{A, B, C, X(7774), X(16997)}}, {{A, B, C, X(7779), X(16995)}}, {{A, B, C, X(8801), X(57830)}}, {{A, B, C, X(9093), X(11604)}}, {{A, B, C, X(15321), X(39983)}}, {{A, B, C, X(16774), X(54454)}}, {{A, B, C, X(17555), X(26118)}}, {{A, B, C, X(18018), X(41013)}}, {{A, B, C, X(19784), X(29679)}}, {{A, B, C, X(20029), X(56208)}}, {{A, B, C, X(20344), X(20516)}}, {{A, B, C, X(22336), X(39960)}}, {{A, B, C, X(26032), X(37055)}}, {{A, B, C, X(27540), X(46878)}}, {{A, B, C, X(30142), X(33091)}}, {{A, B, C, X(32085), X(57831)}}, {{A, B, C, X(37149), X(37181)}}, {{A, B, C, X(38005), X(39982)}}, {{A, B, C, X(39570), X(40940)}}, {{A, B, C, X(39728), X(43733)}}, {{A, B, C, X(39748), X(39978)}}, {{A, B, C, X(39798), X(43726)}}, {{A, B, C, X(39951), X(57666)}}, {{A, B, C, X(43740), X(52133)}}, {{A, B, C, X(52223), X(57866)}}, {{A, B, C, X(56123), X(57825)}}
X(60152) = barycentric quotient X(i)/X(j) for these (i, j): {2, 45962}, {6, 36740}, {25, 45786}

X(60153) = X(2)X(5324)∩X(10)X(2082)

Barycentrics    ((a^2+b^2)^2-2*a*b*(a+b)*c-2*a*b*c^2-c^4)*(a^4-b^4+c^4+2*a^2*c*(-b+c)-2*a*b*c*(b+c)) : :

X(60153) lies on the Kiepert hyperbola and on these lines: {2, 5324}, {4, 33854}, {6, 60152}, {10, 2082}, {30, 54755}, {76, 2478}, {83, 377}, {105, 28739}, {226, 614}, {321, 497}, {376, 54719}, {381, 54754}, {443, 18841}, {475, 52583}, {1029, 7394}, {1370, 60155}, {1446, 7195}, {1751, 26052}, {1851, 40149}, {2051, 26118}, {2475, 5395}, {2996, 5046}, {3545, 54695}, {3839, 54780}, {5084, 18840}, {5276, 60165}, {6827, 54739}, {6957, 54821}, {6997, 60156}, {6998, 60164}, {7380, 60154}, {7386, 60107}, {7390, 60157}, {7391, 55027}, {7392, 60076}, {7407, 60158}, {7410, 60173}, {7736, 45964}, {8889, 60246}, {11677, 13576}, {16998, 54122}, {17559, 60183}, {26096, 60261}, {36907, 51400}, {37162, 60285}, {37456, 45100}, {37462, 43527}, {37670, 60212}, {44431, 54933}, {44442, 54759}

X(60153) = isogonal conjugate of X(36741)
X(60153) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(39732)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(36740)}}, {{A, B, C, X(7), X(1390)}}, {{A, B, C, X(8), X(34)}}, {{A, B, C, X(25), X(210)}}, {{A, B, C, X(37), X(43726)}}, {{A, B, C, X(65), X(39951)}}, {{A, B, C, X(66), X(39798)}}, {{A, B, C, X(67), X(39960)}}, {{A, B, C, X(69), X(33854)}}, {{A, B, C, X(80), X(39954)}}, {{A, B, C, X(87), X(8048)}}, {{A, B, C, X(90), X(26703)}}, {{A, B, C, X(251), X(57705)}}, {{A, B, C, X(291), X(13577)}}, {{A, B, C, X(312), X(36124)}}, {{A, B, C, X(377), X(427)}}, {{A, B, C, X(393), X(57830)}}, {{A, B, C, X(406), X(6997)}}, {{A, B, C, X(443), X(7378)}}, {{A, B, C, X(451), X(7394)}}, {{A, B, C, X(452), X(37394)}}, {{A, B, C, X(475), X(1370)}}, {{A, B, C, X(675), X(57727)}}, {{A, B, C, X(941), X(57858)}}, {{A, B, C, X(1220), X(57923)}}, {{A, B, C, X(1224), X(45132)}}, {{A, B, C, X(1441), X(8801)}}, {{A, B, C, X(1861), X(11677)}}, {{A, B, C, X(2297), X(15314)}}, {{A, B, C, X(2475), X(8889)}}, {{A, B, C, X(2550), X(42318)}}, {{A, B, C, X(2551), X(18228)}}, {{A, B, C, X(3108), X(51223)}}, {{A, B, C, X(3296), X(39728)}}, {{A, B, C, X(3415), X(9309)}}, {{A, B, C, X(4194), X(7392)}}, {{A, B, C, X(4200), X(7386)}}, {{A, B, C, X(4518), X(43740)}}, {{A, B, C, X(5046), X(6353)}}, {{A, B, C, X(5064), X(37462)}}, {{A, B, C, X(5084), X(6995)}}, {{A, B, C, X(5125), X(26052)}}, {{A, B, C, X(5486), X(39982)}}, {{A, B, C, X(5555), X(56358)}}, {{A, B, C, X(6835), X(25985)}}, {{A, B, C, X(6893), X(35973)}}, {{A, B, C, X(6925), X(26020)}}, {{A, B, C, X(7261), X(56164)}}, {{A, B, C, X(7391), X(52252)}}, {{A, B, C, X(7408), X(17559)}}, {{A, B, C, X(7409), X(17582)}}, {{A, B, C, X(7714), X(37162)}}, {{A, B, C, X(7736), X(37670)}}, {{A, B, C, X(7774), X(16998)}}, {{A, B, C, X(11109), X(26118)}}, {{A, B, C, X(13575), X(39748)}}, {{A, B, C, X(16066), X(26096)}}, {{A, B, C, X(17040), X(39975)}}, {{A, B, C, X(19836), X(29667)}}, {{A, B, C, X(30148), X(33090)}}, {{A, B, C, X(30513), X(52133)}}, {{A, B, C, X(32085), X(57877)}}, {{A, B, C, X(37189), X(37330)}}, {{A, B, C, X(38005), X(39974)}}, {{A, B, C, X(39723), X(43733)}}

X(60154) = X(2)X(3193)∩X(46)X(226)

Barycentrics    (a^5+a^4*(b+c)+(b-c)^2*(b+c)^3+a*(b-c)*(b+c)*(b^2-2*b*c-c^2)-2*a^2*(b+c)*(b^2+c^2)-2*a^3*(b^2+b*c+c^2))*(a^5+a^4*(b+c)+(b-c)^2*(b+c)^3+a*(b-c)*(b+c)*(b^2+2*b*c-c^2)-2*a^2*(b+c)*(b^2+c^2)-2*a^3*(b^2+b*c+c^2)) : :

X(60154) lies on the Kiepert hyperbola and on these lines: {1, 60249}, {2, 3193}, {3, 60156}, {4, 36744}, {5, 60155}, {6, 60164}, {20, 1029}, {30, 54756}, {46, 226}, {140, 60169}, {275, 475}, {321, 5552}, {376, 54760}, {377, 6504}, {381, 54766}, {387, 60112}, {406, 2052}, {443, 60114}, {451, 459}, {631, 60076}, {1068, 3085}, {1751, 6832}, {2051, 6834}, {2475, 13579}, {3090, 60107}, {3091, 55027}, {3332, 57710}, {3523, 60258}, {3524, 54788}, {3545, 54759}, {3839, 54794}, {4194, 8796}, {4200, 60161}, {5657, 60321}, {6824, 24624}, {6825, 60071}, {6833, 13478}, {6837, 55944}, {6846, 60168}, {6847, 60167}, {6848, 45100}, {6852, 55962}, {6887, 57721}, {6908, 60170}, {6944, 60087}, {6949, 45098}, {6967, 60085}, {6983, 14554}, {6989, 57722}, {6998, 60152}, {7380, 60153}, {7410, 60165}, {7505, 60246}, {8808, 13411}, {13576, 36672}, {17582, 60237}, {19854, 60243}, {27524, 43533}, {34621, 54780}, {37407, 57826}, {52252, 56346}, {56417, 60091}

X(60154) = isogonal conjugate of X(36742)
X(60154) = trilinear pole of line {46389, 523}
X(60154) = X(i)-cross conjugate of X(j) for these {i, j}: {5706, 4}
X(60154) = pole of line {5706, 60154} with respect to the Kiepert hyperbola
X(60154) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(46)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(37)}}, {{A, B, C, X(5), X(475)}}, {{A, B, C, X(6), X(36754)}}, {{A, B, C, X(7), X(91)}}, {{A, B, C, X(8), X(498)}}, {{A, B, C, X(12), X(68)}}, {{A, B, C, X(20), X(451)}}, {{A, B, C, X(29), X(6889)}}, {{A, B, C, X(40), X(25430)}}, {{A, B, C, X(54), X(941)}}, {{A, B, C, X(64), X(39983)}}, {{A, B, C, X(65), X(2165)}}, {{A, B, C, X(69), X(41013)}}, {{A, B, C, X(78), X(281)}}, {{A, B, C, X(79), X(7318)}}, {{A, B, C, X(86), X(5553)}}, {{A, B, C, X(227), X(57701)}}, {{A, B, C, X(280), X(56027)}}, {{A, B, C, X(377), X(3542)}}, {{A, B, C, X(393), X(51223)}}, {{A, B, C, X(443), X(3089)}}, {{A, B, C, X(461), X(37407)}}, {{A, B, C, X(631), X(4194)}}, {{A, B, C, X(847), X(1441)}}, {{A, B, C, X(860), X(6824)}}, {{A, B, C, X(972), X(52351)}}, {{A, B, C, X(975), X(1766)}}, {{A, B, C, X(1000), X(6684)}}, {{A, B, C, X(1065), X(31359)}}, {{A, B, C, X(1093), X(57831)}}, {{A, B, C, X(1123), X(13388)}}, {{A, B, C, X(1173), X(39956)}}, {{A, B, C, X(1219), X(14497)}}, {{A, B, C, X(1220), X(57884)}}, {{A, B, C, X(1224), X(3577)}}, {{A, B, C, X(1268), X(57724)}}, {{A, B, C, X(1336), X(13389)}}, {{A, B, C, X(1389), X(59760)}}, {{A, B, C, X(1440), X(43733)}}, {{A, B, C, X(1794), X(2335)}}, {{A, B, C, X(2475), X(7505)}}, {{A, B, C, X(2478), X(3541)}}, {{A, B, C, X(3088), X(5084)}}, {{A, B, C, X(3090), X(4200)}}, {{A, B, C, X(3091), X(52252)}}, {{A, B, C, X(3527), X(39798)}}, {{A, B, C, X(3945), X(27524)}}, {{A, B, C, X(5046), X(37119)}}, {{A, B, C, X(5125), X(6832)}}, {{A, B, C, X(5136), X(6825)}}, {{A, B, C, X(5177), X(7537)}}, {{A, B, C, X(5554), X(26364)}}, {{A, B, C, X(5657), X(54396)}}, {{A, B, C, X(6197), X(54283)}}, {{A, B, C, X(6335), X(44059)}}, {{A, B, C, X(6833), X(17555)}}, {{A, B, C, X(6834), X(11109)}}, {{A, B, C, X(6891), X(11105)}}, {{A, B, C, X(6908), X(7498)}}, {{A, B, C, X(7013), X(7952)}}, {{A, B, C, X(7080), X(13411)}}, {{A, B, C, X(7160), X(19605)}}, {{A, B, C, X(7531), X(27531)}}, {{A, B, C, X(7551), X(26027)}}, {{A, B, C, X(9375), X(57707)}}, {{A, B, C, X(9780), X(19854)}}, {{A, B, C, X(10309), X(28626)}}, {{A, B, C, X(10573), X(27529)}}, {{A, B, C, X(15077), X(57865)}}, {{A, B, C, X(15149), X(36672)}}, {{A, B, C, X(15175), X(36626)}}, {{A, B, C, X(20029), X(45838)}}, {{A, B, C, X(25490), X(37414)}}, {{A, B, C, X(34259), X(56254)}}, {{A, B, C, X(34285), X(43712)}}, {{A, B, C, X(34485), X(39711)}}, {{A, B, C, X(39974), X(43908)}}, {{A, B, C, X(44876), X(56248)}}, {{A, B, C, X(46952), X(57705)}}, {{A, B, C, X(51316), X(51502)}}, {{A, B, C, X(51499), X(56259)}}, {{A, B, C, X(56237), X(57671)}}

X(60155) = X(6)X(7382)∩X(10)X(1479)

Barycentrics    ((a-b)*(a+b)^2+(a^2-2*a*b-b^2)*c+(a+b)*c^2+c^3)*(a^3+a^2*(b+c)+(b-c)*(b+c)^2+a*(b^2-2*b*c-c^2)) : :

X(60155) lies on the Kiepert hyperbola and on these lines: {2, 36744}, {3, 60164}, {4, 32911}, {5, 60154}, {6, 7382}, {10, 1479}, {20, 60157}, {30, 54757}, {69, 40013}, {76, 5739}, {81, 60076}, {226, 3946}, {262, 26118}, {321, 14555}, {329, 60265}, {376, 54727}, {377, 43531}, {381, 54758}, {631, 60173}, {801, 26668}, {940, 60169}, {1058, 1255}, {1370, 60153}, {1445, 8808}, {1751, 37185}, {2339, 19822}, {2475, 60077}, {3091, 60158}, {3543, 54726}, {3618, 60082}, {3839, 54688}, {3845, 54789}, {4052, 27826}, {4080, 30699}, {4383, 7381}, {4417, 60242}, {5046, 43533}, {5278, 60206}, {5397, 6826}, {5712, 57722}, {5741, 60254}, {6666, 60243}, {6818, 56161}, {6827, 60112}, {6833, 60162}, {6834, 60159}, {6835, 54972}, {6836, 57719}, {6847, 60174}, {6848, 60166}, {6849, 57710}, {6851, 57720}, {6949, 60160}, {6952, 60163}, {6997, 60152}, {7392, 60165}, {10431, 43672}, {13478, 24597}, {14484, 37456}, {14997, 55027}, {17349, 54119}, {17778, 60236}, {18141, 39994}, {18840, 32782}, {19684, 58012}, {20557, 43677}, {26052, 60081}, {26243, 60212}, {30588, 32774}, {31089, 60232}, {31143, 60143}, {32863, 40021}, {33088, 43534}, {37193, 60110}, {37276, 60137}, {37650, 57721}, {37651, 45098}, {37659, 60237}, {37680, 60107}, {37681, 60168}, {37685, 60258}, {41099, 54947}, {54420, 60249}

X(60155) = isogonal conjugate of X(36743)
X(60155) = trilinear pole of line {21185, 47965}
X(60155) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 36743}, {48, 475}, {63, 44105}, {2206, 42715}
X(60155) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 36743}, {1249, 475}, {3162, 44105}, {40603, 42715}
X(60155) = X(i)-cross conjugate of X(j) for these {i, j}: {4383, 2}, {7381, 60156}, {12699, 7}, {21853, 1}, {57706, 57878}
X(60155) = pole of line {4383, 7381} with respect to the Kiepert hyperbola
X(60155) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(36754)}}, {{A, B, C, X(6), X(1824)}}, {{A, B, C, X(7), X(1255)}}, {{A, B, C, X(8), X(81)}}, {{A, B, C, X(27), X(312)}}, {{A, B, C, X(57), X(80)}}, {{A, B, C, X(66), X(39979)}}, {{A, B, C, X(69), X(32911)}}, {{A, B, C, X(75), X(56224)}}, {{A, B, C, X(79), X(25430)}}, {{A, B, C, X(84), X(56354)}}, {{A, B, C, X(88), X(189)}}, {{A, B, C, X(89), X(43734)}}, {{A, B, C, X(90), X(56231)}}, {{A, B, C, X(92), X(673)}}, {{A, B, C, X(104), X(56352)}}, {{A, B, C, X(149), X(52210)}}, {{A, B, C, X(239), X(33088)}}, {{A, B, C, X(277), X(30690)}}, {{A, B, C, X(278), X(1479)}}, {{A, B, C, X(279), X(10624)}}, {{A, B, C, X(294), X(1857)}}, {{A, B, C, X(329), X(1445)}}, {{A, B, C, X(330), X(34527)}}, {{A, B, C, X(333), X(30513)}}, {{A, B, C, X(335), X(55988)}}, {{A, B, C, X(377), X(469)}}, {{A, B, C, X(406), X(7382)}}, {{A, B, C, X(445), X(6849)}}, {{A, B, C, X(458), X(26118)}}, {{A, B, C, X(475), X(7381)}}, {{A, B, C, X(497), X(16750)}}, {{A, B, C, X(593), X(957)}}, {{A, B, C, X(837), X(7020)}}, {{A, B, C, X(908), X(51432)}}, {{A, B, C, X(941), X(18098)}}, {{A, B, C, X(949), X(41509)}}, {{A, B, C, X(966), X(19684)}}, {{A, B, C, X(967), X(57666)}}, {{A, B, C, X(1000), X(25417)}}, {{A, B, C, X(1010), X(19822)}}, {{A, B, C, X(1156), X(55987)}}, {{A, B, C, X(1171), X(57705)}}, {{A, B, C, X(1214), X(4846)}}, {{A, B, C, X(1246), X(39971)}}, {{A, B, C, X(1389), X(56041)}}, {{A, B, C, X(1434), X(4102)}}, {{A, B, C, X(2006), X(10826)}}, {{A, B, C, X(2221), X(34434)}}, {{A, B, C, X(2476), X(37181)}}, {{A, B, C, X(2481), X(39732)}}, {{A, B, C, X(2982), X(55936)}}, {{A, B, C, X(2990), X(42467)}}, {{A, B, C, X(3062), X(56230)}}, {{A, B, C, X(3296), X(27789)}}, {{A, B, C, X(3427), X(40399)}}, {{A, B, C, X(3618), X(32782)}}, {{A, B, C, X(3678), X(40214)}}, {{A, B, C, X(3832), X(37276)}}, {{A, B, C, X(3946), X(6601)}}, {{A, B, C, X(4011), X(6650)}}, {{A, B, C, X(4358), X(30699)}}, {{A, B, C, X(4417), X(24597)}}, {{A, B, C, X(4441), X(39734)}}, {{A, B, C, X(4671), X(32774)}}, {{A, B, C, X(5046), X(7490)}}, {{A, B, C, X(5084), X(6994)}}, {{A, B, C, X(5125), X(37185)}}, {{A, B, C, X(5278), X(5712)}}, {{A, B, C, X(5551), X(56039)}}, {{A, B, C, X(5556), X(40434)}}, {{A, B, C, X(5558), X(56037)}}, {{A, B, C, X(5559), X(39948)}}, {{A, B, C, X(5560), X(8056)}}, {{A, B, C, X(5741), X(37642)}}, {{A, B, C, X(5905), X(36599)}}, {{A, B, C, X(6557), X(11604)}}, {{A, B, C, X(6819), X(6847)}}, {{A, B, C, X(6820), X(6848)}}, {{A, B, C, X(6834), X(37192)}}, {{A, B, C, X(6836), X(37279)}}, {{A, B, C, X(6851), X(57531)}}, {{A, B, C, X(7017), X(41791)}}, {{A, B, C, X(7224), X(56168)}}, {{A, B, C, X(7261), X(13577)}}, {{A, B, C, X(7357), X(8817)}}, {{A, B, C, X(7736), X(26243)}}, {{A, B, C, X(8048), X(20332)}}, {{A, B, C, X(8814), X(54454)}}, {{A, B, C, X(10309), X(56234)}}, {{A, B, C, X(10431), X(26003)}}, {{A, B, C, X(13567), X(26668)}}, {{A, B, C, X(14377), X(56050)}}, {{A, B, C, X(14997), X(32863)}}, {{A, B, C, X(15314), X(39695)}}, {{A, B, C, X(15998), X(56043)}}, {{A, B, C, X(16989), X(31089)}}, {{A, B, C, X(17349), X(17778)}}, {{A, B, C, X(17501), X(39963)}}, {{A, B, C, X(18139), X(37650)}}, {{A, B, C, X(18141), X(37680)}}, {{A, B, C, X(18928), X(37659)}}, {{A, B, C, X(19742), X(31034)}}, {{A, B, C, X(20028), X(30479)}}, {{A, B, C, X(21739), X(26745)}}, {{A, B, C, X(21853), X(36743)}}, {{A, B, C, X(30701), X(39700)}}, {{A, B, C, X(34234), X(54451)}}, {{A, B, C, X(34529), X(55110)}}, {{A, B, C, X(34546), X(37222)}}, {{A, B, C, X(37456), X(52288)}}, {{A, B, C, X(37656), X(37685)}}, {{A, B, C, X(39721), X(55035)}}, {{A, B, C, X(39957), X(43726)}}, {{A, B, C, X(39980), X(43731)}}, {{A, B, C, X(40435), X(44733)}}, {{A, B, C, X(41506), X(56219)}}, {{A, B, C, X(42304), X(56947)}}, {{A, B, C, X(43758), X(50442)}}, {{A, B, C, X(48357), X(52063)}}, {{A, B, C, X(56157), X(56213)}}
X(60155) = barycentric product X(i)*X(j) for these (i, j): {4, 57878}, {264, 57706}
X(60155) = barycentric quotient X(i)/X(j) for these (i, j): {4, 475}, {6, 36743}, {25, 44105}, {321, 42715}, {57706, 3}, {57878, 69}
X(60155) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 7382, 60156}

X(60156) = X(4)X(81)∩X(10)X(46)

Barycentrics    ((a-b)*(a+b)^2+(a^2+2*a*b-b^2)*c+(a+b)*c^2+c^3)*(a^3+a^2*(b+c)+(b-c)*(b+c)^2+a*(b^2+2*b*c-c^2)) : :

X(60156) lies on these lines: {2, 1444}, {3, 60154}, {4, 81}, {5, 60164}, {6, 7382}, {7, 37181}, {10, 46}, {20, 60158}, {30, 54758}, {57, 60249}, {69, 321}, {77, 226}, {92, 8048}, {98, 26118}, {222, 8736}, {229, 7498}, {286, 2052}, {381, 54757}, {388, 28606}, {394, 1901}, {459, 26540}, {464, 60188}, {527, 60267}, {540, 60079}, {940, 7381}, {969, 21279}, {1029, 14996}, {1150, 60206}, {1370, 60152}, {1446, 7056}, {1751, 24597}, {1790, 5747}, {1814, 5800}, {1836, 5820}, {1867, 57282}, {2475, 14552}, {2478, 43531}, {2995, 26871}, {3090, 60173}, {3091, 60157}, {3424, 37456}, {3434, 5847}, {3543, 54688}, {3545, 54727}, {3830, 54789}, {3839, 54726}, {3936, 60254}, {3945, 60170}, {4052, 31164}, {4648, 57722}, {4911, 13577}, {5046, 60077}, {5278, 32022}, {5307, 19785}, {5397, 6827}, {5712, 60071}, {5739, 34258}, {5745, 60243}, {6514, 27395}, {6539, 20078}, {6817, 56161}, {6826, 60112}, {6833, 60159}, {6834, 60162}, {6835, 57719}, {6836, 54972}, {6847, 60166}, {6848, 60174}, {6849, 57720}, {6851, 57710}, {6949, 60163}, {6952, 60160}, {6997, 60153}, {7386, 60165}, {7490, 60246}, {8808, 56972}, {10431, 56144}, {12115, 54933}, {14555, 60097}, {15309, 60074}, {15682, 54947}, {17185, 37155}, {17300, 60257}, {17778, 60261}, {18134, 60242}, {18141, 40013}, {18840, 33172}, {20171, 43675}, {21582, 26163}, {24553, 56216}, {24624, 37642}, {25080, 60116}, {26052, 60108}, {31015, 40443}, {31266, 56226}, {32911, 60107}, {34284, 60197}, {37191, 60086}, {37193, 40718}, {37276, 38253}, {37462, 52782}, {37633, 60076}, {37652, 60149}, {37653, 56210}, {37666, 60168}, {37674, 60169}, {37683, 54119}, {37685, 55027}, {43363, 59083}, {52392, 60091}, {53421, 54756}, {55868, 60203}

X(60156) = isogonal conjugate of X(36744)
X(60156) = isotomic conjugate of X(5739)
X(60156) = trilinear pole of line {905, 21186}
X(60156) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 36744}, {6, 12514}, {31, 5739}, {42, 27174}, {48, 406}, {55, 45126}, {63, 44086}, {219, 1452}, {2206, 42707}
X(60156) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 5739}, {3, 36744}, {9, 12514}, {223, 45126}, {1249, 406}, {3162, 44086}, {40592, 27174}, {40603, 42707}
X(60156) = X(i)-cross conjugate of X(j) for these {i, j}: {940, 2}, {1867, 2995}, {7381, 60155}, {26933, 693}, {57282, 7}, {57667, 57832}
X(60156) = pole of line {940, 7381} with respect to the Kiepert hyperbola
X(60156) = pole of line {5739, 27174} with respect to the Wallace hyperbola
X(60156) = pole of line {3338, 19785} with respect to the dual conic of Yff parabola
X(60156) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2994)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(36742)}}, {{A, B, C, X(6), X(36743)}}, {{A, B, C, X(7), X(63)}}, {{A, B, C, X(8), X(1255)}}, {{A, B, C, X(21), X(37181)}}, {{A, B, C, X(27), X(85)}}, {{A, B, C, X(29), X(34404)}}, {{A, B, C, X(46), X(57)}}, {{A, B, C, X(65), X(967)}}, {{A, B, C, X(66), X(39957)}}, {{A, B, C, X(68), X(1214)}}, {{A, B, C, X(75), X(19822)}}, {{A, B, C, X(80), X(25430)}}, {{A, B, C, X(88), X(5556)}}, {{A, B, C, X(89), X(32859)}}, {{A, B, C, X(92), X(837)}}, {{A, B, C, X(104), X(56041)}}, {{A, B, C, X(273), X(57911)}}, {{A, B, C, X(278), X(1478)}}, {{A, B, C, X(279), X(4292)}}, {{A, B, C, X(297), X(26118)}}, {{A, B, C, X(312), X(30513)}}, {{A, B, C, X(333), X(43740)}}, {{A, B, C, X(335), X(33163)}}, {{A, B, C, X(345), X(19607)}}, {{A, B, C, X(388), X(5307)}}, {{A, B, C, X(394), X(43724)}}, {{A, B, C, X(406), X(7381)}}, {{A, B, C, X(443), X(6994)}}, {{A, B, C, X(445), X(6851)}}, {{A, B, C, X(469), X(2478)}}, {{A, B, C, X(475), X(7382)}}, {{A, B, C, X(513), X(2221)}}, {{A, B, C, X(514), X(56050)}}, {{A, B, C, X(527), X(4778)}}, {{A, B, C, X(553), X(20078)}}, {{A, B, C, X(758), X(15309)}}, {{A, B, C, X(940), X(1867)}}, {{A, B, C, X(1000), X(27789)}}, {{A, B, C, X(1150), X(5712)}}, {{A, B, C, X(1171), X(51223)}}, {{A, B, C, X(1246), X(37128)}}, {{A, B, C, X(1389), X(56352)}}, {{A, B, C, X(1433), X(6512)}}, {{A, B, C, X(1824), X(8770)}}, {{A, B, C, X(2006), X(10827)}}, {{A, B, C, X(2165), X(7363)}}, {{A, B, C, X(2475), X(7490)}}, {{A, B, C, X(2895), X(14996)}}, {{A, B, C, X(2982), X(55985)}}, {{A, B, C, X(3146), X(37276)}}, {{A, B, C, X(3296), X(21739)}}, {{A, B, C, X(3577), X(56354)}}, {{A, B, C, X(3618), X(33172)}}, {{A, B, C, X(3936), X(37642)}}, {{A, B, C, X(3945), X(14552)}}, {{A, B, C, X(3980), X(6650)}}, {{A, B, C, X(4648), X(5278)}}, {{A, B, C, X(4654), X(55868)}}, {{A, B, C, X(5226), X(31266)}}, {{A, B, C, X(5361), X(37635)}}, {{A, B, C, X(5435), X(31164)}}, {{A, B, C, X(5553), X(42467)}}, {{A, B, C, X(5555), X(34234)}}, {{A, B, C, X(5557), X(39948)}}, {{A, B, C, X(5561), X(8056)}}, {{A, B, C, X(5800), X(40704)}}, {{A, B, C, X(5847), X(28846)}}, {{A, B, C, X(6601), X(30711)}}, {{A, B, C, X(6819), X(6848)}}, {{A, B, C, X(6820), X(6847)}}, {{A, B, C, X(6833), X(37192)}}, {{A, B, C, X(6835), X(37279)}}, {{A, B, C, X(6849), X(57531)}}, {{A, B, C, X(7108), X(34277)}}, {{A, B, C, X(7317), X(56039)}}, {{A, B, C, X(7319), X(40434)}}, {{A, B, C, X(7320), X(56037)}}, {{A, B, C, X(7357), X(39734)}}, {{A, B, C, X(8044), X(57818)}}, {{A, B, C, X(8049), X(8817)}}, {{A, B, C, X(8545), X(9776)}}, {{A, B, C, X(9311), X(56947)}}, {{A, B, C, X(10405), X(12527)}}, {{A, B, C, X(10431), X(37448)}}, {{A, B, C, X(11341), X(26052)}}, {{A, B, C, X(11604), X(43757)}}, {{A, B, C, X(14555), X(37633)}}, {{A, B, C, X(14621), X(26034)}}, {{A, B, C, X(15320), X(39981)}}, {{A, B, C, X(17097), X(55987)}}, {{A, B, C, X(17098), X(55995)}}, {{A, B, C, X(17156), X(17316)}}, {{A, B, C, X(17300), X(37652)}}, {{A, B, C, X(17379), X(37653)}}, {{A, B, C, X(17776), X(20171)}}, {{A, B, C, X(17778), X(37683)}}, {{A, B, C, X(18032), X(56065)}}, {{A, B, C, X(18134), X(24597)}}, {{A, B, C, X(18141), X(32911)}}, {{A, B, C, X(18359), X(56218)}}, {{A, B, C, X(18651), X(41791)}}, {{A, B, C, X(19785), X(19799)}}, {{A, B, C, X(26540), X(37669)}}, {{A, B, C, X(26750), X(55965)}}, {{A, B, C, X(27475), X(40435)}}, {{A, B, C, X(28606), X(30479)}}, {{A, B, C, X(30701), X(40394)}}, {{A, B, C, X(31034), X(37639)}}, {{A, B, C, X(31909), X(37193)}}, {{A, B, C, X(32863), X(37685)}}, {{A, B, C, X(34401), X(55938)}}, {{A, B, C, X(34527), X(39703)}}, {{A, B, C, X(34529), X(37222)}}, {{A, B, C, X(34800), X(45127)}}, {{A, B, C, X(37235), X(37419)}}, {{A, B, C, X(37456), X(52283)}}, {{A, B, C, X(39694), X(54120)}}, {{A, B, C, X(39700), X(55942)}}, {{A, B, C, X(39728), X(40154)}}, {{A, B, C, X(39732), X(57785)}}, {{A, B, C, X(39979), X(43726)}}, {{A, B, C, X(39980), X(43732)}}, {{A, B, C, X(42030), X(43745)}}, {{A, B, C, X(42304), X(43762)}}, {{A, B, C, X(43758), X(56054)}}, {{A, B, C, X(43759), X(56062)}}, {{A, B, C, X(51512), X(55986)}}
X(60156) = barycentric product X(i)*X(j) for these (i, j): {4, 57832}, {264, 57667}, {15413, 59083}, {46010, 76}, {56225, 85}, {59130, 850}
X(60156) = barycentric quotient X(i)/X(j) for these (i, j): {1, 12514}, {2, 5739}, {4, 406}, {6, 36744}, {25, 44086}, {34, 1452}, {57, 45126}, {81, 27174}, {321, 42707}, {26933, 17421}, {46010, 6}, {56225, 9}, {57667, 3}, {57832, 69}, {59083, 1783}, {59130, 110}
X(60156) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 7382, 60155}

X(60157) = X(2)X(36746)∩X(4)X(5120)

Barycentrics    (a^5-2*a^3*(b-c)^2+a^4*(b+c)+(b-c)^2*(b+c)^3+a*(b-c)*(b+c)*(b^2-4*b*c-c^2)-2*a^2*(b+c)*(b^2+c^2))*(a^5-2*a^3*(b-c)^2+a^4*(b+c)+(b-c)^2*(b+c)^3+a*(b-c)*(b+c)*(b^2+4*b*c-c^2)-2*a^2*(b+c)*(b^2+c^2)) : :

X(60157) lies on the Kiepert hyperbola and on these lines: {2, 36746}, {3, 60107}, {4, 5120}, {5, 60076}, {6, 60158}, {10, 53994}, {20, 60155}, {30, 54759}, {226, 3086}, {275, 4194}, {381, 54760}, {406, 56346}, {451, 60137}, {459, 475}, {1029, 3832}, {1751, 6908}, {2051, 6847}, {2052, 4200}, {2478, 60114}, {3091, 60156}, {3146, 55027}, {3541, 60246}, {3543, 54766}, {3545, 54788}, {3597, 14853}, {3839, 54756}, {4052, 45700}, {5046, 6504}, {5056, 60169}, {5068, 60258}, {5084, 60237}, {5721, 43533}, {6825, 55962}, {6833, 45098}, {6837, 60071}, {6838, 24624}, {6848, 13478}, {6886, 57722}, {6890, 60087}, {6926, 14554}, {6964, 60085}, {7380, 60165}, {7390, 60153}, {7407, 60152}, {10200, 56226}, {34621, 54755}, {37108, 60092}, {37112, 57721}, {37407, 60075}, {37421, 60168}, {37427, 60094}, {37434, 45100}, {38253, 52252}, {50687, 54794}

X(60157) = isogonal conjugate of X(36745)
X(60157) = trilinear pole of line {14300, 523}
X(60157) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1440)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(4200)}}, {{A, B, C, X(5), X(4194)}}, {{A, B, C, X(6), X(36746)}}, {{A, B, C, X(7), X(57724)}}, {{A, B, C, X(8), X(1067)}}, {{A, B, C, X(9), X(10396)}}, {{A, B, C, X(20), X(475)}}, {{A, B, C, X(29), X(6846)}}, {{A, B, C, X(37), X(52518)}}, {{A, B, C, X(40), X(8056)}}, {{A, B, C, X(54), X(39975)}}, {{A, B, C, X(64), X(39798)}}, {{A, B, C, X(65), X(46952)}}, {{A, B, C, X(75), X(10309)}}, {{A, B, C, X(80), X(8227)}}, {{A, B, C, X(84), X(2297)}}, {{A, B, C, X(90), X(280)}}, {{A, B, C, X(104), X(1219)}}, {{A, B, C, X(145), X(45700)}}, {{A, B, C, X(277), X(3345)}}, {{A, B, C, X(278), X(937)}}, {{A, B, C, X(281), X(38271)}}, {{A, B, C, X(318), X(5811)}}, {{A, B, C, X(346), X(7040)}}, {{A, B, C, X(377), X(3088)}}, {{A, B, C, X(393), X(57666)}}, {{A, B, C, X(406), X(3091)}}, {{A, B, C, X(451), X(3832)}}, {{A, B, C, X(596), X(10305)}}, {{A, B, C, X(860), X(6838)}}, {{A, B, C, X(941), X(3527)}}, {{A, B, C, X(989), X(57726)}}, {{A, B, C, X(1065), X(10429)}}, {{A, B, C, X(1093), X(57830)}}, {{A, B, C, X(1220), X(3427)}}, {{A, B, C, X(1224), X(3062)}}, {{A, B, C, X(2298), X(55105)}}, {{A, B, C, X(2475), X(3541)}}, {{A, B, C, X(2478), X(3089)}}, {{A, B, C, X(3146), X(52252)}}, {{A, B, C, X(3346), X(39748)}}, {{A, B, C, X(3532), X(39960)}}, {{A, B, C, X(3542), X(5046)}}, {{A, B, C, X(3617), X(10200)}}, {{A, B, C, X(4373), X(5553)}}, {{A, B, C, X(4853), X(14986)}}, {{A, B, C, X(5125), X(6908)}}, {{A, B, C, X(5136), X(6837)}}, {{A, B, C, X(5936), X(57723)}}, {{A, B, C, X(6832), X(7518)}}, {{A, B, C, X(6847), X(11109)}}, {{A, B, C, X(6848), X(17555)}}, {{A, B, C, X(6953), X(11105)}}, {{A, B, C, X(7110), X(33576)}}, {{A, B, C, X(8801), X(20029)}}, {{A, B, C, X(10570), X(55964)}}, {{A, B, C, X(14528), X(39982)}}, {{A, B, C, X(15077), X(57878)}}, {{A, B, C, X(15740), X(57832)}}, {{A, B, C, X(31371), X(57865)}}, {{A, B, C, X(37108), X(57534)}}, {{A, B, C, X(39943), X(40396)}}, {{A, B, C, X(40450), X(43745)}}, {{A, B, C, X(45011), X(57818)}}, {{A, B, C, X(51223), X(52224)}}, {{A, B, C, X(51316), X(51500)}}, {{A, B, C, X(52223), X(57705)}}

X(60158) = X(1)X(8808)∩X(40)X(226)

Barycentrics    (a^5+a^4*(b+c)-2*a^3*(b+c)^2+(b-c)^2*(b+c)^3+a*(b-c)*(b+c)*(b^2-4*b*c-c^2)-2*a^2*(b+c)*(b^2+c^2))*(a^5+a^4*(b+c)-2*a^3*(b+c)^2+(b-c)^2*(b+c)^3+a*(b-c)*(b+c)*(b^2+4*b*c-c^2)-2*a^2*(b+c)*(b^2+c^2)) : :

X(60158) lies on the Kiepert hyperbola and on these lines: {1, 8808}, {2, 5706}, {3, 60076}, {4, 4254}, {5, 60107}, {6, 60157}, {10, 2324}, {20, 60156}, {30, 54760}, {40, 226}, {275, 4200}, {321, 7080}, {347, 1446}, {376, 54788}, {377, 60114}, {381, 54759}, {387, 57719}, {406, 459}, {443, 60237}, {451, 38253}, {475, 56346}, {1029, 3146}, {1751, 6846}, {2051, 6848}, {2052, 4194}, {2475, 6504}, {3091, 60155}, {3332, 54972}, {3522, 60258}, {3523, 60169}, {3542, 60246}, {3543, 54756}, {3832, 55027}, {3839, 54766}, {3931, 7952}, {4052, 45701}, {5711, 15501}, {5712, 6247}, {5713, 56216}, {6776, 57745}, {6824, 55962}, {6834, 45098}, {6837, 24624}, {6838, 60071}, {6847, 13478}, {6886, 57721}, {6926, 60085}, {6953, 60087}, {6964, 14554}, {6998, 60165}, {7390, 60152}, {7407, 60153}, {10198, 56226}, {10528, 43675}, {13576, 36695}, {17758, 37407}, {18391, 60249}, {19855, 60243}, {23555, 43683}, {27522, 43533}, {34621, 54754}, {36672, 56161}, {37108, 57826}, {37112, 57722}, {37421, 60170}, {37427, 60083}, {37434, 60167}, {40942, 47850}, {52252, 60137}

X(60158) = isogonal conjugate of X(36746)
X(60158) = trilinear pole of line {14298, 523}
X(60158) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 36746}, {255, 56864}
X(60158) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 36746}, {6523, 56864}
X(60158) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(40)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(941)}}, {{A, B, C, X(5), X(4200)}}, {{A, B, C, X(6), X(36745)}}, {{A, B, C, X(7), X(158)}}, {{A, B, C, X(8), X(1065)}}, {{A, B, C, X(12), X(6526)}}, {{A, B, C, X(20), X(406)}}, {{A, B, C, X(29), X(6908)}}, {{A, B, C, X(37), X(64)}}, {{A, B, C, X(55), X(37528)}}, {{A, B, C, X(65), X(393)}}, {{A, B, C, X(66), X(51870)}}, {{A, B, C, X(79), X(1440)}}, {{A, B, C, X(86), X(10309)}}, {{A, B, C, X(145), X(45701)}}, {{A, B, C, X(200), X(7160)}}, {{A, B, C, X(253), X(41013)}}, {{A, B, C, X(318), X(5758)}}, {{A, B, C, X(346), X(943)}}, {{A, B, C, X(377), X(3089)}}, {{A, B, C, X(451), X(3146)}}, {{A, B, C, X(461), X(37108)}}, {{A, B, C, X(475), X(3091)}}, {{A, B, C, X(517), X(5711)}}, {{A, B, C, X(646), X(30237)}}, {{A, B, C, X(860), X(6837)}}, {{A, B, C, X(972), X(52500)}}, {{A, B, C, X(989), X(57727)}}, {{A, B, C, X(1000), X(56146)}}, {{A, B, C, X(1012), X(12709)}}, {{A, B, C, X(1093), X(1441)}}, {{A, B, C, X(1173), X(39975)}}, {{A, B, C, X(1219), X(1389)}}, {{A, B, C, X(2475), X(3542)}}, {{A, B, C, X(2478), X(3088)}}, {{A, B, C, X(3176), X(40942)}}, {{A, B, C, X(3427), X(31359)}}, {{A, B, C, X(3527), X(39956)}}, {{A, B, C, X(3541), X(5046)}}, {{A, B, C, X(3577), X(59760)}}, {{A, B, C, X(3615), X(5555)}}, {{A, B, C, X(3617), X(10198)}}, {{A, B, C, X(3701), X(57818)}}, {{A, B, C, X(3811), X(10528)}}, {{A, B, C, X(3832), X(52252)}}, {{A, B, C, X(3945), X(27522)}}, {{A, B, C, X(5125), X(6846)}}, {{A, B, C, X(5136), X(6838)}}, {{A, B, C, X(5552), X(18391)}}, {{A, B, C, X(5553), X(30712)}}, {{A, B, C, X(5556), X(7318)}}, {{A, B, C, X(5657), X(39585)}}, {{A, B, C, X(5665), X(7110)}}, {{A, B, C, X(5936), X(57724)}}, {{A, B, C, X(6355), X(52388)}}, {{A, B, C, X(6553), X(14497)}}, {{A, B, C, X(6738), X(27525)}}, {{A, B, C, X(6847), X(17555)}}, {{A, B, C, X(6848), X(11109)}}, {{A, B, C, X(6889), X(7518)}}, {{A, B, C, X(6890), X(11105)}}, {{A, B, C, X(7105), X(51496)}}, {{A, B, C, X(7412), X(27505)}}, {{A, B, C, X(7498), X(37421)}}, {{A, B, C, X(8232), X(18634)}}, {{A, B, C, X(9780), X(19855)}}, {{A, B, C, X(10365), X(47372)}}, {{A, B, C, X(14004), X(37407)}}, {{A, B, C, X(14528), X(39974)}}, {{A, B, C, X(15077), X(57832)}}, {{A, B, C, X(15149), X(36695)}}, {{A, B, C, X(15740), X(57878)}}, {{A, B, C, X(15749), X(57865)}}, {{A, B, C, X(15909), X(39708)}}, {{A, B, C, X(20029), X(34285)}}, {{A, B, C, X(22334), X(39983)}}, {{A, B, C, X(27530), X(37028)}}, {{A, B, C, X(31503), X(59496)}}, {{A, B, C, X(37054), X(37410)}}, {{A, B, C, X(38307), X(57884)}}, {{A, B, C, X(39798), X(52518)}}, {{A, B, C, X(40396), X(56225)}}, {{A, B, C, X(44059), X(56188)}}, {{A, B, C, X(44861), X(56220)}}, {{A, B, C, X(46952), X(57666)}}, {{A, B, C, X(51223), X(52223)}}, {{A, B, C, X(52224), X(57705)}}, {{A, B, C, X(55091), X(55964)}}
X(60158) = barycentric quotient X(i)/X(j) for these (i, j): {6, 36746}, {393, 56864}

X(60159) = X(2)X(155)∩X(4)X(1609)

Barycentrics    (a^8+(b^2-c^2)^4-4*a^6*(b^2+c^2)+6*a^4*(b^4+c^4)-4*a^2*(b^6-2*b^4*c^2+c^6))*(a^8+(b^2-c^2)^4-4*a^6*(b^2+c^2)+6*a^4*(b^4+c^4)-4*a^2*(b^6-2*b^2*c^4+c^6)) : :

X(60159) lies on the Kiepert hyperbola and on these lines: {2, 155}, {3, 6504}, {4, 1609}, {6, 60162}, {20, 13579}, {30, 54761}, {76, 7383}, {96, 6776}, {98, 58964}, {226, 10044}, {275, 3541}, {376, 54785}, {381, 54764}, {459, 7505}, {499, 60249}, {631, 60114}, {1029, 6847}, {1131, 6807}, {1132, 6808}, {1199, 60163}, {1513, 40178}, {2052, 3542}, {2165, 52582}, {2986, 3546}, {2996, 7400}, {3088, 60161}, {3089, 8796}, {3146, 13585}, {3424, 16659}, {3522, 13582}, {3523, 60255}, {3525, 60237}, {3543, 54762}, {3545, 54797}, {3547, 5392}, {3549, 60256}, {3832, 11538}, {3839, 54765}, {5068, 60191}, {6143, 60137}, {6833, 60156}, {6834, 60155}, {6848, 55027}, {6949, 60107}, {6952, 60076}, {7404, 40393}, {7558, 60221}, {11456, 60166}, {14940, 38253}, {15032, 60160}, {34621, 41895}, {37119, 56346}, {37943, 54710}, {38259, 52404}, {41362, 54943}, {50687, 54601}

X(60159) = isogonal conjugate of X(36747)
X(60159) = trilinear pole of line {14346, 523}
X(60159) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 36747}, {48, 37192}
X(60159) = X(i)-vertex conjugate of X(j) for these {i, j}: {3425, 40178}
X(60159) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 36747}, {1249, 37192}
X(60159) = X(i)-cross conjugate of X(j) for these {i, j}: {1181, 4}
X(60159) = pole of line {1181, 60159} with respect to the Kiepert hyperbola
X(60159) = pole of line {36747, 52014} with respect to the Stammler hyperbola
X(60159) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(17700)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(155)}}, {{A, B, C, X(5), X(66)}}, {{A, B, C, X(6), X(22270)}}, {{A, B, C, X(8), X(10320)}}, {{A, B, C, X(20), X(7505)}}, {{A, B, C, X(24), X(1176)}}, {{A, B, C, X(25), X(7383)}}, {{A, B, C, X(54), X(393)}}, {{A, B, C, X(64), X(2963)}}, {{A, B, C, X(68), X(9722)}}, {{A, B, C, X(69), X(847)}}, {{A, B, C, X(70), X(18855)}}, {{A, B, C, X(74), X(1217)}}, {{A, B, C, X(77), X(1068)}}, {{A, B, C, X(78), X(7040)}}, {{A, B, C, X(91), X(499)}}, {{A, B, C, X(93), X(253)}}, {{A, B, C, X(95), X(1093)}}, {{A, B, C, X(140), X(44658)}}, {{A, B, C, X(252), X(6526)}}, {{A, B, C, X(403), X(3546)}}, {{A, B, C, X(406), X(6833)}}, {{A, B, C, X(451), X(6847)}}, {{A, B, C, X(475), X(6834)}}, {{A, B, C, X(498), X(10044)}}, {{A, B, C, X(523), X(42021)}}, {{A, B, C, X(631), X(3089)}}, {{A, B, C, X(1173), X(46952)}}, {{A, B, C, X(1181), X(52014)}}, {{A, B, C, X(1300), X(15740)}}, {{A, B, C, X(1594), X(7404)}}, {{A, B, C, X(1989), X(14528)}}, {{A, B, C, X(2383), X(56072)}}, {{A, B, C, X(3088), X(3090)}}, {{A, B, C, X(3091), X(37119)}}, {{A, B, C, X(3146), X(14940)}}, {{A, B, C, X(3346), X(3459)}}, {{A, B, C, X(3426), X(14938)}}, {{A, B, C, X(3431), X(51316)}}, {{A, B, C, X(3432), X(19151)}}, {{A, B, C, X(3522), X(37943)}}, {{A, B, C, X(3527), X(15805)}}, {{A, B, C, X(3532), X(52154)}}, {{A, B, C, X(3549), X(18533)}}, {{A, B, C, X(3832), X(6143)}}, {{A, B, C, X(4194), X(6952)}}, {{A, B, C, X(4200), X(6949)}}, {{A, B, C, X(4846), X(9820)}}, {{A, B, C, X(5408), X(13429)}}, {{A, B, C, X(5409), X(13440)}}, {{A, B, C, X(5486), X(45195)}}, {{A, B, C, X(6353), X(7400)}}, {{A, B, C, X(6848), X(52252)}}, {{A, B, C, X(6908), X(7537)}}, {{A, B, C, X(7487), X(7558)}}, {{A, B, C, X(7552), X(37460)}}, {{A, B, C, X(8797), X(11487)}}, {{A, B, C, X(8801), X(13597)}}, {{A, B, C, X(9307), X(36612)}}, {{A, B, C, X(10002), X(16659)}}, {{A, B, C, X(10419), X(56068)}}, {{A, B, C, X(13139), X(43891)}}, {{A, B, C, X(13381), X(43695)}}, {{A, B, C, X(13472), X(52223)}}, {{A, B, C, X(14457), X(43917)}}, {{A, B, C, X(14542), X(34449)}}, {{A, B, C, X(15022), X(35482)}}, {{A, B, C, X(15412), X(56339)}}, {{A, B, C, X(16774), X(18854)}}, {{A, B, C, X(16835), X(46217)}}, {{A, B, C, X(17703), X(45088)}}, {{A, B, C, X(18532), X(45301)}}, {{A, B, C, X(21451), X(35473)}}, {{A, B, C, X(32132), X(34801)}}, {{A, B, C, X(34208), X(46199)}}, {{A, B, C, X(34223), X(52518)}}, {{A, B, C, X(34225), X(34436)}}, {{A, B, C, X(34288), X(43908)}}, {{A, B, C, X(34386), X(42298)}}, {{A, B, C, X(34567), X(52187)}}, {{A, B, C, X(34621), X(52290)}}, {{A, B, C, X(35471), X(58805)}}, {{A, B, C, X(35603), X(57484)}}, {{A, B, C, X(36948), X(45011)}}, {{A, B, C, X(38282), X(52404)}}, {{A, B, C, X(43689), X(58724)}}, {{A, B, C, X(52188), X(57730)}}, {{A, B, C, X(57723), X(57883)}}, {{A, B, C, X(57724), X(57884)}}
X(60159) = barycentric product X(i)*X(j) for these (i, j): {58964, 850}
X(60159) = barycentric quotient X(i)/X(j) for these (i, j): {4, 37192}, {6, 36747}, {8573, 52014}, {58964, 110}

X(60160) = X(2)X(1199)∩X(4)X(8553)

Barycentrics    ((a^2-b^2)^4+2*(-2*a^6+a^4*b^2+a^2*b^4-2*b^6)*c^2+6*(a^4+a^2*b^2+b^4)*c^4-4*(a^2+b^2)*c^6+c^8)*(a^8+(b^2-c^2)^4-4*a^6*(b^2+c^2)+2*a^4*(3*b^4+b^2*c^2+3*c^4)+a^2*(-4*b^6+6*b^4*c^2+2*b^2*c^4-4*c^6)) : :

X(60160) lies on the Kiepert hyperbola and on these lines: {2, 1199}, {3, 13579}, {4, 8553}, {6, 60163}, {20, 13585}, {30, 54762}, {94, 3549}, {140, 60255}, {275, 37119}, {376, 54761}, {381, 54765}, {459, 14940}, {631, 6504}, {1029, 6833}, {1181, 54498}, {2052, 7505}, {2996, 7383}, {3091, 11538}, {3523, 13582}, {3524, 54785}, {3525, 60114}, {3541, 60161}, {3542, 8796}, {3543, 54601}, {3545, 54764}, {5056, 60191}, {5071, 54797}, {5392, 7558}, {6143, 56346}, {6807, 43560}, {6808, 43561}, {6834, 55027}, {6949, 60155}, {6952, 60156}, {7400, 38259}, {7552, 54778}, {15032, 60159}, {18316, 18945}, {34621, 60113}, {37943, 54867}, {40178, 58883}, {44441, 54769}

X(60160) = isogonal conjugate of X(36749)
X(60160) = X(i)-cross conjugate of X(j) for these {i, j}: {7592, 4}
X(60160) = pole of line {7592, 60160} with respect to the Kiepert hyperbola
X(60160) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(2963)}}, {{A, B, C, X(5), X(70)}}, {{A, B, C, X(6), X(22268)}}, {{A, B, C, X(20), X(14940)}}, {{A, B, C, X(24), X(7558)}}, {{A, B, C, X(54), X(2165)}}, {{A, B, C, X(64), X(14938)}}, {{A, B, C, X(66), X(16837)}}, {{A, B, C, X(68), X(252)}}, {{A, B, C, X(69), X(93)}}, {{A, B, C, X(95), X(847)}}, {{A, B, C, X(140), X(45195)}}, {{A, B, C, X(186), X(3549)}}, {{A, B, C, X(254), X(2383)}}, {{A, B, C, X(393), X(1199)}}, {{A, B, C, X(406), X(6952)}}, {{A, B, C, X(451), X(6833)}}, {{A, B, C, X(475), X(6949)}}, {{A, B, C, X(631), X(3542)}}, {{A, B, C, X(1141), X(14542)}}, {{A, B, C, X(1217), X(11270)}}, {{A, B, C, X(1487), X(42021)}}, {{A, B, C, X(1989), X(43908)}}, {{A, B, C, X(3088), X(5067)}}, {{A, B, C, X(3089), X(3525)}}, {{A, B, C, X(3090), X(3541)}}, {{A, B, C, X(3091), X(6143)}}, {{A, B, C, X(3147), X(3547)}}, {{A, B, C, X(3346), X(20421)}}, {{A, B, C, X(3519), X(30542)}}, {{A, B, C, X(3523), X(37943)}}, {{A, B, C, X(3531), X(34223)}}, {{A, B, C, X(3548), X(16868)}}, {{A, B, C, X(6344), X(18951)}}, {{A, B, C, X(6353), X(7383)}}, {{A, B, C, X(6526), X(43891)}}, {{A, B, C, X(6639), X(35471)}}, {{A, B, C, X(6662), X(44157)}}, {{A, B, C, X(6834), X(52252)}}, {{A, B, C, X(6889), X(7537)}}, {{A, B, C, X(7400), X(38282)}}, {{A, B, C, X(7486), X(35482)}}, {{A, B, C, X(7552), X(35486)}}, {{A, B, C, X(7763), X(42354)}}, {{A, B, C, X(13139), X(45736)}}, {{A, B, C, X(13481), X(34483)}}, {{A, B, C, X(14528), X(52154)}}, {{A, B, C, X(14786), X(52295)}}, {{A, B, C, X(15424), X(45011)}}, {{A, B, C, X(16835), X(46223)}}, {{A, B, C, X(17040), X(36612)}}, {{A, B, C, X(18855), X(33565)}}, {{A, B, C, X(20574), X(51336)}}, {{A, B, C, X(21844), X(58805)}}, {{A, B, C, X(34288), X(34567)}}, {{A, B, C, X(46412), X(57713)}}, {{A, B, C, X(51256), X(58727)}}

X(60161) = X(2)X(6748)∩X(4)X(11402)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(3*(a^2-b^2)^2-4*(a^2+b^2)*c^2+c^4)*(3*a^4+b^4-4*b^2*c^2+3*c^4-2*a^2*(2*b^2+3*c^2)) : :

X(60161) lies on the Kiepert hyperbola and on these lines: {2, 6748}, {4, 11402}, {6, 8796}, {20, 13599}, {25, 14494}, {27, 45098}, {30, 54763}, {76, 40684}, {83, 37174}, {96, 4994}, {98, 7378}, {193, 5392}, {262, 6995}, {264, 54636}, {297, 18841}, {381, 54660}, {393, 39284}, {406, 60173}, {427, 7612}, {428, 60127}, {458, 18840}, {468, 53098}, {470, 43446}, {471, 43447}, {472, 43542}, {473, 43543}, {485, 55569}, {486, 55573}, {1585, 3317}, {1586, 3316}, {1598, 11282}, {1993, 2996}, {2051, 6994}, {2052, 3087}, {3088, 60159}, {3089, 60162}, {3091, 40448}, {3146, 31363}, {3399, 6620}, {3424, 7409}, {3523, 60171}, {3535, 34091}, {3536, 34089}, {3541, 60160}, {3542, 60163}, {3543, 60121}, {3830, 54838}, {3839, 60122}, {3845, 54667}, {4194, 60164}, {4200, 60154}, {4232, 7608}, {5032, 54778}, {5064, 60150}, {5094, 60123}, {5485, 52281}, {6353, 10155}, {6819, 60237}, {7408, 14484}, {7487, 57718}, {7518, 57719}, {7607, 52284}, {7714, 54523}, {8889, 53103}, {9221, 18533}, {10110, 32319}, {10301, 60330}, {11433, 56270}, {11547, 60120}, {14004, 45097}, {14129, 53109}, {17907, 54798}, {18842, 52282}, {23292, 60193}, {32022, 54372}, {37119, 43666}, {37645, 43670}, {40065, 54867}, {43981, 54930}, {46924, 54927}, {52253, 60221}, {52280, 56346}, {52285, 54845}, {52288, 60183}, {52301, 53099}, {53857, 60144}

X(60161) = isogonal conjugate of X(36751)
X(60161) = trilinear pole of line {37935, 523}
X(60161) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 36751}, {48, 3090}, {63, 9777}
X(60161) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 36751}, {1249, 3090}, {3162, 9777}
X(60161) = X(i)-cross conjugate of X(j) for these {i, j}: {11427, 2}, {43908, 36948}
X(60161) = pole of line {11427, 60161} with respect to the Kiepert hyperbola
X(60161) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(11426)}}, {{A, B, C, X(6), X(97)}}, {{A, B, C, X(20), X(34287)}}, {{A, B, C, X(25), X(47735)}}, {{A, B, C, X(51), X(51336)}}, {{A, B, C, X(54), X(56338)}}, {{A, B, C, X(64), X(31626)}}, {{A, B, C, X(89), X(40397)}}, {{A, B, C, X(193), X(1993)}}, {{A, B, C, X(253), X(39286)}}, {{A, B, C, X(288), X(3431)}}, {{A, B, C, X(297), X(7378)}}, {{A, B, C, X(343), X(44836)}}, {{A, B, C, X(346), X(53817)}}, {{A, B, C, X(393), X(6748)}}, {{A, B, C, X(394), X(3527)}}, {{A, B, C, X(427), X(37174)}}, {{A, B, C, X(458), X(6995)}}, {{A, B, C, X(1039), X(56352)}}, {{A, B, C, X(1041), X(56041)}}, {{A, B, C, X(1073), X(3531)}}, {{A, B, C, X(1172), X(55989)}}, {{A, B, C, X(1173), X(56266)}}, {{A, B, C, X(1585), X(24243)}}, {{A, B, C, X(1586), X(24244)}}, {{A, B, C, X(3088), X(37192)}}, {{A, B, C, X(3091), X(52280)}}, {{A, B, C, X(3926), X(31804)}}, {{A, B, C, X(4196), X(54372)}}, {{A, B, C, X(4232), X(52281)}}, {{A, B, C, X(4994), X(11547)}}, {{A, B, C, X(6759), X(10110)}}, {{A, B, C, X(6994), X(11109)}}, {{A, B, C, X(7408), X(52288)}}, {{A, B, C, X(7409), X(52283)}}, {{A, B, C, X(7487), X(52253)}}, {{A, B, C, X(7518), X(37279)}}, {{A, B, C, X(8882), X(39109)}}, {{A, B, C, X(11427), X(38442)}}, {{A, B, C, X(11433), X(47392)}}, {{A, B, C, X(14919), X(52518)}}, {{A, B, C, X(15809), X(32974)}}, {{A, B, C, X(18890), X(46736)}}, {{A, B, C, X(22334), X(55982)}}, {{A, B, C, X(25417), X(40396)}}, {{A, B, C, X(27789), X(36121)}}, {{A, B, C, X(34285), X(42300)}}, {{A, B, C, X(36421), X(56200)}}, {{A, B, C, X(37669), X(52452)}}, {{A, B, C, X(39955), X(56364)}}, {{A, B, C, X(40402), X(52223)}}, {{A, B, C, X(43768), X(52661)}}, {{A, B, C, X(52282), X(52284)}}, {{A, B, C, X(56002), X(56362)}}, {{A, B, C, X(56339), X(57875)}}
X(60161) = barycentric product X(i)*X(j) for these (i, j): {264, 43908}, {36948, 4}
X(60161) = barycentric quotient X(i)/X(j) for these (i, j): {4, 3090}, {6, 36751}, {25, 9777}, {36948, 69}, {43908, 3}

X(60162) = X(2)X(36747)∩X(5)X(6504)

Barycentrics    ((a^2-b^2)^4-4*(a^6-2*a^4*b^2-2*a^2*b^4+b^6)*c^2+6*(a^4+b^4)*c^4-4*(a^2+b^2)*c^6+c^8)*(a^8+(b^2-c^2)^4-4*a^6*(b^2+c^2)+a^4*(6*b^4+8*b^2*c^2+6*c^4)-4*a^2*(b^6-2*b^2*c^4+c^6)) : :

X(60162) lies on the Kiepert hyperbola and on these lines: {2, 36747}, {5, 6504}, {6, 60159}, {30, 54764}, {83, 7383}, {96, 47731}, {226, 17437}, {275, 3542}, {376, 54797}, {381, 54761}, {459, 37119}, {1029, 6848}, {1131, 6808}, {1132, 6807}, {1199, 54498}, {2052, 3541}, {3088, 8796}, {3089, 60161}, {3090, 60114}, {3091, 13579}, {3146, 11538}, {3424, 34224}, {3522, 60191}, {3543, 54765}, {3545, 54785}, {3546, 34289}, {3547, 40393}, {3832, 13585}, {3839, 54762}, {5056, 60255}, {5067, 60237}, {5068, 13582}, {5392, 7404}, {5395, 7400}, {6143, 38253}, {6833, 60155}, {6834, 60156}, {6847, 55027}, {6949, 60076}, {6952, 60107}, {7505, 56346}, {7592, 60166}, {13860, 40178}, {14853, 57718}, {14940, 60137}, {18845, 52404}, {34621, 53101}

X(60162) = isogonal conjugate of X(36752)
X(60162) = X(i)-cross conjugate of X(j) for these {i, j}: {10982, 4}
X(60162) = pole of line {10982, 60162} with respect to the Kiepert hyperbola
X(60162) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(17437)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(3541)}}, {{A, B, C, X(5), X(3542)}}, {{A, B, C, X(6), X(254)}}, {{A, B, C, X(20), X(37119)}}, {{A, B, C, X(24), X(7404)}}, {{A, B, C, X(54), X(1217)}}, {{A, B, C, X(64), X(22270)}}, {{A, B, C, X(68), X(3613)}}, {{A, B, C, X(70), X(8801)}}, {{A, B, C, X(252), X(34285)}}, {{A, B, C, X(378), X(3546)}}, {{A, B, C, X(393), X(1173)}}, {{A, B, C, X(406), X(6834)}}, {{A, B, C, X(427), X(7383)}}, {{A, B, C, X(451), X(6848)}}, {{A, B, C, X(475), X(6833)}}, {{A, B, C, X(631), X(3088)}}, {{A, B, C, X(847), X(8797)}}, {{A, B, C, X(1093), X(40410)}}, {{A, B, C, X(1594), X(3547)}}, {{A, B, C, X(2165), X(3527)}}, {{A, B, C, X(2963), X(52518)}}, {{A, B, C, X(3089), X(3090)}}, {{A, B, C, X(3091), X(7505)}}, {{A, B, C, X(3146), X(6143)}}, {{A, B, C, X(3346), X(3431)}}, {{A, B, C, X(3426), X(22268)}}, {{A, B, C, X(3459), X(14491)}}, {{A, B, C, X(3532), X(46412)}}, {{A, B, C, X(3832), X(14940)}}, {{A, B, C, X(4194), X(6949)}}, {{A, B, C, X(4200), X(6952)}}, {{A, B, C, X(5068), X(37943)}}, {{A, B, C, X(5486), X(6662)}}, {{A, B, C, X(6145), X(45090)}}, {{A, B, C, X(6526), X(34110)}}, {{A, B, C, X(6846), X(7537)}}, {{A, B, C, X(6847), X(52252)}}, {{A, B, C, X(7400), X(8889)}}, {{A, B, C, X(10002), X(34224)}}, {{A, B, C, X(13418), X(35510)}}, {{A, B, C, X(13472), X(52224)}}, {{A, B, C, X(13481), X(43834)}}, {{A, B, C, X(14489), X(34428)}}, {{A, B, C, X(14528), X(30537)}}, {{A, B, C, X(14786), X(37122)}}, {{A, B, C, X(15318), X(45857)}}, {{A, B, C, X(15464), X(44157)}}, {{A, B, C, X(15717), X(35482)}}, {{A, B, C, X(16837), X(18855)}}, {{A, B, C, X(17040), X(18853)}}, {{A, B, C, X(18281), X(35485)}}, {{A, B, C, X(18349), X(45833)}}, {{A, B, C, X(22261), X(45108)}}, {{A, B, C, X(34449), X(43726)}}, {{A, B, C, X(34567), X(52188)}}, {{A, B, C, X(35512), X(52717)}}, {{A, B, C, X(41371), X(56298)}}, {{A, B, C, X(43908), X(59496)}}, {{A, B, C, X(52187), X(57730)}}, {{A, B, C, X(52299), X(52404)}}, {{A, B, C, X(57723), X(57884)}}, {{A, B, C, X(57724), X(57883)}}

X(60163) = X(2)X(16266)∩X(5)X(13579)

Barycentrics    (a^8+(b^2-c^2)^4-4*a^6*(b^2+c^2)+6*a^4*(b^4+b^2*c^2+c^4)+a^2*(-4*b^6+6*b^4*c^2+2*b^2*c^4-4*c^6))*(a^8+(b^2-c^2)^4-4*a^6*(b^2+c^2)+6*a^4*(b^4+b^2*c^2+c^4)+a^2*(-4*b^6+2*b^4*c^2+6*b^2*c^4-4*c^6)) : :

X(60163) lies on the Kiepert hyperbola and on these lines: {2, 16266}, {5, 13579}, {6, 60160}, {20, 11538}, {30, 54765}, {76, 45795}, {275, 7505}, {376, 54764}, {381, 54762}, {459, 6143}, {1029, 6834}, {1199, 60159}, {1498, 54942}, {1656, 60255}, {2052, 37119}, {3090, 6504}, {3091, 13585}, {3523, 60191}, {3524, 54797}, {3541, 8796}, {3542, 60161}, {3545, 54761}, {3549, 7578}, {3839, 54601}, {5056, 13582}, {5067, 60114}, {5071, 54785}, {5395, 7383}, {6807, 43561}, {6808, 43560}, {6833, 55027}, {6949, 60156}, {6952, 60155}, {7400, 18845}, {7552, 54792}, {7558, 40393}, {7592, 54498}, {11140, 14786}, {14787, 54782}, {14940, 56346}, {15032, 60166}, {34621, 54476}, {37943, 54531}

X(60163) = isogonal conjugate of X(36753)
X(60163) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(37119)}}, {{A, B, C, X(5), X(7505)}}, {{A, B, C, X(6), X(14938)}}, {{A, B, C, X(20), X(6143)}}, {{A, B, C, X(54), X(1485)}}, {{A, B, C, X(64), X(22268)}}, {{A, B, C, X(66), X(252)}}, {{A, B, C, X(68), X(16837)}}, {{A, B, C, X(70), X(3613)}}, {{A, B, C, X(74), X(22270)}}, {{A, B, C, X(93), X(8797)}}, {{A, B, C, X(140), X(44157)}}, {{A, B, C, X(253), X(13418)}}, {{A, B, C, X(254), X(13472)}}, {{A, B, C, X(393), X(3459)}}, {{A, B, C, X(406), X(6949)}}, {{A, B, C, X(451), X(6834)}}, {{A, B, C, X(475), X(6952)}}, {{A, B, C, X(631), X(3541)}}, {{A, B, C, X(847), X(40410)}}, {{A, B, C, X(1173), X(2165)}}, {{A, B, C, X(1176), X(32132)}}, {{A, B, C, X(1217), X(3431)}}, {{A, B, C, X(1594), X(7558)}}, {{A, B, C, X(2963), X(3527)}}, {{A, B, C, X(3088), X(3525)}}, {{A, B, C, X(3089), X(5067)}}, {{A, B, C, X(3090), X(3542)}}, {{A, B, C, X(3091), X(14940)}}, {{A, B, C, X(3147), X(7404)}}, {{A, B, C, X(3518), X(14786)}}, {{A, B, C, X(3519), X(18575)}}, {{A, B, C, X(3520), X(3548)}}, {{A, B, C, X(3549), X(7577)}}, {{A, B, C, X(5056), X(37943)}}, {{A, B, C, X(5486), X(57640)}}, {{A, B, C, X(6344), X(45011)}}, {{A, B, C, X(6640), X(35481)}}, {{A, B, C, X(6832), X(7537)}}, {{A, B, C, X(6833), X(52252)}}, {{A, B, C, X(7383), X(8889)}}, {{A, B, C, X(7400), X(52299)}}, {{A, B, C, X(8801), X(13139)}}, {{A, B, C, X(10303), X(35482)}}, {{A, B, C, X(11816), X(43726)}}, {{A, B, C, X(17040), X(18349)}}, {{A, B, C, X(18855), X(45736)}}, {{A, B, C, X(18890), X(46089)}}, {{A, B, C, X(20574), X(43718)}}, {{A, B, C, X(30537), X(43908)}}, {{A, B, C, X(34288), X(57730)}}, {{A, B, C, X(34449), X(45108)}}, {{A, B, C, X(42021), X(44658)}}, {{A, B, C, X(43891), X(52487)}}, {{A, B, C, X(45299), X(57387)}}, {{A, B, C, X(45857), X(46199)}}

X(60164) = X(2)X(36742)∩X(275)X(406)

Barycentrics    (a^5+a^4*(b+c)+(b-c)^2*(b+c)^3+a*(b-c)*(b+c)*(b^2-2*b*c-c^2)-2*a^2*(b+c)*(b^2+c^2)-2*a^3*(b^2-b*c+c^2))*(a^5+a^4*(b+c)+(b-c)^2*(b+c)^3+a*(b-c)*(b+c)*(b^2+2*b*c-c^2)-2*a^2*(b+c)*(b^2+c^2)-2*a^3*(b^2-b*c+c^2)) : :

X(60164) lies on the Kiepert hyperbola and on these lines: {2, 36742}, {3, 60155}, {4, 36743}, {5, 60156}, {6, 60154}, {20, 55027}, {30, 54766}, {226, 499}, {275, 406}, {321, 10527}, {376, 54759}, {381, 54756}, {451, 56346}, {459, 52252}, {475, 2052}, {631, 60107}, {1029, 3091}, {1656, 60169}, {1751, 6889}, {2051, 6833}, {2478, 6504}, {3090, 60076}, {3543, 54794}, {3545, 54760}, {4194, 60161}, {4200, 8796}, {5046, 13579}, {5056, 60258}, {5071, 54788}, {5084, 60114}, {5706, 54758}, {6824, 60071}, {6825, 24624}, {6834, 13478}, {6838, 55944}, {6846, 60170}, {6847, 45100}, {6848, 60167}, {6853, 55962}, {6887, 57722}, {6891, 60087}, {6908, 60168}, {6952, 45098}, {6967, 14554}, {6983, 60085}, {6989, 57721}, {6998, 60153}, {7380, 60152}, {17559, 60237}, {37119, 60246}, {37162, 60255}, {37407, 60092}, {37427, 54622}, {54346, 60249}

X(60164) = isogonal conjugate of X(36754)
X(60164) = trilinear pole of line {13401, 523}
X(60164) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3338)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(475)}}, {{A, B, C, X(5), X(406)}}, {{A, B, C, X(6), X(36742)}}, {{A, B, C, X(8), X(499)}}, {{A, B, C, X(9), X(1728)}}, {{A, B, C, X(20), X(52252)}}, {{A, B, C, X(29), X(6832)}}, {{A, B, C, X(37), X(3527)}}, {{A, B, C, X(40), X(39963)}}, {{A, B, C, X(54), X(39945)}}, {{A, B, C, X(68), X(57878)}}, {{A, B, C, X(75), X(5553)}}, {{A, B, C, X(80), X(37692)}}, {{A, B, C, X(84), X(1224)}}, {{A, B, C, X(86), X(57724)}}, {{A, B, C, X(104), X(59760)}}, {{A, B, C, X(254), X(39748)}}, {{A, B, C, X(280), X(55918)}}, {{A, B, C, X(377), X(3541)}}, {{A, B, C, X(393), X(51500)}}, {{A, B, C, X(443), X(3088)}}, {{A, B, C, X(451), X(3091)}}, {{A, B, C, X(452), X(7537)}}, {{A, B, C, X(631), X(4200)}}, {{A, B, C, X(847), X(57830)}}, {{A, B, C, X(860), X(6825)}}, {{A, B, C, X(937), X(2006)}}, {{A, B, C, X(941), X(1173)}}, {{A, B, C, X(943), X(40836)}}, {{A, B, C, X(1000), X(55091)}}, {{A, B, C, X(1093), X(57877)}}, {{A, B, C, X(1217), X(51501)}}, {{A, B, C, X(1220), X(57883)}}, {{A, B, C, X(1268), X(57723)}}, {{A, B, C, X(1440), X(3296)}}, {{A, B, C, X(2165), X(57666)}}, {{A, B, C, X(2475), X(37119)}}, {{A, B, C, X(2478), X(3542)}}, {{A, B, C, X(3086), X(3872)}}, {{A, B, C, X(3089), X(5084)}}, {{A, B, C, X(3090), X(4194)}}, {{A, B, C, X(3467), X(36626)}}, {{A, B, C, X(3613), X(20029)}}, {{A, B, C, X(5046), X(7505)}}, {{A, B, C, X(5125), X(6889)}}, {{A, B, C, X(5136), X(6824)}}, {{A, B, C, X(5936), X(10309)}}, {{A, B, C, X(6833), X(11109)}}, {{A, B, C, X(6834), X(17555)}}, {{A, B, C, X(6846), X(7498)}}, {{A, B, C, X(6883), X(41538)}}, {{A, B, C, X(6944), X(11105)}}, {{A, B, C, X(7110), X(38271)}}, {{A, B, C, X(8797), X(41013)}}, {{A, B, C, X(8801), X(43712)}}, {{A, B, C, X(13472), X(39975)}}, {{A, B, C, X(14528), X(39960)}}, {{A, B, C, X(15740), X(57865)}}, {{A, B, C, X(19843), X(19861)}}, {{A, B, C, X(22268), X(56174)}}, {{A, B, C, X(37407), X(57534)}}, {{A, B, C, X(39708), X(46435)}}, {{A, B, C, X(39982), X(43908)}}, {{A, B, C, X(39983), X(52518)}}, {{A, B, C, X(45011), X(57858)}}, {{A, B, C, X(46952), X(51223)}}, {{A, B, C, X(51502), X(52224)}}

X(60165) = X(4)X(5275)∩X(76)X(443)

Barycentrics    ((a^2+b^2)^2+4*a*b*(a+b)*c+4*a*b*c^2-c^4)*(a^4-b^4+c^4+4*a*b*c*(b+c)+2*a^2*c*(2*b+c)) : :

X(60165) lies on the Kiepert hyperbola and on these lines: {2, 44094}, {4, 5275}, {30, 54780}, {76, 443}, {83, 5084}, {226, 5268}, {376, 54754}, {377, 2996}, {451, 52583}, {975, 36907}, {1029, 1370}, {2475, 38259}, {2478, 5395}, {3524, 54695}, {3545, 54755}, {4052, 51100}, {5046, 18845}, {5071, 54719}, {5276, 60153}, {5292, 60075}, {5816, 43672}, {6854, 54739}, {6916, 54821}, {6997, 55027}, {6998, 60158}, {7380, 60157}, {7386, 60156}, {7392, 60155}, {7410, 60154}, {7735, 60081}, {14494, 37661}, {16999, 54122}, {17559, 18841}, {17582, 18840}, {26052, 60170}, {26118, 60167}, {37162, 60145}, {37394, 40395}, {37462, 60285}, {37664, 40824}, {37675, 60152}, {38282, 60246}, {44442, 54756}, {46336, 60258}, {54433, 60197}

X(60165) = isogonal conjugate of X(37492)
X(60165) = X(i)-cross conjugate of X(j) for these {i, j}: {5800, 4}
X(60165) = pole of line {5800, 60165} with respect to the Kiepert hyperbola
X(60165) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(8817)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(8769)}}, {{A, B, C, X(8), X(5268)}}, {{A, B, C, X(12), X(6340)}}, {{A, B, C, X(25), X(443)}}, {{A, B, C, X(37), X(69)}}, {{A, B, C, X(65), X(8770)}}, {{A, B, C, X(66), X(39983)}}, {{A, B, C, X(105), X(3296)}}, {{A, B, C, X(281), X(3718)}}, {{A, B, C, X(305), X(41013)}}, {{A, B, C, X(377), X(6353)}}, {{A, B, C, X(388), X(31359)}}, {{A, B, C, X(393), X(57831)}}, {{A, B, C, X(406), X(7386)}}, {{A, B, C, X(427), X(5084)}}, {{A, B, C, X(442), X(37394)}}, {{A, B, C, X(451), X(1370)}}, {{A, B, C, X(475), X(7392)}}, {{A, B, C, X(612), X(54433)}}, {{A, B, C, X(941), X(17040)}}, {{A, B, C, X(959), X(28476)}}, {{A, B, C, X(975), X(10327)}}, {{A, B, C, X(1000), X(1390)}}, {{A, B, C, X(1441), X(34208)}}, {{A, B, C, X(2475), X(38282)}}, {{A, B, C, X(2478), X(8889)}}, {{A, B, C, X(2550), X(27475)}}, {{A, B, C, X(5046), X(52299)}}, {{A, B, C, X(5551), X(39723)}}, {{A, B, C, X(5739), X(56213)}}, {{A, B, C, X(6601), X(52133)}}, {{A, B, C, X(6865), X(25985)}}, {{A, B, C, X(6897), X(35973)}}, {{A, B, C, X(6939), X(26020)}}, {{A, B, C, X(6995), X(17582)}}, {{A, B, C, X(6997), X(52252)}}, {{A, B, C, X(7220), X(14943)}}, {{A, B, C, X(7378), X(17559)}}, {{A, B, C, X(7390), X(37276)}}, {{A, B, C, X(7498), X(26052)}}, {{A, B, C, X(7714), X(37462)}}, {{A, B, C, X(7735), X(37664)}}, {{A, B, C, X(7774), X(16999)}}, {{A, B, C, X(8801), X(57877)}}, {{A, B, C, X(9093), X(24298)}}, {{A, B, C, X(9307), X(57866)}}, {{A, B, C, X(16774), X(57818)}}, {{A, B, C, X(17038), X(30479)}}, {{A, B, C, X(20029), X(56237)}}, {{A, B, C, X(26703), X(56027)}}, {{A, B, C, X(34229), X(37661)}}, {{A, B, C, X(34285), X(40412)}}, {{A, B, C, X(37675), X(45962)}}, {{A, B, C, X(38005), X(39960)}}, {{A, B, C, X(39570), X(39595)}}, {{A, B, C, X(39732), X(43733)}}, {{A, B, C, X(39951), X(57705)}}, {{A, B, C, X(57925), X(59760)}}

X(60166) = X(2)X(1181)∩X(4)X(8573)

Barycentrics    ((a^2-b^2)^4-4*(a^2+b^2)*(a^4+b^4)*c^2+6*(a^2+b^2)^2*c^4-4*(a^2+b^2)*c^6+c^8)*(a^8+(b^2-c^2)^4-4*a^6*(b^2+c^2)+a^4*(6*b^4-4*b^2*c^2+6*c^4)-4*a^2*(b^6-3*b^4*c^2+b^2*c^4+c^6)) : :

X(60166) lies on the Kiepert hyperbola and on these lines: {2, 1181}, {3, 60114}, {4, 8573}, {6, 60174}, {20, 6504}, {30, 54785}, {76, 7400}, {98, 34781}, {226, 1158}, {275, 3088}, {381, 54797}, {459, 3542}, {485, 6807}, {486, 6808}, {631, 60237}, {671, 34621}, {1029, 37434}, {1446, 31600}, {2052, 3089}, {2996, 52404}, {3146, 13579}, {3424, 16655}, {3522, 60255}, {3541, 56346}, {3543, 54761}, {3547, 60221}, {3839, 54764}, {3854, 60191}, {5059, 13582}, {5392, 59349}, {5656, 13380}, {6776, 40448}, {6833, 60076}, {6834, 60107}, {6847, 60156}, {6848, 60155}, {7383, 18840}, {7505, 38253}, {7592, 60162}, {11456, 60159}, {11538, 50689}, {13585, 17578}, {14484, 45089}, {15032, 60163}, {15811, 54844}, {15836, 60249}, {18945, 60122}, {37119, 60137}, {50687, 54762}

X(60166) = isogonal conjugate of X(37498)
X(60166) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 37498}, {48, 6820}
X(60166) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 37498}, {1249, 6820}
X(60166) = X(i)-cross conjugate of X(j) for these {i, j}: {1498, 4}
X(60166) = pole of line {1498, 60166} with respect to the Kiepert hyperbola
X(60166) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(393)}}, {{A, B, C, X(5), X(3088)}}, {{A, B, C, X(6), X(34223)}}, {{A, B, C, X(8), X(10321)}}, {{A, B, C, X(20), X(1300)}}, {{A, B, C, X(24), X(56306)}}, {{A, B, C, X(25), X(7400)}}, {{A, B, C, X(40), X(2006)}}, {{A, B, C, X(54), X(52223)}}, {{A, B, C, X(64), X(1217)}}, {{A, B, C, X(66), X(18855)}}, {{A, B, C, X(68), X(6526)}}, {{A, B, C, X(69), X(1093)}}, {{A, B, C, X(70), X(13597)}}, {{A, B, C, X(74), X(254)}}, {{A, B, C, X(84), X(7110)}}, {{A, B, C, X(95), X(45011)}}, {{A, B, C, X(104), X(280)}}, {{A, B, C, X(253), X(847)}}, {{A, B, C, X(347), X(1068)}}, {{A, B, C, X(403), X(13573)}}, {{A, B, C, X(406), X(6847)}}, {{A, B, C, X(451), X(37434)}}, {{A, B, C, X(468), X(34621)}}, {{A, B, C, X(475), X(6848)}}, {{A, B, C, X(631), X(45857)}}, {{A, B, C, X(1105), X(35512)}}, {{A, B, C, X(1141), X(16251)}}, {{A, B, C, X(1173), X(52224)}}, {{A, B, C, X(1297), X(34428)}}, {{A, B, C, X(1299), X(34439)}}, {{A, B, C, X(1440), X(5553)}}, {{A, B, C, X(1976), X(36434)}}, {{A, B, C, X(1989), X(3532)}}, {{A, B, C, X(2963), X(22334)}}, {{A, B, C, X(2980), X(14542)}}, {{A, B, C, X(3091), X(3541)}}, {{A, B, C, X(3146), X(7505)}}, {{A, B, C, X(3459), X(11738)}}, {{A, B, C, X(3527), X(22270)}}, {{A, B, C, X(3531), X(22268)}}, {{A, B, C, X(3546), X(6623)}}, {{A, B, C, X(3547), X(7487)}}, {{A, B, C, X(3832), X(37119)}}, {{A, B, C, X(3926), X(16081)}}, {{A, B, C, X(4194), X(6833)}}, {{A, B, C, X(4200), X(6834)}}, {{A, B, C, X(4846), X(13381)}}, {{A, B, C, X(5059), X(37943)}}, {{A, B, C, X(5486), X(44157)}}, {{A, B, C, X(5552), X(18815)}}, {{A, B, C, X(5900), X(52443)}}, {{A, B, C, X(6143), X(50689)}}, {{A, B, C, X(6344), X(35510)}}, {{A, B, C, X(6353), X(52404)}}, {{A, B, C, X(6523), X(46351)}}, {{A, B, C, X(6530), X(34781)}}, {{A, B, C, X(6995), X(7383)}}, {{A, B, C, X(7318), X(10309)}}, {{A, B, C, X(7537), X(37421)}}, {{A, B, C, X(8749), X(15316)}}, {{A, B, C, X(8791), X(31942)}}, {{A, B, C, X(8884), X(15740)}}, {{A, B, C, X(10002), X(16655)}}, {{A, B, C, X(11270), X(43605)}}, {{A, B, C, X(11744), X(18846)}}, {{A, B, C, X(13481), X(16623)}}, {{A, B, C, X(14376), X(42373)}}, {{A, B, C, X(14457), X(17703)}}, {{A, B, C, X(14528), X(34288)}}, {{A, B, C, X(14860), X(38442)}}, {{A, B, C, X(14938), X(46217)}}, {{A, B, C, X(14940), X(17578)}}, {{A, B, C, X(15318), X(34208)}}, {{A, B, C, X(15319), X(16774)}}, {{A, B, C, X(16263), X(31371)}}, {{A, B, C, X(16620), X(18575)}}, {{A, B, C, X(17983), X(52441)}}, {{A, B, C, X(18317), X(46212)}}, {{A, B, C, X(18850), X(22261)}}, {{A, B, C, X(21451), X(35481)}}, {{A, B, C, X(34802), X(58724)}}, {{A, B, C, X(35603), X(52505)}}, {{A, B, C, X(36612), X(46199)}}, {{A, B, C, X(42021), X(45195)}}, {{A, B, C, X(43660), X(51348)}}, {{A, B, C, X(43908), X(46412)}}, {{A, B, C, X(50480), X(53924)}}
X(60166) = barycentric quotient X(i)/X(j) for these (i, j): {4, 6820}, {6, 37498}

X(60167) = X(10)X(20)∩X(27)X(459)

Barycentrics    (3*a^3+a^2*(b+c)+(b-c)*(b+c)*(3*b+c)+a*(b-c)*(b+3*c))*(3*a^3+a^2*(b+c)-a*(b-c)*(3*b+c)-(b-c)*(b+c)*(b+3*c)) : :
X(60167) = -3*X[2]+2*X[44736]

X(60167) lies on the Kiepert hyperbola and on these lines: {2, 44736}, {4, 37666}, {6, 45100}, {10, 20}, {27, 459}, {30, 54786}, {76, 7406}, {81, 60170}, {144, 321}, {193, 60261}, {226, 1419}, {333, 3146}, {381, 54624}, {391, 34258}, {469, 56346}, {940, 57826}, {1446, 9533}, {1746, 60075}, {1764, 60276}, {2048, 3316}, {2050, 45098}, {2052, 6994}, {2996, 37683}, {3091, 43531}, {3332, 54668}, {3486, 37593}, {3543, 60079}, {3832, 60077}, {3839, 60078}, {3929, 60267}, {4052, 10446}, {5229, 60086}, {5232, 19645}, {5397, 6844}, {6776, 54883}, {6834, 60173}, {6847, 60154}, {6848, 60164}, {6996, 18840}, {6999, 32022}, {7377, 18841}, {7381, 60114}, {7384, 58012}, {7397, 60183}, {7490, 38253}, {19541, 45097}, {19808, 54448}, {24597, 60168}, {26118, 60165}, {36728, 54831}, {37434, 60158}, {37456, 60152}, {37499, 56204}, {37681, 60107}, {40149, 44697}, {50696, 60227}, {50700, 57719}, {50701, 60112}

X(60167) = isogonal conjugate of X(37499)
X(60167) = anticomplement of X(44736)
X(60167) = trilinear pole of line {21172, 523}
X(60167) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 37499}, {6, 12526}
X(60167) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 37499}, {9, 12526}, {44736, 44736}
X(60167) = X(i)-cross conjugate of X(j) for these {i, j}: {9579, 7}, {37642, 2}
X(60167) = pole of line {37642, 60167} with respect to the Kiepert hyperbola
X(60167) = pole of line {37499, 44736} with respect to the Wallace hyperbola
X(60167) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(5234)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(1171)}}, {{A, B, C, X(6), X(37655)}}, {{A, B, C, X(7), X(333)}}, {{A, B, C, X(20), X(27)}}, {{A, B, C, X(25), X(7406)}}, {{A, B, C, X(57), X(144)}}, {{A, B, C, X(63), X(55938)}}, {{A, B, C, X(64), X(967)}}, {{A, B, C, X(69), X(37666)}}, {{A, B, C, X(80), X(56086)}}, {{A, B, C, X(81), X(84)}}, {{A, B, C, X(89), X(10308)}}, {{A, B, C, X(104), X(25417)}}, {{A, B, C, X(193), X(37683)}}, {{A, B, C, X(253), X(8044)}}, {{A, B, C, X(273), X(34404)}}, {{A, B, C, X(278), X(5691)}}, {{A, B, C, X(280), X(19607)}}, {{A, B, C, X(306), X(15077)}}, {{A, B, C, X(312), X(7319)}}, {{A, B, C, X(345), X(52392)}}, {{A, B, C, X(379), X(37104)}}, {{A, B, C, X(391), X(940)}}, {{A, B, C, X(469), X(3091)}}, {{A, B, C, X(514), X(28164)}}, {{A, B, C, X(1105), X(57874)}}, {{A, B, C, X(1156), X(2339)}}, {{A, B, C, X(1219), X(56046)}}, {{A, B, C, X(1255), X(3577)}}, {{A, B, C, X(1389), X(27789)}}, {{A, B, C, X(1407), X(24680)}}, {{A, B, C, X(1440), X(46103)}}, {{A, B, C, X(1826), X(51316)}}, {{A, B, C, X(1848), X(5229)}}, {{A, B, C, X(2006), X(37714)}}, {{A, B, C, X(2982), X(55986)}}, {{A, B, C, X(2985), X(6553)}}, {{A, B, C, X(2994), X(3427)}}, {{A, B, C, X(3088), X(7382)}}, {{A, B, C, X(3089), X(7381)}}, {{A, B, C, X(3146), X(7490)}}, {{A, B, C, X(3332), X(10004)}}, {{A, B, C, X(3486), X(5307)}}, {{A, B, C, X(3600), X(4352)}}, {{A, B, C, X(3668), X(35510)}}, {{A, B, C, X(3929), X(21454)}}, {{A, B, C, X(4196), X(6999)}}, {{A, B, C, X(4198), X(19645)}}, {{A, B, C, X(4207), X(7384)}}, {{A, B, C, X(5232), X(58010)}}, {{A, B, C, X(5556), X(18231)}}, {{A, B, C, X(5560), X(56075)}}, {{A, B, C, X(6837), X(37181)}}, {{A, B, C, X(6895), X(37388)}}, {{A, B, C, X(6995), X(6996)}}, {{A, B, C, X(7224), X(56264)}}, {{A, B, C, X(7320), X(42030)}}, {{A, B, C, X(7377), X(7378)}}, {{A, B, C, X(7397), X(7408)}}, {{A, B, C, X(7402), X(7409)}}, {{A, B, C, X(7554), X(31292)}}, {{A, B, C, X(8051), X(43762)}}, {{A, B, C, X(8605), X(56116)}}, {{A, B, C, X(10431), X(37102)}}, {{A, B, C, X(10435), X(30712)}}, {{A, B, C, X(12512), X(14377)}}, {{A, B, C, X(14018), X(50697)}}, {{A, B, C, X(15314), X(58004)}}, {{A, B, C, X(15320), X(34285)}}, {{A, B, C, X(15740), X(57876)}}, {{A, B, C, X(18141), X(37681)}}, {{A, B, C, X(18848), X(40414)}}, {{A, B, C, X(21739), X(56050)}}, {{A, B, C, X(22334), X(57663)}}, {{A, B, C, X(31042), X(37372)}}, {{A, B, C, X(33893), X(36908)}}, {{A, B, C, X(34234), X(44794)}}, {{A, B, C, X(34991), X(39963)}}, {{A, B, C, X(37279), X(50700)}}, {{A, B, C, X(37389), X(50696)}}, {{A, B, C, X(37642), X(44736)}}, {{A, B, C, X(41890), X(57702)}}, {{A, B, C, X(41894), X(57390)}}, {{A, B, C, X(43733), X(55090)}}, {{A, B, C, X(43757), X(46435)}}, {{A, B, C, X(57671), X(57744)}}
X(60167) = barycentric quotient X(i)/X(j) for these (i, j): {1, 12526}, {6, 37499}, {37642, 44736}

X(60168) = X(2)X(37504)∩X(10)X(452)

Barycentrics    (3*a^3+a^2*(b+c)+a*(b-3*c)*(b+c)+(b-c)*(b+c)*(3*b+c))*(3*a^3+a^2*(b+c)-a*(3*b-c)*(b+c)-(b-c)*(b+c)*(b+3*c)) : :

X(60168) lies on the Kiepert hyperbola and on these lines: {2, 37504}, {6, 60170}, {9, 60267}, {10, 452}, {20, 57719}, {30, 54787}, {76, 14552}, {81, 57826}, {193, 60257}, {226, 1449}, {321, 391}, {329, 4052}, {381, 54790}, {459, 37279}, {1446, 19788}, {2996, 37652}, {3091, 54972}, {3543, 54516}, {3839, 54526}, {3945, 57722}, {5177, 43531}, {5278, 43533}, {5397, 6843}, {5435, 8808}, {5746, 54928}, {6846, 60154}, {6889, 60173}, {6908, 60164}, {6987, 60112}, {7413, 14494}, {7580, 45097}, {11113, 54786}, {12848, 40149}, {17532, 54624}, {18840, 37086}, {18841, 37445}, {20078, 43675}, {24597, 60167}, {32911, 45100}, {37185, 60107}, {37421, 60157}, {37653, 60285}, {37655, 40013}, {37666, 60156}, {37681, 60155}, {43672, 50696}, {50735, 58011}

X(60168) = isogonal conjugate of X(37500)
X(60168) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 37500}, {6, 54422}
X(60168) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 37500}, {9, 54422}
X(60168) = X(i)-cross conjugate of X(j) for these {i, j}: {21866, 1}, {41869, 7}
X(60168) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(2357)}}, {{A, B, C, X(7), X(40435)}}, {{A, B, C, X(8), X(27)}}, {{A, B, C, X(9), X(81)}}, {{A, B, C, X(20), X(37279)}}, {{A, B, C, X(57), X(38271)}}, {{A, B, C, X(63), X(1156)}}, {{A, B, C, X(80), X(278)}}, {{A, B, C, X(84), X(40399)}}, {{A, B, C, X(88), X(2184)}}, {{A, B, C, X(90), X(2982)}}, {{A, B, C, X(92), X(5175)}}, {{A, B, C, X(189), X(673)}}, {{A, B, C, X(193), X(37652)}}, {{A, B, C, X(279), X(2994)}}, {{A, B, C, X(294), X(7008)}}, {{A, B, C, X(329), X(5435)}}, {{A, B, C, X(346), X(5802)}}, {{A, B, C, X(405), X(6994)}}, {{A, B, C, X(469), X(5177)}}, {{A, B, C, X(943), X(25417)}}, {{A, B, C, X(1171), X(57689)}}, {{A, B, C, X(1219), X(40394)}}, {{A, B, C, X(1255), X(5665)}}, {{A, B, C, X(1434), X(42030)}}, {{A, B, C, X(1708), X(20078)}}, {{A, B, C, X(1903), X(39956)}}, {{A, B, C, X(2339), X(55938)}}, {{A, B, C, X(3945), X(5278)}}, {{A, B, C, X(4200), X(37185)}}, {{A, B, C, X(4373), X(15314)}}, {{A, B, C, X(5046), X(37388)}}, {{A, B, C, X(5560), X(37887)}}, {{A, B, C, X(5739), X(37666)}}, {{A, B, C, X(6598), X(56086)}}, {{A, B, C, X(6650), X(39696)}}, {{A, B, C, X(6995), X(37086)}}, {{A, B, C, X(7357), X(56264)}}, {{A, B, C, X(7378), X(37445)}}, {{A, B, C, X(7518), X(7522)}}, {{A, B, C, X(8044), X(57866)}}, {{A, B, C, X(8813), X(57860)}}, {{A, B, C, X(10405), X(15474)}}, {{A, B, C, X(11323), X(50735)}}, {{A, B, C, X(21866), X(37500)}}, {{A, B, C, X(26003), X(50696)}}, {{A, B, C, X(27131), X(54366)}}, {{A, B, C, X(27818), X(56947)}}, {{A, B, C, X(32911), X(37655)}}, {{A, B, C, X(36599), X(39947)}}, {{A, B, C, X(37203), X(41514)}}, {{A, B, C, X(37653), X(51171)}}, {{A, B, C, X(39721), X(56046)}}, {{A, B, C, X(40406), X(55989)}}, {{A, B, C, X(42287), X(56944)}}, {{A, B, C, X(52393), X(56043)}}, {{A, B, C, X(56273), X(56354)}}, {{A, B, C, X(57666), X(57744)}}
X(60168) = barycentric quotient X(i)/X(j) for these (i, j): {1, 54422}, {6, 37500}

X(60169) = X(10)X(3306)∩X(88)X(1056)

Barycentrics    ((a-b)*(a+b)^2+(a^2+6*a*b-b^2)*c+(a+b)*c^2+c^3)*(a^3+a^2*(b+c)+(b-c)*(b+c)^2+a*(b^2+6*b*c-c^2)) : :

X(60169) lies on the Kiepert hyperbola and on these lines: {3, 54758}, {4, 37633}, {5, 54757}, {10, 3306}, {20, 54688}, {30, 54789}, {69, 60097}, {81, 60107}, {88, 1056}, {140, 60154}, {321, 18141}, {376, 54947}, {377, 60079}, {443, 54786}, {940, 60155}, {1150, 32022}, {1656, 60164}, {2478, 60078}, {3090, 54727}, {3091, 54726}, {3523, 60158}, {4648, 60071}, {5046, 54623}, {5056, 60157}, {5084, 54624}, {5712, 60087}, {6692, 60243}, {6826, 54528}, {6827, 54679}, {6835, 54516}, {6836, 54526}, {6847, 54844}, {6850, 54698}, {6864, 54787}, {6865, 54790}, {6925, 54696}, {6952, 54498}, {6957, 54511}, {6996, 54754}, {7377, 54755}, {7381, 54756}, {7382, 54766}, {7384, 54793}, {7397, 54695}, {7402, 54719}, {7406, 54780}, {10431, 54517}, {14458, 26118}, {17234, 60242}, {18139, 60254}, {24597, 60075}, {30852, 56226}, {36662, 54497}, {36698, 54728}, {37162, 60077}, {37185, 54928}, {37276, 54710}, {37434, 54886}, {37456, 54519}, {37642, 57721}, {37674, 60156}, {37684, 60149}, {46336, 60152}

X(60169) = isogonal conjugate of X(37503)
X(60169) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(55995)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(88)}}, {{A, B, C, X(8), X(40434)}}, {{A, B, C, X(27), X(37462)}}, {{A, B, C, X(57), X(3338)}}, {{A, B, C, X(69), X(37633)}}, {{A, B, C, X(79), X(39963)}}, {{A, B, C, X(81), X(5558)}}, {{A, B, C, X(85), X(6336)}}, {{A, B, C, X(89), X(3296)}}, {{A, B, C, X(92), X(56879)}}, {{A, B, C, X(189), X(1255)}}, {{A, B, C, X(333), X(43745)}}, {{A, B, C, X(1000), X(21739)}}, {{A, B, C, X(1150), X(4648)}}, {{A, B, C, X(1214), X(42021)}}, {{A, B, C, X(2994), X(5559)}}, {{A, B, C, X(3522), X(37276)}}, {{A, B, C, X(4997), X(30513)}}, {{A, B, C, X(5226), X(30852)}}, {{A, B, C, X(5486), X(39957)}}, {{A, B, C, X(5739), X(37674)}}, {{A, B, C, X(8046), X(18490)}}, {{A, B, C, X(8056), X(43732)}}, {{A, B, C, X(8817), X(39734)}}, {{A, B, C, X(11331), X(26118)}}, {{A, B, C, X(17234), X(24597)}}, {{A, B, C, X(17300), X(37684)}}, {{A, B, C, X(18139), X(37642)}}, {{A, B, C, X(21446), X(34917)}}, {{A, B, C, X(27475), X(34234)}}, {{A, B, C, X(30608), X(43740)}}, {{A, B, C, X(30690), X(56218)}}, {{A, B, C, X(30701), X(55942)}}, {{A, B, C, X(32021), X(39732)}}, {{A, B, C, X(37518), X(56041)}}, {{A, B, C, X(38005), X(39979)}}, {{A, B, C, X(39723), X(40154)}}, {{A, B, C, X(42318), X(43758)}}, {{A, B, C, X(43741), X(56201)}}, {{A, B, C, X(44794), X(55110)}}

X(60170) = X(2)X(1901)∩X(10)X(329)

Barycentrics    ((a+b)^3+(3*a^2+2*a*b+3*b^2)*c-(a+b)*c^2-3*c^3)*(a^3+3*a^2*(b+c)-a*(b-3*c)*(b+c)-(b-c)*(b+c)*(3*b+c)) : :

X(60170) lies on the Kiepert hyperbola and on these lines: {2, 1901}, {4, 41083}, {6, 60168}, {7, 8808}, {9, 60243}, {10, 329}, {20, 54972}, {30, 54790}, {81, 60167}, {193, 54119}, {226, 347}, {321, 322}, {342, 40149}, {381, 54787}, {452, 17188}, {1446, 31042}, {1750, 54668}, {1751, 5746}, {2996, 17778}, {3091, 57719}, {3543, 54526}, {3839, 54516}, {3945, 60156}, {4869, 40013}, {5397, 6987}, {5739, 43533}, {5802, 54676}, {6832, 60173}, {6843, 60112}, {6846, 60164}, {6908, 60154}, {6994, 40395}, {7413, 7612}, {8226, 45097}, {8232, 60188}, {11113, 54624}, {14552, 60206}, {17532, 54786}, {18840, 37445}, {18841, 37086}, {19542, 45098}, {19684, 60077}, {24624, 37666}, {26052, 60165}, {28609, 60267}, {32911, 60092}, {37185, 60076}, {37279, 56346}, {37388, 60246}, {37421, 60158}, {37681, 57721}, {37685, 55944}, {48612, 60074}, {50696, 56144}

X(60170) = isogonal conjugate of X(37504)
X(60170) = isotomic conjugate of X(14552)
X(60170) = trilinear pole of line {14837, 523}
X(60170) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 37504}, {6, 31424}, {31, 14552}, {48, 7498}
X(60170) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 14552}, {3, 37504}, {9, 31424}, {1249, 7498}
X(60170) = pole of line {5712, 60170} with respect to the Kiepert hyperbola
X(60170) = pole of line {14552, 37504} with respect to the Wallace hyperbola
X(60170) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(37500)}}, {{A, B, C, X(7), X(92)}}, {{A, B, C, X(9), X(1255)}}, {{A, B, C, X(27), X(5177)}}, {{A, B, C, X(57), X(2093)}}, {{A, B, C, X(63), X(17097)}}, {{A, B, C, X(65), X(57744)}}, {{A, B, C, X(79), X(278)}}, {{A, B, C, X(81), X(2184)}}, {{A, B, C, X(189), X(44733)}}, {{A, B, C, X(193), X(17778)}}, {{A, B, C, X(279), X(4295)}}, {{A, B, C, X(280), X(7108)}}, {{A, B, C, X(393), X(1901)}}, {{A, B, C, X(440), X(7518)}}, {{A, B, C, X(442), X(6994)}}, {{A, B, C, X(452), X(469)}}, {{A, B, C, X(941), X(1903)}}, {{A, B, C, X(943), X(27789)}}, {{A, B, C, X(1088), X(58024)}}, {{A, B, C, X(1219), X(39700)}}, {{A, B, C, X(1246), X(57866)}}, {{A, B, C, X(1476), X(56033)}}, {{A, B, C, X(2475), X(37388)}}, {{A, B, C, X(2982), X(17098)}}, {{A, B, C, X(3091), X(37279)}}, {{A, B, C, X(3577), X(40399)}}, {{A, B, C, X(3936), X(37666)}}, {{A, B, C, X(3945), X(5739)}}, {{A, B, C, X(4183), X(31042)}}, {{A, B, C, X(4194), X(37185)}}, {{A, B, C, X(4869), X(32911)}}, {{A, B, C, X(5232), X(19684)}}, {{A, B, C, X(5249), X(8232)}}, {{A, B, C, X(5561), X(37887)}}, {{A, B, C, X(5712), X(14552)}}, {{A, B, C, X(5746), X(56559)}}, {{A, B, C, X(6260), X(17862)}}, {{A, B, C, X(6598), X(30711)}}, {{A, B, C, X(6995), X(37445)}}, {{A, B, C, X(7319), X(40435)}}, {{A, B, C, X(7378), X(37086)}}, {{A, B, C, X(7406), X(25985)}}, {{A, B, C, X(7413), X(37174)}}, {{A, B, C, X(8049), X(56264)}}, {{A, B, C, X(10590), X(40573)}}, {{A, B, C, X(12848), X(31164)}}, {{A, B, C, X(15314), X(30712)}}, {{A, B, C, X(15474), X(55937)}}, {{A, B, C, X(18139), X(37681)}}, {{A, B, C, X(21454), X(28609)}}, {{A, B, C, X(25430), X(38271)}}, {{A, B, C, X(30679), X(59268)}}, {{A, B, C, X(31053), X(54366)}}, {{A, B, C, X(33576), X(40434)}}, {{A, B, C, X(34527), X(54123)}}, {{A, B, C, X(37448), X(50696)}}, {{A, B, C, X(39696), X(54120)}}, {{A, B, C, X(39749), X(56224)}}, {{A, B, C, X(40444), X(50442)}}, {{A, B, C, X(40779), X(41509)}}, {{A, B, C, X(52223), X(57286)}}
X(60170) = barycentric product X(i)*X(j) for these (i, j): {14553, 76}
X(60170) = barycentric quotient X(i)/X(j) for these (i, j): {1, 31424}, {2, 14552}, {4, 7498}, {6, 37504}, {14553, 6}

X(60171) = X(2)X(11431)∩X(4)X(233)

Barycentrics    ((a^2-2*b^2)*(a^2-b^2)^3-(a^2-b^2)^2*(6*a^2+7*b^2)*c^2+(10*a^4+5*a^2*b^2+9*b^4)*c^4-(6*a^2+5*b^2)*c^6+c^8)*((a^2-b^2)^2*(a^4-4*a^2*b^2+b^4)-5*(a^2-b^2)^2*(a^2+b^2)*c^2+(9*a^4+8*a^2*b^2+9*b^4)*c^4-7*(a^2+b^2)*c^6+2*c^8) : :

X(60171) lies on the Kiepert hyperbola and on these lines: {2, 11431}, {3, 60120}, {4, 233}, {5, 39284}, {20, 54892}, {30, 54791}, {140, 275}, {459, 3462}, {598, 7395}, {631, 54531}, {671, 7399}, {1327, 6810}, {1328, 6809}, {1656, 2052}, {3090, 54867}, {3091, 54893}, {3523, 60161}, {3533, 56346}, {5056, 6750}, {5067, 54710}, {6803, 54785}, {6804, 54797}, {6815, 54761}, {6816, 54764}, {7567, 54676}, {8955, 10195}, {13160, 54666}, {14118, 54663}, {14788, 54685}, {16080, 55856}, {17041, 42350}, {17928, 54913}, {22467, 54769}, {34007, 54601}, {34664, 45103}, {43530, 46219}, {46935, 56270}

X(60171) = isogonal conjugate of X(37505)
X(60171) = trilinear pole of line {14460, 35441}
X(60171) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(1656)}}, {{A, B, C, X(5), X(95)}}, {{A, B, C, X(30), X(55856)}}, {{A, B, C, X(54), X(1487)}}, {{A, B, C, X(93), X(18368)}}, {{A, B, C, X(253), X(631)}}, {{A, B, C, X(264), X(2045)}}, {{A, B, C, X(376), X(46935)}}, {{A, B, C, X(381), X(46219)}}, {{A, B, C, X(382), X(55860)}}, {{A, B, C, X(468), X(7399)}}, {{A, B, C, X(546), X(55859)}}, {{A, B, C, X(547), X(15712)}}, {{A, B, C, X(549), X(35018)}}, {{A, B, C, X(550), X(3628)}}, {{A, B, C, X(847), X(45857)}}, {{A, B, C, X(1092), X(17039)}}, {{A, B, C, X(1105), X(14813)}}, {{A, B, C, X(1199), X(1994)}}, {{A, B, C, X(1657), X(5070)}}, {{A, B, C, X(2963), X(8884)}}, {{A, B, C, X(3090), X(3523)}}, {{A, B, C, X(3091), X(3533)}}, {{A, B, C, X(3462), X(38808)}}, {{A, B, C, X(3522), X(5067)}}, {{A, B, C, X(3525), X(5068)}}, {{A, B, C, X(3526), X(3851)}}, {{A, B, C, X(3858), X(16239)}}, {{A, B, C, X(5055), X(15720)}}, {{A, B, C, X(5073), X(55857)}}, {{A, B, C, X(5094), X(7395)}}, {{A, B, C, X(5562), X(10184)}}, {{A, B, C, X(6145), X(53864)}}, {{A, B, C, X(6662), X(26861)}}, {{A, B, C, X(6750), X(45198)}}, {{A, B, C, X(6834), X(37462)}}, {{A, B, C, X(6952), X(37162)}}, {{A, B, C, X(7405), X(34002)}}, {{A, B, C, X(7486), X(10299)}}, {{A, B, C, X(7495), X(14788)}}, {{A, B, C, X(7503), X(52296)}}, {{A, B, C, X(7892), X(37446)}}, {{A, B, C, X(7901), X(37334)}}, {{A, B, C, X(8797), X(15318)}}, {{A, B, C, X(8798), X(55074)}}, {{A, B, C, X(10018), X(13160)}}, {{A, B, C, X(11169), X(45195)}}, {{A, B, C, X(11431), X(46952)}}, {{A, B, C, X(14371), X(57686)}}, {{A, B, C, X(14483), X(26862)}}, {{A, B, C, X(14528), X(41768)}}, {{A, B, C, X(14789), X(52300)}}, {{A, B, C, X(14841), X(57895)}}, {{A, B, C, X(14869), X(44904)}}, {{A, B, C, X(15699), X(33923)}}, {{A, B, C, X(16263), X(46223)}}, {{A, B, C, X(16835), X(34110)}}, {{A, B, C, X(16837), X(17711)}}, {{A, B, C, X(17983), X(43908)}}, {{A, B, C, X(18027), X(42351)}}, {{A, B, C, X(18575), X(44157)}}, {{A, B, C, X(18855), X(36948)}}, {{A, B, C, X(21735), X(46936)}}, {{A, B, C, X(22336), X(46864)}}, {{A, B, C, X(34483), X(57897)}}, {{A, B, C, X(34567), X(41891)}}, {{A, B, C, X(34664), X(52293)}}, {{A, B, C, X(38433), X(45838)}}, {{A, B, C, X(41890), X(57730)}}, {{A, B, C, X(45301), X(51761)}}, {{A, B, C, X(46412), X(52441)}}, {{A, B, C, X(56272), X(57900)}}

X(60172) = X(4)X(3017)∩X(10)X(30)

Barycentrics    (2*a^3+a^2*(b+c)+(b-c)*(b+c)*(2*b+c)+a*(b-c)*(b+2*c))*(2*a^3+a^2*(b+c)-(b-c)*(b+c)*(b+2*c)+a*(-2*b^2+b*c+c^2)) : :
X(60172) = -X[3244]+4*X[46975]

X(60172) lies on these lines: {2, 17190}, {4, 3017}, {6, 54586}, {10, 30}, {27, 16080}, {81, 60139}, {98, 34476}, {115, 55003}, {226, 6357}, {321, 3578}, {381, 43531}, {469, 43530}, {511, 34475}, {514, 2394}, {515, 60116}, {516, 59261}, {519, 43677}, {524, 4052}, {527, 43683}, {542, 11599}, {543, 34899}, {551, 38330}, {553, 24208}, {671, 41629}, {1503, 54668}, {1746, 57721}, {1999, 4080}, {2048, 10195}, {2349, 56947}, {2786, 14223}, {2789, 9180}, {3219, 6539}, {3244, 46975}, {3543, 43533}, {3585, 60086}, {3667, 5466}, {3830, 60079}, {3839, 60077}, {3845, 60078}, {4049, 6002}, {4785, 43665}, {6994, 56270}, {6996, 10159}, {7377, 43527}, {7406, 60285}, {10308, 57419}, {10572, 60321}, {14537, 54701}, {15682, 54786}, {17758, 36728}, {18483, 56402}, {24220, 57722}, {28296, 43674}, {28470, 60106}, {36731, 60075}, {37642, 54587}, {41099, 54624}, {49724, 50118}, {50169, 53004}, {54357, 60203}

X(60172) = reflection of X(i) in X(j) for these {i,j}: {551, 38330}, {55003, 115}, {56402, 18483}
X(60172) = isogonal conjugate of X(37508)
X(60172) = trilinear pole of line {11125, 523}
X(60172) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 37508}, {6, 11684}, {58, 24048}, {1333, 27558}
X(60172) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 54668}
X(60172) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 37508}, {9, 11684}, {10, 24048}, {37, 27558}
X(60172) = pole of line {32636, 52382} with respect to the dual conic of Yff parabola
X(60172) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(5302)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(5325)}}, {{A, B, C, X(27), X(30)}}, {{A, B, C, X(57), X(2349)}}, {{A, B, C, X(58), X(35203)}}, {{A, B, C, X(63), X(34800)}}, {{A, B, C, X(74), X(1171)}}, {{A, B, C, X(75), X(50052)}}, {{A, B, C, X(79), X(333)}}, {{A, B, C, X(80), X(4102)}}, {{A, B, C, X(81), X(553)}}, {{A, B, C, X(84), X(31445)}}, {{A, B, C, X(86), X(49730)}}, {{A, B, C, X(92), X(18480)}}, {{A, B, C, X(189), X(14377)}}, {{A, B, C, X(265), X(306)}}, {{A, B, C, X(278), X(31673)}}, {{A, B, C, X(310), X(50162)}}, {{A, B, C, X(312), X(5560)}}, {{A, B, C, X(376), X(6994)}}, {{A, B, C, X(381), X(469)}}, {{A, B, C, X(428), X(6996)}}, {{A, B, C, X(511), X(4785)}}, {{A, B, C, X(513), X(53083)}}, {{A, B, C, X(516), X(28840)}}, {{A, B, C, X(519), X(1999)}}, {{A, B, C, X(522), X(19607)}}, {{A, B, C, X(524), X(3667)}}, {{A, B, C, X(527), X(6003)}}, {{A, B, C, X(538), X(28470)}}, {{A, B, C, X(540), X(28478)}}, {{A, B, C, X(542), X(2786)}}, {{A, B, C, X(543), X(2789)}}, {{A, B, C, X(596), X(56046)}}, {{A, B, C, X(673), X(49732)}}, {{A, B, C, X(754), X(28487)}}, {{A, B, C, X(903), X(18812)}}, {{A, B, C, X(967), X(3426)}}, {{A, B, C, X(1121), X(57288)}}, {{A, B, C, X(1246), X(57822)}}, {{A, B, C, X(1255), X(16615)}}, {{A, B, C, X(1389), X(56037)}}, {{A, B, C, X(1412), X(48074)}}, {{A, B, C, X(1427), X(47947)}}, {{A, B, C, X(1432), X(48939)}}, {{A, B, C, X(1494), X(3668)}}, {{A, B, C, X(1826), X(1989)}}, {{A, B, C, X(1839), X(2160)}}, {{A, B, C, X(1848), X(3585)}}, {{A, B, C, X(1961), X(50095)}}, {{A, B, C, X(2006), X(18357)}}, {{A, B, C, X(2185), X(3065)}}, {{A, B, C, X(2339), X(36599)}}, {{A, B, C, X(2687), X(40143)}}, {{A, B, C, X(2692), X(35148)}}, {{A, B, C, X(2985), X(39697)}}, {{A, B, C, X(3062), X(4416)}}, {{A, B, C, X(3296), X(30711)}}, {{A, B, C, X(3543), X(7490)}}, {{A, B, C, X(3676), X(9141)}}, {{A, B, C, X(3849), X(28565)}}, {{A, B, C, X(3928), X(41572)}}, {{A, B, C, X(4654), X(54357)}}, {{A, B, C, X(4846), X(48870)}}, {{A, B, C, X(4921), X(42045)}}, {{A, B, C, X(4997), X(33696)}}, {{A, B, C, X(5064), X(7377)}}, {{A, B, C, X(5307), X(10572)}}, {{A, B, C, X(5561), X(44733)}}, {{A, B, C, X(5627), X(31010)}}, {{A, B, C, X(7319), X(56218)}}, {{A, B, C, X(7406), X(7714)}}, {{A, B, C, X(7649), X(16305)}}, {{A, B, C, X(10152), X(36908)}}, {{A, B, C, X(10435), X(39704)}}, {{A, B, C, X(11645), X(30519)}}, {{A, B, C, X(14004), X(36728)}}, {{A, B, C, X(14490), X(57663)}}, {{A, B, C, X(15309), X(28194)}}, {{A, B, C, X(15314), X(30101)}}, {{A, B, C, X(15762), X(31153)}}, {{A, B, C, X(16704), X(50256)}}, {{A, B, C, X(17484), X(37222)}}, {{A, B, C, X(18850), X(57874)}}, {{A, B, C, X(21739), X(52393)}}, {{A, B, C, X(26750), X(34578)}}, {{A, B, C, X(28296), X(52229)}}, {{A, B, C, X(34570), X(57390)}}, {{A, B, C, X(34914), X(49728)}}, {{A, B, C, X(36085), X(53936)}}, {{A, B, C, X(36871), X(50054)}}, {{A, B, C, X(37870), X(43972)}}, {{A, B, C, X(39974), X(43739)}}, {{A, B, C, X(42028), X(49724)}}, {{A, B, C, X(44572), X(49729)}}, {{A, B, C, X(50051), X(57725)}}, {{A, B, C, X(50222), X(52394)}}, {{A, B, C, X(50808), X(55937)}}
X(60172) = barycentric product X(i)*X(j) for these (i, j): {1, 26734}
X(60172) = barycentric quotient X(i)/X(j) for these (i, j): {1, 11684}, {6, 37508}, {10, 27558}, {37, 24048}, {26734, 75}

X(60173) = X(4)X(5124)∩X(5)X(1029)

Barycentrics    (a^5+a^4*(b+c)+(b-c)^2*(b+c)^3+a^3*(-2*b^2+b*c-2*c^2)+a*(b-c)*(b+c)*(b^2-b*c-c^2)-2*a^2*(b+c)*(b^2+c^2))*(a^5+a^4*(b+c)+(b-c)^2*(b+c)^3+a^3*(-2*b^2+b*c-2*c^2)+a*(b-c)*(b+c)*(b^2+b*c-c^2)-2*a^2*(b+c)*(b^2+c^2)) : :

X(60173) lies on the Kiepert hyperbola and on these lines: {2, 36750}, {3, 55027}, {4, 5124}, {5, 1029}, {30, 54794}, {140, 51339}, {226, 3337}, {275, 451}, {376, 54766}, {406, 60161}, {475, 8796}, {631, 60155}, {1656, 60258}, {2051, 6952}, {2052, 52252}, {2475, 11538}, {2478, 13579}, {3090, 60156}, {3524, 54759}, {3525, 60107}, {3545, 54756}, {5046, 13585}, {5067, 60076}, {5071, 54760}, {5084, 6504}, {6143, 60246}, {6825, 55944}, {6832, 60170}, {6833, 45100}, {6834, 60167}, {6852, 60071}, {6853, 24624}, {6889, 60168}, {6949, 13478}, {7410, 60153}, {13582, 37162}, {13584, 13731}, {17559, 60114}, {20107, 56226}

X(60173) = isogonal conjugate of X(37509)
X(60173) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3337)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(5124)}}, {{A, B, C, X(5), X(451)}}, {{A, B, C, X(6), X(36750)}}, {{A, B, C, X(12), X(34110)}}, {{A, B, C, X(37), X(1173)}}, {{A, B, C, X(54), X(39798)}}, {{A, B, C, X(93), X(57830)}}, {{A, B, C, X(104), X(1224)}}, {{A, B, C, X(377), X(37119)}}, {{A, B, C, X(405), X(7537)}}, {{A, B, C, X(406), X(3090)}}, {{A, B, C, X(443), X(3541)}}, {{A, B, C, X(475), X(631)}}, {{A, B, C, X(499), X(4861)}}, {{A, B, C, X(847), X(57877)}}, {{A, B, C, X(860), X(6853)}}, {{A, B, C, X(1440), X(5551)}}, {{A, B, C, X(2165), X(57705)}}, {{A, B, C, X(2475), X(6143)}}, {{A, B, C, X(2478), X(7505)}}, {{A, B, C, X(2962), X(10266)}}, {{A, B, C, X(2963), X(57666)}}, {{A, B, C, X(3088), X(17582)}}, {{A, B, C, X(3089), X(17559)}}, {{A, B, C, X(3296), X(7318)}}, {{A, B, C, X(3459), X(39748)}}, {{A, B, C, X(3525), X(4200)}}, {{A, B, C, X(3527), X(39983)}}, {{A, B, C, X(3542), X(5084)}}, {{A, B, C, X(3613), X(43712)}}, {{A, B, C, X(3615), X(24298)}}, {{A, B, C, X(3617), X(20107)}}, {{A, B, C, X(4194), X(5067)}}, {{A, B, C, X(5046), X(14940)}}, {{A, B, C, X(5136), X(6852)}}, {{A, B, C, X(5553), X(5936)}}, {{A, B, C, X(6832), X(7498)}}, {{A, B, C, X(6949), X(17555)}}, {{A, B, C, X(6952), X(11109)}}, {{A, B, C, X(13418), X(54454)}}, {{A, B, C, X(13472), X(39956)}}, {{A, B, C, X(28650), X(57723)}}, {{A, B, C, X(30598), X(57724)}}, {{A, B, C, X(34567), X(39982)}}, {{A, B, C, X(37162), X(37943)}}, {{A, B, C, X(39960), X(43908)}}, {{A, B, C, X(39974), X(57730)}}, {{A, B, C, X(40410), X(41013)}}, {{A, B, C, X(40437), X(55091)}}, {{A, B, C, X(45299), X(57391)}}, {{A, B, C, X(57883), X(59760)}}

X(60174) = X(2)X(10982)∩X(5)X(60114)

Barycentrics    (a^8+(b^2-c^2)^4-4*a^6*(b^2+c^2)+6*a^4*(b^2+c^2)^2-4*a^2*(b^6+b^4*c^2-3*b^2*c^4+c^6))*(a^8+(b^2-c^2)^4-4*a^6*(b^2+c^2)+6*a^4*(b^2+c^2)^2-4*a^2*(b^6-3*b^4*c^2+b^2*c^4+c^6)) : :

X(60174) lies on the Kiepert hyperbola and on these lines: {2, 10982}, {5, 60114}, {6, 60166}, {30, 54797}, {83, 7400}, {275, 3089}, {381, 54785}, {459, 3541}, {485, 6808}, {486, 6807}, {598, 34621}, {1498, 54844}, {2052, 3088}, {3090, 60237}, {3091, 6504}, {3424, 6146}, {3523, 52014}, {3542, 56346}, {3543, 54764}, {3832, 13579}, {3839, 54761}, {3854, 13582}, {5059, 60191}, {5068, 60255}, {5395, 52404}, {5893, 54941}, {6833, 60107}, {6834, 60076}, {6847, 60155}, {6848, 60156}, {7383, 18841}, {7404, 60221}, {7505, 60137}, {11538, 17578}, {13585, 50689}, {13599, 14853}, {18945, 46727}, {31363, 45089}, {37119, 38253}, {37434, 55027}, {40393, 59349}, {41362, 54870}, {50687, 54765}

X(60174) = isogonal conjugate of X(37514)
X(60174) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 37514}, {48, 6819}
X(60174) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 37514}, {1249, 6819}
X(60174) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(3088)}}, {{A, B, C, X(5), X(3089)}}, {{A, B, C, X(6), X(1217)}}, {{A, B, C, X(20), X(3541)}}, {{A, B, C, X(54), X(3346)}}, {{A, B, C, X(68), X(8801)}}, {{A, B, C, X(254), X(1173)}}, {{A, B, C, X(264), X(45011)}}, {{A, B, C, X(393), X(3527)}}, {{A, B, C, X(406), X(6848)}}, {{A, B, C, X(427), X(7400)}}, {{A, B, C, X(475), X(6847)}}, {{A, B, C, X(1073), X(1181)}}, {{A, B, C, X(1093), X(8797)}}, {{A, B, C, X(1224), X(30500)}}, {{A, B, C, X(2165), X(52518)}}, {{A, B, C, X(3091), X(3542)}}, {{A, B, C, X(3146), X(37119)}}, {{A, B, C, X(3426), X(22270)}}, {{A, B, C, X(3531), X(14938)}}, {{A, B, C, X(3532), X(30537)}}, {{A, B, C, X(3613), X(14457)}}, {{A, B, C, X(3832), X(7505)}}, {{A, B, C, X(3854), X(37943)}}, {{A, B, C, X(4194), X(6834)}}, {{A, B, C, X(4200), X(6833)}}, {{A, B, C, X(5094), X(34621)}}, {{A, B, C, X(6143), X(17578)}}, {{A, B, C, X(6146), X(10002)}}, {{A, B, C, X(7040), X(44861)}}, {{A, B, C, X(7378), X(7383)}}, {{A, B, C, X(7404), X(7487)}}, {{A, B, C, X(8889), X(52404)}}, {{A, B, C, X(9307), X(18853)}}, {{A, B, C, X(11169), X(52441)}}, {{A, B, C, X(13489), X(26862)}}, {{A, B, C, X(14483), X(51316)}}, {{A, B, C, X(14542), X(18850)}}, {{A, B, C, X(14853), X(41365)}}, {{A, B, C, X(14940), X(50689)}}, {{A, B, C, X(15318), X(17040)}}, {{A, B, C, X(16620), X(30542)}}, {{A, B, C, X(16837), X(52487)}}, {{A, B, C, X(18281), X(49670)}}, {{A, B, C, X(22261), X(43726)}}, {{A, B, C, X(22466), X(45090)}}, {{A, B, C, X(28425), X(37074)}}, {{A, B, C, X(35482), X(50693)}}, {{A, B, C, X(37434), X(52252)}}, {{A, B, C, X(38305), X(38436)}}, {{A, B, C, X(43719), X(46412)}}, {{A, B, C, X(43908), X(52188)}}, {{A, B, C, X(44157), X(44658)}}, {{A, B, C, X(45833), X(46199)}}, {{A, B, C, X(45972), X(52443)}}, {{A, B, C, X(51030), X(51990)}}
X(60174) = barycentric quotient X(i)/X(j) for these (i, j): {4, 6819}, {6, 37514}

X(60175) = X(2)X(43150)∩X(76)X(549)

Barycentrics    (4*a^4-2*a^2*b^2+4*b^4-5*(a^2+b^2)*c^2+c^4)*(4*a^4+b^4-5*b^2*c^2+4*c^4-a^2*(5*b^2+2*c^2)) : :

X(60175) lies on the Kiepert hyperbola and on these lines: {2, 43150}, {3, 43676}, {4, 35007}, {5, 53102}, {6, 60192}, {30, 53105}, {76, 549}, {83, 5055}, {115, 54723}, {183, 60202}, {230, 14458}, {262, 5306}, {376, 60219}, {381, 53109}, {383, 43547}, {542, 60104}, {548, 60209}, {598, 5066}, {671, 3534}, {1080, 43546}, {1503, 60323}, {1513, 53100}, {1916, 6055}, {2996, 10304}, {3424, 38227}, {3526, 10159}, {3545, 18843}, {3628, 43527}, {3830, 33698}, {3845, 54494}, {4049, 28553}, {5054, 60210}, {5072, 60146}, {5304, 54522}, {5466, 11633}, {5485, 5569}, {5503, 8667}, {6054, 60073}, {6776, 60102}, {6811, 43570}, {6813, 43571}, {7610, 60181}, {7735, 60127}, {7788, 8781}, {7850, 54841}, {7874, 60183}, {7880, 15709}, {7886, 18841}, {8859, 54540}, {9300, 54645}, {9744, 53103}, {9752, 60327}, {9753, 43951}, {9754, 60336}, {9755, 53108}, {9756, 54890}, {9774, 60218}, {9993, 54582}, {10033, 54539}, {10303, 60285}, {11177, 60136}, {11540, 60277}, {11668, 43461}, {11669, 12007}, {13468, 60180}, {13860, 60142}, {14036, 60151}, {15022, 60145}, {15640, 41895}, {15682, 54720}, {15683, 38259}, {15684, 53106}, {15706, 60250}, {15717, 43681}, {15759, 60228}, {16080, 37453}, {17503, 33699}, {22329, 60095}, {22712, 43688}, {23046, 53107}, {37637, 54644}, {37689, 54520}, {41624, 60211}, {43460, 60150}, {43535, 55177}, {46941, 60200}, {47598, 60278}, {51140, 60233}, {53015, 60325}, {54823, 58849}, {55860, 60182}, {58883, 60337}

X(60175) = reflection of X(i) in X(j) for these {i,j}: {54723, 115}
X(60175) = isogonal conjugate of X(37517)
X(60175) = trilinear pole of line {47465, 523}
X(60175) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 60323}, {25, 14458}, {3425, 53100}
}X(60175) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(5966)}}, {{A, B, C, X(6), X(50664)}}, {{A, B, C, X(25), X(549)}}, {{A, B, C, X(30), X(37453)}}, {{A, B, C, X(66), X(55958)}}, {{A, B, C, X(95), X(34288)}}, {{A, B, C, X(183), X(5306)}}, {{A, B, C, X(230), X(7788)}}, {{A, B, C, X(251), X(57714)}}, {{A, B, C, X(264), X(11058)}}, {{A, B, C, X(427), X(5055)}}, {{A, B, C, X(428), X(3526)}}, {{A, B, C, X(468), X(3534)}}, {{A, B, C, X(519), X(28553)}}, {{A, B, C, X(523), X(48911)}}, {{A, B, C, X(842), X(8770)}}, {{A, B, C, X(1138), X(53935)}}, {{A, B, C, X(1494), X(2165)}}, {{A, B, C, X(1989), X(9307)}}, {{A, B, C, X(2980), X(30537)}}, {{A, B, C, X(3425), X(36616)}}, {{A, B, C, X(3531), X(46123)}}, {{A, B, C, X(3628), X(5064)}}, {{A, B, C, X(4232), X(15698)}}, {{A, B, C, X(5066), X(5094)}}, {{A, B, C, X(5481), X(43662)}}, {{A, B, C, X(5486), X(46204)}}, {{A, B, C, X(6055), X(40820)}}, {{A, B, C, X(6353), X(10304)}}, {{A, B, C, X(6995), X(15709)}}, {{A, B, C, X(7426), X(35472)}}, {{A, B, C, X(7610), X(41624)}}, {{A, B, C, X(7714), X(10303)}}, {{A, B, C, X(7880), X(40022)}}, {{A, B, C, X(8667), X(22329)}}, {{A, B, C, X(8884), X(46412)}}, {{A, B, C, X(10154), X(15750)}}, {{A, B, C, X(11410), X(44212)}}, {{A, B, C, X(12042), X(52145)}}, {{A, B, C, X(13468), X(14614)}}, {{A, B, C, X(13606), X(52133)}}, {{A, B, C, X(14388), X(40103)}}, {{A, B, C, X(15640), X(52290)}}, {{A, B, C, X(15683), X(38282)}}, {{A, B, C, X(15684), X(52297)}}, {{A, B, C, X(18018), X(19307)}}, {{A, B, C, X(21448), X(53890)}}, {{A, B, C, X(23046), X(52298)}}, {{A, B, C, X(29011), X(44763)}}, {{A, B, C, X(29316), X(40801)}}, {{A, B, C, X(31152), X(37942)}}, {{A, B, C, X(32085), X(57895)}}, {{A, B, C, X(32216), X(44957)}}, {{A, B, C, X(32516), X(47643)}}, {{A, B, C, X(33699), X(52292)}}, {{A, B, C, X(34285), X(36889)}}, {{A, B, C, X(36948), X(52188)}}, {{A, B, C, X(38227), X(47382)}}, {{A, B, C, X(40118), X(47847)}}, {{A, B, C, X(44210), X(55572)}}, {{A, B, C, X(45857), X(52187)}}

X(60176) = X(2)X(6321)∩X(30)X(8587)

Barycentrics    (2*a^6-a^4*b^2-a^2*b^4+2*b^6-(6*a^4+a^2*b^2+6*b^4)*c^2+7*(a^2+b^2)*c^4-3*c^6)*(2*a^6-6*a^4*b^2+7*a^2*b^4-3*b^6-(a^4+a^2*b^2-7*b^4)*c^2-(a^2+6*b^2)*c^4+2*c^6) : :

X(60176) lies on the Kiepert hyperbola and on these lines: {2, 6321}, {6, 54482}, {30, 8587}, {76, 38734}, {98, 10631}, {99, 15850}, {114, 60211}, {115, 7607}, {148, 60234}, {262, 1569}, {381, 10484}, {542, 17503}, {543, 42011}, {598, 9880}, {671, 13449}, {1327, 33431}, {1328, 33430}, {1503, 54567}, {2782, 60177}, {2794, 53100}, {3406, 44518}, {5471, 54861}, {5472, 54860}, {5480, 54715}, {6230, 60195}, {7603, 7608}, {9862, 47586}, {10722, 54857}, {10723, 60103}, {10788, 22515}, {12243, 41895}, {13188, 60233}, {14458, 39838}, {14651, 43537}, {22505, 54737}, {22575, 55950}, {22576, 55951}, {35950, 60186}, {36990, 54584}, {38230, 60104}, {38664, 53106}, {38732, 39652}, {43532, 53419}, {44534, 53103}

X(60176) = reflection of X(i) in X(j) for these {i,j}: {7607, 115}, {99, 15850}
X(60176) = isogonal conjugate of X(38225)
X(60176) = trilinear pole of line {3054, 523}
X(60176) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 54567}, {39644, 53103}
X(60176) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(74), X(52239)}}, {{A, B, C, X(115), X(13530)}}, {{A, B, C, X(265), X(53605)}}, {{A, B, C, X(290), X(33813)}}, {{A, B, C, X(511), X(10631)}}, {{A, B, C, X(690), X(11564)}}, {{A, B, C, X(1173), X(3455)}}, {{A, B, C, X(5966), X(10630)}}, {{A, B, C, X(6321), X(9154)}}, {{A, B, C, X(6323), X(14491)}}, {{A, B, C, X(6344), X(39450)}}, {{A, B, C, X(8753), X(38734)}}, {{A, B, C, X(13172), X(35142)}}, {{A, B, C, X(13449), X(44146)}}, {{A, B, C, X(23716), X(34322)}}, {{A, B, C, X(23717), X(34321)}}, {{A, B, C, X(30542), X(57908)}}, {{A, B, C, X(33565), X(39446)}}, {{A, B, C, X(43457), X(56401)}}

X(60177) = X(2)X(20977)∩X(39)X(598)

Barycentrics    (3*a^2*b^2+(a^2+b^2)*c^2-2*c^4)*(-2*b^4+b^2*c^2+a^2*(b^2+3*c^2)) : :
X(60177) = -5*X[7786]+3*X[11149]

X(60177) lies on the Kiepert hyperbola and on these lines: {2, 20977}, {3, 60148}, {4, 32447}, {5, 60126}, {6, 33687}, {10, 22231}, {30, 54805}, {39, 598}, {76, 625}, {83, 574}, {98, 576}, {194, 671}, {325, 43688}, {511, 7607}, {538, 60228}, {631, 8179}, {1007, 35005}, {2023, 60104}, {2080, 3406}, {2782, 60176}, {2996, 20105}, {3094, 60098}, {3095, 43532}, {3266, 40162}, {3407, 5038}, {3767, 54749}, {3934, 60277}, {5286, 54752}, {5395, 6658}, {5466, 23301}, {5485, 20081}, {5969, 15814}, {6194, 53104}, {6683, 43527}, {7612, 44434}, {7617, 10302}, {7709, 54482}, {7735, 60136}, {7736, 60105}, {7752, 10290}, {7757, 17503}, {7763, 54841}, {7774, 11606}, {7779, 54122}, {7786, 11149}, {7867, 10159}, {7921, 54614}, {8586, 60128}, {8587, 13330}, {8781, 8782}, {9464, 40016}, {9466, 60286}, {9770, 60271}, {9865, 60180}, {11163, 54737}, {11170, 18502}, {11172, 44367}, {11668, 22712}, {14231, 45542}, {14245, 45543}, {14458, 44422}, {14881, 55009}, {16925, 18841}, {17578, 54894}, {18840, 32961}, {18842, 33007}, {18843, 33280}, {18906, 43529}, {21057, 60244}, {31239, 60278}, {32450, 53105}, {32452, 33002}, {32469, 60189}, {32969, 60183}, {32984, 60143}, {32985, 54616}, {44562, 51584}, {47586, 51170}, {52942, 60281}, {55801, 60238}

X(60177) = midpoint of X(i) and X(j) for these {i,j}: {7757, 17503}
X(60177) = reflection of X(i) in X(j) for these {i,j}: {51584, 44562}
X(60177) = isogonal conjugate of X(39560)
X(60177) = pole of line {7777, 60177} with respect to the Kiepert hyperbola
X(60177) = pole of line {33687, 39560} with respect to the Wallace hyperbola
X(60177) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(32447)}}, {{A, B, C, X(6), X(7897)}}, {{A, B, C, X(25), X(32966)}}, {{A, B, C, X(39), X(574)}}, {{A, B, C, X(194), X(3266)}}, {{A, B, C, X(251), X(7912)}}, {{A, B, C, X(263), X(41517)}}, {{A, B, C, X(264), X(9227)}}, {{A, B, C, X(276), X(18372)}}, {{A, B, C, X(308), X(45090)}}, {{A, B, C, X(325), X(7766)}}, {{A, B, C, X(427), X(3552)}}, {{A, B, C, X(511), X(576)}}, {{A, B, C, X(625), X(1383)}}, {{A, B, C, X(661), X(21057)}}, {{A, B, C, X(693), X(38247)}}, {{A, B, C, X(1031), X(42407)}}, {{A, B, C, X(1502), X(42286)}}, {{A, B, C, X(1992), X(41136)}}, {{A, B, C, X(2080), X(3095)}}, {{A, B, C, X(2998), X(3613)}}, {{A, B, C, X(3094), X(5038)}}, {{A, B, C, X(3228), X(18575)}}, {{A, B, C, X(3906), X(32479)}}, {{A, B, C, X(4232), X(33006)}}, {{A, B, C, X(4235), X(31857)}}, {{A, B, C, X(6353), X(32993)}}, {{A, B, C, X(6658), X(8889)}}, {{A, B, C, X(6995), X(32961)}}, {{A, B, C, X(7378), X(16925)}}, {{A, B, C, X(7408), X(32969)}}, {{A, B, C, X(7409), X(32970)}}, {{A, B, C, X(7774), X(7779)}}, {{A, B, C, X(7775), X(52898)}}, {{A, B, C, X(7821), X(39955)}}, {{A, B, C, X(7867), X(59180)}}, {{A, B, C, X(8586), X(13330)}}, {{A, B, C, X(8782), X(47734)}}, {{A, B, C, X(9770), X(44367)}}, {{A, B, C, X(10487), X(15814)}}, {{A, B, C, X(11059), X(20081)}}, {{A, B, C, X(17042), X(39389)}}, {{A, B, C, X(18019), X(38256)}}, {{A, B, C, X(20105), X(57518)}}, {{A, B, C, X(22336), X(56057)}}, {{A, B, C, X(23297), X(42551)}}, {{A, B, C, X(26235), X(31276)}}, {{A, B, C, X(32480), X(42008)}}, {{A, B, C, X(32984), X(52301)}}, {{A, B, C, X(33007), X(52284)}}, {{A, B, C, X(40429), X(45819)}}

X(60178) = X(2)X(1570)∩X(4)X(7769)

Barycentrics    (2*(a^2-b^2)^2-3*(a^2+b^2)*c^2+3*c^4)*(2*a^4+3*b^4-3*b^2*c^2+2*c^4-a^2*(3*b^2+4*c^2)) : :

X(60178) lies on the Kiepert hyperbola and on these lines: {2, 1570}, {3, 54873}, {4, 7769}, {6, 60073}, {69, 53103}, {76, 33249}, {83, 31489}, {94, 11059}, {98, 39899}, {99, 60189}, {141, 60248}, {183, 53104}, {262, 10011}, {305, 11140}, {325, 7607}, {381, 54767}, {439, 5475}, {598, 9771}, {671, 8716}, {1007, 7612}, {2996, 7763}, {3055, 60096}, {3406, 7814}, {3407, 17005}, {3815, 60093}, {3926, 43681}, {3972, 5395}, {5392, 57518}, {5476, 54523}, {5485, 7799}, {7736, 60263}, {7752, 60117}, {7757, 54750}, {7777, 60104}, {7778, 60101}, {7786, 60151}, {7868, 60187}, {7925, 60128}, {8176, 54476}, {10153, 11163}, {11057, 54805}, {11167, 41133}, {11174, 60186}, {11184, 60103}, {11668, 37688}, {15491, 43527}, {15589, 53859}, {22110, 60220}, {32829, 38259}, {32832, 60285}, {32833, 60200}, {33235, 53109}, {33250, 53107}, {34229, 60123}, {35927, 53101}, {37690, 60212}, {37803, 60256}, {37804, 60255}, {41895, 53142}, {42535, 54906}, {43688, 51373}, {48784, 60269}, {48785, 60270}, {50974, 60185}

X(60178) = isogonal conjugate of X(39764)
X(60178) = isotomic conjugate of X(37637)
X(60178) = trilinear pole of line {44369, 523}
X(60178) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 39764}, {31, 37637}, {1973, 11898}
X(60178) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 37637}, {3, 39764}, {6337, 11898}
X(60178) = X(i)-cross conjugate of X(j) for these {i, j}: {50644, 35136}
X(60178) = pole of line {11898, 37637} with respect to the Wallace hyperbola
X(60178) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(1570)}}, {{A, B, C, X(25), X(33249)}}, {{A, B, C, X(69), X(34803)}}, {{A, B, C, X(141), X(31489)}}, {{A, B, C, X(183), X(37647)}}, {{A, B, C, X(249), X(40801)}}, {{A, B, C, X(264), X(4590)}}, {{A, B, C, X(305), X(7769)}}, {{A, B, C, X(427), X(33233)}}, {{A, B, C, X(439), X(52299)}}, {{A, B, C, X(458), X(10011)}}, {{A, B, C, X(599), X(9771)}}, {{A, B, C, X(1007), X(55972)}}, {{A, B, C, X(1502), X(42332)}}, {{A, B, C, X(3055), X(15271)}}, {{A, B, C, X(3314), X(17005)}}, {{A, B, C, X(3763), X(15491)}}, {{A, B, C, X(3815), X(7778)}}, {{A, B, C, X(5094), X(35297)}}, {{A, B, C, X(6340), X(34386)}}, {{A, B, C, X(6353), X(32988)}}, {{A, B, C, X(6393), X(14356)}}, {{A, B, C, X(6464), X(34154)}}, {{A, B, C, X(7736), X(37690)}}, {{A, B, C, X(7763), X(57518)}}, {{A, B, C, X(7777), X(7925)}}, {{A, B, C, X(7782), X(57799)}}, {{A, B, C, X(7799), X(11059)}}, {{A, B, C, X(8716), X(14608)}}, {{A, B, C, X(8797), X(40405)}}, {{A, B, C, X(8889), X(32989)}}, {{A, B, C, X(11163), X(41133)}}, {{A, B, C, X(11184), X(22110)}}, {{A, B, C, X(14489), X(56004)}}, {{A, B, C, X(15464), X(44558)}}, {{A, B, C, X(18023), X(57822)}}, {{A, B, C, X(18575), X(36953)}}, {{A, B, C, X(25322), X(52154)}}, {{A, B, C, X(33250), X(52298)}}, {{A, B, C, X(38282), X(52250)}}, {{A, B, C, X(40410), X(42407)}}, {{A, B, C, X(41259), X(51373)}}
X(60178) = barycentric quotient X(i)/X(j) for these (i, j): {2, 37637}, {6, 39764}, {69, 11898}

X(60179) = X(2)X(18020)∩X(76)X(249)

Barycentrics    (a-b)^2*(a+b)^2*(a-c)^2*(a+c)^2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4+b^4-(a^2+b^2)*c^2)*(a^4-a^2*b^2-b^2*c^2+c^4) : :

X(60179) lies on the Kiepert hyperbola and on these lines: {2, 18020}, {4, 23582}, {30, 54808}, {76, 249}, {94, 16081}, {98, 54380}, {99, 52459}, {112, 46040}, {250, 262}, {287, 16080}, {290, 46105}, {459, 44181}, {648, 14223}, {671, 6531}, {685, 4240}, {877, 17932}, {878, 4230}, {1916, 57260}, {2052, 23964}, {2394, 2966}, {2715, 22456}, {4444, 36104}, {4590, 40824}, {9166, 54501}, {9381, 53245}, {12150, 54743}, {15388, 43678}, {20031, 60338}, {31636, 60133}, {32545, 54057}, {32671, 60074}, {32696, 60106}, {35906, 40890}, {37765, 54554}, {41175, 47105}, {45031, 60140}, {53699, 58262}

X(60179) = isogonal conjugate of X(41172)
X(60179) = trilinear pole of line {250, 648}
X(60179) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 41172}, {48, 868}, {63, 44114}, {125, 1755}, {232, 2632}, {237, 20902}, {240, 3269}, {293, 59805}, {304, 58260}, {339, 9417}, {511, 3708}, {656, 3569}, {661, 684}, {798, 6333}, {810, 2799}, {822, 16230}, {1109, 3289}, {1577, 39469}, {1934, 47418}, {1956, 38974}, {1959, 20975}, {2211, 17879}, {2491, 14208}, {2631, 32112}, {2643, 36212}, {3120, 42702}, {4466, 5360}, {6530, 37754}, {15526, 57653}, {17994, 24018}, {23996, 51404}, {36051, 41181}, {36060, 51429}, {53521, 55232}
X(60179) = X(i)-vertex conjugate of X(j) for these {i, j}: {878, 60179}, {14600, 60199}
X(60179) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 41172}, {114, 41181}, {132, 59805}, {1249, 868}, {1560, 51429}, {3162, 44114}, {31998, 6333}, {36830, 684}, {36899, 125}, {39045, 38974}, {39058, 339}, {39062, 2799}, {39085, 3269}, {40596, 3569}, {50938, 57430}
X(60179) = X(i)-Ceva conjugate of X(j) for these {i, j}: {41174, 57991}
X(60179) = X(i)-cross conjugate of X(j) for these {i, j}: {6, 41173}, {98, 22456}, {230, 107}, {287, 2966}, {297, 648}, {1503, 99}, {1691, 112}, {1971, 110}, {6531, 685}, {11646, 935}, {31636, 43187}, {45031, 41074}, {52081, 39291}, {53475, 1289}, {53493, 52998}, {53499, 30247}, {53500, 1301}, {57742, 57991}
X(60179) = pole of line {41181, 51429} with respect to the polar circle
X(60179) = pole of line {41172, 41181} with respect to the Wallace hyperbola
X(60179) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(878)}}, {{A, B, C, X(25), X(50437)}}, {{A, B, C, X(249), X(2715)}}, {{A, B, C, X(287), X(35912)}}, {{A, B, C, X(297), X(47105)}}, {{A, B, C, X(340), X(37765)}}, {{A, B, C, X(524), X(1990)}}, {{A, B, C, X(648), X(53155)}}, {{A, B, C, X(1503), X(6393)}}, {{A, B, C, X(1691), X(2211)}}, {{A, B, C, X(1971), X(3289)}}, {{A, B, C, X(2697), X(53200)}}, {{A, B, C, X(4235), X(4240)}}, {{A, B, C, X(4590), X(32230)}}, {{A, B, C, X(6531), X(53149)}}, {{A, B, C, X(14600), X(40823)}}, {{A, B, C, X(16077), X(18020)}}, {{A, B, C, X(34537), X(34538)}}, {{A, B, C, X(34539), X(53691)}}, {{A, B, C, X(36212), X(43952)}}, {{A, B, C, X(44549), X(51404)}}, {{A, B, C, X(47443), X(55270)}}, {{A, B, C, X(57562), X(57991)}}, {{A, B, C, X(57732), X(57926)}}
X(60179) = barycentric product X(i)*X(j) for these (i, j): {4, 57991}, {107, 17932}, {110, 22456}, {112, 43187}, {162, 36036}, {250, 290}, {264, 57742}, {297, 57562}, {685, 99}, {1910, 46254}, {2395, 55270}, {2715, 6331}, {2966, 648}, {4590, 6531}, {16081, 249}, {18020, 98}, {18024, 57655}, {20031, 4563}, {23357, 60199}, {23582, 287}, {23964, 57799}, {23977, 55274}, {23999, 293}, {24000, 336}, {24041, 36120}, {31614, 53149}, {31636, 44183}, {32230, 6394}, {32696, 670}, {34537, 57260}, {35278, 41074}, {35912, 42308}, {36084, 811}, {36104, 799}, {41173, 877}, {41174, 6}, {43665, 47443}, {43754, 6528}
X(60179) = barycentric quotient X(i)/X(j) for these (i, j): {4, 868}, {6, 41172}, {25, 44114}, {98, 125}, {99, 6333}, {107, 16230}, {110, 684}, {112, 3569}, {230, 41181}, {232, 59805}, {248, 3269}, {249, 36212}, {250, 511}, {287, 15526}, {290, 339}, {293, 2632}, {297, 35088}, {336, 17879}, {468, 51429}, {648, 2799}, {685, 523}, {879, 5489}, {1304, 32112}, {1576, 39469}, {1821, 20902}, {1910, 3708}, {1971, 38974}, {1974, 58260}, {1976, 20975}, {2715, 647}, {2966, 525}, {4230, 41167}, {4590, 6393}, {6531, 115}, {9154, 51258}, {10313, 39000}, {11610, 38356}, {14355, 16186}, {14602, 47418}, {16081, 338}, {16318, 57430}, {17932, 3265}, {17974, 2972}, {18020, 325}, {19128, 38987}, {20031, 2501}, {22456, 850}, {23357, 3289}, {23582, 297}, {23964, 232}, {23977, 55275}, {23999, 40703}, {24000, 240}, {31636, 127}, {32230, 6530}, {32696, 512}, {32713, 17994}, {35912, 1650}, {36036, 14208}, {36084, 656}, {36104, 661}, {36120, 1109}, {37183, 47429}, {41173, 879}, {41174, 76}, {41932, 51404}, {41937, 2211}, {43187, 3267}, {43754, 520}, {44089, 2679}, {44183, 34138}, {46254, 46238}, {47443, 2421}, {52916, 33752}, {53149, 8029}, {53173, 23616}, {53174, 35442}, {53691, 35909}, {55270, 2396}, {57260, 3124}, {57562, 287}, {57655, 237}, {57742, 3}, {57799, 36793}, {57991, 69}, {59153, 58070}, {60199, 23962}
X(60179) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4240, 34761, 685}

X(60180) = X(2)X(59535)∩X(4)X(538)

Barycentrics    (2*a^2*b^2-(a^2+b^2)*c^2-3*c^4)*(a^2*(b^2-2*c^2)+b^2*(3*b^2+c^2)) : :
X(60180) = -3*X[5485]+2*X[14711], -3*X[31981]+X[47102]

X(60180) lies on the Kiepert hyperbola and on these lines: {2, 59535}, {4, 538}, {6, 33685}, {39, 18841}, {76, 33184}, {83, 1975}, {98, 1350}, {99, 54839}, {194, 5395}, {262, 698}, {305, 34087}, {325, 60095}, {511, 3424}, {523, 43668}, {524, 14458}, {525, 60106}, {543, 55009}, {598, 11055}, {599, 60181}, {671, 7788}, {702, 45092}, {712, 54933}, {726, 54668}, {732, 60132}, {2023, 56064}, {2782, 60140}, {2799, 60226}, {3094, 60099}, {3406, 13085}, {3407, 5039}, {3849, 54614}, {3906, 43674}, {3934, 60183}, {5485, 14711}, {5921, 60147}, {5976, 60073}, {6194, 60336}, {7607, 37450}, {7610, 54644}, {7612, 22712}, {7786, 60100}, {7819, 43527}, {7837, 54539}, {7840, 54540}, {7866, 10159}, {8782, 60136}, {9300, 54773}, {9466, 18840}, {9740, 54866}, {9741, 54616}, {9766, 14492}, {9770, 60127}, {9830, 54481}, {9865, 60177}, {10033, 54747}, {10302, 40727}, {11054, 54752}, {11148, 54639}, {11163, 54905}, {11165, 60238}, {11184, 60192}, {11645, 54802}, {13468, 60175}, {14484, 44422}, {14614, 54906}, {16509, 60131}, {20081, 38259}, {31981, 47102}, {32515, 60115}, {33180, 60285}, {33200, 43681}, {37671, 60218}, {40718, 50614}, {44434, 60327}, {44562, 55774}, {47286, 54751}, {51123, 60239}

X(60180) = reflection of X(i) in X(j) for these {i,j}: {32474, 39}
X(60180) = isogonal conjugate of X(41412)
X(60180) = isotomic conjugate of X(14614)
X(60180) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 41412}, {31, 14614}, {163, 32472}, {41622, 46289}
X(60180) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 14614}, {3, 41412}, {39, 41622}, {115, 32472}
X(60180) = pole of line {14614, 33685} with respect to the Wallace hyperbola
X(60180) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(33184)}}, {{A, B, C, X(39), X(9605)}}, {{A, B, C, X(264), X(6664)}}, {{A, B, C, X(305), X(525)}}, {{A, B, C, X(325), X(8667)}}, {{A, B, C, X(427), X(11286)}}, {{A, B, C, X(428), X(7866)}}, {{A, B, C, X(511), X(1350)}}, {{A, B, C, X(524), X(7788)}}, {{A, B, C, X(599), X(41624)}}, {{A, B, C, X(698), X(23878)}}, {{A, B, C, X(1502), X(3228)}}, {{A, B, C, X(1975), X(42551)}}, {{A, B, C, X(2799), X(5969)}}, {{A, B, C, X(3094), X(5039)}}, {{A, B, C, X(3095), X(37479)}}, {{A, B, C, X(3425), X(6464)}}, {{A, B, C, X(3906), X(52229)}}, {{A, B, C, X(5064), X(7819)}}, {{A, B, C, X(5188), X(40268)}}, {{A, B, C, X(6995), X(33196)}}, {{A, B, C, X(7249), X(57725)}}, {{A, B, C, X(7714), X(33180)}}, {{A, B, C, X(7757), X(8024)}}, {{A, B, C, X(7758), X(57852)}}, {{A, B, C, X(9164), X(48911)}}, {{A, B, C, X(9464), X(11055)}}, {{A, B, C, X(9466), X(40022)}}, {{A, B, C, X(9764), X(20023)}}, {{A, B, C, X(9766), X(37671)}}, {{A, B, C, X(11059), X(14711)}}, {{A, B, C, X(14618), X(47847)}}, {{A, B, C, X(14906), X(39951)}}, {{A, B, C, X(17132), X(30519)}}, {{A, B, C, X(18361), X(34898)}}, {{A, B, C, X(18848), X(34129)}}, {{A, B, C, X(25322), X(44558)}}, {{A, B, C, X(29011), X(56004)}}, {{A, B, C, X(29322), X(56362)}}, {{A, B, C, X(33706), X(46807)}}, {{A, B, C, X(36897), X(42359)}}, {{A, B, C, X(37450), X(52282)}}, {{A, B, C, X(40801), X(52581)}}, {{A, B, C, X(41079), X(52752)}}
X(60180) = barycentric product X(i)*X(j) for these (i, j): {1502, 51918}, {39639, 850}
X(60180) = barycentric quotient X(i)/X(j) for these (i, j): {2, 14614}, {6, 41412}, {141, 41622}, {523, 32472}, {39639, 110}, {51918, 32}, {60106, 57459}

X(60181) = X(4)X(754)∩X(262)X(732)

Barycentrics    (a^4+b^4-3*(a^2+b^2)*c^2-2*c^4)*(a^4-3*a^2*b^2-2*b^4-3*b^2*c^2+c^4) : :
X(60181) = -3*X[6308]+2*X[47101]

X(60181) lies on the Kiepert hyperbola and on these lines: {4, 754}, {6, 54773}, {76, 11287}, {83, 5305}, {98, 13468}, {99, 54749}, {115, 54822}, {183, 60218}, {262, 732}, {385, 54539}, {485, 6275}, {486, 6274}, {524, 14492}, {538, 3399}, {543, 9302}, {598, 12156}, {599, 60180}, {671, 37671}, {1352, 14484}, {1916, 14994}, {2896, 2996}, {3424, 29012}, {3767, 18841}, {3830, 54716}, {3849, 54566}, {5485, 11648}, {6054, 54978}, {6292, 7738}, {6308, 47101}, {7610, 60175}, {7612, 9751}, {7615, 54826}, {7620, 54856}, {7788, 60095}, {7795, 60183}, {7828, 60100}, {7832, 56059}, {7837, 54487}, {8290, 60104}, {8357, 43676}, {8362, 10159}, {8556, 11167}, {8667, 14458}, {8781, 9478}, {9166, 54841}, {9300, 54509}, {9740, 54519}, {9770, 54523}, {10302, 52229}, {11160, 54889}, {11165, 60131}, {11184, 54645}, {12073, 43674}, {16509, 60238}, {17766, 54668}, {18845, 20088}, {22329, 54906}, {24273, 60215}, {31268, 60278}, {33025, 43681}, {33202, 60285}, {33706, 34505}, {41624, 54905}, {51122, 60277}, {53475, 60213}

X(60181) = reflection of X(i) in X(j) for these {i,j}: {54822, 115}
X(60181) = isogonal conjugate of X(41413)
X(60181) = isotomic conjugate of X(41624)
X(60181) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 41413}, {31, 41624}, {163, 32473}
X(60181) = X(i)-vertex conjugate of X(j) for these {i, j}: {2353, 60213}
X(60181) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 41624}, {3, 41413}, {115, 32473}, {6292, 41623}
X(60181) = pole of line {41413, 41623} with respect to the Wallace hyperbola
X(60181) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(11287)}}, {{A, B, C, X(95), X(6664)}}, {{A, B, C, X(141), X(32085)}}, {{A, B, C, X(183), X(9766)}}, {{A, B, C, X(251), X(755)}}, {{A, B, C, X(308), X(43098)}}, {{A, B, C, X(325), X(13468)}}, {{A, B, C, X(428), X(6292)}}, {{A, B, C, X(524), X(37671)}}, {{A, B, C, X(525), X(754)}}, {{A, B, C, X(599), X(14614)}}, {{A, B, C, X(695), X(42288)}}, {{A, B, C, X(732), X(14994)}}, {{A, B, C, X(1494), X(9462)}}, {{A, B, C, X(3866), X(7738)}}, {{A, B, C, X(6353), X(33210)}}, {{A, B, C, X(7714), X(33202)}}, {{A, B, C, X(7751), X(57852)}}, {{A, B, C, X(7788), X(8667)}}, {{A, B, C, X(8024), X(14568)}}, {{A, B, C, X(8556), X(11163)}}, {{A, B, C, X(10130), X(12156)}}, {{A, B, C, X(11169), X(25322)}}, {{A, B, C, X(11648), X(52141)}}, {{A, B, C, X(12073), X(52229)}}, {{A, B, C, X(17983), X(44558)}}, {{A, B, C, X(18546), X(30786)}}, {{A, B, C, X(18823), X(40829)}}, {{A, B, C, X(31360), X(57408)}}, {{A, B, C, X(34138), X(44882)}}, {{A, B, C, X(34384), X(53197)}}, {{A, B, C, X(34572), X(38826)}}, {{A, B, C, X(41651), X(44772)}}, {{A, B, C, X(43094), X(51246)}}, {{A, B, C, X(56358), X(57725)}}
X(60181) = barycentric product X(i)*X(j) for these (i, j): {53885, 850}
X(60181) = barycentric quotient X(i)/X(j) for these (i, j): {2, 41624}, {6, 41413}, {523, 32473}, {3589, 41623}, {53885, 110}

X(60182) = X(2)X(55746)∩X(4)X(33751)

Barycentrics    (5*(a^2+b^2)+4*c^2)*(5*a^2+4*b^2+5*c^2) : :

X(60182) lies on the Kiepert hyperbola and on these lines: {2, 55746}, {3, 54582}, {4, 33751}, {5, 54477}, {30, 54813}, {83, 51127}, {98, 55856}, {140, 14492}, {262, 46219}, {297, 54791}, {550, 54717}, {632, 54734}, {1656, 14458}, {3424, 46935}, {3523, 54520}, {3525, 54707}, {3526, 54643}, {3533, 60127}, {3589, 56059}, {3628, 54608}, {5056, 54519}, {5067, 54612}, {5068, 54815}, {5070, 54851}, {6656, 45103}, {6704, 59266}, {6722, 11606}, {7375, 60307}, {7376, 60308}, {7388, 43562}, {7389, 43563}, {7395, 54585}, {7399, 54512}, {7550, 54809}, {7760, 60277}, {7768, 60100}, {7770, 17503}, {7859, 43676}, {7879, 43527}, {7883, 54616}, {7892, 54540}, {7901, 54539}, {8370, 54478}, {9167, 60271}, {10159, 51126}, {11289, 12817}, {11290, 12816}, {11303, 54479}, {11304, 54480}, {11331, 60120}, {14488, 15720}, {14788, 54879}, {15712, 54890}, {16045, 32532}, {32821, 55759}, {32839, 60201}, {32867, 60259}, {32956, 60281}, {32971, 54896}, {32974, 54642}, {34664, 54924}, {35018, 60132}, {39284, 52289}, {47355, 60278}, {52292, 60141}, {52293, 60125}, {54748, 55767}, {55859, 60192}, {55860, 60175}

X(60182) = isogonal conjugate of X(41940)
X(60182) = isotomic conjugate of X(51128)
X(60182) = pole of line {41940, 51128} with respect to the Wallace hyperbola
X(60182) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55672)}}, {{A, B, C, X(140), X(52289)}}, {{A, B, C, X(141), X(51127)}}, {{A, B, C, X(297), X(55856)}}, {{A, B, C, X(458), X(46219)}}, {{A, B, C, X(1656), X(11331)}}, {{A, B, C, X(3589), X(22336)}}, {{A, B, C, X(6656), X(52293)}}, {{A, B, C, X(7770), X(52292)}}, {{A, B, C, X(14387), X(57895)}}, {{A, B, C, X(14861), X(53024)}}, {{A, B, C, X(16045), X(53857)}}, {{A, B, C, X(26861), X(34386)}}, {{A, B, C, X(40421), X(46326)}}, {{A, B, C, X(46935), X(52283)}}

X(60183) = X(2)X(55762)∩X(4)X(3763)

Barycentrics    (3*a^2+5*b^2+3*c^2)*(3*(a^2+b^2)+5*c^2) : :

X(60183) lies on the Kiepert hyperbola and on these lines: {2, 55762}, {3, 55741}, {4, 3763}, {5, 43951}, {20, 60327}, {30, 54815}, {69, 43527}, {83, 3619}, {98, 3525}, {140, 47586}, {141, 18841}, {262, 5067}, {315, 53102}, {376, 54519}, {598, 32006}, {631, 3424}, {632, 54921}, {671, 33230}, {1131, 7376}, {1132, 7375}, {1656, 60118}, {1916, 32951}, {2996, 32956}, {3090, 14484}, {3091, 54706}, {3096, 53109}, {3407, 14069}, {3523, 60324}, {3524, 7822}, {3526, 60336}, {3528, 6292}, {3533, 43537}, {3544, 14488}, {3545, 54520}, {3618, 60100}, {3628, 60331}, {3788, 11167}, {3934, 60180}, {5056, 60328}, {5071, 14492}, {5286, 60143}, {5395, 16045}, {6656, 38259}, {6683, 60099}, {6816, 54705}, {7388, 43561}, {7389, 43560}, {7397, 60167}, {7402, 45100}, {7745, 60284}, {7763, 60217}, {7770, 18845}, {7784, 60281}, {7795, 60181}, {7797, 54748}, {7803, 10302}, {7827, 60286}, {7832, 60218}, {7841, 60113}, {7859, 60277}, {7867, 60142}, {7874, 60175}, {7879, 54639}, {7911, 54646}, {7940, 60220}, {8364, 32872}, {8370, 54476}, {8796, 52283}, {11001, 54477}, {11289, 43556}, {11290, 43557}, {11303, 43552}, {11304, 43553}, {11606, 16043}, {14039, 54539}, {15702, 60150}, {15709, 54866}, {16898, 59266}, {16988, 32960}, {17283, 58012}, {17307, 32022}, {17538, 60326}, {17559, 60153}, {17582, 60152}, {18840, 34573}, {18842, 20582}, {19824, 27797}, {21356, 60238}, {21358, 54616}, {31183, 60243}, {32450, 55744}, {32829, 60212}, {32831, 60259}, {32832, 60202}, {32838, 32953}, {32955, 60260}, {32957, 60190}, {32958, 60234}, {32968, 60105}, {32969, 60177}, {32970, 60184}, {32984, 54737}, {32985, 54901}, {33190, 41895}, {33194, 60201}, {33221, 43688}, {33223, 54823}, {33231, 54906}, {33232, 53105}, {33285, 54540}, {34664, 54552}, {36484, 54946}, {38282, 60125}, {41106, 54582}, {41254, 46214}, {43531, 53665}, {43676, 52713}, {46226, 60214}, {49138, 54917}, {52288, 60161}, {52299, 60141}

X(60183) = isogonal conjugate of X(43136)
X(60183) = trilinear pole of line {47095, 47919}
X(60183) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 43136}, {48, 7408}
X(60183) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 43136}, {1249, 7408}
X(60183) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(31884)}}, {{A, B, C, X(69), X(3763)}}, {{A, B, C, X(141), X(3619)}}, {{A, B, C, X(257), X(7317)}}, {{A, B, C, X(290), X(24861)}}, {{A, B, C, X(297), X(3525)}}, {{A, B, C, X(308), X(36611)}}, {{A, B, C, X(327), X(36948)}}, {{A, B, C, X(335), X(5551)}}, {{A, B, C, X(419), X(32951)}}, {{A, B, C, X(420), X(16043)}}, {{A, B, C, X(458), X(5067)}}, {{A, B, C, X(468), X(33230)}}, {{A, B, C, X(631), X(52283)}}, {{A, B, C, X(966), X(17283)}}, {{A, B, C, X(996), X(56335)}}, {{A, B, C, X(1220), X(40026)}}, {{A, B, C, X(1224), X(56054)}}, {{A, B, C, X(3090), X(52288)}}, {{A, B, C, X(3296), X(39749)}}, {{A, B, C, X(3524), X(11331)}}, {{A, B, C, X(3618), X(6664)}}, {{A, B, C, X(4648), X(17307)}}, {{A, B, C, X(5071), X(52289)}}, {{A, B, C, X(5117), X(14069)}}, {{A, B, C, X(5224), X(53665)}}, {{A, B, C, X(5936), X(42326)}}, {{A, B, C, X(6330), X(18853)}}, {{A, B, C, X(6353), X(32956)}}, {{A, B, C, X(6464), X(14491)}}, {{A, B, C, X(6531), X(46217)}}, {{A, B, C, X(6620), X(32953)}}, {{A, B, C, X(6656), X(38282)}}, {{A, B, C, X(7770), X(52299)}}, {{A, B, C, X(7774), X(16988)}}, {{A, B, C, X(7803), X(26235)}}, {{A, B, C, X(8797), X(14387)}}, {{A, B, C, X(8889), X(16045)}}, {{A, B, C, X(9292), X(41440)}}, {{A, B, C, X(9780), X(31183)}}, {{A, B, C, X(13472), X(40802)}}, {{A, B, C, X(15740), X(48872)}}, {{A, B, C, X(15998), X(41791)}}, {{A, B, C, X(16020), X(17308)}}, {{A, B, C, X(17040), X(42286)}}, {{A, B, C, X(18854), X(42330)}}, {{A, B, C, X(19222), X(34816)}}, {{A, B, C, X(19824), X(24589)}}, {{A, B, C, X(20023), X(31239)}}, {{A, B, C, X(20399), X(57504)}}, {{A, B, C, X(20582), X(21356)}}, {{A, B, C, X(22270), X(40512)}}, {{A, B, C, X(32838), X(40814)}}, {{A, B, C, X(33190), X(52290)}}, {{A, B, C, X(33232), X(37453)}}, {{A, B, C, X(34403), X(48881)}}, {{A, B, C, X(36890), X(40517)}}, {{A, B, C, X(36952), X(42287)}}, {{A, B, C, X(39708), X(42318)}}, {{A, B, C, X(39716), X(43733)}}, {{A, B, C, X(40028), X(56061)}}, {{A, B, C, X(43734), X(57725)}}
X(60183) = barycentric quotient X(i)/X(j) for these (i, j): {4, 7408}, {6, 43136}

X(60184) = X(32)X(671)∩X(76)X(187)

Barycentrics    (2*a^4+a^2*b^2+2*b^4-(a^2+b^2)*c^2)*(2*a^4-b^2*c^2+2*c^4+a^2*(-b^2+c^2)) : :

X(60184) lies on the Kiepert hyperbola and on these lines: {2, 14567}, {3, 60126}, {4, 11842}, {5, 60148}, {6, 33687}, {32, 671}, {76, 187}, {83, 7844}, {182, 7608}, {194, 10290}, {262, 575}, {381, 54805}, {385, 43688}, {598, 7787}, {669, 5466}, {1078, 10302}, {1153, 60131}, {1691, 60128}, {1916, 5939}, {2996, 6658}, {3398, 11170}, {3399, 11171}, {4027, 8781}, {5038, 10484}, {5306, 54823}, {5395, 32993}, {5485, 33007}, {7607, 8590}, {7735, 11606}, {7774, 35005}, {7779, 40824}, {7785, 54841}, {7808, 60238}, {7815, 10159}, {7852, 43527}, {7897, 43529}, {7915, 60278}, {8787, 42010}, {10352, 56064}, {10485, 60098}, {10788, 22515}, {10796, 54482}, {11177, 54731}, {12110, 60189}, {12150, 45103}, {16925, 18840}, {16989, 60105}, {17503, 39563}, {18841, 32961}, {18842, 33006}, {20088, 54822}, {23357, 52940}, {32532, 52942}, {32970, 60183}, {32984, 54616}, {32985, 60143}, {33280, 60219}, {34087, 41309}, {40016, 52898}, {42535, 60233}, {43532, 51523}, {49102, 55009}, {50689, 54894}

X(60184) = isogonal conjugate of X(44453)
X(60184) = isotomic conjugate of X(7897)
X(60184) = X(i)-vertex conjugate of X(j) for these {i, j}: {2, 47643}, {32, 60128}
X(60184) = pole of line {7806, 60184} with respect to the Kiepert hyperbola
X(60184) = pole of line {7897, 44453} with respect to the Wallace hyperbola
X(60184) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(11842)}}, {{A, B, C, X(6), X(39560)}}, {{A, B, C, X(25), X(699)}}, {{A, B, C, X(32), X(187)}}, {{A, B, C, X(111), X(3224)}}, {{A, B, C, X(182), X(575)}}, {{A, B, C, X(251), X(7793)}}, {{A, B, C, X(263), X(1691)}}, {{A, B, C, X(385), X(7766)}}, {{A, B, C, X(427), X(32966)}}, {{A, B, C, X(576), X(8590)}}, {{A, B, C, X(733), X(7816)}}, {{A, B, C, X(1031), X(2165)}}, {{A, B, C, X(2697), X(54114)}}, {{A, B, C, X(2980), X(2998)}}, {{A, B, C, X(3398), X(11171)}}, {{A, B, C, X(4027), X(12829)}}, {{A, B, C, X(4232), X(33007)}}, {{A, B, C, X(4235), X(11636)}}, {{A, B, C, X(4590), X(45819)}}, {{A, B, C, X(5038), X(10485)}}, {{A, B, C, X(5276), X(16996)}}, {{A, B, C, X(5939), X(14382)}}, {{A, B, C, X(6353), X(6658)}}, {{A, B, C, X(6995), X(16925)}}, {{A, B, C, X(7378), X(32961)}}, {{A, B, C, X(7408), X(32970)}}, {{A, B, C, X(7409), X(32969)}}, {{A, B, C, X(7735), X(7779)}}, {{A, B, C, X(7780), X(39955)}}, {{A, B, C, X(7787), X(10130)}}, {{A, B, C, X(7806), X(7897)}}, {{A, B, C, X(7815), X(59180)}}, {{A, B, C, X(7817), X(9464)}}, {{A, B, C, X(7844), X(27366)}}, {{A, B, C, X(7932), X(8024)}}, {{A, B, C, X(8601), X(46316)}}, {{A, B, C, X(8770), X(51450)}}, {{A, B, C, X(8889), X(32993)}}, {{A, B, C, X(15321), X(56057)}}, {{A, B, C, X(16995), X(16998)}}, {{A, B, C, X(32085), X(38262)}}, {{A, B, C, X(32985), X(52301)}}, {{A, B, C, X(33006), X(52284)}}, {{A, B, C, X(34288), X(35511)}}, {{A, B, C, X(39750), X(52996)}}, {{A, B, C, X(40103), X(54413)}}, {{A, B, C, X(45838), X(52395)}}, {{A, B, C, X(46806), X(57692)}}, {{A, B, C, X(52133), X(56042)}}, {{A, B, C, X(52942), X(53857)}}, {{A, B, C, X(55997), X(56353)}}

X(60185) = X(2)X(21968)∩X(4)X(22331)

Barycentrics    (7*a^4-2*a^2*b^2+7*b^4-8*(a^2+b^2)*c^2+c^4)*(7*a^4+b^4-8*b^2*c^2+7*c^4-2*a^2*(4*b^2+c^2)) : :

X(60185) lies on the Kiepert hyperbola and on these lines: {2, 21968}, {3, 43681}, {4, 22331}, {5, 60145}, {6, 54523}, {30, 38259}, {76, 3524}, {83, 5071}, {115, 54767}, {230, 60150}, {376, 2996}, {381, 18845}, {383, 43557}, {542, 60073}, {598, 41106}, {631, 60285}, {671, 11001}, {1080, 43556}, {1285, 54714}, {1370, 13582}, {1503, 60322}, {1513, 47586}, {2394, 59549}, {3525, 10159}, {3528, 43676}, {3544, 53102}, {3545, 5395}, {3830, 60113}, {3845, 54476}, {5067, 43527}, {5304, 54521}, {5306, 60127}, {5485, 13468}, {6055, 8781}, {6353, 56270}, {6776, 53103}, {6811, 60291}, {6813, 60292}, {6997, 60191}, {7386, 60255}, {7710, 60335}, {7714, 8796}, {7735, 14492}, {7736, 54645}, {7837, 60234}, {8556, 60143}, {8889, 60193}, {9300, 14494}, {9744, 11668}, {9752, 60325}, {9753, 54890}, {9755, 60333}, {9756, 52519}, {9766, 60240}, {9862, 54659}, {9993, 54717}, {10155, 14912}, {11177, 60104}, {11179, 60248}, {13579, 44442}, {13860, 60118}, {14039, 60151}, {14651, 60189}, {15682, 41895}, {15698, 60200}, {15702, 18840}, {16080, 38282}, {17008, 60214}, {17538, 60209}, {18362, 54873}, {23055, 60218}, {34229, 60217}, {37671, 40824}, {37689, 54519}, {37943, 52583}, {38227, 60323}, {41099, 53101}, {41151, 50992}, {43460, 54851}, {43530, 52299}, {43537, 58883}, {50974, 60178}, {53015, 60132}

X(60185) = reflection of X(i) in X(j) for these {i,j}: {54767, 115}
X(60185) = isogonal conjugate of X(44456)
X(60185) = trilinear pole of line {47463, 523}
X(60185) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 60322}, {25, 60150}, {3425, 47586}
X(60185) = X(i)-cross conjugate of X(j) for these {i, j}: {39874, 4}
X(60185) = pole of line {39874, 60185} with respect to the Kiepert hyperbola
X(60185) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(22331)}}, {{A, B, C, X(6), X(55705)}}, {{A, B, C, X(25), X(3431)}}, {{A, B, C, X(30), X(38282)}}, {{A, B, C, X(66), X(52154)}}, {{A, B, C, X(69), X(1989)}}, {{A, B, C, X(74), X(8770)}}, {{A, B, C, X(95), X(52187)}}, {{A, B, C, X(111), X(20421)}}, {{A, B, C, X(230), X(5641)}}, {{A, B, C, X(305), X(6344)}}, {{A, B, C, X(376), X(1300)}}, {{A, B, C, X(381), X(52299)}}, {{A, B, C, X(393), X(57822)}}, {{A, B, C, X(427), X(5071)}}, {{A, B, C, X(428), X(3525)}}, {{A, B, C, X(468), X(11001)}}, {{A, B, C, X(631), X(1179)}}, {{A, B, C, X(1138), X(40118)}}, {{A, B, C, X(1370), X(37943)}}, {{A, B, C, X(1494), X(34208)}}, {{A, B, C, X(1992), X(13468)}}, {{A, B, C, X(2165), X(16774)}}, {{A, B, C, X(2980), X(36948)}}, {{A, B, C, X(3147), X(34608)}}, {{A, B, C, X(3545), X(8889)}}, {{A, B, C, X(3563), X(11270)}}, {{A, B, C, X(4231), X(50739)}}, {{A, B, C, X(4232), X(19708)}}, {{A, B, C, X(5064), X(5067)}}, {{A, B, C, X(5094), X(41106)}}, {{A, B, C, X(5551), X(57726)}}, {{A, B, C, X(5627), X(6340)}}, {{A, B, C, X(5900), X(13575)}}, {{A, B, C, X(6055), X(51820)}}, {{A, B, C, X(6325), X(55029)}}, {{A, B, C, X(6531), X(54171)}}, {{A, B, C, X(6995), X(15702)}}, {{A, B, C, X(7317), X(57727)}}, {{A, B, C, X(7505), X(44442)}}, {{A, B, C, X(7735), X(37671)}}, {{A, B, C, X(7837), X(17008)}}, {{A, B, C, X(9300), X(34229)}}, {{A, B, C, X(9766), X(23055)}}, {{A, B, C, X(11738), X(21448)}}, {{A, B, C, X(13377), X(23054)}}, {{A, B, C, X(13452), X(40801)}}, {{A, B, C, X(14489), X(16835)}}, {{A, B, C, X(14491), X(39951)}}, {{A, B, C, X(14583), X(35912)}}, {{A, B, C, X(15464), X(21765)}}, {{A, B, C, X(15682), X(52290)}}, {{A, B, C, X(17040), X(34288)}}, {{A, B, C, X(17983), X(46212)}}, {{A, B, C, X(18361), X(44556)}}, {{A, B, C, X(18490), X(56358)}}, {{A, B, C, X(18852), X(40413)}}, {{A, B, C, X(26255), X(35473)}}, {{A, B, C, X(32085), X(52188)}}, {{A, B, C, X(34449), X(46412)}}, {{A, B, C, X(36612), X(57852)}}, {{A, B, C, X(36890), X(38749)}}, {{A, B, C, X(40103), X(53890)}}, {{A, B, C, X(40119), X(46423)}}, {{A, B, C, X(46087), X(56268)}}, {{A, B, C, X(46952), X(57895)}}

X(60186) = X(4)X(6680)∩X(5)X(60140)

Barycentrics    (3*(a^4+b^4)-(a^2+b^2)*c^2+2*c^4)*(3*a^4-a^2*b^2+2*b^4-b^2*c^2+3*c^4) : :

X(60186) lies on the Kiepert hyperbola and on these lines: {4, 6680}, {5, 60140}, {76, 32954}, {83, 8361}, {230, 60213}, {385, 60231}, {598, 7942}, {671, 7828}, {1352, 43537}, {1506, 18841}, {1916, 16984}, {2996, 33181}, {3054, 60187}, {3090, 54859}, {3399, 6683}, {3589, 7608}, {3767, 5485}, {3815, 56064}, {5395, 10583}, {7792, 8781}, {7795, 60143}, {7804, 54567}, {7806, 43529}, {7808, 60148}, {7832, 10302}, {7875, 60233}, {7886, 55009}, {7930, 8860}, {9873, 54565}, {10159, 37688}, {11159, 17503}, {11174, 60178}, {14484, 58851}, {14485, 18502}, {14568, 60216}, {15491, 53108}, {18840, 33195}, {25555, 53099}, {33201, 38259}, {35950, 60176}, {37350, 45103}, {37637, 60099}, {42011, 47352}, {44381, 53104}

X(60186) = isogonal conjugate of X(44499)
X(60186) = X(i)-vertex conjugate of X(j) for these {i, j}: {25, 60213}
X(60186) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(32954)}}, {{A, B, C, X(95), X(42286)}}, {{A, B, C, X(111), X(38826)}}, {{A, B, C, X(230), X(7792)}}, {{A, B, C, X(385), X(16984)}}, {{A, B, C, X(427), X(8361)}}, {{A, B, C, X(468), X(8369)}}, {{A, B, C, X(1799), X(6680)}}, {{A, B, C, X(2353), X(21448)}}, {{A, B, C, X(3266), X(7828)}}, {{A, B, C, X(3589), X(37688)}}, {{A, B, C, X(3767), X(11059)}}, {{A, B, C, X(4232), X(33197)}}, {{A, B, C, X(5094), X(11318)}}, {{A, B, C, X(6353), X(33181)}}, {{A, B, C, X(6995), X(33195)}}, {{A, B, C, X(7832), X(26235)}}, {{A, B, C, X(7844), X(30786)}}, {{A, B, C, X(7875), X(17004)}}, {{A, B, C, X(7942), X(9464)}}, {{A, B, C, X(8860), X(47352)}}, {{A, B, C, X(8889), X(33199)}}, {{A, B, C, X(9227), X(40405)}}, {{A, B, C, X(9516), X(17983)}}, {{A, B, C, X(11159), X(52292)}}, {{A, B, C, X(11169), X(36953)}}, {{A, B, C, X(11174), X(37637)}}, {{A, B, C, X(14357), X(37860)}}, {{A, B, C, X(14659), X(39389)}}, {{A, B, C, X(18023), X(40416)}}, {{A, B, C, X(25322), X(32085)}}, {{A, B, C, X(30537), X(44571)}}, {{A, B, C, X(33201), X(38282)}}, {{A, B, C, X(34129), X(40413)}}, {{A, B, C, X(37350), X(52293)}}, {{A, B, C, X(37647), X(44381)}}, {{A, B, C, X(40511), X(55958)}}, {{A, B, C, X(42407), X(57408)}}

X(60187) = X(4)X(7815)∩X(5)X(14485)

Barycentrics    (a^4-4*a^2*b^2+b^4-5*(a^2+b^2)*c^2)*(a^4-5*b^2*c^2+c^4-a^2*(5*b^2+4*c^2)) : :

X(60187) lies on the Kiepert hyperbola and on these lines: {3, 60115}, {4, 7815}, {5, 14485}, {32, 18842}, {76, 5024}, {83, 37688}, {98, 58446}, {141, 7608}, {182, 43537}, {183, 60096}, {262, 11477}, {598, 1078}, {626, 54724}, {671, 7847}, {3054, 60186}, {3363, 45103}, {3934, 15483}, {5077, 17503}, {5182, 8587}, {5395, 7793}, {5485, 7738}, {6292, 54822}, {7778, 11669}, {7787, 54639}, {7800, 54826}, {7808, 54616}, {7868, 60178}, {7883, 54804}, {7944, 54841}, {8860, 60239}, {10130, 30505}, {10352, 60136}, {11168, 54509}, {12150, 60283}, {16986, 60233}, {16988, 60231}, {17004, 60129}, {17006, 43528}, {18840, 31401}, {21358, 42011}, {34511, 55794}, {37637, 60215}, {37690, 53098}, {44377, 53108}, {53765, 54840}

X(60187) = isogonal conjugate of X(44500)
X(60187) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(8722)}}, {{A, B, C, X(32), X(5024)}}, {{A, B, C, X(39), X(46316)}}, {{A, B, C, X(95), X(9516)}}, {{A, B, C, X(111), X(42346)}}, {{A, B, C, X(141), X(37688)}}, {{A, B, C, X(182), X(11477)}}, {{A, B, C, X(183), X(14383)}}, {{A, B, C, X(308), X(41909)}}, {{A, B, C, X(468), X(8359)}}, {{A, B, C, X(1078), X(2373)}}, {{A, B, C, X(1799), X(7815)}}, {{A, B, C, X(3363), X(52293)}}, {{A, B, C, X(5077), X(52292)}}, {{A, B, C, X(7830), X(51454)}}, {{A, B, C, X(7868), X(37637)}}, {{A, B, C, X(7931), X(17006)}}, {{A, B, C, X(8770), X(42288)}}, {{A, B, C, X(8860), X(21358)}}, {{A, B, C, X(9462), X(11169)}}, {{A, B, C, X(16984), X(16988)}}, {{A, B, C, X(16986), X(17004)}}, {{A, B, C, X(17983), X(42286)}}, {{A, B, C, X(24861), X(45838)}}, {{A, B, C, X(30786), X(36952)}}, {{A, B, C, X(31401), X(40022)}}, {{A, B, C, X(31622), X(44182)}}, {{A, B, C, X(34161), X(52145)}}, {{A, B, C, X(36953), X(57895)}}, {{A, B, C, X(37860), X(40517)}}, {{A, B, C, X(39968), X(57408)}}, {{A, B, C, X(42351), X(57541)}}, {{A, B, C, X(44558), X(55958)}}

X(60188) = X(2)X(219)∩X(4)X(12)

Barycentrics    (a+b-c)*(a-b+c)*(b+c)*((a-b)^2*(a+b)-2*a*b*c-(a+b)*c^2)*(a^3-a^2*c-b^2*c+c^3-a*(b+c)^2) : :

X(60188) lies on the Kiepert hyperbola and on these lines: {1, 57719}, {2, 219}, {4, 12}, {7, 57722}, {10, 2318}, {37, 40149}, {57, 17758}, {71, 226}, {76, 345}, {94, 41226}, {98, 15439}, {181, 60108}, {200, 60227}, {278, 2197}, {281, 2052}, {321, 3694}, {388, 13726}, {459, 30457}, {464, 60156}, {498, 1754}, {671, 54952}, {1029, 3151}, {1214, 1446}, {1441, 25254}, {1751, 2259}, {2003, 54700}, {2051, 5219}, {2594, 57720}, {3136, 13576}, {3173, 5736}, {3487, 7066}, {3584, 54526}, {3666, 54739}, {3771, 60090}, {4551, 13405}, {5226, 60071}, {6358, 43683}, {7080, 43533}, {8232, 60170}, {8808, 41087}, {10056, 54516}, {10197, 60078}, {10198, 43531}, {11435, 17718}, {14534, 40412}, {15627, 16080}, {16577, 43682}, {17776, 34388}, {18391, 60112}, {23600, 60206}, {26095, 35320}, {26125, 60257}, {26893, 45964}, {28776, 60082}, {30588, 52358}, {33113, 40013}, {34258, 40422}, {37154, 56227}, {37225, 60086}, {37799, 40395}, {45701, 60079}, {48003, 56320}, {52383, 54528}, {56367, 58012}

X(60188) = isogonal conjugate of X(46882)
X(60188) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 46882}, {3, 46884}, {6, 54356}, {21, 2260}, {27, 23207}, {29, 14597}, {57, 8021}, {58, 40937}, {60, 2294}, {78, 46890}, {81, 14547}, {162, 52306}, {219, 46883}, {261, 40978}, {270, 18591}, {283, 1841}, {284, 942}, {333, 40956}, {442, 2150}, {593, 40967}, {604, 51978}, {1172, 4303}, {1333, 6734}, {1414, 33525}, {1789, 44095}, {1790, 1859}, {1838, 2193}, {2185, 40952}, {2189, 56839}, {2194, 5249}, {2299, 18607}, {2326, 39791}, {4282, 45926}, {5546, 50354}, {43729, 46887}
X(60188) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 46882}, {9, 54356}, {10, 40937}, {37, 6734}, {125, 52306}, {226, 18607}, {1214, 5249}, {3161, 51978}, {5452, 8021}, {36103, 46884}, {40586, 14547}, {40590, 942}, {40608, 33525}, {40611, 2260}, {47345, 1838}, {56325, 442}
X(60188) = X(i)-cross conjugate of X(j) for these {i, j}: {37, 943}, {650, 4551}, {11553, 7}, {57099, 4566}
X(60188) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3191)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(12), X(26942)}}, {{A, B, C, X(37), X(55)}}, {{A, B, C, X(63), X(56254)}}, {{A, B, C, X(65), X(278)}}, {{A, B, C, X(92), X(38955)}}, {{A, B, C, X(200), X(56255)}}, {{A, B, C, X(306), X(3085)}}, {{A, B, C, X(406), X(464)}}, {{A, B, C, X(451), X(3151)}}, {{A, B, C, X(525), X(5842)}}, {{A, B, C, X(650), X(14547)}}, {{A, B, C, X(943), X(40447)}}, {{A, B, C, X(1427), X(52422)}}, {{A, B, C, X(1441), X(8817)}}, {{A, B, C, X(2184), X(56195)}}, {{A, B, C, X(2259), X(40572)}}, {{A, B, C, X(2292), X(37225)}}, {{A, B, C, X(3136), X(15149)}}, {{A, B, C, X(3995), X(33113)}}, {{A, B, C, X(4294), X(56382)}}, {{A, B, C, X(4552), X(31615)}}, {{A, B, C, X(4674), X(37887)}}, {{A, B, C, X(5219), X(52358)}}, {{A, B, C, X(5249), X(17924)}}, {{A, B, C, X(6354), X(52383)}}, {{A, B, C, X(7361), X(56027)}}, {{A, B, C, X(10198), X(56810)}}, {{A, B, C, X(11398), X(55399)}}, {{A, B, C, X(11496), X(52037)}}, {{A, B, C, X(16577), X(41226)}}, {{A, B, C, X(16608), X(21911)}}, {{A, B, C, X(17093), X(41539)}}, {{A, B, C, X(18097), X(44733)}}, {{A, B, C, X(18593), X(48003)}}, {{A, B, C, X(20110), X(38300)}}, {{A, B, C, X(25430), X(44692)}}, {{A, B, C, X(27287), X(40152)}}, {{A, B, C, X(40573), X(52560)}}
X(60188) = barycentric product X(i)*X(j) for these (i, j): {12, 40412}, {226, 40435}, {306, 40573}, {523, 54952}, {1175, 34388}, {1214, 40447}, {1441, 943}, {1794, 57809}, {2259, 349}, {2594, 57885}, {2982, 321}, {4552, 56320}, {15439, 850}, {26942, 40395}, {36048, 4086}, {40422, 65}, {40999, 57710}, {52355, 58993}, {52560, 8}
X(60188) = barycentric quotient X(i)/X(j) for these (i, j): {1, 54356}, {6, 46882}, {8, 51978}, {10, 6734}, {12, 442}, {19, 46884}, {34, 46883}, {37, 40937}, {42, 14547}, {55, 8021}, {65, 942}, {73, 4303}, {181, 40952}, {201, 56839}, {225, 1838}, {226, 5249}, {228, 23207}, {608, 46890}, {647, 52306}, {756, 40967}, {943, 21}, {1175, 60}, {1214, 18607}, {1400, 2260}, {1402, 40956}, {1409, 14597}, {1425, 39791}, {1708, 46885}, {1794, 283}, {1824, 1859}, {1825, 1844}, {1880, 1841}, {2171, 2294}, {2197, 18591}, {2259, 284}, {2594, 500}, {2982, 81}, {3678, 31938}, {3709, 33525}, {4017, 50354}, {6354, 55010}, {8736, 1865}, {15439, 110}, {15443, 45038}, {15556, 39772}, {16577, 16585}, {32651, 4565}, {34388, 1234}, {35320, 2617}, {36048, 1414}, {40395, 46103}, {40412, 261}, {40422, 314}, {40435, 333}, {40447, 31623}, {40570, 2189}, {40572, 56000}, {40573, 27}, {40952, 37993}, {41538, 14054}, {52383, 45926}, {52560, 7}, {54952, 99}, {56320, 4560}, {57710, 3615}
X(60188) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13405, 51758, 14547}

X(60189) = X(2)X(9734)∩X(4)X(5477)

Barycentrics    (3*a^6-a^4*b^2-a^2*b^4+3*b^6-2*(4*a^4+a^2*b^2+4*b^4)*c^2+9*(a^2+b^2)*c^4-4*c^6)*(3*a^6-8*a^4*b^2+9*a^2*b^4-4*b^6-(a^4+2*a^2*b^2-9*b^4)*c^2-(a^2+8*b^2)*c^4+3*c^6) : :

X(60189) lies on the Kiepert hyperbola and on these lines: {2, 9734}, {4, 5477}, {5, 60198}, {30, 60103}, {98, 53419}, {99, 60178}, {115, 7612}, {148, 9742}, {381, 60211}, {511, 54750}, {542, 41895}, {543, 60240}, {598, 14848}, {671, 3564}, {690, 60338}, {1503, 54659}, {2782, 60095}, {2794, 60150}, {2996, 10754}, {3424, 10722}, {5254, 54873}, {5480, 54868}, {5485, 14645}, {6321, 6390}, {6776, 54894}, {7607, 13881}, {9112, 54670}, {9113, 54669}, {9752, 39809}, {9862, 60322}, {10153, 38227}, {10723, 39663}, {10753, 54869}, {11623, 60337}, {12110, 60184}, {12243, 32532}, {14494, 31415}, {14651, 60185}, {14853, 53101}, {22515, 60093}, {23234, 42011}, {23235, 60234}, {28526, 34899}, {32469, 60177}, {38664, 53105}, {38732, 60218}, {39647, 43537}, {39838, 54845}, {44518, 60117}, {46034, 54565}, {53023, 54714}

X(60189) = midpoint of X(i) and X(j) for these {i,j}: {148, 9742}
X(60189) = reflection of X(i) in X(j) for these {i,j}: {7612, 115}
X(60189) = isogonal conjugate of X(47113)
X(60189) = isotomic conjugate of X(44369)
X(60189) = trilinear pole of line {37637, 523}
X(60189) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 54659}, {54, 57729}
X(60189) = pole of line {44369, 47113} with respect to the Wallace hyperbola
X(60189) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(9734)}}, {{A, B, C, X(99), X(44768)}}, {{A, B, C, X(265), X(690)}}, {{A, B, C, X(290), X(21166)}}, {{A, B, C, X(523), X(23698)}}, {{A, B, C, X(1173), X(57729)}}, {{A, B, C, X(1499), X(14645)}}, {{A, B, C, X(2065), X(14498)}}, {{A, B, C, X(2374), X(8599)}}, {{A, B, C, X(2789), X(28526)}}, {{A, B, C, X(2987), X(23700)}}, {{A, B, C, X(3426), X(52239)}}, {{A, B, C, X(3455), X(3527)}}, {{A, B, C, X(3613), X(51520)}}, {{A, B, C, X(5641), X(12117)}}, {{A, B, C, X(5966), X(8753)}}, {{A, B, C, X(6321), X(14384)}}, {{A, B, C, X(6323), X(14483)}}, {{A, B, C, X(6337), X(15077)}}, {{A, B, C, X(6530), X(53419)}}, {{A, B, C, X(6531), X(14639)}}, {{A, B, C, X(9880), X(17983)}}, {{A, B, C, X(10630), X(43656)}}, {{A, B, C, X(10722), X(45031)}}, {{A, B, C, X(11564), X(39446)}}, {{A, B, C, X(13881), X(22261)}}, {{A, B, C, X(52094), X(52477)}}

X(60190) = X(2)X(5017)∩X(4)X(3329)

Barycentrics    (a^4+4*a^2*b^2+b^4+2*(a^2+b^2)*c^2-c^4)*(a^4-b^4+2*b^2*c^2+c^4+2*a^2*(b^2+2*c^2)) : :

X(60190) lies on the Kiepert hyperbola and on these lines: {2, 5017}, {4, 3329}, {6, 54122}, {30, 54826}, {69, 42006}, {76, 2548}, {83, 7737}, {98, 14561}, {147, 43532}, {193, 60259}, {262, 31670}, {325, 60232}, {376, 54724}, {381, 54678}, {385, 60212}, {598, 33017}, {671, 7739}, {1007, 43529}, {1916, 7736}, {2996, 16044}, {3314, 18840}, {3406, 7787}, {3407, 3618}, {3424, 51171}, {3545, 9302}, {3815, 60234}, {3839, 54856}, {5395, 6655}, {5485, 32983}, {7391, 30505}, {7394, 55028}, {7612, 7806}, {7694, 60115}, {7735, 60128}, {7752, 10159}, {7771, 43527}, {7777, 40824}, {7840, 60143}, {7846, 60100}, {7899, 56059}, {8182, 60238}, {8290, 14033}, {10352, 60072}, {11179, 14458}, {14484, 40236}, {16043, 18841}, {16984, 60263}, {16990, 60099}, {17008, 60101}, {18842, 32986}, {18843, 33238}, {18845, 33019}, {31120, 60242}, {32957, 60183}, {33006, 54752}, {33018, 38259}, {33020, 37668}, {33255, 54841}, {33279, 53109}, {37187, 56346}, {37242, 53489}, {37337, 52583}, {37690, 60231}, {43535, 59373}, {51224, 60239}

X(60190) = isogonal conjugate of X(50659)
X(60190) = isotomic conjugate of X(16990)
X(60190) = trilinear pole of line {50550, 523}
X(60190) = pole of line {11174, 60190} with respect to the Kiepert hyperbola
X(60190) = pole of line {16990, 50659} with respect to the Wallace hyperbola
X(60190) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(5017)}}, {{A, B, C, X(8), X(40738)}}, {{A, B, C, X(25), X(16924)}}, {{A, B, C, X(32), X(46305)}}, {{A, B, C, X(66), X(39968)}}, {{A, B, C, X(69), X(1031)}}, {{A, B, C, X(193), X(37665)}}, {{A, B, C, X(251), X(2548)}}, {{A, B, C, X(263), X(733)}}, {{A, B, C, X(308), X(43726)}}, {{A, B, C, X(325), X(16989)}}, {{A, B, C, X(385), X(7736)}}, {{A, B, C, X(427), X(7791)}}, {{A, B, C, X(458), X(37182)}}, {{A, B, C, X(468), X(33016)}}, {{A, B, C, X(695), X(39951)}}, {{A, B, C, X(1007), X(7806)}}, {{A, B, C, X(1297), X(30535)}}, {{A, B, C, X(1370), X(37337)}}, {{A, B, C, X(2165), X(52395)}}, {{A, B, C, X(3091), X(37187)}}, {{A, B, C, X(3108), X(7758)}}, {{A, B, C, X(3228), X(38005)}}, {{A, B, C, X(3266), X(7739)}}, {{A, B, C, X(3314), X(3618)}}, {{A, B, C, X(3613), X(44571)}}, {{A, B, C, X(3815), X(17008)}}, {{A, B, C, X(4232), X(32983)}}, {{A, B, C, X(4518), X(14621)}}, {{A, B, C, X(4846), X(57799)}}, {{A, B, C, X(5094), X(33017)}}, {{A, B, C, X(6340), X(7864)}}, {{A, B, C, X(6353), X(16044)}}, {{A, B, C, X(6655), X(8889)}}, {{A, B, C, X(6995), X(32968)}}, {{A, B, C, X(7249), X(17743)}}, {{A, B, C, X(7378), X(16043)}}, {{A, B, C, X(7391), X(37125)}}, {{A, B, C, X(7408), X(32957)}}, {{A, B, C, X(7409), X(32960)}}, {{A, B, C, X(7714), X(33020)}}, {{A, B, C, X(7735), X(7777)}}, {{A, B, C, X(7737), X(23297)}}, {{A, B, C, X(7752), X(59180)}}, {{A, B, C, X(7787), X(45093)}}, {{A, B, C, X(7840), X(46275)}}, {{A, B, C, X(7858), X(39955)}}, {{A, B, C, X(7905), X(55999)}}, {{A, B, C, X(8601), X(47643)}}, {{A, B, C, X(8801), X(9229)}}, {{A, B, C, X(9227), X(52187)}}, {{A, B, C, X(9462), X(22336)}}, {{A, B, C, X(11174), X(16990)}}, {{A, B, C, X(11175), X(34214)}}, {{A, B, C, X(14356), X(32458)}}, {{A, B, C, X(14561), X(46807)}}, {{A, B, C, X(16984), X(37690)}}, {{A, B, C, X(24597), X(31120)}}, {{A, B, C, X(31670), X(44144)}}, {{A, B, C, X(32986), X(52284)}}, {{A, B, C, X(33018), X(38282)}}, {{A, B, C, X(33019), X(52299)}}, {{A, B, C, X(34288), X(40826)}}, {{A, B, C, X(37668), X(51171)}}, {{A, B, C, X(39953), X(39978)}}, {{A, B, C, X(40236), X(52288)}}, {{A, B, C, X(42407), X(45108)}}, {{A, B, C, X(44658), X(57926)}}, {{A, B, C, X(56067), X(57408)}}

X(60191) = X(2)X(11063)∩X(4)X(15037)

Barycentrics    ((a^2-b^2)^3-(a^4+5*a^2*b^2-3*b^4)*c^2-(a^2+3*b^2)*c^4+c^6)*(a^6+(b^2-c^2)^3-a^4*(b^2+3*c^2)-a^2*(b^4+5*b^2*c^2-3*c^4)) : :

X(60191) lies on the Kiepert hyperbola and on these lines: {2, 11063}, {4, 15037}, {5, 54500}, {6, 13582}, {17, 41477}, {18, 41478}, {30, 54827}, {76, 37779}, {94, 56404}, {98, 7533}, {262, 5189}, {384, 54829}, {1370, 54523}, {1656, 43666}, {2475, 54727}, {3091, 54498}, {3522, 60162}, {3523, 60163}, {3839, 54942}, {3854, 60166}, {5056, 60160}, {5059, 60174}, {5068, 60159}, {5422, 11538}, {6655, 54529}, {6997, 60185}, {7391, 60127}, {7394, 60150}, {10155, 46336}, {11004, 60255}, {11818, 54865}, {13585, 34545}, {14458, 37349}, {14494, 16063}, {14957, 54724}, {16044, 54843}, {32979, 54558}, {34007, 60122}, {44263, 54518}, {50689, 54844}

X(60191) = isogonal conjugate of X(50660)
X(60191) = trilinear pole of line {6140, 11620}
X(60191) = pole of line {15018, 60191} with respect to the Kiepert hyperbola
X(60191) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(15037)}}, {{A, B, C, X(6), X(11063)}}, {{A, B, C, X(67), X(30535)}}, {{A, B, C, X(97), X(14861)}}, {{A, B, C, X(251), X(18384)}}, {{A, B, C, X(265), X(55982)}}, {{A, B, C, X(297), X(7533)}}, {{A, B, C, X(458), X(5189)}}, {{A, B, C, X(1117), X(58733)}}, {{A, B, C, X(2981), X(11138)}}, {{A, B, C, X(2987), X(22336)}}, {{A, B, C, X(3519), X(31626)}}, {{A, B, C, X(3521), X(14919)}}, {{A, B, C, X(3854), X(6820)}}, {{A, B, C, X(4846), X(56266)}}, {{A, B, C, X(4993), X(22451)}}, {{A, B, C, X(5059), X(6819)}}, {{A, B, C, X(5068), X(37192)}}, {{A, B, C, X(5422), X(15108)}}, {{A, B, C, X(6151), X(11139)}}, {{A, B, C, X(11004), X(37644)}}, {{A, B, C, X(11331), X(37349)}}, {{A, B, C, X(14593), X(39955)}}, {{A, B, C, X(18370), X(54449)}}, {{A, B, C, X(19778), X(38403)}}, {{A, B, C, X(19779), X(38404)}}, {{A, B, C, X(43731), X(56041)}}, {{A, B, C, X(43732), X(56352)}}, {{A, B, C, X(43908), X(56361)}}, {{A, B, C, X(45821), X(46106)}}, {{A, B, C, X(46104), X(55032)}}, {{A, B, C, X(54124), X(54459)}}, {{A, B, C, X(56002), X(57730)}}

X(60192) = X(4)X(9698)∩X(83)X(549)

Barycentrics    (a^4-8*a^2*b^2+b^4-5*(a^2+b^2)*c^2+4*c^4)*(a^4+4*b^4-5*b^2*c^2+c^4-a^2*(5*b^2+8*c^2)) : :

X(60192) lies on these lines: {2, 37517}, {3, 53102}, {4, 9698}, {5, 43676}, {6, 60175}, {30, 53109}, {76, 5055}, {83, 549}, {98, 9300}, {325, 60217}, {376, 18843}, {381, 53105}, {383, 43546}, {547, 60210}, {548, 60146}, {598, 3534}, {671, 5066}, {1080, 43547}, {1503, 54891}, {1513, 60142}, {1916, 23234}, {3526, 43527}, {3545, 60219}, {3628, 10159}, {3815, 14492}, {3830, 54494}, {3845, 33698}, {5072, 60209}, {5306, 54644}, {5395, 10304}, {5476, 60233}, {6054, 11606}, {6811, 43571}, {6813, 43570}, {7486, 60285}, {7736, 60150}, {7777, 60214}, {7837, 60128}, {7862, 18840}, {9744, 60147}, {9753, 10155}, {9766, 11167}, {9993, 60127}, {10357, 15709}, {11163, 60218}, {11184, 60180}, {11540, 60238}, {13860, 53100}, {14046, 60151}, {14484, 43461}, {14614, 60220}, {14853, 60333}, {15022, 43681}, {15640, 53101}, {15683, 18845}, {15684, 53107}, {15698, 18842}, {15717, 60145}, {15759, 60282}, {18844, 46333}, {23046, 53106}, {31489, 54645}, {33699, 45103}, {37453, 43530}, {37671, 50985}, {38227, 53108}, {38232, 53104}, {41099, 54720}, {42849, 54773}, {43460, 54477}, {44422, 60098}, {47598, 60100}, {55859, 60182}, {58883, 60330}

X(60192) = isogonal conjugate of X(50664)
X(60192) = trilinear pole of line {47445, 523}
X(60192) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 54891}, {3425, 60142}
X(60192) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(53096)}}, {{A, B, C, X(6), X(37517)}}, {{A, B, C, X(25), X(5055)}}, {{A, B, C, X(68), X(31417)}}, {{A, B, C, X(95), X(45090)}}, {{A, B, C, X(251), X(19307)}}, {{A, B, C, X(325), X(9300)}}, {{A, B, C, X(381), X(37453)}}, {{A, B, C, X(427), X(549)}}, {{A, B, C, X(428), X(3628)}}, {{A, B, C, X(468), X(5066)}}, {{A, B, C, X(842), X(3108)}}, {{A, B, C, X(1173), X(5966)}}, {{A, B, C, X(1179), X(34110)}}, {{A, B, C, X(1494), X(3613)}}, {{A, B, C, X(1989), X(40410)}}, {{A, B, C, X(2980), X(57927)}}, {{A, B, C, X(3526), X(5064)}}, {{A, B, C, X(3534), X(5094)}}, {{A, B, C, X(3563), X(34572)}}, {{A, B, C, X(3815), X(37671)}}, {{A, B, C, X(4518), X(13606)}}, {{A, B, C, X(5481), X(29322)}}, {{A, B, C, X(5627), X(53935)}}, {{A, B, C, X(6530), X(12007)}}, {{A, B, C, X(7378), X(15709)}}, {{A, B, C, X(7486), X(7714)}}, {{A, B, C, X(7777), X(7837)}}, {{A, B, C, X(7862), X(42037)}}, {{A, B, C, X(8797), X(52187)}}, {{A, B, C, X(8889), X(10304)}}, {{A, B, C, X(9307), X(52188)}}, {{A, B, C, X(9698), X(34483)}}, {{A, B, C, X(9766), X(11163)}}, {{A, B, C, X(11169), X(18361)}}, {{A, B, C, X(11184), X(14614)}}, {{A, B, C, X(13623), X(30786)}}, {{A, B, C, X(14388), X(39389)}}, {{A, B, C, X(14495), X(36616)}}, {{A, B, C, X(15683), X(52299)}}, {{A, B, C, X(15684), X(52298)}}, {{A, B, C, X(15698), X(52284)}}, {{A, B, C, X(23046), X(52297)}}, {{A, B, C, X(23234), X(40820)}}, {{A, B, C, X(32085), X(52154)}}, {{A, B, C, X(32216), X(35501)}}, {{A, B, C, X(33699), X(52293)}}, {{A, B, C, X(34285), X(52717)}}, {{A, B, C, X(34570), X(45299)}}, {{A, B, C, X(36889), X(46952)}}, {{A, B, C, X(38005), X(46204)}}, {{A, B, C, X(38232), X(56738)}}, {{A, B, C, X(47598), X(52285)}}, {{A, B, C, X(51872), X(52094)}}

X(60193) = X(2)X(6749)∩X(4)X(14530)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(5*(a^2-b^2)^2-4*(a^2+b^2)*c^2-c^4)*(5*a^4-b^4-4*b^2*c^2+5*c^4-2*a^2*(2*b^2+5*c^2)) : :

X(60193) lies on the Kiepert hyperbola and on these lines: {2, 6749}, {3, 54763}, {4, 14530}, {5, 54660}, {6, 56270}, {20, 60121}, {25, 60127}, {27, 54689}, {29, 54787}, {30, 54838}, {98, 52284}, {193, 60256}, {262, 4232}, {297, 18842}, {381, 54667}, {406, 54727}, {427, 60150}, {452, 54559}, {458, 5485}, {467, 54772}, {468, 14494}, {469, 54587}, {470, 43543}, {471, 43542}, {472, 33602}, {473, 33603}, {598, 37174}, {671, 14920}, {1327, 55569}, {1328, 55573}, {1585, 14226}, {1586, 14241}, {1593, 54604}, {2052, 40138}, {2996, 37645}, {3087, 43530}, {3091, 60122}, {3522, 31363}, {3523, 13599}, {3535, 54597}, {3536, 43536}, {3541, 54498}, {3543, 54585}, {3620, 60225}, {3839, 54512}, {4194, 54757}, {4196, 54657}, {4198, 54693}, {4200, 54758}, {4207, 54740}, {4212, 54885}, {5032, 58268}, {5056, 40448}, {5094, 7612}, {5125, 54790}, {5395, 14389}, {6353, 54523}, {6871, 54555}, {6994, 54586}, {6995, 14492}, {7378, 14458}, {7394, 54640}, {7398, 54709}, {7408, 54520}, {7409, 54519}, {7518, 54516}, {7608, 53857}, {7714, 54707}, {8796, 11427}, {8889, 60185}, {9221, 35486}, {10155, 52290}, {10301, 52519}, {11109, 54786}, {11331, 18841}, {14004, 54712}, {14035, 54828}, {14063, 54551}, {14484, 52301}, {14853, 16240}, {15066, 60285}, {17555, 54624}, {17578, 54923}, {18840, 52289}, {23292, 60161}, {26003, 54831}, {32532, 52281}, {32971, 54898}, {32974, 54682}, {34289, 51171}, {35481, 54681}, {37119, 54500}, {37122, 54912}, {37192, 54797}, {37337, 54843}, {37349, 54704}, {37384, 54722}, {40112, 60200}, {40890, 54819}, {43462, 60138}, {43673, 45292}, {50689, 54552}, {52253, 54930}, {52280, 54531}, {52282, 60281}, {52283, 54616}, {52288, 60143}, {52292, 53098}, {52293, 60123}

X(60193) = isogonal conjugate of X(52703)
X(60193) = trilinear pole of line {37934, 523}
X(60193) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 52703}, {48, 3545}
X(60193) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 52703}, {1249, 3545}
X(60193) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(14919)}}, {{A, B, C, X(53), X(46217)}}, {{A, B, C, X(54), X(56266)}}, {{A, B, C, X(64), X(55982)}}, {{A, B, C, X(89), X(40396)}}, {{A, B, C, X(97), X(14528)}}, {{A, B, C, X(193), X(37645)}}, {{A, B, C, X(253), X(55032)}}, {{A, B, C, X(297), X(52284)}}, {{A, B, C, X(393), X(6749)}}, {{A, B, C, X(394), X(43908)}}, {{A, B, C, X(458), X(4232)}}, {{A, B, C, X(1073), X(14530)}}, {{A, B, C, X(1990), X(46809)}}, {{A, B, C, X(2165), X(3087)}}, {{A, B, C, X(3532), X(31626)}}, {{A, B, C, X(3620), X(14389)}}, {{A, B, C, X(5032), X(40112)}}, {{A, B, C, X(5056), X(52280)}}, {{A, B, C, X(5094), X(37174)}}, {{A, B, C, X(5486), X(56267)}}, {{A, B, C, X(6995), X(52289)}}, {{A, B, C, X(7378), X(11331)}}, {{A, B, C, X(11064), X(45088)}}, {{A, B, C, X(11427), X(57875)}}, {{A, B, C, X(14491), X(40384)}}, {{A, B, C, X(14853), X(47388)}}, {{A, B, C, X(15066), X(51171)}}, {{A, B, C, X(16240), X(35906)}}, {{A, B, C, X(18384), X(47735)}}, {{A, B, C, X(25417), X(40397)}}, {{A, B, C, X(34287), X(51348)}}, {{A, B, C, X(34567), X(56347)}}, {{A, B, C, X(39951), X(57409)}}, {{A, B, C, X(40402), X(52224)}}, {{A, B, C, X(52281), X(53857)}}, {{A, B, C, X(52288), X(52301)}}, {{A, B, C, X(56338), X(57713)}}
X(60193) = barycentric quotient X(i)/X(j) for these (i, j): {4, 3545}, {6, 52703}

X(60194) = X(2)X(588)∩X(4)X(9739)

Barycentrics    a^4+b^4-3*b^2*c^2+c^4-2*a^2*(b^2+c^2)+(-2*b^2-2*c^2)*S : :

X(60194) lies on the Kiepert hyperbola and on these lines: {2, 588}, {3, 14234}, {4, 9739}, {5, 14245}, {6, 60274}, {10, 32792}, {17, 33394}, {18, 33393}, {69, 3316}, {76, 45472}, {83, 615}, {98, 8825}, {99, 641}, {141, 5111}, {302, 3391}, {303, 3366}, {316, 23311}, {485, 492}, {486, 32807}, {491, 10195}, {591, 54505}, {639, 1078}, {1131, 3593}, {1270, 3590}, {1271, 60293}, {1328, 35949}, {1916, 13653}, {3069, 60204}, {3071, 6568}, {3317, 32812}, {5058, 60104}, {5490, 7763}, {5491, 5590}, {6118, 44365}, {7612, 49048}, {7878, 45487}, {8252, 33233}, {13757, 54627}, {13783, 60239}, {14229, 26441}, {32786, 60205}, {32806, 34089}, {32808, 43568}, {32810, 43536}, {32813, 43564}, {32814, 60311}, {35297, 53488}, {35947, 54874}, {43620, 54127}, {45577, 55085}

X(60194) = inverse of X(641) in Wallace hyperbola
X(60194) = isogonal conjugate of X(5062)
X(60194) = isotomic conjugate of X(590)
X(60194) = trilinear pole of line {44365, 523}
X(60194) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 5062}, {31, 590}, {48, 52287}
X(60194) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 590}, {3, 5062}, {642, 7749}, {1249, 52287}, {5976, 51395}, {24246, 8035}, {33364, 44647}
X(60194) = X(i)-cross conjugate of X(j) for these {i, j}: {7769, 60196}, {15234, 264}, {54029, 99}
X(60194) = pole of line {7769, 60194} with respect to the Kiepert hyperbola
X(60194) = pole of line {590, 641} with respect to the Wallace hyperbola
X(60194) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(9739)}}, {{A, B, C, X(6), X(1504)}}, {{A, B, C, X(141), X(615)}}, {{A, B, C, X(257), X(3302)}}, {{A, B, C, X(264), X(492)}}, {{A, B, C, X(287), X(55533)}}, {{A, B, C, X(335), X(3300)}}, {{A, B, C, X(1016), X(7090)}}, {{A, B, C, X(1509), X(13390)}}, {{A, B, C, X(1586), X(7763)}}, {{A, B, C, X(5058), X(5111)}}, {{A, B, C, X(11090), X(34386)}}
X(60194) = barycentric product X(i)*X(j) for these (i, j): {588, 76}, {18022, 8825}
X(60194) = barycentric quotient X(i)/X(j) for these (i, j): {2, 590}, {4, 52287}, {6, 5062}, {302, 33393}, {303, 33394}, {325, 51395}, {485, 8035}, {492, 641}, {493, 26460}, {588, 6}, {615, 7749}, {1585, 44637}, {3068, 44647}, {8825, 184}

X(60195) = X(6)X(54503)∩X(30)X(14238)

Barycentrics    a^2*b^2-3*b^4+a^2*c^2+7*b^2*c^2-3*c^4+(4*a^2-2*b^2-2*c^2)*S : :

X(60195) lies on the Kiepert hyperbola and on these lines: {6, 54503}, {30, 14238}, {381, 14231}, {485, 35948}, {486, 14568}, {491, 42024}, {524, 48913}, {590, 54505}, {598, 32787}, {638, 3317}, {671, 1991}, {1271, 54502}, {1327, 13637}, {1328, 45420}, {1992, 14226}, {3068, 54625}, {5485, 32811}, {5861, 60208}, {6230, 60176}, {7771, 53512}, {9166, 13850}, {10195, 39388}, {13639, 43567}, {13690, 14232}, {13757, 43569}, {13846, 54507}, {14236, 49356}, {14244, 33371}, {18362, 44374}, {18424, 44368}, {18546, 44366}, {19054, 54626}, {32788, 54504}, {32808, 60223}, {32809, 42023}, {35297, 53479}, {35878, 60269}, {37785, 54535}, {37786, 54538}

X(60195) = isogonal conjugate of X(9675)
X(60195) = isotomic conjugate of X(591)
X(60195) = pole of line {591, 9675} with respect to the Wallace hyperbola
X(60195) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(493), X(30541)}}, {{A, B, C, X(494), X(21399)}}, {{A, B, C, X(589), X(32420)}}, {{A, B, C, X(755), X(8576)}}, {{A, B, C, X(1502), X(18819)}}, {{A, B, C, X(8577), X(57728)}}, {{A, B, C, X(9289), X(55534)}}

X(60196) = X(2)X(589)∩X(4)X(9738)

Barycentrics    a^4+b^4-3*b^2*c^2+c^4-2*a^2*(b^2+c^2)+(2*b^2+2*c^2)*S : :

X(60196) lies on the Kiepert hyperbola and on these lines: {2, 589}, {3, 14238}, {4, 9738}, {5, 14231}, {6, 60275}, {10, 32791}, {17, 33392}, {18, 33395}, {69, 3317}, {76, 45473}, {83, 590}, {98, 49356}, {99, 642}, {141, 5111}, {302, 3392}, {303, 3367}, {316, 23312}, {485, 39388}, {486, 491}, {492, 10194}, {640, 1078}, {1132, 3595}, {1270, 60294}, {1271, 3591}, {1327, 35948}, {1916, 13773}, {1991, 54504}, {3068, 60205}, {3070, 6569}, {3316, 32813}, {3407, 31481}, {5062, 60104}, {5490, 5591}, {5491, 7763}, {6119, 44364}, {7612, 49049}, {7878, 45486}, {8253, 33233}, {8982, 14244}, {13637, 54628}, {13663, 60239}, {32785, 60204}, {32805, 34091}, {32807, 43559}, {32809, 43569}, {32811, 54597}, {32812, 43565}, {35297, 53487}, {35946, 54876}, {43620, 54126}, {45576, 55085}

X(60196) = inverse of X(642) in Wallace hyperbola
X(60196) = isogonal conjugate of X(5058)
X(60196) = isotomic conjugate of X(615)
X(60196) = trilinear pole of line {44364, 523}
X(60196) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 5058}, {31, 615}, {48, 52286}
X(60196) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 615}, {3, 5058}, {641, 7749}, {1249, 52286}, {5976, 51401}, {24245, 8036}, {33365, 44648}
X(60196) = X(i)-cross conjugate of X(j) for these {i, j}: {7769, 60194}, {15233, 264}, {54028, 99}
X(60196) = pole of line {7769, 60196} with respect to the Kiepert hyperbola
X(60196) = pole of line {615, 642} with respect to the Wallace hyperbola
X(60196) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(9738)}}, {{A, B, C, X(6), X(1505)}}, {{A, B, C, X(141), X(590)}}, {{A, B, C, X(257), X(3300)}}, {{A, B, C, X(264), X(491)}}, {{A, B, C, X(287), X(55534)}}, {{A, B, C, X(335), X(3302)}}, {{A, B, C, X(1016), X(14121)}}, {{A, B, C, X(1509), X(1659)}}, {{A, B, C, X(1585), X(7763)}}, {{A, B, C, X(5062), X(5111)}}, {{A, B, C, X(11091), X(34386)}}
X(60196) = barycentric product X(i)*X(j) for these (i, j): {589, 76}
X(60196) = barycentric quotient X(i)/X(j) for these (i, j): {2, 615}, {4, 52286}, {6, 5058}, {302, 33395}, {303, 33392}, {325, 51401}, {486, 8036}, {491, 642}, {494, 26455}, {589, 6}, {590, 7749}, {1586, 44638}, {3069, 44648}
X(60196) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5491, 26362, 7763}

X(60197) = X(2)X(304)∩X(4)X(75)

Barycentrics    b*c*(b+c)*((a+b)^2+c^2)*(b^2+(a+c)^2) : :

X(60197) lies on the Kiepert hyperbola and on these lines: {2, 304}, {4, 75}, {8, 60152}, {10, 18697}, {76, 40364}, {83, 2281}, {85, 60076}, {98, 336}, {226, 1231}, {274, 14534}, {321, 1228}, {349, 40149}, {459, 57921}, {671, 54982}, {975, 33936}, {1036, 60080}, {1245, 40718}, {1441, 60086}, {1472, 16825}, {1751, 2339}, {1969, 2052}, {2221, 4359}, {4980, 54744}, {5262, 26234}, {6539, 56564}, {9239, 37892}, {10436, 33945}, {16080, 33805}, {16817, 60081}, {24624, 37215}, {26563, 40013}, {27801, 60264}, {33780, 60143}, {33934, 40012}, {33935, 34258}, {33937, 60079}, {34284, 60156}, {36099, 37220}, {39733, 52583}, {40702, 57821}, {40704, 57826}, {43678, 46244}, {54433, 60165}

X(60197) = isotomic conjugate of X(2303)
X(60197) = trilinear pole of line {14208, 523}
X(60197) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 44119}, {31, 2303}, {32, 1010}, {41, 5323}, {48, 4206}, {58, 54416}, {110, 2484}, {163, 8678}, {284, 1460}, {388, 57657}, {612, 1333}, {662, 8646}, {1038, 2204}, {1474, 7085}, {1501, 44154}, {1576, 6590}, {2194, 2285}, {2203, 5227}, {2206, 2345}, {2286, 2299}, {2522, 32676}, {3974, 16947}, {4556, 50494}, {19459, 57386}, {32739, 47844}
X(60197) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 2303}, {9, 44119}, {10, 54416}, {37, 612}, {115, 8678}, {226, 2286}, {244, 2484}, {1084, 8646}, {1214, 2285}, {1249, 4206}, {3160, 5323}, {4858, 6590}, {6376, 1010}, {15526, 2522}, {18589, 1184}, {36901, 2517}, {40590, 1460}, {40603, 2345}, {40619, 47844}, {51574, 7085}, {59608, 4320}
X(60197) = X(i)-cross conjugate of X(j) for these {i, j}: {31993, 1441}
X(60197) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(28), X(257)}}, {{A, B, C, X(72), X(40403)}}, {{A, B, C, X(75), X(304)}}, {{A, B, C, X(85), X(313)}}, {{A, B, C, X(274), X(1228)}}, {{A, B, C, X(594), X(16583)}}, {{A, B, C, X(693), X(38457)}}, {{A, B, C, X(1211), X(1427)}}, {{A, B, C, X(1218), X(40828)}}, {{A, B, C, X(2333), X(52651)}}, {{A, B, C, X(3701), X(36796)}}, {{A, B, C, X(3710), X(58004)}}, {{A, B, C, X(4359), X(56564)}}, {{A, B, C, X(4384), X(57808)}}, {{A, B, C, X(5142), X(19281)}}, {{A, B, C, X(5262), X(52376)}}, {{A, B, C, X(7018), X(44129)}}, {{A, B, C, X(10436), X(33935)}}, {{A, B, C, X(16603), X(49598)}}, {{A, B, C, X(23604), X(39721)}}
X(60197) = barycentric product X(i)*X(j) for these (i, j): {10, 57923}, {313, 56328}, {523, 54982}, {1245, 561}, {1310, 850}, {1441, 30479}, {1502, 2281}, {1577, 37215}, {2221, 27801}, {2339, 349}, {3267, 36099}, {16583, 40831}, {56219, 76}
X(60197) = barycentric quotient X(i)/X(j) for these (i, j): {1, 44119}, {2, 2303}, {4, 4206}, {7, 5323}, {10, 612}, {37, 54416}, {65, 1460}, {72, 7085}, {75, 1010}, {226, 2285}, {306, 5227}, {307, 1038}, {313, 4385}, {321, 2345}, {512, 8646}, {523, 8678}, {525, 2522}, {561, 44154}, {661, 2484}, {693, 47844}, {850, 2517}, {1036, 2194}, {1039, 2299}, {1214, 2286}, {1231, 56367}, {1245, 31}, {1310, 110}, {1441, 388}, {1446, 7365}, {1472, 2206}, {1577, 6590}, {2221, 1333}, {2281, 32}, {2339, 284}, {3668, 4320}, {3701, 3974}, {4036, 48395}, {4705, 50494}, {6046, 10376}, {6354, 8898}, {14208, 23874}, {14258, 27174}, {16583, 1184}, {17094, 51644}, {17441, 19459}, {20235, 7386}, {20336, 54433}, {30479, 21}, {31993, 34261}, {32691, 32676}, {36099, 112}, {36907, 40184}, {37215, 662}, {40071, 19799}, {41013, 7102}, {51686, 2203}, {52369, 3610}, {53510, 5286}, {54982, 99}, {56219, 6}, {56328, 58}, {57923, 86}

X(60198) = X(4)X(9734)∩X(83)X(3055)

Barycentrics    (3*(a^2-b^2)^2-5*(a^2+b^2)*c^2+4*c^4)*(3*a^4+4*b^4-5*b^2*c^2+3*c^4-a^2*(5*b^2+6*c^2)) : :

X(60198) lies on the Kiepert hyperbola and on these lines: {4, 9734}, {5, 60189}, {39, 54750}, {69, 60123}, {83, 3055}, {98, 37647}, {99, 15850}, {183, 11668}, {325, 53104}, {671, 7769}, {1007, 53103}, {1078, 60148}, {1506, 5395}, {2996, 7781}, {3266, 11140}, {3815, 60073}, {3926, 60200}, {5392, 11059}, {5466, 41298}, {5485, 7763}, {6683, 60151}, {7608, 18583}, {7612, 34803}, {7618, 32839}, {7778, 60248}, {7786, 54751}, {7799, 60216}, {7940, 54916}, {8598, 45103}, {9771, 60103}, {10185, 37688}, {17005, 60104}, {25555, 53098}, {31489, 60093}, {32831, 43681}, {32832, 60143}, {32838, 60285}, {32871, 38259}, {32898, 60113}, {35287, 53101}, {44377, 60101}, {54636, 57518}

X(60198) = inverse of X(15850) in Wallace hyperbola
X(60198) = isotomic conjugate of X(3054)
X(60198) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 3054}, {51589, 33554}
X(60198) = pole of line {3054, 15850} with respect to the Wallace hyperbola
X(60198) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(9734)}}, {{A, B, C, X(95), X(18023)}}, {{A, B, C, X(141), X(3055)}}, {{A, B, C, X(308), X(57927)}}, {{A, B, C, X(325), X(37647)}}, {{A, B, C, X(1007), X(34803)}}, {{A, B, C, X(2963), X(25322)}}, {{A, B, C, X(3266), X(7769)}}, {{A, B, C, X(3815), X(44377)}}, {{A, B, C, X(4590), X(55958)}}, {{A, B, C, X(7763), X(11059)}}, {{A, B, C, X(7778), X(31489)}}, {{A, B, C, X(7925), X(17005)}}, {{A, B, C, X(8598), X(52293)}}, {{A, B, C, X(9771), X(22110)}}, {{A, B, C, X(11169), X(40429)}}, {{A, B, C, X(15464), X(56057)}}, {{A, B, C, X(30537), X(40511)}}, {{A, B, C, X(30786), X(34386)}}, {{A, B, C, X(32829), X(57518)}}, {{A, B, C, X(40405), X(40410)}}, {{A, B, C, X(43620), X(56891)}}
X(60198) = barycentric quotient X(i)/X(j) for these (i, j): {2, 3054}, {15534, 33554}

X(60199) = X(2)X(6331)∩X(4)X(290)

Barycentrics    b^4*c^4*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4+b^4-(a^2+b^2)*c^2)*(a^4-a^2*b^2-b^2*c^2+c^4) : :

X(60199) lies on the Kiepert hyperbola and on these lines: {2, 6331}, {4, 290}, {76, 22416}, {83, 6531}, {96, 31635}, {98, 16083}, {99, 46094}, {141, 57790}, {226, 46273}, {262, 264}, {275, 287}, {276, 37125}, {336, 56227}, {671, 59762}, {1235, 3399}, {1502, 40824}, {1821, 60088}, {1916, 44132}, {1969, 60245}, {2052, 53245}, {2986, 43187}, {3289, 44137}, {3406, 14382}, {3407, 57260}, {5392, 57257}, {5466, 46111}, {6394, 40448}, {7607, 52145}, {11140, 55217}, {14265, 60117}, {14618, 46040}, {18817, 54554}, {20573, 39295}, {30505, 30506}, {36120, 40718}, {40016, 42395}, {43532, 44146}, {44129, 60320}, {44145, 54978}, {44155, 52128}, {44173, 52459}, {46511, 54547}, {52491, 55009}, {58782, 60115}

X(60199) = inverse of X(46094) in Wallace hyperbola
X(60199) = isotomic conjugate of X(3289)
X(60199) = trilinear pole of line {264, 34845}
X(60199) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 9417}, {31, 3289}, {48, 237}, {63, 9418}, {163, 39469}, {184, 1755}, {232, 52430}, {240, 14585}, {248, 42075}, {255, 2211}, {293, 9419}, {336, 36425}, {511, 9247}, {560, 36212}, {577, 57653}, {810, 14966}, {1917, 6393}, {1959, 14575}, {2169, 52967}, {2206, 42702}, {2491, 4575}, {3049, 23997}, {4100, 34854}, {14600, 23996}, {23995, 41172}, {40373, 46238}, {51651, 52425}
X(60199) = X(i)-vertex conjugate of X(j) for these {i, j}: {14600, 60179}
X(60199) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 3289}, {115, 39469}, {132, 9419}, {136, 2491}, {1249, 237}, {3162, 9418}, {6374, 36212}, {6523, 2211}, {14363, 52967}, {16081, 57012}, {18314, 41172}, {36103, 9417}, {36899, 184}, {36901, 684}, {38970, 58262}, {39039, 42075}, {39058, 3}, {39062, 14966}, {39085, 14585}, {40603, 42702}
X(60199) = X(i)-cross conjugate of X(j) for these {i, j}: {290, 18024}, {297, 264}, {1503, 44185}, {3981, 36897}, {16089, 57844}, {41760, 34536}, {43665, 22456}, {51257, 57541}, {53245, 290}, {53475, 847}
X(60199) = pole of line {2491, 9419} with respect to the polar circle
X(60199) = pole of line {3289, 46094} with respect to the Wallace hyperbola
X(60199) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(53), X(141)}}, {{A, B, C, X(264), X(44144)}}, {{A, B, C, X(276), X(46104)}}, {{A, B, C, X(287), X(53174)}}, {{A, B, C, X(290), X(57799)}}, {{A, B, C, X(297), X(2967)}}, {{A, B, C, X(308), X(8795)}}, {{A, B, C, X(525), X(14941)}}, {{A, B, C, X(694), X(2211)}}, {{A, B, C, X(695), X(14600)}}, {{A, B, C, X(850), X(16083)}}, {{A, B, C, X(878), X(30496)}}, {{A, B, C, X(1297), X(53200)}}, {{A, B, C, X(1502), X(40822)}}, {{A, B, C, X(1972), X(46271)}}, {{A, B, C, X(1987), X(3289)}}, {{A, B, C, X(2501), X(17980)}}, {{A, B, C, X(2998), X(40807)}}, {{A, B, C, X(3228), X(57732)}}, {{A, B, C, X(6331), X(6528)}}, {{A, B, C, X(6393), X(43702)}}, {{A, B, C, X(9289), X(54032)}}, {{A, B, C, X(14970), X(43717)}}, {{A, B, C, X(17984), X(44132)}}, {{A, B, C, X(18022), X(18027)}}, {{A, B, C, X(18024), X(57541)}}, {{A, B, C, X(20573), X(23962)}}, {{A, B, C, X(23584), X(53700)}}, {{A, B, C, X(30506), X(37125)}}, {{A, B, C, X(34129), X(47110)}}, {{A, B, C, X(34816), X(56341)}}, {{A, B, C, X(38262), X(38264)}}, {{A, B, C, X(40362), X(57904)}}, {{A, B, C, X(40802), X(42374)}}, {{A, B, C, X(40889), X(41203)}}, {{A, B, C, X(46726), X(53701)}}, {{A, B, C, X(47385), X(53229)}}, {{A, B, C, X(52280), X(54004)}}, {{A, B, C, X(57065), X(57257)}}
X(60199) = barycentric product X(i)*X(j) for these (i, j): {264, 290}, {276, 53245}, {297, 57541}, {336, 57806}, {338, 41174}, {1502, 6531}, {1821, 1969}, {1976, 44161}, {2052, 57799}, {4609, 53149}, {14618, 43187}, {16081, 76}, {18022, 98}, {18024, 4}, {18027, 287}, {22456, 850}, {23962, 60179}, {31635, 55553}, {34536, 44132}, {36120, 561}, {40362, 57260}, {43665, 6331}, {44173, 685}, {46111, 52145}, {46273, 92}, {51257, 6330}, {53174, 57844}
X(60199) = barycentric quotient X(i)/X(j) for these (i, j): {2, 3289}, {4, 237}, {19, 9417}, {25, 9418}, {53, 52967}, {76, 36212}, {92, 1755}, {98, 184}, {158, 57653}, {232, 9419}, {240, 42075}, {248, 14585}, {264, 511}, {273, 51651}, {275, 41270}, {287, 577}, {290, 3}, {293, 52430}, {297, 11672}, {305, 51386}, {311, 44716}, {321, 42702}, {331, 43034}, {336, 255}, {338, 41172}, {393, 2211}, {523, 39469}, {648, 14966}, {685, 1576}, {811, 23997}, {850, 684}, {878, 58310}, {879, 39201}, {1093, 34854}, {1502, 6393}, {1821, 48}, {1910, 9247}, {1969, 1959}, {1976, 14575}, {2052, 232}, {2211, 36425}, {2395, 3049}, {2501, 2491}, {2966, 32661}, {2967, 23611}, {2970, 44114}, {5967, 23200}, {6331, 2421}, {6394, 1092}, {6528, 4230}, {6529, 34859}, {6531, 32}, {7017, 59734}, {8754, 58260}, {8795, 19189}, {8884, 58306}, {9154, 14908}, {11610, 22075}, {14265, 52144}, {14601, 40373}, {14618, 3569}, {15352, 58070}, {15628, 52425}, {15630, 23216}, {16081, 6}, {16089, 52128}, {16230, 58262}, {17974, 23606}, {17983, 51980}, {17984, 36213}, {18022, 325}, {18024, 69}, {18027, 297}, {18817, 14356}, {20021, 20775}, {22456, 110}, {31635, 1147}, {31636, 10316}, {32696, 14574}, {34334, 58343}, {34536, 248}, {35142, 34157}, {36036, 4575}, {36120, 31}, {36897, 17970}, {40428, 42065}, {40703, 23996}, {41013, 5360}, {41174, 249}, {41932, 14600}, {43187, 4558}, {43665, 647}, {43920, 22096}, {44129, 17209}, {44132, 36790}, {44145, 51335}, {44146, 9155}, {44173, 6333}, {46104, 51862}, {46107, 53521}, {46111, 5968}, {46273, 63}, {51257, 441}, {51481, 47406}, {51843, 51427}, {52076, 42659}, {52145, 3292}, {52491, 5191}, {52641, 42671}, {53149, 669}, {53173, 32320}, {53174, 418}, {53245, 216}, {53331, 38354}, {54412, 59707}, {57260, 1501}, {57490, 8779}, {57541, 287}, {57796, 51369}, {57799, 394}, {57806, 240}, {57991, 47390}, {60179, 23357}
X(60199) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16083, 16089, 22456}

X(60200) = X(2)X(55788)∩X(4)X(11160)

Barycentrics    (a^2+b^2-11*c^2)*(a^2-11*b^2+c^2) : :
X(60200) = -6*X[5055]+5*X[14494]

X(60200) lies on the Kiepert hyperbola and on these lines: {2, 55788}, {3, 55829}, {4, 11160}, {5, 60330}, {6, 54639}, {20, 53100}, {30, 54845}, {69, 41895}, {98, 8591}, {193, 598}, {316, 54493}, {376, 60322}, {381, 52519}, {524, 53101}, {538, 60096}, {549, 7612}, {599, 2996}, {1992, 5395}, {2482, 60103}, {3091, 60142}, {3424, 15683}, {3523, 60334}, {3526, 60123}, {3534, 60150}, {3543, 60132}, {3620, 5485}, {3628, 53098}, {3839, 14488}, {3926, 60198}, {5032, 18842}, {5055, 14494}, {5056, 60332}, {5066, 60127}, {5286, 60100}, {5461, 8781}, {6392, 18841}, {7486, 7608}, {7607, 10303}, {7620, 7850}, {7788, 54889}, {7840, 14484}, {7841, 60219}, {7877, 53109}, {8352, 54720}, {8370, 18843}, {8596, 15589}, {11054, 60239}, {11185, 45103}, {14046, 32869}, {14458, 14976}, {14711, 60095}, {15022, 53099}, {15533, 54896}, {15684, 60325}, {15692, 60335}, {15698, 60185}, {15709, 53103}, {15717, 43537}, {19570, 60215}, {20080, 54476}, {20081, 60098}, {23334, 54646}, {32833, 60178}, {32874, 60212}, {32892, 60202}, {32971, 53102}, {32974, 43676}, {33272, 60280}, {34505, 38259}, {40112, 60193}, {40344, 60218}, {40727, 60240}, {43150, 54713}, {43448, 60228}, {46941, 60175}, {46951, 60101}, {47286, 60143}, {47586, 50693}, {49140, 54857}, {50074, 54622}, {50133, 54623}, {50692, 60324}, {50992, 54642}, {51171, 54616}

X(60200) = isotomic conjugate of X(5032)
X(60200) = pole of line {21356, 60200} with respect to the Kiepert hyperbola
X(60200) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55724)}}, {{A, B, C, X(69), X(11160)}}, {{A, B, C, X(193), X(599)}}, {{A, B, C, X(253), X(54171)}}, {{A, B, C, X(297), X(10304)}}, {{A, B, C, X(549), X(37174)}}, {{A, B, C, X(597), X(43726)}}, {{A, B, C, X(1992), X(3620)}}, {{A, B, C, X(5032), X(21356)}}, {{A, B, C, X(5461), X(52450)}}, {{A, B, C, X(6620), X(14046)}}, {{A, B, C, X(7486), X(52281)}}, {{A, B, C, X(7840), X(15589)}}, {{A, B, C, X(8753), X(40103)}}, {{A, B, C, X(9462), X(46645)}}, {{A, B, C, X(10303), X(52282)}}, {{A, B, C, X(11331), X(15640)}}, {{A, B, C, X(15683), X(52283)}}, {{A, B, C, X(32836), X(51481)}}, {{A, B, C, X(32869), X(40814)}}, {{A, B, C, X(34897), X(50955)}}, {{A, B, C, X(36588), X(40028)}}, {{A, B, C, X(39721), X(40029)}}, {{A, B, C, X(40802), X(43713)}}, {{A, B, C, X(42313), X(51028)}}, {{A, B, C, X(47735), X(52154)}}
X(60200) = barycentric product X(i)*X(j) for these (i, j): {58091, 850}
X(60200) = barycentric quotient X(i)/X(j) for these (i, j): {2, 5032}, {58091, 110}

X(60201) = X(4)X(3933)∩X(69)X(3424)

Barycentrics    ((a^2-b^2)^2+2*(a^2+b^2)*c^2+5*c^4)*(a^4+5*b^4+2*b^2*c^2+c^4+2*a^2*(b-c)*(b+c)) : :

X(60201) lies on the Kiepert hyperbola and on these lines: {4, 3933}, {69, 3424}, {76, 33180}, {83, 3926}, {98, 10519}, {99, 54800}, {141, 60259}, {147, 60140}, {183, 43537}, {193, 3407}, {305, 37874}, {325, 14484}, {598, 32833}, {671, 32458}, {1007, 53099}, {2052, 8024}, {2996, 3314}, {3329, 32841}, {3620, 54122}, {5395, 7774}, {5485, 32869}, {6393, 60212}, {7612, 37450}, {7763, 43527}, {7778, 60262}, {7788, 54519}, {7799, 60239}, {7819, 18841}, {7840, 53101}, {7866, 18840}, {9464, 34289}, {10008, 60218}, {10159, 32828}, {10302, 46951}, {10513, 60147}, {11180, 14458}, {11286, 18842}, {11824, 14232}, {11825, 14237}, {20081, 60151}, {32817, 54859}, {32829, 60100}, {32832, 60278}, {32837, 60238}, {32838, 56059}, {32839, 60182}, {32868, 60210}, {32874, 33196}, {32875, 60146}, {32877, 53106}, {32878, 60250}, {32879, 60145}, {32880, 38259}, {32882, 43681}, {32885, 60279}, {32892, 60216}, {32896, 60282}, {33194, 60183}, {34229, 60102}, {37671, 54866}, {37689, 60093}, {40022, 59764}, {51373, 60096}

X(60201) = isotomic conjugate of X(5304)
X(60201) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 5304}, {1973, 25406}
X(60201) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 5304}, {6337, 25406}
X(60201) = pole of line {5304, 25406} with respect to the Wallace hyperbola
X(60201) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(33180)}}, {{A, B, C, X(69), X(37668)}}, {{A, B, C, X(141), X(37665)}}, {{A, B, C, X(193), X(3314)}}, {{A, B, C, X(251), X(6464)}}, {{A, B, C, X(253), X(1502)}}, {{A, B, C, X(276), X(1239)}}, {{A, B, C, X(305), X(32830)}}, {{A, B, C, X(325), X(15589)}}, {{A, B, C, X(393), X(6664)}}, {{A, B, C, X(427), X(33198)}}, {{A, B, C, X(1297), X(40802)}}, {{A, B, C, X(2998), X(56334)}}, {{A, B, C, X(3266), X(31621)}}, {{A, B, C, X(3620), X(7774)}}, {{A, B, C, X(3926), X(3933)}}, {{A, B, C, X(4232), X(33184)}}, {{A, B, C, X(4518), X(39749)}}, {{A, B, C, X(6339), X(9229)}}, {{A, B, C, X(6353), X(33200)}}, {{A, B, C, X(6393), X(10519)}}, {{A, B, C, X(6995), X(7866)}}, {{A, B, C, X(7378), X(7819)}}, {{A, B, C, X(7408), X(33194)}}, {{A, B, C, X(7778), X(37689)}}, {{A, B, C, X(9464), X(32833)}}, {{A, B, C, X(11059), X(32869)}}, {{A, B, C, X(11286), X(52284)}}, {{A, B, C, X(11824), X(11825)}}, {{A, B, C, X(18850), X(34129)}}, {{A, B, C, X(18895), X(56264)}}, {{A, B, C, X(25322), X(52187)}}, {{A, B, C, X(26235), X(46951)}}, {{A, B, C, X(30701), X(57996)}}, {{A, B, C, X(31360), X(52224)}}, {{A, B, C, X(32458), X(50567)}}, {{A, B, C, X(32828), X(39998)}}, {{A, B, C, X(32834), X(40022)}}, {{A, B, C, X(33196), X(52301)}}, {{A, B, C, X(35510), X(40405)}}, {{A, B, C, X(37174), X(37450)}}, {{A, B, C, X(42286), X(52188)}}, {{A, B, C, X(43726), X(44571)}}, {{A, B, C, X(57725), X(57726)}}
X(60201) = barycentric quotient X(i)/X(j) for these (i, j): {2, 5304}, {69, 25406}

X(60202) = X(4)X(7796)∩X(83)X(6661)

Barycentrics    ((a^2-b^2)^2+(a^2+b^2)*c^2+4*c^4)*(a^4+4*b^4+b^2*c^2+c^4+a^2*(b^2-2*c^2)) : :

X(60202) lies on the Kiepert hyperbola and on these lines: {4, 7796}, {30, 54846}, {69, 60150}, {76, 33219}, {83, 6661}, {94, 8024}, {98, 37671}, {99, 55009}, {141, 60217}, {183, 60175}, {305, 34289}, {325, 14492}, {524, 54906}, {538, 60151}, {598, 9766}, {599, 60218}, {626, 2996}, {1007, 54523}, {3314, 60214}, {3407, 7837}, {3926, 5395}, {3933, 54858}, {5978, 54561}, {5979, 54562}, {6033, 54659}, {6034, 8781}, {6393, 60101}, {7763, 18841}, {7769, 60100}, {7785, 18845}, {7788, 14458}, {7840, 54539}, {7897, 54823}, {7944, 18840}, {8363, 10159}, {8556, 60220}, {11128, 54485}, {11129, 54484}, {11163, 54773}, {11606, 32458}, {13468, 60103}, {14711, 54750}, {19130, 60127}, {24256, 60096}, {32830, 38259}, {32832, 60183}, {32869, 43681}, {32892, 60200}, {32896, 53101}, {33217, 43527}, {37668, 54519}, {40022, 59763}, {41134, 54839}, {46951, 60285}, {51373, 60098}

X(60202) = isotomic conjugate of X(5306)
X(60202) = trilinear pole of line {523, 53369}
X(60202) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 5306}, {1973, 48906}
X(60202) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 5306}, {6337, 48906}
X(60202) = pole of line {5306, 48906} with respect to the Wallace hyperbola
X(60202) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(33219)}}, {{A, B, C, X(141), X(9300)}}, {{A, B, C, X(305), X(32833)}}, {{A, B, C, X(308), X(55958)}}, {{A, B, C, X(325), X(37671)}}, {{A, B, C, X(427), X(6661)}}, {{A, B, C, X(428), X(8363)}}, {{A, B, C, X(599), X(9766)}}, {{A, B, C, X(1239), X(57899)}}, {{A, B, C, X(1494), X(1502)}}, {{A, B, C, X(1799), X(7809)}}, {{A, B, C, X(1989), X(6664)}}, {{A, B, C, X(3314), X(7837)}}, {{A, B, C, X(4590), X(40829)}}, {{A, B, C, X(5064), X(33217)}}, {{A, B, C, X(6034), X(47734)}}, {{A, B, C, X(6393), X(48876)}}, {{A, B, C, X(7796), X(34386)}}, {{A, B, C, X(7799), X(8024)}}, {{A, B, C, X(7944), X(42037)}}, {{A, B, C, X(8556), X(11184)}}, {{A, B, C, X(8770), X(11060)}}, {{A, B, C, X(9516), X(11058)}}, {{A, B, C, X(13468), X(22110)}}, {{A, B, C, X(18361), X(41909)}}, {{A, B, C, X(31621), X(44168)}}, {{A, B, C, X(32836), X(57518)}}, {{A, B, C, X(42407), X(57822)}}, {{A, B, C, X(57547), X(57558)}}
X(60202) = barycentric quotient X(i)/X(j) for these (i, j): {2, 5306}, {69, 48906}

X(60203) = X(2)X(319)∩X(4)X(2355)

Barycentrics    (b+c)*(2*(a+b)+c)*(2*a+b+2*c) : :

X(60203) lies on the Kiepert hyperbola and on these lines: {2, 319}, {4, 2355}, {9, 54928}, {10, 1962}, {37, 6539}, {63, 60083}, {76, 4359}, {81, 32014}, {83, 29610}, {94, 20566}, {98, 8652}, {226, 40999}, {306, 60243}, {321, 1213}, {671, 32042}, {756, 34475}, {1029, 19808}, {1211, 30588}, {1268, 2160}, {1441, 43682}, {1573, 26747}, {1698, 5278}, {2052, 25001}, {2996, 19822}, {3210, 28651}, {3305, 54586}, {3828, 5294}, {3936, 56226}, {3995, 27797}, {4049, 50457}, {4052, 27823}, {4080, 31993}, {4358, 34258}, {4444, 6546}, {4640, 46896}, {4980, 17248}, {5224, 27186}, {5235, 14534}, {5257, 60267}, {5273, 54760}, {5435, 60076}, {5744, 54788}, {5745, 54768}, {6625, 26044}, {8040, 50312}, {9776, 54831}, {10159, 16815}, {13478, 55867}, {17019, 31248}, {17147, 28633}, {17260, 54686}, {17289, 55027}, {17308, 60075}, {17758, 24603}, {17776, 43533}, {18230, 54759}, {19732, 34819}, {19875, 60079}, {21454, 52422}, {24589, 40013}, {24624, 37211}, {26037, 60110}, {26065, 54770}, {26251, 45964}, {27065, 54648}, {27131, 60071}, {28595, 40718}, {28606, 56210}, {29607, 56059}, {29608, 43527}, {29628, 60278}, {31018, 53854}, {31231, 60085}, {31247, 60251}, {32779, 54119}, {33108, 54883}, {33113, 60206}, {33157, 60149}, {40435, 57710}, {40603, 60244}, {40663, 60321}, {41820, 50095}, {46932, 60077}, {50298, 59261}, {54288, 60116}, {54357, 60172}, {55868, 60156}, {59312, 60109}

X(60203) = isotomic conjugate of X(5333)
X(60203) = complement of X(30562)
X(60203) = trilinear pole of line {4170, 4983}
X(60203) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 4658}, {31, 5333}, {48, 31902}, {56, 4877}, {58, 16777}, {101, 4840}, {110, 4813}, {163, 4802}, {284, 5221}, {662, 4834}, {692, 4960}, {1333, 1698}, {1408, 4007}, {1412, 3715}, {1474, 3927}, {1576, 4823}, {2194, 4654}, {2206, 28605}, {3737, 36074}, {4556, 48005}, {4610, 58290}, {4716, 18268}, {4756, 57129}, {4826, 52935}, {4880, 34079}, {30595, 36142}
X(60203) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 4877}, {2, 5333}, {9, 4658}, {10, 16777}, {37, 1698}, {115, 4802}, {244, 4813}, {1015, 4840}, {1084, 4834}, {1086, 4960}, {1214, 4654}, {1249, 31902}, {4858, 4823}, {6741, 4820}, {23992, 30595}, {35068, 4716}, {35069, 4880}, {40590, 5221}, {40599, 3715}, {40603, 28605}, {40937, 3824}, {51574, 3927}, {52872, 4727}, {55065, 4838}, {59577, 4007}
X(60203) = X(i)-Ceva conjugate of X(j) for these {i, j}: {30598, 56221}
X(60203) = X(i)-cross conjugate of X(j) for these {i, j}: {3841, 1441}, {4841, 3952}, {47678, 190}, {48551, 4033}, {56810, 321}
X(60203) = pole of line {4834, 28328} with respect to the orthoptic circle of the Steiner inellipse
X(60203) = pole of line {56810, 60203} with respect to the Kiepert hyperbola
X(60203) = pole of line {19862, 56221} with respect to the dual conic of Yff parabola
X(60203) = pole of line {4958, 30595} with respect to the dual conic of Wallace hyperbola
X(60203) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(37), X(81)}}, {{A, B, C, X(42), X(29576)}}, {{A, B, C, X(65), X(1255)}}, {{A, B, C, X(75), X(17394)}}, {{A, B, C, X(88), X(56213)}}, {{A, B, C, X(189), X(56157)}}, {{A, B, C, X(210), X(41798)}}, {{A, B, C, X(239), X(50522)}}, {{A, B, C, X(306), X(9780)}}, {{A, B, C, X(313), X(28650)}}, {{A, B, C, X(319), X(1268)}}, {{A, B, C, X(333), X(3701)}}, {{A, B, C, X(335), X(28639)}}, {{A, B, C, X(523), X(4725)}}, {{A, B, C, X(525), X(28146)}}, {{A, B, C, X(693), X(41851)}}, {{A, B, C, X(756), X(16606)}}, {{A, B, C, X(1211), X(5235)}}, {{A, B, C, X(1214), X(3579)}}, {{A, B, C, X(1224), X(40394)}}, {{A, B, C, X(1427), X(30582)}}, {{A, B, C, X(1654), X(26044)}}, {{A, B, C, X(1698), X(30603)}}, {{A, B, C, X(2321), X(30711)}}, {{A, B, C, X(3759), X(3896)}}, {{A, B, C, X(3842), X(50298)}}, {{A, B, C, X(3948), X(47666)}}, {{A, B, C, X(3995), X(24589)}}, {{A, B, C, X(3998), X(25001)}}, {{A, B, C, X(4006), X(46196)}}, {{A, B, C, X(4358), X(31993)}}, {{A, B, C, X(4641), X(33761)}}, {{A, B, C, X(4651), X(24603)}}, {{A, B, C, X(4674), X(25430)}}, {{A, B, C, X(5224), X(5278)}}, {{A, B, C, X(5257), X(21454)}}, {{A, B, C, X(5435), X(52353)}}, {{A, B, C, X(5839), X(14624)}}, {{A, B, C, X(5936), X(51561)}}, {{A, B, C, X(6605), X(53013)}}, {{A, B, C, X(6650), X(56222)}}, {{A, B, C, X(8056), X(56134)}}, {{A, B, C, X(9778), X(56944)}}, {{A, B, C, X(14621), X(56123)}}, {{A, B, C, X(15320), X(28640)}}, {{A, B, C, X(15523), X(29610)}}, {{A, B, C, X(16603), X(28595)}}, {{A, B, C, X(17038), X(28606)}}, {{A, B, C, X(17228), X(48648)}}, {{A, B, C, X(17239), X(55078)}}, {{A, B, C, X(17259), X(33172)}}, {{A, B, C, X(17275), X(56046)}}, {{A, B, C, X(17348), X(56122)}}, {{A, B, C, X(19732), X(32782)}}, {{A, B, C, X(19808), X(42710)}}, {{A, B, C, X(25003), X(26638)}}, {{A, B, C, X(25056), X(43732)}}, {{A, B, C, X(25417), X(56221)}}, {{A, B, C, X(26580), X(31231)}}, {{A, B, C, X(27789), X(53114)}}, {{A, B, C, X(28605), X(30561)}}, {{A, B, C, X(30608), X(30713)}}, {{A, B, C, X(31247), X(35466)}}, {{A, B, C, X(31248), X(41818)}}, {{A, B, C, X(31503), X(56037)}}, {{A, B, C, X(32008), X(56246)}}, {{A, B, C, X(35058), X(42285)}}, {{A, B, C, X(39394), X(40142)}}, {{A, B, C, X(39700), X(39708)}}, {{A, B, C, X(39980), X(56215)}}, {{A, B, C, X(40161), X(52388)}}, {{A, B, C, X(40434), X(56174)}}, {{A, B, C, X(41850), X(43758)}}, {{A, B, C, X(52651), X(56158)}}, {{A, B, C, X(56061), X(56351)}}, {{A, B, C, X(56169), X(56251)}}
X(60203) = barycentric product X(i)*X(j) for these (i, j): {10, 30598}, {226, 42030}, {313, 56343}, {850, 8652}, {1441, 56203}, {1577, 37211}, {4033, 48074}, {25417, 321}, {27801, 34819}, {28625, 76}, {30588, 30590}, {30597, 4066}, {32042, 523}, {56221, 75}
X(60203) = barycentric quotient X(i)/X(j) for these (i, j): {1, 4658}, {2, 5333}, {4, 31902}, {9, 4877}, {10, 1698}, {37, 16777}, {65, 5221}, {72, 3927}, {210, 3715}, {226, 4654}, {313, 30596}, {321, 28605}, {442, 3824}, {512, 4834}, {513, 4840}, {514, 4960}, {523, 4802}, {661, 4813}, {690, 30595}, {740, 4716}, {758, 4880}, {1089, 4066}, {1577, 4823}, {2321, 4007}, {3671, 5586}, {3697, 51572}, {3700, 4820}, {3841, 41862}, {3943, 4727}, {3950, 4898}, {3952, 4756}, {3967, 4942}, {4010, 4810}, {4024, 4838}, {4062, 4938}, {4079, 4826}, {4120, 4958}, {4170, 4961}, {4559, 36074}, {4705, 48005}, {4824, 4963}, {4838, 53585}, {6539, 43260}, {7265, 23883}, {8652, 110}, {14321, 4949}, {25417, 81}, {28625, 6}, {30588, 30589}, {30590, 5235}, {30598, 86}, {32042, 99}, {34819, 1333}, {37211, 662}, {42030, 333}, {47701, 47902}, {48074, 1019}, {50487, 58290}, {56070, 1790}, {56203, 21}, {56221, 1}, {56343, 58}
X(60203) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 25417, 30598}, {2, 30590, 25417}, {25417, 30590, 42030}

X(60204) = X(2)X(6423)∩X(6)X(5490)

Barycentrics    3*a^4+6*a^2*b^2-b^4+6*a^2*c^2+6*b^2*c^2-c^4+(8*a^2+4*b^2+4*c^2)*S : :

X(60204) lies on the Kiepert hyperbola and on these lines: {2, 6423}, {3, 45101}, {4, 43119}, {5, 14229}, {6, 5490}, {76, 3068}, {381, 54652}, {384, 54127}, {485, 11292}, {486, 3618}, {491, 18840}, {590, 5491}, {640, 10195}, {1131, 11294}, {1132, 32489}, {2996, 49220}, {3069, 60194}, {3589, 14064}, {5591, 10159}, {6290, 7612}, {6421, 60260}, {6568, 42561}, {7920, 54126}, {8781, 13989}, {8972, 41485}, {8974, 60259}, {13637, 60143}, {13638, 60212}, {13882, 32973}, {13910, 32828}, {14033, 53482}, {14232, 48467}, {14241, 26619}, {14244, 37343}, {16041, 54626}, {16043, 53487}, {18583, 45102}, {32785, 60196}, {42024, 45576}, {59373, 60223}

X(60204) = isogonal conjugate of X(6422)
X(60204) = isotomic conjugate of X(5590)
X(60204) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 6422}, {31, 5590}, {48, 3127}, {63, 45400}, {19215, 26373}, {19218, 19446}
X(60204) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 5590}, {3, 6422}, {1249, 3127}, {3162, 45400}
X(60204) = pole of line {6422, 32569} with respect to the Stammler hyperbola
X(60204) = pole of line {5590, 6422} with respect to the Wallace hyperbola
X(60204) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(43119)}}, {{A, B, C, X(6), X(3068)}}, {{A, B, C, X(372), X(30535)}}, {{A, B, C, X(491), X(3618)}}, {{A, B, C, X(493), X(8946)}}, {{A, B, C, X(588), X(56004)}}, {{A, B, C, X(590), X(3069)}}, {{A, B, C, X(1123), X(17743)}}, {{A, B, C, X(1336), X(14621)}}, {{A, B, C, X(1659), X(30701)}}, {{A, B, C, X(2987), X(5417)}}, {{A, B, C, X(40416), X(55020)}}
X(60204) = barycentric quotient X(i)/X(j) for these (i, j): {2, 5590}, {4, 3127}, {6, 6422}, {25, 45400}, {493, 45415}, {494, 45726}, {8948, 26373}, {10132, 19446}, {19219, 1165}

X(60205) = X(2)X(6424)∩X(6)X(5491)

Barycentrics    -3*a^4-6*a^2*b^2+b^4-6*a^2*c^2-6*b^2*c^2+c^4+(8*a^2+4*b^2+4*c^2)*S : :

X(60205) lies on the Kiepert hyperbola and on these lines: {2, 6424}, {3, 45102}, {4, 43118}, {5, 14244}, {6, 5491}, {76, 3069}, {381, 54653}, {384, 54126}, {485, 3618}, {486, 11291}, {492, 18840}, {615, 5490}, {639, 10194}, {1131, 32488}, {1132, 11293}, {2996, 49221}, {3068, 60196}, {3589, 14064}, {5590, 10159}, {6289, 7612}, {6422, 60260}, {6569, 31412}, {7920, 54127}, {8781, 8997}, {13757, 60143}, {13758, 60212}, {13934, 32973}, {13941, 41486}, {13950, 60259}, {13972, 32828}, {14033, 53483}, {14069, 32807}, {14226, 26620}, {14229, 37342}, {14237, 48466}, {16041, 54625}, {16043, 53488}, {18583, 45101}, {32786, 60194}, {42023, 45577}, {59373, 60224}

X(60205) = isogonal conjugate of X(6421)
X(60205) = isotomic conjugate of X(5591)
X(60205) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 6421}, {31, 5591}, {48, 3128}, {63, 45401}, {19216, 26374}, {19217, 19447}
X(60205) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 5591}, {3, 6421}, {1249, 3128}, {3162, 45401}
X(60205) = pole of line {6421, 32562} with respect to the Stammler hyperbola
X(60205) = pole of line {5591, 6421} with respect to the Wallace hyperbola
X(60205) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(43118)}}, {{A, B, C, X(6), X(3069)}}, {{A, B, C, X(371), X(30535)}}, {{A, B, C, X(492), X(3618)}}, {{A, B, C, X(494), X(8948)}}, {{A, B, C, X(589), X(56004)}}, {{A, B, C, X(615), X(3068)}}, {{A, B, C, X(1123), X(14621)}}, {{A, B, C, X(1336), X(17743)}}, {{A, B, C, X(2987), X(5419)}}, {{A, B, C, X(13390), X(30701)}}, {{A, B, C, X(40416), X(55021)}}
X(60205) = barycentric quotient X(i)/X(j) for these (i, j): {2, 5591}, {4, 3128}, {6, 6421}, {25, 45401}, {493, 45727}, {494, 45414}, {8946, 26374}, {10133, 19447}, {19219, 1163}

X(60206) = X(2)X(332)∩X(4)X(333)

Barycentrics    ((a-b)^2*(a+b)-(a+b)^2*c-3*(a+b)*c^2-c^3)*(a^3-a^2*(b+c)-(b+c)*(b^2+2*b*c-c^2)-a*(3*b^2+2*b*c+c^2)) : :

X(60206) lies on the Kiepert hyperbola and on these lines: {2, 332}, {4, 333}, {8, 60321}, {10, 345}, {69, 226}, {75, 40149}, {274, 58011}, {321, 3718}, {376, 54677}, {377, 60086}, {391, 45100}, {459, 5931}, {464, 60088}, {940, 58012}, {966, 34258}, {1029, 5361}, {1150, 60156}, {1211, 60254}, {1446, 7182}, {1654, 60261}, {2051, 5816}, {2052, 44130}, {3424, 37443}, {3545, 54722}, {3597, 9534}, {5233, 45098}, {5271, 30479}, {5278, 60155}, {5292, 43531}, {5372, 60258}, {5397, 28935}, {5739, 60071}, {6625, 37683}, {7019, 60245}, {13576, 37193}, {14534, 37642}, {14552, 60170}, {14829, 60076}, {17277, 60107}, {17758, 18141}, {19730, 33026}, {19732, 32022}, {23600, 60188}, {24597, 60082}, {26098, 51196}, {26117, 43533}, {32782, 60242}, {33113, 60203}, {33137, 40718}, {34260, 41015}, {37653, 60257}, {37655, 57826}, {37666, 60077}, {37669, 56216}, {39595, 56226}, {48870, 60078}, {49729, 60079}, {50107, 60267}

X(60206) = isotomic conjugate of X(5712)
X(60206) = trilinear pole of line {6332, 48136}
X(60206) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 54421}, {31, 5712}, {48, 37384}, {1402, 37265}, {2203, 8896}, {23602, 57652}
X(60206) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 5712}, {9, 54421}, {1249, 37384}, {40605, 37265}
X(60206) = X(i)-cross conjugate of X(j) for these {i, j}: {5737, 2}, {50065, 7}
X(60206) = pole of line {5737, 60206} with respect to the Kiepert hyperbola
X(60206) = pole of line {5712, 23602} with respect to the Wallace hyperbola
X(60206) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(37870)}}, {{A, B, C, X(8), X(11679)}}, {{A, B, C, X(27), X(13725)}}, {{A, B, C, X(37), X(940)}}, {{A, B, C, X(57), X(256)}}, {{A, B, C, X(68), X(5788)}}, {{A, B, C, X(69), X(75)}}, {{A, B, C, X(189), X(274)}}, {{A, B, C, X(257), X(278)}}, {{A, B, C, X(280), X(7058)}}, {{A, B, C, X(312), X(57906)}}, {{A, B, C, X(377), X(20911)}}, {{A, B, C, X(391), X(37655)}}, {{A, B, C, X(594), X(2165)}}, {{A, B, C, X(596), X(39696)}}, {{A, B, C, X(967), X(1245)}}, {{A, B, C, X(1000), X(39694)}}, {{A, B, C, X(1150), X(5739)}}, {{A, B, C, X(1211), X(37642)}}, {{A, B, C, X(1219), X(2985)}}, {{A, B, C, X(1222), X(42030)}}, {{A, B, C, X(1257), X(56204)}}, {{A, B, C, X(1654), X(37683)}}, {{A, B, C, X(2895), X(5361)}}, {{A, B, C, X(3617), X(39595)}}, {{A, B, C, X(3661), X(33137)}}, {{A, B, C, X(3666), X(4492)}}, {{A, B, C, X(3926), X(56944)}}, {{A, B, C, X(4648), X(19732)}}, {{A, B, C, X(5232), X(37666)}}, {{A, B, C, X(5271), X(54433)}}, {{A, B, C, X(5292), X(56810)}}, {{A, B, C, X(5372), X(37656)}}, {{A, B, C, X(5559), X(42360)}}, {{A, B, C, X(5712), X(5737)}}, {{A, B, C, X(6734), X(23600)}}, {{A, B, C, X(7018), X(57787)}}, {{A, B, C, X(7490), X(26117)}}, {{A, B, C, X(8770), X(57652)}}, {{A, B, C, X(8797), X(57910)}}, {{A, B, C, X(14555), X(14829)}}, {{A, B, C, X(15149), X(37193)}}, {{A, B, C, X(15232), X(31993)}}, {{A, B, C, X(15315), X(53083)}}, {{A, B, C, X(15474), X(48837)}}, {{A, B, C, X(17275), X(17314)}}, {{A, B, C, X(17277), X(18141)}}, {{A, B, C, X(19804), X(50107)}}, {{A, B, C, X(24597), X(32782)}}, {{A, B, C, X(28605), X(33113)}}, {{A, B, C, X(29593), X(29635)}}, {{A, B, C, X(30701), X(40435)}}, {{A, B, C, X(34277), X(52344)}}, {{A, B, C, X(34527), X(43734)}}, {{A, B, C, X(37443), X(52283)}}, {{A, B, C, X(37652), X(37653)}}, {{A, B, C, X(37887), X(57725)}}, {{A, B, C, X(40412), X(57825)}}, {{A, B, C, X(43740), X(46880)}}, {{A, B, C, X(56046), X(59760)}}, {{A, B, C, X(57705), X(57749)}}, {{A, B, C, X(57824), X(57858)}}
X(60206) = barycentric quotient X(i)/X(j) for these (i, j): {1, 54421}, {2, 5712}, {4, 37384}, {306, 8896}, {333, 37265}, {1812, 23602}

X(60207) = X(2)X(13832)∩X(4)X(33457)

Barycentrics    3*a^4-2*a^2*b^2-9*b^4-2*a^2*c^2+22*b^2*c^2-9*c^4+(8*a^2-4*b^2-4*c^2)*S : :

X(60207) lies on the Kiepert hyperbola and on these lines: {2, 13832}, {4, 33457}, {6, 54626}, {30, 14244}, {69, 42023}, {381, 45102}, {485, 13835}, {486, 12323}, {488, 3317}, {524, 60208}, {598, 19054}, {641, 43559}, {671, 5861}, {1132, 12222}, {1271, 54506}, {1327, 22645}, {1328, 1992}, {3068, 54507}, {3069, 54504}, {3316, 26620}, {3590, 11293}, {3591, 32488}, {3830, 54653}, {5032, 49263}, {5485, 32809}, {5490, 16041}, {6222, 12297}, {10194, 55041}, {10195, 11291}, {12159, 54628}, {12257, 14238}, {12602, 14229}, {12816, 36342}, {12817, 36343}, {12819, 45024}, {13637, 13798}, {13639, 43566}, {13757, 54597}, {13759, 60300}, {13794, 14234}, {13811, 54874}, {13821, 43568}, {14033, 53482}, {14041, 54126}, {14226, 45421}, {18845, 44647}, {19053, 54503}, {19100, 59373}, {22807, 60127}, {22874, 36372}, {22919, 36370}, {32787, 54625}, {32810, 60223}, {32811, 42024}, {33456, 60150}, {36348, 54538}, {36356, 54535}, {36450, 54617}, {36468, 54618}, {45107, 51537}

X(60207) = midpoint of X(i) and X(j) for these {i,j}: {1328, 22485}
X(60207) = reflection of X(i) in X(j) for these {i,j}: {2, 13850}
X(60207) = isotomic conjugate of X(5860)
X(60207) = trilinear pole of line {44400, 523}
X(60207) = pole of line {1991, 60207} with respect to the Kiepert hyperbola
X(60207) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(524), X(5861)}}, {{A, B, C, X(588), X(30541)}}, {{A, B, C, X(589), X(21399)}}, {{A, B, C, X(599), X(19054)}}, {{A, B, C, X(8577), X(14498)}}, {{A, B, C, X(13428), X(41491)}}, {{A, B, C, X(13439), X(32421)}}, {{A, B, C, X(43098), X(55021)}}
X(60207) = barycentric product X(i)*X(j) for these (i, j): {41444, 76}
X(60207) = barycentric quotient X(i)/X(j) for these (i, j): {2, 5860}, {41444, 6}

X(60208) = X(2)X(9600)∩X(4)X(33456)

Barycentrics    -3*a^4+2*a^2*b^2+9*b^4+2*a^2*c^2-22*b^2*c^2+9*c^4+(8*a^2-4*b^2-4*c^2)*S" : :

X(60208) lies on the Kiepert hyperbola and on these lines: {2, 9600}, {4, 33456}, {6, 54625}, {30, 14229}, {69, 42024}, {381, 45101}, {485, 12322}, {486, 13712}, {487, 3316}, {524, 60207}, {598, 19053}, {642, 43558}, {671, 5860}, {1131, 12221}, {1270, 54502}, {1327, 1992}, {1328, 22616}, {3068, 54505}, {3069, 54503}, {3317, 26619}, {3590, 32489}, {3591, 11294}, {3830, 54652}, {5032, 49260}, {5485, 32808}, {5491, 16041}, {5861, 60195}, {6399, 12296}, {10194, 11292}, {10195, 55040}, {12158, 54627}, {12256, 14234}, {12601, 14244}, {12816, 36340}, {12817, 36341}, {12818, 45023}, {13637, 43536}, {13639, 60299}, {13674, 14238}, {13678, 13757}, {13690, 54876}, {13701, 43569}, {13759, 43567}, {14033, 53483}, {14041, 54127}, {14241, 45420}, {18845, 44648}, {19054, 54507}, {19099, 59373}, {22806, 60127}, {22872, 36374}, {22917, 36371}, {32788, 54626}, {32810, 42023}, {32811, 60224}, {33457, 60150}, {36349, 50246}, {36357, 54534}, {36449, 54618}, {36467, 54617}, {45106, 51537}

X(60208) = midpoint of X(i) and X(j) for these {i,j}: {1327, 22484}
X(60208) = reflection of X(i) in X(j) for these {i,j}: {2, 13932}
X(60208) = isotomic conjugate of X(5861)
X(60208) = trilinear pole of line {44393, 523}
X(60208) = pole of line {591, 60208} with respect to the Kiepert hyperbola
X(60208) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(9600)}}, {{A, B, C, X(524), X(5860)}}, {{A, B, C, X(588), X(21399)}}, {{A, B, C, X(589), X(30541)}}, {{A, B, C, X(599), X(19053)}}, {{A, B, C, X(8576), X(14498)}}, {{A, B, C, X(13428), X(32419)}}, {{A, B, C, X(13439), X(41490)}}, {{A, B, C, X(43098), X(55020)}}
X(60208) = barycentric product X(i)*X(j) for these (i, j): {41445, 76}
X(60208) = barycentric quotient X(i)/X(j) for these (i, j): {2, 5861}, {41445, 6}

X(60209) = X(2)X(31457)∩X(98)X(1657)

Barycentrics    (2*(a^2+b^2)-5*c^2)*(2*a^2-5*b^2+2*c^2) : :
X(60209) = -4*X[550]+9*X[60335]

X(60209) lies on the Kiepert hyperbola and on these lines: {2, 31457}, {3, 54644}, {4, 55716}, {5, 54645}, {6, 60146}, {30, 54851}, {98, 1657}, {140, 11668}, {148, 60136}, {262, 3850}, {315, 60219}, {316, 38259}, {381, 54734}, {382, 54934}, {548, 60175}, {550, 60335}, {671, 7860}, {1656, 53108}, {2996, 7768}, {3091, 54522}, {3424, 50691}, {3522, 54921}, {3627, 14458}, {3843, 14492}, {3851, 54920}, {5072, 60192}, {5254, 43527}, {5286, 60145}, {6144, 53106}, {6656, 60277}, {7607, 15712}, {7612, 21735}, {7620, 54639}, {7760, 45103}, {7770, 60238}, {7790, 60278}, {7812, 54494}, {7827, 54616}, {7841, 60216}, {7878, 18842}, {7894, 18845}, {7918, 10159}, {7937, 18840}, {8370, 60283}, {8587, 33268}, {10302, 34505}, {11054, 32532}, {11172, 33247}, {11185, 18841}, {11289, 43548}, {11290, 43549}, {11303, 54593}, {11304, 54594}, {13102, 54561}, {13103, 54562}, {14040, 43528}, {14044, 54540}, {14066, 54539}, {14893, 54582}, {15684, 54608}, {17538, 60185}, {19695, 60218}, {23046, 54643}, {32455, 53107}, {33286, 43529}, {33703, 60150}, {36993, 54849}, {36995, 54850}, {38335, 54477}, {38664, 54659}, {38734, 54723}, {43448, 60285}, {43676, 44518}, {47286, 53105}, {49140, 54866}

X(60209) = isotomic conjugate of X(6144)
X(60209) = X(i)-cross conjugate of X(j) for these {i, j}: {3630, 2}, {31101, 264}
X(60209) = pole of line {3630, 60209} with respect to the Kiepert hyperbola
X(60209) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55716)}}, {{A, B, C, X(6), X(31652)}}, {{A, B, C, X(249), X(3532)}}, {{A, B, C, X(257), X(43732)}}, {{A, B, C, X(297), X(1657)}}, {{A, B, C, X(335), X(43731)}}, {{A, B, C, X(3519), X(9289)}}, {{A, B, C, X(3627), X(11331)}}, {{A, B, C, X(3630), X(6144)}}, {{A, B, C, X(3843), X(52289)}}, {{A, B, C, X(7768), X(54412)}}, {{A, B, C, X(7860), X(44146)}}, {{A, B, C, X(10630), X(57688)}}, {{A, B, C, X(14861), X(42313)}}, {{A, B, C, X(15712), X(52282)}}, {{A, B, C, X(21735), X(37174)}}, {{A, B, C, X(22336), X(31360)}}, {{A, B, C, X(30541), X(43908)}}, {{A, B, C, X(34860), X(35170)}}, {{A, B, C, X(43719), X(56004)}}, {{A, B, C, X(50691), X(52283)}}, {{A, B, C, X(52441), X(53201)}}
X(60209) = barycentric product X(i)*X(j) for these (i, j): {58095, 850}
X(60209) = barycentric quotient X(i)/X(j) for these (i, j): {2, 6144}, {58095, 110}
X(60209) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 31652, 55799}

X(60210) = X(2)X(55782)∩X(4)X(32027)

Barycentrics    (a^2+6*b^2+c^2)*(a^2+b^2+6*c^2) : :

X(60210) lies on the Kiepert hyperbola and on these lines: {2, 55782}, {3, 55727}, {4, 32027}, {30, 54852}, {69, 18843}, {83, 3629}, {98, 3530}, {141, 43676}, {262, 5079}, {315, 53101}, {382, 60326}, {546, 54890}, {547, 60192}, {550, 54857}, {599, 54494}, {632, 53104}, {1916, 33284}, {3096, 5485}, {3407, 14038}, {3529, 60325}, {3631, 53109}, {3851, 60329}, {5054, 60175}, {5070, 11669}, {5254, 60216}, {6656, 60250}, {7754, 43527}, {7760, 18841}, {7790, 43681}, {7812, 60284}, {7827, 60279}, {7883, 17503}, {7894, 60239}, {7909, 60233}, {7911, 53105}, {8703, 54608}, {12103, 54891}, {14047, 60231}, {14061, 35005}, {14458, 15681}, {14492, 38071}, {15692, 54866}, {15710, 60150}, {19709, 54643}, {32868, 60201}, {32886, 60262}, {33229, 53106}, {40341, 53102}, {46936, 60333}, {55864, 60102}

X(60210) = isotomic conjugate of X(6329)
X(60210) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55587)}}, {{A, B, C, X(141), X(3629)}}, {{A, B, C, X(257), X(13602)}}, {{A, B, C, X(297), X(3530)}}, {{A, B, C, X(327), X(57897)}}, {{A, B, C, X(419), X(33284)}}, {{A, B, C, X(458), X(5079)}}, {{A, B, C, X(5117), X(14038)}}, {{A, B, C, X(6292), X(33666)}}, {{A, B, C, X(11331), X(15681)}}, {{A, B, C, X(30495), X(36615)}}, {{A, B, C, X(33229), X(52297)}}, {{A, B, C, X(35140), X(57894)}}, {{A, B, C, X(38071), X(52289)}}, {{A, B, C, X(41440), X(42346)}}, {{A, B, C, X(56353), X(57725)}}

X(60211) = X(2)X(5107)∩X(6)X(60103)

Barycentrics    (2*(a^4-4*a^2*b^2+b^4)-5*(a^2+b^2)*c^2+5*c^4)*(2*a^4+5*b^4-5*b^2*c^2+2*c^4-a^2*(5*b^2+8*c^2)) : :

X(60211) lies on the Kiepert hyperbola and on these lines: {2, 5107}, {6, 60103}, {76, 22110}, {83, 42849}, {98, 11163}, {114, 60176}, {325, 11167}, {381, 60189}, {524, 60220}, {597, 60093}, {598, 3815}, {599, 60101}, {671, 11184}, {1007, 5485}, {1992, 7612}, {2482, 54872}, {2996, 34511}, {3972, 18842}, {5395, 31401}, {5461, 54750}, {5475, 53101}, {5476, 14494}, {7607, 22329}, {7757, 43532}, {7777, 25486}, {7778, 10302}, {7840, 60128}, {8176, 41895}, {8781, 50639}, {8860, 53104}, {9770, 11172}, {10484, 17005}, {11059, 57813}, {11168, 60248}, {14614, 54644}, {22486, 60096}, {23053, 60123}, {23055, 53103}, {34803, 60240}, {37647, 42011}, {41624, 60175}

X(60211) = isotomic conjugate of X(7610)
X(60211) = trilinear pole of line {39905, 523}
X(60211) = pole of line {9771, 60211} with respect to the Kiepert hyperbola
X(60211) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(5107)}}, {{A, B, C, X(141), X(42849)}}, {{A, B, C, X(264), X(18823)}}, {{A, B, C, X(325), X(11163)}}, {{A, B, C, X(524), X(11184)}}, {{A, B, C, X(597), X(7778)}}, {{A, B, C, X(599), X(3815)}}, {{A, B, C, X(1007), X(1992)}}, {{A, B, C, X(3613), X(9164)}}, {{A, B, C, X(5094), X(8598)}}, {{A, B, C, X(7610), X(9771)}}, {{A, B, C, X(7777), X(7840)}}, {{A, B, C, X(8770), X(34154)}}, {{A, B, C, X(8860), X(37647)}}, {{A, B, C, X(8889), X(35287)}}, {{A, B, C, X(11168), X(31489)}}, {{A, B, C, X(11588), X(39955)}}, {{A, B, C, X(14608), X(31859)}}, {{A, B, C, X(21399), X(21448)}}, {{A, B, C, X(23055), X(34803)}}, {{A, B, C, X(34511), X(57518)}}

X(60212) = X(4)X(183)∩X(69)X(262)

Barycentrics    ((a^2-b^2)^2-4*(a^2+b^2)*c^2-c^4)*(a^4-b^4-4*b^2*c^2+c^4-2*a^2*(2*b^2+c^2)) : :

X(60212) lies on the Kiepert hyperbola and on these lines: {4, 183}, {30, 54856}, {69, 262}, {76, 7738}, {83, 7735}, {98, 25406}, {141, 40824}, {316, 54814}, {325, 14494}, {376, 54678}, {385, 60190}, {524, 60268}, {598, 32983}, {671, 32986}, {1007, 7608}, {1078, 53015}, {1370, 55028}, {1916, 16990}, {1992, 54509}, {2052, 37187}, {2996, 7791}, {3266, 59763}, {3314, 60234}, {3407, 17008}, {3424, 37182}, {3524, 5989}, {3545, 54826}, {3619, 60213}, {3620, 60260}, {3926, 18840}, {5071, 54724}, {5392, 39998}, {5395, 16924}, {5485, 46951}, {5503, 21356}, {5976, 43532}, {6393, 60201}, {6655, 32872}, {6997, 30505}, {7612, 37688}, {7736, 60096}, {7763, 10159}, {7769, 60278}, {7774, 60098}, {7788, 54523}, {7792, 18841}, {7799, 60277}, {9466, 54751}, {9478, 33285}, {10153, 23053}, {10302, 32833}, {10513, 60331}, {11056, 43530}, {11168, 11172}, {11185, 22676}, {11669, 34803}, {13638, 60204}, {13758, 60205}, {14484, 15589}, {16044, 18845}, {16986, 60232}, {16989, 60129}, {18842, 22329}, {26235, 34289}, {26243, 60155}, {26244, 32022}, {31276, 60151}, {32829, 60183}, {32830, 60285}, {32836, 60143}, {32874, 60200}, {32886, 60219}, {32893, 33017}, {32985, 54752}, {33016, 53101}, {33020, 60145}, {33021, 43681}, {33238, 53105}, {37637, 60263}, {37647, 53098}, {37668, 53099}, {37670, 60153}, {37671, 60127}, {37690, 60178}, {40016, 40822}, {40236, 60147}, {46336, 60111}, {47061, 54840}, {51373, 60099}, {57518, 59764}

X(60212) = isotomic conjugate of X(7736)
X(60212) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 7736}, {1973, 10519}
X(60212) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 7736}, {6337, 10519}
X(60212) = pole of line {15271, 60212} with respect to the Kiepert hyperbola
X(60212) = pole of line {7736, 10519} with respect to the Wallace hyperbola
X(60212) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(37187)}}, {{A, B, C, X(25), X(16043)}}, {{A, B, C, X(66), X(34816)}}, {{A, B, C, X(69), X(183)}}, {{A, B, C, X(141), X(2165)}}, {{A, B, C, X(182), X(35439)}}, {{A, B, C, X(253), X(56067)}}, {{A, B, C, X(257), X(57727)}}, {{A, B, C, X(305), X(32828)}}, {{A, B, C, X(325), X(34229)}}, {{A, B, C, X(335), X(57726)}}, {{A, B, C, X(385), X(16990)}}, {{A, B, C, X(393), X(31360)}}, {{A, B, C, X(427), X(32968)}}, {{A, B, C, X(468), X(32986)}}, {{A, B, C, X(524), X(42850)}}, {{A, B, C, X(695), X(7738)}}, {{A, B, C, X(1007), X(37688)}}, {{A, B, C, X(1297), X(30541)}}, {{A, B, C, X(1502), X(8797)}}, {{A, B, C, X(1799), X(3785)}}, {{A, B, C, X(2980), X(44571)}}, {{A, B, C, X(2998), X(17040)}}, {{A, B, C, X(3296), X(40738)}}, {{A, B, C, X(3314), X(17008)}}, {{A, B, C, X(3618), X(52395)}}, {{A, B, C, X(3619), X(7792)}}, {{A, B, C, X(3620), X(37667)}}, {{A, B, C, X(4648), X(26244)}}, {{A, B, C, X(5094), X(32983)}}, {{A, B, C, X(5481), X(56004)}}, {{A, B, C, X(5486), X(9462)}}, {{A, B, C, X(5976), X(36892)}}, {{A, B, C, X(6339), X(45857)}}, {{A, B, C, X(6353), X(7791)}}, {{A, B, C, X(6393), X(25406)}}, {{A, B, C, X(6464), X(39951)}}, {{A, B, C, X(6655), X(38282)}}, {{A, B, C, X(6995), X(32960)}}, {{A, B, C, X(6997), X(37125)}}, {{A, B, C, X(7378), X(32957)}}, {{A, B, C, X(7392), X(37337)}}, {{A, B, C, X(7736), X(15271)}}, {{A, B, C, X(7750), X(34403)}}, {{A, B, C, X(7763), X(39998)}}, {{A, B, C, X(8024), X(32832)}}, {{A, B, C, X(8889), X(16924)}}, {{A, B, C, X(9229), X(34208)}}, {{A, B, C, X(9770), X(11168)}}, {{A, B, C, X(11059), X(46951)}}, {{A, B, C, X(13575), X(57903)}}, {{A, B, C, X(14489), X(54998)}}, {{A, B, C, X(14495), X(30535)}}, {{A, B, C, X(15321), X(24861)}}, {{A, B, C, X(16044), X(52299)}}, {{A, B, C, X(16986), X(16989)}}, {{A, B, C, X(17980), X(21448)}}, {{A, B, C, X(20022), X(51373)}}, {{A, B, C, X(21356), X(22329)}}, {{A, B, C, X(23053), X(41133)}}, {{A, B, C, X(26235), X(32833)}}, {{A, B, C, X(30701), X(52133)}}, {{A, B, C, X(32834), X(57518)}}, {{A, B, C, X(33017), X(52290)}}, {{A, B, C, X(33238), X(37453)}}, {{A, B, C, X(34288), X(42286)}}, {{A, B, C, X(36889), X(40826)}}, {{A, B, C, X(36948), X(42407)}}, {{A, B, C, X(37182), X(52283)}}, {{A, B, C, X(37637), X(37690)}}, {{A, B, C, X(39953), X(46735)}}, {{A, B, C, X(41896), X(57899)}}, {{A, B, C, X(46336), X(46511)}}
X(60212) = barycentric product X(i)*X(j) for these (i, j): {14486, 305}
X(60212) = barycentric quotient X(i)/X(j) for these (i, j): {2, 7736}, {69, 10519}, {14486, 25}, {59373, 44839}

X(60213) = X(2)X(4121)∩X(4)X(626)

Barycentrics    (a^4+a^2*b^2+2*b^4+b^2*c^2+c^4)*(a^4+b^4+(a^2+b^2)*c^2+2*c^4) : :

X(60213) lies on the Kiepert hyperbola and on these lines: {2, 4121}, {4, 626}, {6, 60215}, {76, 7851}, {83, 325}, {98, 141}, {99, 51582}, {183, 60093}, {226, 30837}, {230, 60186}, {262, 7778}, {385, 43528}, {598, 7809}, {620, 9751}, {671, 33184}, {1352, 3424}, {1916, 7931}, {2996, 33180}, {3314, 3407}, {3399, 3934}, {3406, 3788}, {3619, 60212}, {3763, 60099}, {3767, 18840}, {5103, 14492}, {5149, 6054}, {5152, 31168}, {5395, 7785}, {5485, 33196}, {5503, 6034}, {6033, 60140}, {7607, 15271}, {7608, 44377}, {7736, 7888}, {7753, 18842}, {7763, 10292}, {7777, 60129}, {7789, 43460}, {7820, 43450}, {7828, 10159}, {7865, 54614}, {7870, 51580}, {7874, 39095}, {7883, 10000}, {7903, 15870}, {7914, 31981}, {7925, 60098}, {7930, 11174}, {7942, 60278}, {7947, 56789}, {9744, 53033}, {9770, 54616}, {9866, 59266}, {10153, 11168}, {10290, 14061}, {10302, 14568}, {11163, 60239}, {11167, 21358}, {11606, 14931}, {14458, 47353}, {14484, 19130}, {14494, 37690}, {16277, 34138}, {16986, 60128}, {22110, 54509}, {23234, 54675}, {23285, 43665}, {33200, 38259}, {34229, 60263}, {37688, 60073}, {43449, 51932}, {48663, 60115}, {53104, 58446}, {53475, 60181}

X(60213) = inverse of X(51582) in Wallace hyperbola
X(60213) = isotomic conjugate of X(7792)
X(60213) = complement of X(10336)
X(60213) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 7792}, {32676, 50547}
X(60213) = X(i)-vertex conjugate of X(j) for these {i, j}: {25, 60186}, {251, 38826}, {2353, 60181}
X(60213) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 7792}, {10335, 51582}, {15526, 50547}
X(60213) = pole of line {7792, 51582} with respect to the Wallace hyperbola
X(60213) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(30270)}}, {{A, B, C, X(6), X(7868)}}, {{A, B, C, X(25), X(7866)}}, {{A, B, C, X(95), X(141)}}, {{A, B, C, X(99), X(30530)}}, {{A, B, C, X(111), X(7919)}}, {{A, B, C, X(183), X(7778)}}, {{A, B, C, X(251), X(7944)}}, {{A, B, C, X(297), X(37450)}}, {{A, B, C, X(305), X(7795)}}, {{A, B, C, X(308), X(36897)}}, {{A, B, C, X(385), X(7931)}}, {{A, B, C, X(427), X(7819)}}, {{A, B, C, X(468), X(33184)}}, {{A, B, C, X(626), X(1799)}}, {{A, B, C, X(694), X(42288)}}, {{A, B, C, X(733), X(39396)}}, {{A, B, C, X(755), X(39389)}}, {{A, B, C, X(761), X(1390)}}, {{A, B, C, X(1105), X(34129)}}, {{A, B, C, X(1494), X(9516)}}, {{A, B, C, X(2353), X(39951)}}, {{A, B, C, X(2710), X(5481)}}, {{A, B, C, X(3108), X(38826)}}, {{A, B, C, X(3425), X(40802)}}, {{A, B, C, X(3619), X(7736)}}, {{A, B, C, X(3734), X(30786)}}, {{A, B, C, X(3763), X(11174)}}, {{A, B, C, X(3767), X(40022)}}, {{A, B, C, X(4074), X(16101)}}, {{A, B, C, X(4232), X(33196)}}, {{A, B, C, X(5094), X(11286)}}, {{A, B, C, X(6330), X(40801)}}, {{A, B, C, X(6353), X(33180)}}, {{A, B, C, X(6464), X(14495)}}, {{A, B, C, X(6664), X(32085)}}, {{A, B, C, X(6995), X(33194)}}, {{A, B, C, X(7777), X(16986)}}, {{A, B, C, X(7809), X(10130)}}, {{A, B, C, X(7828), X(39998)}}, {{A, B, C, X(7832), X(8024)}}, {{A, B, C, X(7851), X(8770)}}, {{A, B, C, X(7869), X(57852)}}, {{A, B, C, X(8842), X(24256)}}, {{A, B, C, X(8889), X(33198)}}, {{A, B, C, X(9229), X(35511)}}, {{A, B, C, X(9462), X(17983)}}, {{A, B, C, X(10415), X(53919)}}, {{A, B, C, X(11060), X(21448)}}, {{A, B, C, X(11163), X(21358)}}, {{A, B, C, X(11168), X(41133)}}, {{A, B, C, X(11169), X(42286)}}, {{A, B, C, X(14568), X(26235)}}, {{A, B, C, X(16084), X(30749)}}, {{A, B, C, X(22336), X(44571)}}, {{A, B, C, X(30495), X(47643)}}, {{A, B, C, X(30837), X(52133)}}, {{A, B, C, X(31360), X(42407)}}, {{A, B, C, X(33200), X(38282)}}, {{A, B, C, X(34229), X(37690)}}, {{A, B, C, X(34816), X(40410)}}, {{A, B, C, X(36212), X(51444)}}, {{A, B, C, X(37688), X(44377)}}, {{A, B, C, X(39749), X(57727)}}, {{A, B, C, X(40428), X(57907)}}, {{A, B, C, X(42373), X(43976)}}, {{A, B, C, X(44165), X(51246)}}, {{A, B, C, X(51450), X(53966)}}, {{A, B, C, X(55958), X(56057)}}
X(60213) = barycentric product X(i)*X(j) for these (i, j): {523, 54990}
X(60213) = barycentric quotient X(i)/X(j) for these (i, j): {2, 7792}, {525, 50547}, {3314, 51582}, {54990, 99}

X(60214) = X(2)X(12055)∩X(4)X(19570)

Barycentrics    (a^4+a^2*b^2+b^4-2*(a^2+b^2)*c^2-2*c^4)*(a^4-2*b^4-2*b^2*c^2+c^4+a^2*(-2*b^2+c^2)) : :

X(60214) lies on the Kiepert hyperbola and on these lines: {2, 12055}, {4, 19570}, {76, 7865}, {83, 5309}, {98, 48898}, {115, 54841}, {141, 54748}, {148, 9302}, {193, 54520}, {385, 14458}, {524, 54540}, {543, 54749}, {598, 18546}, {1916, 7788}, {2996, 7929}, {3314, 60202}, {3399, 13108}, {3407, 5306}, {3818, 7837}, {3830, 54566}, {3845, 54904}, {5989, 60104}, {7607, 37455}, {7774, 60127}, {7777, 60192}, {7783, 47005}, {7797, 18841}, {7822, 56059}, {7834, 60100}, {7840, 60095}, {7876, 10159}, {7884, 43527}, {8667, 43535}, {10334, 60129}, {12188, 55009}, {14614, 54539}, {17004, 54644}, {17008, 60185}, {34505, 60151}, {37667, 54866}, {41135, 54822}, {41624, 54487}, {43453, 54678}, {46226, 60183}

X(60214) = reflection of X(i) in X(j) for these {i,j}: {54841, 115}
X(60214) = isotomic conjugate of X(7837)
X(60214) = pole of line {37671, 60214} with respect to the Kiepert hyperbola
X(60214) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(12055)}}, {{A, B, C, X(25), X(7924)}}, {{A, B, C, X(111), X(11648)}}, {{A, B, C, X(251), X(7865)}}, {{A, B, C, X(305), X(19570)}}, {{A, B, C, X(385), X(5641)}}, {{A, B, C, X(428), X(7876)}}, {{A, B, C, X(733), X(30496)}}, {{A, B, C, X(1494), X(2998)}}, {{A, B, C, X(1502), X(1989)}}, {{A, B, C, X(3228), X(18361)}}, {{A, B, C, X(3314), X(5306)}}, {{A, B, C, X(4590), X(48911)}}, {{A, B, C, X(5309), X(8024)}}, {{A, B, C, X(6353), X(33278)}}, {{A, B, C, X(7837), X(37671)}}, {{A, B, C, X(7840), X(8667)}}, {{A, B, C, X(9229), X(34288)}}, {{A, B, C, X(9462), X(11058)}}, {{A, B, C, X(10351), X(42551)}}, {{A, B, C, X(12188), X(56409)}}, {{A, B, C, X(18546), X(42008)}}, {{A, B, C, X(37455), X(52282)}}

X(60215) = X(4)X(7804)∩X(6)X(60213)

Barycentrics    (2*(a^4+a^2*b^2+b^4)+(a^2+b^2)*c^2+c^4)*(2*a^4+b^4+b^2*c^2+2*c^4+a^2*(b^2+2*c^2)) : :

X(60215) lies on the Kiepert hyperbola and on these lines: {4, 7804}, {6, 60213}, {76, 5305}, {83, 7773}, {98, 10516}, {183, 10159}, {230, 60099}, {262, 3589}, {598, 33184}, {671, 5989}, {1916, 7875}, {2548, 18841}, {2996, 7797}, {3329, 43529}, {3399, 6680}, {3406, 7808}, {3424, 3818}, {3618, 40824}, {5309, 5485}, {5395, 33180}, {5503, 47352}, {5976, 10290}, {7735, 7822}, {7752, 43527}, {7777, 60231}, {7806, 42006}, {7899, 60100}, {7937, 10348}, {8781, 11174}, {9993, 44251}, {10033, 54614}, {10302, 47005}, {11668, 44381}, {11669, 15491}, {14458, 51848}, {14484, 14561}, {14492, 38072}, {14535, 54800}, {16984, 60128}, {16987, 60129}, {16989, 60232}, {18842, 31173}, {18845, 33200}, {19570, 60200}, {22329, 60277}, {22505, 60140}, {24273, 60181}, {31489, 56064}, {37637, 60187}, {46226, 60285}, {53484, 54773}

X(60215) = isotomic conjugate of X(7868)
X(60215) = trilinear pole of line {50253, 523}
X(60215) = X(i)-vertex conjugate of X(j) for these {i, j}: {25, 60099}
X(60215) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(7792)}}, {{A, B, C, X(25), X(7819)}}, {{A, B, C, X(39), X(38905)}}, {{A, B, C, X(183), X(3589)}}, {{A, B, C, X(230), X(11174)}}, {{A, B, C, X(251), X(7846)}}, {{A, B, C, X(264), X(34129)}}, {{A, B, C, X(305), X(7834)}}, {{A, B, C, X(385), X(7875)}}, {{A, B, C, X(427), X(7866)}}, {{A, B, C, X(458), X(37450)}}, {{A, B, C, X(468), X(11286)}}, {{A, B, C, X(699), X(44557)}}, {{A, B, C, X(3108), X(7856)}}, {{A, B, C, X(3115), X(37876)}}, {{A, B, C, X(3266), X(7884)}}, {{A, B, C, X(3329), X(7806)}}, {{A, B, C, X(3618), X(7735)}}, {{A, B, C, X(5094), X(33184)}}, {{A, B, C, X(5305), X(39951)}}, {{A, B, C, X(5309), X(11059)}}, {{A, B, C, X(5989), X(52145)}}, {{A, B, C, X(6353), X(33198)}}, {{A, B, C, X(7378), X(33194)}}, {{A, B, C, X(7752), X(39668)}}, {{A, B, C, X(7777), X(16984)}}, {{A, B, C, X(7797), X(57518)}}, {{A, B, C, X(7804), X(53024)}}, {{A, B, C, X(7808), X(45093)}}, {{A, B, C, X(7822), X(40022)}}, {{A, B, C, X(7934), X(23297)}}, {{A, B, C, X(7943), X(8024)}}, {{A, B, C, X(8770), X(14370)}}, {{A, B, C, X(8840), X(42534)}}, {{A, B, C, X(8889), X(33180)}}, {{A, B, C, X(9469), X(51510)}}, {{A, B, C, X(9515), X(41533)}}, {{A, B, C, X(14489), X(46115)}}, {{A, B, C, X(14495), X(40802)}}, {{A, B, C, X(16986), X(16987)}}, {{A, B, C, X(17381), X(26244)}}, {{A, B, C, X(17980), X(54413)}}, {{A, B, C, X(21448), X(41443)}}, {{A, B, C, X(22329), X(47352)}}, {{A, B, C, X(26235), X(47005)}}, {{A, B, C, X(29316), X(30541)}}, {{A, B, C, X(31360), X(40416)}}, {{A, B, C, X(33196), X(52284)}}, {{A, B, C, X(33200), X(52299)}}, {{A, B, C, X(39716), X(57726)}}, {{A, B, C, X(42286), X(57822)}}

X(60216) = X(2)X(14148)∩X(3)X(55826)

Barycentrics    (a^2+b^2-8*c^2)*(a^2-8*b^2+c^2) : :
X(60216) = -8*X[547]+7*X[7608], -7*X[7616]+5*X[15692]

X(60216) lies on the Kiepert hyperbola and on these lines: {2, 14148}, {3, 55826}, {4, 50992}, {6, 60283}, {30, 54857}, {69, 32532}, {76, 50993}, {83, 11054}, {98, 8703}, {99, 8587}, {262, 19709}, {316, 33698}, {381, 60329}, {524, 45103}, {538, 60098}, {547, 7608}, {598, 15534}, {599, 60228}, {632, 10185}, {671, 22165}, {1916, 14711}, {1992, 60284}, {2996, 7883}, {3407, 14030}, {3530, 60334}, {3534, 60323}, {3830, 60326}, {3845, 54890}, {3860, 14492}, {5054, 7607}, {5070, 60144}, {5079, 60332}, {5254, 60210}, {5485, 50994}, {7612, 15719}, {7616, 15692}, {7620, 60113}, {7760, 53102}, {7762, 53109}, {7790, 60143}, {7799, 60198}, {7812, 18845}, {7827, 60100}, {7841, 60209}, {8352, 53106}, {8370, 60146}, {8584, 60282}, {9166, 42010}, {10153, 41134}, {10302, 47286}, {11055, 60096}, {11160, 54896}, {11185, 53101}, {11317, 53107}, {11540, 53104}, {12156, 59266}, {14568, 60186}, {15533, 17503}, {15681, 53100}, {15682, 60325}, {15710, 60337}, {18546, 54737}, {19569, 54901}, {29620, 30588}, {32836, 60262}, {32892, 60201}, {33458, 54524}, {33459, 54525}, {33699, 54852}, {34505, 53105}, {36521, 60136}, {36523, 60271}, {38071, 60142}, {40727, 42011}, {50990, 54637}, {51185, 60287}, {51186, 60286}, {52713, 54616}, {53859, 55864}

X(60216) = inverse of X(51584) in Wallace hyperbola
X(60216) = isotomic conjugate of X(8584)
X(60216) = pole of line {50991, 60216} with respect to the Kiepert hyperbola
X(60216) = pole of line {8584, 33550} with respect to the Wallace hyperbola
X(60216) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55721)}}, {{A, B, C, X(6), X(50993)}}, {{A, B, C, X(69), X(50992)}}, {{A, B, C, X(297), X(8703)}}, {{A, B, C, X(335), X(13602)}}, {{A, B, C, X(419), X(33291)}}, {{A, B, C, X(458), X(19709)}}, {{A, B, C, X(524), X(22165)}}, {{A, B, C, X(547), X(52281)}}, {{A, B, C, X(597), X(51143)}}, {{A, B, C, X(599), X(15534)}}, {{A, B, C, X(1494), X(57908)}}, {{A, B, C, X(1992), X(50994)}}, {{A, B, C, X(3679), X(29620)}}, {{A, B, C, X(3860), X(52289)}}, {{A, B, C, X(3978), X(14711)}}, {{A, B, C, X(4669), X(29589)}}, {{A, B, C, X(5054), X(52282)}}, {{A, B, C, X(5117), X(14030)}}, {{A, B, C, X(6664), X(34898)}}, {{A, B, C, X(8024), X(11054)}}, {{A, B, C, X(8352), X(52297)}}, {{A, B, C, X(8584), X(50991)}}, {{A, B, C, X(11317), X(52298)}}, {{A, B, C, X(15719), X(37174)}}, {{A, B, C, X(32901), X(40802)}}, {{A, B, C, X(41149), X(51142)}}, {{A, B, C, X(50989), X(51188)}}, {{A, B, C, X(51185), X(51186)}}, {{A, B, C, X(51187), X(51189)}}, {{A, B, C, X(55958), X(57907)}}
X(60216) = barycentric product X(i)*X(j) for these (i, j): {58092, 850}
X(60216) = barycentric quotient X(i)/X(j) for these (i, j): {2, 8584}, {3055, 33550}, {15533, 51584}, {58092, 110}

X(60217) = X(4)X(7811)∩X(83)X(5306)

Barycentrics    ((a^2-b^2)^2-5*(a^2+b^2)*c^2-2*c^4)*(a^4-2*b^4-5*b^2*c^2+c^4-a^2*(5*b^2+2*c^2)) : :

X(60217) lies on the Kiepert hyperbola and on these lines: {4, 7811}, {30, 54858}, {69, 60127}, {83, 5306}, {94, 39998}, {99, 9302}, {141, 60202}, {183, 14458}, {262, 7788}, {305, 59763}, {325, 60192}, {524, 54905}, {598, 8667}, {599, 60095}, {2996, 7800}, {5395, 32828}, {7755, 32885}, {7763, 60183}, {7769, 56059}, {7799, 10159}, {8556, 60218}, {9166, 54822}, {9466, 60151}, {11057, 54716}, {11185, 54856}, {13468, 54906}, {14061, 54841}, {14492, 21850}, {14494, 24206}, {14614, 54773}, {15589, 54520}, {16986, 54748}, {18546, 41895}, {18840, 32833}, {18841, 32832}, {18845, 20065}, {32451, 60096}, {32834, 38259}, {32836, 60285}, {32874, 43681}, {34229, 60185}, {34289, 40022}, {37668, 54522}, {37688, 54644}, {41134, 54749}, {41624, 54509}, {46264, 60150}

X(60217) = isotomic conjugate of X(9300)
X(60217) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(141), X(1989)}}, {{A, B, C, X(183), X(7788)}}, {{A, B, C, X(308), X(1494)}}, {{A, B, C, X(599), X(8667)}}, {{A, B, C, X(1502), X(55958)}}, {{A, B, C, X(1799), X(7811)}}, {{A, B, C, X(6664), X(30537)}}, {{A, B, C, X(7799), X(39998)}}, {{A, B, C, X(8024), X(20573)}}, {{A, B, C, X(8556), X(9766)}}, {{A, B, C, X(8770), X(30495)}}, {{A, B, C, X(9462), X(18361)}}, {{A, B, C, X(9516), X(48911)}}, {{A, B, C, X(31360), X(34288)}}, {{A, B, C, X(31621), X(57545)}}, {{A, B, C, X(32833), X(40022)}}, {{A, B, C, X(36889), X(56067)}}, {{A, B, C, X(40405), X(57822)}}, {{A, B, C, X(46951), X(57518)}}, {{A, B, C, X(57799), X(57852)}}

X(60218) = X(4)X(6179)∩X(6)X(54905)

Barycentrics    (2*(a^4+b^4)-3*(a^2+b^2)*c^2-c^4)*(2*a^4-3*a^2*b^2-b^4-3*b^2*c^2+2*c^4) : :

X(60218) lies on the Kiepert hyperbola and on these lines: {4, 6179}, {6, 54905}, {76, 8356}, {83, 13881}, {98, 55177}, {115, 54872}, {183, 60181}, {262, 3564}, {385, 54540}, {524, 60095}, {542, 54978}, {543, 54750}, {598, 5306}, {599, 60202}, {671, 8667}, {1352, 14494}, {1916, 14645}, {1992, 60127}, {2996, 3785}, {3399, 7757}, {3767, 5395}, {3830, 54718}, {3845, 54714}, {3849, 41895}, {5485, 55164}, {5503, 7788}, {6337, 18840}, {7607, 37451}, {7612, 25406}, {7615, 54753}, {7828, 18841}, {7832, 60183}, {7930, 56059}, {7942, 60100}, {8556, 60217}, {8781, 44531}, {8860, 54644}, {9742, 60333}, {9774, 60175}, {9830, 60103}, {10008, 60201}, {10033, 14492}, {10159, 11285}, {11163, 60192}, {11645, 60150}, {14458, 22329}, {14537, 53101}, {14976, 38259}, {19569, 60113}, {19695, 60209}, {22676, 23698}, {23055, 60185}, {23878, 60338}, {28526, 34475}, {32824, 32990}, {32991, 60145}, {32992, 43527}, {33023, 43681}, {33234, 43676}, {37671, 60180}, {38732, 60189}, {40344, 60200}, {51224, 54678}, {52088, 54839}, {53475, 60093}, {54713, 55007}

X(60218) = reflection of X(i) in X(j) for these {i,j}: {54872, 115}
X(60218) = isotomic conjugate of X(9766)
X(60218) = X(i)-vertex conjugate of X(j) for these {i, j}: {2353, 60093}
X(60218) = pole of line {13468, 60218} with respect to the Kiepert hyperbola
X(60218) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(755)}}, {{A, B, C, X(66), X(56067)}}, {{A, B, C, X(183), X(14970)}}, {{A, B, C, X(264), X(43098)}}, {{A, B, C, X(305), X(14568)}}, {{A, B, C, X(427), X(44543)}}, {{A, B, C, X(428), X(11285)}}, {{A, B, C, X(512), X(8770)}}, {{A, B, C, X(524), X(8667)}}, {{A, B, C, X(599), X(5306)}}, {{A, B, C, X(804), X(14645)}}, {{A, B, C, X(2980), X(31360)}}, {{A, B, C, X(3228), X(57822)}}, {{A, B, C, X(3564), X(23878)}}, {{A, B, C, X(3785), X(6337)}}, {{A, B, C, X(4785), X(28526)}}, {{A, B, C, X(5064), X(32992)}}, {{A, B, C, X(6094), X(18361)}}, {{A, B, C, X(6179), X(57644)}}, {{A, B, C, X(6353), X(33272)}}, {{A, B, C, X(7714), X(32990)}}, {{A, B, C, X(7788), X(22329)}}, {{A, B, C, X(8556), X(9300)}}, {{A, B, C, X(9076), X(18880)}}, {{A, B, C, X(9766), X(13468)}}, {{A, B, C, X(10008), X(25406)}}, {{A, B, C, X(11057), X(51541)}}, {{A, B, C, X(14384), X(44531)}}, {{A, B, C, X(14614), X(37671)}}, {{A, B, C, X(18818), X(40829)}}, {{A, B, C, X(20251), X(39955)}}, {{A, B, C, X(21399), X(39951)}}, {{A, B, C, X(25322), X(30542)}}, {{A, B, C, X(34285), X(40405)}}, {{A, B, C, X(34412), X(53200)}}, {{A, B, C, X(37451), X(52282)}}

X(60219) = X(2)X(32822)∩X(4)X(3629)

Barycentrics    (3*(a^2+b^2)-7*c^2)*(3*a^2-7*b^2+3*c^2) : :
X(60219) = -X[20]+3*X[60336]

X(60219) lies on the Kiepert hyperbola and on these lines: {2, 32822}, {3, 55816}, {4, 3629}, {5, 60333}, {6, 18843}, {10, 52183}, {20, 60336}, {30, 54866}, {69, 43676}, {98, 3529}, {115, 56064}, {148, 60104}, {226, 29602}, {262, 3855}, {315, 60209}, {376, 60175}, {381, 54521}, {382, 3424}, {546, 14484}, {550, 43537}, {631, 53104}, {671, 32006}, {1992, 54494}, {2996, 33229}, {3090, 11669}, {3091, 60331}, {3528, 7612}, {3544, 14494}, {3545, 60192}, {3851, 53099}, {5254, 18841}, {5286, 18842}, {5485, 44518}, {6392, 41895}, {7375, 43559}, {7376, 43558}, {7388, 60294}, {7389, 60293}, {7607, 10299}, {7620, 54616}, {7745, 60281}, {7762, 60113}, {7790, 56059}, {7803, 60238}, {7812, 54646}, {7827, 60287}, {7841, 60200}, {8357, 60259}, {8370, 54639}, {10302, 33190}, {11008, 53105}, {11185, 43527}, {11606, 33279}, {12243, 54659}, {12818, 26339}, {12819, 26340}, {14064, 60231}, {14226, 26288}, {14232, 48477}, {14237, 48476}, {14241, 26289}, {14269, 54520}, {15682, 54608}, {15687, 54519}, {15710, 54644}, {15720, 53859}, {16045, 60100}, {18840, 33232}, {32457, 33703}, {32818, 35005}, {32886, 60212}, {32956, 60278}, {33226, 60128}, {33238, 54122}, {33254, 60136}, {33257, 46453}, {33280, 60184}, {33292, 40824}, {34505, 60143}, {37873, 56346}, {38071, 54522}, {38259, 47286}, {38734, 54475}, {39646, 54859}, {41099, 54643}, {47586, 49135}, {50688, 60147}, {50774, 60322}, {52713, 60285}

X(60219) = reflection of X(i) in X(j) for these {i,j}: {56064, 115}
X(60219) = isotomic conjugate of X(11008)
X(60219) = trilinear pole of line {31250, 31277}
X(60219) = pole of line {40341, 60219} with respect to the Kiepert hyperbola
X(60219) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(5102)}}, {{A, B, C, X(8), X(29602)}}, {{A, B, C, X(69), X(3629)}}, {{A, B, C, X(74), X(6464)}}, {{A, B, C, X(257), X(43733)}}, {{A, B, C, X(265), X(34403)}}, {{A, B, C, X(277), X(40026)}}, {{A, B, C, X(297), X(3529)}}, {{A, B, C, X(335), X(43734)}}, {{A, B, C, X(382), X(52283)}}, {{A, B, C, X(420), X(33279)}}, {{A, B, C, X(458), X(3855)}}, {{A, B, C, X(525), X(15077)}}, {{A, B, C, X(546), X(52288)}}, {{A, B, C, X(2481), X(39709)}}, {{A, B, C, X(2987), X(11270)}}, {{A, B, C, X(3528), X(37174)}}, {{A, B, C, X(3626), X(29624)}}, {{A, B, C, X(5556), X(57725)}}, {{A, B, C, X(5560), X(39749)}}, {{A, B, C, X(6330), X(18846)}}, {{A, B, C, X(6353), X(33229)}}, {{A, B, C, X(6620), X(33292)}}, {{A, B, C, X(6995), X(33232)}}, {{A, B, C, X(8753), X(57688)}}, {{A, B, C, X(10299), X(52282)}}, {{A, B, C, X(10301), X(33190)}}, {{A, B, C, X(11008), X(40341)}}, {{A, B, C, X(13452), X(56004)}}, {{A, B, C, X(13472), X(30541)}}, {{A, B, C, X(14376), X(15749)}}, {{A, B, C, X(14842), X(47735)}}, {{A, B, C, X(14843), X(56267)}}, {{A, B, C, X(16045), X(52285)}}, {{A, B, C, X(16835), X(40802)}}, {{A, B, C, X(18023), X(34208)}}, {{A, B, C, X(18027), X(18852)}}, {{A, B, C, X(18850), X(52581)}}, {{A, B, C, X(20023), X(32450)}}, {{A, B, C, X(20421), X(55999)}}, {{A, B, C, X(31371), X(36952)}}, {{A, B, C, X(32006), X(44146)}}, {{A, B, C, X(32533), X(42287)}}, {{A, B, C, X(32822), X(55972)}}, {{A, B, C, X(34285), X(39142)}}, {{A, B, C, X(35142), X(57823)}}, {{A, B, C, X(36605), X(39697)}}
X(60219) = barycentric product X(i)*X(j) for these (i, j): {58096, 850}
X(60219) = barycentric quotient X(i)/X(j) for these (i, j): {2, 11008}, {58096, 110}

X(60220) = X(4)X(23055)∩X(230)X(598)

Barycentrics    (4*(a^4-a^2*b^2+b^4)-7*(a^2+b^2)*c^2+c^4)*(4*a^4+b^4-7*b^2*c^2+4*c^4-a^2*(7*b^2+4*c^2)) : :

X(60220) lies on the Kiepert hyperbola and on these lines: {4, 23055}, {30, 54869}, {69, 60240}, {76, 11168}, {98, 8860}, {183, 5503}, {230, 598}, {262, 22329}, {325, 42011}, {381, 54868}, {385, 10484}, {524, 60211}, {597, 60096}, {599, 8781}, {671, 7610}, {1992, 14494}, {2482, 54750}, {5395, 7746}, {5461, 54872}, {5466, 36900}, {5485, 34229}, {6055, 43532}, {7608, 11163}, {7612, 11179}, {7735, 60268}, {7737, 53101}, {7757, 60126}, {7801, 60285}, {7840, 60233}, {7870, 18840}, {7940, 60183}, {8182, 41895}, {8556, 60202}, {8587, 9773}, {8593, 37637}, {8859, 54487}, {10302, 15271}, {11167, 37688}, {13468, 60095}, {14614, 60192}, {17004, 43535}, {22110, 60178}, {34507, 53098}, {40824, 42850}, {41624, 54645}, {44401, 60093}

X(60220) = isotomic conjugate of X(11184)
X(60220) = X(i)-vertex conjugate of X(j) for these {i, j}: {25, 598}
X(60220) = pole of line {15597, 60220} with respect to the Kiepert hyperbola
X(60220) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(11168)}}, {{A, B, C, X(69), X(23055)}}, {{A, B, C, X(183), X(22329)}}, {{A, B, C, X(230), X(599)}}, {{A, B, C, X(297), X(40248)}}, {{A, B, C, X(325), X(8860)}}, {{A, B, C, X(468), X(35955)}}, {{A, B, C, X(524), X(7610)}}, {{A, B, C, X(597), X(15271)}}, {{A, B, C, X(843), X(21448)}}, {{A, B, C, X(1007), X(23053)}}, {{A, B, C, X(1383), X(20251)}}, {{A, B, C, X(1992), X(34229)}}, {{A, B, C, X(5306), X(8556)}}, {{A, B, C, X(7735), X(42850)}}, {{A, B, C, X(7771), X(36900)}}, {{A, B, C, X(7778), X(44401)}}, {{A, B, C, X(7840), X(17004)}}, {{A, B, C, X(7870), X(40022)}}, {{A, B, C, X(8667), X(13468)}}, {{A, B, C, X(9164), X(9462)}}, {{A, B, C, X(11163), X(37688)}}, {{A, B, C, X(11184), X(15597)}}, {{A, B, C, X(18823), X(40428)}}, {{A, B, C, X(22110), X(37637)}}, {{A, B, C, X(23054), X(36889)}}, {{A, B, C, X(40118), X(42298)}}, {{A, B, C, X(44557), X(46316)}}, {{A, B, C, X(45838), X(56067)}}

X(60221) = X(4)X(343)∩X(69)X(275)

Barycentrics    ((a^2-b^2)^2*(a^2+b^2)+(a^2-b^2)^2*c^2-5*(a^2+b^2)*c^4+3*c^6)*(a^6+a^4*(b-c)*(b+c)+(b^2-c^2)^2*(3*b^2+c^2)-a^2*(5*b^4+2*b^2*c^2+c^4)) : :

X(60221) lies on the Kiepert hyperbola and on these lines: {2, 52347}, {4, 343}, {22, 3424}, {30, 54870}, {69, 275}, {83, 11433}, {96, 631}, {98, 7494}, {141, 60114}, {311, 2052}, {394, 56346}, {459, 37638}, {467, 8796}, {599, 54784}, {2996, 41237}, {3090, 57718}, {3547, 60166}, {3620, 43670}, {5133, 14484}, {5395, 41231}, {6503, 35921}, {6504, 37636}, {6515, 40393}, {7404, 60174}, {7495, 43537}, {7500, 60147}, {7558, 60159}, {7578, 45794}, {10601, 18841}, {11064, 60137}, {13160, 31363}, {13599, 59197}, {14361, 52583}, {14458, 34608}, {15682, 54879}, {16041, 54824}, {21356, 54774}, {33190, 54513}, {34603, 54519}, {37156, 43533}, {37643, 37874}, {37669, 43530}, {43678, 52283}, {44128, 60120}, {46727, 59346}, {52253, 60161}

X(60221) = isotomic conjugate of X(11427)
X(60221) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 19357}, {31, 11427}, {48, 7487}, {2148, 45089}
X(60221) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 11427}, {6, 19357}, {216, 45089}, {1249, 7487}
X(60221) = X(i)-cross conjugate of X(j) for these {i, j}: {7399, 264}, {9786, 253}
X(60221) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(17834)}}, {{A, B, C, X(22), X(52283)}}, {{A, B, C, X(69), X(311)}}, {{A, B, C, X(95), X(55031)}}, {{A, B, C, X(97), X(30541)}}, {{A, B, C, X(141), X(11433)}}, {{A, B, C, X(297), X(7494)}}, {{A, B, C, X(324), X(18854)}}, {{A, B, C, X(394), X(34403)}}, {{A, B, C, X(467), X(631)}}, {{A, B, C, X(1073), X(34801)}}, {{A, B, C, X(1078), X(32818)}}, {{A, B, C, X(1176), X(33586)}}, {{A, B, C, X(1799), X(55972)}}, {{A, B, C, X(1993), X(3431)}}, {{A, B, C, X(2165), X(6524)}}, {{A, B, C, X(3090), X(52253)}}, {{A, B, C, X(3547), X(6820)}}, {{A, B, C, X(3619), X(10601)}}, {{A, B, C, X(4176), X(57855)}}, {{A, B, C, X(5133), X(52288)}}, {{A, B, C, X(6340), X(34384)}}, {{A, B, C, X(6353), X(41237)}}, {{A, B, C, X(6393), X(26870)}}, {{A, B, C, X(6515), X(37636)}}, {{A, B, C, X(6819), X(7404)}}, {{A, B, C, X(7490), X(37156)}}, {{A, B, C, X(7558), X(37192)}}, {{A, B, C, X(8797), X(41244)}}, {{A, B, C, X(8800), X(22270)}}, {{A, B, C, X(8889), X(41231)}}, {{A, B, C, X(10603), X(57907)}}, {{A, B, C, X(11331), X(34608)}}, {{A, B, C, X(11427), X(14542)}}, {{A, B, C, X(17811), X(37643)}}, {{A, B, C, X(18124), X(42287)}}, {{A, B, C, X(18853), X(57903)}}, {{A, B, C, X(21448), X(39109)}}, {{A, B, C, X(31626), X(56004)}}, {{A, B, C, X(34208), X(42354)}}, {{A, B, C, X(34401), X(52381)}}, {{A, B, C, X(36948), X(46111)}}, {{A, B, C, X(37638), X(37669)}}, {{A, B, C, X(39749), X(56354)}}, {{A, B, C, X(42298), X(56334)}}, {{A, B, C, X(57874), X(57905)}}
X(60221) = barycentric product X(i)*X(j) for these (i, j): {18855, 69}
X(60221) = barycentric quotient X(i)/X(j) for these (i, j): {2, 11427}, {3, 19357}, {4, 7487}, {5, 45089}, {18855, 4}

X(60222) = X(4)X(302)∩X(17)X(69)

Barycentrics    -3*a^4-3*b^4+10*b^2*c^2-3*c^4+6*a^2*(b^2+c^2)+4*sqrt(3)*S*(b^2+c^2) : :

X(60222) lies on the Kiepert hyperbola and on these lines: {4, 302}, {5, 43954}, {13, 16804}, {14, 37172}, {17, 69}, {83, 11489}, {141, 32838}, {298, 32823}, {299, 43554}, {303, 43447}, {376, 54672}, {621, 54848}, {623, 32006}, {627, 54571}, {628, 53104}, {633, 7607}, {635, 34229}, {3366, 32806}, {3367, 32805}, {3926, 44383}, {5392, 41000}, {7763, 40707}, {9761, 54618}, {11133, 43676}, {21356, 55951}, {22495, 33607}, {22890, 54669}, {23303, 32970}, {32828, 60253}, {32832, 40706}, {32883, 44382}, {32961, 34540}, {32978, 53463}, {32985, 33474}, {36764, 56055}, {37640, 60273}, {39899, 54849}, {44030, 59270}

X(60222) = isotomic conjugate of X(11488)
X(60222) = pole of line {32829, 60222} with respect to the Kiepert hyperbola
X(60222) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(15), X(55999)}}, {{A, B, C, X(69), X(300)}}, {{A, B, C, X(298), X(36889)}}, {{A, B, C, X(301), X(8797)}}, {{A, B, C, X(2993), X(18023)}}, {{A, B, C, X(3926), X(40709)}}, {{A, B, C, X(7769), X(16770)}}, {{A, B, C, X(11085), X(40511)}}, {{A, B, C, X(11087), X(25322)}}, {{A, B, C, X(14358), X(54123)}}

X(60223) = X(2)X(13988)∩X(485)X(524)

Barycentrics    4*a^4-7*a^2*b^2+7*b^4-7*a^2*c^2-22*b^2*c^2+7*c^4+6*(a^2-2*b^2-2*c^2)*S : :

X(60223) lies on the Kiepert hyperbola and on these lines: {2, 13988}, {6, 54627}, {30, 54874}, {262, 13681}, {381, 45106}, {485, 524}, {486, 7618}, {492, 671}, {543, 55041}, {591, 1327}, {598, 13669}, {599, 8355}, {615, 54628}, {639, 3316}, {1132, 45508}, {1328, 13712}, {1991, 43568}, {1992, 13662}, {3069, 18842}, {5466, 54029}, {5485, 13831}, {5491, 21356}, {5503, 13653}, {5569, 13835}, {5590, 60143}, {5860, 14241}, {5861, 43536}, {6280, 14244}, {6561, 9894}, {6568, 35949}, {7612, 32419}, {8587, 33343}, {10153, 19057}, {10194, 11315}, {10195, 32491}, {10515, 14245}, {11147, 13789}, {13088, 14229}, {13666, 41490}, {13678, 43567}, {13687, 26288}, {13691, 14458}, {13692, 45107}, {13701, 14226}, {13711, 13927}, {13932, 40727}, {14237, 49355}, {14484, 48778}, {15597, 55040}, {22541, 45421}, {26289, 60102}, {32808, 60195}, {32810, 60207}, {32984, 42009}, {33456, 43566}, {41491, 53103}, {42023, 49261}, {43133, 43560}, {45420, 54505}, {59373, 60204}

X(60223) = isotomic conjugate of X(13637)
X(60223) = X(i)-cross conjugate of X(j) for these {i, j}: {11165, 60224}
X(60223) = pole of line {11165, 60223} with respect to the Kiepert hyperbola
X(60223) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(492), X(524)}}, {{A, B, C, X(3069), X(21356)}}, {{A, B, C, X(7090), X(34892)}}, {{A, B, C, X(13390), X(34914)}}, {{A, B, C, X(34897), X(55533)}}
X(60223) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {599, 16509, 60224}, {13669, 13757, 13769}

X(60224) = X(2)X(13848)∩X(486)X(524)

Barycentrics    4*a^4-7*a^2*b^2+7*b^4-7*a^2*c^2-22*b^2*c^2+7*c^4-6*(a^2-2*b^2-2*c^2)*S : :

X(60224) lies on the Kiepert hyperbola and on these lines: {2, 13848}, {6, 54628}, {30, 54876}, {262, 13801}, {381, 45107}, {485, 7618}, {486, 524}, {491, 671}, {543, 55040}, {590, 54627}, {591, 43569}, {598, 13637}, {599, 8355}, {640, 3317}, {1131, 45509}, {1327, 13835}, {1328, 1991}, {1992, 13782}, {3068, 18842}, {5466, 54028}, {5485, 13832}, {5490, 21356}, {5503, 13773}, {5569, 13712}, {5591, 60143}, {5860, 54597}, {5861, 14226}, {6279, 14229}, {6560, 9892}, {6569, 35948}, {7612, 32421}, {8587, 33342}, {10153, 19058}, {10194, 32490}, {10195, 11316}, {10514, 14231}, {11147, 13669}, {13087, 14244}, {13786, 41491}, {13798, 43566}, {13807, 26289}, {13810, 14458}, {13812, 45106}, {13821, 14241}, {13834, 13874}, {13850, 40727}, {14232, 49356}, {14484, 48779}, {15597, 55041}, {19101, 45420}, {26288, 60102}, {32811, 60208}, {32984, 42060}, {33457, 43567}, {41490, 53103}, {42024, 49262}, {43134, 43561}, {45421, 54504}, {59373, 60205}

X(60224) = isotomic conjugate of X(13757)
X(60224) = X(i)-cross conjugate of X(j) for these {i, j}: {11165, 60223}
X(60224) = pole of line {11165, 60224} with respect to the Kiepert hyperbola
X(60224) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(491), X(524)}}, {{A, B, C, X(1659), X(34914)}}, {{A, B, C, X(3068), X(21356)}}, {{A, B, C, X(14121), X(34892)}}, {{A, B, C, X(34897), X(55534)}}
X(60224) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {599, 16509, 60223}, {13637, 13789, 13833}

X(60225) = X(2)X(231)∩X(4)X(1209)

Barycentrics    ((a^2-b^2)^2*(a^2+b^2)-2*a^2*b^2*c^2-3*(a^2+b^2)*c^4+2*c^6)*(a^6+2*b^6-a^4*c^2-3*b^4*c^2+c^6-a^2*(3*b^4+2*b^2*c^2+c^4)) : :

X(60225) lies on the Kiepert hyperbola and on these lines: {2, 231}, {4, 1209}, {13, 33530}, {14, 33529}, {20, 54870}, {22, 14458}, {30, 54879}, {83, 3580}, {94, 311}, {96, 140}, {98, 7495}, {141, 2986}, {275, 340}, {297, 54685}, {343, 40393}, {467, 39284}, {598, 41231}, {599, 54803}, {671, 41237}, {1656, 57718}, {3620, 60193}, {3763, 59763}, {5025, 54824}, {5133, 14492}, {5392, 57811}, {6656, 54513}, {7387, 54909}, {7403, 54736}, {7494, 60150}, {7500, 54519}, {7503, 60122}, {7512, 54486}, {7558, 54498}, {7770, 54730}, {8781, 11056}, {11331, 43678}, {12088, 54835}, {12225, 54895}, {12605, 54573}, {13160, 60121}, {15066, 43530}, {15760, 60119}, {18316, 35921}, {18534, 54742}, {34289, 37638}, {34603, 54477}, {37156, 60079}, {37231, 54533}, {37804, 60101}, {37900, 60132}, {37925, 54908}, {46727, 58735}, {47096, 54944}, {52069, 54512}, {52253, 60120}, {54844, 59349}

X(60225) = isotomic conjugate of X(14389)
X(60225) = trilinear pole of line {7574, 41078}
X(60225) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 18475}, {31, 14389}, {48, 7576}
X(60225) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 14389}, {6, 18475}, {1249, 7576}
X(60225) = X(i)-cross conjugate of X(j) for these {i, j}: {3581, 1494}, {37347, 264}, {44201, 69}
X(60225) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(37478)}}, {{A, B, C, X(22), X(11331)}}, {{A, B, C, X(54), X(57647)}}, {{A, B, C, X(95), X(311)}}, {{A, B, C, X(97), X(7691)}}, {{A, B, C, X(140), X(467)}}, {{A, B, C, X(141), X(3580)}}, {{A, B, C, X(231), X(2501)}}, {{A, B, C, X(297), X(7495)}}, {{A, B, C, X(308), X(40427)}}, {{A, B, C, X(327), X(2373)}}, {{A, B, C, X(343), X(1209)}}, {{A, B, C, X(468), X(41237)}}, {{A, B, C, X(1176), X(15107)}}, {{A, B, C, X(1656), X(52253)}}, {{A, B, C, X(1799), X(55032)}}, {{A, B, C, X(1993), X(14528)}}, {{A, B, C, X(4550), X(15066)}}, {{A, B, C, X(5094), X(41231)}}, {{A, B, C, X(5133), X(52289)}}, {{A, B, C, X(5486), X(56006)}}, {{A, B, C, X(8800), X(22268)}}, {{A, B, C, X(11056), X(51481)}}, {{A, B, C, X(16230), X(47201)}}, {{A, B, C, X(17983), X(42354)}}, {{A, B, C, X(18020), X(57907)}}, {{A, B, C, X(36948), X(55031)}}, {{A, B, C, X(40410), X(57901)}}, {{A, B, C, X(42021), X(52350)}}, {{A, B, C, X(44134), X(57819)}}, {{A, B, C, X(46808), X(53025)}}
X(60225) = barycentric product X(i)*X(j) for these (i, j): {58975, 850}
X(60225) = barycentric quotient X(i)/X(j) for these (i, j): {2, 14389}, {3, 18475}, {4, 7576}, {58975, 110}

X(60226) = X(2)X(351)∩X(76)X(690)

Barycentrics    (b-c)*(b+c)*(-(a^2*b^2*(a^2+b^2))+2*(a^4+b^4)*c^2-(a^2+b^2)*c^4)*(b^2*c^2*(b^2-2*c^2)+a^4*(-2*b^2+c^2)+a^2*(b^4+c^4)) : :

X(60226) lies on the Kiepert hyperbola and on these lines: {2, 351}, {30, 54881}, {76, 690}, {83, 47646}, {98, 5970}, {110, 52940}, {115, 60106}, {262, 2793}, {512, 671}, {523, 1916}, {542, 54725}, {543, 54603}, {850, 34087}, {887, 36182}, {1499, 43532}, {1503, 54631}, {2782, 54811}, {2789, 60320}, {2794, 54600}, {2799, 60180}, {2996, 53345}, {3124, 5466}, {3566, 54750}, {3849, 54602}, {3906, 10290}, {4374, 40017}, {4444, 53559}, {5485, 58754}, {5503, 23878}, {9830, 54607}, {11632, 54733}, {11645, 54662}, {11646, 44445}, {14931, 46778}, {25423, 43535}, {27550, 43538}, {27551, 43539}, {28470, 55003}, {30217, 55009}, {53263, 60128}, {55122, 60095}

X(60226) = reflection of X(i) in X(j) for these {i,j}: {60106, 115}
X(60226) = isotomic conjugate of X(14607)
X(60226) = trilinear pole of line {21906, 523}
X(60226) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 14607}, {163, 5969}, {662, 5106}, {1101, 11182}, {4575, 56390}, {36142, 45330}, {51494, 56982}
X(60226) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 54631}, {3455, 60111}
X(60226) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 14607}, {115, 5969}, {136, 56390}, {523, 11182}, {1084, 5106}, {23992, 45330}
X(60226) = X(i)-cross conjugate of X(j) for these {i, j}: {11182, 523}
X(60226) = pole of line {1634, 11152} with respect to the 2nd Brocard circle
X(60226) = pole of line {9149, 58765} with respect to the circumcircle
X(60226) = pole of line {1916, 5968} with respect to the orthocentroidal circle
X(60226) = pole of line {2782, 5106} with respect to the orthoptic circle of the Steiner inellipse
X(60226) = pole of line {5969, 56390} with respect to the polar circle
X(60226) = pole of line {14607, 42652} with respect to the Wallace hyperbola
X(60226) = pole of line {11182, 35077} with respect to the dual conic of Wallace hyperbola
X(60226) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(46303)}}, {{A, B, C, X(99), X(9147)}}, {{A, B, C, X(110), X(351)}}, {{A, B, C, X(115), X(850)}}, {{A, B, C, X(290), X(9828)}}, {{A, B, C, X(523), X(670)}}, {{A, B, C, X(2501), X(9293)}}, {{A, B, C, X(2793), X(23878)}}, {{A, B, C, X(2799), X(32472)}}, {{A, B, C, X(4609), X(52618)}}, {{A, B, C, X(8901), X(45689)}}, {{A, B, C, X(9123), X(48951)}}, {{A, B, C, X(11646), X(15321)}}, {{A, B, C, X(13307), X(30492)}}, {{A, B, C, X(20404), X(51480)}}, {{A, B, C, X(22105), X(35138)}}, {{A, B, C, X(31065), X(42345)}}, {{A, B, C, X(38523), X(40352)}}
X(60226) = barycentric product X(i)*X(j) for these (i, j): {5970, 850}, {14606, 76}, {35146, 523}
X(60226) = barycentric quotient X(i)/X(j) for these (i, j): {2, 14607}, {115, 11182}, {512, 5106}, {523, 5969}, {690, 45330}, {882, 51494}, {2086, 42652}, {2501, 56390}, {5970, 110}, {11182, 35077}, {14606, 6}, {35146, 99}, {47646, 17941}

X(60227) = X(4)X(16552)∩X(10)X(3693)

Barycentrics    (a*(a-b)^2*b+(a-b)^2*(a+b)*c-(a^2+3*a*b+b^2)*c^2-(a+b)*c^3+c^4)*(a^3*(b+c)+b*(b-c)^2*(b+c)-a*(b+c)*(b^2+2*b*c-c^2)-a^2*(b^2+b*c+2*c^2)) : :

X(60227) lies on the Kiepert hyperbola and on these lines: {4, 16552}, {8, 60229}, {9, 13576}, {10, 3693}, {30, 54882}, {72, 40515}, {200, 60188}, {226, 518}, {321, 3717}, {405, 60075}, {442, 17758}, {452, 60092}, {1005, 24624}, {1362, 6067}, {1446, 6734}, {1751, 13615}, {1861, 40149}, {2051, 8226}, {2795, 11608}, {3419, 60135}, {4052, 42054}, {4384, 56098}, {4712, 55076}, {5177, 57826}, {5231, 36819}, {7580, 13478}, {9564, 37865}, {10479, 18840}, {11019, 56226}, {11113, 60094}, {14004, 40395}, {14022, 14554}, {14548, 58012}, {17532, 60083}, {26015, 30588}, {27523, 43533}, {36721, 54516}, {36722, 54526}, {37240, 60085}, {37658, 48888}, {50696, 60167}, {50741, 54831}, {52255, 60071}

X(60227) = isotomic conjugate of X(14828)
X(60227) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 14828}, {48, 37389}
X(60227) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 14828}, {1249, 37389}
X(60227) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(5173)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(8), X(4847)}}, {{A, B, C, X(9), X(75)}}, {{A, B, C, X(64), X(51499)}}, {{A, B, C, X(72), X(16552)}}, {{A, B, C, X(142), X(57791)}}, {{A, B, C, X(200), X(318)}}, {{A, B, C, X(257), X(34018)}}, {{A, B, C, X(264), X(2321)}}, {{A, B, C, X(291), X(1174)}}, {{A, B, C, X(309), X(56087)}}, {{A, B, C, X(335), X(42310)}}, {{A, B, C, X(344), X(38057)}}, {{A, B, C, X(391), X(35510)}}, {{A, B, C, X(405), X(3970)}}, {{A, B, C, X(442), X(1089)}}, {{A, B, C, X(452), X(57534)}}, {{A, B, C, X(461), X(5177)}}, {{A, B, C, X(594), X(24006)}}, {{A, B, C, X(596), X(943)}}, {{A, B, C, X(860), X(1005)}}, {{A, B, C, X(903), X(34917)}}, {{A, B, C, X(941), X(3668)}}, {{A, B, C, X(966), X(14548)}}, {{A, B, C, X(1088), X(5665)}}, {{A, B, C, X(1903), X(46772)}}, {{A, B, C, X(2785), X(2795)}}, {{A, B, C, X(2886), X(6598)}}, {{A, B, C, X(3617), X(11019)}}, {{A, B, C, X(3676), X(39954)}}, {{A, B, C, X(3679), X(26015)}}, {{A, B, C, X(3870), X(7162)}}, {{A, B, C, X(3932), X(17277)}}, {{A, B, C, X(4518), X(57815)}}, {{A, B, C, X(5125), X(13615)}}, {{A, B, C, X(5136), X(52255)}}, {{A, B, C, X(5231), X(6735)}}, {{A, B, C, X(6605), X(12867)}}, {{A, B, C, X(7580), X(17555)}}, {{A, B, C, X(8226), X(11109)}}, {{A, B, C, X(8580), X(24982)}}, {{A, B, C, X(11105), X(35990)}}, {{A, B, C, X(13727), X(25985)}}, {{A, B, C, X(19868), X(29667)}}, {{A, B, C, X(20103), X(25005)}}, {{A, B, C, X(28580), X(28851)}}, {{A, B, C, X(36124), X(37887)}}, {{A, B, C, X(37658), X(58024)}}, {{A, B, C, X(38271), X(39708)}}, {{A, B, C, X(40028), X(40719)}}, {{A, B, C, X(41501), X(52651)}}, {{A, B, C, X(44184), X(57881)}}, {{A, B, C, X(56157), X(57830)}}
X(60227) = barycentric quotient X(i)/X(j) for these (i, j): {2, 14828}, {4, 37389}

X(60228) = X(2)X(32457)∩X(4)X(11054)

Barycentrics    (2*(a^2+b^2)-7*c^2)*(2*a^2-7*b^2+2*c^2) : :
X(60228) = -4*X[549]+5*X[7607]

X(60228) lies on the Kiepert hyperbola and on these lines: {2, 32457}, {3, 55820}, {4, 11054}, {5, 60332}, {6, 60282}, {10, 49748}, {30, 53100}, {69, 54637}, {76, 50991}, {83, 34505}, {98, 3534}, {99, 10153}, {115, 42010}, {141, 60286}, {193, 54642}, {262, 5066}, {316, 41895}, {376, 60337}, {381, 60142}, {524, 17503}, {538, 60177}, {542, 54567}, {543, 8587}, {549, 7607}, {597, 60287}, {598, 8584}, {599, 60216}, {671, 7850}, {1916, 36523}, {1992, 60281}, {3424, 15640}, {3526, 10185}, {3545, 60330}, {3628, 60144}, {3830, 60132}, {3845, 14488}, {5055, 7608}, {5254, 60278}, {5485, 50990}, {7612, 15698}, {7620, 53101}, {7757, 60098}, {7790, 60277}, {7812, 53107}, {7827, 18841}, {7841, 43676}, {7878, 60145}, {7883, 60250}, {7894, 18843}, {7918, 18840}, {7937, 10302}, {8352, 53105}, {8370, 53102}, {8703, 60335}, {10303, 53859}, {10304, 43537}, {11001, 60322}, {11057, 43535}, {11185, 18842}, {11317, 53109}, {11540, 11668}, {14036, 43528}, {14046, 43529}, {14458, 33699}, {14711, 43688}, {15300, 60104}, {15534, 45103}, {15682, 54845}, {15683, 47586}, {15684, 54857}, {15709, 60123}, {15759, 60175}, {15850, 53098}, {18546, 54487}, {19709, 54920}, {23046, 60329}, {29622, 30588}, {32532, 50992}, {32833, 60262}, {41099, 52519}, {42011, 52229}, {43448, 60200}, {51140, 54482}, {51187, 54478}

X(60228) = reflection of X(i) in X(j) for these {i,j}: {42010, 115}
X(60228) = inverse of X(51589) in Wallace hyperbola
X(60228) = isotomic conjugate of X(15534)
X(60228) = trilinear pole of line {41133, 523}
X(60228) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 15534}, {15850, 33554}
X(60228) = pole of line {22165, 60228} with respect to the Kiepert hyperbola
X(60228) = pole of line {15534, 33554} with respect to the Wallace hyperbola
X(60228) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55718)}}, {{A, B, C, X(6), X(50991)}}, {{A, B, C, X(141), X(51185)}}, {{A, B, C, X(249), X(43713)}}, {{A, B, C, X(297), X(3534)}}, {{A, B, C, X(305), X(11054)}}, {{A, B, C, X(458), X(5066)}}, {{A, B, C, X(524), X(15533)}}, {{A, B, C, X(549), X(52282)}}, {{A, B, C, X(597), X(51186)}}, {{A, B, C, X(599), X(8584)}}, {{A, B, C, X(903), X(49748)}}, {{A, B, C, X(1502), X(18818)}}, {{A, B, C, X(1992), X(50990)}}, {{A, B, C, X(3679), X(29622)}}, {{A, B, C, X(4677), X(29618)}}, {{A, B, C, X(5055), X(52281)}}, {{A, B, C, X(7850), X(44146)}}, {{A, B, C, X(8352), X(37453)}}, {{A, B, C, X(8770), X(10630)}}, {{A, B, C, X(9289), X(34483)}}, {{A, B, C, X(11055), X(20023)}}, {{A, B, C, X(11331), X(33699)}}, {{A, B, C, X(13622), X(34898)}}, {{A, B, C, X(13623), X(42313)}}, {{A, B, C, X(14711), X(41259)}}, {{A, B, C, X(15534), X(22165)}}, {{A, B, C, X(15640), X(52283)}}, {{A, B, C, X(15698), X(37174)}}, {{A, B, C, X(35140), X(54171)}}, {{A, B, C, X(35146), X(42359)}}, {{A, B, C, X(41149), X(51189)}}, {{A, B, C, X(44763), X(56004)}}, {{A, B, C, X(57822), X(57908)}}
X(60228) = barycentric product X(i)*X(j) for these (i, j): {33638, 850}, {40103, 76}
X(60228) = barycentric quotient X(i)/X(j) for these (i, j): {2, 15534}, {3054, 33554}, {33638, 110}, {40103, 6}, {50992, 51589}

X(60229) = X(2)X(220)∩X(4)X(390)

Barycentrics    (a+b-c)*(a-b+c)*(b+c)*((a-b)^2-(a+b)*c)*(a^2+c*(-b+c)-a*(b+2*c)) : :

X(60229) lies on the Kiepert hyperbola and on these lines: {1, 43672}, {2, 220}, {4, 390}, {7, 3730}, {8, 60227}, {10, 21931}, {12, 13576}, {37, 1446}, {76, 346}, {85, 25237}, {98, 53243}, {226, 1334}, {279, 27253}, {321, 4515}, {651, 54497}, {671, 6606}, {938, 57719}, {1025, 17169}, {1174, 1751}, {1441, 3991}, {1803, 13478}, {2051, 5226}, {2293, 34848}, {2996, 27267}, {3085, 10482}, {3207, 26988}, {3485, 45964}, {3600, 52241}, {3673, 54739}, {3947, 54668}, {3995, 43675}, {4444, 17084}, {4566, 21808}, {5219, 14554}, {6706, 25001}, {10056, 54517}, {10509, 34820}, {14021, 60076}, {14986, 45097}, {17732, 60083}, {17747, 27049}, {17776, 40013}, {20073, 60236}, {20706, 60245}, {27096, 52422}, {27108, 32022}, {28739, 43531}, {28742, 40719}, {29611, 60084}, {31015, 40443}, {34258, 57815}, {34619, 60079}, {41785, 56746}, {43533, 56118}, {47487, 54972}, {52358, 56226}, {54528, 56416}, {54831, 58809}, {56322, 60074}

X(60229) = isotomic conjugate of X(16713)
X(60229) = trilinear pole of line {4524, 523}
X(60229) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 17194}, {21, 1475}, {27, 22079}, {31, 16713}, {41, 17169}, {55, 18164}, {58, 1212}, {60, 21808}, {81, 2293}, {86, 20229}, {110, 21127}, {142, 2194}, {163, 6362}, {212, 53238}, {284, 354}, {593, 21039}, {662, 2488}, {757, 21795}, {1014, 8012}, {1172, 22053}, {1229, 2206}, {1333, 4847}, {1408, 51972}, {1412, 3059}, {1414, 10581}, {1418, 2328}, {1437, 1855}, {1790, 1827}, {1812, 40983}, {2150, 3925}, {2175, 16708}, {2185, 52020}, {3733, 35341}, {3737, 35326}, {4565, 6608}, {4637, 6607}, {5546, 48151}, {7252, 35338}, {9447, 53236}, {20880, 57657}
X(60229) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 16713}, {9, 17194}, {10, 1212}, {37, 4847}, {115, 6362}, {223, 18164}, {244, 21127}, {1084, 2488}, {1214, 142}, {3160, 17169}, {36908, 1418}, {40586, 2293}, {40590, 354}, {40593, 16708}, {40599, 3059}, {40600, 20229}, {40603, 1229}, {40607, 21795}, {40608, 10581}, {40611, 1475}, {40622, 21104}, {40837, 53238}, {55064, 6608}, {56325, 3925}, {59577, 51972}, {59608, 10481}
X(60229) = X(i)-cross conjugate of X(j) for these {i, j}: {37, 56255}, {4041, 4566}, {4077, 4552}, {56255, 56157}
X(60229) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(56320)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(18097)}}, {{A, B, C, X(37), X(220)}}, {{A, B, C, X(65), X(279)}}, {{A, B, C, X(72), X(954)}}, {{A, B, C, X(85), X(56173)}}, {{A, B, C, X(86), X(27039)}}, {{A, B, C, X(189), X(56246)}}, {{A, B, C, X(193), X(27267)}}, {{A, B, C, X(277), X(4674)}}, {{A, B, C, X(307), X(8232)}}, {{A, B, C, X(318), X(27475)}}, {{A, B, C, X(348), X(8543)}}, {{A, B, C, X(390), X(3710)}}, {{A, B, C, X(406), X(31015)}}, {{A, B, C, X(941), X(57660)}}, {{A, B, C, X(1170), X(31618)}}, {{A, B, C, X(1214), X(3295)}}, {{A, B, C, X(1255), X(40447)}}, {{A, B, C, X(1400), X(26125)}}, {{A, B, C, X(1427), X(44794)}}, {{A, B, C, X(1441), X(6604)}}, {{A, B, C, X(2141), X(56156)}}, {{A, B, C, X(2295), X(20706)}}, {{A, B, C, X(3925), X(45226)}}, {{A, B, C, X(3995), X(17776)}}, {{A, B, C, X(4041), X(21808)}}, {{A, B, C, X(4194), X(14021)}}, {{A, B, C, X(4415), X(17056)}}, {{A, B, C, X(4648), X(27108)}}, {{A, B, C, X(5226), X(52358)}}, {{A, B, C, X(6605), X(42310)}}, {{A, B, C, X(10405), X(38955)}}, {{A, B, C, X(21258), X(21931)}}, {{A, B, C, X(26115), X(29611)}}, {{A, B, C, X(27022), X(37908)}}, {{A, B, C, X(27067), X(41003)}}, {{A, B, C, X(27809), X(54123)}}, {{A, B, C, X(30701), X(56186)}}, {{A, B, C, X(32008), X(56127)}}, {{A, B, C, X(33298), X(57809)}}, {{A, B, C, X(36101), X(56195)}}, {{A, B, C, X(42326), X(56135)}}, {{A, B, C, X(53114), X(56043)}}, {{A, B, C, X(55405), X(56219)}}, {{A, B, C, X(55986), X(56254)}}
X(60229) = barycentric product X(i)*X(j) for these (i, j): {10, 21453}, {210, 42311}, {226, 32008}, {523, 6606}, {1170, 321}, {1174, 349}, {1441, 2346}, {1446, 6605}, {3668, 56118}, {3925, 59475}, {4552, 56322}, {10509, 2321}, {31618, 37}, {40443, 41013}, {47487, 57809}, {53243, 850}, {56127, 57}, {56157, 7}, {56255, 85}, {57815, 65}
X(60229) = barycentric quotient X(i)/X(j) for these (i, j): {1, 17194}, {2, 16713}, {7, 17169}, {10, 4847}, {12, 3925}, {37, 1212}, {42, 2293}, {57, 18164}, {65, 354}, {73, 22053}, {85, 16708}, {181, 52020}, {210, 3059}, {213, 20229}, {226, 142}, {228, 22079}, {278, 53238}, {321, 1229}, {349, 1233}, {512, 2488}, {523, 6362}, {661, 21127}, {756, 21039}, {1018, 35341}, {1170, 81}, {1174, 284}, {1334, 8012}, {1400, 1475}, {1427, 1418}, {1441, 20880}, {1446, 59181}, {1500, 21795}, {1803, 1790}, {1824, 1827}, {1826, 1855}, {2171, 21808}, {2321, 51972}, {2346, 21}, {3668, 10481}, {3709, 10581}, {3925, 6067}, {4017, 48151}, {4041, 6608}, {4515, 45791}, {4524, 6607}, {4551, 35338}, {4559, 35326}, {4566, 35312}, {6063, 53236}, {6354, 52023}, {6605, 2287}, {6606, 99}, {7178, 21104}, {8808, 13156}, {10482, 2328}, {10509, 1434}, {14324, 14283}, {17757, 51416}, {18097, 18087}, {21453, 86}, {21859, 35310}, {31618, 274}, {32008, 333}, {40443, 1444}, {40663, 51463}, {41539, 15185}, {42289, 59217}, {42311, 57785}, {47487, 283}, {51421, 51424}, {53243, 110}, {55282, 57252}, {56118, 1043}, {56127, 312}, {56157, 8}, {56255, 9}, {56284, 56283}, {56322, 4560}, {57652, 40983}, {57815, 314}, {58322, 3737}
X(60229) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {21453, 32008, 1170}

X(60230) = X(2)X(1258)∩X(76)X(192)

Barycentrics    (b+c)*(a*b*(a+b)+(a^2+b^2)*c)*(a*c^2+b*c^2+a^2*(b+c)) : :

X(60230) lies on the Kiepert hyperbola and on these lines: {1, 60090}, {2, 1258}, {8, 60110}, {10, 21803}, {37, 56250}, {42, 56211}, {76, 192}, {98, 59102}, {321, 20691}, {594, 53675}, {595, 43531}, {894, 60320}, {1018, 27020}, {1215, 7148}, {1284, 60086}, {2171, 60245}, {2292, 43534}, {3661, 60084}, {3662, 17758}, {3869, 45964}, {3948, 60264}, {3952, 21700}, {4033, 25102}, {4389, 60236}, {4444, 48131}, {6539, 27041}, {6625, 26110}, {14624, 17493}, {16589, 40525}, {16705, 30669}, {17750, 26963}, {18088, 30505}, {20146, 40720}, {20917, 28606}, {23493, 43223}, {24624, 41252}, {26115, 40718}, {26752, 40024}, {26971, 41240}, {27262, 30116}, {27299, 60075}, {27321, 60235}, {29822, 40935}, {32014, 40409}, {33151, 60257}, {35105, 59094}, {35353, 50497}, {56161, 59299}

X(60230) = isotomic conjugate of X(16738)
X(60230) = trilinear pole of line {50491, 523}
X(60230) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 18169}, {27, 22389}, {28, 22065}, {31, 16738}, {58, 1107}, {60, 45208}, {81, 2309}, {86, 1197}, {593, 3728}, {662, 50510}, {757, 21838}, {763, 21700}, {849, 21024}, {1019, 53268}, {1333, 3741}, {2185, 39780}, {2194, 30097}, {2206, 20891}, {7304, 45209}, {40627, 52935}, {53338, 57129}
X(60230) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 16738}, {9, 18169}, {10, 1107}, {37, 3741}, {1084, 50510}, {1214, 30097}, {4075, 21024}, {16587, 51575}, {40586, 2309}, {40591, 22065}, {40600, 1197}, {40603, 20891}, {40607, 21838}
X(60230) = X(i)-cross conjugate of X(j) for these {i, j}: {3835, 4033}, {4079, 3952}, {22041, 1897}, {22046, 1978}, {27042, 2}
X(60230) = pole of line {27042, 60230} with respect to the Kiepert hyperbola
X(60230) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(27809)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(37), X(192)}}, {{A, B, C, X(65), X(330)}}, {{A, B, C, X(85), X(56175)}}, {{A, B, C, X(86), X(26772)}}, {{A, B, C, X(274), X(4674)}}, {{A, B, C, X(595), X(3995)}}, {{A, B, C, X(1218), X(40504)}}, {{A, B, C, X(1221), X(1258)}}, {{A, B, C, X(1284), X(2292)}}, {{A, B, C, X(1441), X(21281)}}, {{A, B, C, X(1500), X(7109)}}, {{A, B, C, X(1654), X(26110)}}, {{A, B, C, X(2171), X(2295)}}, {{A, B, C, X(2296), X(18832)}}, {{A, B, C, X(3661), X(26115)}}, {{A, B, C, X(3971), X(43223)}}, {{A, B, C, X(4079), X(21700)}}, {{A, B, C, X(4651), X(27255)}}, {{A, B, C, X(6376), X(56250)}}, {{A, B, C, X(8025), X(27041)}}, {{A, B, C, X(14621), X(18097)}}, {{A, B, C, X(15320), X(56332)}}, {{A, B, C, X(16589), X(50497)}}, {{A, B, C, X(16738), X(27042)}}, {{A, B, C, X(17152), X(39712)}}, {{A, B, C, X(17381), X(27095)}}, {{A, B, C, X(17743), X(18082)}}, {{A, B, C, X(18793), X(56011)}}, {{A, B, C, X(19874), X(29576)}}, {{A, B, C, X(21674), X(27321)}}, {{A, B, C, X(27269), X(30964)}}, {{A, B, C, X(27320), X(41876)}}, {{A, B, C, X(27801), X(45095)}}, {{A, B, C, X(31359), X(56122)}}, {{A, B, C, X(38247), X(53114)}}, {{A, B, C, X(38955), X(54120)}}, {{A, B, C, X(39736), X(56174)}}, {{A, B, C, X(40005), X(54112)}}, {{A, B, C, X(40720), X(59212)}}, {{A, B, C, X(54123), X(56258)}}, {{A, B, C, X(56044), X(56173)}}, {{A, B, C, X(56046), X(56246)}}, {{A, B, C, X(56051), X(56135)}}
X(60230) = barycentric product X(i)*X(j) for these (i, j): {10, 40418}, {313, 57399}, {1221, 37}, {1258, 321}, {21051, 59094}, {31625, 40525}, {40409, 594}, {59102, 850}
X(60230) = barycentric quotient X(i)/X(j) for these (i, j): {1, 18169}, {2, 16738}, {10, 3741}, {37, 1107}, {42, 2309}, {71, 22065}, {181, 39780}, {213, 1197}, {226, 30097}, {228, 22389}, {321, 20891}, {512, 50510}, {594, 21024}, {756, 3728}, {762, 22206}, {1215, 51575}, {1221, 274}, {1258, 81}, {1500, 21838}, {2171, 45208}, {3778, 23473}, {3952, 53338}, {3971, 59565}, {4079, 40627}, {4557, 53268}, {6535, 21713}, {14624, 56901}, {17757, 51411}, {18082, 18091}, {21803, 27880}, {40409, 1509}, {40418, 86}, {40525, 1015}, {57399, 58}, {59094, 56053}, {59102, 110}, {59158, 17103}

X(60231) = X(4)X(7945)∩X(83)X(7874)

Barycentrics    (2*a^4+3*b^4-a^2*c^2+2*c^4)*(2*a^4-a^2*b^2+2*b^4+3*c^4) : :

X(60231) lies on the Kiepert hyperbola and on these lines: {4, 7945}, {76, 14065}, {83, 7874}, {98, 7931}, {141, 60104}, {325, 43528}, {384, 53109}, {385, 60186}, {549, 55009}, {598, 14036}, {671, 7880}, {3314, 60093}, {3399, 3628}, {3406, 3526}, {3407, 7778}, {3534, 54584}, {5025, 53105}, {5066, 54583}, {5999, 60132}, {7607, 16986}, {7777, 60215}, {7868, 60128}, {7886, 10159}, {7892, 53102}, {7901, 32457}, {10304, 54565}, {11361, 54494}, {13862, 14488}, {14001, 18843}, {14032, 53107}, {14041, 33698}, {14047, 60210}, {14064, 60219}, {16041, 54720}, {16988, 60187}, {16990, 60263}, {33287, 38259}, {33289, 53106}, {37690, 60190}, {44377, 60098}

X(60231) = isotomic conjugate of X(16984)
X(60231) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(14065)}}, {{A, B, C, X(141), X(7925)}}, {{A, B, C, X(305), X(7945)}}, {{A, B, C, X(308), X(40511)}}, {{A, B, C, X(325), X(7931)}}, {{A, B, C, X(427), X(14043)}}, {{A, B, C, X(468), X(14046)}}, {{A, B, C, X(3266), X(7880)}}, {{A, B, C, X(3314), X(7778)}}, {{A, B, C, X(4590), X(9229)}}, {{A, B, C, X(5025), X(37453)}}, {{A, B, C, X(5094), X(14036)}}, {{A, B, C, X(7777), X(7868)}}, {{A, B, C, X(7874), X(8024)}}, {{A, B, C, X(7886), X(39998)}}, {{A, B, C, X(14032), X(52298)}}, {{A, B, C, X(16990), X(37690)}}, {{A, B, C, X(29872), X(30161)}}, {{A, B, C, X(33287), X(38282)}}, {{A, B, C, X(33289), X(52297)}}, {{A, B, C, X(34483), X(51454)}}, {{A, B, C, X(43150), X(44132)}}

X(60232) = X(4)X(3314)∩X(69)X(3407)

Barycentrics    (a^4+2*a^2*b^2+3*b^4+2*b^2*c^2+c^4)*(a^4+b^4+2*(a^2+b^2)*c^2+3*c^4) : :

X(60232) lies on the Kiepert hyperbola and on these lines: {4, 3314}, {69, 3407}, {83, 7774}, {98, 16990}, {114, 54675}, {141, 54122}, {147, 55009}, {325, 60190}, {376, 54614}, {671, 33251}, {1007, 60098}, {1352, 14458}, {2996, 7933}, {3329, 18841}, {3399, 31276}, {3406, 7836}, {3424, 3620}, {3619, 42006}, {3767, 10159}, {5395, 37668}, {5485, 33223}, {7735, 43528}, {7736, 60129}, {7778, 60234}, {7828, 60278}, {7832, 43527}, {7840, 18842}, {7897, 60105}, {7925, 14494}, {7931, 40824}, {8587, 42850}, {10352, 54839}, {14568, 60277}, {16986, 60212}, {16989, 60215}, {17004, 60263}, {17008, 60093}, {18840, 33221}, {21356, 43535}, {31089, 60155}, {31090, 32022}, {32458, 60072}, {33007, 54806}, {34229, 60104}, {37690, 60233}

X(60232) = isotomic conjugate of X(16989)
X(60232) = pole of line {7868, 60232} with respect to the Kiepert hyperbola
X(60232) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(69), X(3314)}}, {{A, B, C, X(141), X(7774)}}, {{A, B, C, X(325), X(16990)}}, {{A, B, C, X(427), X(16898)}}, {{A, B, C, X(468), X(33251)}}, {{A, B, C, X(1297), X(40803)}}, {{A, B, C, X(2353), X(3108)}}, {{A, B, C, X(2998), X(44556)}}, {{A, B, C, X(3329), X(3619)}}, {{A, B, C, X(3620), X(37668)}}, {{A, B, C, X(3767), X(39998)}}, {{A, B, C, X(4232), X(33223)}}, {{A, B, C, X(4648), X(31090)}}, {{A, B, C, X(6340), X(17128)}}, {{A, B, C, X(6353), X(7933)}}, {{A, B, C, X(6664), X(45819)}}, {{A, B, C, X(6995), X(33221)}}, {{A, B, C, X(7735), X(7931)}}, {{A, B, C, X(7736), X(16986)}}, {{A, B, C, X(7778), X(17008)}}, {{A, B, C, X(7795), X(8024)}}, {{A, B, C, X(7840), X(21356)}}, {{A, B, C, X(7868), X(16989)}}, {{A, B, C, X(7925), X(34229)}}, {{A, B, C, X(8797), X(40042)}}, {{A, B, C, X(9865), X(20026)}}, {{A, B, C, X(11169), X(31360)}}, {{A, B, C, X(17004), X(37690)}}, {{A, B, C, X(17980), X(52660)}}, {{A, B, C, X(34138), X(46807)}}

X(60233) = X(2)X(5111)∩X(6)X(60104)

Barycentrics    (a^4-3*a^2*b^2+b^4-2*(a^2+b^2)*c^2+2*c^4)*(a^4+2*b^4-2*b^2*c^2+c^4-a^2*(2*b^2+3*c^2)) : :

X(60233) lies on the Kiepert hyperbola and on these lines: {2, 5111}, {6, 60104}, {76, 7862}, {83, 7907}, {98, 7777}, {193, 60102}, {262, 17005}, {325, 60128}, {381, 54723}, {385, 7607}, {598, 7622}, {1007, 54122}, {1504, 60275}, {1505, 60274}, {2996, 32963}, {3314, 60101}, {3329, 60093}, {3406, 7762}, {3407, 3815}, {3972, 53102}, {5395, 32964}, {5475, 33257}, {5476, 60192}, {7612, 7774}, {7778, 42006}, {7783, 53105}, {7806, 60073}, {7837, 54644}, {7840, 60220}, {7875, 60186}, {7909, 60210}, {7931, 60099}, {8176, 33698}, {8587, 11163}, {9738, 14234}, {9739, 14238}, {9771, 10484}, {11170, 37459}, {11174, 43528}, {11184, 43535}, {11668, 17006}, {13188, 60176}, {16986, 60187}, {16989, 60263}, {17004, 53104}, {17008, 53103}, {18840, 32976}, {18841, 32977}, {18842, 33216}, {18845, 33244}, {19569, 54805}, {19696, 53107}, {31489, 60098}, {32519, 43532}, {33193, 53101}, {34803, 60234}, {37690, 60232}, {42535, 60184}, {43529, 44377}, {51140, 60175}, {51851, 54487}

X(60233) = isotomic conjugate of X(17004)
X(60233) = pole of line {37647, 60233} with respect to the Kiepert hyperbola
X(60233) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(5111)}}, {{A, B, C, X(25), X(32967)}}, {{A, B, C, X(183), X(17005)}}, {{A, B, C, X(251), X(7862)}}, {{A, B, C, X(264), X(35511)}}, {{A, B, C, X(325), X(7777)}}, {{A, B, C, X(427), X(7907)}}, {{A, B, C, X(1007), X(7774)}}, {{A, B, C, X(1297), X(9738)}}, {{A, B, C, X(1504), X(1505)}}, {{A, B, C, X(2998), X(40410)}}, {{A, B, C, X(3314), X(3815)}}, {{A, B, C, X(3329), X(7778)}}, {{A, B, C, X(3425), X(14565)}}, {{A, B, C, X(3613), X(36953)}}, {{A, B, C, X(4590), X(18575)}}, {{A, B, C, X(5094), X(13586)}}, {{A, B, C, X(6353), X(32963)}}, {{A, B, C, X(6995), X(32976)}}, {{A, B, C, X(7378), X(32977)}}, {{A, B, C, X(7622), X(42008)}}, {{A, B, C, X(7806), X(44377)}}, {{A, B, C, X(7840), X(11184)}}, {{A, B, C, X(7908), X(39389)}}, {{A, B, C, X(7931), X(11174)}}, {{A, B, C, X(7947), X(39951)}}, {{A, B, C, X(8024), X(31455)}}, {{A, B, C, X(8889), X(32964)}}, {{A, B, C, X(16989), X(37690)}}, {{A, B, C, X(17004), X(37647)}}, {{A, B, C, X(17008), X(34803)}}, {{A, B, C, X(19696), X(52298)}}, {{A, B, C, X(30537), X(56057)}}, {{A, B, C, X(30542), X(43098)}}, {{A, B, C, X(33216), X(52284)}}, {{A, B, C, X(33244), X(52299)}}, {{A, B, C, X(40416), X(45090)}}, {{A, B, C, X(41909), X(55958)}}, {{A, B, C, X(42332), X(45838)}}

X(60234) = X(4)X(7777)∩X(98)X(7774)

Barycentrics    (a^4-4*a^2*b^2+b^4-2*(a^2+b^2)*c^2+3*c^4)*(a^4+3*b^4-2*b^2*c^2+c^4-2*a^2*(b^2+2*c^2)) : :

X(60234) lies on the Kiepert hyperbola and on these lines: {4, 7777}, {32, 54839}, {69, 60128}, {76, 32961}, {83, 16925}, {98, 7774}, {148, 60176}, {193, 43537}, {194, 43532}, {325, 54122}, {376, 54805}, {385, 7612}, {598, 2548}, {631, 60148}, {671, 7752}, {1007, 1916}, {1992, 8587}, {2996, 32966}, {3090, 60126}, {3146, 54894}, {3314, 60212}, {3406, 7793}, {3407, 7736}, {3552, 5395}, {3618, 43528}, {3815, 60190}, {5013, 54753}, {5485, 32818}, {6337, 54872}, {6658, 18845}, {7607, 17008}, {7608, 14561}, {7694, 54568}, {7735, 60104}, {7763, 60072}, {7766, 60136}, {7778, 60232}, {7785, 55009}, {7806, 60263}, {7823, 54859}, {7837, 60185}, {7840, 11172}, {7846, 60238}, {7899, 10302}, {7925, 40824}, {7931, 18840}, {9770, 43535}, {14229, 43134}, {14244, 43133}, {14494, 17005}, {16989, 60093}, {16990, 60101}, {17004, 53103}, {17006, 60123}, {18841, 32970}, {18842, 32985}, {18843, 33239}, {23235, 60189}, {32958, 60183}, {32993, 38259}, {33280, 53109}, {34803, 60233}, {37667, 60102}, {37690, 43529}, {45103, 52942}

X(60234) = isotomic conjugate of X(17008)
X(60234) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(56057)}}, {{A, B, C, X(25), X(32961)}}, {{A, B, C, X(66), X(57926)}}, {{A, B, C, X(69), X(7777)}}, {{A, B, C, X(111), X(43620)}}, {{A, B, C, X(264), X(41909)}}, {{A, B, C, X(325), X(7774)}}, {{A, B, C, X(385), X(1007)}}, {{A, B, C, X(427), X(16925)}}, {{A, B, C, X(468), X(33006)}}, {{A, B, C, X(1992), X(46275)}}, {{A, B, C, X(2065), X(14565)}}, {{A, B, C, X(2548), X(10130)}}, {{A, B, C, X(2987), X(40803)}}, {{A, B, C, X(2998), X(8797)}}, {{A, B, C, X(3266), X(34161)}}, {{A, B, C, X(3314), X(7736)}}, {{A, B, C, X(3552), X(8889)}}, {{A, B, C, X(3613), X(9516)}}, {{A, B, C, X(3618), X(7931)}}, {{A, B, C, X(3815), X(16990)}}, {{A, B, C, X(4232), X(32984)}}, {{A, B, C, X(4518), X(56353)}}, {{A, B, C, X(5094), X(33007)}}, {{A, B, C, X(5486), X(18023)}}, {{A, B, C, X(6340), X(7783)}}, {{A, B, C, X(6353), X(32966)}}, {{A, B, C, X(6658), X(52299)}}, {{A, B, C, X(6995), X(32969)}}, {{A, B, C, X(7249), X(56042)}}, {{A, B, C, X(7378), X(32970)}}, {{A, B, C, X(7408), X(32958)}}, {{A, B, C, X(7409), X(32959)}}, {{A, B, C, X(7618), X(42008)}}, {{A, B, C, X(7735), X(7925)}}, {{A, B, C, X(7752), X(41896)}}, {{A, B, C, X(7778), X(16989)}}, {{A, B, C, X(7793), X(45093)}}, {{A, B, C, X(7806), X(37690)}}, {{A, B, C, X(7840), X(9770)}}, {{A, B, C, X(8024), X(31401)}}, {{A, B, C, X(9229), X(46952)}}, {{A, B, C, X(9289), X(30786)}}, {{A, B, C, X(14383), X(51373)}}, {{A, B, C, X(17004), X(34803)}}, {{A, B, C, X(17005), X(34229)}}, {{A, B, C, X(17980), X(36615)}}, {{A, B, C, X(18019), X(57771)}}, {{A, B, C, X(30537), X(44558)}}, {{A, B, C, X(32985), X(52284)}}, {{A, B, C, X(32993), X(38282)}}, {{A, B, C, X(34208), X(38262)}}, {{A, B, C, X(34288), X(40429)}}, {{A, B, C, X(35511), X(36889)}}, {{A, B, C, X(40511), X(45819)}}, {{A, B, C, X(45833), X(57857)}}, {{A, B, C, X(52224), X(56334)}}, {{A, B, C, X(52293), X(52942)}}

X(60235) = X(2)X(7058)∩X(10)X(1043)

Barycentrics    (a+b)*(a+c)*((a-b)^2-(a+b)*c-2*c^2)*(a^2-(2*b-c)*(b+c)-a*(b+2*c)) : :

X(60235) lies on the Kiepert hyperbola and on these lines: {2, 7058}, {4, 25446}, {10, 1043}, {75, 43683}, {76, 5737}, {81, 30588}, {86, 56226}, {99, 5745}, {226, 333}, {261, 13478}, {274, 1446}, {321, 5235}, {966, 60254}, {1150, 57722}, {1211, 60251}, {1509, 37642}, {2051, 17277}, {4052, 50093}, {4384, 60245}, {5278, 60071}, {5466, 56321}, {6539, 32849}, {6703, 32014}, {7256, 25006}, {13736, 43533}, {14534, 35466}, {14829, 17758}, {16824, 17097}, {19732, 34258}, {19804, 43682}, {24880, 43531}, {27321, 60230}, {31623, 40149}, {33138, 40718}, {34016, 57826}, {37660, 40012}, {40882, 58463}, {42033, 60267}, {48814, 60079}, {54335, 60116}

X(60235) = inverse of X(5745) in Wallace hyperbola
X(60235) = isotomic conjugate of X(17056)
X(60235) = trilinear pole of line {4833, 4879}
X(60235) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 2650}, {31, 17056}, {32, 18698}, {48, 407}, {56, 21811}, {65, 21748}, {71, 40985}, {213, 3664}, {604, 21677}, {661, 53324}, {667, 22003}, {692, 23755}, {798, 17136}, {1333, 21674}, {1400, 2646}, {1402, 5745}, {1409, 40950}, {1880, 22361}, {2206, 42708}, {7180, 53388}, {30604, 34073}
X(60235) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 21811}, {2, 17056}, {9, 2650}, {37, 21674}, {1086, 23755}, {1249, 407}, {3161, 21677}, {6376, 18698}, {6626, 3664}, {6631, 22003}, {31998, 17136}, {36830, 53324}, {40582, 2646}, {40602, 21748}, {40603, 42708}, {40605, 5745}
X(60235) = X(i)-cross conjugate of X(j) for these {i, j}: {522, 99}, {17588, 86}, {17950, 35145}, {21302, 670}, {53356, 892}, {57668, 57833}
X(60235) = pole of line {3664, 5745} with respect to the Wallace hyperbola
X(60235) = pole of line {24378, 40430} with respect to the dual conic of Yff parabola
X(60235) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(5737)}}, {{A, B, C, X(27), X(1509)}}, {{A, B, C, X(57), X(1247)}}, {{A, B, C, X(63), X(51290)}}, {{A, B, C, X(75), X(33116)}}, {{A, B, C, X(81), X(759)}}, {{A, B, C, X(88), X(1171)}}, {{A, B, C, X(95), X(57911)}}, {{A, B, C, X(99), X(17933)}}, {{A, B, C, X(171), X(40775)}}, {{A, B, C, X(189), X(20569)}}, {{A, B, C, X(249), X(2708)}}, {{A, B, C, X(257), X(37887)}}, {{A, B, C, X(261), X(44130)}}, {{A, B, C, X(274), X(333)}}, {{A, B, C, X(306), X(25446)}}, {{A, B, C, X(393), X(966)}}, {{A, B, C, X(522), X(5745)}}, {{A, B, C, X(662), X(31628)}}, {{A, B, C, X(673), X(40409)}}, {{A, B, C, X(799), X(6632)}}, {{A, B, C, X(940), X(19732)}}, {{A, B, C, X(967), X(3437)}}, {{A, B, C, X(1016), X(30710)}}, {{A, B, C, X(1150), X(5278)}}, {{A, B, C, X(1211), X(35466)}}, {{A, B, C, X(1213), X(6703)}}, {{A, B, C, X(1214), X(46623)}}, {{A, B, C, X(1275), X(57557)}}, {{A, B, C, X(2372), X(43757)}}, {{A, B, C, X(3661), X(33138)}}, {{A, B, C, X(3718), X(57853)}}, {{A, B, C, X(3741), X(27321)}}, {{A, B, C, X(4359), X(32849)}}, {{A, B, C, X(4383), X(37660)}}, {{A, B, C, X(4384), X(7081)}}, {{A, B, C, X(4416), X(34277)}}, {{A, B, C, X(4590), X(53193)}}, {{A, B, C, X(5241), X(37634)}}, {{A, B, C, X(5435), X(50093)}}, {{A, B, C, X(5743), X(37646)}}, {{A, B, C, X(6063), X(57980)}}, {{A, B, C, X(6650), X(55090)}}, {{A, B, C, X(7490), X(13736)}}, {{A, B, C, X(8056), X(17261)}}, {{A, B, C, X(11679), X(16824)}}, {{A, B, C, X(13136), X(32680)}}, {{A, B, C, X(14829), X(17277)}}, {{A, B, C, X(15668), X(19744)}}, {{A, B, C, X(17259), X(37674)}}, {{A, B, C, X(19804), X(34016)}}, {{A, B, C, X(23582), X(57551)}}, {{A, B, C, X(24880), X(56810)}}, {{A, B, C, X(25430), X(32013)}}, {{A, B, C, X(27483), X(33160)}}, {{A, B, C, X(30608), X(33066)}}, {{A, B, C, X(30831), X(31204)}}, {{A, B, C, X(30832), X(41806)}}, {{A, B, C, X(31205), X(41878)}}, {{A, B, C, X(31618), X(35144)}}, {{A, B, C, X(32008), X(32017)}}, {{A, B, C, X(34409), X(58013)}}, {{A, B, C, X(35141), X(51865)}}, {{A, B, C, X(35168), X(36935)}}, {{A, B, C, X(36036), X(57928)}}, {{A, B, C, X(40403), X(56204)}}, {{A, B, C, X(40410), X(57910)}}, {{A, B, C, X(40415), X(56052)}}, {{A, B, C, X(40432), X(53083)}}, {{A, B, C, X(55990), X(56058)}}, {{A, B, C, X(57787), X(57948)}}
X(60235) = barycentric product X(i)*X(j) for these (i, j): {4, 57833}, {264, 57668}, {17097, 314}, {40430, 75}, {40442, 44130}, {56321, 99}
X(60235) = barycentric quotient X(i)/X(j) for these (i, j): {1, 2650}, {2, 17056}, {4, 407}, {8, 21677}, {9, 21811}, {10, 21674}, {21, 2646}, {28, 40985}, {29, 40950}, {75, 18698}, {86, 3664}, {99, 17136}, {110, 53324}, {190, 22003}, {283, 22361}, {284, 21748}, {321, 42708}, {333, 5745}, {514, 23755}, {643, 53388}, {1043, 6737}, {4225, 37836}, {4777, 30604}, {17097, 65}, {40430, 1}, {40442, 73}, {56321, 523}, {57668, 3}, {57833, 69}

X(60236) = X(2)X(4754)∩X(10)X(3662)

Barycentrics    ((b-2*c)*c+a*(b+c))*(b*(-2*b+c)+a*(b+c)) : :

X(60236) lies on the Kiepert hyperbola and on these lines: {2, 4754}, {4, 17300}, {10, 3662}, {20, 54946}, {69, 60149}, {76, 17232}, {83, 17379}, {141, 56210}, {145, 13576}, {193, 60092}, {226, 7185}, {321, 17230}, {330, 20335}, {598, 50266}, {1086, 53675}, {1654, 32022}, {1751, 37683}, {2996, 4869}, {3616, 40718}, {3620, 43533}, {3661, 60267}, {3834, 18144}, {3912, 4052}, {3945, 5395}, {3948, 40012}, {4389, 60230}, {4648, 6625}, {6376, 30044}, {10449, 60079}, {17034, 50133}, {17349, 60075}, {17753, 27295}, {17758, 27269}, {17778, 60155}, {18134, 60261}, {18135, 40017}, {18139, 60257}, {18140, 40031}, {20073, 60229}, {20913, 34258}, {24624, 37684}, {25102, 48629}, {26978, 56167}, {30942, 56211}, {30949, 41838}, {31060, 40013}, {31276, 60090}, {33144, 39724}, {33891, 34860}, {34284, 40024}, {37652, 57721}

X(60236) = isotomic conjugate of X(17349)
X(60236) = trilinear pole of line {3776, 4818}
X(60236) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 8616}, {31, 17349}, {32, 17144}, {101, 48331}, {692, 48008}, {765, 23470}, {1333, 4685}, {2206, 22016}, {4570, 22215}, {23794, 32739}
X(60236) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 17349}, {9, 8616}, {37, 4685}, {513, 23470}, {1015, 48331}, {1086, 48008}, {6376, 17144}, {40603, 22016}, {40619, 23794}, {50330, 22215}
X(60236) = X(i)-cross conjugate of X(j) for these {i, j}: {3971, 75}, {17234, 2}, {33103, 7}, {33890, 330}, {37355, 264}
X(60236) = pole of line {17234, 60236} with respect to the Kiepert hyperbola
X(60236) = pole of line {4382, 20507} with respect to the Steiner circumellipse
X(60236) = pole of line {17349, 17695} with respect to the Wallace hyperbola
X(60236) = pole of line {192, 39742} with respect to the dual conic of Yff parabola
X(60236) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(17230)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(48908)}}, {{A, B, C, X(6), X(17232)}}, {{A, B, C, X(7), X(334)}}, {{A, B, C, X(8), X(17244)}}, {{A, B, C, X(69), X(17300)}}, {{A, B, C, X(75), X(4699)}}, {{A, B, C, X(80), X(32019)}}, {{A, B, C, X(85), X(330)}}, {{A, B, C, X(86), X(17238)}}, {{A, B, C, X(92), X(39703)}}, {{A, B, C, X(141), X(17379)}}, {{A, B, C, X(145), X(3912)}}, {{A, B, C, X(192), X(20923)}}, {{A, B, C, X(193), X(4869)}}, {{A, B, C, X(257), X(27475)}}, {{A, B, C, X(274), X(27494)}}, {{A, B, C, X(277), X(6650)}}, {{A, B, C, X(279), X(24231)}}, {{A, B, C, X(513), X(3834)}}, {{A, B, C, X(514), X(38247)}}, {{A, B, C, X(596), X(20569)}}, {{A, B, C, X(870), X(56124)}}, {{A, B, C, X(979), X(56170)}}, {{A, B, C, X(1121), X(56353)}}, {{A, B, C, X(1218), X(56125)}}, {{A, B, C, X(1220), X(39729)}}, {{A, B, C, X(1278), X(30044)}}, {{A, B, C, X(1654), X(4648)}}, {{A, B, C, X(2994), X(56184)}}, {{A, B, C, X(2998), X(39735)}}, {{A, B, C, X(3616), X(3661)}}, {{A, B, C, X(3620), X(3945)}}, {{A, B, C, X(3624), X(29593)}}, {{A, B, C, X(3632), X(29572)}}, {{A, B, C, X(3835), X(4871)}}, {{A, B, C, X(3936), X(37684)}}, {{A, B, C, X(3948), X(18135)}}, {{A, B, C, X(3963), X(4754)}}, {{A, B, C, X(4213), X(33822)}}, {{A, B, C, X(4369), X(4892)}}, {{A, B, C, X(4373), X(24199)}}, {{A, B, C, X(4668), X(29599)}}, {{A, B, C, X(4885), X(5087)}}, {{A, B, C, X(5376), X(21398)}}, {{A, B, C, X(5560), X(32012)}}, {{A, B, C, X(6376), X(20943)}}, {{A, B, C, X(8049), X(24190)}}, {{A, B, C, X(9311), X(40026)}}, {{A, B, C, X(14377), X(39720)}}, {{A, B, C, X(14621), X(39730)}}, {{A, B, C, X(14996), X(31017)}}, {{A, B, C, X(17234), X(17349)}}, {{A, B, C, X(17297), X(50133)}}, {{A, B, C, X(17313), X(50074)}}, {{A, B, C, X(17696), X(46557)}}, {{A, B, C, X(17743), X(36807)}}, {{A, B, C, X(18032), X(41527)}}, {{A, B, C, X(18134), X(37683)}}, {{A, B, C, X(18139), X(37652)}}, {{A, B, C, X(18140), X(31060)}}, {{A, B, C, X(18152), X(27269)}}, {{A, B, C, X(18832), X(31002)}}, {{A, B, C, X(19877), X(29576)}}, {{A, B, C, X(20052), X(29600)}}, {{A, B, C, X(20053), X(29582)}}, {{A, B, C, X(20057), X(29577)}}, {{A, B, C, X(20335), X(24720)}}, {{A, B, C, X(20913), X(34284)}}, {{A, B, C, X(23493), X(52660)}}, {{A, B, C, X(24603), X(46932)}}, {{A, B, C, X(27303), X(41876)}}, {{A, B, C, X(27483), X(40023)}}, {{A, B, C, X(29583), X(49763)}}, {{A, B, C, X(30636), X(39734)}}, {{A, B, C, X(30690), X(39694)}}, {{A, B, C, X(30701), X(54120)}}, {{A, B, C, X(30712), X(39712)}}, {{A, B, C, X(31359), X(40029)}}, {{A, B, C, X(31503), X(39957)}}, {{A, B, C, X(32009), X(57725)}}, {{A, B, C, X(32018), X(56051)}}, {{A, B, C, X(35170), X(43731)}}, {{A, B, C, X(36952), X(48934)}}, {{A, B, C, X(39721), X(56054)}}, {{A, B, C, X(39722), X(39749)}}, {{A, B, C, X(39741), X(57947)}}, {{A, B, C, X(42313), X(56382)}}, {{A, B, C, X(55995), X(59268)}}
X(60236) = barycentric product X(i)*X(j) for these (i, j): {39742, 75}, {39966, 76}
X(60236) = barycentric quotient X(i)/X(j) for these (i, j): {1, 8616}, {2, 17349}, {10, 4685}, {75, 17144}, {321, 22016}, {513, 48331}, {514, 48008}, {693, 23794}, {1015, 23470}, {3125, 22215}, {17300, 17695}, {39742, 1}, {39966, 6}, {60244, 27438}

X(60237) = X(4)X(17811)∩X(141)X(459)

Barycentrics    ((a^2-b^2)^3+(-a^4+14*a^2*b^2+3*b^4)*c^2-(a^2+3*b^2)*c^4+c^6)*(a^6+(b^2-c^2)^3-a^4*(b^2+3*c^2)+a^2*(-b^4+14*b^2*c^2+3*c^4)) : :

X(60237) lies on the Kiepert hyperbola and on these lines: {4, 17811}, {30, 54886}, {69, 37874}, {83, 37669}, {141, 459}, {376, 54844}, {443, 60158}, {485, 3539}, {486, 3540}, {631, 60166}, {1073, 10996}, {1131, 6805}, {1132, 6806}, {1370, 60147}, {2052, 32000}, {3090, 60174}, {3424, 7386}, {3525, 60159}, {3537, 6509}, {3619, 60241}, {5067, 60162}, {5084, 60157}, {6803, 31363}, {6819, 60161}, {6820, 8796}, {6997, 43951}, {7391, 60327}, {7392, 14484}, {7394, 54706}, {15702, 54498}, {16063, 60324}, {17559, 60164}, {17582, 60154}, {18841, 23292}, {19708, 54942}, {25934, 60076}, {33190, 54779}, {33230, 54558}, {37659, 60155}, {40149, 52457}, {44442, 54519}, {46336, 47586}, {53415, 56346}, {59767, 60137}

X(60237) = isotomic conjugate of X(18928)
X(60237) = trilinear pole of line {47091, 523}
X(60237) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(1032)}}, {{A, B, C, X(8), X(34546)}}, {{A, B, C, X(63), X(52457)}}, {{A, B, C, X(69), X(1073)}}, {{A, B, C, X(141), X(37669)}}, {{A, B, C, X(189), X(6601)}}, {{A, B, C, X(277), X(55110)}}, {{A, B, C, X(327), X(6340)}}, {{A, B, C, X(377), X(37276)}}, {{A, B, C, X(631), X(6820)}}, {{A, B, C, X(1000), X(56354)}}, {{A, B, C, X(1249), X(47633)}}, {{A, B, C, X(2339), X(34401)}}, {{A, B, C, X(2994), X(15998)}}, {{A, B, C, X(3090), X(6819)}}, {{A, B, C, X(3525), X(37192)}}, {{A, B, C, X(3619), X(23292)}}, {{A, B, C, X(6524), X(21448)}}, {{A, B, C, X(7386), X(52283)}}, {{A, B, C, X(7392), X(52288)}}, {{A, B, C, X(8797), X(37873)}}, {{A, B, C, X(8810), X(51498)}}, {{A, B, C, X(14361), X(36876)}}, {{A, B, C, X(14555), X(25934)}}, {{A, B, C, X(17040), X(40802)}}, {{A, B, C, X(18490), X(56041)}}, {{A, B, C, X(19222), X(55023)}}, {{A, B, C, X(20421), X(56361)}}, {{A, B, C, X(26668), X(33172)}}, {{A, B, C, X(34405), X(57817)}}, {{A, B, C, X(36609), X(42021)}}, {{A, B, C, X(39944), X(42290)}}, {{A, B, C, X(40399), X(44178)}}, {{A, B, C, X(41890), X(56363)}}, {{A, B, C, X(44131), X(57909)}}, {{A, B, C, X(45011), X(56345)}}, {{A, B, C, X(51497), X(57418)}}

X(60238) = X(4)X(10168)∩X(98)X(547)

Barycentrics    (5*(a^2+b^2)+2*c^2)*(5*a^2+2*b^2+5*c^2) : :
X(60238) = -16*X[3860]+7*X[54477]

X(60238) lies on the Kiepert hyperbola and on these lines: {2, 55734}, {3, 55771}, {4, 10168}, {5, 54857}, {6, 60277}, {30, 54890}, {76, 47352}, {83, 48310}, {98, 547}, {99, 60271}, {141, 60279}, {262, 5054}, {316, 60282}, {381, 60326}, {524, 10159}, {597, 10302}, {599, 60131}, {632, 7608}, {671, 3589}, {1153, 60098}, {1916, 41134}, {3407, 8176}, {3530, 60142}, {3545, 60325}, {3618, 60143}, {3860, 54477}, {5055, 60323}, {5066, 54852}, {5070, 7607}, {5079, 53100}, {5395, 7911}, {5466, 7927}, {6656, 60146}, {7375, 60303}, {7376, 60304}, {7760, 60285}, {7770, 60209}, {7790, 41895}, {7803, 60219}, {7808, 60184}, {7812, 18841}, {7827, 43676}, {7841, 53107}, {7846, 60234}, {7854, 55740}, {7859, 53109}, {7883, 43527}, {7919, 54901}, {7937, 60287}, {8182, 60190}, {8352, 54646}, {8370, 53106}, {8703, 14492}, {9166, 11606}, {11165, 60180}, {11303, 43551}, {11304, 43550}, {11317, 54493}, {11540, 60192}, {12150, 60129}, {14030, 54540}, {14047, 43528}, {14061, 14762}, {14067, 43529}, {14458, 19709}, {14484, 15692}, {14488, 15681}, {15710, 52519}, {15719, 60127}, {16509, 60181}, {18840, 59373}, {18844, 33190}, {21356, 60183}, {21358, 60278}, {21734, 60328}, {26613, 54905}, {32027, 56059}, {32837, 60201}, {32839, 60262}, {32885, 60259}, {33291, 54539}, {38071, 60132}, {41984, 53108}, {43537, 46936}, {47355, 60239}, {50571, 60095}, {52298, 60124}, {53099, 55864}, {54773, 55164}, {55801, 60177}

X(60238) = isotomic conjugate of X(20582)
X(60238) = trilinear pole of line {37901, 44367}
X(60238) = X(i)-cross conjugate of X(j) for these {i, j}: {12073, 99}
X(60238) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55687)}}, {{A, B, C, X(6), X(47352)}}, {{A, B, C, X(141), X(48310)}}, {{A, B, C, X(287), X(10168)}}, {{A, B, C, X(290), X(57895)}}, {{A, B, C, X(297), X(547)}}, {{A, B, C, X(458), X(5054)}}, {{A, B, C, X(524), X(3589)}}, {{A, B, C, X(597), X(34898)}}, {{A, B, C, X(632), X(52281)}}, {{A, B, C, X(694), X(46123)}}, {{A, B, C, X(981), X(39960)}}, {{A, B, C, X(1016), X(13602)}}, {{A, B, C, X(1509), X(34892)}}, {{A, B, C, X(3055), X(41139)}}, {{A, B, C, X(3978), X(44562)}}, {{A, B, C, X(5070), X(52282)}}, {{A, B, C, X(5641), X(40410)}}, {{A, B, C, X(6094), X(44571)}}, {{A, B, C, X(6531), X(30537)}}, {{A, B, C, X(7841), X(52298)}}, {{A, B, C, X(7883), X(39668)}}, {{A, B, C, X(8370), X(52297)}}, {{A, B, C, X(8703), X(52289)}}, {{A, B, C, X(9487), X(42349)}}, {{A, B, C, X(11331), X(19709)}}, {{A, B, C, X(15491), X(15597)}}, {{A, B, C, X(15692), X(52288)}}, {{A, B, C, X(20251), X(44731)}}, {{A, B, C, X(21358), X(47355)}}, {{A, B, C, X(35140), X(55958)}}, {{A, B, C, X(35146), X(39968)}}, {{A, B, C, X(40425), X(57539)}}, {{A, B, C, X(42346), X(55075)}}
X(60238) = barycentric product X(i)*X(j) for these (i, j): {58120, 850}
X(60238) = barycentric quotient X(i)/X(j) for these (i, j): {2, 20582}, {58120, 110}

X(60239) = X(2)X(5008)∩X(76)X(597)

Barycentrics    (4*(a^2+b^2)+c^2)*(4*a^2+b^2+4*c^2) : :
X(60239) = -12*X[23046]+5*X[60326]

X(60239) lies on the Kiepert hyperbola and on these lines: {2, 5008}, {3, 55778}, {4, 20190}, {5, 53100}, {6, 10302}, {30, 14488}, {76, 597}, {98, 5055}, {99, 51588}, {140, 60332}, {141, 60131}, {262, 549}, {316, 18842}, {376, 52519}, {381, 60132}, {524, 60277}, {547, 60335}, {548, 60329}, {598, 3589}, {599, 7878}, {631, 60330}, {671, 5026}, {1656, 60334}, {1916, 2482}, {1992, 18840}, {2996, 7827}, {3090, 60337}, {3407, 14046}, {3526, 7608}, {3534, 14492}, {3545, 54845}, {3618, 5485}, {3628, 7607}, {3830, 54717}, {3972, 54487}, {5054, 54920}, {5066, 14458}, {5071, 60322}, {5072, 54857}, {5395, 7859}, {5461, 7875}, {5466, 11183}, {5503, 11174}, {6656, 53102}, {7388, 43570}, {7389, 43571}, {7486, 43537}, {7757, 43688}, {7769, 60262}, {7770, 43676}, {7771, 54509}, {7786, 11149}, {7790, 17503}, {7792, 11167}, {7799, 60201}, {7803, 38259}, {7804, 54737}, {7808, 60128}, {7812, 43527}, {7841, 53109}, {7883, 60100}, {7884, 11606}, {7894, 60210}, {7918, 53107}, {7937, 48310}, {8352, 54494}, {8370, 53105}, {8591, 60271}, {8781, 42849}, {8860, 60187}, {9166, 14535}, {10185, 55860}, {10303, 53099}, {10304, 14484}, {10359, 25561}, {10488, 42534}, {11054, 60200}, {11057, 54773}, {11163, 60213}, {11185, 54637}, {11303, 43547}, {11304, 43546}, {11317, 33698}, {11540, 54645}, {11669, 47598}, {13663, 60196}, {13783, 60194}, {14043, 43529}, {14065, 43528}, {14494, 15709}, {15022, 47586}, {15640, 54520}, {15683, 43951}, {15684, 54890}, {15698, 60127}, {15717, 60118}, {15759, 54643}, {17381, 55949}, {18843, 33190}, {19709, 54934}, {20582, 60278}, {21358, 60279}, {22247, 42010}, {22329, 60099}, {23046, 60326}, {26613, 60268}, {33699, 54582}, {37649, 54774}, {40112, 59763}, {44401, 60248}, {44543, 60280}, {47355, 60238}, {50693, 60328}, {51123, 60180}, {51224, 60190}, {53489, 60283}, {55859, 60144}, {59373, 60143}

X(60239) = inverse of X(51588) in Wallace hyperbola
X(60239) = isotomic conjugate of X(21358)
X(60239) = trilinear pole of line {47313, 523}
X(60239) = X(i)-cross conjugate of X(j) for these {i, j}: {7937, 76}, {48310, 2}
X(60239) = pole of line {7937, 48310} with respect to the Kiepert hyperbola
X(60239) = pole of line {21358, 51588} with respect to the Wallace hyperbola
X(60239) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(20190)}}, {{A, B, C, X(6), X(597)}}, {{A, B, C, X(230), X(42849)}}, {{A, B, C, X(264), X(7850)}}, {{A, B, C, X(287), X(38064)}}, {{A, B, C, X(297), X(5055)}}, {{A, B, C, X(419), X(14036)}}, {{A, B, C, X(458), X(549)}}, {{A, B, C, X(524), X(47352)}}, {{A, B, C, X(599), X(3589)}}, {{A, B, C, X(729), X(11175)}}, {{A, B, C, X(981), X(39982)}}, {{A, B, C, X(1016), X(39716)}}, {{A, B, C, X(1992), X(3618)}}, {{A, B, C, X(2482), X(5026)}}, {{A, B, C, X(3224), X(55075)}}, {{A, B, C, X(3526), X(52281)}}, {{A, B, C, X(3534), X(52289)}}, {{A, B, C, X(3628), X(52282)}}, {{A, B, C, X(3978), X(57540)}}, {{A, B, C, X(5066), X(11331)}}, {{A, B, C, X(5117), X(14046)}}, {{A, B, C, X(7757), X(41259)}}, {{A, B, C, X(7792), X(11163)}}, {{A, B, C, X(7812), X(39668)}}, {{A, B, C, X(7827), X(57518)}}, {{A, B, C, X(7840), X(7875)}}, {{A, B, C, X(7848), X(13377)}}, {{A, B, C, X(7878), X(52570)}}, {{A, B, C, X(8370), X(37453)}}, {{A, B, C, X(8753), X(39389)}}, {{A, B, C, X(9164), X(35146)}}, {{A, B, C, X(9169), X(41939)}}, {{A, B, C, X(10304), X(52288)}}, {{A, B, C, X(11166), X(57729)}}, {{A, B, C, X(11174), X(22329)}}, {{A, B, C, X(13606), X(17743)}}, {{A, B, C, X(13623), X(34897)}}, {{A, B, C, X(14621), X(34892)}}, {{A, B, C, X(17381), X(31144)}}, {{A, B, C, X(20582), X(47355)}}, {{A, B, C, X(21358), X(48310)}}, {{A, B, C, X(30535), X(57714)}}, {{A, B, C, X(31489), X(44401)}}, {{A, B, C, X(36948), X(54171)}}, {{A, B, C, X(40112), X(40384)}}, {{A, B, C, X(40425), X(56067)}}, {{A, B, C, X(42313), X(53024)}}, {{A, B, C, X(43950), X(52660)}}, {{A, B, C, X(44557), X(54413)}}, {{A, B, C, X(54124), X(55958)}}
X(60239) = barycentric quotient X(i)/X(j) for these (i, j): {2, 21358}, {59373, 51588}
X(60239) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5008, 55730}

X(60240) = X(4)X(11184)∩X(671)X(1007)

Barycentrics    (5*a^4-14*a^2*b^2+5*b^4-8*(a^2+b^2)*c^2+11*c^4)*(5*a^4+11*b^4-8*b^2*c^2+5*c^4-2*a^2*(4*b^2+7*c^2)) : :
X(60240) = 2*X[11165]+X[41895]

X(60240) lies on the Kiepert hyperbola and on these lines: {4, 11184}, {30, 54894}, {69, 60220}, {98, 9770}, {114, 54475}, {325, 11172}, {524, 7612}, {543, 60189}, {598, 11147}, {671, 1007}, {1992, 60103}, {2996, 32984}, {3566, 43674}, {3815, 18842}, {3849, 60117}, {5395, 32985}, {5466, 30775}, {5485, 22110}, {7610, 53103}, {7735, 10153}, {7774, 8587}, {7778, 60143}, {8176, 54713}, {9740, 50985}, {9766, 60185}, {9771, 14494}, {10159, 32958}, {11165, 41895}, {12040, 53101}, {13681, 45107}, {13801, 45106}, {14484, 50963}, {15597, 60123}, {15702, 60148}, {16925, 60145}, {18845, 33007}, {19708, 54805}, {21356, 60101}, {32959, 43527}, {32961, 43681}, {32969, 60285}, {33006, 38259}, {34803, 60211}, {40727, 60200}, {40824, 41133}, {42849, 54616}, {43667, 55122}, {52942, 54476}, {59373, 60093}

X(60240) = isotomic conjugate of X(23055)
X(60240) = trilinear pole of line {47551, 523}
X(60240) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(69), X(11184)}}, {{A, B, C, X(141), X(52717)}}, {{A, B, C, X(325), X(9770)}}, {{A, B, C, X(428), X(32958)}}, {{A, B, C, X(523), X(1992)}}, {{A, B, C, X(524), X(1007)}}, {{A, B, C, X(599), X(44658)}}, {{A, B, C, X(3566), X(52229)}}, {{A, B, C, X(3815), X(21356)}}, {{A, B, C, X(4235), X(30775)}}, {{A, B, C, X(5064), X(32959)}}, {{A, B, C, X(6353), X(32984)}}, {{A, B, C, X(7610), X(34803)}}, {{A, B, C, X(7714), X(32969)}}, {{A, B, C, X(7735), X(41133)}}, {{A, B, C, X(8889), X(32985)}}, {{A, B, C, X(9771), X(34229)}}, {{A, B, C, X(11147), X(11165)}}, {{A, B, C, X(30786), X(53142)}}, {{A, B, C, X(33006), X(38282)}}, {{A, B, C, X(33007), X(52299)}}

X(60241) = X(2)X(41891)∩X(4)X(14860)

Barycentrics    ((a^2-b^2)^2*(a^2+b^2)-3*(a^2+b^2)*c^4+2*c^6)*(a^6+2*b^6-a^4*c^2-3*b^4*c^2+c^6-a^2*(3*b^4+c^4)) : :

X(60241) lies on the Kiepert hyperbola and on these lines: {2, 41891}, {3, 46729}, {4, 14860}, {30, 54895}, {69, 56346}, {83, 13567}, {98, 6676}, {141, 801}, {275, 343}, {297, 54703}, {394, 43530}, {459, 17907}, {2052, 37638}, {2986, 37636}, {3424, 10565}, {3580, 40393}, {3619, 60237}, {3620, 41899}, {3763, 59764}, {7569, 57718}, {8796, 14129}, {9290, 59197}, {9381, 57811}, {9715, 46727}, {9909, 14458}, {15466, 43678}, {17825, 43527}, {18134, 56216}, {18841, 18928}, {25000, 57721}, {26540, 60082}, {26958, 37874}, {37669, 60137}, {44569, 54926}, {44877, 53415}, {53481, 54911}, {54994, 60122}

X(60241) = isotomic conjugate of X(23292)
X(60241) = trilinear pole of line {3153, 44363}
X(60241) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 13367}, {31, 23292}, {32, 17859}, {48, 3575}, {560, 26166}, {1964, 10548}, {1973, 41008}, {2148, 3574}
X(60241) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 23292}, {6, 13367}, {216, 3574}, {1249, 3575}, {6337, 41008}, {6374, 26166}, {6376, 17859}, {41884, 10548}
X(60241) = X(i)-cross conjugate of X(j) for these {i, j}: {6368, 99}, {13160, 264}, {13568, 253}, {41891, 14860}
X(60241) = pole of line {23292, 41008} with respect to the Wallace hyperbola
X(60241) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(46730)}}, {{A, B, C, X(69), X(41530)}}, {{A, B, C, X(95), X(55553)}}, {{A, B, C, X(97), X(56069)}}, {{A, B, C, X(141), X(13567)}}, {{A, B, C, X(249), X(31626)}}, {{A, B, C, X(287), X(21243)}}, {{A, B, C, X(297), X(6676)}}, {{A, B, C, X(308), X(6330)}}, {{A, B, C, X(324), X(20573)}}, {{A, B, C, X(327), X(40413)}}, {{A, B, C, X(343), X(45793)}}, {{A, B, C, X(394), X(30541)}}, {{A, B, C, X(1275), X(52381)}}, {{A, B, C, X(1502), X(42330)}}, {{A, B, C, X(1799), X(18022)}}, {{A, B, C, X(3523), X(32831)}}, {{A, B, C, X(3580), X(37636)}}, {{A, B, C, X(3619), X(18928)}}, {{A, B, C, X(3763), X(17825)}}, {{A, B, C, X(6394), X(57855)}}, {{A, B, C, X(7058), X(52351)}}, {{A, B, C, X(7569), X(52253)}}, {{A, B, C, X(7769), X(14129)}}, {{A, B, C, X(9909), X(11331)}}, {{A, B, C, X(10565), X(52283)}}, {{A, B, C, X(15466), X(17907)}}, {{A, B, C, X(17811), X(26958)}}, {{A, B, C, X(18139), X(25000)}}, {{A, B, C, X(26540), X(32782)}}, {{A, B, C, X(27364), X(27377)}}, {{A, B, C, X(30710), X(52780)}}, {{A, B, C, X(30786), X(34384)}}, {{A, B, C, X(34386), X(52350)}}, {{A, B, C, X(34412), X(55972)}}, {{A, B, C, X(39287), X(46111)}}, {{A, B, C, X(40405), X(42313)}}, {{A, B, C, X(40410), X(42333)}}, {{A, B, C, X(40414), X(57905)}}, {{A, B, C, X(47296), X(53415)}}
X(60241) = barycentric product X(i)*X(j) for these (i, j): {14860, 69}, {41891, 76}
X(60241) = barycentric quotient X(i)/X(j) for these (i, j): {2, 23292}, {3, 13367}, {4, 3575}, {5, 3574}, {69, 41008}, {75, 17859}, {76, 26166}, {83, 10548}, {5562, 31388}, {7488, 32391}, {14860, 4}, {41891, 6}, {58922, 31976}

X(60242) = X(2)X(55939)∩X(4)X(3936)

Barycentrics    ((a-b)^2*(a+b)-(a^2+b^2)*c+(a+b)*c^2+3*c^3)*(a^3-a^2*(b+c)+a*(b-c)*(b+c)+(b+c)*(3*b^2-2*b*c+c^2)) : :

X(60242) lies on the Kiepert hyperbola and on these lines: {2, 55939}, {4, 3936}, {10, 56136}, {69, 24624}, {226, 2325}, {312, 43675}, {321, 17895}, {346, 4080}, {376, 54564}, {908, 36907}, {1150, 55962}, {1446, 4358}, {1751, 5739}, {3239, 4049}, {3454, 60079}, {4217, 60078}, {4417, 60155}, {5712, 60082}, {5741, 60107}, {11319, 60077}, {14208, 60074}, {14555, 57721}, {17234, 60169}, {17526, 43531}, {17537, 54623}, {18134, 60156}, {18139, 60076}, {18842, 31179}, {24580, 60134}, {30566, 30809}, {30588, 54389}, {30828, 60071}, {30831, 60254}, {31120, 60190}, {32782, 60206}, {39994, 53665}, {50753, 54668}, {51673, 54624}, {57807, 60091}

X(60242) = isotomic conjugate of X(24597)
X(60242) = trilinear pole of line {4528, 50772}
X(60242) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 37817}, {31, 24597}
X(60242) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 24597}, {9, 37817}
X(60242) = pole of line {30811, 60242} with respect to the Kiepert hyperbola
X(60242) = pole of line {17740, 56136} with respect to the dual conic of Yff parabola
X(60242) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(34), X(88)}}, {{A, B, C, X(69), X(3936)}}, {{A, B, C, X(92), X(1222)}}, {{A, B, C, X(278), X(39700)}}, {{A, B, C, X(312), X(17776)}}, {{A, B, C, X(313), X(57818)}}, {{A, B, C, X(318), X(4997)}}, {{A, B, C, X(346), X(2325)}}, {{A, B, C, X(393), X(56123)}}, {{A, B, C, X(469), X(17526)}}, {{A, B, C, X(561), X(13577)}}, {{A, B, C, X(908), X(28739)}}, {{A, B, C, X(1150), X(30828)}}, {{A, B, C, X(1441), X(57825)}}, {{A, B, C, X(2184), X(40406)}}, {{A, B, C, X(2349), X(40436)}}, {{A, B, C, X(4373), X(17895)}}, {{A, B, C, X(4945), X(54389)}}, {{A, B, C, X(5712), X(32782)}}, {{A, B, C, X(5739), X(18134)}}, {{A, B, C, X(5741), X(18141)}}, {{A, B, C, X(6336), X(34860)}}, {{A, B, C, X(6557), X(36624)}}, {{A, B, C, X(6605), X(56207)}}, {{A, B, C, X(8817), X(30636)}}, {{A, B, C, X(14555), X(18139)}}, {{A, B, C, X(14954), X(30809)}}, {{A, B, C, X(16990), X(31120)}}, {{A, B, C, X(18359), X(30701)}}, {{A, B, C, X(21356), X(31179)}}, {{A, B, C, X(24597), X(30811)}}, {{A, B, C, X(27475), X(37842)}}, {{A, B, C, X(29616), X(50753)}}, {{A, B, C, X(30575), X(39956)}}, {{A, B, C, X(30608), X(40029)}}, {{A, B, C, X(30831), X(37642)}}, {{A, B, C, X(31017), X(31034)}}, {{A, B, C, X(31053), X(56366)}}, {{A, B, C, X(32017), X(40447)}}, {{A, B, C, X(34234), X(40014)}}, {{A, B, C, X(37680), X(53665)}}, {{A, B, C, X(39749), X(50442)}}, {{A, B, C, X(52575), X(57874)}}, {{A, B, C, X(55939), X(56136)}}
X(60242) = barycentric product X(i)*X(j) for these (i, j): {321, 55939}, {56136, 75}
X(60242) = barycentric quotient X(i)/X(j) for these (i, j): {1, 37817}, {2, 24597}, {55939, 81}, {56136, 1}

X(60243) = X(2)X(1449)∩X(4)X(165)

Barycentrics    (b+c)*(3*(a+b)+c)*(3*a+b+3*c) : :

X(60243) lies on the Kiepert hyperbola and on these lines: {2, 1449}, {4, 165}, {9, 60170}, {10, 4046}, {37, 60267}, {57, 57826}, {76, 19804}, {98, 28148}, {142, 57722}, {226, 1213}, {306, 60203}, {321, 5257}, {333, 32014}, {459, 56300}, {671, 19808}, {1029, 54357}, {1211, 56226}, {1268, 56078}, {1751, 19744}, {2051, 5316}, {2321, 6539}, {3452, 60071}, {3634, 19732}, {3666, 52708}, {3828, 32777}, {3911, 60076}, {3925, 54668}, {3982, 4748}, {4049, 48402}, {4052, 31993}, {4138, 53039}, {4357, 60257}, {4413, 37078}, {4444, 10196}, {4656, 52706}, {4848, 60321}, {5325, 7110}, {5745, 60156}, {6666, 60155}, {6692, 60169}, {7308, 45100}, {9780, 43533}, {13576, 59306}, {16832, 18840}, {17022, 58859}, {17289, 54686}, {17303, 54928}, {17308, 32022}, {18743, 34258}, {19827, 54549}, {19854, 60154}, {19855, 60158}, {19875, 54786}, {19876, 54624}, {19877, 60077}, {29576, 56210}, {29604, 60075}, {29610, 60149}, {30588, 41809}, {30768, 60080}, {31183, 60183}, {43534, 53663}, {50290, 59261}, {56161, 59312}, {59491, 60258}

X(60243) = isotomic conjugate of X(25507)
X(60243) = complement of X(41930)
X(60243) = trilinear pole of line {4822, 523}
X(60243) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 25507}, {58, 3247}, {110, 48026}, {163, 28147}, {284, 3339}, {662, 50509}, {1333, 9780}, {1474, 3951}, {2150, 3947}, {2206, 42029}
X(60243) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 25507}, {10, 3247}, {37, 9780}, {115, 28147}, {244, 48026}, {1084, 50509}, {40590, 3339}, {40603, 42029}, {51574, 3951}, {56325, 3947}
X(60243) = pole of line {28147, 50449} with respect to the Steiner inellipse
X(60243) = pole of line {3624, 39708} with respect to the dual conic of Yff parabola
X(60243) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(9), X(53013)}}, {{A, B, C, X(27), X(17514)}}, {{A, B, C, X(37), X(57)}}, {{A, B, C, X(42), X(24603)}}, {{A, B, C, X(65), X(25430)}}, {{A, B, C, X(81), X(56221)}}, {{A, B, C, X(165), X(1214)}}, {{A, B, C, X(210), X(19605)}}, {{A, B, C, X(306), X(1698)}}, {{A, B, C, X(307), X(40161)}}, {{A, B, C, X(313), X(56061)}}, {{A, B, C, X(333), X(1213)}}, {{A, B, C, X(525), X(28150)}}, {{A, B, C, X(756), X(56158)}}, {{A, B, C, X(1125), X(56047)}}, {{A, B, C, X(1224), X(39130)}}, {{A, B, C, X(1255), X(53114)}}, {{A, B, C, X(1268), X(3879)}}, {{A, B, C, X(1427), X(39963)}}, {{A, B, C, X(1441), X(32099)}}, {{A, B, C, X(2357), X(38825)}}, {{A, B, C, X(3634), X(56810)}}, {{A, B, C, X(3668), X(5936)}}, {{A, B, C, X(3701), X(56201)}}, {{A, B, C, X(3842), X(50290)}}, {{A, B, C, X(3911), X(3992)}}, {{A, B, C, X(3948), X(47996)}}, {{A, B, C, X(3958), X(4877)}}, {{A, B, C, X(4029), X(52706)}}, {{A, B, C, X(4035), X(6358)}}, {{A, B, C, X(4078), X(50298)}}, {{A, B, C, X(4103), X(37209)}}, {{A, B, C, X(4125), X(5235)}}, {{A, B, C, X(4457), X(56122)}}, {{A, B, C, X(4848), X(18743)}}, {{A, B, C, X(5224), X(19732)}}, {{A, B, C, X(5271), X(19857)}}, {{A, B, C, X(5316), X(52358)}}, {{A, B, C, X(5325), X(42033)}}, {{A, B, C, X(6703), X(41817)}}, {{A, B, C, X(8056), X(56219)}}, {{A, B, C, X(10180), X(27483)}}, {{A, B, C, X(15320), X(42335)}}, {{A, B, C, X(16609), X(53663)}}, {{A, B, C, X(17270), X(28650)}}, {{A, B, C, X(18134), X(19744)}}, {{A, B, C, X(19808), X(42713)}}, {{A, B, C, X(27475), X(46772)}}, {{A, B, C, X(29576), X(43223)}}, {{A, B, C, X(29610), X(29653)}}, {{A, B, C, X(31623), X(55091)}}, {{A, B, C, X(31730), X(56944)}}, {{A, B, C, X(36603), X(56215)}}, {{A, B, C, X(36915), X(40663)}}, {{A, B, C, X(37666), X(46208)}}, {{A, B, C, X(39708), X(41930)}}, {{A, B, C, X(39716), X(56123)}}, {{A, B, C, X(39721), X(56222)}}, {{A, B, C, X(39962), X(56213)}}, {{A, B, C, X(44572), X(52393)}}, {{A, B, C, X(48634), X(48652)}}, {{A, B, C, X(55078), X(56228)}}
X(60243) = barycentric product X(i)*X(j) for these (i, j): {10, 28626}, {226, 30711}, {321, 39948}, {523, 58135}, {28148, 850}
X(60243) = barycentric quotient X(i)/X(j) for these (i, j): {2, 25507}, {10, 9780}, {12, 3947}, {37, 3247}, {65, 3339}, {72, 3951}, {321, 42029}, {512, 50509}, {523, 28147}, {661, 48026}, {28148, 110}, {28626, 86}, {30711, 333}, {39948, 81}, {58135, 99}
X(60243) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 30711, 28626}, {28626, 30711, 39948}

X(60244) = X(2)X(330)∩X(4)X(4645)

Barycentrics    b*c*(b+c)*(a*(b-c)+b*c)*(-a*b+(a+b)*c) : :

X(60244) lies on the Kiepert hyperbola and on these lines: {1, 60109}, {2, 330}, {4, 4645}, {8, 56161}, {10, 3728}, {37, 56250}, {75, 56210}, {76, 3662}, {83, 21759}, {87, 43531}, {98, 932}, {142, 30045}, {226, 3948}, {257, 1920}, {306, 37865}, {312, 60261}, {313, 21025}, {321, 1237}, {334, 1916}, {561, 40162}, {668, 16827}, {671, 18830}, {1089, 34475}, {1240, 27447}, {1258, 17752}, {1441, 60245}, {1751, 2319}, {2051, 3912}, {2053, 60080}, {2162, 19734}, {2228, 25141}, {3125, 21435}, {3407, 40746}, {3661, 34258}, {3701, 43534}, {3831, 60090}, {3834, 18144}, {3959, 4485}, {4033, 21868}, {4044, 4052}, {4358, 18055}, {4391, 4444}, {4598, 24624}, {4721, 29425}, {6378, 16589}, {6381, 17758}, {7153, 60085}, {7209, 57826}, {7275, 31339}, {13478, 24630}, {13576, 17751}, {17033, 56167}, {17786, 21857}, {18040, 25102}, {18050, 21331}, {19810, 54119}, {20255, 20892}, {20440, 28659}, {20606, 21371}, {20691, 56185}, {20706, 21071}, {20888, 60276}, {20899, 35538}, {20913, 60084}, {21057, 60177}, {21257, 22190}, {21904, 24524}, {21951, 35544}, {22036, 27808}, {23493, 40718}, {25614, 56249}, {27436, 29967}, {27569, 43677}, {27641, 32033}, {28660, 40017}, {29960, 30026}, {29974, 46827}, {30001, 30011}, {30022, 40031}, {31008, 56066}, {31060, 60257}, {33930, 43688}, {34071, 60134}, {35353, 58361}, {36907, 44150}, {40603, 60203}, {40936, 46897}, {45782, 60110}, {46902, 56186}, {52353, 58367}, {53677, 58019}, {54933, 58366}

X(60244) = isotomic conjugate of X(27644)
X(60244) = complement of X(36857)
X(60244) = trilinear pole of line {20910, 523}
X(60244) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 38832}, {21, 41526}, {31, 27644}, {32, 33296}, {43, 1333}, {58, 2176}, {81, 2209}, {100, 57074}, {101, 16695}, {110, 20979}, {112, 22090}, {163, 4083}, {192, 2206}, {284, 1403}, {560, 31008}, {604, 56181}, {662, 8640}, {692, 18197}, {849, 20691}, {1110, 16742}, {1178, 51319}, {1408, 3208}, {1423, 2194}, {1474, 20760}, {1576, 3835}, {1918, 7304}, {1980, 36860}, {2203, 22370}, {3212, 57657}, {4556, 50491}, {4567, 38986}, {4570, 6377}, {4600, 21762}, {5009, 51973}, {8750, 23092}, {16947, 27538}, {17217, 32739}, {17921, 32656}, {20284, 38813}, {21835, 24041}, {23824, 23990}, {25098, 32676}, {52923, 57129}
X(60244) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 27644}, {9, 38832}, {10, 2176}, {37, 43}, {115, 4083}, {244, 20979}, {514, 16742}, {1015, 16695}, {1084, 8640}, {1086, 18197}, {1214, 1423}, {3005, 21835}, {3161, 56181}, {4075, 20691}, {4858, 3835}, {4988, 3123}, {6374, 31008}, {6376, 33296}, {8054, 57074}, {15526, 25098}, {16584, 41886}, {16587, 51902}, {16606, 1740}, {26932, 23092}, {34021, 7304}, {34591, 22090}, {36901, 20906}, {40586, 2209}, {40590, 1403}, {40603, 192}, {40611, 41526}, {40619, 17217}, {40622, 43051}, {40624, 27527}, {40627, 38986}, {50330, 6377}, {50497, 21762}, {51574, 20760}, {52872, 52964}, {55065, 21834}, {59577, 3208}
X(60244) = X(i)-Ceva conjugate of X(j) for these {i, j}: {6384, 42027}, {42027, 321}
X(60244) = X(i)-cross conjugate of X(j) for these {i, j}: {313, 321}, {2887, 1441}, {3122, 693}, {21025, 10}, {22171, 37}, {23439, 6}, {59521, 27808}
X(60244) = pole of line {313, 21025} with respect to the Kiepert hyperbola
X(60244) = pole of line {4083, 21438} with respect to the Steiner circumellipse
X(60244) = pole of line {661, 17893} with respect to the dual conic of circumcircle
X(60244) = pole of line {23092, 25098} with respect to the dual conic of polar circle
X(60244) = pole of line {693, 21960} with respect to the dual conic of DeLongchamps ellipse
X(60244) = pole of line {3840, 20891} with respect to the dual conic of Yff parabola
X(60244) = pole of line {3123, 6377} with respect to the dual conic of Wallace hyperbola
X(60244) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(37), X(257)}}, {{A, B, C, X(65), X(335)}}, {{A, B, C, X(75), X(31997)}}, {{A, B, C, X(313), X(6376)}}, {{A, B, C, X(330), X(6383)}}, {{A, B, C, X(334), X(1237)}}, {{A, B, C, X(349), X(20917)}}, {{A, B, C, X(514), X(42471)}}, {{A, B, C, X(525), X(15310)}}, {{A, B, C, X(561), X(9239)}}, {{A, B, C, X(693), X(35532)}}, {{A, B, C, X(1089), X(59212)}}, {{A, B, C, X(1231), X(4645)}}, {{A, B, C, X(1400), X(2275)}}, {{A, B, C, X(1577), X(27801)}}, {{A, B, C, X(3661), X(59305)}}, {{A, B, C, X(3701), X(3948)}}, {{A, B, C, X(3765), X(4710)}}, {{A, B, C, X(3912), X(17751)}}, {{A, B, C, X(3954), X(23660)}}, {{A, B, C, X(4043), X(29982)}}, {{A, B, C, X(4044), X(52353)}}, {{A, B, C, X(4651), X(29968)}}, {{A, B, C, X(4674), X(39970)}}, {{A, B, C, X(7148), X(16606)}}, {{A, B, C, X(9311), X(41683)}}, {{A, B, C, X(9505), X(17924)}}, {{A, B, C, X(10405), X(56258)}}, {{A, B, C, X(14624), X(56044)}}, {{A, B, C, X(15232), X(17743)}}, {{A, B, C, X(15523), X(41240)}}, {{A, B, C, X(16604), X(40085)}}, {{A, B, C, X(18148), X(40010)}}, {{A, B, C, X(18152), X(29983)}}, {{A, B, C, X(19734), X(32782)}}, {{A, B, C, X(20568), X(56186)}}, {{A, B, C, X(20691), X(21025)}}, {{A, B, C, X(20892), X(56185)}}, {{A, B, C, X(20923), X(22016)}}, {{A, B, C, X(21240), X(23632)}}, {{A, B, C, X(23493), X(51837)}}, {{A, B, C, X(27447), X(27455)}}, {{A, B, C, X(29674), X(41233)}}, {{A, B, C, X(30022), X(31060)}}, {{A, B, C, X(30701), X(38955)}}, {{A, B, C, X(33935), X(43997)}}, {{A, B, C, X(39749), X(56173)}}, {{A, B, C, X(40029), X(56127)}}, {{A, B, C, X(56122), X(56237)}}
X(60244) = barycentric product X(i)*X(j) for these (i, j): {10, 6384}, {37, 6383}, {226, 27424}, {310, 7148}, {313, 87}, {321, 330}, {850, 932}, {1240, 45197}, {1441, 7155}, {1502, 21759}, {1577, 4598}, {2162, 27801}, {2319, 349}, {2321, 7209}, {3971, 53679}, {4036, 56053}, {6378, 6385}, {16606, 76}, {16732, 5383}, {18022, 22381}, {18830, 523}, {20948, 34071}, {23493, 561}, {27432, 40012}, {27438, 60236}, {27447, 3963}, {27455, 60264}, {27496, 4052}, {27808, 43931}, {30713, 7153}, {42027, 75}
X(60244) = barycentric quotient X(i)/X(j) for these (i, j): {1, 38832}, {2, 27644}, {8, 56181}, {10, 43}, {37, 2176}, {42, 2209}, {65, 1403}, {72, 20760}, {75, 33296}, {76, 31008}, {87, 58}, {226, 1423}, {274, 7304}, {306, 22370}, {313, 6376}, {321, 192}, {330, 81}, {349, 30545}, {512, 8640}, {513, 16695}, {514, 18197}, {523, 4083}, {525, 25098}, {594, 20691}, {649, 57074}, {656, 22090}, {661, 20979}, {693, 17217}, {850, 20906}, {905, 23092}, {932, 110}, {1086, 16742}, {1089, 3971}, {1111, 23824}, {1215, 51902}, {1237, 41318}, {1400, 41526}, {1441, 3212}, {1577, 3835}, {1978, 36860}, {2053, 2194}, {2162, 1333}, {2295, 51319}, {2319, 284}, {2321, 3208}, {2533, 24533}, {2887, 41886}, {3120, 3123}, {3121, 21762}, {3122, 38986}, {3124, 21835}, {3125, 6377}, {3701, 27538}, {3721, 20284}, {3728, 45216}, {3778, 56806}, {3943, 52964}, {3952, 52923}, {3963, 17752}, {3971, 53676}, {4024, 21834}, {4033, 4595}, {4036, 21051}, {4086, 4147}, {4120, 14408}, {4391, 27527}, {4598, 662}, {4647, 4970}, {4705, 50491}, {5383, 4567}, {6378, 213}, {6383, 274}, {6384, 86}, {7121, 2206}, {7148, 42}, {7153, 1412}, {7155, 21}, {7178, 43051}, {7209, 1434}, {14431, 14426}, {16606, 6}, {16732, 21138}, {17924, 17921}, {18070, 18107}, {18830, 99}, {20234, 33890}, {20691, 53145}, {20727, 20783}, {20892, 16722}, {21051, 25142}, {21052, 24749}, {21257, 14823}, {21759, 32}, {21834, 57050}, {22381, 184}, {23086, 1437}, {23493, 31}, {27424, 333}, {27432, 4383}, {27438, 17349}, {27447, 40432}, {27455, 40153}, {27496, 41629}, {27801, 6382}, {27808, 36863}, {30591, 4992}, {30713, 4110}, {34071, 163}, {34252, 5009}, {34475, 40780}, {40753, 34476}, {42027, 1}, {43534, 41531}, {43931, 3733}, {45197, 1193}, {45218, 2300}, {45782, 3736}, {48643, 4941}, {51837, 40773}, {56053, 52935}, {57264, 57657}
X(60244) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 42027, 7148}, {1237, 3721, 321}, {3125, 27801, 21435}, {6381, 29968, 29983}, {6384, 27424, 330}, {27424, 27432, 27438}, {29968, 29983, 29982}

X(60245) = X(1)X(98)∩X(2)X(257)

Barycentrics    (a+b-c)*(a-b+c)*(b+c)*(b^2+a*c)*(a*b+c^2) : :

X(60245) lies on the Kiepert hyperbola and on these lines: {1, 98}, {2, 257}, {4, 240}, {7, 6625}, {8, 52135}, {10, 7235}, {12, 21941}, {57, 14534}, {65, 40718}, {76, 20236}, {83, 3405}, {85, 40017}, {226, 3721}, {262, 3865}, {321, 4136}, {694, 20271}, {893, 1751}, {904, 3924}, {980, 13478}, {1237, 6358}, {1254, 4032}, {1431, 5883}, {1441, 60244}, {1446, 16888}, {1577, 43665}, {1581, 56171}, {1916, 7179}, {1934, 6376}, {1969, 60199}, {2171, 60230}, {2344, 3407}, {2996, 49518}, {3125, 43686}, {3210, 54119}, {3509, 27994}, {3665, 4444}, {3903, 14923}, {3959, 59480}, {4384, 60235}, {4451, 43533}, {4551, 40936}, {4642, 13576}, {4835, 60077}, {4850, 24595}, {5219, 18055}, {5466, 27710}, {6063, 43684}, {7015, 10441}, {7018, 34258}, {7019, 60206}, {10521, 55949}, {11599, 37049}, {11606, 56928}, {16583, 40729}, {16600, 60135}, {16611, 60075}, {17062, 26538}, {17493, 60149}, {17739, 27958}, {18593, 60085}, {18786, 60081}, {20706, 60229}, {21965, 41003}, {27706, 43685}, {30097, 60320}, {40395, 54373}, {50453, 60074}, {59171, 60110}

X(60245) = isotomic conjugate of X(27958)
X(60245) = X(i)-isoconjugate-of-X(j) for these {i, j}: {21, 172}, {31, 27958}, {41, 17103}, {48, 14006}, {58, 2329}, {60, 2295}, {81, 2330}, {110, 3287}, {163, 3907}, {171, 284}, {249, 40608}, {270, 22061}, {283, 7119}, {333, 7122}, {643, 20981}, {645, 56242}, {849, 4095}, {894, 2194}, {1169, 18235}, {1172, 3955}, {1215, 2150}, {1333, 7081}, {1580, 2311}, {1691, 56154}, {1808, 56828}, {1909, 57657}, {1933, 36800}, {2175, 8033}, {2185, 20964}, {2193, 7009}, {2206, 17787}, {2328, 7175}, {2344, 40731}, {3939, 18200}, {4367, 5546}, {4477, 4565}, {4579, 7252}, {4612, 7234}, {4636, 57234}, {6064, 21755}, {10799, 40432}, {17185, 59159}, {38813, 56558}
X(60245) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 27958}, {10, 2329}, {37, 7081}, {115, 3907}, {244, 3287}, {1214, 894}, {1249, 14006}, {3160, 17103}, {4075, 4095}, {4988, 4459}, {6741, 4529}, {16591, 385}, {36908, 7175}, {39092, 2311}, {40586, 2330}, {40590, 171}, {40593, 8033}, {40603, 17787}, {40611, 172}, {40615, 17212}, {40617, 18200}, {40622, 4369}, {47345, 7009}, {55060, 20981}, {55064, 4477}, {55065, 4140}, {56325, 1215}, {59608, 7176}
X(60245) = X(i)-cross conjugate of X(j) for these {i, j}: {2643, 4077}, {8061, 4551}, {21965, 10}, {41003, 226}
X(60245) = pole of line {21965, 41003} with respect to the Kiepert hyperbola
X(60245) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(240)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(17084)}}, {{A, B, C, X(12), X(85)}}, {{A, B, C, X(37), X(2344)}}, {{A, B, C, X(57), X(1254)}}, {{A, B, C, X(65), X(349)}}, {{A, B, C, X(75), X(1237)}}, {{A, B, C, X(86), X(27688)}}, {{A, B, C, X(257), X(44187)}}, {{A, B, C, X(423), X(37049)}}, {{A, B, C, X(514), X(6757)}}, {{A, B, C, X(523), X(9311)}}, {{A, B, C, X(525), X(29057)}}, {{A, B, C, X(673), X(41501)}}, {{A, B, C, X(756), X(22230)}}, {{A, B, C, X(903), X(27702)}}, {{A, B, C, X(986), X(1214)}}, {{A, B, C, X(1089), X(57725)}}, {{A, B, C, X(1278), X(27705)}}, {{A, B, C, X(1434), X(52382)}}, {{A, B, C, X(1441), X(3212)}}, {{A, B, C, X(2171), X(20567)}}, {{A, B, C, X(2292), X(28659)}}, {{A, B, C, X(3008), X(27690)}}, {{A, B, C, X(3496), X(21016)}}, {{A, B, C, X(3954), X(56533)}}, {{A, B, C, X(4017), X(7153)}}, {{A, B, C, X(4095), X(21965)}}, {{A, B, C, X(4384), X(21674)}}, {{A, B, C, X(4850), X(18593)}}, {{A, B, C, X(5620), X(14377)}}, {{A, B, C, X(6354), X(44733)}}, {{A, B, C, X(6376), X(35544)}}, {{A, B, C, X(8061), X(40936)}}, {{A, B, C, X(8818), X(23902)}}, {{A, B, C, X(10693), X(55965)}}, {{A, B, C, X(12683), X(41081)}}, {{A, B, C, X(14621), X(27713)}}, {{A, B, C, X(16600), X(27712)}}, {{A, B, C, X(17108), X(21124)}}, {{A, B, C, X(17308), X(27714)}}, {{A, B, C, X(17451), X(18785)}}, {{A, B, C, X(18097), X(52383)}}, {{A, B, C, X(20706), X(21808)}}, {{A, B, C, X(21051), X(21941)}}, {{A, B, C, X(24248), X(56382)}}, {{A, B, C, X(24268), X(56827)}}, {{A, B, C, X(25425), X(41013)}}, {{A, B, C, X(27299), X(27701)}}, {{A, B, C, X(27685), X(44331)}}, {{A, B, C, X(27700), X(30107)}}, {{A, B, C, X(27706), X(40874)}}, {{A, B, C, X(27708), X(31191)}}, {{A, B, C, X(30701), X(34895)}}, {{A, B, C, X(32010), X(59191)}}, {{A, B, C, X(39957), X(57905)}}, {{A, B, C, X(52378), X(58737)}}, {{A, B, C, X(52390), X(57243)}}
X(60245) = barycentric product X(i)*X(j) for these (i, j): {10, 7249}, {12, 32010}, {65, 7018}, {225, 7019}, {226, 257}, {349, 893}, {1178, 34388}, {1284, 1934}, {1400, 44187}, {1431, 313}, {1432, 321}, {1441, 256}, {1577, 37137}, {1874, 40708}, {3668, 4451}, {3903, 4077}, {4017, 56241}, {16603, 40738}, {16609, 1916}, {20567, 40729}, {24002, 56257}, {27805, 7178}, {29055, 850}, {40099, 4032}, {40432, 6358}, {52575, 7116}, {52651, 85}, {57185, 7260}, {57809, 7015}, {59191, 60086}
X(60245) = barycentric quotient X(i)/X(j) for these (i, j): {2, 27958}, {4, 14006}, {7, 17103}, {10, 7081}, {12, 1215}, {37, 2329}, {42, 2330}, {65, 171}, {73, 3955}, {85, 8033}, {181, 20964}, {225, 7009}, {226, 894}, {256, 21}, {257, 333}, {321, 17787}, {349, 1920}, {523, 3907}, {594, 4095}, {661, 3287}, {694, 2311}, {893, 284}, {904, 2194}, {1178, 60}, {1284, 1580}, {1365, 53559}, {1400, 172}, {1402, 7122}, {1427, 7175}, {1431, 58}, {1432, 81}, {1441, 1909}, {1446, 7196}, {1469, 40731}, {1581, 56154}, {1874, 419}, {1880, 7119}, {1916, 36800}, {2171, 2295}, {2197, 22061}, {2292, 18235}, {2643, 40608}, {3027, 4154}, {3120, 4459}, {3649, 4697}, {3668, 7176}, {3669, 18200}, {3676, 17212}, {3700, 4529}, {3721, 56558}, {3865, 3794}, {3903, 643}, {4017, 4367}, {4024, 4140}, {4032, 6645}, {4041, 4477}, {4077, 4374}, {4451, 1043}, {4496, 4483}, {4551, 4579}, {4552, 18047}, {4566, 6649}, {4603, 4612}, {6354, 4032}, {6358, 3963}, {7015, 283}, {7018, 314}, {7019, 332}, {7104, 57657}, {7116, 2193}, {7146, 56441}, {7178, 4369}, {7179, 56696}, {7180, 20981}, {7212, 4107}, {7235, 4039}, {7249, 86}, {7260, 4631}, {8736, 1840}, {16609, 385}, {16888, 7187}, {20964, 10799}, {21051, 30584}, {24002, 16737}, {26942, 4019}, {27691, 27954}, {27805, 645}, {29055, 110}, {30572, 4922}, {32010, 261}, {34388, 1237}, {36065, 36084}, {36214, 1808}, {37137, 662}, {40432, 2185}, {40663, 4434}, {40729, 41}, {41003, 59509}, {44187, 28660}, {51641, 56242}, {52651, 9}, {53540, 53541}, {53545, 7200}, {53551, 53553}, {53559, 3023}, {56241, 7257}, {56257, 644}, {57185, 57234}
X(60245) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {257, 7249, 1432}

X(60246) = X(10)X(451)∩X(27)X(1029)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4+b^4-c^4-a*b*c*(b+c)-a^2*b*(2*b+c))*(a^4-b^4+c^4-a*b*c*(b+c)-a^2*c*(b+2*c)) : :

X(60246) lies on the Kiepert hyperbola and on these lines: {2, 40582}, {4, 34435}, {10, 451}, {27, 1029}, {29, 13583}, {30, 54932}, {226, 1781}, {278, 43682}, {281, 43683}, {321, 52412}, {406, 43533}, {469, 55027}, {475, 60077}, {498, 41494}, {1446, 18625}, {2051, 25651}, {3144, 60086}, {3541, 60157}, {3542, 60158}, {4213, 13576}, {6143, 60173}, {6353, 60152}, {6625, 15149}, {6834, 31363}, {6949, 13599}, {6952, 40448}, {7490, 60156}, {7505, 60154}, {7537, 54972}, {8889, 60153}, {13584, 31909}, {17906, 18679}, {18687, 40149}, {28810, 60251}, {37119, 60164}, {37276, 60114}, {37382, 57826}, {37388, 60170}, {37456, 54705}, {38282, 60165}, {43531, 52252}

X(60246) = isotomic conjugate of X(28754)
X(60246) = trilinear pole of line {523, 54244}
X(60246) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 1781}, {6, 52362}, {31, 28754}, {48, 2475}, {71, 229}, {73, 40582}, {212, 18625}, {222, 56317}, {228, 52361}, {656, 57194}, {1409, 52360}, {3211, 56588}
X(60246) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 28754}, {9, 52362}, {1249, 2475}, {36103, 1781}, {40596, 57194}, {40837, 18625}
X(60246) = X(i)-cross conjugate of X(j) for these {i, j}: {1172, 4}, {7110, 7040}, {34435, 54454}, {38336, 7}
X(60246) = pole of line {1172, 60246} with respect to the Kiepert hyperbola
X(60246) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(27), X(451)}}, {{A, B, C, X(37), X(57390)}}, {{A, B, C, X(57), X(1061)}}, {{A, B, C, X(74), X(1214)}}, {{A, B, C, X(92), X(37799)}}, {{A, B, C, X(278), X(6198)}}, {{A, B, C, X(281), X(56316)}}, {{A, B, C, X(406), X(7490)}}, {{A, B, C, X(461), X(37382)}}, {{A, B, C, X(469), X(52252)}}, {{A, B, C, X(1039), X(8056)}}, {{A, B, C, X(1063), X(25430)}}, {{A, B, C, X(1172), X(1781)}}, {{A, B, C, X(1427), X(57392)}}, {{A, B, C, X(1824), X(8791)}}, {{A, B, C, X(2982), X(52351)}}, {{A, B, C, X(3089), X(37276)}}, {{A, B, C, X(4213), X(15149)}}, {{A, B, C, X(6952), X(52280)}}, {{A, B, C, X(7498), X(37388)}}, {{A, B, C, X(8044), X(57865)}}, {{A, B, C, X(8814), X(57878)}}, {{A, B, C, X(17924), X(46103)}}, {{A, B, C, X(25651), X(52358)}}, {{A, B, C, X(28810), X(35466)}}, {{A, B, C, X(39957), X(57388)}}, {{A, B, C, X(39983), X(57702)}}, {{A, B, C, X(40414), X(41013)}}, {{A, B, C, X(43712), X(52388)}}, {{A, B, C, X(43742), X(56201)}}, {{A, B, C, X(54454), X(57797)}}, {{A, B, C, X(56219), X(57391)}}
X(60246) = barycentric product X(i)*X(j) for these (i, j): {4, 54454}, {28, 57797}, {264, 34435}, {273, 56280}, {286, 57646}, {56584, 57794}
X(60246) = barycentric quotient X(i)/X(j) for these (i, j): {1, 52362}, {2, 28754}, {4, 2475}, {19, 1781}, {27, 52361}, {28, 229}, {29, 52360}, {33, 56317}, {112, 57194}, {278, 18625}, {1172, 40582}, {34435, 3}, {41494, 39772}, {41505, 56588}, {54454, 69}, {56280, 78}, {56584, 224}, {57646, 72}, {57797, 20336}

X(60247) = X(3)X(54528)∩X(5)X(54679)

Barycentrics    (2*a^3-a^2*(b+c)+(b-2*c)*(b-c)*(b+c)-a*(2*b^2+c^2))*(2*a^3-a^2*(b+c)+(b-c)*(2*b-c)*(b+c)-a*(b^2+2*c^2)) : :

X(60247) lies on the Kiepert hyperbola and on these lines: {3, 54528}, {5, 54679}, {10, 37571}, {21, 60079}, {83, 31229}, {140, 60112}, {411, 54516}, {1150, 60251}, {1656, 5397}, {1751, 31204}, {2476, 60078}, {2650, 60116}, {3560, 54698}, {6824, 54758}, {6825, 54757}, {6828, 54526}, {6837, 54688}, {6838, 54726}, {6853, 54727}, {6855, 54790}, {6856, 54624}, {6857, 54786}, {6871, 54623}, {6912, 54696}, {6932, 54511}, {6988, 54787}, {6996, 54691}, {7377, 54630}, {8229, 14458}, {10883, 54517}, {20846, 54745}, {24624, 31187}, {35466, 60071}, {36002, 54687}, {37646, 57722}, {41806, 60082}, {46487, 54735}

X(60247) = isotomic conjugate of X(30834)
X(60247) = trilinear pole of line {50767, 523}
X(60247) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(21), X(88)}}, {{A, B, C, X(57), X(37571)}}, {{A, B, C, X(81), X(56062)}}, {{A, B, C, X(85), X(43757)}}, {{A, B, C, X(89), X(56027)}}, {{A, B, C, X(90), X(39963)}}, {{A, B, C, X(141), X(31229)}}, {{A, B, C, X(277), X(37222)}}, {{A, B, C, X(333), X(6336)}}, {{A, B, C, X(1150), X(35466)}}, {{A, B, C, X(1255), X(55938)}}, {{A, B, C, X(2006), X(5559)}}, {{A, B, C, X(2990), X(37518)}}, {{A, B, C, X(3218), X(15446)}}, {{A, B, C, X(3911), X(55918)}}, {{A, B, C, X(3936), X(31187)}}, {{A, B, C, X(5219), X(5560)}}, {{A, B, C, X(5235), X(31359)}}, {{A, B, C, X(5278), X(37646)}}, {{A, B, C, X(8056), X(55936)}}, {{A, B, C, X(8229), X(11331)}}, {{A, B, C, X(15474), X(56201)}}, {{A, B, C, X(17097), X(40434)}}, {{A, B, C, X(18134), X(31204)}}, {{A, B, C, X(18359), X(43731)}}, {{A, B, C, X(32782), X(41806)}}, {{A, B, C, X(36100), X(39962)}}, {{A, B, C, X(55924), X(56060)}}

X(60248) = X(4)X(7771)∩X(69)X(10155)

Barycentrics    (2*(a^2-b^2)^2-5*(a^2+b^2)*c^2+c^4)*(2*a^4+b^4-5*b^2*c^2+2*c^4-a^2*(5*b^2+4*c^2)) : :

X(60248) lies on the Kiepert hyperbola and on these lines: {4, 7771}, {69, 10155}, {76, 58446}, {83, 37637}, {141, 60178}, {183, 7608}, {230, 60096}, {262, 37688}, {325, 11669}, {598, 15597}, {671, 44531}, {1007, 53098}, {2996, 32832}, {3054, 60093}, {3407, 17006}, {6036, 43532}, {7737, 18845}, {7748, 32838}, {7763, 60285}, {7769, 18840}, {7778, 60198}, {7799, 60143}, {7868, 56064}, {7937, 60072}, {8182, 54476}, {8353, 17503}, {8781, 15271}, {8860, 54509}, {11056, 60255}, {11057, 54715}, {11140, 40022}, {11168, 60211}, {11179, 60185}, {14494, 34229}, {17004, 60098}, {18842, 23053}, {32458, 42010}, {32828, 43681}, {32883, 60145}, {37647, 60144}, {39656, 54868}, {44401, 60239}, {51224, 53101}

X(60248) = isotomic conjugate of X(31489)
X(60248) = X(i)-vertex conjugate of X(j) for these {i, j}: {25, 60096}
X(60248) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(95), X(56067)}}, {{A, B, C, X(141), X(37637)}}, {{A, B, C, X(183), X(37688)}}, {{A, B, C, X(230), X(15271)}}, {{A, B, C, X(599), X(15597)}}, {{A, B, C, X(2963), X(31360)}}, {{A, B, C, X(3054), X(7778)}}, {{A, B, C, X(3314), X(17006)}}, {{A, B, C, X(6464), X(55075)}}, {{A, B, C, X(7610), X(11168)}}, {{A, B, C, X(7769), X(40022)}}, {{A, B, C, X(7771), X(57799)}}, {{A, B, C, X(8353), X(52292)}}, {{A, B, C, X(9462), X(15464)}}, {{A, B, C, X(14489), X(30541)}}, {{A, B, C, X(21356), X(23053)}}, {{A, B, C, X(21358), X(44401)}}, {{A, B, C, X(30535), X(43662)}}, {{A, B, C, X(30786), X(53127)}}, {{A, B, C, X(32832), X(57518)}}, {{A, B, C, X(34816), X(53864)}}, {{A, B, C, X(36948), X(40405)}}, {{A, B, C, X(40120), X(42298)}}, {{A, B, C, X(40826), X(57822)}}, {{A, B, C, X(41909), X(44658)}}, {{A, B, C, X(42286), X(52154)}}

X(60249) = X(2)X(914)∩X(4)X(46)

Barycentrics    (a+b-c)*(a-b+c)*(b+c)*(a^3+a^2*(b-c)-(b-c)*(b+c)^2-a*(b^2+c^2))*(a^3+a^2*(-b+c)+(b-c)*(b+c)^2-a*(b^2+c^2)) : :

X(60249) lies on the Kiepert hyperbola and on these lines: {1, 60154}, {2, 914}, {4, 46}, {10, 16577}, {57, 60156}, {63, 6504}, {65, 51557}, {76, 18737}, {91, 52582}, {94, 18815}, {98, 36082}, {226, 7363}, {307, 43675}, {321, 40999}, {485, 13389}, {486, 13388}, {499, 60159}, {553, 60083}, {1069, 1210}, {1751, 2164}, {1817, 24624}, {1836, 32594}, {2003, 7110}, {2982, 57710}, {3668, 43682}, {3911, 13478}, {5745, 6512}, {7072, 56144}, {8287, 18588}, {8808, 18593}, {13579, 55873}, {14837, 60074}, {15836, 60166}, {16609, 36907}, {18391, 60158}, {20262, 56216}, {20570, 34258}, {21044, 40152}, {24914, 37063}, {28808, 60254}, {36626, 43533}, {37787, 55027}, {52422, 58012}, {54346, 60164}, {54420, 60155}, {55869, 60114}, {55872, 60255}

X(60249) = isotomic conjugate of X(31631)
X(60249) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 3193}, {19, 1800}, {21, 2178}, {31, 31631}, {46, 284}, {48, 3559}, {60, 21853}, {110, 46389}, {112, 59973}, {283, 52033}, {453, 2164}, {1068, 2193}, {1172, 3157}, {1333, 5552}, {1406, 2287}, {1813, 57124}, {2150, 21077}, {2194, 5905}, {2299, 6505}, {2328, 56848}, {4282, 56417}, {4636, 55214}, {5546, 51648}, {20930, 57657}, {32660, 57083}
X(60249) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 31631}, {6, 1800}, {9, 3193}, {37, 5552}, {226, 6505}, {244, 46389}, {1214, 5905}, {1249, 3559}, {34591, 59973}, {36908, 56848}, {40590, 46}, {40611, 2178}, {40622, 21188}, {47345, 1068}, {56325, 21077}
X(60249) = X(i)-complementary conjugate of X(j) for these {i, j}: {6, 34853}, {25, 6503}, {254, 141}, {921, 18589}, {2501, 135}, {6504, 1368}, {15316, 6389}, {39109, 2}, {39416, 924}, {41536, 1209}, {46746, 626}, {47732, 34835}, {59189, 343}
X(60249) = X(i)-cross conjugate of X(j) for these {i, j}: {1214, 226}
X(60249) = pole of line {1214, 60249} with respect to the Kiepert hyperbola
X(60249) = pole of line {91, 499} with respect to the dual conic of Yff parabola
X(60249) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(37), X(39943)}}, {{A, B, C, X(46), X(1214)}}, {{A, B, C, X(57), X(225)}}, {{A, B, C, X(63), X(91)}}, {{A, B, C, X(65), X(56231)}}, {{A, B, C, X(72), X(1728)}}, {{A, B, C, X(90), X(6513)}}, {{A, B, C, X(189), X(41013)}}, {{A, B, C, X(306), X(914)}}, {{A, B, C, X(307), X(1708)}}, {{A, B, C, X(333), X(45206)}}, {{A, B, C, X(522), X(1776)}}, {{A, B, C, X(656), X(40152)}}, {{A, B, C, X(860), X(1817)}}, {{A, B, C, X(1158), X(56944)}}, {{A, B, C, X(1427), X(52383)}}, {{A, B, C, X(1442), X(2982)}}, {{A, B, C, X(1709), X(52037)}}, {{A, B, C, X(1770), X(56382)}}, {{A, B, C, X(1779), X(45127)}}, {{A, B, C, X(1826), X(7110)}}, {{A, B, C, X(1940), X(1943)}}, {{A, B, C, X(2321), X(24005)}}, {{A, B, C, X(2994), X(7040)}}, {{A, B, C, X(8777), X(41506)}}, {{A, B, C, X(10395), X(40161)}}, {{A, B, C, X(19605), X(53008)}}, {{A, B, C, X(39708), X(57661)}}
X(60249) = barycentric product X(i)*X(j) for these (i, j): {10, 7318}, {46, 57867}, {226, 2994}, {307, 7040}, {333, 7363}, {1069, 57809}, {1441, 90}, {2164, 349}, {4554, 55248}, {20570, 65}, {20930, 57696}, {36082, 850}, {36626, 3668}, {40149, 6513}
X(60249) = barycentric quotient X(i)/X(j) for these (i, j): {1, 3193}, {2, 31631}, {3, 1800}, {4, 3559}, {10, 5552}, {12, 21077}, {46, 453}, {65, 46}, {73, 3157}, {90, 21}, {225, 1068}, {226, 5905}, {656, 59973}, {661, 46389}, {1042, 1406}, {1069, 283}, {1214, 6505}, {1400, 2178}, {1427, 56848}, {1441, 20930}, {1880, 52033}, {2164, 284}, {2171, 21853}, {2594, 56535}, {2994, 333}, {4017, 51648}, {4554, 55247}, {6512, 6514}, {6513, 1812}, {7040, 29}, {7072, 2328}, {7178, 21188}, {7318, 86}, {7363, 226}, {18344, 57124}, {20570, 314}, {21044, 6506}, {36082, 110}, {36626, 1043}, {40152, 6511}, {44426, 57083}, {52383, 56417}, {55248, 650}, {57185, 55214}, {57696, 90}, {57867, 20570}
X(60249) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 2994, 6513}

X(60250) = X(2)X(55793)∩X(98)X(548)

Barycentrics    (a^2+b^2-6*c^2)*(a^2-6*b^2+c^2) : :
X(60250) = -16*X[3628]+15*X[53108]

X(60250) lies on the Kiepert hyperbola and on these lines: {2, 55793}, {3, 55824}, {4, 55720}, {5, 54920}, {30, 54934}, {98, 548}, {99, 51585}, {262, 5072}, {315, 41895}, {524, 54646}, {549, 54644}, {598, 7754}, {1657, 53100}, {1916, 33289}, {2996, 7911}, {3096, 60143}, {3407, 14032}, {3424, 49140}, {3526, 11668}, {3534, 54851}, {3627, 60132}, {3628, 53108}, {3630, 53106}, {3843, 14488}, {3850, 60142}, {5055, 54645}, {5066, 54734}, {5254, 10302}, {5395, 7760}, {6144, 53107}, {6392, 60145}, {6656, 60210}, {7790, 60285}, {7812, 60281}, {7850, 53105}, {7883, 60228}, {7894, 53102}, {7918, 60286}, {10159, 47286}, {11054, 60282}, {11185, 18845}, {14458, 15684}, {14492, 23046}, {14893, 54717}, {15706, 60175}, {15712, 60334}, {15717, 54921}, {17503, 34505}, {17538, 60322}, {19695, 60280}, {21735, 60337}, {32027, 43676}, {32455, 60146}, {32877, 60262}, {32878, 60201}, {32888, 60259}, {33703, 54845}, {46333, 60150}, {52886, 60104}

X(60250) = inverse of X(51585) in Wallace hyperbola
X(60250) = isotomic conjugate of X(32455)
X(60250) = pole of line {32455, 51585} with respect to the Wallace hyperbola
X(60250) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55720)}}, {{A, B, C, X(290), X(57896)}}, {{A, B, C, X(297), X(548)}}, {{A, B, C, X(335), X(13606)}}, {{A, B, C, X(419), X(33289)}}, {{A, B, C, X(458), X(5072)}}, {{A, B, C, X(525), X(34483)}}, {{A, B, C, X(4668), X(29575)}}, {{A, B, C, X(5117), X(14032)}}, {{A, B, C, X(6664), X(13622)}}, {{A, B, C, X(11331), X(15684)}}, {{A, B, C, X(13623), X(36952)}}, {{A, B, C, X(23046), X(52289)}}, {{A, B, C, X(35140), X(57908)}}, {{A, B, C, X(40802), X(44763)}}, {{A, B, C, X(43713), X(56004)}}, {{A, B, C, X(49140), X(52283)}}, {{A, B, C, X(56042), X(57725)}}
X(60250) = barycentric product X(i)*X(j) for these (i, j): {58094, 850}
X(60250) = barycentric quotient X(i)/X(j) for these (i, j): {2, 32455}, {3630, 51585}, {58094, 110}

X(60251) = X(2)X(645)∩X(10)X(3699)

Barycentrics    ((a-b)^2*(a+b)-(a^2+b^2)*c+2*c^3)*(a^3+2*b^3-a*c^2-b*c^2+c^3-a^2*(b+c)) : :

X(60251) lies on the Kiepert hyperbola and on these lines: {2, 645}, {4, 25650}, {10, 3699}, {69, 55962}, {76, 30811}, {83, 5718}, {98, 6083}, {190, 226}, {312, 43683}, {321, 646}, {671, 20337}, {894, 30588}, {1150, 60247}, {1211, 60235}, {1446, 4554}, {1751, 4417}, {2064, 43675}, {3912, 11608}, {3936, 24624}, {4049, 4997}, {4052, 42033}, {4080, 4582}, {4444, 35354}, {4633, 57826}, {5219, 18055}, {5233, 60075}, {5741, 57721}, {6335, 40149}, {7256, 8286}, {8707, 60086}, {8808, 44327}, {11611, 30823}, {13478, 18134}, {13576, 36802}, {13735, 60078}, {14061, 37691}, {14534, 17056}, {15455, 18743}, {17234, 60085}, {28810, 60246}, {29640, 40718}, {29795, 40515}, {29862, 36801}, {30834, 60071}, {30866, 36795}, {31247, 60203}, {35353, 36798}, {36804, 60091}, {36806, 40017}, {43669, 53339}, {46828, 54119}

X(60251) = isotomic conjugate of X(35466)
X(60251) = trilinear pole of line {8, 4774}
X(60251) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 35466}, {48, 1884}, {163, 6089}, {604, 44669}, {904, 27970}
X(60251) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 35466}, {115, 6089}, {1249, 1884}, {3161, 44669}
X(60251) = X(i)-cross conjugate of X(j) for these {i, j}: {6370, 99}, {6740, 1494}, {49274, 190}
X(60251) = pole of line {49274, 60251} with respect to the dual conic of incircle
X(60251) = pole of line {32851, 34895} with respect to the dual conic of Yff parabola
X(60251) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(30811)}}, {{A, B, C, X(63), X(56833)}}, {{A, B, C, X(69), X(30828)}}, {{A, B, C, X(81), X(30831)}}, {{A, B, C, X(86), X(30832)}}, {{A, B, C, X(92), X(2985)}}, {{A, B, C, X(141), X(5718)}}, {{A, B, C, X(190), X(645)}}, {{A, B, C, X(239), X(29862)}}, {{A, B, C, X(306), X(25650)}}, {{A, B, C, X(312), X(33116)}}, {{A, B, C, X(313), X(40412)}}, {{A, B, C, X(333), X(41878)}}, {{A, B, C, X(334), X(4998)}}, {{A, B, C, X(335), X(2006)}}, {{A, B, C, X(525), X(53794)}}, {{A, B, C, X(561), X(40419)}}, {{A, B, C, X(894), X(5219)}}, {{A, B, C, X(903), X(25529)}}, {{A, B, C, X(1016), X(18359)}}, {{A, B, C, X(1150), X(30834)}}, {{A, B, C, X(1211), X(17056)}}, {{A, B, C, X(1581), X(6015)}}, {{A, B, C, X(2349), X(4567)}}, {{A, B, C, X(3227), X(6336)}}, {{A, B, C, X(3661), X(29640)}}, {{A, B, C, X(3936), X(52503)}}, {{A, B, C, X(4358), X(32849)}}, {{A, B, C, X(4417), X(18134)}}, {{A, B, C, X(4600), X(35141)}}, {{A, B, C, X(4608), X(51561)}}, {{A, B, C, X(5233), X(17234)}}, {{A, B, C, X(5241), X(17245)}}, {{A, B, C, X(5333), X(31247)}}, {{A, B, C, X(5524), X(17266)}}, {{A, B, C, X(5741), X(18139)}}, {{A, B, C, X(6557), X(56078)}}, {{A, B, C, X(6740), X(49274)}}, {{A, B, C, X(17058), X(21944)}}, {{A, B, C, X(17313), X(27739)}}, {{A, B, C, X(17983), X(41683)}}, {{A, B, C, X(18743), X(42033)}}, {{A, B, C, X(18821), X(57995)}}, {{A, B, C, X(20568), X(34234)}}, {{A, B, C, X(24160), X(39700)}}, {{A, B, C, X(24161), X(37887)}}, {{A, B, C, X(28738), X(28793)}}, {{A, B, C, X(28753), X(28807)}}, {{A, B, C, X(28754), X(28810)}}, {{A, B, C, X(28755), X(28811)}}, {{A, B, C, X(28808), X(28974)}}, {{A, B, C, X(30608), X(40014)}}, {{A, B, C, X(30701), X(50442)}}, {{A, B, C, X(31002), X(56365)}}, {{A, B, C, X(35168), X(46638)}}, {{A, B, C, X(40010), X(40410)}}, {{A, B, C, X(40414), X(52575)}}, {{A, B, C, X(52351), X(56951)}}
X(60251) = barycentric product X(i)*X(j) for these (i, j): {6083, 850}, {35354, 799}
X(60251) = barycentric quotient X(i)/X(j) for these (i, j): {2, 35466}, {4, 1884}, {8, 44669}, {523, 6089}, {894, 27970}, {6083, 110}, {35354, 661}, {44669, 34194}, {56648, 1464}

X(60252) = X(4)X(298)∩X(13)X(69)

Barycentrics    -a^4-b^4+14*b^2*c^2-c^4+2*a^2*(b^2+c^2)+4*sqrt(3)*S*(b^2+c^2) : :

X(60252) lies on the Kiepert hyperbola and on these lines: {3, 54850}, {4, 298}, {13, 69}, {17, 33411}, {18, 37177}, {30, 54939}, {83, 37641}, {98, 617}, {141, 33223}, {299, 43542}, {302, 32817}, {303, 43554}, {376, 54484}, {524, 54618}, {616, 54562}, {619, 34229}, {621, 14458}, {627, 54937}, {633, 54847}, {671, 11128}, {3926, 44383}, {5473, 54569}, {5488, 7933}, {7789, 16645}, {9114, 54489}, {9761, 54617}, {11121, 34540}, {11122, 33251}, {11129, 11488}, {12816, 50855}, {12817, 22491}, {14905, 42850}, {18440, 54940}, {18842, 37785}, {21356, 42036}, {25167, 60318}, {25187, 43539}, {32810, 54538}, {32811, 50246}, {32833, 40707}, {32885, 44382}, {34289, 41000}, {41001, 59763}

X(60252) = isotomic conjugate of X(37640)
X(60252) = X(i)-cross conjugate of X(j) for these {i, j}: {32836, 60253}
X(60252) = pole of line {32836, 60252} with respect to the Kiepert hyperbola
X(60252) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(5864)}}, {{A, B, C, X(69), X(298)}}, {{A, B, C, X(300), X(36889)}}, {{A, B, C, X(302), X(36948)}}, {{A, B, C, X(3926), X(40712)}}, {{A, B, C, X(6664), X(11080)}}, {{A, B, C, X(7026), X(30701)}}, {{A, B, C, X(7799), X(19779)}}, {{A, B, C, X(14376), X(52204)}}, {{A, B, C, X(34208), X(53029)}}

X(60253) = X(4)X(299)∩X(14)X(69)

Barycentrics    -a^4-b^4+14*b^2*c^2-c^4+2*a^2*(b^2+c^2)-4*sqrt(3)*S*(b^2+c^2) : :

X(60253) lies on the Kiepert hyperbola and on these lines: {3, 54849}, {4, 299}, {14, 69}, {17, 37178}, {18, 33410}, {30, 54940}, {83, 37640}, {98, 616}, {141, 33223}, {298, 43543}, {302, 43555}, {303, 32817}, {376, 54485}, {524, 54617}, {617, 54561}, {618, 34229}, {622, 14458}, {628, 54938}, {634, 54848}, {671, 11129}, {3926, 44382}, {5474, 54570}, {5487, 7933}, {7789, 16644}, {9116, 54490}, {9763, 54618}, {11121, 33251}, {11122, 34541}, {11128, 11489}, {12816, 22492}, {12817, 50858}, {14904, 42850}, {18440, 54939}, {18842, 37786}, {21356, 42035}, {25157, 60319}, {25183, 43538}, {32810, 54535}, {32811, 54534}, {32828, 60222}, {32833, 40706}, {32885, 44383}, {34289, 41001}, {41000, 59763}

X(60253) = isotomic conjugate of X(37641)
X(60253) = X(i)-cross conjugate of X(j) for these {i, j}: {32836, 60252}
X(60253) = pole of line {32836, 60253} with respect to the Kiepert hyperbola
X(60253) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(5865)}}, {{A, B, C, X(69), X(299)}}, {{A, B, C, X(301), X(36889)}}, {{A, B, C, X(303), X(36948)}}, {{A, B, C, X(3926), X(40711)}}, {{A, B, C, X(6664), X(11085)}}, {{A, B, C, X(7043), X(30701)}}, {{A, B, C, X(7799), X(19778)}}, {{A, B, C, X(14376), X(52203)}}, {{A, B, C, X(34208), X(53030)}}
X(60253) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {141, 46951, 60252}

X(60254) = X(4)X(1043)∩X(10)X(1265)

Barycentrics    ((a-b)^2*(a+b)-(a-b)^2*c+(a+b)*c^2+3*c^3)*(a^3-a^2*(b+c)+a*(b^2+2*b*c-c^2)+(b+c)*(3*b^2-2*b*c+c^2)) : :

X(60254) lies on the Kiepert hyperbola and on these lines: {2, 51612}, {4, 1043}, {10, 1265}, {69, 13478}, {99, 44736}, {226, 345}, {304, 1446}, {312, 40149}, {321, 52406}, {333, 55962}, {966, 60235}, {1211, 60206}, {1230, 5392}, {1751, 14555}, {1992, 54553}, {3926, 17056}, {3936, 60156}, {4052, 50107}, {4195, 60077}, {5226, 60321}, {5233, 60107}, {5712, 14534}, {5739, 24624}, {5741, 60155}, {5743, 32022}, {7763, 32014}, {8808, 44189}, {10436, 56226}, {18134, 60076}, {18139, 60169}, {18141, 60085}, {18697, 43683}, {26872, 60088}, {28808, 60249}, {30588, 33113}, {30831, 60242}, {32830, 57826}, {37176, 43531}, {43672, 50636}, {48817, 60078}

X(60254) = inverse of X(44736) in Wallace hyperbola
X(60254) = isotomic conjugate of X(37642)
X(60254) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 37642}, {32, 44735}, {604, 3486}
X(60254) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 37642}, {3161, 3486}, {6376, 44735}
X(60254) = pole of line {37642, 44736} with respect to the Wallace hyperbola
X(60254) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(69), X(313)}}, {{A, B, C, X(264), X(57825)}}, {{A, B, C, X(304), X(312)}}, {{A, B, C, X(306), X(3926)}}, {{A, B, C, X(333), X(30828)}}, {{A, B, C, X(335), X(56218)}}, {{A, B, C, X(469), X(37176)}}, {{A, B, C, X(561), X(8817)}}, {{A, B, C, X(594), X(966)}}, {{A, B, C, X(908), X(56367)}}, {{A, B, C, X(967), X(6464)}}, {{A, B, C, X(987), X(25430)}}, {{A, B, C, X(1016), X(56086)}}, {{A, B, C, X(1211), X(5712)}}, {{A, B, C, X(1230), X(7763)}}, {{A, B, C, X(2165), X(40085)}}, {{A, B, C, X(2184), X(40403)}}, {{A, B, C, X(3729), X(6557)}}, {{A, B, C, X(3936), X(5739)}}, {{A, B, C, X(4648), X(5743)}}, {{A, B, C, X(4671), X(33113)}}, {{A, B, C, X(5226), X(5936)}}, {{A, B, C, X(5233), X(18141)}}, {{A, B, C, X(8797), X(57824)}}, {{A, B, C, X(13577), X(30635)}}, {{A, B, C, X(14555), X(18134)}}, {{A, B, C, X(17064), X(37887)}}, {{A, B, C, X(18027), X(57874)}}, {{A, B, C, X(18697), X(57818)}}, {{A, B, C, X(18743), X(50107)}}, {{A, B, C, X(24597), X(30831)}}, {{A, B, C, X(30710), X(50442)}}, {{A, B, C, X(31034), X(31037)}}, {{A, B, C, X(34208), X(42027)}}, {{A, B, C, X(34523), X(56075)}}, {{A, B, C, X(37679), X(53665)}}, {{A, B, C, X(40014), X(40420)}}, {{A, B, C, X(40414), X(52581)}}, {{A, B, C, X(44794), X(56335)}}
X(60254) = barycentric quotient X(i)/X(j) for these (i, j): {2, 37642}, {8, 3486}, {75, 44735}

X(60255) = X(4)X(323)∩X(69)X(94)

Barycentrics    ((a^2-b^2)^3+(-a^4+4*a^2*b^2+3*b^4)*c^2-(a^2+3*b^2)*c^4+c^6)*(a^6+(b^2-c^2)^3-a^4*(b^2+3*c^2)+a^2*(-b^4+4*b^2*c^2+3*c^4)) : :

X(60255) lies on the Kiepert hyperbola and on these lines: {2, 52437}, {3, 54498}, {4, 323}, {13, 44719}, {14, 44718}, {30, 54942}, {69, 94}, {98, 16063}, {140, 60160}, {340, 2052}, {394, 13579}, {631, 54500}, {1370, 60150}, {1656, 60163}, {1992, 54807}, {2475, 54758}, {2478, 54727}, {3146, 54844}, {3153, 54943}, {3424, 5189}, {3522, 60166}, {3523, 60159}, {3533, 43666}, {3545, 54827}, {5046, 54757}, {5056, 60162}, {5068, 60174}, {6805, 43536}, {6806, 54597}, {6815, 54763}, {6816, 54660}, {6817, 54885}, {6820, 54710}, {6997, 60127}, {7381, 54587}, {7382, 54689}, {7386, 60185}, {7391, 14458}, {7392, 54523}, {7394, 14492}, {7528, 54912}, {7533, 14484}, {7578, 37645}, {7612, 46336}, {7791, 54843}, {9302, 37190}, {10210, 54939}, {11004, 60191}, {11056, 60248}, {14064, 54829}, {14790, 54486}, {14957, 54678}, {16924, 54529}, {17578, 54886}, {18316, 18531}, {32974, 54558}, {32982, 54779}, {33017, 54733}, {34289, 37644}, {37162, 60164}, {37185, 54499}, {37191, 54677}, {37192, 54867}, {37201, 54604}, {37349, 54520}, {37672, 54765}, {37804, 60178}, {44440, 60119}, {44442, 54612}, {46450, 54865}, {52403, 54941}, {55872, 60249}

X(60255) = isotomic conjugate of X(37644)
X(60255) = trilinear pole of line {7623, 7624}
X(60255) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 18445}, {31, 37644}, {2159, 46817}
X(60255) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 37644}, {6, 18445}, {3163, 46817}
X(60255) = pole of line {15066, 60255} with respect to the Kiepert hyperbola
X(60255) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(67), X(40802)}}, {{A, B, C, X(68), X(14919)}}, {{A, B, C, X(69), X(323)}}, {{A, B, C, X(97), X(16266)}}, {{A, B, C, X(290), X(41896)}}, {{A, B, C, X(297), X(16063)}}, {{A, B, C, X(394), X(3519)}}, {{A, B, C, X(2987), X(5486)}}, {{A, B, C, X(2994), X(34401)}}, {{A, B, C, X(3522), X(6820)}}, {{A, B, C, X(3523), X(37192)}}, {{A, B, C, X(3532), X(56361)}}, {{A, B, C, X(4846), X(55982)}}, {{A, B, C, X(5068), X(6819)}}, {{A, B, C, X(5189), X(52283)}}, {{A, B, C, X(5557), X(56041)}}, {{A, B, C, X(5559), X(56352)}}, {{A, B, C, X(5905), X(55872)}}, {{A, B, C, X(7391), X(11331)}}, {{A, B, C, X(7394), X(52289)}}, {{A, B, C, X(7533), X(52288)}}, {{A, B, C, X(8770), X(18384)}}, {{A, B, C, X(8797), X(57900)}}, {{A, B, C, X(11064), X(45821)}}, {{A, B, C, X(14052), X(45838)}}, {{A, B, C, X(14841), X(36609)}}, {{A, B, C, X(15052), X(15077)}}, {{A, B, C, X(15066), X(37644)}}, {{A, B, C, X(18019), X(55972)}}, {{A, B, C, X(18020), X(57908)}}, {{A, B, C, X(18372), X(42359)}}, {{A, B, C, X(21739), X(43740)}}, {{A, B, C, X(22451), X(37638)}}, {{A, B, C, X(30535), X(38005)}}, {{A, B, C, X(31068), X(56601)}}, {{A, B, C, X(34384), X(44175)}}, {{A, B, C, X(34385), X(44177)}}, {{A, B, C, X(34405), X(55032)}}, {{A, B, C, X(37174), X(46336)}}, {{A, B, C, X(43731), X(56354)}}, {{A, B, C, X(43745), X(54451)}}, {{A, B, C, X(47103), X(52497)}}, {{A, B, C, X(56002), X(57713)}}
X(60255) = barycentric product X(i)*X(j) for these (i, j): {27353, 95}
X(60255) = barycentric quotient X(i)/X(j) for these (i, j): {2, 37644}, {3, 18445}, {30, 46817}, {27353, 5}

X(60256) = X(2)X(14836)∩X(4)X(3580)

Barycentrics    ((a^2-b^2)^2*(a^2+b^2)+(a^2+b^2)^2*c^2-5*(a^2+b^2)*c^4+3*c^6)*(a^6+a^4*(b-c)*(b+c)+(b^2-c^2)^2*(3*b^2+c^2)-a^2*(5*b^4-2*b^2*c^2+c^4)) : :

X(60256) lies on the Kiepert hyperbola and on these lines: {2, 14836}, {4, 3580}, {23, 3424}, {30, 54943}, {69, 2986}, {96, 34853}, {98, 7493}, {193, 60193}, {275, 6515}, {343, 6504}, {376, 18316}, {631, 54969}, {1992, 54803}, {1993, 56346}, {2052, 44138}, {2394, 33294}, {3090, 9221}, {3549, 60159}, {3619, 59763}, {5169, 14484}, {7519, 60147}, {7552, 54498}, {7578, 37644}, {11433, 40393}, {16041, 54899}, {16080, 17907}, {34289, 37643}, {37636, 60114}, {37645, 43530}, {37803, 60178}, {41099, 54809}, {43537, 52300}, {43678, 46106}, {46105, 52283}, {46808, 60119}, {51358, 52583}, {51481, 60266}, {52582, 56272}, {53416, 54778}

X(60256) = isotomic conjugate of X(37645)
X(60256) = trilinear pole of line {6334, 10297}
X(60256) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 47391}, {31, 37645}, {48, 18533}
X(60256) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 37645}, {6, 47391}, {1249, 18533}
X(60256) = X(i)-cross conjugate of X(j) for these {i, j}: {4846, 36889}, {10605, 253}, {15760, 264}, {37638, 2}
X(60256) = pole of line {37638, 60256} with respect to the Kiepert hyperbola
X(60256) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(37489)}}, {{A, B, C, X(23), X(52283)}}, {{A, B, C, X(68), X(14852)}}, {{A, B, C, X(69), X(850)}}, {{A, B, C, X(91), X(15474)}}, {{A, B, C, X(297), X(7493)}}, {{A, B, C, X(323), X(20421)}}, {{A, B, C, X(343), X(6515)}}, {{A, B, C, X(394), X(12163)}}, {{A, B, C, X(1073), X(45788)}}, {{A, B, C, X(1177), X(40802)}}, {{A, B, C, X(1993), X(31626)}}, {{A, B, C, X(2165), X(2501)}}, {{A, B, C, X(2373), X(55972)}}, {{A, B, C, X(2987), X(43697)}}, {{A, B, C, X(2994), X(52351)}}, {{A, B, C, X(3549), X(37192)}}, {{A, B, C, X(4846), X(37638)}}, {{A, B, C, X(5169), X(52288)}}, {{A, B, C, X(5905), X(52381)}}, {{A, B, C, X(8797), X(42355)}}, {{A, B, C, X(11433), X(37636)}}, {{A, B, C, X(11472), X(34802)}}, {{A, B, C, X(12359), X(52350)}}, {{A, B, C, X(12649), X(53816)}}, {{A, B, C, X(13575), X(18022)}}, {{A, B, C, X(14836), X(34288)}}, {{A, B, C, X(14919), X(34403)}}, {{A, B, C, X(15066), X(37643)}}, {{A, B, C, X(15454), X(57482)}}, {{A, B, C, X(17907), X(33294)}}, {{A, B, C, X(18125), X(42287)}}, {{A, B, C, X(18372), X(19222)}}, {{A, B, C, X(26546), X(28420)}}, {{A, B, C, X(34208), X(40427)}}, {{A, B, C, X(36889), X(44134)}}, {{A, B, C, X(37644), X(45972)}}, {{A, B, C, X(40441), X(56002)}}, {{A, B, C, X(41909), X(42313)}}, {{A, B, C, X(46111), X(54124)}}, {{A, B, C, X(52898), X(56601)}}, {{A, B, C, X(55999), X(57647)}}
X(60256) = barycentric product X(i)*X(j) for these (i, j): {264, 34801}, {36889, 59430}, {52487, 69}, {53958, 850}, {57819, 58081}
X(60256) = barycentric quotient X(i)/X(j) for these (i, j): {2, 37645}, {3, 47391}, {4, 18533}, {381, 40909}, {3426, 52168}, {4846, 51471}, {34288, 52165}, {34801, 3}, {52487, 4}, {53958, 110}, {56710, 40138}, {58081, 378}, {58959, 32708}, {59430, 376}, {60119, 40387}

X(60257) = X(2)X(45988)∩X(4)X(17778)

Barycentrics    (a^2*(b+c)+(b-2*c)*c*(b+c)+a*(b^2+b*c-c^2))*(a^2*(b+c)-b*(2*b-c)*(b+c)+a*(-b^2+b*c+c^2)) : :

X(60257) lies on the Kiepert hyperbola and on these lines: {2, 45988}, {4, 17778}, {10, 17889}, {69, 54119}, {75, 38407}, {148, 52025}, {193, 60168}, {226, 41839}, {321, 17786}, {1751, 37652}, {3210, 37865}, {3936, 60261}, {4357, 60243}, {5249, 27269}, {5739, 60149}, {5905, 60088}, {13478, 37684}, {13576, 20012}, {17232, 40013}, {17300, 60156}, {17349, 57721}, {17379, 60082}, {17697, 28620}, {18135, 58025}, {18139, 60236}, {24624, 37683}, {26032, 60152}, {26125, 60188}, {31008, 40031}, {31034, 55027}, {31060, 60244}, {32771, 37164}, {32782, 56210}, {33144, 40718}, {33151, 60230}, {37653, 60206}, {48855, 60078}, {50133, 54735}

X(60257) = isotomic conjugate of X(37652)
X(60257) = trilinear pole of line {17072, 47843}
X(60257) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 54354}, {31, 37652}, {48, 37055}, {560, 30022}, {1333, 59302}
X(60257) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 37652}, {9, 54354}, {37, 59302}, {1249, 37055}, {6374, 30022}
X(60257) = pole of line {18134, 60257} with respect to the Kiepert hyperbola
X(60257) = pole of line {3210, 35633} with respect to the dual conic of Yff parabola
X(60257) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(561)}}, {{A, B, C, X(8), X(56184)}}, {{A, B, C, X(57), X(20568)}}, {{A, B, C, X(69), X(17778)}}, {{A, B, C, X(92), X(335)}}, {{A, B, C, X(278), X(18895)}}, {{A, B, C, X(312), X(41839)}}, {{A, B, C, X(330), X(30690)}}, {{A, B, C, X(334), X(39741)}}, {{A, B, C, X(345), X(17947)}}, {{A, B, C, X(469), X(17697)}}, {{A, B, C, X(983), X(1255)}}, {{A, B, C, X(1221), X(27494)}}, {{A, B, C, X(1502), X(6354)}}, {{A, B, C, X(3112), X(56124)}}, {{A, B, C, X(3263), X(30699)}}, {{A, B, C, X(3681), X(56314)}}, {{A, B, C, X(3912), X(20012)}}, {{A, B, C, X(3936), X(37683)}}, {{A, B, C, X(4357), X(30712)}}, {{A, B, C, X(4373), X(40216)}}, {{A, B, C, X(4417), X(37684)}}, {{A, B, C, X(5249), X(26125)}}, {{A, B, C, X(5712), X(37653)}}, {{A, B, C, X(5739), X(17300)}}, {{A, B, C, X(6358), X(57914)}}, {{A, B, C, X(6650), X(15474)}}, {{A, B, C, X(8049), X(30636)}}, {{A, B, C, X(10405), X(39696)}}, {{A, B, C, X(14996), X(31037)}}, {{A, B, C, X(17230), X(42042)}}, {{A, B, C, X(17232), X(32911)}}, {{A, B, C, X(17238), X(19684)}}, {{A, B, C, X(17349), X(18139)}}, {{A, B, C, X(17379), X(32782)}}, {{A, B, C, X(18032), X(54128)}}, {{A, B, C, X(18134), X(37652)}}, {{A, B, C, X(18359), X(39703)}}, {{A, B, C, X(30022), X(38407)}}, {{A, B, C, X(30635), X(39734)}}, {{A, B, C, X(30701), X(34527)}}, {{A, B, C, X(31008), X(31060)}}, {{A, B, C, X(31017), X(37685)}}, {{A, B, C, X(31034), X(32863)}}, {{A, B, C, X(36807), X(55988)}}, {{A, B, C, X(37870), X(57725)}}, {{A, B, C, X(39720), X(52393)}}, {{A, B, C, X(39976), X(56165)}}, {{A, B, C, X(40014), X(44733)}}, {{A, B, C, X(40026), X(42304)}}, {{A, B, C, X(55985), X(59268)}}
X(60257) = barycentric product X(i)*X(j) for these (i, j): {45988, 76}
X(60257) = barycentric quotient X(i)/X(j) for these (i, j): {1, 54354}, {2, 37652}, {4, 37055}, {10, 59302}, {76, 30022}, {45988, 6}

X(60258) = X(4)X(14996)∩X(10)X(3218)

Barycentrics    ((a-b)*(a+b)^2+(a^2+3*a*b-b^2)*c+(a+b)*c^2+c^3)*(a^3+a^2*(b+c)+(b-c)*(b+c)^2+a*(b^2+3*b*c-c^2)) : :

X(60258) lies on the Kiepert hyperbola and on these lines: {4, 14996}, {5, 54727}, {7, 60091}, {10, 3218}, {20, 54758}, {30, 54947}, {81, 55027}, {89, 1478}, {226, 1443}, {320, 321}, {377, 54786}, {757, 24624}, {940, 1029}, {1656, 60173}, {2475, 60079}, {2478, 54624}, {2895, 34258}, {3091, 54757}, {3146, 54688}, {3522, 60158}, {3523, 60154}, {3543, 54789}, {3832, 54726}, {4080, 17300}, {5046, 60078}, {5056, 60164}, {5068, 60157}, {5372, 60206}, {6539, 37653}, {6833, 54498}, {6835, 54787}, {6836, 54790}, {6839, 54528}, {6840, 54679}, {6894, 54516}, {6895, 54526}, {6952, 54500}, {6996, 54695}, {6999, 54728}, {7192, 60074}, {7272, 8047}, {7377, 54719}, {7381, 54760}, {7382, 54759}, {7384, 54497}, {7406, 54754}, {10431, 54690}, {14458, 37456}, {16063, 60152}, {16704, 60149}, {26118, 60150}, {37162, 43531}, {37434, 54844}, {37437, 54698}, {37635, 60071}, {37639, 54119}, {37656, 60097}, {37685, 60155}, {46336, 60165}, {51558, 54722}, {59491, 60243}

X(60258) = isogonal conjugate of X(54409)
X(60258) = isotomic conjugate of X(37656)
X(60258) = trilinear pole of line {3960, 523}
X(60258) = pole of line {37633, 60258} with respect to the Kiepert hyperbola
X(60258) = pole of line {37656, 54409} with respect to the Wallace hyperbola
X(60258) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(21739)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(51340)}}, {{A, B, C, X(7), X(89)}}, {{A, B, C, X(8), X(17021)}}, {{A, B, C, X(56), X(59265)}}, {{A, B, C, X(57), X(3336)}}, {{A, B, C, X(67), X(39957)}}, {{A, B, C, X(69), X(14996)}}, {{A, B, C, X(79), X(88)}}, {{A, B, C, X(80), X(40434)}}, {{A, B, C, X(81), X(5557)}}, {{A, B, C, X(85), X(21907)}}, {{A, B, C, X(92), X(56880)}}, {{A, B, C, X(97), X(52037)}}, {{A, B, C, X(189), X(2167)}}, {{A, B, C, X(278), X(5270)}}, {{A, B, C, X(333), X(43741)}}, {{A, B, C, X(335), X(33170)}}, {{A, B, C, X(469), X(37162)}}, {{A, B, C, X(593), X(46331)}}, {{A, B, C, X(940), X(2895)}}, {{A, B, C, X(1000), X(56039)}}, {{A, B, C, X(1150), X(37635)}}, {{A, B, C, X(1214), X(3519)}}, {{A, B, C, X(1255), X(5559)}}, {{A, B, C, X(2990), X(34485)}}, {{A, B, C, X(2994), X(7320)}}, {{A, B, C, X(5059), X(37276)}}, {{A, B, C, X(5372), X(5712)}}, {{A, B, C, X(5561), X(39963)}}, {{A, B, C, X(6336), X(20060)}}, {{A, B, C, X(6650), X(39706)}}, {{A, B, C, X(6994), X(37462)}}, {{A, B, C, X(7224), X(39734)}}, {{A, B, C, X(8025), X(37653)}}, {{A, B, C, X(11331), X(37456)}}, {{A, B, C, X(11604), X(30608)}}, {{A, B, C, X(14621), X(33086)}}, {{A, B, C, X(14919), X(43724)}}, {{A, B, C, X(16704), X(17300)}}, {{A, B, C, X(17097), X(55995)}}, {{A, B, C, X(17778), X(37639)}}, {{A, B, C, X(22336), X(39979)}}, {{A, B, C, X(25430), X(43731)}}, {{A, B, C, X(26745), X(34401)}}, {{A, B, C, X(30513), X(56075)}}, {{A, B, C, X(30711), X(43745)}}, {{A, B, C, X(31034), X(37684)}}, {{A, B, C, X(34917), X(36101)}}, {{A, B, C, X(37633), X(37656)}}, {{A, B, C, X(39698), X(54120)}}, {{A, B, C, X(39728), X(57785)}}, {{A, B, C, X(42326), X(43758)}}, {{A, B, C, X(55987), X(56030)}}

X(60259) = X(4)X(7767)∩X(83)X(5304)

Barycentrics    ((a^2-b^2)^2-6*(a^2+b^2)*c^2-3*c^4)*(a^4-3*b^4-6*b^2*c^2+c^4-2*a^2*(3*b^2+c^2)) : :

X(60259) lies on the Kiepert hyperbola and on these lines: {4, 7767}, {69, 14484}, {76, 33202}, {83, 5304}, {98, 14928}, {141, 60201}, {183, 3424}, {193, 60190}, {262, 14994}, {305, 59764}, {325, 53099}, {385, 5395}, {598, 9740}, {671, 33210}, {1007, 60333}, {1916, 3620}, {2052, 39998}, {2996, 16990}, {3314, 60260}, {3407, 37667}, {3543, 54716}, {3926, 10159}, {5485, 11287}, {6194, 60115}, {7763, 60278}, {7788, 54521}, {7799, 60131}, {8357, 60219}, {8362, 18840}, {8974, 60204}, {9464, 59763}, {10302, 32836}, {10513, 60118}, {11160, 54487}, {13950, 60205}, {14492, 54132}, {16986, 60285}, {16988, 32841}, {18842, 32893}, {32829, 56059}, {32831, 60183}, {32832, 43527}, {32833, 60277}, {32837, 60279}, {32838, 60100}, {32867, 60182}, {32868, 43676}, {32869, 60143}, {32885, 60238}, {32886, 53109}, {32888, 60250}, {32894, 43681}, {34229, 43537}, {37671, 54520}, {37688, 60102}, {37874, 40022}, {51171, 60129}

X(60259) = isotomic conjugate of X(37665)
X(60259) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(33202)}}, {{A, B, C, X(69), X(15589)}}, {{A, B, C, X(141), X(393)}}, {{A, B, C, X(183), X(37668)}}, {{A, B, C, X(193), X(16990)}}, {{A, B, C, X(253), X(308)}}, {{A, B, C, X(305), X(32834)}}, {{A, B, C, X(385), X(3620)}}, {{A, B, C, X(468), X(33210)}}, {{A, B, C, X(599), X(9740)}}, {{A, B, C, X(1239), X(57799)}}, {{A, B, C, X(1799), X(34403)}}, {{A, B, C, X(2998), X(45833)}}, {{A, B, C, X(3108), X(6464)}}, {{A, B, C, X(3266), X(46951)}}, {{A, B, C, X(3314), X(37667)}}, {{A, B, C, X(3926), X(7767)}}, {{A, B, C, X(4232), X(11287)}}, {{A, B, C, X(4590), X(9473)}}, {{A, B, C, X(5481), X(40802)}}, {{A, B, C, X(6353), X(33025)}}, {{A, B, C, X(6664), X(46952)}}, {{A, B, C, X(6995), X(8362)}}, {{A, B, C, X(8024), X(18027)}}, {{A, B, C, X(8801), X(34816)}}, {{A, B, C, X(11059), X(32874)}}, {{A, B, C, X(14994), X(44144)}}, {{A, B, C, X(16986), X(51171)}}, {{A, B, C, X(25322), X(52188)}}, {{A, B, C, X(26235), X(32836)}}, {{A, B, C, X(31360), X(52223)}}, {{A, B, C, X(32830), X(40022)}}, {{A, B, C, X(39749), X(52133)}}, {{A, B, C, X(40330), X(46806)}}, {{A, B, C, X(40511), X(41932)}}, {{A, B, C, X(42286), X(52187)}}, {{A, B, C, X(57725), X(57727)}}

X(60260) = X(4)X(10983)∩X(98)X(193)

Barycentrics    (a^4-6*a^2*b^2+b^4-2*(a^2+b^2)*c^2+5*c^4)*(a^4+5*b^4-2*b^2*c^2+c^4-2*a^2*(b^2+3*c^2)) : :

X(60260) lies on the Kiepert hyperbola and on these lines: {2, 51374}, {4, 10983}, {20, 60117}, {76, 32972}, {83, 31400}, {98, 193}, {148, 9742}, {325, 2996}, {385, 43537}, {598, 53142}, {1003, 18842}, {3314, 60259}, {3407, 37665}, {3424, 7774}, {3543, 54659}, {3620, 60212}, {3839, 54713}, {5395, 7736}, {5485, 33228}, {6054, 54767}, {6421, 60204}, {6422, 60205}, {7612, 37667}, {7710, 54894}, {7777, 14484}, {7783, 18845}, {7785, 54846}, {7807, 18841}, {7837, 54866}, {7887, 18840}, {7925, 60262}, {9732, 14229}, {9733, 14244}, {9744, 54873}, {9770, 41895}, {11160, 11172}, {11163, 53101}, {14494, 37071}, {15589, 60128}, {17005, 60333}, {17008, 60102}, {18287, 43670}, {18843, 19687}, {32955, 60183}, {33191, 54616}, {35940, 60133}, {37668, 54122}, {37689, 60104}, {50974, 60150}, {51580, 54833}, {54859, 54996}

X(60260) = isotomic conjugate of X(37667)
X(60260) = trilinear pole of line {44395, 523}}
X(60260) = pole of line {1007, 60260} with respect to the Kiepert hyperbola
X(60260) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(10983)}}, {{A, B, C, X(6), X(56334)}}, {{A, B, C, X(25), X(32972)}}, {{A, B, C, X(66), X(36953)}}, {{A, B, C, X(193), X(253)}}, {{A, B, C, X(264), X(6339)}}, {{A, B, C, X(305), X(56339)}}, {{A, B, C, X(393), X(40429)}}, {{A, B, C, X(427), X(32973)}}, {{A, B, C, X(858), X(35940)}}, {{A, B, C, X(1003), X(52284)}}, {{A, B, C, X(1007), X(37667)}}, {{A, B, C, X(1297), X(9732)}}, {{A, B, C, X(1502), X(46952)}}, {{A, B, C, X(2987), X(40801)}}, {{A, B, C, X(3108), X(6421)}}, {{A, B, C, X(3314), X(37665)}}, {{A, B, C, X(3620), X(7736)}}, {{A, B, C, X(4232), X(33228)}}, {{A, B, C, X(4518), X(54123)}}, {{A, B, C, X(6340), X(9289)}}, {{A, B, C, X(6353), X(32980)}}, {{A, B, C, X(6464), X(14489)}}, {{A, B, C, X(6995), X(7887)}}, {{A, B, C, X(7378), X(7807)}}, {{A, B, C, X(7408), X(32955)}}, {{A, B, C, X(7409), X(33189)}}, {{A, B, C, X(7774), X(37668)}}, {{A, B, C, X(7777), X(15589)}}, {{A, B, C, X(7925), X(37689)}}, {{A, B, C, X(8024), X(31400)}}, {{A, B, C, X(8801), X(42407)}}, {{A, B, C, X(8889), X(32981)}}, {{A, B, C, X(9229), X(52224)}}, {{A, B, C, X(9307), X(57857)}}, {{A, B, C, X(9770), X(11160)}}, {{A, B, C, X(34288), X(56057)}}, {{A, B, C, X(36889), X(41909)}}, {{A, B, C, X(36897), X(38262)}}, {{A, B, C, X(37174), X(56370)}}, {{A, B, C, X(42008), X(53142)}}
X(60260) = barycentric product X(i)*X(j) for these (i, j): {42377, 69}
X(60260) = barycentric quotient X(i)/X(j) for these (i, j): {2, 37667}, {42377, 4}

X(60261) = X(10)X(3944)∩X(192)X(226)

Barycentrics    (a^2*(b+c)+(b-2*c)*c*(b+c)+a*(b^2-b*c-c^2))*(a^2*(b+c)-b*(2*b-c)*(b+c)-a*(b^2+b*c-c^2)) : :

X(60261) lies on the Kiepert hyperbola and on these lines: {4, 20018}, {10, 3944}, {98, 48918}, {192, 226}, {193, 60167}, {194, 10478}, {312, 60244}, {321, 4110}, {908, 37865}, {1029, 31034}, {1211, 56210}, {1446, 30545}, {1654, 60206}, {1751, 17349}, {3663, 56226}, {3936, 60257}, {4052, 50100}, {4195, 4653}, {4352, 26109}, {5712, 6625}, {5739, 54119}, {7783, 19701}, {10446, 13478}, {13576, 20557}, {14534, 17379}, {14555, 60149}, {17232, 40012}, {17238, 60084}, {17300, 60076}, {17778, 60156}, {18134, 60236}, {22019, 56214}, {24624, 37652}, {26096, 60153}, {28606, 30588}, {34020, 40031}, {37759, 60088}, {40718, 59297}, {48817, 54624}, {48850, 60079}, {50133, 54768}

X(60261) = isotomic conjugate of X(37683)
X(60261) = trilinear pole of line {4147, 20316}
X(60261) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 37683}, {48, 16066}, {560, 30092}
X(60261) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 37683}, {1249, 16066}, {6374, 30092}
X(60261) = pole of line {4417, 60261} with respect to the Kiepert hyperbola
X(60261) = pole of line {17490, 59303} with respect to the dual conic of Yff parabola
X(60261) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(7018)}}, {{A, B, C, X(92), X(330)}}, {{A, B, C, X(192), X(312)}}, {{A, B, C, X(257), X(44733)}}, {{A, B, C, X(278), X(3944)}}, {{A, B, C, X(306), X(9289)}}, {{A, B, C, X(313), X(1246)}}, {{A, B, C, X(469), X(4195)}}, {{A, B, C, X(561), X(39741)}}, {{A, B, C, X(941), X(2171)}}, {{A, B, C, X(966), X(26109)}}, {{A, B, C, X(987), X(1255)}}, {{A, B, C, X(1211), X(17379)}}, {{A, B, C, X(1654), X(5712)}}, {{A, B, C, X(2895), X(31034)}}, {{A, B, C, X(3663), X(36606)}}, {{A, B, C, X(3936), X(37652)}}, {{A, B, C, X(4102), X(56353)}}, {{A, B, C, X(4373), X(6063)}}, {{A, B, C, X(4383), X(17232)}}, {{A, B, C, X(4417), X(37683)}}, {{A, B, C, X(4653), X(4671)}}, {{A, B, C, X(5739), X(17778)}}, {{A, B, C, X(5741), X(37684)}}, {{A, B, C, X(6557), X(28659)}}, {{A, B, C, X(6630), X(39696)}}, {{A, B, C, X(7033), X(56124)}}, {{A, B, C, X(7249), X(40028)}}, {{A, B, C, X(7361), X(18359)}}, {{A, B, C, X(8049), X(30635)}}, {{A, B, C, X(8056), X(20568)}}, {{A, B, C, X(14555), X(17300)}}, {{A, B, C, X(17230), X(42043)}}, {{A, B, C, X(17349), X(18134)}}, {{A, B, C, X(17947), X(34277)}}, {{A, B, C, X(20557), X(46108)}}, {{A, B, C, X(27252), X(27319)}}, {{A, B, C, X(27339), X(31053)}}, {{A, B, C, X(27494), X(30710)}}, {{A, B, C, X(31037), X(37685)}}, {{A, B, C, X(31060), X(34020)}}, {{A, B, C, X(35058), X(39768)}}, {{A, B, C, X(39695), X(55024)}}, {{A, B, C, X(39729), X(56224)}}, {{A, B, C, X(54123), X(56086)}}, {{A, B, C, X(56163), X(57947)}}
X(60261) = barycentric quotient X(i)/X(j) for these (i, j): {2, 37683}, {4, 16066}, {76, 30092}

X(60262) = X(2)X(10542)∩X(4)X(6390)

Barycentrics    (3*(a^2-b^2)^2-2*(a^2+b^2)*c^2+7*c^4)*(3*a^4+7*b^4-2*b^2*c^2+3*c^4-2*a^2*(b^2+3*c^2)) : :

X(60262) lies on the Kiepert hyperbola and on these lines: {2, 10542}, {3, 54859}, {4, 6390}, {20, 60140}, {69, 43537}, {76, 33199}, {83, 32829}, {98, 37668}, {183, 60102}, {194, 54751}, {315, 54800}, {325, 3424}, {598, 7763}, {671, 3926}, {1007, 14484}, {2052, 3266}, {2996, 32840}, {3265, 5466}, {3620, 60128}, {5304, 60093}, {5392, 9464}, {5395, 7777}, {5485, 11318}, {6337, 54894}, {7612, 15589}, {7769, 60239}, {7778, 60201}, {7799, 17503}, {7836, 54916}, {7925, 60260}, {7931, 32872}, {8024, 54636}, {8361, 18840}, {8369, 18842}, {8587, 11160}, {9740, 60103}, {10159, 32838}, {10302, 32828}, {10513, 60336}, {11059, 37874}, {11159, 60281}, {12117, 54659}, {18841, 32871}, {20081, 54750}, {32458, 60073}, {32532, 37350}, {32832, 60277}, {32833, 60228}, {32834, 60143}, {32836, 60216}, {32837, 45103}, {32839, 60238}, {32841, 41895}, {32867, 60279}, {32873, 54639}, {32876, 53106}, {32877, 60250}, {32880, 43681}, {32881, 54476}, {32884, 60100}, {32886, 60210}, {32889, 60146}, {33197, 54616}, {34254, 54496}, {34803, 60333}, {37667, 60104}, {37688, 53859}, {37689, 60263}, {43528, 51171}, {51373, 60095}, {53784, 60133}

X(60262) = isotomic conjugate of X(37689)
X(60262) = pole of line {37690, 60262} with respect to the Kiepert hyperbola
X(60262) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(10542)}}, {{A, B, C, X(25), X(33199)}}, {{A, B, C, X(111), X(6464)}}, {{A, B, C, X(253), X(18023)}}, {{A, B, C, X(305), X(32831)}}, {{A, B, C, X(325), X(37668)}}, {{A, B, C, X(393), X(25322)}}, {{A, B, C, X(427), X(33181)}}, {{A, B, C, X(1007), X(15589)}}, {{A, B, C, X(3265), X(3266)}}, {{A, B, C, X(3620), X(7777)}}, {{A, B, C, X(4232), X(11318)}}, {{A, B, C, X(5304), X(7778)}}, {{A, B, C, X(6339), X(9227)}}, {{A, B, C, X(6393), X(56267)}}, {{A, B, C, X(6995), X(8361)}}, {{A, B, C, X(7378), X(32954)}}, {{A, B, C, X(7409), X(33195)}}, {{A, B, C, X(7763), X(9464)}}, {{A, B, C, X(7925), X(37667)}}, {{A, B, C, X(7931), X(51171)}}, {{A, B, C, X(8024), X(32829)}}, {{A, B, C, X(8369), X(52284)}}, {{A, B, C, X(8889), X(33201)}}, {{A, B, C, X(9740), X(22110)}}, {{A, B, C, X(10603), X(52581)}}, {{A, B, C, X(11059), X(32830)}}, {{A, B, C, X(26235), X(32828)}}, {{A, B, C, X(30786), X(34403)}}, {{A, B, C, X(32838), X(39998)}}, {{A, B, C, X(32840), X(57518)}}, {{A, B, C, X(37350), X(53857)}}, {{A, B, C, X(37689), X(37690)}}, {{A, B, C, X(42286), X(46952)}}, {{A, B, C, X(45833), X(56334)}}

X(60263) = X(76)X(32970)∩X(83)X(32969)

Barycentrics    (5*a^4-2*a^2*b^2+5*b^4-4*(a^2+b^2)*c^2+3*c^4)*(5*a^4+3*b^4-4*b^2*c^2+5*c^4-2*a^2*(2*b^2+c^2)) : :

X(60263) lies on the Kiepert hyperbola and on these lines: {76, 32970}, {83, 32969}, {230, 40824}, {598, 32984}, {671, 7857}, {1007, 56064}, {1975, 5485}, {2996, 16925}, {3091, 54894}, {3525, 60126}, {3552, 38259}, {3618, 7608}, {3972, 54568}, {5067, 60148}, {5071, 54805}, {5395, 32961}, {5921, 43537}, {6680, 54915}, {7735, 8781}, {7736, 60178}, {7792, 14494}, {7806, 60234}, {8860, 60143}, {10155, 11174}, {11172, 44401}, {16984, 60190}, {16989, 60233}, {16990, 60231}, {17004, 60232}, {17008, 43529}, {18840, 32959}, {18841, 32958}, {18845, 32966}, {33006, 53101}, {33007, 41895}, {33239, 53105}, {34229, 60213}, {37637, 60212}, {37689, 60262}, {39141, 60128}, {42011, 59373}, {52942, 54896}

X(60263) = isotomic conjugate of X(37690)
X(60263) = trilinear pole of line {47546, 523}
X(60263) = X(i)-vertex conjugate of X(j) for these {i, j}: {25, 40824}
X(60263) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(32970)}}, {{A, B, C, X(66), X(56057)}}, {{A, B, C, X(69), X(57926)}}, {{A, B, C, X(111), X(56004)}}, {{A, B, C, X(230), X(7735)}}, {{A, B, C, X(393), X(41909)}}, {{A, B, C, X(427), X(32969)}}, {{A, B, C, X(468), X(32985)}}, {{A, B, C, X(842), X(56362)}}, {{A, B, C, X(2165), X(9516)}}, {{A, B, C, X(3552), X(38282)}}, {{A, B, C, X(3618), X(37688)}}, {{A, B, C, X(4590), X(44556)}}, {{A, B, C, X(5094), X(32984)}}, {{A, B, C, X(6353), X(16925)}}, {{A, B, C, X(6995), X(32959)}}, {{A, B, C, X(7378), X(32958)}}, {{A, B, C, X(7736), X(37637)}}, {{A, B, C, X(7792), X(34229)}}, {{A, B, C, X(7806), X(17008)}}, {{A, B, C, X(7857), X(52898)}}, {{A, B, C, X(8797), X(40416)}}, {{A, B, C, X(8889), X(32961)}}, {{A, B, C, X(9307), X(56360)}}, {{A, B, C, X(9770), X(44401)}}, {{A, B, C, X(10603), X(44181)}}, {{A, B, C, X(16984), X(16990)}}, {{A, B, C, X(16989), X(17004)}}, {{A, B, C, X(32966), X(52299)}}, {{A, B, C, X(33007), X(52290)}}, {{A, B, C, X(33239), X(37453)}}, {{A, B, C, X(34288), X(36953)}}, {{A, B, C, X(36889), X(40429)}}, {{A, B, C, X(37187), X(37466)}}, {{A, B, C, X(40405), X(51316)}}, {{A, B, C, X(56042), X(57726)}}, {{A, B, C, X(56353), X(57727)}}

X(60264) = X(2)X(1240)∩X(4)X(7017)

Barycentrics    b^2*c^2*(b+c)*(a^2+a*c+b*(b+c))*(a^2+a*b+c*(b+c)) : :

X(60264) lies on the Kiepert hyperbola and on these lines: {2, 1240}, {4, 7017}, {10, 14815}, {75, 60084}, {76, 3782}, {83, 41232}, {98, 8707}, {226, 313}, {312, 2051}, {321, 18202}, {594, 34258}, {1089, 43677}, {1220, 30116}, {1230, 4080}, {1237, 6358}, {2298, 60082}, {2321, 37865}, {3597, 3695}, {3662, 40013}, {3687, 4033}, {3701, 60321}, {3948, 60230}, {3969, 60087}, {4444, 51859}, {11611, 27808}, {13478, 19807}, {14534, 17790}, {17758, 20917}, {27801, 60197}, {29641, 45964}, {31643, 60076}, {32014, 40827}, {36147, 60134}, {40718, 59315}, {42029, 60276}, {42032, 54728}, {42033, 54699}, {56803, 60088}, {58027, 60085}

X(60264) = isotomic conjugate of X(40153)
X(60264) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 40153}, {32, 54308}, {58, 2300}, {163, 6371}, {560, 16705}, {593, 3725}, {604, 4267}, {662, 57157}, {849, 2092}, {960, 16947}, {1106, 46889}, {1193, 1333}, {1397, 17185}, {1408, 2269}, {1412, 20967}, {1437, 2354}, {1474, 22345}, {1501, 16739}, {1576, 48131}, {2203, 22097}, {2206, 3666}, {4509, 14574}, {7342, 21033}, {24471, 57657}, {46877, 52410}, {53280, 57129}
X(60264) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 40153}, {10, 2300}, {37, 1193}, {115, 6371}, {1084, 57157}, {3161, 4267}, {4075, 2092}, {4858, 48131}, {6374, 16705}, {6376, 54308}, {6552, 46889}, {6741, 52326}, {36901, 3004}, {40599, 20967}, {40603, 3666}, {51574, 22345}, {59577, 2269}
X(60264) = X(i)-cross conjugate of X(j) for these {i, j}: {321, 30710}, {4036, 27808}, {4391, 4033}, {5051, 264}
X(60264) = pole of line {14412, 39015} with respect to the dual conic of Wallace hyperbola
X(60264) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(92), X(56186)}}, {{A, B, C, X(313), X(3596)}}, {{A, B, C, X(561), X(56251)}}, {{A, B, C, X(994), X(39700)}}, {{A, B, C, X(1214), X(31785)}}, {{A, B, C, X(2985), X(38955)}}, {{A, B, C, X(3687), X(4391)}}, {{A, B, C, X(3701), X(59761)}}, {{A, B, C, X(3782), X(17053)}}, {{A, B, C, X(3963), X(6358)}}, {{A, B, C, X(4036), X(17790)}}, {{A, B, C, X(4674), X(53083)}}, {{A, B, C, X(7141), X(28654)}}, {{A, B, C, X(14815), X(17946)}}, {{A, B, C, X(15523), X(41232)}}, {{A, B, C, X(17038), X(56122)}}, {{A, B, C, X(21688), X(40859)}}, {{A, B, C, X(30116), X(56810)}}, {{A, B, C, X(35058), X(46720)}}, {{A, B, C, X(39694), X(42471)}}, {{A, B, C, X(44733), X(56175)}}, {{A, B, C, X(56046), X(56133)}}
X(60264) = barycentric product X(i)*X(j) for these (i, j): {10, 1240}, {850, 8707}, {1220, 313}, {2298, 27801}, {3596, 60086}, {14534, 28654}, {14624, 76}, {20948, 36147}, {27808, 4581}, {30710, 321}, {31643, 3701}, {32736, 44173}, {40827, 594}, {57162, 6386}, {57853, 7141}
X(60264) = barycentric quotient X(i)/X(j) for these (i, j): {2, 40153}, {8, 4267}, {10, 1193}, {37, 2300}, {72, 22345}, {75, 54308}, {76, 16705}, {210, 20967}, {306, 22097}, {312, 17185}, {313, 4357}, {321, 3666}, {341, 46877}, {346, 46889}, {349, 3674}, {512, 57157}, {523, 6371}, {561, 16739}, {594, 2092}, {756, 3725}, {850, 3004}, {961, 1408}, {1089, 2292}, {1220, 58}, {1237, 59509}, {1240, 86}, {1441, 24471}, {1577, 48131}, {1791, 1437}, {1826, 2354}, {2298, 1333}, {2321, 2269}, {2363, 849}, {3694, 22074}, {3695, 22076}, {3700, 52326}, {3701, 960}, {3704, 1682}, {3952, 53280}, {3963, 28369}, {4033, 3882}, {4036, 50330}, {4086, 17420}, {4377, 4503}, {4581, 3733}, {6057, 40966}, {6648, 4565}, {7140, 44092}, {7141, 429}, {8707, 110}, {14534, 593}, {14624, 6}, {15420, 7254}, {20948, 4509}, {27801, 20911}, {27808, 53332}, {28654, 1211}, {30710, 81}, {30713, 3687}, {31643, 1014}, {32736, 1576}, {34388, 41003}, {36147, 163}, {40827, 1509}, {41013, 1829}, {52623, 21124}, {53008, 40976}, {57162, 667}, {60086, 56}, {60244, 27455}

X(60265) = X(2)X(277)∩X(4)X(518)

Barycentrics    b*(a^2-2*a*b+(b-c)^2)*c*(b+c)*(a^2+(b-c)^2-2*a*c) : :

X(60265) lies on the Kiepert hyperbola and on these lines: {2, 277}, {4, 518}, {9, 60075}, {10, 53510}, {72, 13576}, {75, 32022}, {76, 57791}, {98, 1292}, {226, 3970}, {262, 6990}, {329, 60155}, {519, 54517}, {527, 54882}, {536, 54728}, {671, 54987}, {1111, 51972}, {1441, 3991}, {1751, 16552}, {2052, 46108}, {2191, 43531}, {3811, 56144}, {4059, 40154}, {4385, 10005}, {4515, 16732}, {10916, 43672}, {17107, 60085}, {20927, 41785}, {22021, 40515}, {24624, 37206}, {28609, 54586}, {31926, 40395}, {34289, 48380}, {34505, 54691}, {34619, 54758}, {37086, 57721}, {37284, 60080}, {37445, 57722}, {57656, 60082}

X(60265) = isotomic conjugate of X(41610)
X(60265) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 41610}, {48, 4233}, {58, 218}, {81, 21059}, {163, 3309}, {284, 1617}, {344, 2206}, {593, 4878}, {662, 8642}, {849, 3991}, {1333, 3870}, {1408, 55337}, {1412, 6600}, {1437, 7719}, {1445, 2194}, {1576, 4468}, {2150, 41539}, {2299, 23144}, {2440, 54353}, {5546, 51652}, {6604, 57657}, {21945, 23357}, {24562, 32676}
X(60265) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 41610}, {10, 218}, {37, 3870}, {115, 3309}, {226, 23144}, {1084, 8642}, {1214, 1445}, {1249, 4233}, {4075, 3991}, {4858, 4468}, {15526, 24562}, {40586, 21059}, {40590, 1617}, {40599, 6600}, {40603, 344}, {40622, 43049}, {56325, 41539}, {56905, 41611}, {59577, 55337}, {59608, 4350}
X(60265) = X(i)-cross conjugate of X(j) for these {i, j}: {210, 1441}, {38930, 6757}
X(60265) = pole of line {3309, 26546} with respect to the Steiner circumellipse
X(60265) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(9), X(3970)}}, {{A, B, C, X(37), X(16601)}}, {{A, B, C, X(65), X(37597)}}, {{A, B, C, X(72), X(518)}}, {{A, B, C, X(210), X(3991)}}, {{A, B, C, X(277), X(57791)}}, {{A, B, C, X(297), X(3651)}}, {{A, B, C, X(313), X(3673)}}, {{A, B, C, X(335), X(943)}}, {{A, B, C, X(349), X(41013)}}, {{A, B, C, X(442), X(31926)}}, {{A, B, C, X(458), X(6990)}}, {{A, B, C, X(1441), X(2481)}}, {{A, B, C, X(1577), X(3701)}}, {{A, B, C, X(1903), X(25066)}}, {{A, B, C, X(2321), X(21096)}}, {{A, B, C, X(2795), X(2799)}}, {{A, B, C, X(3700), X(4515)}}, {{A, B, C, X(4059), X(53478)}}, {{A, B, C, X(4391), X(6598)}}, {{A, B, C, X(4420), X(7265)}}, {{A, B, C, X(5665), X(57725)}}, {{A, B, C, X(7178), X(56174)}}, {{A, B, C, X(14618), X(27801)}}, {{A, B, C, X(15412), X(25257)}}, {{A, B, C, X(16552), X(22021)}}, {{A, B, C, X(17924), X(24781)}}, {{A, B, C, X(25242), X(42027)}}, {{A, B, C, X(25583), X(57924)}}, {{A, B, C, X(42704), X(48380)}}
X(60265) = barycentric product X(i)*X(j) for these (i, j): {37, 57791}, {277, 321}, {523, 54987}, {1292, 850}, {1441, 6601}, {1577, 37206}, {2191, 313}, {3701, 40154}, {17107, 30713}, {27801, 57656}
X(60265) = barycentric quotient X(i)/X(j) for these (i, j): {2, 41610}, {4, 4233}, {10, 3870}, {12, 41539}, {37, 218}, {42, 21059}, {65, 1617}, {210, 6600}, {226, 1445}, {277, 81}, {321, 344}, {349, 21609}, {429, 41611}, {512, 8642}, {523, 3309}, {525, 24562}, {594, 3991}, {756, 4878}, {1109, 21945}, {1214, 23144}, {1292, 110}, {1441, 6604}, {1446, 17093}, {1577, 4468}, {1826, 7719}, {2191, 58}, {2321, 55337}, {3668, 4350}, {3925, 15185}, {4017, 51652}, {4052, 27819}, {4077, 31605}, {4086, 44448}, {6601, 21}, {7178, 43049}, {14268, 4228}, {16732, 4904}, {17107, 1412}, {17757, 51378}, {21044, 38375}, {37206, 662}, {40154, 1014}, {53510, 41785}, {54987, 99}, {55261, 2440}, {57469, 3286}, {57656, 1333}, {57791, 274}

X(60266) = X(2)X(14961)∩X(4)X(2393)

Barycentrics    b^2*c^2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4-4*a^2*b^2+b^4-c^4)*(a^4-b^4-4*a^2*c^2+c^4) : :

X(60266) lies on the Kiepert hyperbola and on these lines: {2, 14961}, {4, 2393}, {6, 60133}, {83, 54412}, {98, 378}, {262, 403}, {264, 671}, {297, 34289}, {324, 54778}, {381, 54919}, {458, 2986}, {598, 37855}, {1235, 2996}, {2052, 5523}, {3407, 15014}, {5094, 60317}, {5254, 43678}, {5286, 52583}, {5392, 47286}, {5466, 14618}, {6504, 40684}, {6623, 14484}, {7607, 37118}, {7841, 54796}, {10604, 11059}, {11165, 34336}, {13608, 43537}, {15652, 60125}, {16080, 40814}, {18842, 40065}, {20774, 60140}, {24624, 37217}, {27377, 54684}, {34505, 54513}, {35908, 60119}, {37077, 54632}, {38259, 44142}, {41511, 58078}, {41760, 46105}, {51481, 60256}, {52281, 54913}, {52282, 54864}, {52713, 60114}, {54347, 57466}

X(60266) = isotomic conjugate of X(41614)
X(60266) = trilinear pole of line {42665, 523}
X(60266) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 41614}, {48, 1995}, {63, 19136}, {163, 30209}, {1576, 14209}, {9247, 11185}, {36060, 53777}
X(60266) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 41614}, {115, 30209}, {1249, 1995}, {1560, 53777}, {3162, 19136}, {4858, 14209}, {40938, 29959}
X(60266) = X(i)-cross conjugate of X(j) for these {i, j}: {5094, 264}, {10602, 305}, {23327, 18018}, {43620, 847}, {54347, 2}, {57466, 60317}
X(60266) = pole of line {30209, 53777} with respect to the polar circle
X(60266) = pole of line {54347, 57466} with respect to the Kiepert hyperbola
X(60266) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(50649)}}, {{A, B, C, X(6), X(525)}}, {{A, B, C, X(54), X(9289)}}, {{A, B, C, X(64), X(36952)}}, {{A, B, C, X(74), X(42313)}}, {{A, B, C, X(249), X(18880)}}, {{A, B, C, X(257), X(1063)}}, {{A, B, C, X(264), X(10604)}}, {{A, B, C, X(276), X(847)}}, {{A, B, C, X(290), X(57819)}}, {{A, B, C, X(297), X(378)}}, {{A, B, C, X(335), X(1061)}}, {{A, B, C, X(403), X(458)}}, {{A, B, C, X(1041), X(57725)}}, {{A, B, C, X(1194), X(15652)}}, {{A, B, C, X(1235), X(54412)}}, {{A, B, C, X(5094), X(37855)}}, {{A, B, C, X(5117), X(15014)}}, {{A, B, C, X(5254), X(8743)}}, {{A, B, C, X(5286), X(41361)}}, {{A, B, C, X(6344), X(42298)}}, {{A, B, C, X(6623), X(52288)}}, {{A, B, C, X(8795), X(57908)}}, {{A, B, C, X(9307), X(15412)}}, {{A, B, C, X(10419), X(53200)}}, {{A, B, C, X(11165), X(15471)}}, {{A, B, C, X(14376), X(14457)}}, {{A, B, C, X(18018), X(46140)}}, {{A, B, C, X(18532), X(30541)}}, {{A, B, C, X(31360), X(57388)}}, {{A, B, C, X(32708), X(53202)}}, {{A, B, C, X(34403), X(45011)}}, {{A, B, C, X(37118), X(52282)}}, {{A, B, C, X(39269), X(57496)}}, {{A, B, C, X(39841), X(57504)}}, {{A, B, C, X(40814), X(52661)}}, {{A, B, C, X(41231), X(45179)}}, {{A, B, C, X(41370), X(43448)}}, {{A, B, C, X(41614), X(54347)}}, {{A, B, C, X(44557), X(57655)}}, {{A, B, C, X(46199), X(54114)}}, {{A, B, C, X(46259), X(54973)}}, {{A, B, C, X(47286), X(57065)}}, {{A, B, C, X(54124), X(57829)}}
X(60266) = barycentric product X(i)*X(j) for these (i, j): {264, 5486}, {1577, 37217}, {18018, 51831}, {30247, 850}, {32133, 58782}, {44146, 60317}
X(60266) = barycentric quotient X(i)/X(j) for these (i, j): {2, 41614}, {4, 1995}, {25, 19136}, {264, 11185}, {427, 29959}, {468, 53777}, {523, 30209}, {1577, 14209}, {5094, 8542}, {5486, 3}, {30247, 110}, {32133, 55977}, {32709, 32729}, {36115, 36142}, {37217, 662}, {37778, 37855}, {37981, 35370}, {51831, 22}, {57466, 14961}, {60317, 895}

X(60267) = X(2)X(2321)∩X(4)X(3679)

Barycentrics    (b+c)*(a+3*b+c)*(a+b+3*c) : :

X(60267) lies on the Kiepert hyperbola and on these lines: {2, 2321}, {4, 3679}, {8, 60077}, {9, 60168}, {10, 3175}, {37, 60243}, {75, 40012}, {76, 30713}, {83, 50095}, {98, 8694}, {210, 54668}, {226, 594}, {306, 30588}, {321, 56253}, {519, 2334}, {527, 60156}, {536, 60084}, {551, 56985}, {553, 60076}, {671, 41816}, {1029, 17781}, {1211, 4052}, {1334, 60092}, {1446, 6358}, {1751, 17281}, {3452, 60087}, {3661, 60236}, {3710, 43533}, {3714, 53004}, {3929, 60167}, {3971, 59261}, {4035, 31025}, {4049, 23879}, {4058, 31993}, {4080, 56810}, {4082, 4733}, {4096, 50312}, {4102, 29574}, {4104, 11599}, {4114, 17118}, {4444, 48399}, {4527, 58381}, {4606, 5325}, {4654, 57826}, {4669, 60078}, {4677, 54624}, {4685, 40718}, {4745, 60079}, {4848, 60086}, {4980, 40013}, {5257, 60203}, {6625, 29615}, {10159, 19796}, {13478, 50048}, {14534, 33766}, {16833, 18841}, {17294, 58012}, {17330, 54676}, {17346, 54549}, {17355, 19723}, {17758, 29594}, {28609, 60170}, {31142, 45100}, {31143, 60139}, {31327, 49757}, {32022, 42032}, {34074, 60134}, {34258, 42034}, {37631, 55949}, {38127, 54035}, {41140, 43527}, {42025, 50292}, {42033, 60235}, {42708, 43682}, {46917, 60336}, {46918, 59584}, {49724, 50118}, {50047, 57719}, {50093, 54119}, {50107, 60206}, {50115, 60082}, {51066, 54786}, {51072, 54623}, {57663, 60085}, {59413, 60327}

X(60267) = isotomic conjugate of X(42028)
X(60267) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 42028}, {48, 31903}, {58, 1449}, {110, 4790}, {163, 4778}, {284, 3361}, {391, 1408}, {593, 37593}, {662, 58140}, {692, 48580}, {849, 5257}, {1014, 4258}, {1169, 4719}, {1333, 3616}, {1412, 4512}, {1474, 4652}, {1576, 4801}, {1790, 5338}, {2150, 3671}, {2194, 21454}, {2206, 19804}, {4556, 4822}, {4673, 16947}, {4832, 52935}, {7342, 42712}, {17553, 28607}
X(60267) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 42028}, {10, 1449}, {37, 3616}, {115, 4778}, {244, 4790}, {1084, 58140}, {1086, 48580}, {1214, 21454}, {1249, 31903}, {4075, 5257}, {4858, 4801}, {6741, 4765}, {36911, 17553}, {40590, 3361}, {40599, 4512}, {40603, 19804}, {40622, 30723}, {51574, 4652}, {52872, 4700}, {55056, 53586}, {55065, 4841}, {56325, 3671}, {59577, 391}
X(60267) = X(i)-Ceva conjugate of X(j) for these {i, j}: {5936, 56237}
X(60267) = X(i)-cross conjugate of X(j) for these {i, j}: {4656, 226}, {50457, 4033}
X(60267) = pole of line {28308, 58140} with respect to the orthoptic circle of the Steiner inellipse
X(60267) = pole of line {4656, 60267} with respect to the Kiepert hyperbola
X(60267) = pole of line {4778, 48551} with respect to the Steiner inellipse
X(60267) = pole of line {1698, 39711} with respect to the dual conic of Yff parabola
X(60267) = pole of line {4773, 4839} with respect to the dual conic of Wallace hyperbola
X(60267) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(37), X(3247)}}, {{A, B, C, X(57), X(56174)}}, {{A, B, C, X(65), X(39948)}}, {{A, B, C, X(75), X(3175)}}, {{A, B, C, X(92), X(39708)}}, {{A, B, C, X(306), X(3679)}}, {{A, B, C, X(313), X(4967)}}, {{A, B, C, X(519), X(23879)}}, {{A, B, C, X(523), X(17133)}}, {{A, B, C, X(524), X(41816)}}, {{A, B, C, X(525), X(28194)}}, {{A, B, C, X(553), X(4647)}}, {{A, B, C, X(594), X(2321)}}, {{A, B, C, X(903), X(56351)}}, {{A, B, C, X(1211), X(4848)}}, {{A, B, C, X(1214), X(7991)}}, {{A, B, C, X(1427), X(56159)}}, {{A, B, C, X(1441), X(32087)}}, {{A, B, C, X(3578), X(31143)}}, {{A, B, C, X(3661), X(4685)}}, {{A, B, C, X(3668), X(36588)}}, {{A, B, C, X(3710), X(26942)}}, {{A, B, C, X(3946), X(4854)}}, {{A, B, C, X(3948), X(48399)}}, {{A, B, C, X(3971), X(40848)}}, {{A, B, C, X(3995), X(4980)}}, {{A, B, C, X(4044), X(21020)}}, {{A, B, C, X(4066), X(43260)}}, {{A, B, C, X(4078), X(50312)}}, {{A, B, C, X(4651), X(29594)}}, {{A, B, C, X(4654), X(5257)}}, {{A, B, C, X(4674), X(39980)}}, {{A, B, C, X(5224), X(19722)}}, {{A, B, C, X(6538), X(28654)}}, {{A, B, C, X(7017), X(55076)}}, {{A, B, C, X(7108), X(55091)}}, {{A, B, C, X(8013), X(29574)}}, {{A, B, C, X(9589), X(56382)}}, {{A, B, C, X(11362), X(56944)}}, {{A, B, C, X(15523), X(50095)}}, {{A, B, C, X(16603), X(53663)}}, {{A, B, C, X(17319), X(42027)}}, {{A, B, C, X(21085), X(29615)}}, {{A, B, C, X(25430), X(40023)}}, {{A, B, C, X(31144), X(37631)}}, {{A, B, C, X(31993), X(42034)}}, {{A, B, C, X(36603), X(56135)}}, {{A, B, C, X(36627), X(53013)}}, {{A, B, C, X(39700), X(42285)}}, {{A, B, C, X(41809), X(42025)}}, {{A, B, C, X(42033), X(42708)}}, {{A, B, C, X(48628), X(48644)}}, {{A, B, C, X(50083), X(57725)}}, {{A, B, C, X(52651), X(56192)}}, {{A, B, C, X(56037), X(56213)}}
X(60267) = barycentric product X(i)*X(j) for these (i, j): {10, 5936}, {37, 40023}, {226, 56086}, {523, 53658}, {850, 8694}, {1089, 56048}, {1441, 4866}, {1577, 4606}, {2321, 57826}, {2334, 313}, {3700, 4624}, {3952, 58860}, {4024, 4633}, {4033, 47915}, {4036, 4614}, {4627, 52623}, {20948, 34074}, {25430, 321}, {27797, 58859}, {30713, 57663}, {34820, 349}, {53008, 57873}, {56204, 6358}, {56237, 75}
X(60267) = barycentric quotient X(i)/X(j) for these (i, j): {2, 42028}, {4, 31903}, {10, 3616}, {12, 3671}, {37, 1449}, {65, 3361}, {72, 4652}, {210, 4512}, {226, 21454}, {321, 19804}, {512, 58140}, {514, 48580}, {523, 4778}, {594, 5257}, {661, 4790}, {756, 37593}, {1334, 4258}, {1577, 4801}, {1824, 5338}, {2292, 4719}, {2321, 391}, {2334, 58}, {3679, 17553}, {3695, 4101}, {3700, 4765}, {3701, 4673}, {3932, 4684}, {3943, 4700}, {3949, 4047}, {3971, 4734}, {3992, 4742}, {3994, 4706}, {4005, 51576}, {4010, 4830}, {4024, 4841}, {4036, 4815}, {4037, 4771}, {4062, 4831}, {4079, 4832}, {4086, 4811}, {4088, 50357}, {4120, 4773}, {4122, 4818}, {4171, 4827}, {4606, 662}, {4614, 52935}, {4624, 4573}, {4627, 4556}, {4633, 4610}, {4705, 4822}, {4841, 53586}, {4866, 21}, {5936, 86}, {6057, 4061}, {7178, 30723}, {8694, 110}, {14626, 3286}, {17757, 51423}, {25430, 81}, {30730, 30728}, {34074, 163}, {34820, 284}, {40023, 274}, {41013, 5342}, {47915, 1019}, {53008, 461}, {53658, 99}, {56048, 757}, {56086, 333}, {56204, 2185}, {56237, 1}, {57663, 1412}, {57826, 1434}, {58859, 26860}, {58860, 7192}
X(60267) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5936, 56086, 25430}

X(60268) = X(2)X(11173)∩X(6)X(11172)

Barycentrics    (a^4+14*a^2*b^2+b^4+8*(a^2+b^2)*c^2-5*c^4)*(a^4-5*b^4+8*b^2*c^2+c^4+2*a^2*(4*b^2+7*c^2)) : :

X(60268) lies on the Kiepert hyperbola and on these lines: {2, 11173}, {6, 11172}, {76, 9770}, {83, 33215}, {98, 59373}, {325, 60143}, {376, 11170}, {381, 54488}, {524, 60212}, {671, 7736}, {1992, 11167}, {2996, 33013}, {3545, 43532}, {5395, 7833}, {5485, 11163}, {7735, 60220}, {8176, 54751}, {8587, 16989}, {8597, 53101}, {9744, 54869}, {10159, 32975}, {11174, 18842}, {11184, 40824}, {14033, 60072}, {14485, 52691}, {15682, 54715}, {16921, 60285}, {18845, 33192}, {21356, 60099}, {25486, 31415}, {26613, 60239}, {32962, 43681}, {32965, 60145}, {32978, 43527}, {33226, 53102}, {33247, 60146}, {38381, 43674}, {41099, 54903}

X(60268) = isotomic conjugate of X(42850)
X(60268) = pole of line {42849, 60268} with respect to the Kiepert hyperbola
X(60268) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(9770)}}, {{A, B, C, X(325), X(57539)}}, {{A, B, C, X(427), X(33215)}}, {{A, B, C, X(428), X(32975)}}, {{A, B, C, X(524), X(7736)}}, {{A, B, C, X(1992), X(11163)}}, {{A, B, C, X(5064), X(32978)}}, {{A, B, C, X(5486), X(13377)}}, {{A, B, C, X(6094), X(38005)}}, {{A, B, C, X(6353), X(33013)}}, {{A, B, C, X(7714), X(16921)}}, {{A, B, C, X(7735), X(11184)}}, {{A, B, C, X(7833), X(8889)}}, {{A, B, C, X(11174), X(21356)}}, {{A, B, C, X(11741), X(29316)}}, {{A, B, C, X(33192), X(52299)}}, {{A, B, C, X(36897), X(46275)}}, {{A, B, C, X(42286), X(46645)}}, {{A, B, C, X(42849), X(42850)}}

X(60269) = X(2)X(7599)∩X(115)X(486)

Barycentrics    4*a^4*b^2*c^2-a^6*(b^2+c^2)-(b^2-c^2)^2*(b^4-3*b^2*c^2+c^4)+a^2*(2*b^6-3*b^4*c^2-3*b^2*c^4+2*c^6)+2*(a^6+a^2*b^2*c^2-a^4*(b^2+c^2)-(b^2-c^2)^2*(b^2+c^2))*S : :

X(60269) lies on these lines: {2, 7599}, {4, 32492}, {76, 6229}, {99, 642}, {115, 486}, {148, 487}, {262, 6564}, {371, 14238}, {372, 60275}, {485, 8997}, {542, 1328}, {543, 55040}, {598, 35822}, {671, 32419}, {1132, 32498}, {1916, 9867}, {2459, 60104}, {2782, 6290}, {2794, 14237}, {3023, 12958}, {3027, 12948}, {3564, 5111}, {5466, 13842}, {6033, 22596}, {6119, 14061}, {6251, 14231}, {6321, 44394}, {6561, 54876}, {6569, 10723}, {7607, 13653}, {7612, 13873}, {9921, 39832}, {9986, 43449}, {10194, 13989}, {10722, 54936}, {12188, 48659}, {12210, 44586}, {12237, 58538}, {12256, 14651}, {12268, 38220}, {12601, 38732}, {12819, 50723}, {13081, 13183}, {13182, 18989}, {13773, 35879}, {13928, 22602}, {13929, 22604}, {13934, 49267}, {14232, 45023}, {14234, 35825}, {14236, 35833}, {14645, 42023}, {15980, 53512}, {19055, 54503}, {22484, 36523}, {22502, 54874}, {22562, 54628}, {32471, 45543}, {35821, 54878}, {35831, 60117}, {35878, 60195}, {35938, 60274}, {38224, 49103}, {39875, 54626}, {43571, 50721}, {48784, 60178}

X(60269) = midpoint of X(i) and X(j) for these {i,j}: {148, 487}, {12188, 48659}
X(60269) = reflection of X(i) in X(j) for these {i,j}: {12237, 58538}, {486, 115}, {6033, 22596}, {99, 642}
X(60269) = isogonal conjugate of X(2460)
X(60269) = isotomic conjugate of X(44364)
X(60269) = trilinear pole of line {615, 523}
X(60269) = X(i)-vertex conjugate of X(j) for these {i, j}: {3455, 60270}
X(60269) = X(i)-cross conjugate of X(j) for these {i, j}: {6321, 60270}, {44394, 2}
X(60269) = pole of line {6321, 44394} with respect to the Kiepert hyperbola
X(60269) = pole of line {2460, 44364} with respect to the Wallace hyperbola
X(60269) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(371), X(9738)}}, {{A, B, C, X(372), X(1505)}}, {{A, B, C, X(690), X(32419)}}, {{A, B, C, X(2459), X(5111)}}, {{A, B, C, X(3455), X(5417)}}, {{A, B, C, X(6564), X(56401)}}, {{A, B, C, X(14498), X(32420)}}, {{A, B, C, X(23698), X(54029)}}

X(60270) = X(2)X(7598)∩X(115)X(485)

Barycentrics    4*a^4*b^2*c^2-a^6*(b^2+c^2)-(b^2-c^2)^2*(b^4-3*b^2*c^2+c^4)+a^2*(2*b^6-3*b^4*c^2-3*b^2*c^4+2*c^6)-2*(a^6+a^2*b^2*c^2-a^4*(b^2+c^2)-(b^2-c^2)^2*(b^2+c^2))*S : :

X(60270) lies on the Kiepert hyperbola and on these lines: {2, 7598}, {4, 32495}, {76, 6228}, {99, 641}, {115, 485}, {148, 488}, {262, 6565}, {371, 60274}, {372, 14234}, {486, 9739}, {542, 1327}, {543, 55041}, {598, 35823}, {671, 32421}, {1131, 32499}, {1916, 9868}, {2460, 60104}, {2782, 6289}, {2794, 14232}, {3023, 12959}, {3027, 12949}, {3564, 5111}, {5466, 13719}, {6033, 22625}, {6118, 14061}, {6250, 14245}, {6321, 44392}, {6560, 54874}, {6568, 10723}, {7607, 13773}, {7612, 13926}, {8997, 10195}, {9922, 39832}, {9987, 43449}, {10722, 54935}, {12188, 48660}, {12211, 44587}, {12238, 58538}, {12257, 14651}, {12269, 38220}, {12602, 38732}, {12818, 50724}, {13082, 13183}, {13182, 18988}, {13653, 35878}, {13875, 22631}, {13876, 22633}, {13882, 49266}, {14237, 45024}, {14238, 35824}, {14240, 35832}, {14645, 42024}, {15980, 53515}, {19056, 54507}, {22485, 36523}, {22501, 54876}, {22563, 54627}, {32470, 45542}, {35820, 54877}, {35830, 60117}, {35939, 60275}, {38224, 49104}, {39876, 54625}, {43570, 50722}, {48785, 60178}

X(60270) = midpoint of X(i) and X(j) for these {i,j}: {148, 488}, {12188, 48660}
X(60270) = reflection of X(i) in X(j) for these {i,j}: {12238, 58538}, {485, 115}, {6033, 22625}, {99, 641}
X(60270) = isogonal conjugate of X(2459)
X(60270) = isotomic conjugate of X(44365)
X(60270) = trilinear pole of line {590, 523}
X(60270) = X(i)-vertex conjugate of X(j) for these {i, j}: {3455, 60269}
X(60270) = X(i)-cross conjugate of X(j) for these {i, j}: {6321, 60269}, {44392, 2}
X(60270) = pole of line {6321, 44392} with respect to the Kiepert hyperbola
X(60270) = pole of line {2459, 44365} with respect to the Wallace hyperbola
X(60270) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(371), X(1504)}}, {{A, B, C, X(372), X(9739)}}, {{A, B, C, X(690), X(32421)}}, {{A, B, C, X(2460), X(5111)}}, {{A, B, C, X(3455), X(5419)}}, {{A, B, C, X(6565), X(56401)}}, {{A, B, C, X(14498), X(32422)}}, {{A, B, C, X(23698), X(54028)}}

X(60271) = X(83)X(543)∩X(148)X(598)

Barycentrics    (a^4+5*a^2*b^2+b^4-(a^2+b^2)*c^2-5*c^4)*(a^4-5*b^4-b^2*c^2+c^4-a^2*(b^2-5*c^2)) : :

X(60271) lies on the Kiepert hyperbola and on these lines: {76, 41135}, {83, 543}, {98, 19924}, {99, 60238}, {114, 54920}, {115, 10302}, {147, 14488}, {148, 598}, {524, 11606}, {542, 60132}, {671, 7779}, {826, 9180}, {1916, 41136}, {1992, 54901}, {5461, 60279}, {5466, 9479}, {5969, 42006}, {5984, 54845}, {6054, 60142}, {6055, 60334}, {6321, 54567}, {7774, 54737}, {8591, 60239}, {8596, 18842}, {8782, 60099}, {8859, 60136}, {9166, 10159}, {9167, 60182}, {9770, 60177}, {9830, 54539}, {11177, 53100}, {14971, 56059}, {19689, 43527}, {20094, 54616}, {32473, 43667}, {35369, 54639}, {36523, 60216}, {41134, 60100}, {43535, 44367}, {45109, 60127}, {52229, 54822}, {54644, 55178}

X(60271) = reflection of X(i) in X(j) for these {i,j}: {10302, 115}
X(60271) = isotomic conjugate of X(44367)
X(60271) = trilinear pole of line {20582, 45692}
X(60271) = pole of line {7840, 60271} with respect to the Kiepert hyperbola
X(60271) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(111), X(41135)}}, {{A, B, C, X(148), X(42008)}}, {{A, B, C, X(385), X(41136)}}, {{A, B, C, X(524), X(7779)}}, {{A, B, C, X(543), X(826)}}, {{A, B, C, X(1383), X(52239)}}, {{A, B, C, X(2799), X(19924)}}, {{A, B, C, X(3228), X(36882)}}, {{A, B, C, X(5064), X(19689)}}, {{A, B, C, X(6094), X(18023)}}, {{A, B, C, X(7840), X(44367)}}, {{A, B, C, X(18823), X(25322)}}, {{A, B, C, X(31068), X(51226)}}, {{A, B, C, X(34572), X(41533)}}, {{A, B, C, X(34898), X(35511)}}, {{A, B, C, X(36889), X(43664)}}

X(60272) = X(4)X(6774)∩X(18)X(619)

Barycentrics    a^4-11*a^2*b^2+4*b^4-11*a^2*c^2-11*b^2*c^2+4*c^4+4*sqrt(3)*(2*a^2+b^2+c^2)*S : :

X(60272) lies on the Kiepert hyperbola and on these lines: {4, 6774}, {5, 54938}, {13, 6670}, {14, 6672}, {18, 619}, {76, 16645}, {98, 52263}, {99, 11121}, {299, 56056}, {395, 40706}, {531, 33606}, {617, 43543}, {635, 10187}, {3589, 60273}, {3618, 43554}, {5460, 12817}, {5464, 54594}, {6303, 54534}, {6307, 54535}, {6674, 16529}, {6773, 54849}, {10159, 44383}, {10302, 33474}, {11128, 11489}, {11603, 14139}, {12816, 22490}, {14905, 42063}, {21359, 43549}, {22797, 54673}, {23303, 40707}, {33603, 59379}, {33605, 51483}, {35020, 43547}, {41134, 42035}, {44250, 54572}, {47611, 54561}, {48312, 54593}, {48656, 54847}, {54848, 59384}

X(60272) = inverse of X(22848) in Wallace hyperbola
X(60272) = isotomic conjugate of X(44382)
X(60272) = trilinear pole of line {3180, 44462}
X(60272) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 44382}, {619, 22848}, {10639, 16022}
X(60272) = pole of line {22848, 44382} with respect to the Wallace hyperbola
X(60272) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(395), X(1989)}}, {{A, B, C, X(619), X(6672)}}, {{A, B, C, X(2380), X(6151)}}, {{A, B, C, X(2981), X(34322)}}
X(60272) = barycentric quotient X(i)/X(j) for these (i, j): {2, 44382}, {62, 16022}, {395, 22848}

X(60273) = X(4)X(6771)∩X(17)X(618)

Barycentrics    a^4-11*a^2*b^2+4*b^4-11*a^2*c^2-11*b^2*c^2+4*c^4-4*sqrt(3)*(2*a^2+b^2+c^2)*S : :

X(60273) lies on the Kiepert hyperbola and on these lines: {4, 6771}, {5, 54937}, {13, 6671}, {14, 6669}, {17, 618}, {76, 16644}, {98, 52266}, {99, 11122}, {298, 56055}, {396, 40707}, {530, 33607}, {616, 43542}, {636, 10188}, {3589, 60272}, {3618, 43555}, {5459, 12816}, {5463, 54593}, {6302, 50246}, {6306, 54538}, {6673, 16530}, {6770, 54850}, {10159, 44382}, {10302, 33475}, {11129, 11488}, {11602, 14138}, {12817, 22489}, {14904, 42062}, {21360, 43548}, {22796, 54672}, {23302, 40706}, {33602, 59378}, {33604, 51482}, {35019, 43546}, {36770, 43544}, {37640, 60222}, {41134, 42036}, {47610, 54562}, {48311, 54594}, {48655, 54848}, {54847, 59383}

X(60273) = inverse of X(22892) in Wallace hyperbola
X(60273) = isotomic conjugate of X(44383)
X(60273) = trilinear pole of line {3181, 44466}
X(60273) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 44383}, {618, 22892}, {10640, 16021}
X(60273) = pole of line {22892, 44383} with respect to the Wallace hyperbola
X(60273) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(396), X(1989)}}, {{A, B, C, X(618), X(6671)}}, {{A, B, C, X(2381), X(2981)}}, {{A, B, C, X(6151), X(34321)}}
X(60273) = barycentric quotient X(i)/X(j) for these (i, j): {2, 44383}, {61, 16021}, {396, 22892}

X(60274) = X(2)X(5062)∩X(3)X(14245)

Barycentrics    3*a^2*b^2-b^4+3*a^2*c^2+3*b^2*c^2-c^4+(4*a^2+2*b^2+2*c^2)*S : :

X(60274) lies on the Kiepert hyperbola and on these lines: {2, 5062}, {3, 14245}, {4, 43120}, {5, 14234}, {6, 60194}, {76, 590}, {99, 13882}, {371, 60270}, {485, 490}, {486, 7828}, {492, 19103}, {638, 3316}, {671, 13663}, {1131, 42838}, {1327, 35949}, {1505, 60233}, {3068, 5490}, {3317, 3618}, {3589, 7942}, {3767, 54126}, {5491, 32785}, {6568, 14061}, {7607, 49356}, {7771, 53487}, {7857, 45871}, {8253, 33233}, {10159, 45473}, {12297, 35945}, {13879, 44365}, {13885, 60072}, {14229, 45511}, {14568, 42023}, {18840, 32806}, {35297, 53479}, {35938, 60269}, {35947, 45106}

X(60274) = midpoint of X(i) and X(j) for these {i,j}: {2, 13657}
X(60274) = inverse of X(13882) in Wallace hyperbola
X(60274) = isogonal conjugate of X(1504)
X(60274) = isotomic conjugate of X(45472)
X(60274) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 1504}, {31, 45472}, {48, 32588}
X(60274) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 45472}, {3, 1504}, {1249, 32588}, {10962, 32568}, {13934, 7888}, {33364, 13882}
X(60274) = X(i)-cross conjugate of X(j) for these {i, j}: {7857, 60275}, {45871, 2}
X(60274) = pole of line {7857, 45871} with respect to the Kiepert hyperbola
X(60274) = pole of line {1504, 32568} with respect to the Stammler hyperbola
X(60274) = pole of line {1504, 7888} with respect to the Wallace hyperbola
X(60274) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(43120)}}, {{A, B, C, X(6), X(590)}}, {{A, B, C, X(249), X(371)}}, {{A, B, C, X(393), X(3068)}}, {{A, B, C, X(493), X(56004)}}, {{A, B, C, X(1016), X(1123)}}, {{A, B, C, X(1336), X(1509)}}, {{A, B, C, X(3300), X(17743)}}, {{A, B, C, X(3302), X(14621)}}, {{A, B, C, X(8576), X(38826)}}, {{A, B, C, X(13440), X(42298)}}, {{A, B, C, X(18820), X(42332)}}, {{A, B, C, X(32436), X(54029)}}, {{A, B, C, X(42313), X(55534)}}
X(60274) = barycentric product X(i)*X(j) for these (i, j): {18819, 492}
X(60274) = barycentric quotient X(i)/X(j) for these (i, j): {2, 45472}, {4, 32588}, {6, 1504}, {371, 32568}, {492, 42009}, {494, 26338}, {3068, 13882}, {5200, 45478}, {18819, 485}, {45473, 7888}

X(60275) = X(2)X(5058)∩X(3)X(14231)

Barycentrics    3*a^2*b^2-b^4+3*a^2*c^2+3*b^2*c^2-c^4-(4*a^2+2*b^2+2*c^2)*S : :

X(60275) lies on the Kiepert hyperbola and on these lines: {2, 5058}, {3, 14231}, {4, 43121}, {5, 14238}, {6, 60196}, {76, 615}, {99, 13934}, {372, 60269}, {485, 7828}, {486, 489}, {491, 19104}, {637, 3317}, {671, 13783}, {1132, 42840}, {1328, 35948}, {1504, 60233}, {3069, 5491}, {3316, 3618}, {3589, 7942}, {3767, 54127}, {5490, 32786}, {6569, 14061}, {7607, 49355}, {7771, 53488}, {7832, 32807}, {7857, 45872}, {8252, 33233}, {10159, 45472}, {12296, 35944}, {13933, 44364}, {13938, 60072}, {14244, 45510}, {14568, 42024}, {18840, 32805}, {35297, 53480}, {35939, 60270}, {35946, 45107}

X(60275) = midpoint of X(i) and X(j) for these {i,j}: {2, 13777}
X(60275) = inverse of X(13934) in Wallace hyperbola
X(60275) = isogonal conjugate of X(1505)
X(60275) = isotomic conjugate of X(45473)
X(60275) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 1505}, {31, 45473}, {48, 32587}
X(60275) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 45473}, {3, 1505}, {1249, 32587}, {10960, 32575}, {13882, 7888}, {33365, 13934}
X(60275) = X(i)-cross conjugate of X(j) for these {i, j}: {7857, 60274}, {45872, 2}
X(60275) = pole of line {7857, 45872} with respect to the Kiepert hyperbola
X(60275) = pole of line {1505, 32575} with respect to the Stammler hyperbola
X(60275) = pole of line {1505, 7888} with respect to the Wallace hyperbola
X(60275) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(43121)}}, {{A, B, C, X(6), X(615)}}, {{A, B, C, X(249), X(372)}}, {{A, B, C, X(393), X(3069)}}, {{A, B, C, X(494), X(56004)}}, {{A, B, C, X(1016), X(1336)}}, {{A, B, C, X(1123), X(1509)}}, {{A, B, C, X(3300), X(14621)}}, {{A, B, C, X(3302), X(17743)}}, {{A, B, C, X(8577), X(38826)}}, {{A, B, C, X(13429), X(42298)}}, {{A, B, C, X(18819), X(42332)}}, {{A, B, C, X(32433), X(54028)}}, {{A, B, C, X(42313), X(55533)}}
X(60275) = barycentric product X(i)*X(j) for these (i, j): {18820, 491}
X(60275) = barycentric quotient X(i)/X(j) for these (i, j): {2, 45473}, {4, 32587}, {6, 1505}, {372, 32575}, {491, 42060}, {493, 26337}, {3069, 13934}, {18820, 486}, {45472, 7888}, {52291, 45479}

X(60276) = X(10)X(536)∩X(98)X(13634)

Barycentrics    (a*(b+c)+b*(3*b+c))*(a*(b+c)+c*(b+3*c)) : :

X(60276) lies on the Kiepert hyperbola and on these lines: {10, 536}, {69, 54770}, {75, 60288}, {98, 13634}, {226, 29594}, {321, 6381}, {514, 35353}, {517, 54668}, {519, 40718}, {524, 60078}, {527, 60089}, {538, 60090}, {594, 13466}, {598, 17346}, {599, 60083}, {671, 17271}, {712, 34475}, {824, 4049}, {1654, 54795}, {1764, 60167}, {3339, 60086}, {3661, 4080}, {3666, 52708}, {3679, 13576}, {3912, 30588}, {3948, 60097}, {10449, 60077}, {11599, 35103}, {13478, 47039}, {17251, 60079}, {17281, 60135}, {17330, 60094}, {17392, 55949}, {17758, 21024}, {18145, 40024}, {18822, 57038}, {18842, 37654}, {20888, 60244}, {20913, 39994}, {27797, 29593}, {29600, 44417}, {30942, 36871}, {31143, 54648}, {41816, 54686}, {42029, 60264}, {47037, 48863}, {48852, 56161}, {49724, 54676}, {50163, 50318}

X(60276) = isotomic conjugate of X(46922)
X(60276) = trilinear pole of line {4728, 47756}
X(60276) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 46922}, {692, 47763}, {1333, 29822}
X(60276) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 46922}, {37, 29822}, {1086, 47763}
X(60276) = pole of line {4003, 4688} with respect to the dual conic of Yff parabola
X(60276) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(40023)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(44572)}}, {{A, B, C, X(8), X(29594)}}, {{A, B, C, X(27), X(50058)}}, {{A, B, C, X(75), X(514)}}, {{A, B, C, X(85), X(39708)}}, {{A, B, C, X(87), X(48587)}}, {{A, B, C, X(257), X(596)}}, {{A, B, C, X(297), X(13634)}}, {{A, B, C, X(334), X(4665)}}, {{A, B, C, X(335), X(42285)}}, {{A, B, C, X(517), X(59215)}}, {{A, B, C, X(519), X(824)}}, {{A, B, C, X(524), X(17271)}}, {{A, B, C, X(527), X(23876)}}, {{A, B, C, X(551), X(29593)}}, {{A, B, C, X(594), X(1577)}}, {{A, B, C, X(599), X(17346)}}, {{A, B, C, X(673), X(48821)}}, {{A, B, C, X(712), X(4785)}}, {{A, B, C, X(903), X(4364)}}, {{A, B, C, X(2786), X(35103)}}, {{A, B, C, X(3512), X(56149)}}, {{A, B, C, X(3551), X(48074)}}, {{A, B, C, X(3617), X(29600)}}, {{A, B, C, X(3626), X(29577)}}, {{A, B, C, X(3666), X(39980)}}, {{A, B, C, X(3679), X(3912)}}, {{A, B, C, X(3828), X(29576)}}, {{A, B, C, X(4391), X(55076)}}, {{A, B, C, X(4664), X(56128)}}, {{A, B, C, X(4669), X(17230)}}, {{A, B, C, X(4674), X(39957)}}, {{A, B, C, X(4708), X(39704)}}, {{A, B, C, X(4745), X(17244)}}, {{A, B, C, X(4980), X(17147)}}, {{A, B, C, X(6376), X(20888)}}, {{A, B, C, X(9311), X(39711)}}, {{A, B, C, X(9328), X(34860)}}, {{A, B, C, X(17132), X(28468)}}, {{A, B, C, X(17251), X(17378)}}, {{A, B, C, X(17297), X(17330)}}, {{A, B, C, X(17392), X(31144)}}, {{A, B, C, X(18145), X(20913)}}, {{A, B, C, X(19875), X(24603)}}, {{A, B, C, X(20568), X(27483)}}, {{A, B, C, X(21024), X(43265)}}, {{A, B, C, X(21356), X(37654)}}, {{A, B, C, X(27494), X(39697)}}, {{A, B, C, X(29571), X(53620)}}, {{A, B, C, X(29572), X(38098)}}, {{A, B, C, X(29615), X(49560)}}, {{A, B, C, X(29674), X(50095)}}, {{A, B, C, X(35168), X(40098)}}, {{A, B, C, X(39721), X(50091)}}, {{A, B, C, X(39735), X(46772)}}, {{A, B, C, X(39797), X(56174)}}, {{A, B, C, X(39798), X(47947)}}, {{A, B, C, X(40014), X(56051)}}, {{A, B, C, X(42034), X(44417)}}, {{A, B, C, X(50042), X(56947)}}, {{A, B, C, X(50067), X(52374)}}
X(60276) = barycentric quotient X(i)/X(j) for these (i, j): {2, 46922}, {10, 29822}, {514, 47763}

X(60277) = X(83)X(599)∩X(141)X(598)

Barycentrics    (2*a^2+5*b^2+2*c^2)*(2*(a^2+b^2)+5*c^2) : :
X(60277) = -7*X[14488]+12*X[38071]

X(60277) lies on the Kiepert hyperbola and on these lines: {2, 55771}, {3, 54857}, {4, 25561}, {5, 60329}, {6, 60238}, {30, 60326}, {69, 54616}, {76, 20582}, {83, 599}, {98, 5054}, {141, 598}, {262, 547}, {315, 18843}, {316, 53101}, {376, 60325}, {381, 54890}, {524, 60239}, {549, 60323}, {597, 43527}, {632, 7607}, {671, 7937}, {1916, 5461}, {1992, 18841}, {2482, 16986}, {2996, 7918}, {3096, 53105}, {3407, 47005}, {3424, 15692}, {3530, 11149}, {3534, 54852}, {3619, 5485}, {3620, 54639}, {3763, 10302}, {3860, 54582}, {3934, 60177}, {5070, 7608}, {5079, 60142}, {5466, 45692}, {5503, 7868}, {6656, 60209}, {7375, 60304}, {7376, 60303}, {7757, 42006}, {7760, 60182}, {7768, 60145}, {7770, 60146}, {7790, 60228}, {7799, 60212}, {7810, 14038}, {7812, 53102}, {7820, 55730}, {7827, 18840}, {7840, 60129}, {7841, 53106}, {7850, 50993}, {7859, 60183}, {7870, 60128}, {7878, 11160}, {7883, 53109}, {7930, 8860}, {7931, 10484}, {7934, 54737}, {8352, 54493}, {8370, 53107}, {8587, 22247}, {8591, 11606}, {8703, 14458}, {9466, 43688}, {11054, 60143}, {11057, 14030}, {11167, 12040}, {11168, 60093}, {11185, 32532}, {11303, 43550}, {11304, 43551}, {11317, 54646}, {11540, 60175}, {11668, 41984}, {14047, 43529}, {14067, 43528}, {14488, 38071}, {14492, 19709}, {14568, 60232}, {15271, 60103}, {15681, 31168}, {15710, 54845}, {15719, 60150}, {17234, 55949}, {17503, 51143}, {18842, 21356}, {21734, 60324}, {22110, 60096}, {22165, 60287}, {22329, 60215}, {25562, 55009}, {29629, 30588}, {31144, 60075}, {32832, 60262}, {32833, 60259}, {33291, 54540}, {34573, 60131}, {35404, 54917}, {43537, 55864}, {45103, 51186}, {46936, 53099}, {50991, 60283}, {51122, 60181}, {52297, 60124}, {54901, 55164}

X(60277) = isotomic conjugate of X(47352)
X(60277) = trilinear pole of line {47314, 523}
X(60277) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55606)}}, {{A, B, C, X(6), X(20582)}}, {{A, B, C, X(141), X(599)}}, {{A, B, C, X(297), X(5054)}}, {{A, B, C, X(327), X(57822)}}, {{A, B, C, X(458), X(547)}}, {{A, B, C, X(524), X(21358)}}, {{A, B, C, X(597), X(3763)}}, {{A, B, C, X(632), X(52282)}}, {{A, B, C, X(1992), X(3619)}}, {{A, B, C, X(3679), X(29629)}}, {{A, B, C, X(5070), X(52281)}}, {{A, B, C, X(7757), X(43094)}}, {{A, B, C, X(7778), X(11168)}}, {{A, B, C, X(7827), X(40022)}}, {{A, B, C, X(7840), X(16986)}}, {{A, B, C, X(7841), X(52297)}}, {{A, B, C, X(7868), X(22329)}}, {{A, B, C, X(7937), X(51541)}}, {{A, B, C, X(8370), X(52298)}}, {{A, B, C, X(8703), X(11331)}}, {{A, B, C, X(8797), X(54171)}}, {{A, B, C, X(9466), X(41259)}}, {{A, B, C, X(13602), X(34892)}}, {{A, B, C, X(14608), X(45692)}}, {{A, B, C, X(15271), X(22110)}}, {{A, B, C, X(15533), X(51143)}}, {{A, B, C, X(15692), X(52283)}}, {{A, B, C, X(17234), X(31144)}}, {{A, B, C, X(19709), X(52289)}}, {{A, B, C, X(22165), X(51186)}}, {{A, B, C, X(31143), X(33172)}}, {{A, B, C, X(34897), X(42313)}}, {{A, B, C, X(40802), X(44731)}}, {{A, B, C, X(41440), X(44557)}}, {{A, B, C, X(42351), X(46921)}}, {{A, B, C, X(46140), X(57817)}}, {{A, B, C, X(50991), X(50993)}}, {{A, B, C, X(54124), X(57895)}}

X(60278) = X(2)X(5041)∩X(4)X(7937)

Barycentrics    (2*a^2+3*b^2+2*c^2)*(2*(a^2+b^2)+3*c^2) : :

X(60278) lies on the Kiepert hyperbola and on these lines: {2, 5041}, {3, 55743}, {4, 7937}, {5, 14488}, {6, 60100}, {10, 17370}, {76, 34573}, {83, 3763}, {98, 3526}, {140, 53100}, {141, 43527}, {262, 3628}, {315, 18842}, {316, 18845}, {321, 29613}, {381, 54717}, {548, 60326}, {549, 14458}, {598, 3096}, {631, 54845}, {632, 60335}, {671, 7918}, {1656, 60142}, {1916, 6722}, {3090, 52519}, {3407, 7815}, {3424, 10303}, {3525, 60322}, {3533, 60337}, {3534, 54477}, {3619, 7878}, {3934, 43688}, {3972, 59266}, {5054, 54934}, {5055, 7944}, {5066, 42787}, {5070, 54920}, {5072, 54890}, {5254, 60228}, {6292, 14036}, {6656, 53105}, {7375, 60306}, {7376, 60305}, {7388, 12819}, {7389, 12818}, {7486, 14484}, {7607, 55859}, {7608, 55860}, {7752, 54773}, {7754, 10159}, {7757, 55745}, {7760, 56059}, {7763, 60259}, {7769, 60212}, {7770, 53109}, {7783, 47005}, {7786, 42006}, {7790, 60209}, {7793, 55738}, {7803, 60285}, {7812, 60283}, {7814, 60129}, {7822, 11606}, {7827, 60143}, {7828, 60232}, {7832, 54122}, {7841, 33698}, {7859, 18840}, {7860, 60146}, {7867, 54487}, {7883, 60282}, {7884, 54748}, {7899, 54905}, {7914, 14046}, {7915, 60184}, {7940, 60128}, {7942, 60213}, {8370, 54494}, {9167, 43535}, {10292, 55009}, {10304, 54519}, {11285, 60280}, {11289, 43546}, {11290, 43547}, {11303, 12820}, {11304, 12821}, {11540, 54851}, {15022, 43951}, {15683, 54815}, {15704, 54917}, {15706, 54852}, {15709, 60150}, {15717, 60147}, {16045, 18843}, {17265, 32014}, {17283, 43531}, {17307, 60075}, {20582, 60239}, {21358, 60238}, {26162, 54683}, {29628, 60203}, {31239, 60177}, {31268, 60181}, {31630, 41259}, {32832, 60201}, {32956, 60219}, {33190, 54720}, {37453, 60125}, {46219, 60334}, {47355, 60182}, {47598, 60175}, {50693, 60327}, {55856, 60332}

X(60278) = isotomic conjugate of X(47355)
X(60278) = trilinear pole of line {47650, 47651}
X(60278) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 47355}, {692, 48138}
X(60278) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 47355}, {1086, 48138}
X(60278) = pole of line {51128, 60278} with respect to the Kiepert hyperbola
X(60278) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(29613)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(14810)}}, {{A, B, C, X(6), X(5041)}}, {{A, B, C, X(39), X(52660)}}, {{A, B, C, X(75), X(17370)}}, {{A, B, C, X(141), X(3763)}}, {{A, B, C, X(264), X(40045)}}, {{A, B, C, X(297), X(3526)}}, {{A, B, C, X(305), X(40036)}}, {{A, B, C, X(308), X(7894)}}, {{A, B, C, X(327), X(7871)}}, {{A, B, C, X(335), X(25539)}}, {{A, B, C, X(419), X(14065)}}, {{A, B, C, X(458), X(3628)}}, {{A, B, C, X(514), X(39729)}}, {{A, B, C, X(549), X(11331)}}, {{A, B, C, X(596), X(39730)}}, {{A, B, C, X(1213), X(17265)}}, {{A, B, C, X(1235), X(7850)}}, {{A, B, C, X(1509), X(39749)}}, {{A, B, C, X(1698), X(29628)}}, {{A, B, C, X(2481), X(28650)}}, {{A, B, C, X(2963), X(5346)}}, {{A, B, C, X(3096), X(10130)}}, {{A, B, C, X(3224), X(41440)}}, {{A, B, C, X(3314), X(16988)}}, {{A, B, C, X(3739), X(29802)}}, {{A, B, C, X(3934), X(41259)}}, {{A, B, C, X(5055), X(52289)}}, {{A, B, C, X(5117), X(14043)}}, {{A, B, C, X(5224), X(17283)}}, {{A, B, C, X(6656), X(37453)}}, {{A, B, C, X(7486), X(52288)}}, {{A, B, C, X(7754), X(52570)}}, {{A, B, C, X(7805), X(34816)}}, {{A, B, C, X(7855), X(9516)}}, {{A, B, C, X(7859), X(40022)}}, {{A, B, C, X(7937), X(40050)}}, {{A, B, C, X(9289), X(13623)}}, {{A, B, C, X(10303), X(52283)}}, {{A, B, C, X(13606), X(49534)}}, {{A, B, C, X(17042), X(36615)}}, {{A, B, C, X(17234), X(17307)}}, {{A, B, C, X(17245), X(17327)}}, {{A, B, C, X(17292), X(29660)}}, {{A, B, C, X(18896), X(57926)}}, {{A, B, C, X(20582), X(21358)}}, {{A, B, C, X(21448), X(56344)}}, {{A, B, C, X(29596), X(36534)}}, {{A, B, C, X(30541), X(44763)}}, {{A, B, C, X(34412), X(40421)}}, {{A, B, C, X(34483), X(42313)}}, {{A, B, C, X(35140), X(36948)}}, {{A, B, C, X(35146), X(40511)}}, {{A, B, C, X(35172), X(39736)}}, {{A, B, C, X(39951), X(57421)}}, {{A, B, C, X(40512), X(53200)}}, {{A, B, C, X(47355), X(51128)}}, {{A, B, C, X(48943), X(53024)}}, {{A, B, C, X(52281), X(55860)}}, {{A, B, C, X(52282), X(55859)}}
X(60278) = barycentric product X(i)*X(j) for these (i, j): {58121, 850}
X(60278) = barycentric quotient X(i)/X(j) for these (i, j): {2, 47355}, {514, 48138}, {58121, 110}
X(60278) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5041, 55759}

X(60279) = X(2)X(55761)∩X(3)X(55742)

Barycentrics    (5*a^2+8*b^2+5*c^2)*(5*(a^2+b^2)+8*c^2) : :

X(60279) lies on the Kiepert hyperbola and on these lines: {2, 55761}, {3, 55742}, {4, 55637}, {83, 20582}, {98, 11539}, {141, 60238}, {262, 15703}, {549, 54891}, {597, 60100}, {598, 3763}, {599, 43527}, {2482, 11606}, {3096, 18845}, {3424, 15721}, {3619, 54616}, {5395, 7883}, {5461, 60271}, {7607, 55858}, {7608, 48154}, {7790, 54637}, {7812, 60145}, {7827, 60210}, {7877, 18841}, {7937, 54493}, {10109, 14492}, {10302, 34573}, {12108, 54857}, {14458, 15693}, {15689, 60326}, {15705, 60147}, {16988, 43535}, {17283, 55949}, {19710, 54477}, {21358, 60239}, {31168, 59266}, {32837, 60259}, {32867, 60262}, {32885, 60201}, {34200, 60132}, {35005, 38223}, {40344, 54539}, {42006, 44562}, {53100, 55863}

X(60279) = isotomic conjugate of X(48310)
X(60279) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55637)}}, {{A, B, C, X(141), X(20582)}}, {{A, B, C, X(297), X(11539)}}, {{A, B, C, X(327), X(57895)}}, {{A, B, C, X(458), X(15703)}}, {{A, B, C, X(597), X(34573)}}, {{A, B, C, X(599), X(3763)}}, {{A, B, C, X(7840), X(16988)}}, {{A, B, C, X(10109), X(52289)}}, {{A, B, C, X(11331), X(15693)}}, {{A, B, C, X(11588), X(30535)}}, {{A, B, C, X(15721), X(52283)}}, {{A, B, C, X(17283), X(31144)}}, {{A, B, C, X(48154), X(52281)}}, {{A, B, C, X(52282), X(55858)}}

X(60280) = X(114)X(10155)∩X(115)X(5395)

Barycentrics    (3*a^4+2*a^2*b^2+3*b^4-3*(a^2+b^2)*c^2-2*c^4)*(3*a^4-2*b^4-3*b^2*c^2+3*c^4+a^2*(-3*b^2+2*c^2)) : :

X(60280) lies on the Kiepert hyperbola and on these lines: {76, 33234}, {99, 18840}, {114, 10155}, {115, 5395}, {147, 53099}, {148, 43681}, {262, 18440}, {542, 60127}, {2996, 7751}, {5485, 7811}, {5503, 54103}, {5984, 43951}, {6036, 60123}, {6054, 54645}, {7612, 35021}, {7789, 10159}, {7800, 60285}, {8356, 10302}, {8781, 11646}, {9166, 54616}, {10723, 43532}, {11177, 54519}, {11285, 60278}, {11632, 54659}, {12829, 53107}, {14061, 43527}, {14269, 54714}, {15687, 54718}, {19695, 60250}, {20065, 38259}, {32451, 60095}, {32990, 35022}, {32992, 60100}, {33272, 60200}, {36523, 54896}, {37451, 53104}, {41134, 60131}, {41135, 54476}, {44534, 60103}, {44543, 60239}

X(60280) = reflection of X(i) in X(j) for these {i,j}: {5395, 115}
X(60280) = isotomic conjugate of X(50771)
X(60280) = trilinear pole of line {3618, 523}
X(60280) = X(i)-vertex conjugate of X(j) for these {i, j}: {3455, 8781}, {17980, 32901}, {39644, 60103}, {41533, 60073}
X(60280) = pole of line {50774, 60280} with respect to the Kiepert hyperbola
X(60280) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(33234)}}, {{A, B, C, X(99), X(42396)}}, {{A, B, C, X(249), X(29180)}}, {{A, B, C, X(755), X(57260)}}, {{A, B, C, X(2980), X(44558)}}, {{A, B, C, X(6323), X(41533)}}, {{A, B, C, X(8356), X(10301)}}, {{A, B, C, X(14486), X(30541)}}, {{A, B, C, X(17983), X(43098)}}, {{A, B, C, X(18440), X(56401)}}, {{A, B, C, X(29316), X(32901)}}, {{A, B, C, X(32992), X(52285)}}, {{A, B, C, X(43664), X(57894)}}, {{A, B, C, X(50771), X(50774)}}

X(60281) = X(2)X(15655)∩X(6)X(32532)

Barycentrics    (11*(a^2+b^2)-7*c^2)*(11*a^2-7*b^2+11*c^2) : :

X(60281) lies on the Kiepert hyperbola and on these lines: {2, 15655}, {5, 53859}, {6, 32532}, {30, 53099}, {76, 50992}, {98, 41099}, {262, 15682}, {316, 60131}, {376, 7608}, {381, 43537}, {597, 60284}, {631, 60144}, {671, 41672}, {1992, 60228}, {2996, 11317}, {3090, 10185}, {3424, 3845}, {3524, 53098}, {3529, 60332}, {3534, 60333}, {3543, 60118}, {3545, 7607}, {3618, 60283}, {3830, 14484}, {3839, 47586}, {3855, 60334}, {5066, 60102}, {5071, 60123}, {5395, 8352}, {5475, 42011}, {5476, 54568}, {5485, 15534}, {5503, 15300}, {7612, 41106}, {7745, 60219}, {7784, 60183}, {7812, 60250}, {8370, 60285}, {8584, 54637}, {10153, 14971}, {10155, 19708}, {10302, 50994}, {11001, 14494}, {11159, 60262}, {11167, 14537}, {11669, 15698}, {12101, 54520}, {14033, 43529}, {15640, 60331}, {15719, 53108}, {16041, 43528}, {18840, 50993}, {18842, 53418}, {20094, 45111}, {22165, 60143}, {23334, 51143}, {27088, 32898}, {32956, 60182}, {33190, 43527}, {33699, 54521}, {39874, 54903}, {42010, 52695}, {43448, 54720}, {45103, 59373}, {50687, 60328}, {50990, 60286}, {52281, 56270}, {52282, 60193}, {52283, 60138}, {52942, 60177}

X(60281) = isotomic conjugate of X(50990)
X(60281) = pole of line {51185, 60281} with respect to the Kiepert hyperbola
X(60281) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(11736)}}, {{A, B, C, X(6), X(15655)}}, {{A, B, C, X(297), X(41099)}}, {{A, B, C, X(376), X(52281)}}, {{A, B, C, X(458), X(15682)}}, {{A, B, C, X(597), X(50994)}}, {{A, B, C, X(1992), X(15534)}}, {{A, B, C, X(3545), X(52282)}}, {{A, B, C, X(3618), X(50993)}}, {{A, B, C, X(3830), X(52288)}}, {{A, B, C, X(3845), X(52283)}}, {{A, B, C, X(5064), X(33190)}}, {{A, B, C, X(5556), X(34892)}}, {{A, B, C, X(6353), X(11317)}}, {{A, B, C, X(7319), X(34914)}}, {{A, B, C, X(7714), X(8370)}}, {{A, B, C, X(8352), X(8889)}}, {{A, B, C, X(8770), X(47060)}}, {{A, B, C, X(10630), X(39955)}}, {{A, B, C, X(11738), X(30535)}}, {{A, B, C, X(13377), X(44556)}}, {{A, B, C, X(14487), X(40802)}}, {{A, B, C, X(18550), X(42287)}}, {{A, B, C, X(34898), X(43726)}}, {{A, B, C, X(37174), X(41106)}}, {{A, B, C, X(41672), X(56395)}}, {{A, B, C, X(50990), X(51185)}}

X(60282) = X(2)X(55820)∩X(3)X(55796)

Barycentrics    (7*(a^2+b^2)-2*c^2)*(7*a^2-2*b^2+7*c^2) : :

X(60282) lies on the Kiepert hyperbola and on these lines: {2, 55820}, {3, 55796}, {4, 55708}, {5, 60334}, {6, 60228}, {30, 60142}, {76, 15534}, {98, 5066}, {262, 3534}, {316, 60238}, {376, 60330}, {381, 53100}, {549, 7608}, {597, 45103}, {671, 53489}, {3526, 60144}, {3545, 60337}, {3618, 60284}, {3628, 10185}, {3830, 14488}, {3845, 60132}, {3860, 54934}, {3972, 42011}, {5055, 7607}, {7486, 53859}, {7745, 60100}, {7760, 43681}, {7790, 53101}, {7803, 18844}, {7812, 18840}, {7827, 53106}, {7841, 53102}, {7850, 50993}, {7883, 60278}, {7911, 18841}, {8352, 53109}, {8370, 43676}, {8584, 60216}, {8587, 14061}, {8703, 54920}, {10159, 51143}, {10302, 22165}, {10304, 53099}, {11054, 60250}, {11317, 53105}, {11540, 53108}, {12101, 54717}, {12150, 60128}, {12156, 42006}, {14036, 43529}, {14046, 43528}, {14484, 15640}, {14492, 33699}, {14494, 15698}, {15533, 60286}, {15682, 52519}, {15683, 60118}, {15684, 60329}, {15709, 53098}, {15759, 60192}, {17503, 51185}, {19709, 60335}, {23046, 54857}, {32532, 59373}, {32896, 60201}, {41099, 54845}, {41106, 60322}, {41134, 42010}, {41153, 54478}, {47352, 60283}, {50992, 60143}, {51171, 54896}

X(60282) = isotomic conjugate of X(50991)
X(60282) = trilinear pole of line {37909, 523}
X(60282) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55708)}}, {{A, B, C, X(6), X(15534)}}, {{A, B, C, X(67), X(597)}}, {{A, B, C, X(249), X(57714)}}, {{A, B, C, X(287), X(13623)}}, {{A, B, C, X(297), X(5066)}}, {{A, B, C, X(458), X(3534)}}, {{A, B, C, X(549), X(52281)}}, {{A, B, C, X(729), X(43950)}}, {{A, B, C, X(1509), X(13606)}}, {{A, B, C, X(3108), X(10630)}}, {{A, B, C, X(3589), X(51143)}}, {{A, B, C, X(3618), X(50994)}}, {{A, B, C, X(5055), X(52282)}}, {{A, B, C, X(7812), X(42037)}}, {{A, B, C, X(8753), X(34572)}}, {{A, B, C, X(11317), X(37453)}}, {{A, B, C, X(15533), X(51185)}}, {{A, B, C, X(15640), X(52288)}}, {{A, B, C, X(18818), X(52395)}}, {{A, B, C, X(30535), X(32901)}}, {{A, B, C, X(33699), X(52289)}}, {{A, B, C, X(36882), X(44571)}}, {{A, B, C, X(47352), X(50993)}}

X(60283) = X(2)X(55826)∩X(3)X(55791)

Barycentrics    (8*(a^2+b^2)-c^2)*(8*a^2-b^2+8*c^2) : :

X(60283) lies on the Kiepert hyperbola and on these lines: {2, 55826}, {3, 55791}, {4, 55704}, {6, 60216}, {30, 60329}, {76, 8584}, {98, 19709}, {262, 8703}, {316, 54616}, {381, 54857}, {524, 60286}, {547, 7607}, {597, 17503}, {620, 42010}, {632, 60144}, {671, 51185}, {1916, 14030}, {3407, 33291}, {3530, 60332}, {3589, 60287}, {3618, 60281}, {3830, 54890}, {3845, 60326}, {3860, 14458}, {3972, 10484}, {5054, 7608}, {5066, 60323}, {5070, 10185}, {5079, 60334}, {7784, 60100}, {7790, 54494}, {7812, 60278}, {7827, 38259}, {7841, 60146}, {7878, 43676}, {8352, 53107}, {8370, 60209}, {8587, 14971}, {10159, 51186}, {10302, 15533}, {11054, 43681}, {11055, 43688}, {11317, 53106}, {11540, 11669}, {12150, 60187}, {14494, 15719}, {15681, 60142}, {15692, 53099}, {15710, 60330}, {18840, 50990}, {38071, 53100}, {41099, 60325}, {46936, 53859}, {47352, 60282}, {50991, 60277}, {53489, 60239}, {54637, 59373}

X(60283) = isotomic conjugate of X(50993)
X(60283) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55704)}}, {{A, B, C, X(6), X(8584)}}, {{A, B, C, X(249), X(44731)}}, {{A, B, C, X(297), X(19709)}}, {{A, B, C, X(419), X(14030)}}, {{A, B, C, X(458), X(8703)}}, {{A, B, C, X(524), X(51185)}}, {{A, B, C, X(547), X(52282)}}, {{A, B, C, X(597), X(15533)}}, {{A, B, C, X(3589), X(51186)}}, {{A, B, C, X(3618), X(50990)}}, {{A, B, C, X(3860), X(11331)}}, {{A, B, C, X(5054), X(52281)}}, {{A, B, C, X(5117), X(33291)}}, {{A, B, C, X(8352), X(52298)}}, {{A, B, C, X(10630), X(39951)}}, {{A, B, C, X(11055), X(41259)}}, {{A, B, C, X(11317), X(52297)}}, {{A, B, C, X(13377), X(44571)}}, {{A, B, C, X(13602), X(14621)}}, {{A, B, C, X(18818), X(56067)}}, {{A, B, C, X(41153), X(51188)}}, {{A, B, C, X(47352), X(50991)}}

X(60284) = X(4)X(51185)∩X(6)X(54637)

Barycentrics    (13*(a^2+b^2)-5*c^2)*(13*a^2-5*b^2+13*c^2) : :

X(60284) lies on the Kiepert hyperbola and on these lines: {4, 51185}, {6, 54637}, {30, 60118}, {69, 60286}, {98, 41106}, {262, 11001}, {376, 53099}, {381, 47586}, {597, 60281}, {1992, 60216}, {3090, 53859}, {3424, 41099}, {3524, 7608}, {3525, 60144}, {3528, 60332}, {3534, 60331}, {3543, 60328}, {3544, 60334}, {3545, 43537}, {3618, 60282}, {3830, 43951}, {3839, 60324}, {3845, 60147}, {5066, 60336}, {5067, 10185}, {5071, 7607}, {5485, 8584}, {5503, 36521}, {6722, 10153}, {7745, 60183}, {7812, 60210}, {7841, 60145}, {8352, 18845}, {8370, 43681}, {10302, 50990}, {11317, 38259}, {12040, 51589}, {14039, 43529}, {14484, 15682}, {14494, 19708}, {15533, 60143}, {15698, 60333}, {15702, 53098}, {17503, 59373}, {18840, 50991}, {19709, 54921}, {33230, 43527}, {33285, 43528}, {51171, 54642}, {53101, 53489}

X(60284) = isotomic conjugate of X(50994)
X(60284) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(69), X(51185)}}, {{A, B, C, X(297), X(41106)}}, {{A, B, C, X(458), X(11001)}}, {{A, B, C, X(597), X(50990)}}, {{A, B, C, X(1992), X(8584)}}, {{A, B, C, X(3524), X(52281)}}, {{A, B, C, X(3618), X(50991)}}, {{A, B, C, X(5064), X(33230)}}, {{A, B, C, X(5071), X(52282)}}, {{A, B, C, X(5486), X(15533)}}, {{A, B, C, X(8352), X(52299)}}, {{A, B, C, X(11317), X(38282)}}, {{A, B, C, X(15682), X(52288)}}, {{A, B, C, X(18847), X(42330)}}, {{A, B, C, X(20421), X(30535)}}, {{A, B, C, X(31371), X(34897)}}, {{A, B, C, X(34892), X(43733)}}, {{A, B, C, X(34914), X(43734)}}, {{A, B, C, X(36611), X(52395)}}, {{A, B, C, X(41099), X(52283)}}, {{A, B, C, X(44571), X(46645)}}

X(60285) = X(4)X(3620)∩X(83)X(193)

Barycentrics    (a^2+5*b^2+c^2)*(a^2+b^2+5*c^2) : :
X(60285) = -14*X[3851]+9*X[52519]

X(60285) lies on the Kiepert hyperbola and on these lines: {2, 9606}, {3, 55729}, {4, 3620}, {5, 60127}, {10, 17304}, {20, 14458}, {69, 5395}, {83, 193}, {98, 3523}, {140, 7612}, {141, 2996}, {194, 60099}, {226, 29579}, {262, 5056}, {297, 54867}, {315, 53109}, {376, 54612}, {458, 54531}, {459, 11331}, {524, 54639}, {550, 54845}, {598, 7768}, {599, 32979}, {631, 60185}, {671, 32974}, {1352, 54846}, {1654, 60092}, {1656, 14494}, {1657, 60325}, {1916, 33283}, {2896, 49135}, {3090, 54523}, {3091, 14492}, {3096, 43676}, {3146, 54519}, {3314, 5068}, {3407, 14037}, {3424, 3522}, {3533, 53103}, {3543, 54477}, {3545, 54707}, {3832, 54520}, {3839, 54582}, {3851, 52519}, {3854, 43951}, {3926, 55797}, {3934, 32825}, {4045, 32878}, {4232, 60125}, {4869, 6625}, {5032, 16045}, {5059, 17128}, {5232, 60149}, {5254, 43681}, {5286, 10159}, {5485, 6656}, {5503, 33199}, {6392, 18840}, {6658, 54901}, {6722, 7869}, {6823, 54604}, {6996, 54587}, {7375, 54597}, {7376, 43536}, {7377, 54689}, {7383, 54498}, {7388, 14226}, {7389, 14241}, {7395, 54660}, {7399, 54763}, {7406, 60172}, {7486, 60192}, {7607, 7836}, {7608, 46935}, {7760, 60238}, {7763, 60248}, {7765, 32892}, {7770, 11160}, {7789, 55819}, {7790, 60250}, {7794, 32987}, {7795, 60093}, {7800, 60280}, {7801, 60220}, {7803, 60278}, {7824, 11172}, {7827, 60131}, {7841, 32532}, {7860, 53107}, {7864, 32882}, {7867, 32886}, {7876, 32869}, {7878, 60287}, {7881, 10155}, {7883, 33698}, {7885, 54706}, {7891, 60336}, {7892, 37667}, {7898, 54917}, {7901, 32834}, {7904, 60324}, {7912, 60142}, {7925, 60333}, {7931, 32872}, {8352, 54647}, {8370, 60281}, {8587, 33206}, {8796, 37636}, {9167, 60103}, {9466, 32972}, {9740, 19689}, {10299, 51579}, {10303, 60175}, {10304, 54608}, {10484, 33270}, {10519, 54858}, {11185, 53106}, {11289, 43542}, {11290, 43543}, {11303, 33602}, {11304, 33603}, {11606, 35369}, {12040, 32978}, {12815, 32885}, {13727, 54690}, {13740, 54624}, {14035, 54539}, {14063, 54540}, {15022, 54521}, {15066, 60193}, {15482, 32875}, {15692, 54851}, {15717, 54866}, {15720, 60337}, {16043, 51122}, {16062, 54786}, {16063, 40178}, {16921, 60268}, {16986, 60259}, {17130, 33272}, {17232, 57826}, {17238, 43533}, {17300, 60077}, {17578, 54815}, {17811, 41899}, {18841, 51171}, {20080, 60145}, {20081, 42006}, {21356, 32982}, {22235, 34541}, {22237, 34540}, {31450, 32896}, {32824, 32990}, {32830, 60212}, {32832, 60178}, {32836, 60217}, {32838, 60198}, {32893, 33248}, {32956, 60143}, {32962, 54487}, {32965, 43535}, {32969, 60240}, {32973, 54906}, {32980, 54889}, {32993, 54737}, {33020, 37668}, {33021, 54122}, {33180, 60180}, {33190, 54637}, {33202, 60181}, {33226, 59780}, {33229, 54720}, {33838, 54831}, {34507, 60117}, {34664, 54667}, {35018, 60330}, {36652, 54712}, {36670, 54740}, {37162, 60153}, {37174, 39284}, {37186, 54547}, {37462, 60165}, {37653, 60168}, {37665, 60129}, {37689, 43528}, {39998, 40831}, {40107, 54718}, {40814, 59764}, {41231, 54772}, {41237, 54930}, {41238, 54784}, {41366, 52583}, {43448, 60209}, {46219, 60123}, {46226, 60215}, {46936, 54645}, {46951, 60202}, {49140, 54852}, {50690, 60327}, {50691, 60326}, {50991, 54896}, {50994, 54642}, {52283, 54710}, {52284, 60141}, {52289, 56346}, {52404, 54844}, {52713, 60219}, {53033, 60073}, {53098, 55856}, {53857, 60124}, {54097, 60113}, {54644, 55864}

X(60285) = isotomic conjugate of X(51171)
X(60285) = trilinear pole of line {47315, 523}
X(60285) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 51171}, {48, 7714}
X(60285) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 51171}, {1249, 7714}
X(60285) = pole of line {3619, 60285} with respect to the Kiepert hyperbola
X(60285) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(33878)}}, {{A, B, C, X(8), X(29579)}}, {{A, B, C, X(20), X(11331)}}, {{A, B, C, X(68), X(18358)}}, {{A, B, C, X(69), X(3620)}}, {{A, B, C, X(140), X(37174)}}, {{A, B, C, X(141), X(193)}}, {{A, B, C, X(253), X(327)}}, {{A, B, C, X(257), X(7320)}}, {{A, B, C, X(263), X(17042)}}, {{A, B, C, X(277), X(32018)}}, {{A, B, C, X(279), X(27494)}}, {{A, B, C, X(297), X(3523)}}, {{A, B, C, X(308), X(56334)}}, {{A, B, C, X(330), X(49446)}}, {{A, B, C, X(335), X(5558)}}, {{A, B, C, X(391), X(17232)}}, {{A, B, C, X(419), X(33283)}}, {{A, B, C, X(458), X(5056)}}, {{A, B, C, X(468), X(32974)}}, {{A, B, C, X(989), X(40434)}}, {{A, B, C, X(1220), X(40029)}}, {{A, B, C, X(1654), X(4869)}}, {{A, B, C, X(2481), X(39736)}}, {{A, B, C, X(2963), X(47735)}}, {{A, B, C, X(2987), X(43908)}}, {{A, B, C, X(3091), X(52289)}}, {{A, B, C, X(3314), X(15589)}}, {{A, B, C, X(3519), X(14376)}}, {{A, B, C, X(3522), X(52283)}}, {{A, B, C, X(3619), X(51171)}}, {{A, B, C, X(3926), X(36952)}}, {{A, B, C, X(3945), X(17238)}}, {{A, B, C, X(4232), X(6656)}}, {{A, B, C, X(4373), X(17304)}}, {{A, B, C, X(5068), X(52288)}}, {{A, B, C, X(5094), X(32971)}}, {{A, B, C, X(5117), X(14037)}}, {{A, B, C, X(5232), X(17300)}}, {{A, B, C, X(5286), X(39998)}}, {{A, B, C, X(5559), X(30701)}}, {{A, B, C, X(5936), X(40028)}}, {{A, B, C, X(6339), X(31360)}}, {{A, B, C, X(6392), X(40022)}}, {{A, B, C, X(6464), X(30535)}}, {{A, B, C, X(6620), X(7901)}}, {{A, B, C, X(6664), X(38005)}}, {{A, B, C, X(6722), X(52450)}}, {{A, B, C, X(7770), X(52284)}}, {{A, B, C, X(7841), X(53857)}}, {{A, B, C, X(7879), X(55032)}}, {{A, B, C, X(7931), X(37689)}}, {{A, B, C, X(9292), X(52660)}}, {{A, B, C, X(9606), X(46952)}}, {{A, B, C, X(10405), X(39722)}}, {{A, B, C, X(11160), X(21356)}}, {{A, B, C, X(14387), X(54171)}}, {{A, B, C, X(14528), X(40802)}}, {{A, B, C, X(15066), X(55978)}}, {{A, B, C, X(16986), X(37665)}}, {{A, B, C, X(16990), X(37668)}}, {{A, B, C, X(17230), X(50316)}}, {{A, B, C, X(20023), X(31276)}}, {{A, B, C, X(20568), X(59760)}}, {{A, B, C, X(27483), X(56054)}}, {{A, B, C, X(30541), X(56362)}}, {{A, B, C, X(32821), X(55972)}}, {{A, B, C, X(32828), X(51481)}}, {{A, B, C, X(32834), X(40814)}}, {{A, B, C, X(32956), X(52301)}}, {{A, B, C, X(32982), X(52290)}}, {{A, B, C, X(34403), X(42313)}}, {{A, B, C, X(35142), X(36948)}}, {{A, B, C, X(38748), X(57504)}}, {{A, B, C, X(39721), X(40023)}}, {{A, B, C, X(39730), X(55937)}}, {{A, B, C, X(40014), X(56044)}}, {{A, B, C, X(41361), X(41366)}}, {{A, B, C, X(41791), X(43741)}}, {{A, B, C, X(42352), X(54114)}}, {{A, B, C, X(42377), X(45857)}}, {{A, B, C, X(46935), X(52281)}}, {{A, B, C, X(56004), X(57713)}}, {{A, B, C, X(56067), X(57857)}}
X(60285) = barycentric product X(i)*X(j) for these (i, j): {58116, 850}
X(60285) = barycentric quotient X(i)/X(j) for these (i, j): {2, 51171}, {4, 7714}, {58116, 110}

X(60286) = X(2)X(55781)∩X(3)X(55728)

Barycentrics    (2*a^2+11*b^2+2*c^2)*(2*(a^2+b^2)+11*c^2) : :

X(60286) lies on the Kiepert hyperbola and on these lines: {2, 55781}, {3, 55728}, {4, 50994}, {69, 60284}, {76, 51143}, {83, 15534}, {98, 15693}, {141, 60228}, {262, 10109}, {316, 54476}, {524, 60283}, {598, 22165}, {599, 45103}, {620, 8587}, {671, 50993}, {3534, 54891}, {3620, 54896}, {5485, 7937}, {7607, 11539}, {7608, 15703}, {7784, 53106}, {7827, 60183}, {7918, 60250}, {8584, 60287}, {9466, 60177}, {10185, 55858}, {11054, 18840}, {11055, 60099}, {11057, 54901}, {11167, 51123}, {11185, 54720}, {14458, 19710}, {14971, 42010}, {15300, 43535}, {15533, 60282}, {15689, 54857}, {15705, 47586}, {15721, 43537}, {17503, 50991}, {18842, 50992}, {21356, 32532}, {34200, 53100}, {39785, 55796}, {48154, 60144}, {50990, 60281}, {51186, 60216}, {55863, 60334}

X(60286) = isotomic conjugate of X(51185)
X(60286) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55588)}}, {{A, B, C, X(6), X(51143)}}, {{A, B, C, X(69), X(50994)}}, {{A, B, C, X(141), X(15534)}}, {{A, B, C, X(297), X(15693)}}, {{A, B, C, X(458), X(10109)}}, {{A, B, C, X(524), X(50993)}}, {{A, B, C, X(599), X(22165)}}, {{A, B, C, X(8584), X(51186)}}, {{A, B, C, X(11054), X(40022)}}, {{A, B, C, X(11331), X(19710)}}, {{A, B, C, X(11539), X(52282)}}, {{A, B, C, X(15533), X(50991)}}, {{A, B, C, X(15703), X(52281)}}, {{A, B, C, X(21356), X(50992)}}, {{A, B, C, X(31360), X(34898)}}, {{A, B, C, X(41152), X(51189)}}, {{A, B, C, X(50989), X(51142)}}, {{A, B, C, X(57822), X(57907)}}

X(60287) = X(2)X(55725)∩X(3)X(55786)

Barycentrics    (10*(a^2+b^2)+c^2)*(10*a^2+b^2+10*c^2) : :

X(60287) lies on the Kiepert hyperbola and on these lines: {2, 55725}, {3, 55786}, {4, 46267}, {262, 12100}, {316, 54639}, {597, 60228}, {1916, 36521}, {3407, 33288}, {3589, 60283}, {3618, 32532}, {3845, 54917}, {6722, 8587}, {7607, 15699}, {7608, 15694}, {7790, 54493}, {7827, 60219}, {7878, 60285}, {7879, 56059}, {7918, 18845}, {7937, 60238}, {8584, 60286}, {9167, 42010}, {10159, 50993}, {10185, 55857}, {10302, 15534}, {11737, 53100}, {14484, 15697}, {14492, 15685}, {14869, 60332}, {15686, 60329}, {15688, 60142}, {15708, 53099}, {16239, 60144}, {18840, 50992}, {22165, 60277}, {44562, 51584}, {45103, 47352}, {51143, 60131}, {51185, 60216}

X(60287) = isotomic conjugate of X(51186)
X(60287) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55698)}}, {{A, B, C, X(458), X(12100)}}, {{A, B, C, X(597), X(15534)}}, {{A, B, C, X(3589), X(50993)}}, {{A, B, C, X(3618), X(50992)}}, {{A, B, C, X(5117), X(33288)}}, {{A, B, C, X(8584), X(51185)}}, {{A, B, C, X(15685), X(52289)}}, {{A, B, C, X(15694), X(52281)}}, {{A, B, C, X(15697), X(52288)}}, {{A, B, C, X(15699), X(52282)}}, {{A, B, C, X(22165), X(42286)}}, {{A, B, C, X(44557), X(46123)}}

X(60288) = X(2)X(668)∩X(4)X(6335)

Barycentrics    b*c*(b+c)*(a*(b-2*c)+b*c)*(-2*a*b+(a+b)*c) : :

X(60288) lies on the Kiepert hyperbola and on these lines: {2, 668}, {4, 6335}, {10, 3122}, {75, 60276}, {76, 1086}, {98, 898}, {321, 3125}, {334, 3762}, {344, 54728}, {671, 889}, {739, 839}, {1500, 56197}, {1751, 51566}, {2051, 18061}, {3661, 60097}, {3912, 14554}, {3948, 4080}, {3992, 43534}, {4125, 34475}, {4607, 24624}, {4714, 59261}, {5466, 18003}, {6376, 17758}, {11611, 42713}, {14431, 35353}, {16589, 40525}, {18149, 35957}, {19804, 60084}, {20566, 60074}, {29593, 39997}, {30114, 56167}, {30116, 60109}, {30566, 30830}, {30588, 59212}, {30709, 43928}, {33116, 54699}, {34075, 60134}, {34087, 57994}, {36872, 50301}, {37129, 37218}, {37788, 54739}, {39994, 52043}, {40515, 56250}, {40718, 56191}, {41245, 60085}, {42716, 54548}, {42724, 54933}, {52754, 54533}

X(60288) = isotomic conjugate of X(52897)
X(60288) = trilinear pole of line {321, 8034}
X(60288) = perspector of circumconic {{A, B, C, X(889), X(57994)}}
X(60288) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 52897}, {48, 52890}, {58, 3230}, {110, 3768}, {163, 891}, {536, 2206}, {662, 890}, {849, 52959}, {899, 1333}, {1576, 4728}, {1646, 4570}, {2194, 52896}, {4009, 16947}, {4556, 14404}, {23343, 57129}, {43037, 57657}
X(60288) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 52897}, {10, 3230}, {37, 899}, {115, 891}, {244, 3768}, {1084, 890}, {1214, 52896}, {1249, 52890}, {4075, 52959}, {4858, 4728}, {4988, 19945}, {6741, 4526}, {40603, 536}, {50330, 1646}, {52875, 59797}
X(60288) = X(i)-Ceva conjugate of X(j) for these {i, j}: {31002, 41683}
X(60288) = X(i)-cross conjugate of X(j) for these {i, j}: {14431, 27808}
X(60288) = pole of line {42764, 52626} with respect to the dual conic of Stammler hyperbola
X(60288) = pole of line {4871, 41683} with respect to the dual conic of Yff parabola
X(60288) = pole of line {1646, 14434} with respect to the dual conic of Wallace hyperbola
X(60288) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(37), X(6383)}}, {{A, B, C, X(85), X(56186)}}, {{A, B, C, X(330), X(42471)}}, {{A, B, C, X(334), X(668)}}, {{A, B, C, X(335), X(4674)}}, {{A, B, C, X(514), X(27809)}}, {{A, B, C, X(523), X(33908)}}, {{A, B, C, X(525), X(29349)}}, {{A, B, C, X(1015), X(1086)}}, {{A, B, C, X(1016), X(38955)}}, {{A, B, C, X(1500), X(21025)}}, {{A, B, C, X(3227), X(41683)}}, {{A, B, C, X(3661), X(56191)}}, {{A, B, C, X(3762), X(3948)}}, {{A, B, C, X(4125), X(59212)}}, {{A, B, C, X(9263), X(21100)}}, {{A, B, C, X(13466), X(14431)}}, {{A, B, C, X(16589), X(21024)}}, {{A, B, C, X(17734), X(27709)}}, {{A, B, C, X(17743), X(56133)}}, {{A, B, C, X(17790), X(18003)}}, {{A, B, C, X(18785), X(57944)}}, {{A, B, C, X(18832), X(40005)}}, {{A, B, C, X(20255), X(22171)}}, {{A, B, C, X(20336), X(41316)}}, {{A, B, C, X(24190), X(40147)}}, {{A, B, C, X(27475), X(56175)}}, {{A, B, C, X(27810), X(57162)}}, {{A, B, C, X(30701), X(56173)}}, {{A, B, C, X(31061), X(40098)}}, {{A, B, C, X(33934), X(41245)}}, {{A, B, C, X(36871), X(56281)}}, {{A, B, C, X(40014), X(56127)}}, {{A, B, C, X(56122), X(56134)}}, {{A, B, C, X(56251), X(57947)}}
X(60288) = barycentric product X(i)*X(j) for these (i, j): {10, 31002}, {313, 37129}, {321, 3227}, {512, 57994}, {523, 889}, {850, 898}, {1441, 36798}, {1577, 4607}, {16732, 5381}, {20948, 34075}, {27801, 739}, {27808, 43928}, {32718, 44173}, {35353, 668}, {41683, 75}
X(60288) = barycentric quotient X(i)/X(j) for these (i, j): {2, 52897}, {4, 52890}, {10, 899}, {37, 3230}, {226, 52896}, {313, 6381}, {321, 536}, {512, 890}, {523, 891}, {594, 52959}, {661, 3768}, {739, 1333}, {889, 99}, {898, 110}, {1089, 3994}, {1441, 43037}, {1577, 4728}, {3120, 19945}, {3125, 1646}, {3227, 81}, {3700, 4526}, {3701, 4009}, {3948, 4465}, {3952, 23343}, {3994, 42083}, {4033, 23891}, {4036, 14431}, {4080, 52900}, {4086, 14430}, {4120, 14437}, {4125, 4937}, {4607, 662}, {4705, 14404}, {5381, 4567}, {8034, 33917}, {13576, 52902}, {14431, 14434}, {16732, 52626}, {21051, 14426}, {23892, 57129}, {27801, 35543}, {27808, 41314}, {30588, 52901}, {30591, 30592}, {31002, 86}, {32718, 1576}, {34075, 163}, {35353, 513}, {35532, 52882}, {36798, 21}, {36872, 52680}, {37129, 58}, {38955, 45145}, {41683, 1}, {43928, 3733}, {52754, 51420}, {52757, 16702}, {52959, 59797}, {57994, 670}

X(60289) = X(2)X(6408)∩X(4)X(6470)

Barycentrics    -65*(b^2-c^2)^2+a^2*(33*a^2+32*b^2+32*c^2)+112*a^2*S : :
Barycentrics    1 / (4*S + 7*SA) : :

X(60289) lies on these lines: {2, 6408}, {3, 60311}, {4, 6470}, {5, 60312}, {6, 60290}, {98, 43122}, {372, 60298}, {485, 17538}, {486, 6436}, {1131, 6221}, {1132, 13665}, {1151, 14241}, {1327, 42570}, {1328, 35771}, {1587, 54597}, {1657, 60291}, {3070, 34089}, {3311, 54599}, {3312, 3591}, {3316, 42259}, {3317, 3594}, {3590, 21735}, {3627, 43560}, {3843, 43561}, {3850, 6501}, {6396, 43558}, {6419, 12819}, {6426, 43518}, {6434, 60315}, {6459, 12818}, {6482, 52667}, {6499, 43387}, {6500, 23046}, {6564, 43571}, {6568, 50722}, {6811, 54921}, {7582, 60302}, {7584, 60300}, {10194, 31412}, {13886, 43570}, {13935, 43565}, {14893, 54543}, {15684, 60295}, {23251, 60301}, {23267, 34091}, {23269, 43209}, {35821, 43562}, {35822, 60314}, {38335, 54542}, {41954, 43517}, {42540, 49140}, {43340, 60294}, {43434, 43512}, {43791, 49138}, {46333, 60299}, {53513, 60305}

X(60289) = isogonal conjugate of X(6407)
X(60289) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(6470)}}, {{A, B, C, X(6), X(6408)}}, {{A, B, C, X(74), X(1151)}}, {{A, B, C, X(372), X(6436)}}, {{A, B, C, X(493), X(13452)}}, {{A, B, C, X(1173), X(3312)}}, {{A, B, C, X(1585), X(17538)}}, {{A, B, C, X(1659), X(7317)}}, {{A, B, C, X(3535), X(33703)}}, {{A, B, C, X(5417), X(6396)}}, {{A, B, C, X(5551), X(14121)}}, {{A, B, C, X(6199), X(43713)}}, {{A, B, C, X(6426), X(6501)}}, {{A, B, C, X(6434), X(6500)}}, {{A, B, C, X(6491), X(6499)}}

X(60290) = X(2)X(6407)∩X(4)X(6471)

Barycentrics    -65*(b^2-c^2)^2+a^2*(33*a^2+32*b^2+32*c^2)-112*a^2*S : :
Barycentrics    1 / (4*S - 7*SA) : :

X(60290) lies on the Kiepert hyperbola and on these lines: {2, 6407}, {3, 60312}, {4, 6471}, {5, 60311}, {6, 60289}, {98, 43123}, {371, 60297}, {485, 6435}, {486, 17538}, {1131, 13785}, {1132, 6398}, {1152, 14226}, {1327, 35770}, {1328, 42571}, {1588, 43536}, {1657, 60292}, {3071, 34091}, {3311, 3590}, {3312, 54598}, {3316, 3592}, {3317, 42258}, {3591, 21735}, {3627, 43561}, {3843, 43560}, {3850, 6500}, {6200, 43559}, {6420, 12818}, {6425, 43517}, {6433, 60316}, {6460, 12819}, {6483, 52666}, {6498, 43386}, {6501, 23046}, {6565, 43570}, {6569, 50721}, {6813, 54921}, {7581, 60301}, {7583, 60299}, {9540, 43564}, {10195, 42561}, {13939, 43571}, {14893, 54542}, {15684, 60296}, {23261, 60302}, {23273, 34089}, {23275, 43210}, {35820, 43563}, {35823, 60313}, {38335, 54543}, {41953, 43518}, {42539, 49140}, {43341, 60293}, {43435, 43511}, {43792, 49138}, {46333, 60300}, {53516, 60306}

X(60290) = isogonal conjugate of X(6408)
X(60290) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(6471)}}, {{A, B, C, X(6), X(6407)}}, {{A, B, C, X(74), X(1152)}}, {{A, B, C, X(371), X(6435)}}, {{A, B, C, X(494), X(13452)}}, {{A, B, C, X(1173), X(3311)}}, {{A, B, C, X(1586), X(17538)}}, {{A, B, C, X(3536), X(33703)}}, {{A, B, C, X(5419), X(6200)}}, {{A, B, C, X(5551), X(7090)}}, {{A, B, C, X(6395), X(43713)}}, {{A, B, C, X(6425), X(6500)}}, {{A, B, C, X(6433), X(6501)}}, {{A, B, C, X(6490), X(6498)}}, {{A, B, C, X(7317), X(13390)}}

X(60291) = X(2)X(6426)∩X(4)X(6199)

Barycentrics    -25*(b^2-c^2)^2+a^2*(7*a^2+18*b^2+18*c^2)+48*a^2*S : :
Barycentrics    1 / (3*S + 4*SA) : :

X(60291) lies on the Kiepert hyperbola and on these lines: {2, 6426}, {3, 43536}, {4, 6199}, {5, 54597}, {6, 60292}, {20, 14241}, {30, 60301}, {140, 34089}, {226, 31602}, {372, 42604}, {381, 60302}, {485, 3522}, {486, 5068}, {1131, 1151}, {1132, 3854}, {1327, 3146}, {1328, 3832}, {1585, 54710}, {1587, 10194}, {1656, 34091}, {1657, 60289}, {2043, 33604}, {2044, 33605}, {2045, 43554}, {2046, 43555}, {3068, 43560}, {3069, 60312}, {3070, 3590}, {3091, 14226}, {3312, 3317}, {3316, 3523}, {3533, 6408}, {3543, 6447}, {3592, 54599}, {3839, 60308}, {3850, 6500}, {5072, 43386}, {5490, 32814}, {6396, 10195}, {6425, 42537}, {6431, 42539}, {6451, 23269}, {6459, 41954}, {6460, 43409}, {6472, 35405}, {6519, 58208}, {6564, 12819}, {6568, 50724}, {6807, 54498}, {6811, 60185}, {6813, 54523}, {7000, 60127}, {7374, 60150}, {7388, 54616}, {7389, 60143}, {7583, 60306}, {7585, 43561}, {8972, 42414}, {9543, 13886}, {10147, 42538}, {13939, 43316}, {15022, 35822}, {15683, 42525}, {15717, 43256}, {17578, 43566}, {18538, 43565}, {19054, 60296}, {21734, 43879}, {21735, 45384}, {23249, 43570}, {23251, 41969}, {23267, 43564}, {32787, 54543}, {35018, 42523}, {35770, 42605}, {41950, 43338}, {42197, 50245}, {42265, 43411}, {42273, 43377}, {42417, 54598}, {42600, 43558}, {43212, 46936}, {43562, 50687}, {43567, 50689}, {50691, 60309}, {50692, 60295}, {50693, 60299}, {54531, 55569}, {54867, 55573}

X(60291) = isogonal conjugate of X(6425)
X(60291) = X(i)-cross conjugate of X(j) for these {i, j}: {8972, 2}, {42414, 1132}, {42568, 3317}, {42570, 1131}, {42578, 3316}, {43519, 43561}, {43785, 43571}
X(60291) = pole of line {8972, 42414} with respect to the Kiepert hyperbola
X(60291) = pole of line {6425, 32564} with respect to the Stammler hyperbola
X(60291) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(6199)}}, {{A, B, C, X(6), X(6426)}}, {{A, B, C, X(54), X(6396)}}, {{A, B, C, X(372), X(57730)}}, {{A, B, C, X(493), X(1151)}}, {{A, B, C, X(588), X(14528)}}, {{A, B, C, X(1123), X(43731)}}, {{A, B, C, X(1336), X(43732)}}, {{A, B, C, X(1585), X(3522)}}, {{A, B, C, X(1586), X(5068)}}, {{A, B, C, X(1659), X(7320)}}, {{A, B, C, X(3311), X(6497)}}, {{A, B, C, X(3523), X(55573)}}, {{A, B, C, X(3535), X(5059)}}, {{A, B, C, X(3536), X(3854)}}, {{A, B, C, X(5056), X(55569)}}, {{A, B, C, X(5417), X(34567)}}, {{A, B, C, X(5558), X(14121)}}, {{A, B, C, X(6408), X(6500)}}, {{A, B, C, X(6447), X(6451)}}, {{A, B, C, X(8946), X(39955)}}, {{A, B, C, X(22334), X(41438)}}, {{A, B, C, X(24244), X(35510)}}, {{A, B, C, X(25417), X(46434)}}, {{A, B, C, X(30557), X(56030)}}, {{A, B, C, X(51316), X(53513)}}
X(60291) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1131, 1151, 42540}, {3312, 3317, 42541}, {42414, 42578, 8972}

X(60292) = X(2)X(6425)∩X(4)X(6395)

Barycentrics    -25*(b^2-c^2)^2+a^2*(7*a^2+18*b^2+18*c^2)-48*a^2*S : :
Barycentrics    1 / (3*S - 4*SA) : :

X(60292) lies on the Kiepert hyperbola and on these lines: {2, 6425}, {3, 54597}, {4, 6395}, {5, 43536}, {6, 60291}, {20, 14226}, {30, 60302}, {140, 34091}, {226, 31601}, {371, 42605}, {381, 60301}, {485, 5068}, {486, 3522}, {1131, 3854}, {1132, 1152}, {1327, 3832}, {1328, 3146}, {1586, 54710}, {1588, 10195}, {1656, 34089}, {1657, 60290}, {2043, 33605}, {2044, 33604}, {2045, 43555}, {2046, 43554}, {3068, 60311}, {3069, 43561}, {3071, 3591}, {3091, 14241}, {3311, 3316}, {3317, 3523}, {3533, 6407}, {3543, 6448}, {3594, 54598}, {3839, 60307}, {3850, 6501}, {5072, 43387}, {6200, 10194}, {6426, 42538}, {6432, 42540}, {6452, 23275}, {6459, 43410}, {6460, 41953}, {6473, 35405}, {6522, 58208}, {6565, 12818}, {6569, 50723}, {6808, 54498}, {6811, 54523}, {6813, 60185}, {7000, 60150}, {7374, 60127}, {7388, 60143}, {7389, 54616}, {7584, 60305}, {7586, 43560}, {9542, 55859}, {9543, 42601}, {10148, 42537}, {13886, 43317}, {13939, 49135}, {13941, 42413}, {15022, 35823}, {15683, 42524}, {15717, 43257}, {17578, 43567}, {17851, 49133}, {18762, 43564}, {19053, 60295}, {21734, 43880}, {21735, 45385}, {23259, 43571}, {23261, 41970}, {23273, 43565}, {32788, 54542}, {35018, 42522}, {35771, 42604}, {41949, 43339}, {42262, 43412}, {42270, 43376}, {42418, 54599}, {43211, 46936}, {43563, 50687}, {43566, 50689}, {45870, 53099}, {50691, 60310}, {50692, 60296}, {50693, 60300}, {54531, 55573}, {54867, 55569}

X(60292) = isogonal conjugate of X(6426)
X(60292) = X(i)-cross conjugate of X(j) for these {i, j}: {13941, 2}, {42413, 1131}, {42569, 3316}, {42571, 1132}, {42579, 3317}, {43520, 43560}, {43786, 43570}
X(60292) = pole of line {13941, 42413} with respect to the Kiepert hyperbola
X(60292) = pole of line {6426, 32571} with respect to the Stammler hyperbola
X(60292) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(6395)}}, {{A, B, C, X(6), X(6425)}}, {{A, B, C, X(54), X(6200)}}, {{A, B, C, X(371), X(57730)}}, {{A, B, C, X(494), X(1152)}}, {{A, B, C, X(589), X(14528)}}, {{A, B, C, X(1123), X(43732)}}, {{A, B, C, X(1336), X(43731)}}, {{A, B, C, X(1585), X(5068)}}, {{A, B, C, X(1586), X(3522)}}, {{A, B, C, X(3312), X(6496)}}, {{A, B, C, X(3523), X(55569)}}, {{A, B, C, X(3535), X(3854)}}, {{A, B, C, X(3536), X(5059)}}, {{A, B, C, X(5056), X(55573)}}, {{A, B, C, X(5419), X(34567)}}, {{A, B, C, X(5558), X(7090)}}, {{A, B, C, X(6407), X(6501)}}, {{A, B, C, X(6448), X(6452)}}, {{A, B, C, X(7320), X(13390)}}, {{A, B, C, X(8948), X(39955)}}, {{A, B, C, X(22334), X(41437)}}, {{A, B, C, X(24243), X(35510)}}, {{A, B, C, X(25417), X(46433)}}, {{A, B, C, X(30556), X(56030)}}, {{A, B, C, X(51316), X(53516)}}
X(60292) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3311, 3316, 42542}, {42413, 42579, 13941}

X(60293) = X(2)X(6432)∩X(4)X(6449)

Barycentrics    a^2*(21*a^2-50*b^2-50*c^2)+29*(b^2-c^2)^2-40*a^2*S : :
Barycentrics    1 / (5*S + 2*SA) : :

X(60293) lies on the Kiepert hyperbola and on these lines: {2, 6432}, {3, 60305}, {4, 6449}, {5, 60306}, {6, 60294}, {20, 12818}, {140, 10138}, {485, 10303}, {486, 7486}, {548, 60309}, {549, 14241}, {590, 1132}, {631, 43382}, {1131, 15717}, {1151, 54543}, {1271, 60194}, {1327, 10304}, {1328, 10576}, {1587, 43568}, {3068, 3591}, {3071, 60296}, {3091, 12819}, {3316, 3526}, {3317, 3628}, {3523, 43570}, {3534, 60307}, {3543, 54595}, {3590, 8253}, {3595, 5490}, {3839, 54596}, {5055, 14226}, {5056, 43571}, {5066, 60308}, {5072, 60310}, {5418, 49140}, {5420, 60297}, {6459, 43561}, {6811, 54845}, {6813, 52519}, {7000, 14488}, {7374, 60132}, {7388, 18843}, {7389, 60219}, {7583, 60315}, {7584, 54597}, {7586, 10194}, {8976, 34089}, {8981, 60302}, {9540, 43383}, {9543, 43508}, {10195, 13935}, {11540, 43505}, {13886, 43564}, {13941, 34091}, {15640, 42602}, {15683, 43566}, {15698, 60301}, {15706, 23269}, {15709, 43536}, {15721, 43342}, {19117, 43565}, {23249, 58186}, {35821, 43563}, {41950, 43338}, {41951, 60300}, {42262, 43412}, {42265, 50692}, {42273, 54598}, {43341, 60290}, {43376, 60303}, {43512, 43567}, {43560, 50693}, {43879, 60311}

X(60293) = isogonal conjugate of X(6431)
X(60293) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(6449)}}, {{A, B, C, X(6), X(6432)}}, {{A, B, C, X(372), X(57714)}}, {{A, B, C, X(1123), X(13606)}}, {{A, B, C, X(1585), X(10303)}}, {{A, B, C, X(1586), X(7486)}}, {{A, B, C, X(3526), X(55573)}}, {{A, B, C, X(3535), X(15717)}}, {{A, B, C, X(3536), X(15022)}}, {{A, B, C, X(3628), X(55569)}}, {{A, B, C, X(8946), X(39389)}}, {{A, B, C, X(40434), X(46434)}}, {{A, B, C, X(41438), X(43713)}}

X(60294) = X(2)X(6431)∩X(4)X(6450)

Barycentrics    a^2*(21*a^2-50*b^2-50*c^2)+29*(b^2-c^2)^2+40*a^2*S : :
Barycentrics    1 / (5*S - 2*SA) : :

X(60294) lies on the Kiepert hyperbola and on these lines: {2, 6431}, {3, 60306}, {4, 6450}, {5, 60305}, {6, 60293}, {20, 12819}, {140, 10137}, {226, 21170}, {485, 7486}, {486, 10303}, {548, 60310}, {549, 14226}, {615, 1131}, {631, 43383}, {1132, 15717}, {1152, 54542}, {1270, 60196}, {1327, 10577}, {1328, 10304}, {1588, 43569}, {3069, 3590}, {3070, 60295}, {3091, 12818}, {3316, 3628}, {3317, 3526}, {3523, 43571}, {3534, 60308}, {3543, 54596}, {3591, 8252}, {3593, 5491}, {3839, 54595}, {5055, 14241}, {5056, 43570}, {5066, 60307}, {5072, 60309}, {5418, 60298}, {5420, 49140}, {6460, 43560}, {6811, 52519}, {6813, 54845}, {7000, 60132}, {7374, 14488}, {7388, 60219}, {7389, 18843}, {7583, 43536}, {7584, 60316}, {7585, 10195}, {8972, 34089}, {9540, 10194}, {11540, 43506}, {13935, 43382}, {13939, 43565}, {13951, 34091}, {13966, 60301}, {15640, 42603}, {15683, 43567}, {15698, 60302}, {15706, 23275}, {15709, 52047}, {15721, 43343}, {19116, 43564}, {23259, 58186}, {35820, 43562}, {41949, 43339}, {41952, 60299}, {42262, 50692}, {42265, 43411}, {42270, 54599}, {43340, 60289}, {43377, 60304}, {43511, 43566}, {43561, 50693}, {43880, 60312}

X(60294) = isogonal conjugate of X(6432)
X(60294) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(6450)}}, {{A, B, C, X(6), X(6431)}}, {{A, B, C, X(371), X(57714)}}, {{A, B, C, X(1336), X(13606)}}, {{A, B, C, X(1585), X(7486)}}, {{A, B, C, X(1586), X(10303)}}, {{A, B, C, X(3526), X(55569)}}, {{A, B, C, X(3535), X(15022)}}, {{A, B, C, X(3536), X(15717)}}, {{A, B, C, X(3628), X(55573)}}, {{A, B, C, X(8948), X(39389)}}, {{A, B, C, X(40434), X(46433)}}, {{A, B, C, X(41437), X(43713)}}

X(60295) = X(2)X(6434)∩X(6)X(60296)

Barycentrics    119*a^4+50*a^2*b^2+50*a^2*c^2-169*(b^2-c^2)^2+240*a^2*S : :
Barycentrics    1 / (5*S + 12*SA) : :

X(60295) lies on the Kiepert hyperbola and on these lines: {2, 6434}, {6, 60296}, {485, 15683}, {549, 34089}, {1131, 41945}, {3070, 60294}, {3146, 43570}, {3316, 10304}, {3534, 43536}, {3543, 60305}, {3590, 50693}, {3591, 3594}, {3832, 43571}, {3839, 60306}, {5055, 34091}, {5066, 54597}, {6221, 14241}, {6408, 60316}, {6470, 43520}, {6501, 23046}, {7000, 60330}, {7374, 60337}, {7486, 43565}, {7585, 54542}, {8976, 58197}, {10194, 15022}, {10195, 15717}, {10303, 43564}, {12818, 50687}, {12819, 35771}, {13665, 60307}, {13847, 60312}, {15684, 60289}, {15709, 60315}, {19053, 60292}, {19054, 54543}, {23249, 42608}, {32787, 43560}, {33699, 60301}, {41948, 43519}, {41961, 60299}, {42537, 43383}, {42575, 42577}, {43340, 60309}, {43438, 43883}, {43513, 60297}, {43562, 43791}, {43566, 52666}, {49140, 60303}, {50692, 60291}

X(60295) = isogonal conjugate of X(6433)
X(60295) = X(i)-cross conjugate of X(j) for these {i, j}: {42575, 3591}, {42577, 14226}, {51850, 14241}
X(60295) = pole of line {42575, 42577} with respect to the Kiepert hyperbola
X(60295) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(6434)}}, {{A, B, C, X(54), X(35771)}}, {{A, B, C, X(588), X(43713)}}, {{A, B, C, X(1585), X(15683)}}, {{A, B, C, X(6408), X(6501)}}, {{A, B, C, X(10304), X(55573)}}

X(60296) = X(2)X(6433)∩X(6)X(60295)

Barycentrics    119*a^4+50*a^2*b^2+50*a^2*c^2-169*(b^2-c^2)^2-240*a^2*S : :
Barycentrics    1 / (5*S - 12*SA) : :

X(60296) lies on the Kiepert hyperbola and on these lines: {2, 6433}, {6, 60295}, {486, 15683}, {549, 34091}, {1132, 41946}, {3071, 60293}, {3146, 43571}, {3317, 10304}, {3534, 54597}, {3543, 60306}, {3590, 3592}, {3591, 50693}, {3832, 43570}, {3839, 60305}, {5055, 34089}, {5066, 43536}, {6398, 14226}, {6407, 60315}, {6471, 43519}, {6500, 23046}, {7000, 60337}, {7374, 60330}, {7486, 43564}, {7586, 54543}, {10194, 15717}, {10195, 15022}, {10303, 43565}, {12818, 35770}, {12819, 50687}, {13785, 60308}, {13846, 60311}, {13951, 58197}, {15684, 60290}, {15709, 60316}, {19053, 54542}, {19054, 60291}, {23259, 42609}, {32788, 43561}, {33699, 60302}, {41947, 43520}, {41962, 60300}, {42538, 43382}, {42574, 42576}, {43341, 60310}, {43439, 43884}, {43514, 60298}, {43563, 43792}, {43567, 52667}, {49140, 60304}, {50692, 60292}

X(60296) = isogonal conjugate of X(6434)
X(60296) = X(i)-cross conjugate of X(j) for these {i, j}: {42574, 3590}, {42576, 14241}, {51849, 14226}
X(60296) = pole of line {42574, 42576} with respect to the Kiepert hyperbola
X(60296) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(6433)}}, {{A, B, C, X(54), X(35770)}}, {{A, B, C, X(589), X(43713)}}, {{A, B, C, X(1586), X(15683)}}, {{A, B, C, X(6407), X(6500)}}, {{A, B, C, X(10304), X(55569)}}

X(60297) = X(2)X(6436)∩X(4)X(42537)

Barycentrics    -56*a^4+121*a^2*b^2+121*a^2*c^2-65*(b^2-c^2)^2+66*a^2*S : :
Barycentrics    1 / (11*S + 3*SA) : :

X(60297) lies on the Kiepert hyperbola and on these lines: {2, 6436}, {4, 42537}, {6, 60298}, {371, 60290}, {372, 60311}, {485, 6408}, {486, 6470}, {590, 43569}, {1131, 15708}, {1151, 11737}, {1327, 8253}, {1328, 6221}, {3312, 43322}, {3317, 35771}, {3591, 6419}, {3594, 10195}, {5420, 60293}, {6199, 42573}, {6200, 54599}, {6396, 14241}, {6426, 42639}, {6561, 60308}, {10124, 42578}, {10194, 32787}, {10576, 43560}, {12818, 15688}, {13821, 41895}, {13847, 43559}, {14226, 32785}, {14869, 43570}, {15685, 43562}, {15686, 43254}, {15697, 43566}, {19053, 34091}, {31414, 60303}, {32789, 41966}, {35823, 60304}, {42261, 43380}, {42274, 60314}, {42277, 54595}, {42526, 42601}, {43513, 60295}, {43563, 53130}, {52667, 60307}

X(60297) = isogonal conjugate of X(6435)
X(60297) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(6436)}}, {{A, B, C, X(371), X(6408)}}, {{A, B, C, X(372), X(6470)}}, {{A, B, C, X(1585), X(15694)}}, {{A, B, C, X(1586), X(15699)}}, {{A, B, C, X(3312), X(35771)}}, {{A, B, C, X(3535), X(15708)}}, {{A, B, C, X(3594), X(6419)}}, {{A, B, C, X(6221), X(6396)}}

X(60298) = X(2)X(6435)∩X(4)X(42538)

Barycentrics    -56*a^4+121*a^2*b^2+121*a^2*c^2-65*(b^2-c^2)^2-66*a^2*S : :
Barycentrics    1 / (11*S - 3*SA) : :

X(60298) lies on the Kiepert hyperbola and on these lines: {2, 6435}, {4, 42538}, {6, 60297}, {371, 60312}, {372, 60289}, {485, 6471}, {486, 6407}, {615, 43568}, {1132, 15708}, {1152, 11737}, {1327, 6398}, {1328, 8252}, {3311, 43323}, {3316, 35770}, {3590, 6420}, {3592, 10194}, {5418, 60294}, {6200, 14226}, {6395, 42572}, {6396, 54598}, {6425, 42640}, {6560, 60307}, {10124, 42579}, {10195, 32788}, {10577, 43561}, {12819, 15688}, {13701, 41895}, {13846, 43558}, {14241, 32786}, {14869, 43571}, {15685, 43563}, {15686, 43255}, {15697, 43567}, {19054, 34089}, {32790, 41965}, {35822, 60303}, {42260, 43381}, {42274, 54596}, {42277, 60313}, {42527, 42600}, {43514, 60296}, {43562, 53131}, {52666, 60308}

X(60298) = isogonal conjugate of X(6436)
X(60298) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(6435)}}, {{A, B, C, X(371), X(6471)}}, {{A, B, C, X(372), X(6407)}}, {{A, B, C, X(1585), X(15699)}}, {{A, B, C, X(1586), X(15694)}}, {{A, B, C, X(3311), X(35770)}}, {{A, B, C, X(3536), X(15708)}}, {{A, B, C, X(3592), X(6420)}}, {{A, B, C, X(6200), X(6398)}}

X(60299) = X(2)X(6438)∩X(4)X(31487)

Barycentrics    11*a^4+50*a^2*b^2+50*a^2*c^2-61*(b^2-c^2)^2+120*a^2*S : :
Barycentrics    1 / (5*S + 6*SA) : :

X(60299) lies on the Kiepert hyperbola and on these lines: {2, 6438}, {4, 31487}, {6, 60300}, {20, 43570}, {30, 10137}, {226, 17801}, {376, 43340}, {381, 60306}, {485, 10304}, {548, 60303}, {549, 3316}, {590, 43384}, {1131, 13846}, {1132, 19054}, {1327, 6476}, {1328, 7585}, {1587, 43559}, {1991, 54502}, {3068, 43380}, {3091, 43571}, {3317, 5055}, {3526, 43564}, {3534, 8972}, {3543, 12818}, {3590, 15717}, {3591, 15022}, {3628, 43565}, {3830, 42643}, {3839, 12819}, {5066, 14226}, {5072, 60304}, {6492, 43512}, {6564, 43563}, {6811, 60337}, {6813, 60330}, {7000, 60142}, {7374, 53100}, {7486, 10194}, {7583, 60290}, {7586, 43386}, {10195, 10303}, {13639, 60208}, {13665, 15698}, {13886, 15684}, {13925, 58202}, {13966, 34091}, {15704, 43521}, {15709, 34089}, {15759, 45384}, {23046, 60310}, {23249, 60313}, {23259, 42608}, {31412, 43561}, {32785, 41958}, {32787, 43567}, {33699, 43383}, {35815, 43257}, {41952, 60294}, {41961, 60295}, {42265, 60312}, {42522, 43504}, {42540, 43318}, {43406, 54542}, {43438, 43879}, {43508, 54599}, {43525, 43558}, {46333, 60289}, {49140, 53130}, {50693, 60291}, {52048, 60315}

X(60299) = isogonal conjugate of X(6437)
X(60299) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(6438)}}, {{A, B, C, X(493), X(43713)}}, {{A, B, C, X(549), X(55573)}}, {{A, B, C, X(1585), X(10304)}}, {{A, B, C, X(3535), X(15683)}}, {{A, B, C, X(5055), X(55569)}}, {{A, B, C, X(6200), X(6476)}}, {{A, B, C, X(6409), X(6492)}}, {{A, B, C, X(8946), X(34572)}}

X(60300) = X(2)X(6437)∩X(30)X(10138)

Barycentrics    11*a^4+50*a^2*b^2+50*a^2*c^2-61*(b^2-c^2)^2-120*a^2*S : :
Barycentrics    1 / (5*S - 6*SA) : :

X(60300) lies on the Kiepert hyperbola and on these lines: {2, 6437}, {6, 60299}, {20, 43571}, {30, 10138}, {226, 17804}, {376, 43341}, {381, 60305}, {486, 10304}, {548, 60304}, {549, 3317}, {591, 54506}, {615, 43385}, {1131, 19053}, {1132, 13847}, {1327, 7586}, {1328, 6477}, {1588, 43558}, {3069, 43381}, {3091, 43570}, {3316, 5055}, {3526, 43565}, {3534, 13941}, {3543, 12819}, {3590, 15022}, {3591, 15717}, {3628, 43564}, {3830, 42644}, {3839, 12818}, {5066, 14241}, {5072, 60303}, {6493, 43511}, {6565, 43562}, {6811, 60330}, {6813, 60337}, {7000, 53100}, {7374, 60142}, {7486, 10195}, {7584, 60289}, {7585, 43387}, {8981, 34089}, {10194, 10303}, {13759, 60207}, {13785, 15698}, {13939, 15684}, {13993, 58202}, {15704, 43522}, {15709, 34091}, {15759, 45385}, {23046, 60309}, {23249, 42609}, {23259, 60314}, {32786, 41957}, {32788, 43566}, {33699, 43382}, {35814, 43256}, {41951, 60293}, {41962, 60296}, {42262, 60311}, {42523, 43503}, {42539, 43319}, {42561, 43560}, {43405, 54543}, {43439, 43880}, {43507, 54598}, {43526, 43559}, {46333, 60290}, {49140, 53131}, {50693, 60292}, {52047, 60316}

X(60300) = isogonal conjugate of X(6438)
X(60300) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(6437)}}, {{A, B, C, X(494), X(43713)}}, {{A, B, C, X(549), X(55569)}}, {{A, B, C, X(1586), X(10304)}}, {{A, B, C, X(3536), X(15683)}}, {{A, B, C, X(5055), X(55573)}}, {{A, B, C, X(6396), X(6477)}}, {{A, B, C, X(6410), X(6493)}}, {{A, B, C, X(8948), X(34572)}}

X(60301) = X(2)X(6446)∩X(6)X(60302)

Barycentrics    65*a^4+32*a^2*b^2+32*a^2*c^2-97*(b^2-c^2)^2+144*a^2*S : :
Barycentrics    1 / (4*S + 9*SA) : :

X(60301) lies on the Kiepert hyperbola and on these lines: {2, 6446}, {6, 60302}, {30, 60291}, {376, 3590}, {381, 60292}, {485, 6486}, {486, 41106}, {1131, 15682}, {1132, 6499}, {1328, 43791}, {3068, 60313}, {3070, 34091}, {3316, 19708}, {3317, 42273}, {3524, 10195}, {3525, 42524}, {3545, 3591}, {3830, 42522}, {3845, 43561}, {3860, 43387}, {5071, 10194}, {6490, 9541}, {6564, 43569}, {7581, 60290}, {7585, 54598}, {8703, 60311}, {9681, 43570}, {12101, 54542}, {12819, 35822}, {13665, 43566}, {13966, 60294}, {15698, 60293}, {15702, 43564}, {19054, 43563}, {19709, 60312}, {21735, 42526}, {23249, 43536}, {23251, 60289}, {23267, 54597}, {23269, 34089}, {31412, 43558}, {32787, 60307}, {33699, 60295}, {41955, 43522}, {41964, 43565}, {43257, 51850}, {43386, 43567}, {43413, 43432}, {50724, 54655}

X(60301) = isogonal conjugate of X(6445)
X(60301) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(6446)}}, {{A, B, C, X(371), X(6486)}}, {{A, B, C, X(493), X(11738)}}, {{A, B, C, X(588), X(20421)}}, {{A, B, C, X(1152), X(6499)}}, {{A, B, C, X(1585), X(11001)}}, {{A, B, C, X(1586), X(41106)}}, {{A, B, C, X(3535), X(15682)}}, {{A, B, C, X(3536), X(41099)}}, {{A, B, C, X(6221), X(6490)}}, {{A, B, C, X(19708), X(55573)}}, {{A, B, C, X(41515), X(46212)}}

X(60302) = X(2)X(6445)∩X(6)X(60301)

Barycentrics    65*a^4+32*a^2*b^2+32*a^2*c^2-97*(b^2-c^2)^2-144*a^2*S : :
Barycentrics    1 / (4*S - 9*SA) : :

X(60302) lies on the Kiepert hyperbola and on these lines: {2, 6445}, {6, 60301}, {30, 60292}, {376, 3591}, {381, 60291}, {485, 41106}, {486, 6487}, {1131, 6498}, {1132, 15682}, {1327, 43792}, {3069, 60314}, {3071, 34089}, {3316, 42270}, {3317, 19708}, {3524, 10194}, {3525, 42525}, {3545, 3590}, {3830, 42523}, {3845, 43560}, {3860, 43386}, {5071, 10195}, {6491, 14226}, {6565, 43568}, {7582, 60289}, {7586, 54599}, {8703, 60312}, {8981, 60293}, {12101, 54543}, {12818, 35823}, {13785, 43567}, {15698, 60294}, {15702, 43565}, {19053, 43562}, {19709, 60311}, {21735, 42527}, {23259, 54597}, {23261, 60290}, {23273, 43536}, {23275, 34091}, {32788, 60308}, {33699, 60296}, {41956, 43521}, {41963, 43564}, {42561, 43559}, {43256, 51849}, {43387, 43566}, {43414, 43433}, {50723, 54656}

X(60302) = isogonal conjugate of X(6446)
X(60302) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(6445)}}, {{A, B, C, X(372), X(6487)}}, {{A, B, C, X(494), X(11738)}}, {{A, B, C, X(589), X(20421)}}, {{A, B, C, X(1151), X(6498)}}, {{A, B, C, X(1585), X(41106)}}, {{A, B, C, X(1586), X(11001)}}, {{A, B, C, X(3535), X(41099)}}, {{A, B, C, X(3536), X(15682)}}, {{A, B, C, X(6398), X(6491)}}, {{A, B, C, X(19708), X(55569)}}, {{A, B, C, X(41516), X(46212)}}

X(60303) = X(2)X(6448)∩X(6)X(60304)

Barycentrics    13*a^4+72*a^2*b^2+72*a^2*c^2-85*(b^2-c^2)^2+168*a^2*S : :
Barycentrics    1 / (6*S + 7*SA) : :

X(60303) lies on the Kiepert hyperbola and on these lines: {2, 6448}, {6, 60304}, {485, 21735}, {548, 60299}, {1131, 1657}, {1132, 3850}, {1152, 34089}, {1327, 6453}, {1587, 43565}, {3311, 43561}, {3316, 6410}, {3523, 60311}, {3590, 15712}, {3591, 7581}, {3627, 43566}, {3843, 43567}, {5056, 60312}, {5072, 60300}, {6200, 43570}, {6420, 43569}, {6425, 60307}, {6451, 23269}, {6813, 54522}, {7375, 60238}, {7376, 60277}, {7582, 43571}, {8960, 12818}, {10195, 23267}, {12819, 31412}, {13886, 43560}, {14241, 17538}, {14893, 54599}, {31414, 60297}, {35822, 60298}, {38335, 54598}, {41961, 60305}, {41963, 43521}, {43376, 60293}, {43409, 43510}, {43536, 53513}, {46333, 60313}, {49140, 60295}

X(60303) = isogonal conjugate of X(6447)
X(60303) = X(i)-cross conjugate of X(j) for these {i, j}: {43787, 14226}
X(60303) = pole of line {43787, 60303} with respect to the Kiepert hyperbola
X(60303) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(6448)}}, {{A, B, C, X(1152), X(6417)}}, {{A, B, C, X(1585), X(21735)}}, {{A, B, C, X(1657), X(3535)}}, {{A, B, C, X(3311), X(6410)}}, {{A, B, C, X(6200), X(6453)}}, {{A, B, C, X(6425), X(6451)}}, {{A, B, C, X(41438), X(57715)}}

X(60304) = X(2)X(6447)∩X(6)X(60303)

Barycentrics    13*a^4+72*a^2*b^2+72*a^2*c^2-85*(b^2-c^2)^2-168*a^2*S : :
Barycentrics    1 / (6*S - 7*SA) : :

X(60304) lies on the Kiepert hyperbola and on these lines: {2, 6447}, {6, 60303}, {486, 21735}, {548, 60300}, {1131, 3850}, {1132, 1657}, {1151, 34091}, {1328, 6454}, {1588, 43564}, {3312, 43560}, {3317, 6409}, {3523, 60312}, {3590, 7582}, {3591, 15712}, {3627, 43567}, {3843, 43566}, {5056, 60311}, {5072, 60299}, {6396, 43571}, {6419, 43568}, {6426, 60308}, {6452, 23275}, {6811, 54522}, {7375, 60277}, {7376, 60238}, {7581, 43570}, {10194, 23273}, {12818, 42561}, {12819, 58866}, {13939, 43561}, {14226, 17538}, {14893, 54598}, {31414, 60313}, {35823, 60297}, {38335, 54599}, {41962, 60306}, {41964, 43522}, {43377, 60294}, {43410, 43509}, {46333, 60314}, {49140, 60296}, {53516, 54597}

X(60304) = isogonal conjugate of X(6448)
X(60304) = X(i)-cross conjugate of X(j) for these {i, j}: {43788, 14241}
X(60304) = pole of line {43788, 60304} with respect to the Kiepert hyperbola
X(60304) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(6447)}}, {{A, B, C, X(1151), X(6418)}}, {{A, B, C, X(1586), X(21735)}}, {{A, B, C, X(1657), X(3536)}}, {{A, B, C, X(3312), X(6409)}}, {{A, B, C, X(6396), X(6454)}}, {{A, B, C, X(6426), X(6452)}}, {{A, B, C, X(41437), X(57715)}}

X(60305) = X(2)X(6450)∩X(4)X(6431)

Barycentrics    21*a^4+8*a^2*b^2+8*a^2*c^2-29*(b^2-c^2)^2+40*a^2*S : :
Barycentrics    1 / (2*S + 5*SA) : :

X(60305) lies on the Kiepert hyperbola and on these lines: {2, 6450}, {3, 60293}, {4, 6431}, {5, 60294}, {6, 60306}, {30, 10137}, {226, 17803}, {376, 43568}, {381, 60300}, {382, 1131}, {485, 3529}, {486, 3855}, {546, 1132}, {550, 3590}, {631, 43558}, {1327, 6459}, {1328, 7582}, {1587, 14226}, {1588, 60310}, {3068, 43570}, {3070, 3317}, {3071, 60308}, {3090, 43559}, {3311, 54542}, {3316, 3528}, {3543, 60295}, {3545, 43569}, {3591, 3851}, {3839, 60296}, {3861, 43889}, {5067, 42567}, {5871, 54875}, {6564, 10194}, {6811, 60102}, {6813, 60333}, {7000, 60331}, {7374, 60336}, {7375, 60100}, {7376, 60278}, {7584, 60292}, {8976, 42540}, {9543, 13886}, {10195, 10299}, {10783, 14234}, {11737, 13961}, {12818, 35821}, {12819, 23275}, {13665, 43560}, {13749, 14228}, {13935, 34091}, {13939, 38071}, {14227, 54874}, {14241, 23251}, {14269, 19117}, {15682, 35815}, {15687, 43566}, {15702, 43380}, {17578, 43340}, {19054, 54596}, {23273, 43561}, {33703, 43337}, {34089, 42259}, {35820, 43314}, {35822, 43563}, {41099, 60314}, {41958, 43506}, {41961, 60303}, {41967, 43521}, {42262, 54597}, {42265, 60315}, {42269, 43571}, {42284, 60309}, {43384, 43505}, {43410, 43797}, {43510, 43565}, {43516, 54595}, {53513, 60289}

X(60305) = isogonal conjugate of X(6449)
X(60305) = X(i)-cross conjugate of X(j) for these {i, j}: {23253, 4}
X(60305) = pole of line {23253, 60305} with respect to the Kiepert hyperbola
X(60305) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(6431)}}, {{A, B, C, X(6), X(6450)}}, {{A, B, C, X(371), X(13452)}}, {{A, B, C, X(372), X(14491)}}, {{A, B, C, X(382), X(3535)}}, {{A, B, C, X(493), X(16835)}}, {{A, B, C, X(546), X(3536)}}, {{A, B, C, X(588), X(11270)}}, {{A, B, C, X(1585), X(3529)}}, {{A, B, C, X(1586), X(3855)}}, {{A, B, C, X(1659), X(43734)}}, {{A, B, C, X(3311), X(43713)}}, {{A, B, C, X(3431), X(5417)}}, {{A, B, C, X(3528), X(55573)}}, {{A, B, C, X(3544), X(55569)}}, {{A, B, C, X(14121), X(43733)}}, {{A, B, C, X(24244), X(57897)}}, {{A, B, C, X(31371), X(55534)}}, {{A, B, C, X(39707), X(55154)}}, {{A, B, C, X(43699), X(53517)}}

X(60306) = X(2)X(6449)∩X(4)X(6432)

Barycentrics    21*a^4+8*a^2*b^2+8*a^2*c^2-29*(b^2-c^2)^2-40*a^2*S : :
Barycentrics    1 / (2*S - 5*SA) : :

X(60306) lies on the Kiepert hyperbola and on these lines: {2, 6449}, {3, 60294}, {4, 6432}, {5, 60293}, {6, 60305}, {30, 10138}, {226, 17806}, {376, 43569}, {381, 60299}, {382, 1132}, {485, 3855}, {486, 3529}, {546, 1131}, {550, 3591}, {631, 43559}, {1327, 7581}, {1328, 6460}, {1587, 60309}, {1588, 14241}, {3069, 43571}, {3070, 60307}, {3071, 3316}, {3090, 43558}, {3312, 54543}, {3317, 3528}, {3543, 60296}, {3545, 43568}, {3590, 3851}, {3839, 60295}, {3861, 43890}, {5067, 42566}, {6565, 10195}, {6811, 60333}, {6813, 60102}, {7000, 60336}, {7374, 60331}, {7375, 60278}, {7376, 60100}, {7583, 60291}, {9540, 34089}, {10194, 10299}, {10784, 14238}, {11737, 13903}, {12818, 23269}, {12819, 35820}, {13748, 14243}, {13785, 43561}, {13886, 38071}, {13939, 49135}, {13951, 42539}, {14226, 23261}, {14233, 54875}, {14242, 54876}, {14269, 19116}, {15682, 35814}, {15687, 43567}, {15702, 43381}, {17578, 43341}, {19053, 54595}, {23267, 43560}, {33703, 43336}, {34091, 42258}, {35821, 43315}, {35823, 43562}, {41099, 60313}, {41957, 43505}, {41962, 60304}, {41968, 43522}, {42262, 60316}, {42265, 43536}, {42268, 43570}, {42283, 60310}, {43385, 43506}, {43409, 43798}, {43509, 43564}, {43515, 54596}, {53516, 60290}

X(60306) = isogonal conjugate of X(6450)
X(60306) = X(i)-cross conjugate of X(j) for these {i, j}: {23263, 4}
X(60306) = pole of line {23263, 60306} with respect to the Kiepert hyperbola
X(60306) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(6432)}}, {{A, B, C, X(6), X(6449)}}, {{A, B, C, X(371), X(14491)}}, {{A, B, C, X(372), X(13452)}}, {{A, B, C, X(382), X(3536)}}, {{A, B, C, X(494), X(16835)}}, {{A, B, C, X(546), X(3535)}}, {{A, B, C, X(589), X(11270)}}, {{A, B, C, X(1585), X(3855)}}, {{A, B, C, X(1586), X(3529)}}, {{A, B, C, X(3312), X(43713)}}, {{A, B, C, X(3431), X(5419)}}, {{A, B, C, X(3528), X(55569)}}, {{A, B, C, X(3544), X(55573)}}, {{A, B, C, X(7090), X(43733)}}, {{A, B, C, X(13390), X(43734)}}, {{A, B, C, X(24243), X(57897)}}, {{A, B, C, X(31371), X(55533)}}, {{A, B, C, X(39707), X(55155)}}, {{A, B, C, X(43699), X(53520)}}

X(60307) = X(2)X(6452)∩X(30)X(3590)

Barycentrics    77*a^4+8*a^2*b^2+8*a^2*c^2-85*(b^2-c^2)^2+72*a^2*S : :
Barycentrics    1 / (2*S + 9*SA) : :

X(60307) lies on the Kiepert hyperbola and on these lines: {2, 6452}, {6, 60308}, {30, 3590}, {376, 10195}, {381, 3591}, {485, 15682}, {486, 41099}, {1131, 3830}, {1132, 3845}, {1152, 34091}, {1327, 43795}, {1328, 23267}, {1587, 60310}, {3070, 60306}, {3311, 43560}, {3316, 6409}, {3317, 23251}, {3524, 43564}, {3534, 60293}, {3536, 60138}, {3543, 6447}, {3545, 6454}, {3839, 60292}, {3860, 6395}, {5066, 60294}, {5071, 43565}, {6200, 43568}, {6420, 43571}, {6425, 60303}, {6560, 60298}, {6564, 42538}, {6811, 53859}, {7375, 60182}, {7581, 43561}, {7582, 12819}, {12101, 43566}, {13665, 60295}, {14226, 23249}, {14228, 14230}, {14241, 42284}, {15698, 43558}, {19053, 60314}, {19054, 43562}, {19708, 34089}, {19710, 43507}, {23273, 43312}, {31412, 42525}, {32787, 60301}, {33699, 43383}, {42269, 43506}, {43211, 60311}, {43503, 60313}, {43509, 43536}, {52667, 60297}

X(60307) = isogonal conjugate of X(6451)
X(60307) = X(i)-cross conjugate of X(j) for these {i, j}: {43522, 14226}
X(60307) = pole of line {43522, 60307} with respect to the Kiepert hyperbola
X(60307) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(6452)}}, {{A, B, C, X(64), X(3311)}}, {{A, B, C, X(493), X(13603)}}, {{A, B, C, X(494), X(14487)}}, {{A, B, C, X(588), X(6200)}}, {{A, B, C, X(1152), X(3527)}}, {{A, B, C, X(1585), X(15682)}}, {{A, B, C, X(1586), X(41099)}}, {{A, B, C, X(3535), X(3830)}}, {{A, B, C, X(3536), X(3845)}}, {{A, B, C, X(5417), X(13452)}}, {{A, B, C, X(6420), X(6454)}}, {{A, B, C, X(6425), X(6447)}}, {{A, B, C, X(11001), X(55573)}}, {{A, B, C, X(41106), X(55569)}}

X(60308) = X(2)X(6451)∩X(30)X(3591)

Barycentrics    77*a^4+8*a^2*b^2+8*a^2*c^2-85*(b^2-c^2)^2-72*a^2*S : :
Barycentrics    1 / (2*S - 9*SA) : :

X(60308) lies on the Kiepert hyperbola and on these lines: {2, 6451}, {6, 60307}, {30, 3591}, {376, 10194}, {381, 3590}, {485, 41099}, {486, 15682}, {1131, 3845}, {1132, 3830}, {1151, 34089}, {1327, 23273}, {1328, 43796}, {1588, 60309}, {3071, 60305}, {3312, 43561}, {3316, 23261}, {3317, 6410}, {3524, 43565}, {3534, 60294}, {3535, 60138}, {3543, 6448}, {3545, 6453}, {3839, 60291}, {3860, 6199}, {5066, 60293}, {5071, 43564}, {6396, 43569}, {6419, 43570}, {6426, 60304}, {6561, 60297}, {6565, 42537}, {6813, 53859}, {7376, 60182}, {7581, 12818}, {7582, 43560}, {12101, 43567}, {13785, 60296}, {14226, 42283}, {14233, 14243}, {14241, 23259}, {15698, 43559}, {19053, 43563}, {19054, 60313}, {19708, 34091}, {19710, 43508}, {23267, 43313}, {32788, 60302}, {33699, 43382}, {42268, 43505}, {42524, 42561}, {43212, 60312}, {43504, 60314}, {43510, 53519}, {52666, 60298}

X(60308) = isogonal conjugate of X(6452)
X(60308) = X(i)-cross conjugate of X(j) for these {i, j}: {43521, 14241}
X(60308) = pole of line {43521, 60308} with respect to the Kiepert hyperbola
X(60308) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(6451)}}, {{A, B, C, X(64), X(3312)}}, {{A, B, C, X(493), X(14487)}}, {{A, B, C, X(494), X(13603)}}, {{A, B, C, X(589), X(6396)}}, {{A, B, C, X(1151), X(3527)}}, {{A, B, C, X(1585), X(41099)}}, {{A, B, C, X(1586), X(15682)}}, {{A, B, C, X(3535), X(3845)}}, {{A, B, C, X(3536), X(3830)}}, {{A, B, C, X(5419), X(13452)}}, {{A, B, C, X(6419), X(6453)}}, {{A, B, C, X(6426), X(6448)}}, {{A, B, C, X(11001), X(55569)}}, {{A, B, C, X(41106), X(55573)}}
X(60308) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {41106, 42417, 3316}

X(60309) = X(2)X(6456)∩X(4)X(43789)

Barycentrics    45*a^4-53*(b^2-c^2)^2+4*a^2*(2*b^2+2*c^2+14*S) : :
Barycentrics    1 / (2*S + 7*SA) : :

X(60309) lies on the Kiepert hyperbola and on these lines: {2, 6456}, {4, 43789}, {6, 60310}, {20, 60311}, {371, 60313}, {485, 6480}, {486, 23269}, {548, 60293}, {1131, 3627}, {1132, 3843}, {1328, 7581}, {1587, 60306}, {1588, 60308}, {1657, 3590}, {3070, 14226}, {3091, 60312}, {3316, 17538}, {3317, 23249}, {3591, 3850}, {5072, 60294}, {6460, 6479}, {6564, 43505}, {7374, 54921}, {7376, 56059}, {7582, 43561}, {7583, 43560}, {8972, 58207}, {8976, 58204}, {9540, 41952}, {10195, 21735}, {12819, 23273}, {13749, 54875}, {13886, 15684}, {13939, 42540}, {14230, 14243}, {14241, 23253}, {14242, 54874}, {14893, 23275}, {23046, 60300}, {31412, 43568}, {34089, 42265}, {34091, 41960}, {35822, 54595}, {38335, 43522}, {42269, 43569}, {42284, 60305}, {42525, 42608}, {43340, 60295}, {50691, 60291}

X(60309) = isogonal conjugate of X(6455)
X(60309) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(6456)}}, {{A, B, C, X(371), X(6480)}}, {{A, B, C, X(493), X(57715)}}, {{A, B, C, X(588), X(13452)}}, {{A, B, C, X(1585), X(33703)}}, {{A, B, C, X(3311), X(43691)}}, {{A, B, C, X(3535), X(3627)}}, {{A, B, C, X(3536), X(3843)}}, {{A, B, C, X(5417), X(11270)}}, {{A, B, C, X(6420), X(6479)}}, {{A, B, C, X(17538), X(55573)}}, {{A, B, C, X(18296), X(55533)}}, {{A, B, C, X(24244), X(57896)}}

X(60310) = X(2)X(6455)∩X(4)X(43790)

Barycentrics    45*a^4-53*(b^2-c^2)^2+4*a^2*(2*b^2+2*c^2-14*S) : :
Barycentrics    1 / (2*S - 7*SA) : :

X(60310) lies on the Kiepert hyperbola and on these lines: {2, 6455}, {4, 43790}, {6, 60309}, {20, 60312}, {372, 60314}, {485, 23275}, {486, 6481}, {548, 60294}, {1131, 3843}, {1132, 3627}, {1327, 7582}, {1587, 60307}, {1588, 60305}, {1657, 3591}, {3071, 14241}, {3091, 60311}, {3316, 23259}, {3317, 17538}, {3590, 3850}, {5072, 60293}, {6459, 6478}, {6565, 43506}, {7000, 54921}, {7375, 56059}, {7581, 43560}, {7584, 43561}, {9680, 43558}, {10194, 21735}, {12818, 23267}, {13886, 42539}, {13935, 41951}, {13939, 15684}, {13941, 58207}, {13951, 58204}, {14226, 23263}, {14227, 54876}, {14228, 14233}, {14893, 23269}, {23046, 60299}, {34089, 41959}, {34091, 42262}, {35823, 54596}, {38335, 43521}, {42268, 43568}, {42283, 60306}, {42524, 42609}, {42561, 43569}, {43341, 60296}, {50691, 60292}

X(60310) = isogonal conjugate of X(6456)
X(60310) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(6455)}}, {{A, B, C, X(372), X(6481)}}, {{A, B, C, X(494), X(57715)}}, {{A, B, C, X(589), X(13452)}}, {{A, B, C, X(1586), X(33703)}}, {{A, B, C, X(3312), X(43691)}}, {{A, B, C, X(3535), X(3843)}}, {{A, B, C, X(3536), X(3627)}}, {{A, B, C, X(5419), X(11270)}}, {{A, B, C, X(6419), X(6478)}}, {{A, B, C, X(17538), X(55569)}}, {{A, B, C, X(18296), X(55534)}}, {{A, B, C, X(24243), X(57896)}}

X(60311) = X(2)X(6471)∩X(4)X(6407)

Barycentrics    -33*a^4-65*(b^2-c^2)^2+14*a^2*(7*b^2+7*c^2+8*S) : :
Barycentrics    1 / (7*S + 4*SA) : :

X(60311) lies on the Kiepert hyperbola and on these lines: {2, 6471}, {3, 60289}, {4, 6407}, {5, 60290}, {6, 60312}, {20, 60309}, {83, 43123}, {372, 60297}, {486, 6435}, {547, 6500}, {590, 43560}, {632, 34089}, {1131, 21734}, {1132, 3592}, {1151, 54598}, {1152, 3590}, {3068, 60292}, {3091, 60310}, {3311, 14226}, {3316, 6398}, {3317, 8976}, {3523, 60303}, {5054, 43536}, {5056, 60304}, {5070, 34091}, {6200, 12818}, {6395, 60315}, {6420, 43559}, {6425, 43520}, {6459, 43567}, {7374, 60325}, {7585, 42579}, {8703, 60301}, {8972, 43561}, {10194, 35770}, {10303, 43316}, {10576, 43569}, {13846, 60296}, {13886, 43565}, {13935, 43558}, {14241, 15692}, {19709, 60302}, {32814, 60194}, {35786, 54595}, {35815, 60314}, {41948, 43519}, {42262, 60300}, {42413, 54542}, {43211, 60307}, {43257, 54596}, {43512, 54599}, {43879, 60293}

X(60311) = isogonal conjugate of X(6470)
X(60311) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(6407)}}, {{A, B, C, X(6), X(6471)}}, {{A, B, C, X(372), X(6435)}}, {{A, B, C, X(493), X(1152)}}, {{A, B, C, X(3311), X(6398)}}, {{A, B, C, X(3535), X(21734)}}, {{A, B, C, X(6395), X(6500)}}, {{A, B, C, X(6420), X(35770)}}, {{A, B, C, X(46936), X(55569)}}, {{A, B, C, X(55573), X(55864)}}

X(60312) = X(2)X(6470)∩X(4)X(6408)

Barycentrics    -33*a^4-65*(b^2-c^2)^2+14*a^2*(7*b^2+7*c^2-8*S) : :
Barycentrics    1 / (7*S - 4*SA) : :

X(60312) lies on the Kiepert hyperbola and on these lines: {2, 6470}, {3, 60290}, {4, 6408}, {5, 60289}, {6, 60311}, {20, 60310}, {83, 43122}, {371, 60298}, {485, 6436}, {547, 6501}, {615, 43561}, {632, 34091}, {1131, 3594}, {1132, 21734}, {1151, 3591}, {1152, 54599}, {3069, 60291}, {3091, 60309}, {3312, 14241}, {3316, 13951}, {3317, 6221}, {3523, 60304}, {5054, 54597}, {5056, 60303}, {5070, 34089}, {6199, 60316}, {6396, 12819}, {6419, 43558}, {6426, 43519}, {6460, 43566}, {7000, 60325}, {7586, 42578}, {8703, 60302}, {9540, 43559}, {10195, 35771}, {10303, 43317}, {10577, 43568}, {13847, 60295}, {13939, 43564}, {13941, 43560}, {14226, 15692}, {19709, 60301}, {35787, 54596}, {35814, 60313}, {41947, 43520}, {42265, 60299}, {42414, 54543}, {43212, 60308}, {43256, 54595}, {43511, 54598}, {43880, 60294}

X(60312) = isogonal conjugate of X(6471)
X(60312) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(6408)}}, {{A, B, C, X(6), X(6470)}}, {{A, B, C, X(371), X(6436)}}, {{A, B, C, X(494), X(1151)}}, {{A, B, C, X(3312), X(6221)}}, {{A, B, C, X(3536), X(21734)}}, {{A, B, C, X(6199), X(6501)}}, {{A, B, C, X(6419), X(35771)}}, {{A, B, C, X(46936), X(55573)}}, {{A, B, C, X(55569), X(55864)}}

X(60313) = X(2)X(6481)∩X(6)X(60314)

Barycentrics    28*a^4-53*(b^2-c^2)^2+5*a^2*(5*b^2+5*c^2+18*S) : :
Barycentrics    1 / (5*S + 9*SA) : :

X(60313) lies on these lines: {2, 6481}, {6, 60314}, {30, 43570}, {371, 60309}, {381, 43571}, {485, 3534}, {486, 5066}, {549, 10195}, {1131, 6478}, {1132, 35822}, {1327, 33699}, {1328, 13665}, {3068, 60301}, {3070, 42608}, {3316, 15698}, {3590, 10304}, {3830, 12818}, {3845, 12819}, {3857, 43439}, {5055, 10194}, {5420, 60316}, {5490, 22485}, {6561, 43566}, {6564, 14226}, {6811, 60334}, {6813, 60332}, {7581, 42609}, {7585, 54599}, {12101, 54595}, {13925, 42576}, {14241, 43791}, {15682, 35815}, {15683, 42525}, {15684, 53513}, {15706, 41952}, {15709, 43564}, {15713, 43338}, {15759, 43568}, {18512, 43381}, {19054, 60308}, {19709, 43431}, {23249, 60299}, {31412, 34091}, {31414, 60304}, {32787, 43562}, {34089, 42602}, {35814, 60312}, {35823, 60290}, {41099, 60306}, {41983, 43378}, {42269, 43561}, {42274, 54597}, {42277, 60298}, {42572, 54596}, {42600, 43382}, {43336, 43536}, {43432, 49136}, {43503, 60307}, {46333, 60303}, {50720, 54655}

X(60313) = isogonal conjugate of X(6480)
X(60313) = X(i)-cross conjugate of X(j) for these {i, j}: {43526, 43569}
X(60313) = pole of line {43526, 60313} with respect to the Kiepert hyperbola
X(60313) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(6481)}}, {{A, B, C, X(371), X(6455)}}, {{A, B, C, X(1151), X(6478)}}, {{A, B, C, X(1585), X(3534)}}, {{A, B, C, X(1586), X(5066)}}, {{A, B, C, X(3535), X(15640)}}, {{A, B, C, X(11091), X(13623)}}, {{A, B, C, X(15698), X(55573)}}

X(60314) = X(2)X(6480)∩X(6)X(60313)

Barycentrics    28*a^4-53*(b^2-c^2)^2+5*a^2*(5*b^2+5*c^2-18*S) : :
Barycentrics    1 / (5*S - 9*SA) : :

X(60314) lies on the Kiepert hyperbola and on these lines: {2, 6480}, {6, 60313}, {30, 43571}, {372, 60310}, {381, 43570}, {485, 5066}, {486, 3534}, {549, 10194}, {1131, 35823}, {1132, 6479}, {1327, 13785}, {1328, 33699}, {3069, 60302}, {3071, 42609}, {3317, 15698}, {3591, 10304}, {3830, 12819}, {3845, 12818}, {3857, 43438}, {5055, 10195}, {5418, 60315}, {5491, 22484}, {6560, 43567}, {6565, 14241}, {6811, 60332}, {6813, 60334}, {7582, 42608}, {7586, 54598}, {12101, 54596}, {13993, 42577}, {14226, 43792}, {15682, 35814}, {15683, 42524}, {15684, 53516}, {15706, 41951}, {15709, 43565}, {15713, 43339}, {15759, 43569}, {18510, 43380}, {19053, 60307}, {19709, 43430}, {23259, 60300}, {32788, 43563}, {34089, 42561}, {34091, 42603}, {35815, 60311}, {35822, 60289}, {41099, 60305}, {41983, 43379}, {42268, 43560}, {42274, 60297}, {42277, 43536}, {42573, 54595}, {42601, 43383}, {43337, 54597}, {43433, 49136}, {43504, 60308}, {46333, 60304}, {50719, 54656}

X(60314) = isogonal conjugate of X(6481)
X(60314) = X(i)-cross conjugate of X(j) for these {i, j}: {43525, 43568}
X(60314) = pole of line {43525, 60314} with respect to the Kiepert hyperbola
X(60314) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(6480)}}, {{A, B, C, X(372), X(6456)}}, {{A, B, C, X(1152), X(6479)}}, {{A, B, C, X(1585), X(5066)}}, {{A, B, C, X(1586), X(3534)}}, {{A, B, C, X(3536), X(15640)}}, {{A, B, C, X(11090), X(13623)}}, {{A, B, C, X(15698), X(55569)}}
X(60314) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14226, 43792, 53131}

X(60315) = X(2)X(6501)∩X(6)X(60316)

Barycentrics    -63*a^4-65*(b^2-c^2)^2+16*a^2*(8*b^2+8*c^2+2*S) : :
Barycentrics    1 / (8*S + SA) : :

X(60315) lies on the Kiepert hyperbola and on these lines: {2, 6501}, {6, 60316}, {376, 54542}, {590, 43565}, {631, 43560}, {1131, 3525}, {1132, 5067}, {1152, 14241}, {1327, 15702}, {3090, 43561}, {3311, 3591}, {3316, 3594}, {3317, 32789}, {3524, 43566}, {3533, 6408}, {3539, 13579}, {3545, 54543}, {5071, 43567}, {5418, 60314}, {6200, 12819}, {6395, 60311}, {6407, 60296}, {6420, 43558}, {6425, 43517}, {6434, 60289}, {6460, 43570}, {6470, 42579}, {6471, 43518}, {6496, 41106}, {6805, 13585}, {6806, 11538}, {6811, 60327}, {6813, 54706}, {7375, 18845}, {7376, 38259}, {7583, 60293}, {8253, 34091}, {9540, 14226}, {10194, 35771}, {11001, 54598}, {12818, 42267}, {15709, 60295}, {19708, 43562}, {32785, 43559}, {41957, 43505}, {42265, 60305}, {52048, 60299}

X(60315) = isogonal conjugate of X(6500)
X(60315) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(6501)}}, {{A, B, C, X(588), X(6420)}}, {{A, B, C, X(1152), X(3431)}}, {{A, B, C, X(3302), X(18490)}}, {{A, B, C, X(3311), X(3594)}}, {{A, B, C, X(3525), X(3535)}}, {{A, B, C, X(3536), X(5067)}}, {{A, B, C, X(6395), X(6470)}}, {{A, B, C, X(6407), X(6434)}}, {{A, B, C, X(6408), X(6425)}}, {{A, B, C, X(14843), X(55533)}}

X(60316) = X(2)X(6500)∩X(6)X(60315)

Barycentrics    -63*a^4-65*(b^2-c^2)^2+16*a^2*(8*b^2+8*c^2-2*S) : :
Barycentrics    1 / (8*S - SA) : :

X(60316) lies on the Kiepert hyperbola and on these lines: {2, 6500}, {6, 60315}, {376, 54543}, {615, 43564}, {631, 43561}, {1131, 5067}, {1132, 3525}, {1151, 14226}, {1328, 15702}, {3090, 43560}, {3312, 3590}, {3316, 32790}, {3317, 3592}, {3524, 43567}, {3533, 6407}, {3540, 13579}, {3545, 54542}, {5071, 43566}, {5420, 60313}, {6199, 60312}, {6396, 12818}, {6408, 60295}, {6419, 43559}, {6426, 43518}, {6433, 60290}, {6459, 43571}, {6470, 43517}, {6471, 42578}, {6497, 41106}, {6805, 11538}, {6806, 13585}, {6811, 54706}, {6813, 60327}, {7375, 38259}, {7376, 18845}, {7584, 60294}, {8252, 34089}, {10195, 35770}, {11001, 54599}, {12819, 42266}, {13935, 14241}, {15709, 60296}, {19708, 43563}, {31414, 43375}, {32786, 43558}, {41958, 43506}, {42262, 60306}, {52047, 60300}

X(60316) = isogonal conjugate of X(6501)
X(60316) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(6500)}}, {{A, B, C, X(589), X(6419)}}, {{A, B, C, X(1151), X(3431)}}, {{A, B, C, X(3300), X(18490)}}, {{A, B, C, X(3312), X(3592)}}, {{A, B, C, X(3525), X(3536)}}, {{A, B, C, X(3535), X(5067)}}, {{A, B, C, X(6199), X(6471)}}, {{A, B, C, X(6407), X(6426)}}, {{A, B, C, X(6408), X(6433)}}, {{A, B, C, X(14843), X(55534)}}

X(60317) = X(2)X(895)∩X(4)X(111)

Barycentrics    (a^2+b^2-2*c^2)*(a^2-2*b^2+c^2)*(a^4-4*a^2*b^2+b^4-c^4)*(a^4-b^4-4*a^2*c^2+c^4) : :

X(60317) lies on the Kiepert hyperbola and on these lines: {2, 895}, {4, 111}, {76, 30786}, {94, 46783}, {98, 5913}, {262, 9745}, {427, 54825}, {468, 10422}, {598, 1995}, {671, 858}, {1513, 60119}, {2052, 17983}, {2394, 9191}, {2996, 31125}, {3260, 57813}, {3546, 54558}, {5094, 60266}, {5466, 47138}, {5485, 16051}, {5968, 34289}, {6642, 54730}, {7464, 34320}, {7607, 20481}, {9139, 16080}, {9185, 43674}, {9759, 54819}, {10415, 46105}, {10511, 11580}, {11585, 54513}, {15638, 46959}, {16092, 58268}, {16277, 40326}, {17503, 31133}, {17928, 54682}, {18842, 40132}, {24855, 42007}, {31099, 41895}, {39169, 52300}, {41238, 54916}, {51831, 52290}, {52189, 57491}, {54381, 54685}

X(60317) = isogonal conjugate of X(53777)
X(60317) = trilinear pole of line {2549, 5486}
X(60317) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 53777}, {48, 37855}, {163, 55135}, {896, 1995}, {922, 11185}, {14210, 19136}
X(60317) = X(i)-vertex conjugate of X(j) for these {i, j}: {23, 17983}, {1177, 10422}, {3424, 22455}, {3425, 60119}
X(60317) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 53777}, {115, 55135}, {1249, 37855}, {15477, 19136}, {15899, 1995}, {39061, 11185}
X(60317) = X(i)-cross conjugate of X(j) for these {i, j}: {5094, 10415}, {24855, 2}, {42007, 671}, {43620, 57539}, {57466, 60266}, {59893, 39296}
X(60317) = pole of line {23287, 34519} with respect to the circumcircle
X(60317) = pole of line {24855, 42007} with respect to the Kiepert hyperbola
X(60317) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(67), X(468)}}, {{A, B, C, X(111), X(895)}}, {{A, B, C, X(183), X(9745)}}, {{A, B, C, X(325), X(5913)}}, {{A, B, C, X(523), X(9084)}}, {{A, B, C, X(525), X(23699)}}, {{A, B, C, X(842), X(48362)}}, {{A, B, C, X(892), X(1302)}}, {{A, B, C, X(1494), X(2770)}}, {{A, B, C, X(1995), X(5094)}}, {{A, B, C, X(2374), X(10424)}}, {{A, B, C, X(3260), X(9191)}}, {{A, B, C, X(3266), X(41909)}}, {{A, B, C, X(3563), X(14536)}}, {{A, B, C, X(4232), X(16051)}}, {{A, B, C, X(5481), X(22455)}}, {{A, B, C, X(5486), X(32133)}}, {{A, B, C, X(5505), X(10102)}}, {{A, B, C, X(7495), X(54381)}}, {{A, B, C, X(8791), X(15118)}}, {{A, B, C, X(9178), X(52152)}}, {{A, B, C, X(9213), X(46783)}}, {{A, B, C, X(11564), X(40118)}}, {{A, B, C, X(11636), X(32583)}}, {{A, B, C, X(14908), X(34158)}}, {{A, B, C, X(14910), X(53929)}}, {{A, B, C, X(15464), X(16511)}}, {{A, B, C, X(18018), X(40323)}}, {{A, B, C, X(18023), X(44182)}}, {{A, B, C, X(23287), X(34898)}}, {{A, B, C, X(24855), X(52477)}}, {{A, B, C, X(25322), X(53773)}}, {{A, B, C, X(30745), X(37777)}}, {{A, B, C, X(31099), X(52290)}}, {{A, B, C, X(31133), X(52292)}}, {{A, B, C, X(34336), X(41498)}}, {{A, B, C, X(39446), X(52094)}}, {{A, B, C, X(40132), X(52284)}}, {{A, B, C, X(42008), X(52141)}}, {{A, B, C, X(53080), X(53690)}}
X(60317) = barycentric product X(i)*X(j) for these (i, j): {3267, 32709}, {5486, 671}, {14208, 36115}, {14977, 30247}, {32133, 52141}, {35188, 850}, {60266, 895}
X(60317) = barycentric quotient X(i)/X(j) for these (i, j): {4, 37855}, {6, 53777}, {111, 1995}, {523, 55135}, {671, 11185}, {895, 41614}, {5486, 524}, {10097, 30209}, {13608, 27088}, {30247, 4235}, {32709, 112}, {32740, 19136}, {35188, 110}, {36115, 162}, {42007, 8542}, {46154, 29959}, {53764, 18800}, {57466, 5181}, {60266, 44146}

X(60318) = X(13)X(39)∩X(15)X(83)

Barycentrics    2*b^2*c^2*(b^2-c^2)^2-a^4*(3*b^4+7*b^2*c^2+3*c^4)+a^2*(3*b^6-4*b^4*c^2-4*b^2*c^4+3*c^6)+2*sqrt(3)*a^2*(b^2-b*c+c^2)*(b^2+b*c+c^2)*S : :

X(60318) lies on the Kiepert hyperbola and on these lines: {2, 3104}, {4, 3107}, {5, 43538}, {13, 39}, {14, 3105}, {15, 83}, {17, 3106}, {18, 511}, {62, 98}, {76, 624}, {194, 11122}, {262, 51753}, {636, 42006}, {732, 22850}, {754, 22745}, {1506, 3094}, {1916, 6114}, {2782, 11603}, {3095, 43539}, {3102, 3366}, {3103, 3367}, {3399, 7684}, {3406, 36760}, {3407, 54298}, {6294, 50858}, {6581, 42036}, {6694, 43527}, {6695, 43528}, {10653, 54485}, {11257, 54860}, {16268, 36385}, {16964, 31702}, {16965, 22694}, {16967, 24256}, {18581, 54115}, {22690, 40694}, {22693, 43953}, {22702, 42153}, {22708, 42813}, {22714, 42489}, {23024, 40335}, {23873, 43665}, {25167, 60252}, {33482, 42035}, {36252, 43532}, {36969, 54561}, {36992, 54873}, {37835, 40707}, {42814, 54572}

X(60318) = isogonal conjugate of X(54297)
X(60318) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 54297}, {48, 16250}
X(60318) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 54297}, {1249, 16250}
X(60318) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(301)}}, {{A, B, C, X(15), X(39)}}, {{A, B, C, X(62), X(511)}}, {{A, B, C, X(298), X(30537)}}, {{A, B, C, X(300), X(3613)}}, {{A, B, C, X(303), X(15321)}}, {{A, B, C, X(624), X(3457)}}, {{A, B, C, X(3094), X(54298)}}, {{A, B, C, X(3095), X(36760)}}, {{A, B, C, X(3490), X(46286)}}, {{A, B, C, X(34288), X(53030)}}, {{A, B, C, X(53029), X(55958)}}
X(60318) = barycentric quotient X(i)/X(j) for these (i, j): {4, 16250}, {6, 54297}

X(60319) = X(14)X(39)∩X(16)X(83)

Barycentrics    2*b^2*c^2*(b^2-c^2)^2-a^4*(3*b^4+7*b^2*c^2+3*c^4)+a^2*(3*b^6-4*b^4*c^2-4*b^2*c^4+3*c^6)-2*sqrt(3)*a^2*(b^2-b*c+c^2)*(b^2+b*c+c^2)*S : :

X(60319) lies on the Kiepert hyperbola and on these lines: {2, 3105}, {4, 3106}, {5, 43539}, {13, 3104}, {14, 39}, {16, 83}, {17, 511}, {18, 3107}, {61, 98}, {76, 623}, {194, 11121}, {262, 51754}, {635, 42006}, {732, 22894}, {754, 22746}, {1506, 3094}, {1916, 6115}, {2782, 11602}, {3095, 43538}, {3102, 3391}, {3103, 3392}, {3399, 7685}, {3406, 36759}, {3407, 54297}, {6294, 42035}, {6581, 50855}, {6694, 43528}, {6695, 43527}, {10654, 54484}, {11257, 54861}, {16267, 36384}, {16964, 22693}, {16965, 31701}, {16966, 24256}, {18582, 54116}, {22688, 40693}, {22694, 43954}, {22701, 42156}, {22707, 42814}, {22715, 42488}, {23018, 40334}, {23872, 43665}, {25157, 60253}, {33483, 42036}, {36251, 43532}, {36970, 54562}, {36994, 54873}, {37832, 40706}, {42813, 54571}

X(60319) = isogonal conjugate of X(54298)
X(60319) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 54298}, {48, 16249}
X(60319) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 54298}, {1249, 16249}
X(60319) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(300)}}, {{A, B, C, X(16), X(39)}}, {{A, B, C, X(61), X(511)}}, {{A, B, C, X(299), X(30537)}}, {{A, B, C, X(301), X(3613)}}, {{A, B, C, X(302), X(15321)}}, {{A, B, C, X(623), X(3458)}}, {{A, B, C, X(3094), X(54297)}}, {{A, B, C, X(3095), X(36759)}}, {{A, B, C, X(3489), X(46286)}}, {{A, B, C, X(34288), X(53029)}}, {{A, B, C, X(53030), X(55958)}}
X(60319) = barycentric quotient X(i)/X(j) for these (i, j): {4, 16249}, {6, 54298}

X(60320) = X(10)X(511)∩X(58)X(98)

Barycentrics    (a^2*b^2*(a+b)+a^2*b^2*c+(a^3+b^3)*c^2+a*b*c^3-(a+b)*c^4)*(-(b^4*c)+b^2*c^3+a*b^3*(-b+c)+a^2*c^2*(b+c)+a^3*(b^2+c^2)) : :

X(60320) lies on the Kiepert hyperbola and on these lines: {2, 17209}, {3, 60109}, {4, 5145}, {5, 60090}, {10, 511}, {39, 2051}, {58, 98}, {76, 24220}, {83, 572}, {194, 10478}, {226, 24215}, {321, 1959}, {514, 43665}, {538, 4052}, {726, 43677}, {894, 60230}, {946, 2782}, {2394, 30519}, {2786, 46040}, {2789, 60226}, {3667, 60106}, {5466, 28565}, {5969, 34899}, {7184, 60086}, {9840, 40718}, {11257, 54883}, {13576, 15971}, {16080, 31916}, {26764, 56197}, {27436, 29967}, {28296, 43668}, {30030, 43685}, {30092, 40162}, {30097, 60245}, {32515, 34475}, {43683, 46180}, {44129, 60199}

X(60320) = isogonal conjugate of X(54388)
X(60320) = trilinear pole of line {20508, 523}
X(60320) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 54388}, {6, 11688}
X(60320) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 54388}, {9, 11688}
X(60320) = X(i)-cross conjugate of X(j) for these {i, j}: {45208, 1}
X(60320) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(27424)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(5145)}}, {{A, B, C, X(6), X(57906)}}, {{A, B, C, X(7), X(20258)}}, {{A, B, C, X(27), X(15973)}}, {{A, B, C, X(30), X(30519)}}, {{A, B, C, X(39), X(572)}}, {{A, B, C, X(57), X(30076)}}, {{A, B, C, X(58), X(511)}}, {{A, B, C, X(85), X(87)}}, {{A, B, C, X(86), X(15985)}}, {{A, B, C, X(194), X(30092)}}, {{A, B, C, X(256), X(28660)}}, {{A, B, C, X(261), X(7261)}}, {{A, B, C, X(274), X(894)}}, {{A, B, C, X(279), X(30082)}}, {{A, B, C, X(524), X(28565)}}, {{A, B, C, X(538), X(3667)}}, {{A, B, C, X(698), X(28470)}}, {{A, B, C, X(726), X(6002)}}, {{A, B, C, X(732), X(28487)}}, {{A, B, C, X(1423), X(29967)}}, {{A, B, C, X(2664), X(30030)}}, {{A, B, C, X(2705), X(53195)}}, {{A, B, C, X(2782), X(2786)}}, {{A, B, C, X(2789), X(5969)}}, {{A, B, C, X(3062), X(40775)}}, {{A, B, C, X(3613), X(57905)}}, {{A, B, C, X(3674), X(3865)}}, {{A, B, C, X(4219), X(30031)}}, {{A, B, C, X(4391), X(55089)}}, {{A, B, C, X(4785), X(32515)}}, {{A, B, C, X(6003), X(46180)}}, {{A, B, C, X(7249), X(18299)}}, {{A, B, C, X(9840), X(31909)}}, {{A, B, C, X(15149), X(15971)}}, {{A, B, C, X(17789), X(23605)}}, {{A, B, C, X(20892), X(26764)}}, {{A, B, C, X(23841), X(53688)}}, {{A, B, C, X(24220), X(27375)}}, {{A, B, C, X(27455), X(39949)}}, {{A, B, C, X(29092), X(31737)}}, {{A, B, C, X(30038), X(40790)}}, {{A, B, C, X(40827), X(42027)}}, {{A, B, C, X(45208), X(54388)}}
X(60320) = barycentric quotient X(i)/X(j) for these (i, j): {1, 11688}, {6, 54388}

X(60321) = X(2)X(65)∩X(4)X(941)

Barycentrics    (a+b-c)*(a-b+c)*(b+c)*(c*(b+c)+a*(2*b+c))*(b*(b+c)+a*(b+2*c)) : :

X(60321) lies on the Kiepert hyperbola and on these lines: {1, 13478}, {2, 65}, {4, 941}, {7, 58012}, {8, 60206}, {10, 2171}, {12, 321}, {21, 961}, {37, 60086}, {40, 54972}, {76, 1441}, {83, 8543}, {85, 40030}, {98, 32693}, {192, 2996}, {226, 1254}, {388, 28606}, {429, 40149}, {671, 32038}, {1214, 60076}, {1400, 58386}, {1409, 57745}, {1411, 5331}, {1446, 6046}, {1722, 60075}, {1751, 2258}, {2051, 4424}, {2285, 12514}, {2476, 34258}, {3339, 31312}, {3486, 37593}, {3649, 30588}, {3671, 56226}, {3696, 43533}, {3701, 60264}, {3743, 60089}, {3896, 5086}, {3947, 4052}, {4642, 37865}, {4646, 13576}, {4848, 60243}, {5226, 60254}, {5257, 53004}, {5290, 60083}, {5657, 60154}, {5698, 60077}, {5977, 8781}, {7233, 40017}, {7235, 56210}, {7612, 44430}, {10106, 54768}, {10408, 56214}, {10572, 60172}, {11114, 54549}, {11237, 54775}, {11681, 26587}, {12617, 43672}, {12709, 52931}, {15888, 21333}, {16824, 17097}, {17577, 54686}, {24547, 25466}, {37232, 56288}, {37558, 60085}, {40395, 54340}, {40663, 60203}, {45784, 55962}, {56908, 56914}

X(60321) = isogonal conjugate of X(54417)
X(60321) = trilinear pole of line {523, 57185}
X(60321) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 54417}, {21, 1468}, {48, 44734}, {58, 958}, {60, 59305}, {81, 2268}, {110, 17418}, {163, 23880}, {283, 4185}, {284, 940}, {333, 5019}, {849, 3714}, {1333, 11679}, {1412, 3713}, {1414, 58332}, {1437, 54396}, {2150, 31993}, {2193, 5307}, {2194, 10436}, {4636, 8672}, {5546, 48144}, {34284, 57657}, {52378, 53561}
X(60321) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 54417}, {10, 958}, {37, 11679}, {115, 23880}, {244, 17418}, {1214, 10436}, {1249, 44734}, {4075, 3714}, {4988, 53526}, {40586, 2268}, {40590, 940}, {40599, 3713}, {40608, 58332}, {40611, 1468}, {40622, 43067}, {47345, 5307}, {56325, 31993}
X(60321) = X(i)-cross conjugate of X(j) for these {i, j}: {47842, 4551}, {56908, 40149}, {56914, 34258}
X(60321) = pole of line {959, 3486} with respect to the Feuerbach hyperbola
X(60321) = pole of line {56908, 56914} with respect to the Kiepert hyperbola
X(60321) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3869)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(225)}}, {{A, B, C, X(8), X(1826)}}, {{A, B, C, X(12), X(65)}}, {{A, B, C, X(21), X(37)}}, {{A, B, C, X(86), X(55089)}}, {{A, B, C, X(442), X(54340)}}, {{A, B, C, X(523), X(31503)}}, {{A, B, C, X(941), X(34259)}}, {{A, B, C, X(959), X(50040)}}, {{A, B, C, X(1156), X(25917)}}, {{A, B, C, X(1214), X(3695)}}, {{A, B, C, X(1400), X(43074)}}, {{A, B, C, X(1402), X(52567)}}, {{A, B, C, X(1426), X(7249)}}, {{A, B, C, X(1788), X(56173)}}, {{A, B, C, X(2476), X(4185)}}, {{A, B, C, X(3649), X(4870)}}, {{A, B, C, X(3665), X(8543)}}, {{A, B, C, X(3668), X(51512)}}, {{A, B, C, X(3812), X(55924)}}, {{A, B, C, X(3932), X(4646)}}, {{A, B, C, X(3947), X(4848)}}, {{A, B, C, X(4424), X(37558)}}, {{A, B, C, X(4674), X(17098)}}, {{A, B, C, X(5530), X(17751)}}, {{A, B, C, X(6757), X(53114)}}, {{A, B, C, X(8818), X(15232)}}, {{A, B, C, X(11375), X(52383)}}, {{A, B, C, X(12514), X(28606)}}, {{A, B, C, X(12709), X(17757)}}, {{A, B, C, X(15065), X(56027)}}, {{A, B, C, X(15320), X(28628)}}, {{A, B, C, X(16824), X(21674)}}, {{A, B, C, X(18123), X(57853)}}, {{A, B, C, X(27475), X(28659)}}, {{A, B, C, X(30712), X(45104)}}, {{A, B, C, X(35576), X(52382)}}, {{A, B, C, X(36100), X(56219)}}, {{A, B, C, X(36599), X(56134)}}, {{A, B, C, X(41505), X(54418)}}, {{A, B, C, X(46878), X(46880)}}
X(60321) = barycentric product X(i)*X(j) for these (i, j): {10, 44733}, {12, 37870}, {37, 58008}, {226, 31359}, {321, 959}, {1402, 40828}, {1441, 941}, {2258, 349}, {4391, 52931}, {5331, 6358}, {31643, 56914}, {31993, 50040}, {32038, 523}, {32693, 850}, {34258, 65}, {34259, 40149}
X(60321) = barycentric quotient X(i)/X(j) for these (i, j): {4, 44734}, {6, 54417}, {10, 11679}, {12, 31993}, {37, 958}, {42, 2268}, {65, 940}, {210, 3713}, {225, 5307}, {226, 10436}, {523, 23880}, {594, 3714}, {661, 17418}, {931, 4612}, {941, 21}, {959, 81}, {1400, 1468}, {1402, 5019}, {1441, 34284}, {1826, 54396}, {1880, 4185}, {2171, 59305}, {2258, 284}, {3120, 53526}, {3709, 58332}, {4017, 48144}, {4516, 53561}, {5331, 2185}, {7178, 43067}, {8736, 1867}, {30572, 53536}, {31359, 333}, {32038, 99}, {32693, 110}, {34258, 314}, {34259, 1812}, {34263, 16049}, {37870, 261}, {40828, 40072}, {43703, 34279}, {44733, 86}, {50040, 37870}, {52931, 651}, {53540, 53543}, {56914, 960}, {57185, 8672}, {58008, 274}
X(60321) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {31359, 44733, 959}

X(60322) = X(2)X(50954)∩X(76)X(3528)

Barycentrics    (9*a^4+2*a^2*b^2+9*b^4-8*(a^2+b^2)*c^2-c^4)*(9*a^4-8*a^2*b^2-b^4+2*(a^2-4*b^2)*c^2+9*c^4) : :
X(60322) = -2*X[382]+5*X[38259], -13*X[10299]+10*X[51579], -8*X[35021]+5*X[60073]

X(60322) lies on the Kiepert hyperbola and on these lines: {2, 50954}, {76, 3528}, {83, 3544}, {230, 60337}, {376, 60200}, {382, 38259}, {546, 18845}, {550, 43681}, {1503, 60185}, {1513, 60336}, {2794, 54767}, {2996, 3529}, {3524, 10302}, {3525, 60278}, {3545, 54639}, {3851, 60145}, {3855, 5395}, {5067, 60100}, {5071, 60239}, {6776, 10155}, {7607, 7710}, {7735, 60132}, {7736, 60332}, {9744, 60144}, {9748, 54520}, {9752, 60150}, {9753, 54477}, {9754, 54644}, {9755, 14484}, {9756, 14494}, {9862, 60189}, {10299, 51579}, {11001, 60228}, {11177, 42010}, {13860, 60331}, {14269, 54476}, {14492, 53015}, {14651, 54659}, {14853, 54707}, {14912, 54523}, {15687, 60113}, {15715, 60143}, {17538, 60250}, {35021, 60073}, {39874, 53103}, {41106, 60282}, {50774, 60219}, {58883, 60102}

X(60322) = isogonal conjugate of X(55584)
X(60322) = trilinear pole of line {47461, 523}
X(60322) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 60185}, {25, 60337}, {3425, 60336}, {8770, 11270}
X(60322) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(55697)}}, {{A, B, C, X(25), X(3528)}}, {{A, B, C, X(64), X(43662)}}, {{A, B, C, X(264), X(14842)}}, {{A, B, C, X(305), X(14843)}}, {{A, B, C, X(382), X(38282)}}, {{A, B, C, X(393), X(57823)}}, {{A, B, C, X(427), X(3544)}}, {{A, B, C, X(523), X(16774)}}, {{A, B, C, X(546), X(52299)}}, {{A, B, C, X(2980), X(17040)}}, {{A, B, C, X(3425), X(20421)}}, {{A, B, C, X(3524), X(10301)}}, {{A, B, C, X(3529), X(6353)}}, {{A, B, C, X(3563), X(13452)}}, {{A, B, C, X(3855), X(8889)}}, {{A, B, C, X(5067), X(52285)}}, {{A, B, C, X(6997), X(35482)}}, {{A, B, C, X(7714), X(10299)}}, {{A, B, C, X(8770), X(16835)}}, {{A, B, C, X(11008), X(50774)}}, {{A, B, C, X(11738), X(40801)}}, {{A, B, C, X(13472), X(14486)}}, {{A, B, C, X(14489), X(57715)}}, {{A, B, C, X(14491), X(54172)}}, {{A, B, C, X(15715), X(52301)}}, {{A, B, C, X(15749), X(34223)}}, {{A, B, C, X(18490), X(52133)}}, {{A, B, C, X(18851), X(40413)}}, {{A, B, C, X(21765), X(45838)}}, {{A, B, C, X(34208), X(57897)}}, {{A, B, C, X(34285), X(57894)}}, {{A, B, C, X(36616), X(43719)}}

X(60323) = X(2)X(44108)∩X(76)X(548)

Barycentrics    (6*a^4+2*a^2*b^2+6*b^4-5*(a^2+b^2)*c^2-c^4)*(6*a^4-b^4-5*b^2*c^2+6*c^4+a^2*(-5*b^2+2*c^2)) : :
X(60323) = -4*X[3627]+7*X[53105]

X(60323) lies on the Kiepert hyperbola and on these lines: {2, 44108}, {3, 55727}, {76, 548}, {83, 5072}, {262, 12007}, {549, 60277}, {598, 23046}, {671, 15684}, {1503, 60175}, {1513, 60335}, {1657, 43676}, {2794, 54723}, {2996, 49140}, {3526, 56059}, {3534, 60216}, {3627, 53105}, {3843, 53109}, {3850, 53102}, {4052, 28550}, {5055, 60238}, {5066, 60283}, {5485, 46333}, {6776, 60333}, {7608, 9756}, {7710, 53103}, {7735, 60325}, {9744, 53098}, {9748, 54706}, {9752, 47586}, {9753, 54519}, {9754, 60102}, {9755, 14492}, {9993, 54917}, {10302, 15706}, {13860, 54920}, {14032, 60151}, {14890, 60131}, {14893, 54494}, {32457, 33703}, {33698, 38335}, {36990, 54891}, {38227, 60185}, {43460, 43537}, {53015, 60127}

X(60323) = isogonal conjugate of X(55587)
X(60323) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 60175}, {3425, 60335}
X(60323) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(55695)}}, {{A, B, C, X(25), X(548)}}, {{A, B, C, X(64), X(5966)}}, {{A, B, C, X(66), X(57896)}}, {{A, B, C, X(95), X(21765)}}, {{A, B, C, X(427), X(5072)}}, {{A, B, C, X(468), X(15684)}}, {{A, B, C, X(2980), X(13622)}}, {{A, B, C, X(3425), X(43713)}}, {{A, B, C, X(3627), X(37453)}}, {{A, B, C, X(3667), X(28550)}}, {{A, B, C, X(4232), X(46333)}}, {{A, B, C, X(5094), X(23046)}}, {{A, B, C, X(5481), X(57714)}}, {{A, B, C, X(6353), X(49140)}}, {{A, B, C, X(10301), X(15706)}}, {{A, B, C, X(11816), X(46259)}}, {{A, B, C, X(12007), X(33971)}}, {{A, B, C, X(13606), X(56358)}}, {{A, B, C, X(14840), X(18575)}}, {{A, B, C, X(29011), X(43691)}}, {{A, B, C, X(37899), X(55572)}}

X(60324) = X(2)X(55684)∩X(3)X(55737)

Barycentrics    (11*a^4+10*a^2*b^2+11*b^4-6*(a^2+b^2)*c^2-5*c^4)*(11*a^4-5*b^4-6*b^2*c^2+11*c^4+a^2*(-6*b^2+10*c^2)) : :

X(60324) lies on the Kiepert hyperbola and on these lines: {2, 55684}, {3, 55737}, {6, 60328}, {20, 60143}, {76, 5059}, {83, 3854}, {459, 52301}, {598, 50689}, {671, 17578}, {1503, 53099}, {2996, 50690}, {3091, 54616}, {3146, 5485}, {3522, 18840}, {3523, 60183}, {3543, 54637}, {3832, 18842}, {3839, 60284}, {4232, 38253}, {5068, 18841}, {5189, 60114}, {5304, 60327}, {6776, 60142}, {6995, 54710}, {7000, 54597}, {7374, 43536}, {7408, 54867}, {7409, 54531}, {7904, 60285}, {8550, 14484}, {9748, 54917}, {10302, 50693}, {16063, 60237}, {21734, 60277}, {32532, 50687}, {36990, 47586}, {37349, 54797}, {37434, 54695}, {37456, 54788}, {50692, 60200}, {52284, 60137}, {53015, 60102}, {54097, 54916}

X(60324) = isogonal conjugate of X(55614)
X(60324) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 53099}
X(60324) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(55684)}}, {{A, B, C, X(20), X(52301)}}, {{A, B, C, X(25), X(5059)}}, {{A, B, C, X(64), X(1383)}}, {{A, B, C, X(66), X(52443)}}, {{A, B, C, X(67), X(52223)}}, {{A, B, C, X(111), X(22334)}}, {{A, B, C, X(251), X(3532)}}, {{A, B, C, X(427), X(3854)}}, {{A, B, C, X(468), X(17578)}}, {{A, B, C, X(2373), X(31361)}}, {{A, B, C, X(2697), X(46081)}}, {{A, B, C, X(2980), X(46208)}}, {{A, B, C, X(3088), X(7533)}}, {{A, B, C, X(3089), X(5189)}}, {{A, B, C, X(3146), X(4232)}}, {{A, B, C, X(3522), X(6995)}}, {{A, B, C, X(3523), X(7408)}}, {{A, B, C, X(3832), X(52284)}}, {{A, B, C, X(5056), X(7409)}}, {{A, B, C, X(5068), X(7378)}}, {{A, B, C, X(5094), X(50689)}}, {{A, B, C, X(6353), X(50690)}}, {{A, B, C, X(7519), X(37460)}}, {{A, B, C, X(9095), X(56263)}}, {{A, B, C, X(10301), X(50693)}}, {{A, B, C, X(10415), X(38443)}}, {{A, B, C, X(13472), X(53890)}}, {{A, B, C, X(13574), X(23590)}}, {{A, B, C, X(13575), X(51348)}}, {{A, B, C, X(14002), X(49670)}}, {{A, B, C, X(14486), X(43719)}}, {{A, B, C, X(14490), X(40103)}}, {{A, B, C, X(14495), X(57713)}}, {{A, B, C, X(14528), X(29180)}}, {{A, B, C, X(15321), X(51316)}}, {{A, B, C, X(17703), X(45096)}}, {{A, B, C, X(18296), X(30786)}}, {{A, B, C, X(22336), X(52224)}}, {{A, B, C, X(32085), X(35510)}}, {{A, B, C, X(34285), X(38005)}}, {{A, B, C, X(50687), X(53857)}}

X(60325) = X(2)X(50957)∩X(3)X(55739)

Barycentrics    (9*a^4+10*a^2*b^2+9*b^4-4*(a^2+b^2)*c^2-5*c^4)*(9*a^4-5*b^4-4*b^2*c^2+9*c^4+a^2*(-4*b^2+10*c^2)) : :
X(60325) = -10*X[3843]+7*X[5395]

X(60325) lies on the Kiepert hyperbola and on these lines: {2, 50957}, {3, 55739}, {76, 33703}, {376, 60277}, {631, 56059}, {1503, 60127}, {1657, 60285}, {2996, 3627}, {3529, 60210}, {3545, 60238}, {3843, 5395}, {6776, 52519}, {7000, 60312}, {7374, 60311}, {7608, 7710}, {7612, 36990}, {7735, 60323}, {8781, 14928}, {9744, 60332}, {9748, 54519}, {9752, 60185}, {9753, 54608}, {9755, 60147}, {9756, 53103}, {9993, 54891}, {10159, 21735}, {10302, 46333}, {11668, 58883}, {14484, 39874}, {14492, 14912}, {14893, 53101}, {15682, 60216}, {15684, 60200}, {16654, 54604}, {16658, 54763}, {17538, 18840}, {23046, 54639}, {38335, 41895}, {41099, 60283}, {43460, 60144}, {43681, 50691}, {53015, 60175}

X(60325) = isogonal conjugate of X(55629)
X(60325) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(55682)}}, {{A, B, C, X(25), X(33703)}}, {{A, B, C, X(69), X(21765)}}, {{A, B, C, X(251), X(13452)}}, {{A, B, C, X(393), X(57896)}}, {{A, B, C, X(428), X(21735)}}, {{A, B, C, X(1657), X(7714)}}, {{A, B, C, X(3425), X(11738)}}, {{A, B, C, X(3563), X(22334)}}, {{A, B, C, X(3627), X(6353)}}, {{A, B, C, X(3843), X(8889)}}, {{A, B, C, X(5481), X(14491)}}, {{A, B, C, X(6340), X(21400)}}, {{A, B, C, X(6995), X(17538)}}, {{A, B, C, X(8797), X(14840)}}, {{A, B, C, X(10301), X(46333)}}, {{A, B, C, X(11270), X(14495)}}, {{A, B, C, X(13472), X(29180)}}, {{A, B, C, X(13603), X(18847)}}, {{A, B, C, X(14486), X(16835)}}, {{A, B, C, X(14912), X(16264)}}, {{A, B, C, X(14928), X(36875)}}, {{A, B, C, X(15321), X(34208)}}, {{A, B, C, X(29316), X(39955)}}, {{A, B, C, X(38335), X(52290)}}, {{A, B, C, X(43662), X(46851)}}

X(60326) = X(2)X(32237)∩X(3)X(55745)

Barycentrics    (4*a^4+6*a^2*b^2+4*b^4-(a^2+b^2)*c^2-3*c^4)*(4*a^4-3*b^4-b^2*c^2+4*c^4-a^2*(b^2-6*c^2)) : :
X(60326) = -12*X[23046]+7*X[60239]

X(60326) lies on the Kiepert hyperbola and on these lines: {2, 32237}, {3, 55745}, {6, 54890}, {30, 60277}, {76, 3627}, {83, 3843}, {381, 60238}, {382, 60210}, {383, 43549}, {548, 60278}, {598, 14893}, {671, 38335}, {1080, 43548}, {1503, 14488}, {1513, 11668}, {1657, 10159}, {3830, 60216}, {3845, 60283}, {3850, 43527}, {5072, 60100}, {5480, 54582}, {6776, 54520}, {7761, 18840}, {9744, 54523}, {9753, 47586}, {9755, 54891}, {9993, 53100}, {10302, 15684}, {13860, 53108}, {14066, 60151}, {14492, 36990}, {14494, 43460}, {14639, 54800}, {14853, 54706}, {15686, 60131}, {15689, 60279}, {17538, 60183}, {23046, 60239}, {37463, 43441}, {37464, 43440}, {38227, 60102}, {39838, 43532}, {50691, 60285}, {53015, 60337}

X(60326) = isogonal conjugate of X(55649)
X(60326) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 14488}, {3425, 11668}
X(60326) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(29316)}}, {{A, B, C, X(25), X(3627)}}, {{A, B, C, X(251), X(57715)}}, {{A, B, C, X(264), X(48889)}}, {{A, B, C, X(305), X(21400)}}, {{A, B, C, X(427), X(3843)}}, {{A, B, C, X(428), X(1657)}}, {{A, B, C, X(468), X(38335)}}, {{A, B, C, X(842), X(14486)}}, {{A, B, C, X(1297), X(13603)}}, {{A, B, C, X(1494), X(21765)}}, {{A, B, C, X(3062), X(53899)}}, {{A, B, C, X(3425), X(22334)}}, {{A, B, C, X(3426), X(14495)}}, {{A, B, C, X(3531), X(53890)}}, {{A, B, C, X(3613), X(14840)}}, {{A, B, C, X(5072), X(52285)}}, {{A, B, C, X(5094), X(14893)}}, {{A, B, C, X(6995), X(33703)}}, {{A, B, C, X(7408), X(17538)}}, {{A, B, C, X(7714), X(50691)}}, {{A, B, C, X(9106), X(39732)}}, {{A, B, C, X(9307), X(15321)}}, {{A, B, C, X(10301), X(15684)}}, {{A, B, C, X(11169), X(43726)}}, {{A, B, C, X(11738), X(29322)}}, {{A, B, C, X(13452), X(39955)}}, {{A, B, C, X(14483), X(29180)}}, {{A, B, C, X(16264), X(36990)}}, {{A, B, C, X(17501), X(56358)}}, {{A, B, C, X(18494), X(37899)}}, {{A, B, C, X(22336), X(57822)}}, {{A, B, C, X(32085), X(57896)}}

X(60327) = X(2)X(50960)∩X(6)X(54706)

Barycentrics    (9*a^4+14*a^2*b^2+9*b^4-2*(a^2+b^2)*c^2-7*c^4)*(9*a^4-7*b^4-2*b^2*c^2+9*c^4-2*a^2*(b^2-7*c^2)) : :
X(60327) = -7*X[3832]+4*X[18841]

X(60327) lies on these lines: {2, 50960}, {6, 54706}, {20, 60183}, {76, 17578}, {83, 50689}, {459, 7408}, {1503, 54520}, {3146, 18840}, {3543, 60143}, {3832, 18841}, {3839, 54616}, {3854, 43527}, {4052, 9812}, {5059, 10159}, {5304, 60324}, {5485, 50687}, {6776, 54890}, {6811, 60315}, {6813, 60316}, {6995, 38253}, {7000, 34091}, {7374, 34089}, {7378, 60137}, {7391, 60237}, {7409, 56346}, {7710, 53099}, {9748, 14458}, {9752, 60175}, {9753, 54851}, {9755, 54845}, {9756, 60102}, {14853, 54582}, {14930, 60328}, {21734, 56059}, {36990, 43951}, {43460, 60332}, {44434, 60180}, {50690, 60285}, {50693, 60278}, {59413, 60267}

X(60327) = isogonal conjugate of X(55651)
X(60327) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 54520}
X(60327) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(55673)}}, {{A, B, C, X(20), X(7408)}}, {{A, B, C, X(25), X(17578)}}, {{A, B, C, X(64), X(39955)}}, {{A, B, C, X(251), X(22334)}}, {{A, B, C, X(305), X(18296)}}, {{A, B, C, X(427), X(50689)}}, {{A, B, C, X(428), X(5059)}}, {{A, B, C, X(1383), X(14490)}}, {{A, B, C, X(3088), X(37349)}}, {{A, B, C, X(3091), X(7409)}}, {{A, B, C, X(3146), X(6995)}}, {{A, B, C, X(3425), X(13603)}}, {{A, B, C, X(3531), X(5481)}}, {{A, B, C, X(3532), X(34572)}}, {{A, B, C, X(3543), X(52301)}}, {{A, B, C, X(3832), X(7378)}}, {{A, B, C, X(3854), X(5064)}}, {{A, B, C, X(4232), X(50687)}}, {{A, B, C, X(7714), X(50690)}}, {{A, B, C, X(8801), X(46208)}}, {{A, B, C, X(9109), X(24680)}}, {{A, B, C, X(9464), X(46731)}}, {{A, B, C, X(13575), X(31361)}}, {{A, B, C, X(14495), X(57715)}}, {{A, B, C, X(15314), X(56200)}}, {{A, B, C, X(15321), X(21765)}}, {{A, B, C, X(18575), X(51316)}}, {{A, B, C, X(29180), X(52518)}}

X(60328) = X(2)X(55614)∩X(4)X(22246)

Barycentrics    (5*a^4+22*a^2*b^2+5*b^4+6*(a^2+b^2)*c^2-11*c^4)*(5*a^4-11*b^4+6*b^2*c^2+5*c^4+a^2*(6*b^2+22*c^2)) : :

X(60328) lies on the Kiepert hyperbola and on these lines: {2, 55614}, {3, 55768}, {4, 22246}, {6, 60324}, {20, 54616}, {76, 3854}, {83, 5059}, {598, 17578}, {671, 50689}, {3091, 60143}, {3146, 18842}, {3522, 18841}, {3543, 60284}, {3832, 5485}, {3839, 54637}, {4232, 60137}, {5056, 60183}, {5068, 18840}, {5395, 50690}, {5480, 43537}, {7000, 43536}, {7374, 54597}, {7378, 54710}, {7408, 54531}, {7409, 54867}, {7533, 60114}, {9748, 60335}, {14853, 53100}, {14930, 60327}, {21734, 60238}, {37349, 54785}, {37434, 54719}, {37665, 54706}, {38253, 52284}, {50687, 60281}, {50692, 54639}, {50693, 60239}, {52301, 56346}, {52854, 54814}, {53023, 60118}, {54097, 54915}

X(60328) = isogonal conjugate of X(55684)
X(60328) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(22246)}}, {{A, B, C, X(6), X(52443)}}, {{A, B, C, X(25), X(3854)}}, {{A, B, C, X(67), X(52224)}}, {{A, B, C, X(427), X(5059)}}, {{A, B, C, X(468), X(50689)}}, {{A, B, C, X(1383), X(52518)}}, {{A, B, C, X(3088), X(5189)}}, {{A, B, C, X(3089), X(7533)}}, {{A, B, C, X(3091), X(52301)}}, {{A, B, C, X(3108), X(3532)}}, {{A, B, C, X(3146), X(52284)}}, {{A, B, C, X(3522), X(7378)}}, {{A, B, C, X(3523), X(7409)}}, {{A, B, C, X(3527), X(11181)}}, {{A, B, C, X(3613), X(46208)}}, {{A, B, C, X(3832), X(4232)}}, {{A, B, C, X(5056), X(7408)}}, {{A, B, C, X(5068), X(6995)}}, {{A, B, C, X(5094), X(17578)}}, {{A, B, C, X(8801), X(38005)}}, {{A, B, C, X(8889), X(50690)}}, {{A, B, C, X(13481), X(22336)}}, {{A, B, C, X(18018), X(51348)}}, {{A, B, C, X(22334), X(39389)}}, {{A, B, C, X(31857), X(49670)}}, {{A, B, C, X(43458), X(43726)}}, {{A, B, C, X(45011), X(54459)}}

X(60329) = X(2)X(55606)∩X(83)X(1657)

Barycentrics    (2*(a^4+5*a^2*b^2+b^4)+3*(a^2+b^2)*c^2-5*c^4)*(2*a^4-5*b^4+3*b^2*c^2+2*c^4+a^2*(3*b^2+10*c^2)) : :

X(60329) lies on the Kiepert hyperbola and on these lines: {2, 55606}, {3, 55771}, {5, 60277}, {6, 54857}, {30, 60283}, {76, 3850}, {83, 1657}, {381, 60216}, {383, 54593}, {548, 60239}, {598, 3627}, {625, 18840}, {671, 3843}, {1080, 54594}, {1513, 54645}, {1656, 56059}, {3851, 60210}, {5072, 7922}, {5395, 50691}, {5480, 7607}, {5485, 7758}, {8550, 14458}, {9744, 52519}, {9753, 60102}, {9993, 11669}, {12812, 60131}, {13860, 54644}, {14066, 54872}, {14853, 47586}, {14893, 17503}, {15684, 60282}, {15686, 60287}, {15712, 43527}, {17538, 54616}, {18841, 21735}, {18842, 33703}, {23046, 60228}, {37463, 43549}, {37464, 43548}, {37874, 47315}, {38227, 60123}, {38335, 45103}, {43460, 43951}, {43461, 60332}, {49140, 54639}, {50280, 54637}, {53023, 60142}

X(60329) = isogonal conjugate of X(55687)
X(60329) = X(i)-vertex conjugate of X(j) for these {i, j}: {3425, 54645}
X(60329) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(55606)}}, {{A, B, C, X(264), X(22336)}}, {{A, B, C, X(305), X(14861)}}, {{A, B, C, X(427), X(1657)}}, {{A, B, C, X(468), X(3843)}}, {{A, B, C, X(842), X(3527)}}, {{A, B, C, X(1297), X(57730)}}, {{A, B, C, X(1593), X(47315)}}, {{A, B, C, X(3627), X(5094)}}, {{A, B, C, X(4518), X(43732)}}, {{A, B, C, X(5064), X(15712)}}, {{A, B, C, X(5072), X(10301)}}, {{A, B, C, X(7249), X(43731)}}, {{A, B, C, X(7378), X(21735)}}, {{A, B, C, X(7758), X(13608)}}, {{A, B, C, X(8889), X(50691)}}, {{A, B, C, X(9307), X(38005)}}, {{A, B, C, X(13472), X(14388)}}, {{A, B, C, X(14528), X(29011)}}, {{A, B, C, X(14840), X(45090)}}, {{A, B, C, X(14893), X(52292)}}, {{A, B, C, X(17983), X(43726)}}, {{A, B, C, X(21765), X(55958)}}, {{A, B, C, X(22334), X(53890)}}, {{A, B, C, X(29316), X(39951)}}, {{A, B, C, X(33703), X(52284)}}, {{A, B, C, X(38335), X(52293)}}, {{A, B, C, X(39389), X(57715)}}

X(60330) = X(2)X(55724)∩X(3)X(54639)

Barycentrics    (a^4-22*a^2*b^2+b^4-12*(a^2+b^2)*c^2+11*c^4)*(a^4+11*b^4-12*b^2*c^2+c^4-2*a^2*(6*b^2+11*c^2)) : :

X(60330) lies on the Kiepert hyperbola and on these lines: {2, 55724}, {3, 54639}, {5, 60200}, {6, 60337}, {83, 10299}, {376, 60282}, {382, 53101}, {546, 41895}, {550, 5395}, {598, 3529}, {631, 60239}, {671, 3855}, {1513, 54521}, {2996, 3851}, {3090, 10302}, {3528, 18842}, {3533, 60100}, {3544, 5485}, {3545, 60228}, {6811, 60300}, {6813, 60299}, {7000, 60295}, {7374, 60296}, {7736, 60132}, {7906, 43681}, {8550, 60150}, {9744, 54917}, {10301, 60161}, {13860, 54866}, {14269, 54896}, {14853, 53098}, {14912, 47586}, {15687, 54642}, {15710, 60283}, {18845, 49135}, {33238, 54753}, {33239, 54833}, {35018, 60285}, {39874, 54857}, {50688, 54476}, {52285, 54893}, {58883, 60192}

X(60330) = isogonal conjugate of X(55701)
X(60330) = X(i)-vertex conjugate of X(j) for these {i, j}: {3425, 54521}
X(60330) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(55724)}}, {{A, B, C, X(427), X(10299)}}, {{A, B, C, X(468), X(3855)}}, {{A, B, C, X(546), X(52290)}}, {{A, B, C, X(550), X(8889)}}, {{A, B, C, X(3090), X(10301)}}, {{A, B, C, X(3528), X(52284)}}, {{A, B, C, X(3529), X(5094)}}, {{A, B, C, X(3533), X(52285)}}, {{A, B, C, X(3544), X(4232)}}, {{A, B, C, X(3851), X(6353)}}, {{A, B, C, X(5486), X(45090)}}, {{A, B, C, X(7714), X(35018)}}, {{A, B, C, X(8797), X(38005)}}, {{A, B, C, X(8801), X(57894)}}, {{A, B, C, X(11270), X(39389)}}, {{A, B, C, X(14536), X(18853)}}, {{A, B, C, X(14842), X(40410)}}, {{A, B, C, X(15321), X(52717)}}, {{A, B, C, X(16063), X(35482)}}, {{A, B, C, X(17040), X(57897)}}, {{A, B, C, X(34208), X(45108)}}, {{A, B, C, X(34567), X(40801)}}, {{A, B, C, X(39951), X(57713)}}, {{A, B, C, X(45011), X(46081)}}, {{A, B, C, X(46848), X(54172)}}, {{A, B, C, X(46952), X(57823)}}, {{A, B, C, X(49135), X(52299)}}

X(60331) = X(2)X(55722)∩X(3)X(55790)

Barycentrics    (a^4-18*a^2*b^2+b^4-10*(a^2+b^2)*c^2+9*c^4)*(a^4+9*b^4-10*b^2*c^2+c^4-2*a^2*(5*b^2+9*c^2)) : :

X(60331) lies on the Kiepert hyperbola and on these lines: {2, 55722}, {3, 55790}, {6, 60336}, {20, 18843}, {76, 15022}, {83, 15717}, {98, 14930}, {549, 54616}, {598, 15683}, {3091, 60219}, {3146, 53109}, {3522, 53102}, {3534, 60284}, {3628, 60183}, {3815, 60118}, {3832, 53105}, {3839, 54720}, {5055, 60143}, {5066, 54637}, {5068, 43676}, {5304, 54921}, {5395, 50693}, {5480, 54521}, {6776, 54608}, {7000, 60305}, {7374, 60306}, {7486, 18840}, {7736, 60147}, {9744, 54477}, {9748, 53108}, {9753, 60144}, {10303, 18841}, {10304, 18842}, {10513, 60212}, {11669, 14853}, {12007, 54866}, {13860, 60322}, {15640, 60281}, {18844, 49140}, {18845, 50692}, {33287, 60151}, {37453, 60137}, {37665, 47586}, {43461, 54734}, {50687, 54494}

X(60331) = isogonal conjugate of X(55703)
X(60331) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(55722)}}, {{A, B, C, X(25), X(15022)}}, {{A, B, C, X(253), X(11169)}}, {{A, B, C, X(325), X(14930)}}, {{A, B, C, X(427), X(15717)}}, {{A, B, C, X(1383), X(14489)}}, {{A, B, C, X(3526), X(7409)}}, {{A, B, C, X(3613), X(52224)}}, {{A, B, C, X(3628), X(7408)}}, {{A, B, C, X(3832), X(22466)}}, {{A, B, C, X(5055), X(52301)}}, {{A, B, C, X(5094), X(15683)}}, {{A, B, C, X(5481), X(44763)}}, {{A, B, C, X(5966), X(14491)}}, {{A, B, C, X(6995), X(7486)}}, {{A, B, C, X(7378), X(10303)}}, {{A, B, C, X(7736), X(10513)}}, {{A, B, C, X(8889), X(50693)}}, {{A, B, C, X(10304), X(52284)}}, {{A, B, C, X(13622), X(35510)}}, {{A, B, C, X(14486), X(40103)}}, {{A, B, C, X(18575), X(52188)}}, {{A, B, C, X(39389), X(43713)}}, {{A, B, C, X(45088), X(46455)}}, {{A, B, C, X(45108), X(52223)}}, {{A, B, C, X(45819), X(51316)}}, {{A, B, C, X(50692), X(52299)}}, {{A, B, C, X(52487), X(53963)}}

X(60332) = X(2)X(55718)∩X(3)X(55796)

Barycentrics    (2*(a^4-7*a^2*b^2+b^4)-9*(a^2+b^2)*c^2+7*c^4)*(2*a^4+7*b^4-9*b^2*c^2+2*c^4-a^2*(9*b^2+14*c^2)) : :

X(60332) lies on the Kiepert hyperbola and on these lines: {2, 55718}, {3, 55796}, {5, 60228}, {6, 60334}, {76, 35018}, {83, 15720}, {140, 60239}, {382, 45103}, {546, 17503}, {550, 598}, {671, 3851}, {1513, 54643}, {1656, 10302}, {3523, 54639}, {3528, 60284}, {3529, 60281}, {3530, 60283}, {3544, 54637}, {3815, 14488}, {3855, 32532}, {5056, 60200}, {5079, 60216}, {6811, 60314}, {6813, 60313}, {7736, 60322}, {9744, 60325}, {10299, 18842}, {10301, 60120}, {13860, 54608}, {14034, 54872}, {14269, 54478}, {14869, 60287}, {18841, 58448}, {33606, 37463}, {33607, 37464}, {38227, 53098}, {43460, 60327}, {43461, 60329}, {46219, 60100}, {49135, 53101}, {49139, 53109}, {50688, 54642}, {55856, 60278}

X(60332) = isogonal conjugate of X(55708)
X(60332) = X(i)-vertex conjugate of X(j) for these {i, j}: {3425, 54643}
X(60332) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(55718)}}, {{A, B, C, X(25), X(35018)}}, {{A, B, C, X(305), X(26861)}}, {{A, B, C, X(382), X(52293)}}, {{A, B, C, X(427), X(15720)}}, {{A, B, C, X(468), X(3851)}}, {{A, B, C, X(546), X(52292)}}, {{A, B, C, X(550), X(5094)}}, {{A, B, C, X(842), X(43908)}}, {{A, B, C, X(1656), X(10301)}}, {{A, B, C, X(3516), X(47629)}}, {{A, B, C, X(3613), X(57823)}}, {{A, B, C, X(3855), X(53857)}}, {{A, B, C, X(5486), X(57897)}}, {{A, B, C, X(10299), X(52284)}}, {{A, B, C, X(15464), X(45090)}}, {{A, B, C, X(37900), X(52296)}}, {{A, B, C, X(38005), X(40410)}}, {{A, B, C, X(39389), X(57713)}}, {{A, B, C, X(46219), X(52285)}}

X(60333) = X(2)X(5102)∩X(3)X(18843)

Barycentrics    (3*a^4-14*a^2*b^2+3*b^4-10*(a^2+b^2)*c^2+7*c^4)*(3*a^4+7*b^4-10*b^2*c^2+3*c^4-2*a^2*(5*b^2+7*c^2)) : :

X(60333) lies on the Kiepert hyperbola and on these lines: {2, 5102}, {3, 18843}, {4, 31467}, {5, 60219}, {6, 60102}, {20, 53109}, {76, 7486}, {83, 10303}, {230, 53859}, {381, 54720}, {548, 18844}, {549, 18842}, {598, 10304}, {671, 36519}, {1007, 60259}, {1513, 52519}, {2996, 15022}, {3091, 53105}, {3424, 3815}, {3523, 53102}, {3526, 18841}, {3534, 60281}, {3543, 54494}, {3628, 18840}, {3839, 33698}, {4052, 10171}, {5055, 5485}, {5056, 43676}, {5066, 32532}, {5304, 7607}, {5395, 15717}, {6194, 60096}, {6776, 60323}, {6811, 60306}, {6813, 60305}, {7000, 12818}, {7374, 12819}, {7608, 9752}, {7612, 37665}, {7710, 60147}, {7736, 43537}, {7925, 60285}, {9742, 60218}, {9744, 54857}, {9748, 14494}, {9753, 54645}, {9754, 11669}, {9755, 60185}, {9756, 47586}, {12007, 60336}, {13860, 54845}, {14853, 60192}, {15640, 45103}, {15683, 53101}, {15698, 60284}, {15709, 54616}, {17005, 60260}, {18845, 50693}, {31489, 53099}, {34803, 60262}, {37453, 56346}, {37668, 60101}, {37689, 53103}, {43461, 54890}, {44434, 60098}, {46936, 60210}, {49140, 53107}, {51171, 60104}

X(60333) = isogonal conjugate of X(55711)
X(60333) = X(i)-vertex conjugate of X(j) for these {i, j}: {25, 53859}, {3425, 52519}
X(60333) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(5102)}}, {{A, B, C, X(25), X(7486)}}, {{A, B, C, X(95), X(52717)}}, {{A, B, C, X(253), X(13622)}}, {{A, B, C, X(254), X(34110)}}, {{A, B, C, X(427), X(10303)}}, {{A, B, C, X(523), X(45833)}}, {{A, B, C, X(549), X(52284)}}, {{A, B, C, X(1007), X(37665)}}, {{A, B, C, X(2963), X(21765)}}, {{A, B, C, X(3091), X(37453)}}, {{A, B, C, X(3108), X(14489)}}, {{A, B, C, X(3425), X(57714)}}, {{A, B, C, X(3526), X(7378)}}, {{A, B, C, X(3613), X(44658)}}, {{A, B, C, X(3628), X(6995)}}, {{A, B, C, X(3815), X(37668)}}, {{A, B, C, X(4232), X(5055)}}, {{A, B, C, X(5066), X(53857)}}, {{A, B, C, X(5094), X(10304)}}, {{A, B, C, X(5481), X(43713)}}, {{A, B, C, X(6353), X(15022)}}, {{A, B, C, X(7925), X(51171)}}, {{A, B, C, X(8797), X(52224)}}, {{A, B, C, X(8889), X(15717)}}, {{A, B, C, X(11410), X(30769)}}, {{A, B, C, X(13606), X(57726)}}, {{A, B, C, X(15640), X(52293)}}, {{A, B, C, X(17005), X(37667)}}, {{A, B, C, X(30537), X(50973)}}, {{A, B, C, X(31467), X(34483)}}, {{A, B, C, X(34285), X(45090)}}, {{A, B, C, X(34803), X(37689)}}, {{A, B, C, X(39389), X(40801)}}, {{A, B, C, X(40410), X(52223)}}, {{A, B, C, X(43726), X(46217)}}, {{A, B, C, X(49140), X(52298)}}, {{A, B, C, X(50693), X(52299)}}, {{A, B, C, X(51132), X(52188)}}, {{A, B, C, X(51214), X(55958)}}

X(60334) = X(2)X(33749)∩X(3)X(55820)

Barycentrics    (7*a^4-4*a^2*b^2+7*b^4-9*(a^2+b^2)*c^2+2*c^4)*(7*a^4+2*b^4-9*b^2*c^2+7*c^4-a^2*(9*b^2+4*c^2)) : :

X(60334) lies on the Kiepert hyperbola and on these lines: {2, 33749}, {3, 55820}, {5, 60282}, {6, 60332}, {76, 15720}, {83, 35018}, {140, 10302}, {230, 60132}, {382, 17503}, {546, 45103}, {550, 671}, {598, 3851}, {1513, 54608}, {1656, 60239}, {3523, 60200}, {3528, 54637}, {3529, 32532}, {3530, 60216}, {3544, 60284}, {3855, 60281}, {5056, 54639}, {5079, 60283}, {5485, 10299}, {6055, 60271}, {6811, 60313}, {6813, 60314}, {8550, 10185}, {9993, 54706}, {10301, 39284}, {11606, 35021}, {13860, 54643}, {14045, 54872}, {15687, 54478}, {15712, 60250}, {33606, 37464}, {33607, 37463}, {37900, 54666}, {38227, 54857}, {41895, 49135}, {43461, 60123}, {46219, 60278}, {49139, 53105}, {50688, 54896}, {52285, 54791}, {55856, 60100}, {55863, 60286}

X(60334) = isogonal conjugate of X(55718)
X(60334) = trilinear pole of line {47466, 523}
X(60334) = X(i)-vertex conjugate of X(j) for these {i, j}: {25, 60132}, {3425, 54608}
X(60334) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(43656)}}, {{A, B, C, X(6), X(55708)}}, {{A, B, C, X(25), X(15720)}}, {{A, B, C, X(67), X(57897)}}, {{A, B, C, X(69), X(14842)}}, {{A, B, C, X(95), X(33749)}}, {{A, B, C, X(111), X(57713)}}, {{A, B, C, X(140), X(10301)}}, {{A, B, C, X(382), X(52292)}}, {{A, B, C, X(427), X(35018)}}, {{A, B, C, X(468), X(550)}}, {{A, B, C, X(546), X(52293)}}, {{A, B, C, X(1799), X(26861)}}, {{A, B, C, X(2165), X(57823)}}, {{A, B, C, X(3519), X(52192)}}, {{A, B, C, X(3529), X(53857)}}, {{A, B, C, X(3532), X(14388)}}, {{A, B, C, X(3851), X(5094)}}, {{A, B, C, X(4232), X(10299)}}, {{A, B, C, X(10018), X(37900)}}, {{A, B, C, X(11270), X(40103)}}, {{A, B, C, X(15398), X(43689)}}, {{A, B, C, X(15464), X(32085)}}, {{A, B, C, X(17983), X(45838)}}, {{A, B, C, X(21448), X(43719)}}, {{A, B, C, X(22336), X(53864)}}, {{A, B, C, X(37453), X(49139)}}, {{A, B, C, X(45819), X(57895)}}, {{A, B, C, X(49135), X(52290)}}, {{A, B, C, X(52285), X(55856)}}

X(60335) = X(2)X(55706)∩X(3)X(55824)

Barycentrics    (6*a^4-2*a^2*b^2+6*b^4-7*(a^2+b^2)*c^2+c^4)*(6*a^4+b^4-7*b^2*c^2+6*c^4-a^2*(7*b^2+2*c^2)) : :
X(60335) = 4*X[550]+5*X[60209]

X(60335) lies on the Kiepert hyperbola and on these lines: {2, 55706}, {3, 55824}, {6, 54920}, {76, 3530}, {83, 5079}, {230, 53100}, {382, 53106}, {546, 53107}, {547, 60239}, {550, 60209}, {598, 38071}, {632, 60278}, {671, 15681}, {1503, 54851}, {1513, 60323}, {1916, 35021}, {3851, 60146}, {3855, 18844}, {5054, 10302}, {5070, 60100}, {5485, 15710}, {6055, 42010}, {7608, 9755}, {7710, 60185}, {7735, 52519}, {8703, 60228}, {9744, 60123}, {9748, 60328}, {9752, 60147}, {9753, 54520}, {9754, 43537}, {9756, 14492}, {14038, 60151}, {14269, 54646}, {15687, 54493}, {15692, 60200}, {19709, 60282}, {38227, 60150}, {43460, 47586}

X(60335) = isogonal conjugate of X(55720)
X(60335) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 54851}, {25, 53100}, {3425, 60323}
X(60335) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(55706)}}, {{A, B, C, X(25), X(3530)}}, {{A, B, C, X(382), X(13381)}}, {{A, B, C, X(427), X(5079)}}, {{A, B, C, X(468), X(15681)}}, {{A, B, C, X(523), X(57823)}}, {{A, B, C, X(546), X(52298)}}, {{A, B, C, X(2165), X(57897)}}, {{A, B, C, X(3425), X(54172)}}, {{A, B, C, X(4232), X(15710)}}, {{A, B, C, X(5054), X(10301)}}, {{A, B, C, X(5070), X(52285)}}, {{A, B, C, X(5094), X(38071)}}, {{A, B, C, X(8770), X(29011)}}, {{A, B, C, X(9307), X(57894)}}, {{A, B, C, X(13602), X(52133)}}, {{A, B, C, X(14842), X(34285)}}, {{A, B, C, X(32085), X(44658)}}, {{A, B, C, X(35021), X(40820)}}, {{A, B, C, X(37897), X(55576)}}, {{A, B, C, X(38005), X(57895)}}, {{A, B, C, X(40801), X(53890)}}

X(60336) = X(2)X(50958)∩X(3)X(55827)

Barycentrics    (9*a^4-2*a^2*b^2+9*b^4-10*(a^2+b^2)*c^2+c^4)*(9*a^4+b^4-10*b^2*c^2+9*c^4-2*a^2*(5*b^2+c^2)) : :
X(60336) = X[20]+2*X[60219]

X(60336) lies on the Kiepert hyperbola and on these lines: {2, 50958}, {3, 55827}, {6, 60331}, {20, 60219}, {76, 15717}, {83, 15022}, {165, 4052}, {230, 47586}, {549, 60143}, {671, 15683}, {1503, 54866}, {1513, 60322}, {2996, 50693}, {3091, 18843}, {3146, 53105}, {3522, 43676}, {3526, 60183}, {3534, 54637}, {3543, 54720}, {3832, 53109}, {5055, 54616}, {5066, 60284}, {5068, 53102}, {5304, 60118}, {5485, 10304}, {5984, 60073}, {6194, 60180}, {6776, 53104}, {7000, 60306}, {7374, 60305}, {7486, 18841}, {7710, 43537}, {7735, 43951}, {7891, 60285}, {9744, 10185}, {9748, 14492}, {9752, 14458}, {9753, 54582}, {9754, 60175}, {9755, 14494}, {9756, 14484}, {10153, 11177}, {10303, 18840}, {10513, 60262}, {12007, 60333}, {14651, 54723}, {14853, 54643}, {14930, 53099}, {15640, 32532}, {20080, 35005}, {33698, 50687}, {37453, 38253}, {37689, 60147}, {38227, 54851}, {38259, 50692}, {44434, 60095}, {46917, 60267}, {53015, 54519}

X(60336) = isogonal conjugate of X(55722)
X(60336) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 54866}, {25, 47586}, {3425, 60322}
X(60336) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(55703)}}, {{A, B, C, X(25), X(15717)}}, {{A, B, C, X(67), X(51027)}}, {{A, B, C, X(69), X(46208)}}, {{A, B, C, X(105), X(165)}}, {{A, B, C, X(111), X(43713)}}, {{A, B, C, X(393), X(13622)}}, {{A, B, C, X(427), X(15022)}}, {{A, B, C, X(468), X(15683)}}, {{A, B, C, X(523), X(34285)}}, {{A, B, C, X(549), X(52301)}}, {{A, B, C, X(1297), X(44763)}}, {{A, B, C, X(1383), X(5481)}}, {{A, B, C, X(2980), X(44658)}}, {{A, B, C, X(3146), X(37453)}}, {{A, B, C, X(3526), X(7408)}}, {{A, B, C, X(3628), X(7409)}}, {{A, B, C, X(3832), X(38443)}}, {{A, B, C, X(4232), X(10304)}}, {{A, B, C, X(5966), X(11270)}}, {{A, B, C, X(6353), X(50693)}}, {{A, B, C, X(6995), X(10303)}}, {{A, B, C, X(7378), X(7486)}}, {{A, B, C, X(8770), X(29180)}}, {{A, B, C, X(10513), X(37689)}}, {{A, B, C, X(13481), X(14842)}}, {{A, B, C, X(14658), X(34130)}}, {{A, B, C, X(15321), X(46217)}}, {{A, B, C, X(15640), X(53857)}}, {{A, B, C, X(21765), X(46952)}}, {{A, B, C, X(30542), X(52187)}}, {{A, B, C, X(34208), X(52443)}}, {{A, B, C, X(38282), X(50692)}}, {{A, B, C, X(39954), X(46917)}}, {{A, B, C, X(40103), X(40801)}}, {{A, B, C, X(44836), X(46455)}}, {{A, B, C, X(45838), X(52223)}}

X(60337) = X(2)X(55701)∩X(3)X(55829)

Barycentrics    (11*a^4-2*a^2*b^2+11*b^4-12*(a^2+b^2)*c^2+c^4)*(11*a^4+b^4-12*b^2*c^2+11*c^4-2*a^2*(6*b^2+c^2)) : :

X(60337) lies on the Kiepert hyperbola and on these lines: {2, 55701}, {3, 55829}, {5, 54639}, {6, 60330}, {76, 10299}, {230, 60322}, {376, 60228}, {382, 41895}, {546, 53101}, {550, 2996}, {598, 3855}, {631, 10302}, {671, 3529}, {1513, 54866}, {3090, 60239}, {3528, 5485}, {3533, 60278}, {3544, 18842}, {3545, 60282}, {3851, 5395}, {6776, 60123}, {6811, 60299}, {6813, 60300}, {7000, 60296}, {7374, 60295}, {7608, 14912}, {7735, 14488}, {8550, 53098}, {8781, 35021}, {8796, 10301}, {10991, 54659}, {11623, 60189}, {13860, 54521}, {14269, 54642}, {14651, 54475}, {15687, 54896}, {15710, 60216}, {15720, 60285}, {21735, 60250}, {38259, 49135}, {39874, 43537}, {41899, 47629}, {50688, 60113}, {52285, 54892}, {53015, 60326}, {58883, 60175}

X(60337) = isogonal conjugate of X(55724)
X(60337) = trilinear pole of line {47462, 523}
X(60337) = X(i)-vertex conjugate of X(j) for these {i, j}: {25, 60322}, {3425, 54866}
X(60337) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(55701)}}, {{A, B, C, X(25), X(10299)}}, {{A, B, C, X(54), X(54172)}}, {{A, B, C, X(67), X(34208)}}, {{A, B, C, X(111), X(11270)}}, {{A, B, C, X(376), X(13530)}}, {{A, B, C, X(382), X(40347)}}, {{A, B, C, X(393), X(57894)}}, {{A, B, C, X(468), X(3529)}}, {{A, B, C, X(550), X(6353)}}, {{A, B, C, X(631), X(10301)}}, {{A, B, C, X(3147), X(37900)}}, {{A, B, C, X(3528), X(4232)}}, {{A, B, C, X(3532), X(3563)}}, {{A, B, C, X(3544), X(52284)}}, {{A, B, C, X(3851), X(8889)}}, {{A, B, C, X(3855), X(5094)}}, {{A, B, C, X(7714), X(15720)}}, {{A, B, C, X(8770), X(43719)}}, {{A, B, C, X(9076), X(55029)}}, {{A, B, C, X(10603), X(18851)}}, {{A, B, C, X(13597), X(18852)}}, {{A, B, C, X(14486), X(57730)}}, {{A, B, C, X(14842), X(16774)}}, {{A, B, C, X(16835), X(21448)}}, {{A, B, C, X(17983), X(34285)}}, {{A, B, C, X(35021), X(51820)}}, {{A, B, C, X(36948), X(38005)}}, {{A, B, C, X(38282), X(49135)}}, {{A, B, C, X(40118), X(41522)}}

X(60338) = X(2)X(2501)∩X(4)X(3566)

Barycentrics    (b-c)*(b+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*((a^2-b^2)^2-(a^2+b^2)*c^2+2*c^4)*(a^4+2*b^4-b^2*c^2+c^4-a^2*(b^2+2*c^2)) : :

X(60338) lies on the Kiepert hyperbola and on these lines: {2, 2501}, {4, 3566}, {69, 55278}, {76, 14618}, {83, 47736}, {96, 15412}, {98, 3563}, {275, 15422}, {485, 54028}, {486, 54029}, {512, 60117}, {523, 7612}, {525, 2996}, {671, 35142}, {690, 60189}, {850, 5392}, {1499, 54894}, {2489, 60093}, {2799, 8781}, {2986, 2987}, {3429, 28529}, {4235, 32697}, {5466, 35235}, {6504, 33294}, {11140, 55251}, {14273, 60103}, {17994, 54978}, {18808, 54495}, {20031, 60179}, {23878, 60218}, {36891, 54925}, {40428, 53173}, {42065, 53345}, {53101, 58780}, {53156, 54554}, {54872, 59775}

X(60338) = isogonal conjugate of X(56389)
X(60338) = trilinear pole of line {8754, 34981}
X(60338) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 56389}, {48, 4226}, {163, 3564}, {230, 4575}, {662, 52144}, {1692, 4592}, {1733, 32661}, {4558, 8772}, {17462, 43754}, {36084, 47406}
X(60338) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 56389}, {115, 3564}, {136, 230}, {1084, 52144}, {1249, 4226}, {2501, 57154}, {5139, 1692}, {38970, 114}, {38987, 47406}, {47898, 6782}, {47899, 6783}, {48317, 5477}
X(60338) = X(i)-cross conjugate of X(j) for these {i, j}: {125, 40428}, {2799, 14618}
X(60338) = pole of line {3564, 39813} with respect to the anticomplementary circle
X(60338) = pole of line {3564, 39818} with respect to the circumcircle of the Johnson triangle
X(60338) = pole of line {114, 230} with respect to the polar circle
X(60338) = pole of line {2987, 3564} with respect to the Steiner circumellipse
X(60338) = pole of line {8781, 39816} with respect to the dual conic of orthic inconic
X(60338) = pole of line {35067, 47406} with respect to the dual conic of Wallace hyperbola
X(60338) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(125), X(53173)}}, {{A, B, C, X(287), X(52473)}}, {{A, B, C, X(338), X(14977)}}, {{A, B, C, X(525), X(3566)}}, {{A, B, C, X(648), X(18808)}}, {{A, B, C, X(850), X(6563)}}, {{A, B, C, X(2395), X(2799)}}, {{A, B, C, X(2501), X(14618)}}, {{A, B, C, X(3563), X(57493)}}, {{A, B, C, X(3926), X(18347)}}, {{A, B, C, X(4235), X(35235)}}, {{A, B, C, X(4558), X(43709)}}, {{A, B, C, X(14341), X(42399)}}, {{A, B, C, X(39183), X(58784)}}
X(60338) = barycentric product X(i)*X(j) for these (i, j): {264, 35364}, {1109, 36105}, {2501, 8781}, {3563, 850}, {10425, 2970}, {14618, 2987}, {16230, 40428}, {18808, 36891}, {24006, 8773}, {30786, 52476}, {32697, 338}, {35142, 523}, {43665, 57493}, {57872, 58757}
X(60338) = barycentric quotient X(i)/X(j) for these (i, j): {4, 4226}, {6, 56389}, {136, 57154}, {512, 52144}, {523, 3564}, {879, 53783}, {2065, 43754}, {2489, 1692}, {2501, 230}, {2971, 42663}, {2987, 4558}, {3563, 110}, {3569, 47406}, {8754, 55122}, {8773, 4592}, {8781, 4563}, {14273, 5477}, {14618, 51481}, {16230, 114}, {17983, 52035}, {17994, 51335}, {18808, 36875}, {24006, 1733}, {32654, 32661}, {32697, 249}, {35142, 99}, {35364, 3}, {36051, 4575}, {36105, 24041}, {40428, 17932}, {47736, 17941}, {52476, 468}, {53149, 51820}, {56689, 57625}, {57493, 2421}, {57609, 38359}, {58757, 460}

X(60339) = X(6)X(2431)∩X(9)X(650)

Barycentrics    a*(a - b - c)*(b - c)*(a^2*b - b^3 + a^2*c - 2*a*b*c + b^2*c + b*c^2 - c^3)^2 : :

X(60339) lies on these lines: {6, 2431}, {9, 650}, {119, 20623}, {223, 3669}, {226, 14837}, {478, 46389}, {521, 9817}, {661, 18591}, {770, 47765}, {1211, 1577}, {1638, 39063}, {1643, 5452}, {1769, 3310}, {2423, 40134}, {2427, 23706}, {3064, 53009}, {3239, 20262}, {6364, 13388}, {6365, 13389}, {6544, 46384}, {17435, 45950}, {21011, 55232}, {35015, 55153}, {40584, 57174}, {40590, 57185}

X(60339) = complement of the isotomic conjugate of X(53151)
X(60339) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 35014}, {1785, 21252}, {1875, 17059}, {2427, 18589}, {4246, 3741}, {8750, 517}, {14571, 116}, {21801, 127}, {23706, 2886}, {23981, 34822}, {24029, 18639}, {32676, 15325}, {42072, 57434}, {42078, 10017}, {51377, 34846}, {53151, 2887}
X(60339) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 35014}, {651, 517}, {4391, 2804}, {21664, 41215}, {26611, 3326}
X(60339) = X(i)-isoconjugate of X(j) for these (i,j): {104, 37136}, {109, 59196}, {664, 41933}, {909, 54953}, {2720, 34234}, {18816, 32669}, {34051, 36037}
X(60339) = X(i)-Dao conjugate of X(j) for these (i,j): {11, 59196}, {517, 651}, {1145, 13136}, {2804, 4391}, {3259, 34051}, {23980, 54953}, {35014, 2}, {38981, 34234}, {39025, 41933}, {40613, 37136}, {40624, 57550}, {55153, 18816}, {57293, 222}
X(60339) = crossdifference of every pair of points on line {104, 1319}
X(60339) = barycentric product X(i)*X(j) for these {i,j}: {8, 42757}, {11, 15632}, {100, 3326}, {513, 55016}, {517, 2804}, {521, 21664}, {522, 24028}, {650, 26611}, {651, 55153}, {908, 46393}, {1361, 4397}, {1769, 6735}, {3262, 53549}, {4391, 23980}, {6073, 46041}, {18026, 41215}, {23101, 43728}, {35014, 53151}, {35518, 42072}, {35519, 42078}, {39534, 51379}
X(60339) = barycentric quotient X(i)/X(j) for these {i,j}: {517, 54953}, {650, 59196}, {1361, 934}, {2183, 37136}, {2804, 18816}, {3063, 41933}, {3310, 34051}, {3326, 693}, {4391, 57550}, {15632, 4998}, {21664, 18026}, {23980, 651}, {24028, 664}, {26611, 4554}, {41215, 521}, {41220, 23224}, {42072, 108}, {42078, 109}, {42757, 7}, {42771, 57468}, {46393, 34234}, {52315, 42455}, {53549, 104}, {55016, 668}, {55153, 4391}, {59800, 1415}

X(60340) = X(3)X(690)∩X(30)X(14566)

Barycentrics    (b^2 - c^2)*(-a^2 + b^2 - b*c + c^2)*(-a^2 + b^2 + b*c + c^2)*(-2*a^6 + 2*a^4*b^2 - a^2*b^4 + b^6 + 2*a^4*c^2 - b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6)^2 : :

X(60340) lies on these lines: {3, 690}, {30, 14566}, {523, 24975}, {1640, 6041}, {1649, 41167}, {5664, 31378}, {8552, 47055}, {14993, 15475}, {15295, 46608}, {16188, 18556}, {23283, 40578}, {23284, 40579}

X(60340) lies on these lines: midpoint of X(18556) and X(57603)
X(60340) lies on these lines: complement of the isogonal conjugate of X(51262)
X(60340) lies on these lines: X(i)-complementary conjugate of X(j) for these (i,j): {31, 57464}, {35200, 37987}, {36034, 542}, {48451, 8287}, {51227, 21253}, {51262, 10}
X(60340) lies on these lines: X(i)-Ceva conjugate of X(j) for these (i,j): {2, 57464}, {476, 542}
X(60340) lies on these lines: X(842)-isoconjugate of X(36096)
X(60340) lies on these lines: X(i)-Dao conjugate of X(j) for these (i,j): {542, 476}, {57464, 2}
X(60340) lies on these lines: crossdifference of every pair of points on line {842, 2493}
X(60340) lies on these lines: barycentric product X(i)*X(j) for these {i,j}: {3268, 23967}, {8552, 38552}, {14999, 53132}
X(60340) lies on these lines: barycentric quotient X(i)/X(j) for these {i,j}: {1640, 54554}, {2247, 36096}, {3268, 57547}, {5191, 23969}, {23967, 476}, {38552, 46456}, {46048, 23968}, {53132, 14223}

X(60341) = X(3)X(525)∩X(132)X(133)

Barycentrics    (b^2 - c^2)*(-a^2 + b^2 + c^2)^2*(-2*a^6 + a^4*b^2 + b^6 + a^4*c^2 - b^4*c^2 - b^2*c^4 + c^6)^2 : :

X(60341) lies on these lines: {3, 525}, {4, 58342}, {132, 133}, {523, 1249}, {6523, 58757}, {6793, 9475}, {8057, 20208}, {16253, 42733}, {52613, 53844}

X(60341) lies on these lines: X(i)-complementary conjugate of X(j) for these (i,j): {31, 57296}, {2409, 20308}, {8766, 35968}, {19614, 57606}
X(60341) lies on these lines: X(i)-Ceva conjugate of X(j) for these (i,j): {2, 57296}, {107, 1503}, {3265, 39473}
X(60341) lies on these lines: X(i)-isoconjugate of X(j) for these (i,j): {1297, 36092}, {6330, 36046}, {8767, 44770}
X(60341) = X(i)-Dao conjugate of X(j) for these (i,j): {1503, 107}, {33504, 6330}, {39071, 44770}, {39473, 3265}, {57296, 2}
X(60341) = crossdifference of every pair of points on line {232, 1297}
X(60341) = barycentric product X(i)*X(j) for these {i,j}: {1503, 39473}, {3265, 23976}, {24018, 24023}
X(60341) = barycentric quotient X(i)/X(j) for these {i,j}: {2312, 36092}, {3265, 57549}, {8779, 44770}, {15639, 32230}, {23976, 107}, {24023, 823}, {39473, 35140}, {42671, 32687}

X(60342) = X(5)X(543)∩X(6)X(647)

Barycentrics    a^2*(b^2 - c^2)*(a^2 - b^2 - b*c - c^2)*(a^2 - b^2 + b*c - c^2)*(a^4*b^2 - 2*a^2*b^4 + b^6 + a^4*c^2 + 2*a^2*b^2*c^2 - b^4*c^2 - 2*a^2*c^4 - b^2*c^4 + c^6) : :
X[14380] + 3 X[34291], 4 X[8562] - 3 X[44814]

X(60342) lies on the Jerabek circumhyperbola of the medial triangle and these lines: {2, 15328}, {3, 924}, {5, 523}, {6, 647}, {110, 15453}, {113, 131}, {141, 30511}, {186, 53234}, {206, 8651}, {512, 4550}, {520, 1147}, {526, 1511}, {684, 1649}, {942, 31947}, {1510, 14809}, {3258, 16186}, {6132, 6593}, {9033, 46085}, {10190, 57592}, {14385, 15470}, {14940, 57120}, {16171, 18577}, {20184, 44866}, {21196, 34830}, {23992, 39021}, {24975, 31945}, {47138, 55267}

X(60342) = midpoint of X(i) and X(j) for these {i,j}: {110, 15453}, {14270, 14314}
X(60342) = reflection of X(i) in X(j) for these {i,j}: {30511, 38401}, {44808, 44816}
X(60342) = complement of X(15328)
X(60342) = complement of the isogonal conjugate of X(15329)
X(60342) = medial-isogonal conjugate of X(3134)
X(60342) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 3134}, {31, 2088}, {162, 13754}, {163, 11064}, {1101, 55121}, {1725, 125}, {2315, 15526}, {3003, 8287}, {3580, 21253}, {4575, 10257}, {6149, 56792}, {13754, 34846}, {15329, 10}, {16237, 20305}, {18609, 116}, {21731, 24040}, {23995, 47230}, {23997, 47049}, {32676, 16310}, {32678, 58416}, {36034, 6699}, {36061, 12358}, {36134, 14156}
X(60342) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 2088}, {110, 13754}, {523, 55121}, {4558, 50}, {14385, 16186}, {14618, 2081}, {53958, 3581}
X(60342) = X(i)-isoconjugate of X(j) for these (i,j): {162, 12028}, {163, 40427}, {265, 36114}, {476, 36053}, {1300, 36061}, {2166, 10420}, {2986, 32678}, {5504, 36129}, {14910, 32680}, {36034, 39375}, {36047, 39986}, {36096, 51456}
X(60342) = X(i)-Dao conjugate of X(j) for these (i,j): {113, 476}, {115, 40427}, {125, 12028}, {526, 15470}, {2088, 2}, {3258, 39375}, {3580, 99}, {6334, 850}, {11597, 10420}, {16178, 6344}, {16221, 1300}, {17433, 60035}, {18334, 2986}, {34834, 35139}, {35235, 58084}, {35581, 39986}, {35588, 5961}, {39005, 265}, {39021, 94}, {40604, 18878}, {47230, 14618}, {56792, 5627}
X(60342) = crossdifference of every pair of points on line {30, 50}
X(60342) = X(5)-line conjugate of X(51847)
X(60342) = barycentric product X(i)*X(j) for these {i,j}: {186, 6334}, {323, 55121}, {340, 686}, {403, 8552}, {523, 34834}, {525, 1986}, {526, 3580}, {1725, 32679}, {3003, 3268}, {4558, 16221}, {5627, 58872}, {5664, 14264}, {7799, 21731}, {10419, 58790}, {13754, 44427}, {16186, 16237}, {44084, 45792}, {44808, 52504}, {47236, 52437}
X(60342) = barycentric quotient X(i)/X(j) for these {i,j}: {50, 10420}, {186, 687}, {323, 18878}, {340, 57932}, {403, 46456}, {523, 40427}, {526, 2986}, {647, 12028}, {686, 265}, {1637, 39375}, {1725, 32680}, {1986, 648}, {2081, 60035}, {2088, 15328}, {2315, 36061}, {2624, 36053}, {3003, 476}, {3268, 40832}, {3580, 35139}, {5664, 52552}, {6334, 328}, {8552, 57829}, {13754, 60053}, {14264, 39290}, {14270, 14910}, {15329, 39295}, {16186, 15421}, {16221, 14618}, {18334, 15470}, {21731, 1989}, {22115, 43755}, {34397, 32708}, {34834, 99}, {44808, 52505}, {47230, 1300}, {47236, 6344}, {52603, 18879}, {52743, 15454}, {55121, 94}, {55130, 52498}, {55265, 14254}, {57136, 52557}, {58872, 6148}, {58940, 54959}
X(60342) = {X(57122),X(57123)}-harmonic conjugate of X(52743)





leftri   Points associated with hyperbolas: X(60343) - X(60352)  rightri

Contributed by Clark Kimberling and Peter Moses, November 3, 2023

Let H be a hyperbola. Let W be the center of H, and let L and L' be the asymptotes of H. There exists a unique hyperbola H' other than H that has center W and asymptotes L and L'. The hyperbola H' is the called the conjugate of H. If H is a circumhyperbola and L is given by

u x + v y + w z = 0,

then L' is given by

v w x + w u y + u v z = 0.

The hyperbola H is given by u(v - w)^2 y z + (cyclic) = 0, with center u(v^2 - w^2) : : and perspector u(v - w)^2 y z : : .

The conjugate hyperbola H' is given by u(v+w)^2 y z + (cyclic) + 2 u v w (x^2 + y^2 + z^2) = 0, with center u(v^2 - w^2) : : and perspector

u*(v - w)*(3*u*v + v^2 + u*w + 3*v*w)*(u*v + 3*u*w + 3*v*w + w^2) : : .

Example 1. H = Kiepert hyperbola

Center of H and H': X(115)

Asymptotes, L and L', are the lines u x + v y + w z = 0, where u:v:w = X(30508) and u:v:w = X(30509).

Equation for H: (b^2 - c^2) b y + (cyclic) = 0

Equation for H': 2*((a^2 - b^2)^3*x*y + (-a^2 + c^2)^3*x*z + (b^2 - c^2)^3*y*z) - (a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2)*(x^2 + y^2 + z^2) = 0

The point X(i) lies on H' for these i: 3413, 3414, 39107, 39108. The perspector of H' is X(9293).

Example 2. H = Jerabek hyperbola

Center of H and H': X(125)

Asymptotes, L and L', are the lines u x + v y + w z = 0, where u:v:w = X(50944) and u:v:w = X(50945).

Equation for H: a^2(b^2 - c^2)SA y z + (cyclic) = 0

Equation for H': 2*(a^2*b^2*(a^2 - b^2)^3*(-a^2 - b^2 + c^2)*x*y + a^2*c^2*(-a^2 + b^2 - c^2)*(-a^2 + c^2)^3*x*z + b^2*c^2*(a^2 - b^2 - c^2)*(b^2 - c^2)^3*y*z) - (a^2 - b^2)*(a^2 - c^2)*(a^2 - b^2 - c^2)*(b^2 - c^2)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(x^2 + y^2 + z^2) = 0

The point X(i) lies on H' for these i: 2574, 2575. The perspector of H' is X(60478).

Example 3. H = Feuerbach hyperbola

Center of H and H': X(11)

Asymptotes, L and L', are the lines u x + v y + w z = 0, where u:v:w = X(60476) and u:v:w = X(60477).

Equation for H: a(b - c)(b + c - a) y z + (cyclic) = 0

Equation for H': 2*(a*(a - b)^3*b*(a + b - c)*x*y + a*c*(-a + c)^3*(a - b + c)*x*z + b*(b - c)^3*c*(-a + b + c)*y*z) + (a - b)*(b - c)*(a + b - c)*(-a + c)*(a - b + c)*(-a + b + c)*(x^2 + y^2 + z^2) = 0

The point X(i) passes through H' for these i: 3307, 3308. The perspector of H' is X(42552).

Starting with a line L, the L-asymptotic circumhyperbola is the hyperbola that passes through the vertices A,B,C and has L as an asymptote.

Example 4. L = Brocard axis, X(3)X(6). Here, the other asymptote, L', is the line through X(i) for these i: 115, 127, 338, 339, 2799, 6334, 15526, 16732, 18312, 21207.

The L-asymptotic hyperbola, H, passes through X(i) for these i: 511, 1297, 1916, 1972, 2799, 2967, 2987, 32458, 36426, 36790, 44132, 46787, 46807, 53229.

The conjugate of the L-asymptotic hyperbola passes through X(511) and X(2799).

Example 5. L = Lemoine axis, X(187)X(237). Here, the other asymptote, L', passes through X(i) for these i: 325, 523, 684, 693, 850, 858, 1273, 1491, 2512, 2513

The L-asymptotic hyperbola, H, passes through X(i) for these i: 512, 523, 691, 876, 882, 2422, 2489, 4079, 4705, 9124, 9178, 14560, 15475, 18105, 18829, 32696, 35364, 41880, 41881, 46001, 46005, 50344, 51441, 52618, 52631, 57993, 58756, 58757, 58825, 58827, 58869, 58870, 60028, 60031, 60037, 60045, 60050, 60054, 60057.

The conjugate, H', of the L-asymptotic hyperbola passes through X(i) for these i: 512, 523, 21006, 47133, 57082.

Example 6. L = anti-orthic axis, X(44)X(513). Here, the other asymptote, L', passes through X(i) for these i: 514, 661, 693, 857, 908, 914, 1577, 1959, 2084, 2582

The L-asymptotic hyperbola, H, passes through X(i) for these i: 513, 514, 876, 1019, 1022, 1027, 1308, 3257, 3669, 4562, 7199, 35355, 36146, 39179, 47915, 47947, 48070, 48074, 48587, 57200, 58794, 58817. The center of H is X(661), and the perspector, X(244).

The conjugate, H', of the L-asymptotic hyperbola, given by

a(b + c)^2 y z + b(c + a)^2 z x + c(a + b)^2 x y + 2a b c(x^2 + y^2 + z^2) = 0,

passes through X(i) for these i: 513, 514, 4063, 20954, 47921, 48085, 48128, 48624, 60343, 60344, 60345, 60346, 60347, 60348, 60349, 60350, 60351. The center of H' is X(661), and the perspector, X(60529.

Example 7. The Kiepert circumhyperbola of the anticomplementary triangle, given by

(b^2 - c^2) x^2 + (c^2 - a^2) y^2 + (a^2 - b^2) z^2 = 0.

is discussed as the "superior Kiepert hyperbola" in Yiu's Introduction to the Geometry of the Triangle (2013 revision, page 136). This hyperbola passes through X(i) for these i: 1, 2, 20, 63, 147, 194, 368, 487, 488, 616, 617, 627, 628, 1670, 1671, 1764, 2128, 2582, 2583, 2896, 3413, 3414, 6194, 6462, 6463, 7616, 8591, 8782, 9742, 10336, 11148, 13174, 13678, 13798, 16552, 16563, 17147, 18301, 18596, 20371, 21378, 30562, 30564, 30579, 33404, 33405, 33608, 33609, 33610, 33611, 33612, 33613, 36857, 41914, 41923, 41930, 44010, 45029, 46625, 46717, 46944, 51860, 51952, 51953, 52025, 52676, 53856, 56471, 56472, 58035, and also the vertices of the excentral and anticomplementary triangles. The center of this hyperbola, H is X(99).

The conjugate hyperbola, H', given by

(b^2 - c^2)*(a^4 - a^2*b^2 - b^4 - a^2*c^2 + 3*b^2*c^2 - c^4)*x^2 - 4*(a^2 - b^2)*(b^2 - c^2)*(-a^2 + c^2)*x*y + (-a^2 + c^2)*(-a^4 - a^2*b^2 + b^4 + 3*a^2*c^2 - b^2*c^2 - c^4)*y^2 - 4*(a^2 - b^2)*(b^2 - c^2)*(-a^2 + c^2)*x*z - 4*(a^2 - b^2)*(b^2 - c^2)*(-a^2 + c^2)*y*z + (a^2 - b^2)*(-a^4 + 3*a^2*b^2 - b^4 - a^2*c^2 - b^2*c^2 + c^4)*z^2 = 0, passes through X(3413) and X(3414).

Recall that a hyperbola is a rectangular hyperbola if its asymptotes are perpendicular, and that if one asymptote is given by ux + vy + wz =0, then the other given by x/u +y/v + z/w =0. The locus of the point u:v:w for which these asymptotes are perpendicular is the cubic K010, given by b c cos(A) x (y -z)^2 + (cyclic) = 0. This cubic passes through X(i) for these i: 2, 2394, 2395, 2396, 2397, 2398, 2399, 2400, 2401, 2402, 2403, 2404, 2405, 2406, 2407, 2408, 2409, 2410, 2411, 2412, 2413, 2414, 2415, 2416, 2417, 2418, 2419, 30508, 30509, 50941, 50942, 50943, 50944, 50945, 57455, 57456, 57457, 57458, 57459, 57460. The intersection of the perpendicular asymptotes, hence the center of the hyperbola, lies on the nine-point circle.

Example 8. The Moses-Feuerbach circumhyperbola and its conjugate are introduced at X(60478).

underbar



X(60343) = X(9)X(513)∩X(514)X(48304)

Barycentrics    a*(b - c)*(a^4 - 5*a^3*b + 7*a^2*b^2 - 3*a*b^3 - 5*a^3*c + 5*a^2*b*c + 9*a*b^2*c - 5*b^3*c + 7*a^2*c^2 + 9*a*b*c^2 + 6*b^2*c^2 - 3*a*c^3 - 5*b*c^3) : :
X(60343) = 3 X[4040] - 2 X[45695]

X(60343) lies on these lines: {9, 513}, {514, 48304}, {3309, 47921}, {3667, 56322}, {4040, 45695}, {4063, 42325}, {48081, 48128}, {48085, 48116}

X(60344) = X(10)X(514)∩X(512)X(47948)

Barycentrics    a*(b - c)*(a*b^3 + a^2*b*c + 4*a*b^2*c + 2*b^3*c + 4*a*b*c^2 + 3*b^2*c^2 + a*c^3 + 2*b*c^3) : :
X(60344) = 2 X[665] - 3 X[47827]

X(60344) lies on these lines: {10, 514}, {512, 47948}, {513, 21832}, {523, 3766}, {661, 30665}, {665, 47827}, {784, 47679}, {3250, 48030}, {4040, 38348}, {4063, 4784}, {4083, 48027}, {4802, 21113}, {20295, 50538}, {29198, 47921}, {47658, 58360}, {47659, 58289}

X(60344) = reflection of X(i) in X(j) for these {i,j}: {876, 1491}, {3250, 48030}
X(60344) = crossdifference of every pair of points on line {1914, 4649}

X(60345) = X(1)X(667)∩X(512)X(48624)

Barycentrics    a*(b - c)*(3*a^2*b^2 + 2*a*b^3 + 2*a^2*b*c + 2*a*b^2*c - 2*b^3*c + 3*a^2*c^2 + 2*a*b*c^2 - 3*b^2*c^2 + 2*a*c^3 - 2*b*c^3) : :

X(603455) lies on these lines: {1, 667}, {512, 48624}, {513, 4826}, {514, 4806}, {3250, 48030}, {4802, 18080}, {17230, 31040}, {20954, 28195}, {29198, 48085}, {29226, 47921}, {30665, 50335}

X(60345) = reflection of X(48030) in X(3250)
X(60345) = crossdifference of every pair of points on line {1575, 16468}

X(60346) = X(1)X(513)∩X(514)X(4120)

Barycentrics    a*(b - c)*(a^2 + 5*a*b + 4*b^2 + 5*a*c - b*c + 4*c^2) : :
X(60346) = X[48320] - 4 X[48335], 7 X[1019] - 4 X[48624], 4 X[1635] - 3 X[4063], 5 X[1635] - 6 X[14838], X[1635] - 3 X[48131], 5 X[4063] - 8 X[14838], X[4063] - 4 X[48131], 2 X[14838] - 5 X[48131], 3 X[14349] - 2 X[47777], 5 X[14349] - 2 X[47921], 5 X[47777] - 3 X[47921], X[47947] - 4 X[48128], X[47970] - 4 X[48129], X[48085] + 2 X[48334], 5 X[48085] - 2 X[48582], 5 X[48334] + X[48582], 2 X[48122] + X[48337]

X(60346) lies on these lines: {1, 513}, {514, 4120}, {1019, 48624}, {1635, 4063}, {4083, 4825}, {4893, 21385}, {14349, 47777}, {17217, 47683}, {21130, 48558}, {23888, 48550}, {47947, 48128}, {47970, 48129}, {48085, 48334}, {48122, 48337}

X(60346) = reflection of X(i) in X(j) for these {i,j}: {1022, 48335}, {21130, 48558}, {21385, 4893}, {48320, 1022}
X(60346) = crossdifference of every pair of points on line {44, 21747}

X(60347) = X(2)X(514)∩X(513)X(3245)

Barycentrics    a*(b - c)*(a^2 - a*b - 2*b^2 - a*c - 13*b*c - 2*c^2) : :
X(60347) = X[1019] - 4 X[47921], 2 X[3251] - 3 X[4040], 5 X[4063] - 2 X[48149], 5 X[4498] - 2 X[48624], 4 X[9269] - 3 X[48282], 4 X[47918] - X[48085], 5 X[47918] - 2 X[48612], 5 X[48085] - 8 X[48612], 4 X[47922] - X[48086], 5 X[47959] - 2 X[48128], 4 X[47966] - X[48337]

X(60347) lies on these lines: {2, 514}, {513, 3245}, {1019, 47921}, {1635, 48320}, {3251, 4040}, {3762, 20954}, {4063, 48149}, {4498, 48624}, {9269, 48282}, {28175, 47725}, {47777, 48335}, {47918, 48085}, {47922, 48086}, {47959, 48128}, {47966, 48337}

X(60347) = reflection of X(i) in X(j) for these {i,j}: {1022, 4893}, {21116, 21198}, {48320, 1635}, {48335, 47777}
X(60347) = crossdifference of every pair of points on line {902, 16666}

X(60348) = X(512)X(47921)∩X(513)X(665)

Barycentrics    a*(b - c)*(6*a^2*b^2 + 2*a*b^3 + 11*a^2*b*c + 14*a*b^2*c + b^3*c + 6*a^2*c^2 + 14*a*b*c^2 + 6*b^2*c^2 + 2*a*c^3 + b*c^3) : :

X(60348) lies on these lines: {512, 47921}, {513, 665}, {514, 4170}, {1027, 48367}, {4063, 4724}, {4778, 20954}, {6372, 48128}, {48085, 48122}

X(60349 = X(37)X(513)∩X(512)X(659)

Barycentrics    a*(b - c)*(2*a^2*b^2 + a*b^3 + 3*a^2*b*c + 4*a*b^2*c + 2*a^2*c^2 + 4*a*b*c^2 + b^2*c^2 + a*c^3) : :
X(60349) = 4 X[40549] - 3 X[47824]

X(60349) lies on these lines: {37, 513}, {512, 659}, {514, 4010}, {661, 30665}, {665, 4784}, {784, 7265}, {1491, 24290}, {3766, 4806}, {4083, 47921}, {4977, 20954}, {6005, 48624}, {6372, 48085}, {8663, 17494}, {20295, 58296}, {23791, 24083}, {29198, 48128}, {40549, 47824}

X(60349) = reflection of X(i) in X(j) for these {i,j}: {876, 3250}, {3766, 4806}, {4784, 665}
X(60349 = crossdifference of every pair of points on line {238, 24512}
X(60349 = barycentric product X(513)*X(31323)
X(60349 = barycentric quotient X(31323)/X(668)

X(60350) = X(75)X(522)∩X(512)X(2526)

Barycentrics    a*(b - c)*(2*a^2*b^2 - 2*a*b^3 + 3*a^2*b*c - 2*a*b^2*c - 3*b^3*c + 2*a^2*c^2 - 2*a*b*c^2 - 2*b^2*c^2 - 2*a*c^3 - 3*b*c^3) : :

X(60350) lies on these lines: {75, 522}, {512, 2526}, {513, 4832}, {514, 1734}, {784, 7178}, {1027, 45755}, {1491, 24290}, {3766, 50356}, {4063, 47929}, {4151, 49285}, {4492, 24873}, {6005, 48023}, {6372, 7659}, {17756, 47828}, {20520, 47123}, {30665, 50335}

X(60350) = midpoint of X(3766) and X(50356)
X(60350) = reflection of X(47123) in X(20520)
X(60350) = crossdifference of every pair of points on line {2280, 9454}

X(60351) = X(513)X(4729)∩X(514)X(4521)

Barycentrics    a*(b - c)*(a^2 - 2*a*b - 3*b^2 - 2*a*c - 22*b*c - 3*c^2) : :
X(60351) = 3 X[4394] - 2 X[48144], 3 X[47921] - X[48144], 5 X[47955] - 3 X[48085], 3 X[47915] - X[48597], 3 X[47918] - X[48128], 3 X[47966] - X[48333], X[48336] - 3 X[48618]

X(60351) lies on these lines: {513, 4729}, {514, 4521}, {2516, 48341}, {4394, 47921}, {4462, 20954}, {8712, 47955}, {47915, 48597}, {47918, 48128}, {47966, 48333}, {48336, 48618}

X(60351) = reflection of X(i) in X(j) for these {i,j}: {4394, 47921}, {48341, 2516}
X(60351) = crossdifference of every pair of points on line {3052, 16667}

X(60352) = X(110)X(40173)∩X(526)X(1112)

Barycentrics    a^2*(b^2 - c^2)*(a^2 - b^2 - c^2)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - a^4*c^2 + a^2*b^2*c^2 - b^4*c^2 + a^2*c^4 + b^2*c^4 - c^6)*(a^6 - a^4*b^2 + a^2*b^4 - b^6 - a^4*c^2 + a^2*b^2*c^2 + b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6) : :

X(60352) lies on these lines: {110, 40173}, {526, 1112}, {684, 22085}, {850, 3448}, {924, 3447}, {3569, 14397}, {6333, 9517}, {9514, 46246}, {13198, 35909}

X(60352) = isogonal conjugate of X(30716)
X(60352) = perspector of conjugate of Jerabek circumhyperbola (see preamble just before X(60343)
X(60352) = X(i)-isoconjugate of X(j) for these (i,j): {1, 30716}, {92, 36830}, {112, 20941}, {162, 3448}, {648, 16562}, {811, 7669}, {823, 22146}, {5379, 21203}, {8574, 46254}, {14366, 24006}
X(60352) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 30716}, {125, 3448}, {17423, 7669}, {22391, 36830}, {34591, 20941}, {55066, 16562}
X(60352) = crossdifference of every pair of points on line {3448, 22146}
X(60352) = X(850)-line conjugate of X(3448)
X(60352) = barycentric product X(i)*X(j) for these {i,j}: {125, 40173}, {525, 3447}, {647, 13485}, {4558, 6328}
X(60352) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 30716}, {184, 36830}, {647, 3448}, {656, 20941}, {810, 16562}, {3049, 7669}, {3447, 648}, {6328, 14618}, {13485, 6331}, {20975, 45801}, {32661, 14366}, {39201, 22146}, {39469, 34349}, {40173, 18020}, {55230, 21092}



?

leftri  Common point of radical axes: X(60353) - X(60475)  rightri

This preamble and centers X(60353)-X(60475) were contributed by César Eliud Lozada, November 5, 2023.

Let ω be a circle and P, Q two distinct fixed points, none on ω. Then the radical axes of ω and all the circles through P and Q have a common point X(ω, P, Q).

The pencil or set of circles through P, Q is denoted here OO(P, Q).

Some properties:

  1. The common point X(ω, P, Q) lies on the line PQ. Therefore, it is the intersection of this line with the radical axis of ω and any chosen circle in O(P, Q). A very simple proof of this fact can be seen here.
  2. X(ω, P, Q) is the radical center of ω and any pair of circles in O(P,Q).
  3. When P, Q and the center of ω are not collinear, X(ω, P, Q) = PQ∩P'Q', where P' and Q' are the respective inverses of P, Q in ω.
  4. If P or Q is the center of ω then X(ω, P, Q) is the inverse of the other in ω.
  5. If ω is the circumcircle of ABC then X(ω, P, Q) concides with the Vu (P,Q)-circle point (see preamble just before X(38458)).
  6. If ω is the circumcircle of ABC and P or Q is the centroid X(2) of ABC, then X(ω, P, Q) coincides with the Vu pole of P and Q (see preamble just before X(37756)).
underbar

X(60353) = COMMON POINT OF RADICAL AXES OF { CIRCUMCIRCLE, OO( X(1), X(10) ) }

Barycentrics    a*(a^3+b*c*a+(b+c)*(b^2-3*b*c+c^2)) : :
X(60353) = X(1)-2*X(30117) = 2*X(10)-X(16086) = X(484)+2*X(1168) = X(3465)-4*X(15898) = 2*X(4432)-3*X(33309)

X(60353) lies on these lines: {1, 2}, {3, 24440}, {6, 50014}, {9, 3735}, {12, 24161}, {21, 4642}, {30, 8481}, {34, 979}, {35, 3987}, {36, 1054}, {38, 54315}, {40, 49128}, {44, 44663}, {46, 37397}, {56, 24174}, {58, 3754}, {65, 1046}, {75, 24291}, {80, 3465}, {86, 49779}, {87, 998}, {100, 4695}, {101, 16611}, {169, 54329}, {171, 3753}, {172, 21951}, {238, 517}, {244, 54391}, {269, 31598}, {355, 30448}, {392, 17123}, {405, 37598}, {484, 759}, {495, 33130}, {514, 4581}, {515, 1738}, {529, 1086}, {666, 35176}, {748, 3877}, {758, 1757}, {846, 4424}, {859, 5143}, {956, 982}, {958, 986}, {984, 9708}, {993, 17596}, {996, 7194}, {999, 17063}, {1048, 37558}, {1104, 5255}, {1220, 17789}, {1279, 3880}, {1319, 16610}, {1411, 26727}, {1420, 11512}, {1421, 16576}, {1449, 50028}, {1455, 9364}, {1478, 17889}, {1616, 10912}, {1706, 37552}, {1707, 2093}, {1716, 18506}, {1724, 3460}, {1740, 29331}, {1742, 30503}, {1743, 18421}, {1807, 11545}, {1870, 17927}, {2099, 4383}, {2170, 33854}, {2191, 56150}, {2292, 5260}, {2329, 16583}, {2345, 49781}, {2802, 40091}, {2886, 37717}, {2975, 24443}, {3073, 37562}, {3120, 5080}, {3125, 3509}, {3230, 4919}, {3290, 56530}, {3340, 54386}, {3419, 32865}, {3421, 33144}, {3496, 3959}, {3501, 16968}, {3550, 37817}, {3670, 5258}, {3681, 49454}, {3698, 37539}, {3749, 16485}, {3751, 8539}, {3752, 37617}, {3772, 37716}, {3782, 34606}, {3812, 37607}, {3902, 32943}, {3915, 14923}, {3925, 5724}, {3953, 5288}, {3976, 12513}, {4000, 24249}, {4051, 16502}, {4315, 24175}, {4363, 48832}, {4390, 26242}, {4432, 33309}, {4534, 57019}, {4645, 38456}, {4646, 37573}, {4650, 36279}, {4653, 4868}, {4659, 48812}, {4675, 48825}, {4723, 32927}, {4737, 32920}, {5119, 8616}, {5176, 33129}, {5252, 24789}, {5289, 37679}, {5298, 43055}, {5434, 40688}, {5440, 56009}, {5587, 17064}, {5710, 16478}, {5722, 33141}, {5725, 33111}, {5795, 13161}, {5902, 32913}, {6001, 9355}, {6004, 59834}, {6187, 37311}, {6547, 46100}, {7281, 50896}, {7290, 10800}, {8056, 13462}, {8666, 24046}, {8706, 12029}, {9260, 48283}, {9363, 37566}, {10106, 24178}, {10436, 20924}, {10899, 11010}, {10914, 37588}, {11113, 33095}, {11114, 33094}, {11260, 52541}, {13541, 16489}, {15934, 49490}, {15950, 37663}, {16370, 17601}, {16784, 60361}, {17290, 48801}, {17606, 33177}, {17719, 17757}, {17735, 21888}, {17737, 21044}, {17906, 37168}, {20805, 38286}, {20893, 25590}, {21147, 43040}, {21896, 56176}, {24281, 50025}, {24358, 35101}, {24693, 48816}, {24806, 57277}, {24851, 57288}, {27003, 54310}, {27660, 41723}, {32860, 49492}, {33096, 39542}, {33135, 37715}, {33771, 35016}, {33895, 45219}, {36926, 37759}, {38458, 60358}, {38459, 60364}, {41015, 41239}, {43059, 52089}, {43065, 60369}, {49755, 50029}, {49778, 59772}

X(60353) = reflection of X(i) in X(j) for these (i, j): (1, 30117), (16086, 10)
X(60353) = complement of X(60452)
X(60353) = cross-difference of every pair of points on the line X(649)X(2269)
X(60353) = crosspoint of X(655) and X(7035)
X(60353) = crosssum of X(i) and X(j) for these {i, j}: {1, 5529}, {654, 3248}, {2245, 3725}
X(60353) = X(i)-aleph conjugate of-X(j) for these (i, j): (1, 6326), (266, 6127), (509, 16554), (2222, 23703)
X(60353) = X(i)-beth conjugate of-X(j) for these (i, j): (8, 16086), (21, 47623), (36926, 36926)
X(60353) = X(i)-Ceva conjugate of-X(j) for these (i, j): (1411, 1), (40663, 484)
X(60353) = X(2)-daleth conjugate of-X(39595)
X(60353) = X(i)-Dao conjugate of-X(j) for these (i, j): (10, 34895), (15898, 36935)
X(60353) = X(2)-hirst inverse of-X(1999)
X(60353) = X(i)-isoconjugate of-X(j) for these {i, j}: {36, 36935}, {58, 34895}
X(60353) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (37, 34895), (2161, 36935), (36926, 312), (37759, 75), (37791, 86), (41873, 20924), (47056, 903)
X(60353) = X(i)-zayin conjugate of-X(j) for these (i, j): (1404, 1743), (1457, 978), (42753, 1054), (51646, 21173)
X(60353) = Gibert-Burek-Moses concurrent circles image of X(6790)
X(60353) = perspector of the circumconic through X(190) and X(47056)
X(60353) = inverse of X(1999) in Steiner circumellipse
X(60353) = inverse of X(39595) in Steiner inellipse
X(60353) = pole of the line {4057, 24457} with respect to the circumcircle
X(60353) = pole of the line {3667, 12545} with respect to the Conway circle
X(60353) = pole of the line {3667, 4298} with respect to the incircle
X(60353) = pole of the line {7649, 46878} with respect to the polar circle
X(60353) = pole of the line {2, 24319} with respect to the circumhyperbola dual of Yff parabola
X(60353) = pole of the line {1213, 2161} with respect to the Kiepert circumhyperbola
X(60353) = pole of the line {58, 214} with respect to the Stammler hyperbola
X(60353) = pole of the line {514, 1999} with respect to the Steiner circumellipse
X(60353) = pole of the line {514, 39595} with respect to the Steiner inellipse
X(60353) = pole of the line {86, 1227} with respect to the Steiner-Wallace hyperbola
X(60353) = pole of the line {190, 6002} with respect to the Yff parabola
X(60353) = barycentric product X(i)*X(j) for these {i, j}: {1, 37759}, {10, 37791}, {57, 36926}, {519, 47056}, {2161, 41873}
X(60353) = trilinear product X(i)*X(j) for these {i, j}: {6, 37759}, {37, 37791}, {44, 47056}, {56, 36926}, {6187, 41873}
X(60353) = trilinear quotient X(i)/X(j) for these (i, j): (10, 34895), (80, 36935), (36926, 8), (37759, 2), (37791, 81), (41873, 320), (47056, 88)
X(60353) = X(16086)-of-outer-Garcia triangle
X(60353) = X(30117)-of-Aquila triangle
X(60353) = center of circle {{X(901), X(6163), X(15343)}}
X(60353) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 1722, 978), (1, 6048, 78), (1, 16569, 997), (1, 56191, 1961), (2, 49487, 1), (8, 3924, 1), (36, 1739, 1054), (65, 5247, 1046), (145, 28082, 1), (386, 30147, 1), (614, 3872, 1), (1046, 1247, 56289), (1104, 5836, 5255), (1125, 15955, 1), (1149, 38460, 1), (1201, 4861, 1), (3125, 5291, 3509), (3720, 17015, 1), (3959, 4426, 3496), (4424, 5251, 846), (4674, 52680, 484), (5262, 10459, 1), (7292, 38460, 1149), (12513, 17054, 3976), (17016, 59305, 1), (17735, 21888, 41322), (19860, 54418, 1), (28011, 36846, 1), (30115, 49682, 1), (30148, 50637, 1), (37817, 54286, 3550)

X(60354) = COMMON POINT OF RADICAL AXES OF { CIRCUMCIRCLE, OO( X(2), X(11) ) }

Barycentrics    3*a^5-3*(b+c)*a^4+(2*b^2-b*c+2*c^2)*a^3-2*(b^2-c^2)*(b-c)*a^2-(b^2+3*b*c+c^2)*(b-c)^2*a+(b^4-c^4)*(b-c) : :

X(60354) lies on these lines: {2, 11}, {23, 14667}, {108, 4232}, {347, 7493}, {468, 60356}, {495, 4223}, {631, 15251}, {676, 47884}, {1421, 3911}, {3598, 40615}, {3689, 60459}, {4293, 37254}, {4904, 35280}, {6995, 20621}, {7427, 12248}, {9318, 24322}, {10578, 11028}, {11580, 60362}, {14197, 46784}, {15252, 40132}, {17724, 51406}, {20999, 46586}, {26228, 40127}, {34547, 57600}, {36122, 38300}, {37760, 60359}, {37761, 60365}, {37762, 60368}, {37763, 60370}, {37764, 60371}, {37907, 47140}, {48680, 57605}

X(60354) = pole of the line {659, 59842} with respect to the circumcircle

X(60355) = COMMON POINT OF RADICAL AXES OF { CIRCUMCIRCLE, OO( X(4), X(9) ) }

Barycentrics    a*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^2-2*(b+c)*a+b^2+b*c+c^2) : :

X(60355) lies on these lines: {4, 9}, {24, 38902}, {104, 911}, {186, 32625}, {468, 37763}, {607, 6198}, {653, 38461}, {813, 40101}, {1436, 10623}, {1735, 35349}, {1752, 54361}, {1783, 1870}, {2287, 34790}, {3064, 14330}, {3520, 34867}, {3697, 4222}, {3911, 5236}, {5235, 31925}, {5279, 59578}, {5744, 37382}, {6065, 41391}, {8164, 40131}, {8568, 52252}, {8744, 60360}, {18908, 59681}, {37787, 57435}, {37943, 60357}, {38462, 60366}, {40117, 53911}, {60356, 60370}

X(60355) = polar conjugate of the isotomic conjugate of X(3935)
X(60355) = polar conjugate of the isogonal conjugate of X(19624)
X(60355) = cross-difference of every pair of points on the line X(1459)X(22053)
X(60355) = X(19624)-cross conjugate of-X(3935)
X(60355) = X(i)-Dao conjugate of-X(j) for these (i, j): (35125, 4025), (36103, 34578)
X(60355) = X(i)-isoconjugate of-X(j) for these {i, j}: {3, 34578}, {222, 3254}, {905, 1308}, {1459, 37143}, {7177, 42064}, {22383, 35171}
X(60355) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (19, 34578), (33, 3254), (1783, 37143), (1897, 35171), (2078, 77), (3887, 4025), (3935, 69), (5526, 63), (7071, 42064), (8645, 1459), (8750, 1308), (17264, 304), (19624, 3), (22108, 905), (28345, 26006), (30565, 15413), (37787, 348), (38459, 7056)
X(60355) = X(1638)-zayin conjugate of-X(652)
X(60355) = pole of the line {48387, 59846} with respect to the circumcircle
X(60355) = pole of the line {142, 514} with respect to the polar circle
X(60355) = pole of the line {1465, 3100} with respect to the Stevanovic circle
X(60355) = barycentric product X(i)*X(j) for these {i, j}: {4, 3935}, {19, 17264}, {92, 5526}, {264, 19624}, {281, 37787}, {318, 2078}, {1783, 30565}, {1897, 3887}, {6335, 22108}, {7046, 38459}, {7079, 37757}, {28345, 52781}
X(60355) = trilinear product X(i)*X(j) for these {i, j}: {4, 5526}, {19, 3935}, {25, 17264}, {33, 37787}, {92, 19624}, {281, 2078}, {1783, 3887}, {1897, 22108}, {6335, 8645}, {7071, 37757}, {7079, 38459}, {8750, 30565}, {28345, 36122}, {43050, 56183}
X(60355) = trilinear quotient X(i)/X(j) for these (i, j): (4, 34578), (281, 3254), (1783, 1308), (1897, 37143), (2078, 222), (3887, 905), (3935, 63), (5526, 3), (6335, 35171), (6594, 6510), (7079, 42064), (8645, 22383), (17264, 69), (19624, 48), (22108, 1459), (30565, 4025), (37757, 7056), (37787, 77), (38459, 7177)
X(60355) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (607, 17916, 6198), (1783, 5089, 1870), (7079, 7719, 4)

X(60356) = COMMON POINT OF RADICAL AXES OF { CIRCUMCIRCLE, OO( X(4), X(11) ) }

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^5-(b+c)*a^4-(2*b-c)*(b-2*c)*a^3+2*(b^2-c^2)*(b-c)*a^2+(b^2-b*c+c^2)*(b-c)^2*a-(b^4-c^4)*(b-c)) : :

X(60356) lies on these lines: {1, 451}, {2, 1897}, {4, 11}, {105, 6353}, {149, 4242}, {186, 14667}, {208, 50443}, {406, 14986}, {468, 60354}, {496, 7412}, {497, 37441}, {499, 7952}, {676, 14312}, {1068, 2006}, {1210, 6198}, {1421, 1870}, {1737, 15500}, {1785, 3582}, {1845, 16173}, {3035, 56183}, {3089, 15251}, {3176, 7505}, {3542, 15253}, {4081, 10271}, {5603, 59816}, {5704, 56876}, {6834, 18283}, {8744, 60362}, {8889, 20621}, {10072, 34231}, {13462, 52848}, {15171, 37289}, {15325, 37305}, {16082, 21666}, {17923, 37769}, {17927, 60371}, {20999, 46588}, {21664, 57298}, {23710, 37799}, {26000, 60246}, {30239, 51762}, {31231, 40971}, {36110, 57441}, {37943, 47191}, {38282, 38300}, {38461, 60365}, {38462, 60368}, {60355, 60370}

X(60356) = polar conjugate of the cyclocevian conjugate of X(100)
X(60356) = polar conjugate of the isotomic conjugate of X(37781)
X(60356) = cross-difference of every pair of points on the line X(22055)X(22346)
X(60356) = crosssum of X(20752) and X(47422)
X(60356) = X(44426)-Ceva conjugate of-X(4)
X(60356) = X(i)-Dao conjugate of-X(j) for these (i, j): (651, 6516), (36103, 29374)
X(60356) = X(3)-isoconjugate of-X(29374)
X(60356) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (19, 29374), (1768, 63), (37781, 69), (57105, 44717)
X(60356) = orthoassociate of X(56890)
X(60356) = inverse of X(56890) in polar circle
X(60356) = pole of the line {53304, 59848} with respect to the circumcircle
X(60356) = pole of the line {676, 2804} with respect to the polar circle
X(60356) = pole of the line {34050, 37799} with respect to the circumhyperbola dual of Yff parabola
X(60356) = barycentric product X(i)*X(j) for these {i, j}: {4, 37781}, {92, 1768}, {16082, 34345}
X(60356) = trilinear product X(i)*X(j) for these {i, j}: {4, 1768}, {19, 37781}, {34345, 36123}
X(60356) = trilinear quotient X(i)/X(j) for these (i, j): (4, 29374), (1768, 3), (34345, 22350), (37781, 63)
X(60356) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (11, 108, 4), (11, 23711, 108), (499, 7952, 52252), (1737, 15500, 56877), (7681, 38870, 4), (44675, 51359, 1870)

X(60357) = COMMON POINT OF RADICAL AXES OF { CIRCUMCIRCLE, OO( X(5), X(9) ) }

Barycentrics    a*(a^9-3*(b+c)*a^8+2*(b^2+b*c+c^2)*a^7+2*(b+c)*(b^2+b*c+c^2)*a^6-(2*b^2-b*c+2*c^2)*(2*b^2+b*c+2*c^2)*a^5+(b+c)*(2*b^2-3*b*c+2*c^2)*(2*b^2+b*c+2*c^2)*a^4-(2*b^6+2*c^6+(6*b^4+6*c^4-b*c*(5*b^2-2*b*c+5*c^2))*b*c)*a^3-(b^2-c^2)*(b-c)*(2*b^4+2*c^4+b*c*(2*b^2+b*c+2*c^2))*a^2+(3*b^4+3*c^4+2*b*c*(2*b^2-3*b*c+2*c^2))*(b^2-c^2)^2*a-(b^2-c^2)^4*(b+c)) : :

X(60357) lies on these lines: {2, 60464}, {5, 9}, {2070, 32625}, {13621, 38902}, {34864, 34867}, {37760, 37763}, {37943, 60355}, {38458, 43065}, {38463, 60360}, {38464, 60363}, {38465, 60366}, {60358, 60369}, {60359, 60370}

X(60357) = complement of X(60464)

X(60358) = COMMON POINT OF RADICAL AXES OF { CIRCUMCIRCLE, OO( X(5), X(10) ) }

Barycentrics    (b+c)*a^6+(b^2+c^2)*a^5-(b+c)*(b^2+c^2)*a^4-(b^4+c^4-b*c*(b+c)^2)*a^3-(b^3+c^3)*b*c*a^2-(b^2-c^2)^2*b*c*a+(b^2-c^2)^2*(b+c)*b*c : :

X(60358) lies on these lines: {2, 60447}, {5, 10}, {859, 15065}, {1324, 2070}, {2758, 26711}, {7081, 13595}, {13621, 38903}, {17927, 37943}, {34864, 34868}, {37760, 37764}, {38458, 60353}, {38463, 60361}, {38464, 60364}, {38465, 60367}, {50757, 60359}, {60357, 60369}

X(60358) = complement of X(60447)
X(60358) = pole of the line {52356, 59853} with respect to the circumcircle

X(60359) = COMMON POINT OF RADICAL AXES OF { CIRCUMCIRCLE, OO( X(5), X(11) ) }

Barycentrics    2*a^6-2*(b+c)*a^5-(b^2-4*b*c+c^2)*a^4+2*(b^2-c^2)*(b-c)*a^3-(2*b^2+3*b*c+2*c^2)*(b-c)^2*a^2+(b^2-c^2)*(b-c)*b*c*a+(b^2-c^2)^2*(b-c)^2 : :

X(60359) lies on these lines: {1, 5}, {81, 17061}, {100, 24145}, {105, 13595}, {106, 26709}, {108, 3518}, {109, 11246}, {244, 37646}, {676, 59918}, {2070, 14667}, {6126, 6147}, {10096, 47140}, {18180, 18984}, {25466, 52368}, {37760, 60354}, {37798, 41341}, {37943, 47191}, {38463, 60362}, {38464, 60365}, {38465, 60368}, {47203, 59837}, {50757, 60358}, {60357, 60370}

X(60359) = pole of the line {39200, 59854} with respect to the circumcircle
X(60359) = (X(15253), X(45946))-harmonic conjugate of X(11)

X(60360) = COMMON POINT OF RADICAL AXES OF { CIRCUMCIRCLE, OO( X(6), X(9) ) }

Barycentrics    a^2*(a^4-2*(b+c)*a^3+(2*b^2+7*b*c+2*c^2)*a^2-2*(b+c)*(b^2+c^2)*a+(b^2+3*b*c+c^2)*(b-c)^2) : :

X(60360) lies on these lines: {1, 6}, {187, 32625}, {574, 34867}, {902, 919}, {1055, 3220}, {1384, 21002}, {1462, 3911}, {1471, 56546}, {1914, 52969}, {3052, 55163}, {5276, 50294}, {8744, 60355}, {11580, 37763}, {38463, 60357}, {38466, 60363}, {38467, 60366}, {59920, 59921}, {60361, 60369}, {60362, 60370}

X(60360) = pole of the line {667, 59857} with respect to the circumcircle

X(60361) = COMMON POINT OF RADICAL AXES OF { CIRCUMCIRCLE, OO( X(6), X(10) ) }

Barycentrics    a^2*(a^5+(b^2+b*c+c^2)*a^3+(b^3+c^3)*a^2+(b^2+c^2)*b*c*a+(b^2-3*b*c+c^2)*(b+c)^3) : :

X(60361) lies on these lines: {6, 10}, {187, 1324}, {574, 34868}, {1384, 38903}, {4006, 5293}, {8744, 17927}, {11580, 37764}, {16784, 60353}, {38463, 60358}, {38466, 60364}, {38467, 60367}, {60360, 60369}, {60362, 60371}

X(60361) = pole of the line {8637, 59858} with respect to the circumcircle

X(60362) = COMMON POINT OF RADICAL AXES OF { CIRCUMCIRCLE, OO( X(6), X(11) ) }

Barycentrics    a^2*(a^7-(b+c)*a^6+(b^2+b*c+c^2)*a^5-(b+c)*(b^2+c^2)*a^4-(b^4+c^4-2*b*c*(b^2+c^2))*a^3+(b^4-c^4)*(b-c)*a^2-(b^2+3*b*c+c^2)*(b-c)^4*a+(b^2-c^2)*(b-c)*(b^4-4*b^2*c^2+c^4)) : :

X(60362) lies on these lines: {6, 11}, {19, 47232}, {187, 14667}, {1279, 53413}, {1421, 16784}, {2207, 23711}, {8744, 60356}, {11580, 60354}, {38463, 60359}, {38466, 60365}, {38467, 60368}, {60360, 60370}, {60361, 60371}

X(60362) = pole of the line {20989, 51775} with respect to the circumhyperbola dual of Yff parabola

X(60363) = COMMON POINT OF RADICAL AXES OF { CIRCUMCIRCLE, OO( X(7), X(9) ) }

Barycentrics    a*(a+b-c)*(a-b+c)*(a^5-3*(b+c)*a^4+(2*b^2+7*b*c+2*c^2)*a^3+(2*b-c)*(b-2*c)*(b+c)*a^2-(3*b^4+3*c^4+b*c*(3*b^2-8*b*c+3*c^2))*a+(b^2-c^2)*(b-c)*(b^2+3*b*c+c^2)) : :

X(60363) lies on these lines: {2, 7}, {104, 971}, {190, 38468}, {392, 8543}, {514, 59930}, {651, 38459}, {653, 38461}, {655, 43762}, {912, 12755}, {1159, 7672}, {1443, 43047}, {1512, 45043}, {1776, 5851}, {2310, 18461}, {4293, 54370}, {5265, 7330}, {5732, 17010}, {5768, 52684}, {7288, 15297}, {7671, 10246}, {8074, 38948}, {8544, 52027}, {10394, 18444}, {11570, 41700}, {17613, 30295}, {18467, 30318}, {21578, 51768}, {32624, 32625}, {34865, 34867}, {35514, 36976}, {37141, 56763}, {38464, 60357}, {38466, 60360}, {38900, 38902}, {39778, 41554}, {60364, 60369}, {60365, 60370}

X(60363) = X(650)-isoconjugate of-X(53184)
X(60363) = X(109)-reciprocal conjugate of-X(53184)
X(60363) = pole of the line {649, 20014} with respect to the Bevan circle
X(60363) = pole of the line {23865, 59860} with respect to the circumcircle
X(60363) = pole of the line {3064, 59986} with respect to the polar circle
X(60363) = pole of the line {522, 1998} with respect to the Steiner circumellipse
X(60363) = pole of the line {100, 16189} with respect to the Yff parabola
X(60363) = trilinear quotient X(651)/X(53184)
X(60363) = X(34397)-of-Honsberger triangle, when ABC is acute
X(60363) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (7, 37787, 3218), (37787, 37789, 1445)

X(60364) = COMMON POINT OF RADICAL AXES OF { CIRCUMCIRCLE, OO( X(7), X(10) ) }

Barycentrics    (a+b-c)*(a-b+c)*(a^5-3*(b^2+3*b*c+c^2)*a^3+(b+c)*(b^2+b*c+c^2)*a^2+(2*b^4+2*c^4+b*c*(3*b^2-2*b*c+3*c^2))*a-(b^2-c^2)*(b-c)*(b^2+5*b*c+c^2)) : :

X(60364) lies on these lines: {7, 10}, {514, 37797}, {515, 1447}, {1324, 32624}, {3212, 3487}, {5715, 33867}, {17927, 38461}, {34865, 34868}, {37761, 37764}, {38459, 60353}, {38464, 60358}, {38466, 60361}, {38468, 60367}, {38900, 38903}, {60363, 60369}, {60365, 60371}

X(60364) = pole of the line {41575, 48268} with respect to the Steiner circumellipse

X(60365) = COMMON POINT OF RADICAL AXES OF { CIRCUMCIRCLE, OO( X(7), X(11) ) }

Barycentrics    (a+b-c)^2*(a-b+c)^2*(a^5-3*(b+c)*a^4+(b+2*c)*(2*b+c)*a^3+2*(b+c)*(b^2-3*b*c+c^2)*a^2-(3*b^2+7*b*c+3*c^2)*(b-c)^2*a+(b^2-c^2)*(b-c)*(b^2+4*b*c+c^2)) : :

X(60365) lies on these lines: {7, 11}, {279, 2006}, {1421, 38459}, {3160, 45946}, {14667, 32624}, {37757, 37797}, {37761, 60354}, {38461, 60356}, {38464, 60359}, {38466, 60362}, {38468, 60368}, {60363, 60370}, {60364, 60371}

X(60366) = COMMON POINT OF RADICAL AXES OF { CIRCUMCIRCLE, OO( X(8), X(9) ) }

Barycentrics    a*(-a+b+c)*(a^5-3*(b+c)*a^4+(2*b^2+7*b*c+2*c^2)*a^3+(b+c)*(2*b^2-9*b*c+2*c^2)*a^2-(3*b^4+3*c^4-5*b*c*(b^2+c^2))*a+(b^3+c^3)*(b-c)^2) : :

X(60366) lies on these lines: {8, 9}, {104, 6078}, {190, 38468}, {644, 38460}, {997, 59216}, {17100, 32625}, {28982, 43047}, {34758, 34867}, {37762, 37763}, {38462, 60355}, {38465, 60357}, {38467, 60360}, {38901, 38902}, {60367, 60369}, {60368, 60370}

X(60366) = X(7259)-beth conjugate of-X(43065)
X(60366) = X(37788)-Ceva conjugate of-X(3935)

X(60367) = COMMON POINT OF RADICAL AXES OF { CIRCUMCIRCLE, OO( X(8), X(10) ) }

Barycentrics    a^4+(b+c)*a^3-(2*b^2+3*b*c+2*c^2)*a^2-(b+c)*(b^2-6*b*c+c^2)*a+(b^2-3*b*c+c^2)*(b+c)^2 : :

X(60367) lies on these lines: {1, 2}, {36, 21290}, {100, 855}, {104, 19335}, {121, 40091}, {341, 37828}, {672, 27546}, {901, 5080}, {1222, 6691}, {1324, 17100}, {3699, 40663}, {3880, 37758}, {4645, 6163}, {4695, 37759}, {4962, 59913}, {5100, 17619}, {5123, 32850}, {5265, 6556}, {5657, 27538}, {7288, 42020}, {8706, 43081}, {17072, 20293}, {17927, 38462}, {24914, 44720}, {34758, 34868}, {38465, 60358}, {38467, 60361}, {38468, 60364}, {38901, 38903}, {43290, 44669}, {52353, 56313}, {60366, 60369}, {60368, 60371}

X(60367) = pole of the line {4057, 59864} with respect to the circumcircle

X(60368) = COMMON POINT OF RADICAL AXES OF { CIRCUMCIRCLE, OO( X(8), X(11) ) }

Barycentrics    (-a+b+c)*(a^5-(b+c)*a^4-(2*b-c)*(b-2*c)*a^3+2*(b^2-c^2)*(b-c)*a^2+(b^2-9*b*c+c^2)*(b-c)^2*a-(b^2-c^2)*(b-c)*(b^2-4*b*c+c^2)) : :

X(60368) lies on these lines: {2, 4939}, {8, 11}, {1421, 38460}, {1997, 43290}, {2006, 6553}, {3086, 24034}, {14304, 37771}, {14667, 17100}, {37762, 60354}, {38462, 60356}, {38465, 60359}, {38467, 60362}, {38468, 60365}, {60366, 60370}, {60367, 60371}

X(60369) = COMMON POINT OF RADICAL AXES OF { CIRCUMCIRCLE, OO( X(9), X(10) ) }

Barycentrics    a*(a^6-3*(b+c)*a^5+3*(b^2+b*c+c^2)*a^4-4*(b+c)*b*c*a^3-(3*b^4+3*c^4-2*b*c*(b^2+3*b*c+c^2))*a^2+3*(b^2-c^2)^2*(b+c)*a-(b+c)*(b^2-c^2)*(b^3-c^3)) : :

X(60369) lies on these lines: {2, 60451}, {4, 9}, {1324, 32625}, {4515, 54316}, {34867, 34868}, {37763, 37764}, {38902, 38903}, {43065, 60353}, {60357, 60358}, {60360, 60361}, {60363, 60364}, {60366, 60367}, {60370, 60371}

X(60369) = complement of X(60451)
X(60369) = pole of the line {48387, 59866} with respect to the circumcircle

X(60370) = COMMON POINT OF RADICAL AXES OF { CIRCUMCIRCLE, OO( X(9), X(11) ) }

Barycentrics    a*(-a+b+c)*(a^7-3*(b+c)*a^6+3*(b^2+b*c+c^2)*a^5-(b+c)*(b^2+c^2)*a^4-(b-c)^4*a^3+3*(b^4-c^4)*(b-c)*a^2-(3*b^4+3*c^4+b*c*(5*b^2-8*b*c+5*c^2))*(b-c)^2*a+(b^2-c^2)^3*(b-c)) : :

X(60370) lies on these lines: {1, 38375}, {9, 11}, {1421, 43065}, {3756, 8557}, {14667, 32625}, {37763, 60354}, {60355, 60356}, {60357, 60359}, {60360, 60362}, {60363, 60365}, {60366, 60368}, {60369, 60371}

X(60371) = COMMON POINT OF RADICAL AXES OF { CIRCUMCIRCLE, OO( X(10), X(11) ) }

Barycentrics    (b+c)*a^5-4*b*c*a^4-(b+c)*(b^2-3*b*c+c^2)*a^3+(b-c)^2*b*c*a^2-3*(b^2-c^2)*(b-c)*b*c*a+(b^2-c^2)^2*b*c : :

X(60371) lies on these lines: {10, 11}, {105, 1261}, {759, 14204}, {1324, 14667}, {1421, 16576}, {4124, 5400}, {4516, 26095}, {5659, 33138}, {6677, 15252}, {17611, 59638}, {17927, 60356}, {24026, 28353}, {37764, 60354}, {50757, 60358}, {60361, 60362}, {60364, 60365}, {60367, 60368}, {60369, 60370}

X(60372) = COMMON POINT OF RADICAL AXES OF { CIRCUMCIRCLE, OO( BICENTRIC PAIR PU(11) ) }

Barycentrics    (b^2-c^2)*((b^2+c^2)*a^4-b^2*c^2*a^2+(b^2+c^2)*b^2*c^2) : :
X(60372) = 2*X(141)-X(50549) = 2*X(5113)-X(55974) = 3*X(14428)-4*X(44451) = X(22260)-2*X(54262) = 3*X(53369)+X(58784)

X(60372) lies on these lines: {141, 523}, {512, 35522}, {670, 805}, {688, 3267}, {808, 21006}, {826, 47138}, {850, 888}, {3221, 23285}, {3231, 47229}, {5027, 9030}, {5113, 55974}, {14428, 44451}, {53369, 58784}

X(60372) = reflection of X(i) in X(j) for these (i, j): (22260, 54262), (50549, 141), (55974, 5113)
X(60372) = cross-difference of every pair of points on the line X(1691)X(19127)
X(60372) = perspector of the circumconic through X(1916) and X(45096)
X(60372) = pole of the line {6660, 34360} with respect to the circumcircle
X(60372) = pole of the line {9479, 55974} with respect to the Kiepert parabola
X(60372) = pole of the line {7779, 9464} with respect to the Steiner circumellipse
X(60372) = pole of the line {325, 30749} with respect to the Steiner inellipse
X(60372) = pole of the line {17941, 58752} with respect to the Steiner-Wallace hyperbola
X(60372) = center of circle {{X(69), X(316), X(47285)}}

X(60373) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(1), X(6) ) }

Barycentrics    a*((b+c)*a^5-3*(b^2+c^2)*a^4+2*(b+c)*(2*b^2-3*b*c+2*c^2)*a^3-2*(2*b^2+3*b*c+2*c^2)*(b-c)^2*a^2+3*(b^4-c^4)*(b-c)*a-(b-c)^2*(b^2+c^2)^2) : :

X(60373) lies on these lines: {1, 6}, {519, 59814}, {1323, 60401}, {1438, 15636}, {2725, 58944}, {3309, 4897}, {5533, 60396}, {5570, 40460}, {8193, 51622}, {14760, 44675}, {39541, 59953}, {39545, 59949}, {51615, 60379}, {51616, 60391}, {53618, 60404}, {60374, 60402}

X(60373) = cross-difference of every pair of points on the line X(513)X(5452)
X(60373) = crosspoint of X(7) and X(9061)
X(60373) = crosssum of X(55) and X(9004)
X(60373) = inverse of X(51540) in incircle
X(60373) = pole of the line {667, 3433} with respect to the circumcircle
X(60373) = pole of the line {6, 3309} with respect to the incircle
X(60373) = pole of the line {55, 1565} with respect to the Feuerbach circumhyperbola
X(60373) = pole of the line {521, 34960} with respect to the MacBeath circumconic
X(60373) = pole of the line {650, 20269} with respect to the Steiner inellipse
X(60373) = X(13509)-of-inverse-in-incircle triangle, when ABC is acute
X(60373) = X(54074)-of-intouch triangle, when ABC is acute
X(60373) = reflection of X(i) in the line X(j)X(k) for these (i, j, k): (1, 3309, 39541), (6, 2498, 3309), (72, 3309, 4925)

X(60374) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(1), X(8) ) }

Barycentrics    2*a^4-5*(b+c)*a^3-(7*b^2-30*b*c+7*c^2)*a^2+(b+c)*(b^2-6*b*c+c^2)*a+(b^2-c^2)^2 : :
X(60374) = 2*X(1)-X(37743) = 2*X(1)+X(51615) = 5*X(1)+X(53614) = 3*X(1)+X(53619) = X(8)-4*X(60380) = X(8)-3*X(60409) = X(145)+5*X(60382)

X(60374) lies on these lines: {1, 2}, {56, 11067}, {515, 39752}, {517, 59812}, {1320, 15637}, {1323, 60405}, {1837, 13625}, {3445, 21627}, {3667, 3669}, {5048, 14027}, {5533, 60398}, {5570, 60387}, {6553, 28661}, {7963, 12632}, {12541, 45047}, {12577, 33097}, {12640, 38496}, {26718, 58793}, {51616, 60393}, {60373, 60402}, {60375, 60408}

X(60374) = midpoint of X(i) and X(j) for these (i, j): {1, 53618}, {5048, 14027}, {37743, 51615}
X(60374) = reflection of X(i) in X(j) for these (i, j): (37743, 1), (51615, 53618)
X(60374) = X(i)-complementary conjugate of-X(j) for these (i, j): (8686, 2885), (16945, 52871), (37627, 5510)
X(60374) = perspector of the circumconic through X(190) and X(8051)
X(60374) = inverse of X(8) in incircle
X(60374) = pole of the line {8, 3667} with respect to the incircle
X(60374) = pole of the line {2, 27825} with respect to the circumhyperbola dual of Yff parabola
X(60374) = pole of the line {1357, 3057} with respect to the Feuerbach circumhyperbola
X(60374) = pole of the line {514, 8056} with respect to the Steiner inellipse
X(60374) = X(6760)-of-incircle-circles triangle, when ABC is acute
X(60374) = X(11589)-of-Hutson intouch triangle, when ABC is acute
X(60374) = X(12096)-of-intouch triangle, when ABC is acute
X(60374) = X(34170)-of-inverse-in-incircle triangle, when ABC is acute
X(60374) = X(53618)-of-anti-Aquila triangle
X(60374) = center of circle {{X(11), X(5048), X(14027)}}

X(60375) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(1), X(9) ) }

Barycentrics    a*((b+c)*a^5-5*(b^2+c^2)*a^4+2*(b+c)*(5*b^2-6*b*c+5*c^2)*a^3-2*(5*b^4+5*c^4-2*b*c*(b^2+b*c+c^2))*a^2+(b^2-c^2)*(b-c)*(5*b^2-2*b*c+5*c^2)*a-(b^2+c^2)*(b-c)^4) : :

X(60375) lies on these lines: {1, 6}, {294, 15636}, {517, 59814}, {1323, 60406}, {3309, 3676}, {5533, 60399}, {5570, 60388}, {18839, 47007}, {51615, 60381}, {51616, 60394}, {53618, 60410}, {60374, 60408}

X(60375) = midpoint of X(18839) and X(47007)
X(60375) = inverse of X(9) in incircle
X(60375) = pole of the line {9, 3309} with respect to the incircle
X(60375) = pole of the line {142, 40615} with respect to the circumhyperbola dual of Yff parabola
X(60375) = pole of the line {55, 1292} with respect to the Feuerbach circumhyperbola
X(60375) = pole of the line {277, 650} with respect to the Steiner inellipse
X(60375) = X(5523)-of-inverse-in-incircle triangle, when ABC is acute
X(60375) = X(54075)-of-intouch triangle, when ABC is acute
X(60375) = reflection of X(i) in the line X(j)X(k) for these (i, j, k): (1, 3309, 30723), (72, 3309, 20318)
X(60375) = center of circle {{X(11), X(18839), X(47007)}}

X(60376) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(2), X(3) ) }

Barycentrics    2*a^6+3*(b^2-4*b*c+c^2)*a^4-6*(b^2-c^2)*(b-c)*a^3-2*(b^2+c^2)*(b^2-3*b*c+c^2)*a^2+6*(b^4-c^4)*(b-c)*a-3*(b^2-c^2)^2*(b-c)^2 : :

X(60376) lies on these lines: {2, 3}, {5570, 51615}, {22166, 31515}, {39386, 59943}, {60379, 60385}, {60380, 60387}, {60381, 60388}, {60382, 60389}

X(60376) = pole of the line {44409, 59870} with respect to the incircle

X(60377) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(2), X(4) ) }

Barycentrics    2*a^6-(7*b^2-12*b*c+7*c^2)*a^4+6*(b^2-c^2)*(b-c)*a^3-2*(b^2+5*b*c+c^2)*(b-c)^2*a^2-6*(b^4-c^4)*(b-c)*a+(7*b^2-6*b*c+7*c^2)*(b^2-c^2)^2 : :

X(60377) lies on these lines: {2, 3}, {676, 4926}, {22166, 31516}, {51615, 51616}, {60379, 60391}, {60380, 60393}, {60381, 60394}, {60382, 60395}

X(60377) = pole of the line {44409, 59871} with respect to the incircle

X(60378) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(2), X(5) ) }

Barycentrics    (5*b^2-12*b*c+5*c^2)*a^4-6*(b^2-c^2)*(b-c)*a^3+2*(3*b^2-5*b*c+3*c^2)*b*c*a^2+6*(b^4-c^4)*(b-c)*a-(5*b^2-6*b*c+5*c^2)*(b^2-c^2)^2 : :

X(60378) lies on these lines: {2, 3}, {3837, 59943}, {5533, 51615}, {22166, 31517}, {60379, 60396}, {60380, 60398}, {60381, 60399}, {60382, 60400}

X(60378) = pole of the line {44409, 59872} with respect to the incircle
X(60378) = (X(60376), X(60377))-harmonic conjugate of X(2)

X(60379) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(2), X(6) ) }

Barycentrics    2*a^6+(b^2-12*b*c+c^2)*a^4+6*(b^2-c^2)*(b-c)*a^3-2*(b^2+3*b*c-2*c^2)*(2*b^2-3*b*c-c^2)*a^2+6*(b^4-c^4)*(b-c)*a-3*(b-c)^2*(b^2+c^2)^2 : :

X(60379) lies on these lines: {2, 6}, {22166, 31518}, {51615, 60373}, {59948, 59949}, {60376, 60385}, {60377, 60391}, {60378, 60396}, {60380, 60402}, {60381, 60403}, {60382, 60404}

X(60379) = pole of the line {4897, 59873} with respect to the incircle

X(60380) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(2), X(8) ) }

Barycentrics    2*a^3-5*(b+c)*a^2-16*(b^2-3*b*c+c^2)*a+(b+c)*(7*b^2-18*b*c+7*c^2) : :
X(60380) = 3*X(2)+X(51615) = 3*X(2)+5*X(60382) = X(8)+3*X(60374) = X(8)-9*X(60409)

X(60380) lies on these lines: {1, 2}, {2487, 2496}, {4997, 15637}, {6557, 26718}, {60376, 60387}, {60377, 60393}, {60378, 60398}, {60379, 60402}, {60381, 60408}

X(60380) = midpoint of X(51615) and X(52907)
X(60380) = complement of X(52907)
X(60380) = X(31316)-complementary conjugate of-X(1329)
X(60380) = inverse of X(21267) in incircle
X(60380) = inverse of X(39567) in orthoptic circle of Steiner inellipse
X(60380) = pole of the line {3667, 21267} with respect to the incircle
X(60380) = pole of the line {3667, 39567} with respect to the orthoptic circle of Steiner inellipse
X(60380) = pole of the line {2, 40621} with respect to the circumhyperbola dual of Yff parabola
X(60380) = pole of the line {514, 4373} with respect to the Steiner inellipse
X(60380) = pole of the line {190, 42343} with respect to the Yff parabola
X(60380) = X(46057)-of-Wasat triangle, when ABC is acute

X(60381) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(2), X(9) ) }

Barycentrics    2*a^6-3*(b+c)*a^5-(7*b^2-10*b*c+7*c^2)*a^4+2*(b+c)*(11*b^2-16*b*c+11*c^2)*a^3-4*(6*b^4+6*c^4-b*c*(b^2+6*b*c+c^2))*a^2+(b^2-c^2)*(b-c)*(13*b^2-6*b*c+13*c^2)*a-3*(b-c)^6 : :

X(60381) lies on these lines: {2, 7}, {22166, 31519}, {51615, 60375}, {60376, 60388}, {60377, 60394}, {60378, 60399}, {60379, 60403}, {60380, 60408}, {60382, 60410}

X(60382) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(2), X(10) ) }

Barycentrics    (b+c)*a^2+6*(2*b-c)*(b-2*c)*a-(b+c)*(5*b^2-12*b*c+5*c^2) : :
X(60382) = 3*X(2)+2*X(51615) = 9*X(2)-4*X(52907) = 3*X(2)-8*X(60380) = 2*X(10)+3*X(53618) = 4*X(10)-9*X(60409) = X(145)-6*X(60374) = 4*X(1125)+X(53614) = 2*X(5087)+3*X(14027)

X(60382) lies on these lines: {1, 2}, {3756, 28582}, {4080, 15637}, {5087, 14027}, {60376, 60389}, {60377, 60395}, {60378, 60400}, {60379, 60404}, {60381, 60410}

X(60382) = (X(51615), X(60380))-harmonic conjugate of X(2)

X(60383) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(3), X(4) ) }

Barycentrics    2*a^10-(5*b^2-4*b*c+5*c^2)*a^8+2*(b^2-c^2)*(b-c)*a^7+2*(b^4+c^4-5*(b-c)^2*b*c)*a^6-6*(b^4-c^4)*(b-c)*a^5+2*(2*b^4+2*c^4+b*c*(7*b^2+6*b*c+7*c^2))*(b-c)^2*a^4+2*(b^2-c^2)*(b-c)*(3*b^4+2*b^2*c^2+3*c^4)*a^3-2*(b^4-c^4)*(b^2-c^2)*(2*b^2-b*c+2*c^2)*a^2-2*(b^4-c^4)*(b^2-c^2)^2*(b-c)*a+(b^2-c^2)^4*(b-c)^2 : :

X(60383) lies on these lines: {2, 3}, {900, 59944}, {5570, 51616}, {31515, 31516}, {60385, 60391}, {60386, 60392}, {60387, 60393}, {60388, 60394}, {60389, 60395}

X(60383) = pole of the line {44409, 59875} with respect to the incircle
X(60383) = center of circle {{X(5533), X(34464), X(56423)}}

X(60384) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(3), X(5) ) }

Barycentrics    (b^2-4*b*c+c^2)*a^8-2*(b^2-c^2)*(b-c)*a^7-2*(b^4+c^4-5*b*c*(b^2-b*c+c^2))*a^6+6*(b^4-c^4)*(b-c)*a^5-2*(3*b^4+3*c^4-b*c*(3*b^2-2*b*c+3*c^2))*b*c*a^4-2*(b^2-c^2)*(b-c)*(3*b^4+2*b^2*c^2+3*c^4)*a^3+2*(b-c)*(b^3+c^3)*(b^4-c^4)*a^2+2*(b^4-c^4)*(b^2-c^2)^2*(b-c)*a-(b^2-c^2)^4*(b-c)^2 : :

X(60384) lies on these lines: {2, 3}, {2771, 5533}, {7701, 17437}, {28217, 59871}, {31515, 31517}, {60385, 60396}, {60386, 60397}, {60387, 60398}, {60388, 60399}, {60389, 60400}

X(60384) = pole of the line {44409, 59876} with respect to the incircle

X(60385) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(3), X(6) ) }

Barycentrics    a^2*((b^2+c^2)*a^6-2*(b^2-c^2)*(b-c)*a^5+(b^4+c^4-2*b*c*(b+c)^2)*a^4-(b^6+c^6-b^2*c^2*(5*b^2-4*b*c+5*c^2))*a^2+2*(b^4-c^4)*(b^2+c^2)*(b-c)*a-(b^2+c^2)*(b^4+c^4)*(b-c)^2) : :

X(60385) lies on these lines: {3, 6}, {2473, 2488}, {5570, 40460}, {31515, 31518}, {39641, 39642}, {60376, 60379}, {60383, 60391}, {60384, 60396}, {60386, 60401}, {60387, 60402}, {60388, 60403}, {60389, 60404}

X(60385) = pole of the line {44410, 59877} with respect to the incircle

X(60386) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(3), X(7) ) }

Barycentrics    (a+b-c)*(a-b+c)*(2*a^8-2*(b+c)*a^7-(7*b^2-4*b*c+7*c^2)*a^6+8*(b^3+c^3)*a^5+(b^2+c^2)*(7*b^2-8*b*c+7*c^2)*a^4-2*(b+c)*(5*b^4+5*c^4-2*b*c*(5*b^2-7*b*c+5*c^2))*a^3-(b^4+c^4+2*b*c*(b^2-b*c+c^2))*(b-c)^2*a^2+4*(b^2-c^2)*(b-c)^2*(b^3-c^3)*a-(b^2-c^2)^2*(b-c)^4) : :

X(60386) lies on these lines: {3, 7}, {1323, 5570}, {17437, 21314}, {20121, 31515}, {60383, 60392}, {60384, 60397}, {60385, 60401}, {60387, 60405}, {60388, 60406}, {60389, 60407}

X(60387) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(3), X(8) ) }

Barycentrics    2*a^7-4*(b+c)*a^6-(11*b^2-28*b*c+11*c^2)*a^5+(b+c)*(5*b^2-4*b*c+5*c^2)*a^4+2*(6*b^4+6*c^4-b*c*(15*b^2-8*b*c+15*c^2))*a^3-2*(b+c)*(b^2+c^2)*(b^2-3*b*c+c^2)*a^2-(b^2-c^2)^2*(3*b^2-2*b*c+3*c^2)*a+(b^2-c^2)^3*(b-c) : :

X(60387) lies on these lines: {3, 8}, {5570, 60374}, {21267, 31515}, {28217, 59956}, {60376, 60380}, {60383, 60393}, {60384, 60398}, {60385, 60402}, {60386, 60405}, {60388, 60408}, {60389, 60409}

X(60388) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(3), X(9) ) }

Barycentrics    a*((b+c)*a^8-6*(b^2-b*c+c^2)*a^7+14*(b^2-c^2)*(b-c)*a^6-2*(7*b^4+7*c^4-b*c*(3*b^2+14*b*c+3*c^2))*a^5-4*(b^3+c^3)*b*c*a^4+2*(b^2+c^2)*(7*b^2+15*b*c+7*c^2)*(b-c)^2*a^3-2*(b^2-c^2)*(b-c)*(7*b^4+8*b^2*c^2+7*c^4)*a^2+2*(b^3-c^3)*(b-c)^3*(3*b^2+2*b*c+3*c^2)*a-(b^2-c^2)^3*(b-c)^3) : :

X(60388) lies on these lines: {3, 9}, {5570, 60375}, {31515, 31519}, {60376, 60381}, {60383, 60394}, {60384, 60399}, {60385, 60403}, {60386, 60406}, {60387, 60408}, {60389, 60410}

X(60389) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(3), X(10) ) }

Barycentrics    (b+c)*a^6+2*(2*b-c)*(b-2*c)*a^5-(b+c)*(b^2+c^2)*a^4-2*(3*b^4+3*c^4-b*c*(5*b^2-2*b*c+5*c^2))*a^3+(b^4-c^4)*(b-c)*a^2+2*(b^4-c^4)*(b^2-c^2)*a-(b^2-c^2)^3*(b-c) : :

X(60389) lies on these lines: {3, 10}, {5570, 53618}, {31515, 31520}, {60376, 60382}, {60383, 60395}, {60384, 60400}, {60385, 60404}, {60386, 60407}, {60387, 60409}, {60388, 60410}

X(60390) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(4), X(5) ) }

Barycentrics    (3*b^2-4*b*c+3*c^2)*a^8-2*(b^2-c^2)*(b-c)*a^7-2*(3*b^4+3*c^4-5*b*c*(b^2-b*c+c^2))*a^6+6*(b^4-c^4)*(b-c)*a^5-2*(3*b^2+2*b*c+3*c^2)*(b-c)^2*b*c*a^4-2*(b^2-c^2)*(b-c)*(3*b^4+2*b^2*c^2+3*c^4)*a^3+2*(b^2-c^2)^2*(3*b^4+3*c^4-b*c*(b^2-b*c+c^2))*a^2+2*(b^4-c^4)*(b^2-c^2)^2*(b-c)*a-(b^2-c^2)^4*(3*b^2-2*b*c+3*c^2) : :

X(60390) lies on these lines: {2, 3}, {5533, 51616}, {28221, 59945}, {31516, 31517}, {60391, 60396}, {60392, 60397}, {60393, 60398}, {60394, 60399}, {60395, 60400}

X(60390) = pole of the line {44409, 59879} with respect to the incircle

X(60391) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(4), X(6) ) }

Barycentrics    2*a^10-(3*b^2-4*b*c+3*c^2)*a^8+6*(b^2-c^2)*(b-c)*a^7-2*(4*b^2+7*b*c+4*c^2)*(b-c)^2*a^6+2*(b^4-c^4)*(b-c)*a^5+2*(b^3-c^3)*(b-c)*(b^2+c^2)*a^4-2*(b^2-c^2)*(b-c)*(3*b^4+2*b^2*c^2+3*c^4)*a^3+2*(b^2-c^2)^2*(3*b^4+3*c^4-b*c*(b^2+c^2))*a^2-2*(b^4-c^4)*(b^2-c^2)^2*(b-c)*a+(b^4-c^4)^2*(b-c)^2 : :

X(60391) lies on these lines: {4, 6}, {31516, 31518}, {51616, 60373}, {59958, 59959}, {60377, 60379}, {60383, 60385}, {60390, 60396}, {60392, 60401}, {60393, 60402}, {60394, 60403}, {60395, 60404}

X(60392) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(4), X(7) ) }

Barycentrics    (a+b-c)*(a-b+c)*((b+c)*a^7-2*(b^2-b*c+c^2)*a^6-(b^2-c^2)*(b-c)*a^5+4*(b^3-c^3)*(b-c)*a^4-(b^2-c^2)^2*(b+c)*a^3-2*(b^4+c^4+b*c*(3*b^2+8*b*c+3*c^2))*(b-c)^2*a^2+(b^2-c^2)*(b-c)*(b^4+14*b^2*c^2+c^4)*a+4*(b^2-c^2)^2*(b-c)^2*b*c) : :

X(60392) lies on these lines: {4, 7}, {1323, 51616}, {6362, 59960}, {20121, 31516}, {60383, 60386}, {60390, 60397}, {60391, 60401}, {60393, 60405}, {60394, 60406}, {60395, 60407}

X(60392) = pole of the line {905, 59881} with respect to the incircle

X(60393) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(4), X(8) ) }

Barycentrics    (b+c)*a^6+3*(b^2-4*b*c+c^2)*a^5+2*(b^3+c^3)*a^4-2*(b^2+3*b*c+c^2)*(b-c)^2*a^3-3*(b^4-c^4)*(b-c)*a^2-(b^2-c^2)^2*(b^2-14*b*c+c^2)*a-4*(b^2-c^2)^2*(b+c)*b*c : :

X(60393) lies on these lines: {4, 8}, {900, 7661}, {21267, 31516}, {51616, 60374}, {60377, 60380}, {60383, 60387}, {60390, 60398}, {60391, 60402}, {60392, 60405}, {60394, 60408}, {60395, 60409}

X(60394) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(4), X(9) ) }

Barycentrics    2*a^7-3*(b+c)*a^6-4*(b^2-3*b*c+c^2)*a^5+15*(b^2-c^2)*(b-c)*a^4-2*(11*b^2+14*b*c+11*c^2)*(b-c)^2*a^3+(b^2-c^2)*(b-c)*(19*b^2+10*b*c+19*c^2)*a^2-4*(b^2-c^2)^2*(2*b^2-b*c+2*c^2)*a+(b^2-c^2)*(b-c)^5 : :

X(60394) lies on these lines: {4, 9}, {31516, 31519}, {51616, 60375}, {60377, 60381}, {60383, 60388}, {60390, 60399}, {60391, 60403}, {60392, 60406}, {60393, 60408}

X(60395) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(4), X(10) ) }

Barycentrics    (b+c)*a^5-(5*b^2-8*b*c+5*c^2)*a^4+2*(b^2-c^2)*(b-c)*a^3+2*(b^2-c^2)^2*a^2-(b^2-c^2)*(b-c)*(b+3*c)*(3*b+c)*a+3*(b^4-c^4)*(b^2-c^2) : :

X(60395) lies on these lines: {4, 9}, {1769, 4962}, {31516, 31520}, {51616, 53618}, {60377, 60382}, {60383, 60389}, {60390, 60400}, {60391, 60404}, {60392, 60407}, {60393, 60409}

X(60396) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(5), X(6) ) }

Barycentrics    (b^2-4*b*c+c^2)*a^8-2*(b^2-c^2)*(b-c)*a^7+2*(b^4+c^4+b*c*(b^2-b*c+c^2))*a^6-2*(b^4-c^4)*(b-c)*a^5+2*(b^2-4*b*c+c^2)*(b^2-b*c+c^2)*b*c*a^4+2*(b^2-c^2)^3*(b-c)*a^3-2*(b^6+c^6+3*(b^4+c^4-b*c*(b+c)^2)*b*c)*(b-c)^2*a^2+2*(b^4-c^4)*(b^2-c^2)^2*(b-c)*a-(b^4-c^4)^2*(b-c)^2 : :

X(60396) lies on these lines: {5, 6}, {5533, 60373}, {31517, 31518}, {59964, 59965}, {60378, 60379}, {60384, 60385}, {60390, 60391}, {60397, 60401}, {60398, 60402}, {60399, 60403}, {60400, 60404}

X(60397) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(5), X(7) ) }

Barycentrics    (a+b-c)*(a-b+c)*((3*b^2-4*b*c+3*c^2)*a^6-6*(b^2-c^2)*(b-c)*a^5-(3*b^4+3*c^4-4*b*c*(b^2-3*b*c+c^2))*a^4+4*(b+c)*(3*b^4+3*c^4-5*b*c*(b^2-b*c+c^2))*a^3-3*(b^4+c^4+2*b*c*(b^2+4*b*c+c^2))*(b-c)^2*a^2-2*(b^2-c^2)*(b-c)^3*(3*b^2+8*b*c+3*c^2)*a+3*(b^2-c^2)^4) : :

X(60397) lies on these lines: {5, 7}, {1323, 5533}, {20121, 31517}, {60384, 60386}, {60390, 60392}, {60396, 60401}, {60398, 60405}, {60399, 60406}, {60400, 60407}

X(60398) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(5), X(8) ) }

Barycentrics    (3*b^2-4*b*c+3*c^2)*a^5-(b+c)*(7*b^2-8*b*c+7*c^2)*a^4-2*(5*b^4+5*c^4-(17*b^2-13*b*c+17*c^2)*b*c)*a^3+2*(b+c)*(5*b^4+5*c^4-(9*b^2-5*b*c+9*c^2)*b*c)*a^2+(7*b^2-30*b*c+7*c^2)*(b^2-c^2)^2*a-(b^2-c^2)^2*(b+c)*(3*b-c)*(b-3*c) : :

X(60398) lies on these lines: {5, 8}, {5533, 60374}, {21267, 31517}, {60378, 60380}, {60384, 60387}, {60390, 60393}, {60396, 60402}, {60397, 60405}, {60399, 60408}, {60400, 60409}

X(60399) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(5), X(9) ) }

Barycentrics    (b^2-4*b*c+c^2)*a^8-2*(b+c)*(3*b^2-8*b*c+3*c^2)*a^7+2*(7*b^4+7*c^4-5*b*c*(b^2+b*c+c^2))*a^6-2*(b+c)*(7*b^4+7*c^4-b*c*(8*b^2-7*b*c+8*c^2))*a^5+2*(3*b^4+3*c^4+b*c*(b^2+c^2))*b*c*a^4+2*(b^2-c^2)*(b-c)*(7*b^4+7*c^4+b*c*(6*b^2-b*c+6*c^2))*a^3-2*(7*b^6+7*c^6+(13*b^4+13*c^4-b*c*(3*b^2+2*b*c+3*c^2))*b*c)*(b-c)^2*a^2+2*(b^2-c^2)^3*(b-c)*(3*b^2-2*b*c+3*c^2)*a-(b^2-c^2)^2*(b-c)^6 : :

X(60399) lies on these lines: {5, 9}, {5533, 60375}, {31517, 31519}, {60378, 60381}, {60384, 60388}, {60390, 60394}, {60396, 60403}, {60397, 60406}, {60398, 60408}, {60400, 60410}

X(60400) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(5), X(10) ) }

Barycentrics    (b^2-c^2)*(b-c)*a^4+(b^2-4*b*c+c^2)*(b^2-b*c+c^2)*a^3-(b+c)*(b^4+c^4-3*b*c*(b^2-b*c+c^2))*a^2-(b^2-c^2)^2*(b^2-5*b*c+c^2)*a-(b^2-c^2)^2*(b+c)*b*c : :

X(60400) lies on these lines: {5, 10}, {5533, 53618}, {6681, 24867}, {31517, 31520}, {60378, 60382}, {60384, 60389}, {60390, 60395}, {60396, 60404}, {60397, 60407}, {60398, 60409}, {60399, 60410}

X(60401) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(6), X(7) ) }

Barycentrics    (a+b-c)*(a-b+c)*(2*a^8-2*(b+c)*a^7-(5*b^2-4*b*c+5*c^2)*a^6+4*(b+c)*(3*b^2-4*b*c+3*c^2)*a^5-(17*b^4+17*c^4-2*b*c*(4*b^2+5*b*c+4*c^2))*a^4+2*(b^2-c^2)*(b-c)*(9*b^2+4*b*c+9*c^2)*a^3-(11*b^4+11*c^4+2*b*c*(7*b^2+5*b*c+7*c^2))*(b-c)^2*a^2+4*(b^3+c^3)*(b-c)^2*(b^2+c^2)*a-(b^2+c^2)^2*(b-c)^4) : :

X(60401) lies on these lines: {6, 7}, {1323, 60373}, {20121, 31518}, {60385, 60386}, {60391, 60392}, {60396, 60397}, {60402, 60405}, {60403, 60406}, {60404, 60407}

X(60401) = pole of the line {43042, 59884} with respect to the incircle

X(60402) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(6), X(8) ) }

Barycentrics    2*a^7-4*(b+c)*a^6-(9*b^2-28*b*c+9*c^2)*a^5+3*(b+c)*(b^2-4*b*c+c^2)*a^4-2*(7*b^4+7*c^4-b*c*(15*b^2-4*b*c+15*c^2))*a^3+2*(b+c)*(4*b^4+4*c^4-b*c*(7*b^2-2*b*c+7*c^2))*a^2-(b^2+c^2)*(3*b^2+4*b*c+3*c^2)*(b-c)^2*a+(b^4-c^4)*(b^2+c^2)*(b-c) : :

X(60402) lies on these lines: {6, 8}, {21267, 31518}, {60373, 60374}, {60379, 60380}, {60385, 60387}, {60391, 60393}, {60396, 60398}, {60401, 60405}, {60403, 60408}, {60404, 60409}

X(60403) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(6), X(9) ) }

Barycentrics    a*((b+c)*a^7-(5*b^2-4*b*c+5*c^2)*a^6+(b+c)*(11*b^2-24*b*c+11*c^2)*a^5-(15*b^4+15*c^4-2*b*c*(10*b^2+7*b*c+10*c^2))*a^4+(b+c)*(15*b^4+15*c^4-2*b*c*(20*b^2-21*b*c+20*c^2))*a^3-(11*b^4+11*c^4+2*b*c*(b^2+5*b*c+c^2))*(b-c)^2*a^2+(b^4-c^4)*(b-c)*(5*b^2-6*b*c+5*c^2)*a-(b^2+c^2)^2*(b-c)^4) : :

X(60403) lies on these lines: {1, 6}, {2195, 15636}, {60379, 60381}, {60385, 60388}, {60391, 60394}, {60396, 60399}, {60401, 60406}, {60402, 60408}, {60404, 60410}

X(60404) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(6), X(10) ) }

Barycentrics    (b+c)*a^6+2*(2*b-c)*(b-2*c)*a^5-(b+c)*(b^2+c^2)*a^4+2*(3*b^4+3*c^4-b*c*(5*b^2-2*b*c+5*c^2))*a^3-(b+c)*(3*b^4+3*c^4-2*b*c*(b^2+3*b*c+c^2))*a^2+2*(b^4-c^4)*(b^2-c^2)*a-(b^4-c^4)*(b^2+c^2)*(b-c) : :

X(60404) lies on these lines: {6, 10}, {31518, 31520}, {53618, 60373}, {60379, 60382}, {60385, 60389}, {60391, 60395}, {60396, 60400}, {60401, 60407}, {60402, 60409}, {60403, 60410}

X(60405) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(7), X(8) ) }

Barycentrics    (a+b-c)*(a-b+c)*((b+c)*a^4-(b^2+8*b*c+c^2)*a^3-(b+c)*(b^2-10*b*c+c^2)*a^2+(b^4+c^4-2*b*c*(7*b^2-9*b*c+7*c^2))*a+4*(b^2-c^2)*(b-c)*b*c) : :

X(60405) lies on these lines: {7, 8}, {1323, 60374}, {6919, 24797}, {9436, 60407}, {17535, 24805}, {20121, 21267}, {59966, 59967}, {60386, 60387}, {60392, 60393}, {60397, 60398}, {60401, 60402}, {60406, 60408}

X(60405) = pole of the line {3669, 4859} with respect to the incircle

X(60406) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(7), X(9) ) }

Barycentrics    (a+b-c)*(a-b+c)*(2*a^6-3*(b+c)*a^5-(9*b^2-14*b*c+9*c^2)*a^4+2*(b+c)*(13*b^2-20*b*c+13*c^2)*a^3-4*(6*b^4+6*c^4-b*c*(b^2+6*b*c+c^2))*a^2+(b^2-c^2)*(b-c)*(9*b^2+2*b*c+9*c^2)*a-(b-c)^6) : :

X(60406) lies on these lines: {2, 7}, {1323, 60375}, {5853, 43762}, {20121, 31519}, {60386, 60388}, {60392, 60394}, {60397, 60399}, {60401, 60403}, {60405, 60408}, {60407, 60410}

X(60407) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(7), X(10) ) }

Barycentrics    (a+b-c)*(a-b+c)*((b+c)*a^4-2*(2*b-c)*(b-2*c)*a^3+2*(b+c)*(b^2-7*b*c+c^2)*a^2+2*(2*b^4+2*c^4+b*c*(11*b^2-18*b*c+11*c^2))*a+(b^2-c^2)*(b-c)*(-3*b^2-8*b*c-3*c^2)) : :

X(60407) lies on these lines: {7, 10}, {1323, 53618}, {9436, 60405}, {20121, 31520}, {60386, 60389}, {60392, 60395}, {60397, 60400}, {60401, 60404}, {60406, 60410}

X(60408) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(8), X(9) ) }

Barycentrics    (-a+b+c)*(2*a^6-7*(b+c)*a^5-(5*b^2-46*b*c+5*c^2)*a^4+10*(b+c)*(3*b^2-8*b*c+3*c^2)*a^3-4*(7*b^4+7*c^4-3*b*c*(5*b^2-4*b*c+5*c^2))*a^2+(b^2-c^2)*(b-c)*(9*b^2-14*b*c+9*c^2)*a-(b-c)^6) : :

X(60408) lies on these lines: {8, 9}, {21267, 31519}, {60374, 60375}, {60380, 60381}, {60387, 60388}, {60393, 60394}, {60398, 60399}, {60402, 60403}, {60405, 60406}, {60409, 60410}

X(60409) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(8), X(10) ) }

Barycentrics    (b+c)*a^3-(7*b^2-4*b*c+7*c^2)*a^2-(b+c)*(5*b^2-18*b*c+5*c^2)*a+(3*b^2-8*b*c+3*c^2)*(b+c)^2 : :
X(60409) = X(8)+2*X(60374) = X(8)+8*X(60380) = 2*X(10)+X(53618) = 4*X(10)+5*X(60382) = 2*X(5123)+X(14027)

X(60409) lies on these lines: {1, 2}, {5123, 14027}, {9436, 60405}, {11067, 26062}, {24797, 27813}, {25919, 48696}, {60387, 60389}, {60393, 60395}, {60398, 60400}, {60402, 60404}, {60408, 60410}

X(60409) = X(23835)-complementary conjugate of-X(5510)
X(60409) = pole of the line {1213, 40621} with respect to the Kiepert circumhyperbola
X(60409) = pole of the line {514, 4052} with respect to the Steiner inellipse
X(60409) = reflection of X(2) in the line X(3667)X(25996)

X(60410) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(9), X(10) ) }

Barycentrics    (b+c)*a^6+2*(b^2-7*b*c+c^2)*a^5-(b+c)*(15*b^2-38*b*c+15*c^2)*a^4+4*(6*b^4+6*c^4-b*c*(5*b^2+4*b*c+5*c^2))*a^3-(b^2-c^2)*(b-c)*(17*b^2+6*b*c+17*c^2)*a^2+6*(b^2-c^2)*(b-c)*(b^3+c^3)*a-(b^2-c^2)*(b-c)^5 : :

X(60410) lies on these lines: {4, 9}, {31519, 31520}, {53618, 60375}, {60381, 60382}, {60388, 60389}, {60399, 60400}, {60403, 60404}, {60406, 60407}, {60408, 60409}

X(60411) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( X(13), X(14) ) }

Barycentrics    2*a^8+4*(b^2-3*b*c+c^2)*a^6-12*(b^2-c^2)*(b-c)*a^5-(3*b^4+3*c^4-4*b*c*(3*b^2-4*b*c+3*c^2))*a^4+6*(b^4-c^4)*(b-c)*a^3+2*(2*b^2+3*b*c+2*c^2)*(b^2-b*c+c^2)*(b-c)^2*a^2+6*(b^2-c^2)^3*(b-c)*a+(b^2-c^2)^2*(b-c)^2*(-7*b^2-8*b*c-7*c^2) : :

X(60411) lies on these lines: {6, 13}, {24224, 50802}

X(60412) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( BICENTRIC PAIR PU(1) ) }

Barycentrics    a^2*(b-c)*((b+c)*(b^2+c^2)*a^4-2*(b^4+c^4)*a^3+(b+c)*(b^2+b*c+c^2)*(b^2-3*b*c+c^2)*a^2+2*(b^2+c^2)*b^2*c^2*a+(b^2-c^2)*(b-c)*b^2*c^2) : :

X(60412) lies on these lines: {39, 512}, {2473, 2488}, {2495, 59877}, {2497, 3309}, {39541, 40458}

X(60412) = cross-difference of every pair of points on the line X(385)X(40461)
X(60412) = perspector of the circumconic through X(694) and X(46324)

X(60413) = COMMON POINT OF RADICAL AXES OF { INCIRCLE, OO( BICENTRIC PAIR PU(11) ) }

Barycentrics    (b-c)*((b+c)*a^6-2*(b^2+c^2)*a^5-(b+c)^3*a^4-4*b^2*c^2*a^3+(b+c)*(3*b^4+3*c^4-2*b*c*(2*b-c)*(b-2*c))*a^2+2*(b^2+c^2)*(b^4+c^4)*a+(b+c)*(b^2+c^2)*(b^4+c^4-2*b*c*(b^2+b*c+c^2))) : :

X(60413) lies on these lines: {141, 523}

X(60414) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(1), X(2) ) }

Barycentrics    2*a^3-3*(b+c)*a^2-4*(b^2-3*b*c+c^2)*a+3*(b^2-c^2)*(b-c) : :

X(60414) lies on these lines: {1, 2}, {468, 1877}, {858, 39692}, {896, 3911}, {908, 18201}, {1155, 3259}, {1279, 31235}, {1470, 11284}, {1738, 31272}, {3452, 36263}, {3816, 4689}, {3977, 11814}, {4187, 37599}, {4346, 30740}, {4663, 37663}, {4887, 33864}, {4896, 26229}, {4926, 47800}, {5087, 43055}, {5159, 60415}, {5204, 37366}, {5370, 33849}, {6667, 16610}, {6931, 11512}, {7302, 19649}, {9350, 24386}, {13747, 37589}, {15601, 31231}, {16670, 40128}, {24183, 30799}, {24855, 60416}, {26476, 30739}, {31224, 36277}, {35996, 59319}, {60417, 60420}, {60419, 60422}

X(60414) = complement of X(37762)
X(60414) = pole of the line {3667, 11238} with respect to the incircle
X(60414) = pole of the line {44316, 59887} with respect to the nine-point circle
X(60414) = pole of the line {944, 3667} with respect to the orthoptic circle of Steiner inellipse
X(60414) = pole of the line {514, 17276} with respect to the Steiner inellipse
X(60414) = (X(2), X(5121))-harmonic conjugate of X(3011)

X(60415) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(1), X(3) ) }

Barycentrics    a*(-a^2+b^2+c^2)*((b+c)*a^3+(b^2-4*b*c+c^2)*a^2-(b^2-c^2)*(b-c)*a-(b^2-c^2)^2) : :

X(60415) lies on these lines: {1, 3}, {2, 38462}, {5, 1074}, {30, 1465}, {33, 6911}, {73, 13369}, {84, 8757}, {119, 10017}, {223, 7171}, {225, 37356}, {227, 18481}, {376, 17080}, {404, 6198}, {474, 37696}, {496, 3914}, {515, 24025}, {522, 8062}, {912, 7004}, {1012, 37697}, {1068, 6890}, {1210, 26741}, {1785, 6882}, {1807, 5440}, {1829, 7428}, {1854, 45770}, {1858, 54427}, {1870, 6909}, {1878, 13744}, {2072, 39692}, {2968, 6735}, {3100, 6905}, {3488, 4850}, {3562, 26877}, {3752, 5722}, {3814, 51889}, {3916, 52408}, {4075, 34851}, {4188, 9538}, {4296, 37403}, {4646, 37739}, {4719, 12710}, {5044, 35194}, {5123, 56416}, {5159, 60414}, {5396, 10391}, {5399, 12675}, {5552, 33113}, {5554, 25876}, {6001, 34586}, {6350, 11239}, {6891, 7952}, {6924, 8144}, {6948, 34231}, {7078, 24467}, {7515, 27385}, {9645, 37034}, {9729, 34956}, {9730, 20122}, {10200, 34120}, {10257, 47140}, {10915, 34823}, {11363, 20842}, {11373, 52541}, {11585, 26476}, {12608, 40677}, {13730, 26378}, {14961, 60416}, {15654, 52359}, {17073, 17382}, {17441, 23206}, {18210, 23205}, {18491, 36985}, {18732, 22344}, {19372, 37234}, {22072, 31837}, {22144, 51376}, {23169, 34381}, {27506, 41013}, {34822, 48843}, {35072, 35113}, {36636, 58808}, {37694, 40263}, {40644, 46850}, {44222, 54346}, {52384, 59653}, {60417, 60424}, {60418, 60425}

X(60415) = midpoint of X(i) and X(j) for these (i, j): {1, 45269}, {7004, 22350}
X(60415) = complementary conjugate of the complement of X(36058)
X(60415) = complement of X(38462)
X(60415) = cross-difference of every pair of points on the line X(650)X(2178)
X(60415) = crosspoint of X(77) and X(52351)
X(60415) = crosssum of X(33) and X(52413)
X(60415) = X(51562)-Ceva conjugate of-X(521)
X(60415) = X(i)-complementary conjugate of-X(j) for these (i, j): (3, 121), (48, 16594), (88, 20305), (106, 5), (184, 4370), (603, 1145), (901, 20316), (903, 21243), (1417, 1210), (1437, 34587), (1459, 3259), (1795, 56750), (1797, 141), (2316, 41883), (4591, 30476), (4622, 21259), (8752, 13567), (9456, 226), (32656, 6544), (32659, 2), (32719, 3239), (35186, 32475), (36058, 10), (52759, 34517)
X(60415) = X(6)-Dao conjugate of-X(55995)
X(60415) = X(19)-isoconjugate of-X(55995)
X(60415) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (3, 55995), (30384, 92)
X(60415) = center of the circumconic through X(30384) and X(51562)
X(60415) = perspector of the circumconic through X(651) and X(2994)
X(60415) = pole of the line {513, 9798} with respect to the circumcircle
X(60415) = pole of the line {513, 1479} with respect to the incircle
X(60415) = pole of the line {1068, 44426} with respect to the polar circle
X(60415) = pole of the line {910, 8756} with respect to the Stevanovic circle
X(60415) = pole of the line {513, 1479} with respect to the de Longchamps ellipse
X(60415) = pole of the line {21, 55995} with respect to the Stammler hyperbola
X(60415) = pole of the line {17496, 20078} with respect to the Steiner circumellipse
X(60415) = pole of the line {63, 905} with respect to the Steiner inellipse
X(60415) = barycentric product X(63)*X(30384)
X(60415) = trilinear product X(3)*X(30384)
X(60415) = trilinear quotient X(i)/X(j) for these (i, j): (63, 55995), (30384, 4)
X(60415) = X(45269)-of-anti-Aquila triangle

X(60416) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(1), X(6) ) }

Barycentrics    a*((b+c)*a^5-(b^2+4*b*c+c^2)*a^4+2*(b+c)*b*c*a^3-4*(b-c)^2*b*c*a^2-(b^4-c^4)*(b-c)*a+(b^4-c^4)*(b^2-c^2)) : :

X(60416) lies on these lines: {1, 6}, {1877, 60428}, {6735, 60438}, {14961, 60415}, {16583, 28074}, {24855, 60414}, {39692, 49123}, {59977, 59978}, {60417, 60435}, {60418, 60436}

X(60416) = pole of the line {3309, 12589} with respect to the incircle

X(60417) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(1), X(7) ) }

Barycentrics    (-a+b+c)*(2*a^2-(b+c)*a-(b-c)^2)*(a^4-4*(b-c)^2*a^2+4*(b^2-c^2)*(b-c)*a-(b-c)^4) : :

X(60417) lies on these lines: {1, 7}, {1086, 56741}, {1638, 17427}, {1877, 60429}, {6735, 60441}, {39692, 60432}, {60414, 60420}, {60415, 60424}, {60416, 60435}, {60418, 60439}, {60419, 60440}

X(60418) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(1), X(8) ) }

Barycentrics    2*a^4-5*(b+c)*a^3-(3*b^2-22*b*c+3*c^2)*a^2+(b-3*c)*(3*b-c)*(b+c)*a-(b^2-c^2)^2 : :

X(60418) lies on these lines: {1, 2}, {513, 14284}, {515, 17460}, {1317, 1455}, {1837, 38496}, {1862, 1877}, {3259, 5048}, {3756, 44784}, {9260, 59980}, {10700, 30384}, {10912, 23675}, {12640, 32577}, {16610, 32426}, {39692, 60433}, {60415, 60425}, {60416, 60436}, {60417, 60439}, {60419, 60442}

X(60418) = pole of the line {2098, 3667} with respect to the incircle
X(60418) = pole of the line {44316, 59892} with respect to the nine-point circle
X(60418) = pole of the line {7649, 59913} with respect to the polar circle
X(60418) = pole of the line {3057, 3756} with respect to the Feuerbach circumhyperbola

X(60419) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(1), X(9) ) }

Barycentrics    a*(-a+b+c)^2*((b+c)*a^3-(b^2+c^2)*a^2-(b^2-c^2)*(b-c)*a+(b-c)^4) : :

X(60419) lies on these lines: {1, 6}, {2, 38468}, {119, 1566}, {169, 11248}, {241, 908}, {294, 45393}, {650, 6362}, {672, 18838}, {910, 2077}, {1146, 3693}, {1323, 16578}, {1470, 40131}, {1519, 17747}, {1826, 1907}, {1877, 5089}, {2082, 26358}, {2340, 55380}, {2635, 35293}, {3359, 42316}, {3730, 37562}, {3991, 49169}, {5552, 6554}, {7368, 10965}, {10915, 41006}, {20927, 25242}, {24036, 40869}, {24635, 31018}, {25066, 26364}, {25083, 34852}, {30513, 40779}, {35072, 35113}, {35110, 43064}, {35111, 35128}, {39692, 60434}, {41572, 45227}, {41698, 44424}, {52334, 52614}, {60414, 60422}, {60417, 60440}, {60418, 60442}

X(60419) = complement of X(38468)
X(60419) = cross-difference of every pair of points on the line X(513)X(1617)
X(60419) = crosspoint of X(2) and X(34894)
X(60419) = crosssum of X(6) and X(3660)
X(60419) = X(i)-complementary conjugate of-X(j) for these (i, j): (2742, 17072), (34894, 2887), (51567, 17047)
X(60419) = X(18839)-reciprocal conjugate of-X(7)
X(60419) = center of the inconic with perspector X(34894)
X(60419) = perspector of the circumconic through X(100) and X(6601)
X(60419) = pole of the line {11, 2078} with respect to the Stevanovic circle
X(60419) = pole of the line {142, 18240} with respect to the circumhyperbola dual of Yff parabola
X(60419) = pole of the line {442, 38055} with respect to the Kiepert circumhyperbola
X(60419) = pole of the line {521, 4863} with respect to the Mandart inellipse
X(60419) = pole of the line {17494, 20111} with respect to the Steiner circumellipse
X(60419) = pole of the line {220, 650} with respect to the Steiner inellipse
X(60419) = barycentric product X(8)*X(18839)
X(60419) = trilinear product X(9)*X(18839)
X(60419) = trilinear quotient X(18839)/X(57)
X(60419) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (9, 34526, 220), (34522, 34524, 220)

X(60420) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(2), X(7) ) }

Barycentrics    2*a^6-(b+c)*a^5-(13*b^2-18*b*c+13*c^2)*a^4+4*(b+c)*(6*b^2-11*b*c+6*c^2)*a^3-2*(7*b^2+22*b*c+7*c^2)*(b-c)^2*a^2+(b^2-c^2)*(b-c)*(b^2+18*b*c+c^2)*a+(b^2+6*b*c+c^2)*(b-c)^4 : :

X(60420) lies on these lines: {2, 7}, {468, 60429}, {858, 60432}, {5159, 60424}, {24855, 60435}, {59984, 59985}, {60414, 60417}, {60421, 60439}, {60423, 60441}

X(60420) = inverse of X(50092) in Steiner inellipse
X(60420) = pole of the line {3576, 5511} with respect to the orthoptic circle of Steiner inellipse
X(60420) = pole of the line {1, 24685} with respect to the circumhyperbola dual of Yff parabola
X(60420) = pole of the line {522, 50092} with respect to the Steiner inellipse

X(60421) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(2), X(8) ) }

Barycentrics    2*a^3-5*(b+c)*a^2-4*(b^2-6*b*c+c^2)*a+(b+c)*(b^2-6*b*c+c^2) : :

X(60421) lies on these lines: {1, 2}, {468, 60430}, {858, 60433}, {2505, 7659}, {4009, 58413}, {5057, 31271}, {5159, 60425}, {24855, 60436}, {60420, 60439}, {60422, 60442}

X(60421) = pole of the line {7628, 44316} with respect to the nine-point circle
X(60421) = pole of the line {3667, 12245} with respect to the orthoptic circle of Steiner inellipse
X(60421) = (X(2), X(50535))-harmonic conjugate of X(3011)

X(60422) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(2), X(9) ) }

Barycentrics    (-a+b+c)*(2*a^5-(b+c)*a^4-8*(b^2-b*c+c^2)*a^3+4*(b+c)*(2*b^2-3*b*c+2*c^2)*a^2+2*(b^2+c^2)*(b-c)^2*a-3*(b^2-c^2)*(b-c)^3) : :

X(60422) lies on these lines: {2, 7}, {468, 60431}, {858, 60434}, {3011, 6603}, {5159, 60426}, {5199, 50752}, {5513, 46415}, {24855, 60437}, {29639, 34522}, {47766, 59984}, {60414, 60419}, {60421, 60442}, {60423, 60444}

X(60422) = complement of X(37761)
X(60422) = pole of the line {5759, 28292} with respect to the orthoptic circle of Steiner inellipse
X(60422) = pole of the line {14100, 57443} with respect to the Feuerbach circumhyperbola

X(60423) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(2), X(10) ) }

Barycentrics    (b+c)*a^2-6*b*c*a+(b+c)*(b^2+c^2) : :
X(60423) = 3*X(2)+X(60459)

X(60423) lies on these lines: {1, 2}, {11, 3823}, {44, 4831}, {120, 3259}, {142, 32931}, {226, 25961}, {244, 3717}, {305, 20943}, {341, 23675}, {373, 17792}, {468, 1861}, {553, 32938}, {661, 4521}, {726, 24200}, {750, 17353}, {858, 3814}, {908, 3836}, {993, 40916}, {1054, 3977}, {1086, 4009}, {1155, 4422}, {1211, 58451}, {1266, 3263}, {1329, 30739}, {1376, 11284}, {1575, 3291}, {1738, 4358}, {1995, 25440}, {2325, 32845}, {3266, 6381}, {3290, 3943}, {3336, 59639}, {3452, 25957}, {3681, 59684}, {3685, 26073}, {3701, 24178}, {3703, 16602}, {3710, 24174}, {3712, 41310}, {3782, 59506}, {3790, 24620}, {3826, 30818}, {3834, 51400}, {3844, 5241}, {3868, 59685}, {3883, 17125}, {3911, 33115}, {3914, 18743}, {3932, 16610}, {3952, 24231}, {3967, 40688}, {4023, 17231}, {4029, 26242}, {4078, 4850}, {4082, 17155}, {4104, 33172}, {4126, 21342}, {4138, 27131}, {4389, 30758}, {4413, 17279}, {4414, 25101}, {4429, 30829}, {4434, 31289}, {4656, 33125}, {4684, 21805}, {4700, 33854}, {4874, 59895}, {4899, 17449}, {5094, 46878}, {5123, 6075}, {5159, 60427}, {5249, 59511}, {5267, 7496}, {5294, 17122}, {5316, 25760}, {5370, 13587}, {5423, 15590}, {5437, 33163}, {5750, 37675}, {5847, 37680}, {6376, 11059}, {6666, 32917}, {6692, 33119}, {7308, 26034}, {7628, 47123}, {7777, 25140}, {9342, 33157}, {9347, 38049}, {9352, 59544}, {10712, 24709}, {11814, 21241}, {13161, 17674}, {13407, 59666}, {14774, 36951}, {14996, 59408}, {14997, 51196}, {16051, 34823}, {16434, 18481}, {17265, 17718}, {17356, 17602}, {17719, 31252}, {18492, 26118}, {20888, 26235}, {21060, 33069}, {21255, 33065}, {23536, 46937}, {24164, 24168}, {24169, 59517}, {24177, 32925}, {24855, 60438}, {25531, 32850}, {30748, 34824}, {30860, 33329}, {32948, 40998}, {33078, 37687}, {33086, 35595}, {33131, 46938}, {33849, 45281}, {35263, 56010}, {40131, 54389}, {40132, 59572}, {43957, 57288}, {48062, 59887}, {60420, 60441}, {60422, 60444}

X(60423) = midpoint of X(7292) and X(60459)
X(60423) = complement of X(7292)
X(60423) = complementary conjugate of the complement of X(34893)
X(60423) = cross-difference of every pair of points on the line X(649)X(3915)
X(60423) = X(i)-complementary conjugate of-X(j) for these (i, j): (2748, 513), (5387, 27076), (34892, 141), (34893, 10), (51561, 3741)
X(60423) = perspector of the circumconic through X(190) and X(34860)
X(60423) = pole of the line {4786, 39592} with respect to the Bevan circle
X(60423) = pole of the line {44316, 59895} with respect to the nine-point circle
X(60423) = pole of the line {40, 3667} with respect to the orthoptic circle of Steiner inellipse
X(60423) = pole of the line {7649, 59839} with respect to the polar circle
X(60423) = pole of the line {2, 4986} with respect to the circumhyperbola dual of Yff parabola
X(60423) = pole of the line {3057, 9041} with respect to the Feuerbach circumhyperbola
X(60423) = pole of the line {1213, 3756} with respect to the Kiepert circumhyperbola
X(60423) = pole of the line {3239, 21627} with respect to the Mandart inellipse
X(60423) = pole of the line {514, 2321} with respect to the Steiner inellipse
X(60423) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (2, 5205, 3011), (2, 5297, 1125), (3836, 24003, 908), (4082, 24175, 17155), (4358, 24988, 1738), (50535, 50752, 2), (60414, 60421, 2)

X(60424) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(3), X(7) ) }

Barycentrics    (-a^2+b^2+c^2)*(2*a^8-2*(b+c)*a^7-3*(3*b^2-4*b*c+3*c^2)*a^6+2*(b+c)*(9*b^2-16*b*c+9*c^2)*a^5-(11*b^2+30*b*c+11*c^2)*(b-c)^2*a^4+2*(b^2-c^2)*(b-c)*(b^2+8*b*c+c^2)*a^3+(b^2+4*b*c+c^2)*(b-c)^4*a^2-2*(b^2-c^2)^3*(b-c)*a+(b^2-c^2)^2*(b-c)^4) : :

X(60424) lies on these lines: {3, 7}, {30, 60429}, {2072, 60432}, {3900, 17069}, {5159, 60420}, {14961, 60435}, {60415, 60417}, {60425, 60439}, {60426, 60440}, {60427, 60441}

X(60425) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(3), X(8) ) }

Barycentrics    (-a^2+b^2+c^2)*(2*a^5-4*(b+c)*a^4-(3*b^2-16*b*c+3*c^2)*a^3+(b+c)*(b^2-4*b*c+c^2)*a^2-(b^2-c^2)^2*a+(b^2-c^2)^2*(b+c)) : :

X(60425) lies on these lines: {3, 8}, {30, 60430}, {513, 20315}, {2072, 60433}, {5159, 60421}, {14961, 60436}, {46974, 53618}, {60415, 60418}, {60424, 60439}, {60426, 60442}, {60427, 60443}

X(60425) = X(43081)-complementary conjugate of-X(1210)
X(60425) = perspector of the circumconic through X(13136) and X(39696)
X(60425) = pole of the line {900, 12410} with respect to the circumcircle

X(60426) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(3), X(9) ) }

Barycentrics    a*(-a+b+c)*(-a^2+b^2+c^2)*((b+c)*a^5-(3*b^2-4*b*c+3*c^2)*a^4+2*(b^2-c^2)*(b-c)*a^3+2*(b^3-c^3)*(b-c)*a^2-(b^2-c^2)*(b-c)*(3*b^2+2*b*c+3*c^2)*a+(b^2-c^2)^2*(b-c)^2) : :

X(60426) lies on these lines: {2, 38461}, {3, 9}, {30, 60431}, {514, 28984}, {912, 34591}, {1062, 34526}, {1212, 37565}, {1214, 43064}, {2072, 60434}, {3560, 7079}, {5030, 8558}, {5159, 60422}, {5526, 46974}, {14961, 60437}, {25932, 31018}, {35072, 35113}, {40616, 60427}, {46830, 57282}, {60424, 60440}, {60425, 60442}

X(60426) = complement of X(38461)
X(60426) = X(37143)-Ceva conjugate of-X(521)
X(60426) = X(i)-complementary conjugate of-X(j) for these (i, j): (212, 10427), (219, 31844), (2291, 16608), (4845, 5), (18889, 226), (32728, 21172), (34068, 1210), (41798, 20305), (52425, 35110), (57108, 46415), (60047, 2886)
X(60426) = perspector of the circumconic through X(13138) and X(39695)
X(60426) = pole of the line {23710, 51361} with respect to the Stevanovic circle
X(60426) = pole of the line {78, 57055} with respect to the Steiner inellipse

X(60427) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(3), X(10) ) }

Barycentrics    (-a^2+b^2+c^2)*((b+c)*a^4-2*b*c*a^3-(b^2-c^2)^2*(b+c)) : :

X(60427) lies on these lines: {2, 1060}, {3, 10}, {5, 46878}, {8, 1062}, {9, 18595}, {30, 1861}, {72, 343}, {123, 5123}, {127, 20541}, {216, 1573}, {281, 6826}, {339, 6381}, {406, 37696}, {441, 25007}, {475, 52366}, {514, 20315}, {517, 46100}, {519, 18455}, {912, 26932}, {956, 25947}, {960, 1209}, {1038, 1698}, {1040, 3679}, {1074, 53008}, {1125, 18447}, {1211, 5044}, {1329, 11585}, {1368, 3820}, {1574, 22401}, {1575, 14961}, {1737, 35466}, {1809, 40437}, {2072, 3814}, {2550, 15941}, {2551, 6643}, {2886, 15760}, {2968, 6735}, {3035, 10257}, {3100, 56877}, {3547, 19843}, {3548, 26364}, {3549, 26363}, {4296, 52252}, {4426, 10316}, {4999, 7542}, {5090, 13730}, {5159, 60423}, {5236, 8728}, {5396, 45206}, {5692, 18588}, {5887, 20306}, {6347, 55885}, {6348, 55890}, {6376, 41009}, {6708, 6881}, {6734, 7515}, {6823, 31419}, {6917, 54396}, {7291, 37179}, {7386, 29679}, {7494, 29667}, {10024, 25639}, {10039, 17102}, {10897, 31453}, {12605, 57288}, {15252, 51359}, {16196, 47742}, {16585, 18641}, {17073, 17327}, {17239, 18642}, {17792, 37511}, {20262, 42018}, {20831, 49542}, {24914, 56414}, {24984, 41013}, {24987, 37565}, {26687, 28695}, {27091, 28407}, {27505, 56876}, {28146, 45281}, {30445, 44417}, {31458, 47525}, {39585, 44229}, {40616, 60426}, {60424, 60441}, {60425, 60443}

X(60427) = midpoint of X(3100) and X(56877)
X(60427) = complementary conjugate of the complement of X(1807)
X(60427) = complement of X(1870)
X(60427) = cross-difference of every pair of points on the line X(5301)X(6589)
X(60427) = X(i)-complementary conjugate of-X(j) for these (i, j): (3, 214), (35, 1511), (48, 16586), (72, 31845), (73, 6739), (80, 5), (228, 35069), (265, 25639), (652, 46398), (655, 46396), (759, 942), (1411, 1210), (1459, 51402), (1793, 960), (1807, 10), (1946, 35128), (2006, 16608), (2161, 226), (2222, 521), (2341, 6708), (6187, 6), (6740, 34831), (8606, 34544), (18359, 20305), (20566, 21243), (24624, 34830), (32662, 21192), (32675, 14837), (34079, 40940), (34857, 50036), (36058, 52537), (36069, 21187), (36910, 41883), (47318, 30476), (51562, 20316), (52153, 1100), (52351, 141), (52371, 20262), (52391, 442), (52392, 2886), (52431, 2), (57736, 1125), (57985, 3741)
X(60427) = perspector of the circumconic through X(39700) and X(44765)
X(60427) = pole of the line {522, 49553} with respect to the circumcircle
X(60427) = pole of the line {522, 11247} with respect to the Spieker circle
X(60427) = pole of the line {306, 6332} with respect to the Steiner inellipse
X(60427) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (10, 34823, 3), (1038, 1698, 34120)

X(60428) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(4), X(6) ) }

Barycentrics    (2*a^2-b^2-c^2)*(a^2+b^2-c^2)^2*(a^2-b^2+c^2)^2 : :
X(60428) = 3*X(37855)-X(44146)

X(60428) lies on these lines: {2, 10603}, {4, 6}, {5, 1968}, {25, 7737}, {30, 232}, {32, 235}, {39, 1885}, {107, 843}, {112, 230}, {113, 38970}, {115, 10151}, {127, 44340}, {187, 468}, {216, 34664}, {249, 297}, {264, 8370}, {325, 15014}, {378, 3815}, {419, 9217}, {427, 5475}, {428, 14537}, {431, 2204}, {458, 37648}, {460, 512}, {524, 37778}, {598, 2052}, {648, 47286}, {935, 47245}, {1007, 35940}, {1552, 8749}, {1593, 2548}, {1596, 10311}, {1597, 15484}, {1625, 44665}, {1783, 21956}, {1861, 60438}, {1877, 60416}, {2079, 37951}, {2549, 44438}, {2682, 44102}, {3053, 3542}, {3055, 37118}, {3147, 5023}, {3163, 47162}, {3172, 3767}, {3199, 3575}, {3269, 15311}, {3516, 31401}, {4235, 32459}, {5052, 39871}, {5094, 31415}, {5095, 52477}, {5139, 44099}, {5203, 5477}, {5210, 35486}, {5305, 44226}, {5913, 37962}, {6103, 37984}, {6528, 35146}, {6531, 20031}, {6623, 7735}, {6781, 37931}, {6819, 55446}, {7071, 31409}, {7576, 33885}, {7694, 37074}, {7753, 33843}, {7762, 54412}, {7763, 37199}, {7812, 21447}, {7841, 17907}, {8352, 37765}, {8779, 51403}, {8791, 37981}, {9308, 11185}, {9675, 13884}, {10019, 39565}, {10313, 47096}, {10317, 11799}, {11547, 52282}, {11744, 43717}, {13449, 39569}, {13851, 51363}, {14120, 47151}, {14273, 52475}, {14569, 34154}, {14585, 16252}, {15355, 38323}, {15387, 34169}, {16227, 59533}, {16303, 52219}, {16310, 52952}, {16320, 46619}, {18325, 22121}, {18533, 59229}, {18560, 39575}, {21843, 37453}, {22120, 31725}, {22240, 52069}, {23047, 27371}, {27373, 40325}, {28419, 32006}, {31467, 55575}, {32269, 54082}, {32661, 51425}, {32687, 47105}, {32713, 32741}, {35325, 45938}, {35485, 53095}, {35906, 57608}, {36416, 53414}, {36794, 53489}, {37174, 37645}, {37196, 43618}, {39176, 47144}, {40856, 46942}, {41254, 51358}, {47296, 50188}, {47336, 52951}, {47339, 52945}, {51394, 59558}, {52058, 52403}, {52283, 59767}, {53109, 54703}, {53156, 58780}, {55275, 58346}, {60429, 60435}, {60430, 60436}, {60431, 60437}

X(60428) = polar conjugate of X(30786)
X(60428) = isogonal conjugate of the isotomic conjugate of X(37778)
X(60428) = cevapoint of X(1648) and X(14273)
X(60428) = cross-difference of every pair of points on the line X(394)X(520)
X(60428) = crosspoint of X(4) and X(60133)
X(60428) = crosssum of X(i) and X(j) for these {i, j}: {3, 14961}, {577, 58357}
X(60428) = X(37778)-Ceva conjugate of-X(468)
X(60428) = X(i)-cross conjugate of-X(j) for these (i, j): (1648, 14273), (2682, 52475), (44102, 468)
X(60428) = X(i)-Dao conjugate of-X(j) for these (i, j): (136, 14977), (1249, 30786), (1560, 69), (1649, 15526), (2482, 3926), (3162, 895), (5139, 10097), (6523, 671), (6593, 394), (15259, 111), (21905, 3269), (23992, 3265), (38988, 520), (42426, 51405), (48317, 525), (50938, 36894), (52881, 4176)
X(60428) = X(i)-isoconjugate of-X(j) for these {i, j}: {48, 30786}, {63, 895}, {69, 36060}, {111, 326}, {255, 671}, {304, 14908}, {394, 897}, {520, 36085}, {577, 46277}, {691, 24018}, {822, 892}, {923, 3926}, {1102, 8753}, {3265, 36142}, {3719, 7316}, {3964, 36128}, {4091, 5380}, {4100, 46111}, {4575, 14977}, {4592, 10097}, {5547, 7183}, {6507, 17983}, {14585, 57999}, {18023, 52430}
X(60428) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (4, 30786), (25, 895), (107, 892), (158, 46277), (187, 394), (351, 520), (393, 671), (468, 69), (524, 3926), (690, 3265), (896, 326), (922, 255), (1093, 46111), (1096, 897), (1648, 15526), (1973, 36060), (1974, 14908), (2052, 18023), (2207, 111), (2393, 51253), (2489, 10097), (2501, 14977), (2642, 24018), (2682, 1650), (3292, 3964), (3712, 1264), (4062, 52396), (4235, 4563), (4750, 30805), (5095, 6390), (5203, 6340), (5967, 6394), (6059, 5547), (6103, 51405), (6390, 4176), (6524, 17983), (6528, 53080), (7181, 7055), (7337, 7316), (8744, 57481), (8753, 15398), (8754, 51258), (9155, 51386), (14273, 525), (14417, 4143), (14419, 4131), (14432, 52616), (14567, 577), (15352, 59762), (16318, 36894)
X(60428) = X(53412)-zayin conjugate of-X(822)
X(60428) = trilinear pole of the line {351, 14273} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(60428) = orthoassociate of X(35902)
X(60428) = Zosma transform of X(18669)
X(60428) = perspector of the circumconic through X(107) and X(393)
X(60428) = inverse of X(35902) in polar circle
X(60428) = pole of the line {1609, 39201} with respect to the circumcircle
X(60428) = pole of the line {47097, 47202} with respect to the Dao-Moses-Telv circle
X(60428) = pole of the line {125, 511} with respect to the Dou circles radical circle
X(60428) = pole of the line {525, 1843} with respect to the incircle-of-orthic triangle
X(60428) = pole of the line {800, 39201} with respect to the 1st Lozada circle
X(60428) = pole of the line {468, 44436} with respect to the Moses circles radical circle
X(60428) = pole of the line {6103, 14961} with respect to the Moses-Parry circle
X(60428) = pole of the line {59745, 59900} with respect to the nine-point circle
X(60428) = pole of the line {9209, 9752} with respect to the orthoptic circle of Steiner inellipse
X(60428) = pole of the line {69, 525} with respect to the polar circle
X(60428) = pole of the line {800, 39201} with respect to the Brocard inellipse
X(60428) = pole of the line {115, 427} with respect to the Hatzipolakis-Lozada hyperbola
X(60428) = pole of the line {51, 1562} with respect to the Jerabek circumhyperbola
X(60428) = pole of the line {4, 1177} with respect to the Kiepert circumhyperbola
X(60428) = pole of the line {1632, 6562} with respect to the Kiepert parabola
X(60428) = pole of the line {8057, 52077} with respect to the MacBeath circumconic
X(60428) = pole of the line {25, 523} with respect to the orthic inconic
X(60428) = pole of the line {394, 3269} with respect to the Stammler hyperbola
X(60428) = pole of the line {6392, 33294} with respect to the Steiner circumellipse
X(60428) = pole of the line {3767, 6587} with respect to the Steiner inellipse
X(60428) = pole of the line {3926, 15526} with respect to the Steiner-Wallace hyperbola
X(60428) = barycentric product X(i)*X(j) for these {i, j}: {4, 468}, {6, 37778}, {25, 44146}, {107, 690}, {158, 896}, {187, 2052}, {264, 44102}, {351, 6528}, {393, 524}, {648, 14273}, {823, 2642}, {922, 57806}, {1093, 3292}, {1096, 14210}, {1118, 3712}, {1300, 12828}, {1560, 60133}, {1648, 23582}, {1857, 7181}, {2207, 3266}
X(60428) = trilinear product X(i)*X(j) for these {i, j}: {19, 468}, {31, 37778}, {92, 44102}, {107, 2642}, {158, 187}, {162, 14273}, {351, 823}, {393, 896}, {524, 1096}, {690, 24019}, {922, 2052}, {1648, 24000}, {1857, 51653}, {1973, 44146}, {2207, 14210}, {3292, 6520}, {4062, 5317}, {5095, 36128}, {6521, 23200}, {8747, 21839}
X(60428) = trilinear quotient X(i)/X(j) for these (i, j): (19, 895), (25, 36060), (92, 30786), (107, 36085), (158, 671), (187, 255), (351, 822), (393, 897), (468, 63), (524, 326), (690, 24018), (823, 892), (896, 394), (922, 577), (1096, 111), (1648, 2632), (1973, 14908), (2052, 46277), (2207, 923), (2642, 520)
X(60428) = X(43065)-of-orthic triangle, when ABC is acute
X(60428) = (2nd anti-Conway)-isotomic conjugate-of-X(32246)
X(60428) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (4, 8743, 5254), (4, 8744, 5523), (4, 41370, 6), (53, 53418, 4), (112, 403, 230), (115, 14581, 16318), (297, 41253, 11064), (468, 1560, 24855), (1596, 18907, 10311), (1990, 53419, 5523), (3172, 37197, 3767), (3199, 7747, 3575), (5523, 8744, 1990), (6530, 35907, 1990), (7812, 58782, 27377), (10151, 16318, 115), (27371, 39590, 23047), (41336, 49123, 230), (44438, 45141, 2549)

X(60429) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(4), X(7) ) }

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*((b+c)*a^5-2*(2*b^2-3*b*c+2*c^2)*a^4+6*(b^2-c^2)*(b-c)*a^3-4*(b^2+4*b*c+c^2)*(b-c)^2*a^2+(b^2-c^2)*(b-c)*(b^2+6*b*c+c^2)*a+2*b*c*(b-c)^4) : :

X(60429) lies on these lines: {4, 7}, {30, 60424}, {403, 60432}, {468, 60420}, {1861, 60441}, {1877, 60417}, {3064, 48026}, {60428, 60435}, {60430, 60439}, {60431, 60440}

X(60429) = pole of the line {144, 3900} with respect to the polar circle
X(60429) = pole of the line {1836, 38388} with respect to the Feuerbach circumhyperbola

X(60430) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(4), X(8) ) }

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*((b+c)*a^2+(b^2-8*b*c+c^2)*a+2*b*c*(b+c)) : :

X(60430) lies on these lines: {4, 8}, {30, 60425}, {403, 60433}, {468, 60421}, {900, 7649}, {1785, 5151}, {1861, 60443}, {1862, 1877}, {17516, 23832}, {24828, 51432}, {60428, 60436}, {60429, 60439}, {60431, 60442}

X(60430) = cross-difference of every pair of points on the line X(20818)X(22383)
X(60430) = crosssum of X(3) and X(23205)
X(60430) = Zosma transform of X(1149)
X(60430) = pole of the line {513, 12135} with respect to the incircle-of-orthic triangle
X(60430) = pole of the line {145, 513} with respect to the polar circle
X(60430) = pole of the line {1837, 38389} with respect to the Feuerbach circumhyperbola
X(60430) = pole of the line {281, 6591} with respect to the orthic inconic
X(60430) = (X(4), X(38462))-harmonic conjugate of X(1878)

X(60431) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(4), X(9) ) }

Barycentrics    (-a+b+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(2*a^2-(b+c)*a-(b-c)^2) : :

X(60431) lies on these lines: {4, 9}, {6, 53009}, {30, 60426}, {33, 28120}, {34, 34526}, {44, 8755}, {48, 20263}, {92, 55954}, {220, 225}, {278, 31142}, {403, 60434}, {407, 38930}, {430, 52818}, {468, 60422}, {515, 34591}, {527, 37805}, {653, 50573}, {860, 40869}, {908, 4564}, {910, 5514}, {960, 1840}, {1055, 33573}, {1155, 46415}, {1212, 40950}, {1737, 8558}, {1783, 1785}, {1802, 21075}, {1877, 5089}, {2324, 52033}, {3064, 3700}, {3197, 54009}, {3715, 53008}, {5290, 5747}, {5307, 18228}, {5691, 56857}, {6603, 23710}, {6745, 52891}, {7003, 55931}, {7282, 25993}, {7291, 60468}, {7354, 46830}, {10895, 46835}, {13609, 54079}, {17757, 51376}, {17916, 56814}, {21871, 53998}, {21935, 52530}, {28044, 28060}, {37448, 54357}, {44425, 56858}, {60428, 60437}, {60429, 60440}, {60430, 60442}

X(60431) = polar conjugate of the isotomic conjugate of X(6745)
X(60431) = cross-difference of every pair of points on the line X(222)X(1459)
X(60431) = X(37805)-Ceva conjugate of-X(23710)
X(60431) = X(i)-Dao conjugate of-X(j) for these (i, j): (5452, 60047), (6594, 63), (7952, 1121), (23050, 41798), (35091, 4025), (35110, 348), (36103, 34056), (38966, 23893), (52870, 7056), (52879, 7177), (52880, 7183)
X(60431) = X(i)-isoconjugate of-X(j) for these {i, j}: {3, 34056}, {57, 60047}, {77, 2291}, {222, 1156}, {348, 34068}, {603, 1121}, {905, 14733}, {1459, 37139}, {1813, 35348}, {4025, 36141}, {4845, 7177}, {7053, 41798}, {7056, 18889}, {15413, 32728}, {22383, 35157}
X(60431) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (19, 34056), (33, 1156), (55, 60047), (281, 1121), (527, 348), (607, 2291), (1055, 222), (1155, 77), (1323, 7056), (1783, 37139), (1897, 35157), (2212, 34068), (6139, 1459), (6366, 4025), (6510, 7183), (6603, 63), (6610, 7177), (6745, 69), (7071, 4845), (7079, 41798), (8750, 14733), (14392, 521), (14414, 4131), (18344, 35348), (23710, 7), (30574, 17094), (30806, 7182), (33573, 26932), (37805, 85), (38461, 1088), (52891, 86), (56763, 41081)
X(60431) = Zosma transform of X(43065)
X(60431) = perspector of the circumconic through X(281) and X(1897)
X(60431) = pole of the line {7, 514} with respect to the polar circle
X(60431) = pole of the line {1465, 15252} with respect to the Stevanovic circle
X(60431) = pole of the line {1146, 1864} with respect to the Feuerbach circumhyperbola
X(60431) = pole of the line {55, 8058} with respect to the Mandart inellipse
X(60431) = pole of the line {33, 7649} with respect to the orthic inconic
X(60431) = pole of the line {25259, 30694} with respect to the Steiner circumellipse
X(60431) = pole of the line {3239, 46835} with respect to the Steiner inellipse
X(60431) = barycentric product X(i)*X(j) for these {i, j}: {4, 6745}, {8, 23710}, {9, 37805}, {10, 52891}, {33, 30806}, {92, 6603}, {200, 38461}, {281, 527}, {318, 1155}, {1055, 7017}, {1323, 7046}, {1897, 6366}, {6610, 7101}, {7079, 37780}, {14392, 18026}, {30574, 36797}, {33573, 46102}
X(60431) = trilinear product X(i)*X(j) for these {i, j}: {4, 6603}, {9, 23710}, {19, 6745}, {33, 527}, {37, 52891}, {55, 37805}, {220, 38461}, {281, 1155}, {318, 1055}, {607, 30806}, {653, 14392}, {1323, 7079}, {1638, 56183}, {1783, 6366}, {1857, 6510}, {6139, 6335}, {6610, 7046}, {7012, 33573}, {7071, 37780}, {7952, 56763}
X(60431) = trilinear quotient X(i)/X(j) for these (i, j): (4, 34056), (9, 60047), (33, 2291), (281, 1156), (318, 1121), (527, 77), (607, 34068), (1055, 603), (1155, 222), (1323, 7177), (1783, 14733), (1897, 37139), (3064, 35348), (6068, 6510), (6139, 22383), (6335, 35157), (6366, 905), (6510, 1804), (6603, 3), (6610, 7053)
X(60431) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (4, 7079, 1855), (1783, 1785, 1886)

X(60432) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(5), X(7) ) }

Barycentrics    (b^2+c^2)*a^8-2*(5*b^4+5*c^4-b*c*(6*b^2-7*b*c+6*c^2))*a^6+4*(b+c)*(4*b^4+4*c^4-7*b*c*(b^2-b*c+c^2))*a^5-24*(b^3-c^3)*(b-c)*b*c*a^4-4*(b^2-c^2)*(b-c)*(4*b^4+4*c^4-b*c*(2*b^2+7*b*c+2*c^2))*a^3+2*(5*b^4+5*c^4+13*b*c*(2*b^2+3*b*c+2*c^2))*(b-c)^4*a^2-12*(b^2-c^2)^3*(b-c)*b*c*a-(b^2-c^2)^2*(b-c)^4*(b^2+4*b*c+c^2) : :

X(60432) lies on these lines: {5, 7}, {403, 60429}, {858, 60420}, {2072, 60424}, {3814, 60441}, {39692, 60417}, {49123, 60435}, {60433, 60439}, {60434, 60440}

X(60432) = complement of the circumperp conjugate of X(36996)
X(60432) = inverse of X(7) in nine-point circle
X(60432) = reflection of X(7) in the line X(59891)X(59894)

X(60433) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(5), X(8) ) }

Barycentrics    (b^2+c^2)*a^5-3*(b+c)*(b^2+c^2)*a^4-2*(2*b^4+2*c^4-b*c*(8*b^2-b*c+8*c^2))*a^3+2*(b+c)*(2*b^4+2*c^4-b*c*(2*b^2+3*b*c+2*c^2))*a^2+(3*b^2-16*b*c+3*c^2)*(b^2-c^2)^2*a-(b^2-c^2)^2*(b+c)*(b^2-4*b*c+c^2) : :

X(60433) lies on these lines: {5, 8}, {403, 60430}, {858, 60421}, {2072, 60425}, {3814, 60443}, {8068, 53618}, {28217, 44316}, {39508, 59970}, {39692, 60418}, {49123, 60436}, {60432, 60439}, {60434, 60442}

X(60433) = complement of the circumperp conjugate of X(12245)
X(60433) = inverse of X(8) in nine-point circle
X(60433) = pole of the line {8, 28217} with respect to the nine-point circle
X(60433) = reflection of X(i) in the line X(j)X(k) for these (i, j, k): (5, 28217, 39508), (8, 7628, 28217)

X(60434) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(5), X(9) ) }

Barycentrics    (-a+b+c)*((b^2+c^2)*a^7-(b+c)*(b^2+c^2)*a^6-(3*b^4+3*c^4-2*b*c*(b-c)^2)*a^5+(b+c)*(b^2+c^2)*(3*b^2-4*b*c+3*c^2)*a^4+(3*b^4+3*c^4+2*b*c*(b^2+c^2))*(b-c)^2*a^3-(b^2-c^2)*(b-c)^3*(3*b^2+4*b*c+3*c^2)*a^2-(b^4-c^4)*(b^2-c^2)*(b-c)^2*a+(b^2-c^2)^3*(b-c)^3) : :

X(60434) lies on these lines: {2, 32624}, {5, 9}, {403, 60431}, {858, 60422}, {2072, 60426}, {3814, 60444}, {5526, 8068}, {7741, 34526}, {39692, 60419}, {49123, 60437}, {60432, 60440}, {60433, 60442}

X(60434) = complement of X(32624)
X(60434) = inverse of X(9) in nine-point circle
X(60434) = reflection of X(9) in the line X(59979)X(59986)

X(60435) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(6), X(7) ) }

Barycentrics    2*a^10-2*(b+c)*a^9-3*(3*b^2-4*b*c+3*c^2)*a^8+4*(b+c)*(5*b^2-8*b*c+5*c^2)*a^7-4*(5*b^4+5*c^4-b*c*(b^2+6*b*c+c^2))*a^6+4*(b^2-c^2)*(b-c)*(4*b^2+5*b*c+4*c^2)*a^5-2*(3*b^4+3*c^4+2*b*c*(7*b^2+5*b*c+7*c^2))*(b-c)^2*a^4-4*(b^2-c^2)*(b-c)*(b^4+c^4-2*b*c*(b^2+b*c+c^2))*a^3+2*(b^4+c^4+2*b*c*(b^2-b*c+c^2))*(b-c)^4*a^2+2*(b^4-c^4)*(b^2-c^2)^2*(b-c)*a-(b^4-c^4)*(b^2-c^2)*(b-c)^4 : :

X(60435) lies on these lines: {6, 7}, {14961, 60424}, {24855, 60420}, {49123, 60432}, {60416, 60417}, {60428, 60429}, {60436, 60439}, {60437, 60440}, {60438, 60441}

X(60436) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(6), X(8) ) }

Barycentrics    2*a^7-4*(b+c)*a^6-(3*b^2-16*b*c+3*c^2)*a^5-(b+c)*(b^2+4*b*c+c^2)*a^4-4*(b^4+c^4-4*b*c*(b^2+c^2))*a^3+2*(b+c)*(b^4+c^4-2*b*c*(b^2+b*c+c^2))*a^2+(b^4-c^4)*(b^2-c^2)*a-(b^4-c^4)*(b^2-c^2)*(b+c) : :

X(60436) lies on these lines: {6, 8}, {14961, 60425}, {24855, 60421}, {49123, 60433}, {60416, 60418}, {60428, 60430}, {60435, 60439}, {60437, 60442}, {60438, 60443}

X(60437) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(6), X(9) ) }

Barycentrics    a*(-a+b+c)*((b+c)*a^6-2*(b^2-b*c+c^2)*a^5+(b+c)*(b^2-6*b*c+c^2)*a^4+2*(b+c)^2*b*c*a^3-(b^2-c^2)*(b-c)*(b^2+4*b*c+c^2)*a^2+2*(b^4-c^4)*(b^2-c^2)*a-(b^4-c^4)*(b-c)^3) : :

X(60437) lies on these lines: {1, 6}, {1566, 20623}, {14961, 60426}, {16611, 31896}, {24855, 60422}, {49123, 60434}, {59978, 59979}, {60428, 60431}, {60435, 60440}, {60436, 60442}, {60438, 60444}

X(60438) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(6), X(10) ) }

Barycentrics    (b+c)*a^6-2*b*c*a^5-(b+c)*(b^2+c^2)*a^4-2*(b^2+c^2)*b*c*a^3-((b^2-c^2)^2-4*b^2*c^2)*(b+c)*a^2+(b^4-c^4)*(b^2-c^2)*(b+c) : :

X(60438) lies on these lines: {6, 10}, {1575, 14961}, {1861, 60428}, {3814, 49123}, {6735, 60416}, {11064, 25007}, {24855, 60423}, {60435, 60441}, {60436, 60443}, {60437, 60444}

X(60439) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(7), X(8) ) }

Barycentrics    (b+c)*a^6-(3*b^2+4*b*c+3*c^2)*a^5+4*(b+c)*(b^2+c^2)*a^4-2*(2*b^4+2*c^4+3*b*c*(b-c)^2)*a^3+(b^2-c^2)*(b-c)*(3*b^2+4*b*c+3*c^2)*a^2-(b^4+c^4-2*b*c*(2*b^2-7*b*c+2*c^2))*(b-c)^2*a-2*(b^2-c^2)*(b-c)^3*b*c : :

X(60439) lies on these lines: {7, 8}, {60417, 60418}, {60420, 60421}, {60424, 60425}, {60429, 60430}, {60432, 60433}, {60435, 60436}, {60440, 60442}, {60441, 60443}

X(60440) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(7), X(9) ) }

Barycentrics    (-a+b+c)^2*(2*a^6+(b+c)*a^5-(11*b^2-18*b*c+11*c^2)*a^4+8*(b^2-c^2)*(b-c)*a^3+2*(b^2-8*b*c+c^2)*(b-c)^2*a^2-(b^2-c^2)*(b-c)^3*a-(b-c)^6) : :

X(60440) lies on these lines: {2, 7}, {3900, 59985}, {6068, 51418}, {13609, 44785}, {60417, 60419}, {60424, 60426}, {60429, 60431}, {60432, 60434}, {60435, 60437}, {60439, 60442}, {60441, 60444}

X(60440) = pole of the line {3064, 59930} with respect to the polar circle
X(60440) = pole of the line {14100, 43960} with respect to the Feuerbach circumhyperbola

X(60441) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(7), X(10) ) }

Barycentrics    (-a+b+c)*((b+c)*a^5+(b^2+4*b*c+c^2)*a^4-4*(b+c)*(2*b^2-3*b*c+2*c^2)*a^3+8*(b^2-c^2)^2*a^2-(b^2-c^2)*(b-c)*(b^2+10*b*c+c^2)*a-(b^2+4*b*c+c^2)*(b-c)^4) : :

X(60441) lies on these lines: {7, 10}, {1861, 60429}, {3814, 60432}, {4147, 4521}, {6735, 60417}, {60420, 60423}, {60424, 60427}, {60435, 60438}, {60439, 60443}, {60440, 60444}

X(60441) = pole of the line {3672, 24775} with respect to the circumhyperbola dual of Yff parabola

X(60442) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(8), X(9) ) }

Barycentrics    (-a+b+c)*(2*a^6-7*(b+c)*a^5+3*(b^2+10*b*c+c^2)*a^4+4*(b+c)*(2*b^2-9*b*c+2*c^2)*a^3-2*(3*b^4+3*c^4-2*b*c*(6*b^2-5*b*c+6*c^2))*a^2-(b^2-c^2)^2*(b+c)*a+(b^2-c^2)^2*(b-c)^2) : :

X(60442) lies on these lines: {8, 9}, {5526, 53618}, {60418, 60419}, {60421, 60422}, {60425, 60426}, {60430, 60431}, {60433, 60434}, {60436, 60437}, {60439, 60440}, {60443, 60444}

X(60443) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(8), X(10) ) }

Barycentrics    (b+c)*a^3-(3*b^2+4*b*c+3*c^2)*a^2-(b+c)*(3*b^2-14*b*c+3*c^2)*a+(b^2-4*b*c+c^2)*(b+c)^2 : :

X(60443) lies on these lines: {1, 2}, {121, 30384}, {1861, 60430}, {2885, 3057}, {3259, 5123}, {3814, 60433}, {4487, 24216}, {6006, 59970}, {24003, 51433}, {33119, 44848}, {60425, 60427}, {60436, 60438}, {60439, 60441}, {60442, 60444}

X(60443) = pole of the line {44316, 59909} with respect to the nine-point circle

X(60444) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( X(9), X(10) ) }

Barycentrics    (-a+b+c)^2*((b+c)*a^4-2*b*c*a^3-2*(b^2-c^2)*(b-c)*a^2-2*(b-c)^2*b*c*a+(b^2-c^2)*(b-c)^3) : :

X(60444) lies on these lines: {2, 34525}, {4, 9}, {8, 34526}, {220, 6734}, {908, 26001}, {938, 3553}, {1146, 3693}, {1212, 24987}, {1737, 5526}, {3035, 54079}, {3814, 60434}, {4521, 8713}, {5123, 5514}, {6603, 26015}, {7680, 23840}, {10039, 41006}, {17044, 51364}, {17112, 46415}, {21258, 21617}, {24005, 27508}, {24982, 46835}, {25005, 27541}, {25007, 37774}, {34619, 53994}, {40616, 60426}, {60422, 60423}, {60437, 60438}, {60440, 60441}, {60442, 60443}

X(60444) = complement of X(38459)
X(60444) = complementary conjugate of the complement of X(42064)
X(60444) = X(i)-complementary conjugate of-X(j) for these (i, j): (55, 6594), (657, 40629), (1308, 3900), (3254, 2886), (8641, 35125), (34578, 21258), (37143, 46399), (42064, 10)
X(60444) = pole of the line {514, 4341} with respect to the polar circle
X(60444) = pole of the line {4000, 24025} with respect to the circumhyperbola dual of Yff parabola
X(60444) = pole of the line {3239, 42455} with respect to the Steiner inellipse

X(60445) = COMMON POINT OF RADICAL AXES OF { NINE-POINT CIRCLE, OO( BICENTRIC PAIR PU(11) ) }

Barycentrics    (b^2-c^2)*(a^6-3*(b^2+c^2)*a^4+(b^4+4*b^2*c^2+c^4)*a^2+(b^2+c^2)*(b^4-4*b^2*c^2+c^4)) : :

X(60445) lies on these lines: {141, 523}, {525, 47138}, {2451, 20806}, {2501, 9035}, {9033, 30476}, {11064, 47229}, {15066, 53347}, {15526, 36471}, {28408, 55190}

X(60445) = cross-difference of every pair of points on the line X(1691)X(19153)
X(60445) = X(30541)-complementary conjugate of-X(34846)
X(60445) = pole of the line {21531, 59911} with respect to the nine-point circle
X(60445) = pole of the line {419, 41370} with respect to the polar circle
X(60445) = pole of the line {7779, 31099} with respect to the Steiner circumellipse
X(60445) = pole of the line {325, 5094} with respect to the Steiner inellipse

X(60446) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(1), X(2) ) }

Barycentrics    a^3+(4*b^2-3*b*c+4*c^2)*a-3*c^3-3*b^3 : :

X(60446) lies on these lines: {1, 2}, {147, 30579}, {149, 26097}, {325, 17160}, {346, 9599}, {896, 32844}, {3932, 26139}, {3936, 58371}, {3999, 33891}, {4346, 37668}, {4388, 36263}, {4440, 7840}, {4442, 41136}, {4514, 4689}, {4645, 18201}, {4663, 33071}, {5015, 37599}, {5189, 60448}, {9464, 18835}, {17070, 32922}, {17161, 44435}, {17280, 17721}, {20090, 33070}, {20095, 56755}, {30867, 49527}, {32851, 49704}, {60447, 60455}, {60449, 60456}, {60450, 60457}, {60451, 60458}, {60453, 60460}

X(60446) = anticomplement of X(37764)
X(60446) = crosspoint of X(1016) and X(46143)
X(60446) = X(i)-anticomplementary conjugate of-X(j) for these (i, j): (2705, 513), (34899, 21287), (46143, 21301)
X(60446) = X(37764)-Dao conjugate of-X(37764)
X(60446) = pole of the line {20294, 59839} with respect to the power circles radical circle
X(60446) = pole of the line {514, 53598} with respect to the Steiner circumellipse
X(60446) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (3006, 5211, 2), (3705, 29840, 2)

X(60447) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(1), X(3) ) }

Barycentrics    a*(b*c*a^4+(b^3+c^3)*a^3+(b^4+c^4-b*c*(b^2-b*c+c^2))*a^2-(b^3+c^3)*(b^2+c^2)*a-(b^4-c^4)*(b^2-c^2)) : :

X(60447) lies on these lines: {1, 3}, {2, 60358}, {3705, 31074}, {4777, 50345}, {30781, 31236}, {46450, 60448}, {60446, 60455}, {60449, 60462}, {60450, 60463}, {60451, 60464}, {60452, 60465}

X(60447) = anticomplement of X(60358)
X(60447) = X(60358)-Dao conjugate of-X(60358)

X(60448) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(1), X(4) ) }

Barycentrics    a^7+b*c*a^5+(b^3+c^3)*a^4-(b^2+c^2)^2*a^3-(b^2-c^2)^2*b*c*a-(b^3+c^3)*(b^2-c^2)^2 : :
X(60448) = 5*X(631)-4*X(54090)

X(60448) lies on these lines: {1, 4}, {2, 1324}, {30, 35455}, {35, 36575}, {315, 18835}, {443, 51637}, {522, 44444}, {631, 54090}, {1330, 35614}, {1370, 3705}, {2550, 50368}, {2886, 37098}, {3771, 6818}, {3980, 52121}, {4294, 36496}, {5080, 17777}, {5081, 44662}, {5189, 60446}, {5842, 51414}, {6817, 29635}, {6997, 29634}, {7382, 29841}, {7391, 29840}, {7394, 29838}, {9798, 17555}, {10591, 36557}, {17677, 34634}, {18531, 20254}, {20242, 52367}, {23850, 27531}, {26308, 54343}, {46450, 60447}, {60449, 60466}, {60450, 60467}, {60451, 60468}

X(60448) = anticomplement of X(1324)
X(60448) = X(1324)-Dao conjugate of-X(1324)
X(60448) = orthoassociate of X(49542)
X(60448) = inverse of X(18483) in Johnson triangle circumcircle
X(60448) = inverse of X(34937) in incircle
X(60448) = inverse of X(39642) in anticomplementary circle
X(60448) = inverse of X(49542) in polar circle
X(60448) = pole of the line {1, 522} with respect to the anticomplementary circle
X(60448) = pole of the line {522, 34937} with respect to the incircle
X(60448) = pole of the line {522, 18483} with respect to the Johnson triangle circumcircle
X(60448) = pole of the line {522, 49542} with respect to the polar circle
X(60448) = reflection of X(1) in the line X(522)X(2530)

X(60449) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(1), X(5) ) }

Barycentrics    a^7+(b^2+c^2)*a^5-(3*b^4+3*c^4-b*c*(2*b^2-9*b*c+2*c^2))*a^3+2*(b^3+c^3)*(b^2+c^2)*a^2+(b^2-c^2)^2*(b-c)^2*a-2*(b^3+c^3)*(b^2-c^2)^2 : :

X(60449) lies on these lines: {1, 5}, {60446, 60456}, {60447, 60462}, {60448, 60466}, {60450, 60469}, {60451, 60470}, {60452, 60471}

X(60450) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(1), X(6) ) }

Barycentrics    a*(b*c*a^4+(b^3+c^3)*a^3-(b^4+c^4-b*c*(b^2-3*b*c+c^2))*a^2+(b^3+c^3)*(b^2+c^2)*a-(b^2+c^2)*(b^4+c^4)) : :

X(60450) lies on these lines: {1, 6}, {8301, 16546}, {9025, 18728}, {18715, 25048}, {20544, 24205}, {60446, 60457}, {60447, 60463}, {60448, 60467}, {60449, 60469}, {60451, 60472}, {60452, 60473}

X(60451) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(1), X(7) ) }

Barycentrics    a^7-2*(b+c)*a^6+5*b*c*a^5+(b+c)*(3*b^2-11*b*c+3*c^2)*a^4-(3*b^4+3*c^4+2*b*c*(b^2-9*b*c+c^2))*a^3+6*(b^2-c^2)*(b-c)*b*c*a^2+(2*b^4+2*c^4+b*c*(b+c)^2)*(b-c)^2*a-(b^3+c^3)*(b-c)^4 : :

X(60451) lies on these lines: {1, 7}, {2, 60369}, {30806, 60452}, {60446, 60458}, {60447, 60464}, {60448, 60468}, {60449, 60470}, {60450, 60472}

X(60451) = anticomplement of X(60369)
X(60451) = X(60369)-Dao conjugate of-X(60369)

X(60452) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(1), X(8) ) }

Barycentrics    a^4-(b+c)*a^3+5*b*c*a^2+(b^2-c^2)*(b-c)*a-(b^3+c^3)*(b+c) : :
X(60452) = X(8)-2*X(16086)

X(60452) lies on these lines: {1, 2}, {7, 20924}, {59, 1016}, {69, 49779}, {80, 4975}, {150, 14210}, {190, 529}, {304, 56928}, {312, 5252}, {320, 44663}, {341, 32049}, {345, 3476}, {346, 24247}, {388, 17789}, {442, 30543}, {515, 3685}, {517, 4645}, {944, 49128}, {966, 50014}, {1000, 43749}, {1056, 24349}, {1319, 32851}, {1330, 3878}, {1482, 30448}, {2099, 18134}, {2292, 5484}, {2975, 52273}, {3057, 7270}, {3161, 51280}, {3421, 27538}, {3436, 19582}, {3672, 50010}, {3710, 9369}, {3869, 32859}, {3877, 4388}, {3880, 32850}, {3884, 36974}, {3885, 5300}, {3890, 5016}, {3932, 38455}, {3992, 21290}, {4071, 4919}, {4126, 34689}, {4201, 37598}, {4358, 5176}, {4389, 48801}, {4417, 5289}, {4427, 20067}, {4514, 5919}, {4544, 16503}, {4555, 57887}, {4673, 5794}, {4695, 26073}, {4781, 36004}, {4966, 5855}, {5015, 9957}, {5080, 17777}, {5123, 37758}, {5296, 49758}, {5434, 32939}, {5724, 32942}, {7283, 45287}, {17298, 18421}, {17354, 48832}, {17461, 48835}, {20060, 25253}, {20893, 31995}, {21296, 49780}, {21299, 29331}, {21605, 30617}, {30225, 49753}, {30806, 60451}, {31165, 33066}, {31359, 49760}, {32933, 34605}, {60447, 60465}, {60449, 60471}, {60450, 60473}

X(60452) = reflection of X(8) in X(16086)
X(60452) = anticomplement of X(60353)
X(60452) = X(i)-anticomplementary conjugate of-X(j) for these (i, j): (34895, 1330), (36935, 5080)
X(60452) = X(60353)-Dao conjugate of-X(60353)
X(60452) = X(2)-hirst inverse of-X(3687)
X(60452) = inverse of X(3687) in Steiner circumellipse
X(60452) = pole of the line {3667, 12527} with respect to the incircle of anticomplementary triangle
X(60452) = pole of the line {4296, 20294} with respect to the power circles radical circle
X(60452) = pole of the line {58, 54081} with respect to the Stammler hyperbola
X(60452) = pole of the line {514, 3687} with respect to the Steiner circumellipse
X(60452) = pole of the line {190, 3910} with respect to the Yff parabola
X(60452) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (4358, 5176, 36926), (10327, 12648, 8)

X(60453) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(1), X(9) ) }

Barycentrics    a*((b^2-c^2)*(b-c)*a^3-(3*b^4+2*b^2*c^2+3*c^4)*a^2+(b+c)*(b^2+c^2)*(3*b^2-4*b*c+3*c^2)*a-(b^4+c^4)*(b-c)^2) : :

X(60453) lies on these lines: {1, 6}, {3004, 47712}, {60446, 60460}

X(60454) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(1), X(10) ) }

Barycentrics    a^4+(2*b^2+b*c+2*c^2)*a^2+(b^3+c^3)*a-2*(b^3+c^3)*(b+c) : :

X(60454) lies on these lines: {1, 2}, {3419, 32855}, {3703, 37717}, {3994, 37375}, {4680, 17596}, {5429, 33119}, {5722, 33092}, {5725, 33169}, {17532, 49493}, {28161, 47712}

X(60454) = pole of the line {20294, 59914} with respect to the power circles radical circle

X(60455) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(2), X(3) ) }

Barycentrics    a^6+3*(b^2+c^2)*a^4-(b^4+5*b^2*c^2+c^4)*a^2-3*(b^4-c^4)*(b^2-c^2) : :
X(60455) = 9*X(2)-4*X(23) = 3*X(2)-8*X(858) = 3*X(2)+2*X(5189) = 13*X(2)-8*X(7426) = X(2)+4*X(10989) = 6*X(2)-X(20063) = 3*X(2)-4*X(30745) = 7*X(2)-2*X(37901) = 11*X(2)-6*X(37909) = 3*X(2)+7*X(60456) = 14*X(3)-9*X(35489) = 4*X(3)-9*X(44450) = 2*X(3)+3*X(46450) = X(3)+9*X(60462) = 3*X(4)+2*X(35001) = X(20)+4*X(7574) = 3*X(20)-8*X(37950) = X(23)-6*X(858) = 3*X(23)-8*X(5159) = 2*X(23)+3*X(5189) = X(23)+9*X(10989) = 8*X(23)-3*X(20063) = X(23)-3*X(30745) = 2*X(23)-3*X(37760) = 11*X(23)-6*X(37900) = 14*X(23)-9*X(37901) = X(23)+4*X(46517) = 3*X(193)-8*X(15826) = 8*X(3292)-3*X(14683) = 3*X(3448)+2*X(23061) = X(3448)+4*X(51360) = X(14094)-6*X(51392) = X(23061)-6*X(51360) = 3*X(44367)-8*X(47242) = 13*X(46934)-8*X(51693)

X(60455) lies on these lines: {2, 3}, {193, 15826}, {671, 40343}, {3292, 14683}, {3448, 5965}, {3620, 8705}, {4678, 47492}, {5160, 5274}, {5261, 7286}, {13391, 15027}, {14094, 51392}, {15034, 44407}, {15039, 46114}, {15059, 29317}, {15899, 31125}, {23293, 52987}, {44367, 47242}, {46934, 51693}, {60446, 60447}, {60457, 60463}, {60458, 60464}, {60459, 60465}

X(60455) = midpoint of X(5189) and X(37760)
X(60455) = reflection of X(i) in X(j) for these (i, j): (30745, 858), (37760, 30745), (37923, 632)
X(60455) = anticomplement of X(37760)
X(60455) = X(37760)-Dao conjugate of-X(37760)
X(60455) = perspector of the circumconic through X(648) and X(60210)
X(60455) = inverse of X(3530) in orthoptic circle of Steiner inellipse
X(60455) = pole of the line {523, 3530} with respect to the orthoptic circle of Steiner inellipse
X(60455) = pole of the line {525, 3631} with respect to the Steiner circumellipse
X(60455) = pole of the line {69, 25336} with respect to the Steiner-Wallace hyperbola
X(60455) = reflection of X(23) in the line X(523)X(31209)
X(60455) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (858, 5189, 2), (858, 46517, 23), (1368, 37349, 2), (14002, 16051, 2), (16063, 31857, 2), (30745, 37760, 2), (37900, 47316, 23), (37909, 47097, 2)

X(60456) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(2), X(5) ) }

Barycentrics    3*a^6+5*(b^2+c^2)*a^4-(3*b^4+7*b^2*c^2+3*c^4)*a^2-5*(b^4-c^4)*(b^2-c^2) : :
X(60456) = 15*X(2)-8*X(23) = 3*X(2)+4*X(5189) = X(2)-8*X(10989) = 9*X(2)-2*X(20063) = 11*X(2)-4*X(37901) = 3*X(2)-10*X(60455) = 10*X(5)-3*X(37949) = 2*X(5)-9*X(60462) = 4*X(5)+3*X(60466) = X(20)+6*X(46450) = 3*X(23)-10*X(858) = 2*X(23)+5*X(5189) = 12*X(23)-5*X(20063) = 17*X(23)-10*X(37900) = 3*X(23)+4*X(47095) = X(23)+6*X(47314) = X(23)-8*X(47315) = X(14683)-8*X(51360)

X(60456) lies on these lines: {2, 3}, {14683, 51360}, {60446, 60449}, {60457, 60469}, {60458, 60470}, {60459, 60471}

X(60456) = inverse of X(12108) in orthoptic circle of Steiner inellipse
X(60456) = pole of the line {523, 12108} with respect to the orthoptic circle of Steiner inellipse
X(60456) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (858, 20063, 2), (858, 47095, 23), (5189, 60455, 2), (47314, 47315, 23)

X(60457) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(2), X(6) ) }

Barycentrics    a^6+5*(b^2+c^2)*a^4+(b^4-b^2*c^2+c^4)*a^2-3*(b^2+c^2)*(b^4+c^4) : :

X(60457) lies on these lines: {2, 6}, {316, 20099}, {5189, 60467}, {7813, 14360}, {7903, 8585}, {10415, 31068}, {14931, 50711}, {19570, 31132}, {22121, 28413}, {60446, 60450}, {60455, 60463}, {60456, 60469}, {60458, 60472}, {60459, 60473}

X(60457) = pole of the line {18311, 44445} with respect to the anticomplementary circle

X(60458) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(2), X(7) ) }

Barycentrics    a^6-2*(b+c)*a^5+(b^2+3*b*c+c^2)*a^4-7*(b+c)*b*c*a^3-(b^4+c^4-b*c*(b^2+12*b*c+c^2))*a^2+(b^2-c^2)*(b-c)*(2*b^2+3*b*c+2*c^2)*a-(b^2+c^2)*(b-c)^4 : :

X(60458) lies on these lines: {2, 7}, {5189, 60468}, {30806, 60459}, {60446, 60451}, {60455, 60464}, {60456, 60470}, {60457, 60472}

X(60458) = anticomplement of X(37763)
X(60458) = X(37763)-Dao conjugate of-X(37763)

X(60459) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(2), X(8) ) }

Barycentrics    a^3-(b+c)*a^2+(b^2+3*b*c+c^2)*a-(b^2+c^2)*(b+c) : :
X(60459) = 3*X(2)-4*X(60423)

X(60459) lies on these lines: {1, 2}, {7, 53661}, {12, 31100}, {23, 100}, {120, 4152}, {149, 4358}, {171, 33166}, {210, 2895}, {312, 33110}, {320, 3263}, {329, 53673}, {341, 20060}, {468, 56877}, {497, 46938}, {594, 37675}, {668, 3266}, {750, 33165}, {756, 24697}, {858, 17757}, {956, 40916}, {984, 33086}, {1016, 38310}, {1376, 32862}, {1739, 24164}, {1995, 5687}, {2325, 16548}, {2475, 3701}, {2550, 4671}, {2551, 31106}, {2975, 7496}, {3218, 3717}, {3290, 4727}, {3291, 52959}, {3306, 4901}, {3315, 9053}, {3416, 37656}, {3421, 46336}, {3436, 16063}, {3681, 32863}, {3685, 20095}, {3689, 60354}, {3695, 4239}, {3699, 3936}, {3740, 33075}, {3773, 46918}, {3823, 33129}, {3836, 32927}, {3873, 30615}, {3883, 35595}, {3952, 4645}, {3967, 20292}, {3971, 32948}, {3974, 28605}, {3992, 5080}, {3994, 24715}, {4009, 5057}, {4030, 5284}, {4090, 32949}, {4096, 4683}, {4232, 56876}, {4387, 49719}, {4413, 33089}, {4429, 33155}, {4430, 18141}, {4434, 33115}, {4439, 32845}, {4468, 4778}, {4518, 21739}, {4553, 56878}, {4756, 17768}, {4767, 10712}, {4779, 20075}, {4873, 40131}, {4894, 26127}, {4914, 58451}, {4938, 21805}, {4969, 33854}, {4997, 31126}, {5014, 18743}, {5015, 37162}, {5046, 5300}, {5169, 11681}, {5276, 17369}, {5303, 15246}, {5338, 52301}, {5380, 15899}, {5423, 5905}, {5846, 37680}, {6057, 49732}, {6327, 26792}, {7270, 52353}, {7493, 59591}, {7533, 52367}, {8229, 24808}, {9330, 50295}, {9347, 38047}, {9350, 32855}, {10609, 37449}, {11002, 25304}, {13574, 42713}, {14594, 37798}, {14996, 59406}, {14997, 51192}, {15302, 16975}, {15680, 56311}, {16434, 18526}, {17122, 33162}, {17124, 33169}, {17125, 49506}, {17143, 26235}, {17145, 49707}, {17165, 26842}, {17360, 30758}, {17483, 32937}, {17495, 26073}, {17615, 37781}, {17719, 21026}, {17737, 20483}, {17777, 21282}, {18480, 37456}, {18524, 37959}, {19649, 34773}, {20553, 20947}, {21226, 31088}, {24003, 32844}, {24988, 32922}, {25957, 33153}, {25961, 32920}, {26097, 36926}, {26685, 30653}, {30806, 60458}, {31073, 51583}, {31130, 42697}, {31151, 32856}, {32635, 49716}, {32848, 56009}, {32919, 49693}, {32925, 33102}, {32926, 33150}, {32931, 33112}, {32944, 50288}, {32947, 59517}, {33067, 42054}, {33072, 33107}, {33161, 56010}, {33761, 44419}, {37633, 49524}, {37635, 46897}, {39728, 57925}, {43214, 56564}, {54265, 57077}, {60455, 60465}, {60456, 60471}, {60457, 60473}

X(60459) = reflection of X(7292) in X(60423)
X(60459) = anticomplement of X(7292)
X(60459) = anticomplementary conjugate of the anticomplement of X(34893)
X(60459) = crosssum of X(1015) and X(8650)
X(60459) = X(i)-anticomplementary conjugate of-X(j) for these (i, j): (2748, 513), (5387, 668), (34892, 69), (34893, 8), (51561, 17135)
X(60459) = X(36802)-beth conjugate of-X(46784)
X(60459) = X(i)-Dao conjugate of-X(j) for these (i, j): (9, 7313), (7292, 7292)
X(60459) = X(6)-isoconjugate of-X(7313)
X(60459) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 7313), (5525, 1)
X(60459) = pole of the line {3667, 17781} with respect to the incircle of anticomplementary triangle
X(60459) = pole of the line {44316, 59841} with respect to the nine-point circle
X(60459) = pole of the line {3667, 6684} with respect to the orthoptic circle of Steiner inellipse
X(60459) = pole of the line {34460, 44424} with respect to the Stevanovic circle
X(60459) = pole of the line {514, 2321} with respect to the Steiner circumellipse
X(60459) = pole of the line {190, 4467} with respect to the Yff parabola
X(60459) = barycentric product X(75)*X(5525)
X(60459) = trilinear product X(2)*X(5525)
X(60459) = trilinear quotient X(i)/X(j) for these (i, j): (2, 7313), (5525, 6)
X(60459) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (10, 5297, 2), (100, 3932, 32849), (210, 33078, 2895), (612, 29679, 2), (750, 33165, 33170), (756, 33079, 33083), (1376, 32862, 33168), (3006, 5205, 2), (3836, 32927, 33148), (3952, 4645, 17484), (3971, 32948, 33100), (4009, 5057, 30578), (4358, 32850, 149), (5268, 29667, 2), (5300, 46937, 5046), (6327, 27538, 26792), (7292, 60423, 2), (16830, 26251, 2), (17483, 53660, 32937), (17484, 53672, 3952), (33072, 59511, 33107)

X(60460) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(2), X(9) ) }

Barycentrics    a^6-3*(b+c)*a^5+(7*b^2-b*c+7*c^2)*a^4-2*(b+c)*(5*b^2-b*c+5*c^2)*a^3+(b^2+c^2)*(3*b^2+8*b*c+3*c^2)*a^2+5*(b^4-c^4)*(b-c)*a-3*(b^3-c^3)*(b-c)^3 : :

X(60460) lies on these lines: {2, 7}, {60446, 60453}

X(60461) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(2), X(10) ) }

Barycentrics    3*a^3-2*(b+c)*a^2+3*(2*b^2+b*c+2*c^2)*a-(b+c)*(5*b^2-3*b*c+5*c^2) : :

X(60461) lies on these lines: {1, 2}

X(60461) = pole of the line {20294, 59829} with respect to the power circles radical circle
X(60461) = (X(60446), X(60459))-harmonic conjugate of X(2)

X(60462) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(3), X(5) ) }

Barycentrics    a^10-(4*b^4+11*b^2*c^2+4*c^4)*a^6+(b^2+2*c^2)*(2*b^2+c^2)*(b^2+c^2)*a^4+(3*b^4+4*b^2*c^2+3*c^4)*(b^2-c^2)^2*a^2-2*(b^4-c^4)*(b^2-c^2)^3 : :
X(60462) = 2*X(2)-X(37956) = 3*X(3)-2*X(35489) = X(3)-2*X(44450) = X(3)+2*X(46450) = X(3)-10*X(60455) = 4*X(5)-X(37949) = 2*X(5)+7*X(60456) = 2*X(5)+X(60466) = X(381)+8*X(10989) = X(382)-4*X(3153) = X(382)+2*X(35452) = X(399)-4*X(51392) = 2*X(25739)+X(37496)

X(60462) lies on these lines: {2, 3}, {399, 51392}, {539, 51360}, {1853, 54048}, {5448, 52100}, {6101, 12280}, {9641, 11238}, {10193, 32395}, {12284, 15101}, {12307, 20299}, {13391, 38724}, {25739, 37496}, {32609, 44407}, {60447, 60449}, {60463, 60469}, {60464, 60470}, {60465, 60471}

X(60462) = midpoint of X(i) and X(j) for these (i, j): {5189, 37943}, {44450, 46450}
X(60462) = reflection of X(i) in X(j) for these (i, j): (3, 44450), (5899, 37943), (37943, 37938), (37956, 2)
X(60462) = pole of the line {3, 46440} with respect to the Stammler hyperbola
X(60462) = X(44450)-of-X3-ABC reflections triangle
X(60462) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1656, 5064, 381), (3153, 35452, 382), (16072, 38335, 381)

X(60463) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(3), X(6) ) }

Barycentrics    a^2*(b^2+c^2)^2*(a^4-b^4+b^2*c^2-c^4) : :

X(60463) lies on these lines: {3, 6}, {99, 16095}, {826, 2474}, {1236, 8024}, {3933, 14378}, {6292, 22424}, {7764, 28674}, {7794, 28666}, {7796, 28677}, {7810, 23635}, {7818, 56920}, {7820, 20819}, {8891, 31236}, {39641, 39642}, {39842, 46450}, {60447, 60450}, {60455, 60457}, {60462, 60469}, {60464, 60472}, {60465, 60473}

X(60463) = cross-difference of every pair of points on the line X(251)X(523)
X(60463) = crosspoint of X(141) and X(18019)
X(60463) = crosssum of X(251) and X(18374)
X(60463) = X(i)-Ceva conjugate of-X(j) for these (i, j): (18019, 141), (36827, 57132)
X(60463) = X(i)-Dao conjugate of-X(j) for these (i, j): (141, 9076), (6665, 18019), (7664, 308), (9019, 23), (40583, 52395), (40585, 37221), (52042, 3455)
X(60463) = X(i)-isoconjugate of-X(j) for these {i, j}: {82, 9076}, {251, 37221}, {2157, 52395}
X(60463) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (23, 52395), (38, 37221), (39, 9076), (7794, 18019), (8041, 67), (9019, 83), (18374, 59996), (18715, 3112), (52630, 52936), (59994, 3455)
X(60463) = perspector of the circumconic through X(110) and X(141)
X(60463) = pole of the line {512, 2916} with respect to the circumcircle
X(60463) = pole of the line {512, 23642} with respect to the Moses circle
X(60463) = pole of the line {5996, 9751} with respect to the orthoptic circle of Steiner inellipse
X(60463) = pole of the line {14618, 32085} with respect to the polar circle
X(60463) = pole of the line {512, 23642} with respect to the Brocard inellipse
X(60463) = pole of the line {1634, 2528} with respect to the Kiepert parabola
X(60463) = pole of the line {2, 827} with respect to the Stammler hyperbola
X(60463) = pole of the line {2896, 31296} with respect to the Steiner circumellipse
X(60463) = pole of the line {647, 6292} with respect to the Steiner inellipse
X(60463) = pole of the line {76, 4577} with respect to the Steiner-Wallace hyperbola
X(60463) = barycentric product X(i)*X(j) for these {i, j}: {23, 7794}, {38, 18715}, {141, 9019}, {316, 8041}, {2528, 52630}, {4175, 8744}, {18374, 59995}, {40074, 59994}, {55226, 57132}
X(60463) = trilinear product X(i)*X(j) for these {i, j}: {38, 9019}, {39, 18715}, {8041, 16568}, {20944, 59994}
X(60463) = trilinear quotient X(i)/X(j) for these (i, j): (38, 9076), (141, 37221), (8041, 2157), (9019, 82), (16568, 52395), (18715, 83)
X(60463) = center of circle {{X(110), X(691), X(5189)}}
X(60463) = (X(22424), X(42442))-harmonic conjugate of X(6292)

X(60464) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(3), X(7) ) }

Barycentrics    a^10-2*(b+c)*a^9-(b^2-4*b*c+c^2)*a^8+4*(b^2-c^2)*(b-c)*a^7-(2*b^4+2*c^4+b*c*(4*b-c)*(b-4*c))*a^6+2*(b+c)*(6*b^2-5*b*c+6*c^2)*b*c*a^5+2*(b^2+c^2)*(b^4-10*b^2*c^2+c^4)*a^4-2*(b^2-c^2)*(b-c)*(2*b^4+2*c^4+b*c*(4*b^2+3*b*c+4*c^2))*a^3+(b^4+b^2*c^2+c^4)*(b-c)^4*a^2+2*(b^4-c^4)*(b^2-c^2)^2*(b-c)*a-(b^4-c^4)*(b^2-c^2)*(b-c)^4 : :

X(60464) lies on these lines: {2, 60357}, {3, 7}, {30806, 60465}, {46450, 60468}, {60447, 60451}, {60455, 60458}, {60462, 60470}, {60463, 60472}

X(60464) = anticomplement of X(60357)
X(60464) = X(60357)-Dao conjugate of-X(60357)

X(60465) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(3), X(8) ) }

Barycentrics    a^7-(b+c)*a^6-(b^2-4*b*c+c^2)*a^5+(b^2+c^2)*(b+c)*a^4-(b^4+c^4+b*c*(4*b^2+b*c+4*c^2))*a^3+(b^3+c^3)*(b^2+b*c+c^2)*a^2+(b^4-c^4)*(b^2-c^2)*a-(b^4-c^4)*(b^2-c^2)*(b+c) : :

X(60465) lies on these lines: {2, 38458}, {3, 8}, {72, 5900}, {1330, 3952}, {1532, 38465}, {2475, 15065}, {5080, 46450}, {12532, 15095}, {17751, 56952}, {30806, 60464}, {35489, 56877}, {60447, 60452}, {60455, 60459}, {60462, 60471}, {60463, 60473}

X(60465) = anticomplement of X(38458)
X(60465) = X(38458)-Dao conjugate of-X(38458)
X(60465) = pole of the line {3904, 3969} with respect to the Steiner circumellipse

X(60466) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(4), X(5) ) }

Barycentrics    a^10-(b^2+c^2)*a^8-(2*b^4+11*b^2*c^2+2*c^4)*a^6+2*(b^2+c^2)^3*a^4+(b^4+5*b^2*c^2+c^4)*(b^2-c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)^3 : :
X(60466) = 9*X(2)-8*X(10096) = 3*X(4)-4*X(3153) = X(4)-4*X(5189) = 5*X(4)-8*X(7574) = 11*X(4)-8*X(18325) = 7*X(4)-8*X(18403) = 9*X(4)-8*X(31726) = X(4)-2*X(46450) = 5*X(4)-4*X(52403) = 2*X(5)-X(37949) = 4*X(5)-7*X(60456) = 2*X(5)-3*X(60462) = X(20)-2*X(35452) = 3*X(23)-4*X(44452) = 4*X(140)-3*X(37956) = 8*X(186)-9*X(3524) = 7*X(186)-8*X(16976) = 3*X(186)-4*X(47090) = 3*X(376)-4*X(18859) = 4*X(14157)-5*X(20125) = X(14157)-2*X(51360) = 5*X(20125)-8*X(51360)

X(60466) lies on these lines: {2, 3}, {1154, 12317}, {1899, 48914}, {3357, 32346}, {3410, 13340}, {3448, 13391}, {3818, 54041}, {4846, 38006}, {5080, 60471}, {12325, 37484}, {12383, 44407}, {13203, 18400}, {13434, 17712}, {14157, 20125}, {14677, 36853}, {15045, 48901}, {29012, 43574}, {29323, 51394}, {31383, 43579}, {36987, 41171}, {43808, 45186}, {43818, 44829}, {60448, 60449}, {60467, 60469}, {60468, 60470}

X(60466) = reflection of X(i) in X(j) for these (i, j): (4, 46450), (20, 35452), (403, 46517), (10295, 47091), (13619, 7464), (14157, 51360), (20063, 2070), (37900, 10257), (37924, 37938), (37925, 858), (37945, 2072), (37946, 403), (37949, 5), (46450, 5189), (47093, 47315), (52403, 7574)
X(60466) = anticomplement of X(5899)
X(60466) = anticomplementary conjugate of the anticomplement of X(5900)
X(60466) = circumperp conjugate of X(37126)
X(60466) = X(5900)-anticomplementary conjugate of-X(8)
X(60466) = X(5899)-Dao conjugate of-X(5899)
X(60466) = inverse of X(5) in anticomplementary circle
X(60466) = inverse of X(3861) in Johnson triangle circumcircle
X(60466) = inverse of X(34939) in: nine-point circle, MacBeath inconic
X(60466) = pole of the line {5, 523} with respect to the anticomplementary circle
X(60466) = pole of the line {523, 3861} with respect to the Johnson triangle circumcircle
X(60466) = pole of the line {523, 34939} with respect to the nine-point circle
X(60466) = pole of the line {520, 34942} with respect to the Johnson circumconic
X(60466) = pole of the line {523, 34939} with respect to the MacBeath inconic
X(60466) = X(37949)-of-Johnson triangle
X(60466) = X(46450)-of-anti-Euler triangle
X(60466) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (20, 18570, 376), (376, 7391, 4), (3529, 14790, 4), (14807, 14808, 5), (15682, 18531, 4), (33703, 37444, 4), (37949, 60462, 5)

X(60467) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(4), X(6) ) }

Barycentrics    a^10+(b^2+c^2)*a^8+b^2*c^2*a^6-2*(b^2+c^2)*b^2*c^2*a^4-(b^2-c^2)^2*(b^4+3*b^2*c^2+c^4)*a^2-(b^8-c^8)*(b^2-c^2) : :

X(60467) lies on these lines: {2, 5938}, {4, 6}, {525, 44445}, {1370, 32817}, {5080, 60473}, {5189, 60457}, {7386, 54075}, {7494, 54060}, {12317, 43453}, {18840, 34138}, {37190, 54076}, {39842, 46450}, {60448, 60450}, {60466, 60469}, {60468, 60472}

X(60467) = anticomplement of X(5938)
X(60467) = polar conjugate of the isotomic conjugate of X(28413)
X(60467) = X(5938)-Dao conjugate of-X(5938)
X(60467) = X(28413)-reciprocal conjugate of-X(69)
X(60467) = inverse of X(51540) in anticomplementary circle
X(60467) = pole of the line {6, 525} with respect to the anticomplementary circle
X(60467) = pole of the line {28413, 44436} with respect to the Moses circles radical circle
X(60467) = pole of the line {8057, 34945} with respect to the MacBeath circumconic
X(60467) = pole of the line {6656, 33294} with respect to the Steiner circumellipse
X(60467) = pole of the line {6587, 8364} with respect to the Steiner inellipse
X(60467) = barycentric product X(4)*X(28413)
X(60467) = trilinear product X(19)*X(28413)
X(60467) = trilinear quotient X(28413)/X(63)

X(60468) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(4), X(7) ) }

Barycentrics    a^7-(b+c)*a^6-(b^2-7*b*c+c^2)*a^5+(b+c)*(b^2-4*b*c+c^2)*a^4-(b^2-c^2)^2*a^3+(b^2-c^2)*(b-c)*(b^2+4*b*c+c^2)*a^2+(b^4+c^4-b*c*(5*b^2+8*b*c+5*c^2))*(b-c)^2*a-(b^2-c^2)^3*(b-c) : :

X(60468) lies on these lines: {2, 32625}, {4, 7}, {30, 35454}, {497, 56741}, {3160, 12667}, {3900, 4106}, {4872, 5080}, {5189, 60458}, {5273, 56763}, {5328, 54079}, {7291, 60431}, {17112, 18228}, {37108, 39558}, {46450, 60464}, {60448, 60451}, {60466, 60470}, {60467, 60472}

X(60468) = anticomplement of X(32625)
X(60468) = X(34902)-anticomplementary conjugate of-X(56943)
X(60468) = X(32625)-Dao conjugate of-X(32625)
X(60468) = inverse of X(7) in anticomplementary circle
X(60468) = inverse of X(18482) in Johnson triangle circumcircle
X(60468) = pole of the line {7, 3900} with respect to the anticomplementary circle
X(60468) = pole of the line {3900, 18482} with respect to the Johnson triangle circumcircle
X(60468) = pole of the line {17896, 26563} with respect to the Steiner circumellipse
X(60468) = X(49123)-of-2nd Conway triangle, when ABC is acute

X(60469) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(5), X(6) ) }

Barycentrics    a^10+2*(b^2+c^2)*a^8-(2*b^4+7*b^2*c^2+2*c^4)*a^6-5*(b^2+c^2)*b^2*c^2*a^4+(b^8+c^8+2*b^2*c^2*(b^4+5*b^2*c^2+c^4))*a^2-2*(b^4-c^4)*(b^2-c^2)*(b^4+c^4) : :

X(60469) lies on these lines: {5, 6}, {13175, 37949}, {60449, 60450}, {60456, 60457}, {60462, 60463}, {60466, 60467}, {60470, 60472}, {60471, 60473}

X(60470) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(5), X(7) ) }

Barycentrics    a^10-2*(b+c)*a^9-(b^2+c^2)*a^8+4*(b^3+c^3)*a^7-(2*b^4+2*c^4+b*c*(4*b^2+19*b*c+4*c^2))*a^6+2*(b+c)*(6*b^2+11*b*c+6*c^2)*b*c*a^5+2*(b^6+c^6+(6*b^4+6*c^4-b*c*(21*b^2+4*b*c+21*c^2))*b*c)*a^4-2*(b^2-c^2)*(b-c)*(2*b^4+2*c^4+b*c*(10*b^2+23*b*c+10*c^2))*a^3+(b^6+c^6-2*(5*b^4+5*c^4-b*c*(23*b^2+27*b*c+23*c^2))*b*c)*(b-c)^2*a^2+2*(b^2-c^2)^3*(b-c)*(b^2+4*b*c+c^2)*a-(b^4-c^4)*(b^2-c^2)*(b-c)^4 : :

X(60470) lies on these lines: {5, 7}, {30806, 60471}, {60449, 60451}, {60456, 60458}, {60462, 60464}, {60466, 60468}, {60469, 60472}

X(60471) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(5), X(8) ) }

Barycentrics    a^7-(b+c)*a^6-(b^2+c^2)*a^5+(b+c)*(b^2+c^2)*a^4-(b^4+c^4+b*c*(8*b^2+13*b*c+8*c^2))*a^3+(b+c)*(b^4+13*b^2*c^2+c^4)*a^2+(b^2+8*b*c+c^2)*(b^2-c^2)^2*a-(b^4-c^4)*(b^2-c^2)*(b+c) : :

X(60471) lies on these lines: {5, 8}, {100, 37949}, {5080, 60466}, {30806, 60470}, {60449, 60452}, {60456, 60459}, {60462, 60465}, {60469, 60473}

X(60472) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(6), X(7) ) }

Barycentrics    a^10-2*(b+c)*a^9+(b^2+4*b*c+c^2)*a^8-8*(b+c)*b*c*a^7+(4*b^2+21*b*c+4*c^2)*b*c*a^6-2*(b+2*c)*(2*b+c)*(b+c)*b*c*a^5+18*(b^2+c^2)*b^2*c^2*a^4-2*(b+c)^3*b^2*c^2*a^3-(b^4+3*b^2*c^2+c^4)*(b-c)^4*a^2+2*(b^8-c^8)*(b-c)*a-(b^2+c^2)*(b^4+c^4)*(b-c)^4 : :

X(60472) lies on these lines: {6, 7}, {30806, 60473}, {60450, 60451}, {60457, 60458}, {60463, 60464}, {60467, 60468}, {60469, 60470}

X(60473) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(6), X(8) ) }

Barycentrics    a^7-(b+c)*a^6+(b^2+4*b*c+c^2)*a^5-(b+c)*(b^2+c^2)*a^4+(b^4+c^4+b*c*(4*b^2+3*b*c+4*c^2))*a^3-(b+c)*(b^4+3*b^2*c^2+c^4)*a^2+(b^2+c^2)*(b^4+c^4)*a-(b^2+c^2)*(b+c)*(b^4+c^4) : :

X(60473) lies on these lines: {6, 8}, {5080, 60467}, {30806, 60472}, {60450, 60452}, {60457, 60459}, {60463, 60465}, {60469, 60471}

X(60474) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( X(13), X(14) ) }

Barycentrics    a^8+2*(b^2+c^2)*a^6-11*b^2*c^2*a^4-(b^2+c^2)*(b^4-5*b^2*c^2+c^4)*a^2-2*(b^6-c^6)*(b^2-c^2) : :
X(60474) = 2*X(3506)-3*X(47352)

X(60474) lies on these lines: {6, 13}, {305, 670}, {648, 5064}, {868, 32255}, {3448, 36207}, {3506, 47352}, {4363, 24694}, {5063, 55007}, {7779, 10989}, {7837, 8878}, {18935, 33223}

X(60474) = pole of the line {323, 9407} with respect to the Stammler hyperbola
X(60474) = pole of the line {1495, 7799} with respect to the Steiner-Wallace hyperbola

X(60475) = COMMON POINT OF RADICAL AXES OF { ANTICOMPLEMENTARY CIRCLE, OO( BICENTRIC PAIR PU(11) ) }

Barycentrics    (b^4-c^4)*(2*a^4+(b^2+c^2)*a^2+2*b^2*c^2) : :
X(60475) = X(6)-2*X(54263) = 4*X(141)-3*X(57132)

X(60475) lies on these lines: {6, 54263}, {141, 523}, {826, 41583}, {2528, 33907}, {7927, 35522}

X(60475) = reflection of X(6) in X(54263)
X(60475) = cross-difference of every pair of points on the line X(1691)X(58761)
X(60475) = X(36886)-Ceva conjugate of-X(39)
X(60475) = X(7804)-reciprocal conjugate of-X(4577)
X(60475) = perspector of the circumconic through X(1916) and X(7804)
X(60475) = pole of the line {419, 32581} with respect to the polar circle
X(60475) = pole of the line {7779, 31078} with respect to the Steiner circumellipse
X(60475) = barycentric product X(826)*X(7804)
X(60475) = trilinear product X(7804)*X(8061)
X(60475) = trilinear quotient X(7804)/X(4599)

X(60476) = TRILINEAR POLE OF X(11)X(2447)

Barycentrics    (a - b)*(a - c)*(a + b - c)*(a - b + c)*(a^3*b - a^2*b^2 - a*b^3 + b^4 + a^3*c + a*b^2*c - a^2*c^2 + a*b*c^2 - 2*b^2*c^2 - a*c^3 + c^4 + 2*a*Sqrt[a*b*c*(a^3 - a^2*b - a*b^2 + b^3 - a^2*c + 3*a*b*c - b^2*c - a*c^2 - b*c^2 + c^3)]) : :

X(60476) lies on the cubics K0101 and K013 and these lines: {190, 644}, {390, 3308}, {1381, 47805}

X(60476) = isotomic conjugate of X(60477)
X(60476) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1381, 150}, {2149, 3308}
X(60476) = X(i)-isoconjugate of X(j) for these (i,j): {101, 2446}, {1382, 2590}, {14504, 32669}
X(60476) = X(i)-Dao conjugate of X(j) for these (i,j): {1015, 2446}, {3308, 650}, {55153, 14504}
X(60476) = cevapoint of X(650) and X(3308)
X(60476) = trilinear pole of line {11, 2447}
X(60476) = pole of line {4560, 60477} with respect to the Kiepert circumhyperbola of the anticomplementary triangle
X(60476) = pole of line {100, 1381} with respect to the Steiner circumellipse
X(60476) = pole of line {3035, 3307} with respect to the Steiner inellipse
X(60476) = pole of line {8, 3308} with respect to the Yff parabola
X(60476) = barycentric product X(i)*X(j) for these {i,j}: {668, 2447}, {14503, 54953}
X(60476) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 2446}, {1381, 1382}, {2447, 513}, {2591, 2590}, {2804, 14504}, {3308, 3307}, {14503, 2804}
X(60476) = {X(190),X(2397)}-harmonic conjugate of X(60477)

X(60477) = TRILINEAR POLE OF X(11)X(2446)

Barycentrics    (a - b)*(a - c)*(a + b - c)*(a - b + c)*(a^3*b - a^2*b^2 - a*b^3 + b^4 + a^3*c + a*b^2*c - a^2*c^2 + a*b*c^2 - 2*b^2*c^2 - a*c^3 + c^4 - 2*a*Sqrt[a*b*c*(a^3 - a^2*b - a*b^2 + b^3 - a^2*c + 3*a*b*c - b^2*c - a*c^2 - b*c^2 + c^3)]) : :

X(60477) lies on the cubics K0101 and K013 and these lines: {190, 644}, {390, 3307}, {1382, 47805}

X(60477) = isotomic conjugate of X(60476)
X(60477) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1382, 150}, {2149, 3307}
X(60477) = X(i)-isoconjugate of X(j) for these (i,j): {101, 2447}, {1381, 2591}, {14503, 32669}
X(60477) = X(i)-Dao conjugate of X(j) for these (i,j): {1015, 2447}, {3307, 650}, {55153, 14503}
X(60477) = cevapoint of X(650) and X(3307)
X(60477) = trilinear pole of line {11, 2446}
X(60477) = pole of line {4560, 60476} with respect to the Kiepert circumhyperbola of the anticomplementary triangle
X(60477) = pole of line {100, 1382} with respect to the Steiner circumellipse
X(60477) = pole of line {3035, 3308} with respect to the Steiner inellipse
X(60477) = pole of line {8, 3307} with respect to the Yff parabola
X(60477) = barycentric product X(i)*X(j) for these {i,j}: {668, 2446}, {14504, 54953}
X(60477) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 2447}, {1382, 1381}, {2446, 513}, {2590, 2591}, {2804, 14503}, {3307, 3308}, {14504, 2804}
X(60477) = {X(190),X(2397)}-harmonic conjugate of X(60476)

X(60478) = PERSPECTOR OF CONJUGATE OF MOSES-FEUERBACH CIRCUMHYPERBOLA

Barycentrics    (a - b - c)*(b - c)*(a*b - b^2 + a*c + b*c)*(a*b + a*c + b*c - c^2) : :
X(60478) = 4 X[650] - 3 X[42454]

The Moses-Feuerbach circumhyperbola, H, is introduced here as the hyperbola that passes through the points A, B, C, X(514), and X(522). This hyperbola, given by the barycentric equation

(b + c - a)(b - c)^2 y z + (c + a - b)(c - a)^2 z x + (a + b - c)(a - b) x y = 0,

has center X(650). The perspector of H is the Feuerbach point, X(11), and H is the trilinear pole of X(11) and the line at infinity. The hyperbola H passes through X(i) for these i: 514, 522, 655, 666, 885, 929, 2401, 4391, 4560, 4581, 4582, 17924, 24002, 50039, 56320, 56322, 58838, 58840, 60074, 60476, 60477.

The conjugate of H is the hyperbola H' that has the same center and asymptotes as H. The conjugate of the Moses-Feuerbach circumhyperbola. The hyperbola H', given by

(a - b - c)*(a + b - c)*(a - b + c)*x^2 - 2*(a + b - c)*c^2*x*y + (a - b - c)*(a + b - c)*(a - b + c)*y^2 - 2*b^2*(a - b + c)*x*z + 2*a^2*(a - b - c)*y*z + (a - b - c)*(a + b - c)*(a - b + c)*z^2 = 0,

has center X(650) and perspector X(60478), and it passes through X(i) for these i: 514, 522, 6332, 31605.

X(60478) lies on these lines: {100, 17494}, {514, 44319}, {522, 50518}, {523, 2254}, {650, 5432}, {693, 2886}, {784, 48397}, {2350, 48277}, {2689, 43076}, {2826, 48046}, {3064, 56324}, {3700, 6362}, {4077, 23599}, {4086, 50333}, {4500, 17758}, {4762, 34612}, {4777, 13476}, {8760, 11827}, {9397, 10950}, {15280, 52061}, {17418, 23289}, {23761, 57252}, {24006, 48396}, {26824, 33110}, {35154, 53649}, {47033, 47724}

X(60478) = X(i)-isoconjugate of X(j) for these (i,j): {59, 4040}, {100, 55086}, {109, 1621}, {651, 4251}, {692, 55082}, {1110, 57167}, {1252, 58324}, {1415, 17277}, {2149, 17494}, {3294, 4565}, {3939, 38859}, {4556, 20616}, {4564, 21007}, {4619, 38347}, {7012, 22160}, {14004, 36059}, {23990, 57247}, {31615, 38346}, {53243, 55340}
X(60478) = X(i)-Dao conjugate of X(j) for these (i,j): {11, 1621}, {514, 57167}, {650, 17494}, {661, 58324}, {1086, 55082}, {1146, 17277}, {1577, 20954}, {2968, 3996}, {6615, 4040}, {6741, 4651}, {8054, 55086}, {20620, 14004}, {38991, 4251}, {40615, 33765}, {40617, 38859}, {40624, 17143}, {55064, 3294}
X(60478) = cevapoint of X(4516) and X(21132)
X(60478) = trilinear pole of line {17435, 21044}
X(60478) = crossdifference of every pair of points on line {4251, 55086}
X(60478) = barycentric product X(i)*X(j) for these {i,j}: {11, 54118}, {514, 55076}, {522, 17758}, {650, 40216}, {2350, 35519}, {3700, 39734}, {4041, 40004}, {4086, 39950}, {4391, 13476}, {21044, 53649}
X(60478) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 17494}, {244, 58324}, {514, 55082}, {522, 17277}, {649, 55086}, {650, 1621}, {663, 4251}, {1086, 57167}, {1111, 57247}, {2170, 4040}, {2350, 109}, {3064, 14004}, {3239, 3996}, {3271, 21007}, {3669, 38859}, {3676, 33765}, {3700, 4651}, {4041, 3294}, {4086, 4043}, {4391, 17143}, {4705, 20616}, {4858, 20954}, {7117, 22160}, {13476, 651}, {17758, 664}, {18191, 57148}, {21044, 4151}, {21127, 55340}, {21132, 17761}, {35519, 18152}, {39734, 4573}, {39950, 1414}, {40004, 4625}, {40166, 40619}, {40216, 4554}, {42454, 26846}, {43076, 52378}, {48264, 29773}, {53649, 4620}, {54118, 4998}, {55076, 190}, {55195, 2486}
X(60478) = {X(650),X(15584)}-harmonic conjugate of X(5432)

X(60479) = TRILINEAR POLE OF X(11)X(514)

Barycentrics    (b - c)*(a^2 - 2*a*b + b^2 + a*c + b*c - 2*c^2)*(-a^2 - a*b + 2*b^2 + 2*a*c - b*c - c^2) : :
X(60479) = 5 X[7] - 2 X[23730], X[7] + 2 X[42462], X[23730] + 5 X[42462]

X(60479) lies on the Moses-Feuerbach circumhyperbola, the circumhyperbola {{A,B,C,X(2),X(7)}} and these lines: {2, 522}, {7, 514}, {11, 52333}, {75, 4391}, {86, 4560}, {273, 17924}, {527, 53362}, {655, 37139}, {666, 28132}, {673, 885}, {675, 2291}, {903, 918}, {929, 14733}, {1088, 24002}, {1659, 58840}, {2401, 34056}, {2989, 60047}, {3676, 56274}, {4582, 42720}, {4762, 39704}, {4777, 27475}, {5308, 23757}, {6006, 55937}, {9318, 31992}, {13390, 58838}, {18815, 60074}, {21453, 56322}, {30565, 41798}, {31605, 36620}, {40424, 57066}, {44428, 52781}, {52709, 53583}, {56320, 60041}

X(60479) = reflection of X(57457) in X(35348)
X(60479) = X(15734)-anticomplementary conjugate of X(33650)
X(60479) = X(35157)-Ceva conjugate of X(1156)
X(60479) = X(i)-isoconjugate of X(j) for these (i,j): {9, 23346}, {41, 56543}, {55, 23890}, {100, 1055}, {101, 1155}, {109, 6603}, {527, 692}, {906, 23710}, {919, 35293}, {1110, 1638}, {1252, 14413}, {1262, 14392}, {1415, 6745}, {2149, 6366}, {3939, 6610}, {4564, 6139}, {6068, 36141}, {6174, 32665}, {6510, 8750}, {7115, 14414}, {24685, 34067}, {30806, 32739}, {32656, 37805}, {36059, 60431}, {56763, 57118}
X(60479) = X(i)-Dao conjugate of X(j) for these (i,j): {11, 6603}, {223, 23890}, {478, 23346}, {514, 1638}, {650, 6366}, {661, 14413}, {1015, 1155}, {1086, 527}, {1146, 6745}, {3160, 56543}, {4988, 30574}, {5190, 23710}, {6544, 30573}, {8054, 1055}, {16592, 6647}, {20620, 60431}, {26932, 6510}, {35091, 6068}, {35092, 6174}, {35119, 24685}, {35125, 6594}, {38980, 35293}, {40615, 1323}, {40617, 6610}, {40619, 30806}, {40628, 14414}, {40629, 35110}
X(60479) = cevapoint of X(i) and X(j) for these (i,j): {11, 52334}, {514, 1638}, {650, 3887}, {23893, 35348}
X(60479) = trilinear pole of line {11, 514}
X(60479) = barycentric product X(i)*X(j) for these {i,j}: {11, 35157}, {75, 35348}, {85, 23893}, {514, 1121}, {693, 1156}, {1638, 57565}, {2291, 3261}, {4391, 34056}, {4845, 52621}, {4858, 37139}, {6063, 23351}, {6548, 52746}, {14733, 34387}, {24002, 41798}, {34068, 40495}, {46107, 60047}, {52334, 57563}
X(60479) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 56543}, {11, 6366}, {56, 23346}, {57, 23890}, {244, 14413}, {513, 1155}, {514, 527}, {522, 6745}, {649, 1055}, {650, 6603}, {693, 30806}, {812, 24685}, {900, 6174}, {905, 6510}, {1086, 1638}, {1121, 190}, {1156, 100}, {1638, 35110}, {1647, 30573}, {2254, 35293}, {2291, 101}, {2310, 14392}, {2826, 10427}, {3064, 60431}, {3120, 30574}, {3271, 6139}, {3669, 6610}, {3676, 1323}, {3887, 6594}, {4369, 6647}, {4845, 3939}, {6366, 6068}, {6548, 36887}, {7004, 14414}, {7649, 23710}, {10426, 2742}, {14413, 42082}, {14733, 59}, {17924, 37805}, {23351, 55}, {23893, 9}, {24002, 37780}, {34056, 651}, {34068, 692}, {35157, 4998}, {35348, 1}, {36141, 2149}, {37139, 4564}, {41798, 644}, {42462, 33573}, {42754, 42762}, {43050, 15730}, {52334, 35091}, {52746, 17780}, {53522, 51408}, {55126, 12831}, {60047, 1331}

X(60480) = TRILINEAR POLE OF X(11)X(522)

Barycentrics    (a + b - 2*c)*(a - b - c)*(b - c)*(a - 2*b + c) : :
X(60480) = 3 X[2] - 4 X[21198], 2 X[1022] - 3 X[6548], X[1022] - 3 X[23598], X[2403] - 4 X[4049], X[2403] - 3 X[6548], X[2403] - 6 X[23598], 4 X[4049] - 3 X[6548], 2 X[4049] - 3 X[23598], 3 X[8] - 2 X[4543], X[8] + 2 X[21132], X[4543] + 3 X[21132], 4 X[10015] - X[21222], X[145] - 4 X[21201], 3 X[4391] - 2 X[4944], X[4560] - 4 X[21120], 2 X[764] + X[24128], 5 X[3616] - 2 X[21105], 4 X[3762] - X[49274], X[23764] - 4 X[44314], 2 X[30573] - 3 X[38314]

X(60480) lies on the Moses-Feuerbach circumhyperbola and these lines: {2, 514}, {8, 522}, {11, 52337}, {85, 20949}, {88, 2401}, {92, 4462}, {106, 1311}, {145, 21201}, {257, 28863}, {312, 4391}, {333, 4560}, {519, 53361}, {523, 23352}, {650, 30608}, {655, 3257}, {666, 4555}, {764, 24128}, {885, 1320}, {900, 36593}, {901, 929}, {903, 918}, {1220, 4581}, {1577, 31037}, {1639, 3904}, {1797, 2988}, {2397, 46779}, {2804, 36596}, {3239, 56075}, {3616, 21105}, {3762, 4080}, {3910, 4102}, {4468, 50442}, {4518, 14430}, {4582, 30731}, {4671, 52627}, {4674, 53356}, {4707, 21739}, {4762, 55954}, {4777, 50075}, {4791, 17230}, {4792, 53343}, {4802, 31359}, {4945, 30565}, {6332, 6557}, {6336, 52780}, {7026, 54023}, {7043, 54021}, {7090, 58840}, {7178, 40420}, {7192, 55942}, {14121, 58838}, {16816, 48321}, {17494, 30564}, {17743, 28882}, {17960, 24402}, {18011, 50351}, {18031, 20568}, {21130, 47894}, {21140, 43922}, {21297, 23888}, {23764, 44314}, {23880, 42030}, {23887, 53364}, {25057, 31150}, {28132, 52334}, {28855, 54120}, {30573, 38314}, {30725, 31227}, {32008, 56322}, {40435, 43991}, {42026, 48571}, {47043, 52478}, {47965, 56062}, {48172, 50316}, {48177, 48298}

X(60480) = reflection of X(i) in X(j) for these {i,j}: {1022, 4049}, {2403, 1022}, {3904, 1639}, {4453, 10015}, {6548, 23598}, {21222, 4453}, {30725, 44902}, {47772, 3762}, {47894, 21130}, {48298, 48177}, {49274, 47772}
X(60480) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1168, 150}, {32665, 6224}
X(60480) = X(i)-Ceva conjugate of X(j) for these (i,j): {3257, 4080}, {4555, 1320}, {4582, 4997}
X(60480) = X(i)-isoconjugate of X(j) for these (i,j): {6, 23703}, {44, 109}, {56, 1023}, {57, 23344}, {59, 1635}, {100, 1404}, {101, 1319}, {108, 22356}, {163, 40663}, {214, 32675}, {519, 1415}, {604, 17780}, {651, 902}, {653, 23202}, {664, 2251}, {692, 3911}, {900, 2149}, {906, 1877}, {919, 53531}, {1106, 30731}, {1110, 30725}, {1145, 32669}, {1252, 53528}, {1262, 4895}, {1317, 32665}, {1397, 24004}, {1405, 52924}, {1408, 4169}, {1409, 46541}, {1414, 52963}, {1417, 53582}, {1420, 2429}, {1461, 3689}, {1639, 24027}, {1960, 4564}, {1983, 14584}, {2222, 17455}, {3285, 4551}, {4554, 9459}, {4559, 52680}, {4565, 21805}, {4730, 52378}, {4768, 23979}, {5440, 32674}, {6174, 36141}, {7012, 22086}, {7115, 53532}, {7339, 14427}, {8756, 36059}, {14439, 32735}, {32641, 53530}, {32656, 37790}, {32660, 38462}, {34073, 36920}, {36039, 53529}
X(60480) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 1023}, {9, 23703}, {11, 44}, {115, 40663}, {514, 30725}, {522, 1639}, {650, 900}, {656, 14418}, {661, 53528}, {1015, 1319}, {1086, 3911}, {1146, 519}, {1566, 53529}, {1577, 3762}, {2968, 2325}, {3161, 17780}, {4988, 30572}, {5190, 1877}, {5452, 23344}, {6544, 39771}, {6552, 30731}, {6608, 14427}, {6615, 1635}, {6741, 3943}, {7358, 52978}, {8054, 1404}, {9460, 664}, {20620, 8756}, {35072, 5440}, {35076, 5298}, {35090, 41541}, {35091, 6174}, {35092, 1317}, {35125, 41553}, {35128, 214}, {35508, 3689}, {38980, 53531}, {38983, 22356}, {38984, 17455}, {38991, 902}, {39025, 2251}, {40594, 651}, {40595, 109}, {40608, 52963}, {40624, 4358}, {40625, 16704}, {40626, 3977}, {40628, 53532}, {45247, 2427}, {46398, 52659}, {51402, 4370}, {52871, 53582}, {55062, 52964}, {55064, 21805}, {55067, 52680}, {55153, 1145}, {59577, 4169}
X(60480) = cevapoint of X(i) and X(j) for these (i,j): {11, 52338}, {514, 10015}, {522, 1639}, {650, 3738}, {4530, 21132}, {54021, 54023}
X(60480) = trilinear pole of line {11, 522}
X(60480) = crossdifference of every pair of points on line {902, 1404}
X(60480) = barycentric product X(i)*X(j) for these {i,j}: {8, 6548}, {11, 4555}, {75, 23838}, {88, 4391}, {106, 35519}, {312, 1022}, {314, 55244}, {333, 4049}, {514, 4997}, {522, 903}, {650, 20568}, {663, 57995}, {679, 4768}, {693, 1320}, {901, 34387}, {1086, 4582}, {1639, 54974}, {1797, 46110}, {2316, 3261}, {2403, 6557}, {3257, 4858}, {3596, 23345}, {3699, 6549}, {3738, 57788}, {4080, 4560}, {4397, 56049}, {4453, 36590}, {4516, 4634}, {4615, 21044}, {4674, 18155}, {4895, 57929}, {4944, 40833}, {5376, 40166}, {5548, 23989}, {6332, 6336}, {6635, 7336}, {21183, 36596}, {23598, 30608}, {28660, 55263}, {35518, 36125}, {52338, 57564}, {52356, 52553}
X(60480) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 23703}, {8, 17780}, {9, 1023}, {11, 900}, {29, 46541}, {55, 23344}, {88, 651}, {106, 109}, {244, 53528}, {312, 24004}, {314, 55243}, {346, 30731}, {513, 1319}, {514, 3911}, {521, 5440}, {522, 519}, {523, 40663}, {649, 1404}, {650, 44}, {652, 22356}, {654, 17455}, {663, 902}, {676, 53529}, {900, 1317}, {901, 59}, {903, 664}, {1022, 57}, {1086, 30725}, {1146, 1639}, {1168, 2222}, {1318, 901}, {1320, 100}, {1639, 4370}, {1647, 39771}, {1769, 53530}, {1797, 1813}, {1946, 23202}, {2170, 1635}, {2254, 53531}, {2310, 4895}, {2316, 101}, {2320, 52924}, {2321, 4169}, {2325, 53582}, {2401, 40218}, {2403, 5435}, {2804, 1145}, {2826, 41556}, {2827, 41554}, {3063, 2251}, {3064, 8756}, {3119, 14427}, {3120, 30572}, {3239, 2325}, {3257, 4564}, {3271, 1960}, {3700, 3943}, {3709, 52963}, {3716, 4432}, {3737, 52680}, {3738, 214}, {3837, 24816}, {3887, 41553}, {3900, 3689}, {3904, 51583}, {3907, 4434}, {4041, 21805}, {4049, 226}, {4080, 4552}, {4081, 4528}, {4086, 3992}, {4124, 4448}, {4391, 4358}, {4397, 4723}, {4453, 41801}, {4459, 4922}, {4516, 4730}, {4522, 4439}, {4528, 4152}, {4530, 6544}, {4534, 14425}, {4542, 33922}, {4543, 8028}, {4555, 4998}, {4560, 16704}, {4582, 1016}, {4591, 52378}, {4615, 4620}, {4674, 4551}, {4765, 4700}, {4768, 4738}, {4777, 36920}, {4811, 4742}, {4820, 4727}, {4843, 4819}, {4858, 3762}, {4895, 678}, {4913, 4753}, {4944, 4908}, {4976, 4969}, {4977, 5298}, {4985, 4975}, {4997, 190}, {5376, 31615}, {5548, 1252}, {6332, 3977}, {6336, 653}, {6362, 51463}, {6366, 6174}, {6548, 7}, {6549, 3676}, {6550, 14027}, {6557, 2415}, {7004, 53532}, {7117, 22086}, {7252, 3285}, {7336, 6550}, {7649, 1877}, {8674, 41541}, {8752, 32674}, {9456, 1415}, {10015, 52659}, {10428, 2720}, {14260, 23981}, {15637, 58858}, {17924, 37790}, {18155, 30939}, {20568, 4554}, {21044, 4120}, {21120, 51415}, {21132, 1647}, {23345, 56}, {23352, 2099}, {23598, 5219}, {23836, 56642}, {23838, 1}, {23884, 36913}, {24026, 4768}, {28660, 55262}, {32659, 32660}, {32665, 2149}, {34230, 2283}, {34591, 14418}, {35015, 23757}, {35519, 3264}, {36058, 36059}, {36125, 108}, {36590, 51562}, {36596, 51564}, {36887, 56543}, {39534, 1846}, {42462, 4530}, {43728, 36944}, {43922, 43924}, {44426, 38462}, {45247, 23832}, {46041, 52479}, {46110, 46109}, {46150, 46153}, {52031, 24029}, {52337, 46050}, {52338, 35092}, {52356, 51975}, {53240, 35312}, {53522, 51422}, {53523, 53534}, {53525, 53535}, {53526, 53536}, {53527, 53537}, {54021, 36668}, {54023, 36669}, {55126, 12832}, {55244, 65}, {55263, 1400}, {55376, 33905}, {56049, 934}, {57055, 52978}, {57788, 35174}, {57995, 4572}, {60074, 14628}
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1022, 4049, 6548}, {1022, 23598, 4049}, {2403, 6548, 1022}, {6548, 53362, 46790}

X(60481) = TRILINEAR POLE OF X(11)X(918)

Barycentrics    (b - c)*(-(a*b^3) + b^4 + a^3*c + a*b^2*c - b^3*c - 2*a^2*c^2 + a*c^3)*(a^3*b - 2*a^2*b^2 + a*b^3 + a*b*c^2 - a*c^3 - b*c^3 + c^4) : :
X(60481) = 5 X[31209] - 4 X[40540]

X(60481) lies on the Moses-Feuerbach circumhyperbola and these lines: {2, 885}, {514, 9436}, {522, 3912}, {650, 666}, {693, 35094}, {929, 53607}, {2862, 59049}, {3263, 4391}, {4560, 30941}, {4762, 18821}, {4885, 56365}, {6063, 40166}, {8047, 17494}, {13577, 43991}, {26533, 43974}, {31209, 40540}

X(60481) = midpoint of X(17494) and X(39353)
X(60481) = reflection of X(i) in X(j) for these {i,j}: {666, 650}, {693, 35094}
X(60481) = isotomic conjugate of X(40865)
X(60481) = antitomic conjugate of X(693)
X(60481) = X(i)-isoconjugate of X(j) for these (i,j): {31, 40865}, {101, 5091}, {692, 9318}, {2223, 34906}, {54325, 56896}
X(60481) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 40865}, {1015, 5091}, {1086, 9318}
X(60481) = trilinear pole of line {11, 918}
X(60481) = barycentric product X(i)*X(j) for these {i,j}: {693, 14947}, {918, 53214}, {3261, 9319}, {18031, 34905}, {34387, 53607}
X(60481) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 40865}, {513, 5091}, {514, 9318}, {673, 34906}, {9319, 101}, {14947, 100}, {34905, 672}, {53214, 666}, {53607, 59}, {59049, 919}

X(60482) = TRILINEAR POLE OF X(11)X(1357)

Barycentrics    (b - c)*(-a + b - c)*(a + b - c)*(a^2 - 2*a*b + b^2 + a*c + b*c)*(a^2 + a*b - 2*a*c + b*c + c^2) : :

X(60482) lies on the Moses-Feuerbach circumhyperbola and these lines: {7, 48334}, {514, 37789}, {522, 4318}, {651, 50039}, {666, 6613}, {885, 1476}, {929, 59123}, {3669, 4391}, {3676, 27830}, {4308, 48150}, {4552, 4582}, {4560, 18199}, {5261, 48556}, {5265, 47817}, {5382, 25268}, {7178, 40420}, {8706, 59117}, {18625, 60074}, {24232, 40451}, {48341, 57167}

X(60482) = isotomic conjugate of X(25268)
X(60482) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {3451, 34548}, {59095, 3436}
X(60482) = X(6613)-Ceva conjugate of X(1476)
X(60482) = X(i)-isoconjugate of X(j) for these (i,j): {9, 23845}, {31, 25268}, {33, 23113}, {41, 21272}, {55, 21362}, {100, 2347}, {101, 3057}, {110, 21809}, {163, 21031}, {212, 17906}, {643, 21796}, {644, 1201}, {692, 3452}, {1110, 21120}, {1252, 6615}, {1332, 40982}, {1415, 6736}, {1783, 22072}, {1828, 4587}, {2149, 42337}, {2175, 21580}, {3699, 20228}, {3752, 3939}, {4557, 18163}, {4578, 59173}, {4642, 5546}, {6065, 48334}, {12640, 34080}, {20895, 32739}
X(60482) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 25268}, {115, 21031}, {223, 21362}, {244, 21809}, {478, 23845}, {514, 21120}, {650, 42337}, {661, 6615}, {1015, 3057}, {1086, 3452}, {1146, 6736}, {3160, 21272}, {4521, 14284}, {8054, 2347}, {39006, 22072}, {40593, 21580}, {40615, 3663}, {40617, 3752}, {40619, 20895}, {40620, 17183}, {40621, 12640}, {40622, 4415}, {40837, 17906}, {55060, 21796}
X(60482) = cevapoint of X(i) and X(j) for these (i,j): {514, 3669}, {650, 3667}, {7180, 51662}
X(60482) = trilinear pole of line {11, 1357}
X(60482) = barycentric product X(i)*X(j) for these {i,j}: {7, 56323}, {11, 6613}, {514, 40420}, {664, 40451}, {693, 1476}, {1222, 3676}, {1261, 59941}, {1358, 8706}, {3261, 3451}, {3669, 32017}, {4025, 40446}, {4569, 40528}, {7192, 56173}, {17096, 56258}, {23617, 24002}, {34387, 59123}, {51476, 52621}, {52549, 58817}
X(60482) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 25268}, {7, 21272}, {11, 42337}, {56, 23845}, {57, 21362}, {85, 21580}, {222, 23113}, {244, 6615}, {278, 17906}, {513, 3057}, {514, 3452}, {522, 6736}, {523, 21031}, {649, 2347}, {661, 21809}, {693, 20895}, {1019, 18163}, {1086, 21120}, {1222, 3699}, {1261, 4578}, {1357, 6363}, {1459, 22072}, {1476, 100}, {3451, 101}, {3667, 12640}, {3669, 3752}, {3676, 3663}, {3756, 14284}, {4017, 4642}, {6613, 4998}, {7178, 4415}, {7180, 21796}, {7192, 17183}, {7200, 28006}, {8706, 4076}, {10566, 18086}, {17096, 18600}, {23617, 644}, {24002, 26563}, {30719, 45204}, {30725, 51415}, {32017, 646}, {40420, 190}, {40446, 1897}, {40451, 522}, {40528, 3900}, {43923, 1828}, {43924, 1201}, {43931, 52195}, {43932, 1122}, {51476, 3939}, {51656, 45219}, {52549, 6558}, {53538, 48334}, {56173, 3952}, {56190, 4069}, {56258, 30730}, {56323, 8}, {57181, 20228}, {58817, 52563}, {59123, 59}, {59478, 8706}

X(60483) = TRILINEAR POLE OF X(11)X(3900)

Barycentrics    (a - b - c)*(b - c)*(a^3 - a^2*b - a*b^2 + b^3 - 2*a^2*c + 2*a*b*c - 2*b^2*c + a*c^2 + b*c^2)*(a^3 - 2*a^2*b + a*b^2 - a^2*c + 2*a*b*c + b^2*c - a*c^2 - 2*b*c^2 + c^3) : :

X(60483) lies on the Moses-Feuerbach circumhyperbola and these lines: {2, 24002}, {9, 514}, {200, 522}, {281, 17924}, {346, 4391}, {655, 53337}, {666, 2397}, {885, 2804}, {918, 2401}, {929, 2742}, {2287, 4560}, {4130, 40166}, {4468, 34525}, {4581, 48250}, {4762, 36916}, {6366, 23351}, {6605, 43991}, {30565, 41798}, {36101, 43762}, {36910, 60074}

X(60483) = X(10426)-anticomplementary conjugate of X(150)
X(60483) = X(i)-isoconjugate of X(j) for these (i,j): {101, 3660}, {109, 43065}, {692, 30379}, {1415, 26015}, {1461, 15733}, {2149, 2826}, {10427, 36141}, {32665, 41556}, {32739, 38468}
X(60483) = X(i)-Dao conjugate of X(j) for these (i,j): {11, 43065}, {650, 2826}, {1015, 3660}, {1086, 30379}, {1146, 26015}, {35091, 10427}, {35092, 41556}, {35508, 15733}, {40619, 38468}, {40624, 37788}
X(60483) = cevapoint of X(i) and X(j) for these (i,j): {527, 16578}, {650, 6366}, {21132, 33573}
X(60483) = trilinear pole of line {11, 3900}
X(60483) = barycentric product X(i)*X(j) for these {i,j}: {522, 51567}, {693, 34894}, {2742, 34387}, {3239, 43762}, {4397, 15728}
X(60483) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 2826}, {513, 3660}, {514, 30379}, {522, 26015}, {650, 43065}, {693, 38468}, {885, 56850}, {900, 41556}, {2742, 59}, {3900, 15733}, {4391, 37788}, {6362, 41555}, {6366, 10427}, {10426, 14733}, {15728, 934}, {34894, 100}, {43762, 658}, {51567, 664}

X(60484) = TRILINEAR POLE OF X(11)X(3910)

Barycentrics    (a - b - c)*(b - c)*(-b^3 + a^2*c - a*b*c + a*c^2)*(a^2*b + a*b^2 - a*b*c - c^3) : :

X(60484) lies on the Moses-Feuerbach circumhyperbola and these lines: {2, 4581}, {514, 4357}, {522, 3687}, {666, 35147}, {885, 11609}, {929, 2703}, {2401, 17946}, {4391, 55195}, {11611, 60074}, {17924, 54314}

X(60484) = X(35147)-Ceva conjugate of X(11609)
X(60484) = X(i)-isoconjugate of X(j) for these (i,j): {101, 5061}, {109, 5291}, {1400, 17944}, {1415, 17763}, {2149, 2787}, {4551, 5006}, {4564, 5040}, {17977, 32674}, {17987, 32660}, {17989, 52378}
X(60484) = X(i)-Dao conjugate of X(j) for these (i,j): {11, 5291}, {650, 2787}, {1015, 5061}, {1146, 17763}, {35072, 17977}, {40582, 17944}, {40624, 17790}, {40625, 19623}
X(60484) = trilinear pole of line {11, 3910}
X(60484) = barycentric product X(i)*X(j) for these {i,j}: {11, 35147}, {314, 18015}, {693, 11609}, {2703, 34387}, {4391, 17946}, {4560, 11611}, {17954, 35519}, {17981, 35518}, {18002, 40072}
X(60484) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 2787}, {21, 17944}, {314, 17935}, {513, 5061}, {521, 17977}, {522, 17763}, {650, 5291}, {2703, 59}, {3271, 5040}, {4391, 17790}, {4516, 17989}, {4560, 19623}, {7252, 5006}, {11609, 100}, {11611, 4552}, {17946, 651}, {17954, 109}, {17961, 1415}, {17971, 36059}, {17981, 108}, {18002, 1402}, {18015, 65}, {18155, 5209}, {35147, 4998}, {44426, 17987}, {53689, 8687}, {57680, 23067}

X(60485) = TRILINEAR POLE OF X(11)X(4777)

Barycentrics    (b - c)*(a^3 - 4*a^2*b - a*b^2 + 4*b^3 - a^2*c + 6*a*b*c - b^2*c - a*c^2 - 4*b*c^2 + c^3)*(a^3 - a^2*b - a*b^2 + b^3 - 4*a^2*c + 6*a*b*c - 4*b^2*c - a*c^2 - b*c^2 + 4*c^3) : :

X(60485) lies on the Moses-Feuerbach circumhyperbola and these lines: {514, 5219}, {522, 3679}, {885, 24297}, {1638, 2401}, {4391, 4671}, {4560, 5235}, {4945, 30565}, {5603, 28537}

X(60485) = X(i)-isoconjugate of X(j) for these (i,j): {101, 5126}, {1983, 34232}, {32665, 50843}
X(60485) = X(i)-Dao conjugate of X(j) for these (i,j): {1015, 5126}, {35092, 50843}
X(60485) = trilinear pole of line {11, 4777}
X(60485) = barycentric product X(693)*X(24297)
X(60485) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 5126}, {900, 50843}, {24297, 100}

X(60486) = TRILINEAR POLE OF X(11)X(4977)

Barycentrics    (b - c)*(a^3 - a^2*b - a*b^2 + b^3 + a^2*c + a*b*c + b^2*c - a*c^2 - b*c^2 - c^3)*(-a^3 - a^2*b + a*b^2 + b^3 + a^2*c - a*b*c + b^2*c + a*c^2 - b*c^2 - c^3) : :

X(60486) lies on the Moses-Feuerbach circumhyperbola and these lines: {514, 553}, {522, 1125}, {655, 14147}, {885, 3065}, {929, 34921}, {4359, 4391}, {4560, 8025}, {4707, 21739}, {4977, 24470}

X(60486) = X(i)-isoconjugate of X(j) for these (i,j): {100, 19297}, {101, 484}, {110, 21864}, {662, 58285}, {692, 17484}, {1252, 59837}, {1783, 23071}, {2222, 26744}, {4564, 42657}, {17791, 32739}, {23344, 47058}
X(60486) = X(i)-Dao conjugate of X(j) for these (i,j): {244, 21864}, {661, 59837}, {1015, 484}, {1084, 58285}, {1086, 17484}, {8054, 19297}, {38984, 26744}, {39006, 23071}, {40619, 17791}, {40620, 56935}
X(60486) = cevapoint of X(i) and X(j) for these (i,j): {4988, 53527}, {42462, 53525}
X(60486) = trilinear pole of line {11, 4977}
X(60486) = crossdifference of every pair of points on line {19297, 58285}
X(60486) = barycentric product X(i)*X(j) for these {i,j}: {513, 40716}, {514, 21739}, {693, 3065}, {3261, 19302}, {3904, 26743}, {34387, 34921}
X(60486) = barycentric quotient X(i)/X(j) for these {i,j}: {244, 59837}, {512, 58285}, {513, 484}, {514, 17484}, {649, 19297}, {654, 26744}, {661, 21864}, {693, 17791}, {1022, 47058}, {1459, 23071}, {3065, 100}, {3271, 42657}, {3337, 17404}, {3960, 40612}, {7192, 56935}, {18191, 35055}, {19302, 101}, {21739, 190}, {26743, 655}, {34921, 59}, {40716, 668}, {53314, 6126}

X(60487) = TRILINEAR POLE OF X(7)X(11)

Barycentrics    (a - b)*(a - c)*(a + b - c)^2*(a - b + c)^2*(a^2 - 2*a*b + b^2 + a*c + b*c - 2*c^2)*(a^2 + a*b - 2*b^2 - 2*a*c + b*c + c^2) : :
X(60487) = 2 X[658] - 3 X[59457]

X(60487) lies on the Moses-Feuerbach circumhyperbola and these lines: {7, 3328}, {514, 658}, {522, 664}, {885, 927}, {929, 59105}, {1121, 17078}, {1156, 14189}, {1323, 37757}, {2401, 57455}, {4391, 4554}, {4560, 4573}, {13149, 17924}, {24002, 24011}, {24015, 60074}, {34018, 34056}, {37780, 41798}

X(60487) = reflection of X(658) in the Soddy line
X(60487) = X(i)-isoconjugate of X(j) for these (i,j): {6, 14392}, {9, 6139}, {41, 6366}, {220, 14413}, {527, 8641}, {607, 14414}, {657, 1155}, {663, 6603}, {692, 33573}, {1055, 3900}, {1110, 52334}, {1253, 1638}, {1323, 57180}, {1946, 60431}, {3022, 23890}, {3063, 6745}, {3119, 23346}, {4105, 6610}
X(60487) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 14392}, {478, 6139}, {514, 52334}, {1086, 33573}, {3160, 6366}, {10001, 6745}, {17113, 1638}, {39053, 60431}, {40629, 35091}, {59608, 30574}
X(60487) = cevapoint of X(i) and X(j) for these (i,j): {7, 1638}, {514, 1323}, {650, 15726}, {52334, 55370}
X(60487) = trilinear pole of line {7, 11}
X(60487) = barycentric product X(i)*X(j) for these {i,j}: {7, 35157}, {85, 37139}, {658, 1121}, {1156, 4569}, {1638, 57563}, {2291, 46406}, {4554, 34056}, {4845, 52937}, {6063, 14733}, {20567, 36141}, {32728, 41283}, {34387, 59105}, {36838, 41798}
X(60487) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 14392}, {7, 6366}, {56, 6139}, {77, 14414}, {269, 14413}, {279, 1638}, {514, 33573}, {651, 6603}, {653, 60431}, {658, 527}, {664, 6745}, {934, 1155}, {1086, 52334}, {1121, 3239}, {1156, 3900}, {1461, 1055}, {1638, 35091}, {2291, 657}, {3668, 30574}, {4569, 30806}, {4617, 6610}, {4626, 1323}, {4845, 4105}, {7339, 23346}, {13149, 37805}, {14733, 55}, {18889, 57180}, {23351, 3022}, {23893, 3119}, {32728, 2175}, {34056, 650}, {34068, 8641}, {35157, 8}, {35348, 2310}, {36118, 23710}, {36141, 41}, {36838, 37780}, {37139, 9}, {37141, 56763}, {41353, 35293}, {41798, 4130}, {52746, 4528}, {56543, 6068}, {59105, 59}, {59457, 56543}, {60047, 57108}

X(60488) = TRILINEAR POLE OF X(9)X(11)

Barycentrics    (a - b)*(a - c)*(a - b - c)*(a^2 + a*b + b^2 - 2*a*c - 2*b*c + c^2)*(a^2 - 2*a*b + b^2 + a*c - 2*b*c + c^2) : :

X(60488) lies on the Moses-Feuerbach circumhyperbola and these lines: {100, 514}, {519, 1280}, {522, 644}, {643, 4560}, {664, 24002}, {765, 56322}, {1026, 51562}, {1120, 32922}, {1320, 3254}, {1897, 17924}, {2398, 2401}, {2742, 2826}, {3699, 4391}, {3904, 36802}, {3935, 30806}, {4427, 56320}, {4511, 14942}, {4581, 36147}, {5199, 6745}, {5548, 53523}, {6065, 6362}

X(60488) = X(35171)-Ceva conjugate of X(37143)
X(60488) = X(i)-isoconjugate of X(j) for these (i,j): {6, 43050}, {7, 8645}, {56, 3887}, {57, 22108}, {513, 2078}, {604, 30565}, {649, 37787}, {663, 38459}, {1308, 47007}, {3063, 37757}, {3669, 5526}, {3676, 19624}, {3935, 43924}, {17264, 57181}, {23345, 41553}, {32669, 57435}, {36141, 40629}
X(60488) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 3887}, {9, 43050}, {3161, 30565}, {5375, 37787}, {5452, 22108}, {10001, 37757}, {35091, 40629}, {39026, 2078}, {55153, 57435}
X(60488) = cevapoint of X(i) and X(j) for these (i,j): {1, 2826}, {522, 6745}, {650, 15733}, {3900, 60419}
X(60488) = trilinear pole of line {9, 11}
X(60488) = barycentric product X(i)*X(j) for these {i,j}: {8, 37143}, {9, 35171}, {190, 3254}, {312, 1308}, {3699, 34578}, {4554, 42064}
X(60488) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 43050}, {8, 30565}, {9, 3887}, {41, 8645}, {55, 22108}, {100, 37787}, {101, 2078}, {644, 3935}, {651, 38459}, {664, 37757}, {1023, 41553}, {1308, 57}, {2804, 57435}, {3254, 514}, {3699, 17264}, {3939, 5526}, {6366, 40629}, {15734, 35348}, {22108, 47007}, {34578, 3676}, {35171, 85}, {37143, 7}, {42064, 650}, {56183, 60355}

X(60489) = TRILINEAR POLE OF X(11)X(6362)

Barycentrics    b*(b - c)*c*(-a + b + c)*(a^2 + a*b + b^2 - 2*a*c - 2*b*c + c^2)*(a^2 - 2*a*b + b^2 + a*c - 2*b*c + c^2) : :

X(60489) lies on the Moses-Feuerbach circumhyperbola and these lines: {2, 56322}, {142, 514}, {522, 4847}, {655, 1025}, {666, 4585}, {885, 3254}, {918, 60074}, {929, 1308}, {1229, 4391}, {2401, 34578}, {4560, 16713}, {4978, 56320}, {24002, 59181}

X(60489) = X(35171)-Ceva conjugate of X(3254)
X(60489) = X(i)-isoconjugate of X(j) for these (i,j): {59, 22108}, {101, 2078}, {109, 5526}, {651, 19624}, {692, 37787}, {1110, 43050}, {1415, 3935}, {2149, 3887}, {4564, 8645}, {6594, 36141}, {32665, 41553}, {36059, 60355}
X(60489) = X(i)-Dao conjugate of X(j) for these (i,j): {11, 5526}, {514, 43050}, {650, 3887}, {1015, 2078}, {1086, 37787}, {1146, 3935}, {1577, 30565}, {6615, 22108}, {20620, 60355}, {35091, 6594}, {35092, 41553}, {38991, 19624}, {40615, 38459}, {40624, 17264}, {40629, 15730}
X(60489) = trilinear pole of line {11, 6362}
X(60489) = barycentric product X(i)*X(j) for these {i,j}: {11, 35171}, {693, 3254}, {1308, 34387}, {4391, 34578}, {4858, 37143}, {42064, 52621}
X(60489) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 3887}, {513, 2078}, {514, 37787}, {522, 3935}, {650, 5526}, {663, 19624}, {900, 41553}, {1086, 43050}, {1308, 59}, {1638, 15730}, {2170, 22108}, {3064, 60355}, {3254, 100}, {3271, 8645}, {3676, 38459}, {4391, 17264}, {4858, 30565}, {6366, 6594}, {24002, 37757}, {34578, 651}, {35171, 4998}, {37143, 4564}, {42064, 3939}

X(60490) = TRILINEAR POLE OF X(11)X(3835)

Barycentrics    (b - c)*(a^3*b - 2*a^2*b^2 + a*b^3 + a^3*c + b^3*c - a^2*c^2 - b^2*c^2)*(-(a^3*b) + a^2*b^2 - a^3*c + 2*a^2*c^2 + b^2*c^2 - a*c^3 - b*c^3) : :

X(60490) lies on the Moses-Feuerbach circumhyperbola and these lines: {192, 522}, {514, 3212}, {659, 885}, {2254, 40848}, {3287, 56322}, {4391, 6376}, {4560, 33296}, {9311, 29226}, {17092, 24002}, {17494, 52136}, {41527, 48008}

X(60490) = X(i)-isoconjugate of X(j) for these (i,j): {100, 20459}, {101, 20358}, {110, 20706}, {163, 20486}, {692, 20335}, {1110, 20507}, {1783, 20731}, {20435, 32739}
X(60490) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 20486}, {244, 20706}, {514, 20507}, {1015, 20358}, {1086, 20335}, {8054, 20459}, {39006, 20731}, {40619, 20435}
X(60490) = cevapoint of X(i) and X(j) for these (i,j): {514, 665}, {650, 812}
X(60490) = trilinear pole of line {11, 3835}
X(60490) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 20358}, {514, 20335}, {523, 20486}, {649, 20459}, {661, 20706}, {693, 20435}, {1086, 20507}, {1459, 20731}

X(60491) = TRILINEAR POLE OF X(11)X(52305)

Barycentrics    (a - b - c)*(b - c)^2*(a^3 - a^2*b - a*b^2 + b^3 - a^2*c - b^2*c + 2*a*c^2 + 2*b*c^2 - 2*c^3)*(a^3 - a^2*b + 2*a*b^2 - 2*b^3 - a^2*c + 2*b^2*c - a*c^2 - b*c^2 + c^3) : :

X(60491) lies on the Moses-Feuerbach circumhyperbola and these lines: {2, 666}, {7, 655}, {11, 885}, {141, 50039}, {346, 4582}, {514, 4089}, {545, 46791}, {840, 929}, {952, 14191}, {1111, 60074}, {2401, 4904}, {59021, 60354}

X(60491) = X(i)-isoconjugate of X(j) for these (i,j): {59, 2246}, {109, 52985}, {528, 2149}, {1110, 5723}, {2283, 52227}, {7045, 52969}
X(60491) = X(i)-Dao conjugate of X(j) for these (i,j): {11, 52985}, {514, 5723}, {650, 528}, {3126, 1642}, {6615, 2246}, {17115, 52969}, {40624, 42722}, {52873, 35113}
X(60491) = cevapoint of X(i) and X(j) for these (i,j): {11, 52946}, {1086, 57442}, {14393, 52304}
X(60491) = trilinear pole of line {11, 52305}
X(60491) = barycentric product X(i)*X(j) for these {i,j}: {11, 18821}, {840, 34387}, {4858, 37131}
X(60491) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 528}, {650, 52985}, {840, 59}, {1024, 52227}, {1086, 5723}, {2170, 2246}, {4391, 42722}, {14936, 52969}, {17435, 1642}, {18821, 4998}, {37131, 4564}, {52228, 1025}, {52946, 35113}, {59021, 59101}

X(60492) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(42)X(604)

Barycentrics    (a - b - c)*(b - c)*(a^2 + 2*a*b + b^2 + 2*a*c + c^2) : :
X(60492) = 2 X[1019] - 3 X[4786], 3 X[4025] - 4 X[21192], 3 X[4750] - X[48341], X[17496] - 3 X[27486], 2 X[905] - 3 X[47785], 2 X[3239] - 3 X[47793], 4 X[4129] - 3 X[47786], 4 X[4521] - 3 X[57066], 2 X[4978] - 3 X[21183], 3 X[21183] - 4 X[21188], 2 X[4992] - 3 X[48555], 4 X[7658] - 3 X[47796], 2 X[8045] - 3 X[47766], 2 X[14349] - 3 X[47783], 2 X[30719] - 3 X[44550], 2 X[30723] - 3 X[44551], X[47719] - 3 X[47836], 3 X[47886] - X[48334]

X(60492) lies on the conjugate of the Moses-Feuerbach circumhyperbola and these lines: {10, 29190}, {239, 514}, {449, 525}, {512, 48006}, {522, 3717}, {650, 3910}, {661, 28478}, {693, 14837}, {824, 47130}, {905, 3310}, {918, 47921}, {1577, 25007}, {3004, 8712}, {3239, 27526}, {3309, 48014}, {3566, 48029}, {3669, 17069}, {3676, 4801}, {3700, 20317}, {3810, 4913}, {3900, 50347}, {4129, 47786}, {4142, 47123}, {4151, 21185}, {4462, 4467}, {4521, 57066}, {4705, 48039}, {4729, 47972}, {4762, 7178}, {4885, 48280}, {4976, 21120}, {4978, 21183}, {4992, 48555}, {6050, 48290}, {7649, 57215}, {7658, 47796}, {8045, 47766}, {10015, 23882}, {11068, 48300}, {14349, 47783}, {14838, 26641}, {17072, 49285}, {23876, 48003}, {23879, 33294}, {28468, 47883}, {28481, 48035}, {28487, 48017}, {28493, 49284}, {28846, 47918}, {29017, 48062}, {29078, 48401}, {29142, 48069}, {29200, 48040}, {29202, 48056}, {29302, 50453}, {29312, 50504}, {30719, 44550}, {30723, 44551}, {47719, 47836}, {47886, 48334}, {47955, 48034}, {47959, 48038}, {47966, 48036}, {47995, 48402}

X(60492) = midpoint of X(i) and X(j) for these {i,j}: {4462, 4467}, {4498, 21124}, {4729, 47972}, {4976, 21120}, {23755, 47926}
X(60492) = reflection of X(i) in X(j) for these {i,j}: {693, 14837}, {3669, 17069}, {3700, 20317}, {4468, 47965}, {4560, 4765}, {4801, 3676}, {4978, 21188}, {6332, 650}, {44448, 4041}, {47123, 4142}, {47995, 48402}, {48034, 47955}, {48036, 47966}, {48038, 47959}, {48039, 4705}, {48060, 4063}, {48069, 50501}, {48144, 3798}, {48268, 1577}, {48280, 4885}, {48290, 6050}, {48300, 11068}, {49285, 17072}
X(60492) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {937, 150}, {2255, 149}, {58957, 962}, {58991, 69}
X(60492) = X(i)-isoconjugate of X(j) for these (i,j): {37, 59069}, {692, 60076}, {1415, 59760}
X(60492) = X(i)-Dao conjugate of X(j) for these (i,j): {1086, 60076}, {1146, 59760}, {40589, 59069}
X(60492) = crossdifference of every pair of points on line {42, 604}
X(60492) = barycentric product X(i)*X(j) for these {i,j}: {8, 47995}, {314, 50332}, {333, 48402}, {514, 14555}, {522, 17321}, {693, 5250}, {3261, 4254}, {3931, 18155}, {4025, 4194}, {4391, 5256}, {7713, 35518}, {16466, 35519}, {28660, 50492}, {44426, 54404}
X(60492) = barycentric quotient X(i)/X(j) for these {i,j}: {58, 59069}, {514, 60076}, {522, 59760}, {3931, 4551}, {4194, 1897}, {4254, 101}, {5250, 100}, {5256, 651}, {7713, 108}, {14555, 190}, {16466, 109}, {17321, 664}, {47995, 7}, {48402, 226}, {50332, 65}, {50492, 1400}, {54404, 6516}
X(60492) = {X(4978),X(21188)}-harmonic conjugate of X(21183)

X(60493) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1193)X(2268)

Barycentrics    (b - c)*(a^4 + 4*a^3*b + 2*a^2*b^2 + b^4 + 4*a^3*c + 2*a^2*b*c + 4*a*b^2*c + 2*b^3*c + 2*a^2*c^2 + 4*a*b*c^2 + 2*b^2*c^2 + 2*b*c^3 + c^4) : :
X(60493) = 2 X[21172] - 3 X[47820], 3 X[47787] - 2 X[50331]

X(60493) lies on the conjugate of the Moses-Feuerbach circumhyperbola and these lines: {513, 6332}, {514, 4017}, {522, 649}, {647, 48006}, {3667, 8045}, {4468, 8672}, {7661, 47708}, {21172, 47820}, {23800, 48015}, {31605, 43067}, {47787, 50331}, {47995, 50330}, {48039, 52355}

X(60493) = reflection of X(i) in X(j) for these {i,j}: {47708, 7661}, {47995, 50330}, {48015, 23800}, {48039, 52355}
X(60493) = crossdifference of every pair of points on line {1193, 2268}

X(60494) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(25)X(48)

Barycentrics    (b - c)*(a^2 - b^2 - c^2)*(a^4 - 2*a^2*b^2 + b^4 - 4*a^2*b*c - 2*a^2*c^2 - 2*b^2*c^2 + c^4) : :

X(60495) lies on the conjugate of the Moses-Feuerbach circumhyperbola and these lines: {240, 522}, {441, 525}, {514, 652}, {1021, 57073}, {4077, 21188}, {7658, 21192}, {10015, 23882}, {17926, 57224}, {23146, 57223}, {23806, 29216}, {41800, 47787}, {45745, 46382}

X(60494) = midpoint of X(i) and X(j) for these {i,j}: {652, 57243}, {4025, 57245}
X(60494) = reflection of X(i) in X(j) for these {i,j}: {4077, 21188}, {17924, 14837}
X(60494) = X(i)-complementary conjugate of X(j) for these (i,j): {2219, 124}, {58987, 960}
X(60494) = X(i)-isoconjugate of X(j) for these (i,j): {3, 58965}, {19, 58992}, {101, 55105}, {32656, 55107}, {32739, 55106}
X(60494) = X(i)-Dao conjugate of X(j) for these (i,j): {6, 58992}, {1015, 55105}, {31653, 1}, {36103, 58965}, {40619, 55106}, {49183, 1783}
X(60494) = crossdifference of every pair of points on line {25, 48}
X(60494) = barycentric product X(i)*X(j) for these {i,j}: {514, 26872}, {664, 26956}, {693, 55104}, {3085, 4025}, {3265, 37383}, {3553, 15413}, {19349, 35519}, {35518, 37550}
X(60494) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 58992}, {19, 58965}, {513, 55105}, {693, 55106}, {3085, 1897}, {3553, 1783}, {17924, 55107}, {19349, 109}, {26872, 190}, {26956, 522}, {37383, 107}, {37550, 108}, {55104, 100}

X(60495) = X(6)X(66)∩X(39)X(184)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^4 + b^4 - c^4)*(a^4 - b^4 + c^4) : :

X(60495) lies on the cubic K1352 and these lines: {2, 34137}, {3, 22075}, {4, 56364}, {6, 66}, {22, 46243}, {25, 38356}, {39, 184}, {69, 28412}, {125, 42295}, {157, 58358}, {262, 16277}, {275, 40814}, {287, 1993}, {305, 20806}, {394, 441}, {426, 577}, {1289, 26717}, {1409, 2156}, {1501, 3269}, {1843, 22262}, {3049, 23616}, {3051, 14003}, {3060, 10766}, {3167, 22146}, {3173, 23137}, {3289, 41168}, {3796, 54060}, {3978, 40421}, {5359, 34237}, {5422, 37801}, {6776, 34945}, {8041, 14585}, {11206, 13509}, {11427, 56347}, {14533, 16030}, {14580, 53851}, {17409, 34146}, {18396, 44415}, {18877, 46147}, {19125, 39951}, {29011, 58113}, {32064, 41363}, {35264, 35901}, {41382, 54384}, {41580, 52905}

X(60495) = isogonal conjugate of X(17907)
X(60495) = isogonal conjugate of the isotomic conjugate of X(14376)
X(60495) = isotomic conjugate of the polar conjugate of X(2353)
X(60495) = isogonal conjugate of the polar conjugate of X(66)
X(60495) = X(i)-Ceva conjugate of X(j) for these (i,j): {66, 2353}, {40404, 14376}
X(60495) = X(i)-isoconjugate of X(j) for these (i,j): {1, 17907}, {4, 1760}, {19, 315}, {22, 92}, {25, 20641}, {27, 4463}, {28, 4150}, {33, 17076}, {63, 52448}, {75, 8743}, {127, 24000}, {158, 20806}, {162, 33294}, {206, 1969}, {240, 31636}, {264, 2172}, {278, 4123}, {281, 7210}, {286, 4456}, {561, 17409}, {662, 59932}, {811, 2485}, {823, 8673}, {1096, 34254}, {1577, 52915}, {1783, 21178}, {1897, 16757}, {1973, 40073}, {3112, 40938}, {4548, 57787}, {4611, 24006}, {10316, 57806}, {11605, 16568}, {11610, 40703}, {16715, 18082}, {17453, 18022}, {21034, 57796}, {23999, 38356}, {24019, 57069}, {34055, 41375}, {36126, 58359}
X(60495) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 17907}, {6, 315}, {125, 33294}, {206, 8743}, {1084, 59932}, {1147, 20806}, {3162, 52448}, {6337, 40073}, {6503, 34254}, {6505, 20641}, {17423, 2485}, {22391, 22}, {34452, 40938}, {34467, 16757}, {35071, 57069}, {36033, 1760}, {39006, 21178}, {39085, 31636}, {40368, 17409}, {40591, 4150}, {46093, 58359}
X(60495) = cevapoint of X(i) and X(j) for these (i,j): {3, 23163}, {3049, 3269}, {22383, 22432}
X(60495) = trilinear pole of line {23228, 39201}
X(60495) = crossdifference of every pair of points on line {8673, 33294}
X(60495) = barycentric product X(i)*X(j) for these {i,j}: {3, 66}, {6, 14376}, {39, 40404}, {54, 41168}, {63, 2156}, {67, 54060}, {69, 2353}, {95, 27372}, {141, 46765}, {184, 18018}, {248, 34138}, {305, 40146}, {394, 13854}, {520, 1289}, {577, 43678}, {647, 44766}, {2525, 58113}, {3269, 44183}, {3917, 16277}, {9247, 46244}, {14575, 40421}, {15388, 15526}
X(60495) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 315}, {6, 17907}, {25, 52448}, {32, 8743}, {48, 1760}, {63, 20641}, {66, 264}, {69, 40073}, {71, 4150}, {184, 22}, {212, 4123}, {222, 17076}, {228, 4463}, {248, 31636}, {394, 34254}, {512, 59932}, {520, 57069}, {577, 20806}, {603, 7210}, {647, 33294}, {1289, 6528}, {1459, 21178}, {1501, 17409}, {1576, 52915}, {1843, 41375}, {2156, 92}, {2200, 4456}, {2353, 4}, {3049, 2485}, {3051, 40938}, {3269, 127}, {3455, 11605}, {4558, 55225}, {9247, 2172}, {13854, 2052}, {14376, 76}, {14575, 206}, {14585, 10316}, {14600, 11610}, {15388, 23582}, {16277, 46104}, {18018, 18022}, {20775, 3313}, {20975, 53569}, {22075, 36414}, {22383, 16757}, {23208, 59165}, {27369, 27373}, {27372, 5}, {32320, 58359}, {32661, 4611}, {34138, 44132}, {34980, 47413}, {39201, 8673}, {39643, 28405}, {40146, 25}, {40373, 20968}, {40404, 308}, {40421, 44161}, {40947, 41761}, {41168, 311}, {43678, 18027}, {44766, 6331}, {46765, 83}, {54060, 316}, {58113, 42396}
{X(3),X(22135)}-harmonic conjugate of X(22075)

X(60496) = X(2)X(17708)∩X(6)X(67)

Barycentrics    (a^4 - a^2*b^2 + b^4 - c^4)*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*(a^4 - b^4 - a^2*c^2 + c^4) : :

X(60496) lies on the cubic K1352 and these lines: {2, 17708}, {4, 1554}, {6, 67}, {39, 647}, {262, 10511}, {935, 6794}, {1650, 3284}, {1990, 58261}, {2420, 51360}, {3148, 3455}, {3258, 35906}, {5024, 15900}, {5063, 32663}, {5967, 10415}, {13366, 59175}, {14356, 23588}, {15048, 46338}, {18019, 59771}, {23292, 57496}, {40814, 43530}, {51254, 57431}, {53955, 58953}

X(60496) = X(i)-isoconjugate of X(j) for these (i,j): {23, 2349}, {74, 16568}, {316, 2159}, {9979, 36034}, {18374, 33805}, {20944, 40352}, {22151, 36119}, {35200, 37765}
X(60496) = X(i)-Dao conjugate of X(j) for these (i,j): {133, 37765}, {1511, 22151}, {3163, 316}, {3258, 9979}, {15900, 1494}
X(60496) = cevapoint of X(i) and X(j) for these (i,j): {2682, 14398}, {5642, 51360}
X(60496) = crossdifference of every pair of points on line {23, 9517}
X(60496) = barycentric product X(i)*X(j) for these {i,j}: {30, 67}, {935, 9033}, {1495, 18019}, {1637, 17708}, {1990, 34897}, {2157, 14206}, {3260, 3455}, {3284, 46105}, {5642, 10415}, {8791, 11064}, {9076, 51360}, {9214, 14357}, {10511, 13857}
X(60496) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 316}, {67, 1494}, {935, 16077}, {1495, 23}, {1637, 9979}, {1990, 37765}, {2157, 2349}, {2173, 16568}, {2407, 55226}, {2420, 52630}, {2682, 5099}, {3260, 40074}, {3284, 22151}, {3455, 74}, {5642, 7664}, {6357, 17088}, {8791, 16080}, {9214, 52551}, {9407, 18374}, {9408, 52951}, {9409, 9517}, {11064, 37804}, {11125, 21205}, {14206, 20944}, {14357, 36890}, {14398, 2492}, {14581, 8744}, {14583, 52449}, {23347, 52916}, {59175, 9717}

X(60497) = X(6)X(3613)∩X(39)X(51)

Barycentrics    a^2*(a^4 - a^2*b^2 - a^2*c^2 - 2*b^2*c^2)*(a^2*b^2 - b^4 + a^2*c^2 + b^2*c^2)*(a^2*b^2 + a^2*c^2 + b^2*c^2 - c^4) : :

X(60497) lies on the cubic K1352 and these lines: {2, 36952}, {4, 30505}, {6, 3613}, {39, 51}, {217, 7753}, {3051, 7755}, {3289, 54002}, {14096, 59208}, {14957, 41334}, {14994, 59197}

X(60497) = X(i)-isoconjugate of X(j) for these (i,j): {262, 18042}, {263, 33764}, {1078, 2186}, {3402, 33769}, {33778, 46319}
X(60497) = X(i)-Dao conjugate of X(j) for these (i,j): {38997, 31296}, {51580, 33769}
X(60497) = crossdifference of every pair of points on line {11450, 31296}
X(60497) = barycentric product X(i)*X(j) for these {i,j}: {182, 3613}, {183, 27375}, {3288, 11794}, {10311, 36952}, {14096, 30505}, {33971, 42487}
X(60497) = barycentric quotient X(i)/X(j) for these {i,j}: {182, 1078}, {183, 33769}, {3288, 31296}, {3403, 33778}, {3613, 327}, {6784, 7668}, {10311, 36794}, {23878, 57082}, {27375, 262}, {33971, 54100}, {34396, 5012}, {42487, 59257}, {52134, 33764}, {53701, 53196}

X(60498) = X(4)X(1499)∩X(6)X(110)

Barycentrics    a^2*(a^2 + b^2 - 2*c^2)*(a^2 - 2*b^2 + c^2)*(a^4*b^2 - 2*a^2*b^4 + b^6 + a^4*c^2 + 2*a^2*b^2*c^2 - b^4*c^2 - 2*a^2*c^4 - b^2*c^4 + c^6) : :

X(60498) lies on the cubic K1352 and these lines: {4, 1499}, {6, 110}, {25, 32729}, {39, 51253}, {51, 51980}, {262, 9745}, {511, 52152}, {671, 34289}, {858, 1648}, {1351, 32583}, {1993, 57491}, {2088, 14609}, {2393, 46589}, {2433, 9213}, {3003, 15329}, {3053, 36830}, {3060, 36827}, {3148, 14908}, {3260, 52756}, {5422, 57481}, {7464, 13192}, {9139, 52933}, {9159, 44526}, {9777, 10558}, {9969, 51962}, {9971, 52197}, {11002, 46783}, {11433, 36894}, {11477, 53770}, {12099, 44468}, {17810, 52142}, {20423, 52232}, {31133, 36821}, {34320, 54131}, {35188, 40119}, {37644, 51405}, {41512, 56403}, {52451, 55265}

X(60498) = X(i)-isoconjugate of X(j) for these (i,j): {524, 36053}, {896, 2986}, {922, 40832}, {2642, 18878}, {14210, 14910}, {14417, 36114}, {15328, 23889}, {51653, 56103}
X(60498) = X(i)-Dao conjugate of X(j) for these (i,j): {113, 524}, {2088, 45808}, {15477, 14910}, {15899, 2986}, {34834, 3266}, {39005, 14417}, {39021, 35522}, {39061, 40832}
X(60498) = trilinear pole of line {3003, 21731}
X(60498) = crossdifference of every pair of points on line {690, 3292}
X(60498) = barycentric product X(i)*X(j) for these {i,j}: {111, 3580}, {113, 9139}, {403, 895}, {671, 3003}, {691, 55121}, {892, 21731}, {897, 1725}, {5466, 15329}, {5968, 52451}, {9213, 41512}, {9214, 14264}, {10097, 16237}, {10415, 12824}, {10422, 12827}, {12828, 15398}, {13754, 17983}, {14908, 44138}, {30786, 44084}, {52668, 57486}
X(60498) = barycentric quotient X(i)/X(j) for these {i,j}: {111, 2986}, {403, 44146}, {671, 40832}, {686, 14417}, {691, 18878}, {895, 57829}, {923, 36053}, {1725, 14210}, {3003, 524}, {3580, 3266}, {5547, 56103}, {6334, 45807}, {8753, 1300}, {9139, 40423}, {9178, 15328}, {9214, 52552}, {10097, 15421}, {12824, 7664}, {12828, 34336}, {13754, 6390}, {14264, 36890}, {14908, 5504}, {15329, 5468}, {18609, 16741}, {21731, 690}, {32729, 10420}, {32740, 14910}, {44084, 468}, {51821, 9717}, {52451, 52145}, {55121, 35522}, {56403, 43084}, {60342, 45808}

X(60499) = X(2)X(525)∩X(6)X(74)

Barycentrics    a^2*(a^4 - 2*a^2*b^2 + b^4 + a^2*c^2 + b^2*c^2 - 2*c^4)*(a^4 + a^2*b^2 - 2*b^4 - 2*a^2*c^2 + b^2*c^2 + c^4)*(a^4*b^2 - b^6 + a^4*c^2 - 2*a^2*b^2*c^2 + b^4*c^2 + b^2*c^4 - c^6) : :

X(60499) lies on the cubics K280 and K1352 and these lines: {2, 525}, {3, 32640}, {6, 74}, {39, 14264}, {154, 34190}, {216, 51964}, {262, 60119}, {574, 48451}, {1304, 35901}, {1494, 7757}, {1625, 54037}, {1995, 46341}, {2071, 2420}, {2393, 46592}, {2549, 34150}, {2693, 32681}, {3003, 46585}, {3148, 40352}, {3470, 22332}, {5013, 14385}, {5024, 9717}, {7736, 52488}, {7738, 56686}, {7739, 40630}, {8743, 32695}, {9818, 50464}, {10419, 14355}, {12079, 15048}, {12099, 44468}, {14989, 44526}, {16080, 40814}, {19153, 32715}, {36823, 41511}, {36896, 52703}, {39575, 52646}, {41614, 44769}, {54995, 58347}

X(60499) = X(i)-isoconjugate of X(j) for these (i,j): {1177, 14206}, {1495, 37220}, {1784, 18876}, {2173, 2373}, {9033, 36095}, {9406, 46140}
X(60499) = X(i)-Dao conjugate of X(j) for these (i,j): {5181, 11064}, {9410, 46140}, {36896, 2373}, {38971, 41079}
X(60499) = trilinear pole of line {2393, 42665}
X(60499) = crossdifference of every pair of points on line {1495, 9033}
X(60499) = barycentric product X(i)*X(j) for these {i,j}: {74, 858}, {1236, 40352}, {1494, 2393}, {2159, 20884}, {2349, 18669}, {5181, 9139}, {5523, 14919}, {9717, 59422}, {10419, 12827}, {14961, 16080}, {16077, 42665}, {34767, 46592}, {35910, 52672}, {36890, 57485}, {44769, 47138}
X(60499) = barycentric quotient X(i)/X(j) for these {i,j}: {74, 2373}, {858, 3260}, {1494, 46140}, {2349, 37220}, {2393, 30}, {2433, 60040}, {5523, 46106}, {8749, 60133}, {14580, 1990}, {14961, 11064}, {18669, 14206}, {18877, 18876}, {20884, 46234}, {32715, 10423}, {35908, 52486}, {36131, 36095}, {40352, 1177}, {42665, 9033}, {46147, 46165}, {46592, 4240}, {47138, 41079}, {47426, 5642}, {57485, 9214}

X(60500) = X(6)X(35912)∩X(39)X(51254)

Barycentrics    (b - c)^2*(b + c)^2*(a^6*b^2 - a^4*b^4 - a^2*b^6 + b^8 + 3*a^6*c^2 - a^4*b^2*c^2 + 3*a^2*b^4*c^2 - b^6*c^2 - 6*a^4*c^4 - a^2*b^2*c^4 - b^4*c^4 + 3*a^2*c^6 + b^2*c^6)*(3*a^6*b^2 - 6*a^4*b^4 + 3*a^2*b^6 + a^6*c^2 - a^4*b^2*c^2 - a^2*b^4*c^2 + b^6*c^2 - a^4*c^4 + 3*a^2*b^2*c^4 - b^4*c^4 - a^2*c^6 - b^2*c^6 + c^8) : :

X(60500) lies on the cubic K1352 and these lines: {6, 35912}, {39, 51254}, {125, 55265}, {1640, 36189}, {1648, 1650}, {3124, 14401}, {3269, 58780}, {5489, 51429}, {20975, 58262}, {44114, 58907}

X(60500) = X(1101)-isoconjugate of X(41254)
X(60500) = X(523)-Dao conjugate of X(41254)
X(60500) = barycentric quotient X(i)/X(j) for these {i,j}: {115, 41254}, {20975, 5622}, {44114, 7418}

X(60501) = X(5)X(6)∩X(32)X(51)

Barycentrics    a^2*(a^4 - 2*a^2*b^2 + b^4 - 2*b^2*c^2 + c^4)*(a^4 + b^4 - 2*a^2*c^2 - 2*b^2*c^2 + c^4) : :

X(60501) lies on the cubic K1352 and these lines: {2, 55550}, {3, 32654}, {5, 6}, {24, 58312}, {25, 41271}, {32, 51}, {39, 16391}, {83, 5392}, {91, 40747}, {96, 262}, {115, 39643}, {213, 21807}, {230, 41587}, {460, 2207}, {570, 15827}, {571, 5446}, {729, 925}, {847, 6531}, {1084, 46394}, {1093, 8745}, {1181, 7694}, {1196, 46680}, {1504, 26922}, {1640, 30442}, {1692, 1974}, {1820, 2281}, {1968, 50387}, {1993, 7752}, {3114, 57904}, {3124, 14585}, {3172, 40354}, {3225, 46134}, {3527, 57703}, {5013, 44415}, {5058, 6413}, {5062, 6414}, {5359, 42346}, {5966, 9707}, {6388, 7749}, {6423, 44193}, {6424, 44192}, {6464, 10607}, {6663, 46200}, {7846, 37802}, {7899, 15066}, {9781, 14495}, {10601, 52350}, {11426, 14489}, {11441, 39839}, {14601, 20968}, {14669, 53775}, {18268, 36145}, {19153, 32734}, {19156, 40825}, {21637, 39764}, {23700, 58961}, {31404, 34945}, {31406, 39524}, {34756, 39416}, {37637, 58923}, {41334, 56272}, {41614, 41909}

X(60501) = isogonal conjugate of X(7763)
X(60501) = isogonal conjugate of the anticomplement of X(7746)
X(60501) = isogonal conjugate of the isotomic conjugate of X(2165)
X(60501) = isogonal conjugate of the polar conjugate of X(14593)
X(60501) = polar conjugate of the isotomic conjugate of X(2351)
X(60501) = X(31)-complementary conjugate of X(37864)
X(60501) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 37864}, {2165, 2351}, {39416, 34952}
X(60501) = X(i)-isoconjugate of X(j) for these (i,j): {1, 7763}, {2, 44179}, {24, 304}, {47, 76}, {63, 317}, {69, 1748}, {75, 1993}, {86, 42700}, {92, 9723}, {249, 17881}, {313, 18605}, {326, 11547}, {491, 55398}, {492, 55397}, {523, 55249}, {561, 571}, {563, 18022}, {656, 55227}, {662, 6563}, {670, 55216}, {799, 924}, {811, 52584}, {1147, 1969}, {1821, 51439}, {1928, 52436}, {1959, 31635}, {1978, 34948}, {2167, 39113}, {2180, 34384}, {2616, 55252}, {4592, 57065}, {4602, 34952}, {6507, 59139}, {6753, 55202}, {14208, 41679}, {24037, 47421}, {30451, 57968}, {33805, 51393}, {33808, 57484}, {40364, 44077}, {40440, 52032}, {40703, 51776}
X(60501) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 7763}, {206, 1993}, {512, 47421}, {1084, 6563}, {3162, 317}, {5139, 57065}, {14713, 41770}, {15259, 11547}, {15295, 18883}, {17423, 52584}, {22391, 9723}, {24245, 45805}, {24246, 45806}, {32664, 44179}, {34853, 76}, {37864, 2}, {38996, 924}, {40368, 571}, {40369, 52436}, {40588, 39113}, {40596, 55227}, {40600, 42700}, {40601, 51439}
X(60501) = cevapoint of X(3049) and X(3124)
X(60501) = X(60501) = trilinear pole of line {669, 55219}
X(60501) = crossdifference of every pair of points on line {924, 6563}
X(60501) = barycentric product X(i)*X(j) for these {i,j}: {3, 14593}, {4, 2351}, {5, 41271}, {6, 2165}, {19, 1820}, {25, 68}, {31, 91}, {32, 5392}, {51, 96}, {53, 57703}, {155, 59189}, {163, 55250}, {184, 847}, {393, 55549}, {485, 8576}, {486, 8577}, {512, 925}, {523, 32734}, {560, 20571}, {661, 36145}, {669, 46134}, {1093, 59176}, {1501, 57904}, {1625, 55253}, {1799, 27367}, {1924, 55215}, {1953, 2168}, {1974, 20563}, {2207, 52350}, {2971, 57763}, {3049, 30450}, {3199, 57875}, {3426, 40348}, {5962, 52153}, {6413, 41516}, {6414, 41515}, {6524, 16391}, {8754, 44174}, {8770, 56891}, {9247, 57716}, {11060, 37802}, {12077, 32692}, {14575, 55553}, {34385, 40981}, {34428, 39111}, {34853, 39109}, {44078, 57415}, {54030, 58825}, {54031, 58827}, {54034, 56272}
X(60501) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 7763}, {25, 317}, {31, 44179}, {32, 1993}, {51, 39113}, {68, 305}, {91, 561}, {96, 34384}, {112, 55227}, {163, 55249}, {184, 9723}, {213, 42700}, {217, 52032}, {237, 51439}, {485, 45806}, {486, 45805}, {512, 6563}, {560, 47}, {669, 924}, {847, 18022}, {925, 670}, {1084, 47421}, {1501, 571}, {1625, 55252}, {1820, 304}, {1924, 55216}, {1973, 1748}, {1974, 24}, {1976, 31635}, {1980, 34948}, {2165, 76}, {2207, 11547}, {2351, 69}, {2489, 57065}, {2643, 17881}, {2971, 136}, {3049, 52584}, {3199, 467}, {5392, 1502}, {6524, 59139}, {8576, 492}, {8577, 491}, {9233, 52436}, {9407, 51393}, {9426, 34952}, {11060, 18883}, {14575, 1147}, {14593, 264}, {14600, 51776}, {16391, 4176}, {20563, 40050}, {20571, 1928}, {27367, 427}, {32734, 99}, {36145, 799}, {36417, 8745}, {40348, 44133}, {40373, 52435}, {40981, 52}, {41271, 95}, {42295, 41770}, {42663, 57154}, {44077, 55551}, {44162, 44077}, {44174, 47389}, {46134, 4609}, {55250, 20948}, {55549, 3926}, {55553, 44161}, {56891, 57518}, {57204, 6753}, {57703, 34386}, {57904, 40362}, {58825, 54028}, {58827, 54029}, {59176, 3964}, {59189, 46746}
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 2165, 55549}, {6, 13881, 23128}, {2165, 56891, 68}, {3124, 14585, 44527}, {8576, 8577, 2351}

X(60502) = X(2)X(339)∩X(4)X(94)

Barycentrics    b^2*c^2*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2)*(-2*a^6 + 2*a^4*b^2 - a^2*b^4 + b^6 + 2*a^4*c^2 - b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6) : :

X(60502) lies on the cubic K1353 and these lines: {2, 339}, {4, 94}, {6, 264}, {23, 41377}, {25, 5986}, {53, 53495}, {76, 6331}, {83, 9381}, {98, 36176}, {107, 38664}, {297, 525}, {323, 56016}, {324, 35318}, {401, 10317}, {419, 34397}, {468, 44420}, {567, 37124}, {671, 2052}, {1232, 53481}, {1235, 14389}, {1236, 11064}, {1990, 44138}, {2781, 47110}, {2782, 4230}, {2967, 57583}, {2986, 7754}, {3260, 56021}, {3581, 35474}, {5094, 32447}, {5191, 7473}, {5392, 56296}, {6392, 51968}, {6515, 34163}, {7391, 12918}, {13200, 36181}, {16237, 47228}, {18438, 37190}, {18472, 51350}, {25051, 46151}, {30737, 40884}, {34990, 41677}, {35311, 46512}, {37200, 37489}, {37778, 50187}, {40138, 44135}, {41238, 56015}, {41392, 57486}, {55973, 56270}, {58268, 60266}

X(60502) = reflection of X(i) in X(j) for these {i,j}: {4230, 47202}, {16237, 47228}
X(60502) = polar conjugate of X(842)
X(60502) = isotomic conjugate of the isogonal conjugate of X(6103)
X(60502) = polar conjugate of the isogonal conjugate of X(542)
X(60502) = X(2697)-anticomplementary conjugate of X(4329)
X(60502) = X(264)-Ceva conjugate of X(38552)
X(60502) = X(i)-isoconjugate of X(j) for these (i,j): {48, 842}, {163, 35909}, {293, 52199}, {810, 5649}, {4575, 14998}, {5641, 9247}, {32676, 35911}, {35200, 48453}
X(60502) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 35909}, {132, 52199}, {133, 48453}, {136, 14998}, {1249, 842}, {2493, 14984}, {6103, 2781}, {15526, 35911}, {23967, 3}, {23976, 40080}, {38970, 23350}, {39062, 5649}, {40938, 46157}, {42426, 6}, {60340, 47414}
X(60502) = cevapoint of X(i) and X(j) for these (i,j): {542, 6103}, {2493, 2781}
X(60502) = trilinear pole of line {16188, 18312}
X(60502) = crossdifference of every pair of points on line {184, 39469}
X(60502) = barycentric product X(i)*X(j) for these {i,j}: {76, 6103}, {264, 542}, {290, 54380}, {297, 46786}, {325, 52491}, {340, 43087}, {648, 18312}, {850, 7473}, {1640, 6331}, {1969, 2247}, {3260, 17986}, {3267, 35907}, {5191, 18022}, {5641, 38552}, {14618, 14999}, {16092, 44146}, {30737, 47105}, {34369, 44132}, {35522, 53155}, {37778, 51405}, {44138, 51456}, {45662, 46111}, {46106, 51227}
X(60502) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 842}, {186, 52179}, {232, 52199}, {264, 5641}, {297, 46787}, {427, 46157}, {523, 35909}, {525, 35911}, {542, 3}, {648, 5649}, {685, 53691}, {1503, 40080}, {1640, 647}, {1990, 48453}, {2247, 48}, {2501, 14998}, {2781, 51472}, {4240, 51263}, {5191, 184}, {6041, 3049}, {6103, 6}, {6331, 6035}, {6344, 54554}, {6530, 52492}, {7473, 110}, {14618, 14223}, {14999, 4558}, {16092, 895}, {16188, 14984}, {16230, 23350}, {17984, 57452}, {17986, 74}, {18312, 525}, {23968, 32662}, {34366, 10766}, {34369, 248}, {34761, 43754}, {35907, 112}, {36129, 36096}, {38552, 542}, {42426, 2781}, {43087, 265}, {44145, 34174}, {44146, 52094}, {45662, 3292}, {46106, 51228}, {46786, 287}, {47105, 1297}, {48451, 18877}, {51227, 14919}, {51428, 20975}, {51456, 5504}, {52491, 98}, {53132, 16186}, {53155, 691}, {54380, 511}, {55142, 9517}, {57464, 47414}, {58087, 2697}
X(60502) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {648, 41254, 41253}, {648, 48540, 9308}, {1990, 53474, 44138}, {2592, 2593, 297}, {3580, 5523, 297}, {35360, 53346, 4}, {41194, 41195, 338}, {41253, 41254, 458}, {41760, 48540, 338}, {44146, 46106, 297}, {46106, 51481, 44146}, {47286, 51358, 297}, {50188, 54395, 297}

X(60503) = X(6)X(67)∩X(110)X(525)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(2*a^2 - b^2 - c^2)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^4 - a^2*b^2 + b^4 - c^4)*(a^4 - b^4 - a^2*c^2 + c^4) : :

X(60503) lies on the cubic K1353 and these lines: {6, 67}, {107, 14223}, {110, 525}, {648, 34574}, {2781, 51823}, {4563, 59152}, {5467, 14417}, {5468, 45807}, {5967, 57496}, {6331, 35138}, {6593, 34336}, {9717, 14357}, {10415, 32234}, {11061, 56569}, {15471, 52234}, {32228, 57602}

X(60503) = midpoint of X(11061) and X(56569)
X(60503) = X(i)-isoconjugate of X(j) for these (i,j): {63, 10561}, {656, 14246}, {661, 57481}, {810, 52551}, {897, 9517}, {4575, 10555}, {9979, 36060}, {10097, 16568}, {14208, 52142}, {22151, 23894}, {42659, 46277}
X(60503) = X(i)-Dao conjugate of X(j) for these (i,j): {136, 10555}, {1560, 9979}, {3162, 10561}, {6593, 9517}, {15900, 14977}, {36830, 57481}, {39062, 52551}, {40596, 14246}
X(60503) = cevapoint of X(i) and X(j) for these (i,j): {690, 5095}, {44102, 58780}
X(60503) = trilinear pole of line {187, 14357}
X(60503) = barycentric product X(i)*X(j) for these {i,j}: {67, 4235}, {110, 57496}, {468, 17708}, {524, 935}, {648, 14357}, {5467, 46105}, {5468, 8791}, {6331, 59175}
X(60503) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 10561}, {67, 14977}, {110, 57481}, {112, 14246}, {187, 9517}, {468, 9979}, {648, 52551}, {935, 671}, {2501, 10555}, {3455, 10097}, {4235, 316}, {5095, 18311}, {5467, 22151}, {5468, 37804}, {8791, 5466}, {14357, 525}, {14567, 42659}, {17708, 30786}, {44102, 2492}, {46105, 52632}, {53232, 51405}, {54274, 47415}, {57496, 850}, {58780, 5099}, {59175, 647}

X(60504) = X(4)X(32)∩X(99)X(249)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^4 + b^4 - a^2*c^2 - b^2*c^2)*(2*a^4 - a^2*b^2 + b^4 - a^2*c^2 - 2*b^2*c^2 + c^4)*(a^4 - a^2*b^2 - b^2*c^2 + c^4) : :

X(60504) lies on the cubic K1353 and these lines: {4, 32}, {99, 249}, {110, 46606}, {114, 53783}, {230, 34174}, {542, 51963}, {648, 57562}, {878, 53273}, {1562, 35912}, {1625, 2422}, {1640, 35278}, {1692, 46039}, {5477, 36875}, {5967, 41672}, {6037, 59007}, {6054, 23967}, {10753, 47388}, {12829, 14265}, {18858, 26714}, {20031, 57219}, {22664, 47382}, {35606, 40820}, {39860, 40079}, {41675, 56788}, {41932, 48721}, {51431, 51820}, {53173, 53737}

X(60504) = reflection of X(i) in X(j) for these {i,j}: {98, 34156}, {56687, 114}
X(60504) = antigonal image of X(56687)
X(60504) = symgonal image of X(34156)
X(60504) = X(i)-Ceva conjugate of X(j) for these (i,j): {2966, 4226}, {4590, 40820}, {57562, 98}
X(60504) = X(i)-isoconjugate of X(j) for these (i,j): {656, 57493}, {661, 52091}, {1577, 34157}, {1959, 35364}, {2799, 36051}, {3569, 8773}, {32679, 39374}, {36105, 41172}
X(60504) = X(i)-Dao conjugate of X(j) for these (i,j): {114, 2799}, {868, 35088}, {34156, 525}, {35067, 6333}, {36830, 52091}, {39001, 41172}, {39072, 3569}, {40596, 57493}, {51610, 41181}, {55152, 868}, {56788, 115}
X(60504) = cevapoint of X(230) and X(55267)
X(60504) = trilinear pole of line {230, 51820}
X(60504) = crossdifference of every pair of points on line {684, 44114}
X(60504) = barycentric product X(i)*X(j) for these {i,j}: {98, 4226}, {99, 51820}, {107, 53783}, {110, 14265}, {114, 41173}, {230, 2966}, {460, 17932}, {685, 3564}, {1692, 43187}, {1733, 36084}, {2715, 51481}, {5967, 52035}, {8772, 36036}, {12829, 39291}, {16081, 56389}, {22456, 52144}, {34174, 34761}, {43754, 44145}, {55122, 57991}, {55267, 57562}
X(60504) = barycentric quotient X(i)/X(j) for these {i,j}: {110, 52091}, {112, 57493}, {230, 2799}, {460, 16230}, {685, 35142}, {1576, 34157}, {1692, 3569}, {1976, 35364}, {2715, 2987}, {2966, 8781}, {3564, 6333}, {4226, 325}, {6531, 60338}, {14265, 850}, {14560, 39374}, {17932, 57872}, {32696, 3563}, {34174, 34765}, {36084, 8773}, {41173, 40428}, {42663, 44114}, {43754, 43705}, {44099, 17994}, {51335, 41167}, {51820, 523}, {52144, 684}, {53783, 3265}, {55122, 868}, {55267, 35088}, {56389, 36212}, {57562, 55266}, {57742, 10425}

X(60505) = X(4)X(54527)∩X(6)X(35912)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(2*a^6 - 2*a^4*b^2 + a^2*b^4 - b^6 - 2*a^4*c^2 + b^4*c^2 + a^2*c^4 + b^2*c^4 - c^6)^2 : :

X(60505) lies on the cubic K1353 and these lines: {4, 54527}, {6, 35912}, {110, 14401}, {112, 20404}, {525, 2420}, {542, 6103}, {648, 14223}, {1625, 57203}, {1640, 7473}, {2501, 4240}, {17708, 23616}, {35907, 53155}

X(60505) = X(i)-Ceva conjugate of X(j) for these (i,j): {648, 7473}, {60179, 54380}
X(60505) = X(810)-isoconjugate of X(57547)
X(60505) = X(i)-Dao conjugate of X(j) for these (i,j): {542, 525}, {39062, 57547}, {42426, 14223}
X(60505) = barycentric product X(i)*X(j) for these {i,j}: {110, 38552}, {542, 7473}, {648, 23967}, {6103, 14999}, {34761, 54380}, {42743, 52491}, {45662, 53155}
X(60505) = barycentric quotient X(i)/X(j) for these {i,j}: {648, 57547}, {5191, 35909}, {6103, 14223}, {7473, 5641}, {23967, 525}, {38552, 850}, {54380, 34765}

X(60506) = X(2)X(98)∩X(107)X(685)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^4 + b^4 - a^2*c^2 - b^2*c^2)*(a^4 - a^2*b^2 - b^2*c^2 + c^4)*(2*a^6 - a^4*b^2 - b^6 - a^4*c^2 + b^4*c^2 + b^2*c^4 - c^6) : :

X(60506) lies on the cubic K1353 and these lines: {2, 98}, {107, 685}, {878, 1624}, {1640, 35278}, {4563, 57991}, {6037, 59136}, {6793, 51963}, {17932, 44326}, {34156, 35282}, {36793, 52145}, {43754, 44766}, {52913, 60179}

X(60506) = X(i)-Ceva conjugate of X(j) for these (i,j): {685, 2409}, {32230, 32545}, {57991, 441}
X(60506) = X(i)-isoconjugate of X(j) for these (i,j): {240, 2435}, {656, 39265}, {684, 8767}, {1755, 43673}, {1959, 34212}, {2419, 57653}, {14208, 51822}
X(60506) = X(i)-Dao conjugate of X(j) for these (i,j): {15595, 6333}, {23976, 2799}, {36899, 43673}, {39071, 684}, {39073, 41167}, {39085, 2435}, {40596, 39265}, {50938, 16230}
X(60506) = cevapoint of X(2445) and X(15639)
X(60506) = trilinear pole of line {1503, 34156}
X(60506) = barycentric product X(i)*X(j) for these {i,j}: {98, 34211}, {99, 51963}, {110, 57490}, {287, 2409}, {441, 685}, {648, 34156}, {1503, 2966}, {1576, 51257}, {2312, 36036}, {2445, 57799}, {2715, 30737}, {4558, 52641}, {6394, 23977}, {8779, 22456}, {15595, 41173}, {15639, 57761}, {16318, 17932}, {42671, 43187}
X(60506) = barycentric quotient X(i)/X(j) for these {i,j}: {98, 43673}, {112, 39265}, {248, 2435}, {287, 2419}, {441, 6333}, {685, 6330}, {1503, 2799}, {1976, 34212}, {2409, 297}, {2445, 232}, {2715, 1297}, {2966, 35140}, {8779, 684}, {9475, 41167}, {15639, 132}, {16318, 16230}, {23977, 6530}, {28343, 33752}, {32696, 43717}, {34156, 525}, {34211, 325}, {36104, 8767}, {41173, 9476}, {42671, 3569}, {51257, 44173}, {51437, 17994}, {51963, 523}, {52641, 14618}, {57490, 850}
X(60506) = {X(47200),X(51820)}-harmonic conjugate of X(98)

X(60507) = X(2)X(339)∩X(112)X(523)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^4 - a^2*b^2 + b^4 - c^4)*(a^4 - b^4 - a^2*c^2 + c^4)*(a^4*b^2 - b^6 + a^4*c^2 - 2*a^2*b^2*c^2 + b^4*c^2 + b^2*c^4 - c^6) : :

X(60507) lies on the cubic K1353 and these lines: {2, 339}, {67, 3269}, {99, 59059}, {112, 523}, {1289, 58980}, {1560, 57485}, {6103, 14357}, {15900, 47427}, {30247, 39413}, {39269, 52672}, {46592, 47138}

X(60507) = X(935)-Ceva conjugate of X(46592)
X(60507) = X(i)-isoconjugate of X(j) for these (i,j): {656, 60002}, {37220, 42659}
X(60507) = X(i)-Dao conjugate of X(j) for these (i,j): {468, 18311}, {14357, 525}, {40596, 60002}
X(60507) = cevapoint of X(1560) and X(47138)
X(60507) = barycentric product X(i)*X(j) for these {i,j}: {110, 39269}, {112, 57476}, {858, 935}, {5523, 17708}, {18019, 46592}
X(60507) = barycentric quotient X(i)/X(j) for these {i,j}: {112, 60002}, {935, 2373}, {1560, 18311}, {2393, 9517}, {5523, 9979}, {8791, 60040}, {14580, 2492}, {39269, 850}, {46592, 23}, {57476, 3267}
X(60507) = {X(44467),X(57496)}-harmonic conjugate of X(8791)

X(60508) = X(74)X(525)∩X(98)X(523)

Barycentrics    (2*a^6 - 2*a^4*b^2 + a^2*b^4 - b^6 - 2*a^4*c^2 + b^4*c^2 + a^2*c^4 + b^2*c^4 - c^6)*(a^8 - a^6*b^2 - a^4*b^4 + a^2*b^6 - a^6*c^2 + 3*a^4*b^2*c^2 - a^2*b^4*c^2 + 3*b^6*c^2 - a^4*c^4 - a^2*b^2*c^4 - 6*b^4*c^4 + a^2*c^6 + 3*b^2*c^6) : :
X(60508) = 3 X[12188] + X[38582], 2 X[12188] + X[47291], 2 X[38582] - 3 X[47291], 3 X[98] - X[842], 2 X[842] - 3 X[36166], 3 X[403] - 4 X[43291], 3 X[1551] - 4 X[16188], 3 X[16092] - 2 X[16188], 3 X[671] - X[44969], 3 X[7472] - 4 X[38611], 2 X[38611] - 3 X[46633], 3 X[6055] - 2 X[16760], 4 X[16760] - 3 X[53136], 3 X[34366] - 2 X[42426], 4 X[12042] - X[47289], 2 X[14120] - 3 X[14651], 3 X[14568] - 2 X[46999], 3 X[14639] - 2 X[46988], 5 X[15081] - 6 X[34953], 3 X[21445] - 2 X[36180], 3 X[22329] - 2 X[47584], X[23235] - 3 X[38702], 3 X[34473] - 2 X[46987], 3 X[34473] - X[47288], 3 X[38227] - 4 X[47238], X[47292] + 4 X[51523], X[52090] - 3 X[57307]

X(60508) lies on the cubic K1353 and these lines: {2, 9717}, {3, 47293}, {4, 51258}, {6, 36183}, {30, 148}, {74, 525}, {98, 523}, {99, 46981}, {111, 2501}, {147, 36170}, {183, 6795}, {323, 858}, {339, 46637}, {403, 8744}, {468, 41204}, {542, 1550}, {648, 9139}, {671, 44969}, {691, 38664}, {1316, 9755}, {1495, 47207}, {1499, 22265}, {1503, 47242}, {1513, 16315}, {2452, 13860}, {2782, 7472}, {3906, 53709}, {5099, 11623}, {5191, 7473}, {5627, 41392}, {5912, 47229}, {5970, 43654}, {5984, 36173}, {6054, 46980}, {6055, 16760}, {6070, 47200}, {6103, 17986}, {7426, 47146}, {8667, 59231}, {10295, 14654}, {10415, 32234}, {10722, 46982}, {11632, 36196}, {12042, 46634}, {14120, 14651}, {14568, 46999}, {14639, 46988}, {14981, 40544}, {15081, 34953}, {16306, 53475}, {21445, 36180}, {22329, 47584}, {23235, 38702}, {31510, 47202}, {34473, 46987}, {34536, 53937}, {37930, 40947}, {38227, 47238}, {40355, 41512}, {41932, 48721}, {47292, 51523}, {52090, 57307}, {52229, 54995}

X(60508) = midpoint of X(i) and X(j) for these {i,j}: {691, 38664}, {5984, 36173}
X(60508) = reflection of X(i) in X(j) for these {i,j}: {4, 51258}, {99, 46981}, {147, 36170}, {1513, 16315}, {1550, 51428}, {1551, 16092}, {5099, 11623}, {6054, 46980}, {7472, 46633}, {10722, 46982}, {14981, 40544}, {36166, 98}, {36196, 11632}, {46634, 12042}, {47288, 46987}, {47289, 46634}, {47293, 3}, {53136, 6055}
X(60508) = X(i)-Ceva conjugate of X(j) for these (i,j): {98, 7418}, {648, 1640}, {34536, 34369}, {40423, 51227}
X(60508) = barycentric product X(i)*X(j) for these {i,j}: {542, 41254}, {7418, 46786}
X(60508) = barycentric quotient X(i)/X(j) for these {i,j}: {7418, 46787}, {41254, 5641}
X(60508) = {X(34473),X(47288)}-harmonic conjugate of X(46987)

X(60509) = X(4)X(690)∩X(113)X(525)

Barycentrics    (b^2 - c^2)*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2)*(-2*a^6 + 2*a^4*b^2 - a^2*b^4 + b^6 + 2*a^4*c^2 - b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6)*(-a^6 + 4*a^4*b^2 - 5*a^2*b^4 + 2*b^6 + 4*a^4*c^2 - 3*a^2*b^2*c^2 + b^4*c^2 - 5*a^2*c^4 + b^2*c^4 + 2*c^6) : :

X(60509) lies on the Feuerbach circumhyperbola of the orthic triangle, the cubic K1353, and these lines: {4, 690}, {6, 14273}, {52, 9517}, {113, 525}, {193, 9033}, {512, 1986}, {523, 5095}, {526, 1843}, {648, 18808}, {826, 2914}, {924, 40949}, {1640, 6103}, {2501, 12828}, {3566, 13202}, {3906, 10294}, {4232, 14932}, {5139, 35582}, {5642, 47217}, {7473, 14999}, {8723, 15463}, {18947, 57221}, {45147, 46026}

X(60509) = polar-circle-inverse of X(34174)
X(60509) = X(648)-Ceva conjugate of X(6103)
X(60509) = X(1640)-Dao conjugate of X(525)
X(60509) = barycentric product X(16077)*X(57465)
X(60509) = barycentric quotient X(57465)/X(9033)

X(60510) = X(2)X(1637)∩X(6)X(9033)

Barycentrics    (b^2 - c^2)*(-2*a^6 + 2*a^4*b^2 - a^2*b^4 + b^6 + 2*a^4*c^2 - b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6)*(a^8 + a^6*b^2 - 3*a^4*b^4 - a^2*b^6 + 2*b^8 + a^6*c^2 - a^4*b^2*c^2 + 3*a^2*b^4*c^2 - 3*b^6*c^2 - 3*a^4*c^4 + 3*a^2*b^2*c^4 + 2*b^4*c^4 - a^2*c^6 - 3*b^2*c^6 + 2*c^8) : :

X(60510) lies on the cubic K1353 and these lines: {2, 1637}, {6, 9033}, {115, 46416}, {122, 42306}, {216, 2492}, {523, 3163}, {525, 15595}, {542, 1640}, {648, 14977}, {1196, 2508}, {1249, 14273}, {1560, 2501}, {3162, 47236}, {5972, 14401}, {6795, 8429}, {7473, 35907}, {12077, 40583}, {14582, 41512}, {15526, 18310}, {18311, 23583}, {40938, 47230}, {41145, 45327}, {45237, 58900}

X(60510) = midpoint of X(648) and X(14977)
X(60510) = reflection of X(i) in X(j) for these {i,j}: {15526, 18310}, {18311, 23583}, {41145, 45327}
X(60510) = complement of the isotomic conjugate of X(7473)
X(60510) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 37987}, {2247, 127}, {5191, 34846}, {6103, 21253}, {7473, 2887}, {32676, 542}, {35907, 20305}, {53155, 21256}
X(60510) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 37987}, {648, 542}, {14977, 55142}
X(60510) = X(37987)-Dao conjugate of X(2)
X(60510) = crossdifference of every pair of points on line {2781, 5191}
X(60510) = barycentric product X(7473)*X(37987)

X(60511) = X(4)X(5968)∩X(99)X(5649)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(2*a^6 - 2*a^4*b^2 + a^2*b^4 - b^6 - 2*a^4*c^2 + b^4*c^2 + a^2*c^4 + b^2*c^4 - c^6)*(a^6*b^2 - a^4*b^4 - a^2*b^6 + b^8 + a^6*c^2 - 2*a^4*b^2*c^2 + 2*a^2*b^4*c^2 - 3*b^6*c^2 - a^4*c^4 + 2*a^2*b^2*c^4 + 4*b^4*c^4 - a^2*c^6 - 3*b^2*c^6 + c^8) : :

X(60511) lies on the cubic K1353 and these lines: {4, 5968}, {99, 5649}, {311, 43084}, {523, 2407}, {525, 2421}, {691, 16220}, {1640, 14999}, {2493, 54395}, {2782, 57603}, {4235, 57065}, {7757, 54725}, {14570, 18311}, {16237, 57071}, {20577, 52630}, {45331, 50187}

X(60511) = reflection of X(54395) in X(2493)
X(60511) = X(i)-Ceva conjugate of X(j) for these (i,j): {99, 7468}, {648, 14999}
X(60511) = X(i)-Dao conjugate of X(j) for these (i,j): {2493, 523}, {16188, 14998}, {23967, 51480}
X(60511) = barycentric product X(i)*X(j) for these {i,j}: {99, 16188}, {542, 14221}, {14999, 54395}
X(60511) = barycentric quotient X(i)/X(j) for these {i,j}: {542, 51480}, {2493, 14998}, {7468, 842}, {7473, 40118}, {14221, 5641}, {14984, 35909}, {16188, 523}, {42743, 40083}, {54395, 14223}

X(60512) = X(2)X(35908)∩X(107)X(14223)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^2 + b^2 - c^2)^2*(a^2 - b^2 + c^2)^2*(2*a^6 - 2*a^4*b^2 + a^2*b^4 - b^6 - 2*a^4*c^2 + b^4*c^2 + a^2*c^4 + b^2*c^4 - c^6)*(a^8*b^2 - 2*a^6*b^4 + 2*a^2*b^8 - b^10 + a^8*c^2 + a^4*b^4*c^2 - 2*a^2*b^6*c^2 - 2*a^6*c^4 + a^4*b^2*c^4 + b^6*c^4 - 2*a^2*b^2*c^6 + b^4*c^6 + 2*a^2*c^8 - c^10) : :

X(60512) lies on the cubic K1353 and these lines: {2, 35908}, {107, 14223}, {523, 2409}, {1640, 35907}, {2501, 58070}, {2781, 50188}, {4240, 33294}, {6035, 42308}, {46587, 47216}, {47202, 57632}

X(60512) = inner-Soddy-circle-inverse of X(40817)
X(60512) = X(i)-Ceva conjugate of X(j) for these (i,j): {107, 37937}, {648, 35907}
X(60512) = X(6103)-Dao conjugate of X(525)
X(60512) = trilinear pole of line {42426, 47427}
X(60512) = barycentric product X(i)*X(j) for these {i,j}: {648, 42426}, {6528, 47427}, {7473, 50188}
X(60512) = barycentric quotient X(i)/X(j) for these {i,j}: {2781, 35911}, {35907, 2697}, {42426, 525}, {47427, 520}

X(60513) = X(2)X(44817)∩X(4)X(9517)

Barycentrics    b^2*(b^2 - c^2)*c^2*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2)*(-2*a^6 + 2*a^4*b^2 - a^2*b^4 + b^6 + 2*a^4*c^2 - b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6)*(-a^10 + 2*a^8*b^2 - 2*a^4*b^6 + a^2*b^8 + 2*a^8*c^2 - a^6*b^2*c^2 - a^4*b^4*c^2 - a^2*b^6*c^2 + b^8*c^2 - a^4*b^2*c^4 + 4*a^2*b^4*c^4 - b^6*c^4 - 2*a^4*c^6 - a^2*b^2*c^6 - b^4*c^6 + a^2*c^8 + b^2*c^8) : :

X(60513) lies on the cubic K1353 and these lines: {2, 44817}, {4, 9517}, {264, 14223}, {324, 9979}, {523, 2967}, {648, 43665}, {850, 14920}, {1235, 14295}, {6103, 18312}, {14592, 41392}, {14999, 35907}, {15928, 31953}, {35522, 35911}

X(60513) = X(264)-Ceva conjugate of X(36189)
X(60513) = X(18312)-Dao conjugate of X(525)
X(60513) = barycentric product X(18312)*X(41253)
X(60513) = barycentric quotient X(i)/X(j) for these {i,j}: {36189, 35909}, {41253, 5649}

X(60514) = X(2)X(160)∩X(6)X(25)

Barycentrics    a^2*(a^6*b^2 - a^2*b^6 + a^6*c^2 - b^6*c^2 + 2*b^4*c^4 - a^2*c^6 - b^2*c^6) : :
X(60514) = 3 X[46511] - 2 X[53570]

X(60514) lies on the cubic K1354 and these lines: {2, 160}, {3, 3734}, {4, 15270}, {5, 23208}, {6, 25}, {22, 157}, {23, 385}, {24, 39646}, {26, 2353}, {30, 53273}, {98, 34133}, {115, 21177}, {141, 7467}, {148, 37896}, {230, 237}, {325, 1634}, {1196, 41331}, {1503, 53174}, {1576, 10313}, {1625, 2387}, {1691, 15630}, {1995, 11174}, {2070, 5938}, {2967, 44668}, {3124, 56915}, {3148, 9609}, {3203, 27375}, {3233, 37980}, {3329, 13595}, {3511, 6660}, {3767, 20960}, {3815, 20775}, {3852, 51324}, {5020, 58464}, {5254, 27369}, {5306, 40981}, {5899, 9301}, {7418, 43460}, {7669, 33983}, {7736, 34098}, {7746, 11360}, {7792, 35222}, {8667, 9909}, {9766, 20794}, {10312, 15257}, {10540, 18322}, {11185, 35924}, {11325, 44518}, {13207, 35265}, {14965, 58355}, {16318, 52604}, {16950, 18092}, {17938, 36897}, {20885, 37637}, {20897, 46319}, {20989, 51928}, {20998, 51983}, {21284, 30715}, {21525, 36822}, {26184, 39784}, {33651, 33769}, {33875, 40350}, {33900, 37914}, {34229, 37184}, {34787, 40801}, {34809, 41266}, {36851, 37187}, {40643, 41334}, {42444, 58486}, {44886, 47200}, {46511, 53570}, {46522, 53419}

X(60514) = isogonal conjugate of X(55033)
X(60514) = isogonal conjugate of the anticomplement of X(40601)
X(60514) = isogonal conjugate of the isotomic conjugate of X(14957)
X(60514) = polar conjugate of the isotomic conjugate of X(14965)
X(60514) = tangential isogonal conjugate of X(52162)
X(60514) = X(82)-complementary conjugate of X(52878)
X(60514) = X(i)-Ceva conjugate of X(j) for these (i,j): {290, 6}, {14957, 14965}
X(60514) = X(1)-isoconjugate of X(55033)
X(60514) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 55033}, {237, 511}
X(60514) = crossdifference of every pair of points on line {39, 525}
X(60514) = barycentric product X(i)*X(j) for these {i,j}: {1, 16564}, {4, 14965}, {6, 14957}, {290, 40601}, {2052, 58355}
X(60514) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 55033}, {14957, 76}, {14965, 69}, {16564, 75}, {40601, 511}, {58355, 394}
X(60514) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {22, 183, 8266}, {23, 385, 51862}, {23, 9149, 5201}, {385, 51862, 5201}, {2070, 5938, 39857}, {9149, 51862, 385}, {20987, 44524, 25}, {45428, 45429, 20987}

X(60515) = X(2)X(1235)∩X(66)X(68)

Barycentrics    b^2*c^2*(-a^4 + b^4 - c^4)*(a^4 + b^4 - c^4)*(-(a^2*b^2) + b^4 - a^2*c^2 - 2*b^2*c^2 + c^4) : :

X(60515) lies on the cubic K1354 and these lines: {2, 1235}, {5, 41168}, {26, 2353}, {52, 27372}, {66, 68}, {290, 11610}, {339, 27376}, {343, 41480}, {1289, 3518}, {7512, 41377}, {7516, 60007}, {10002, 18855}, {10316, 30737}, {28405, 59156}, {34138, 36952}

X(60515) = polar conjugate of the isogonal conjugate of X(41168)
X(60515) = X(18018)-Ceva conjugate of X(41168)
X(60515) = X(i)-isoconjugate of X(j) for these (i,j): {22, 2148}, {54, 2172}, {95, 17453}, {206, 2167}, {1760, 54034}, {2169, 8743}, {2190, 10316}, {2485, 36134}, {7251, 44687}, {14573, 20641}, {17186, 56254}, {22075, 40440}
X(60515) = X(i)-Dao conjugate of X(j) for these (i,j): {5, 10316}, {137, 2485}, {216, 22}, {338, 33294}, {14363, 8743}, {35441, 47413}, {39019, 8673}, {40588, 206}, {52032, 20806}, {52869, 52950}
X(60515) = barycentric product X(i)*X(j) for these {i,j}: {5, 18018}, {51, 40421}, {66, 311}, {264, 41168}, {324, 14376}, {343, 43678}, {1953, 46244}, {13854, 28706}, {18022, 27372}, {18314, 44766}, {34138, 53245}
X(60515) = barycentric quotient X(i)/X(j) for these {i,j}: {5, 22}, {51, 206}, {53, 8743}, {66, 54}, {216, 10316}, {217, 22075}, {311, 315}, {324, 17907}, {343, 20806}, {1289, 933}, {1953, 2172}, {2156, 2148}, {2179, 17453}, {2353, 54034}, {3199, 17409}, {6368, 8673}, {12077, 2485}, {13450, 52448}, {13854, 8882}, {14213, 1760}, {14376, 97}, {14391, 14396}, {14570, 4611}, {18018, 95}, {18314, 33294}, {21011, 4456}, {23290, 59932}, {27371, 40938}, {27372, 184}, {28706, 34254}, {35360, 52915}, {35442, 47413}, {40146, 14573}, {40421, 34384}, {40981, 20968}, {41168, 3}, {43678, 275}, {44766, 18315}, {52945, 52950}, {53245, 31636}
X(60515) = {X(18018),X(43678)}-harmonic conjugate of X(14376)

X(60516) = X(2)X(1235)∩X(4)X(51)

Barycentrics    b^2*c^2*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2)*(-2*a^6 + a^4*b^2 + b^6 + a^4*c^2 - b^4*c^2 - b^2*c^4 + c^6) : :

X(60516) lies on the cubic K1354 and these lines: {2, 1235}, {4, 51}, {23, 53769}, {76, 459}, {94, 60133}, {107, 41377}, {112, 401}, {186, 47207}, {196, 26735}, {232, 44893}, {237, 47202}, {264, 1249}, {287, 41363}, {290, 9476}, {297, 525}, {311, 17907}, {324, 458}, {338, 1990}, {339, 44334}, {393, 41760}, {394, 56015}, {419, 685}, {441, 9475}, {460, 2970}, {648, 3260}, {1316, 58311}, {2393, 46151}, {2409, 34156}, {2782, 15143}, {2967, 21531}, {3978, 44132}, {5392, 52583}, {6248, 59529}, {8744, 41254}, {9308, 26206}, {9512, 44096}, {13567, 27376}, {14615, 56013}, {14957, 35360}, {15595, 51434}, {16080, 46105}, {17555, 26592}, {18687, 31623}, {19222, 43710}, {20300, 41170}, {21243, 39604}, {21447, 33630}, {23300, 41375}, {26541, 37448}, {35474, 40664}, {36212, 41676}, {36851, 41766}, {37124, 43651}, {37765, 44138}, {40684, 41366}, {41253, 46571}, {44143, 56301}, {44549, 60428}, {51334, 59533}, {56270, 60266}
on K1354

X(60516) = polar conjugate of X(1297)
X(60516) = isotomic conjugate of the isogonal conjugate of X(16318)
X(60516) = polar conjugate of the isotomic conjugate of X(30737)
X(60516) = polar conjugate of the isogonal conjugate of X(1503)
X(60516) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {8767, 56570}, {34168, 4329}
X(60516) = X(i)-Ceva conjugate of X(j) for these (i,j): {290, 4}, {16081, 57490}
X(60516) = X(i)-isoconjugate of X(j) for these (i,j): {48, 1297}, {163, 2435}, {255, 43717}, {520, 36046}, {577, 8767}, {822, 44770}, {1755, 15407}, {4575, 34212}, {6330, 52430}, {9247, 35140}, {9417, 57761}, {24018, 32649}, {32320, 36092}, {35200, 51937}
X(60516) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 2435}, {133, 51937}, {136, 34212}, {232, 511}, {441, 36212}, {1249, 1297}, {1503, 8779}, {6523, 43717}, {15595, 394}, {16318, 34146}, {23976, 3}, {33504, 520}, {36899, 15407}, {36901, 2419}, {39058, 57761}, {39071, 577}, {39073, 3289}, {40938, 46164}, {50938, 6}, {56794, 206}, {60341, 47409}
X(60516) = cevapoint of X(i) and X(j) for these (i,j): {6, 34131}, {232, 34146}, {1503, 16318}
X(60516) = trilinear pole of line {132, 50938}
X(60516) = crossdifference of every pair of points on line {184, 32320}
X(60516) = barycentric product X(i)*X(j) for these {i,j}: {4, 30737}, {76, 16318}, {132, 290}, {232, 51257}, {264, 1503}, {276, 51363}, {297, 57490}, {308, 51434}, {325, 52641}, {340, 43089}, {441, 2052}, {850, 2409}, {1235, 21458}, {1502, 51437}, {1529, 59256}, {1969, 2312}, {2445, 44173}, {3267, 23977}, {7017, 43045}, {8766, 57806}, {8779, 18027}, {9475, 60199}, {14208, 24024}, {14249, 16096}, {14618, 34211}, {15352, 39473}, {15595, 16081}, {16089, 51960}, {17875, 36120}, {18022, 42671}, {32230, 58258}, {35282, 46111}, {36894, 37778}, {41174, 57430}, {43187, 55275}, {44132, 51963}, {44145, 56572}
X(60516) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 1297}, {98, 15407}, {107, 44770}, {132, 511}, {158, 8767}, {264, 35140}, {290, 57761}, {393, 43717}, {419, 51343}, {427, 46164}, {441, 394}, {523, 2435}, {850, 2419}, {1289, 46967}, {1503, 3}, {1529, 1350}, {1990, 51937}, {2052, 6330}, {2312, 48}, {2409, 110}, {2445, 1576}, {2501, 34212}, {6529, 32687}, {6530, 39265}, {6793, 3284}, {8766, 255}, {8779, 577}, {9475, 3289}, {14249, 14944}, {14618, 43673}, {15595, 36212}, {16081, 9476}, {16096, 15394}, {16318, 6}, {21458, 1176}, {23976, 8779}, {23977, 112}, {24019, 36046}, {24023, 8766}, {24024, 162}, {28343, 10317}, {30737, 69}, {32713, 32649}, {34156, 17974}, {34211, 4558}, {34854, 51822}, {35282, 3292}, {36126, 36092}, {37778, 56601}, {39473, 52613}, {42671, 184}, {43045, 222}, {43089, 265}, {43187, 55274}, {44145, 56687}, {50938, 34146}, {51257, 57799}, {51363, 216}, {51434, 39}, {51437, 32}, {51647, 603}, {51960, 14941}, {51963, 248}, {52641, 98}, {52661, 52485}, {53568, 13754}, {55129, 8673}, {55275, 3569}, {56572, 43705}, {57296, 47409}, {57430, 41172}, {57490, 287}
X(60516) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {76, 15466, 52283}, {297, 51481, 44146}, {324, 458, 44142}, {338, 1990, 37778}, {393, 41760, 44131}, {458, 56296, 8743}, {2052, 40814, 4}, {2592, 2593, 50188}, {5523, 51358, 50188}, {17907, 59156, 311}, {41361, 43678, 1235}, {46106, 51481, 297}

X(60517) = X(2)X(290)∩X(4)X(32)

Barycentrics    (a^4 + b^4 - a^2*c^2 - b^2*c^2)*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)*(a^4 - a^2*b^2 - b^2*c^2 + c^4) : :

X(60517) lies on the circumconic {{A,B,C,X(4),X(5)}}, the cubics K1354 and 1355, and these lines:{2, 290}, {4, 32}, {5, 217}, {6, 3613}, {39, 37121}, {51, 52878}, {53, 40981}, {148, 54086}, {187, 34175}, {206, 1976}, {216, 311}, {230, 237}, {232, 44893}, {287, 3618}, {393, 15352}, {569, 17974}, {879, 1987}, {1141, 2715}, {1316, 57261}, {1910, 32675}, {1989, 2395}, {2422, 60037}, {2548, 16837}, {2782, 47406}, {2966, 40853}, {2980, 51542}, {3016, 43620}, {3199, 13450}, {3289, 21531}, {3331, 43291}, {5106, 36874}, {5167, 15630}, {5254, 54003}, {5309, 54991}, {5523, 40079}, {6394, 34229}, {7745, 54005}, {7746, 14265}, {7797, 39685}, {8901, 35325}, {11674, 13137}, {13881, 32445}, {14600, 34449}, {14601, 51820}, {15081, 31415}, {16083, 46511}, {16989, 31636}, {17008, 31635}, {17500, 36412}, {17703, 38297}, {20026, 36897}, {21458, 41932}, {21731, 53149}, {27364, 42459}, {32828, 37186}, {34579, 41079}, {36822, 37637}, {37114, 56688}, {38227, 39682}, {43665, 54547}, {47202, 51334}, {47635, 53416}

X(60517) = isogonal conjugate of the isotomic conjugate of X(53245)
X(60517) = polar conjugate of the isotomic conjugate of X(53174)
X(60517) = X(i)-Ceva conjugate of X(j) for these (i,j): {2715, 2395}, {53245, 53174}
X(60517) = X(i)-isoconjugate of X(j) for these (i,j): {54, 1959}, {63, 19189}, {75, 41270}, {95, 1755}, {97, 240}, {297, 2169}, {304, 58306}, {325, 2148}, {511, 2167}, {2168, 51439}, {2190, 36212}, {2421, 2616}, {2799, 36134}, {3289, 40440}, {3405, 16030}, {9417, 34384}, {14533, 40703}, {15412, 23997}, {17209, 56254}, {34386, 57653}, {43034, 44687}, {46238, 54034}
X(60517) = X(i)-Dao conjugate of X(j) for these (i,j): {5, 36212}, {137, 2799}, {206, 41270}, {216, 325}, {3162, 19189}, {14363, 297}, {15450, 684}, {36899, 95}, {39019, 6333}, {39058, 34384}, {39085, 97}, {40588, 511}, {52032, 6393}, {52869, 51389}, {52878, 11672}
X(60517) = cevapoint of X(i) and X(j) for these (i,j): {51, 52967}, {6130, 7668}
X(60517) = trilinear pole of line {51, 12077}
X(60517) = crossdifference of every pair of points on line {684, 9420}
X(60517) = barycentric product X(i)*X(j) for these {i,j}: {4, 53174}, {5, 98}, {6, 53245}, {51, 290}, {53, 287}, {216, 16081}, {217, 60199}, {248, 324}, {311, 1976}, {336, 2181}, {343, 6531}, {685, 6368}, {879, 35360}, {1625, 43665}, {1821, 1953}, {1910, 14213}, {2179, 46273}, {2395, 14570}, {2618, 36084}, {2715, 18314}, {2966, 12077}, {3199, 57799}, {6394, 14569}, {9154, 41586}, {9476, 51363}, {13450, 17974}, {15451, 22456}, {17500, 20021}, {17932, 51513}, {18024, 40981}, {23290, 43754}, {28706, 57260}, {35362, 58784}, {36120, 44706}, {39569, 47388}, {41221, 57991}, {43187, 55219}, {52451, 60035}, {52967, 57541}
X(60517) = barycentric quotient X(i)/X(j) for these {i,j}: {5, 325}, {25, 19189}, {32, 41270}, {51, 511}, {52, 51439}, {53, 297}, {98, 95}, {143, 51440}, {216, 36212}, {217, 3289}, {248, 97}, {287, 34386}, {290, 34384}, {324, 44132}, {343, 6393}, {685, 18831}, {878, 23286}, {1154, 51383}, {1625, 2421}, {1910, 2167}, {1953, 1959}, {1974, 58306}, {1976, 54}, {2179, 1755}, {2181, 240}, {2395, 15412}, {2422, 2623}, {2715, 18315}, {3199, 232}, {5562, 51386}, {6368, 6333}, {6531, 275}, {7069, 44694}, {12077, 2799}, {14213, 46238}, {14569, 6530}, {14570, 2396}, {14600, 14533}, {14601, 54034}, {15451, 684}, {16081, 276}, {17167, 51370}, {17500, 20022}, {18180, 51369}, {20031, 16813}, {32696, 933}, {35360, 877}, {35362, 4576}, {35906, 43768}, {36120, 40440}, {40981, 237}, {41221, 868}, {41586, 50567}, {41588, 51374}, {43187, 55218}, {51363, 15595}, {51404, 53576}, {51441, 8901}, {51513, 16230}, {51869, 16030}, {52604, 4230}, {52945, 51389}, {52967, 11672}, {53173, 15414}, {53174, 69}, {53245, 76}, {55219, 3569}, {57260, 8882}, {59197, 51373}, {60199, 57790}
X(60517) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {98, 6531, 248}, {230, 51441, 48452}, {248, 6531, 35906}

X(60518) = X(2)X(6)∩X(51)X(311)

Barycentrics    (a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)*(a^6 - 2*a^4*b^2 + a^2*b^4 - 2*a^4*c^2 - a^2*b^2*c^2 + b^4*c^2 + a^2*c^4 + b^2*c^4) : :

X(60518) lies on the cubic K1354 and these lines: {2, 6}, {51, 311}, {52, 28706}, {76, 3567}, {290, 20022}, {315, 18912}, {316, 25739}, {850, 924}, {1078, 43651}, {1273, 41586}, {1899, 44128}, {3135, 40697}, {3266, 51439}, {4558, 41270}, {4576, 51440}, {5207, 13137}, {6337, 37114}, {9418, 25314}, {12215, 37123}, {25053, 30737}, {40981, 41588}, {44146, 52000}

X(60518) = X(60037)-anticomplementary conjugate of X(21221)
X(60518) = X(290)-Ceva conjugate of X(311)
X(60518) = barycentric product X(i)*X(j) for these {i,j}: {14570, 53331}, {19128, 28706}, {45123, 57799}
X(60518) = barycentric quotient X(i)/X(j) for these {i,j}: {19128, 8882}, {45123, 232}, {53263, 2623}, {53331, 15412}
X(60518) = {X({}),X(1)}-harmonic conjugate of X({}[[1]][[3]])

X(60519) = X(2)X(311)∩X(6)X(14768)

Barycentrics    b^2*c^2*(a^4 - 2*a^2*b^2 + b^4 - 2*b^2*c^2 + c^4)*(a^4 + b^4 - 2*a^2*c^2 - 2*b^2*c^2 + c^4)*(2*a^4 - a^2*b^2 + b^4 - a^2*c^2 - 2*b^2*c^2 + c^4) : :

X(60519) lies on the cubic K1354 and these lines: {2, 311}, {6, 14768}, {51, 14593}, {68, 54393}, {230, 2974}, {686, 2501}, {847, 47735}, {9418, 32734}, {11610, 41932}, {41334, 56272}

X(60519) = X(i)-isoconjugate of X(j) for these (i,j): {47, 2987}, {563, 35142}, {571, 8773}, {1748, 42065}, {1993, 36051}, {10425, 55216}, {30451, 36105}, {32654, 44179}
X(60519) = X(i)-Dao conjugate of X(j) for these (i,j): {114, 1993}, {230, 51439}, {34156, 51776}, {34853, 2987}, {35067, 9723}, {37864, 32654}, {39001, 30451}, {39069, 47}, {39072, 571}, {55152, 924}
X(60519) = crossdifference of every pair of points on line {1147, 34952}
X(60519) = barycentric product X(i)*X(j) for these {i,j}: {68, 44145}, {91, 1733}, {230, 5392}, {460, 20563}, {847, 3564}, {1692, 57904}, {2165, 51481}, {8772, 20571}, {46134, 55122}, {52144, 55553}
X(60519) = barycentric quotient X(i)/X(j) for these {i,j}: {68, 43705}, {91, 8773}, {114, 51439}, {230, 1993}, {460, 24}, {847, 35142}, {925, 10425}, {1692, 571}, {1733, 44179}, {2165, 2987}, {2351, 42065}, {3564, 9723}, {5392, 8781}, {8772, 47}, {14265, 31635}, {14593, 3563}, {20563, 57872}, {42663, 34952}, {44099, 44077}, {44145, 317}, {51431, 51393}, {51481, 7763}, {52144, 1147}, {55122, 924}

X(60520) = X(2)X(11794)∩X(4)X(27370)

Barycentrics    b^2*c^2*(a^4 + b^4 - a^2*c^2 - b^2*c^2)*(-(a^2*b^2) + b^4 - a^2*c^2 - b^2*c^2)*(-a^4 + a^2*b^2 + b^2*c^2 - c^4)*(a^2*b^2 + a^2*c^2 + b^2*c^2 - c^4) : :

X(60520) lies on the Kiepert circumhjyperbola, the cubic K1354, and these lines: {2, 11794}, {4, 27370}, {51, 30505}, {76, 36952}, {83, 290}, {98, 34133}, {262, 3613}, {275, 16081}, {287, 40393}, {338, 9419}, {511, 35098}, {3406, 14265}, {7607, 51259}, {18024, 31630}, {20021, 55028}, {34845, 36200}, {52145, 60128}, {53174, 54832}, {57799, 60101}

X(60520) = X(53701)-Ceva conjugate of X(43665)
X(60520) = X(i)-isoconjugate of X(j) for these (i,j): {237, 18042}, {1078, 9417}, {1755, 5012}, {3050, 23997}, {3203, 3405}, {9418, 33764}
X(60520) = X(i)-Dao conjugate of X(j) for these (i,j): {36899, 5012}, {39058, 1078}
X(60520) = cevapoint of X(338) and X(3569)
X(60520) = trilinear pole of line {523, 3613}
X(60520) = barycentric product X(i)*X(j) for these {i,j}: {290, 3613}, {850, 53701}, {11794, 43665}, {16081, 36952}, {18024, 27375}
X(60520) = barycentric quotient X(i)/X(j) for these {i,j}: {98, 5012}, {290, 1078}, {1821, 18042}, {2395, 3050}, {3613, 511}, {6531, 10312}, {11794, 2421}, {16081, 36794}, {18024, 33769}, {20021, 41328}, {27375, 237}, {30505, 51862}, {36952, 36212}, {43665, 31296}, {46273, 33764}, {51404, 38352}, {51869, 3203}, {53701, 110}

X(60521) = X(4)X(27370)∩X(6)X(157)

Barycentrics    a^2*(a^4 + b^4 - a^2*c^2 - b^2*c^2)*(a^2*b^2 - b^4 + a^2*c^2 - b^2*c^2 - c^4)*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)*(a^4 - a^2*b^2 - b^2*c^2 + c^4) : :
X(60521) = 3 X[51] - 2 X[52878], 4 X[52878] - 3 X[52926]

X(60521) lies on the cubic K1354 and these lines: {4, 27370}, {6, 157}, {26, 17974}, {51, 52878}, {52, 27372}, {98, 3567}, {290, 3060}, {3202, 39575}, {5890, 55006}, {7731, 52190}, {9969, 20021}, {10263, 53795}

X(60521) = reflection of X(52926) in X(51)
X(60521) = X(51)-Dao conjugate of X(511)
X(60521) = barycentric product X(i)*X(j) for these {i,j}: {98, 41480}, {160, 53245}, {290, 40588}, {15897, 57799}, {39575, 53174}
X(60521) = barycentric quotient X(i)/X(j) for these {i,j}: {3202, 41270}, {15897, 232}, {40588, 511}, {41480, 325}, {53245, 44185}

X(60522) = X(2)X(3)∩X(51)X(41334)

Barycentrics    a^2*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)*(a^8 - a^6*b^2 - a^4*b^4 + a^2*b^6 - a^6*c^2 - a^4*b^2*c^2 + a^2*b^4*c^2 + b^6*c^2 - a^4*c^4 + a^2*b^2*c^4 - 2*b^4*c^4 + a^2*c^6 + b^2*c^6) : :

X(60522) lies on the cubic K1354 and these lines: {2, 3}, {51, 41334}, {154, 3202}, {161, 2387}, {290, 51862}, {512, 34983}, {2055, 19173}, {10313, 38368}, {10317, 58311}, {11365, 51703}, {15649, 51735}, {32428, 53245}, {34417, 50678}, {40981, 42459}, {52604, 52945}

X(60522) = X(i)-Ceva conjugate of X(j) for these (i,j): {290, 41334}, {1297, 216}, {35098, 6}
X(60522) = crossdifference of every pair of points on line {647, 14773}
X(60522) = barycentric product X(i)*X(j) for these {i,j}: {5, 10313}, {1625, 53345}, {14570, 53265}
X(60522) = barycentric quotient X(i)/X(j) for these {i,j}: {10313, 95}, {53265, 15412}, {58317, 2623}
X(60522) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {22, 458, 3}, {23, 7473, 2070}, {237, 460, 21177}, {297, 44894, 56961}, {3129, 3130, 44890}

X(60523) = X(2)X(34157)∩X(230)X(237)

Barycentrics    (a^4 + b^4 - a^2*c^2 - b^2*c^2)*(a^4 - a^2*b^2 - b^2*c^2 + c^4)*(a^4*b^2 - 2*a^2*b^4 + b^6 + a^4*c^2 - a^2*b^2*c^2 - 2*b^4*c^2 + a^2*c^4 + b^2*c^4)*(a^4*b^2 + a^2*b^4 + a^4*c^2 - a^2*b^2*c^2 + b^4*c^2 - 2*a^2*c^4 - 2*b^2*c^4 + c^6) : :

X(60523) lies on the cubic K1354 and these lines: {2, 34157}, {32, 51820}, {98, 46518}, {230, 237}, {290, 20022}, {460, 2211}, {511, 14957}, {2698, 34536}, {6531, 58306}, {14251, 47734}, {36874, 52765}, {51980, 52450}

X(60523) = X(i)-isoconjugate of X(j) for these (i,j): {811, 38354}, {23997, 53331}, {24041, 38987}
X(60523) = X(i)-Dao conjugate of X(j) for these (i,j): {3005, 38987}, {17423, 38354}
X(60523) = cevapoint of X(512) and X(51441)
X(60523) = trilinear pole of line {2491, 55122}
X(60523) = barycentric quotient X(i)/X(j) for these {i,j}: {2395, 53331}, {2422, 53263}, {3049, 38354}, {3124, 38987}, {3199, 45123}, {57260, 19128}

X(60524) = X(2)X(32)∩X(5)X(51)

Barycentrics    (a^2*b^2 - b^4 + a^2*c^2 - c^4)*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4) : :

X(60524) lies on the cubic K1355 and these lines: {2, 32}, {5, 51}, {23, 38745}, {39, 41237}, {50, 46184}, {53, 52347}, {76, 52247}, {99, 40853}, {114, 237}, {115, 51481}, {125, 21531}, {127, 441}, {216, 39113}, {231, 44376}, {232, 297}, {233, 57805}, {287, 5207}, {311, 36412}, {316, 401}, {324, 27371}, {340, 40888}, {394, 7776}, {458, 7773}, {467, 3199}, {511, 2450}, {524, 16310}, {577, 44128}, {620, 35296}, {625, 3580}, {648, 44363}, {868, 23098}, {1273, 14570}, {1634, 45918}, {1975, 52282}, {1993, 7759}, {1994, 7838}, {2072, 47207}, {2393, 45921}, {2794, 37183}, {3001, 53569}, {3003, 44388}, {3148, 54393}, {3260, 15526}, {3313, 23333}, {3767, 6515}, {3788, 52275}, {3926, 37174}, {3934, 37636}, {5025, 40814}, {5112, 59707}, {5422, 7834}, {5461, 44555}, {5475, 41231}, {5965, 41205}, {6033, 6660}, {6503, 7387}, {7751, 45794}, {7778, 37344}, {7799, 40885}, {7802, 51350}, {7805, 41628}, {7813, 54395}, {7829, 34545}, {7844, 37644}, {7866, 10601}, {11064, 44334}, {11433, 14064}, {11623, 41724}, {12077, 18314}, {13567, 40379}, {14790, 34225}, {15595, 40601}, {20399, 35298}, {20541, 25007}, {20854, 38743}, {21243, 37988}, {21245, 26543}, {21536, 51360}, {22151, 23583}, {32006, 37188}, {32152, 37457}, {32458, 46807}, {32823, 52283}, {36426, 44132}, {36790, 51371}, {39569, 44716}, {40588, 52032}, {44347, 51430}

X(60524) = reflection of X(50) in X(46184)
X(60524) = isotomic conjugate of the polar conjugate of X(39569)
X(60524) = polar conjugate of the isogonal conjugate of X(44716)
X(60524) = X(661)-complementary conjugate of X(38987)
X(60524) = X(i)-Ceva conjugate of X(j) for these (i,j): {325, 44716}, {2421, 2799}
X(60524) = X(i)-isoconjugate of X(j) for these (i,j): {54, 1910}, {98, 2148}, {248, 2190}, {293, 8882}, {1821, 54034}, {1976, 2167}, {2169, 6531}, {2395, 36134}, {2616, 2715}, {2623, 36084}, {14533, 36120}, {14573, 46273}, {14600, 40440}, {23286, 36104}
X(60524) = X(i)-Dao conjugate of X(j) for these (i,j): {5, 248}, {132, 8882}, {137, 2395}, {216, 98}, {338, 43665}, {343, 51776}, {511, 41270}, {5976, 95}, {11672, 54}, {14363, 6531}, {15450, 878}, {35088, 15412}, {38987, 2623}, {39000, 23286}, {39019, 879}, {39039, 2190}, {39040, 2167}, {40588, 1976}, {40601, 54034}, {46094, 14533}, {52032, 287}, {52869, 35906}, {52878, 32}, {55267, 8901}
X(60524) = crossdifference of every pair of points on line {878, 2623}
X(60524) = barycentric product X(i)*X(j) for these {i,j}: {5, 325}, {53, 6393}, {69, 39569}, {216, 44132}, {232, 28706}, {240, 18695}, {264, 44716}, {297, 343}, {311, 511}, {324, 36212}, {877, 6368}, {1273, 14356}, {1502, 52967}, {1953, 46238}, {1959, 14213}, {2396, 12077}, {2421, 18314}, {2799, 14570}, {6333, 35360}, {6530, 52347}, {13450, 51386}, {14966, 15415}, {17500, 51371}, {18180, 42703}, {21011, 51370}, {25043, 51440}, {27364, 51374}, {36790, 53245}, {40703, 44706}, {46807, 59197}, {51439, 56272}
X(60524) = barycentric quotient X(i)/X(j) for these {i,j}: {5, 98}, {51, 1976}, {53, 6531}, {216, 248}, {217, 14600}, {232, 8882}, {237, 54034}, {240, 2190}, {297, 275}, {311, 290}, {324, 16081}, {325, 95}, {343, 287}, {511, 54}, {684, 23286}, {868, 8901}, {877, 18831}, {1154, 14355}, {1568, 35912}, {1625, 2715}, {1755, 2148}, {1953, 1910}, {1959, 2167}, {2421, 18315}, {2617, 36084}, {2799, 15412}, {2967, 19189}, {3199, 57260}, {3289, 14533}, {3569, 2623}, {4230, 933}, {5562, 17974}, {5891, 11653}, {6368, 879}, {6393, 34386}, {6530, 8884}, {9418, 14573}, {11672, 41270}, {12077, 2395}, {14213, 1821}, {14356, 1141}, {14570, 2966}, {14966, 14586}, {15451, 878}, {17994, 58756}, {18314, 43665}, {18695, 336}, {20022, 39287}, {23181, 43754}, {23997, 36134}, {28706, 57799}, {32428, 32545}, {35360, 685}, {36212, 97}, {39113, 31635}, {39469, 58308}, {39569, 4}, {40703, 40440}, {40804, 1298}, {40981, 14601}, {41221, 51441}, {41586, 5967}, {42703, 56189}, {44132, 276}, {44694, 44687}, {44704, 38808}, {44706, 293}, {44716, 3}, {45123, 19128}, {45793, 53245}, {46807, 42300}, {51363, 51963}, {51389, 43768}, {51513, 53149}, {52032, 51776}, {52347, 6394}, {52604, 32696}, {52926, 32716}, {52945, 35906}, {52967, 32}, {53174, 47388}, {53245, 34536}, {55219, 2422}, {59197, 46806}, {59208, 51542}
X(60524) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 343, 59197}, {297, 325, 36212}, {297, 36212, 51389}, {7776, 52251, 394}, {33529, 33530, 41586}

X(60525) = X(2)X(3613)∩X(51)X(216)

Barycentrics    a^4*(a^4 - a^2*b^2 - a^2*c^2 - b^2*c^2)*(a^2*b^2 - b^4 + a^2*c^2 - c^4)*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4) : :

X(60525) lies on the cubic K1355 and these lines: {2, 3613}, {51, 216}, {132, 39569}, {160, 60106}, {237, 3289}, {511, 46094}, {3618, 26874}, {5188, 52042}, {6638, 21970}, {30737, 36901}

X(60525) = X(53245)-Ceva conjugate of X(217)
X(60525) = X(i)-Dao conjugate of X(j) for these (i,j): {46394, 53245}, {52878, 3613}
X(60525) = crossdifference of every pair of points on line {15412, 43665}
X(60525) = barycentric product X(i)*X(j) for these {i,j}: {511, 41334}, {1078, 52967}, {3289, 30506}, {10312, 44716}
X(60525) = barycentric quotient X(i)/X(j) for these {i,j}: {30506, 60199}, {41334, 290}, {52967, 3613}
X(60525) = {X(418),X(40981)}-harmonic conjugate of X(59208)

X(60526) = X(5)X(39)∩X(51)X(1196)

Barycentrics    a^2*(a^4*b^2 - 2*a^2*b^4 + b^6 + a^4*c^2 - a^2*b^2*c^2 - 2*b^4*c^2 + a^2*c^4 + b^2*c^4)*(a^4*b^2 + a^2*b^4 + a^4*c^2 - a^2*b^2*c^2 + b^4*c^2 - 2*a^2*c^4 - 2*b^2*c^4 + c^6) : :

X(60526) lies on the cubic K1355 and these lines: {5, 39}, {32, 51906}, {51, 1196}, {98, 46039}, {216, 2974}, {232, 44145}, {511, 51455}, {1194, 31613}, {1692, 9418}, {2021, 21177}, {2491, 55122}, {2971, 3199}, {3291, 46156}, {5661, 44531}, {21807, 21814}

X(60526) = X(i)-isoconjugate of X(j) for these (i,j): {304, 19128}, {662, 53331}, {799, 53263}
X(60526) = X(i)-Dao conjugate of X(j) for these (i,j): {1084, 53331}, {38996, 53263}
X(60526) = cevapoint of X(i) and X(j) for these (i,j): {1084, 42663}, {2491, 3124}, {3005, 44114}, {21637, 52144}
X(60526) = trilinear pole of line {688, 22260}
X(60526) = crossdifference of every pair of points on line {38354, 53263}
X(60526) = barycentric quotient X(i)/X(j) for these {i,j}: {512, 53331}, {669, 53263}, {1974, 19128}, {58260, 38987}

X(60527) = X(6)X(19166)∩X(51)X(125)

Barycentrics    (a^6*b^2 - a^4*b^4 - a^2*b^6 + b^8 + a^6*c^2 + a^4*b^2*c^2 - a^2*b^4*c^2 - b^6*c^2 - 2*a^4*c^4 + a^2*b^2*c^4 - b^4*c^4 + a^2*c^6 + b^2*c^6)*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + a^6*c^2 + a^4*b^2*c^2 + a^2*b^4*c^2 + b^6*c^2 - a^4*c^4 - a^2*b^2*c^4 - b^4*c^4 - a^2*c^6 - b^2*c^6 + c^8) : :

X(60527) lies on the cubic K1355 and these lines: {6, 19166}, {51, 125}, {53, 338}, {141, 216}, {206, 45838}, {237, 1503}, {297, 53245}, {343, 8024}, {2351, 15577}, {3580, 31125}, {3613, 6697}, {5596, 34285}, {23292, 35325}, {23297, 37648}, {53864, 58450}

X(60527) = isogonal conjugate of X(10313)
X(60527) = X(i)-isoconjugate of X(j) for these (i,j): {1, 10313}, {163, 53345}, {662, 53265}, {799, 58317}
X(60527) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 10313}, {115, 53345}, {647, 3150}, {1084, 53265}, {38996, 58317}, {41167, 39000}
X(60527) = cevapoint of X(i) and X(j) for these (i,j): {125, 3569}, {868, 12077}, {3575, 16318}
X(60527) = trilinear pole of line {826, 3574}
X(60527) = crossdifference of every pair of points on line {53265, 58317}
X(60527) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 10313}, {125, 3150}, {512, 53265}, {523, 53345}, {669, 58317}, {34221, 5005}, {34222, 5004}, {41172, 39000}, {44114, 38368}

X(60528) = X(2)X(52878)∩X(5)X(127)

Barycentrics    a^2*(a^6*b^2 + a^4*b^4 - a^2*b^6 - b^8 + a^6*c^2 - a^4*b^2*c^2 + a^2*b^4*c^2 - b^6*c^2 - 2*a^4*c^4 - a^2*b^2*c^4 + b^4*c^4 + a^2*c^6 + b^2*c^6)*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + a^6*c^2 - a^4*b^2*c^2 - a^2*b^4*c^2 + b^6*c^2 + a^4*c^4 + a^2*b^2*c^4 + b^4*c^4 - a^2*c^6 - b^2*c^6 - c^8) : :

X(60528) lies on the cubic K1355 and these lines: {2, 52878}, {5, 127}, {206, 8266}, {216, 9475}, {1843, 15526}, {2871, 3313}, {2979, 59257}, {3819, 52926}, {3917, 11672}, {5188, 5562}, {14957, 30737}, {34218, 40080}

X(60528) = reflection of X(52926) in X(3819)
X(60528) = anticomplement of X(52878)
X(60528) = isotomic conjugate of the anticomplement of X(52967)
X(60528) = cevapoint of X(i) and X(j) for these (i,j): {511, 3819}, {2972, 39469}, {3005, 41172}, {5007, 42671}
X(60528) = trilinear pole of line {11205, 17434}
X(60528) = barycentric quotient X(52967)/X(52878)

X(60529) = X(3952)X(31290)∩X(4010)X(4977)

Barycentrics    a*(b - c)*(3*a*b + b^2 + a*c + 3*b*c)*(a*b + 3*a*c + 3*b*c + c^2) : :

X(60529) lies on these lines: {3952, 31290}, {4010, 4977}, {4979, 6372}, {28840, 58784}, {47906, 54256}

X(60529) = X(i)-isoconjugate of X(j) for these (i,j): {1018, 33766}, {1252, 31290}, {3952, 33774}, {4557, 33770}, {4629, 55343}, {24185, 59149}
X(60529) = X(i)-Dao conjugate of X(j) for these (i,j): {661, 31290}, {40620, 33779}
X(60529) = barycentric product X(514)*X(34585)
X(60529) = barycentric quotient X(i)/X(j) for these {i,j}: {244, 31290}, {764, 24185}, {1019, 33770}, {3733, 33766}, {4983, 55343}, {7192, 33779}, {8042, 40620}, {16726, 57059}, {34585, 190}, {57129, 33774}





leftri  Dao-Lozada circum-bicevian-perspectors: X(60530) - X(60551)  rightri

This preamble and centers X(60530)-X(60551) were contributed by César Eliud Lozada, November 10, 2023.

Let ABC be a triangle with circumcircle ω. Let P', P" be two interior points to ABC and A'B'C', A"B"C" their respective cevian triangles. Denote at the circle through A' and A" tangent to ω at At, with At lying on the arc BC of ω not containing A. Define bt, Bt, ct, Ct cyclically. Then the lines AAt, BBt, CCt concur at a point Q(P', P"). (Dao Thanh Oai, November 6, 2023).

The point Q(P', P") is named here the Dao-Lozada circum-bicevian-perspector of P' and P".

If P' = x' : y' : z' and P" = x" : y" : z" (barycentrics), then

At = -a^2/(c*Y + b*Z) : b/Z : c/Y
and
Q(P', P") = a*X : b*Y : c*Z
where X = sqrt(x'*x"), Y = sqrt(y'*y"), Z = sqrt(z'*z").

In general, the above concurrence does not occur for the second circles through the traces of P', P", tangent to ω and touching it at points on its positive arcs.

The appearance of (i, j, k) in the following list means that Q(X(i), X(j)) = X(k):

(1, 2, 365), (1, 6, 18753), (1, 7, 266), (1, 8, 259), (1, 9, 60530), (1, 10, 60531), (1, 11, 60532), (1, 12, 60533), (2, 6, 6), (2, 7, 509), (2, 8, 60534), (2, 9, 259), (2, 10, 60535), (2, 11, 60536), (2, 12, 60537), (6, 7, 60538), (6, 8, 60530), (6, 9, 60539), (6, 10, 60540), (6, 11, 60541), (6, 12, 60542), (7, 8, 1), (7, 9, 365), (7, 10, 60543), (7, 11, 14079), (7, 12, 65), (8, 9, 4166), (8, 10, 60544), (8, 11, 60545), (8, 12, 37), (9, 10, 60546), (9, 11, 60547), (9, 12, 60548), (10, 11, 60549), (10, 12, 60550), (11, 12, 60551)

underbar

X(60530) = DAO-LOZADA CIRCUM-BICEVIAN-PERSPECTOR OF X(1) AND X(9)

Barycentrics    a^(3/2)*cos(A/2) : :

X(60530) lies on these lines: {60538, 60542}

X(60530) = isogonal conjugate of X(508)
X(60530) = crosspoint of X(509) and X(60534)
X(60530) = crosssum of X(i) and X(j) for these {i, j}: {509, 60534}, {514, 5997}
X(60530) = X(509)-Ceva conjugate of-X(60538)
X(60530) = X(i)-Dao conjugate of-X(j) for these (i, j): (206, 60538), (5452, 55336), (32664, 509), (40600, 60537)
X(60530) = X(i)-isoconjugate of-X(j) for these {i, j}: {2, 509}, {7, 60534}, {57, 55336}, {75, 60538}, {86, 60537}, {174, 366}, {266, 18297}, {274, 60542}, {365, 4146}, {555, 4166}, {4182, 7371}
X(60530) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (31, 509), (32, 60538), (41, 60534), (55, 55336), (213, 60537), (259, 18297), (365, 4146), (508, 6063), (509, 85), (1918, 60542), (4166, 556), (18753, 174), (55336, 76), (60534, 75), (60536, 14080), (60537, 1441), (60538, 7), (60539, 366), (60541, 14078), (60542, 226)
X(60530) = NK-transform of X(i) for these i: {509, 60534}
X(60530) = pole of the line {508, 60538} with respect to the Stammler hyperbola
X(60530) = barycentric product X(i)*X(j) for these {i, j}: {1, 60534}, {6, 55336}, {8, 60538}, {9, 509}, {21, 60537}, {55, 508}, {174, 4166}, {188, 365}, {259, 366}, {266, 4182}, {333, 60542}, {556, 18753}, {4179, 6727}, {14087, 60541}, {18297, 60539}
X(60530) = trilinear product X(i)*X(j) for these {i, j}: {6, 60534}, {9, 60538}, {21, 60542}, {31, 55336}, {41, 508}, {55, 509}, {188, 18753}, {259, 365}, {266, 4166}, {284, 60537}, {366, 60539}, {6727, 60548}, {14085, 60536}
X(60530) = trilinear quotient X(i)/X(j) for these (i, j): (6, 509), (9, 55336), (31, 60538), (41, 60530), (42, 60537), (55, 60534), (188, 18297), (213, 60542), (259, 366), (365, 174), (366, 4146), (508, 85), (509, 7), (4166, 188), (4182, 556), (6726, 4182), (18753, 266), (55336, 75)

X(60531) = DAO-LOZADA CIRCUM-BICEVIAN-PERSPECTOR OF X(1) AND X(10)

Barycentrics    sqrt(a^3*(b+c)) : :

X(60531) lies on the cubics K362, K750, K1090, the curve Q182 and these lines: {}

X(60531) = X(40586)-Dao conjugate of-X(39131)
X(60531) = X(81)-isoconjugate of-X(39131)
X(60531) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (42, 39131), (39131, 75), (60535, 18297), (60540, 366), (60543, 4146), (60544, 556), (60546, 55336)
X(60531) = barycentric product X(i)*X(j) for these {i, j}: {1, 39131}, {174, 60544}, {188, 60543}, {366, 60535}, {508, 60546}, {18297, 60540}
X(60531) = trilinear product X(i)*X(j) for these {i, j}: {6, 39131}, {259, 60543}, {266, 60544}, {365, 60535}, {366, 60540}, {509, 60546}, {6727, 60550}
X(60531) = trilinear quotient X(i)/X(j) for these (i, j): (37, 39131), (42, 60531), (39131, 2)

X(60532) = DAO-LOZADA CIRCUM-BICEVIAN-PERSPECTOR OF X(1) AND X(11)

Barycentrics    a*abs(b-c)*cos(A/2) : :

X(60532) lies on these lines: {}

X(60532) = X(i)-isoconjugate of-X(j) for these {i, j}: {266, 14087}, {4146, 14085}, {14089, 60533}
X(60532) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (259, 14087), (6727, 14089), (14079, 4146), (14088, 174), (14090, 6724), (60536, 18297), (60541, 366), (60545, 556), (60547, 55336)
X(60532) = barycentric product X(i)*X(j) for these {i, j}: {174, 60545}, {188, 14079}, {259, 14078}, {366, 60536}, {508, 60547}, {556, 14088}, {6727, 14086}, {14080, 60539}, {18297, 60541}
X(60532) = trilinear product X(i)*X(j) for these {i, j}: {188, 14088}, {259, 14079}, {266, 60545}, {365, 60536}, {366, 60541}, {509, 60547}, {6727, 60551}, {14078, 60539}
X(60532) = trilinear quotient X(i)/X(j) for these (i, j): (188, 14087), (3271, 60532), (14078, 4146), (14079, 174), (14088, 266), (14090, 60533)

X(60533) = DAO-LOZADA CIRCUM-BICEVIAN-PERSPECTOR OF X(1) AND X(12)

Barycentrics    a*(b+c)*sin(A/2) : :

X(60533) lies on these lines: {174, 556}, {259, 260}, {5935, 8092}, {6724, 6725}

X(60533) = polar conjugate of the isotomic conjugate of X(7591)
X(60533) = crosspoint of X(174) and X(266)
X(60533) = crosssum of X(188) and X(259)
X(60533) = X(6725)-beth conjugate of-X(6725)
X(60533) = X(174)-Ceva conjugate of-X(6724)
X(60533) = X(i)-Dao conjugate of-X(j) for these (i, j): (10, 556), (236, 314), (1084, 6728), (15495, 274), (32664, 6727), (36908, 555), (38986, 6729), (40586, 188), (40590, 4146), (40599, 7027), (40600, 259), (40607, 6725), (40608, 6730), (40611, 174)
X(60533) = X(i)-isoconjugate of-X(j) for these {i, j}: {2, 6727}, {21, 174}, {58, 556}, {81, 188}, {86, 259}, {99, 6729}, {266, 333}, {274, 60539}, {284, 4146}, {555, 2328}, {662, 6728}, {757, 6725}, {1014, 6731}, {1043, 7370}, {1412, 7027}, {1414, 6730}, {1434, 6726}, {2185, 6724}, {2287, 7371}, {4560, 6733}, {7591, 46103}, {14089, 60532}
X(60533) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (31, 6727), (37, 556), (42, 188), (65, 4146), (174, 274), (181, 6724), (188, 314), (210, 7027), (213, 259), (259, 333), (266, 86), (512, 6728), (556, 28660), (798, 6729), (1042, 7371), (1334, 6731), (1400, 174), (1402, 266), (1427, 555), (1500, 6725), (1918, 60539), (3709, 6730), (4146, 310), (6724, 75), (6725, 312), (6726, 1043), (6727, 261), (6728, 18155), (6729, 4560), (6733, 99), (7370, 1434), (7371, 57785), (7591, 69), (60537, 18297), (60539, 21), (60542, 366), (60548, 55336)
X(60533) = barycentric product X(i)*X(j) for these {i, j}: {1, 6724}, {4, 7591}, {10, 266}, {12, 6727}, {37, 174}, {42, 4146}, {57, 6725}, {65, 188}, {210, 7371}, {226, 259}, {366, 60537}, {508, 60548}, {509, 4179}, {523, 6733}, {555, 1334}, {556, 1400}, {1020, 6730}, {1042, 7027}, {1427, 6731}, {1441, 60539}
X(60533) = trilinear product X(i)*X(j) for these {i, j}: {6, 6724}, {19, 7591}, {37, 266}, {42, 174}, {56, 6725}, {65, 259}, {188, 1400}, {210, 7370}, {213, 4146}, {226, 60539}, {365, 60537}, {366, 60542}, {509, 60548}, {556, 1402}, {661, 6733}, {1042, 6731}, {1334, 7371}, {1427, 6726}, {2171, 6727}, {4179, 60538}
X(60533) = trilinear quotient X(i)/X(j) for these (i, j): (6, 6727), (10, 556), (37, 188), (42, 259), (65, 174), (174, 86), (181, 60533), (188, 333), (210, 6731), (213, 60539), (226, 4146), (259, 21), (266, 81), (512, 6729), (555, 57785), (556, 314), (661, 6728), (756, 6725), (1042, 7370), (1334, 6726)

X(60534) = DAO-LOZADA CIRCUM-BICEVIAN-PERSPECTOR OF X(2) AND X(8)

Barycentrics    sqrt(a)*cos(A/2) : :

X(60534) lies on the cubic K984 and these lines: {509, 60537}

X(60534) = isogonal conjugate of X(509)
X(60534) = crosspoint of X(508) and X(55336)
X(60534) = crosssum of X(i) and X(j) for these {i, j}: {60530, 60538}, {60537, 60542}
X(60534) = X(508)-Ceva conjugate of-X(509)
X(60534) = X(60530)-cross conjugate of-X(509)
X(60534) = X(i)-Dao conjugate of-X(j) for these (i, j): (1, 55336), (9, 508), (236, 18297), (32664, 60538), (40374, 4146), (40586, 60537), (40600, 60542)
X(60534) = X(i)-isoconjugate of-X(j) for these {i, j}: {2, 60538}, {6, 508}, {7, 60530}, {56, 55336}, {81, 60537}, {86, 60542}, {174, 365}, {266, 366}, {4146, 18753}, {4166, 7371}, {4182, 7370}
X(60534) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 508), (9, 55336), (31, 60538), (41, 60530), (42, 60537), (188, 18297), (213, 60542), (259, 366), (365, 174), (366, 4146), (508, 85), (509, 7), (4166, 188), (4182, 556), (6726, 4182), (18753, 266), (55336, 75), (60530, 1), (60536, 14078), (60537, 226), (60538, 57), (60539, 365), (60540, 60543), (60541, 14079), (60542, 65), (60546, 39131), (60548, 6724)
X(60534) = barycentric product X(i)*X(j) for these {i, j}: {1, 55336}, {8, 509}, {9, 508}, {75, 60530}, {174, 4182}, {188, 366}, {259, 18297}, {312, 60538}, {314, 60542}, {333, 60537}, {365, 556}, {4146, 4166}, {14087, 60536}
X(60534) = trilinear product X(i)*X(j) for these {i, j}: {2, 60530}, {6, 55336}, {8, 60538}, {9, 509}, {21, 60537}, {55, 508}, {174, 4166}, {188, 365}, {259, 366}, {266, 4182}, {333, 60542}, {556, 18753}, {4179, 6727}, {14087, 60541}, {18297, 60539}
X(60534) = trilinear quotient X(i)/X(j) for these (i, j): (2, 508), (6, 60538), (8, 55336), (9, 60534), (37, 60537), (42, 60542), (55, 60530), (188, 366), (259, 365), (365, 266), (366, 174), (508, 7), (509, 57), (556, 18297), (4166, 259), (4179, 6724), (4182, 188), (6725, 4179), (6726, 4166), (6731, 4182)
X(60534) = (X(60537), X(60538))-harmonic conjugate of X(509)

X(60535) = DAO-LOZADA CIRCUM-BICEVIAN-PERSPECTOR OF X(2) AND X(10)

Barycentrics    a*sqrt(b+c) : :

X(60535) lies on the curve Q066 and these lines: {}

X(60535) = X(40600)-Dao conjugate of-X(60540)
X(60535) = X(86)-isoconjugate of-X(60540)
X(60535) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (213, 60540), (39131, 18297), (60531, 366), (60540, 1), (60542, 60543), (60543, 508), (60544, 55336), (60546, 188), (60548, 39131)
X(60535) = barycentric product X(i)*X(j) for these {i, j}: {75, 60540}, {366, 39131}, {508, 60544}, {4146, 60546}, {18297, 60531}, {55336, 60543}
X(60535) = trilinear product X(i)*X(j) for these {i, j}: {2, 60540}, {174, 60546}, {365, 39131}, {366, 60531}, {509, 60544}
X(60535) = trilinear quotient X(i)/X(j) for these (i, j): (37, 60535), (42, 60540), (4179, 39131), (39131, 366)

X(60536) = DAO-LOZADA CIRCUM-BICEVIAN-PERSPECTOR OF X(2) AND X(11)

Barycentrics    sqrt(a)*abs(b-c)*cos(A/2) : :

X(60536) lies on these lines: {}

X(60536) = X(i)-isoconjugate of-X(j) for these {i, j}: {508, 14085}, {4998, 60541}, {14087, 60538}, {14089, 60542}
X(60536) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (14079, 508), (14088, 509), (14090, 60537), (60532, 366), (60534, 14087), (60541, 1), (60545, 55336), (60547, 188)
X(60536) = barycentric product X(i)*X(j) for these {i, j}: {75, 60541}, {508, 60545}, {4146, 60547}, {14078, 60534}, {14079, 55336}, {14080, 60530}, {18297, 60532}
X(60536) = trilinear product X(i)*X(j) for these {i, j}: {2, 60541}, {174, 60547}, {366, 60532}, {509, 60545}, {14078, 60530}, {14079, 60534}, {14088, 55336}
X(60536) = trilinear quotient X(i)/X(j) for these (i, j): (2170, 60536), (3271, 60541), (14078, 508), (14079, 509), (14088, 60538), (14090, 60542), (55336, 14087)

X(60537) = DAO-LOZADA CIRCUM-BICEVIAN-PERSPECTOR OF X(2) AND X(12)

Barycentrics    sqrt(a)*(b+c)*sin(A/2) : :

X(60537) lies on these lines: {509, 60534}

X(60537) = crosspoint of X(508) and X(509)
X(60537) = crosssum of X(60530) and X(60534)
X(60537) = X(509)-Ceva conjugate of-X(60542)
X(60537) = X(i)-Dao conjugate of-X(j) for these (i, j): (10, 55336), (40586, 60534), (40590, 508), (40600, 60530), (40611, 509)
X(60537) = X(i)-isoconjugate of-X(j) for these {i, j}: {21, 509}, {58, 55336}, {81, 60534}, {86, 60530}, {261, 60542}, {284, 508}, {333, 60538}, {366, 6727}, {14089, 60541}
X(60537) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (37, 55336), (42, 60534), (65, 508), (213, 60530), (508, 274), (509, 86), (1400, 509), (1402, 60538), (4179, 556), (6724, 18297), (14090, 60536), (18753, 6727), (55336, 314), (60530, 21), (60533, 366), (60534, 333), (60538, 81), (60542, 1), (60548, 188)
X(60537) = barycentric product X(i)*X(j) for these {i, j}: {10, 509}, {37, 508}, {65, 55336}, {75, 60542}, {174, 4179}, {226, 60534}, {321, 60538}, {366, 6724}, {1441, 60530}, {4146, 60548}, {18297, 60533}
X(60537) = trilinear product X(i)*X(j) for these {i, j}: {2, 60542}, {10, 60538}, {37, 509}, {42, 508}, {65, 60534}, {174, 60548}, {226, 60530}, {266, 4179}, {365, 6724}, {366, 60533}, {1400, 55336}
X(60537) = trilinear quotient X(i)/X(j) for these (i, j): (10, 55336), (37, 60534), (42, 60530), (65, 509), (181, 60542), (226, 508), (365, 6727), (508, 86), (509, 81), (1400, 60538), (2171, 60537), (4179, 188), (6724, 366), (6725, 4182), (14090, 60541), (55336, 333)
X(60537) = (X(509), X(60534))-harmonic conjugate of X(60538)

X(60538) = DAO-LOZADA CIRCUM-BICEVIAN-PERSPECTOR OF X(6) AND X(7)

Barycentrics    a^(3/2)*sin(A/2) : :

X(60538) lies on these lines: {509, 60534}, {60530, 60542}

X(60538) = isogonal conjugate of X(55336)
X(60538) = X(60534)-beth conjugate of-X(60534)
X(60538) = X(509)-Ceva conjugate of-X(60530)
X(60538) = X(60542)-cross conjugate of-X(509)
X(60538) = X(i)-Dao conjugate of-X(j) for these (i, j): (206, 60530), (478, 508), (32664, 60534)
X(60538) = X(i)-isoconjugate of-X(j) for these {i, j}: {2, 60534}, {8, 509}, {9, 508}, {75, 60530}, {174, 4182}, {188, 366}, {259, 18297}, {314, 60542}, {333, 60537}, {365, 556}, {4146, 4166}, {14087, 60536}
X(60538) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (31, 60534), (32, 60530), (56, 508), (266, 18297), (365, 556), (508, 76), (509, 75), (604, 509), (1402, 60537), (4166, 7027), (18753, 188), (55336, 3596), (60530, 8), (60534, 312), (60537, 321), (60539, 4182), (60542, 10)
X(60538) = pole of the line {55336, 60530} with respect to the Stammler hyperbola
X(60538) = barycentric product X(i)*X(j) for these {i, j}: {1, 509}, {6, 508}, {7, 60530}, {56, 55336}, {57, 60534}, {81, 60537}, {86, 60542}, {174, 365}, {266, 366}, {4146, 18753}, {4166, 7371}, {4182, 7370}
X(60538) = trilinear product X(i)*X(j) for these {i, j}: {6, 509}, {31, 508}, {56, 60534}, {57, 60530}, {58, 60537}, {81, 60542}, {174, 18753}, {266, 365}, {604, 55336}, {4166, 7370}
X(60538) = trilinear quotient X(i)/X(j) for these (i, j): (6, 60534), (31, 60530), (56, 509), (57, 508), (174, 18297), (259, 4182), (266, 366), (365, 188), (366, 556), (508, 75), (509, 2), (604, 60538), (1400, 60537), (1402, 60542), (4166, 6731), (4182, 7027), (14088, 60536), (18753, 259), (55336, 312)
X(60538) = (X(509), X(60534))-harmonic conjugate of X(60537)

X(60539) = DAO-LOZADA CIRCUM-BICEVIAN-PERSPECTOR OF X(6) AND X(9)

Barycentrics    a^2*cos(A/2) : :

X(60539) lies on these lines: {1, 362}, {6, 42622}, {174, 6733}, {188, 6727}, {259, 6726}, {266, 7370}, {289, 45874}

X(60539) = isogonal conjugate of X(4146)
X(60539) = crosspoint of X(259) and X(266)
X(60539) = crosssum of X(i) and X(j) for these {i, j}: {1, 362}, {2, 7057}, {174, 188}, {514, 10504}
X(60539) = X(6726)-beth conjugate of-X(6726)
X(60539) = X(i)-Ceva conjugate of-X(j) for these (i, j): (6727, 259), (6733, 6729)
X(60539) = X(i)-Dao conjugate of-X(j) for these (i, j): (206, 266), (236, 76), (478, 555), (5452, 556), (6600, 7027), (15495, 6063), (32664, 174), (39025, 6728), (40600, 6724)
X(60539) = X(i)-isoconjugate of-X(j) for these {i, j}: {2, 174}, {7, 188}, {8, 7371}, {9, 555}, {57, 556}, {75, 266}, {85, 259}, {86, 6724}, {176, 5451}, {236, 21456}, {269, 7027}, {274, 60533}, {279, 6731}, {286, 7591}, {312, 7370}, {366, 508}, {509, 18297}, {557, 1143}, {558, 1274}, {658, 6730}, {664, 6728}, {693, 6733}, {1088, 6726}, {1434, 6725}, {1441, 6727}, {1488, 7057}, {1489, 46892}, {2089, 7048}, {4554, 6729}, {7001, 53121}, {7010, 53120}, {7028, 18886}, {10492, 55341}, {16017, 16664}, {41885, 46891}
X(60539) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (31, 174), (32, 266), (41, 188), (55, 556), (56, 555), (174, 6063), (188, 76), (213, 6724), (220, 7027), (259, 75), (266, 85), (556, 561), (604, 7371), (1253, 6731), (1397, 7370), (1918, 60533), (2175, 259), (2200, 7591), (3063, 6728), (4146, 20567), (6724, 349), (6725, 313), (6726, 312), (6727, 274), (6728, 3261), (6729, 693), (6730, 35519), (6731, 3596), (6733, 4554), (7027, 28659), (7370, 1088), (7371, 57792), (7591, 1231), (8641, 6730), (14827, 6726), (18753, 508), (32739, 6733), (57657, 6727), (60530, 18297), (60532, 14080), (60533, 1441)
X(60539) = pole of the line {266, 4146} with respect to the Stammler hyperbola
X(60539) = barycentric product X(i)*X(j) for these {i, j}: {1, 259}, {6, 188}, {9, 266}, {21, 60533}, {31, 556}, {37, 6727}, {41, 4146}, {55, 174}, {56, 6731}, {57, 6726}, {58, 6725}, {100, 6729}, {101, 6728}, {109, 6730}, {173, 53119}, {200, 7370}, {220, 7371}, {258, 53118}, {260, 7707}, {284, 6724}
X(60539) = trilinear product X(i)*X(j) for these {i, j}: {6, 259}, {31, 188}, {32, 556}, {41, 174}, {42, 6727}, {55, 266}, {56, 6726}, {101, 6729}, {220, 7370}, {284, 60533}, {365, 60530}, {555, 14827}, {604, 6731}, {663, 6733}, {692, 6728}, {1253, 7371}, {1333, 6725}, {1397, 7027}, {1415, 6730}, {2175, 4146}
X(60539) = trilinear quotient X(i)/X(j) for these (i, j): (6, 174), (9, 556), (31, 266), (41, 259), (42, 6724), (55, 188), (56, 7371), (57, 555), (174, 85), (188, 75), (200, 7027), (213, 60533), (220, 6731), (228, 7591), (259, 2), (266, 7), (289, 21456), (365, 508), (555, 57792), (556, 76)

X(60540) = DAO-LOZADA CIRCUM-BICEVIAN-PERSPECTOR OF X(6) AND X(10)

Barycentrics    a^2*sqrt(b+c) : :

X(60540) lies on the curve Q182 and these lines: {}

X(60540) = X(40600)-Dao conjugate of-X(60535)
X(60540) = X(86)-isoconjugate of-X(60535)
X(60540) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (213, 60535), (60531, 18297), (60535, 75), (60546, 556)
X(60540) = barycentric product X(i)*X(j) for these {i, j}: {1, 60535}, {174, 60546}, {365, 39131}, {366, 60531}, {509, 60544}
X(60540) = trilinear product X(i)*X(j) for these {i, j}: {6, 60535}, {266, 60546}, {365, 60531}, {18753, 39131}
X(60540) = trilinear quotient X(i)/X(j) for these (i, j): (42, 60535), (213, 60540), (39131, 18297)

X(60541) = DAO-LOZADA CIRCUM-BICEVIAN-PERSPECTOR OF X(6) AND X(11)

Barycentrics    a^(3/2)*abs(b-c)*cos(A/2) : :

X(60541) lies on these lines: {}

X(60541) = X(i)-isoconjugate of-X(j) for these {i, j}: {509, 14087}, {4998, 60536}, {14089, 60537}
X(60541) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (14088, 508), (60530, 14087), (60532, 18297), (60536, 75), (60547, 556)
X(60541) = barycentric product X(i)*X(j) for these {i, j}: {1, 60536}, {174, 60547}, {366, 60532}, {509, 60545}, {14078, 60530}, {14079, 60534}, {14088, 55336}
X(60541) = trilinear product X(i)*X(j) for these {i, j}: {6, 60536}, {266, 60547}, {365, 60532}, {14079, 60530}, {14088, 60534}
X(60541) = trilinear quotient X(i)/X(j) for these (i, j): (3271, 60536), (14079, 508), (14088, 509), (14090, 60537)

X(60542) = DAO-LOZADA CIRCUM-BICEVIAN-PERSPECTOR OF X(6) AND X(12)

Barycentrics    a^(3/2)*(b+c)*sin(A/2) : :

X(60542) lies on these lines: {508, 509}, {60530, 60538}

X(60542) = crosspoint of X(509) and X(60538)
X(60542) = crosssum of X(55336) and X(60534)
X(60542) = X(509)-Ceva conjugate of-X(60537)
X(60542) = X(i)-Dao conjugate of-X(j) for these (i, j): (40586, 55336), (40600, 60534), (40611, 508)
X(60542) = X(i)-isoconjugate of-X(j) for these {i, j}: {21, 508}, {81, 55336}, {86, 60534}, {261, 60537}, {274, 60530}, {314, 60538}, {333, 509}, {6727, 18297}, {14089, 60536}
X(60542) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (42, 55336), (213, 60534), (508, 310), (509, 274), (1400, 508), (1402, 509), (1918, 60530), (55336, 28660), (60530, 333), (60533, 18297), (60534, 314), (60537, 75), (60538, 86), (60548, 556)
X(60542) = barycentric product X(i)*X(j) for these {i, j}: {1, 60537}, {10, 60538}, {37, 509}, {42, 508}, {65, 60534}, {174, 60548}, {226, 60530}, {266, 4179}, {365, 6724}, {366, 60533}, {1400, 55336}
X(60542) = trilinear product X(i)*X(j) for these {i, j}: {6, 60537}, {37, 60538}, {42, 509}, {65, 60530}, {213, 508}, {266, 60548}, {365, 60533}, {1400, 60534}, {1402, 55336}, {6724, 18753}
X(60542) = trilinear quotient X(i)/X(j) for these (i, j): (37, 55336), (42, 60534), (65, 508), (181, 60537), (213, 60530), (508, 274), (509, 86), (1400, 509), (1402, 60538), (4179, 556), (6724, 18297), (14090, 60536), (18753, 6727), (55336, 314)

X(60543) = DAO-LOZADA CIRCUM-BICEVIAN-PERSPECTOR OF X(7) AND X(10)

Barycentrics    sqrt(a*(b+c))*sin(A/2) : :

X(60543) lies on the curve Q066 and these lines: {60544, 60550}

X(60543) = X(40586)-Dao conjugate of-X(60544)
X(60543) = X(i)-isoconjugate of-X(j) for these {i, j}: {81, 60544}, {2185, 60550}, {6727, 39131}
X(60543) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (42, 60544), (181, 60550), (14090, 60549), (39131, 556), (60531, 188), (60533, 39131), (60535, 55336), (60540, 60534), (60542, 60535), (60544, 8), (60546, 4182), (60550, 10)
X(60543) = barycentric product X(i)*X(j) for these {i, j}: {7, 60544}, {86, 60550}, {174, 39131}, {508, 60535}, {4146, 60531}
X(60543) = trilinear product X(i)*X(j) for these {i, j}: {57, 60544}, {81, 60550}, {174, 60531}, {266, 39131}, {508, 60540}, {509, 60535}
X(60543) = trilinear quotient X(i)/X(j) for these (i, j): (37, 60544), (65, 60543), (2171, 60550), (6724, 39131), (39131, 188)

X(60544) = DAO-LOZADA CIRCUM-BICEVIAN-PERSPECTOR OF X(8) AND X(10)

Barycentrics    sqrt(a*(b+c))*cos(A/2) : :

X(60544) lies on these lines: {60543, 60550}

X(60544) = X(i)-Dao conjugate of-X(j) for these (i, j): (40586, 60543), (40607, 60550)
X(60544) = X(i)-isoconjugate of-X(j) for these {i, j}: {81, 60543}, {757, 60550}
X(60544) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (42, 60543), (1500, 60550), (39131, 4146), (60531, 174), (60535, 508), (60540, 509), (60543, 7), (60546, 366), (60549, 14078), (60550, 226)
X(60544) = barycentric product X(i)*X(j) for these {i, j}: {8, 60543}, {188, 39131}, {333, 60550}, {556, 60531}, {14087, 60549}, {18297, 60546}, {55336, 60535}
X(60544) = trilinear product X(i)*X(j) for these {i, j}: {9, 60543}, {21, 60550}, {188, 60531}, {259, 39131}, {366, 60546}, {55336, 60540}
X(60544) = trilinear quotient X(i)/X(j) for these (i, j): (37, 60543), (210, 60544), (756, 60550), (6725, 39131), (39131, 174)

X(60545) = DAO-LOZADA CIRCUM-BICEVIAN-PERSPECTOR OF X(8) AND X(11)

Barycentrics    a*abs(b-c)*(-a+b+c) : :

X(60545) lies on the cubic K925 and these lines: {14079, 14088}

X(60545) = X(14078)-Ceva conjugate of-X(14079)
X(60545) = X(i)-Dao conjugate of-X(j) for these (i, j): (1, 14087), (650, 14080), (6615, 14078), (40582, 14089)
X(60545) = X(i)-isoconjugate of-X(j) for these {i, j}: {7, 14085}, {56, 14087}, {59, 14078}, {1400, 14089}, {2149, 14080}, {4564, 14079}, {4620, 14090}, {4998, 14088}, {14086, 52378}
X(60545) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (9, 14087), (11, 14080), (21, 14089), (41, 14085), (2170, 14078), (3271, 14079), (4516, 14086), (14078, 85), (14079, 7), (14080, 6063), (14085, 4564), (14086, 1441), (14088, 57), (14090, 65), (60532, 174), (60536, 508), (60541, 509), (60547, 366), (60551, 226)
X(60545) = center of the central inconic through X(513) and X(3900)
X(60545) = pole of the line {6144, 20014} with respect to the Feuerbach circumhyperbola
X(60545) = barycentric product X(i)*X(j) for these {i, j}: {8, 14079}, {9, 14078}, {21, 14086}, {55, 14080}, {312, 14088}, {314, 14090}, {333, 60551}, {556, 60532}, {2170, 14087}, {4516, 14089}, {4858, 14085}, {18297, 60547}, {55336, 60536}
X(60545) = trilinear product X(i)*X(j) for these {i, j}: {8, 14088}, {9, 14079}, {11, 14085}, {21, 60551}, {41, 14080}, {55, 14078}, {188, 60532}, {284, 14086}, {333, 14090}, {366, 60547}, {3271, 14087}, {55336, 60541}
X(60545) = trilinear quotient X(i)/X(j) for these (i, j): (8, 14087), (11, 14078), (55, 14085), (333, 14089), (2170, 14079), (2310, 60545), (3271, 14088), (4516, 60551), (4858, 14080), (14078, 7), (14079, 57), (14080, 85), (14085, 59), (14086, 226), (14087, 4998), (14088, 56), (14089, 4620), (14090, 1400), (21044, 14086)
X(60545) = X(14086)-of-Ursa-minor triangle, when ABC is acute
X(60545) = (X(14088), X(60551))-harmonic conjugate of X(14079)

X(60546) = DAO-LOZADA CIRCUM-BICEVIAN-PERSPECTOR OF X(9) AND X(10)

Barycentrics    a*sqrt(b+c)*cos(A/2) : :

X(60546) lies on these lines: {}

X(60546) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (60531, 508), (60535, 4146), (60540, 174), (60544, 18297)
X(60546) = barycentric product X(i)*X(j) for these {i, j}: {188, 60535}, {366, 60544}, {556, 60540}, {4182, 60543}, {39131, 60534}, {55336, 60531}
X(60546) = trilinear product X(i)*X(j) for these {i, j}: {188, 60540}, {259, 60535}, {365, 60544}, {4166, 60543}, {39131, 60530}
X(60546) = trilinear quotient X(i)/X(j) for these (i, j): (1334, 60546), (39131, 508)

X(60547) = DAO-LOZADA CIRCUM-BICEVIAN-PERSPECTOR OF X(9) AND X(11)

Barycentrics    a^(3/2)*(-a+b+c)*abs(b-c) : :

X(60547) lies on these lines: {}

X(60547) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (4166, 14087), (60532, 508), (60536, 4146), (60541, 174), (60545, 18297)
X(60547) = barycentric product X(i)*X(j) for these {i, j}: {188, 60536}, {366, 60545}, {556, 60541}, {4166, 14078}, {4182, 14079}, {55336, 60532}
X(60547) = trilinear product X(i)*X(j) for these {i, j}: {188, 60541}, {259, 60536}, {365, 60545}, {4166, 14079}, {4182, 14088}
X(60547) = trilinear quotient X(i)/X(j) for these (i, j): (4182, 14087), (14936, 60547)

X(60548) = DAO-LOZADA CIRCUM-BICEVIAN-PERSPECTOR OF X(9) AND X(12)

Barycentrics    a^(3/2)*(b+c) : :

X(60548) lies on these lines: {10, 20485}, {37, 20682}, {365, 4166}, {366, 18297}

X(60548) = crosspoint of X(365) and X(366)
X(60548) = crosssum of X(365) and X(366)
X(60548) = X(366)-Ceva conjugate of-X(4179)
X(60548) = X(i)-Dao conjugate of-X(j) for these (i, j): (10, 18297), (40374, 274), (40586, 366), (40600, 365), (40607, 4179)
X(60548) = X(i)-isoconjugate of-X(j) for these {i, j}: {58, 18297}, {81, 366}, {86, 365}, {274, 18753}, {508, 6727}, {757, 4179}, {1014, 4182}, {1434, 4166}
X(60548) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (37, 18297), (42, 366), (213, 365), (365, 86), (366, 274), (1334, 4182), (1500, 4179), (1918, 18753), (4166, 333), (4179, 75), (4182, 314), (18297, 310), (18753, 81), (60533, 508), (60537, 4146), (60542, 174)
X(60548) = NK-transform of X(i) for these i: {365, 366}
X(60548) = barycentric product X(i)*X(j) for these {i, j}: {1, 4179}, {10, 365}, {37, 366}, {42, 18297}, {65, 4182}, {188, 60537}, {226, 4166}, {321, 18753}, {509, 6725}, {556, 60542}, {6724, 60534}, {39131, 60535}, {55336, 60533}
X(60548) = trilinear product X(i)*X(j) for these {i, j}: {6, 4179}, {10, 18753}, {37, 365}, {42, 366}, {65, 4166}, {188, 60542}, {213, 18297}, {259, 60537}, {1400, 4182}, {6724, 60530}, {6725, 60538}, {39131, 60540}
X(60548) = trilinear quotient X(i)/X(j) for these (i, j): (10, 18297), (37, 366), (42, 365), (210, 4182), (213, 18753), (365, 81), (366, 86), (756, 4179), (1334, 4166), (1500, 60548), (4166, 21), (4179, 2), (4182, 333), (6724, 508), (6725, 55336), (18297, 274), (18753, 58), (20682, 40378), (20695, 40374)
X(60548) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (10, 20497, 20485), (37, 20695, 20682), (365, 4166, 18753)

X(60549) = DAO-LOZADA CIRCUM-BICEVIAN-PERSPECTOR OF X(10) AND X(11)

Barycentrics    abs(b-c)*sqrt(a*(b+c))*cos(A/2) : :

X(60549) lies on these lines: {}

X(60549) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (14090, 60543), (60544, 14087)
X(60549) = center of the central inconic through X(512) and X(522)
X(60549) = barycentric product X(14078)*X(60544)
X(60549) = trilinear product X(i)*X(j) for these {i, j}: {14079, 60544}, {39131, 60532}
X(60549) = trilinear quotient X(4516)/X(60549)

X(60550) = DAO-LOZADA CIRCUM-BICEVIAN-PERSPECTOR OF X(10) AND X(12)

Barycentrics    sqrt(a)*(b+c)^(3/2)*sin(A/2) : :

X(60550) lies on these lines: {60543, 60544}

X(60550) = X(40607)-Dao conjugate of-X(60544)
X(60550) = X(i)-isoconjugate of-X(j) for these {i, j}: {757, 60544}, {2185, 60543}
X(60550) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (181, 60543), (1500, 60544), (60543, 86), (60544, 333)
X(60550) = barycentric product X(i)*X(j) for these {i, j}: {10, 60543}, {226, 60544}, {6724, 39131}
X(60550) = trilinear product X(i)*X(j) for these {i, j}: {37, 60543}, {65, 60544}, {6724, 60531}, {39131, 60533}
X(60550) = trilinear quotient X(i)/X(j) for these (i, j): (756, 60544), (2171, 60543)

X(60551) = DAO-LOZADA CIRCUM-BICEVIAN-PERSPECTOR OF X(11) AND X(12)

Barycentrics    a*abs(b^2-c^2) : :

X(60551) lies on these lines: {14078, 14080}, {14079, 14088}

X(60551) = crosspoint of X(14078) and X(14079)
X(60551) = X(i)-Ceva conjugate of-X(j) for these (i, j): (14078, 14086), (14079, 14090)
X(60551) = X(i)-Dao conjugate of-X(j) for these (i, j): (9, 14089), (10, 14087), (4988, 14080), (40600, 14085), (40627, 14079), (50330, 14078), (50497, 14088)
X(60551) = X(i)-isoconjugate of-X(j) for these {i, j}: {6, 14089}, {58, 14087}, {86, 14085}, {249, 14086}, {4567, 14079}, {4570, 14078}, {4590, 14090}, {4600, 14088}
X(60551) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 14089), (37, 14087), (213, 14085), (2643, 14086), (3120, 14080), (3121, 14088), (3122, 14079), (3125, 14078), (14078, 274), (14079, 86), (14080, 310), (14085, 4567), (14086, 75), (14087, 4601), (14088, 81), (14089, 24037), (14090, 1), (60545, 333)
X(60551) = center of the central inconic through X(512) and X(523)
X(60551) = barycentric product X(i)*X(j) for these {i, j}: {1, 14086}, {10, 14079}, {37, 14078}, {42, 14080}, {75, 14090}, {226, 60545}, {321, 14088}, {2643, 14089}, {3125, 14087}, {14085, 16732}
X(60551) = trilinear product X(i)*X(j) for these {i, j}: {2, 14090}, {6, 14086}, {10, 14088}, {37, 14079}, {42, 14078}, {65, 60545}, {213, 14080}, {3120, 14085}, {3122, 14087}, {3124, 14089}, {6724, 60532}
X(60551) = trilinear quotient X(i)/X(j) for these (i, j): (2, 14089), (10, 14087), (42, 14085), (115, 14086), (2643, 60551), (3120, 14078), (3122, 14088), (3124, 14090), (3125, 14079), (4516, 60545), (14078, 86), (14079, 81), (14080, 274), (14085, 4570), (14086, 2), (14087, 4600), (14088, 58), (14089, 4590), (14090, 6), (16732, 14080)
X(60551) = (X(14079), X(60545))-harmonic conjugate of X(14088)


leftri  Circumtangential-bicevian-perspectors: X(60552) - X(60564)  rightri

This preamble and centers X(60552)-X(60564) were contributed by César Eliud Lozada, November 10, 2023.

Continuing with the construction and notations in the previous section (see preamble just before X(60530)), let A*B*C* be the triangle bounded by the tangent lines to ω at At, Bt, Ct. Then A*B*C* is perspective to ABC with perspector Q*(P', P").

This new perspector is referred here as the circumtangential-bicevian-perspector of P' and P". Corresponding barycentrics coordinates are:

A* = -a*(2*b*c*X^2 + a*(a*Y*Z + b*Z*X + c*X*Y)) : b^2*(a*Y*Z + b*Z*X - c*X*Y) : c^2*(a*Y*Z - b*Z*X + c*X*Y)
and
Q*(P', P") = a^2/(-a*Y*Z + b*Z*X + c*X*Y) : b^2/(a*Y*Z - b*Z*X + c*X*Y) : c^2/(a*Y*Z + b*Z*X - c*X*Y)

The circumtangential-bicevian-perspector of P' and P" results to be the U-vertex conjugate of-U, where U is the Dao-Lozada-circum-bicevian perspector of P' and P" explained in the previous section.

underbar

X(60552) = CIRCUMTANGENTIAL-BICEVIAN-PERSPECTOR OF X(1) AND X(2)

Barycentrics    a^2*(a-(sqrt(b)-sqrt(c))^2) : :

X(60552) lies on these lines: {55, 365}, {3207, 18753}

X(60552) = isogonal conjugate of X(20534)
X(60552) = crosssum of X(i) and X(j) for these {i, j}: {4180, 20527}, {20673, 20763}
X(60552) = X(18753)-cross conjugate of-X(6)
X(60552) = X(i)-Dao conjugate of-X(j) for these (i, j): (206, 20673), (22391, 20763), (32664, 364), (40600, 20695)
X(60552) = X(i)-isoconjugate of-X(j) for these {i, j}: {2, 364}, {75, 20673}, {86, 20695}, {92, 20763}, {366, 40374}
X(60552) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (31, 364), (32, 20673), (184, 20763), (213, 20695), (18753, 40374)
X(60552) = X(365)-vertex conjugate of-X(365)
X(60552) = pole of the line {20534, 20673} with respect to the Stammler hyperbola
X(60552) = trilinear quotient X(i)/X(j) for these (i, j): (6, 364), (31, 20673), (42, 20695), (48, 20763), (365, 40374)
X(60552) = (X(55), X(365))-harmonic conjugate of X(20673)

X(60553) = CIRCUMTANGENTIAL-BICEVIAN-PERSPECTOR OF X(1) AND X(6)

Barycentrics    a^2*(b*c-a*(sqrt(b)-sqrt(c))^2) : :

X(60553) lies on these lines: {365, 21780}, {2176, 18753}

X(60553) = isogonal conjugate of X(40383)
X(60553) = X(365)-cross conjugate of-X(6)
X(60553) = X(i)-Dao conjugate of-X(j) for these (i, j): (22391, 20798), (32664, 40375)
X(60553) = X(i)-isoconjugate of-X(j) for these {i, j}: {2, 40375}, {92, 20798}
X(60553) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (31, 40375), (184, 20798)
X(60553) = X(18753)-vertex conjugate of-X(18753)
X(60553) = trilinear quotient X(i)/X(j) for these (i, j): (6, 40375), (48, 20798)

X(60554) = CIRCUMTANGENTIAL-BICEVIAN-PERSPECTOR OF X(1) AND X(7)

Barycentrics    a^2*(a^2-4*sin(A/2)*b*c-(b-c)^2) : :

X(60554) lies on the cubic K967 and these lines: {1, 3659}, {3, 10231}, {55, 53119}, {56, 266}, {164, 8081}, {188, 7588}, {258, 260}, {361, 5247}, {999, 1130}, {3052, 60539}, {3304, 53118}, {5563, 52802}, {12523, 58777}

X(60554) = isogonal conjugate of X(7057)
X(60554) = crosssum of X(i) and X(j) for these {i, j}: {177, 178}, {188, 12646}
X(60554) = X(i)-Ceva conjugate of-X(j) for these (i, j): (260, 53119), (289, 6)
X(60554) = X(60539)-cross conjugate of-X(6)
X(60554) = X(i)-Dao conjugate of-X(j) for these (i, j): (206, 42622), (478, 18886), (32664, 173)
X(60554) = X(i)-isoconjugate of-X(j) for these {i, j}: {2, 173}, {9, 18886}, {75, 42622}, {174, 236}, {188, 2089}, {266, 53122}, {4146, 53118}, {7001, 53076}, {7010, 53077}, {7048, 52999}, {45877, 55341}
X(60554) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (31, 173), (32, 42622), (56, 18886), (258, 75), (259, 53122), (289, 4146), (7048, 76), (21456, 6063), (45874, 55341), (53119, 556), (60539, 236)
X(60554) = X(266)-vertex conjugate of-X(266)
X(60554) = pole of the the tripolar of X(289) with respect to the circumcircle
X(60554) = pole of the line {7057, 42622} with respect to the Stammler hyperbola
X(60554) = barycentric product X(i)*X(j) for these {i, j}: {1, 258}, {6, 7048}, {55, 21456}, {174, 53119}, {188, 289}, {259, 1488}, {260, 16015}, {266, 7028}, {3659, 10492}, {10495, 45875}, {18887, 59467}
X(60554) = trilinear product X(i)*X(j) for these {i, j}: {6, 258}, {31, 7048}, {41, 21456}, {259, 289}, {260, 16011}, {266, 53119}, {1488, 60539}, {10495, 45874}
X(60554) = trilinear quotient X(i)/X(j) for these (i, j): (6, 173), (31, 42622), (57, 18886), (188, 53122), (258, 2), (259, 236), (266, 2089), (289, 174), (1488, 4146), (3659, 55342), (7001, 53077), (7010, 53076), (7028, 556), (7048, 75), (15997, 178), (16011, 177), (21456, 85), (41799, 234), (42622, 52999), (45874, 43192)
X(60554) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (56, 266, 42622), (266, 289, 16011), (10231, 42614, 3)

X(60555) = CIRCUMTANGENTIAL-BICEVIAN-PERSPECTOR OF X(1) AND X(8)

Barycentrics    a^2*(a^3+(b+c)*a^2-(b+c)^2*a-(b^2-c^2)*(b-c)+4*b*c*(-a+b+c)*sin(A/2)) : :

X(60555) lies on these lines: {168, 505}, {198, 259}

X(60555) = isogonal conjugate of X(16017)
X(60555) = X(32664)-Dao conjugate of-X(164)
X(60555) = X(i)-isoconjugate of-X(j) for these {i, j}: {2, 164}, {188, 15495}
X(60555) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (31, 164), (505, 75)
X(60555) = X(259)-vertex conjugate of-X(259)
X(60555) = barycentric product X(i)*X(j) for these {i, j}: {1, 505}, {259, 16664}
X(60555) = trilinear product X(i)*X(j) for these {i, j}: {6, 505}, {16664, 60539}
X(60555) = trilinear quotient X(i)/X(j) for these (i, j): (6, 164), (266, 15495), (505, 2), (16664, 4146)

X(60556) = CIRCUMTANGENTIAL-BICEVIAN-PERSPECTOR OF X(1) AND X(10)

Barycentrics    a^2*(a^3+(b+c)*a^2-(b^2+b*c+c^2)*a-(b+c)*(b^2+c^2)+2*sqrt(b*c)*sqrt(a+b)*sqrt(a+c)*(b+c)) : :

X(60556) lies on these lines: {1030, 60531}

X(60556) = X(60531)-vertex conjugate of-X(60531)

X(60557) = CIRCUMTANGENTIAL-BICEVIAN-PERSPECTOR OF X(2) AND X(7)

Barycentrics    a^2*(a^3-(b+c)*a^2+(b^2+c^2)*a-(b^2-c^2)*(b-c)-4*b*c*sqrt(b*c)*sin(A/2)) : :

X(60557) lies on these lines: {509, 1486}

X(60557) = isogonal conjugate of the anticomplement of X(60534)
X(60557) = X(509)-vertex conjugate of-X(509)

X(60558) = CIRCUMTANGENTIAL-BICEVIAN-PERSPECTOR OF X(2) AND X(8)

Barycentrics    a^2*(a^4+2*b*c*a^2-2*(b+c)*b*c*a-(b^2-c^2)^2+4*b*c*(-a+b+c)*sqrt(b*c)*sin(A/2)) : :

X(60558) lies on these lines: {197, 60534}

X(60558) = isogonal conjugate of the anticomplement of X(509)
X(60558) = X(60534)-vertex conjugate of-X(60534)

X(60559) = CIRCUMTANGENTIAL-BICEVIAN-PERSPECTOR OF X(2) AND X(10)

Barycentrics    a^2*(a^4+(b+c)*a^3+b*c*a^2-(b+c)*(b^2+c^2)*a-(b^3+c^3)*(b+c)+2*sqrt(a+b)*sqrt(a+c)*b*c*(b+c)) : :

X(60559) lies on these lines: {199, 60535}

X(60559) = X(60535)-vertex conjugate of-X(60535)

X(60560) = CIRCUMTANGENTIAL-BICEVIAN-PERSPECTOR OF X(6) AND X(7)

Barycentrics    a^2*(3*a-b-c-4*sqrt(b*c)*sin(A/2)) : :

X(60560) lies on these lines: {3052, 60538}

X(60560) = isogonal conjugate of the anticomplement of X(55336)
X(60560) = X(60530)-cross conjugate of-X(6)
X(60560) = X(60538)-vertex conjugate of-X(60538)

X(60561) = CIRCUMTANGENTIAL-BICEVIAN-PERSPECTOR OF X(6) AND X(8)

Barycentrics    a^2*(3*a^2-2*(b+c)*a-(b-c)^2+4*sqrt(b*c)*(-a+b+c)*sin(A/2)) : :

X(60561) lies on these lines: {3207, 60530}

X(60561) = isogonal conjugate of the anticomplement of X(508)
X(60561) = X(60538)-cross conjugate of-X(6)
X(60561) = X(60530)-vertex conjugate of-X(60530)

X(60562) = CIRCUMTANGENTIAL-BICEVIAN-PERSPECTOR OF X(6) AND X(10)

Barycentrics    a^2*(a^2-(b+c)*a-b^2-b*c-c^2+2*sqrt(a+b)*sqrt(a+c)*(b+c)) : :

X(60562) lies on these lines: {18755, 60540}

X(60562) = X(60540)-vertex conjugate of-X(60540)

X(60563) = CIRCUMTANGENTIAL-BICEVIAN-PERSPECTOR OF X(7) AND X(10)

Barycentrics    a^2*(a^5-(b^2+b*c+c^2)*a^3+(b^3+c^3)*a^2+(b+c)^2*b*c*a-(b^2-c^2)*(b^3-c^3)-4*b*c*sqrt(b*c*(a+b)*(a+c))*(b+c)*sin(A/2)) : :

X(60563) lies on these lines: {3145, 60543}

X(60563) = X(60543)-vertex conjugate of-X(60543)

X(60564) = CIRCUMTANGENTIAL-BICEVIAN-PERSPECTOR OF X(8) AND X(10)

Barycentrics    a^2*(a^6+(b+c)*a^5-(b^2-3*b*c+c^2)*a^4+2*(b+c)*b*c*a^3+(b^4+c^4-2*b*c*(b^2+b*c+c^2))*a^2-(b+c)*(b^4+c^4+2*b*c*(b^2-b*c+c^2))*a-(b^3-c^3)*(b^2-c^2)*(b+c)+4*sqrt((a+b)*b*c*(a+c))*b*c*(b+c)*(-a+b+c)*sin(A/2)) : :

X(60564) lies on these lines: {}

X(60564) = X(60544)-vertex conjugate of-X(60544)

X(60565) = TRILINEAR POLE OF X(11)X(22383)

Barycentrics    (b - c)*(a^7 - a^6*b - a^5*b^2 + a^4*b^3 + a^3*b^4 - a^2*b^5 - a*b^6 + b^7 + a^5*b*c - 2*a^3*b^3*c + a*b^5*c - 2*a^5*c^2 + a^4*b*c^2 + a^3*b^2*c^2 + a^2*b^3*c^2 + a*b^4*c^2 - 2*b^5*c^2 - a^3*b*c^3 - a*b^3*c^3 + a^3*c^4 + b^3*c^4)*(a^7 - 2*a^5*b^2 + a^3*b^4 - a^6*c + a^5*b*c + a^4*b^2*c - a^3*b^3*c - a^5*c^2 + a^3*b^2*c^2 + a^4*c^3 - 2*a^3*b*c^3 + a^2*b^2*c^3 - a*b^3*c^3 + b^4*c^3 + a^3*c^4 + a*b^2*c^4 - a^2*c^5 + a*b*c^5 - 2*b^2*c^5 - a*c^6 + c^7) : :

X(60565) lies on the Moses-Feuerbach circumhyperbola and these lines: {3, 4391}, {48, 522}, {56, 17924}, {104, 39429}, {514, 603}, {885, 32658}, {1437, 4560}, {7053, 24002}, {17971, 60484}, {36058, 60480}, {53063, 58840}, {53064, 58838}

X(60565) = X(101)-isoconjugate of X(45266)
X(60565) = X(1015)-Dao conjugate of X(45266)
X(60565) = trilinear pole of line {11, 22383}
X(60565) = barycentric product X(905)*X(39429)
X(60565) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 45266}, {39429, 6335}

X(60566) = TRILINEAR POLE OF X(11)X(1946)

Barycentrics    (a - b - c)*(b - c)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - a^5*c + a^3*b^2*c + a^2*b^3*c - b^5*c - a^4*c^2 - b^4*c^2 + a^3*c^3 + b^3*c^3)*(a^6 - a^5*b - a^4*b^2 + a^3*b^3 - a^4*c^2 + a^3*b*c^2 + a^2*b*c^3 + b^3*c^3 - a^2*c^4 - b^2*c^4 - b*c^5 + c^6) : :

X(60566) lies on the Moses-Feuerbach circumhyperbola and these lines: {6, 17924}, {48, 514}, {212, 522}, {219, 4391}, {222, 24002}, {2193, 4560}, {2401, 14578}, {52431, 60074}, {53065, 58838}, {53066, 58840}

X(60566) = trilinear pole of line {11, 1946}

X(60567) = TRILINEAR POLE OF X(11)X(1459)

Barycentrics    (b - c)*(a^6 - a^5*b - a^4*b^2 + 2*a^3*b^3 - a^2*b^4 - a*b^5 + b^6 + a^4*b*c - a^3*b^2*c - a^2*b^3*c + a*b^4*c - 2*a^4*c^2 + a^3*b*c^2 + 2*a^2*b^2*c^2 + a*b^3*c^2 - 2*b^4*c^2 - a^2*b*c^3 - a*b^2*c^3 + a^2*c^4 + b^2*c^4)*(a^6 - 2*a^4*b^2 + a^2*b^4 - a^5*c + a^4*b*c + a^3*b^2*c - a^2*b^3*c - a^4*c^2 - a^3*b*c^2 + 2*a^2*b^2*c^2 - a*b^3*c^2 + b^4*c^2 + 2*a^3*c^3 - a^2*b*c^3 + a*b^2*c^3 - a^2*c^4 + a*b*c^4 - 2*b^2*c^4 - a*c^5 + c^6) : :

X(60567) lies on the Moses-Feuerbach circumhyperbola and these lines: {3, 522}, {57, 17924}, {63, 4391}, {103, 32706}, {222, 514}, {295, 2812}, {885, 36057}, {929, 35187}, {1790, 4560}, {1797, 2988}, {1803, 56322}, {2067, 58840}, {6502, 58838}, {7177, 24002}, {29013, 42467}

X(60567) = X(i)-isoconjugate of X(j) for these (i,j): {37, 7450}, {100, 8607}, {101, 1735}, {2149, 55124}
X(60567) = X(i)-Dao conjugate of X(j) for these (i,j): {650, 55124}, {1015, 1735}, {8054, 8607}, {40589, 7450}
X(60567) = cevapoint of X(649) and X(53522)
X(60567) = trilinear pole of line {11, 1459}
X(60567) = barycentric product X(i)*X(j) for these {i,j}: {514, 2988}, {4025, 32706}, {17880, 36113}, {34387, 35187}, {53522, 57751}
X(60567) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 55124}, {58, 7450}, {513, 1735}, {649, 8607}, {2988, 190}, {32706, 1897}, {32707, 7115}, {35187, 59}, {36113, 7012}, {53522, 117}

X(60568) = TRILINEAR POLE OF X(11)X(7252)

Barycentrics    (a + b)*(a - b - c)*(b - c)*(a + c)*(a^4 + b^4 - a^2*c^2 - b^2*c^2)*(a^4 - a^2*b^2 - b^2*c^2 + c^4) : :

X(60568) lies on the Moses-Feuerbach circumhyperbola and these lines: {21, 1946}, {28, 667}, {58, 514}, {60, 4560}, {98, 759}, {261, 23189}, {284, 522}, {422, 55259}, {448, 10099}, {655, 36084}, {666, 2966}, {879, 1175}, {929, 2715}, {1014, 17212}, {1169, 2395}, {1178, 3737}, {2189, 55195}, {2311, 15628}, {32682, 53701}

X(60568) = X(36084)-Ceva conjugate of X(98)
X(60568) = X(i)-isoconjugate of X(j) for these (i,j): {12, 23997}, {201, 4230}, {240, 23067}, {511, 4551}, {653, 42702}, {664, 5360}, {684, 7012}, {813, 16591}, {1018, 43034}, {1020, 59734}, {1400, 42717}, {1755, 4552}, {1959, 4559}, {2149, 2799}, {2171, 2421}, {3569, 4564}, {3952, 51651}, {6358, 14966}, {17209, 21859}, {44694, 53321}
X(60568) = X(i)-Dao conjugate of X(j) for these (i,j): {650, 2799}, {905, 6333}, {36899, 4552}, {39025, 5360}, {39085, 23067}, {40582, 42717}, {40623, 16591}, {40624, 42703}, {40625, 325}, {55067, 1959}, {55068, 44694}
X(60568) = cevapoint of X(4435) and X(21789)
X(60568) = trilinear pole of line {11, 7252}
X(60568) = barycentric product X(i)*X(j) for these {i,j}: {11, 2966}, {60, 43665}, {98, 4560}, {261, 2395}, {290, 7252}, {293, 57215}, {645, 43920}, {685, 26932}, {879, 46103}, {1821, 3737}, {1910, 18155}, {2170, 36036}, {2422, 18021}, {2715, 34387}, {3271, 43187}, {4858, 36084}, {7117, 22456}, {7192, 15628}, {8735, 17932}, {16081, 23189}, {17880, 36104}, {27010, 53701}, {51441, 55196}, {55195, 57991}
X(60568) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 2799}, {21, 42717}, {60, 2421}, {98, 4552}, {248, 23067}, {261, 2396}, {659, 16591}, {685, 46102}, {878, 2197}, {879, 26942}, {1021, 44694}, {1910, 4551}, {1946, 42702}, {1976, 4559}, {2150, 23997}, {2189, 4230}, {2395, 12}, {2422, 181}, {2715, 59}, {2966, 4998}, {3063, 5360}, {3271, 3569}, {3733, 43034}, {3737, 1959}, {4391, 42703}, {4435, 50440}, {4560, 325}, {4976, 51417}, {7117, 684}, {7252, 511}, {8735, 16230}, {15628, 3952}, {18155, 46238}, {21789, 59734}, {23189, 36212}, {26932, 6333}, {32696, 7115}, {36084, 4564}, {36104, 7012}, {43665, 34388}, {43754, 44717}, {43920, 7178}, {46103, 877}, {51441, 55197}, {53149, 8736}, {55195, 868}, {57129, 51651}, {57215, 40703}, {57991, 55194}

X(60569) = TRILINEAR POLE OF X(11)X(652)

Barycentrics    (a - b - c)*(b - c)*(a^5 - a^3*b^2 - a^2*b^3 + b^5 - a^4*c + 2*a^2*b^2*c - b^4*c - a^3*c^2 - b^3*c^2 + a^2*c^3 + b^2*c^3)*(a^5 - a^4*b - a^3*b^2 + a^2*b^3 - a^3*c^2 + 2*a^2*b*c^2 + b^3*c^2 - a^2*c^3 - b^2*c^3 - b*c^4 + c^5) : :

X(60569) lies on the Moses-Feuerbach circumhyperbola, the circumconic {{A,B,C,X(1),X(3)}}, and these lines: {1, 17924}, {3, 514}, {77, 24002}, {78, 4391}, {102, 917}, {219, 522}, {283, 4560}, {296, 3738}, {929, 35182}, {1794, 56320}, {1795, 2401}, {1807, 60074}, {2066, 58838}, {2359, 4581}, {2989, 60047}, {5414, 58840}, {47487, 56322}, {56110, 60480}, {57997, 60046}

X(60569) = X(i)-isoconjugate of X(j) for these (i,j): {57, 56742}, {65, 4243}, {108, 916}, {109, 1736}, {651, 8608}, {653, 2253}, {1415, 48381}, {2149, 55125}
X(60569) = X(i)-Dao conjugate of X(j) for these (i,j): {11, 1736}, {650, 55125}, {1146, 48381}, {5452, 56742}, {38983, 916}, {38991, 8608}, {40602, 4243}
X(60569) = trilinear pole of line {11, 652}
X(60569) = crossdifference of every pair of points on line {2253, 8608}
X(60569) = barycentric product X(i)*X(j) for these {i,j}: {514, 56110}, {522, 2989}, {652, 57997}, {917, 6332}, {17880, 36107}, {34387, 35182}
X(60569) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 55125}, {55, 56742}, {284, 4243}, {522, 48381}, {650, 1736}, {652, 916}, {663, 8608}, {917, 653}, {1946, 2253}, {2989, 664}, {32699, 7115}, {35182, 59}, {36107, 7012}, {56110, 190}, {57997, 46404}

X(60570) = TRILINEAR POLE OF X(11)X(654)

Barycentrics    (b - c)*(-a + b + c)*(a^5 - a^3*b^2 - a^2*b^3 + b^5 - a^4*c + a^3*b*c + 2*a^2*b^2*c + a*b^3*c - b^4*c - a^3*c^2 - a^2*b*c^2 - a*b^2*c^2 - b^3*c^2 + a^2*c^3 + b^2*c^3)*(a^5 - a^4*b - a^3*b^2 + a^2*b^3 + a^3*b*c - a^2*b^2*c - a^3*c^2 + 2*a^2*b*c^2 - a*b^2*c^2 + b^3*c^2 - a^2*c^3 + a*b*c^3 - b^2*c^3 - b*c^4 + c^5) : :

X(60570) lies on the Moses-Feuerbach circumhyperbola and these lines: {1, 60074}, {36, 514}, {59, 523}, {60, 56283}, {239, 60481}, {522, 2323}, {953, 19628}, {1090, 3737}, {1443, 24002}, {1870, 17924}, {2605, 40450}, {4391, 4511}

X(60570) = X(109)-isoconjugate of X(24433)
X(60570) = X(11)-Dao conjugate of X(24433)
X(60570) = trilinear pole of line {11, 654}
X(60570) = barycentric product X(3904)*X(19628)
X(60570) = barycentric quotient X(i)/X(j) for these {i,j}: {650, 24433}, {19628, 655}

X(60571) = TRILINEAR POLE OF X(11)X(3737)

Barycentrics    (a + b)^2*(a - b - c)*(b - c)*(a + c)^2*(a^2 - a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2) : :

X(60571) lies on the Moses-Feuerbach circumhyperbola and these lines: {21, 522}, {27, 17924}, {60, 56283}, {81, 514}, {333, 4391}, {655, 37140}, {759, 53707}, {885, 52380}, {929, 36069}, {1019, 52393}, {1434, 24002}, {2185, 4560}, {2363, 4581}, {5331, 48297}, {6740, 56154}, {24624, 60074}, {37009, 56645}, {47318, 50039}

X(60571) = X(37140)-Ceva conjugate of X(24624)
X(60571) = X(i)-isoconjugate of X(j) for these (i,j): {12, 1983}, {36, 21859}, {59, 2610}, {109, 4053}, {181, 4585}, {758, 4559}, {1018, 1464}, {1252, 51663}, {1835, 4574}, {2149, 6370}, {2197, 4242}, {2222, 35069}, {2245, 4551}, {2361, 4605}, {3724, 4552}, {4103, 52440}, {4557, 18593}, {4564, 42666}, {4736, 32675}
X(60571) = X(i)-Dao conjugate of X(j) for these (i,j): {11, 4053}, {650, 6370}, {661, 51663}, {6615, 2610}, {15898, 21859}, {35128, 4736}, {36909, 4103}, {38984, 35069}, {40620, 41804}, {40625, 3936}, {55067, 758}
X(60571) = cevapoint of X(654) and X(3737)
X(60571) = trilinear pole of line {11, 3737}
X(60571) = barycentric product X(i)*X(j) for these {i,j}: {654, 57555}, {655, 26856}, {693, 52380}, {757, 52356}, {759, 18155}, {2185, 60074}, {2341, 7199}, {3737, 14616}, {4560, 24624}, {4858, 37140}, {6740, 7192}, {17197, 47318}, {34387, 36069}
X(60571) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 6370}, {244, 51663}, {270, 4242}, {650, 4053}, {654, 35069}, {759, 4551}, {1019, 18593}, {2006, 4605}, {2150, 1983}, {2161, 21859}, {2170, 2610}, {2185, 4585}, {2341, 1018}, {3271, 42666}, {3733, 1464}, {3737, 758}, {3738, 4736}, {4560, 3936}, {6740, 3952}, {7192, 41804}, {7252, 2245}, {17197, 4707}, {18155, 35550}, {18191, 53527}, {24624, 4552}, {26856, 3904}, {32671, 2149}, {34079, 4559}, {36069, 59}, {36910, 4103}, {37140, 4564}, {52356, 1089}, {52371, 40521}, {52380, 100}, {53314, 3028}, {57200, 1835}, {57555, 46405}, {57736, 23067}, {60074, 6358}

X(60572) = TRILINEAR POLE OF X(11)X(3063)

Barycentrics    (a - b - c)*(b - c)*(a^4 + b^4 - a^3*c - b^3*c)*(a^4 - a^3*b - b*c^3 + c^4) : :

X(60572) lies on the Moses-Feuerbach circumhyperbola and these lines: {25, 17924}, {31, 514}, {41, 522}, {55, 4391}, {56, 24002}, {105, 767}, {2194, 4560}, {2401, 34858}, {6187, 60074}, {34068, 60479}

X(60572) = X(i)-isoconjugate of X(j) for these (i,j): {101, 45267}, {109, 35552}, {664, 766}, {4572, 8629}
X(60572) = X(i)-Dao conjugate of X(j) for these (i,j): {11, 35552}, {1015, 45267}, {39025, 766}
X(60572) = trilinear pole of line {11, 3063}
X(60572) = barycentric product X(i)*X(j) for these {i,j}: {650, 767}, {3063, 57951}
X(60572) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 45267}, {650, 35552}, {767, 4554}, {3063, 766}

X(60573) = TRILINEAR POLE OF X(11)X(663)

Barycentrics    (a - b - c)*(b - c)*(a^3 + b^3 - a^2*c - b^2*c)*(a^3 - a^2*b - b*c^2 + c^3) : :

X(60573) lies on the Moses-Feuerbach circumhyperbola and these lines: {6, 514}, {9, 4391}, {19, 4063}, {55, 522}, {57, 24002}, {284, 4560}, {655, 36087}, {673, 37130}, {675, 2291}, {812, 2161}, {885, 2195}, {909, 2224}, {929, 32682}, {1174, 56322}, {1945, 43050}, {2259, 56320}, {2316, 60480}, {3451, 60482}, {3738, 7077}, {9319, 60481}, {19302, 60486}, {43093, 60014}, {50039, 53337}

X(60573) = X(36087)-Ceva conjugate of X(60135)
X(60573) = X(i)-isoconjugate of X(j) for these (i,j): {56, 42723}, {100, 43039}, {109, 57015}, {190, 51657}, {651, 674}, {664, 2225}, {1214, 4249}, {1415, 3006}, {2149, 23887}, {4551, 14964}, {4554, 8618}
X(60573) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 42723}, {11, 57015}, {650, 23887}, {1146, 3006}, {8054, 43039}, {38991, 674}, {39025, 2225}, {55053, 51657}
X(60573) = trilinear pole of line {11, 663}
X(60573) = crossdifference of every pair of points on line {674, 43039}
X(60573) = barycentric product X(i)*X(j) for these {i,j}: {522, 675}, {650, 37130}, {663, 43093}, {2224, 4391}, {4560, 60135}, {4858, 36087}, {32682, 34387}
X(60573) = barycentric quotient X(i)/X(j) for these {i,j}: {9, 42723}, {11, 23887}, {522, 3006}, {649, 43039}, {650, 57015}, {663, 674}, {667, 51657}, {675, 664}, {2224, 651}, {2299, 4249}, {3063, 2225}, {7252, 14964}, {32682, 59}, {36087, 4564}, {37130, 4554}, {43093, 4572}, {60135, 4552}

X(60574) = TRILINEAR POLE OF X(11)X(661)

Barycentrics    (b - c)*(a^3*b - 2*a^2*b^2 + a*b^3 + a^3*c + b^3*c - a*c^3 - b*c^3)*(-(a^3*b) + a*b^3 - a^3*c + b^3*c + 2*a^2*c^2 - a*c^3 - b*c^3) : :

X(60574) lies on the Moses-Feuerbach circumhyperbola and these lines: {1, 4151}, {10, 1734}, {37, 522}, {65, 514}, {75, 57214}, {225, 17924}, {512, 34434}, {513, 40504}, {523, 13476}, {666, 53644}, {759, 53707}, {885, 18785}, {3668, 24002}, {4674, 53356}, {28623, 46772}, {50346, 56322}, {52383, 60074}, {53600, 60484}

X(60574) = X(i)-isoconjugate of X(j) for these (i,j): {3, 4250}, {100, 20470}, {101, 20367}, {110, 20718}, {692, 20347}, {1110, 20520}, {1783, 20744}, {20448, 32739}, {36086, 39046}
X(60574) = X(i)-Dao conjugate of X(j) for these (i,j): {244, 20718}, {514, 20520}, {1015, 20367}, {1086, 20347}, {8054, 20470}, {36103, 4250}, {38989, 39046}, {39006, 20744}, {40619, 20448}
X(60574) = cevapoint of X(523) and X(2254)
X(60574) = trilinear pole of line {11, 661}
X(60574) = crossdifference of every pair of points on line {20470, 39046}
X(60574) = barycentric product X(i)*X(j) for these {i,j}: {11, 53644}, {1577, 53707}
X(60574) = barycentric quotient X(i)/X(j) for these {i,j}: {19, 4250}, {513, 20367}, {514, 20347}, {649, 20470}, {661, 20718}, {665, 39046}, {693, 20448}, {1086, 20520}, {1459, 20744}, {53644, 4998}, {53707, 662}

X(60575) = TRILINEAR POLE OF X(11)X(4041)

Barycentrics    (b - c)*(-a + b + c)*(a^2*b + a*b^2 + a^2*c - 2*a*b*c + b^2*c - a*c^2 - b*c^2)*(-(a^2*b) + a*b^2 - a^2*c + 2*a*b*c + b^2*c - a*c^2 - b*c^2) : :

X(60575) lies on the Moses-Feuerbach circumhyperbola and these lines: {9, 4560}, {37, 514}, {210, 522}, {226, 4776}, {929, 59071}, {1826, 17924}, {2250, 2401}, {2321, 4391}, {2786, 60486}, {4129, 8818}, {53339, 60479}, {56255, 56322}

X(60575) = X(i)-isoconjugate of X(j) for these (i,j): {109, 45751}, {1415, 29824}, {4565, 44671}
X(60575) = X(i)-Dao conjugate of X(j) for these (i,j): {11, 45751}, {1146, 29824}, {55064, 44671}
X(60575) = cevapoint of X(3700) and X(14430)
X(60575) = trilinear pole of line {11, 4041}
X(60575) = barycentric product X(34387)*X(59071)
X(60575) = barycentric quotient X(i)/X(j) for these {i,j}: {522, 29824}, {650, 45751}, {4041, 44671}, {4526, 40614}, {59071, 59}

X(60576) = TRILINEAR POLE OF X(11)X(3239)

Barycentrics    (a - b - c)*(b - c)*(a^2 - a*b + 2*b^2 - 2*a*c - b*c + c^2)*(a^2 - 2*a*b + b^2 - a*c - b*c + 2*c^2) : :

X(60576) lies on the Moses-Feuerbach circumhyperbola and these lines: {8, 514}, {75, 24002}, {318, 17924}, {341, 4391}, {346, 522}, {666, 39272}, {885, 6559}, {929, 6078}, {1043, 4560}, {1219, 37626}, {1222, 60482}, {1280, 2401}, {1477, 2370}, {3667, 4488}, {4081, 52304}, {4163, 6556}, {4768, 60489}, {18025, 35160}, {28161, 56349}, {28576, 48077}, {30188, 39749}, {30731, 60488}, {36807, 60479}, {52409, 60074}, {56118, 56322}

X(60576) = X(i)-isoconjugate of X(j) for these (i,j): {59, 48032}, {108, 20780}, {109, 1279}, {604, 53337}, {934, 8647}, {1407, 23704}, {1415, 3008}, {1461, 2348}, {2149, 6084}, {4564, 8659}, {20662, 36146}, {24027, 53523}, {32669, 51419}, {32735, 53552}, {36059, 54234}
X(60576) = X(i)-Dao conjugate of X(j) for these (i,j): {11, 1279}, {522, 53523}, {650, 6084}, {1146, 3008}, {2968, 5853}, {3161, 53337}, {6615, 48032}, {14714, 8647}, {20620, 54234}, {24771, 23704}, {35508, 2348}, {38983, 20780}, {39014, 20662}, {51402, 53534}, {55153, 51419}
X(60576) = cevapoint of X(522) and X(50333)
X(60576) = trilinear pole of line {11, 3239}
X(60576) = barycentric product X(i)*X(j) for these {i,j}: {312, 35355}, {341, 37626}, {522, 36807}, {1280, 4391}, {1477, 52622}, {1810, 46110}, {3239, 35160}, {4397, 43760}, {6078, 34387}
X(60576) = barycentric quotient X(i)/X(j) for these {i,j}: {8, 53337}, {11, 6084}, {200, 23704}, {522, 3008}, {650, 1279}, {652, 20780}, {657, 8647}, {885, 52210}, {926, 20662}, {1146, 53523}, {1280, 651}, {1477, 1461}, {1639, 53534}, {1810, 1813}, {2170, 48032}, {2804, 51419}, {3064, 54234}, {3239, 5853}, {3271, 8659}, {3900, 2348}, {4534, 2976}, {6078, 59}, {21044, 53558}, {35160, 658}, {35355, 57}, {36807, 664}, {37626, 269}, {43760, 934}, {50333, 16593}

X(60577) = TRILINEAR POLE OF X(11)X(3700)

Barycentrics    (a - b - c)*(b - c)*(-b^2 + a*c)*(a*b - c^2) : :

X(60777) lies on the Moses-Feuerbach circumhyperbola and these lines: {8, 3907}, {10, 514}, {141, 523}, {281, 55206}, {291, 2401}, {295, 2812}, {335, 60479}, {513, 17351}, {522, 2321}, {655, 660}, {661, 19584}, {666, 1026}, {693, 48647}, {813, 929}, {875, 8678}, {885, 3716}, {996, 4160}, {1441, 20504}, {1577, 29674}, {1654, 56157}, {1769, 41531}, {1808, 56103}, {2254, 40848}, {2311, 15628}, {3572, 4581}, {3596, 4086}, {3701, 3810}, {3737, 27958}, {3738, 7077}, {3762, 3864}, {4088, 30639}, {4107, 9508}, {4122, 9237}, {4151, 49560}, {4518, 14430}, {4582, 23838}, {4804, 17230}, {6740, 56154}, {7192, 33170}, {14838, 16825}, {15065, 18003}, {17924, 21108}, {18827, 35141}, {23902, 55076}, {24093, 48401}, {25380, 43041}, {28470, 50355}, {28487, 48265}, {28840, 50313}, {29051, 56320}, {29116, 49303}, {30671, 47975}, {40217, 60481}, {47918, 47992}, {56173, 60482}

X(60577) = reflection of X(i) in X(j) for these {i,j}: {4107, 9508}, {4444, 23596}, {43041, 25380}
X(60577) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {24479, 150}, {30648, 149}, {51614, 20554}
X(60577) = X(i)-Ceva conjugate of X(j) for these (i,j): {660, 43534}, {4562, 4876}, {36801, 4518}
X(60577) = X(i)-isoconjugate of X(j) for these (i,j): {56, 3573}, {59, 659}, {100, 1428}, {101, 1429}, {108, 7193}, {109, 238}, {110, 1284}, {163, 16609}, {239, 1415}, {242, 36059}, {604, 3570}, {651, 1914}, {660, 12835}, {664, 2210}, {692, 1447}, {812, 2149}, {874, 1397}, {919, 34253}, {1110, 43041}, {1262, 4435}, {1414, 3747}, {1461, 3684}, {1580, 29055}, {1691, 37137}, {1813, 2201}, {1874, 4575}, {2238, 4565}, {2715, 16591}, {2720, 15507}, {3716, 24027}, {4551, 5009}, {4554, 14599}, {4564, 8632}, {4572, 18892}, {4573, 41333}, {6516, 57654}, {6614, 58327}, {7012, 22384}, {8299, 32735}, {8685, 56805}, {10030, 32739}, {20769, 32674}, {21832, 52378}, {24685, 36141}, {27950, 32675}, {32666, 39775}, {32669, 51381}, {36065, 36213}, {36086, 51329}, {38989, 59101}
X(60577) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 3573}, {11, 238}, {115, 16609}, {136, 1874}, {244, 1284}, {514, 43041}, {522, 3716}, {650, 812}, {1015, 1429}, {1086, 1447}, {1146, 239}, {1577, 3766}, {2968, 3685}, {3161, 3570}, {4988, 7212}, {5518, 56413}, {6615, 659}, {6741, 740}, {8054, 1428}, {9470, 109}, {20620, 242}, {35072, 20769}, {35091, 24685}, {35094, 39775}, {35128, 27950}, {35508, 3684}, {36906, 651}, {38980, 34253}, {38981, 15507}, {38983, 7193}, {38989, 51329}, {38991, 1914}, {39025, 2210}, {39092, 29055}, {40608, 3747}, {40619, 10030}, {40624, 350}, {40625, 33295}, {51402, 4432}, {52656, 1025}, {55064, 2238}, {55065, 7235}, {55153, 51381}
X(60577) = trilinear pole of line {11, 3700}
X(60577) = crossdifference of every pair of points on line {1428, 1691}
X(60577) = barycentric product X(i)*X(j) for these {i,j}: {8, 4444}, {11, 4562}, {291, 4391}, {292, 35519}, {295, 46110}, {312, 876}, {333, 35352}, {334, 650}, {335, 522}, {337, 3064}, {514, 4518}, {523, 36800}, {660, 4858}, {663, 18895}, {693, 4876}, {813, 34387}, {850, 2311}, {875, 28659}, {885, 40217}, {918, 33676}, {1086, 36801}, {1577, 56154}, {1808, 14618}, {1916, 3907}, {1934, 3287}, {2170, 4583}, {2643, 36806}, {3063, 44172}, {3239, 7233}, {3261, 7077}, {3572, 3596}, {3700, 18827}, {3716, 40098}, {4041, 40017}, {4086, 37128}, {4516, 4639}, {4560, 43534}, {4589, 21044}, {5378, 40166}, {21438, 43748}, {23596, 52133}, {40495, 51858}, {50333, 52209}, {55206, 57987}
X(60577) = barycentric quotient X(i)/X(j) for these {i,j}: {8, 3570}, {9, 3573}, {11, 812}, {291, 651}, {292, 109}, {295, 1813}, {312, 874}, {334, 4554}, {335, 664}, {513, 1429}, {514, 1447}, {521, 20769}, {522, 239}, {523, 16609}, {649, 1428}, {650, 238}, {652, 7193}, {660, 4564}, {661, 1284}, {663, 1914}, {665, 51329}, {693, 10030}, {694, 29055}, {741, 4565}, {813, 59}, {875, 604}, {876, 57}, {885, 6654}, {918, 39775}, {1086, 43041}, {1146, 3716}, {1581, 37137}, {1639, 4432}, {1808, 4558}, {1911, 1415}, {2170, 659}, {2196, 36059}, {2254, 34253}, {2310, 4435}, {2311, 110}, {2501, 1874}, {2804, 51381}, {3063, 2210}, {3064, 242}, {3120, 7212}, {3239, 3685}, {3252, 2283}, {3261, 18033}, {3271, 8632}, {3287, 1580}, {3572, 56}, {3596, 27853}, {3700, 740}, {3709, 3747}, {3716, 4366}, {3738, 27950}, {3810, 33891}, {3900, 3684}, {3907, 385}, {4024, 7235}, {4041, 2238}, {4081, 4148}, {4086, 3948}, {4124, 4375}, {4130, 58327}, {4140, 4039}, {4171, 4433}, {4391, 350}, {4397, 3975}, {4435, 8300}, {4444, 7}, {4459, 4107}, {4474, 4396}, {4516, 21832}, {4518, 190}, {4522, 3797}, {4530, 4448}, {4534, 53580}, {4560, 33295}, {4562, 4998}, {4589, 4620}, {4820, 4716}, {4843, 4771}, {4858, 3766}, {4876, 100}, {4913, 20142}, {4944, 4693}, {4976, 4974}, {5378, 31615}, {6366, 24685}, {7077, 101}, {7117, 22384}, {7233, 658}, {7252, 5009}, {8632, 12835}, {14430, 4465}, {14432, 4760}, {17072, 39930}, {17926, 14024}, {18155, 30940}, {18191, 50456}, {18265, 32739}, {18344, 2201}, {18827, 4573}, {18895, 4572}, {21044, 4010}, {21132, 27918}, {21348, 56413}, {21438, 56930}, {22116, 1025}, {23596, 7179}, {23655, 51956}, {27958, 17941}, {30669, 6649}, {30671, 1469}, {33676, 666}, {34067, 2149}, {35352, 226}, {35519, 1921}, {36800, 99}, {36801, 1016}, {36806, 24037}, {37128, 1414}, {40017, 4625}, {40217, 883}, {42462, 4124}, {43534, 4552}, {46110, 40717}, {46393, 15507}, {50333, 17755}, {51858, 692}, {51866, 32735}, {52030, 36146}, {52209, 927}, {52622, 4087}, {53239, 35312}, {53560, 53556}, {55206, 862}, {56154, 662}, {57987, 55205}, {60480, 27922}
X(60577) = {X(876),X(35352)}-harmonic conjugate of X(4444)

X(60578) = TRILINEAR POLE OF X(11)X(21132)

Barycentrics    (a + b - 2*c)*(a - b - c)*(b - c)^2*(a - 2*b + c) : :
X(60578) = 3 X[11] - X[4542], X[11] - 3 X[7336], 5 X[11] - 3 X[55376], X[4542] - 9 X[7336], 5 X[4542] - 9 X[55376], 5 X[7336] - X[55376], 3 X[3911] - 2 X[38326], 3 X[17067] - X[38326], 3 X[903] + X[3257], X[3257] - 3 X[46790]

X(60578) lies on the Moses-Feuerbach circumhyperbola and these lines: {11, 522}, {88, 655}, {106, 929}, {226, 52031}, {514, 1086}, {515, 1168}, {516, 14190}, {527, 666}, {553, 40215}, {726, 4013}, {885, 23838}, {908, 1266}, {1022, 2401}, {1111, 21130}, {1320, 3254}, {1731, 3218}, {1738, 4674}, {2325, 4582}, {2403, 23766}, {3452, 52140}, {3663, 52900}, {3982, 47058}, {4049, 60074}, {4342, 45247}, {4391, 4858}, {4530, 60480}, {4560, 17197}, {4581, 43922}, {4778, 43909}, {4792, 28234}, {4887, 51908}, {4945, 28301}, {4957, 30519}, {5542, 34230}, {6173, 36887}, {6548, 60479}, {7332, 24224}, {17960, 32857}, {23598, 60485}, {24177, 52206}, {24870, 38941}, {25342, 27922}, {28194, 39148}, {42462, 60491}, {50092, 52755}, {53545, 60482}

X(60578) = midpoint of X(i) and X(j) for these {i,j}: {903, 46790}, {908, 1266}, {14190, 19636}
X(60578) = reflection of X(3911) in X(17067)
X(60578) = X(i)-Ceva conjugate of X(j) for these (i,j): {88, 4049}, {903, 23838}, {4997, 60480}, {6336, 1022}
X(60578) = X(i)-isoconjugate of X(j) for these (i,j): {44, 59}, {101, 23703}, {109, 1023}, {519, 2149}, {651, 23344}, {765, 1404}, {902, 4564}, {1110, 3911}, {1252, 1319}, {1262, 3689}, {1415, 17780}, {1960, 31615}, {2251, 4998}, {2325, 24027}, {4619, 4895}, {4723, 23979}, {5440, 7115}, {7012, 22356}, {14427, 59151}, {17455, 52377}, {21805, 52378}, {23202, 46102}, {53528, 59149}
X(60578) = X(i)-Dao conjugate of X(j) for these (i,j): {11, 1023}, {513, 1404}, {514, 3911}, {522, 2325}, {650, 519}, {656, 52978}, {661, 1319}, {905, 3977}, {1015, 23703}, {1146, 17780}, {1577, 4358}, {2968, 30731}, {3126, 14439}, {4988, 40663}, {6544, 1317}, {6615, 44}, {6741, 4169}, {9460, 4998}, {38991, 23344}, {40594, 4564}, {40595, 59}, {40624, 24004}, {40628, 5440}, {51402, 53582}
X(60578) = cevapoint of X(i) and X(j) for these (i,j): {11, 4530}, {1086, 42754}, {2170, 53525}, {7336, 52338}
X(60578) = trilinear pole of line {11, 21132}
X(60578) = barycentric product X(i)*X(j) for these {i,j}: {8, 6549}, {11, 903}, {88, 4858}, {106, 34387}, {514, 60480}, {522, 6548}, {693, 23838}, {1022, 4391}, {1086, 4997}, {1111, 1320}, {2170, 20568}, {2316, 23989}, {3257, 40166}, {3271, 57995}, {3596, 43922}, {4049, 4560}, {4080, 17197}, {4089, 36590}, {4530, 54974}, {4555, 21132}, {4582, 6545}, {4615, 55195}, {5548, 23100}, {6336, 26932}, {17880, 36125}, {18155, 55244}, {23345, 35519}, {24026, 56049}, {46790, 60491}, {53525, 57788}
X(60578) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 519}, {88, 4564}, {106, 59}, {244, 1319}, {513, 23703}, {522, 17780}, {650, 1023}, {663, 23344}, {764, 53528}, {903, 4998}, {1015, 1404}, {1022, 651}, {1086, 3911}, {1146, 2325}, {1168, 52377}, {1318, 9268}, {1320, 765}, {1417, 24027}, {1639, 53582}, {1647, 1317}, {1797, 44717}, {2170, 44}, {2310, 3689}, {2316, 1252}, {2969, 1877}, {3120, 40663}, {3239, 30731}, {3257, 31615}, {3271, 902}, {3675, 53531}, {3700, 4169}, {4049, 4552}, {4089, 41801}, {4124, 4432}, {4391, 24004}, {4459, 4434}, {4516, 21805}, {4530, 4370}, {4542, 8028}, {4582, 6632}, {4615, 55194}, {4858, 4358}, {4939, 4487}, {4997, 1016}, {5548, 59149}, {6336, 46102}, {6545, 30725}, {6548, 664}, {6549, 7}, {6550, 39771}, {7004, 5440}, {7117, 22356}, {7336, 1647}, {8735, 8756}, {8752, 7115}, {9456, 2149}, {15637, 6049}, {17197, 16704}, {17435, 14439}, {18155, 55243}, {18191, 52680}, {21044, 3943}, {21132, 900}, {21140, 24816}, {23345, 109}, {23615, 4528}, {23838, 100}, {24026, 4723}, {24188, 14027}, {26856, 30606}, {26932, 3977}, {34387, 3264}, {34591, 52978}, {35015, 1145}, {36125, 7012}, {40166, 3762}, {42455, 4768}, {42462, 1639}, {42753, 53530}, {42754, 52659}, {43922, 56}, {52338, 6544}, {53525, 214}, {55195, 4120}, {55244, 4551}, {55263, 4559}, {56049, 7045}, {60480, 190}, {60491, 46791}

X(60579) = TRILINEAR POLE OF X(11)X(42462)

Barycentrics    (a - b - c)*(b - c)^2*(a^2 - 2*a*b + b^2 + a*c + b*c - 2*c^2)*(a^2 + a*b - 2*b^2 - 2*a*c + b*c + c^2) : :
X(60579) = 3 X[11] - X[3328], X[11] - 3 X[5532], 5 X[11] - 3 X[55370], X[3328] - 9 X[5532], 5 X[3328] - 9 X[55370], 5 X[5532] - X[55370], 3 X[1737] - X[53617]

X(60579) lies on the Moses-Feuerbach circumhyperbola and these lines: {10, 56665}, {11, 514}, {80, 516}, {519, 666}, {522, 1146}, {885, 4530}, {929, 2291}, {1090, 1111}, {1323, 37757}, {1737, 43672}, {1776, 5011}, {2401, 35348}, {3679, 52746}, {3717, 4582}, {4089, 15634}, {4293, 18328}, {4302, 31852}, {4391, 24026}, {5199, 6745}, {12019, 53801}, {14505, 59951}, {14733, 53878}, {21132, 60491}, {24232, 40451}, {26015, 53382}, {34056, 44675}, {35015, 60485}

X(60579) = reflection of X(6745) in X(5199)
X(60579) = X(1121)-Ceva conjugate of X(23893)
X(60579) = X(i)-isoconjugate of X(j) for these (i,j): {59, 1155}, {100, 23346}, {101, 23890}, {527, 2149}, {692, 56543}, {1055, 4564}, {1110, 1323}, {1252, 6610}, {1262, 6603}, {6510, 7115}, {6745, 24027}, {14392, 59151}, {23990, 37780}
X(60579) = X(i)-Dao conjugate of X(j) for these (i,j): {514, 1323}, {522, 6745}, {650, 527}, {661, 6610}, {1015, 23890}, {1086, 56543}, {1577, 30806}, {3126, 35293}, {6615, 1155}, {8054, 23346}, {40628, 6510}
X(60579) = cevapoint of X(i) and X(j) for these (i,j): {1638, 23730}, {5532, 52334}
X(60579) = trilinear pole of line {11, 42462}
X(60579) = barycentric product X(i)*X(j) for these {i,j}: {11, 1121}, {522, 60479}, {693, 23893}, {1111, 41798}, {1156, 4858}, {2291, 34387}, {3261, 23351}, {4391, 35348}, {4845, 23989}, {23615, 60487}, {24026, 34056}, {35157, 42462}, {37139, 42455}
X(60579) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 527}, {244, 6610}, {513, 23890}, {514, 56543}, {649, 23346}, {1086, 1323}, {1111, 37780}, {1121, 4998}, {1146, 6745}, {1156, 4564}, {2170, 1155}, {2291, 59}, {2310, 6603}, {3271, 1055}, {4124, 24685}, {4459, 6647}, {4530, 6174}, {4845, 1252}, {4858, 30806}, {5532, 33573}, {7004, 6510}, {8735, 23710}, {14733, 4619}, {17435, 35293}, {18889, 1110}, {21132, 1638}, {23351, 101}, {23893, 100}, {33573, 6068}, {34056, 7045}, {34068, 2149}, {35348, 651}, {41798, 765}, {42069, 60431}, {42462, 6366}, {52338, 30573}, {55195, 30574}, {60047, 44717}, {60479, 664}

X(60580) = TRILINEAR POLE OF X(11)X(649)

Barycentrics    (b - c)*(a^4 - a^3*b - a*b^3 + b^4 + a^2*b*c + a*b^2*c - a^2*c^2 - b^2*c^2)*(-a^4 + a^2*b^2 + a^3*c - a^2*b*c - a*b*c^2 + b^2*c^2 + a*c^3 - c^4) : :

X(60580) lies on the Moses-Feuerbach circumhyperbola, the circumconic {{A,B,C,X(1),X(6)}} and these lines: {1, 4391}, {6, 522}, {34, 17924}, {56, 514}, {58, 4560}, {106, 1311}, {269, 24002}, {655, 36094}, {885, 1438}, {929, 32689}, {998, 29066}, {1411, 60074}, {2827, 9432}, {3445, 52596}, {4582, 9268}, {17954, 60484}, {23887, 36052}

X(60580) = X(i)-isoconjugate of X(j) for these (i,j): {72, 7463}, {100, 8679}, {692, 33864}
X(60580) = X(i)-Dao conjugate of X(j) for these (i,j): {1086, 33864}, {8054, 8679}
X(60580) = trilinear pole of line {11, 649}
X(60580) = barycentric product X(i)*X(j) for these {i,j}: {514, 1311}, {4858, 36094}, {32689, 34387}
X(60580) = barycentric quotient X(i)/X(j) for these {i,j}: {514, 33864}, {649, 8679}, {1311, 190}, {1474, 7463}, {32689, 59}, {36094, 4564}

X(60581) = TRILINEAR POLE OF X(11)X(3323)

Barycentrics    (b - c)*(-a + b - c)*(a + b - c)*(a^3 - a^2*b - a*b^2 + b^3 + a*c^2 + b*c^2 - 2*c^3)*(-a^3 - a*b^2 + 2*b^3 + a^2*c - b^2*c + a*c^2 - c^3) : :

X(60581 lies on the Moses-Feuerbach circumhyperbola and these lines: {7, 522}, {85, 4391}, {103, 2369}, {279, 514}, {676, 885}, {929, 24016}, {1358, 52304}, {1434, 4560}, {1847, 17924}, {4089, 15634}, {4293, 59925}, {10509, 56322}, {18025, 35160}, {23062, 24002}, {36101, 43762}, {42462, 58817}, {52156, 60480}

X(60581) = X(i)-isoconjugate of X(j) for these (i,j): {9, 2426}, {41, 2398}, {59, 46392}, {101, 41339}, {109, 51418}, {212, 41321}, {643, 51436}, {692, 40869}, {910, 3939}, {2175, 42719}, {4241, 52370}, {6602, 23973}, {8750, 51376}, {9502, 52927}, {36086, 56785}, {54325, 56900}
X(60581) = X(i)-Dao conjugate of X(j) for these (i,j): {11, 51418}, {478, 2426}, {1015, 41339}, {1086, 40869}, {3160, 2398}, {6615, 46392}, {26932, 51376}, {38989, 56785}, {40593, 42719}, {40615, 516}, {40617, 910}, {40622, 17747}, {40837, 41321}, {55060, 51436}
X(60581) = cevapoint of X(i) and X(j) for these (i,j): {241, 59813}, {514, 43042}, {650, 2820}
X(60581) = trilinear pole of line {11, 3323}
X(60581) = barycentric product X(i)*X(j) for these {i,j}: {7, 2400}, {103, 52621}, {348, 53150}, {514, 52156}, {664, 15634}, {693, 43736}, {1358, 57928}, {2424, 6063}, {3669, 57996}, {3676, 18025}, {24002, 36101}, {24016, 34387}
X(60581) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 2398}, {56, 2426}, {85, 42719}, {103, 3939}, {278, 41321}, {479, 23973}, {513, 41339}, {514, 40869}, {650, 51418}, {665, 56785}, {677, 6065}, {905, 51376}, {1358, 676}, {1815, 4587}, {2170, 46392}, {2400, 8}, {2424, 55}, {3669, 910}, {3676, 516}, {7178, 17747}, {7180, 51436}, {15634, 522}, {17094, 51366}, {17096, 14953}, {18025, 3699}, {23062, 24015}, {24002, 30807}, {24016, 59}, {30719, 53579}, {30725, 51406}, {32642, 6066}, {32668, 2149}, {36101, 644}, {36122, 56183}, {43035, 3234}, {43041, 51435}, {43042, 50441}, {43050, 28345}, {43736, 100}, {43930, 56639}, {43932, 1456}, {52156, 190}, {52213, 2284}, {52621, 35517}, {53150, 281}, {53544, 9502}, {55257, 1334}, {56668, 42720}, {56787, 52614}, {57928, 4076}, {57996, 646}, {58817, 43035}

X(60582) = TRILINEAR POLE OF X(11)X(51442)

Barycentrics    (a - b - c)*(b - c)^2*(a^4 - 2*a^2*b^2 + b^4 - 2*a^3*c + 2*a^2*b*c + 2*a*b^2*c - 2*b^3*c + a^2*c^2 - 4*a*b*c^2 + b^2*c^2 + 2*a*c^3 + 2*b*c^3 - 2*c^4)*(a^4 - 2*a^3*b + a^2*b^2 + 2*a*b^3 - 2*b^4 + 2*a^2*b*c - 4*a*b^2*c + 2*b^3*c - 2*a^2*c^2 + 2*a*b*c^2 + b^2*c^2 - 2*b*c^3 + c^4) : :

X(60582) lies on the Moses-Feuerbach circumhyperbola and these lines: {2, 655}, {278, 40218}, {345, 4582}, {514, 42754}, {522, 35015}, {528, 52479}, {666, 46136}, {885, 46041}, {929, 953}, {1086, 2401}, {1146, 60485}, {4858, 60074}, {5741, 50039}, {17079, 60487}, {26932, 60480}

X(60582) = X(46136)-Ceva conjugate of X(46041)
X(60582) = X(i)-isoconjugate of X(j) for these (i,j): {59, 2265}, {952, 2149}, {1110, 43043}
X(60582) = X(i)-Dao conjugate of X(j) for these (i,j): {514, 43043}, {650, 952}, {6615, 2265}
X(60582) = cevapoint of X(1146) and X(51442)
X(60582) = barycentric product X(i)*X(j) for these {i,j}: {11, 46136}, {693, 46041}, {953, 34387}, {50943, 60480}
X(60582) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 952}, {953, 59}, {1086, 43043}, {2170, 2265}, {3326, 6073}, {6075, 3319}, {7336, 6075}, {46041, 100}, {46136, 4998}, {60480, 57456}

X(60583) = TRILINEAR POLE OF X(11)X(3064)

Barycentrics    (b - c)*(-a + b + c)*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2)*(a^3 - a^2*b - a*b^2 + b^3 + a*c^2 + b*c^2 - 2*c^3)*(-a^3 - a*b^2 + 2*b^3 + a^2*c - b^2*c + a*c^2 - c^3) : :

X(60583 lies on the Moses-Feuerbach circumhyperbola and these lines: {4, 514}, {29, 4560}, {103, 32706}, {158, 17924}, {273, 2400}, {278, 23615}, {281, 522}, {318, 4391}, {929, 40116}, {2401, 2424}, {10731, 44978}, {36101, 43764}, {40446, 60482}, {44428, 52781}

X(60583) = Yff-central-circle-inverse of X(47267)
X(60583) = X(i)-isoconjugate of X(j) for these (i,j): {77, 2426}, {212, 23973}, {516, 36059}, {603, 2398}, {906, 43035}, {910, 1813}, {1331, 1456}, {1415, 26006}, {1461, 51376}, {2149, 39470}, {4241, 22341}, {7125, 41321}, {20752, 56786}, {24015, 52425}, {30807, 32660}, {42719, 52411}
X(60583) = X(i)-Dao conjugate of X(j) for these (i,j): {650, 39470}, {1146, 26006}, {5190, 43035}, {5521, 1456}, {6741, 51366}, {7952, 2398}, {20620, 516}, {35508, 51376}, {38966, 41339}, {40837, 23973}, {53985, 53529}
X(60583) = trilinear pole of line {11, 3064}
X(60583) = barycentric product X(i)*X(j) for these {i,j}: {8, 53150}, {103, 46110}, {281, 2400}, {522, 52781}, {2338, 46107}, {2424, 7017}, {3064, 18025}, {4391, 36122}, {8735, 57928}, {18344, 57996}, {34387, 40116}, {36101, 44426}, {44130, 55257}
X(60583) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 39470}, {103, 1813}, {273, 24015}, {278, 23973}, {281, 2398}, {318, 42719}, {522, 26006}, {607, 2426}, {677, 44717}, {911, 36059}, {1815, 6517}, {1857, 41321}, {2338, 1331}, {2400, 348}, {2424, 222}, {3064, 516}, {3700, 51366}, {3900, 51376}, {6591, 1456}, {7649, 43035}, {8735, 676}, {8748, 4241}, {18344, 910}, {23615, 57292}, {36101, 6516}, {36122, 651}, {36124, 56786}, {40116, 59}, {44130, 55256}, {44426, 30807}, {46110, 35517}, {52781, 664}, {53150, 7}, {55257, 73}, {56787, 53550}, {60001, 2284}

X(60584) = TRILINEAR POLE OF X(11)X(7649)

Barycentrics    (b - c)*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2)*(a^4 - 2*a^2*b^2 + b^4 - a^3*c + a^2*b*c + a*b^2*c - b^3*c + a^2*c^2 - 2*a*b*c^2 + b^2*c^2 + a*c^3 + b*c^3 - 2*c^4)*(-a^4 + a^3*b - a^2*b^2 - a*b^3 + 2*b^4 - a^2*b*c + 2*a*b^2*c - b^3*c + 2*a^2*c^2 - a*b*c^2 - b^2*c^2 + b*c^3 - c^4)

: : X(60584) lies on the Moses-Feuerbach circumhyperbola and these lines: {4, 522}, {27, 4560}, {92, 2399}, {102, 917}, {278, 514}, {513, 53813}, {885, 36121}, {929, 36067}, {1847, 24002}, {2432, 40573}, {6336, 52780}, {36100, 37203}

X(60584) = X(i)-isoconjugate of X(j) for these (i,j): {59, 46391}, {78, 2425}, {101, 46974}, {184, 42718}, {212, 2406}, {515, 906}, {1331, 2182}, {1455, 4587}, {1813, 51361}, {2149, 39471}, {2289, 23987}, {3990, 7452}, {6056, 24035}
X(60584) = X(i)-Dao conjugate of X(j) for these (i,j): {650, 39471}, {1015, 46974}, {5190, 515}, {5521, 2182}, {6615, 46391}, {40622, 51368}, {40837, 2406}
X(60584) = cevapoint of X(3064) and X(39534)
X(60584) = trilinear pole of line {11, 7649}
X(60584) = barycentric product X(i)*X(j) for these {i,j}: {7, 53152}, {102, 46107}, {278, 2399}, {331, 2432}, {514, 52780}, {693, 36121}, {7649, 34393}, {15633, 36118}, {17924, 36100}, {34387, 36067}, {44129, 55255}
X(60584) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 39471}, {92, 42718}, {102, 1331}, {278, 2406}, {513, 46974}, {608, 2425}, {1118, 23987}, {2170, 46391}, {2399, 345}, {2432, 219}, {2969, 53522}, {6591, 2182}, {7178, 51368}, {7649, 515}, {8747, 7452}, {15629, 4587}, {18344, 51361}, {32667, 2149}, {32677, 906}, {34393, 4561}, {36067, 59}, {36100, 1332}, {36121, 100}, {38362, 6087}, {43923, 1455}, {43933, 56638}, {44129, 55254}, {46107, 35516}, {52780, 190}, {53152, 8}, {53522, 38554}, {54239, 51375}, {55255, 71}

X(60585) = TRILINEAR POLE OF X(11)X(6591)

Barycentrics    (b - c)*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2)*(a^5 - a^4*b - a*b^4 + b^5 + 2*a*b*c^3 - a*c^4 - b*c^4)*(-a^5 + a*b^4 + a^4*c - 2*a*b^3*c + b^4*c + a*c^4 - c^5) : :

X(60585 lies on the Moses-Feuerbach circumhyperbola and these lines: {4, 4391}, {19, 522}, {28, 4560}, {34, 514}, {655, 36093}, {885, 8751}, {915, 7427}, {929, 32688}, {1118, 17924}, {1119, 24002}, {17981, 60484}, {36125, 60480}

X(60585) = X(i)-isoconjugate of X(j) for these (i,j): {1026, 34160}, {1331, 3827}, {3682, 4244}, {4571, 51655}
X(60585) = X(5521)-Dao conjugate of X(3827)
X(60585) = trilinear pole of line {11, 6591}
X(60585) = barycentric product X(i)*X(j) for these {i,j}: {4858, 36093}, {17924, 26703}, {32688, 34387}
X(60585) = barycentric quotient X(i)/X(j) for these {i,j}: {5317, 4244}, {6591, 3827}, {26703, 1332}, {32688, 59}, {36093, 4564}, {43929, 34160}

X(60586) = X(1)X(6)∩X(4)X(3735)

Barycentrics    a*(b + c)*(a^3*b^2 - a^2*b^3 - a*b^4 + b^5 - 2*a^3*b*c - a^2*b^2*c - b^4*c + a^3*c^2 - a^2*b*c^2 - 2*a*b^2*c^2 - a^2*c^3 - a*c^4 - b*c^4 + c^5) : :

X(60586) lies on the cubic K1352 and these lines: {1, 6}, {4, 3735}, {38, 22070}, {39, 42702}, {51, 5360}, {226, 3721}, {228, 3148}, {321, 40814}, {442, 3125}, {950, 3727}, {976, 52425}, {1640, 55232}, {1708, 54317}, {1901, 4016}, {1953, 50621}, {2238, 40661}, {2292, 53560}, {2295, 15556}, {4037, 51972}, {4531, 21804}, {7738, 24274}, {20271, 25525}

X(60586) = barycentric product X(i)*X(j) for these {i,j}: {10, 11031}, {37, 26543}, {72, 37362}
X(60586) = barycentric quotient X(i)/X(j) for these {i,j}: {11031, 86}, {26543, 274}, {37362, 286}
X(60586) = {X(72),X(218)}-harmonic conjugate of X(21839)

X(60587) = X(4)X(30505)∩X(6)X(22)

Barycentrics    a^2*(a^2 + b^2)*(a^2 + c^2)*(a^4*b^2 - 2*a^2*b^4 + b^6 + a^4*c^2 - 2*a^2*b^2*c^2 - b^4*c^2 - 2*a^2*c^4 - b^2*c^4 + c^6) : :

X(60587) lies on the cubic K1352 and these lines: {4, 30505}, {6, 22}, {39, 51252}, {83, 5392}, {184, 10551}, {262, 16277}, {308, 56017}, {311, 18092}, {394, 10130}, {401, 10548}, {1692, 59188}, {1799, 1993}, {1994, 52898}, {2623, 58784}, {3051, 7495}, {3148, 10547}, {5133, 20965}, {10601, 39668}, {20022, 41237}, {34545, 59180}, {41334, 52580}, {42295, 43977}, {46104, 52253}

X(60587) = isogonal conjugate of the polar conjugate of X(10550)
X(60587) = X(i)-isoconjugate of X(j) for these (i,j): {38, 40393}, {141, 2216}, {1964, 57903}, {20883, 40441}
X(60587) = X(i)-Dao conjugate of X(j) for these (i,j): {1209, 141}, {41884, 57903}
X(60587) = barycentric product X(i)*X(j) for these {i,j}: {3, 10550}, {83, 570}, {251, 37636}, {1176, 1594}, {1216, 32085}, {1799, 47328}, {16698, 18098}, {17500, 51255}, {23195, 46104}, {50947, 58784}
X(60587) = barycentric quotient X(i)/X(j) for these {i,j}: {83, 57903}, {251, 40393}, {570, 141}, {1216, 3933}, {1594, 1235}, {4630, 59004}, {10547, 40441}, {10550, 264}, {16698, 16703}, {17500, 59137}, {18105, 50946}, {23195, 3917}, {37636, 8024}, {46289, 2216}, {47328, 427}, {50947, 4576}, {59172, 16030}

X(60588) = X(2)X(30539)∩X(6)X(30)

Barycentrics    (a^2 - 2*b^2 - 2*c^2)*(a^4 + 4*a^2*b^2 + b^4 - 2*a^2*c^2 - 2*b^2*c^2 + c^4)*(a^4 - 2*a^2*b^2 + b^4 + 4*a^2*c^2 - 2*b^2*c^2 + c^4) : :

X(60588) lies on the cubic K1352 and these lines: {2, 30539}, {6, 30}, {51, 11648}, {262, 60119}, {574, 13857}, {671, 34289}, {1302, 6323}, {2088, 30495}, {3148, 3455}, {6128, 7706}, {32681, 53955}

X(60588) = X(15066)-isoconjugate of X(55927)
X(60588) = X(i)-Dao conjugate of X(j) for these (i,j): {8542, 15066}, {11165, 32833}, {17413, 8675}, {17416, 30474}
X(60588) = barycentric product X(i)*X(j) for these {i,j}: {574, 34289}, {599, 34288}, {1302, 3906}, {4846, 5094}, {8541, 57819}, {13857, 60119}
X(60588) = barycentric quotient X(i)/X(j) for these {i,j}: {574, 15066}, {599, 32833}, {1302, 35138}, {3906, 30474}, {5094, 44134}, {8541, 378}, {17414, 8675}, {32738, 11636}, {34288, 598}, {34289, 40826}

X(60589) = X(2)X(36952)∩X(6)X(24)

Barycentrics    a^2*(a^4 - 2*a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2)*(a^4 - a^2*b^2 - 2*a^2*c^2 - b^2*c^2 + c^4)*(a^4*b^2 - b^6 + a^4*c^2 + 2*a^2*b^2*c^2 + b^4*c^2 + b^2*c^4 - c^6) : :

X(60589) lies on the cubic K1352 and these lines: {2, 36952}, {6, 24}, {39, 41270}, {51, 58306}, {95, 7786}, {96, 262}, {97, 23115}, {112, 19172}, {217, 7576}, {275, 40814}, {1640, 2623}, {2207, 58785}, {3148, 54034}, {3289, 14788}, {5305, 8901}, {7401, 60106}, {7488, 41334}, {8743, 8884}, {9605, 16030}, {10548, 15412}, {16035, 30435}, {19173, 45141}, {19174, 41361}, {19210, 22120}, {20806, 34386}

X(60589) = barycentric product X(i)*X(j) for these {i,j}: {54, 5133}, {95, 9969}, {19174, 51252}, {39287, 42442}
X(60589) = barycentric quotient X(i)/X(j) for these {i,j}: {5133, 311}, {9969, 5}
X(60589) = {X(39),X(41270)}-harmonic conjugate of X(51255)

X(60590) = ISOGONAL CONJUGATE OF X(5622)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^6*b^2-a^4*b^4-a^2*b^6+b^8+3*a^6*c^2-a^4*b^2*c^2+3*a^2*b^4*c^2-b^6*c^2-6*a^4*c^4-a^2*b^2*c^4-b^4*c^4+3*a^2*c^6+b^2*c^6)*(3*a^6*b^2-6*a^4*b^4+3*a^2*b^6+a^6*c^2-a^4*b^2*c^2-a^2*b^4*c^2+b^6*c^2-a^4*c^4+3*a^2*b^2*c^4-b^4*c^4-a^2*c^6-b^2*c^6+c^8) : :
X(60590) = 3 X[403]-X[44146],3 X[2967]+X[38552]

X(60590) lies on the cubic K1353 and these lines: {2,35908},{4,5968},{6,35912},{23,19189},{25,3233},{30,232},{98,46426},{112,46981},{113,525},{132,36170},{186,51862},{235,58080},{250,36166},{262,57583},{264,36183},{325,403},{427,14356},{468,511},{523,2967},{648,9139},{842,7473},{858,6530},{1316,40801},{1560,2501},{2065,60506},{2697,35907},{3265,34336},{3425,36176},{5186,5203},{6720,10257},{6795,45141},{7426,46809},{9970,60503},{10295,52692},{12028,41392},{14999,40118},{23350,53156},{34334,58757},{34370,52464},{37930,56307},{37984,52477},{46619,46987},{47151,56370},{47475,50387}

X(60590) = isogonal conjugate of X(5622)
X(60590) = polar conjugate of X(41254)
X(60590) = X(i)-isoconjugate of X(j) for these (i,j):{1,5622},{48,41254},{293,7418}
X(60590) = X(i)-Dao conjugate of X(j) for these (i,j):{3,5622},{132,7418},{1249,41254},{42426,60508}
X(60590) = cevapoint of X(i) and X(j) for these (i,j):{3,45016},{2967,54380},{5095,45662}
X(60590) = trilinear pole of line {3569,9033}
X(60590) = barycentric product X(18020)*X(60500)
X(60590) = barycentric quotient X(i)/X(j) for these {i,j}:{4,41254},{6,5622},{232,7418},{6103,60508},{60500,125}

X(60591) = ISOGONAL CONJUGATE OF X(37937)

Barycentrics    (b^2-c^2)*(-a^2+b^2+c^2)*(a^10-a^6*b^4-a^4*b^6+b^10-2*a^8*c^2+2*a^6*b^2*c^2+2*a^2*b^6*c^2-2*b^8*c^2-a^4*b^2*c^4-a^2*b^4*c^4+2*a^4*c^6+2*b^4*c^6-a^2*c^8-b^2*c^8)*(-a^10+2*a^8*b^2-2*a^4*b^6+a^2*b^8-2*a^6*b^2*c^2+a^4*b^4*c^2+b^8*c^2+a^6*c^4+a^2*b^4*c^4-2*b^6*c^4+a^4*c^6-2*a^2*b^2*c^6+2*b^2*c^8-c^10) : :

X(60591) lies on the Jerabek hyperbola, the cubic K1353, and these lines: {3,41077},{4,9517},{6,9033},{64,690},{66,526},{67,520},{74,525},{125,2435},{265,8673},{512,11744},{523,1177},{648,60512},{895,8057},{1562,10097},{2501,43717},{2780,35512},{5505,9007},{6368,34437},{10293,30209},{14316,57388},{14380,15526},{32661,60505},{34207,55121},{35909,37987},{39447,59108},{45327,57665},{57742,60506}

X(60591) = reflection of X(2435) in X(125)
X(60591) = isogonal conjugate of X(37937)
X(60591) = antigonal image of X(2435)
X(60591) = X(i)-isoconjugate of X(j) for these (i,j):{1,37937},{162,2781},{163,50188}
X(60591) = X(i)-Dao conjugate of X(j) for these (i,j):{3,37937},{115,50188},{125,2781},{42426,60512}
X(60591) = trilinear pole of line {647,1650}
X(60591) = barycentric product X(i)*X(j) for these {i,j}:{525,2697},{35911,58087},{47110,53173}
X(60591) = barycentric quotient X(i)/X(j) for these {i,j}:{6,37937},{523,50188},{647,2781},{1640,42426},{2697,648},{6103,60512},{14582,43090},{46340,52916}

X(60592) = X(51)X(14593)∩X(66)X(68)

Barycentrics    (a^4-2*a^2*b^2+b^4-2*b^2*c^2+c^4)*(a^4+b^4-2*a^2*c^2-2*b^2*c^2+c^4)*(a^6-a^4*b^2+a^2*b^4-b^6-a^4*c^2+b^4*c^2+a^2*c^4+b^2*c^4-c^6) : :

X(60592) lies on the cubic K1354 and these lines: {51,14593},{66,68},{159,11360},{161,2351},{206,1976},{290,55553},{847,18912},{1209,34853},{1502,46134},{9969,27367},{38317,56892},{41761,53245},{44176,60518}

X(60592) = X(i)-Ceva conjugate of X(j) for these (i,j):{290,60519},{55553,2165}
X(60592) = X(i)-isoconjugate of X(j) for these (i,j):{47,44175},{1485,44179},{1748,59169}
X(60592) = X(i)-Dao conjugate of X(j) for these (i,j):{184,1147},{34853,44175},{37864,1485}
X(60592) = barycentric product X(i)*X(j) for these {i,j}:{91,21374},{157,5392},{847,23128},{2165,11442},{2351,59156},{2909,57904},{22391,55553}
X(60592) = barycentric quotient X(i)/X(j) for these {i,j}:{157,1993},{2165,44175},{2351,59169},{2909,571},{5392,57771},{11442,7763},{21374,44179},{22391,1147},{23128,9723},{60501,1485}

X(60593) = X(51)X(14593)∩X(66)X(68)

Barycentrics    (a^2*b^2-b^4+a^2*c^2+2*b^2*c^2-c^4)*(a^8+a^6*b^2-a^4*b^4-a^2*b^6+a^6*c^2-a^4*b^2*c^2+a^2*b^4*c^2-b^6*c^2-a^4*c^4+a^2*b^2*c^4+2*b^4*c^4-a^2*c^6-b^2*c^6) : :

X(60593) lies on the cubic K1354 and these lines: {2,40588},{4,6},{311,60515},{1976,60523},{3164,31276},{11610,21458},{12384,13236},{17500,41334},{19570,23878},{33754,57137},{39569,51363},{52967,60517}

X(60593) = X(290)-Ceva conjugate of X(51)
X(60593) = X(2167)-isoconjugate of X(60528)
X(60593) = X(i)-Dao conjugate of X(j) for these (i,j):{40588,60528},{52967,511}
X(60593) = barycentric product X(290)*X(52878)
X(60593) = barycentric quotient X(i)/X(j) for these {i,j}:{51,60528},{52878,511}

X(60594) = X(290)X(511)∩X(419)X(685)

Barycentrics    b^2*c^2*(a^4+b^4-a^2*c^2-b^2*c^2)^2*(-a^4+a^2*b^2+b^2*c^2-c^4)^2*(-(a^2*b^2)+b^4-a^2*c^2-2*b^2*c^2+c^4) : :

X(60594) lies on the cubic K1354 and these lines: {6,14265},{98,34133},{290,511},{419,685},{9755,57490},{11610,41932},{32428,53245},{33971,52641},{52967,60517},{53174,60518}

X(60594) = X(i)-isoconjugate of X(j) for these (i,j):{54,23996},{95,42075},{1355,44687},{1959,41270},{2148,36790},{2167,11672},{2169,2967},{36134,41167}
X(60594) = X(i)-Dao conjugate of X(j) for these (i,j):{137,41167},{216,36790},{14363,2967},{40588,11672},{52878,23611}
X(60594) = cevapoint of X(51) and X(60517)
barycentric product X(i)*X(j) for these {i,j}:{5,34536},{51,57541},{98,53245},{290,60517},{311,41932},{324,47388},{16081,53174},{18314,41173}
X(60594) = barycentric quotient X(i)/X(j) for these {i,j}:{5,36790},{51,11672},{53,2967},{311,32458},{1953,23996},{1976,41270},{2179,42075},{6531,19189},{12077,41167},{13450,36426},{14569,51334},{14570,15631},{18180,16725},{34536,95},{40981,9419},{41173,18315},{41221,59805},{41932,54},{47388,97},{52967,23611},{53174,36212},{53245,325},{55219,58262},{57260,58306},{57541,34384},{60517,511}

X(60595) = X(2)X(136)∩X(5)X(27367)

Barycentrics    (a^2*b^2-b^4+a^2*c^2-c^4)*(a^4-2*a^2*b^2+b^4-2*b^2*c^2+c^4)*(a^4+b^4-2*a^2*c^2-2*b^2*c^2+c^4)*(2*a^4-a^2*b^2+b^4-a^2*c^2-2*b^2*c^2+c^4) : :

X(60595) lies on the cubic K1355 and these lines: {2,136},{5,27367},{206,1976},{216,8754},{511,2450},{847,37446},{2351,14713},{3148,35067},{5392,54978},{17994,55267},{40588,60526}

X(60595) = X(8772)-complementary conjugate of X(22391)
X(60595) = X(32734)-Ceva conjugate of X(55122)
X(60595) = X(i)-isoconjugate of X(j) for these (i,j):{47,40428},{2065,44179},{31635,36051},{55216,55266}
X(60595) = X(i)-Dao conjugate of X(j) for these (i,j):{114,31635},{230,7763},{868,6563},{34853,40428},{37864,2065}
X(60595) = barycentric product X(i)*X(j) for these {i,j}:{91,17462},{114,2165},{511,60519},{847,47406},{925,55267},{5392,51335}
X(60595) = barycentric quotient X(i)/X(j) for these {i,j}:{114,7763},{230,31635},{925,55266},{2165,40428},{17462,44179},{47406,9723},{51335,1993},{52144,51776},{55267,6563},{60501,2065},{60519,290}

X(60596) = X(216)X(311)∩X(237)X(511)

Barycentrics    a^2*(a^2*b^2-b^4+a^2*c^2-c^4)*(a^2*b^2-b^4+a^2*c^2+2*b^2*c^2-c^4)*(a^6-2*a^4*b^2+a^2*b^4-2*a^4*c^2-a^2*b^2*c^2+b^4*c^2+a^2*c^4+b^2*c^4) : :

X(60596) lies on the cubic K1355 and these lines: {2,60526},{51,23181},{206,8266},{216,311},{237,511},{343,35319},{570,3589},{1194,23584},{6676,46832},{52967,60524}

X(60596) = midpoint of X(311) and X(14570)
X(60596) = reflection of X(570) in X(34990)
X(60596) = isotomic conjugate of the polar conjugate of X(45123)
X(60596) = X(i)-complementary conjugate of X(j) for these (i,j):{31,60524},{163,53567},{19128,20305},{53263,21253}
X(60596) = X(2)-Ceva conjugate of X(60524)
X(60596) = X(2167)-isoconjugate of X(60523)
X(60596) = X(i)-Dao conjugate of X(j) for these (i,j):{3569,8901},{40588,60523},{52878,60526},{60524,2}
X(60596) = barycentric product X(i)*X(j) for these {i,j}:{69,45123},{511,60518}
X(60596) = barycentric quotient X(i)/X(j) for these {i,j}:{51,60523},{38354,23286},{38987,8901},{45123,4},{52967,60526},{60518,290}

X(60597) = ISOTOMIC CONJUGATE OF X(16813)

Barycentrics    (a^2 - b^2 - c^2)^2*(b^2 - c^2)*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4) : :
X(60597) = X[2525] + 2 X[6334], 3 X[3265] - X[20580], 4 X[3265] - X[41077], 3 X[14417] - 2 X[52584], 4 X[20580] - 3 X[41077], 2 X[20580] - 3 X[52613], 3 X[12077] - 2 X[20577], X[12077] + 2 X[41078], 3 X[18314] - X[20577], X[20577] + 3 X[41078]

X(60597) lies on these lines: {441, 525}, {684, 826}, {690, 22089}, {801, 2394}, {1225, 18312}, {1568, 6368}, {2419, 42330}, {2799, 3267}, {5562, 58305}, {12077, 18314}, {14273, 57070}, {15414, 39181}, {15526, 18557}, {23685, 35518}, {23878, 57069}, {28724, 53173}, {30476, 57065}, {33294, 52585}, {45147, 47193}, {52624, 57811}

X(60597) = midpoint of X(18314) and X(41078)
X(60597) = reflection of X(i) in X(j) for these {i,j}: {12077, 18314}, {33294, 52585}, {41077, 52613}, {52613, 3265}, {57065, 30476}
X(60597) = isotomic conjugate of X(16813)
X(60597) = complement of the isotomic conjugate of X(16039)
X(60597) = isotomic conjugate of the isogonal conjugate of X(17434)
X(60597) = isotomic conjugate of the polar conjugate of X(6368)
X(60597) = X(15319)-anticomplementary conjugate of X(21294)
X(60597) = X(i)-complementary conjugate of X(j) for these (i,j): {163, 32391}, {6145, 21253}, {16039, 2887}, {20626, 20305}
X(60597) = X(i)-Ceva conjugate of X(j) for these (i,j): {394, 15526}, {14570, 343}, {20563, 125}, {52347, 35442}
X(60597) = X(i)-isoconjugate of X(j) for these (i,j): {19, 933}, {31, 16813}, {54, 24019}, {107, 2148}, {112, 2190}, {158, 14586}, {162, 8882}, {163, 8884}, {275, 32676}, {393, 36134}, {560, 42405}, {823, 54034}, {1096, 18315}, {1101, 15422}, {1973, 18831}, {2167, 32713}, {2168, 52917}, {2169, 6529}, {2616, 23964}, {2623, 24000}, {6520, 15958}, {9247, 52779}, {14533, 36126}, {14573, 57973}, {19174, 34072}, {19189, 36104}, {24021, 46088}
X(60597) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 16813}, {5, 112}, {6, 933}, {115, 8884}, {125, 8882}, {130, 32}, {134, 36416}, {137, 393}, {216, 107}, {338, 2052}, {343, 41679}, {520, 46088}, {523, 15422}, {525, 15412}, {1147, 14586}, {2972, 6}, {3269, 16035}, {6337, 18831}, {6368, 12077}, {6374, 42405}, {6503, 18315}, {14363, 6529}, {15449, 19174}, {15450, 25}, {15526, 275}, {17433, 52418}, {17434, 23286}, {34591, 2190}, {35071, 54}, {35441, 523}, {35442, 6748}, {36901, 8795}, {37867, 15958}, {38985, 2148}, {39000, 19189}, {39019, 4}, {39020, 38808}, {40588, 32713}, {45249, 57219}, {46093, 14533}, {47421, 24}, {52032, 648}, {52878, 34859}, {55073, 571}
X(60597) = crossdifference of every pair of points on line {25, 8745}
X(60597) = barycentric product X(i)*X(j) for these {i,j}: {5, 3265}, {51, 52617}, {53, 4143}, {69, 6368}, {76, 17434}, {99, 35442}, {216, 3267}, {305, 15451}, {311, 520}, {324, 52613}, {326, 2618}, {339, 23181}, {343, 525}, {394, 18314}, {418, 44173}, {523, 52347}, {577, 15415}, {647, 28706}, {656, 18695}, {850, 5562}, {905, 42698}, {1273, 43083}, {1502, 42293}, {1568, 34767}, {1625, 36793}, {2617, 17879}, {3926, 12077}, {3964, 23290}, {4176, 51513}, {6333, 53174}, {13157, 20580}, {14208, 44706}, {14213, 24018}, {14570, 15526}, {14638, 42459}, {15414, 36412}, {18022, 58305}, {21011, 30805}, {21102, 52396}, {34384, 34983}, {34386, 57195}, {41168, 57069}, {53173, 60524}, {58359, 60515}
X(60597) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 16813}, {3, 933}, {5, 107}, {51, 32713}, {52, 52917}, {53, 6529}, {69, 18831}, {76, 42405}, {115, 15422}, {216, 112}, {255, 36134}, {264, 52779}, {311, 6528}, {324, 15352}, {343, 648}, {394, 18315}, {418, 1576}, {520, 54}, {523, 8884}, {525, 275}, {577, 14586}, {647, 8882}, {656, 2190}, {684, 19189}, {822, 2148}, {826, 19174}, {850, 8795}, {1092, 15958}, {1154, 53176}, {1568, 4240}, {1625, 23964}, {1953, 24019}, {1972, 41210}, {2081, 52418}, {2617, 24000}, {2618, 158}, {2632, 2616}, {2972, 23286}, {3265, 95}, {3267, 276}, {3269, 2623}, {4143, 34386}, {5489, 8901}, {5562, 110}, {6368, 4}, {8057, 38808}, {8798, 1301}, {12077, 393}, {14208, 40440}, {14213, 823}, {14391, 1990}, {14570, 23582}, {14618, 8794}, {15415, 18027}, {15451, 25}, {15526, 15412}, {17167, 52919}, {17434, 6}, {18022, 54950}, {18027, 42401}, {18180, 52920}, {18314, 2052}, {18695, 811}, {20975, 58756}, {21102, 8747}, {23181, 250}, {23290, 1093}, {23616, 53576}, {23974, 15414}, {24018, 2167}, {24862, 51513}, {28706, 6331}, {32320, 14533}, {34386, 52939}, {34900, 52998}, {34980, 58308}, {34983, 51}, {34987, 38848}, {35071, 46088}, {35360, 32230}, {35441, 6748}, {35442, 523}, {37084, 25044}, {39019, 12077}, {39201, 54034}, {39469, 58306}, {41077, 43768}, {41078, 14165}, {41168, 1289}, {41212, 15451}, {41219, 39201}, {41221, 58757}, {42293, 32}, {42353, 35278}, {42459, 57219}, {42698, 6335}, {43083, 1141}, {44088, 14574}, {44173, 57844}, {44706, 162}, {44713, 36306}, {44714, 36309}, {44715, 1304}, {44716, 4230}, {50463, 46966}, {51363, 23977}, {51513, 6524}, {52032, 41679}, {52317, 8745}, {52347, 99}, {52613, 97}, {52617, 34384}, {52967, 34859}, {53174, 685}, {55219, 2207}, {55549, 32692}, {57109, 56254}, {57135, 3518}, {57195, 53}, {57241, 35196}, {58305, 184}, {58310, 14573}, {58796, 33629}, {60517, 20031}

X(60598) = X(1)X(188)∩X(174)X(178)

Barycentrics    Cos[A/2]*(Sin[A/2] - Sin[B/2] - Sin[C/2]) : :

X(60598) lies on the cubic K199 and these lines: {1, 188}, {164, 9837}, {174, 178}, {483, 7090}, {2090, 11924}, {3082, 14121}, {3576, 10023}, {7027, 55332}, {7057, 8125}, {8080, 8422}, {8095, 53810}, {8392, 53118}, {11691, 55342}

X(60598) = X(8)-Ceva conjugate of X(188)
X(60598) = X(i)-isoconjugate of X(j) for these (i,j): {6, 16664}, {174, 60555}, {266, 505}
X(60598) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 16664}, {174, 7}
X(60598) = barycentric product X(i)*X(j) for these {i,j}: {8, 15495}, {164, 556}, {188, 16017}
X(60598) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 16664}, {164, 174}, {259, 505}, {15495, 7}, {16017, 4146}, {60539, 60555}
X(60598) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 42017, 188}, {7028, 12646, 188}

X(60599) = X(1)X(280)∩X(189)X(626)

Barycentrics    (a - b - c)*(a^3 - a^2*b - a*b^2 + b^3 + a^2*c + 2*a*b*c + b^2*c - a*c^2 - b*c^2 - c^3)*(a^3 + a^2*b - a*b^2 - b^3 - a^2*c + 2*a*b*c - b^2*c - a*c^2 + b*c^2 + c^3)*(3*a^6 + 2*a^5*b - 7*a^4*b^2 - 4*a^3*b^3 + 5*a^2*b^4 + 2*a*b^5 - b^6 + 2*a^5*c + 6*a^4*b*c + 4*a^3*b^2*c - 4*a^2*b^3*c - 6*a*b^4*c - 2*b^5*c - 7*a^4*c^2 + 4*a^3*b*c^2 - 2*a^2*b^2*c^2 + 4*a*b^3*c^2 + b^4*c^2 - 4*a^3*c^3 - 4*a^2*b*c^3 + 4*a*b^2*c^3 + 4*b^3*c^3 + 5*a^2*c^4 - 6*a*b*c^4 + b^2*c^4 + 2*a*c^5 - 2*b*c^5 - c^6) : :

X(60599) lies on the cubic K199 and these lines: {1, 280}, {189, 946}, {271, 31435}, {7020, 34231}, {7078, 13138}, {7080, 44327}, {7090, 34907}, {9581, 20263}, {14121, 34908}, {47436, 53997}

X(60599) = X(8)-Ceva conjugate of X(280)
X(60599) = X(189)-Dao conjugate of X(7)
X(60599) = barycentric product X(i)*X(j) for these {i,j}: {280, 20211}, {2956, 34404}
X(60599) = barycentric quotient X(i)/X(j) for these {i,j}: {2956, 223}, {20211, 347}
X(60599) = {X(1),X(46355)}-harmonic conjugate of X(280)

X(60600) = X(4)X(2896)∩X(39)X(694)

Barycentrics    a^2*(2*a^2*b^2 + b^4 + a^2*c^2 + 2*b^2*c^2)*(a^2*b^2 + 2*a^2*c^2 + 2*b^2*c^2 + c^4)*(a^4*b^2 - a^2*b^4 + a^4*c^2 + a^2*b^2*c^2 + b^4*c^2 - a^2*c^4 + b^2*c^4) : :

X(60600) lies on the cubic K0202 and these lines: {4, 2896}, {39, 694}, {76, 3498}, {3095, 40803}, {3224, 3499}, {3398, 43357}, {3494, 3503}, {3500, 8865}, {8864, 8870}, {19602, 51997}, {51246, 60602}

X(60600) = midpoint of X(76) and X(3498)
X(60600) = barycentric product X(i)*X(j) for these {i,j}: {11328, 42006}, {43357, 54262}
X(60600) = barycentric quotient X(i)/X(j) for these {i,j}: {11328, 3329}, {54276, 14318}

X(60601) = X(4)X(39)∩X(384)X(57259)

Barycentrics    (a^2*b^2 - b^4 + 2*a^2*c^2 + b^2*c^2)*(2*a^2*b^2 + a^2*c^2 + b^2*c^2 - c^4)*(2*a^8 - a^6*b^2 - a^2*b^6 - a^6*c^2 + a^4*b^2*c^2 - a^2*b^4*c^2 + b^6*c^2 - a^2*b^2*c^4 - 2*b^4*c^4 - a^2*c^6 + b^2*c^6) : :

X(60601) lies on the cubic K020 and these lines: {4, 39}, {384, 57259}, {695, 3498}, {2896, 42313}, {3224, 8870}, {3402, 3500}, {3499, 51246}, {7900, 46807}

X(60601) = X(384)-Ceva conjugate of X(3498)
X(60601) = barycentric product X(i)*X(j) for these {i,j}: {262, 56377}, {263, 8920}, {42313, 56867}
X(60601) = barycentric quotient X(i)/X(j) for these {i,j}: {8920, 20023}, {56377, 183}, {56867, 458}

X(60602) = X(1)X(51251)∩X(3)X(8928)

Barycentrics    (a^2 + b^2)*(a^2 + c^2)*(a^8*b^4 + a^6*b^6 - a^4*b^8 + a^8*b^2*c^2 + a^6*b^4*c^2 + a^4*b^6*c^2 + a^2*b^8*c^2 + a^8*c^4 + a^6*b^2*c^4 + 2*a^4*b^4*c^4 + a^2*b^6*c^4 + b^8*c^4 + a^6*c^6 + a^4*b^2*c^6 + a^2*b^4*c^6 + b^6*c^6 - a^4*c^8 + a^2*b^2*c^8 + b^4*c^8) : :

X(60602) lies on the cubic K020 and these lines: {1, 51251}, {3, 8928}, {32, 39953}, {76, 14370}, {83, 695}, {194, 38817}, {3405, 3495}, {3502, 7346}, {51244, 51249}, {51246, 60600}

X(60602) = X(384)-Ceva conjugate of X(83)





leftri   Points associated with the Neuberg-Gibert hyperbola: X(60603) - X(60611)  rightri

This preamble, based on notes about "hyperbola (P)" in Bernard Gibert's webpage, K001, the Neuberg cubic, was submitted by Peter Moses, November 14, 2023.

Gibert's notes include the following:

(P) is a very remarkable hyperbola passing through X(476) and the vertices of the circumtangential triangle TaTbTc. It has two asymptotes making an angle of 60 degrees, so that its eccentricity is 2. X(110) is one of its foci and the related directrix is the Euler line. The tangent at X(476) is the real asymptote of the Neuberg cubic.
The hyperbola (P) is here named the Neuberg-Gibert hyperbola. Associated triangle centers include the following:

X(60603) = center
X(60604) = focus, other than X(110)
Pass-through points: X(476) and X(i) for these i: 60605, 60606, 60607, 60608, 60609, 60610, 60611. The asmptotes meet the infinity line in PU(215).

underbar



X(60603) = CENTER OF THE NEUBERG-GIBERT HYPERBOLA

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(3*a^8 - 3*a^6*b^2 - a^4*b^4 - a^2*b^6 + 2*b^8 - 3*a^6*c^2 + 5*a^4*b^2*c^2 + a^2*b^4*c^2 - 8*b^6*c^2 - a^4*c^4 + a^2*b^2*c^4 + 12*b^4*c^4 - a^2*c^6 - 8*b^2*c^6 + 2*c^8) : :
X(60603) = 2 X[5] + X[52056], 3 X[14644] - 4 X[21315], 2 X[21315] - 3 X[57305], X[74] + 2 X[36193], X[74] - 4 X[38609], X[36193] + 2 X[38609], X[110] + 2 X[476], 5 X[110] - 8 X[3233], X[110] - 4 X[7471], 5 X[110] - 2 X[14480], 7 X[110] - 4 X[14611], 17 X[110] - 8 X[30221], 5 X[476] + 4 X[3233], X[476] + 2 X[7471], and many others

X(60603) lies on these lines: {5, 52056}, {20, 18279}, {23, 58849}, {30, 14644}, {74, 36193}, {107, 1291}, {110, 476}, {250, 31941}, {477, 15051}, {549, 14851}, {925, 16166}, {1316, 10545}, {1511, 38580}, {1637, 36830}, {2453, 10546}, {3448, 31876}, {3523, 60008}, {4240, 30716}, {5972, 14731}, {7426, 44401}, {8371, 60606}, {9060, 53693}, {10733, 25641}, {12121, 18319}, {13434, 36159}, {14508, 15021}, {14643, 51345}, {14934, 15020}, {14993, 32423}, {15035, 16168}, {15036, 38610}, {15054, 46632}, {15059, 17511}, {15107, 36188}, {16163, 34193}, {23236, 31874}, {30512, 47053}, {30789, 36173}, {36169, 44967}, {38678, 47084}, {41724, 47146}, {52603, 53319}, {53705, 53957}

X(60603) = midpoint of X(i) and X(j) for these {i,j}: {110, 60604}, {476, 60605}, {14643, 51345}
X(60603) = reflection of X(i) in X(j) for these {i,j}: {110, 60605}, {14644, 57305}, {14851, 549}, {15055, 38700}, {60604, 476}, {60605, 7471}
X(60603) = reflection of X(60605) in the Euler line
X(60603) = barycentric product X(648)*X(12902)
X(60603) = barycentric quotient X(12902)/X(525)
X(60603) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {476, 7471, 110}, {3233, 14480, 110}, {17511, 22104, 15059}, {36188, 47327, 15107}, {36193, 38609, 74}

X(60604) = FOCUS, OTHER THAN X(110), OF THE NEUBERG-GIBERT HYPERBOLA

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(3*a^8 - 3*a^6*b^2 + a^4*b^4 - 5*a^2*b^6 + 4*b^8 - 3*a^6*c^2 + a^4*b^2*c^2 + 5*a^2*b^4*c^2 - 16*b^6*c^2 + a^4*c^4 + 5*a^2*b^2*c^4 + 24*b^4*c^4 - 5*a^2*c^6 - 16*b^2*c^6 + 4*c^8) : :
X(60604) = X[74] + 2 X[38580], X[110] - 4 X[476], 13 X[110] - 16 X[3233], 5 X[110] - 8 X[7471], 7 X[110] - 4 X[14480], 11 X[110] - 8 X[14611], 25 X[110] - 16 X[30221], 3 X[110] - 4 X[60605], 13 X[476] - 4 X[3233], 5 X[476] - 2 X[7471], 7 X[476] - X[14480], 11 X[476] - 2 X[14611], 25 X[476] - 4 X[30221], 3 X[476] - X[60605], and many others

X(60604) lies on these lines: {74, 38580}, {110, 476}, {925, 53705}, {1138, 38793}, {2453, 10545}, {8029, 60606}, {10546, 47284}, {10721, 18319}, {11749, 38728}, {14644, 14993}, {14731, 15059}, {15021, 38677}, {15023, 47084}, {15051, 38609}, {15055, 16168}, {20417, 60008}, {20957, 21315}, {32423, 51345}

X(60604) = reflection of X(i) in X(j) for these {i,j}: {110, 60603}, {1138, 38793}, {14644, 14993}, {20957, 21315}, {60603, 476}

X(60605) = REFLECTION OF X(60603) IN THE EULER LINE

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(3*a^8 - 3*a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + b^8 - 3*a^6*c^2 + 7*a^4*b^2*c^2 - a^2*b^4*c^2 - 4*b^6*c^2 - 2*a^4*c^4 - a^2*b^2*c^4 + 6*b^4*c^4 + a^2*c^6 - 4*b^2*c^6 + c^8) : :
X(60605) = 4 X[3] - X[14508], X[20] + 2 X[1553], 2 X[110] + X[476], X[110] - 4 X[3233], X[110] + 2 X[7471], 4 X[110] - X[14480], 5 X[110] - 2 X[14611], 13 X[110] - 4 X[30221], 3 X[110] + X[60604], X[476] + 8 X[3233], X[476] - 4 X[7471], 2 X[476] + X[14480], 5 X[476] + 4 X[14611], 13 X[476] + 8 X[30221], 3 X[476] - 2 X[60604], and many others

X(60605) lies on the Neuberg-Gibert hyperbola and these lines: {2, 60606}, {3, 14508}, {20, 1553}, {23, 60610}, {30, 14643}, {110, 476}, {113, 44967}, {250, 4240}, {265, 21315}, {323, 47327}, {399, 38609}, {477, 1511}, {930, 1304}, {1316, 10546}, {1325, 60609}, {1495, 36188}, {1576, 31941}, {1637, 23357}, {2979, 37926}, {3109, 18357}, {3268, 18020}, {3448, 22104}, {3523, 55319}, {4226, 60611}, {5627, 32423}, {5642, 34312}, {5663, 38700}, {5972, 17511}, {6030, 47509}, {6070, 14683}, {6800, 9159}, {7426, 22110}, {7468, 15724}, {7472, 60608}, {7480, 52913}, {9158, 35266}, {9209, 36830}, {10272, 20957}, {10420, 53957}, {10733, 36169}, {11657, 41724}, {12068, 15059}, {12121, 14989}, {12383, 25641}, {14094, 46632}, {14731, 55308}, {14934, 15034}, {15020, 47084}, {15040, 38610}, {15051, 36164}, {15107, 47351}, {15342, 53738}, {16163, 36172}, {16166, 20189}, {16167, 58948}, {16168, 32609}, {16340, 38794}, {20126, 47852}, {23234, 37907}, {23236, 34209}, {26881, 36192}, {30510, 30512}, {36159, 43598}, {36161, 43614}, {52722, 53163}, {52723, 53162}, {57368, 57370}

X(60605) = midpoint of X(110) and X(60603)
X(60605) = reflection of X(i) in X(j) for these {i,j}: {265, 21315}, {476, 60603}, {5627, 57305}, {20126, 47852}, {38701, 15035}, {60603, 7471}
X(60605) = reflection of X(60603) in the Euler line
X(60605) = barycentric product X(i)*X(j) for these {i,j}: {249, 18039}, {648, 12121}, {2407, 14989}
X(60605) = barycentric quotient X(i)/X(j) for these {i,j}: {12121, 525}, {14989, 2394}, {18039, 338}
X(60605) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 476, 14480}, {110, 7471, 476}, {1511, 36193, 477}, {3233, 7471, 110}

X(60606) = X(2)X(60605)∩X(3)X(60610)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(3*a^12 - 6*a^10*b^2 + 7*a^8*b^4 - 9*a^6*b^6 + 7*a^4*b^8 - 3*a^2*b^10 + b^12 - 6*a^10*c^2 + 4*a^8*b^2*c^2 + 3*a^6*b^4*c^2 - 4*a^4*b^6*c^2 + 4*a^2*b^8*c^2 - 2*b^10*c^2 + 7*a^8*c^4 + 3*a^6*b^2*c^4 - 3*a^4*b^4*c^4 - a^2*b^6*c^4 - b^8*c^4 - 9*a^6*c^6 - 4*a^4*b^2*c^6 - a^2*b^4*c^6 + 4*b^6*c^6 + 7*a^4*c^8 + 4*a^2*b^2*c^8 - b^4*c^8 - 3*a^2*c^10 - 2*b^2*c^10 + c^12) : :

X(60606) lies on the Neuberg-Gibert hyperbola and these lines: {2, 60605}, {3, 60610}, {110, 1649}, {476, 691}, {1640, 36830}, {3268, 57991}, {5467, 53379}, {6287, 15000}, {8029, 60604}, {8371, 60603}, {9140, 14830}, {9177, 9888}, {14480, 44010}, {15329, 60607}, {17708, 34761}, {37619, 60609}, {57742, 60340}

X(60606) = barycentric product X(99)*X(51894)
X(60606) = barycentric quotient X(51894)/X(523)

X(60607) = X(3)X(60611)∩X(23)X(94)

Barycentrics    a^4*(a^2 - b^2)*(a^2 - c^2)*(a^4*b^4 - 2*a^2*b^6 + b^8 - a^4*b^2*c^2 + a^2*b^4*c^2 - 3*b^6*c^2 + a^4*c^4 + a^2*b^2*c^4 + 5*b^4*c^4 - 2*a^2*c^6 - 3*b^2*c^6 + c^8) : :

X(60607) lies on the Neuberg-Gibert hyperbola and these lines: {3, 60611}, {23, 94}, {110, 669}, {237, 38225}, {691, 14270}, {5640, 11332}, {5926, 7472}, {7468, 15724}, {9218, 34952}, {14510, 15107}, {15329, 60606}, {32729, 52603}, {35268, 47049}, {35298, 60608}, {37916, 51942}, {42659, 43754}, {53263, 53379}

X(60608) = X(110)X(6082)∩X(111)X(230)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^8 - 3*a^6*b^2 + 22*a^4*b^4 - 9*a^2*b^6 + b^8 - 3*a^6*c^2 - 35*a^4*b^2*c^2 + 7*a^2*b^4*c^2 + 22*a^4*c^4 + 7*a^2*b^2*c^4 - 2*b^4*c^4 - 9*a^2*c^6 + c^8) : :

X(60608) lies on the Neuberg-Gibert hyperbola and these lines: {99, 15724}, {110, 6082}, {111, 230}, {892, 9123}, {2696, 9126}, {2770, 9130}, {7472, 60605}, {14515, 15360}, {35298, 60607}, {47047, 60611}

X(60609) = X(100)X(476)∩X(110)X(901)

Barycentrics    a^2*(a^2 - b^2)*(a^2 - c^2)*(a^4*b^2 - 2*a^2*b^4 + b^6 + a^4*b*c - 3*a^3*b^2*c + a^2*b^3*c + 3*a*b^4*c - 2*b^5*c + a^4*c^2 - 3*a^3*b*c^2 + 5*a^2*b^2*c^2 - 3*a*b^3*c^2 - b^4*c^2 + a^2*b*c^3 - 3*a*b^2*c^3 + 4*b^3*c^3 - 2*a^2*c^4 + 3*a*b*c^4 - b^2*c^4 - 2*b*c^5 + c^6) : :

X(60609) lies on the Neuberg-Gibert hyperbola and these lines: {100, 476}, {110, 901}, {859, 35000}, {930, 53702}, {1325, 60605}, {10546, 57520}, {15329, 23832}, {23981, 52603}, {37619, 60606}

X(60610) = X(99)X(476)∩X(110)X(669)

Barycentrics    a^4*(a^2 - b^2)*(a^2 - c^2)*(a^4*b^4 - 2*a^2*b^6 + b^8 + a^4*b^2*c^2 - a^2*b^4*c^2 - b^6*c^2 + a^4*c^4 - a^2*b^2*c^4 + 3*b^4*c^4 - 2*a^2*c^6 - b^2*c^6 + c^8) : :

X(60610) lies on the Neuberg-Gibert hyperbola and these lines: {3, 60606}, {23, 60605}, {99, 476}, {110, 669}, {237, 15107}, {249, 14270}, {323, 56393}, {930, 53701}, {4230, 30530}, {7698, 37338}, {9218, 42660}, {10546, 11332}, {14966, 23357}, {15329, 41337}, {15483, 35298}, {37465, 47047}

X(60610) = barycentric product X(4590)*X(45911)
X(60610) = barycentric quotient X(45911)/X(115)

X(60611) = X(2)X(476)∩X(110)X(1649)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^12 - 2*a^10*b^2 + 5*a^8*b^4 - 11*a^6*b^6 + 11*a^4*b^8 - 5*a^2*b^10 + b^12 - 2*a^10*c^2 - 4*a^8*b^2*c^2 + 9*a^6*b^4*c^2 - 12*a^4*b^6*c^2 + 8*a^2*b^8*c^2 - 2*b^10*c^2 + 5*a^8*c^4 + 9*a^6*b^2*c^4 + 3*a^4*b^4*c^4 - 3*a^2*b^6*c^4 - b^8*c^4 - 11*a^6*c^6 - 12*a^4*b^2*c^6 - 3*a^2*b^4*c^6 + 4*b^6*c^6 + 11*a^4*c^8 + 8*a^2*b^2*c^8 - b^4*c^8 - 5*a^2*c^10 - 2*b^2*c^10 + c^12) : :

X(60611) lies on the Neuberg-Gibert hyperbola and these lines: {2, 476}, {3, 60607}, {99, 44814}, {110, 1649}, {3268, 6035}, {4226, 60605}, {5468, 52603}, {5649, 60340}, {9168, 14480}, {10190, 14611}, {15329, 41337}, {35443, 36840}, {35444, 36839}, {45662, 54439}, {47047, 60608}

X(60612) = X(3)X(39164)∩X(4)X(39165)

Barycentrics    3*(3*a^4-(b^2-c^2)^2-2*a^2*(b^2+c^2))*(2*a^12-3*a^10*(b^2+c^2)+a^4*(b^2-c^2)^2*(2*b^2+c^2)*(b^2+2*c^2)+2*a^8*(b^4+b^2*c^2+c^4)-a^6*(b^2+c^2)*(2*b^4-3*b^2*c^2+2*c^4)-a^2*(b^2-c^2)^2*(b^2+c^2)*(3*b^4+b^2*c^2+3*c^4)+(b^2-c^2)^2*(2*b^8+2*c^8+b^2*c^2*(b^2+c^2)^2)+2*(a^10+a^6*b^2*c^2-a^8*(b^2+c^2)-a^2*(b^2-c^2)*(b^6-c^6)+(b^2-c^2)*(b^8-c^8))*sqrt(-3*S^2+SW^2))-4*S*(6*a^10-6*a^8*(b^2+c^2)-3*a^4*(b^2-c^2)^2*(b^2+c^2)+a^2*(b^2-c^2)^2*(b^4+4*b^2*c^2+c^4)-(b^2-c^2)^2*(b^2+c^2)*(3*b^4-2*b^2*c^2+3*c^4)+a^6*(5*b^4-4*b^2*c^2+5*c^4)+(6*a^8+a^4*(b^2-c^2)^2-3*a^6*(b^2+c^2)-a^2*(b^2-c^2)^2*(b^2+c^2)-(b^2-c^2)^2*(3*b^4+2*b^2*c^2+3*c^4))*sqrt(-3*S^2+SW^2))*sqrt(-(S^2*(3*S^2+18*R^2*SW-5*SW^2+2*(9*R^2-2*SW)*sqrt(-3*S^2+SW^2)))) : :
X(60612) = 4*X(3)-3*X(39164) = 2*X(4)-3*X(39165) = X(3146)-3*X(39161) = 5*X(3522)-3*X(39160)

The locus of P such that the circumconic with perspector P has concurrent A-, B-, C- normals is the cubic K002, and the locus of these points of concurrence Q(P) is the cubic K004.
The appearance of (i, j) in the following list means that Q(X(i)) = X(j): (1, 1), (2, 4), (3, 64), (4, 20), (6, 3), (9, 84), (57, 40), (223, 3345), (282, 1490), (1073, 1498), (1249, 3346), (3341, 3347), (3342, 3182), (3343, 3348), (3344, 3183), (3349, 2130), (3350, 2131), (3351, 3354), (3352, 3353), (3356, 3355), (14481, 3637), (39162, 42412), (39163, 42411), (39164, 60612), (39165, 60613), (40989, 40993), (40990, 40994), (40991, 40851), (40992, 40852), (46978, 3473), (46979, 3472).
César E. Lozada - November 13, 2023.

X(60612) lies on the cubics K004, K187, K852, K855 and these lines: {3, 39164}, {4, 39165}, {20, 51898}, {3146, 39161}, {3522, 39160}

X(60612) = isogonal conjugate of X(60613)
X(60612) = reflection of X(60613) in X(20)
X(60612) = point of concurrence of the A-, B-, C- normals of the circumonic with perspector X(39164)
X(60612) = 1st imaginary focus of the inconic with center X(20)

X(60613) = X(3)X(39165)∩X(4)X(39164)

Barycentrics    3*(3*a^4-(b^2-c^2)^2-2*a^2*(b^2+c^2))*(2*a^12-3*a^10*(b^2+c^2)+a^4*(b^2-c^2)^2*(2*b^2+c^2)*(b^2+2*c^2)+2*a^8*(b^4+b^2*c^2+c^4)-a^6*(b^2+c^2)*(2*b^4-3*b^2*c^2+2*c^4)-a^2*(b^2-c^2)^2*(b^2+c^2)*(3*b^4+b^2*c^2+3*c^4)+(b^2-c^2)^2*(2*b^8+2*c^8+b^2*c^2*(b^2+c^2)^2)+2*(a^10+a^6*b^2*c^2-a^8*(b^2+c^2)-a^2*(b^2-c^2)*(b^6-c^6)+(b^2-c^2)*(b^8-c^8))*sqrt(-3*S^2+SW^2))+4*S*(6*a^10-6*a^8*(b^2+c^2)-3*a^4*(b^2-c^2)^2*(b^2+c^2)+a^2*(b^2-c^2)^2*(b^4+4*b^2*c^2+c^4)-(b^2-c^2)^2*(b^2+c^2)*(3*b^4-2*b^2*c^2+3*c^4)+a^6*(5*b^4-4*b^2*c^2+5*c^4)+(6*a^8+a^4*(b^2-c^2)^2-3*a^6*(b^2+c^2)-a^2*(b^2-c^2)^2*(b^2+c^2)-(b^2-c^2)^2*(3*b^4+2*b^2*c^2+3*c^4))*sqrt(-3*S^2+SW^2))*sqrt(-(S^2*(3*S^2+18*R^2*SW-5*SW^2+2*(9*R^2-2*SW)*sqrt(-3*S^2+SW^2)))) : :
X(60613) = 4*X(3)-3*X(39165) = 2*X(4)-3*X(39164) = X(3146)-3*X(39160) = 5*X(3522)-3*X(39161)

See X(60612). César E. Lozada - November 13, 2023.

X(60613) lies on the cubics K004, K187, K852, K855 and these lines: {3, 39165}, {4, 39164}, {20, 51898}, {3146, 39160}, {3522, 39161}

X(60613) = isogonal conjugate of X(60612)
X(60613) = reflection of X(60612) in X(20)
X(60613) = point of concurrence of the A-, B-, C- normals of the circumonic with perspector X(39165)
X(60613) = 2nd imaginary focus of the inconic with center X(20)


leftri

Bicevian Chordal Triangles: X(60614)-X(60737)

rightri

This preamble and centers X(60614)-X(60737) were contributed by Ivan Pavlov on November 18, 2023.

Let (c) be the bicevian conic of P=u:v:w and Q=p:q:r in barycentrics. Denote by Ap, Aq the intersection points of AP, AQ and (c), and similarly define Bp, Bq, Cp, and Cq. The lines ApAq, BpBq, and CpCq form a triangle A'B'C' which we call the bicevian chordal triangle of P and Q (wrt ABC).

A'B'C' and ABC are perspective with center which lies on the circumconic through P and Q. We call this center the bicevian chordal perspector of P and Q (wrt ABC).
A first barycentric coordinate is p*u*(r^2*u*v+2*r*(q*u+p*v)*w+p*q*w^2)*(p*r*v^2+q^2*u*w+2*q*v*(r*u+p*w))

For details, see Euclid 6040.

X(60614) = X(2)X(35002)∩X(30)X(3407)

Barycentrics    (a^6-a^4*(b^2-2*c^2)-(b-c)*(b+c)*(2*b^4+c^4)+a^2*(2*b^4+3*b^2*c^2+2*c^4))*(a^6+a^4*(2*b^2-c^2)+(b-c)*(b+c)*(b^4+2*c^4)+a^2*(2*b^4+3*b^2*c^2+2*c^4)) : :

X(60614) lies on the Kiepert hyperbola and on these lines: {2, 35002}, {3, 43528}, {5, 43529}, {6, 55009}, {30, 3407}, {76, 10356}, {83, 5476}, {94, 56409}, {98, 5309}, {115, 54731}, {381, 1916}, {419, 43530}, {671, 3818}, {3545, 40824}, {3830, 54539}, {3845, 54540}, {5055, 60231}, {5117, 16080}, {5475, 14492}, {5480, 11170}, {5503, 8176}, {6620, 60193}, {7607, 37334}, {7608, 37446}, {7834, 60186}, {7841, 60151}, {7884, 60093}, {10722, 54481}, {11317, 54872}, {11606, 12243}, {11645, 54806}, {11648, 14458}, {12188, 43535}, {14880, 60184}, {18546, 60180}, {19130, 54841}, {19570, 54122}, {37345, 60128}, {43448, 54678}, {47286, 60214}, {53419, 54903}, {53504, 54724}

X(60614) = reflection of X(i) in X(j) for these {i,j}: {54731, 115}
X(60614) = isogonal conjugate of X(26316)
X(60614) = orthology center of ABC and bicevian chordal triangle of X(2) and X(3407)
X(60614) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(5641)}}, {{A, B, C, X(30), X(5117)}}, {{A, B, C, X(74), X(9515)}}, {{A, B, C, X(264), X(43453)}}, {{A, B, C, X(297), X(55008)}}, {{A, B, C, X(327), X(1989)}}, {{A, B, C, X(381), X(419)}}, {{A, B, C, X(1494), X(19222)}}, {{A, B, C, X(1976), X(11178)}}, {{A, B, C, X(2980), X(57907)}}, {{A, B, C, X(3527), X(14370)}}, {{A, B, C, X(3545), X(6620)}}, {{A, B, C, X(3818), X(44146)}}, {{A, B, C, X(4846), X(40708)}}, {{A, B, C, X(5309), X(14356)}}, {{A, B, C, X(5627), X(53197)}}, {{A, B, C, X(6531), X(55958)}}, {{A, B, C, X(9154), X(18575)}}, {{A, B, C, X(9487), X(13377)}}, {{A, B, C, X(15321), X(57908)}}, {{A, B, C, X(37334), X(52282)}}, {{A, B, C, X(37446), X(52281)}}, {{A, B, C, X(43696), X(57822)}}, {{A, B, C, X(51980), X(52492)}}, {{A, B, C, X(52187), X(55972)}}

X(60615) = X(2)X(4268)∩X(10)X(36)

Barycentrics    (a^3+b^3+2*a*b*c-(a+b)*c^2)*(a^3-a*b*(b-2*c)-b^2*c+c^3) : :

X(60615) lies on the Kiepert hyperbola and on these lines: {2, 4268}, {6, 60087}, {10, 36}, {30, 54698}, {57, 60091}, {81, 2051}, {94, 52393}, {226, 17074}, {321, 3218}, {333, 60097}, {593, 24624}, {940, 60071}, {1019, 60074}, {1150, 34258}, {4080, 17483}, {4190, 43533}, {4193, 43531}, {5187, 60077}, {5397, 6882}, {6890, 60158}, {6891, 60154}, {6911, 60112}, {6915, 57719}, {6943, 54972}, {6944, 60164}, {6953, 60157}, {13576, 33142}, {14554, 32911}, {17015, 54933}, {17579, 60079}, {18047, 33113}, {18139, 60251}, {18141, 60242}, {24597, 60107}, {28452, 54528}, {29845, 40718}, {35466, 57721}, {35990, 60227}, {37356, 57710}, {37375, 60078}, {37642, 60155}, {37674, 57722}, {37684, 60261}

X(60615) = isogonal conjugate of X(4271)
X(60615) = isotomic conjugate of X(5741)
X(60615) = trilinear pole of line {21173, 48281}
X(60615) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 4271}, {6, 3878}, {31, 5741}, {48, 11105}, {219, 1866}, {1964, 29534}
X(60615) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 5741}, {3, 4271}, {9, 3878}, {1249, 11105}, {41884, 29534}
X(60615) = X(i)-cross conjugate of X(j) for these {i, j}: {18990, 7}, {37634, 2}
X(60615) = pole of line {37634, 60615} with respect to the Kiepert hyperbola
X(60615) = pole of line {4271, 5741} with respect to the Wallace hyperbola
X(60615) = pole of line {5563, 33133} with respect to the dual conic of Yff parabola
X(60615) = orthology center of ABC and bicevian chordal triangle of X(2) and X(54698)
X(60615) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(5258)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(4268)}}, {{A, B, C, X(7), X(95)}}, {{A, B, C, X(27), X(88)}}, {{A, B, C, X(36), X(57)}}, {{A, B, C, X(79), X(5445)}}, {{A, B, C, X(81), X(1476)}}, {{A, B, C, X(92), X(5176)}}, {{A, B, C, X(278), X(45287)}}, {{A, B, C, X(279), X(4311)}}, {{A, B, C, X(333), X(1255)}}, {{A, B, C, X(335), X(33119)}}, {{A, B, C, X(379), X(35994)}}, {{A, B, C, X(445), X(37356)}}, {{A, B, C, X(469), X(4193)}}, {{A, B, C, X(673), X(39962)}}, {{A, B, C, X(675), X(57785)}}, {{A, B, C, X(693), X(7224)}}, {{A, B, C, X(940), X(1150)}}, {{A, B, C, X(1220), X(56058)}}, {{A, B, C, X(2006), X(30690)}}, {{A, B, C, X(2339), X(55961)}}, {{A, B, C, X(2963), X(8818)}}, {{A, B, C, X(2982), X(55995)}}, {{A, B, C, X(2985), X(39698)}}, {{A, B, C, X(2994), X(56218)}}, {{A, B, C, X(2995), X(58014)}}, {{A, B, C, X(3661), X(29845)}}, {{A, B, C, X(3676), X(39728)}}, {{A, B, C, X(3911), X(17483)}}, {{A, B, C, X(3912), X(33142)}}, {{A, B, C, X(3936), X(6354)}}, {{A, B, C, X(4190), X(7490)}}, {{A, B, C, X(4850), X(19811)}}, {{A, B, C, X(4998), X(8049)}}, {{A, B, C, X(5278), X(37674)}}, {{A, B, C, X(5372), X(14996)}}, {{A, B, C, X(5741), X(37634)}}, {{A, B, C, X(6915), X(37279)}}, {{A, B, C, X(6994), X(17567)}}, {{A, B, C, X(6996), X(35973)}}, {{A, B, C, X(7357), X(32023)}}, {{A, B, C, X(8044), X(57830)}}, {{A, B, C, X(14377), X(26745)}}, {{A, B, C, X(14621), X(32918)}}, {{A, B, C, X(18139), X(35466)}}, {{A, B, C, X(18141), X(24597)}}, {{A, B, C, X(19607), X(36795)}}, {{A, B, C, X(19645), X(37253)}}, {{A, B, C, X(19684), X(37660)}}, {{A, B, C, X(24614), X(52394)}}, {{A, B, C, X(25430), X(56152)}}, {{A, B, C, X(27475), X(56062)}}, {{A, B, C, X(30710), X(55942)}}, {{A, B, C, X(30711), X(56089)}}, {{A, B, C, X(31002), X(40415)}}, {{A, B, C, X(32017), X(40394)}}, {{A, B, C, X(35990), X(37389)}}, {{A, B, C, X(36805), X(55990)}}, {{A, B, C, X(37683), X(37684)}}, {{A, B, C, X(39734), X(40419)}}, {{A, B, C, X(40434), X(40435)}}
X(60615) = barycentric product X(i)*X(j) for these (i, j): {56133, 86}, {56143, 7}
X(60615) = barycentric quotient X(i)/X(j) for these (i, j): {1, 3878}, {2, 5741}, {4, 11105}, {6, 4271}, {34, 1866}, {83, 29534}, {56133, 10}, {56143, 8}

X(60616) = X(2)X(55737)∩X(3)X(55768)

Barycentrics    (11*(a^2+b^2)+5*c^2)*(11*a^2+5*b^2+11*c^2) : :

X(60616) lies on the Kiepert hyperbola and on these lines: {2, 55737}, {3, 55768}, {4, 50975}, {5, 60324}, {6, 60629}, {30, 54706}, {69, 60131}, {262, 15702}, {376, 43951}, {381, 60327}, {524, 60643}, {597, 18840}, {599, 60183}, {631, 60118}, {1992, 10159}, {3090, 47586}, {3424, 5071}, {3524, 14484}, {3525, 53099}, {3545, 60147}, {3589, 5485}, {3618, 10302}, {5067, 43537}, {5395, 33230}, {5503, 22247}, {7375, 60291}, {7376, 60292}, {7877, 56059}, {11001, 54520}, {14492, 19708}, {15709, 60331}, {15715, 52519}, {16045, 43681}, {18842, 48310}, {18845, 33190}, {21356, 60279}, {32898, 60262}, {32952, 43529}, {32953, 43528}, {32956, 60145}, {33223, 59266}, {33231, 60260}, {40344, 54773}, {41099, 54815}, {41106, 54519}, {47352, 60143}, {47355, 54616}, {51126, 60646}, {59373, 60277}

X(60616) = isogonal conjugate of X(22246)
X(60616) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 22246}, {75, 31885}
X(60616) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 22246}, {206, 31885}
X(60616) = pole of line {22246, 31885} with respect to the Stammler hyperbola
X(60616) = orthology center of ABC and bicevian chordal triangle of X(2) and X(54706)
X(60616) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55684)}}, {{A, B, C, X(458), X(15702)}}, {{A, B, C, X(597), X(3618)}}, {{A, B, C, X(599), X(16774)}}, {{A, B, C, X(1992), X(3589)}}, {{A, B, C, X(3524), X(52288)}}, {{A, B, C, X(5071), X(52283)}}, {{A, B, C, X(8889), X(33230)}}, {{A, B, C, X(9476), X(40506)}}, {{A, B, C, X(11736), X(30541)}}, {{A, B, C, X(15491), X(23053)}}, {{A, B, C, X(18490), X(34892)}}, {{A, B, C, X(19708), X(52289)}}, {{A, B, C, X(21356), X(48310)}}, {{A, B, C, X(33190), X(52299)}}, {{A, B, C, X(34898), X(47352)}}, {{A, B, C, X(42287), X(50983)}}
X(60616) = barycentric quotient X(i)/X(j) for these (i, j): {6, 22246}, {32, 31885}

X(60617) = X(2)X(3286)∩X(10)X(672)

Barycentrics    (a*b*(a^2+b^2)+(a+b)*(a^2+a*b+b^2)*c-(a+b)*c^3)*(2*a^2*b*c-b^3*c+b*c^3+a^3*(b+c)+a*(-b^3+2*b*c^2+c^3)) : :

X(60617) lies on the Kiepert hyperbola and on these lines: {1, 40515}, {2, 3286}, {6, 13576}, {10, 672}, {30, 54728}, {76, 30941}, {226, 1458}, {321, 518}, {377, 32022}, {379, 3423}, {381, 54497}, {388, 60229}, {1011, 60188}, {1446, 4059}, {1478, 60135}, {1724, 60075}, {1876, 40149}, {1916, 19635}, {2475, 60149}, {2478, 58012}, {2795, 11611}, {3252, 43534}, {3839, 54793}, {3970, 56282}, {4052, 42057}, {4080, 11330}, {4212, 60246}, {5046, 6625}, {5087, 30588}, {6817, 60107}, {6818, 60076}, {8049, 55026}, {14626, 60267}, {14956, 60071}, {17758, 26100}, {20880, 60197}, {25501, 56226}, {30962, 40030}, {36672, 60164}, {36695, 60157}, {37657, 56161}, {57469, 60265}

X(60617) = isogonal conjugate of X(5132)
X(60617) = trilinear pole of line {665, 523}
X(60617) = pole of line {24512, 60617} with respect to the Kiepert hyperbola
X(60617) = orthology center of ABC and bicevian chordal triangle of X(2) and X(54728)
X(60617) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(16552)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(7)}}, {{A, B, C, X(8), X(3691)}}, {{A, B, C, X(27), X(52245)}}, {{A, B, C, X(42), X(57666)}}, {{A, B, C, X(65), X(2350)}}, {{A, B, C, X(79), X(291)}}, {{A, B, C, X(80), X(30571)}}, {{A, B, C, X(86), X(55035)}}, {{A, B, C, X(87), X(20028)}}, {{A, B, C, X(105), X(57785)}}, {{A, B, C, X(145), X(42057)}}, {{A, B, C, X(286), X(2298)}}, {{A, B, C, X(310), X(1220)}}, {{A, B, C, X(377), X(4196)}}, {{A, B, C, X(379), X(948)}}, {{A, B, C, X(388), X(20880)}}, {{A, B, C, X(405), X(16601)}}, {{A, B, C, X(752), X(28851)}}, {{A, B, C, X(985), X(7192)}}, {{A, B, C, X(1011), X(14547)}}, {{A, B, C, X(1244), X(3108)}}, {{A, B, C, X(1246), X(39956)}}, {{A, B, C, X(1390), X(2481)}}, {{A, B, C, X(1724), X(3970)}}, {{A, B, C, X(1826), X(57830)}}, {{A, B, C, X(2475), X(4212)}}, {{A, B, C, X(2478), X(4207)}}, {{A, B, C, X(2787), X(2795)}}, {{A, B, C, X(3240), X(49999)}}, {{A, B, C, X(3241), X(50001)}}, {{A, B, C, X(3613), X(8818)}}, {{A, B, C, X(3617), X(25501)}}, {{A, B, C, X(4184), X(52185)}}, {{A, B, C, X(4194), X(6818)}}, {{A, B, C, X(4200), X(6817)}}, {{A, B, C, X(4213), X(5046)}}, {{A, B, C, X(5087), X(32631)}}, {{A, B, C, X(5136), X(14956)}}, {{A, B, C, X(5556), X(39741)}}, {{A, B, C, X(5561), X(52654)}}, {{A, B, C, X(11330), X(37168)}}, {{A, B, C, X(14624), X(57824)}}, {{A, B, C, X(15320), X(39798)}}, {{A, B, C, X(18082), X(40010)}}, {{A, B, C, X(18152), X(26100)}}, {{A, B, C, X(30513), X(56102)}}, {{A, B, C, X(30947), X(49984)}}, {{A, B, C, X(30962), X(37657)}}, {{A, B, C, X(37235), X(37400)}}, {{A, B, C, X(39698), X(56138)}}, {{A, B, C, X(39713), X(57944)}}, {{A, B, C, X(39925), X(54120)}}, {{A, B, C, X(39961), X(57705)}}, {{A, B, C, X(39965), X(51223)}}, {{A, B, C, X(39966), X(56173)}}, {{A, B, C, X(39983), X(56157)}}, {{A, B, C, X(41506), X(56236)}}

X(60618) = X(2)X(11425)∩X(3)X(459)

Barycentrics    (3*a^8+(b^2-c^2)^3*(3*b^2+c^2)-4*a^6*(b^2+2*c^2)+2*a^4*(b^2+c^2)*(b^2+3*c^2)-4*a^2*(b^3-b*c^2)^2)*(3*a^8-4*a^6*(2*b^2+c^2)+2*a^4*(b^2+c^2)*(3*b^2+c^2)-(b^2-c^2)^3*(b^2+3*c^2)-4*a^2*(-(b^2*c)+c^3)^2) : :

X(60618) lies on the Kiepert hyperbola and on these lines: {2, 11425}, {3, 459}, {4, 15905}, {5, 56346}, {6, 31363}, {20, 2052}, {30, 54867}, {98, 18945}, {193, 9290}, {275, 3091}, {376, 54710}, {381, 54531}, {631, 38253}, {2996, 56290}, {3090, 60137}, {3146, 8796}, {3316, 6809}, {3317, 6810}, {3522, 56270}, {3523, 16080}, {3543, 39284}, {3832, 60161}, {3839, 60120}, {5056, 43530}, {5068, 60193}, {5485, 34664}, {6146, 60166}, {6776, 13380}, {6804, 60237}, {6816, 60114}, {6833, 60246}, {7395, 18840}, {7399, 18841}, {7400, 52583}, {7503, 60221}, {12022, 60159}, {12233, 36413}, {14118, 60256}, {16655, 54844}, {16656, 54886}, {16657, 60174}, {34286, 59660}, {38323, 54771}, {40149, 50701}, {46935, 60138}, {50687, 54893}, {52069, 54930}

X(60618) = isogonal conjugate of X(9786)
X(60618) = trilinear pole of line {523, 58796}
X(60618) = orthology center of ABC and bicevian chordal triangle of X(2) and X(54867)
X(60618) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(20)}}, {{A, B, C, X(5), X(3091)}}, {{A, B, C, X(6), X(11425)}}, {{A, B, C, X(21), X(50701)}}, {{A, B, C, X(30), X(3523)}}, {{A, B, C, X(54), X(41894)}}, {{A, B, C, X(64), X(34285)}}, {{A, B, C, X(68), X(253)}}, {{A, B, C, X(69), X(1105)}}, {{A, B, C, X(95), X(15740)}}, {{A, B, C, X(140), X(3543)}}, {{A, B, C, X(193), X(56290)}}, {{A, B, C, X(264), X(15077)}}, {{A, B, C, X(265), X(18855)}}, {{A, B, C, X(280), X(56261)}}, {{A, B, C, X(376), X(3522)}}, {{A, B, C, X(377), X(6847)}}, {{A, B, C, X(381), X(5056)}}, {{A, B, C, X(382), X(10303)}}, {{A, B, C, X(393), X(12241)}}, {{A, B, C, X(405), X(50700)}}, {{A, B, C, X(411), X(6987)}}, {{A, B, C, X(443), X(37434)}}, {{A, B, C, X(452), X(3149)}}, {{A, B, C, X(546), X(7486)}}, {{A, B, C, X(549), X(49135)}}, {{A, B, C, X(550), X(10304)}}, {{A, B, C, X(631), X(3146)}}, {{A, B, C, X(1006), X(50695)}}, {{A, B, C, X(1012), X(6904)}}, {{A, B, C, X(1093), X(51316)}}, {{A, B, C, X(1249), X(14365)}}, {{A, B, C, X(1294), X(18851)}}, {{A, B, C, X(1300), X(45833)}}, {{A, B, C, X(1370), X(7400)}}, {{A, B, C, X(1498), X(17811)}}, {{A, B, C, X(1513), X(32974)}}, {{A, B, C, X(1532), X(6919)}}, {{A, B, C, X(1656), X(3839)}}, {{A, B, C, X(1657), X(15692)}}, {{A, B, C, X(2165), X(6526)}}, {{A, B, C, X(2475), X(6833)}}, {{A, B, C, X(2476), X(6844)}}, {{A, B, C, X(2478), X(6848)}}, {{A, B, C, X(3088), X(6815)}}, {{A, B, C, X(3089), X(6816)}}, {{A, B, C, X(3090), X(3832)}}, {{A, B, C, X(3153), X(3549)}}, {{A, B, C, X(3521), X(22270)}}, {{A, B, C, X(3524), X(5059)}}, {{A, B, C, X(3525), X(17578)}}, {{A, B, C, X(3526), X(50688)}}, {{A, B, C, X(3527), X(41891)}}, {{A, B, C, X(3528), X(50693)}}, {{A, B, C, X(3529), X(15717)}}, {{A, B, C, X(3530), X(49140)}}, {{A, B, C, X(3533), X(50687)}}, {{A, B, C, X(3545), X(5068)}}, {{A, B, C, X(3546), X(44440)}}, {{A, B, C, X(3547), X(37444)}}, {{A, B, C, X(3548), X(50009)}}, {{A, B, C, X(3613), X(38443)}}, {{A, B, C, X(3627), X(55864)}}, {{A, B, C, X(3843), X(46936)}}, {{A, B, C, X(3845), X(46935)}}, {{A, B, C, X(3854), X(5071)}}, {{A, B, C, X(3855), X(15022)}}, {{A, B, C, X(4188), X(6938)}}, {{A, B, C, X(4189), X(6934)}}, {{A, B, C, X(4190), X(6906)}}, {{A, B, C, X(4198), X(7549)}}, {{A, B, C, X(4208), X(8727)}}, {{A, B, C, X(4232), X(34664)}}, {{A, B, C, X(4846), X(18846)}}, {{A, B, C, X(5046), X(6834)}}, {{A, B, C, X(5054), X(50691)}}, {{A, B, C, X(5067), X(50689)}}, {{A, B, C, X(5073), X(15708)}}, {{A, B, C, X(5129), X(19541)}}, {{A, B, C, X(5154), X(6968)}}, {{A, B, C, X(5177), X(6831)}}, {{A, B, C, X(5187), X(6941)}}, {{A, B, C, X(5891), X(10539)}}, {{A, B, C, X(5907), X(9306)}}, {{A, B, C, X(6145), X(8801)}}, {{A, B, C, X(6530), X(18945)}}, {{A, B, C, X(6759), X(11793)}}, {{A, B, C, X(6776), X(46735)}}, {{A, B, C, X(6823), X(7396)}}, {{A, B, C, X(6824), X(6839)}}, {{A, B, C, X(6825), X(6840)}}, {{A, B, C, X(6826), X(6837)}}, {{A, B, C, X(6827), X(6838)}}, {{A, B, C, X(6828), X(6843)}}, {{A, B, C, X(6829), X(6870)}}, {{A, B, C, X(6830), X(6871)}}, {{A, B, C, X(6832), X(6894)}}, {{A, B, C, X(6835), X(6846)}}, {{A, B, C, X(6836), X(6908)}}, {{A, B, C, X(6841), X(6993)}}, {{A, B, C, X(6849), X(6886)}}, {{A, B, C, X(6850), X(6890)}}, {{A, B, C, X(6851), X(37112)}}, {{A, B, C, X(6865), X(37421)}}, {{A, B, C, X(6869), X(37106)}}, {{A, B, C, X(6872), X(6905)}}, {{A, B, C, X(6884), X(44229)}}, {{A, B, C, X(6888), X(6917)}}, {{A, B, C, X(6889), X(6895)}}, {{A, B, C, X(6891), X(37437)}}, {{A, B, C, X(6893), X(6953)}}, {{A, B, C, X(6923), X(6972)}}, {{A, B, C, X(6925), X(6926)}}, {{A, B, C, X(6928), X(6960)}}, {{A, B, C, X(6929), X(6979)}}, {{A, B, C, X(6935), X(37435)}}, {{A, B, C, X(6942), X(15680)}}, {{A, B, C, X(6944), X(13729)}}, {{A, B, C, X(6950), X(37256)}}, {{A, B, C, X(6957), X(6964)}}, {{A, B, C, X(6977), X(31295)}}, {{A, B, C, X(6985), X(6992)}}, {{A, B, C, X(6989), X(37433)}}, {{A, B, C, X(6995), X(7395)}}, {{A, B, C, X(6996), X(7390)}}, {{A, B, C, X(6998), X(7406)}}, {{A, B, C, X(7377), X(7407)}}, {{A, B, C, X(7378), X(7399)}}, {{A, B, C, X(7383), X(7391)}}, {{A, B, C, X(7384), X(36672)}}, {{A, B, C, X(7385), X(36670)}}, {{A, B, C, X(7386), X(52404)}}, {{A, B, C, X(7398), X(11479)}}, {{A, B, C, X(7404), X(7544)}}, {{A, B, C, X(7487), X(7503)}}, {{A, B, C, X(7500), X(7509)}}, {{A, B, C, X(7518), X(7567)}}, {{A, B, C, X(7519), X(7550)}}, {{A, B, C, X(7580), X(37423)}}, {{A, B, C, X(8797), X(14860)}}, {{A, B, C, X(8884), X(45011)}}, {{A, B, C, X(10299), X(15683)}}, {{A, B, C, X(10431), X(37407)}}, {{A, B, C, X(10565), X(12362)}}, {{A, B, C, X(11676), X(32965)}}, {{A, B, C, X(12028), X(16104)}}, {{A, B, C, X(12103), X(58188)}}, {{A, B, C, X(13573), X(16934)}}, {{A, B, C, X(13860), X(32971)}}, {{A, B, C, X(14035), X(37334)}}, {{A, B, C, X(14037), X(55008)}}, {{A, B, C, X(14063), X(37446)}}, {{A, B, C, X(14118), X(18533)}}, {{A, B, C, X(14542), X(46952)}}, {{A, B, C, X(14861), X(46412)}}, {{A, B, C, X(14938), X(21400)}}, {{A, B, C, X(15318), X(18852)}}, {{A, B, C, X(15319), X(18853)}}, {{A, B, C, X(15619), X(43726)}}, {{A, B, C, X(15640), X(15720)}}, {{A, B, C, X(15697), X(33923)}}, {{A, B, C, X(15702), X(50690)}}, {{A, B, C, X(16263), X(52224)}}, {{A, B, C, X(16837), X(43949)}}, {{A, B, C, X(17538), X(21734)}}, {{A, B, C, X(17558), X(20420)}}, {{A, B, C, X(18296), X(46455)}}, {{A, B, C, X(18404), X(58805)}}, {{A, B, C, X(18550), X(22268)}}, {{A, B, C, X(19262), X(50702)}}, {{A, B, C, X(21448), X(31942)}}, {{A, B, C, X(31304), X(35921)}}, {{A, B, C, X(31305), X(37126)}}, {{A, B, C, X(31371), X(36948)}}, {{A, B, C, X(34007), X(37119)}}, {{A, B, C, X(34449), X(45088)}}, {{A, B, C, X(34570), X(43908)}}, {{A, B, C, X(34621), X(46336)}}, {{A, B, C, X(34781), X(41372)}}, {{A, B, C, X(35732), X(52401)}}, {{A, B, C, X(36526), X(36692)}}, {{A, B, C, X(36659), X(36693)}}, {{A, B, C, X(36660), X(36694)}}, {{A, B, C, X(36662), X(36695)}}, {{A, B, C, X(37104), X(37275)}}, {{A, B, C, X(37431), X(50698)}}, {{A, B, C, X(37436), X(37447)}}, {{A, B, C, X(38445), X(51032)}}, {{A, B, C, X(40410), X(43699)}}, {{A, B, C, X(42021), X(51348)}}, {{A, B, C, X(42282), X(52402)}}, {{A, B, C, X(42333), X(57677)}}, {{A, B, C, X(43695), X(45838)}}, {{A, B, C, X(44658), X(46255)}}, {{A, B, C, X(46087), X(50480)}}, {{A, B, C, X(51254), X(52485)}}, {{A, B, C, X(54114), X(56267)}}

X(60619) = X(2)X(6248)∩X(4)X(5052)

Barycentrics    (2*a^2*b^2*(a^2+b^2)+3*(a^4+b^4)*c^2-4*(a^2+b^2)*c^4+c^6)*(b^6-4*b^4*c^2+3*b^2*c^4+a^4*(3*b^2+2*c^2)+2*a^2*(-2*b^4+c^4)) : :
X(60619) = -2*X[115]+X[54978], -2*X[3095]+3*X[60095], 2*X[52854]+3*X[60150]

X(60619) lies on the Kiepert hyperbola and on these lines: {2, 6248}, {3, 60101}, {4, 5052}, {5, 60096}, {30, 60218}, {39, 14494}, {76, 48876}, {83, 5050}, {98, 3053}, {115, 54978}, {194, 60260}, {262, 5254}, {381, 54905}, {382, 60280}, {511, 2996}, {542, 54872}, {1503, 60117}, {2782, 8781}, {3095, 60095}, {3406, 5033}, {3424, 36998}, {3566, 43665}, {5395, 6776}, {5485, 12251}, {7709, 10155}, {11147, 46941}, {12243, 54822}, {13108, 60202}, {13330, 54869}, {13674, 54625}, {13794, 54626}, {22682, 52519}, {22712, 60212}, {32448, 60211}, {33706, 34505}, {36990, 54846}, {38642, 60073}, {38664, 60072}, {43532, 54152}, {46040, 55122}, {49111, 60217}, {52854, 60150}, {54412, 60199}

X(60619) = reflection of X(i) in X(j) for these {i,j}: {11257, 40923}, {54978, 115}
X(60619) = isogonal conjugate of X(5171)
X(60619) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 60117}
X(60619) = orthology center of ABC and bicevian chordal triangle of X(2) and X(60218)
X(60619) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(5052)}}, {{A, B, C, X(6), X(13334)}}, {{A, B, C, X(32), X(54998)}}, {{A, B, C, X(39), X(3527)}}, {{A, B, C, X(64), X(511)}}, {{A, B, C, X(66), X(35142)}}, {{A, B, C, X(253), X(42377)}}, {{A, B, C, X(264), X(6248)}}, {{A, B, C, X(290), X(9307)}}, {{A, B, C, X(726), X(28529)}}, {{A, B, C, X(2065), X(2353)}}, {{A, B, C, X(2782), X(14265)}}, {{A, B, C, X(3095), X(5033)}}, {{A, B, C, X(3531), X(41440)}}, {{A, B, C, X(5254), X(33971)}}, {{A, B, C, X(6530), X(52581)}}, {{A, B, C, X(6776), X(15077)}}, {{A, B, C, X(8704), X(47588)}}, {{A, B, C, X(15318), X(48259)}}, {{A, B, C, X(16000), X(53912)}}, {{A, B, C, X(17042), X(30499)}}, {{A, B, C, X(19222), X(32522)}}, {{A, B, C, X(27376), X(39646)}}, {{A, B, C, X(36998), X(45031)}}, {{A, B, C, X(38664), X(51259)}}, {{A, B, C, X(42299), X(57908)}}, {{A, B, C, X(44176), X(47847)}}

X(60620) = X(6)X(60621)∩X(485)X(3528)

Barycentrics    9*a^4-41*(b^2-c^2)^2+16*a^2*(2*(b^2+c^2)+5*S) : :

X(60620) lies on the Kiepert hyperbola and on these lines: {6, 60621}, {30, 60295}, {371, 43562}, {376, 43340}, {381, 60296}, {382, 43560}, {485, 3528}, {486, 3544}, {546, 43561}, {550, 60291}, {631, 43382}, {1131, 3529}, {1132, 3855}, {1327, 13886}, {1328, 31412}, {1587, 34091}, {1588, 60302}, {3068, 12818}, {3070, 15715}, {3090, 60294}, {3316, 41948}, {3317, 6442}, {3524, 43568}, {3525, 6483}, {3530, 60311}, {3545, 60300}, {3590, 10299}, {3851, 60292}, {5067, 43559}, {5071, 43569}, {5079, 60312}, {6460, 10195}, {6811, 60336}, {6813, 60331}, {7389, 60639}, {7581, 54597}, {7582, 60290}, {8976, 15710}, {9540, 14241}, {11001, 60313}, {13664, 54720}, {13903, 49135}, {14226, 42270}, {14269, 54543}, {15687, 54542}, {17538, 42570}, {17578, 42643}, {23249, 60289}, {23267, 34089}, {35820, 43570}, {41106, 60314}, {41966, 43518}, {42258, 60309}, {42269, 54596}, {43386, 60623}, {43412, 43571}, {43566, 52047}

X(60620) = X(i)-cross conjugate of X(j) for these {i, j}: {23269, 4}
X(60620) = pole of line {23269, 60620} with respect to the Kiepert hyperbola
X(60620) = orthology center of ABC and bicevian chordal triangle of X(2) and X(60295)
X(60620) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(371), X(20421)}}, {{A, B, C, X(493), X(11270)}}, {{A, B, C, X(1152), X(57714)}}, {{A, B, C, X(1585), X(3528)}}, {{A, B, C, X(1586), X(3544)}}, {{A, B, C, X(3312), X(6442)}}, {{A, B, C, X(3529), X(3535)}}, {{A, B, C, X(3536), X(3855)}}, {{A, B, C, X(6483), X(35771)}}, {{A, B, C, X(11090), X(14843)}}, {{A, B, C, X(14121), X(18490)}}, {{A, B, C, X(14842), X(41515)}}, {{A, B, C, X(24244), X(57823)}}, {{A, B, C, X(39709), X(55154)}}

X(60621) = X(6)X(60620)∩X(486)X(3528)

Barycentrics    9*a^4-41*(b^2-c^2)^2+16*a^2*(2*(b^2+c^2)-5*S) : :

X(60621) lies on the Kiepert hyperbola and on these lines: {6, 60620}, {30, 60296}, {372, 43563}, {376, 43341}, {381, 60295}, {382, 43561}, {485, 3544}, {486, 3528}, {546, 43560}, {550, 60292}, {631, 43383}, {1131, 3855}, {1132, 3529}, {1327, 42561}, {1328, 13939}, {1587, 60301}, {1588, 34089}, {3069, 12819}, {3071, 15715}, {3090, 60293}, {3316, 6441}, {3317, 9541}, {3524, 43569}, {3525, 6482}, {3530, 60312}, {3545, 60299}, {3591, 10299}, {3851, 60291}, {5067, 43558}, {5071, 43568}, {5079, 60311}, {6459, 10194}, {6811, 60331}, {6813, 60336}, {7388, 60639}, {7581, 60289}, {7582, 43536}, {11001, 60314}, {13784, 54720}, {13935, 14226}, {13951, 15710}, {13961, 49135}, {14241, 42273}, {14269, 54542}, {15687, 54543}, {17538, 42571}, {17578, 42644}, {23259, 60290}, {23273, 34091}, {35821, 43571}, {41106, 60313}, {41965, 43517}, {42259, 60310}, {42268, 54595}, {43387, 60622}, {43411, 43570}, {43567, 52048}

X(60621) = X(i)-cross conjugate of X(j) for these {i, j}: {23275, 4}
X(60621) = pole of line {23275, 60621} with respect to the Kiepert hyperbola
X(60621) = orthology center of ABC and bicevian chordal triangle of X(2) and X(60296)
X(60621) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(372), X(20421)}}, {{A, B, C, X(494), X(11270)}}, {{A, B, C, X(1151), X(57714)}}, {{A, B, C, X(1585), X(3544)}}, {{A, B, C, X(1586), X(3528)}}, {{A, B, C, X(3311), X(6441)}}, {{A, B, C, X(3529), X(3536)}}, {{A, B, C, X(3535), X(3855)}}, {{A, B, C, X(6482), X(35770)}}, {{A, B, C, X(7090), X(18490)}}, {{A, B, C, X(11091), X(14843)}}, {{A, B, C, X(14842), X(41516)}}, {{A, B, C, X(24243), X(57823)}}, {{A, B, C, X(39709), X(55155)}}

X(60622) = X(3)X(60303)∩X(4)X(6447)

Barycentrics    13*a^4+85*(b^2-c^2)^2-14*a^2*(7*b^2+7*c^2+12*S) : :

X(60622) lies on the Kiepert hyperbola and on these lines: {3, 60303}, {4, 6447}, {5, 60304}, {6, 60623}, {30, 60309}, {376, 60289}, {381, 60310}, {485, 15692}, {547, 3317}, {590, 43384}, {632, 43564}, {1131, 6409}, {1132, 32787}, {1151, 43560}, {1327, 8972}, {3068, 41955}, {3312, 34091}, {3316, 5054}, {3530, 43376}, {3545, 60290}, {3590, 31414}, {3591, 19053}, {3860, 6199}, {5070, 43565}, {6396, 43568}, {6419, 43571}, {6452, 15719}, {6454, 10195}, {6564, 54595}, {7000, 60329}, {7374, 54857}, {7585, 14226}, {7586, 43569}, {8703, 14241}, {8976, 15710}, {9690, 60307}, {10194, 46936}, {12818, 42266}, {13846, 42537}, {13847, 60294}, {13886, 38071}, {13925, 35434}, {15681, 60305}, {15697, 43314}, {18538, 60302}, {19054, 60300}, {21734, 43879}, {22235, 42252}, {22237, 42253}, {23251, 35414}, {35822, 43558}, {41952, 43512}, {41970, 60293}, {42417, 43508}, {42540, 60295}, {42604, 43890}, {43212, 60316}, {43380, 43507}, {43387, 60621}, {53519, 54598}

X(60622) = orthology center of ABC and bicevian chordal triangle of X(2) and X(60309)
X(60622) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(6447)}}, {{A, B, C, X(547), X(55569)}}, {{A, B, C, X(588), X(44731)}}, {{A, B, C, X(1151), X(6409)}}, {{A, B, C, X(1585), X(15692)}}, {{A, B, C, X(3312), X(6418)}}, {{A, B, C, X(5054), X(55573)}}, {{A, B, C, X(6199), X(6452)}}, {{A, B, C, X(6419), X(6454)}}, {{A, B, C, X(46434), X(56037)}}

X(60623) = X(3)X(60304)∩X(4)X(6448)

Barycentrics    13*a^4+85*(b^2-c^2)^2-14*a^2*(7*b^2+7*c^2-12*S) : :

X(60623) lies on the Kiepert hyperbola and on these lines: {3, 60304}, {4, 6448}, {5, 60303}, {6, 60622}, {30, 60310}, {376, 60290}, {381, 60309}, {486, 15692}, {547, 3316}, {615, 43385}, {632, 43565}, {1131, 32788}, {1132, 6410}, {1152, 43561}, {1328, 13941}, {3069, 41956}, {3311, 34089}, {3317, 5054}, {3530, 43377}, {3545, 60289}, {3590, 19054}, {3860, 6395}, {5070, 43564}, {6200, 43569}, {6420, 43570}, {6451, 15719}, {6453, 10194}, {6565, 54596}, {7000, 54857}, {7374, 60329}, {7585, 43568}, {7586, 14241}, {8703, 14226}, {10195, 46936}, {12819, 42267}, {13759, 60195}, {13846, 60293}, {13847, 42538}, {13939, 38071}, {13951, 15710}, {13993, 35434}, {15681, 60306}, {15697, 43315}, {18762, 60301}, {19053, 60299}, {21734, 43880}, {22235, 42250}, {22237, 42251}, {23261, 35414}, {35823, 43559}, {41951, 43511}, {41969, 60294}, {42418, 43507}, {42539, 60296}, {42605, 43889}, {43211, 60315}, {43381, 43508}, {43386, 60620}, {43415, 60308}, {53518, 54599}

X(60623) = orthology center of ABC and bicevian chordal triangle of X(2) and X(60310)
X(60623) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(6448)}}, {{A, B, C, X(547), X(55573)}}, {{A, B, C, X(589), X(44731)}}, {{A, B, C, X(1152), X(6410)}}, {{A, B, C, X(1586), X(15692)}}, {{A, B, C, X(3311), X(6417)}}, {{A, B, C, X(5054), X(55569)}}, {{A, B, C, X(6395), X(6451)}}, {{A, B, C, X(6420), X(6453)}}, {{A, B, C, X(46433), X(56037)}}

X(60624) = X(2)X(902)∩X(76)X(519)

Barycentrics    (b+c)*(2*a^2+a*b+2*b^2-(a+b)*c)*(2*a^2+a*(-b+c)+c*(-b+2*c)) : :

X(60624) lies on the Kiepert hyperbola and on these lines: {1, 60236}, {2, 902}, {4, 50287}, {10, 52963}, {30, 60320}, {42, 4080}, {76, 519}, {98, 30554}, {262, 516}, {321, 4090}, {512, 3919}, {551, 17758}, {726, 43688}, {740, 34475}, {752, 60090}, {1916, 2796}, {2051, 48940}, {2784, 43532}, {2996, 50282}, {3097, 28550}, {3679, 56210}, {3755, 11599}, {3845, 54701}, {3849, 50180}, {3993, 43534}, {4052, 4780}, {4444, 4785}, {4651, 27797}, {4669, 60276}, {11645, 60172}, {14537, 60078}, {17132, 60180}, {17766, 42006}, {18840, 50311}, {30588, 43223}, {40013, 42057}, {40031, 50301}, {42042, 60257}, {42043, 60261}, {43531, 56969}, {48813, 48822}, {48829, 60109}, {48830, 57826}, {48900, 49545}, {50316, 60285}

X(60624) = trilinear pole of line {14407, 523}
X(60624) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 31916}, {58, 49448}, {110, 50335}, {163, 30519}, {1333, 17230}, {4622, 9461}
X(60624) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 49448}, {37, 17230}, {115, 30519}, {244, 50335}, {1249, 31916}
X(60624) = X(i)-cross conjugate of X(j) for these {i, j}: {4085, 10}
X(60624) = pole of line {4085, 60624} with respect to the Kiepert hyperbola
X(60624) = orthology center of ABC and bicevian chordal triangle of X(2) and X(60320)
X(60624) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4685)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(56196)}}, {{A, B, C, X(37), X(3551)}}, {{A, B, C, X(42), X(512)}}, {{A, B, C, X(65), X(3550)}}, {{A, B, C, X(80), X(40418)}}, {{A, B, C, X(225), X(33106)}}, {{A, B, C, X(306), X(50287)}}, {{A, B, C, X(469), X(56969)}}, {{A, B, C, X(502), X(32948)}}, {{A, B, C, X(516), X(23878)}}, {{A, B, C, X(523), X(28562)}}, {{A, B, C, X(551), X(4651)}}, {{A, B, C, X(726), X(25423)}}, {{A, B, C, X(740), X(3993)}}, {{A, B, C, X(804), X(2796)}}, {{A, B, C, X(903), X(15320)}}, {{A, B, C, X(994), X(3223)}}, {{A, B, C, X(996), X(39741)}}, {{A, B, C, X(1826), X(4660)}}, {{A, B, C, X(2238), X(50359)}}, {{A, B, C, X(2296), X(42285)}}, {{A, B, C, X(2321), X(43749)}}, {{A, B, C, X(2350), X(43950)}}, {{A, B, C, X(3293), X(42057)}}, {{A, B, C, X(3679), X(43223)}}, {{A, B, C, X(3755), X(6541)}}, {{A, B, C, X(3950), X(4780)}}, {{A, B, C, X(4028), X(50282)}}, {{A, B, C, X(4061), X(48830)}}, {{A, B, C, X(4133), X(4356)}}, {{A, B, C, X(4207), X(48813)}}, {{A, B, C, X(4669), X(29822)}}, {{A, B, C, X(4674), X(16606)}}, {{A, B, C, X(4946), X(51093)}}, {{A, B, C, X(5561), X(6384)}}, {{A, B, C, X(5620), X(33104)}}, {{A, B, C, X(8049), X(39697)}}, {{A, B, C, X(14624), X(36588)}}, {{A, B, C, X(17132), X(32472)}}, {{A, B, C, X(18152), X(48844)}}, {{A, B, C, X(18822), X(40747)}}, {{A, B, C, X(19998), X(51071)}}, {{A, B, C, X(21241), X(45095)}}, {{A, B, C, X(21282), X(52618)}}, {{A, B, C, X(23604), X(33109)}}, {{A, B, C, X(28658), X(56160)}}, {{A, B, C, X(30571), X(43972)}}, {{A, B, C, X(31144), X(50180)}}, {{A, B, C, X(32631), X(48646)}}, {{A, B, C, X(39961), X(44557)}}, {{A, B, C, X(39982), X(40504)}}, {{A, B, C, X(45989), X(56131)}}, {{A, B, C, X(52654), X(56174)}}, {{A, B, C, X(56157), X(56222)}}
X(60624) = barycentric product X(i)*X(j) for these (i, j): {30554, 850}
X(60624) = barycentric quotient X(i)/X(j) for these (i, j): {4, 31916}, {10, 17230}, {37, 49448}, {523, 30519}, {661, 50335}, {14407, 9461}, {30554, 110}

X(60625) = X(6)X(60650)∩X(83)X(7620)

Barycentrics    (7*(a^2+b^2)-17*c^2)*(7*a^2-17*b^2+7*c^2) : :
X(60625) = -2*X[3534]+5*X[60185]

X(60625) lies on the Kiepert hyperbola and on these lines: {6, 60650}, {20, 60337}, {30, 60322}, {69, 60635}, {83, 7620}, {98, 15683}, {148, 60103}, {193, 60113}, {524, 38259}, {543, 60073}, {549, 53103}, {671, 20080}, {1992, 54476}, {3091, 60330}, {3146, 53100}, {3522, 60334}, {3534, 60185}, {3543, 54845}, {3832, 60142}, {3839, 52519}, {5032, 18845}, {5055, 10155}, {5066, 54523}, {5068, 60332}, {5286, 60649}, {5466, 59549}, {6392, 53106}, {7486, 53098}, {7607, 15717}, {7608, 15022}, {7612, 10304}, {7841, 60636}, {7850, 60626}, {8352, 60631}, {8596, 10153}, {8781, 41135}, {10302, 43448}, {10303, 60123}, {11054, 60630}, {11148, 60240}, {11185, 60238}, {12243, 54567}, {15640, 60150}, {17503, 23334}, {21356, 60639}, {32480, 32897}, {32532, 47286}, {32879, 60262}, {32883, 55803}, {32979, 53102}, {32982, 43676}, {33287, 43529}, {33699, 54612}, {34505, 60285}, {43537, 50693}, {47586, 50692}, {50687, 60132}, {51170, 53101}, {52713, 60641}, {53419, 60632}, {59373, 60145}

X(60625) = pole of line {11160, 60625} with respect to the Kiepert hyperbola
X(60625) = orthology center of ABC and bicevian chordal triangle of X(2) and X(60322)
X(60625) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(297), X(15683)}}, {{A, B, C, X(524), X(6339)}}, {{A, B, C, X(2987), X(43713)}}, {{A, B, C, X(5032), X(17040)}}, {{A, B, C, X(5641), X(35510)}}, {{A, B, C, X(6464), X(44763)}}, {{A, B, C, X(7620), X(31125)}}, {{A, B, C, X(10304), X(37174)}}, {{A, B, C, X(15022), X(52281)}}, {{A, B, C, X(15717), X(52282)}}, {{A, B, C, X(30541), X(57714)}}, {{A, B, C, X(41135), X(52450)}}, {{A, B, C, X(43691), X(56362)}}, {{A, B, C, X(57539), X(57857)}}

X(60626) = X(2)X(15301)∩X(98)X(12355)

Barycentrics    (4*(a^2+b^2)-11*c^2)*(4*a^2-11*b^2+4*c^2) : :
X(60626) = -4*X[8703]+7*X[60175]

X(60626) lies on the Kiepert hyperbola and on these lines: {2, 15301}, {30, 60323}, {98, 12355}, {262, 38071}, {316, 32532}, {382, 54857}, {524, 53105}, {543, 60104}, {546, 60329}, {547, 11669}, {598, 20583}, {671, 40341}, {3530, 7607}, {3629, 54494}, {3830, 54852}, {3860, 54643}, {5054, 53104}, {5079, 7608}, {5254, 60644}, {5395, 7620}, {7612, 15710}, {7790, 60131}, {7827, 60647}, {7841, 60250}, {7850, 60625}, {8352, 60630}, {8370, 60649}, {8703, 60175}, {9166, 56064}, {10159, 34505}, {11008, 54720}, {11054, 41895}, {11185, 54616}, {14038, 43528}, {14269, 54890}, {15687, 60326}, {15692, 60102}, {17503, 47286}, {19709, 60192}, {23334, 60113}, {33229, 60209}, {33284, 43529}, {35005, 41135}, {43448, 60628}, {53144, 60098}

X(60626) = orthology center of ABC and bicevian chordal triangle of X(2) and X(60323)
X(60626) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(297), X(15681)}}, {{A, B, C, X(458), X(38071)}}, {{A, B, C, X(524), X(30477)}}, {{A, B, C, X(599), X(20583)}}, {{A, B, C, X(3530), X(52282)}}, {{A, B, C, X(5079), X(52281)}}, {{A, B, C, X(5641), X(57823)}}, {{A, B, C, X(15301), X(35146)}}, {{A, B, C, X(15710), X(37174)}}, {{A, B, C, X(17132), X(28553)}}, {{A, B, C, X(30541), X(44731)}}

X(60627) = X(4)X(15533)∩X(69)X(17503)

Barycentrics    (a^2+b^2-17*c^2)*(a^2-17*b^2+c^2) : :
X(60627) = -5*X[5071]+4*X[53099]

X(60627) lies on the Kiepert hyperbola and on these lines: {4, 15533}, {30, 60324}, {69, 17503}, {98, 15300}, {141, 60637}, {262, 14711}, {376, 47586}, {381, 60328}, {524, 60281}, {598, 52713}, {599, 54637}, {620, 10153}, {671, 50990}, {1992, 60282}, {3424, 11001}, {3524, 43537}, {3525, 53859}, {3545, 60118}, {3830, 60327}, {3845, 54706}, {5071, 53099}, {5485, 50991}, {7607, 15702}, {7620, 54720}, {7784, 60219}, {8584, 18842}, {8587, 52695}, {11054, 43527}, {11160, 54642}, {11185, 54494}, {14484, 41106}, {15534, 60284}, {15682, 60147}, {15698, 60336}, {15715, 60337}, {15719, 54921}, {21356, 60216}, {22165, 32532}, {32833, 60198}, {32869, 60262}, {32892, 40824}, {33190, 43681}, {33230, 60285}, {39785, 60144}, {41099, 43951}, {45103, 50992}, {47286, 60628}, {50994, 60228}, {51143, 60641}, {51185, 54616}, {51186, 60143}, {59373, 60287}

X(60627) = pole of line {50993, 60627} with respect to the Kiepert hyperbola
X(60627) = orthology center of ABC and bicevian chordal triangle of X(2) and X(60324)
X(60627) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(69), X(15533)}}, {{A, B, C, X(297), X(19708)}}, {{A, B, C, X(524), X(50990)}}, {{A, B, C, X(1992), X(50991)}}, {{A, B, C, X(5551), X(34914)}}, {{A, B, C, X(7317), X(34892)}}, {{A, B, C, X(7714), X(33230)}}, {{A, B, C, X(8584), X(21356)}}, {{A, B, C, X(11001), X(52283)}}, {{A, B, C, X(14376), X(14843)}}, {{A, B, C, X(14711), X(20023)}}, {{A, B, C, X(15534), X(50994)}}, {{A, B, C, X(15702), X(52282)}}, {{A, B, C, X(17040), X(34898)}}, {{A, B, C, X(18490), X(57725)}}, {{A, B, C, X(20421), X(40802)}}, {{A, B, C, X(22165), X(50992)}}, {{A, B, C, X(23054), X(56057)}}, {{A, B, C, X(32892), X(40814)}}, {{A, B, C, X(36609), X(55978)}}, {{A, B, C, X(36889), X(57908)}}, {{A, B, C, X(41106), X(52288)}}

X(60628) = X(4)X(54174)∩X(6)X(60648)

Barycentrics    (a^2+13*b^2+c^2)*(a^2+b^2+13*c^2) : :
X(60628) = -10*X[19709]+7*X[60127]

X(60628) lies on the Kiepert hyperbola and on these lines: {4, 54174}, {6, 60648}, {20, 54857}, {30, 60325}, {69, 53101}, {83, 5032}, {98, 15692}, {141, 60200}, {193, 18842}, {524, 5395}, {543, 60280}, {547, 14494}, {598, 11160}, {599, 41895}, {620, 60103}, {632, 60123}, {671, 3620}, {1992, 54639}, {2996, 21356}, {3091, 60329}, {3407, 9740}, {3530, 60337}, {3543, 60326}, {3839, 54890}, {5054, 7612}, {5070, 53098}, {5079, 60330}, {5286, 56059}, {6390, 55805}, {6392, 60183}, {7388, 60304}, {7389, 60303}, {7607, 55864}, {7608, 46936}, {7620, 53105}, {7784, 38259}, {8370, 18844}, {8703, 60150}, {8781, 14971}, {9466, 60096}, {10304, 60323}, {11054, 60131}, {11148, 11167}, {11185, 33698}, {15640, 54852}, {15681, 54845}, {15710, 60322}, {15719, 60185}, {15810, 60218}, {16509, 60240}, {19709, 60127}, {20080, 60650}, {20094, 43535}, {21358, 60285}, {21734, 47586}, {22165, 54642}, {23334, 45103}, {32459, 55829}, {32532, 52713}, {32828, 60198}, {32833, 60248}, {32836, 60101}, {32869, 60212}, {32874, 40824}, {32892, 60217}, {32971, 60146}, {32974, 60209}, {37668, 54487}, {38071, 52519}, {43448, 60626}, {47286, 60627}, {50990, 54896}, {50994, 60632}, {51171, 60239}, {59373, 60647}

X(60628) = orthology center of ABC and bicevian chordal triangle of X(2) and X(60325)
X(60628) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55580)}}, {{A, B, C, X(141), X(5032)}}, {{A, B, C, X(193), X(21356)}}, {{A, B, C, X(253), X(57907)}}, {{A, B, C, X(297), X(15692)}}, {{A, B, C, X(327), X(54171)}}, {{A, B, C, X(524), X(3620)}}, {{A, B, C, X(599), X(11160)}}, {{A, B, C, X(2987), X(44731)}}, {{A, B, C, X(3314), X(9740)}}, {{A, B, C, X(5054), X(37174)}}, {{A, B, C, X(13602), X(57725)}}, {{A, B, C, X(14971), X(52450)}}, {{A, B, C, X(21358), X(51171)}}, {{A, B, C, X(32874), X(40814)}}, {{A, B, C, X(42313), X(54174)}}, {{A, B, C, X(46936), X(52281)}}, {{A, B, C, X(46951), X(51481)}}, {{A, B, C, X(52282), X(55864)}}, {{A, B, C, X(56334), X(57539)}}

X(60629) = X(2)X(22246)∩X(4)X(21358)

Barycentrics    (5*a^2+11*b^2+5*c^2)*(5*(a^2+b^2)+11*c^2) : :
X(60629) = -7*X[41106]+4*X[54520]

X(60629) lies on the Kiepert hyperbola and on these lines: {2, 22246}, {3, 55737}, {4, 21358}, {5, 60328}, {6, 60616}, {30, 60327}, {69, 60239}, {83, 21356}, {98, 9167}, {141, 18842}, {376, 60147}, {381, 54706}, {524, 18841}, {597, 60646}, {599, 54616}, {631, 47586}, {671, 3619}, {1992, 60238}, {2996, 33230}, {3090, 60118}, {3424, 3524}, {3525, 43537}, {3545, 43951}, {3618, 60645}, {3620, 60648}, {3763, 60143}, {5067, 53099}, {5071, 14484}, {5395, 7879}, {5485, 20582}, {5503, 6722}, {5590, 54628}, {5591, 54627}, {7375, 60292}, {7376, 60291}, {7827, 60642}, {9741, 60181}, {11001, 54519}, {11185, 60630}, {14458, 15810}, {14762, 54773}, {15682, 54815}, {15709, 60336}, {15715, 54845}, {16045, 60145}, {23334, 51143}, {32837, 60212}, {32870, 60262}, {32885, 40824}, {32893, 60201}, {32952, 43528}, {32953, 43529}, {32956, 43681}, {33190, 38259}, {34573, 60643}, {41106, 54520}, {43527, 59373}, {44562, 60099}, {50571, 60150}, {50994, 60287}, {51186, 60284}, {52713, 60228}

X(60629) = orthology center of ABC and bicevian chordal triangle of X(2) and X(60327)
X(60629) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55614)}}, {{A, B, C, X(6), X(22246)}}, {{A, B, C, X(69), X(21358)}}, {{A, B, C, X(141), X(21356)}}, {{A, B, C, X(297), X(15702)}}, {{A, B, C, X(524), X(3619)}}, {{A, B, C, X(1992), X(20582)}}, {{A, B, C, X(3524), X(52283)}}, {{A, B, C, X(5071), X(52288)}}, {{A, B, C, X(5641), X(36948)}}, {{A, B, C, X(6353), X(33230)}}, {{A, B, C, X(9487), X(40511)}}, {{A, B, C, X(11331), X(19708)}}, {{A, B, C, X(18490), X(34914)}}, {{A, B, C, X(32885), X(40814)}}, {{A, B, C, X(33190), X(38282)}}, {{A, B, C, X(50990), X(51143)}}, {{A, B, C, X(50994), X(51186)}}
X(60629) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 22246, 55768}

X(60630) = X(2)X(15602)∩X(98)X(15684)

Barycentrics    (8*(a^2+b^2)-13*c^2)*(8*a^2-13*b^2+8*c^2) : :
X(60630) = 4*X[33699]+5*X[54851]

X(60630) lies on the Kiepert hyperbola and on these lines: {2, 15602}, {30, 60335}, {98, 15684}, {262, 23046}, {316, 54637}, {381, 54920}, {524, 60209}, {548, 7607}, {549, 11668}, {671, 6144}, {1657, 60334}, {3534, 54644}, {3627, 53100}, {3830, 54934}, {3843, 60142}, {3850, 60332}, {5055, 53108}, {5066, 54645}, {5072, 7608}, {5485, 7850}, {7612, 46333}, {7620, 60285}, {7827, 60145}, {7841, 60210}, {8352, 60626}, {9880, 54567}, {11054, 60625}, {11185, 60629}, {14032, 43528}, {14488, 14893}, {15683, 54921}, {15706, 53104}, {23334, 38259}, {32455, 54493}, {33289, 43529}, {33699, 54851}, {33703, 60337}, {38335, 60132}, {41135, 60136}, {43448, 54639}, {43537, 49140}, {44518, 60100}, {53419, 60228}

X(60630) = orthology center of ABC and bicevian chordal triangle of X(2) and X(60335)
X(60630) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(15602)}}, {{A, B, C, X(297), X(15684)}}, {{A, B, C, X(458), X(23046)}}, {{A, B, C, X(524), X(6144)}}, {{A, B, C, X(548), X(52282)}}, {{A, B, C, X(5072), X(52281)}}, {{A, B, C, X(37174), X(46333)}}

X(60631) = X(30)X(60336)∩X(671)X(11008)

Barycentrics    (11*(a^2+b^2)-19*c^2)*(11*a^2-19*b^2+11*c^2) : :
X(60631) = X[15682]+2*X[54866]

X(60631) lies on the Kiepert hyperbola and on these lines: {30, 60336}, {376, 60102}, {381, 60331}, {382, 47586}, {524, 60219}, {543, 56064}, {546, 60118}, {671, 11008}, {1992, 33698}, {3524, 53104}, {3528, 7607}, {3529, 43537}, {3544, 7608}, {3545, 60333}, {3629, 54720}, {3855, 53099}, {5071, 11669}, {6329, 18842}, {7620, 18840}, {7841, 60639}, {8352, 60625}, {10159, 33232}, {10299, 53859}, {11001, 60175}, {11185, 60131}, {11317, 60650}, {12243, 54475}, {14269, 43951}, {15681, 54921}, {15682, 54866}, {15687, 60147}, {15715, 53103}, {21356, 60210}, {23334, 32532}, {33229, 43681}, {33230, 60278}, {33285, 60231}, {33292, 43529}, {38734, 54800}, {41099, 54521}, {41106, 60192}, {41135, 60104}, {43448, 54616}, {44518, 60183}, {50688, 60324}, {52713, 60638}, {53102, 59373}, {53144, 60187}, {53419, 54637}

X(60631) = orthology center of ABC and bicevian chordal triangle of X(2) and X(60336)
X(60631) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(428), X(33232)}}, {{A, B, C, X(524), X(11008)}}, {{A, B, C, X(3528), X(52282)}}, {{A, B, C, X(3544), X(52281)}}, {{A, B, C, X(6329), X(21356)}}, {{A, B, C, X(11736), X(56004)}}, {{A, B, C, X(15749), X(34897)}}, {{A, B, C, X(36611), X(57539)}}, {{A, B, C, X(39453), X(46645)}}

X(60632) = X(20)X(60334)∩X(98)X(15640)

Barycentrics    (13*(a^2+b^2)-23*c^2)*(13*a^2-23*b^2+13*c^2) : :

X(60632) lies on the Kiepert hyperbola and on these lines: {20, 60334}, {30, 60337}, {98, 15640}, {193, 32532}, {381, 60330}, {549, 60123}, {1992, 54896}, {2996, 50992}, {3091, 60332}, {3534, 7612}, {3543, 53100}, {3620, 60638}, {3830, 54845}, {3839, 60142}, {3845, 52519}, {5032, 45103}, {5055, 53098}, {5066, 14494}, {7486, 60144}, {7607, 10304}, {7620, 60277}, {8352, 60219}, {8584, 54642}, {10153, 41135}, {10185, 10303}, {11160, 60228}, {11185, 60279}, {11317, 18843}, {15534, 41895}, {15682, 60322}, {15683, 43537}, {15698, 53103}, {15717, 53859}, {22165, 60200}, {32974, 60642}, {33699, 60150}, {36523, 60103}, {43448, 60239}, {46210, 54395}, {50993, 60285}, {50994, 60628}, {51123, 60240}, {51171, 60283}, {53419, 60625}

X(60632) = orthology center of ABC and bicevian chordal triangle of X(2) and X(60337)
X(60632) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(67), X(11160)}}, {{A, B, C, X(193), X(50992)}}, {{A, B, C, X(297), X(15640)}}, {{A, B, C, X(3534), X(37174)}}, {{A, B, C, X(5032), X(5486)}}, {{A, B, C, X(10304), X(52282)}}, {{A, B, C, X(11741), X(56004)}}, {{A, B, C, X(21399), X(57714)}}, {{A, B, C, X(44763), X(55999)}}, {{A, B, C, X(50993), X(51171)}}

X(60633) = X(2)X(9821)∩X(4)X(13331)

Barycentrics    (3*a^2*b^2*(a^2+b^2)+(2*a^2+b^2)*(a^2+2*b^2)*c^2-(a^2+b^2)*c^4-c^6)*(a^4*(2*b^2+3*c^2)-b^2*(b^4+b^2*c^2-2*c^4)+a^2*(-b^4+5*b^2*c^2+3*c^4)) : :

X(60633) lies on the Kiepert hyperbola and on these lines: {2, 9821}, {3, 60129}, {4, 13331}, {5, 42006}, {39, 14492}, {76, 19130}, {83, 5092}, {98, 5007}, {262, 9698}, {381, 60214}, {511, 10159}, {626, 60099}, {1916, 44230}, {3095, 43688}, {3399, 5480}, {3406, 59232}, {5286, 54678}, {6033, 11606}, {6034, 9302}, {6248, 43676}, {6309, 60180}, {7709, 43951}, {7745, 55009}, {7753, 14458}, {7785, 54122}, {7809, 60217}, {7927, 43665}, {11257, 14488}, {12251, 60285}, {12252, 59266}, {18840, 24256}, {22682, 60132}, {43527, 58445}, {43538, 51754}, {43539, 51753}, {44142, 60199}, {44422, 60202}, {44518, 54903}, {48673, 54748}, {56789, 60105}

X(60633) = isogonal conjugate of X(12054)
X(60633) = orthology center of ABC and bicevian chordal triangle of X(2) and the isogonal conjugate of X(12055)
X(60633) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(13331)}}, {{A, B, C, X(6), X(9821)}}, {{A, B, C, X(39), X(74)}}, {{A, B, C, X(54), X(30499)}}, {{A, B, C, X(290), X(45108)}}, {{A, B, C, X(327), X(45090)}}, {{A, B, C, X(419), X(44230)}}, {{A, B, C, X(427), X(7470)}}, {{A, B, C, X(511), X(1173)}}, {{A, B, C, X(592), X(43702)}}, {{A, B, C, X(842), X(57421)}}, {{A, B, C, X(3095), X(59232)}}, {{A, B, C, X(3426), X(17042)}}, {{A, B, C, X(3613), X(14881)}}, {{A, B, C, X(8704), X(46672)}}, {{A, B, C, X(10357), X(43696)}}, {{A, B, C, X(11060), X(14483)}}, {{A, B, C, X(13603), X(41440)}}, {{A, B, C, X(51244), X(51872)}}

X(60634) = X(2)X(40)∩X(4)X(2331)

Barycentrics    (b+c)*((a+b)^3+(a-b)^2*c-(a+b)*c^2-c^3)*((a-b)*(a+b)^2+(a-b)*(3*a+b)*c+(3*a+b)*c^2+c^3) : :

X(60634) lies on the Kiepert hyperbola and on these lines: {1, 60076}, {2, 40}, {4, 2331}, {10, 21068}, {65, 8808}, {76, 322}, {98, 58946}, {226, 227}, {321, 21075}, {515, 60156}, {516, 37062}, {517, 60084}, {944, 54788}, {1029, 31673}, {1519, 45098}, {1699, 60107}, {2052, 47372}, {3672, 21620}, {4052, 21077}, {4205, 53004}, {4444, 28478}, {4848, 60249}, {5485, 17133}, {5587, 43533}, {5691, 54760}, {5706, 13478}, {5711, 12053}, {5799, 57719}, {5818, 54786}, {5882, 60258}, {6260, 60170}, {10444, 58012}, {10863, 60097}, {12608, 60071}, {12609, 56226}, {12610, 17758}, {12705, 60157}, {13464, 60169}, {13583, 18406}, {14534, 37422}, {18483, 60155}, {19925, 60079}, {21628, 43672}, {26332, 60114}, {31730, 37402}, {39579, 40149}, {39591, 60108}, {41869, 60077}, {51118, 60078}

X(60634) = trilinear pole of line {523, 55212}
X(60634) = X(i)-isoconjugate-of-X(j) for these {i, j}: {21, 34046}, {58, 57279}, {81, 54322}, {1333, 34255}
X(60634) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 57279}, {37, 34255}, {40586, 54322}, {40611, 34046}
X(60634) = X(i)-cross conjugate of X(j) for these {i, j}: {4646, 10}
X(60634) = pole of line {4646, 60634} with respect to the Kiepert hyperbola
X(60634) = orthology center of ABC and bicevian chordal triangle of X(2) and the isogonal conjugate of X(41816)
X(60634) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2321)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(4270)}}, {{A, B, C, X(7), X(3701)}}, {{A, B, C, X(37), X(84)}}, {{A, B, C, X(40), X(65)}}, {{A, B, C, X(42), X(947)}}, {{A, B, C, X(57), X(39592)}}, {{A, B, C, X(79), X(41012)}}, {{A, B, C, X(102), X(1245)}}, {{A, B, C, X(104), X(56221)}}, {{A, B, C, X(210), X(7160)}}, {{A, B, C, X(225), X(946)}}, {{A, B, C, X(429), X(37422)}}, {{A, B, C, X(469), X(37062)}}, {{A, B, C, X(502), X(16615)}}, {{A, B, C, X(516), X(23879)}}, {{A, B, C, X(523), X(28194)}}, {{A, B, C, X(740), X(28478)}}, {{A, B, C, X(962), X(3668)}}, {{A, B, C, X(963), X(52555)}}, {{A, B, C, X(1292), X(4103)}}, {{A, B, C, X(1389), X(53114)}}, {{A, B, C, X(1400), X(28270)}}, {{A, B, C, X(1499), X(17133)}}, {{A, B, C, X(1848), X(3704)}}, {{A, B, C, X(1869), X(5587)}}, {{A, B, C, X(1903), X(56195)}}, {{A, B, C, X(3296), X(3671)}}, {{A, B, C, X(3646), X(56237)}}, {{A, B, C, X(3649), X(16005)}}, {{A, B, C, X(3695), X(3755)}}, {{A, B, C, X(4424), X(5711)}}, {{A, B, C, X(4646), X(14551)}}, {{A, B, C, X(4848), X(21077)}}, {{A, B, C, X(5556), X(26129)}}, {{A, B, C, X(6260), X(21933)}}, {{A, B, C, X(6684), X(15232)}}, {{A, B, C, X(7350), X(56192)}}, {{A, B, C, X(8227), X(45091)}}, {{A, B, C, X(8806), X(52560)}}, {{A, B, C, X(8818), X(56174)}}, {{A, B, C, X(10429), X(56157)}}, {{A, B, C, X(10435), X(57723)}}, {{A, B, C, X(15909), X(23604)}}, {{A, B, C, X(26062), X(56173)}}, {{A, B, C, X(28291), X(56257)}}, {{A, B, C, X(30500), X(56259)}}, {{A, B, C, X(31162), X(52382)}}, {{A, B, C, X(34485), X(35576)}}
X(60634) = barycentric product X(i)*X(j) for these (i, j): {34244, 60267}, {58946, 850}
X(60634) = barycentric quotient X(i)/X(j) for these (i, j): {10, 34255}, {37, 57279}, {42, 54322}, {1400, 34046}, {4656, 28616}, {34244, 42028}, {58946, 110}

X(60635) = X(4)X(50962)∩X(98)X(8596)

Barycentrics    (5*(a^2+b^2)-19*c^2)*(5*a^2-19*b^2+5*c^2) : :
X(60635) = -6*X[5054]+7*X[53103]

X(60635) lies on the Kiepert hyperbola and on these lines: {4, 50962}, {69, 60625}, {98, 8596}, {193, 54476}, {524, 60113}, {547, 10155}, {598, 51170}, {599, 43681}, {1992, 18845}, {2482, 60073}, {3146, 54857}, {3543, 60325}, {3832, 60329}, {3860, 54707}, {5032, 60650}, {5054, 53103}, {5395, 34505}, {6392, 53109}, {7612, 15692}, {7620, 45103}, {8591, 60103}, {8703, 60185}, {10513, 60271}, {11054, 54494}, {11160, 38259}, {11185, 60282}, {15681, 60322}, {15683, 60323}, {18842, 47286}, {19709, 54523}, {20080, 41895}, {21734, 43537}, {32835, 60198}, {32837, 60178}, {32885, 60248}, {32893, 60101}, {32979, 60146}, {32982, 60209}, {43448, 60216}, {44367, 60147}, {46936, 53098}, {50687, 60326}, {52713, 60643}, {55864, 60123}

X(60635) = orthology center of ABC and bicevian chordal triangle of X(2) and the isogonal conjugate of X(55593)
X(60635) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(599), X(51170)}}, {{A, B, C, X(10513), X(44367)}}, {{A, B, C, X(11160), X(20080)}}, {{A, B, C, X(15692), X(37174)}}, {{A, B, C, X(35510), X(54171)}}, {{A, B, C, X(51215), X(56267)}}

X(60636) = X(2)X(55790)∩X(4)X(40341)

Barycentrics    (a^2+b^2-9*c^2)*(a^2-9*b^2+c^2) : :
X(60636) = -7*X[3090]+6*X[60333]

X(60636) lies on the Kiepert hyperbola and on these lines: {2, 55790}, {3, 55827}, {4, 40341}, {5, 60331}, {69, 53105}, {76, 33232}, {83, 52713}, {98, 3528}, {262, 3544}, {315, 17503}, {376, 54866}, {382, 60147}, {546, 43951}, {550, 47586}, {631, 60102}, {1916, 33292}, {2996, 7879}, {3090, 60333}, {3096, 60638}, {3424, 3529}, {3524, 60175}, {3525, 51587}, {3530, 54921}, {3545, 54521}, {3629, 18843}, {3631, 60219}, {3851, 60118}, {3855, 14484}, {5067, 11669}, {5071, 60192}, {5254, 60143}, {5395, 7754}, {6248, 54814}, {6392, 60647}, {6656, 60639}, {6722, 56064}, {7375, 60294}, {7376, 60293}, {7790, 60640}, {7803, 60182}, {7841, 60625}, {7894, 60649}, {7982, 54668}, {8370, 60650}, {10299, 43537}, {10302, 33230}, {11001, 54608}, {11008, 53109}, {11054, 60287}, {11185, 53107}, {11541, 17131}, {11606, 33238}, {12251, 60115}, {15687, 54815}, {15715, 60185}, {17538, 60323}, {18842, 20583}, {32532, 34505}, {32868, 60212}, {32951, 60231}, {33190, 60200}, {33229, 38259}, {33236, 60093}, {33239, 60184}, {33253, 35369}, {41106, 54643}, {47286, 60285}, {49135, 60324}, {50688, 60327}, {50771, 52519}

X(60636) = trilinear pole of line {523, 55188}
X(60636) = orthology center of ABC and bicevian chordal triangle of X(2) and the isogonal conjugate of X(55607)
X(60636) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55722)}}, {{A, B, C, X(25), X(33232)}}, {{A, B, C, X(69), X(40341)}}, {{A, B, C, X(257), X(18490)}}, {{A, B, C, X(277), X(40029)}}, {{A, B, C, X(287), X(14843)}}, {{A, B, C, X(297), X(3528)}}, {{A, B, C, X(419), X(33292)}}, {{A, B, C, X(420), X(33238)}}, {{A, B, C, X(458), X(3544)}}, {{A, B, C, X(1235), X(52713)}}, {{A, B, C, X(3296), X(57725)}}, {{A, B, C, X(3525), X(31617)}}, {{A, B, C, X(3529), X(52283)}}, {{A, B, C, X(3626), X(29621)}}, {{A, B, C, X(3631), X(11008)}}, {{A, B, C, X(3855), X(52288)}}, {{A, B, C, X(4391), X(15998)}}, {{A, B, C, X(5551), X(56042)}}, {{A, B, C, X(6330), X(18851)}}, {{A, B, C, X(6464), X(13472)}}, {{A, B, C, X(6531), X(14842)}}, {{A, B, C, X(6664), X(17040)}}, {{A, B, C, X(7982), X(59215)}}, {{A, B, C, X(9516), X(16774)}}, {{A, B, C, X(10301), X(33230)}}, {{A, B, C, X(11270), X(40802)}}, {{A, B, C, X(18853), X(52581)}}, {{A, B, C, X(20421), X(56004)}}, {{A, B, C, X(20583), X(21356)}}, {{A, B, C, X(33229), X(38282)}}, {{A, B, C, X(33236), X(57533)}}, {{A, B, C, X(39710), X(40028)}}, {{A, B, C, X(39711), X(55948)}}, {{A, B, C, X(39749), X(43734)}}, {{A, B, C, X(55972), X(57823)}}

X(60637) = X(4)X(22165)∩X(98)X(15698)

Barycentrics    (a^2+19*b^2+c^2)*(a^2+b^2+19*c^2) : :

X(60637) lies on the Kiepert hyperbola and on these lines: {4, 22165}, {69, 45103}, {98, 15698}, {141, 60627}, {376, 53100}, {524, 60284}, {549, 43537}, {598, 50992}, {599, 32532}, {631, 60334}, {671, 50994}, {1992, 60283}, {3090, 60332}, {3424, 3534}, {3524, 60337}, {3526, 53859}, {3545, 60142}, {5055, 53099}, {5066, 14484}, {5071, 60330}, {5485, 50993}, {7607, 15709}, {7850, 54494}, {7879, 38259}, {9167, 10153}, {10304, 47586}, {11001, 54845}, {11054, 60278}, {11185, 54493}, {14488, 41099}, {14711, 60099}, {15533, 60281}, {15534, 18842}, {15640, 60147}, {15682, 60132}, {15683, 60324}, {15719, 60335}, {15759, 54866}, {17503, 50990}, {19708, 60322}, {21356, 60228}, {21358, 60641}, {32874, 60262}, {32892, 60212}, {32956, 60642}, {33190, 43676}, {33699, 54519}, {41106, 52519}, {41895, 52713}, {46333, 54857}, {50991, 54637}, {51143, 60143}, {51189, 54647}

X(60637) = pole of line {51186, 60637} with respect to the Kiepert hyperbola
X(60637) = orthology center of ABC and bicevian chordal triangle of X(2) and the isogonal conjugate of X(55626)
X(60637) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(69), X(22165)}}, {{A, B, C, X(297), X(15698)}}, {{A, B, C, X(524), X(50994)}}, {{A, B, C, X(599), X(50992)}}, {{A, B, C, X(1992), X(50993)}}, {{A, B, C, X(3534), X(52283)}}, {{A, B, C, X(5066), X(52288)}}, {{A, B, C, X(5486), X(15534)}}, {{A, B, C, X(15533), X(50990)}}, {{A, B, C, X(15709), X(52282)}}, {{A, B, C, X(21358), X(22336)}}, {{A, B, C, X(34403), X(34483)}}, {{A, B, C, X(36889), X(57907)}}

X(60638) = X(2)X(55786)∩X(3)X(55725)

Barycentrics    (a^2+10*b^2+c^2)*(a^2+b^2+10*c^2) : :
X(60638) = -16*X[11737]+11*X[60142]

X(60638) lies on the Kiepert hyperbola and on these lines: {2, 55786}, {3, 55725}, {4, 50990}, {6, 60287}, {69, 60281}, {76, 51186}, {83, 8584}, {98, 12100}, {141, 60216}, {316, 54646}, {524, 60282}, {598, 15533}, {599, 17503}, {671, 50991}, {1916, 33288}, {3096, 60636}, {3424, 15697}, {3620, 60632}, {3830, 54917}, {5395, 7877}, {7607, 15694}, {7608, 15699}, {7760, 60647}, {7790, 60200}, {7812, 18843}, {7827, 56059}, {7883, 53105}, {7911, 38259}, {8587, 41134}, {9466, 60098}, {10159, 11054}, {10185, 16239}, {11167, 51122}, {11185, 60113}, {11737, 60142}, {14061, 42010}, {14458, 15685}, {14711, 42006}, {14869, 60334}, {14976, 54901}, {15534, 60283}, {15686, 54857}, {15688, 53100}, {15708, 43537}, {21356, 54637}, {21358, 60286}, {22165, 45103}, {32027, 53106}, {32532, 50994}, {32892, 60259}, {40344, 43535}, {41152, 54478}, {46951, 60262}, {50992, 60284}, {50993, 60228}, {51185, 60239}, {52713, 60631}, {55857, 60144}

X(60638) = trilinear pole of line {41136, 523}
X(60638) = pole of line {51143, 60638} with respect to the Kiepert hyperbola
X(60638) = orthology center of ABC and bicevian chordal triangle of X(2) and the isogonal conjugate of X(55631)
X(60638) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55583)}}, {{A, B, C, X(6), X(51186)}}, {{A, B, C, X(69), X(50990)}}, {{A, B, C, X(141), X(8584)}}, {{A, B, C, X(297), X(12100)}}, {{A, B, C, X(419), X(33288)}}, {{A, B, C, X(524), X(50991)}}, {{A, B, C, X(599), X(15533)}}, {{A, B, C, X(1494), X(57907)}}, {{A, B, C, X(11054), X(39998)}}, {{A, B, C, X(11331), X(15685)}}, {{A, B, C, X(14711), X(60707)}}, {{A, B, C, X(15534), X(50993)}}, {{A, B, C, X(15694), X(52282)}}, {{A, B, C, X(15697), X(52283)}}, {{A, B, C, X(15699), X(52281)}}, {{A, B, C, X(21358), X(51185)}}, {{A, B, C, X(50989), X(51189)}}, {{A, B, C, X(50992), X(50994)}}, {{A, B, C, X(55958), X(57908)}}

X(60639) = X(2)X(55785)∩X(3)X(60322)

Barycentrics    (a^2+9*b^2+c^2)*(a^2+b^2+9*c^2) : :

X(60639) lies on the Kiepert hyperbola and on these lines: {2, 55785}, {3, 60322}, {4, 55584}, {20, 54845}, {69, 18845}, {83, 51170}, {98, 15717}, {141, 43681}, {193, 60145}, {262, 15022}, {315, 45103}, {549, 60185}, {599, 60113}, {1916, 33287}, {3091, 52519}, {3096, 60216}, {3146, 60132}, {3424, 50693}, {3522, 53100}, {3523, 60337}, {3526, 53103}, {3534, 54612}, {3620, 38259}, {3628, 10155}, {3832, 14488}, {3926, 60248}, {5055, 54523}, {5056, 60330}, {5066, 54707}, {5068, 60142}, {5254, 60200}, {5286, 60278}, {5395, 20080}, {6392, 10159}, {6656, 60636}, {7388, 60621}, {7389, 60620}, {7486, 14494}, {7612, 10303}, {7754, 18841}, {7793, 54906}, {7841, 60631}, {7850, 53107}, {7897, 60118}, {7929, 54477}, {8781, 32834}, {10304, 60150}, {10513, 60105}, {11160, 60650}, {14458, 15683}, {18843, 32971}, {20081, 60099}, {21356, 60625}, {31274, 60073}, {31276, 60096}, {32828, 60178}, {32830, 60101}, {32869, 60217}, {32874, 60202}, {32882, 60259}, {32894, 60201}, {32974, 60219}, {32979, 53109}, {32982, 53105}, {33023, 60280}, {45017, 60323}, {49140, 60325}, {50692, 60147}, {51481, 59764}, {55825, 59545}

X(60639) = orthology center of ABC and bicevian chordal triangle of X(2) and the isogonal conjugate of X(55632)
X(60639) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55584)}}, {{A, B, C, X(141), X(6339)}}, {{A, B, C, X(297), X(15717)}}, {{A, B, C, X(308), X(57857)}}, {{A, B, C, X(419), X(33287)}}, {{A, B, C, X(458), X(15022)}}, {{A, B, C, X(2207), X(40103)}}, {{A, B, C, X(3620), X(20080)}}, {{A, B, C, X(3926), X(34483)}}, {{A, B, C, X(6392), X(39998)}}, {{A, B, C, X(10303), X(37174)}}, {{A, B, C, X(11331), X(15683)}}, {{A, B, C, X(13606), X(54123)}}, {{A, B, C, X(27494), X(56335)}}, {{A, B, C, X(32834), X(51481)}}, {{A, B, C, X(32982), X(37453)}}, {{A, B, C, X(35510), X(57907)}}, {{A, B, C, X(36952), X(56339)}}, {{A, B, C, X(39749), X(56353)}}, {{A, B, C, X(40029), X(56044)}}, {{A, B, C, X(43713), X(56362)}}, {{A, B, C, X(50693), X(52283)}}

X(60640) = X(2)X(55784)∩X(3)X(54851)

Barycentrics    (a^2+8*b^2+c^2)*(a^2+b^2+8*c^2) : :

X(60640) lies on the Kiepert hyperbola and on these lines: {2, 55784}, {3, 54851}, {4, 55585}, {5, 54734}, {69, 18844}, {83, 32455}, {98, 15712}, {140, 54644}, {141, 60250}, {548, 54608}, {550, 54934}, {599, 54493}, {620, 60136}, {1656, 54645}, {1657, 14458}, {1916, 33286}, {3096, 43681}, {3407, 14040}, {3627, 54477}, {3630, 60146}, {3843, 54582}, {3850, 14492}, {5056, 54522}, {5072, 54643}, {6144, 60649}, {6656, 60216}, {7760, 60239}, {7768, 53109}, {7770, 60283}, {7784, 53105}, {7790, 60636}, {7812, 60650}, {7883, 41895}, {11289, 54593}, {11290, 54594}, {11668, 46219}, {14893, 54813}, {15720, 60335}, {17538, 54612}, {21735, 60150}, {32878, 60259}, {32888, 60201}, {32956, 60641}, {35018, 54920}, {50691, 54519}, {53108, 55856}

X(60640) = orthology center of ABC and bicevian chordal triangle of X(2) and the isogonal conjugate of X(55634)
X(60640) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55585)}}, {{A, B, C, X(141), X(32455)}}, {{A, B, C, X(287), X(14841)}}, {{A, B, C, X(297), X(15712)}}, {{A, B, C, X(327), X(57896)}}, {{A, B, C, X(419), X(33286)}}, {{A, B, C, X(1657), X(11331)}}, {{A, B, C, X(5117), X(14040)}}, {{A, B, C, X(6531), X(14840)}}, {{A, B, C, X(26861), X(36952)}}, {{A, B, C, X(39711), X(54974)}}

X(60641) = X(4)X(50991)∩X(98)X(15719)

Barycentrics    (5*a^2+23*b^2+5*c^2)*(5*(a^2+b^2)+23*c^2) : :

X(60641) lies on the Kiepert hyperbola and on these lines: {4, 50991}, {69, 60282}, {98, 15719}, {141, 54637}, {376, 54857}, {547, 53099}, {598, 50990}, {599, 60281}, {632, 53859}, {1992, 60287}, {3424, 8703}, {3545, 60329}, {3619, 60286}, {3620, 54642}, {3860, 54520}, {5054, 43537}, {5485, 51186}, {8584, 54616}, {10153, 31274}, {11001, 60325}, {11054, 60642}, {11540, 60102}, {14484, 19709}, {15533, 18842}, {15682, 60326}, {15692, 47586}, {15698, 60323}, {15710, 53100}, {17503, 21356}, {18841, 51185}, {21358, 60637}, {22165, 60284}, {32532, 50993}, {32893, 60262}, {32956, 60640}, {33190, 60209}, {41099, 54890}, {45103, 50994}, {50992, 60283}, {51143, 60627}, {52713, 60625}

X(60641) = orthology center of ABC and bicevian chordal triangle of X(2) and the isogonal conjugate of X(55641)
X(60641) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(69), X(50991)}}, {{A, B, C, X(297), X(15719)}}, {{A, B, C, X(599), X(50990)}}, {{A, B, C, X(1992), X(51186)}}, {{A, B, C, X(3619), X(51185)}}, {{A, B, C, X(8703), X(52283)}}, {{A, B, C, X(13602), X(39749)}}, {{A, B, C, X(15533), X(21356)}}, {{A, B, C, X(19709), X(52288)}}, {{A, B, C, X(22165), X(50994)}}, {{A, B, C, X(50992), X(50993)}}

X(60642) = X(2)X(55776)∩X(3)X(54608)

Barycentrics    (2*a^2+7*b^2+2*c^2)*(2*(a^2+b^2)+7*c^2) : :

X(60642) lies on the Kiepert hyperbola and on these lines: {2, 55776}, {3, 54608}, {4, 55594}, {5, 54643}, {83, 40341}, {98, 15720}, {140, 60175}, {141, 53105}, {262, 35018}, {315, 18844}, {382, 54477}, {546, 54582}, {550, 14458}, {1656, 60192}, {1657, 54852}, {2996, 7937}, {3096, 60209}, {3523, 54866}, {3528, 54612}, {3530, 54851}, {3544, 54707}, {3631, 53102}, {3851, 14492}, {5056, 54521}, {5079, 54734}, {5395, 7768}, {6656, 60228}, {7388, 60314}, {7389, 60313}, {7760, 60645}, {7770, 60282}, {7827, 60629}, {7860, 53109}, {7869, 60233}, {7878, 54616}, {7883, 54646}, {7918, 43676}, {10299, 60150}, {11054, 60641}, {11289, 33607}, {11290, 33606}, {11669, 55856}, {14034, 54539}, {14045, 54540}, {14269, 54813}, {15712, 60323}, {17503, 33229}, {20583, 60239}, {31274, 60104}, {32956, 60637}, {32974, 60632}, {33232, 54637}, {46219, 53104}, {46935, 60333}, {49135, 54519}, {49139, 60132}

X(60642) = orthology center of ABC and bicevian chordal triangle of X(2) and the isogonal conjugate of X(55642)
X(60642) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55594)}}, {{A, B, C, X(141), X(40341)}}, {{A, B, C, X(297), X(15720)}}, {{A, B, C, X(327), X(57823)}}, {{A, B, C, X(458), X(35018)}}, {{A, B, C, X(550), X(11331)}}, {{A, B, C, X(3851), X(52289)}}, {{A, B, C, X(9307), X(40042)}}, {{A, B, C, X(20583), X(21358)}}, {{A, B, C, X(26861), X(42313)}}, {{A, B, C, X(33229), X(52292)}}

X(60643) = X(4)X(20582)∩X(6)X(60646)

Barycentrics    (7*a^2+13*b^2+7*c^2)*(7*(a^2+b^2)+13*c^2) : :

X(60643) lies on the Kiepert hyperbola and on these lines: {4, 20582}, {6, 60646}, {69, 60238}, {98, 15709}, {141, 54616}, {376, 60132}, {524, 60616}, {549, 3424}, {598, 3619}, {599, 18841}, {631, 53100}, {1992, 43527}, {3090, 60142}, {3524, 54845}, {3525, 60337}, {3526, 43537}, {3533, 60334}, {3534, 54519}, {3545, 14488}, {3628, 53099}, {3763, 5485}, {5055, 14484}, {5066, 54520}, {5067, 60330}, {5071, 52519}, {7375, 43571}, {7376, 43570}, {7486, 60118}, {7758, 55768}, {7850, 60283}, {7868, 60268}, {10303, 47586}, {10304, 60147}, {14458, 15698}, {15022, 60328}, {15640, 54815}, {15683, 60327}, {15702, 60322}, {15717, 60324}, {15719, 54934}, {16045, 53102}, {18842, 21358}, {21356, 60239}, {32897, 60262}, {32956, 43676}, {33190, 53105}, {33230, 60219}, {34573, 60629}, {41099, 54717}, {42850, 60215}, {46333, 60326}, {47598, 60102}, {52713, 60635}, {53665, 55949}, {53859, 55859}, {54901, 60728}, {59373, 60645}

X(60643) = orthology center of ABC and bicevian chordal triangle of X(2) and the isogonal conjugate of X(55654)
X(60643) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55626)}}, {{A, B, C, X(67), X(21356)}}, {{A, B, C, X(69), X(20582)}}, {{A, B, C, X(297), X(15709)}}, {{A, B, C, X(549), X(52283)}}, {{A, B, C, X(599), X(3619)}}, {{A, B, C, X(1992), X(3763)}}, {{A, B, C, X(5055), X(52288)}}, {{A, B, C, X(7868), X(42850)}}, {{A, B, C, X(11331), X(15698)}}, {{A, B, C, X(31144), X(53665)}}, {{A, B, C, X(33190), X(37453)}}, {{A, B, C, X(40410), X(54171)}}, {{A, B, C, X(40802), X(57714)}}, {{A, B, C, X(51026), X(53024)}}, {{A, B, C, X(55972), X(57895)}}

X(60644) = X(2)X(7882)∩X(3)X(54890)

Barycentrics    (4*(a^2+b^2)+3*c^2)*(4*a^2+3*b^2+4*c^2) : :

X(60644) lies on the Kiepert hyperbola and on these lines: {2, 7882}, {3, 54890}, {4, 48891}, {5, 60326}, {6, 56059}, {76, 51126}, {98, 5070}, {140, 60329}, {262, 632}, {315, 54616}, {316, 18843}, {547, 14458}, {1656, 54857}, {1916, 14067}, {2996, 7859}, {3090, 60325}, {3096, 60239}, {3407, 14047}, {3424, 46936}, {3530, 14488}, {3589, 60278}, {3628, 60323}, {5054, 14492}, {5055, 54852}, {5079, 49112}, {5254, 60626}, {6656, 53107}, {6704, 54539}, {7375, 60309}, {7376, 60310}, {7754, 10302}, {7762, 43527}, {7769, 60201}, {7770, 53106}, {7786, 43688}, {7803, 43681}, {7812, 60287}, {7815, 60129}, {7816, 54823}, {7827, 60200}, {7841, 54646}, {7846, 54773}, {7860, 60145}, {7878, 60100}, {7894, 10159}, {7918, 17503}, {7930, 60232}, {7937, 53102}, {7942, 54122}, {7943, 11606}, {8370, 54493}, {8703, 54582}, {11289, 43551}, {11290, 43550}, {11303, 54592}, {11304, 54591}, {11540, 54643}, {12811, 54917}, {14484, 55864}, {15681, 54717}, {15692, 54520}, {18844, 32956}, {19709, 54477}, {21734, 54706}, {41984, 54645}, {48310, 60131}, {52297, 60141}, {52298, 60125}

X(60644) = orthology center of ABC and bicevian chordal triangle of X(2) and the isogonal conjugate of X(55665)
X(60644) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55674)}}, {{A, B, C, X(6), X(51126)}}, {{A, B, C, X(39), X(36615)}}, {{A, B, C, X(297), X(5070)}}, {{A, B, C, X(419), X(14067)}}, {{A, B, C, X(458), X(632)}}, {{A, B, C, X(547), X(11331)}}, {{A, B, C, X(3589), X(14381)}}, {{A, B, C, X(3763), X(51127)}}, {{A, B, C, X(5054), X(52289)}}, {{A, B, C, X(5117), X(14047)}}, {{A, B, C, X(6656), X(52298)}}, {{A, B, C, X(7770), X(52297)}}, {{A, B, C, X(7786), X(41259)}}, {{A, B, C, X(7859), X(57518)}}, {{A, B, C, X(7894), X(52570)}}, {{A, B, C, X(8770), X(57421)}}, {{A, B, C, X(9289), X(48891)}}, {{A, B, C, X(13602), X(56353)}}, {{A, B, C, X(14970), X(24861)}}, {{A, B, C, X(39951), X(59996)}}, {{A, B, C, X(44731), X(56004)}}, {{A, B, C, X(46936), X(52283)}}, {{A, B, C, X(52288), X(55864)}}, {{A, B, C, X(52660), X(55075)}}, {{A, B, C, X(54124), X(57927)}}

X(60645) = X(2)X(14075)∩X(4)X(25565)

Barycentrics    (7*(a^2+b^2)+4*c^2)*(7*a^2+4*b^2+7*c^2) : :

X(60645) lies on the Kiepert hyperbola and on these lines: {2, 14075}, {3, 55764}, {4, 25565}, {6, 60131}, {98, 15699}, {262, 15694}, {381, 54917}, {524, 60279}, {597, 10159}, {598, 47355}, {599, 60278}, {671, 48310}, {1992, 60183}, {2482, 60271}, {3589, 10302}, {3618, 60629}, {5461, 11606}, {7607, 55857}, {7608, 16239}, {7760, 60642}, {7762, 60100}, {7790, 32532}, {7812, 60647}, {7827, 60250}, {7859, 53106}, {7883, 18841}, {11737, 60132}, {12100, 14492}, {12812, 54857}, {14484, 15708}, {14488, 15688}, {14869, 60142}, {15685, 54582}, {15686, 54890}, {15697, 54520}, {16987, 43535}, {20582, 56059}, {33288, 54539}, {47352, 60277}, {51126, 60238}, {59373, 60643}

X(60645) = orthology center of ABC and bicevian chordal triangle of X(2) and the isogonal conjugate of X(55670)
X(60645) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55681)}}, {{A, B, C, X(6), X(14075)}}, {{A, B, C, X(297), X(15699)}}, {{A, B, C, X(458), X(15694)}}, {{A, B, C, X(524), X(48310)}}, {{A, B, C, X(597), X(3589)}}, {{A, B, C, X(599), X(47355)}}, {{A, B, C, X(2987), X(11588)}}, {{A, B, C, X(7840), X(16987)}}, {{A, B, C, X(12100), X(52289)}}, {{A, B, C, X(15491), X(44401)}}, {{A, B, C, X(15708), X(52288)}}, {{A, B, C, X(16239), X(52281)}}, {{A, B, C, X(20582), X(51126)}}, {{A, B, C, X(34897), X(53024)}}, {{A, B, C, X(52282), X(55857)}}
X(60645) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14075, 55740}

X(60646) = X(4)X(48310)∩X(6)X(60643)

Barycentrics    (13*(a^2+b^2)+7*c^2)*(13*a^2+7*b^2+13*c^2) : :

X(60646) lies on the Kiepert hyperbola and on these lines: {4, 48310}, {6, 60643}, {69, 60279}, {262, 15709}, {376, 14488}, {524, 60183}, {549, 14484}, {597, 60629}, {631, 60142}, {1992, 60131}, {3090, 53100}, {3424, 5055}, {3524, 52519}, {3525, 60330}, {3526, 53099}, {3533, 60332}, {3534, 54520}, {3545, 60132}, {3589, 60143}, {3618, 60277}, {3628, 43537}, {5066, 54519}, {5067, 60337}, {5071, 54845}, {5503, 31274}, {7375, 43570}, {7376, 43571}, {7486, 47586}, {10159, 59373}, {10303, 60118}, {10304, 43951}, {11540, 54522}, {14458, 14762}, {14492, 15698}, {15022, 60324}, {15682, 54717}, {15683, 54706}, {15717, 60328}, {15810, 54773}, {16045, 43676}, {18840, 47352}, {18842, 47355}, {18843, 33230}, {21356, 60278}, {23334, 60284}, {32956, 53102}, {33190, 53109}, {46333, 54890}, {47598, 60333}, {51126, 60616}, {53859, 55860}

X(60646) = orthology center of ABC and bicevian chordal triangle of X(2) and the isogonal conjugate of X(55671)
X(60646) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(66), X(21356)}}, {{A, B, C, X(69), X(48310)}}, {{A, B, C, X(458), X(15709)}}, {{A, B, C, X(549), X(52288)}}, {{A, B, C, X(3618), X(47352)}}, {{A, B, C, X(5055), X(52283)}}, {{A, B, C, X(11165), X(37863)}}, {{A, B, C, X(15321), X(21358)}}, {{A, B, C, X(15698), X(52289)}}

X(60647) = X(2)X(55729)∩X(4)X(12017)

Barycentrics    (5*(a^2+b^2)+c^2)*(5*a^2+b^2+5*c^2) : :

X(60647) lies on the Kiepert hyperbola and on these lines: {2, 55729}, {3, 55780}, {4, 12017}, {5, 60150}, {6, 60285}, {20, 14492}, {76, 51171}, {98, 5056}, {140, 14494}, {182, 54858}, {193, 18840}, {262, 3523}, {297, 54531}, {315, 60100}, {316, 60649}, {376, 54707}, {458, 54867}, {459, 52289}, {550, 52519}, {597, 60200}, {598, 32974}, {631, 54523}, {671, 32971}, {1656, 7612}, {1916, 14037}, {2996, 3618}, {3090, 60185}, {3091, 14458}, {3096, 60182}, {3146, 54520}, {3329, 32841}, {3407, 33283}, {3424, 5068}, {3522, 14484}, {3533, 10155}, {3543, 54582}, {3545, 54612}, {3589, 5395}, {3620, 7877}, {3832, 54519}, {3839, 54477}, {3850, 60325}, {3851, 54845}, {3854, 60147}, {4232, 60141}, {5032, 10302}, {5059, 43951}, {5286, 43676}, {5304, 42006}, {5485, 7770}, {5503, 33181}, {6392, 60636}, {6656, 18842}, {6658, 54737}, {6680, 60198}, {6996, 54689}, {7375, 43536}, {7376, 54597}, {7377, 54587}, {7388, 14241}, {7389, 14226}, {7395, 54763}, {7399, 54660}, {7406, 54586}, {7486, 60175}, {7607, 46935}, {7608, 10583}, {7745, 60145}, {7755, 32885}, {7760, 60638}, {7767, 55735}, {7768, 60278}, {7803, 53105}, {7808, 32867}, {7812, 60645}, {7824, 60268}, {7827, 60626}, {7841, 60281}, {7859, 53102}, {7860, 60239}, {7878, 11160}, {7892, 32835}, {7923, 60327}, {7932, 53100}, {8370, 32532}, {8587, 33270}, {8781, 31274}, {10303, 60192}, {10304, 54643}, {10484, 33206}, {11172, 16921}, {11174, 60260}, {11289, 43543}, {11290, 43542}, {11303, 33603}, {11304, 33602}, {11317, 54647}, {11331, 56346}, {11479, 54604}, {13727, 54712}, {13740, 54786}, {14035, 54540}, {14063, 54539}, {14488, 49135}, {14976, 33202}, {15022, 54866}, {15692, 54734}, {15717, 54521}, {15720, 60330}, {16045, 60143}, {16062, 54624}, {16984, 60102}, {16989, 60259}, {17681, 54831}, {32837, 60202}, {32870, 60212}, {32956, 54616}, {32962, 43535}, {32965, 54487}, {32970, 60240}, {32972, 54906}, {32973, 44562}, {32979, 41895}, {32981, 54889}, {32982, 53101}, {32987, 60218}, {32990, 54905}, {32993, 54901}, {33020, 54122}, {33021, 60190}, {33190, 60284}, {33198, 60180}, {33269, 60214}, {34007, 54704}, {34664, 54838}, {35018, 60337}, {36652, 54690}, {36670, 54657}, {37162, 60152}, {37174, 60120}, {37649, 43670}, {37665, 60232}, {37667, 60099}, {37681, 56210}, {41231, 54930}, {41237, 54772}, {41238, 54771}, {43678, 56865}, {46214, 54395}, {46219, 53098}, {46936, 54644}, {50688, 54717}, {50689, 54815}, {50690, 54706}, {50691, 54890}, {52284, 60125}, {52288, 54710}, {54097, 54476}, {54645, 55864}, {55819, 60096}, {55856, 60123}, {59373, 60628}

X(60647) = trilinear pole of line {37910, 523}
X(60647) = orthology center of ABC and bicevian chordal triangle of X(2) and the isogonal conjugate of X(55678)
X(60647) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(12017)}}, {{A, B, C, X(6), X(51171)}}, {{A, B, C, X(20), X(52289)}}, {{A, B, C, X(32), X(46123)}}, {{A, B, C, X(66), X(3589)}}, {{A, B, C, X(68), X(53024)}}, {{A, B, C, X(88), X(989)}}, {{A, B, C, X(193), X(3618)}}, {{A, B, C, X(297), X(5056)}}, {{A, B, C, X(393), X(40425)}}, {{A, B, C, X(419), X(14037)}}, {{A, B, C, X(458), X(3523)}}, {{A, B, C, X(468), X(32971)}}, {{A, B, C, X(597), X(5032)}}, {{A, B, C, X(981), X(39975)}}, {{A, B, C, X(1656), X(37174)}}, {{A, B, C, X(2207), X(3108)}}, {{A, B, C, X(3091), X(11331)}}, {{A, B, C, X(3224), X(11175)}}, {{A, B, C, X(3329), X(5304)}}, {{A, B, C, X(3522), X(52288)}}, {{A, B, C, X(4232), X(7770)}}, {{A, B, C, X(4373), X(39729)}}, {{A, B, C, X(5068), X(52283)}}, {{A, B, C, X(5094), X(32974)}}, {{A, B, C, X(5117), X(33283)}}, {{A, B, C, X(5557), X(30701)}}, {{A, B, C, X(5558), X(14621)}}, {{A, B, C, X(6531), X(52224)}}, {{A, B, C, X(6620), X(7892)}}, {{A, B, C, X(6656), X(52284)}}, {{A, B, C, X(7320), X(17743)}}, {{A, B, C, X(7875), X(37668)}}, {{A, B, C, X(8370), X(53857)}}, {{A, B, C, X(8743), X(56865)}}, {{A, B, C, X(10405), X(39730)}}, {{A, B, C, X(11160), X(47352)}}, {{A, B, C, X(11174), X(37667)}}, {{A, B, C, X(14376), X(14861)}}, {{A, B, C, X(16045), X(52301)}}, {{A, B, C, X(16989), X(37665)}}, {{A, B, C, X(17379), X(37681)}}, {{A, B, C, X(30535), X(43908)}}, {{A, B, C, X(31274), X(52450)}}, {{A, B, C, X(32835), X(40814)}}, {{A, B, C, X(32839), X(51481)}}, {{A, B, C, X(32979), X(52290)}}, {{A, B, C, X(34567), X(56004)}}, {{A, B, C, X(38110), X(42021)}}, {{A, B, C, X(39722), X(55937)}}, {{A, B, C, X(39968), X(56360)}}, {{A, B, C, X(42287), X(56339)}}, {{A, B, C, X(46935), X(52282)}}, {{A, B, C, X(51348), X(54114)}}, {{A, B, C, X(54413), X(55075)}}, {{A, B, C, X(56362), X(57713)}}

X(60648) = X(4)X(38079)∩X(6)X(60628)

Barycentrics    (13*(a^2+b^2)+c^2)*(13*a^2+b^2+13*c^2) : :

X(60648) lies on the Kiepert hyperbola and on these lines: {4, 38079}, {6, 60628}, {20, 60329}, {193, 10302}, {262, 15692}, {381, 60325}, {547, 7612}, {597, 2996}, {632, 53098}, {1992, 60285}, {3091, 54857}, {3530, 60330}, {3543, 54890}, {3589, 54639}, {3618, 41895}, {3620, 60629}, {3839, 60326}, {5032, 60143}, {5054, 14494}, {5070, 60123}, {5079, 60337}, {5485, 51171}, {7388, 60303}, {7389, 60304}, {7607, 46936}, {7608, 55864}, {7762, 60183}, {7790, 54478}, {7812, 60182}, {7841, 18844}, {7873, 55760}, {8703, 60127}, {8781, 22247}, {11160, 18840}, {15681, 52519}, {15719, 54523}, {19569, 54773}, {19709, 60150}, {21734, 60118}, {32971, 60209}, {32974, 60146}, {38071, 54845}, {47352, 53101}, {59373, 60200}

X(60648) = orthology center of ABC and bicevian chordal triangle of X(2) and the isogonal conjugate of X(55682)
X(60648) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(67), X(47352)}}, {{A, B, C, X(193), X(597)}}, {{A, B, C, X(458), X(15692)}}, {{A, B, C, X(547), X(37174)}}, {{A, B, C, X(1992), X(51171)}}, {{A, B, C, X(3618), X(11160)}}, {{A, B, C, X(5032), X(41909)}}, {{A, B, C, X(11741), X(30541)}}, {{A, B, C, X(22247), X(52450)}}, {{A, B, C, X(30535), X(44731)}}, {{A, B, C, X(30537), X(47735)}}, {{A, B, C, X(46936), X(52282)}}, {{A, B, C, X(52281), X(55864)}}

X(60649) = X(2)X(55824)∩X(262)X(548)

Barycentrics    (6*(a^2+b^2)-c^2)*(6*a^2-b^2+6*c^2) : :

X(60649) lies on the Kiepert hyperbola and on these lines: {2, 55824}, {3, 54920}, {4, 55706}, {5, 60335}, {6, 60250}, {76, 32455}, {98, 5072}, {262, 548}, {316, 60647}, {381, 54934}, {549, 54645}, {597, 54493}, {1657, 60142}, {1916, 14032}, {2996, 7878}, {3407, 33289}, {3526, 53108}, {3534, 54734}, {3618, 18844}, {3627, 14488}, {3628, 11668}, {3843, 60132}, {3850, 53100}, {5055, 54644}, {5066, 54851}, {5286, 60625}, {5395, 7918}, {6144, 60640}, {7745, 60239}, {7770, 60210}, {7803, 53101}, {7812, 60131}, {7827, 32532}, {7850, 10159}, {7859, 54616}, {7860, 60182}, {7894, 60636}, {7937, 60100}, {8370, 60626}, {10304, 54522}, {14458, 23046}, {14484, 49140}, {14492, 15684}, {15022, 54921}, {15706, 60192}, {15712, 60332}, {21735, 60330}, {33703, 52519}, {38335, 54717}, {43527, 53489}, {46333, 60127}

X(60649) = orthology center of ABC and bicevian chordal triangle of X(2) and the isogonal conjugate of X(55689)
X(60649) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(55706)}}, {{A, B, C, X(6), X(32455)}}, {{A, B, C, X(297), X(5072)}}, {{A, B, C, X(419), X(14032)}}, {{A, B, C, X(458), X(548)}}, {{A, B, C, X(5117), X(33289)}}, {{A, B, C, X(7850), X(44142)}}, {{A, B, C, X(11331), X(23046)}}, {{A, B, C, X(13606), X(14621)}}, {{A, B, C, X(15684), X(52289)}}, {{A, B, C, X(30496), X(46123)}}, {{A, B, C, X(34412), X(39289)}}, {{A, B, C, X(49140), X(52288)}}, {{A, B, C, X(54124), X(57896)}}

X(60650) = X(6)X(60625)∩X(20)X(60330)

Barycentrics    (17*(a^2+b^2)-7*c^2)*(17*a^2-7*b^2+17*c^2) : :

X(60650) lies on the Kiepert hyperbola and on these lines: {6, 60625}, {20, 60330}, {262, 15683}, {381, 60322}, {549, 10155}, {597, 18845}, {1992, 43681}, {3091, 60337}, {3146, 60142}, {3522, 60332}, {3534, 54523}, {3543, 52519}, {3832, 53100}, {3839, 54845}, {5032, 60635}, {5055, 53103}, {5066, 60185}, {5068, 60334}, {5485, 51170}, {7486, 60123}, {7607, 15022}, {7608, 15717}, {7812, 60640}, {8370, 60636}, {10303, 53098}, {10304, 14494}, {11160, 60639}, {11317, 60631}, {14488, 50687}, {14930, 60271}, {15640, 60127}, {20080, 60628}, {32895, 60262}, {32979, 43676}, {32982, 53102}, {33287, 43528}, {33699, 54707}, {50692, 60118}, {50693, 53099}, {51171, 54476}, {53489, 60281}, {59373, 60113}

X(60650) = orthology center of ABC and bicevian chordal triangle of X(2) and the isogonal conjugate of X(55697)
X(60650) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(66), X(597)}}, {{A, B, C, X(458), X(15683)}}, {{A, B, C, X(1992), X(51170)}}, {{A, B, C, X(11160), X(17040)}}, {{A, B, C, X(14248), X(34572)}}, {{A, B, C, X(14930), X(44367)}}, {{A, B, C, X(15022), X(52282)}}, {{A, B, C, X(15717), X(52281)}}, {{A, B, C, X(30535), X(43713)}}

X(60651) = X(2)X(3)∩X(147)X(1350)

Barycentrics    2*a^8-b^8+b^6*c^2+b^2*c^6-c^8+4*a^6*(b^2+c^2)-a^4*(3*b^4+b^2*c^2+3*c^4)-2*a^2*(b^6+2*b^4*c^2+2*b^2*c^4+c^6) : :
X(60651) = -2*X[5188]+X[7811], -X[7893]+4*X[9821], -5*X[7904]+2*X[9873], -X[14458]+3*X[22712]

X(60651) lies on these lines: {2, 3}, {98, 48898}, {114, 48885}, {147, 1350}, {183, 48905}, {262, 29317}, {325, 48881}, {385, 46264}, {511, 7837}, {516, 49563}, {538, 34624}, {542, 33706}, {754, 9764}, {1503, 6194}, {2794, 9772}, {3098, 3314}, {3329, 31670}, {3818, 16986}, {5092, 7875}, {5188, 7811}, {5306, 44882}, {5309, 12203}, {5987, 12121}, {7757, 54222}, {7766, 48906}, {7777, 48880}, {7779, 33878}, {7799, 30270}, {7802, 51373}, {7806, 48892}, {7868, 55646}, {7893, 9821}, {7904, 9873}, {8667, 11177}, {8721, 32833}, {8725, 14880}, {9300, 29181}, {9744, 48873}, {9751, 38317}, {9774, 19924}, {11174, 48910}, {11179, 35431}, {12122, 54393}, {14458, 22712}, {14492, 48901}, {14614, 43273}, {14931, 38730}, {15072, 55005}, {15819, 29323}, {17004, 48891}, {19570, 39646}, {35021, 60175}, {39750, 56980}, {39899, 50248}, {43461, 48920}, {48872, 59236}, {48879, 58851}, {50977, 55178}

X(60651) = midpoint of X(i) and X(j) for these {i,j}: {33706, 55177}
X(60651) = reflection of X(i) in X(j) for these {i,j}: {3543, 8370}, {7811, 5188}, {7833, 376}, {9863, 7811}
X(60651) = pole of line {185, 7876} with respect to the Jerabek hyperbola
X(60651) = orthology center of the bicevian chordal triangle of X(2) and X(76) and ABC
X(60651) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1105), X(7876)}}, {{A, B, C, X(1294), X(55008)}}, {{A, B, C, X(7470), X(60122)}}, {{A, B, C, X(11331), X(42006)}}, {{A, B, C, X(15740), X(16898)}}, {{A, B, C, X(21513), X(40801)}}, {{A, B, C, X(52289), X(60129)}}
X(60651) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 4, 7876}, {30, 376, 7833}, {30, 8370, 3543}, {2043, 2044, 7470}, {5092, 9993, 7875}, {33706, 55177, 542}

X(60652) = X(2)X(3)∩X(147)X(14810)

Barycentrics    5*a^8-b^8+b^6*c^2+b^2*c^6-c^8+7*a^6*(b^2+c^2)-a^2*(b^2+c^2)*(5*b^4+8*b^2*c^2+5*c^4)-a^4*(6*b^4+7*b^2*c^2+6*c^4) : :
X(60652) = -3*X[9751]+X[14492]

X(60652) lies on circumconic {{A, B, C, X(1297), X(21513)}} and on these lines: {2, 3}, {98, 33751}, {147, 14810}, {542, 55178}, {1350, 7837}, {3098, 7779}, {3314, 55646}, {3329, 48881}, {3818, 60728}, {5984, 37671}, {5987, 38726}, {7788, 31884}, {7868, 55656}, {7875, 55676}, {9300, 59236}, {9751, 14492}, {9764, 47101}, {9772, 38742}, {9774, 41136}, {9993, 55672}, {10335, 25406}, {12203, 19570}, {14458, 48898}, {14931, 38736}, {16986, 48905}, {33706, 44367}, {41624, 50965}, {43460, 55653}, {48906, 50248}, {50977, 55177}

X(60652) = orthology center of the bicevian chordal triangle of X(2) and X(83) and ABC
X(60652) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 7892, 15717}

X(60653) = X(2)X(3)∩X(99)X(19905)

Barycentrics    2*a^8-12*a^6*(b^2+c^2)+8*a^2*b^2*c^2*(b^2+c^2)-(b^2-c^2)^2*(b^4-b^2*c^2+c^4)+11*a^4*(b^4+b^2*c^2+c^4) : :
X(60653) = X[6194]+X[32480], 2*X[7810]+X[11257], -X[7812]+4*X[13334], X[7893]+8*X[32516], -X[9863]+4*X[34510], X[9939]+5*X[32522], -X[34733]+4*X[44562]

X(60653) lies on circumconic {{A, B, C, X(11676), X(57822)}} and on these lines: {2, 3}, {99, 19905}, {182, 51224}, {183, 12243}, {511, 52691}, {524, 7709}, {542, 22677}, {543, 11167}, {597, 10788}, {2794, 9774}, {3314, 8724}, {3849, 21163}, {3972, 10168}, {5171, 7827}, {6054, 7761}, {6055, 7771}, {6194, 32480}, {7610, 14651}, {7612, 55823}, {7619, 46941}, {7757, 52996}, {7810, 11257}, {7812, 13334}, {7831, 11178}, {7893, 32516}, {8182, 21445}, {8719, 21358}, {9862, 43273}, {9863, 34510}, {9939, 32522}, {10519, 53142}, {11163, 52771}, {11170, 54509}, {11171, 22503}, {11179, 14907}, {14494, 55794}, {15993, 54169}, {17004, 49102}, {19911, 21166}, {19924, 22676}, {22521, 59373}, {31173, 43461}, {34733, 44562}, {39656, 47352}, {41146, 51737}, {54041, 55005}, {54903, 60187}

X(60653) = midpoint of X(i) and X(j) for these {i,j}: {6194, 32480}
X(60653) = inverse of X(37946) in 2nd Brocard circle
X(60653) = orthology center of the bicevian chordal triangle of X(2) and X(262) and ABC
X(60653) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 376, 11676}, {549, 15980, 2}

X(60654) = X(2)X(3)∩X(147)X(599)

Barycentrics    2*a^8+6*a^6*(b^2+c^2)-10*a^2*b^2*c^2*(b^2+c^2)-(b^2-c^2)^2*(b^4-b^2*c^2+c^4)-7*a^4*(b^4+b^2*c^2+c^4) : :
X(60654) = X[598]+X[22676], 2*X[5188]+X[7812], -4*X[7810]+X[9863], X[7837]+2*X[33706], 5*X[7921]+4*X[9821], 2*X[9466]+X[34624], -2*X[14762]+X[22682], -2*X[21163]+X[52691]

X(60654) lies on circumconic {{A, B, C, X(5999), X(57822)}} and on these lines: {2, 3}, {147, 599}, {183, 11177}, {262, 19924}, {325, 54169}, {385, 11179}, {524, 6194}, {542, 8592}, {598, 22676}, {1350, 11163}, {2794, 9743}, {3098, 7777}, {3314, 6054}, {3329, 20423}, {3815, 50965}, {5092, 7806}, {5188, 7812}, {5306, 39560}, {5569, 9877}, {6055, 17004}, {7710, 21356}, {7736, 54170}, {7766, 50979}, {7774, 50967}, {7792, 50983}, {7810, 9863}, {7811, 51373}, {7827, 37479}, {7837, 33706}, {7840, 9744}, {7875, 10168}, {7920, 12054}, {7921, 9821}, {8719, 11164}, {8722, 51224}, {9300, 44453}, {9466, 34624}, {9753, 38064}, {9759, 15055}, {10033, 29012}, {11168, 44882}, {11174, 54131}, {11178, 16986}, {11180, 16990}, {11184, 31884}, {11645, 15819}, {14762, 22682}, {14810, 43461}, {17508, 38227}, {20791, 55005}, {21163, 52691}, {22329, 51737}, {37665, 51028}, {50971, 58446}

X(60654) = midpoint of X(i) and X(j) for these {i,j}: {598, 22676}, {9774, 22712}
X(60654) = reflection of X(i) in X(j) for these {i,j}: {22682, 14762}, {52691, 21163}
X(60654) = orthology center of the bicevian chordal triangle of X(2) and X(598) and ABC
X(60654) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 376, 5999}, {183, 43273, 11177}, {549, 1513, 2}, {9774, 22712, 542}

X(60655) = X(2)X(3)∩X(141)X(13812)

Barycentrics    3*a^2*(a^4-(b^2+c^2)^2)+2*(4*a^4+(b^2-c^2)^2-5*a^2*(b^2+c^2))*S : :

X(60655) lies on these lines: {2, 3}, {141, 13812}, {485, 7690}, {488, 32837}, {492, 12042}, {542, 55041}, {1327, 12124}, {1503, 13692}, {2794, 9757}, {6055, 9894}, {6200, 21843}, {6221, 44595}, {6396, 31463}, {6398, 31403}, {6561, 50721}, {8252, 49115}, {9300, 39679}, {9732, 52045}, {9733, 32787}, {11179, 41490}, {11645, 49786}, {12017, 35256}, {12257, 32810}, {12305, 13846}, {12974, 53130}, {13088, 32419}, {13638, 35002}, {13708, 32421}, {13794, 32805}, {13836, 42225}, {19053, 45411}, {19054, 45488}, {26361, 45375}, {26516, 45489}, {32788, 43119}, {32809, 33370}, {32811, 48773}, {33878, 35255}, {35822, 45498}, {35874, 43619}, {41491, 54173}, {43118, 52046}, {43141, 53131}, {50977, 55040}

X(60655) = midpoint of X(i) and X(j) for these {i,j}: {1327, 12124}, {12257, 32810}, {12305, 13846}
X(60655) = reflection of X(i) in X(j) for these {i,j}: {13846, 49104}, {53130, 12974}
X(60655) = orthology center of the bicevian chordal triangle of X(2) and X(1327) and ABC
X(60655) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {15765, 18585, 11315}

X(60656) = X(2)X(3)∩X(141)X(13692)

Barycentrics    3*a^2*(a^4-(b^2+c^2)^2)-2*(4*a^4+(b^2-c^2)^2-5*a^2*(b^2+c^2))*S : :

X(60656) lies on these lines: {2, 3}, {141, 13692}, {486, 7692}, {487, 32837}, {491, 12042}, {542, 55040}, {1328, 12123}, {1503, 13812}, {2794, 9758}, {6055, 9892}, {6396, 21843}, {6398, 44596}, {6560, 50722}, {8253, 49114}, {9300, 39648}, {9732, 32788}, {9733, 52046}, {11179, 41491}, {11645, 49787}, {12017, 35255}, {12256, 32811}, {12306, 13847}, {12975, 53131}, {13087, 32421}, {13674, 32806}, {13713, 42226}, {13758, 35002}, {13828, 32419}, {19053, 45489}, {19054, 45410}, {26362, 45376}, {26521, 45488}, {32787, 43118}, {32808, 33371}, {32810, 48772}, {33878, 35256}, {35823, 45499}, {35873, 43619}, {41490, 54173}, {43119, 52045}, {43144, 53130}, {50977, 55041}

X(60656) = midpoint of X(i) and X(j) for these {i,j}: {1328, 12123}, {12256, 32811}, {12306, 13847}
X(60656) = reflection of X(i) in X(j) for these {i,j}: {13847, 49103}, {53131, 12975}
X(60656) = orthology center of the bicevian chordal triangle of X(2) and X(1328) and ABC
X(60656) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {15765, 18585, 11316}

X(60657) = X(2)X(3)∩X(98)X(60185)

Barycentrics    a^8-22*a^6*(b^2+c^2)-10*a^2*(b^2-c^2)^2*(b^2+c^2)+4*a^4*(6*b^4+b^2*c^2+6*c^4)+(b^2-c^2)^2*(7*b^4-2*b^2*c^2+7*c^4) : :

X(60657) lies on these lines: {2, 3}, {98, 60185}, {230, 39874}, {262, 54523}, {1184, 15032}, {1503, 7612}, {1611, 11456}, {5306, 9752}, {5480, 14494}, {5969, 54978}, {6036, 14927}, {6721, 48873}, {7607, 54612}, {7608, 54707}, {7710, 38227}, {9742, 34380}, {9754, 53015}, {10155, 14492}, {10753, 50992}, {11180, 13468}, {14458, 53103}, {14651, 15428}, {31670, 34803}, {40178, 54500}, {44381, 48905}, {60175, 60322}

X(60657) = pole of line {523, 47463} with respect to the orthoptic circle of the Steiner inellipse
X(60657) = orthology center of the bicevian chordal triangle of X(2) and X(2996) and ABC
X(60657) = intersection, other than A, B, C, of circumconics {{A, B, C, X(297), X(60185)}}, {{A, B, C, X(458), X(54523)}}, {{A, B, C, X(10155), X(52289)}}, {{A, B, C, X(11331), X(53103)}}, {{A, B, C, X(32971), X(54763)}}, {{A, B, C, X(32974), X(54660)}}, {{A, B, C, X(32979), X(60121)}}, {{A, B, C, X(32982), X(60122)}}, {{A, B, C, X(37174), X(60150)}}, {{A, B, C, X(52281), X(54707)}}, {{A, B, C, X(52282), X(54612)}}
X(60657) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {376, 3545, 7841}, {383, 1080, 3146}, {6811, 6813, 3522}

X(60658) = X(2)X(3)∩X(147)X(11160)

Barycentrics    5*a^8+24*a^6*(b^2+c^2)-16*a^2*b^2*c^2*(b^2+c^2)-(b^2-c^2)^2*(7*b^4+2*b^2*c^2+7*c^4)-2*a^4*(11*b^4+2*b^2*c^2+11*c^4) : :

X(60658) lies on these lines: {2, 3}, {147, 11160}, {183, 51023}, {325, 54170}, {524, 7710}, {542, 9740}, {2777, 9759}, {2794, 9877}, {3424, 11167}, {3815, 51024}, {5304, 11179}, {5485, 15428}, {6054, 37668}, {7610, 53015}, {7615, 46034}, {7694, 23334}, {7735, 43273}, {7736, 54131}, {7774, 51028}, {7778, 50965}, {7840, 54174}, {9742, 41136}, {9744, 54132}, {9748, 59373}, {9753, 9774}, {11163, 51212}, {11168, 36990}, {11177, 37667}, {11180, 15589}, {11184, 29181}, {11580, 35237}, {14484, 54509}, {14927, 23055}, {20423, 37665}, {20481, 33534}, {37689, 38010}, {37690, 48881}, {42850, 47353}, {51022, 58446}, {54519, 60187}

X(60658) = midpoint of X(i) and X(j) for these {i,j}: {5485, 15428}
X(60658) = reflection of X(i) in X(j) for these {i,j}: {23334, 7694}, {46034, 7615}, {53015, 7610}
X(60658) = orthology center of the bicevian chordal triangle of X(2) and X(5485) and ABC
X(60658) = intersection, other than A, B, C, of circumconics {{A, B, C, X(5077), X(18850)}}, {{A, B, C, X(11167), X(52283)}}, {{A, B, C, X(52288), X(54509)}}
X(60658) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15683, 5999}, {4, 376, 5077}, {376, 1513, 2}, {5077, 11288, 8359}, {6054, 50967, 37668}

X(60659) = X(2)X(3)∩X(39)X(10357)

Barycentrics    a^8+b^8-b^6*c^2-b^2*c^6+c^8+5*a^6*(b^2+c^2)-a^2*(b^2+c^2)*(b^4+10*b^2*c^2+c^4)-a^4*(6*b^4+11*b^2*c^2+6*c^4) : :
X(60659) = X[2896]+2*X[12054]

X(60659) lies on these lines: {2, 3}, {39, 10357}, {182, 7811}, {538, 13086}, {542, 31168}, {2782, 9302}, {2794, 9751}, {2896, 12054}, {4045, 43453}, {5092, 7831}, {5309, 22712}, {5476, 34615}, {5890, 52658}, {5892, 33873}, {7709, 32833}, {7739, 12251}, {7757, 50977}, {7799, 13334}, {7865, 37479}, {7880, 21163}, {9466, 12243}, {10168, 12150}, {10796, 54724}, {11178, 34624}, {11179, 34623}, {12122, 14492}, {13188, 39091}, {14651, 15819}, {19570, 49111}, {22521, 38110}, {22676, 38317}, {34236, 36987}, {35431, 59373}, {38064, 39750}, {52997, 54173}

X(60659) = midpoint of X(i) and X(j) for these {i,j}: {12122, 14492}
X(60659) = orthology center of the bicevian chordal triangle of X(2) and X(11606) and ABC
X(60659) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 7876, 4}, {5092, 7831, 9862}

X(60660) = X(2)X(3)∩X(16)X(43273)

Barycentrics    (a^2+b^2+c^2)*(2*a^4-a^2*b^2-b^4-a^2*c^2+2*b^2*c^2-c^4)-3*sqrt(3)*a^2*(-a^2+b^2+c^2)*S : :

X(60660) lies on these lines: {2, 3}, {15, 54131}, {16, 43273}, {187, 42154}, {530, 11165}, {574, 42155}, {599, 14538}, {1350, 5464}, {1384, 10654}, {2482, 5473}, {2794, 9760}, {5024, 10653}, {5463, 47353}, {7776, 9989}, {8588, 42096}, {8589, 42097}, {8724, 48656}, {9736, 11645}, {9749, 11184}, {9761, 41022}, {9886, 41023}, {10645, 48910}, {10646, 48905}, {11178, 36755}, {11179, 11486}, {11180, 52194}, {11480, 51024}, {11485, 20423}, {14981, 35751}, {15655, 42085}, {16942, 42940}, {18860, 50858}, {21158, 53023}, {21159, 59411}, {21163, 22694}, {25154, 42128}, {25164, 42126}, {31670, 42116}, {36761, 42035}, {40922, 41119}, {42115, 46264}, {42974, 47857}, {50967, 52193}, {54569, 55950}

X(60660) = midpoint of X(i) and X(j) for these {i,j}: {36761, 42035}
X(60660) = orthology center of the bicevian chordal triangle of X(2) and X(42035) and ABC
X(60660) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {376, 383, 11295}, {11296, 13860, 381}

X(60661) = X(2)X(3)∩X(15)X(43273)

Barycentrics    (a^2+b^2+c^2)*(2*a^4-a^2*b^2-b^4-a^2*c^2+2*b^2*c^2-c^4)+3*sqrt(3)*a^2*(-a^2+b^2+c^2)*S : :

X(60661) lies on these lines: {2, 3}, {15, 43273}, {16, 54131}, {187, 42155}, {531, 11165}, {542, 36775}, {574, 42154}, {599, 14539}, {1350, 5463}, {1384, 10653}, {2482, 5474}, {2794, 9762}, {5024, 10654}, {5464, 47353}, {7776, 9988}, {8588, 42097}, {8589, 42096}, {8724, 48655}, {9735, 11645}, {9750, 11184}, {9763, 41023}, {9885, 41022}, {10645, 48905}, {10646, 48910}, {11178, 36756}, {11179, 11485}, {11180, 52193}, {11481, 51024}, {11486, 20423}, {14981, 36329}, {15655, 42086}, {16943, 42941}, {18860, 50855}, {21158, 59411}, {21159, 53023}, {21163, 22693}, {25154, 42127}, {25164, 42125}, {31670, 42115}, {40921, 41120}, {41458, 42036}, {42116, 46264}, {42975, 47858}, {50967, 52194}, {54570, 55951}

X(60661) = midpoint of X(i) and X(j) for these {i,j}: {41458, 42036}
X(60661) = orthology center of the bicevian chordal triangle of X(2) and X(42036) and ABC
X(60661) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {376, 1080, 11296}, {1080, 11296, 381}

X(60662) = BICEVIAN CHORDAL PERSPECTOR OF X(1) AND X(4)

Barycentrics    a*(a-b-c)*(a*b*(a+b)^2+2*(a+b)*(a^2+b^2)*c-(a^2+a*b+b^2)*c^2-2*(a+b)*c^3+c^4)*(b*(b-2*c)*(b-c)*(b+c)+a^3*(2*b+c)-a*(b-c)*(b+c)*(2*b+c)+a^2*(-b^2+2*b*c+2*c^2)) : :

X(60662) lies on the Feuerbach hyperbola and on these lines: {1, 851}, {4, 2650}, {21, 1936}, {65, 1937}, {73, 17097}, {84, 52524}, {90, 1046}, {104, 54310}, {896, 55918}, {941, 2294}, {943, 59305}, {1172, 2202}, {1745, 17098}, {1896, 40950}, {2335, 17452}, {2635, 55924}, {2648, 56904}, {7162, 59311}

X(60662) = isogonal conjugate of X(60682)
X(60662) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 60682}, {3, 60681}, {6, 60705}, {65, 51290}, {73, 1982}, {77, 60712}
X(60662) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 60682}, {9, 60705}, {36103, 60681}, {40602, 51290}
X(60662) = pole of line {51290, 60682} with respect to the Stammler hyperbola
X(60662) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(29), X(65)}}, {{A, B, C, X(73), X(283)}}, {{A, B, C, X(81), X(17947)}}, {{A, B, C, X(225), X(2654)}}, {{A, B, C, X(284), X(53114)}}, {{A, B, C, X(1046), X(3193)}}, {{A, B, C, X(1243), X(36123)}}, {{A, B, C, X(1425), X(2660)}}, {{A, B, C, X(2183), X(54310)}}, {{A, B, C, X(2294), X(6734)}}, {{A, B, C, X(2316), X(60078)}}, {{A, B, C, X(2990), X(54120)}}, {{A, B, C, X(3072), X(24474)}}, {{A, B, C, X(4674), X(7110)}}, {{A, B, C, X(13476), X(51565)}}, {{A, B, C, X(37530), X(37625)}}, {{A, B, C, X(39739), X(56094)}}, {{A, B, C, X(40442), X(57672)}}, {{A, B, C, X(44426), X(54933)}}, {{A, B, C, X(56136), X(56225)}}
X(60662) = barycentric quotient X(i)/X(j) for these (i, j): {1, 60705}, {6, 60682}, {19, 60681}, {284, 51290}, {607, 60712}, {1172, 1982}

X(60663) = BICEVIAN CHORDAL PERSPECTOR OF X(1) AND X(43)

Barycentrics    a^2*(a*b-(a+b)*c-2*c^2)*(-(b*c)+a*(b+c))*(a*(b-c)+b*(2*b+c)) : :

X(60663) lies on these lines: {1, 1575}, {2, 55997}, {6, 727}, {42, 2162}, {43, 17459}, {2176, 20971}, {3210, 27494}, {3736, 51449}, {4360, 56247}, {8025, 55971}, {16557, 42043}, {17318, 31625}, {33296, 53675}, {34475, 60109}, {38832, 53145}, {53641, 53648}

X(60663) = isogonal conjugate of X(40720)
X(60663) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 40720}, {2, 40753}, {87, 4393}, {330, 16468}, {932, 4785}, {2162, 30963}, {4598, 4782}, {6384, 21793}, {7121, 10009}, {14621, 40783}, {34476, 60244}
X(60663) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 40720}, {32664, 40753}, {40598, 10009}
X(60663) = X(i)-Ceva conjugate of X(j) for these {i, j}: {40735, 60665}
X(60663) = X(i)-cross conjugate of X(j) for these {i, j}: {40780, 60665}
X(60663) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(43)}}, {{A, B, C, X(2), X(16604)}}, {{A, B, C, X(6), X(192)}}, {{A, B, C, X(42), X(20691)}}, {{A, B, C, X(291), X(6376)}}, {{A, B, C, X(1002), X(4083)}}, {{A, B, C, X(2276), X(19584)}}, {{A, B, C, X(3208), X(4050)}}, {{A, B, C, X(3240), X(52895)}}, {{A, B, C, X(3736), X(3795)}}, {{A, B, C, X(17318), X(21762)}}, {{A, B, C, X(27538), X(56154)}}, {{A, B, C, X(31008), X(39966)}}, {{A, B, C, X(39972), X(53676)}}, {{A, B, C, X(40780), X(52654)}}
X(60663) = barycentric product X(i)*X(j) for these (i, j): {1, 40780}, {43, 52654}, {192, 60665}, {2176, 27494}, {3835, 43077}, {3971, 51449}, {20691, 55971}, {20979, 53648}, {34475, 38832}, {40735, 6376}, {40756, 984}
X(60663) = barycentric quotient X(i)/X(j) for these (i, j): {6, 40720}, {31, 40753}, {43, 30963}, {192, 10009}, {869, 40783}, {2176, 4393}, {2209, 16468}, {8640, 4782}, {20691, 59212}, {20979, 4785}, {23643, 25376}, {27494, 6383}, {40735, 87}, {40756, 870}, {40780, 75}, {43077, 4598}, {50491, 4806}, {52654, 6384}, {60665, 330}

X(60664) = BICEVIAN CHORDAL PERSPECTOR OF X(1) AND X(75)

Barycentrics    a*(a^2*b^2+2*(a^2+b^2)*c^2+c^4)*(b^4+2*b^2*c^2+a^2*(2*b^2+c^2)) : :

X(60664) lies on these lines: {1, 2236}, {10, 33891}, {19, 16556}, {37, 56805}, {38, 1581}, {75, 17457}, {82, 1580}, {759, 43357}, {982, 16587}, {1740, 23051}, {1926, 18833}, {2186, 17471}, {2234, 55930}, {2244, 55927}, {3116, 51844}, {18827, 42055}, {18832, 39731}, {40747, 60672}

X(60664) = isogonal conjugate of X(60686)
X(60664) = isotomic conjugate of X(60683)
X(60664) = trilinear pole of line {661, 3808}
X(60664) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 60686}, {2, 12212}, {6, 3329}, {25, 60702}, {31, 60683}, {32, 60707}, {38, 51312}, {99, 14318}, {141, 41295}, {237, 39685}, {251, 10007}, {3051, 59249}
X(60664) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 60683}, {3, 60686}, {9, 3329}, {6376, 60707}, {6505, 60702}, {32664, 12212}, {38986, 14318}, {40585, 10007}
X(60664) = pole of line {60683, 60686} with respect to the Wallace hyperbola
X(60664) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(2), X(982)}}, {{A, B, C, X(38), X(661)}}, {{A, B, C, X(291), X(40763)}}, {{A, B, C, X(756), X(42055)}}, {{A, B, C, X(870), X(30663)}}, {{A, B, C, X(984), X(19222)}}, {{A, B, C, X(1002), X(45782)}}, {{A, B, C, X(1244), X(45989)}}, {{A, B, C, X(1740), X(39731)}}, {{A, B, C, X(1930), X(17445)}}, {{A, B, C, X(1964), X(17457)}}, {{A, B, C, X(2329), X(43696)}}, {{A, B, C, X(3862), X(25426)}}, {{A, B, C, X(3961), X(56245)}}, {{A, B, C, X(7146), X(27494)}}, {{A, B, C, X(7166), X(39798)}}, {{A, B, C, X(7194), X(49612)}}, {{A, B, C, X(16556), X(34055)}}, {{A, B, C, X(16603), X(51836)}}, {{A, B, C, X(30701), X(56332)}}, {{A, B, C, X(39977), X(43747)}}, {{A, B, C, X(49563), X(52654)}}, {{A, B, C, X(56329), X(57925)}}, {{A, B, C, X(56357), X(57923)}}
X(60664) = barycentric product X(i)*X(j) for these (i, j): {1, 42006}, {561, 60672}, {1577, 43357}, {3112, 59262}, {18833, 59273}, {39684, 46273}, {60667, 75}
X(60664) = barycentric quotient X(i)/X(j) for these (i, j): {1, 3329}, {2, 60683}, {6, 60686}, {31, 12212}, {38, 10007}, {63, 60702}, {75, 60707}, {251, 51312}, {798, 14318}, {1821, 39685}, {3112, 59249}, {39684, 1755}, {42006, 75}, {43357, 662}, {46289, 41295}, {59262, 38}, {59273, 1964}, {60600, 19591}, {60667, 1}, {60672, 31}

X(60665) = BICEVIAN CHORDAL PERSPECTOR OF X(1) AND X(87)

Barycentrics    a^2*(a*b-(a+b)*c-2*c^2)*(a*(b-c)+b*(2*b+c)) : :

X(60665) lies on cubic K1017 and on these lines: {1, 1575}, {2, 3226}, {6, 3009}, {9, 36598}, {37, 87}, {44, 55933}, {45, 37129}, {55, 17962}, {56, 16969}, {58, 2176}, {86, 192}, {106, 574}, {213, 56343}, {292, 16515}, {594, 26077}, {649, 23355}, {869, 25426}, {870, 16826}, {937, 16968}, {979, 1107}, {984, 40789}, {1100, 39972}, {1120, 36534}, {1126, 56800}, {1438, 16524}, {2162, 21827}, {2163, 3230}, {2215, 16520}, {2279, 16514}, {2665, 25427}, {2983, 16516}, {3294, 36604}, {3445, 31477}, {4775, 23892}, {5283, 39748}, {7312, 24423}, {15668, 55975}, {16519, 56220}, {16672, 55919}, {16884, 40433}, {17084, 24654}, {17448, 39969}, {21010, 21793}, {21769, 57399}, {21785, 57400}, {23493, 53146}, {23538, 40148}, {24275, 34475}, {28366, 56328}, {40750, 40756}

X(60665) = isogonal conjugate of X(4393)
X(60665) = isotomic conjugate of X(10009)
X(60665) = trilinear pole of line {649, 6373}
X(60665) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 4393}, {2, 16468}, {6, 30963}, {31, 10009}, {43, 40720}, {58, 59212}, {72, 31912}, {75, 21793}, {81, 3993}, {86, 21904}, {88, 4759}, {92, 23095}, {100, 4785}, {190, 4782}, {192, 40753}, {321, 34476}, {662, 4806}, {870, 40733}, {985, 27481}, {1255, 4991}, {3257, 45314}, {3795, 14621}, {21010, 56664}, {40783, 52136}
X(60665) = X(i)-vertex conjugate of X(j) for these {i, j}: {40746, 40746}
X(60665) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 10009}, {3, 4393}, {9, 30963}, {10, 59212}, {206, 21793}, {1084, 4806}, {3789, 27481}, {8054, 4785}, {21250, 25376}, {22391, 23095}, {32664, 16468}, {40586, 3993}, {40600, 21904}, {55053, 4782}, {55055, 45314}
X(60665) = X(i)-Ceva conjugate of X(j) for these {i, j}: {40735, 60663}, {51449, 40735}, {55971, 52654}
X(60665) = X(i)-cross conjugate of X(j) for these {i, j}: {2276, 6}, {40780, 60663}
X(60665) = pole of line {4393, 21793} with respect to the Stammler hyperbola
X(60665) = pole of line {4393, 10009} with respect to the Wallace hyperbola
X(60665) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6)}}, {{A, B, C, X(2), X(649)}}, {{A, B, C, X(3), X(29080)}}, {{A, B, C, X(9), X(4050)}}, {{A, B, C, X(31), X(1255)}}, {{A, B, C, X(37), X(192)}}, {{A, B, C, X(42), X(27789)}}, {{A, B, C, X(45), X(3230)}}, {{A, B, C, X(55), X(17735)}}, {{A, B, C, X(75), X(46032)}}, {{A, B, C, X(81), X(39966)}}, {{A, B, C, X(213), X(16777)}}, {{A, B, C, X(238), X(16515)}}, {{A, B, C, X(330), X(16604)}}, {{A, B, C, X(405), X(16520)}}, {{A, B, C, X(513), X(41527)}}, {{A, B, C, X(518), X(16524)}}, {{A, B, C, X(574), X(3285)}}, {{A, B, C, X(663), X(40779)}}, {{A, B, C, X(713), X(3224)}}, {{A, B, C, X(739), X(40434)}}, {{A, B, C, X(869), X(16826)}}, {{A, B, C, X(876), X(59255)}}, {{A, B, C, X(893), X(25430)}}, {{A, B, C, X(1001), X(16514)}}, {{A, B, C, X(1002), X(28600)}}, {{A, B, C, X(1104), X(16516)}}, {{A, B, C, X(1107), X(21769)}}, {{A, B, C, X(1125), X(56800)}}, {{A, B, C, X(1149), X(36534)}}, {{A, B, C, X(1258), X(2214)}}, {{A, B, C, X(1333), X(56066)}}, {{A, B, C, X(1386), X(16523)}}, {{A, B, C, X(1459), X(43718)}}, {{A, B, C, X(1616), X(16517)}}, {{A, B, C, X(1914), X(27922)}}, {{A, B, C, X(2053), X(4876)}}, {{A, B, C, X(2160), X(39970)}}, {{A, B, C, X(2186), X(3862)}}, {{A, B, C, X(2242), X(4363)}}, {{A, B, C, X(2256), X(16968)}}, {{A, B, C, X(2276), X(3795)}}, {{A, B, C, X(2345), X(28366)}}, {{A, B, C, X(2350), X(25417)}}, {{A, B, C, X(3052), X(31477)}}, {{A, B, C, X(3223), X(55997)}}, {{A, B, C, X(3227), X(39960)}}, {{A, B, C, X(3242), X(16782)}}, {{A, B, C, X(3252), X(52127)}}, {{A, B, C, X(3731), X(36647)}}, {{A, B, C, X(4492), X(39717)}}, {{A, B, C, X(5283), X(16685)}}, {{A, B, C, X(6382), X(21040)}}, {{A, B, C, X(7033), X(40737)}}, {{A, B, C, X(7050), X(8770)}}, {{A, B, C, X(7241), X(18827)}}, {{A, B, C, X(7290), X(16518)}}, {{A, B, C, X(16483), X(16521)}}, {{A, B, C, X(16606), X(39694)}}, {{A, B, C, X(16672), X(54981)}}, {{A, B, C, X(16781), X(16973)}}, {{A, B, C, X(16884), X(20963)}}, {{A, B, C, X(17084), X(45240)}}, {{A, B, C, X(17303), X(27641)}}, {{A, B, C, X(17448), X(21785)}}, {{A, B, C, X(18268), X(32014)}}, {{A, B, C, X(20532), X(52656)}}, {{A, B, C, X(21788), X(40742)}}, {{A, B, C, X(23532), X(38247)}}, {{A, B, C, X(24661), X(33296)}}, {{A, B, C, X(26077), X(28244)}}, {{A, B, C, X(28607), X(45785)}}, {{A, B, C, X(30496), X(31359)}}, {{A, B, C, X(31308), X(59272)}}, {{A, B, C, X(32013), X(54413)}}, {{A, B, C, X(36494), X(60677)}}, {{A, B, C, X(39698), X(56162)}}, {{A, B, C, X(40418), X(56357)}}, {{A, B, C, X(40735), X(55971)}}, {{A, B, C, X(40750), X(56441)}}, {{A, B, C, X(40770), X(40834)}}, {{A, B, C, X(40775), X(50344)}}, {{A, B, C, X(51449), X(52654)}}, {{A, B, C, X(56037), X(57397)}}
X(60665) = barycentric product X(i)*X(j) for these (i, j): {1, 52654}, {10, 51449}, {37, 55971}, {42, 55947}, {321, 59192}, {330, 60663}, {27494, 6}, {34475, 58}, {40735, 75}, {40756, 45782}, {40780, 87}, {43077, 514}, {53648, 649}
X(60665) = barycentric quotient X(i)/X(j) for these (i, j): {1, 30963}, {2, 10009}, {6, 4393}, {31, 16468}, {32, 21793}, {37, 59212}, {42, 3993}, {184, 23095}, {213, 21904}, {512, 4806}, {649, 4785}, {667, 4782}, {869, 3795}, {902, 4759}, {1474, 31912}, {1960, 45314}, {2162, 40720}, {2206, 34476}, {2276, 27481}, {2308, 4991}, {7121, 40753}, {27494, 76}, {34475, 313}, {40728, 40733}, {40735, 1}, {40780, 6376}, {43077, 190}, {51449, 86}, {52654, 75}, {53648, 1978}, {55947, 310}, {55971, 274}, {59192, 81}, {60663, 192}

X(60666) = BICEVIAN CHORDAL PERSPECTOR OF X(1) AND X(105)

Barycentrics    a*(3*a^2-2*a*b+3*b^2-4*(a+b)*c+c^2)*(3*a^2+(b-3*c)*(b-c)-2*a*(2*b+c)) : :

X(60666) lies on these lines: {1, 2348}, {2, 3158}, {9, 1280}, {55, 8056}, {57, 1279}, {81, 44841}, {88, 35445}, {105, 35227}, {165, 36603}, {274, 52352}, {277, 3601}, {278, 54234}, {279, 1420}, {291, 52155}, {354, 39980}, {513, 37626}, {1001, 39959}, {1002, 7290}, {1170, 3340}, {1219, 5436}, {1477, 19604}, {3227, 31169}, {3576, 28915}, {16485, 57664}, {30701, 49466}, {31435, 56137}, {38315, 39948}

X(60666) = isogonal conjugate of X(3243)
X(60666) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 3243}, {6, 29627}, {8, 42314}, {9, 51302}, {55, 51351}, {56, 10005}, {57, 59216}, {604, 59201}
X(60666) = X(i)-vertex conjugate of X(j) for these {i, j}: {56, 57}
X(60666) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 10005}, {3, 3243}, {9, 29627}, {223, 51351}, {478, 51302}, {3161, 59201}, {5452, 59216}
X(60666) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(6), X(38316)}}, {{A, B, C, X(7), X(41441)}}, {{A, B, C, X(8), X(40154)}}, {{A, B, C, X(9), X(513)}}, {{A, B, C, X(19), X(10390)}}, {{A, B, C, X(21), X(2137)}}, {{A, B, C, X(55), X(1420)}}, {{A, B, C, X(56), X(1174)}}, {{A, B, C, X(65), X(44841)}}, {{A, B, C, X(103), X(945)}}, {{A, B, C, X(106), X(1057)}}, {{A, B, C, X(269), X(2346)}}, {{A, B, C, X(354), X(3340)}}, {{A, B, C, X(392), X(16485)}}, {{A, B, C, X(479), X(7320)}}, {{A, B, C, X(518), X(35227)}}, {{A, B, C, X(614), X(49466)}}, {{A, B, C, X(672), X(48572)}}, {{A, B, C, X(953), X(2078)}}, {{A, B, C, X(1001), X(7290)}}, {{A, B, C, X(1014), X(56028)}}, {{A, B, C, X(1036), X(1617)}}, {{A, B, C, X(1191), X(5436)}}, {{A, B, C, X(1319), X(35445)}}, {{A, B, C, X(1411), X(39393)}}, {{A, B, C, X(1419), X(58320)}}, {{A, B, C, X(1697), X(56937)}}, {{A, B, C, X(2161), X(51102)}}, {{A, B, C, X(2218), X(7091)}}, {{A, B, C, X(2279), X(2280)}}, {{A, B, C, X(2291), X(41436)}}, {{A, B, C, X(2320), X(15728)}}, {{A, B, C, X(3247), X(38315)}}, {{A, B, C, X(3660), X(7962)}}, {{A, B, C, X(3680), X(24392)}}, {{A, B, C, X(3887), X(28915)}}, {{A, B, C, X(5173), X(11518)}}, {{A, B, C, X(6598), X(55013)}}, {{A, B, C, X(7162), X(45818)}}, {{A, B, C, X(7220), X(58322)}}, {{A, B, C, X(7285), X(20615)}}, {{A, B, C, X(10426), X(43081)}}, {{A, B, C, X(16475), X(16484)}}, {{A, B, C, X(40779), X(59216)}}, {{A, B, C, X(42315), X(42318)}}, {{A, B, C, X(50839), X(55920)}}, {{A, B, C, X(59193), X(59242)}}
X(60666) = barycentric product X(i)*X(j) for these (i, j): {1, 42318}, {42315, 8}, {56088, 57}
X(60666) = barycentric quotient X(i)/X(j) for these (i, j): {1, 29627}, {6, 3243}, {8, 59201}, {9, 10005}, {55, 59216}, {56, 51302}, {57, 51351}, {604, 42314}, {42315, 7}, {42318, 75}, {56088, 312}

X(60667) = BICEVIAN CHORDAL PERSPECTOR OF X(2) AND X(6)

Barycentrics    a^2*(a^2*b^2+2*(a^2+b^2)*c^2+c^4)*(b^4+2*b^2*c^2+a^2*(2*b^2+c^2)) : :
X(60667) = -X[308]+4*X[3589], 2*X[39080]+X[39939]

X(60667) lies on cubics K423 and K422 and on these lines: {2, 732}, {6, 8623}, {25, 10329}, {37, 56805}, {39, 694}, {111, 43357}, {141, 39968}, {182, 18898}, {237, 12055}, {251, 1691}, {263, 3094}, {308, 3589}, {393, 47738}, {597, 3228}, {695, 14822}, {702, 9462}, {1383, 8627}, {1613, 39951}, {1976, 5038}, {2275, 19586}, {2998, 3618}, {3051, 3108}, {3117, 52660}, {3231, 39389}, {3329, 8842}, {5116, 21512}, {12212, 14096}, {14389, 18372}, {16081, 52289}, {17795, 56533}, {18818, 52758}, {20023, 40332}, {21513, 36213}, {32449, 60707}, {34816, 47355}, {38262, 51171}, {39080, 39939}, {46123, 51906}

X(60667) = isogonal conjugate of X(3329)
X(60667) = isotomic conjugate of X(60707)
X(60667) = trilinear pole of line {39684, 512}
X(60667) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 3329}, {2, 60686}, {6, 60683}, {19, 60702}, {31, 60707}, {75, 12212}, {82, 10007}, {141, 51312}, {799, 14318}, {1755, 39685}, {1930, 41295}, {1964, 59249}
X(60667) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 60707}, {3, 3329}, {6, 60702}, {9, 60683}, {141, 10007}, {206, 12212}, {32664, 60686}, {36899, 39685}, {38996, 14318}, {41884, 59249}
X(60667) = X(i)-cross conjugate of X(j) for these {i, j}: {59262, 42006}, {59273, 60672}
X(60667) = pole of line {3329, 10007} with respect to the Stammler hyperbola
X(60667) = pole of line {3329, 60707} with respect to the Wallace hyperbola
X(60667) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1428)}}, {{A, B, C, X(2), X(6)}}, {{A, B, C, X(3), X(50659)}}, {{A, B, C, X(4), X(17042)}}, {{A, B, C, X(32), X(13331)}}, {{A, B, C, X(39), X(83)}}, {{A, B, C, X(54), X(34130)}}, {{A, B, C, X(74), X(54724)}}, {{A, B, C, X(76), X(10014)}}, {{A, B, C, X(98), X(30499)}}, {{A, B, C, X(141), X(20965)}}, {{A, B, C, X(182), X(262)}}, {{A, B, C, X(187), X(44672)}}, {{A, B, C, X(232), X(42330)}}, {{A, B, C, X(237), X(52289)}}, {{A, B, C, X(420), X(21513)}}, {{A, B, C, X(511), X(5038)}}, {{A, B, C, X(575), X(5111)}}, {{A, B, C, X(592), X(3399)}}, {{A, B, C, X(597), X(3231)}}, {{A, B, C, X(598), X(30495)}}, {{A, B, C, X(671), X(41440)}}, {{A, B, C, X(702), X(9009)}}, {{A, B, C, X(729), X(60238)}}, {{A, B, C, X(850), X(33873)}}, {{A, B, C, X(1176), X(10329)}}, {{A, B, C, X(1469), X(52654)}}, {{A, B, C, X(1576), X(9211)}}, {{A, B, C, X(1613), X(3618)}}, {{A, B, C, X(2024), X(34870)}}, {{A, B, C, X(2162), X(39716)}}, {{A, B, C, X(2276), X(17754)}}, {{A, B, C, X(2279), X(52655)}}, {{A, B, C, X(2330), X(56547)}}, {{A, B, C, X(3051), X(3589)}}, {{A, B, C, X(3117), X(41259)}}, {{A, B, C, X(3224), X(18841)}}, {{A, B, C, X(3426), X(54826)}}, {{A, B, C, X(3455), X(54841)}}, {{A, B, C, X(3456), X(57421)}}, {{A, B, C, X(3531), X(54678)}}, {{A, B, C, X(3532), X(5013)}}, {{A, B, C, X(3613), X(18024)}}, {{A, B, C, X(3815), X(51543)}}, {{A, B, C, X(3862), X(27483)}}, {{A, B, C, X(4590), X(46278)}}, {{A, B, C, X(5034), X(13330)}}, {{A, B, C, X(5092), X(12055)}}, {{A, B, C, X(5395), X(30496)}}, {{A, B, C, X(6664), X(31630)}}, {{A, B, C, X(8041), X(17949)}}, {{A, B, C, X(8617), X(51185)}}, {{A, B, C, X(8627), X(17414)}}, {{A, B, C, X(9139), X(46296)}}, {{A, B, C, X(9292), X(60647)}}, {{A, B, C, X(9302), X(14483)}}, {{A, B, C, X(9463), X(47352)}}, {{A, B, C, X(10155), X(40803)}}, {{A, B, C, X(10159), X(27375)}}, {{A, B, C, X(11169), X(46302)}}, {{A, B, C, X(11170), X(54998)}}, {{A, B, C, X(12212), X(42288)}}, {{A, B, C, X(13622), X(55033)}}, {{A, B, C, X(14389), X(18371)}}, {{A, B, C, X(14621), X(52205)}}, {{A, B, C, X(14908), X(53024)}}, {{A, B, C, X(15321), X(20021)}}, {{A, B, C, X(17743), X(59480)}}, {{A, B, C, X(17795), X(40790)}}, {{A, B, C, X(17980), X(60129)}}, {{A, B, C, X(21001), X(51171)}}, {{A, B, C, X(21531), X(35476)}}, {{A, B, C, X(22336), X(60111)}}, {{A, B, C, X(31360), X(40162)}}, {{A, B, C, X(31622), X(42292)}}, {{A, B, C, X(34087), X(42286)}}, {{A, B, C, X(34238), X(43528)}}, {{A, B, C, X(41517), X(60098)}}, {{A, B, C, X(42287), X(43718)}}, {{A, B, C, X(42346), X(60100)}}, {{A, B, C, X(43716), X(54804)}}, {{A, B, C, X(44168), X(54621)}}, {{A, B, C, X(44557), X(54413)}}, {{A, B, C, X(44571), X(46001)}}, {{A, B, C, X(51542), X(60670)}}, {{A, B, C, X(52239), X(54840)}}, {{A, B, C, X(56179), X(56329)}}, {{A, B, C, X(56328), X(56357)}}
X(60667) = barycentric product X(i)*X(j) for these (i, j): {1, 60664}, {290, 39684}, {308, 59273}, {19222, 60600}, {42006, 6}, {43357, 523}, {59262, 83}, {60672, 76}
X(60667) = barycentric quotient X(i)/X(j) for these (i, j): {1, 60683}, {2, 60707}, {3, 60702}, {6, 3329}, {31, 60686}, {32, 12212}, {39, 10007}, {83, 59249}, {98, 39685}, {669, 14318}, {39684, 511}, {42006, 76}, {43357, 99}, {46288, 41295}, {46289, 51312}, {59262, 141}, {59273, 39}, {60600, 18906}, {60664, 75}, {60672, 6}

X(60668) = BICEVIAN CHORDAL PERSPECTOR OF X(2) AND X(8)

Barycentrics    (a-b-c)*((b-c)*c+a*(2*b+c))*(b*(-b+c)+a*(b+2*c)) : :
X(60668) = -2*X[1]+5*X[31269], X[8]+2*X[1212], -4*X[10]+X[85], X[3177]+5*X[3617], -X[3241]+4*X[44570], -X[3243]+4*X[10012], -4*X[6706]+7*X[9780]

X(60668) lies on these lines: {1, 31269}, {2, 210}, {8, 1212}, {9, 14942}, {10, 85}, {29, 7079}, {75, 4712}, {92, 1861}, {189, 53013}, {200, 333}, {257, 21677}, {312, 3717}, {341, 28660}, {390, 56088}, {519, 55954}, {765, 17335}, {1001, 60709}, {1121, 3679}, {1125, 56060}, {1220, 2279}, {1311, 8693}, {1698, 32015}, {3059, 26059}, {3177, 3617}, {3241, 44570}, {3243, 10012}, {3706, 56086}, {3751, 14828}, {3870, 40435}, {3886, 59216}, {4009, 56075}, {4113, 30711}, {4384, 39959}, {4385, 40011}, {4518, 40609}, {4678, 36605}, {4866, 14007}, {4944, 28143}, {4997, 5231}, {5220, 10025}, {5223, 40719}, {5772, 31993}, {5880, 40868}, {6557, 27538}, {6706, 9780}, {6735, 55984}, {6745, 30608}, {7174, 24600}, {8580, 40420}, {10580, 44307}, {13576, 51052}, {13727, 41229}, {15481, 51352}, {17277, 56179}, {19868, 37036}, {20173, 40967}, {27424, 44720}, {27549, 56102}, {28043, 56098}, {31359, 60677}, {33165, 40845}, {34234, 36819}, {35026, 53210}, {36905, 52156}, {37658, 40739}, {40333, 51351}, {44664, 53620}, {44798, 56164}, {51443, 55942}

X(60668) = isogonal conjugate of X(1471)
X(60668) = isotomic conjugate of X(40719)
X(60668) = trilinear pole of line {4171, 21127}
X(60668) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 1471}, {6, 5228}, {7, 60722}, {31, 40719}, {32, 60720}, {41, 42309}, {55, 59242}, {56, 1001}, {57, 2280}, {58, 42289}, {109, 4724}, {604, 4384}, {608, 23151}, {1106, 3886}, {1397, 4441}, {1400, 60721}, {1407, 37658}, {1408, 3696}, {1409, 31926}, {1412, 59207}, {1415, 4762}, {1417, 4702}, {1437, 1893}, {1461, 45755}, {2206, 60734}, {4044, 16947}, {5597, 5598}, {7053, 28044}, {28809, 52410}, {40746, 40784}, {43924, 54440}
X(60668) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 1001}, {2, 40719}, {3, 1471}, {9, 5228}, {10, 42289}, {11, 4724}, {142, 59217}, {223, 59242}, {1146, 4762}, {3160, 42309}, {3161, 4384}, {5452, 2280}, {6376, 60720}, {6552, 3886}, {6741, 4804}, {19584, 40784}, {23050, 28044}, {24771, 37658}, {35508, 45755}, {40582, 60721}, {40599, 59207}, {40603, 60734}, {52871, 4702}, {59577, 3696}
X(60668) = X(i)-Ceva conjugate of X(j) for these {i, j}: {59255, 27475}
X(60668) = X(i)-cross conjugate of X(j) for these {i, j}: {24393, 8}, {40779, 27475}
X(60668) = pole of line {390, 4517} with respect to the Feuerbach hyperbola
X(60668) = pole of line {4762, 54264} with respect to the Steiner inellipse
X(60668) = pole of line {1471, 40719} with respect to the Wallace hyperbola
X(60668) = pole of line {29571, 59255} with respect to the dual conic of Yff parabola
X(60668) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(354)}}, {{A, B, C, X(2), X(8)}}, {{A, B, C, X(4), X(3475)}}, {{A, B, C, X(7), X(11038)}}, {{A, B, C, X(9), X(75)}}, {{A, B, C, X(10), X(200)}}, {{A, B, C, X(21), X(1280)}}, {{A, B, C, X(55), X(291)}}, {{A, B, C, X(78), X(25006)}}, {{A, B, C, X(79), X(54687)}}, {{A, B, C, X(80), X(17718)}}, {{A, B, C, X(82), X(39943)}}, {{A, B, C, X(86), X(6601)}}, {{A, B, C, X(87), X(40505)}}, {{A, B, C, X(91), X(7161)}}, {{A, B, C, X(158), X(7162)}}, {{A, B, C, X(273), X(2346)}}, {{A, B, C, X(281), X(1268)}}, {{A, B, C, X(284), X(749)}}, {{A, B, C, X(294), X(1390)}}, {{A, B, C, X(307), X(3692)}}, {{A, B, C, X(318), X(3681)}}, {{A, B, C, X(346), X(5686)}}, {{A, B, C, X(390), X(10005)}}, {{A, B, C, X(461), X(14007)}}, {{A, B, C, X(519), X(5231)}}, {{A, B, C, X(650), X(7220)}}, {{A, B, C, X(751), X(2316)}}, {{A, B, C, X(903), X(34919)}}, {{A, B, C, X(943), X(57724)}}, {{A, B, C, X(960), X(16739)}}, {{A, B, C, X(984), X(19586)}}, {{A, B, C, X(996), X(56094)}}, {{A, B, C, X(1000), X(45097)}}, {{A, B, C, X(1002), X(40757)}}, {{A, B, C, X(1043), X(59760)}}, {{A, B, C, X(1067), X(60164)}}, {{A, B, C, X(1098), X(56220)}}, {{A, B, C, X(1126), X(2299)}}, {{A, B, C, X(1215), X(21677)}}, {{A, B, C, X(1222), X(24477)}}, {{A, B, C, X(1223), X(30705)}}, {{A, B, C, X(1224), X(56146)}}, {{A, B, C, X(1253), X(21039)}}, {{A, B, C, X(1265), X(57873)}}, {{A, B, C, X(2297), X(42015)}}, {{A, B, C, X(2335), X(40433)}}, {{A, B, C, X(2648), X(40401)}}, {{A, B, C, X(3177), X(31627)}}, {{A, B, C, X(3254), X(39704)}}, {{A, B, C, X(3255), X(39707)}}, {{A, B, C, X(3296), X(54712)}}, {{A, B, C, X(3679), X(4944)}}, {{A, B, C, X(3680), X(3742)}}, {{A, B, C, X(3700), X(59261)}}, {{A, B, C, X(3706), X(4673)}}, {{A, B, C, X(3740), X(19605)}}, {{A, B, C, X(3789), X(30966)}}, {{A, B, C, X(3790), X(27495)}}, {{A, B, C, X(3848), X(31509)}}, {{A, B, C, X(3870), X(6734)}}, {{A, B, C, X(3872), X(21183)}}, {{A, B, C, X(3883), X(4901)}}, {{A, B, C, X(3886), X(24393)}}, {{A, B, C, X(4009), X(52755)}}, {{A, B, C, X(4384), X(30854)}}, {{A, B, C, X(4430), X(56203)}}, {{A, B, C, X(4492), X(9365)}}, {{A, B, C, X(4661), X(52344)}}, {{A, B, C, X(4712), X(23612)}}, {{A, B, C, X(4853), X(11019)}}, {{A, B, C, X(4858), X(17335)}}, {{A, B, C, X(4876), X(56093)}}, {{A, B, C, X(4900), X(42285)}}, {{A, B, C, X(5558), X(56348)}}, {{A, B, C, X(5559), X(17728)}}, {{A, B, C, X(5560), X(54517)}}, {{A, B, C, X(6366), X(28143)}}, {{A, B, C, X(6598), X(40415)}}, {{A, B, C, X(6736), X(8580)}}, {{A, B, C, X(7045), X(56139)}}, {{A, B, C, X(7101), X(56157)}}, {{A, B, C, X(7110), X(28650)}}, {{A, B, C, X(7160), X(56330)}}, {{A, B, C, X(7218), X(8056)}}, {{A, B, C, X(7241), X(34820)}}, {{A, B, C, X(7319), X(56331)}}, {{A, B, C, X(7320), X(36620)}}, {{A, B, C, X(9311), X(34018)}}, {{A, B, C, X(9442), X(52013)}}, {{A, B, C, X(18815), X(55920)}}, {{A, B, C, X(25568), X(56026)}}, {{A, B, C, X(27475), X(40739)}}, {{A, B, C, X(27483), X(27484)}}, {{A, B, C, X(27538), X(44720)}}, {{A, B, C, X(30513), X(51567)}}, {{A, B, C, X(31169), X(37780)}}, {{A, B, C, X(31269), X(59181)}}, {{A, B, C, X(34894), X(58028)}}, {{A, B, C, X(36798), X(51055)}}, {{A, B, C, X(36905), X(50441)}}, {{A, B, C, X(36916), X(55955)}}, {{A, B, C, X(39708), X(44040)}}, {{A, B, C, X(39737), X(56232)}}, {{A, B, C, X(40430), X(56278)}}, {{A, B, C, X(40719), X(55983)}}, {{A, B, C, X(41798), X(56115)}}, {{A, B, C, X(42470), X(58001)}}, {{A, B, C, X(46897), X(56175)}}, {{A, B, C, X(52549), X(56205)}}, {{A, B, C, X(56208), X(60110)}}
X(60668) = barycentric product X(i)*X(j) for these (i, j): {57, 59260}, {314, 60677}, {341, 42290}, {1002, 312}, {1229, 59193}, {2279, 3596}, {3661, 40739}, {3700, 51563}, {3701, 42302}, {27475, 8}, {30713, 51443}, {32041, 522}, {33931, 40757}, {35519, 8693}, {37138, 4391}, {40779, 75}, {42310, 4847}, {59255, 9}, {59269, 85}, {60673, 76}
X(60668) = barycentric quotient X(i)/X(j) for these (i, j): {1, 5228}, {2, 40719}, {6, 1471}, {7, 42309}, {8, 4384}, {9, 1001}, {21, 60721}, {29, 31926}, {37, 42289}, {41, 60722}, {55, 2280}, {57, 59242}, {75, 60720}, {78, 23151}, {200, 37658}, {210, 59207}, {312, 4441}, {314, 60735}, {321, 60734}, {341, 28809}, {346, 3886}, {522, 4762}, {644, 54440}, {650, 4724}, {984, 40784}, {1002, 57}, {1212, 59217}, {1229, 59202}, {1826, 1893}, {2279, 56}, {2321, 3696}, {2325, 4702}, {3596, 21615}, {3700, 4804}, {3701, 4044}, {3790, 27474}, {3900, 45755}, {7079, 28044}, {8693, 109}, {14430, 45338}, {27475, 7}, {32041, 664}, {36138, 32735}, {37138, 651}, {40739, 14621}, {40757, 985}, {40779, 1}, {42290, 269}, {42302, 1014}, {42310, 21453}, {51443, 1412}, {51563, 4573}, {53227, 34085}, {59193, 1170}, {59255, 85}, {59260, 312}, {59269, 9}, {60673, 6}, {60677, 65}

X(60669) = BICEVIAN CHORDAL PERSPECTOR OF X(2) AND X(86)

Barycentrics    (3*a^2+7*a*b+3*b^2+5*(a+b)*c+c^2)*(3*a^2+5*a*b+b^2+7*a*c+5*b*c+3*c^2) : :

X(60669) lies on these lines: {2, 1051}, {75, 28640}, {86, 25358}, {335, 31310}, {675, 59080}, {1125, 6650}, {1268, 6542}, {1654, 30598}, {4971, 55955}, {5333, 40164}, {5625, 60710}, {5936, 29570}, {9791, 39720}, {20090, 28626}, {20142, 42335}, {25354, 59267}, {27483, 29586}, {48635, 56061}

X(60669) = reflection of X(i) in X(j) for these {i,j}: {31350, 31336}
X(60669) = isotomic conjugate of X(60710)
X(60669) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 60688}, {31, 60710}, {213, 60708}
X(60669) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 60710}, {9, 60688}, {6626, 60708}
X(60669) = pole of line {60708, 60710} with respect to the Wallace hyperbola
X(60669) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(29592)}}, {{A, B, C, X(2), X(7)}}, {{A, B, C, X(514), X(1125)}}, {{A, B, C, X(524), X(28179)}}, {{A, B, C, X(1051), X(1255)}}, {{A, B, C, X(1213), X(6539)}}, {{A, B, C, X(1654), X(5333)}}, {{A, B, C, X(3616), X(29570)}}, {{A, B, C, X(4080), X(25358)}}, {{A, B, C, X(4971), X(28209)}}, {{A, B, C, X(5550), X(29593)}}, {{A, B, C, X(6651), X(41841)}}, {{A, B, C, X(6707), X(8025)}}, {{A, B, C, X(7312), X(40434)}}, {{A, B, C, X(16826), X(29586)}}, {{A, B, C, X(17397), X(29569)}}, {{A, B, C, X(20090), X(25507)}}, {{A, B, C, X(20142), X(31336)}}, {{A, B, C, X(25417), X(28640)}}, {{A, B, C, X(26626), X(29595)}}, {{A, B, C, X(27789), X(39956)}}, {{A, B, C, X(29578), X(29590)}}, {{A, B, C, X(29585), X(46934)}}, {{A, B, C, X(29587), X(29603)}}, {{A, B, C, X(29591), X(29609)}}, {{A, B, C, X(30571), X(31308)}}, {{A, B, C, X(34585), X(37128)}}
X(60669) = barycentric product X(i)*X(j) for these (i, j): {3261, 59080}
X(60669) = barycentric quotient X(i)/X(j) for these (i, j): {1, 60688}, {2, 60710}, {86, 60708}, {59080, 101}

X(60670) = BICEVIAN CHORDAL PERSPECTOR OF X(4) AND X(6)

Barycentrics    a^2*(a^2*b^2*(a^2-b^2)^2+2*(a^2-b^2)^2*(a^2+b^2)*c^2-(5*a^4+3*a^2*b^2+5*b^4)*c^4+4*(a^2+b^2)*c^6-c^8)*(a^6*(2*b^2+c^2)-(b^2-2*c^2)*(b^3-b*c^2)^2-a^4*(5*b^4+2*b^2*c^2+2*c^4)+a^2*(4*b^6-3*b^4*c^2-2*b^2*c^4+c^6)) : :

X(60670) lies on the Jerabek hyperbola and on these lines: {3, 54991}, {51, 1987}, {54, 1971}, {69, 17035}, {217, 1173}, {290, 52281}, {3087, 43710}, {3331, 14483}, {3527, 32445}, {6748, 8795}, {6749, 57732}, {14533, 59143}, {38264, 40065}, {38297, 52518}, {38449, 53023}, {42021, 49111}

X(60670) = isogonal conjugate of X(60700)
X(60670) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 60700}, {63, 60693}, {2167, 10003}, {14213, 59241}
X(60670) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 60700}, {3162, 60693}, {40588, 10003}
X(60670) = pole of line {39682, 42300} with respect to the Kiepert hyperbola
X(60670) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(3), X(4)}}, {{A, B, C, X(51), X(275)}}, {{A, B, C, X(184), X(60120)}}, {{A, B, C, X(217), X(6748)}}, {{A, B, C, X(232), X(14492)}}, {{A, B, C, X(237), X(52281)}}, {{A, B, C, X(251), X(57253)}}, {{A, B, C, X(262), X(10311)}}, {{A, B, C, X(263), X(47735)}}, {{A, B, C, X(288), X(51477)}}, {{A, B, C, X(598), X(40799)}}, {{A, B, C, X(1988), X(60161)}}, {{A, B, C, X(2963), X(59142)}}, {{A, B, C, X(3087), X(32445)}}, {{A, B, C, X(3331), X(6749)}}, {{A, B, C, X(5480), X(51543)}}, {{A, B, C, X(6531), X(27375)}}, {{A, B, C, X(7578), X(60039)}}, {{A, B, C, X(8601), X(32654)}}, {{A, B, C, X(8882), X(17035)}}, {{A, B, C, X(17810), X(36616)}}, {{A, B, C, X(21638), X(55084)}}, {{A, B, C, X(23357), X(54663)}}, {{A, B, C, X(30537), X(54547)}}, {{A, B, C, X(38297), X(40065)}}, {{A, B, C, X(51336), X(54531)}}
X(60670) = barycentric quotient X(i)/X(j) for these (i, j): {6, 60700}, {25, 60693}, {51, 10003}, {54034, 59241}

X(60671) = BICEVIAN CHORDAL PERSPECTOR OF X(6) AND X(31)

Barycentrics    a^3*(a*b+2*(a+b)*c+c^2)*(a*(2*b+c)+b*(b+2*c)) : :

X(60671) lies on these lines: {6, 2667}, {31, 21753}, {42, 57397}, {81, 238}, {86, 59147}, {213, 1911}, {739, 21747}, {922, 28607}, {1333, 2210}, {1918, 28615}, {2162, 21779}, {2214, 60676}, {2298, 60675}, {4384, 14621}, {16469, 18789}, {16477, 20332}, {17156, 56046}, {20663, 51333}, {40728, 40735}, {59261, 60082}

X(60671) = isogonal conjugate of X(60706)
X(60671) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 60706}, {2, 16826}, {4, 60729}, {6, 60719}, {7, 60731}, {8, 60717}, {9, 60732}, {10, 51356}, {37, 51314}, {57, 60730}, {69, 60699}, {75, 4649}, {76, 60697}, {81, 60736}, {85, 60711}, {86, 3842}, {92, 60701}, {99, 4824}, {190, 28840}, {264, 60703}, {274, 60724}, {306, 31904}, {312, 60715}, {313, 59243}, {321, 51311}, {335, 20142}, {664, 4913}, {668, 4784}, {870, 40774}, {903, 4753}, {1171, 59203}, {1268, 5625}, {4597, 4948}, {4963, 32042}, {6063, 60713}, {14621, 27495}, {16369, 40017}, {31336, 42335}, {32014, 59218}, {40439, 59219}
X(60671) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 60706}, {9, 60719}, {206, 4649}, {478, 60732}, {5452, 60730}, {22391, 60701}, {32664, 16826}, {36033, 60729}, {38986, 4824}, {39025, 4913}, {40586, 60736}, {40589, 51314}, {40600, 3842}, {55053, 28840}
X(60671) = pole of line {4649, 40734} with respect to the Stammler hyperbola
X(60671) = pole of line {59219, 60706} with respect to the Wallace hyperbola
X(60671) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(31)}}, {{A, B, C, X(25), X(55967)}}, {{A, B, C, X(32), X(56343)}}, {{A, B, C, X(42), X(86)}}, {{A, B, C, X(58), X(213)}}, {{A, B, C, X(87), X(2258)}}, {{A, B, C, X(292), X(39971)}}, {{A, B, C, X(649), X(42302)}}, {{A, B, C, X(673), X(2350)}}, {{A, B, C, X(869), X(2279)}}, {{A, B, C, X(872), X(2054)}}, {{A, B, C, X(893), X(37128)}}, {{A, B, C, X(1400), X(55968)}}, {{A, B, C, X(1402), X(4038)}}, {{A, B, C, X(1918), X(2206)}}, {{A, B, C, X(3736), X(24342)}}, {{A, B, C, X(4068), X(5284)}}, {{A, B, C, X(4649), X(51449)}}, {{A, B, C, X(5331), X(23493)}}, {{A, B, C, X(9258), X(45965)}}, {{A, B, C, X(9309), X(45966)}}, {{A, B, C, X(16468), X(40728)}}, {{A, B, C, X(16477), X(21760)}}, {{A, B, C, X(21779), X(27644)}}, {{A, B, C, X(25426), X(60680)}}, {{A, B, C, X(30571), X(59272)}}, {{A, B, C, X(30650), X(39952)}}, {{A, B, C, X(40148), X(40433)}}, {{A, B, C, X(42346), X(57535)}}
X(60671) = barycentric product X(i)*X(j) for these (i, j): {1, 25426}, {32, 60678}, {42, 60680}, {56, 60675}, {58, 60676}, {1333, 59261}, {1962, 59194}, {2276, 40748}, {27483, 31}, {28841, 513}, {30571, 6}, {59272, 81}
X(60671) = barycentric quotient X(i)/X(j) for these (i, j): {1, 60719}, {6, 60706}, {31, 16826}, {32, 4649}, {41, 60731}, {42, 60736}, {48, 60729}, {55, 60730}, {56, 60732}, {58, 51314}, {184, 60701}, {213, 3842}, {560, 60697}, {604, 60717}, {667, 28840}, {798, 4824}, {869, 27495}, {1333, 51356}, {1397, 60715}, {1918, 60724}, {1919, 4784}, {1962, 59203}, {1973, 60699}, {2175, 60711}, {2203, 31904}, {2206, 51311}, {2210, 20142}, {2251, 4753}, {3063, 4913}, {9247, 60703}, {9447, 60713}, {21753, 59219}, {25426, 75}, {27483, 561}, {28841, 668}, {30571, 76}, {40728, 40774}, {59261, 27801}, {59272, 321}, {60675, 3596}, {60676, 313}, {60678, 1502}, {60680, 310}
X(60671) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16468, 40749, 20142}

X(60672) = BICEVIAN CHORDAL PERSPECTOR OF X(6) AND X(32)

Barycentrics    a^4*(a^2*b^2+2*(a^2+b^2)*c^2+c^4)*(b^4+2*b^2*c^2+a^2*(2*b^2+c^2)) : :

X(60672) lies on these lines: {6, 8623}, {32, 39684}, {39, 42346}, {83, 385}, {729, 5008}, {2207, 34096}, {3051, 9468}, {3114, 7766}, {3117, 46319}, {3224, 3499}, {3225, 38382}, {7735, 20024}, {14602, 46288}, {34097, 52958}, {34252, 51917}, {40747, 60664}, {43183, 56344}, {51322, 51326}, {54413, 57016}

X(60672) = isogonal conjugate of X(60707)
X(60672) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 60707}, {2, 60683}, {38, 59249}, {75, 3329}, {76, 60686}, {92, 60702}, {561, 12212}, {1959, 39685}, {3112, 10007}, {4602, 14318}, {8024, 51312}
X(60672) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 60707}, {206, 3329}, {22391, 60702}, {32664, 60683}, {34452, 10007}, {40368, 12212}
X(60672) = X(i)-cross conjugate of X(j) for these {i, j}: {43977, 51948}, {59273, 60667}
X(60672) = pole of line {3329, 60707} with respect to the Stammler hyperbola
X(60672) = pole of line {10007, 60707} with respect to the Wallace hyperbola
X(60672) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(32)}}, {{A, B, C, X(31), X(34252)}}, {{A, B, C, X(39), X(308)}}, {{A, B, C, X(251), X(385)}}, {{A, B, C, X(263), X(3117)}}, {{A, B, C, X(290), X(27375)}}, {{A, B, C, X(512), X(42299)}}, {{A, B, C, X(574), X(34097)}}, {{A, B, C, X(695), X(14970)}}, {{A, B, C, X(1501), X(39955)}}, {{A, B, C, X(1911), X(40763)}}, {{A, B, C, X(3329), X(51450)}}, {{A, B, C, X(3456), X(42444)}}, {{A, B, C, X(5007), X(41331)}}, {{A, B, C, X(5008), X(33875)}}, {{A, B, C, X(7766), X(18899)}}, {{A, B, C, X(9229), X(56978)}}, {{A, B, C, X(9489), X(57016)}}, {{A, B, C, X(10547), X(22138)}}, {{A, B, C, X(12212), X(43977)}}, {{A, B, C, X(14251), X(18873)}}, {{A, B, C, X(14575), X(43706)}}, {{A, B, C, X(17970), X(43722)}}, {{A, B, C, X(30495), X(42359)}}, {{A, B, C, X(34096), X(43718)}}, {{A, B, C, X(38382), X(51322)}}, {{A, B, C, X(40746), X(51856)}}, {{A, B, C, X(42006), X(59273)}}, {{A, B, C, X(44772), X(59994)}}, {{A, B, C, X(51902), X(51917)}}
X(60672) = barycentric product X(i)*X(j) for these (i, j): {6, 60667}, {31, 60664}, {32, 42006}, {251, 59262}, {39684, 98}, {43357, 512}, {47643, 60600}, {59273, 83}
X(60672) = barycentric quotient X(i)/X(j) for these (i, j): {6, 60707}, {31, 60683}, {32, 3329}, {184, 60702}, {251, 59249}, {560, 60686}, {1501, 12212}, {1976, 39685}, {3051, 10007}, {9426, 14318}, {39684, 325}, {42006, 1502}, {43357, 670}, {59262, 8024}, {59273, 141}, {60664, 561}, {60667, 76}

X(60673) = BICEVIAN CHORDAL PERSPECTOR OF X(6) AND X(55)

Barycentrics    a^2*(a-b-c)*((b-c)*c+a*(2*b+c))*(b*(-b+c)+a*(b+2*c)) : :

X(60673) lies on these lines: {1, 673}, {6, 2223}, {9, 2293}, {19, 2356}, {31, 1174}, {41, 2195}, {42, 57}, {55, 20229}, {200, 333}, {210, 56208}, {269, 10509}, {284, 1253}, {612, 1751}, {663, 1024}, {869, 7290}, {991, 3751}, {2160, 18791}, {2177, 2291}, {2258, 5364}, {2259, 21059}, {2319, 3158}, {2339, 3190}, {3009, 35227}, {3689, 56116}, {3736, 42302}, {3886, 40739}, {4251, 7084}, {6169, 9439}, {10389, 56717}, {10436, 59255}, {11051, 20995}, {32041, 50127}

X(60673) = isogonal conjugate of X(40719)
X(60673) = trilinear pole of line {663, 46388}
X(60673) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 40719}, {2, 5228}, {6, 60720}, {7, 1001}, {8, 59242}, {9, 42309}, {56, 4441}, {57, 4384}, {58, 60734}, {75, 1471}, {85, 2280}, {86, 42289}, {226, 60721}, {269, 3886}, {278, 23151}, {279, 37658}, {604, 21615}, {651, 4762}, {658, 45755}, {664, 4724}, {1014, 3696}, {1214, 31926}, {1400, 60735}, {1407, 28809}, {1412, 4044}, {1414, 4804}, {1434, 59207}, {1444, 1893}, {3676, 54440}, {4334, 56705}, {4702, 56049}, {6063, 60722}, {7056, 28044}, {14621, 40784}, {21453, 59217}, {56658, 60715}
X(60673) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 4441}, {3, 40719}, {9, 60720}, {10, 60734}, {142, 59202}, {206, 1471}, {478, 42309}, {3161, 21615}, {5452, 4384}, {6600, 3886}, {24771, 28809}, {32664, 5228}, {38991, 4762}, {39025, 4724}, {40582, 60735}, {40599, 4044}, {40600, 42289}, {40608, 4804}
X(60673) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1002, 2279}, {40739, 9}, {59193, 1002}
X(60673) = pole of line {1471, 40719} with respect to the Stammler hyperbola
X(60673) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(41)}}, {{A, B, C, X(6), X(9)}}, {{A, B, C, X(31), X(269)}}, {{A, B, C, X(33), X(15624)}}, {{A, B, C, X(42), X(200)}}, {{A, B, C, X(73), X(1802)}}, {{A, B, C, X(78), X(41265)}}, {{A, B, C, X(210), X(40504)}}, {{A, B, C, X(220), X(2334)}}, {{A, B, C, X(607), X(1126)}}, {{A, B, C, X(612), X(3190)}}, {{A, B, C, X(649), X(42315)}}, {{A, B, C, X(672), X(21446)}}, {{A, B, C, X(991), X(2263)}}, {{A, B, C, X(1002), X(59269)}}, {{A, B, C, X(1260), X(57701)}}, {{A, B, C, X(1334), X(4866)}}, {{A, B, C, X(1419), X(20995)}}, {{A, B, C, X(1462), X(9315)}}, {{A, B, C, X(1911), X(2175)}}, {{A, B, C, X(2082), X(4251)}}, {{A, B, C, X(2141), X(17682)}}, {{A, B, C, X(2191), X(2194)}}, {{A, B, C, X(2279), X(40779)}}, {{A, B, C, X(3063), X(40735)}}, {{A, B, C, X(3693), X(39957)}}, {{A, B, C, X(3709), X(59272)}}, {{A, B, C, X(3736), X(3886)}}, {{A, B, C, X(4183), X(37262)}}, {{A, B, C, X(4845), X(41434)}}, {{A, B, C, X(5364), X(10436)}}, {{A, B, C, X(6605), X(39961)}}, {{A, B, C, X(7050), X(10579)}}, {{A, B, C, X(13404), X(51476)}}, {{A, B, C, X(14547), X(21059)}}, {{A, B, C, X(18889), X(52429)}}, {{A, B, C, X(19605), X(39967)}}, {{A, B, C, X(20967), X(54308)}}, {{A, B, C, X(25426), X(42317)}}, {{A, B, C, X(39341), X(40730)}}
X(60673) = barycentric product X(i)*X(j) for these (i, j): {1, 40779}, {6, 60668}, {21, 60677}, {41, 59255}, {57, 59269}, {200, 42290}, {210, 42302}, {522, 8693}, {1002, 9}, {1212, 59193}, {2276, 40739}, {2279, 8}, {2293, 42310}, {2321, 51443}, {3709, 51563}, {27475, 55}, {32041, 663}, {36138, 50333}, {37138, 650}, {40757, 984}, {46388, 53227}, {59260, 604}
X(60673) = barycentric quotient X(i)/X(j) for these (i, j): {1, 60720}, {6, 40719}, {8, 21615}, {9, 4441}, {21, 60735}, {31, 5228}, {32, 1471}, {37, 60734}, {41, 1001}, {55, 4384}, {56, 42309}, {200, 28809}, {210, 4044}, {212, 23151}, {213, 42289}, {220, 3886}, {604, 59242}, {663, 4762}, {869, 40784}, {1002, 85}, {1212, 59202}, {1253, 37658}, {1334, 3696}, {2175, 2280}, {2194, 60721}, {2279, 7}, {2299, 31926}, {2333, 1893}, {3063, 4724}, {3709, 4804}, {4517, 27474}, {8641, 45755}, {8693, 664}, {9447, 60722}, {20229, 59217}, {27475, 6063}, {32041, 4572}, {32724, 36146}, {36138, 927}, {37138, 4554}, {40757, 870}, {40779, 75}, {42290, 1088}, {42302, 57785}, {51443, 1434}, {59193, 31618}, {59255, 20567}, {59260, 28659}, {59269, 312}, {60668, 76}, {60677, 1441}

X(60674) = BICEVIAN CHORDAL PERSPECTOR OF X(6) AND X(64)

Barycentrics    a^2*(a^2-b^2-c^2)*(3*a^4+2*a^2*b^2+3*b^4-2*(a^2+b^2)*c^2-c^4)*(3*a^4-2*a^2*b^2-b^4+2*(a-b)*(a+b)*c^2+3*c^4) : :

X(60674) lies on the Jerabek hyperbola and on these lines: {3, 8779}, {4, 3172}, {6, 33582}, {25, 43717}, {32, 64}, {39, 14528}, {54, 9605}, {69, 441}, {74, 1384}, {187, 43713}, {290, 14614}, {577, 34817}, {647, 2435}, {1609, 34436}, {1853, 23976}, {3053, 3532}, {3167, 36214}, {3284, 55977}, {3426, 21309}, {3431, 5024}, {3527, 43136}, {4846, 15341}, {5007, 52518}, {5008, 14490}, {6391, 38292}, {7767, 28425}, {7792, 52251}, {8573, 34207}, {10317, 34801}, {11328, 43727}, {14642, 52559}, {15316, 22120}, {15655, 20421}, {19222, 56372}, {22246, 44731}, {22331, 43691}, {40825, 43702}

X(60674) = isogonal conjugate of X(52283)
X(60674) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 52283}, {2, 23052}, {4, 51304}, {19, 37668}, {63, 10002}, {75, 45141}, {92, 1350}, {1895, 40813}, {1959, 45031}, {12037, 24000}
X(60674) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 52283}, {6, 37668}, {206, 45141}, {3162, 10002}, {22391, 1350}, {32664, 23052}, {36033, 51304}
X(60674) = pole of line {37668, 45141} with respect to the Stammler hyperbola
X(60674) = pole of line {50642, 54260} with respect to the Steiner inellipse
X(60674) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(3), X(4)}}, {{A, B, C, X(25), X(441)}}, {{A, B, C, X(32), X(3172)}}, {{A, B, C, X(97), X(39955)}}, {{A, B, C, X(216), X(9605)}}, {{A, B, C, X(219), X(9439)}}, {{A, B, C, X(251), X(394)}}, {{A, B, C, X(393), X(14376)}}, {{A, B, C, X(577), X(10547)}}, {{A, B, C, X(1383), X(14919)}}, {{A, B, C, X(1384), X(3284)}}, {{A, B, C, X(1433), X(1438)}}, {{A, B, C, X(1609), X(22120)}}, {{A, B, C, X(2351), X(39951)}}, {{A, B, C, X(2353), X(20208)}}, {{A, B, C, X(3049), X(46319)}}, {{A, B, C, X(3053), X(38292)}}, {{A, B, C, X(3148), X(52251)}}, {{A, B, C, X(3289), X(14614)}}, {{A, B, C, X(3926), X(52223)}}, {{A, B, C, X(5013), X(15851)}}, {{A, B, C, X(5024), X(5158)}}, {{A, B, C, X(5305), X(55549)}}, {{A, B, C, X(6394), X(32085)}}, {{A, B, C, X(7053), X(40746)}}, {{A, B, C, X(7084), X(32658)}}, {{A, B, C, X(8573), X(23115)}}, {{A, B, C, X(8882), X(28783)}}, {{A, B, C, X(9409), X(51937)}}, {{A, B, C, X(9748), X(54032)}}, {{A, B, C, X(9755), X(10311)}}, {{A, B, C, X(11328), X(56372)}}, {{A, B, C, X(14486), X(17974)}}, {{A, B, C, X(14908), X(40799)}}, {{A, B, C, X(15400), X(20402)}}, {{A, B, C, X(21448), X(52153)}}, {{A, B, C, X(22331), X(33636)}}, {{A, B, C, X(34288), X(34897)}}, {{A, B, C, X(36609), X(51336)}}, {{A, B, C, X(36748), X(43136)}}
X(60674) = barycentric product X(i)*X(j) for these (i, j): {3, 3424}, {184, 59256}, {525, 58963}, {35571, 42658}, {42287, 6}
X(60674) = barycentric quotient X(i)/X(j) for these (i, j): {3, 37668}, {6, 52283}, {25, 10002}, {31, 23052}, {32, 45141}, {48, 51304}, {184, 1350}, {1976, 45031}, {3269, 12037}, {3424, 264}, {14642, 40813}, {42287, 76}, {42658, 14343}, {42671, 1529}, {58963, 648}, {59256, 18022}

X(60675) = BICEVIAN CHORDAL PERSPECTOR OF X(8) AND X(9)

Barycentrics    a*(a-b-c)*(a*b+2*(a+b)*c+c^2)*(a*(2*b+c)+b*(b+2*c)) : :

X(60675) lies on the Feuerbach hyperbola and on these lines: {1, 1573}, {4, 59261}, {7, 1654}, {8, 3985}, {9, 4111}, {21, 3684}, {79, 17746}, {84, 35203}, {104, 28841}, {210, 4876}, {256, 4489}, {314, 3686}, {391, 7155}, {941, 3728}, {966, 25124}, {1334, 32635}, {1655, 4771}, {2298, 60671}, {2344, 37658}, {2481, 50095}, {3208, 4866}, {3707, 36798}, {4034, 56087}, {8846, 43747}, {24603, 30966}, {25946, 60715}, {27644, 56048}, {35355, 50328}

X(60675) = isogonal conjugate of X(60715)
X(60675) = isotomic conjugate of X(60732)
X(60675) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 60715}, {6, 60717}, {7, 60697}, {31, 60732}, {34, 60701}, {56, 16826}, {57, 4649}, {65, 51311}, {73, 31904}, {109, 28840}, {222, 60699}, {226, 59243}, {269, 60711}, {278, 60703}, {279, 60713}, {604, 60706}, {608, 60729}, {651, 4784}, {1014, 60724}, {1106, 60730}, {1397, 60719}, {1400, 51356}, {1402, 51314}, {1407, 60731}, {1408, 60736}, {1412, 3842}, {1461, 4913}, {4565, 4824}
X(60675) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 16826}, {2, 60732}, {3, 60715}, {9, 60717}, {11, 28840}, {3161, 60706}, {5452, 4649}, {6552, 60730}, {6600, 60711}, {11517, 60701}, {24771, 60731}, {35508, 4913}, {38991, 4784}, {40582, 51356}, {40599, 3842}, {40602, 51311}, {40605, 51314}, {55064, 4824}, {59577, 60736}
X(60675) = X(i)-Ceva conjugate of X(j) for these {i, j}: {27483, 30571}
X(60675) = pole of line {51311, 60715} with respect to the Stammler hyperbola
X(60675) = pole of line {51314, 60715} with respect to the Wallace hyperbola
X(60675) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(55), X(42030)}}, {{A, B, C, X(210), X(333)}}, {{A, B, C, X(284), X(1334)}}, {{A, B, C, X(312), X(56208)}}, {{A, B, C, X(346), X(4699)}}, {{A, B, C, X(391), X(3208)}}, {{A, B, C, X(1001), X(55983)}}, {{A, B, C, X(1654), X(2287)}}, {{A, B, C, X(2319), X(30711)}}, {{A, B, C, X(2321), X(3691)}}, {{A, B, C, X(2340), X(50095)}}, {{A, B, C, X(2348), X(50328)}}, {{A, B, C, X(3789), X(30966)}}, {{A, B, C, X(4489), X(7081)}}, {{A, B, C, X(4517), X(40733)}}, {{A, B, C, X(7110), X(46196)}}, {{A, B, C, X(17746), X(52405)}}, {{A, B, C, X(27484), X(59269)}}
X(60675) = barycentric product X(i)*X(j) for these (i, j): {21, 59261}, {55, 60678}, {314, 59272}, {333, 60676}, {2321, 60680}, {3596, 60671}, {3790, 40748}, {25426, 312}, {27483, 9}, {28841, 4391}, {30571, 8}, {40779, 56658}
X(60675) = barycentric quotient X(i)/X(j) for these (i, j): {1, 60717}, {2, 60732}, {6, 60715}, {8, 60706}, {9, 16826}, {21, 51356}, {33, 60699}, {41, 60697}, {55, 4649}, {78, 60729}, {200, 60731}, {210, 3842}, {212, 60703}, {219, 60701}, {220, 60711}, {284, 51311}, {312, 60719}, {333, 51314}, {346, 60730}, {650, 28840}, {663, 4784}, {1172, 31904}, {1253, 60713}, {1334, 60724}, {2194, 59243}, {2321, 60736}, {3683, 5625}, {3684, 20142}, {3689, 4753}, {3900, 4913}, {4041, 4824}, {4111, 59219}, {4517, 40774}, {4814, 4948}, {25426, 57}, {27483, 85}, {28841, 651}, {30571, 7}, {56658, 60720}, {59261, 1441}, {59272, 65}, {60671, 56}, {60676, 226}, {60678, 6063}, {60680, 1434}
X(60675) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {25426, 60676, 30571}

X(60676) = BICEVIAN CHORDAL PERSPECTOR OF X(37) AND X(10)

Barycentrics    a*(b+c)*(a*b+2*(a+b)*c+c^2)*(a*(2*b+c)+b*(b+2*c)) : :

X(60676) lies on cubic K286 and on these lines: {1, 1573}, {2, 18827}, {6, 24944}, {9, 13610}, {10, 4037}, {19, 862}, {37, 21699}, {43, 9280}, {44, 55925}, {45, 897}, {65, 21879}, {75, 1213}, {661, 876}, {759, 4262}, {1100, 46971}, {1581, 19584}, {1931, 37675}, {2092, 17038}, {2214, 60671}, {2276, 30570}, {2363, 5275}, {3124, 9330}, {3668, 27691}, {3730, 57419}, {3943, 56126}, {4687, 56703}, {4770, 23894}, {5257, 42027}, {6376, 18298}, {6537, 29674}, {10026, 17244}, {16369, 40747}, {20691, 56237}, {21024, 31359}, {21839, 52708}, {25614, 56174}, {40750, 51311}, {52706, 56125}, {52959, 56134}

X(60676) = isogonal conjugate of X(51311)
X(60676) = isotomic conjugate of X(51314)
X(60676) = trilinear pole of line {661, 8663}
X(60676) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 51311}, {2, 59243}, {3, 31904}, {6, 51356}, {21, 60715}, {27, 60703}, {28, 60701}, {31, 51314}, {58, 16826}, {81, 4649}, {86, 60697}, {110, 28840}, {284, 60717}, {593, 3842}, {662, 4784}, {741, 20142}, {757, 60724}, {849, 60736}, {1014, 60711}, {1171, 5625}, {1333, 60706}, {1408, 60730}, {1412, 60731}, {1434, 60713}, {1474, 60729}, {1790, 60699}, {2194, 60732}, {2206, 60719}, {4556, 4824}, {4565, 4913}, {14621, 40734}, {52558, 59218}
X(60676) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 51314}, {3, 51311}, {9, 51356}, {10, 16826}, {37, 60706}, {244, 28840}, {1084, 4784}, {1214, 60732}, {4075, 60736}, {8299, 20142}, {32664, 59243}, {36103, 31904}, {40586, 4649}, {40590, 60717}, {40591, 60701}, {40599, 60731}, {40600, 60697}, {40603, 60719}, {40607, 60724}, {40611, 60715}, {51574, 60729}, {55064, 4913}, {59577, 60730}
X(60676) = X(i)-Ceva conjugate of X(j) for these {i, j}: {27483, 59261}, {30571, 59272}
X(60676) = X(i)-cross conjugate of X(j) for these {i, j}: {984, 52651}
X(60676) = pole of line {3661, 3826} with respect to the Kiepert hyperbola
X(60676) = pole of line {20142, 51311} with respect to the Wallace hyperbola
X(60676) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(2), X(661)}}, {{A, B, C, X(6), X(1213)}}, {{A, B, C, X(9), X(21879)}}, {{A, B, C, X(42), X(29576)}}, {{A, B, C, X(45), X(4770)}}, {{A, B, C, X(57), X(9281)}}, {{A, B, C, X(76), X(594)}}, {{A, B, C, X(181), X(39967)}}, {{A, B, C, X(321), X(56236)}}, {{A, B, C, X(523), X(59255)}}, {{A, B, C, X(740), X(870)}}, {{A, B, C, X(762), X(6543)}}, {{A, B, C, X(941), X(7148)}}, {{A, B, C, X(984), X(3842)}}, {{A, B, C, X(1002), X(60724)}}, {{A, B, C, X(1211), X(5275)}}, {{A, B, C, X(1400), X(17248)}}, {{A, B, C, X(1423), X(5257)}}, {{A, B, C, X(1962), X(25417)}}, {{A, B, C, X(2054), X(40746)}}, {{A, B, C, X(2171), X(56210)}}, {{A, B, C, X(2245), X(4262)}}, {{A, B, C, X(2321), X(27424)}}, {{A, B, C, X(2345), X(27565)}}, {{A, B, C, X(3780), X(14624)}}, {{A, B, C, X(3789), X(7179)}}, {{A, B, C, X(3950), X(25614)}}, {{A, B, C, X(3986), X(21868)}}, {{A, B, C, X(4041), X(40779)}}, {{A, B, C, X(4205), X(37101)}}, {{A, B, C, X(4492), X(55246)}}, {{A, B, C, X(6057), X(56208)}}, {{A, B, C, X(8818), X(17758)}}, {{A, B, C, X(25426), X(27483)}}, {{A, B, C, X(25427), X(27475)}}, {{A, B, C, X(25430), X(52208)}}, {{A, B, C, X(27481), X(40733)}}, {{A, B, C, X(30570), X(30571)}}, {{A, B, C, X(40776), X(51311)}}, {{A, B, C, X(52900), X(52959)}}
X(60676) = barycentric product X(i)*X(j) for these (i, j): {1, 59261}, {10, 30571}, {42, 60678}, {226, 60675}, {313, 60671}, {594, 60680}, {1577, 28841}, {3773, 40748}, {25426, 321}, {27483, 37}, {56658, 60677}, {59272, 75}
X(60676) = barycentric quotient X(i)/X(j) for these (i, j): {1, 51356}, {2, 51314}, {6, 51311}, {10, 60706}, {19, 31904}, {31, 59243}, {37, 16826}, {42, 4649}, {65, 60717}, {71, 60701}, {72, 60729}, {210, 60731}, {213, 60697}, {226, 60732}, {228, 60703}, {321, 60719}, {512, 4784}, {594, 60736}, {661, 28840}, {756, 3842}, {869, 40734}, {1334, 60711}, {1400, 60715}, {1500, 60724}, {1824, 60699}, {1962, 5625}, {2238, 20142}, {2321, 60730}, {4041, 4913}, {4705, 4824}, {4770, 4948}, {21699, 59219}, {21805, 4753}, {21816, 59218}, {25426, 81}, {27483, 274}, {28841, 662}, {30571, 86}, {48005, 4963}, {56658, 60735}, {59261, 75}, {59272, 1}, {60671, 58}, {60675, 333}, {60678, 310}, {60680, 1509}
X(60676) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {30571, 60675, 25426}

X(60677) = BICEVIAN CHORDAL PERSPECTOR OF X(37) AND X(65)

Barycentrics    a*(b+c)*((b-c)*c+a*(2*b+c))*(b*(-b+c)+a*(b+2*c)) : :

X(60677) lies on these lines: {1, 672}, {10, 3930}, {19, 2356}, {37, 4890}, {42, 18785}, {65, 1500}, {75, 142}, {354, 6184}, {594, 46772}, {759, 8693}, {876, 50359}, {897, 37138}, {1174, 1438}, {2171, 3668}, {2214, 8053}, {2218, 54416}, {2329, 40430}, {2938, 13610}, {3501, 11518}, {3943, 56125}, {3950, 42027}, {4029, 41683}, {4044, 21101}, {4356, 20706}, {4876, 18827}, {9278, 20692}, {16589, 56237}, {17023, 39717}, {17316, 55945}, {17760, 18298}, {20691, 56174}, {21872, 31503}, {22021, 24090}, {29674, 39708}, {31359, 60668}, {33635, 40438}, {40504, 56926}, {40747, 60724}, {40775, 40790}, {42285, 57015}, {52708, 56134}, {52959, 56159}, {60711, 60721}

X(60677) = isogonal conjugate of X(60721)
X(60677) = isotomic conjugate of X(60735)
X(60677) = trilinear pole of line {661, 2512}
X(60677) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 60721}, {3, 31926}, {21, 5228}, {28, 23151}, {31, 60735}, {58, 4384}, {81, 1001}, {86, 2280}, {110, 4762}, {274, 60722}, {284, 40719}, {333, 1471}, {593, 3696}, {662, 4724}, {757, 59207}, {849, 4044}, {1014, 37658}, {1019, 54440}, {1333, 4441}, {1408, 28809}, {1412, 3886}, {1414, 45755}, {2150, 60734}, {2185, 42289}, {2194, 60720}, {2206, 21615}, {2287, 59242}, {2328, 42309}, {4556, 4804}, {56658, 59243}
X(60677) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 60735}, {3, 60721}, {10, 4384}, {37, 4441}, {244, 4762}, {1084, 4724}, {1214, 60720}, {4075, 4044}, {36103, 31926}, {36908, 42309}, {40586, 1001}, {40590, 40719}, {40591, 23151}, {40599, 3886}, {40600, 2280}, {40603, 21615}, {40607, 59207}, {40608, 45755}, {40611, 5228}, {56325, 60734}, {59577, 28809}
X(60677) = pole of line {60721, 60735} with respect to the Wallace hyperbola
X(60677) = pole of line {984, 30949} with respect to the dual conic of Yff parabola
X(60677) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(2), X(56192)}}, {{A, B, C, X(4), X(52241)}}, {{A, B, C, X(6), X(3970)}}, {{A, B, C, X(25), X(37097)}}, {{A, B, C, X(42), X(226)}}, {{A, B, C, X(76), X(941)}}, {{A, B, C, X(142), X(1400)}}, {{A, B, C, X(213), X(51058)}}, {{A, B, C, X(306), X(41265)}}, {{A, B, C, X(334), X(40433)}}, {{A, B, C, X(514), X(25426)}}, {{A, B, C, X(893), X(55090)}}, {{A, B, C, X(1002), X(59255)}}, {{A, B, C, X(1334), X(1500)}}, {{A, B, C, X(1432), X(4890)}}, {{A, B, C, X(1824), X(56255)}}, {{A, B, C, X(1826), X(3730)}}, {{A, B, C, X(2051), X(39967)}}, {{A, B, C, X(2092), X(3674)}}, {{A, B, C, X(2238), X(50359)}}, {{A, B, C, X(2279), X(27475)}}, {{A, B, C, X(2318), X(37755)}}, {{A, B, C, X(2344), X(11608)}}, {{A, B, C, X(3755), X(42289)}}, {{A, B, C, X(3864), X(34475)}}, {{A, B, C, X(3950), X(20691)}}, {{A, B, C, X(3997), X(34892)}}, {{A, B, C, X(4029), X(52959)}}, {{A, B, C, X(4044), X(7146)}}, {{A, B, C, X(4052), X(52651)}}, {{A, B, C, X(4053), X(16785)}}, {{A, B, C, X(4080), X(56156)}}, {{A, B, C, X(5257), X(16589)}}, {{A, B, C, X(8053), X(21070)}}, {{A, B, C, X(8818), X(17240)}}, {{A, B, C, X(14624), X(30701)}}, {{A, B, C, X(16606), X(56226)}}, {{A, B, C, X(17018), X(30636)}}, {{A, B, C, X(17241), X(28625)}}, {{A, B, C, X(19584), X(19587)}}, {{A, B, C, X(22021), X(54416)}}, {{A, B, C, X(23493), X(49528)}}, {{A, B, C, X(25092), X(40085)}}, {{A, B, C, X(39961), X(57722)}}, {{A, B, C, X(52155), X(54668)}}, {{A, B, C, X(54123), X(56258)}}
X(60677) = barycentric product X(i)*X(j) for these (i, j): {10, 1002}, {42, 59255}, {226, 40779}, {1042, 59260}, {1089, 51443}, {1441, 60673}, {1577, 8693}, {2279, 321}, {2321, 42290}, {3668, 59269}, {3925, 59193}, {4705, 51563}, {16603, 40757}, {21808, 42310}, {27475, 37}, {32041, 661}, {37138, 523}, {42302, 594}, {60668, 65}
X(60677) = barycentric quotient X(i)/X(j) for these (i, j): {2, 60735}, {6, 60721}, {10, 4441}, {12, 60734}, {19, 31926}, {37, 4384}, {42, 1001}, {65, 40719}, {71, 23151}, {181, 42289}, {210, 3886}, {213, 2280}, {226, 60720}, {321, 21615}, {512, 4724}, {594, 4044}, {661, 4762}, {756, 3696}, {1002, 86}, {1042, 59242}, {1334, 37658}, {1400, 5228}, {1402, 1471}, {1427, 42309}, {1500, 59207}, {1918, 60722}, {2279, 81}, {2321, 28809}, {3709, 45755}, {3925, 59202}, {4557, 54440}, {4705, 4804}, {8693, 662}, {21805, 4702}, {27475, 274}, {32041, 799}, {37138, 99}, {40779, 333}, {42290, 1434}, {42302, 1509}, {51443, 757}, {51563, 4623}, {52020, 59217}, {59255, 310}, {59269, 1043}, {60668, 314}, {60673, 21}, {60676, 56658}
X(60677) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1002, 40779, 2279}

X(60678) = BICEVIAN CHORDAL PERSPECTOR OF X(75) AND X(76)

Barycentrics    b*c*(a*b+2*(a+b)*c+c^2)*(a*(2*b+c)+b*(b+2*c)) : :

X(60678) lies on these lines: {10, 32018}, {75, 1213}, {76, 4647}, {79, 33297}, {85, 3649}, {274, 350}, {286, 1839}, {319, 15320}, {321, 334}, {767, 28841}, {870, 4393}, {1218, 59272}, {1269, 6385}, {2481, 50095}, {4044, 60706}, {4479, 50180}, {6376, 40023}, {14210, 20569}, {30570, 30966}, {33931, 59255}

X(60678) = isotomic conjugate of X(4649)
X(60678) = trilinear pole of line {693, 4988}
X(60678) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 60697}, {25, 60703}, {31, 4649}, {32, 16826}, {41, 60715}, {42, 59243}, {56, 60713}, {184, 60699}, {213, 51311}, {560, 60706}, {604, 60711}, {692, 4784}, {1333, 60724}, {1397, 60731}, {1501, 60719}, {1576, 4824}, {1918, 51356}, {1922, 20142}, {1973, 60701}, {1974, 60729}, {2175, 60717}, {2200, 31904}, {2205, 51314}, {2206, 3842}, {9447, 60732}, {16369, 18268}, {28840, 32739}
X(60678) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 60713}, {2, 4649}, {9, 60697}, {37, 60724}, {1086, 4784}, {3160, 60715}, {3161, 60711}, {4858, 4824}, {6337, 60701}, {6374, 60706}, {6376, 16826}, {6505, 60703}, {6626, 51311}, {27481, 40774}, {34021, 51356}, {35068, 16369}, {39028, 20142}, {40592, 59243}, {40593, 60717}, {40603, 3842}, {40619, 28840}, {40624, 4913}
X(60678) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {40748, 41821}
X(60678) = X(i)-cross conjugate of X(j) for these {i, j}: {3775, 2}, {59261, 27483}
X(60678) = pole of line {4649, 51311} with respect to the Wallace hyperbola
X(60678) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(29576)}}, {{A, B, C, X(7), X(17248)}}, {{A, B, C, X(10), X(79)}}, {{A, B, C, X(75), X(76)}}, {{A, B, C, X(226), X(56052)}}, {{A, B, C, X(257), X(18827)}}, {{A, B, C, X(310), X(321)}}, {{A, B, C, X(313), X(20888)}}, {{A, B, C, X(314), X(17762)}}, {{A, B, C, X(319), X(33297)}}, {{A, B, C, X(320), X(50450)}}, {{A, B, C, X(335), X(31323)}}, {{A, B, C, X(514), X(55947)}}, {{A, B, C, X(596), X(3226)}}, {{A, B, C, X(903), X(4364)}}, {{A, B, C, X(1268), X(17758)}}, {{A, B, C, X(3661), X(4393)}}, {{A, B, C, X(3775), X(4649)}}, {{A, B, C, X(3864), X(60664)}}, {{A, B, C, X(3912), X(50095)}}, {{A, B, C, X(4373), X(17247)}}, {{A, B, C, X(4441), X(33931)}}, {{A, B, C, X(4505), X(46132)}}, {{A, B, C, X(4791), X(14210)}}, {{A, B, C, X(6384), X(34258)}}, {{A, B, C, X(6539), X(39734)}}, {{A, B, C, X(7179), X(43688)}}, {{A, B, C, X(17246), X(39710)}}, {{A, B, C, X(18822), X(40098)}}, {{A, B, C, X(19975), X(27922)}}, {{A, B, C, X(27475), X(31322)}}, {{A, B, C, X(29594), X(50019)}}, {{A, B, C, X(30570), X(30571)}}, {{A, B, C, X(30966), X(40721)}}, {{A, B, C, X(31002), X(60097)}}, {{A, B, C, X(32853), X(33084)}}, {{A, B, C, X(32864), X(33081)}}, {{A, B, C, X(39714), X(56130)}}, {{A, B, C, X(39994), X(56169)}}, {{A, B, C, X(40012), X(56212)}}, {{A, B, C, X(40033), X(57815)}}, {{A, B, C, X(40415), X(54119)}}, {{A, B, C, X(40418), X(60084)}}, {{A, B, C, X(55945), X(57725)}}
X(60678) = barycentric product X(i)*X(j) for these (i, j): {274, 59261}, {310, 60676}, {313, 60680}, {1502, 60671}, {6063, 60675}, {25426, 561}, {27483, 75}, {28841, 40495}, {30571, 76}, {56658, 59255}, {59272, 6385}
X(60678) = barycentric quotient X(i)/X(j) for these (i, j): {1, 60697}, {2, 4649}, {7, 60715}, {8, 60711}, {9, 60713}, {10, 60724}, {63, 60703}, {69, 60701}, {75, 16826}, {76, 60706}, {81, 59243}, {85, 60717}, {86, 51311}, {92, 60699}, {274, 51356}, {286, 31904}, {304, 60729}, {310, 51314}, {312, 60731}, {313, 60736}, {321, 3842}, {350, 20142}, {514, 4784}, {561, 60719}, {693, 28840}, {740, 16369}, {1577, 4824}, {3596, 60730}, {3661, 40774}, {4358, 4753}, {4359, 5625}, {4391, 4913}, {4647, 59218}, {4791, 4948}, {4823, 4963}, {6063, 60732}, {25426, 31}, {27483, 1}, {28841, 692}, {30571, 6}, {33931, 27495}, {40748, 40746}, {40773, 40734}, {53478, 59219}, {56658, 1001}, {56703, 40749}, {59261, 37}, {59272, 213}, {60671, 32}, {60675, 55}, {60676, 42}, {60680, 58}

X(60679) = BICEVIAN CHORDAL PERSPECTOR OF X(27) AND X(86)

Barycentrics    (a+b)*(a+c)*(2*a^2*b^2+(a^2+b^2)*c^2-c^4)*(-b^4+b^2*c^2+a^2*(b^2+2*c^2)) : :

X(60679) lies on these lines: {2, 51}, {7, 43034}, {27, 17187}, {75, 1953}, {81, 56358}, {86, 17209}, {273, 31917}, {310, 17167}, {327, 57824}, {675, 26714}, {1240, 29967}, {1246, 43718}, {1790, 52394}, {2296, 3402}, {2700, 6037}, {2989, 7419}, {6384, 27460}, {6650, 26839}, {31916, 52781}, {53194, 53196}, {57825, 59257}

X(60679) = isogonal conjugate of X(60726)
X(60679) = isotomic conjugate of X(60737)
X(60679) = trilinear pole of line {514, 53521}
X(60679) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 60726}, {6, 60723}, {31, 60737}, {32, 42711}, {37, 182}, {42, 52134}, {71, 60685}, {72, 10311}, {100, 3288}, {183, 213}, {228, 458}, {321, 34396}, {692, 23878}, {1334, 60716}, {1918, 3403}, {2205, 20023}, {3990, 33971}, {4055, 51315}, {4567, 6784}, {5360, 46806}, {14096, 18098}, {56254, 59208}
X(60679) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 60737}, {3, 60726}, {9, 60723}, {1086, 23878}, {6376, 42711}, {6626, 183}, {8054, 3288}, {34021, 3403}, {40589, 182}, {40592, 52134}, {40627, 6784}
X(60679) = X(i)-cross conjugate of X(j) for these {i, j}: {7146, 81}
X(60679) = pole of line {182, 60726} with respect to the Stammler hyperbola
X(60679) = pole of line {183, 52134} with respect to the Wallace hyperbola
X(60679) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7)}}, {{A, B, C, X(51), X(1474)}}, {{A, B, C, X(57), X(30035)}}, {{A, B, C, X(58), X(511)}}, {{A, B, C, X(81), X(3794)}}, {{A, B, C, X(92), X(9309)}}, {{A, B, C, X(226), X(28402)}}, {{A, B, C, X(263), X(2186)}}, {{A, B, C, X(649), X(47638)}}, {{A, B, C, X(1201), X(30059)}}, {{A, B, C, X(1423), X(30985)}}, {{A, B, C, X(1790), X(3917)}}, {{A, B, C, X(3060), X(18041)}}, {{A, B, C, X(5331), X(27424)}}, {{A, B, C, X(5943), X(17868)}}, {{A, B, C, X(7146), X(52658)}}, {{A, B, C, X(7199), X(42302)}}, {{A, B, C, X(8747), X(14853)}}, {{A, B, C, X(10519), X(17206)}}, {{A, B, C, X(13857), X(18653)}}, {{A, B, C, X(14953), X(31916)}}, {{A, B, C, X(28371), X(30030)}}, {{A, B, C, X(28660), X(40432)}}
X(60679) = barycentric product X(i)*X(j) for these (i, j): {27, 42313}, {262, 86}, {263, 310}, {327, 58}, {2186, 274}, {3402, 6385}, {16887, 42299}, {17167, 42300}, {26714, 3261}, {43718, 44129}, {52612, 52631}, {53196, 53521}, {59257, 8747}
X(60679) = barycentric quotient X(i)/X(j) for these (i, j): {1, 60723}, {2, 60737}, {6, 60726}, {27, 458}, {28, 60685}, {58, 182}, {75, 42711}, {81, 52134}, {86, 183}, {262, 10}, {263, 42}, {274, 3403}, {310, 20023}, {327, 313}, {514, 23878}, {649, 3288}, {1014, 60716}, {1474, 10311}, {2186, 37}, {2206, 34396}, {3122, 6784}, {3402, 213}, {8747, 33971}, {16887, 14994}, {17167, 59197}, {17187, 14096}, {18653, 51372}, {26714, 101}, {42299, 18082}, {42300, 56246}, {42313, 306}, {43718, 71}, {44129, 44144}, {46319, 1918}, {51370, 51373}, {52631, 4079}, {54032, 3682}, {59257, 52396}

X(60680) = BICEVIAN CHORDAL PERSPECTOR OF X(81) AND X(86)

Barycentrics    a*(a+b)*(a+c)*(a*b+2*(a+b)*c+c^2)*(a*(2*b+c)+b*(b+2*c)) : :

X(60680) lies on these lines: {1, 4094}, {2, 40439}, {6, 24944}, {81, 238}, {83, 20132}, {86, 239}, {757, 18166}, {873, 8025}, {1001, 51311}, {1014, 1429}, {1509, 4366}, {1931, 16484}, {1963, 16503}, {2669, 29584}, {3736, 55971}, {4393, 51314}, {14621, 51356}, {15569, 40773}, {17103, 56042}, {21904, 60708}, {24512, 39971}, {27644, 56048}, {28841, 37633}, {34476, 40748}, {39914, 39915}, {42025, 56658}, {50302, 59261}

X(60680) = isogonal conjugate of X(60724)
X(60680) = isotomic conjugate of X(60736)
X(60680) = trilinear pole of line {659, 1019}
X(60680) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 60724}, {6, 3842}, {10, 60697}, {31, 60736}, {37, 4649}, {42, 16826}, {65, 60711}, {71, 60699}, {101, 4824}, {210, 60715}, {213, 60706}, {226, 60713}, {291, 16369}, {594, 59243}, {756, 51311}, {872, 51314}, {1018, 4784}, {1126, 59218}, {1334, 60717}, {1400, 60731}, {1402, 60730}, {1500, 51356}, {1824, 60701}, {1826, 60703}, {1918, 60719}, {2333, 60729}, {3690, 31904}, {4557, 28840}, {4559, 4913}, {5625, 52555}, {40747, 40774}, {57397, 59219}
X(60680) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 60736}, {3, 60724}, {9, 3842}, {1015, 4824}, {3647, 59218}, {6626, 60706}, {34021, 60719}, {39029, 16369}, {40582, 60731}, {40589, 4649}, {40592, 16826}, {40602, 60711}, {40605, 60730}, {55067, 4913}
X(60680) = X(i)-cross conjugate of X(j) for these {i, j}: {3802, 33295}
X(60680) = pole of line {4649, 40774} with respect to the Stammler hyperbola
X(60680) = pole of line {16826, 60706} with respect to the Wallace hyperbola
X(60680) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(83)}}, {{A, B, C, X(2), X(3720)}}, {{A, B, C, X(6), X(593)}}, {{A, B, C, X(37), X(6650)}}, {{A, B, C, X(42), X(51333)}}, {{A, B, C, X(57), X(4038)}}, {{A, B, C, X(81), X(86)}}, {{A, B, C, X(87), X(39948)}}, {{A, B, C, X(88), X(42335)}}, {{A, B, C, X(89), X(39981)}}, {{A, B, C, X(513), X(40776)}}, {{A, B, C, X(673), X(1255)}}, {{A, B, C, X(940), X(16738)}}, {{A, B, C, X(1001), X(15569)}}, {{A, B, C, X(1002), X(31306)}}, {{A, B, C, X(1434), X(55968)}}, {{A, B, C, X(1829), X(16705)}}, {{A, B, C, X(2185), X(2905)}}, {{A, B, C, X(2296), X(55975)}}, {{A, B, C, X(3736), X(34476)}}, {{A, B, C, X(4094), X(4366)}}, {{A, B, C, X(4359), X(24944)}}, {{A, B, C, X(4492), X(39720)}}, {{A, B, C, X(4833), X(16702)}}, {{A, B, C, X(6625), X(47915)}}, {{A, B, C, X(7199), X(27475)}}, {{A, B, C, X(9421), X(40725)}}, {{A, B, C, X(17379), X(40153)}}, {{A, B, C, X(17946), X(44572)}}, {{A, B, C, X(20332), X(40433)}}, {{A, B, C, X(25426), X(60671)}}, {{A, B, C, X(26860), X(52897)}}, {{A, B, C, X(27483), X(30571)}}, {{A, B, C, X(27644), X(42028)}}, {{A, B, C, X(31335), X(52654)}}, {{A, B, C, X(32014), X(39950)}}, {{A, B, C, X(37222), X(37633)}}, {{A, B, C, X(39734), X(55025)}}, {{A, B, C, X(39949), X(40408)}}, {{A, B, C, X(39952), X(55919)}}, {{A, B, C, X(40735), X(57129)}}, {{A, B, C, X(40773), X(60721)}}, {{A, B, C, X(43972), X(48587)}}
X(60680) = barycentric product X(i)*X(j) for these (i, j): {58, 60678}, {310, 60671}, {1434, 60675}, {1509, 60676}, {4359, 59194}, {25426, 274}, {27483, 81}, {28841, 7199}, {30571, 86}, {30966, 40748}, {42302, 56658}, {59261, 757}, {59272, 873}
X(60680) = barycentric quotient X(i)/X(j) for these (i, j): {1, 3842}, {2, 60736}, {6, 60724}, {21, 60731}, {28, 60699}, {58, 4649}, {81, 16826}, {86, 60706}, {274, 60719}, {284, 60711}, {333, 60730}, {513, 4824}, {593, 51311}, {757, 51356}, {849, 59243}, {1014, 60717}, {1019, 28840}, {1100, 59218}, {1333, 60697}, {1412, 60715}, {1434, 60732}, {1437, 60703}, {1444, 60729}, {1509, 51314}, {1790, 60701}, {1914, 16369}, {2194, 60713}, {3720, 59219}, {3733, 4784}, {3736, 40774}, {3737, 4913}, {4359, 59203}, {4833, 4948}, {4840, 4963}, {25426, 37}, {27483, 321}, {28841, 1018}, {30571, 10}, {40748, 40718}, {40773, 27495}, {52680, 4753}, {56658, 4044}, {59194, 1255}, {59261, 1089}, {59272, 756}, {60671, 42}, {60675, 2321}, {60676, 594}, {60678, 313}

X(60681) = X(1)X(4)∩X(29)X(65)

Barycentrics    (a+b-c)*(a-b+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4-2*a^3*(b+c)+b*c*(b+c)^2+2*a*(b+c)*(b^2+c^2)-a^2*(b^2+b*c+c^2)) : :

X(60681) lies on these lines: {1, 4}, {12, 5174}, {21, 22341}, {29, 65}, {46, 7531}, {55, 37258}, {56, 1013}, {92, 2099}, {158, 7524}, {318, 12635}, {411, 40946}, {412, 2646}, {960, 1887}, {1038, 30943}, {1118, 7518}, {1452, 37055}, {1737, 7551}, {1784, 5425}, {1788, 7498}, {1837, 52248}, {1875, 14004}, {1888, 7513}, {1896, 17097}, {1982, 51290}, {2651, 59482}, {2886, 5081}, {3340, 39585}, {3474, 37028}, {3560, 20764}, {3869, 27410}, {4296, 14956}, {5125, 11375}, {5727, 39531}, {7049, 17098}, {7282, 41003}, {7510, 39542}, {7541, 17605}, {9579, 43160}, {11509, 37253}, {15950, 17923}, {17555, 28628}, {18588, 37098}, {26013, 46878}, {37234, 38284}, {37278, 59691}, {37393, 37541}, {37730, 44225}, {39529, 50194}, {40395, 54340}, {40663, 52412}, {44916, 46974}, {56261, 60691}, {60682, 60712}

X(60681) = perspector of circumconic {{A, B, C, X(653), X(41207)}}
X(60681) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 60662}
X(60681) = X(i)-Dao conjugate of X(j) for these {i, j}: {36103, 60662}
X(60681) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1982, 60682}
X(60681) = pole of line {65, 243} with respect to the Feuerbach hyperbola
X(60681) = pole of line {283, 40946} with respect to the Stammler hyperbola
X(60681) = isogonal conjugate of the bicevian chordal perspector of X(1) and X(3)
X(60681) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(37142)}}, {{A, B, C, X(4), X(1982)}}, {{A, B, C, X(21), X(2654)}}, {{A, B, C, X(29), X(243)}}, {{A, B, C, X(73), X(296)}}, {{A, B, C, X(226), X(1952)}}, {{A, B, C, X(515), X(54526)}}, {{A, B, C, X(1248), X(1745)}}, {{A, B, C, X(1699), X(54900)}}, {{A, B, C, X(1896), X(40950)}}, {{A, B, C, X(2635), X(55924)}}, {{A, B, C, X(5307), X(40395)}}, {{A, B, C, X(34299), X(56825)}}, {{A, B, C, X(51282), X(56261)}}
X(60681) = barycentric product X(i)*X(j) for these (i, j): {4, 60705}, {1982, 226}, {40149, 51290}, {60682, 92}, {60712, 85}
X(60681) = barycentric quotient X(i)/X(j) for these (i, j): {19, 60662}, {1982, 333}, {51290, 1812}, {60682, 63}, {60705, 69}, {60712, 9}
X(60681) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2655, 73}, {1, 4, 243}, {4, 17985, 225}, {29, 65, 1940}, {2654, 8763, 1}

X(60682) = X(1)X(3)∩X(21)X(73)

Barycentrics    a*(a+b-c)*(a-b+c)*(a^4-2*a^3*(b+c)+b*c*(b+c)^2+2*a*(b+c)*(b^2+c^2)-a^2*(b^2+b*c+c^2)) : :

X(60682) lies on these lines: {1, 3}, {12, 29640}, {21, 73}, {29, 225}, {33, 37258}, {34, 1013}, {37, 17966}, {201, 34772}, {212, 37106}, {222, 16370}, {226, 4653}, {255, 6875}, {388, 10448}, {405, 37694}, {411, 2654}, {412, 40950}, {603, 4189}, {774, 45230}, {1006, 22350}, {1068, 7531}, {1450, 7677}, {1451, 19767}, {1457, 1621}, {1745, 3560}, {2000, 4855}, {2003, 52680}, {2006, 56950}, {2594, 5247}, {2635, 6912}, {2650, 7098}, {2659, 59482}, {3485, 4331}, {3562, 22361}, {3822, 38945}, {3911, 4256}, {4303, 6906}, {4337, 10058}, {4551, 5251}, {4559, 60711}, {4649, 5427}, {4848, 33771}, {5248, 10571}, {5260, 56198}, {5428, 52408}, {5433, 33140}, {5436, 19372}, {6690, 51421}, {6734, 7572}, {6909, 22053}, {6986, 22072}, {7004, 18444}, {7288, 11269}, {7508, 52407}, {8609, 21008}, {9817, 52026}, {10198, 25490}, {11109, 58411}, {11194, 55405}, {11501, 59311}, {15950, 16484}, {16418, 34048}, {16503, 43039}, {16577, 30115}, {17010, 37469}, {17074, 17549}, {17095, 33954}, {17320, 22464}, {18162, 18606}, {18446, 24430}, {18540, 56824}, {23071, 28443}, {24987, 34831}, {29675, 36487}, {35258, 54400}, {35981, 57283}, {37298, 43043}, {37817, 45126}, {40663, 60714}, {46889, 55323}, {54346, 57287}, {55101, 59301}, {60681, 60712}

X(60682) = isogonal conjugate of X(60662)
X(60682) = perspector of circumconic {{A, B, C, X(651), X(41206)}}
X(60682) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1982, 60681}
X(60682) = pole of line {1, 17975} with respect to the Feuerbach hyperbola
X(60682) = pole of line {21, 1936} with respect to the Stammler hyperbola
X(60682) = pole of line {314, 60662} with respect to the Wallace hyperbola
X(60682) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(37142)}}, {{A, B, C, X(3), X(1982)}}, {{A, B, C, X(21), X(1936)}}, {{A, B, C, X(29), X(2646)}}, {{A, B, C, X(46), X(1247)}}, {{A, B, C, X(65), X(1937)}}, {{A, B, C, X(283), X(40946)}}, {{A, B, C, X(897), X(36279)}}, {{A, B, C, X(942), X(5331)}}, {{A, B, C, X(1214), X(40843)}}, {{A, B, C, X(3362), X(3612)}}, {{A, B, C, X(22341), X(40442)}}, {{A, B, C, X(23707), X(37600)}}, {{A, B, C, X(34234), X(37520)}}, {{A, B, C, X(37606), X(55917)}}, {{A, B, C, X(51281), X(56261)}}
X(60682) = barycentric product X(i)*X(j) for these (i, j): {1, 60705}, {226, 51290}, {348, 60712}, {1214, 1982}, {60681, 63}
X(60682) = barycentric quotient X(i)/X(j) for these (i, j): {6, 60662}, {1982, 31623}, {51290, 333}, {60681, 92}, {60705, 75}, {60712, 281}
X(60682) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1758, 65}, {1, 3, 1936}, {1, 36152, 3072}, {1, 37583, 54339}, {1, 51281, 60691}, {1, 54320, 37591}, {3, 60691, 51281}, {21, 73, 1935}, {24299, 37565, 1}

X(60683) = X(1)X(75)∩X(2)X(7033)

Barycentrics    b*c*(a^4+b^2*c^2+2*a^2*(b^2+c^2)) : :

X(60683) lies on these lines: {1, 75}, {2, 7033}, {38, 799}, {76, 49455}, {82, 1923}, {190, 56533}, {870, 18906}, {984, 39044}, {1920, 17598}, {1932, 56971}, {3113, 52134}, {3508, 17277}, {3677, 6384}, {4393, 52652}, {5207, 43749}, {6376, 7174}, {6382, 29652}, {7018, 29840}, {8033, 42055}, {9417, 18042}, {10009, 36480}, {10030, 25303}, {16496, 24524}, {16706, 27020}, {17116, 39914}, {17117, 17752}, {17152, 17153}, {17289, 26959}, {17319, 17787}, {17469, 33764}, {18064, 20889}, {18140, 52662}, {18832, 23051}, {18834, 20883}, {19566, 51974}, {19579, 24330}, {20179, 21760}, {21443, 49464}, {28288, 40093}, {29668, 59518}, {29832, 30632}, {30113, 30892}, {43270, 50285}

X(60683) = isotomic conjugate of X(60664)
X(60683) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 60672}, {6, 60667}, {31, 60664}, {32, 42006}, {83, 59273}, {98, 39684}, {251, 59262}, {47643, 60600}
X(60683) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 60664}, {9, 60667}, {6376, 42006}, {32664, 60672}, {39054, 43357}, {40585, 59262}
X(60683) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {40738, 1330}, {40763, 2895}
X(60683) = pole of line {3808, 7192} with respect to the Steiner circumellipse
X(60683) = pole of line {3808, 4369} with respect to the Steiner inellipse
X(60683) = pole of line {1, 2236} with respect to the Wallace hyperbola
X(60683) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(43763)}}, {{A, B, C, X(82), X(17445)}}, {{A, B, C, X(86), X(3329)}}, {{A, B, C, X(274), X(60707)}}, {{A, B, C, X(304), X(18834)}}, {{A, B, C, X(740), X(43265)}}, {{A, B, C, X(1740), X(23051)}}, {{A, B, C, X(1930), X(1934)}}, {{A, B, C, X(1964), X(1967)}}, {{A, B, C, X(1966), X(3112)}}, {{A, B, C, X(2234), X(55930)}}, {{A, B, C, X(3113), X(3403)}}, {{A, B, C, X(3736), X(12212)}}, {{A, B, C, X(7033), X(30940)}}, {{A, B, C, X(10007), X(32010)}}, {{A, B, C, X(18832), X(39731)}}, {{A, B, C, X(46281), X(52138)}}, {{A, B, C, X(51974), X(51985)}}
X(60683) = barycentric product X(i)*X(j) for these (i, j): {1, 60707}, {38, 59249}, {1959, 39685}, {3329, 75}, {10007, 3112}, {12212, 561}, {14318, 4602}, {51312, 8024}, {60686, 76}, {60702, 92}
X(60683) = barycentric quotient X(i)/X(j) for these (i, j): {1, 60667}, {2, 60664}, {31, 60672}, {38, 59262}, {75, 42006}, {662, 43357}, {1755, 39684}, {1964, 59273}, {3329, 1}, {10007, 38}, {12212, 31}, {14318, 798}, {19591, 60600}, {39685, 1821}, {41295, 46289}, {51312, 251}, {59249, 3112}, {60686, 6}, {60702, 63}, {60707, 75}
X(60683) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3403, 52138}, {1, 75, 1966}, {38, 3112, 1965}, {75, 52138, 3403}, {17445, 51907, 1}, {43749, 56928, 5207}

X(60684) = X(1)X(2)∩X(21)X(5143)

Barycentrics    a^4+a^3*(b+c)+b*c*(b+c)^2+a^2*(2*b+c)*(b+2*c)+2*a*(b+c)*(b^2+c^2) : :

X(60684) lies on these lines: {1, 2}, {21, 5143}, {65, 4670}, {190, 1220}, {392, 32944}, {495, 32775}, {517, 32772}, {964, 37598}, {1010, 4642}, {1478, 32776}, {3754, 25526}, {3812, 50362}, {3877, 25496}, {3931, 54331}, {4026, 5724}, {4364, 34606}, {4418, 4424}, {4425, 5080}, {4657, 5252}, {4702, 37548}, {4781, 11115}, {4868, 25060}, {5260, 58386}, {5725, 25760}, {5793, 17318}, {5903, 43531}, {6682, 54391}, {6703, 40663}, {11533, 56318}, {16393, 17601}, {16454, 24440}, {17335, 31359}, {17556, 25378}, {17592, 49492}, {24174, 24594}, {24325, 54315}, {24593, 37607}, {24627, 54310}, {24715, 50171}, {33083, 38456}

X(60684) = isogonal conjugate of the bicevian chordal perspector of X(1) and X(58)
X(60684) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1193), X(17954)}}, {{A, B, C, X(1220), X(17763)}}, {{A, B, C, X(2363), X(10459)}}
X(60684) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 10, 17763}, {10, 17016, 27368}

X(60685) = X(1)X(19)∩X(31)X(92)

Barycentrics    a*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4-2*b^2*c^2-a^2*(b^2+c^2)) : :

X(60685) lies on these lines: {1, 19}, {4, 983}, {7, 56909}, {29, 3915}, {31, 92}, {33, 3749}, {38, 1748}, {47, 1733}, {58, 56014}, {75, 255}, {82, 158}, {171, 278}, {238, 281}, {242, 2212}, {243, 52428}, {458, 60737}, {595, 39585}, {607, 613}, {608, 611}, {612, 55472}, {614, 55478}, {653, 1471}, {748, 52412}, {750, 17923}, {811, 52138}, {902, 1013}, {985, 56867}, {986, 6197}, {1201, 37253}, {1386, 14571}, {1395, 7009}, {1430, 17126}, {1725, 1747}, {1738, 1771}, {1760, 44706}, {1783, 16468}, {1785, 1890}, {1838, 5264}, {1859, 3744}, {1861, 10039}, {1871, 5266}, {1966, 1969}, {2181, 17469}, {2331, 16475}, {2345, 3074}, {3011, 30687}, {3075, 4000}, {3087, 23693}, {3550, 4219}, {3923, 46108}, {4183, 8616}, {4334, 32714}, {5236, 50307}, {5710, 54394}, {7076, 17127}, {7501, 37617}, {10311, 60723}, {10459, 54343}, {15975, 28369}, {16483, 37393}, {16568, 18477}, {17122, 17917}, {17717, 37799}, {17913, 50302}, {33104, 37371}, {33106, 37372}, {36119, 55927}, {36263, 52414}, {37552, 57276}, {38832, 44734}, {41263, 55393}

X(60685) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 43718}, {3, 262}, {4, 54032}, {5, 51444}, {6, 42313}, {25, 59257}, {63, 2186}, {69, 263}, {71, 60679}, {184, 327}, {216, 42300}, {248, 46807}, {265, 57268}, {287, 51543}, {304, 3402}, {305, 46319}, {525, 26714}, {684, 6037}, {3917, 42299}, {3933, 42288}, {4563, 52631}, {6333, 32716}, {6776, 40803}, {14941, 39682}, {35909, 36885}, {39469, 53196}, {51338, 56267}
X(60685) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 42313}, {3162, 2186}, {6505, 59257}, {32664, 43718}, {36033, 54032}, {36103, 262}, {38997, 656}, {39039, 46807}, {51580, 304}
X(60685) = pole of line {1577, 3810} with respect to the polar circle
X(60685) = pole of line {304, 44706} with respect to the Wallace hyperbola
X(60685) = isogonal conjugate of the bicevian chordal perspector of X(1) and X(63)
X(60685) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1821)}}, {{A, B, C, X(19), X(36120)}}, {{A, B, C, X(28), X(458)}}, {{A, B, C, X(31), X(9417)}}, {{A, B, C, X(48), X(82)}}, {{A, B, C, X(75), X(1953)}}, {{A, B, C, X(92), X(240)}}, {{A, B, C, X(158), X(17442)}}, {{A, B, C, X(182), X(284)}}, {{A, B, C, X(183), X(2303)}}, {{A, B, C, X(1172), X(33971)}}, {{A, B, C, X(1474), X(10311)}}, {{A, B, C, X(1973), X(2190)}}, {{A, B, C, X(2173), X(55927)}}, {{A, B, C, X(2186), X(4008)}}, {{A, B, C, X(3288), X(42669)}}, {{A, B, C, X(17438), X(56034)}}, {{A, B, C, X(23878), X(44661)}}
X(60685) = barycentric product X(i)*X(j) for these (i, j): {1, 458}, {3, 51315}, {4, 52134}, {25, 3403}, {27, 60723}, {28, 60737}, {31, 44144}, {162, 23878}, {182, 92}, {183, 19}, {240, 46806}, {281, 60716}, {286, 60726}, {1474, 42711}, {1969, 34396}, {1973, 20023}, {2167, 39530}, {2190, 59197}, {3288, 811}, {10311, 75}, {33971, 63}, {36119, 51372}, {40440, 59208}, {40703, 51542}, {46254, 6784}, {52414, 56401}, {56828, 8842}
X(60685) = barycentric quotient X(i)/X(j) for these (i, j): {1, 42313}, {19, 262}, {25, 2186}, {28, 60679}, {31, 43718}, {48, 54032}, {63, 59257}, {92, 327}, {182, 63}, {183, 304}, {240, 46807}, {458, 75}, {1973, 263}, {1974, 3402}, {2148, 51444}, {2190, 42300}, {3288, 656}, {3403, 305}, {6784, 3708}, {10311, 1}, {20023, 40364}, {23878, 14208}, {32676, 26714}, {32696, 36132}, {33971, 92}, {34396, 48}, {36104, 6037}, {39530, 14213}, {42711, 40071}, {44144, 561}, {46806, 336}, {51315, 264}, {51542, 293}, {52134, 69}, {57653, 51543}, {59197, 18695}, {59208, 44706}, {60716, 348}, {60723, 306}, {60726, 72}, {60737, 20336}
X(60685) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 19, 240}, {1, 1955, 48}, {1, 51288, 23052}, {19, 23052, 51288}, {19, 56828, 1973}, {31, 92, 1957}, {1953, 8766, 1}

X(60686) = X(1)X(21)∩X(6)X(983)

Barycentrics    a^5+a*b^2*c^2+2*a^3*(b^2+c^2) : :

X(60686) lies on these lines: {1, 21}, {6, 983}, {82, 662}, {100, 17795}, {171, 56805}, {238, 40790}, {869, 8300}, {985, 11328}, {1009, 5255}, {1432, 6660}, {1930, 3112}, {1953, 16559}, {2223, 12194}, {2344, 21793}, {3061, 17716}, {3113, 52138}, {3502, 35975}, {3507, 32911}, {3550, 21495}, {3749, 9575}, {3750, 51319}, {3961, 33299}, {4112, 7976}, {5192, 29674}, {7191, 18208}, {13732, 16478}, {16689, 16877}, {17442, 39725}, {17445, 33760}, {18788, 19649}, {21214, 56774}, {23538, 54416}, {24598, 58863}

X(60686) = isogonal conjugate of X(60664)
X(60686) = perspector of circumconic {{A, B, C, X(662), X(8684)}}
X(60686) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 60664}, {2, 60667}, {6, 42006}, {76, 60672}, {83, 59262}, {290, 39684}, {308, 59273}, {19222, 60600}
X(60686) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 60664}, {9, 42006}, {32664, 60667}
X(60686) = pole of line {1, 2236} with respect to the Stammler hyperbola
X(60686) = pole of line {75, 17457} with respect to the Wallace hyperbola
X(60686) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(43763)}}, {{A, B, C, X(38), X(1581)}}, {{A, B, C, X(58), X(12212)}}, {{A, B, C, X(63), X(39725)}}, {{A, B, C, X(81), X(3329)}}, {{A, B, C, X(82), X(1580)}}, {{A, B, C, X(1923), X(1927)}}, {{A, B, C, X(2186), X(51836)}}, {{A, B, C, X(3112), X(17469)}}, {{A, B, C, X(3113), X(51291)}}, {{A, B, C, X(3747), X(14318)}}, {{A, B, C, X(3794), X(4876)}}, {{A, B, C, X(40773), X(60707)}}
X(60686) = barycentric product X(i)*X(j) for these (i, j): {1, 3329}, {6, 60683}, {19, 60702}, {31, 60707}, {141, 51312}, {1755, 39685}, {1930, 41295}, {1964, 59249}, {10007, 82}, {12212, 75}, {14318, 799}
X(60686) = barycentric quotient X(i)/X(j) for these (i, j): {1, 42006}, {6, 60664}, {31, 60667}, {163, 43357}, {560, 60672}, {1923, 59273}, {1964, 59262}, {3329, 75}, {9417, 39684}, {10007, 1930}, {12212, 1}, {14318, 661}, {39685, 46273}, {41295, 82}, {51312, 83}, {59249, 18833}, {60683, 76}, {60702, 304}, {60707, 561}
X(60686) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 17799, 38}, {1, 31, 1580}, {1, 51291, 52134}, {31, 52134, 51291}, {82, 1964, 1582}, {1959, 17469, 1}

X(60687) = X(1)X(3)∩X(104)X(651)

Barycentrics    a*(a*(a-2*b)*(a^2-b^2)^2-(a-b)*(2*a-b)*(a+b)*(a^2-3*a*b+b^2)*c-a*(a-b)*(2*a-b)*(a+3*b)*c^2+(4*a^3-6*a^2*b-3*a*b^2+2*b^3)*c^3+a*(a+5*b)*c^4-(2*a+b)*c^5) : :

X(60687) lies on these lines: {1, 3}, {2, 36590}, {5, 18340}, {11, 56754}, {104, 651}, {106, 1086}, {109, 38602}, {214, 1807}, {997, 24433}, {1000, 37222}, {1001, 24457}, {1054, 6797}, {1125, 51889}, {1317, 56756}, {1647, 5722}, {2222, 38617}, {3058, 56421}, {3616, 37043}, {4256, 37728}, {4551, 12773}, {5886, 35015}, {6265, 7004}, {6788, 37730}, {10703, 19907}, {11373, 32577}, {11700, 53748}, {11715, 24025}, {11729, 38357}, {12515, 53530}, {12737, 24028}, {15898, 52537}, {22758, 52005}, {24864, 56750}, {35281, 51636}, {43048, 56426}, {52148, 56752}, {53535, 59234}

X(60687) = isogonal conjugate of the bicevian chordal perspector of X(1) and X(80)
X(60687) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(517), X(36590)}}, {{A, B, C, X(1319), X(40437)}}, {{A, B, C, X(23703), X(39444)}}
X(60687) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 41343, 999}, {1, 46820, 5902}

X(60688) = X(1)X(6)∩X(100)X(1255)

Barycentrics    a*(a^2+3*b^2+7*b*c+3*c^2+5*a*(b+c)) : :

X(60688) lies on these lines: {1, 6}, {100, 1255}, {190, 5625}, {846, 17019}, {1051, 27065}, {1054, 17021}, {1125, 4431}, {1698, 17233}, {2108, 3720}, {3216, 24944}, {3622, 49455}, {3624, 3875}, {3743, 20360}, {3746, 51621}, {3790, 48822}, {3821, 29569}, {3842, 50016}, {3923, 29570}, {3993, 16826}, {4384, 31319}, {4413, 17592}, {4687, 50281}, {4698, 4716}, {5018, 16133}, {5263, 50111}, {5287, 17596}, {5293, 58380}, {5524, 21806}, {6542, 25354}, {9332, 37595}, {9345, 28606}, {10180, 34064}, {13610, 56221}, {15668, 49452}, {16569, 25430}, {16831, 49474}, {17117, 19862}, {17127, 27789}, {17315, 50298}, {17318, 40328}, {17390, 24697}, {17763, 27811}, {24248, 29624}, {24295, 29586}, {27268, 49488}, {29574, 33082}, {29580, 33682}, {29597, 43997}, {30571, 60724}, {33087, 41312}, {36494, 49445}, {36531, 49470}, {39586, 49469}, {50309, 51093}

X(60688) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 60669}, {514, 59080}
X(60688) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 60669}
X(60688) = X(i)-Ceva conjugate of X(j) for these {i, j}: {60708, 60710}
X(60688) = pole of line {4063, 48609} with respect to the Bevan circle
X(60688) = pole of line {17494, 53587} with respect to the Steiner circumellipse
X(60688) = pole of line {1018, 6540} with respect to the Yff parabola
X(60688) = pole of line {100, 59080} with respect to the Hutson-Moses hyperbola
X(60688) = isogonal conjugate of the bicevian chordal perspector of X(1) and X(81)
X(60688) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(53688)}}, {{A, B, C, X(1100), X(1929)}}, {{A, B, C, X(1255), X(1757)}}, {{A, B, C, X(3723), X(40438)}}, {{A, B, C, X(13610), X(16777)}}, {{A, B, C, X(21879), X(56221)}}, {{A, B, C, X(39260), X(55925)}}, {{A, B, C, X(46845), X(46971)}}
X(60688) = barycentric product X(i)*X(j) for these (i, j): {1, 60710}, {37, 60708}
X(60688) = barycentric quotient X(i)/X(j) for these (i, j): {1, 60669}, {692, 59080}, {60708, 274}, {60710, 75}
X(60688) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 37, 1757}, {1, 51294, 4649}, {37, 20698, 21816}, {37, 4649, 51294}, {238, 3723, 1}, {1001, 51058, 5223}, {1255, 1962, 1961}, {3993, 16826, 24342}

X(60689) = X(1)X(3)∩X(8)X(221)

Barycentrics    a*(a+b-c)*(a-b+c)*(a^4+a^3*(b+c)-2*b*c*(b+c)^2-a*(b+c)*(b^2-6*b*c+c^2)-a^2*(b^2+4*b*c+c^2)) : :

X(60689) lies on these lines: {1, 3}, {8, 221}, {10, 34040}, {34, 5836}, {73, 3913}, {77, 3895}, {109, 956}, {145, 34046}, {222, 519}, {280, 1222}, {518, 54400}, {603, 12513}, {1191, 1788}, {1376, 1457}, {1394, 4853}, {1406, 10944}, {1407, 3476}, {1455, 3872}, {1465, 54286}, {1480, 5722}, {1616, 7288}, {2122, 56942}, {3241, 17074}, {3419, 34032}, {3434, 51421}, {3632, 34043}, {3679, 34048}, {3698, 19372}, {3753, 34036}, {3869, 26264}, {3911, 16483}, {4296, 14923}, {4383, 40663}, {4417, 7080}, {4559, 37658}, {4723, 28997}, {4848, 16466}, {4915, 34033}, {5121, 24914}, {5192, 56173}, {5252, 6180}, {5289, 25934}, {5687, 10571}, {6604, 17378}, {7074, 59417}, {7078, 11362}, {10914, 21147}, {16236, 16474}, {16486, 56758}, {17757, 34029}, {17784, 56821}, {18360, 22759}, {22129, 51422}, {23071, 34718}, {24390, 34030}, {27739, 52659}, {34051, 36944}, {34606, 53529}, {34744, 55405}, {41006, 50115}, {43043, 45700}

X(60689) = X(i)-isoconjugate-of-X(j) for these {i, j}: {9, 59263}
X(60689) = X(i)-Dao conjugate of X(j) for these {i, j}: {478, 59263}
X(60689) = isogonal conjugate of the bicevian chordal perspector of X(1) and X(84)
X(60689) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(51284)}}, {{A, B, C, X(8), X(9371)}}, {{A, B, C, X(40), X(1222)}}, {{A, B, C, X(56), X(9372)}}, {{A, B, C, X(280), X(3057)}}, {{A, B, C, X(979), X(15803)}}, {{A, B, C, X(17595), X(36100)}}
X(60689) = barycentric product X(i)*X(j) for these (i, j): {51284, 57}, {59221, 7}
X(60689) = barycentric quotient X(i)/X(j) for these (i, j): {56, 59263}, {51284, 312}, {59221, 8}
X(60689) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 40, 9371}, {1, 9364, 56}, {8, 221, 9370}

X(60690) = X(1)X(6)∩X(2)X(4693)

Barycentrics    a*(a^2-2*b^2-7*b*c-2*c^2-4*a*(b+c)) : :

X(60690) lies on these lines: {1, 6}, {2, 4693}, {35, 23854}, {88, 17593}, {89, 9345}, {100, 40434}, {171, 17021}, {190, 551}, {239, 50111}, {662, 4653}, {678, 5297}, {740, 16815}, {748, 17013}, {752, 29569}, {846, 37520}, {968, 17122}, {1125, 1266}, {1962, 17012}, {3622, 32935}, {3624, 5695}, {3634, 17263}, {3685, 29578}, {3923, 41847}, {3993, 17160}, {4029, 50305}, {4085, 9780}, {4363, 25055}, {4432, 16826}, {4495, 30963}, {4664, 24331}, {4689, 9324}, {4702, 4755}, {4716, 16816}, {4759, 46922}, {4860, 52155}, {4868, 25077}, {5284, 17600}, {5308, 50301}, {5550, 17302}, {6542, 50297}, {16706, 19862}, {16832, 50086}, {17244, 31151}, {17256, 49764}, {17259, 49469}, {17260, 49471}, {17271, 49767}, {17277, 50018}, {17316, 50296}, {17354, 48822}, {17595, 26102}, {21806, 35595}, {24693, 29581}, {24715, 29571}, {24841, 50777}, {25351, 29626}, {25378, 27759}, {27268, 32941}, {27784, 37573}, {27811, 32944}, {29570, 50300}, {29579, 32784}, {29583, 50295}, {29591, 50298}, {29595, 50302}, {29596, 50290}, {29601, 32846}, {29624, 50303}, {29640, 37691}, {29659, 41313}, {29660, 41312}, {29814, 54352}, {30564, 32919}, {32847, 49740}, {33076, 49766}, {36478, 41310}, {36480, 51488}, {44307, 60714}, {49708, 50286}, {49721, 51110}

X(60690) = pole of line {667, 47922} with respect to the circumcircle
X(60690) = pole of line {17494, 28886} with respect to the Steiner circumellipse
X(60690) = pole of line {650, 28886} with respect to the Steiner inellipse
X(60690) = pole of line {274, 49780} with respect to the Wallace hyperbola
X(60690) = pole of line {142, 17271} with respect to the dual conic of Yff parabola
X(60690) = isogonal conjugate of the bicevian chordal perspector of X(1) and X(89)
X(60690) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(44), X(30571)}}, {{A, B, C, X(88), X(4649)}}, {{A, B, C, X(40434), X(49712)}}, {{A, B, C, X(49490), X(56151)}}
X(60690) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 15254, 16477}, {1, 16676, 984}, {1, 44, 4649}, {1, 45, 49712}, {1, 60688, 39260}, {1001, 16672, 1}, {4702, 4755, 36531}

X(60691) = X(1)X(3)∩X(4)X(651)

Barycentrics    a*(a^6+a^5*(b+c)+2*b*c*(b^2-c^2)^2+a*(b-c)^2*(b+c)*(b^2+c^2)+a^2*(b^2+c^2)^2-2*a^4*(b^2+b*c+c^2)-2*a^3*(b^3+c^3)) : :

X(60691) lies on these lines: {1, 3}, {4, 651}, {5, 7078}, {6, 5179}, {29, 1069}, {30, 222}, {33, 912}, {72, 2000}, {73, 6985}, {81, 3488}, {155, 7524}, {212, 6883}, {219, 59483}, {221, 12699}, {255, 2654}, {355, 17814}, {376, 17074}, {381, 23071}, {382, 23070}, {394, 3419}, {405, 52408}, {412, 1068}, {429, 10071}, {496, 11269}, {611, 37715}, {950, 36742}, {1012, 52407}, {1013, 3868}, {1058, 30943}, {1172, 3211}, {1191, 11373}, {1210, 36754}, {1387, 16483}, {1406, 1770}, {1480, 30305}, {1498, 5787}, {1785, 37826}, {1870, 37258}, {1877, 44413}, {1935, 37234}, {2003, 3586}, {2323, 23058}, {2883, 48482}, {3173, 18451}, {3362, 38248}, {3894, 9577}, {3927, 35194}, {3955, 56960}, {4551, 18491}, {4658, 54411}, {5315, 37704}, {5398, 57278}, {5399, 11500}, {5906, 11105}, {6734, 7532}, {6911, 22350}, {6913, 22117}, {7074, 26446}, {7352, 37194}, {8144, 24475}, {8609, 14974}, {8614, 12953}, {9370, 18480}, {9581, 54301}, {10527, 25490}, {10529, 26091}, {10826, 56535}, {10916, 34831}, {11113, 55400}, {11236, 56416}, {11240, 34234}, {13352, 36059}, {14054, 54299}, {14058, 49627}, {16473, 37702}, {18391, 44414}, {18481, 34046}, {21258, 49738}, {22124, 59657}, {22753, 34586}, {22791, 34040}, {26884, 37241}, {34043, 41869}, {34231, 56294}, {36747, 56293}, {37235, 43740}, {40960, 51755}, {53996, 54286}, {55917, 60047}, {56261, 60681}

X(60691) = X(i)-Ceva conjugate of X(j) for these {i, j}: {56261, 3}
X(60691) = pole of line {3064, 36054} with respect to the MacBeath circumconic
X(60691) = pole of line {21, 3157} with respect to the Stammler hyperbola
X(60691) = isogonal conjugate of the bicevian chordal perspector of X(1) and X(90)
X(60691) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(43764)}}, {{A, B, C, X(3), X(8759)}}, {{A, B, C, X(4), X(8758)}}, {{A, B, C, X(29), X(46)}}, {{A, B, C, X(65), X(7040)}}, {{A, B, C, X(1069), X(22341)}}, {{A, B, C, X(1155), X(55917)}}, {{A, B, C, X(1214), X(2994)}}, {{A, B, C, X(3362), X(58887)}}, {{A, B, C, X(20764), X(38248)}}, {{A, B, C, X(37565), X(43740)}}
X(60691) = barycentric product X(i)*X(j) for these (i, j): {51282, 63}, {59223, 69}
X(60691) = barycentric quotient X(i)/X(j) for these (i, j): {51282, 92}, {59223, 4}
X(60691) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1936, 3}, {1, 46, 8758}, {1, 51281, 60682}, {1, 5709, 37565}, {4, 3157, 8757}, {4, 3562, 3157}, {255, 2654, 3560}, {381, 23071, 34048}, {1936, 60682, 51281}, {15934, 45923, 37543}

X(60692) = X(1)X(514)∩X(2)X(4530)

Barycentrics    a^4-a^2*(b-2*c)*(2*b-c)-b*(b-c)^2*c-a^3*(b+c)+2*a*(b-c)^2*(b+c) : :
X(60692) = -5*X[3616]+4*X[25342]

X(60692) lies on these lines: {1, 514}, {2, 4530}, {8, 24318}, {41, 4564}, {390, 527}, {519, 43282}, {544, 7972}, {664, 673}, {908, 17316}, {952, 24712}, {1086, 43038}, {1317, 5845}, {2082, 25716}, {2087, 24281}, {3218, 4393}, {3257, 4664}, {3616, 25342}, {3732, 17439}, {3910, 24415}, {3911, 5222}, {4041, 24396}, {4534, 17044}, {4850, 37222}, {5048, 44664}, {6173, 36887}, {9055, 9457}, {11200, 28234}, {14190, 28910}, {17484, 29588}, {21044, 39351}, {21139, 24203}, {21272, 31020}, {24447, 48323}, {24806, 49487}, {26007, 35110}, {38460, 46180}

X(60692) = reflection of X(i) in X(j) for these {i,j}: {8, 24318}, {9318, 1}
X(60692) = pole of line {239, 47785} with respect to the Steiner circumellipse
X(60692) = pole of line {812, 36237} with respect to the Yff parabola
X(60692) = isogonal conjugate of the bicevian chordal perspector of X(1) and X(101)
X(60692) = intersection, other than A, B, C, of circumconics {{A, B, C, X(85), X(21105)}}, {{A, B, C, X(663), X(9319)}}, {{A, B, C, X(664), X(9318)}}, {{A, B, C, X(885), X(53214)}}, {{A, B, C, X(4449), X(4564)}}, {{A, B, C, X(9311), X(21132)}}, {{A, B, C, X(27475), X(30573)}}
X(60692) = barycentric product X(i)*X(j) for these (i, j): {10006, 664}, {60698, 75}
X(60692) = barycentric quotient X(i)/X(j) for these (i, j): {10006, 522}, {60698, 1}
X(60692) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 514, 9318}, {664, 2170, 9317}

X(60693) = X(4)X(6)∩X(51)X(107)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^8-b^2*c^2*(b^2-c^2)^2-4*a^6*(b^2+c^2)-2*a^2*(b^2-c^2)^2*(b^2+c^2)+a^4*(5*b^4+3*b^2*c^2+5*c^4)) : :

X(60693) lies on these lines: {4, 6}, {5, 17035}, {51, 107}, {54, 44088}, {112, 22521}, {143, 37127}, {182, 35474}, {262, 10311}, {264, 576}, {297, 18583}, {317, 14561}, {324, 53863}, {340, 24206}, {378, 10788}, {401, 30258}, {419, 6403}, {427, 45867}, {450, 5640}, {458, 1351}, {511, 36794}, {648, 5097}, {1173, 4994}, {1629, 13366}, {1994, 30506}, {2052, 15004}, {3090, 32001}, {3168, 9777}, {3284, 44924}, {3518, 19189}, {3527, 43710}, {3567, 46866}, {5050, 37200}, {5052, 6531}, {5093, 9308}, {5158, 42329}, {5999, 60694}, {6755, 56297}, {7577, 44375}, {8537, 44145}, {8541, 43976}, {8884, 37505}, {10003, 60700}, {10312, 37334}, {10358, 54412}, {10796, 15014}, {11170, 60266}, {14389, 41203}, {14483, 57732}, {14494, 38282}, {14848, 52282}, {15019, 46106}, {32002, 39569}, {34565, 42400}, {35930, 40807}, {38264, 52518}, {39081, 42350}, {39099, 44144}, {43768, 54375}, {44443, 44492}, {45105, 54867}, {48876, 52289}, {50649, 53485}, {56022, 59661}

X(60693) = reflection of X(i) in X(j) for these {i,j}: {37124, 36794}
X(60693) = perspector of circumconic {{A, B, C, X(107), X(41210)}}
X(60693) = X(i)-isoconjugate-of-X(j) for these {i, j}: {63, 60670}
X(60693) = X(i)-Dao conjugate of X(j) for these {i, j}: {3162, 60670}, {53827, 525}
X(60693) = pole of line {51, 1629} with respect to the Jerabek hyperbola
X(60693) = pole of line {33294, 57195} with respect to the Steiner circumellipse
X(60693) = isogonal conjugate of the bicevian chordal perspector of X(2) and X(3)
X(60693) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(60700)}}, {{A, B, C, X(6), X(1298)}}, {{A, B, C, X(53), X(10003)}}, {{A, B, C, X(217), X(1173)}}, {{A, B, C, X(275), X(41204)}}, {{A, B, C, X(1503), X(54664)}}, {{A, B, C, X(3087), X(43710)}}, {{A, B, C, X(3331), X(14483)}}, {{A, B, C, X(3527), X(32445)}}, {{A, B, C, X(6748), X(8795)}}, {{A, B, C, X(6749), X(57732)}}, {{A, B, C, X(9792), X(60670)}}, {{A, B, C, X(14912), X(54531)}}, {{A, B, C, X(38264), X(40065)}}, {{A, B, C, X(38297), X(52518)}}, {{A, B, C, X(38449), X(53023)}}
X(60693) = barycentric product X(i)*X(j) for these (i, j): {4, 60700}, {324, 59241}, {10003, 275}
X(60693) = barycentric quotient X(i)/X(j) for these (i, j): {25, 60670}, {10003, 343}, {59241, 97}, {60700, 69}
X(60693) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 6, 41204}, {51, 275, 436}, {275, 55084, 51}, {511, 36794, 37124}, {1173, 4994, 13450}, {3087, 14853, 4}, {5097, 39530, 648}

X(60694) = X(6)X(22)∩X(76)X(827)

Barycentrics    a^2*(a^8-2*b^4*c^4-a^4*(b^4+c^4)) : :

X(60694) lies on these lines: {2, 37893}, {6, 22}, {20, 3398}, {23, 56920}, {76, 827}, {183, 1576}, {250, 9832}, {384, 44162}, {385, 14575}, {699, 3565}, {858, 7792}, {1370, 16989}, {1975, 15257}, {2071, 26316}, {3095, 7488}, {4027, 10342}, {5999, 60693}, {6636, 50666}, {7493, 7774}, {7754, 10547}, {7766, 19222}, {10298, 35002}, {10317, 35924}, {10420, 53704}, {11380, 14035}, {14574, 54332}, {14601, 36822}, {16932, 37891}, {18018, 38830}, {19154, 37123}, {26881, 56923}

X(60694) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {43722, 21289}
X(60694) = X(i)-cross conjugate of X(j) for these {i, j}: {59204, 59248}
X(60694) = pole of line {141, 19602} with respect to the Stammler hyperbola
X(60694) = pole of line {8024, 23293} with respect to the Wallace hyperbola
X(60694) = isogonal conjugate of the bicevian chordal perspector of X(2) and X(66)
X(60694) = intersection, other than A, B, C, of circumconics {{A, B, C, X(22), X(38830)}}, {{A, B, C, X(699), X(33632)}}, {{A, B, C, X(18018), X(20859)}}, {{A, B, C, X(42826), X(46288)}}
X(60694) = barycentric product X(i)*X(j) for these (i, j): {6, 60727}, {32, 59248}, {40416, 59204}, {42826, 76}
X(60694) = barycentric quotient X(i)/X(j) for these (i, j): {42826, 6}, {59204, 626}, {59248, 1502}, {60727, 76}
X(60694) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 51320, 1501}, {10313, 19121, 22}

X(60695) = X(2)X(5467)∩X(6)X(23)

Barycentrics    a^2*(2*a^8+2*b^6*c^2-5*b^4*c^4+2*b^2*c^6-a^6*(b^2+c^2)+a^4*(-2*b^4+b^2*c^2-2*c^4)+a^2*(b^2+c^2)*(b^4+c^4)) : :

X(60695) lies on these lines: {2, 5467}, {6, 23}, {30, 10788}, {32, 691}, {61, 11629}, {62, 11630}, {110, 34383}, {182, 6785}, {187, 15925}, {194, 36156}, {250, 10311}, {251, 14948}, {385, 1316}, {468, 7777}, {523, 7766}, {576, 842}, {598, 15918}, {671, 11636}, {858, 7806}, {1351, 37930}, {1495, 52693}, {2080, 37991}, {2086, 59232}, {2453, 14614}, {3095, 38613}, {3329, 9832}, {5007, 38526}, {5099, 7812}, {5304, 36181}, {5968, 14002}, {5999, 60696}, {6194, 36177}, {7492, 46127}, {7575, 32447}, {7737, 36174}, {7757, 47326}, {7787, 36165}, {7793, 36157}, {7797, 36187}, {7798, 47288}, {7875, 11007}, {8859, 23200}, {9149, 35357}, {9753, 36173}, {10313, 37918}, {10567, 47442}, {11163, 37907}, {16320, 41624}, {16986, 57588}, {16989, 36163}, {19136, 21460}, {30435, 37915}, {32455, 47245}, {34574, 52142}, {37647, 47243}, {37901, 50149}, {44089, 54094}, {44367, 50146}

X(60695) = pole of line {5169, 41939} with respect to the Kiepert hyperbola
X(60695) = pole of line {599, 45330} with respect to the Stammler hyperbola
X(60695) = isogonal conjugate of the bicevian chordal perspector of X(2) and X(67)
X(60695) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(10415), X(20977)}}, {{A, B, C, X(14948), X(30489)}}

X(60696) = X(4)X(2407)∩X(6)X(30)

Barycentrics    a^12+b^2*c^2*(b^2-c^2)^4-5*a^10*(b^2+c^2)+7*a^8*(b^4+b^2*c^2+c^4)-a^6*(b^2+c^2)*(b^4+6*b^2*c^2+c^4)+2*a^2*(b^2-c^2)^2*(b^6+c^6)-4*a^4*(b^8-2*b^6*c^2+b^4*c^4-2*b^2*c^6+c^8) : :
X(60696) = -2*X[576]+X[2452], -X[1350]+2*X[36177], X[2453]+X[11477], -X[5112]+2*X[47581], -2*X[5476]+X[36194], -2*X[11007]+3*X[14561], -3*X[14848]+2*X[50147], -3*X[14853]+X[36163], -2*X[34094]+X[54173], 2*X[37517]+X[47285], X[47283]+4*X[55718]

X(60696) lies on these lines: {2, 15919}, {3, 35345}, {4, 2407}, {6, 30}, {23, 47579}, {25, 3233}, {51, 36192}, {183, 36183}, {262, 9832}, {317, 403}, {381, 40879}, {394, 34093}, {476, 3060}, {511, 1316}, {523, 1351}, {542, 1561}, {576, 2452}, {858, 9753}, {1302, 2986}, {1350, 36177}, {1384, 46981}, {1993, 14611}, {2453, 11477}, {2782, 9970}, {2799, 60509}, {3329, 15915}, {3830, 34810}, {4226, 14687}, {5112, 47581}, {5476, 36194}, {5999, 60695}, {7464, 10788}, {7472, 39656}, {9159, 15019}, {9512, 56401}, {10223, 16266}, {10311, 14966}, {10601, 47509}, {11002, 36188}, {11007, 14561}, {11173, 48721}, {14614, 60508}, {14848, 50147}, {14853, 36163}, {14894, 37498}, {15066, 46868}, {16319, 37645}, {30226, 39099}, {32460, 47576}, {32461, 47575}, {33586, 36178}, {34094, 54173}, {36160, 36747}, {37517, 47285}, {47283, 55718}

X(60696) = midpoint of X(i) and X(j) for these {i,j}: {2453, 11477}
X(60696) = reflection of X(i) in X(j) for these {i,j}: {1350, 36177}, {16279, 20423}, {2452, 576}, {36194, 5476}, {5112, 47581}, {54173, 34094}, {56925, 47571}, {6795, 6}
X(60696) = pole of line {42660, 44221} with respect to the circumcircle
X(60696) = pole of line {15066, 15920} with respect to the Stammler hyperbola
X(60696) = isogonal conjugate of the bicevian chordal perspector of X(2) and X(74)
X(60696) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2986), X(6795)}}, {{A, B, C, X(4846), X(54925)}}
X(60696) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 2407, 15928}, {6, 30, 6795}, {30, 20423, 16279}, {30, 47571, 56925}

X(60697) = X(6)X(31)∩X(37)X(81)

Barycentrics    a^2*(a^2+b*c+2*a*(b+c)) : :

X(60697) lies on these lines: {1, 9346}, {6, 31}, {9, 1961}, {35, 20970}, {37, 81}, {39, 1203}, {44, 5276}, {58, 101}, {63, 16972}, {65, 36074}, {86, 24690}, {100, 21904}, {106, 41415}, {111, 4588}, {171, 2238}, {218, 7296}, {238, 24512}, {387, 9598}, {574, 5313}, {594, 32864}, {595, 20963}, {739, 28210}, {750, 37673}, {757, 2106}, {894, 33295}, {896, 21840}, {985, 16468}, {1015, 5315}, {1046, 3721}, {1100, 1621}, {1107, 57280}, {1185, 4275}, {1193, 33863}, {1197, 4264}, {1333, 2205}, {1399, 36075}, {1400, 2248}, {1428, 56556}, {1449, 8616}, {1468, 2176}, {1475, 20672}, {1509, 31996}, {1575, 32911}, {1724, 17750}, {1965, 41250}, {1999, 4037}, {2242, 54981}, {2275, 5021}, {2279, 40746}, {2295, 5247}, {2305, 35216}, {2344, 51291}, {2345, 37652}, {2712, 28875}, {3017, 5134}, {3285, 34869}, {3509, 46907}, {3726, 32913}, {3735, 49500}, {3758, 16998}, {3780, 5255}, {3868, 16974}, {3930, 4722}, {3989, 16777}, {3997, 5291}, {4109, 8258}, {4286, 5161}, {4376, 49496}, {4386, 17126}, {4396, 24514}, {4400, 17499}, {4649, 40774}, {5007, 6184}, {5019, 16778}, {5278, 17303}, {5312, 31451}, {5524, 16670}, {6629, 30106}, {8300, 16477}, {9259, 54310}, {9506, 51866}, {10026, 29846}, {12194, 24578}, {16369, 16826}, {16514, 20985}, {16589, 37559}, {16669, 44798}, {16785, 52963}, {16827, 17103}, {16968, 54421}, {16971, 40091}, {17362, 32945}, {17731, 31027}, {20142, 60706}, {20483, 33118}, {21010, 40733}, {21839, 30115}, {21874, 37539}, {26242, 56513}, {27274, 34016}, {28471, 28899}, {28482, 59054}, {29473, 58452}, {32912, 49509}, {36086, 40761}, {37596, 56834}, {39252, 40747}, {40734, 59243}, {40736, 51321}, {40750, 59207}, {41422, 55163}, {48870, 56746}, {52635, 55086}, {54317, 54386}

X(60697) = isogonal conjugate of X(27483)
X(60697) = perspector of circumconic {{A, B, C, X(101), X(4596)}}
X(60697) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 27483}, {2, 30571}, {6, 60678}, {7, 60675}, {10, 60680}, {75, 25426}, {76, 60671}, {81, 59261}, {86, 60676}, {274, 59272}, {693, 28841}, {1002, 56658}, {3661, 40748}, {4647, 59194}, {30570, 40721}, {40775, 56703}
X(60697) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 27483}, {9, 60678}, {206, 25426}, {32664, 30571}, {40586, 59261}, {40600, 60676}
X(60697) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4649, 60713}, {16826, 60703}, {51311, 4649}
X(60697) = pole of line {86, 239} with respect to the Stammler hyperbola
X(60697) = pole of line {6586, 8043} with respect to the Steiner inellipse
X(60697) = pole of line {662, 52923} with respect to the Hutson-Moses hyperbola
X(60697) = pole of line {310, 1921} with respect to the Wallace hyperbola
X(60697) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(741)}}, {{A, B, C, X(31), X(1171)}}, {{A, B, C, X(37), X(59218)}}, {{A, B, C, X(42), X(292)}}, {{A, B, C, X(55), X(2248)}}, {{A, B, C, X(58), X(1914)}}, {{A, B, C, X(71), X(295)}}, {{A, B, C, X(81), X(2308)}}, {{A, B, C, X(111), X(2177)}}, {{A, B, C, X(213), X(16369)}}, {{A, B, C, X(672), X(4784)}}, {{A, B, C, X(674), X(28840)}}, {{A, B, C, X(739), X(21747)}}, {{A, B, C, X(985), X(21793)}}, {{A, B, C, X(1011), X(31904)}}, {{A, B, C, X(1918), X(1922)}}, {{A, B, C, X(2249), X(54296)}}, {{A, B, C, X(2276), X(2279)}}, {{A, B, C, X(2280), X(40746)}}, {{A, B, C, X(3842), X(56926)}}, {{A, B, C, X(17735), X(51866)}}, {{A, B, C, X(20142), X(60671)}}, {{A, B, C, X(25426), X(51443)}}, {{A, B, C, X(28471), X(41423)}}
X(60697) = barycentric product X(i)*X(j) for these (i, j): {1, 4649}, {3, 60699}, {4, 60703}, {10, 59243}, {19, 60701}, {25, 60729}, {31, 60706}, {32, 60719}, {37, 51311}, {41, 60732}, {42, 51356}, {55, 60717}, {56, 60731}, {57, 60711}, {100, 4784}, {101, 28840}, {106, 4753}, {109, 4913}, {110, 4824}, {213, 51314}, {604, 60730}, {1126, 5625}, {1171, 59218}, {1333, 60736}, {3842, 58}, {4588, 4948}, {4963, 8652}, {16369, 37128}, {16826, 6}, {20142, 292}, {27495, 40746}, {31904, 71}, {40718, 40734}, {40774, 985}, {60713, 7}, {60715, 9}, {60724, 81}
X(60697) = barycentric quotient X(i)/X(j) for these (i, j): {1, 60678}, {6, 27483}, {31, 30571}, {32, 25426}, {41, 60675}, {42, 59261}, {213, 60676}, {560, 60671}, {1333, 60680}, {1918, 59272}, {2280, 56658}, {3842, 313}, {4649, 75}, {4753, 3264}, {4784, 693}, {4824, 850}, {4913, 35519}, {5625, 1269}, {16369, 3948}, {16826, 76}, {20142, 1921}, {28840, 3261}, {31904, 44129}, {32739, 28841}, {40734, 30966}, {40774, 33931}, {51311, 274}, {51314, 6385}, {51356, 310}, {59218, 1230}, {59243, 86}, {60699, 264}, {60701, 304}, {60703, 69}, {60706, 561}, {60711, 312}, {60713, 8}, {60715, 85}, {60717, 6063}, {60719, 1502}, {60724, 321}, {60729, 305}, {60730, 28659}, {60731, 3596}, {60732, 20567}, {60736, 27801}
X(60697) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 17735, 42}, {6, 21793, 2280}, {31, 2280, 21793}, {58, 213, 172}, {63, 16972, 41269}, {672, 2308, 6}, {2280, 21793, 1914}, {4649, 60711, 60724}, {17126, 37657, 4386}, {39252, 40749, 40747}, {39673, 57397, 2205}

X(60698) = X(1)X(36280)∩X(6)X(513)

Barycentrics    a*(a^4-a^2*(b-2*c)*(2*b-c)-b*(b-c)^2*c-a^3*(b+c)+2*a*(b-c)^2*(b+c)) : :

X(60698) lies on these lines: {1, 36280}, {6, 513}, {7, 7336}, {36, 16468}, {59, 2175}, {69, 24250}, {105, 651}, {511, 59787}, {517, 1351}, {527, 8540}, {576, 24695}, {901, 3240}, {995, 2718}, {1083, 4585}, {1155, 16670}, {1319, 7290}, {1633, 20958}, {2687, 2714}, {3243, 5048}, {3259, 11269}, {3557, 36735}, {3558, 36736}, {3888, 31073}, {3908, 4370}, {4000, 43909}, {4383, 34583}, {4516, 9355}, {5176, 50289}, {5990, 7766}, {6550, 24281}, {7083, 51682}, {8614, 57666}, {10755, 14839}, {11477, 38531}, {14513, 17126}, {17350, 39185}, {19890, 50295}, {31847, 36742}, {35338, 58368}

X(60698) = midpoint of X(i) and X(j) for these {i,j}: {11477, 38531}
X(60698) = reflection of X(i) in X(j) for these {i,j}: {5091, 6}, {69, 24250}
X(60698) = inverse of X(3063) in cosine circle
X(60698) = pole of line {517, 3063} with respect to the cosine circle
X(60698) = isogonal conjugate of the bicevian chordal perspector of X(2) and X(100)
X(60698) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(53607)}}, {{A, B, C, X(59), X(20980)}}, {{A, B, C, X(651), X(5091)}}, {{A, B, C, X(3063), X(18771)}}
X(60698) = barycentric product X(i)*X(j) for these (i, j): {1, 60692}, {10006, 651}
X(60698) = barycentric quotient X(i)/X(j) for these (i, j): {10006, 4391}, {60692, 75}
X(60698) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 513, 5091}

X(60699) = X(4)X(9)∩X(27)X(295)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^2+b*c+2*a*(b+c)) : :

X(60699) lies on these lines: {4, 9}, {27, 295}, {28, 32009}, {33, 1961}, {34, 39972}, {92, 1889}, {225, 13610}, {286, 31902}, {428, 34337}, {430, 52412}, {475, 19865}, {653, 1893}, {1711, 3474}, {1848, 4212}, {1900, 37390}, {1944, 48902}, {2355, 14004}, {3144, 39579}, {3842, 60711}, {4872, 25365}, {6198, 31900}, {6994, 7102}, {7071, 37396}, {11363, 31903}, {15496, 27287}, {16826, 31904}, {24320, 51063}, {32118, 53591}, {46468, 46976}, {60719, 60729}, {60731, 60736}

X(60699) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 30571}, {48, 27483}, {63, 25426}, {69, 60671}, {71, 60680}, {184, 60678}, {222, 60675}, {905, 28841}, {1437, 59261}, {1444, 59272}, {1790, 60676}, {3781, 40748}, {3958, 59194}
X(60699) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 27483}, {3162, 25426}, {36103, 30571}
X(60699) = X(i)-cross conjugate of X(j) for these {i, j}: {60697, 16826}
X(60699) = pole of line {514, 4010} with respect to the polar circle
X(60699) = pole of line {1790, 7193} with respect to the Stammler hyperbola
X(60699) = pole of line {3916, 17206} with respect to the Wallace hyperbola
X(60699) = pole of line {4000, 53590} with respect to the dual conic of Yff parabola
X(60699) = isogonal conjugate of the bicevian chordal perspector of X(3) and X(63)
X(60699) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(31904)}}, {{A, B, C, X(9), X(4649)}}, {{A, B, C, X(10), X(335)}}, {{A, B, C, X(27), X(242)}}, {{A, B, C, X(28), X(40975)}}, {{A, B, C, X(40), X(60715)}}, {{A, B, C, X(71), X(295)}}, {{A, B, C, X(286), X(1839)}}, {{A, B, C, X(516), X(28840)}}, {{A, B, C, X(573), X(59243)}}, {{A, B, C, X(966), X(51356)}}, {{A, B, C, X(2183), X(4784)}}, {{A, B, C, X(3730), X(57419)}}, {{A, B, C, X(5587), X(54510)}}, {{A, B, C, X(5657), X(54677)}}, {{A, B, C, X(12514), X(51311)}}, {{A, B, C, X(14534), X(50314)}}, {{A, B, C, X(50295), X(54119)}}
X(60699) = barycentric product X(i)*X(j) for these (i, j): {10, 31904}, {19, 60706}, {25, 60719}, {27, 3842}, {28, 60736}, {33, 60732}, {34, 60730}, {158, 60701}, {264, 60697}, {273, 60711}, {278, 60731}, {281, 60717}, {286, 60724}, {318, 60715}, {331, 60713}, {393, 60729}, {1824, 51314}, {1826, 51356}, {1897, 28840}, {2052, 60703}, {4649, 92}, {4753, 6336}, {4784, 6335}, {4824, 648}, {4913, 653}, {16826, 4}, {41013, 51311}
X(60699) = barycentric quotient X(i)/X(j) for these (i, j): {4, 27483}, {19, 30571}, {25, 25426}, {28, 60680}, {33, 60675}, {92, 60678}, {1824, 60676}, {1826, 59261}, {1973, 60671}, {2333, 59272}, {3842, 306}, {4649, 63}, {4753, 3977}, {4784, 905}, {4824, 525}, {4913, 6332}, {4948, 49280}, {5625, 4001}, {8750, 28841}, {16826, 69}, {28840, 4025}, {31904, 86}, {51311, 1444}, {51356, 17206}, {59218, 41014}, {59243, 1790}, {60697, 3}, {60701, 326}, {60703, 394}, {60706, 304}, {60711, 78}, {60713, 219}, {60715, 77}, {60717, 348}, {60719, 305}, {60724, 72}, {60729, 3926}, {60730, 3718}, {60731, 345}, {60732, 7182}, {60736, 20336}
X(60699) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 17927, 1826}, {4, 19, 242}, {27, 1824, 7009}, {1839, 1861, 4}

X(60700) = X(2)X(3)∩X(95)X(216)

Barycentrics    a^8-b^2*c^2*(b^2-c^2)^2-4*a^6*(b^2+c^2)-2*a^2*(b^2-c^2)^2*(b^2+c^2)+a^4*(5*b^4+3*b^2*c^2+5*c^4) : :

X(60700) lies on these lines: {2, 3}, {6, 43980}, {95, 216}, {99, 59197}, {141, 40867}, {182, 42313}, {183, 59211}, {233, 32002}, {264, 10979}, {276, 324}, {287, 5092}, {290, 54439}, {323, 50678}, {566, 44375}, {574, 40814}, {1078, 36212}, {1350, 47740}, {1993, 7793}, {1994, 41334}, {3164, 36751}, {3329, 46807}, {5481, 46806}, {6709, 36412}, {7769, 60524}, {7783, 51481}, {7836, 37636}, {7906, 45794}, {8589, 41254}, {10003, 60693}, {12042, 40870}, {13571, 41628}, {14389, 54082}, {14767, 46724}, {14806, 41760}, {17006, 54395}, {21445, 34396}, {22052, 36794}, {27377, 40897}, {35178, 60034}, {36422, 36426}, {37871, 46760}, {39530, 42351}, {40684, 54100}, {47383, 52712}, {54973, 55982}

X(60700) = isogonal conjugate of X(60670)
X(60700) = perspector of circumconic {{A, B, C, X(648), X(41208)}}
X(60700) = X(i)-Dao conjugate of X(j) for these {i, j}: {53827, 523}
X(60700) = X(i)-Ceva conjugate of X(j) for these {i, j}: {42351, 2}
X(60700) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {42351, 6327}
X(60700) = pole of line {3, 54991} with respect to the Stammler hyperbola
X(60700) = pole of line {69, 17035} with respect to the Wallace hyperbola
X(60700) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(31617)}}, {{A, B, C, X(5), X(1972)}}, {{A, B, C, X(95), X(401)}}, {{A, B, C, X(140), X(276)}}, {{A, B, C, X(290), X(52281)}}, {{A, B, C, X(297), X(57907)}}, {{A, B, C, X(324), X(3078)}}, {{A, B, C, X(418), X(31626)}}, {{A, B, C, X(549), X(54973)}}, {{A, B, C, X(631), X(54114)}}, {{A, B, C, X(852), X(55982)}}, {{A, B, C, X(3523), X(38256)}}, {{A, B, C, X(42313), X(52247)}}
X(60700) = barycentric product X(i)*X(j) for these (i, j): {311, 59241}, {10003, 95}, {60693, 69}
X(60700) = barycentric quotient X(i)/X(j) for these (i, j): {10003, 5}, {59241, 54}, {60693, 4}
X(60700) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3, 401}, {95, 216, 56290}, {140, 297, 2}, {22052, 58454, 36794}

X(60701) = X(3)X(63)∩X(71)X(1332)

Barycentrics    a*(a^2-b^2-c^2)*(a^2+b*c+2*a*(b+c)) : :

X(60701) lies on these lines: {3, 63}, {9, 11329}, {35, 18206}, {41, 21508}, {42, 56834}, {57, 16367}, {71, 1332}, {81, 37573}, {100, 28842}, {171, 40773}, {218, 16436}, {238, 24598}, {239, 7783}, {306, 1796}, {307, 25950}, {321, 24053}, {672, 21511}, {894, 24700}, {1790, 2200}, {1931, 5247}, {1959, 56288}, {3219, 19308}, {3305, 16412}, {3666, 33863}, {3912, 24047}, {4189, 54419}, {4229, 57287}, {4416, 37508}, {4640, 17798}, {4641, 18755}, {4649, 51311}, {4847, 48925}, {5021, 5256}, {5030, 17023}, {5273, 37274}, {5285, 16876}, {5294, 16060}, {5744, 24591}, {5745, 37233}, {6626, 19808}, {6996, 59491}, {8822, 29967}, {9441, 24635}, {10436, 16349}, {11343, 56507}, {15803, 19314}, {16054, 54357}, {16061, 54311}, {16826, 60711}, {17316, 41423}, {17729, 24588}, {17735, 37596}, {19310, 31424}, {19329, 31445}, {20347, 31016}, {21371, 54322}, {21477, 56508}, {21495, 56509}, {21514, 56510}, {21537, 25940}, {21981, 37597}, {21989, 25066}, {21997, 56520}, {22127, 55466}, {22267, 26065}, {25946, 59207}, {26243, 56024}, {28606, 37607}, {31904, 60706}, {35258, 37580}, {44416, 59625}, {44447, 48900}

X(60701) = X(i)-isoconjugate-of-X(j) for these {i, j}: {4, 25426}, {19, 30571}, {25, 27483}, {27, 59272}, {28, 60676}, {34, 60675}, {92, 60671}, {430, 59194}, {1474, 59261}, {1824, 60680}, {1973, 60678}, {7649, 28841}
X(60701) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 30571}, {6337, 60678}, {6505, 27483}, {11517, 60675}, {22391, 60671}, {36033, 25426}, {40591, 60676}, {51574, 59261}
X(60701) = X(i)-Ceva conjugate of X(j) for these {i, j}: {60706, 4649}
X(60701) = pole of line {28, 2201} with respect to the Stammler hyperbola
X(60701) = pole of line {286, 1839} with respect to the Wallace hyperbola
X(60701) = pole of line {693, 4988} with respect to the dual conic of polar circle
X(60701) = isogonal conjugate of the bicevian chordal perspector of X(4) and X(19)
X(60701) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(28842)}}, {{A, B, C, X(63), X(51311)}}, {{A, B, C, X(72), X(4649)}}, {{A, B, C, X(78), X(16826)}}, {{A, B, C, X(228), X(1796)}}, {{A, B, C, X(912), X(28840)}}, {{A, B, C, X(1444), X(20769)}}, {{A, B, C, X(1790), X(22060)}}, {{A, B, C, X(3916), X(17206)}}
X(60701) = barycentric product X(i)*X(j) for these (i, j): {1, 60729}, {3, 60706}, {48, 60719}, {219, 60732}, {222, 60730}, {304, 60697}, {306, 51311}, {326, 60699}, {345, 60715}, {348, 60711}, {1332, 28840}, {1444, 3842}, {1790, 60736}, {4561, 4784}, {4592, 4824}, {4649, 69}, {4913, 6516}, {16826, 63}, {17206, 60724}, {20336, 59243}, {31904, 3998}, {51314, 71}, {51356, 72}, {60703, 75}, {60713, 7182}, {60717, 78}, {60731, 77}
X(60701) = barycentric quotient X(i)/X(j) for these (i, j): {3, 30571}, {48, 25426}, {63, 27483}, {69, 60678}, {71, 60676}, {72, 59261}, {184, 60671}, {219, 60675}, {228, 59272}, {906, 28841}, {1790, 60680}, {3842, 41013}, {4649, 4}, {4753, 38462}, {4784, 7649}, {4824, 24006}, {4913, 44426}, {5625, 56875}, {16826, 92}, {23151, 56658}, {28840, 17924}, {51311, 27}, {51314, 44129}, {51356, 286}, {59243, 28}, {60697, 19}, {60699, 158}, {60703, 1}, {60706, 264}, {60711, 281}, {60713, 33}, {60715, 278}, {60717, 273}, {60719, 1969}, {60724, 1826}, {60729, 75}, {60730, 7017}, {60731, 318}, {60732, 331}
X(60701) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 20796, 228}, {3, 63, 20769}, {3916, 25083, 63}, {5744, 37416, 24591}, {20777, 22060, 3}, {60711, 60715, 16826}

X(60702) = X(2)X(5017)∩X(3)X(69)

Barycentrics    (a^2-b^2-c^2)*(a^4+b^2*c^2+2*a^2*(b^2+c^2)) : :

X(60702) lies on these lines: {2, 5017}, {3, 69}, {6, 7793}, {20, 46311}, {39, 6308}, {76, 3098}, {83, 41413}, {98, 50640}, {99, 14810}, {141, 384}, {182, 7771}, {183, 1350}, {193, 33004}, {315, 35424}, {316, 24206}, {325, 37455}, {385, 3094}, {511, 1078}, {524, 5116}, {574, 32451}, {599, 4048}, {626, 35374}, {698, 17129}, {732, 7783}, {1003, 21356}, {1352, 11676}, {1799, 3917}, {1975, 31884}, {2056, 59696}, {3231, 26257}, {3266, 41462}, {3329, 10007}, {3523, 35423}, {3552, 3620}, {3618, 11285}, {3619, 7770}, {3631, 33276}, {3763, 7773}, {3818, 7802}, {3819, 33651}, {5031, 7885}, {5039, 7786}, {5092, 43459}, {5103, 32967}, {5104, 24256}, {5149, 7848}, {5152, 50567}, {5162, 7810}, {5182, 46893}, {5480, 37688}, {5569, 41137}, {5989, 11177}, {6636, 10330}, {6655, 53475}, {7768, 35422}, {7782, 55649}, {7811, 50977}, {7836, 59695}, {7924, 51848}, {7998, 26233}, {8177, 44453}, {8617, 16055}, {9225, 35301}, {10130, 46900}, {11056, 51360}, {11057, 11178}, {11185, 48873}, {11261, 22521}, {13334, 39872}, {13468, 44531}, {13860, 34229}, {14853, 50685}, {14927, 54993}, {14928, 33751}, {15031, 48895}, {15107, 26235}, {15577, 57275}, {20080, 33022}, {22712, 35387}, {26156, 26221}, {28419, 37186}, {29181, 59635}, {31670, 32832}, {32449, 59236}, {32521, 35456}, {32819, 48881}, {34507, 43152}, {34817, 43714}, {34885, 35375}, {35383, 49111}, {35474, 44144}, {35925, 41400}, {35930, 40330}, {37668, 51580}, {45803, 46283}, {51396, 58445}

X(60702) = anticomplement of X(53484)
X(60702) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 60667}, {25, 60664}, {92, 60672}, {1973, 42006}, {36120, 39684}
X(60702) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 60667}, {6337, 42006}, {6505, 60664}, {22391, 60672}, {46094, 39684}, {53484, 53484}
X(60702) = X(i)-Ceva conjugate of X(j) for these {i, j}: {60707, 3329}
X(60702) = pole of line {3917, 12215} with respect to the Jerabek hyperbola
X(60702) = pole of line {7797, 11174} with respect to the Kiepert hyperbola
X(60702) = pole of line {4558, 4577} with respect to the Kiepert parabola
X(60702) = pole of line {25, 10329} with respect to the Stammler hyperbola
X(60702) = pole of line {2528, 6563} with respect to the Steiner circumellipse
X(60702) = pole of line {4, 2896} with respect to the Wallace hyperbola
X(60702) = isogonal conjugate of the bicevian chordal perspector of X(4) and X(25)
X(60702) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(12212)}}, {{A, B, C, X(69), X(1031)}}, {{A, B, C, X(1176), X(22062)}}, {{A, B, C, X(1799), X(12215)}}, {{A, B, C, X(3785), X(43714)}}, {{A, B, C, X(3926), X(60707)}}, {{A, B, C, X(3933), X(10007)}}, {{A, B, C, X(17970), X(20775)}}, {{A, B, C, X(20794), X(34817)}}
X(60702) = barycentric product X(i)*X(j) for these (i, j): {3, 60707}, {304, 60686}, {3329, 69}, {3917, 59249}, {10007, 1799}, {12212, 305}, {14318, 52608}, {36212, 39685}, {60683, 63}
X(60702) = barycentric quotient X(i)/X(j) for these (i, j): {3, 60667}, {63, 60664}, {69, 42006}, {184, 60672}, {3289, 39684}, {3329, 4}, {3917, 59262}, {4558, 43357}, {10007, 427}, {12212, 25}, {14318, 2489}, {20775, 59273}, {39685, 16081}, {59249, 46104}, {60683, 92}, {60686, 19}, {60707, 264}
X(60702) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 69, 12215}, {141, 2076, 384}, {141, 7750, 5207}, {183, 1350, 18906}, {183, 5999, 46318}, {193, 33004, 50659}, {1799, 3917, 37894}, {3785, 10519, 69}, {7998, 26233, 56430}, {10007, 12212, 3329}, {14810, 14994, 99}

X(60703) = X(3)X(48)∩X(228)X(295)

Barycentrics    a^2*(a^2-b^2-c^2)*(a^2+b*c+2*a*(b+c)) : :

X(60703) lies on these lines: {3, 48}, {36, 4260}, {41, 37507}, {72, 1444}, {101, 28842}, {172, 3736}, {198, 37474}, {228, 295}, {284, 37609}, {604, 37502}, {991, 41323}, {1958, 54410}, {2174, 3286}, {2293, 51621}, {2317, 37510}, {2323, 48886}, {3207, 24320}, {3220, 48929}, {4184, 26885}, {4210, 26889}, {4649, 60713}, {5132, 7113}, {11340, 26893}, {15931, 52823}, {16826, 31904}, {20761, 22053}, {24332, 30273}, {40734, 59243}, {48893, 57281}

X(60703) = X(i)-isoconjugate-of-X(j) for these {i, j}: {4, 30571}, {19, 27483}, {25, 60678}, {27, 60676}, {28, 59261}, {92, 25426}, {264, 60671}, {278, 60675}, {286, 59272}, {1826, 60680}, {17924, 28841}
X(60703) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 27483}, {6505, 60678}, {22391, 25426}, {36033, 30571}, {40591, 59261}
X(60703) = X(i)-Ceva conjugate of X(j) for these {i, j}: {16826, 60697}
X(60703) = pole of line {3955, 20733} with respect to the Jerabek hyperbola
X(60703) = pole of line {27, 242} with respect to the Stammler hyperbola
X(60703) = pole of line {40717, 44129} with respect to the Wallace hyperbola
X(60703) = pole of line {3261, 30591} with respect to the dual conic of polar circle
X(60703) = isogonal conjugate of the bicevian chordal perspector of X(4) and X(92)
X(60703) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(28842)}}, {{A, B, C, X(48), X(57685)}}, {{A, B, C, X(71), X(295)}}, {{A, B, C, X(219), X(1808)}}, {{A, B, C, X(916), X(28840)}}, {{A, B, C, X(1444), X(22054)}}, {{A, B, C, X(1790), X(7193)}}, {{A, B, C, X(2252), X(4784)}}, {{A, B, C, X(3682), X(16826)}}, {{A, B, C, X(3781), X(40734)}}, {{A, B, C, X(5625), X(7100)}}
X(60703) = barycentric product X(i)*X(j) for these (i, j): {1, 60701}, {6, 60729}, {48, 60706}, {184, 60719}, {212, 60732}, {219, 60717}, {222, 60731}, {228, 51314}, {306, 59243}, {348, 60713}, {394, 60699}, {603, 60730}, {1331, 28840}, {1332, 4784}, {1437, 60736}, {1444, 60724}, {1790, 3842}, {1796, 5625}, {1797, 4753}, {1813, 4913}, {4558, 4824}, {4649, 63}, {16369, 57738}, {16826, 3}, {20142, 295}, {31904, 3682}, {51311, 72}, {51356, 71}, {57685, 59218}, {60697, 69}, {60711, 77}, {60715, 78}
X(60703) = barycentric quotient X(i)/X(j) for these (i, j): {3, 27483}, {48, 30571}, {63, 60678}, {71, 59261}, {184, 25426}, {212, 60675}, {228, 60676}, {1437, 60680}, {2200, 59272}, {4649, 92}, {4753, 46109}, {4784, 17924}, {4824, 14618}, {4913, 46110}, {9247, 60671}, {16826, 264}, {20142, 40717}, {28840, 46107}, {32656, 28841}, {40734, 31909}, {51311, 286}, {51314, 57796}, {51356, 44129}, {59218, 44143}, {59243, 27}, {60697, 4}, {60699, 2052}, {60701, 75}, {60706, 1969}, {60711, 318}, {60713, 281}, {60715, 273}, {60717, 331}, {60719, 18022}, {60724, 41013}, {60729, 76}, {60731, 7017}, {60732, 57787}
X(60703) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 17976, 71}, {3, 48, 7193}, {228, 1790, 3955}, {1818, 22054, 3}

X(60704) = X(3)X(525)∩X(6)X(4235)

Barycentrics    (a^2-b^2-c^2)*(a^8-b^2*c^2*(b^2-c^2)^2-a^6*(b^2+c^2)+2*a^2*(b^2-c^2)^2*(b^2+c^2)+a^4*(-2*b^4+5*b^2*c^2-2*c^4)) : :
X(60704) = -5*X[631]+2*X[47616], -3*X[5054]+2*X[33509]

X(60704) lies on these lines: {2, 30227}, {3, 525}, {6, 4235}, {99, 287}, {125, 543}, {141, 35902}, {184, 5118}, {217, 7783}, {249, 7782}, {323, 51350}, {376, 524}, {538, 21663}, {599, 36890}, {620, 1562}, {631, 47616}, {1204, 7781}, {1992, 58347}, {2502, 48991}, {2799, 6795}, {5026, 10766}, {5054, 33509}, {5108, 35901}, {5622, 5969}, {6146, 18347}, {6467, 59796}, {7618, 45662}, {8779, 32456}, {11064, 37188}, {13188, 53174}, {15080, 17708}, {15098, 33928}, {15341, 32459}, {17974, 33813}, {18396, 52473}, {22151, 35952}, {37446, 54168}, {43448, 47296}, {44769, 47383}

X(60704) = pole of line {6530, 39533} with respect to the polar circle
X(60704) = pole of line {3111, 5108} with respect to the Jerabek hyperbola
X(60704) = pole of line {4230, 6787} with respect to the Stammler hyperbola
X(60704) = pole of line {401, 47258} with respect to the Steiner circumellipse
X(60704) = pole of line {441, 47249} with respect to the Steiner inellipse
X(60704) = pole of line {877, 32815} with respect to the Wallace hyperbola
X(60704) = isogonal conjugate of the bicevian chordal perspector of X(4) and X(112)
X(60704) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(249), X(22089)}}, {{A, B, C, X(878), X(53700)}}, {{A, B, C, X(879), X(2452)}}, {{A, B, C, X(5489), X(9289)}}
X(60704) = barycentric product X(i)*X(j) for these (i, j): {2452, 69}, {22264, 99}
X(60704) = barycentric quotient X(i)/X(j) for these (i, j): {2452, 4}, {22264, 523}
X(60704) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7782, 9289, 14585}

X(60705) = X(2)X(7)∩X(10)X(1758)

Barycentrics    (a+b-c)*(a-b+c)*(a^4-2*a^3*(b+c)+b*c*(b+c)^2+2*a*(b+c)*(b^2+c^2)-a^2*(b^2+b*c+c^2)) : :

X(60705) lies on these lines: {2, 7}, {10, 1758}, {65, 11110}, {225, 25446}, {333, 664}, {1155, 13727}, {1330, 54346}, {1441, 5235}, {1442, 16704}, {1443, 30564}, {1465, 17277}, {1737, 17596}, {1788, 13725}, {1982, 51290}, {1999, 16577}, {2982, 37870}, {3673, 17595}, {4551, 60731}, {5241, 43056}, {5278, 17080}, {6708, 54107}, {7364, 53042}, {7677, 46909}, {9534, 54320}, {10538, 38945}, {12514, 25513}, {15932, 16828}, {16062, 24914}, {16817, 37591}, {17349, 56418}, {17594, 18391}, {19853, 37550}, {23151, 28920}, {26942, 33116}, {28936, 49753}, {31623, 40149}, {32779, 40999}, {37558, 46877}, {37652, 45126}, {52357, 56311}, {54119, 60249}

X(60705) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 60662}
X(60705) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 60662}
X(60705) = pole of line {1943, 17056} with respect to the Kiepert hyperbola
X(60705) = pole of line {284, 1951} with respect to the Stammler hyperbola
X(60705) = pole of line {333, 1944} with respect to the Wallace hyperbola
X(60705) = isogonal conjugate of the bicevian chordal perspector of X(6) and X(19)
X(60705) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(1982)}}, {{A, B, C, X(57), X(60682)}}, {{A, B, C, X(63), X(51290)}}, {{A, B, C, X(226), X(1952)}}, {{A, B, C, X(307), X(57801)}}, {{A, B, C, X(333), X(1944)}}, {{A, B, C, X(671), X(31164)}}, {{A, B, C, X(1400), X(1945)}}, {{A, B, C, X(5249), X(37870)}}, {{A, B, C, X(5745), X(31623)}}, {{A, B, C, X(5905), X(54119)}}, {{A, B, C, X(7361), X(55868)}}, {{A, B, C, X(10436), X(40412)}}, {{A, B, C, X(18816), X(50116)}}, {{A, B, C, X(28921), X(56201)}}
X(60705) = barycentric product X(i)*X(j) for these (i, j): {1441, 51290}, {1982, 307}, {60681, 69}, {60682, 75}, {60712, 7182}
X(60705) = barycentric quotient X(i)/X(j) for these (i, j): {1, 60662}, {1982, 29}, {51290, 21}, {60681, 4}, {60682, 1}, {60712, 33}
X(60705) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17950, 226}, {2, 63, 1944}, {333, 1214, 1943}

X(60706) = X(2)X(37)∩X(10)X(274)

Barycentrics    b*c*(a^2+b*c+2*a*(b+c)) : :

X(60706) lies on these lines: {2, 37}, {7, 26038}, {8, 25303}, {10, 274}, {39, 16819}, {42, 86}, {43, 2663}, {69, 26040}, {76, 1698}, {85, 1788}, {99, 5251}, {171, 33295}, {172, 16917}, {183, 4413}, {190, 59207}, {239, 24512}, {257, 21951}, {310, 313}, {314, 43223}, {319, 4651}, {325, 3925}, {594, 31027}, {672, 17277}, {693, 48225}, {870, 2279}, {873, 17731}, {889, 25382}, {894, 2238}, {899, 37678}, {903, 56169}, {1002, 49450}, {1009, 16817}, {1015, 16829}, {1086, 31004}, {1125, 17143}, {1213, 25349}, {1240, 56052}, {1269, 18152}, {1376, 16992}, {1441, 7196}, {1500, 31996}, {1574, 27020}, {1654, 24690}, {1914, 17000}, {1920, 27798}, {1930, 28611}, {2275, 27318}, {2295, 16827}, {3228, 56158}, {3240, 41847}, {3261, 47828}, {3264, 30970}, {3293, 17175}, {3294, 29460}, {3596, 59312}, {3616, 17144}, {3617, 24524}, {3624, 32104}, {3634, 18140}, {3661, 30945}, {3679, 52716}, {3696, 28600}, {3720, 4360}, {3741, 4967}, {3758, 37657}, {3761, 19875}, {3766, 48244}, {3783, 24325}, {3789, 24349}, {3795, 40328}, {3807, 21101}, {3826, 37664}, {3828, 6381}, {3842, 40774}, {3875, 26102}, {3879, 4685}, {3926, 19855}, {3934, 20671}, {3945, 59295}, {3975, 29576}, {3993, 30571}, {4044, 60678}, {4066, 32018}, {4212, 54314}, {4218, 39556}, {4357, 24169}, {4361, 17027}, {4363, 24514}, {4374, 47827}, {4386, 16998}, {4396, 16999}, {4406, 4893}, {4411, 48213}, {4416, 4987}, {4426, 16915}, {4553, 22327}, {4554, 60734}, {4647, 33939}, {4649, 40734}, {4665, 30967}, {4670, 21904}, {4705, 16737}, {4713, 17118}, {4714, 14210}, {4948, 45657}, {4968, 33938}, {5224, 26037}, {5247, 17103}, {5564, 17135}, {5936, 6384}, {6376, 9780}, {6533, 29637}, {7179, 10030}, {7199, 47825}, {7321, 20347}, {7763, 19854}, {8299, 16823}, {9596, 33028}, {9598, 33029}, {10009, 52654}, {10453, 42696}, {10459, 34063}, {15668, 17032}, {16569, 25590}, {16589, 25264}, {16604, 26801}, {16606, 54117}, {16705, 19874}, {16712, 19870}, {16739, 33118}, {16748, 56249}, {16815, 20331}, {16826, 60724}, {16828, 25599}, {17018, 17394}, {17050, 29991}, {17116, 24330}, {17151, 25502}, {17160, 30950}, {17210, 52572}, {17275, 24691}, {17285, 30821}, {17286, 30822}, {17393, 29814}, {17398, 20174}, {17762, 25585}, {17794, 49483}, {18037, 31090}, {18135, 19877}, {18146, 19876}, {18698, 20437}, {19856, 33941}, {20142, 60697}, {20156, 42316}, {20179, 33854}, {20335, 24199}, {20483, 30179}, {20880, 33944}, {20906, 47823}, {20907, 47830}, {20911, 33943}, {20913, 29610}, {20943, 46932}, {20949, 47824}, {20954, 48242}, {21857, 26110}, {21868, 24656}, {23807, 47835}, {24165, 49521}, {24342, 40718}, {24437, 31330}, {24592, 37686}, {25508, 56926}, {25614, 40908}, {26045, 46714}, {26643, 41258}, {26959, 40479}, {26978, 27026}, {27324, 52538}, {27855, 36848}, {28248, 40418}, {28612, 33935}, {29591, 52151}, {29631, 35550}, {29822, 30939}, {29861, 35548}, {30946, 42697}, {30965, 56810}, {31002, 55955}, {31006, 33077}, {31028, 48628}, {31402, 33026}, {31448, 33036}, {31460, 33033}, {31904, 60701}, {33035, 54416}, {33296, 59305}, {33775, 42031}, {33933, 33945}, {33936, 50287}, {34282, 42043}, {34884, 37311}, {35152, 35171}, {35538, 40087}, {37668, 40333}, {40533, 56660}, {46277, 52747}, {50314, 54291}, {54308, 59315}, {59212, 60710}, {60717, 60729}

X(60706) = inverse of X(350) in 1st Yff-Moses hyperbola
X(60706) = isogonal conjugate of X(60671)
X(60706) = isotomic conjugate of X(30571)
X(60706) = perspector of circumconic {{A, B, C, X(668), X(4639)}}
X(60706) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 60671}, {6, 25426}, {31, 30571}, {32, 27483}, {58, 59272}, {213, 60680}, {560, 60678}, {604, 60675}, {649, 28841}, {869, 40748}, {1333, 60676}, {2206, 59261}, {20970, 59194}
X(60706) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 30571}, {3, 60671}, {9, 25426}, {10, 59272}, {37, 60676}, {3161, 60675}, {5375, 28841}, {6374, 60678}, {6376, 27483}, {6626, 60680}, {24603, 15569}, {40603, 59261}, {56696, 40773}
X(60706) = X(i)-Ceva conjugate of X(j) for these {i, j}: {51314, 16826}, {60719, 60730}
X(60706) = X(i)-cross conjugate of X(j) for these {i, j}: {3842, 16826}, {16826, 60732}, {59219, 3842}, {60731, 60730}, {60736, 60719}
X(60706) = pole of line {350, 514} with respect to the 1st Yff-Moses hyperbola
X(60706) = pole of line {21005, 23401} with respect to the circumcircle
X(60706) = pole of line {1211, 31027} with respect to the Kiepert hyperbola
X(60706) = pole of line {1333, 2210} with respect to the Stammler hyperbola
X(60706) = pole of line {81, 238} with respect to the Wallace hyperbola
X(60706) = pole of line {4391, 4458} with respect to the dual conic of Bevan circle
X(60706) = pole of line {905, 53556} with respect to the dual conic of polar circle
X(60706) = pole of line {190, 4625} with respect to the dual conic of Feuerbach hyperbola
X(60706) = pole of line {10, 350} with respect to the dual conic of Yff parabola
X(60706) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(16826)}}, {{A, B, C, X(7), X(4699)}}, {{A, B, C, X(10), X(4037)}}, {{A, B, C, X(37), X(291)}}, {{A, B, C, X(42), X(21820)}}, {{A, B, C, X(75), X(40017)}}, {{A, B, C, X(86), X(3739)}}, {{A, B, C, X(192), X(5936)}}, {{A, B, C, X(274), X(350)}}, {{A, B, C, X(310), X(4359)}}, {{A, B, C, X(312), X(51865)}}, {{A, B, C, X(321), X(334)}}, {{A, B, C, X(536), X(28840)}}, {{A, B, C, X(870), X(4441)}}, {{A, B, C, X(903), X(4688)}}, {{A, B, C, X(1441), X(27569)}}, {{A, B, C, X(1575), X(4784)}}, {{A, B, C, X(2276), X(2279)}}, {{A, B, C, X(3228), X(4664)}}, {{A, B, C, X(3666), X(56052)}}, {{A, B, C, X(3693), X(4913)}}, {{A, B, C, X(3797), X(20142)}}, {{A, B, C, X(3995), X(40093)}}, {{A, B, C, X(4043), X(40094)}}, {{A, B, C, X(4261), X(59243)}}, {{A, B, C, X(4358), X(56169)}}, {{A, B, C, X(4373), X(4772)}}, {{A, B, C, X(4671), X(46277)}}, {{A, B, C, X(4687), X(28650)}}, {{A, B, C, X(4698), X(56061)}}, {{A, B, C, X(4739), X(39710)}}, {{A, B, C, X(4751), X(30598)}}, {{A, B, C, X(4753), X(4908)}}, {{A, B, C, X(6384), X(19804)}}, {{A, B, C, X(16606), X(21883)}}, {{A, B, C, X(17205), X(27918)}}, {{A, B, C, X(17264), X(35152)}}, {{A, B, C, X(24589), X(31002)}}, {{A, B, C, X(24944), X(40438)}}, {{A, B, C, X(28606), X(51311)}}, {{A, B, C, X(30571), X(55947)}}, {{A, B, C, X(31993), X(40418)}}, {{A, B, C, X(32011), X(44417)}}, {{A, B, C, X(33891), X(33947)}}, {{A, B, C, X(33931), X(59255)}}, {{A, B, C, X(35144), X(50107)}}, {{A, B, C, X(52893), X(56158)}}
X(60706) = barycentric product X(i)*X(j) for these (i, j): {1, 60719}, {10, 51314}, {264, 60701}, {274, 3842}, {304, 60699}, {310, 60724}, {312, 60717}, {313, 51311}, {321, 51356}, {561, 60697}, {1969, 60703}, {1978, 4784}, {3596, 60715}, {4554, 4913}, {4649, 76}, {4824, 799}, {6063, 60711}, {16826, 75}, {20142, 334}, {20336, 31904}, {20567, 60713}, {20568, 4753}, {27495, 870}, {27801, 59243}, {28840, 668}, {32018, 5625}, {40438, 59203}, {60729, 92}, {60730, 7}, {60731, 85}, {60732, 8}, {60736, 86}
X(60706) = barycentric quotient X(i)/X(j) for these (i, j): {1, 25426}, {2, 30571}, {6, 60671}, {8, 60675}, {10, 60676}, {37, 59272}, {75, 27483}, {76, 60678}, {86, 60680}, {100, 28841}, {321, 59261}, {3842, 37}, {4441, 56658}, {4649, 6}, {4753, 44}, {4784, 649}, {4824, 661}, {4913, 650}, {4948, 4893}, {4963, 4813}, {5625, 1100}, {14621, 40748}, {16369, 3747}, {16826, 1}, {20142, 238}, {27495, 984}, {28840, 513}, {31336, 15569}, {31904, 28}, {40438, 59194}, {40774, 2276}, {45657, 52745}, {51311, 58}, {51314, 86}, {51356, 81}, {59203, 4647}, {59218, 1962}, {59219, 16589}, {59243, 1333}, {60697, 31}, {60699, 19}, {60701, 3}, {60703, 48}, {60711, 55}, {60713, 41}, {60715, 56}, {60717, 57}, {60719, 75}, {60724, 42}, {60729, 63}, {60730, 8}, {60731, 9}, {60732, 7}, {60736, 10}
X(60706) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17759, 37}, {2, 4441, 30963}, {2, 75, 350}, {8, 31997, 25303}, {10, 1909, 25280}, {10, 274, 1909}, {43, 10436, 37632}, {75, 20947, 321}, {75, 30758, 33931}, {75, 30963, 4441}, {1500, 36812, 31996}, {1575, 3739, 2}, {3263, 4359, 75}, {3634, 20888, 18140}, {4363, 37673, 24514}, {4651, 30941, 319}, {4670, 21904, 40721}, {9780, 34284, 6376}, {28612, 33942, 33935}, {60717, 60731, 60729}

X(60707) = X(2)X(39)∩X(141)X(308)

Barycentrics    b^2*c^2*(a^4+b^2*c^2+2*a^2*(b^2+c^2)) : :

X(60707) lies on these lines: {2, 39}, {75, 41531}, {83, 3051}, {99, 14096}, {141, 308}, {183, 327}, {237, 1078}, {290, 37688}, {311, 39999}, {316, 11673}, {350, 40790}, {384, 8623}, {420, 1235}, {850, 45692}, {1221, 26149}, {1502, 3763}, {1613, 7770}, {1909, 30982}, {1915, 56976}, {1978, 29587}, {3096, 33734}, {3589, 33769}, {3619, 6374}, {3661, 56660}, {5117, 17984}, {5651, 60727}, {6382, 29611}, {7760, 20965}, {7768, 20022}, {7771, 37184}, {7793, 41278}, {7804, 52083}, {7831, 11229}, {8920, 40330}, {9208, 14295}, {9210, 44173}, {10010, 52660}, {10159, 40016}, {10302, 34087}, {11185, 37190}, {11331, 18022}, {11338, 21001}, {12212, 59249}, {14617, 24273}, {14994, 34236}, {16988, 35540}, {17143, 56802}, {17292, 18891}, {18840, 40162}, {18906, 52658}, {20582, 30736}, {21356, 44152}, {21531, 59635}, {29579, 59518}, {29591, 40087}, {32449, 60667}, {33301, 44530}, {34885, 37183}, {39266, 47638}, {40877, 44155}, {44144, 52283}, {59213, 60728}

X(60707) = isogonal conjugate of X(60672)
X(60707) = isotomic conjugate of X(60667)
X(60707) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 60672}, {31, 60667}, {32, 60664}, {82, 59273}, {560, 42006}, {798, 43357}, {1910, 39684}, {46289, 59262}
X(60707) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 60667}, {3, 60672}, {39, 59262}, {141, 59273}, {3329, 5116}, {6374, 42006}, {6376, 60664}, {11672, 39684}, {31998, 43357}
X(60707) = X(i)-Ceva conjugate of X(j) for these {i, j}: {59249, 3329}
X(60707) = X(i)-cross conjugate of X(j) for these {i, j}: {10007, 3329}
X(60707) = pole of line {141, 3978} with respect to the Kiepert hyperbola
X(60707) = pole of line {32, 39684} with respect to the Stammler hyperbola
X(60707) = pole of line {6, 8623} with respect to the Wallace hyperbola
X(60707) = pole of line {850, 32193} with respect to the dual conic of 2nd Brocard circle
X(60707) = pole of line {850, 9479} with respect to the dual conic of circumcircle
X(60707) = pole of line {3124, 41178} with respect to the dual conic of Wallace hyperbola
X(60707) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(3329)}}, {{A, B, C, X(4), X(31276)}}, {{A, B, C, X(39), X(694)}}, {{A, B, C, X(76), X(31622)}}, {{A, B, C, X(83), X(3934)}}, {{A, B, C, X(194), X(18840)}}, {{A, B, C, X(308), X(3978)}}, {{A, B, C, X(538), X(10302)}}, {{A, B, C, X(671), X(9466)}}, {{A, B, C, X(1180), X(41295)}}, {{A, B, C, X(1235), X(28677)}}, {{A, B, C, X(3114), X(20023)}}, {{A, B, C, X(3117), X(46319)}}, {{A, B, C, X(3229), X(14318)}}, {{A, B, C, X(6683), X(56059)}}, {{A, B, C, X(7757), X(43094)}}, {{A, B, C, X(7786), X(60278)}}, {{A, B, C, X(7801), X(54816)}}, {{A, B, C, X(8024), X(18896)}}, {{A, B, C, X(8840), X(51373)}}, {{A, B, C, X(9865), X(42006)}}, {{A, B, C, X(14711), X(60638)}}, {{A, B, C, X(20081), X(60285)}}, {{A, B, C, X(26235), X(34087)}}, {{A, B, C, X(31078), X(60111)}}, {{A, B, C, X(31239), X(60100)}}, {{A, B, C, X(39998), X(40016)}}, {{A, B, C, X(40022), X(40162)}}, {{A, B, C, X(40773), X(60686)}}, {{A, B, C, X(44562), X(60279)}}
X(60707) = barycentric product X(i)*X(j) for these (i, j): {141, 59249}, {264, 60702}, {325, 39685}, {561, 60686}, {3329, 76}, {10007, 308}, {12212, 1502}, {14318, 4609}, {41295, 52568}, {60683, 75}
X(60707) = barycentric quotient X(i)/X(j) for these (i, j): {2, 60667}, {6, 60672}, {39, 59273}, {75, 60664}, {76, 42006}, {99, 43357}, {141, 59262}, {511, 39684}, {3329, 6}, {10007, 39}, {12212, 32}, {14318, 669}, {18906, 60600}, {39685, 98}, {41295, 46288}, {51312, 46289}, {59249, 83}, {60683, 1}, {60686, 31}, {60702, 3}
X(60707) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20023, 41259}, {2, 40858, 39}, {2, 76, 3978}, {76, 41259, 20023}, {141, 308, 9230}, {308, 55081, 141}, {3229, 3934, 2}

X(60708) = X(2)X(6)∩X(99)X(1125)

Barycentrics    (a+b)*(a+c)*(a^2+3*b^2+7*b*c+3*c^2+5*a*(b+c)) : :

X(60708) lies on these lines: {2, 6}, {99, 1125}, {190, 59218}, {274, 28618}, {350, 33779}, {757, 17123}, {859, 34889}, {1268, 8013}, {1509, 19862}, {1698, 32004}, {3624, 6626}, {3634, 33770}, {3848, 51369}, {4423, 56934}, {5550, 17103}, {5937, 16374}, {14007, 49488}, {17397, 24378}, {18827, 29578}, {21085, 28653}, {21904, 60680}, {25496, 30598}, {28620, 49560}, {30963, 51314}, {34016, 34595}

X(60708) = X(i)-isoconjugate-of-X(j) for these {i, j}: {213, 60669}, {661, 59080}
X(60708) = X(i)-Dao conjugate of X(j) for these {i, j}: {6626, 60669}, {36830, 59080}
X(60708) = pole of line {99, 59080} with respect to the Kiepert parabola
X(60708) = pole of line {2, 1051} with respect to the Wallace hyperbola
X(60708) = pole of line {1125, 17731} with respect to the dual conic of Yff parabola
X(60708) = isogonal conjugate of the bicevian chordal perspector of X(6) and X(42)
X(60708) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(53688)}}, {{A, B, C, X(1213), X(11599)}}, {{A, B, C, X(1268), X(6707)}}, {{A, B, C, X(1654), X(30598)}}, {{A, B, C, X(5333), X(40164)}}, {{A, B, C, X(10026), X(30586)}}, {{A, B, C, X(17731), X(32014)}}, {{A, B, C, X(20090), X(28626)}}, {{A, B, C, X(20142), X(42335)}}
X(60708) = barycentric product X(i)*X(j) for these (i, j): {274, 60688}, {60710, 86}
X(60708) = barycentric quotient X(i)/X(j) for these (i, j): {86, 60669}, {110, 59080}, {60688, 37}, {60710, 10}
X(60708) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20536, 1213}, {2, 86, 17731}, {6707, 10026, 2}, {32014, 55083, 1125}

X(60709) = X(1)X(43984)∩X(2)X(7)

Barycentrics    a^4-b*(b-c)^2*c-4*a^3*(b+c)-2*a*(b-c)^2*(b+c)+a^2*(5*b^2+3*b*c+5*c^2) : :

X(60709) lies on these lines: {1, 43984}, {2, 7}, {10, 52164}, {44, 14828}, {220, 31269}, {664, 1212}, {1001, 60668}, {2481, 16815}, {3693, 17277}, {3730, 27000}, {3731, 24600}, {3870, 17349}, {3957, 17121}, {4384, 59216}, {4666, 27268}, {4712, 16823}, {4847, 25101}, {6603, 44570}, {6605, 8551}, {6706, 32024}, {10012, 60733}, {14942, 15254}, {16572, 27253}, {17095, 58458}, {17263, 51384}, {17268, 26593}, {17280, 25006}, {17335, 37658}, {27021, 46196}, {27304, 55337}, {31618, 59181}

X(60709) = pole of line {651, 6606} with respect to the Hutson-Moses hyperbola
X(60709) = isogonal conjugate of the bicevian chordal perspector of X(6) and X(57)
X(60709) = intersection, other than A, B, C, of circumconics {{A, B, C, X(142), X(10012)}}, {{A, B, C, X(6666), X(31618)}}, {{A, B, C, X(10025), X(32008)}}, {{A, B, C, X(18230), X(56265)}}
X(60709) = barycentric product X(i)*X(j) for these (i, j): {10012, 32008}, {60733, 8}
X(60709) = barycentric quotient X(i)/X(j) for these (i, j): {10012, 142}, {60733, 7}
X(60709) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 40868, 142}, {2, 51352, 40719}, {2, 9, 10025}, {9, 40719, 51352}, {6666, 9436, 2}

X(60710) = X(1)X(2)∩X(190)X(1213)

Barycentrics    a^2+3*b^2+7*b*c+3*c^2+5*a*(b+c) : :

X(60710) lies on these lines: {1, 2}, {37, 43985}, {99, 59214}, {190, 1213}, {594, 31248}, {1278, 5936}, {1654, 4670}, {3696, 31308}, {3739, 33888}, {3759, 28650}, {3842, 27483}, {4357, 41844}, {4440, 4708}, {4472, 20072}, {4659, 17248}, {4748, 6646}, {4781, 46896}, {5224, 7232}, {5260, 19308}, {5333, 32004}, {5625, 60669}, {6625, 26044}, {6666, 41845}, {6707, 32025}, {6999, 9956}, {7384, 26446}, {8025, 32014}, {17160, 25358}, {17270, 36834}, {17289, 41843}, {17303, 17335}, {17307, 40480}, {17322, 28633}, {17390, 32101}, {20337, 41809}, {21858, 24944}, {24628, 32780}, {25457, 56249}, {26045, 27102}, {28605, 33932}, {28626, 31313}, {28652, 46707}, {31314, 40328}, {32029, 34573}, {35595, 41322}, {40092, 51225}, {59212, 60706}

X(60710) = isotomic conjugate of X(60669)
X(60710) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 60669}, {513, 59080}
X(60710) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 60669}, {39026, 59080}
X(60710) = X(i)-Ceva conjugate of X(j) for these {i, j}: {60708, 60688}
X(60710) = pole of line {1213, 4478} with respect to the Kiepert hyperbola
X(60710) = pole of line {86, 25358} with respect to the Wallace hyperbola
X(60710) = pole of line {3120, 57461} with respect to the dual conic of Wallace hyperbola
X(60710) = isogonal conjugate of the bicevian chordal perspector of X(6) and X(58)
X(60710) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(75), X(29592)}}, {{A, B, C, X(671), X(3828)}}, {{A, B, C, X(1125), X(6650)}}, {{A, B, C, X(1268), X(6542)}}, {{A, B, C, X(1698), X(6625)}}, {{A, B, C, X(3634), X(32014)}}, {{A, B, C, X(5936), X(29570)}}, {{A, B, C, X(6543), X(8013)}}, {{A, B, C, X(18827), X(29580)}}, {{A, B, C, X(27483), X(29586)}}
X(60710) = barycentric product X(i)*X(j) for these (i, j): {10, 60708}, {60688, 75}
X(60710) = barycentric quotient X(i)/X(j) for these (i, j): {2, 60669}, {101, 59080}, {60688, 1}, {60708, 86}
X(60710) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20016, 1125}, {2, 29588, 29612}, {2, 29593, 29569}, {2, 3617, 29570}, {2, 46933, 29593}, {2, 51353, 16826}, {2, 8, 29592}, {10, 16826, 51353}, {1213, 1268, 28604}, {1698, 19875, 25352}, {3679, 29612, 29588}, {3828, 24603, 29610}, {4472, 31144, 20072}, {16826, 51353, 6542}, {16832, 29608, 2}, {50095, 51073, 29609}

X(60711) = X(1)X(5021)∩X(9)X(55)

Barycentrics    a*(a-b-c)*(a^2+b*c+2*a*(b+c)) : :

X(60711) lies on these lines: {1, 5021}, {2, 41423}, {6, 3750}, {9, 55}, {21, 644}, {35, 3294}, {37, 171}, {43, 31477}, {45, 4386}, {63, 51058}, {100, 59207}, {190, 21101}, {191, 3970}, {213, 37573}, {238, 2276}, {333, 2321}, {344, 24586}, {385, 17261}, {405, 3501}, {527, 14828}, {551, 5030}, {594, 33164}, {595, 25092}, {672, 1621}, {748, 17756}, {902, 5276}, {910, 36528}, {940, 3247}, {958, 3208}, {966, 34607}, {978, 31448}, {993, 56530}, {1001, 17754}, {1018, 5251}, {1054, 31443}, {1055, 17549}, {1107, 37588}, {1125, 24047}, {1213, 49732}, {1400, 8238}, {1429, 16367}, {1500, 5247}, {1571, 24174}, {1575, 17123}, {1697, 4051}, {1722, 31426}, {2177, 37657}, {2238, 60714}, {2319, 34820}, {2344, 40757}, {2646, 4520}, {3061, 5250}, {3219, 3930}, {3230, 37617}, {3290, 17596}, {3295, 21384}, {3496, 16601}, {3550, 3731}, {3686, 3996}, {3691, 3871}, {3729, 16992}, {3730, 5248}, {3746, 16552}, {3749, 16517}, {3753, 41322}, {3822, 5134}, {3842, 60699}, {3985, 7081}, {3986, 37508}, {3991, 31445}, {3997, 4653}, {4007, 4042}, {4038, 16777}, {4071, 33116}, {4095, 56311}, {4136, 56313}, {4189, 9310}, {4294, 26036}, {4414, 26242}, {4515, 5302}, {4559, 60682}, {4649, 40774}, {4872, 25353}, {5013, 21214}, {5255, 5283}, {5259, 16549}, {5272, 9574}, {6690, 17747}, {8301, 15254}, {10198, 17732}, {10389, 51194}, {11512, 31421}, {16484, 24512}, {16673, 37604}, {16676, 37540}, {16785, 52680}, {16826, 60701}, {16914, 17743}, {16968, 37598}, {16970, 17594}, {16972, 17592}, {16973, 17715}, {16994, 17116}, {16996, 25269}, {17050, 17687}, {17314, 32853}, {17315, 17731}, {17753, 25500}, {19584, 19591}, {19732, 59772}, {20616, 54339}, {20834, 56956}, {21795, 59734}, {21808, 56288}, {21904, 59238}, {21956, 33138}, {23397, 23853}, {24333, 51052}, {24498, 36265}, {28920, 55869}, {31490, 59310}, {33106, 37661}, {34486, 58036}, {35258, 40131}, {37673, 56009}, {38874, 40796}, {54330, 59337}, {54354, 54416}, {60677, 60721}

X(60711) = perspector of circumconic {{A, B, C, X(644), X(29199)}}
X(60711) = X(i)-isoconjugate-of-X(j) for these {i, j}: {7, 25426}, {56, 27483}, {57, 30571}, {65, 60680}, {85, 60671}, {269, 60675}, {604, 60678}, {1014, 60676}, {1412, 59261}, {1434, 59272}, {3649, 59194}, {3676, 28841}, {7146, 40748}
X(60711) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 27483}, {3161, 60678}, {5452, 30571}, {6600, 60675}, {40599, 59261}, {40602, 60680}
X(60711) = X(i)-Ceva conjugate of X(j) for these {i, j}: {16826, 4649}
X(60711) = X(i)-cross conjugate of X(j) for these {i, j}: {60713, 4649}
X(60711) = pole of line {4394, 7234} with respect to the circumcircle
X(60711) = pole of line {1014, 1429} with respect to the Stammler hyperbola
X(60711) = pole of line {21383, 35341} with respect to the Yff parabola
X(60711) = pole of line {553, 10030} with respect to the Wallace hyperbola
X(60711) = isogonal conjugate of the bicevian chordal perspector of X(7) and X(57)
X(60711) = intersection, other than A, B, C, of circumconics {{A, B, C, X(9), X(4649)}}, {{A, B, C, X(21), X(3684)}}, {{A, B, C, X(55), X(2248)}}, {{A, B, C, X(200), X(16826)}}, {{A, B, C, X(210), X(4102)}}, {{A, B, C, X(333), X(3683)}}, {{A, B, C, X(2319), X(4512)}}, {{A, B, C, X(2329), X(16369)}}, {{A, B, C, X(2344), X(37658)}}, {{A, B, C, X(2348), X(4784)}}, {{A, B, C, X(3693), X(4913)}}, {{A, B, C, X(3694), X(3842)}}, {{A, B, C, X(4254), X(59243)}}, {{A, B, C, X(13615), X(31904)}}, {{A, B, C, X(15733), X(28840)}}, {{A, B, C, X(33635), X(51858)}}, {{A, B, C, X(40774), X(40777)}}, {{A, B, C, X(42033), X(59218)}}
X(60711) = barycentric product X(i)*X(j) for these (i, j): {1, 60731}, {6, 60730}, {21, 3842}, {33, 60729}, {41, 60719}, {55, 60706}, {100, 4913}, {200, 60717}, {210, 51356}, {220, 60732}, {281, 60701}, {284, 60736}, {312, 60697}, {318, 60703}, {333, 60724}, {346, 60715}, {1320, 4753}, {1334, 51314}, {2321, 51311}, {2344, 27495}, {3699, 4784}, {3701, 59243}, {4649, 8}, {4824, 643}, {16369, 36800}, {16826, 9}, {20142, 4876}, {28840, 644}, {31904, 3694}, {32635, 5625}, {40774, 52133}, {60699, 78}, {60713, 75}
X(60711) = barycentric quotient X(i)/X(j) for these (i, j): {8, 60678}, {9, 27483}, {41, 25426}, {55, 30571}, {210, 59261}, {220, 60675}, {284, 60680}, {1334, 60676}, {2175, 60671}, {3842, 1441}, {4649, 7}, {4784, 3676}, {4824, 4077}, {4913, 693}, {16369, 16609}, {16826, 85}, {20142, 10030}, {28840, 24002}, {37658, 56658}, {40774, 7179}, {51311, 1434}, {51356, 57785}, {59243, 1014}, {60697, 57}, {60699, 273}, {60701, 348}, {60703, 77}, {60706, 6063}, {60713, 1}, {60715, 279}, {60717, 1088}, {60719, 20567}, {60724, 226}, {60729, 7182}, {60730, 76}, {60731, 75}, {60732, 57792}, {60736, 349}
X(60711) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 55, 3684}, {21, 1334, 2329}, {37, 17735, 171}, {37, 4640, 3509}, {672, 1621, 16503}, {1001, 42316, 17754}, {3550, 3731, 5275}, {3683, 3693, 9}, {3730, 5248, 41239}, {4877, 33635, 2321}, {16826, 60701, 60715}, {60697, 60724, 4649}

X(60712) = X(1)X(1013)∩X(19)X(25)

Barycentrics    a*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4-2*a^3*(b+c)+b*c*(b+c)^2+2*a*(b+c)*(b^2+c^2)-a^2*(b^2+b*c+c^2)) : :

X(60712) lies on these lines: {1, 1013}, {19, 25}, {27, 4304}, {29, 37573}, {42, 1783}, {92, 3750}, {108, 42289}, {162, 4649}, {281, 2177}, {415, 5174}, {756, 56316}, {1096, 37553}, {1785, 1860}, {1897, 3993}, {1957, 17018}, {2292, 6198}, {2326, 56919}, {2328, 4055}, {3720, 4219}, {5247, 11107}, {14954, 29822}, {16484, 17923}, {26102, 35994}, {29640, 37371}, {29678, 37372}, {36119, 53114}, {37253, 37574}, {52412, 60714}, {60681, 60682}

X(60712) = X(i)-isoconjugate-of-X(j) for these {i, j}: {77, 60662}
X(60712) = isogonal conjugate of the bicevian chordal perspector of X(7) and X(77)
X(60712) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(25), X(1982)}}, {{A, B, C, X(55), X(60682)}}, {{A, B, C, X(968), X(51290)}}
X(60712) = barycentric product X(i)*X(j) for these (i, j): {33, 60705}, {281, 60682}, {1826, 51290}, {1982, 37}, {60681, 9}
X(60712) = barycentric quotient X(i)/X(j) for these (i, j): {607, 60662}, {1982, 274}, {51290, 17206}, {60681, 85}, {60682, 348}, {60705, 7182}
X(60712) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1013, 1430}, {42, 4183, 7076}

X(60713) = X(21)X(210)∩X(41)X(55)

Barycentrics    a^2*(a-b-c)*(a^2+b*c+2*a*(b+c)) : :

X(60713) lies on these lines: {21, 210}, {35, 20683}, {41, 55}, {42, 172}, {100, 40744}, {181, 37583}, {209, 54371}, {284, 2311}, {354, 11349}, {379, 17718}, {518, 21511}, {584, 15624}, {674, 54409}, {869, 1914}, {1030, 22277}, {1376, 54419}, {1428, 37502}, {1468, 4255}, {1580, 60714}, {2174, 35327}, {2223, 4251}, {2245, 8539}, {2280, 21010}, {2329, 4433}, {3056, 4254}, {3475, 4209}, {3779, 36744}, {3811, 13723}, {4223, 37080}, {4262, 37586}, {4266, 8540}, {4289, 47373}, {4649, 60703}, {4663, 56834}, {5547, 5549}, {8298, 40790}, {11328, 19586}, {20715, 34772}, {25946, 28600}, {33124, 33826}

X(60713) = X(i)-isoconjugate-of-X(j) for these {i, j}: {7, 30571}, {56, 60678}, {57, 27483}, {85, 25426}, {226, 60680}, {279, 60675}, {1014, 59261}, {1434, 60676}, {6063, 60671}, {7179, 40748}, {24002, 28841}, {42290, 56658}, {57785, 59272}
X(60713) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 60678}, {5452, 27483}
X(60713) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4649, 60697}
X(60713) = pole of line {1434, 1447} with respect to the Stammler hyperbola
X(60713) = isogonal conjugate of the bicevian chordal perspector of X(7) and X(85)
X(60713) = intersection, other than A, B, C, of circumconics {{A, B, C, X(41), X(18757)}}, {{A, B, C, X(55), X(2248)}}, {{A, B, C, X(220), X(4649)}}, {{A, B, C, X(1334), X(7077)}}, {{A, B, C, X(2053), X(4258)}}, {{A, B, C, X(2318), X(15377)}}, {{A, B, C, X(2340), X(16826)}}, {{A, B, C, X(2389), X(28840)}}
X(60713) = barycentric product X(i)*X(j) for these (i, j): {1, 60711}, {6, 60731}, {21, 60724}, {31, 60730}, {33, 60701}, {41, 60706}, {101, 4913}, {200, 60715}, {210, 51311}, {219, 60699}, {220, 60717}, {281, 60703}, {284, 3842}, {607, 60729}, {1253, 60732}, {1334, 51356}, {2175, 60719}, {2194, 60736}, {2316, 4753}, {2318, 31904}, {2321, 59243}, {2344, 40774}, {4649, 9}, {4784, 644}, {4824, 5546}, {4948, 5549}, {16369, 56154}, {16826, 55}, {20142, 7077}, {28840, 3939}, {33635, 5625}, {60697, 8}
X(60713) = barycentric quotient X(i)/X(j) for these (i, j): {9, 60678}, {41, 30571}, {55, 27483}, {1253, 60675}, {1334, 59261}, {2175, 25426}, {2194, 60680}, {3842, 349}, {4649, 85}, {4784, 24002}, {4913, 3261}, {9447, 60671}, {16826, 6063}, {20142, 18033}, {28840, 52621}, {51311, 57785}, {59243, 1434}, {60697, 7}, {60699, 331}, {60701, 7182}, {60703, 348}, {60706, 20567}, {60711, 75}, {60715, 1088}, {60717, 57792}, {60719, 41283}, {60724, 1441}, {60729, 57918}, {60730, 561}, {60731, 76}
X(60713) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {42, 18266, 172}, {584, 15624, 19133}

X(60714) = X(1)X(474)∩X(43)X(55)

Barycentrics    a*(a^2+b*c-2*a*(b+c)) : :

X(60714) lies on these lines: {1, 474}, {2, 2177}, {3, 50581}, {6, 3550}, {8, 19278}, {9, 31477}, {10, 1043}, {21, 3214}, {31, 3240}, {35, 3293}, {37, 59238}, {38, 3935}, {39, 50028}, {42, 81}, {43, 55}, {57, 49490}, {58, 50587}, {63, 17601}, {75, 29670}, {78, 37598}, {106, 51071}, {165, 1350}, {183, 3875}, {190, 4090}, {192, 56180}, {197, 37576}, {200, 984}, {210, 846}, {213, 51296}, {218, 51300}, {226, 24715}, {228, 5143}, {240, 56316}, {244, 3957}, {284, 60726}, {306, 33079}, {312, 4693}, {333, 4685}, {345, 33165}, {354, 1054}, {386, 5255}, {392, 5529}, {405, 6048}, {480, 4335}, {516, 33096}, {518, 17596}, {519, 4256}, {528, 33106}, {573, 50584}, {612, 17592}, {614, 17715}, {678, 17012}, {740, 7081}, {748, 17782}, {750, 4038}, {799, 25286}, {874, 41318}, {893, 3774}, {899, 1621}, {902, 32911}, {908, 33095}, {940, 42042}, {958, 37574}, {970, 50583}, {978, 3295}, {982, 3870}, {986, 3811}, {988, 6765}, {995, 25439}, {1001, 16569}, {1045, 37619}, {1046, 3579}, {1155, 32913}, {1193, 3871}, {1215, 32932}, {1266, 59730}, {1326, 6043}, {1575, 16503}, {1580, 60713}, {1698, 56993}, {1707, 35445}, {1714, 31452}, {1738, 13405}, {1742, 6244}, {1743, 31508}, {1757, 4640}, {1758, 41539}, {1918, 59304}, {1935, 14882}, {1961, 37593}, {1962, 5297}, {1979, 21757}, {1999, 4434}, {2003, 23703}, {2209, 59300}, {2238, 60711}, {2271, 3501}, {2276, 3684}, {2280, 17756}, {2292, 4420}, {2321, 26244}, {2329, 3507}, {2550, 33111}, {2663, 59254}, {2999, 3749}, {3011, 33132}, {3030, 5943}, {3052, 16468}, {3058, 37663}, {3072, 32141}, {3073, 11849}, {3210, 32920}, {3216, 3746}, {3219, 21805}, {3242, 17591}, {3243, 18193}, {3256, 4551}, {3303, 21214}, {3434, 17717}, {3617, 10448}, {3623, 32577}, {3666, 3689}, {3679, 5737}, {3681, 4414}, {3685, 59511}, {3687, 33076}, {3699, 3971}, {3712, 33164}, {3717, 59547}, {3722, 7191}, {3741, 3996}, {3744, 29821}, {3748, 16610}, {3755, 33135}, {3769, 49488}, {3771, 4429}, {3821, 33126}, {3836, 29839}, {3873, 18201}, {3896, 17763}, {3898, 45763}, {3914, 17719}, {3920, 17600}, {3925, 29640}, {3931, 5293}, {3936, 32948}, {3938, 4850}, {3946, 41457}, {3952, 32936}, {3993, 43290}, {3995, 17780}, {4028, 32846}, {4030, 32866}, {4061, 42334}, {4062, 33078}, {4096, 17261}, {4104, 24697}, {4258, 54329}, {4277, 40401}, {4362, 4716}, {4413, 26102}, {4417, 4660}, {4418, 46897}, {4427, 32938}, {4428, 15485}, {4433, 40790}, {4450, 32843}, {4641, 21870}, {4642, 34772}, {4651, 32917}, {4661, 36263}, {4674, 5425}, {4677, 16499}, {4709, 55095}, {4734, 32921}, {4743, 37764}, {4863, 29676}, {4868, 30115}, {4954, 31136}, {4970, 32926}, {4972, 29846}, {4995, 35466}, {5014, 29849}, {5015, 17748}, {5132, 15621}, {5218, 33137}, {5251, 31855}, {5256, 17716}, {5263, 6685}, {5264, 5312}, {5268, 25430}, {5272, 10389}, {5313, 37610}, {5429, 37589}, {5432, 33140}, {5712, 50301}, {5718, 33109}, {5741, 32947}, {5745, 49772}, {5752, 50585}, {5853, 24239}, {5919, 47623}, {6174, 37634}, {6600, 41886}, {6690, 33138}, {6745, 24210}, {7257, 59643}, {7262, 35258}, {8666, 50575}, {9324, 37520}, {9342, 30950}, {9441, 12782}, {9574, 51194}, {9778, 24695}, {10327, 33092}, {11248, 37699}, {11491, 37570}, {11499, 37529}, {11679, 49459}, {13161, 59722}, {13587, 54310}, {14555, 50296}, {16497, 16833}, {16602, 42819}, {16706, 29656}, {16785, 35342}, {16814, 58629}, {16999, 17319}, {17019, 21806}, {17056, 49732}, {17124, 29814}, {17135, 32918}, {17147, 32927}, {17165, 32845}, {17262, 59597}, {17380, 29842}, {17495, 32923}, {17595, 41711}, {17718, 17889}, {17720, 36485}, {17724, 33147}, {17725, 19785}, {17735, 21904}, {17740, 33169}, {17765, 29840}, {17766, 33071}, {17769, 20056}, {17784, 26098}, {18134, 31151}, {18165, 22278}, {18185, 18792}, {19054, 41421}, {19744, 19875}, {19765, 59311}, {19804, 29651}, {19998, 32864}, {20011, 32919}, {20012, 32853}, {20045, 32924}, {20095, 33107}, {20965, 59797}, {21077, 24851}, {21384, 31448}, {21760, 21792}, {22314, 53412}, {23705, 24429}, {23958, 54352}, {24169, 33124}, {24248, 25568}, {24789, 29675}, {24929, 60353}, {24988, 29851}, {25101, 59684}, {25440, 37607}, {25507, 43223}, {25961, 29830}, {26034, 33084}, {26109, 50299}, {26227, 32860}, {26250, 32928}, {26724, 29689}, {26740, 41553}, {27065, 54309}, {29642, 31252}, {29649, 49470}, {29665, 33128}, {29671, 32850}, {29673, 32851}, {29678, 33108}, {29679, 33156}, {29837, 58443}, {29848, 32774}, {30331, 45204}, {31053, 33094}, {32781, 33175}, {32848, 33091}, {32856, 33102}, {32929, 32931}, {32934, 32937}, {32950, 33065}, {33064, 33068}, {33074, 33077}, {33081, 33086}, {33082, 44419}, {33104, 49719}, {33105, 33110}, {33113, 33117}, {33122, 33125}, {33127, 33131}, {33144, 33149}, {33145, 33153}, {33159, 59692}, {33162, 33168}, {33167, 49524}, {33171, 33174}, {34611, 37651}, {37482, 50578}, {37525, 49494}, {37556, 56630}, {37642, 50282}, {37657, 41423}, {37683, 49497}, {37703, 40688}, {37716, 45701}, {38000, 49457}, {39594, 49678}, {39595, 59593}, {40375, 60552}, {40663, 60682}, {40728, 53145}, {41333, 51319}, {41629, 49685}, {44307, 60690}, {49736, 51415}, {50302, 59297}, {50590, 56018}, {52412, 60712}, {53053, 53089}, {54316, 56926}, {59624, 60731}

X(60714) = reflection of X(i) in X(j) for these {i,j}: {14829, 59679}, {33106, 37662}, {37617, 4256}
X(60714) = perspector of circumconic {{A, B, C, X(4584), X(27834)}}
X(60714) = pole of line {984, 2098} with respect to the Feuerbach hyperbola
X(60714) = pole of line {238, 5253} with respect to the Stammler hyperbola
X(60714) = pole of line {3669, 28851} with respect to the Steiner inellipse
X(60714) = pole of line {350, 3664} with respect to the Wallace hyperbola
X(60714) = isogonal conjugate of the bicevian chordal perspector of X(7) and X(87)
X(60714) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(291), X(4096)}}, {{A, B, C, X(741), X(3445)}}, {{A, B, C, X(3550), X(56353)}}, {{A, B, C, X(3680), X(7220)}}, {{A, B, C, X(3880), X(4964)}}, {{A, B, C, X(8056), X(17261)}}, {{A, B, C, X(8616), X(56358)}}, {{A, B, C, X(9309), X(17063)}}, {{A, B, C, X(17122), X(23617)}}, {{A, B, C, X(24174), X(57705)}}
X(60714) = barycentric product X(i)*X(j) for these (i, j): {1, 17261}, {100, 25666}, {190, 4879}, {4096, 81}, {25280, 6}, {27834, 4964}
X(60714) = barycentric quotient X(i)/X(j) for these (i, j): {4096, 321}, {4879, 514}, {4964, 4462}, {17261, 75}, {25280, 76}, {25666, 693}
X(60714) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1376, 17122}, {2, 2177, 3750}, {2, 3750, 16484}, {6, 4421, 3550}, {10, 33771, 37573}, {35, 3293, 5247}, {42, 100, 171}, {42, 171, 4649}, {43, 55, 238}, {43, 8616, 4383}, {55, 4383, 8616}, {165, 3751, 4650}, {200, 17594, 984}, {210, 4689, 846}, {519, 4256, 37617}, {528, 37662, 33106}, {750, 17018, 4038}, {846, 5524, 210}, {899, 1621, 17123}, {1054, 3979, 354}, {1193, 3871, 37588}, {1738, 13405, 33130}, {3550, 42043, 6}, {3666, 3689, 3961}, {3748, 16610, 29820}, {3750, 56009, 2}, {3913, 4255, 1}, {3920, 46904, 17600}, {3938, 4850, 17598}, {4428, 37679, 15485}, {4640, 4849, 1757}, {5718, 34612, 33109}, {15485, 36634, 37679}, {18755, 20691, 2329}, {24169, 50748, 33124}, {37553, 46917, 5268}, {37574, 59294, 958}, {42042, 56010, 940}, {45701, 48837, 37716}

X(60715) = X(1)X(3)∩X(226)X(1434)

Barycentrics    a*(a+b-c)*(a-b+c)*(a^2+b*c+2*a*(b+c)) : :

X(60715) lies on these lines: {1, 3}, {86, 24705}, {108, 28842}, {226, 1434}, {553, 55082}, {651, 1014}, {1412, 40408}, {1418, 2114}, {1427, 2248}, {1447, 16994}, {1471, 42290}, {1475, 11349}, {3684, 11329}, {3911, 24603}, {4649, 60703}, {5030, 29571}, {5219, 19749}, {5244, 7181}, {5253, 56509}, {7153, 16606}, {7176, 16609}, {16412, 21384}, {16503, 21511}, {16826, 60701}, {17315, 37212}, {18162, 21773}, {25946, 60675}, {29624, 41423}, {51314, 60732}

X(60715) = isogonal conjugate of X(60675)
X(60715) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 60675}, {8, 25426}, {9, 30571}, {21, 60676}, {41, 60678}, {55, 27483}, {210, 60680}, {284, 59261}, {312, 60671}, {333, 59272}, {522, 28841}, {4046, 59194}, {56658, 60673}
X(60715) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 60675}, {223, 27483}, {478, 30571}, {3160, 60678}, {40590, 59261}, {40611, 60676}
X(60715) = X(i)-Ceva conjugate of X(j) for these {i, j}: {60717, 4649}
X(60715) = X(i)-cross conjugate of X(j) for these {i, j}: {60697, 4649}
X(60715) = pole of line {21, 3684} with respect to the Stammler hyperbola
X(60715) = pole of line {314, 3686} with respect to the Wallace hyperbola
X(60715) = pole of line {226, 4038} with respect to the dual conic of Yff parabola
X(60715) = isogonal conjugate of the bicevian chordal perspector of X(8) and X(9)
X(60715) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4649)}}, {{A, B, C, X(2), X(17592)}}, {{A, B, C, X(3), X(28842)}}, {{A, B, C, X(55), X(2248)}}, {{A, B, C, X(81), X(4038)}}, {{A, B, C, X(88), X(17593)}}, {{A, B, C, X(517), X(28840)}}, {{A, B, C, X(940), X(51356)}}, {{A, B, C, X(1014), X(1429)}}, {{A, B, C, X(1155), X(4784)}}, {{A, B, C, X(1403), X(57663)}}, {{A, B, C, X(1434), X(32636)}}, {{A, B, C, X(3361), X(7153)}}, {{A, B, C, X(3666), X(56052)}}, {{A, B, C, X(3842), X(3931)}}, {{A, B, C, X(4913), X(9371)}}, {{A, B, C, X(7146), X(42290)}}, {{A, B, C, X(16606), X(37593)}}, {{A, B, C, X(20142), X(27644)}}
X(60715) = barycentric product X(i)*X(j) for these (i, j): {1, 60717}, {6, 60732}, {34, 60729}, {56, 60706}, {226, 51311}, {269, 60731}, {273, 60703}, {278, 60701}, {279, 60711}, {604, 60719}, {1014, 3842}, {1088, 60713}, {1214, 31904}, {1400, 51314}, {1407, 60730}, {1412, 60736}, {1414, 4824}, {1434, 60724}, {1441, 59243}, {4649, 7}, {4753, 56049}, {4784, 664}, {4913, 934}, {16826, 57}, {28840, 651}, {51356, 65}, {60697, 85}, {60699, 77}
X(60715) = barycentric quotient X(i)/X(j) for these (i, j): {6, 60675}, {7, 60678}, {56, 30571}, {57, 27483}, {65, 59261}, {604, 25426}, {1397, 60671}, {1400, 60676}, {1402, 59272}, {1412, 60680}, {1415, 28841}, {3842, 3701}, {4649, 8}, {4753, 4723}, {4784, 522}, {4824, 4086}, {4913, 4397}, {5228, 56658}, {5625, 3702}, {16369, 3985}, {16826, 312}, {20142, 3975}, {28840, 4391}, {31904, 31623}, {40734, 3786}, {40774, 3790}, {51311, 333}, {51314, 28660}, {51356, 314}, {59243, 21}, {60697, 9}, {60699, 318}, {60701, 345}, {60703, 78}, {60706, 3596}, {60711, 346}, {60713, 200}, {60717, 75}, {60719, 28659}, {60724, 2321}, {60729, 3718}, {60730, 59761}, {60731, 341}, {60732, 76}, {60736, 30713}
X(60715) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {56, 57, 1429}, {241, 32636, 57}, {1014, 1400, 7175}, {13388, 13389, 17592}, {16826, 60701, 60711}, {37772, 37773, 17593}

X(60716) = X(7)X(171)∩X(57)X(77)

Barycentrics    a*(a+b-c)*(a-b+c)*(a^4-2*b^2*c^2-a^2*(b^2+c^2)) : :

X(60716) lies on these lines: {7, 171}, {31, 1447}, {57, 77}, {85, 603}, {109, 40719}, {273, 1395}, {601, 3673}, {651, 17754}, {750, 7179}, {982, 1442}, {985, 1471}, {1106, 7176}, {1393, 7210}, {1443, 7204}, {1468, 3212}, {1935, 52422}, {2199, 41246}, {2275, 40765}, {3075, 17170}, {3598, 17126}, {3674, 37522}, {4386, 34253}, {5269, 7190}, {5932, 45984}, {7223, 52440}, {7269, 17716}, {9436, 54325}, {16997, 39930}, {17077, 24586}, {40750, 40784}, {40757, 42290}

X(60716) = X(i)-isoconjugate-of-X(j) for these {i, j}: {8, 263}, {9, 2186}, {55, 262}, {281, 43718}, {312, 3402}, {327, 2175}, {607, 42313}, {645, 52631}, {1334, 60679}, {1857, 54032}, {3596, 46319}, {3688, 42299}, {3700, 26714}, {3703, 42288}, {6059, 59257}, {15628, 51543}
X(60716) = X(i)-Dao conjugate of X(j) for these {i, j}: {223, 262}, {478, 2186}, {16603, 3773}, {38997, 4041}, {40593, 327}, {51580, 312}
X(60716) = X(i)-cross conjugate of X(j) for these {i, j}: {182, 52134}
X(60716) = pole of line {312, 7069} with respect to the Wallace hyperbola
X(60716) = pole of line {7272, 12047} with respect to the dual conic of Yff parabola
X(60716) = isogonal conjugate of the bicevian chordal perspector of X(9) and X(33)
X(60716) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(81), X(183)}}, {{A, B, C, X(182), X(284)}}, {{A, B, C, X(458), X(1817)}}, {{A, B, C, X(982), X(33103)}}, {{A, B, C, X(1449), X(60723)}}, {{A, B, C, X(1790), X(52394)}}, {{A, B, C, X(2280), X(60726)}}, {{A, B, C, X(3403), X(54308)}}, {{A, B, C, X(4850), X(42711)}}, {{A, B, C, X(7182), X(44708)}}
X(60716) = barycentric product X(i)*X(j) for these (i, j): {182, 85}, {183, 57}, {348, 60685}, {458, 77}, {1014, 60737}, {1412, 42711}, {1414, 23878}, {1434, 60723}, {1804, 51315}, {3288, 4625}, {3403, 56}, {10311, 7182}, {20023, 604}, {20567, 34396}, {33971, 7183}, {44144, 603}, {52134, 7}, {57785, 60726}
X(60716) = barycentric quotient X(i)/X(j) for these (i, j): {56, 2186}, {57, 262}, {77, 42313}, {85, 327}, {182, 9}, {183, 312}, {458, 318}, {603, 43718}, {604, 263}, {1014, 60679}, {1397, 3402}, {3288, 4041}, {3403, 3596}, {7125, 54032}, {7183, 59257}, {10311, 33}, {14096, 33299}, {20023, 28659}, {23878, 4086}, {34396, 41}, {42711, 30713}, {51641, 52631}, {51651, 51543}, {52134, 8}, {59208, 7069}, {60685, 281}, {60723, 2321}, {60726, 210}, {60737, 3701}

X(60717) = X(2)X(7)∩X(65)X(664)

Barycentrics    (a+b-c)*(a-b+c)*(a^2+b*c+2*a*(b+c)) : :

X(60717) lies on these lines: {1, 48925}, {2, 7}, {65, 664}, {85, 5221}, {86, 4640}, {269, 39972}, {273, 1889}, {319, 49732}, {430, 7282}, {1014, 1402}, {1155, 14828}, {1441, 52421}, {1475, 27000}, {3212, 3339}, {3338, 17753}, {3474, 14548}, {3649, 17095}, {3664, 17596}, {3668, 13610}, {3671, 17084}, {3673, 5708}, {3685, 30962}, {3945, 17594}, {4298, 56928}, {4428, 17394}, {4872, 11246}, {4911, 24470}, {4955, 32636}, {5088, 5902}, {5228, 40747}, {7061, 24472}, {7198, 32007}, {7240, 18786}, {7247, 52783}, {10404, 33298}, {10481, 52160}, {16824, 17206}, {16826, 60701}, {17082, 17156}, {17169, 56288}, {24241, 32857}, {27475, 42316}, {30941, 32932}, {31904, 51311}, {33765, 34855}, {33867, 53597}, {36687, 57282}, {39594, 42027}, {60706, 60729}

X(60717) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 60675}, {8, 60671}, {9, 25426}, {21, 59272}, {41, 27483}, {55, 30571}, {284, 60676}, {650, 28841}, {1334, 60680}, {2175, 60678}, {2194, 59261}, {4517, 40748}
X(60717) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 60675}, {223, 30571}, {478, 25426}, {1214, 59261}, {3160, 27483}, {40590, 60676}, {40593, 60678}, {40611, 59272}
X(60717) = X(i)-Ceva conjugate of X(j) for these {i, j}: {60732, 16826}
X(60717) = X(i)-cross conjugate of X(j) for these {i, j}: {4649, 16826}
X(60717) = pole of line {333, 3683} with respect to the Wallace hyperbola
X(60717) = isogonal conjugate of the bicevian chordal perspector of X(9) and X(55)
X(60717) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(16826)}}, {{A, B, C, X(9), X(4649)}}, {{A, B, C, X(57), X(60715)}}, {{A, B, C, X(63), X(51311)}}, {{A, B, C, X(75), X(17248)}}, {{A, B, C, X(226), X(7233)}}, {{A, B, C, X(527), X(28840)}}, {{A, B, C, X(553), X(57785)}}, {{A, B, C, X(579), X(59243)}}, {{A, B, C, X(672), X(4784)}}, {{A, B, C, X(903), X(17254)}}, {{A, B, C, X(1434), X(1447)}}, {{A, B, C, X(3668), X(27691)}}, {{A, B, C, X(3842), X(5257)}}, {{A, B, C, X(4913), X(40869)}}, {{A, B, C, X(10436), X(40409)}}, {{A, B, C, X(35143), X(50127)}}, {{A, B, C, X(40747), X(59207)}}
X(60717) = barycentric product X(i)*X(j) for these (i, j): {1, 60732}, {56, 60719}, {57, 60706}, {226, 51356}, {269, 60730}, {273, 60701}, {278, 60729}, {279, 60731}, {307, 31904}, {331, 60703}, {348, 60699}, {349, 59243}, {1014, 60736}, {1088, 60711}, {1434, 3842}, {1441, 51311}, {4554, 4784}, {4573, 4824}, {4649, 85}, {4913, 658}, {6063, 60697}, {16826, 7}, {20142, 7233}, {28840, 664}, {51314, 65}, {57785, 60724}, {57792, 60713}, {60715, 75}
X(60717) = barycentric quotient X(i)/X(j) for these (i, j): {1, 60675}, {7, 27483}, {56, 25426}, {57, 30571}, {65, 60676}, {85, 60678}, {109, 28841}, {226, 59261}, {604, 60671}, {1014, 60680}, {1400, 59272}, {3842, 2321}, {4649, 9}, {4753, 2325}, {4784, 650}, {4824, 3700}, {4913, 3239}, {4948, 4944}, {4963, 4820}, {5625, 3686}, {16369, 4433}, {16826, 8}, {20142, 3685}, {27495, 3790}, {28840, 522}, {31904, 29}, {40719, 56658}, {51311, 21}, {51314, 314}, {51356, 333}, {59218, 4046}, {59243, 284}, {60697, 55}, {60699, 281}, {60701, 78}, {60703, 219}, {60706, 312}, {60711, 200}, {60713, 220}, {60715, 1}, {60719, 3596}, {60724, 210}, {60729, 345}, {60730, 341}, {60731, 346}, {60732, 75}, {60736, 3701}
X(60717) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 57, 1447}, {65, 1434, 7176}, {553, 9436, 7}, {60706, 60729, 60731}

X(60718) = X(1)X(7)∩X(65)X(513)

Barycentrics    (a+b-c)*(a-b+c)*(2*a^4+2*a^2*b*c-2*a^3*(b+c)-a*(b-c)^2*(b+c)+(b^2-c^2)^2) : :

X(60718) lies on these lines: {1, 7}, {8, 24411}, {56, 38530}, {57, 1647}, {65, 513}, {79, 52377}, {109, 2006}, {222, 33094}, {226, 23703}, {241, 28534}, {244, 24465}, {528, 53531}, {651, 24715}, {883, 25719}, {1086, 53529}, {1106, 12699}, {1446, 54619}, {1836, 9316}, {2183, 9596}, {2796, 4552}, {3339, 6788}, {4014, 53548}, {4660, 28968}, {5057, 9364}, {8270, 33098}, {9355, 45043}, {9579, 18340}, {11246, 53525}, {14882, 59247}, {17074, 33095}, {17095, 24723}, {17350, 25005}, {17768, 24433}, {24725, 37541}, {24836, 53545}, {28075, 28096}, {39293, 40724}

X(60718) = perspector of circumconic {{A, B, C, X(658), X(2006)}}
X(60718) = pole of line {5172, 44408} with respect to the circumcircle
X(60718) = pole of line {514, 1319} with respect to the incircle
X(60718) = pole of line {354, 35015} with respect to the Feuerbach hyperbola
X(60718) = pole of line {4025, 37759} with respect to the Steiner circumellipse
X(60718) = pole of line {36, 514} with respect to the Suppa-Cucoanes circle
X(60718) = isogonal conjugate of the bicevian chordal perspector of X(21) and X(100)
X(60718) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(54619)}}, {{A, B, C, X(4), X(38941)}}, {{A, B, C, X(7), X(19628)}}, {{A, B, C, X(79), X(4089)}}, {{A, B, C, X(513), X(1443)}}, {{A, B, C, X(1442), X(52377)}}
X(60718) = barycentric product X(i)*X(j) for these (i, j): {19636, 3911}
X(60718) = barycentric quotient X(i)/X(j) for these (i, j): {19636, 4997}
X(60718) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {481, 482, 4089}

X(60719) = X(10)X(75)∩X(37)X(274)

Barycentrics    b^2*c^2*(a^2+b*c+2*a*(b+c)) : :
X(60719) = -4*X[3842]+3*X[40774], -5*X[4687]+4*X[25092]

X(60719) lies on these lines: {10, 75}, {37, 274}, {85, 7201}, {190, 60735}, {192, 34284}, {304, 51058}, {310, 321}, {334, 3773}, {349, 7205}, {350, 24325}, {518, 17143}, {537, 56660}, {561, 28605}, {668, 3696}, {740, 1909}, {870, 32921}, {871, 27494}, {873, 17019}, {894, 30940}, {1002, 4441}, {1975, 54410}, {1999, 8033}, {2481, 12721}, {3403, 4659}, {3739, 18140}, {3761, 49474}, {3774, 17759}, {3797, 20913}, {3842, 40774}, {3995, 16748}, {4043, 18157}, {4044, 27478}, {4359, 18152}, {4365, 18059}, {4451, 20436}, {4479, 31178}, {4687, 25092}, {4688, 18145}, {4699, 18135}, {4732, 25280}, {4980, 40087}, {6382, 42029}, {6383, 40023}, {6385, 27801}, {7018, 48643}, {16826, 51314}, {17144, 49490}, {17756, 27298}, {18298, 42027}, {19565, 40908}, {20917, 27474}, {24524, 49459}, {25303, 49471}, {27162, 27261}, {27483, 59212}, {27495, 60736}, {28898, 40495}, {30963, 40328}, {31004, 40024}, {31008, 31993}, {32104, 49448}, {33935, 49509}, {34020, 44417}, {42034, 59518}, {60699, 60729}, {60730, 60732}

X(60719) = reflection of X(i) in X(j) for these {i,j}: {25264, 37}, {75, 20888}
X(60719) = isotomic conjugate of X(25426)
X(60719) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 60671}, {31, 25426}, {32, 30571}, {560, 27483}, {667, 28841}, {1333, 59272}, {1397, 60675}, {1501, 60678}, {1918, 60680}, {2206, 60676}, {40728, 40748}
X(60719) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 25426}, {9, 60671}, {37, 59272}, {6374, 27483}, {6376, 30571}, {6631, 28841}, {34021, 60680}, {40603, 60676}, {56696, 3736}
X(60719) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {50520, 39345}
X(60719) = X(i)-cross conjugate of X(j) for these {i, j}: {60736, 60706}
X(60719) = pole of line {2206, 14599} with respect to the Stammler hyperbola
X(60719) = pole of line {20295, 50520} with respect to the Steiner circumellipse
X(60719) = pole of line {58, 1914} with respect to the Wallace hyperbola
X(60719) = pole of line {3261, 28147} with respect to the dual conic of Brocard inellipse
X(60719) = isogonal conjugate of the bicevian chordal perspector of X(31) and X(32)
X(60719) = intersection, other than A, B, C, of circumconics {{A, B, C, X(10), X(335)}}, {{A, B, C, X(37), X(21699)}}, {{A, B, C, X(75), X(40017)}}, {{A, B, C, X(274), X(20888)}}, {{A, B, C, X(310), X(1921)}}, {{A, B, C, X(313), X(18895)}}, {{A, B, C, X(726), X(28840)}}, {{A, B, C, X(871), X(10009)}}, {{A, B, C, X(984), X(1002)}}, {{A, B, C, X(986), X(60715)}}, {{A, B, C, X(1269), X(6385)}}, {{A, B, C, X(2228), X(4784)}}, {{A, B, C, X(4824), X(56125)}}, {{A, B, C, X(5224), X(51356)}}, {{A, B, C, X(6376), X(18298)}}, {{A, B, C, X(16062), X(31904)}}, {{A, B, C, X(20142), X(30965)}}, {{A, B, C, X(27801), X(52576)}}, {{A, B, C, X(42328), X(56023)}}
X(60719) = barycentric product X(i)*X(j) for these (i, j): {264, 60729}, {274, 60736}, {305, 60699}, {310, 3842}, {312, 60732}, {313, 51356}, {321, 51314}, {1502, 60697}, {1969, 60701}, {1978, 28840}, {3596, 60717}, {4572, 4913}, {4649, 561}, {4753, 57995}, {4784, 6386}, {4824, 670}, {6063, 60731}, {16826, 76}, {18022, 60703}, {18895, 20142}, {20567, 60711}, {27801, 51311}, {28659, 60715}, {31904, 40071}, {32014, 59203}, {40774, 871}, {41283, 60713}, {60706, 75}, {60724, 6385}, {60730, 85}
X(60719) = barycentric quotient X(i)/X(j) for these (i, j): {1, 60671}, {2, 25426}, {10, 59272}, {75, 30571}, {76, 27483}, {190, 28841}, {274, 60680}, {312, 60675}, {313, 59261}, {321, 60676}, {561, 60678}, {870, 40748}, {3842, 42}, {4649, 31}, {4753, 902}, {4784, 667}, {4824, 512}, {4913, 663}, {4948, 4775}, {4963, 4834}, {5625, 2308}, {16369, 41333}, {16826, 6}, {20142, 1914}, {21615, 56658}, {27495, 2276}, {28840, 649}, {31904, 1474}, {32014, 59194}, {40774, 869}, {51311, 1333}, {51314, 81}, {51356, 58}, {59203, 1213}, {59218, 20970}, {59219, 2667}, {59243, 2206}, {60697, 32}, {60699, 25}, {60701, 48}, {60703, 184}, {60706, 1}, {60711, 41}, {60713, 2175}, {60715, 604}, {60717, 56}, {60724, 213}, {60729, 3}, {60730, 9}, {60731, 55}, {60732, 57}, {60736, 37}
X(60719) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 21615, 10009}, {75, 52049, 10}, {76, 10009, 21615}, {310, 321, 1920}, {4043, 18157, 33939}, {10009, 21615, 1921}, {21443, 50117, 75}

X(60720) = X(2)X(4554)∩X(7)X(8)

Barycentrics    b*(a+b-c)*c*(a-b+c)*(a^2-2*b*c-a*(b+c)) : :

X(60720) lies on these lines: {2, 4554}, {7, 8}, {57, 24592}, {76, 346}, {226, 7243}, {274, 279}, {278, 17087}, {304, 1229}, {321, 21609}, {333, 33765}, {344, 349}, {345, 1233}, {348, 17075}, {390, 2481}, {668, 10005}, {870, 41354}, {1088, 19804}, {1111, 24248}, {1323, 52716}, {1434, 29767}, {1446, 32022}, {1458, 9312}, {1462, 20172}, {1921, 20567}, {3160, 31997}, {3674, 29960}, {3886, 4441}, {3963, 4461}, {3996, 21453}, {4359, 7182}, {4384, 42309}, {4569, 10004}, {4572, 10009}, {4625, 51314}, {4699, 7205}, {5226, 30545}, {5228, 60735}, {5263, 56783}, {5435, 7196}, {5543, 17144}, {7056, 16708}, {7209, 27496}, {8817, 40216}, {10481, 32092}, {14189, 16823}, {16748, 21454}, {17170, 17866}, {17257, 25001}, {17860, 21436}, {17950, 33934}, {18142, 56084}, {20917, 39749}, {20924, 30225}, {21615, 28809}, {24589, 37780}, {25002, 30694}, {25303, 25718}, {27855, 43930}, {28287, 45738}, {30036, 30097}, {32104, 58816}, {40333, 56264}, {43983, 50560}

X(60720) = isotomic conjugate of X(40779)
X(60720) = perspector of circumconic {{A, B, C, X(4554), X(46135)}}
X(60720) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 60673}, {31, 40779}, {32, 60668}, {41, 1002}, {55, 2279}, {604, 59269}, {663, 8693}, {869, 40757}, {926, 36138}, {1253, 42290}, {1334, 51443}, {2175, 27475}, {2194, 60677}, {3063, 37138}, {9447, 59255}, {20229, 59193}, {40728, 40739}
X(60720) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 40779}, {9, 60673}, {223, 2279}, {1214, 60677}, {2276, 4517}, {3160, 1002}, {3161, 59269}, {6376, 60668}, {10001, 37138}, {17113, 42290}, {39012, 926}, {40593, 27475}, {55059, 3709}
X(60720) = X(i)-cross conjugate of X(j) for these {i, j}: {4384, 4441}, {40784, 7}
X(60720) = pole of line {2194, 14827} with respect to the Stammler hyperbola
X(60720) = pole of line {693, 926} with respect to the Steiner circumellipse
X(60720) = pole of line {926, 4885} with respect to the Steiner inellipse
X(60720) = pole of line {21, 220} with respect to the Wallace hyperbola
X(60720) = pole of line {3261, 4130} with respect to the dual conic of incircle
X(60720) = pole of line {883, 3952} with respect to the dual conic of Feuerbach hyperbola
X(60720) = isogonal conjugate of the bicevian chordal perspector of X(31) and X(41)
X(60720) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(518)}}, {{A, B, C, X(7), X(31618)}}, {{A, B, C, X(8), X(274)}}, {{A, B, C, X(65), X(279)}}, {{A, B, C, X(75), X(4441)}}, {{A, B, C, X(76), X(20880)}}, {{A, B, C, X(346), X(3059)}}, {{A, B, C, X(377), X(31926)}}, {{A, B, C, X(883), X(4554)}}, {{A, B, C, X(941), X(2280)}}, {{A, B, C, X(1441), X(57792)}}, {{A, B, C, X(1469), X(1471)}}, {{A, B, C, X(2550), X(39721)}}, {{A, B, C, X(3212), X(27818)}}, {{A, B, C, X(3868), X(60721)}}, {{A, B, C, X(4059), X(57826)}}, {{A, B, C, X(4702), X(49702)}}, {{A, B, C, X(5369), X(60722)}}, {{A, B, C, X(5880), X(6650)}}, {{A, B, C, X(5936), X(56705)}}, {{A, B, C, X(6063), X(40704)}}, {{A, B, C, X(7209), X(39126)}}, {{A, B, C, X(14624), X(59207)}}, {{A, B, C, X(17792), X(54117)}}, {{A, B, C, X(20569), X(30806)}}, {{A, B, C, X(24349), X(39749)}}, {{A, B, C, X(24471), X(59242)}}, {{A, B, C, X(36807), X(49499)}}, {{A, B, C, X(41228), X(58004)}}
X(60720) = barycentric product X(i)*X(j) for these (i, j): {226, 60735}, {279, 28809}, {310, 42289}, {312, 42309}, {349, 60721}, {1001, 6063}, {1088, 3886}, {1231, 31926}, {1434, 4044}, {1471, 561}, {3596, 59242}, {3696, 57785}, {4384, 85}, {4441, 7}, {4554, 4762}, {4572, 4724}, {4625, 4804}, {5228, 76}, {20567, 2280}, {21453, 59202}, {21615, 57}, {23151, 331}, {37658, 57792}, {40719, 75}, {41283, 60722}, {45755, 46406}, {52621, 54440}, {56658, 60732}, {60734, 86}
X(60720) = barycentric quotient X(i)/X(j) for these (i, j): {1, 60673}, {2, 40779}, {7, 1002}, {8, 59269}, {57, 2279}, {75, 60668}, {85, 27475}, {226, 60677}, {279, 42290}, {651, 8693}, {664, 37138}, {870, 40739}, {1001, 55}, {1014, 51443}, {1434, 42302}, {1471, 31}, {1893, 1824}, {2280, 41}, {3596, 59260}, {3696, 210}, {3789, 4517}, {3886, 200}, {4044, 2321}, {4384, 9}, {4441, 8}, {4554, 32041}, {4625, 51563}, {4702, 3689}, {4724, 663}, {4762, 650}, {4804, 4041}, {5228, 6}, {6063, 59255}, {14621, 40757}, {21453, 59193}, {21615, 312}, {23151, 219}, {28044, 7071}, {28809, 346}, {31618, 42310}, {31926, 1172}, {32735, 32724}, {36146, 36138}, {37658, 220}, {40719, 1}, {40784, 2276}, {42289, 42}, {42309, 57}, {45338, 4526}, {45755, 657}, {46135, 53227}, {54440, 3939}, {56658, 60675}, {56705, 7220}, {59202, 4847}, {59207, 1334}, {59217, 2293}, {59242, 56}, {60721, 284}, {60722, 2175}, {60734, 10}, {60735, 333}
X(60720) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 33677, 8}, {75, 85, 40704}, {85, 10030, 7}, {349, 52422, 18135}, {3886, 59202, 4441}, {4359, 59181, 7182}

X(60721) = X(1)X(21)∩X(2)X(4251)

Barycentrics    a*(a+b)*(a+c)*(a^2-2*b*c-a*(b+c)) : :

X(60721) lies on these lines: {1, 21}, {2, 4251}, {9, 41610}, {32, 940}, {41, 16831}, {75, 4483}, {86, 142}, {101, 16826}, {190, 22048}, {274, 55946}, {333, 1174}, {386, 19314}, {552, 553}, {572, 10446}, {584, 15668}, {894, 55100}, {1001, 23151}, {1014, 17207}, {1043, 49466}, {1125, 20769}, {1333, 18166}, {1444, 18164}, {1474, 31906}, {1790, 8025}, {1814, 55340}, {1973, 31919}, {2174, 28639}, {2210, 3720}, {2268, 10889}, {2280, 4384}, {2327, 16713}, {2329, 5325}, {2332, 15149}, {2344, 51356}, {3061, 56439}, {3219, 3970}, {3286, 37580}, {3522, 19783}, {3684, 24603}, {4184, 40910}, {4228, 4666}, {4229, 31730}, {4253, 16367}, {4256, 24598}, {4258, 16412}, {4262, 11329}, {4273, 52897}, {4278, 37576}, {4390, 29605}, {4754, 24271}, {4877, 51058}, {4890, 8424}, {4921, 29573}, {5053, 46922}, {5060, 7146}, {5235, 17284}, {5249, 53591}, {5333, 29598}, {5337, 24512}, {6904, 19766}, {7058, 30038}, {7768, 18134}, {8049, 18656}, {9310, 29597}, {9327, 29580}, {14548, 24609}, {14828, 37086}, {16502, 40153}, {16704, 16788}, {16779, 27644}, {17175, 26643}, {17758, 50200}, {18180, 36017}, {19716, 19763}, {19767, 56777}, {20602, 21808}, {22097, 40955}, {24587, 31006}, {24632, 30941}, {25083, 37080}, {25665, 31089}, {25940, 29603}, {25946, 35342}, {26243, 29456}, {27950, 29586}, {28620, 29646}, {31926, 40719}, {34476, 40748}, {37244, 50628}, {37783, 56532}, {40214, 42025}, {49476, 56018}, {56019, 58788}, {60677, 60711}

X(60721) = isogonal conjugate of X(60677)
X(60721) = perspector of circumconic {{A, B, C, X(662), X(55281)}}
X(60721) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 60677}, {10, 2279}, {37, 1002}, {42, 27475}, {65, 40779}, {210, 42290}, {213, 59255}, {226, 60673}, {512, 32041}, {523, 8693}, {594, 51443}, {756, 42302}, {1400, 60668}, {1427, 59269}, {4079, 51563}, {4088, 36138}, {21808, 59193}, {42310, 52020}
X(60721) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 60677}, {2276, 3773}, {6626, 59255}, {36830, 37138}, {39012, 4088}, {39054, 32041}, {40582, 60668}, {40589, 1002}, {40592, 27475}, {40602, 40779}, {55059, 4024}
X(60721) = X(i)-cross conjugate of X(j) for these {i, j}: {5228, 31926}
X(60721) = pole of line {5949, 17337} with respect to the Kiepert hyperbola
X(60721) = pole of line {1, 672} with respect to the Stammler hyperbola
X(60721) = pole of line {4458, 14838} with respect to the Steiner inellipse
X(60721) = pole of line {75, 142} with respect to the Wallace hyperbola
X(60721) = pole of line {238, 5249} with respect to the dual conic of Yff parabola
X(60721) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(673)}}, {{A, B, C, X(2), X(3873)}}, {{A, B, C, X(21), X(1509)}}, {{A, B, C, X(31), X(1174)}}, {{A, B, C, X(37), X(24803)}}, {{A, B, C, X(63), X(23151)}}, {{A, B, C, X(81), X(552)}}, {{A, B, C, X(86), X(18206)}}, {{A, B, C, X(142), X(3912)}}, {{A, B, C, X(333), X(17194)}}, {{A, B, C, X(553), X(1962)}}, {{A, B, C, X(593), X(39673)}}, {{A, B, C, X(662), X(54353)}}, {{A, B, C, X(758), X(4762)}}, {{A, B, C, X(846), X(43747)}}, {{A, B, C, X(896), X(4724)}}, {{A, B, C, X(1429), X(3747)}}, {{A, B, C, X(1432), X(2650)}}, {{A, B, C, X(1468), X(1471)}}, {{A, B, C, X(2185), X(2328)}}, {{A, B, C, X(2292), X(3674)}}, {{A, B, C, X(2346), X(6185)}}, {{A, B, C, X(3573), X(39272)}}, {{A, B, C, X(3696), X(3743)}}, {{A, B, C, X(3877), X(16712)}}, {{A, B, C, X(3886), X(5250)}}, {{A, B, C, X(3889), X(30701)}}, {{A, B, C, X(3892), X(34892)}}, {{A, B, C, X(4441), X(8049)}}, {{A, B, C, X(4512), X(37658)}}, {{A, B, C, X(5208), X(37870)}}, {{A, B, C, X(14621), X(23407)}}, {{A, B, C, X(16053), X(18164)}}, {{A, B, C, X(17169), X(33297)}}, {{A, B, C, X(28044), X(35935)}}, {{A, B, C, X(40749), X(40763)}}, {{A, B, C, X(40773), X(60680)}}, {{A, B, C, X(40784), X(51836)}}
X(60721) = barycentric product X(i)*X(j) for these (i, j): {6, 60735}, {21, 40719}, {60, 60734}, {261, 42289}, {284, 60720}, {310, 60722}, {333, 5228}, {1001, 86}, {1014, 3886}, {1043, 59242}, {1333, 21615}, {1412, 28809}, {1434, 37658}, {1471, 314}, {1509, 59207}, {2280, 274}, {2287, 42309}, {3696, 757}, {4044, 593}, {4384, 81}, {4441, 58}, {4573, 45755}, {4724, 99}, {4762, 662}, {4804, 52935}, {23151, 27}, {31926, 63}, {51311, 56658}, {54440, 7192}
X(60721) = barycentric quotient X(i)/X(j) for these (i, j): {6, 60677}, {21, 60668}, {58, 1002}, {81, 27475}, {86, 59255}, {110, 37138}, {163, 8693}, {284, 40779}, {593, 42302}, {662, 32041}, {849, 51443}, {1001, 10}, {1043, 59260}, {1333, 2279}, {1412, 42290}, {1471, 65}, {1893, 56285}, {2194, 60673}, {2280, 37}, {2328, 59269}, {3696, 1089}, {3789, 3773}, {3886, 3701}, {4044, 28654}, {4384, 321}, {4441, 313}, {4702, 3992}, {4724, 523}, {4762, 1577}, {4804, 4036}, {5228, 226}, {21615, 27801}, {23151, 306}, {28044, 53008}, {28809, 30713}, {31926, 92}, {37658, 2321}, {40719, 1441}, {40784, 16603}, {42289, 12}, {42309, 1446}, {45755, 3700}, {52935, 51563}, {54440, 3952}, {59207, 594}, {59217, 3925}, {59242, 3668}, {60720, 349}, {60722, 42}, {60734, 34388}, {60735, 76}
X(60721) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {21, 81, 18206}, {2185, 42028, 1412}, {8025, 14953, 17169}, {16826, 40744, 101}

X(60722) = X(31)X(32)∩X(56)X(58)

Barycentrics    a^3*(a^2-2*b*c-a*(b+c)) : :

X(60722) lies on these lines: {6, 692}, {9, 19133}, {31, 32}, {42, 8647}, {44, 47373}, {55, 218}, {56, 58}, {72, 3683}, {101, 21010}, {110, 51311}, {182, 6210}, {184, 1475}, {238, 5138}, {239, 24264}, {284, 20992}, {354, 52015}, {560, 5019}, {572, 36635}, {579, 23868}, {583, 1631}, {584, 8053}, {672, 37586}, {985, 40749}, {1001, 23151}, {1055, 21747}, {1083, 17316}, {1402, 54321}, {1428, 16469}, {1460, 44098}, {1580, 16476}, {1621, 56542}, {1743, 2330}, {1836, 53591}, {1918, 16946}, {1974, 2354}, {1980, 8657}, {2174, 3941}, {2241, 3747}, {2242, 20985}, {2245, 4471}, {2264, 12723}, {2279, 40746}, {2344, 39252}, {2911, 3688}, {3204, 20990}, {3207, 20986}, {3449, 9309}, {3573, 4393}, {3601, 54354}, {3792, 47038}, {4026, 51743}, {4253, 17798}, {4260, 7295}, {4381, 18805}, {4517, 5526}, {4643, 16792}, {4890, 54358}, {5034, 20669}, {5042, 7122}, {5091, 5222}, {5228, 39792}, {5311, 21802}, {5324, 10473}, {5880, 24588}, {6056, 22131}, {7193, 16475}, {8772, 53165}, {10822, 19763}, {11246, 14377}, {11428, 30223}, {17745, 40910}, {20978, 21748}, {23407, 40744}, {23524, 34543}, {34068, 34073}, {35892, 41610}, {37577, 53005}, {50284, 56529}

X(60722) = isogonal conjugate of X(59255)
X(60722) = perspector of circumconic {{A, B, C, X(692), X(919)}}
X(60722) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 59255}, {2, 27475}, {7, 60668}, {75, 1002}, {76, 2279}, {85, 40779}, {142, 42310}, {269, 59260}, {274, 60677}, {312, 42290}, {313, 51443}, {321, 42302}, {514, 32041}, {523, 51563}, {693, 37138}, {1088, 59269}, {2254, 53227}, {3261, 8693}, {6063, 60673}, {7179, 40739}, {20880, 59193}
X(60722) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 59255}, {206, 1002}, {6600, 59260}, {32664, 27475}, {55059, 850}
X(60722) = X(i)-Ceva conjugate of X(j) for these {i, j}: {40746, 32}, {58989, 665}
X(60722) = pole of line {665, 2605} with respect to the circumcircle
X(60722) = pole of line {665, 1459} with respect to the Brocard inellipse
X(60722) = pole of line {16601, 54430} with respect to the Feuerbach hyperbola
X(60722) = pole of line {8, 274} with respect to the Stammler hyperbola
X(60722) = pole of line {3596, 6385} with respect to the Wallace hyperbola
X(60722) = isogonal conjugate of the bicevian chordal perspector of X(75) and X(85)
X(60722) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(6), X(2223)}}, {{A, B, C, X(7), X(20683)}}, {{A, B, C, X(31), X(1174)}}, {{A, B, C, X(32), X(1408)}}, {{A, B, C, X(41), X(58)}}, {{A, B, C, X(55), X(20229)}}, {{A, B, C, X(56), X(213)}}, {{A, B, C, X(222), X(228)}}, {{A, B, C, X(766), X(4762)}}, {{A, B, C, X(859), X(28044)}}, {{A, B, C, X(869), X(2279)}}, {{A, B, C, X(1002), X(39792)}}, {{A, B, C, X(1245), X(2198)}}, {{A, B, C, X(1397), X(2205)}}, {{A, B, C, X(1401), X(4441)}}, {{A, B, C, X(1437), X(52425)}}, {{A, B, C, X(1475), X(3730)}}, {{A, B, C, X(2194), X(14827)}}, {{A, B, C, X(2225), X(4724)}}, {{A, B, C, X(2258), X(5364)}}, {{A, B, C, X(3423), X(37580)}}, {{A, B, C, X(3500), X(42309)}}, {{A, B, C, X(5360), X(43034)}}, {{A, B, C, X(9309), X(21746)}}, {{A, B, C, X(14267), X(20455)}}, {{A, B, C, X(14620), X(21615)}}, {{A, B, C, X(20662), X(40730)}}, {{A, B, C, X(20967), X(37658)}}, {{A, B, C, X(31926), X(33718)}}, {{A, B, C, X(40147), X(59207)}}
X(60722) = barycentric product X(i)*X(j) for these (i, j): {1, 2280}, {31, 4384}, {32, 4441}, {42, 60721}, {58, 59207}, {101, 4724}, {109, 45755}, {163, 4804}, {220, 59242}, {222, 28044}, {228, 31926}, {284, 42289}, {1001, 6}, {1174, 59217}, {1253, 42309}, {1333, 3696}, {1397, 28809}, {1471, 9}, {1893, 2193}, {1918, 60735}, {2175, 60720}, {2206, 4044}, {3789, 40746}, {3886, 604}, {4702, 9456}, {4762, 692}, {5228, 55}, {14621, 40732}, {21615, 560}, {23151, 25}, {32718, 45338}, {37658, 56}, {40719, 41}, {54440, 649}, {57657, 60734}
X(60722) = barycentric quotient X(i)/X(j) for these (i, j): {6, 59255}, {31, 27475}, {32, 1002}, {41, 60668}, {163, 51563}, {220, 59260}, {560, 2279}, {692, 32041}, {919, 53227}, {1001, 76}, {1397, 42290}, {1471, 85}, {1893, 52575}, {1918, 60677}, {2175, 40779}, {2206, 42302}, {2280, 75}, {3696, 27801}, {3886, 28659}, {4384, 561}, {4441, 1502}, {4724, 3261}, {4762, 40495}, {4804, 20948}, {5228, 6063}, {9447, 60673}, {14827, 59269}, {21615, 1928}, {23151, 305}, {28044, 7017}, {28809, 40363}, {31926, 57796}, {32739, 37138}, {37658, 3596}, {40719, 20567}, {40732, 3661}, {42289, 349}, {45755, 35519}, {54440, 1978}, {59207, 313}, {59217, 1233}, {59242, 57792}, {60720, 41283}, {60721, 310}
X(60722) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 1486, 52020}, {6, 7083, 21746}, {31, 2210, 32}, {31, 41, 2223}, {55, 218, 20683}, {53065, 53066, 20229}

X(60723) = X(1)X(6)∩X(98)X(100)

Barycentrics    a*(b+c)*(a^4-2*b^2*c^2-a^2*(b^2+c^2)) : :

X(60723) lies on these lines: {1, 6}, {3, 3729}, {8, 31394}, {10, 1284}, {21, 17261}, {35, 8424}, {55, 3175}, {63, 37521}, {78, 46475}, {95, 7523}, {98, 100}, {182, 52134}, {183, 3403}, {242, 4222}, {306, 21319}, {404, 17116}, {474, 25590}, {516, 22019}, {536, 5132}, {668, 43664}, {726, 37575}, {851, 4054}, {894, 37609}, {942, 25099}, {1009, 17355}, {1011, 56082}, {1215, 1402}, {1403, 4413}, {1696, 19309}, {1756, 17792}, {1824, 14486}, {2223, 3923}, {2901, 25439}, {3159, 8669}, {3161, 52241}, {3216, 28358}, {3219, 3794}, {3286, 17351}, {3681, 7611}, {3685, 22016}, {3696, 4557}, {3710, 37225}, {3811, 50602}, {3840, 44304}, {3869, 31395}, {3875, 37502}, {3883, 15507}, {3967, 52139}, {3977, 30944}, {3993, 25425}, {4026, 17757}, {4133, 4433}, {4189, 25269}, {4199, 4656}, {4223, 38869}, {4279, 54282}, {4362, 20967}, {4447, 50307}, {4463, 14495}, {4516, 4523}, {5144, 22011}, {5695, 15624}, {6675, 25589}, {6685, 22020}, {6910, 25601}, {8731, 56078}, {10311, 60685}, {11169, 42724}, {11679, 20760}, {16058, 30568}, {17447, 34378}, {18754, 37573}, {20229, 21369}, {20236, 29010}, {20470, 49483}, {20498, 43223}, {21075, 50290}, {21320, 49511}, {21327, 21750}, {22004, 22027}, {22060, 32933}, {23629, 40934}, {23681, 50199}, {26223, 40956}, {32929, 54327}, {33971, 51315}, {34247, 50314}, {37507, 50127}, {45838, 52086}, {52345, 57408}, {52923, 60731}

X(60723) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 60679}, {27, 43718}, {58, 262}, {81, 2186}, {86, 263}, {274, 3402}, {310, 46319}, {327, 2206}, {514, 26714}, {1474, 42313}, {4610, 52631}, {6037, 53521}, {8747, 54032}, {16887, 42288}, {17187, 42299}
X(60723) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 60679}, {10, 262}, {3815, 16740}, {16603, 7179}, {38997, 513}, {40586, 2186}, {40600, 263}, {40603, 327}, {51574, 42313}, {51580, 274}, {55051, 2530}
X(60723) = X(i)-Ceva conjugate of X(j) for these {i, j}: {183, 60737}, {52133, 10}, {52134, 60726}
X(60723) = pole of line {667, 53257} with respect to the circumcircle
X(60723) = pole of line {2530, 17924} with respect to the polar circle
X(60723) = pole of line {100, 26714} with respect to the Hutson-Moses hyperbola
X(60723) = pole of line {274, 18180} with respect to the Wallace hyperbola
X(60723) = pole of line {16732, 18188} with respect to the dual conic of Wallace hyperbola
X(60723) = isogonal conjugate of the bicevian chordal perspector of X(81) and X(28)
X(60723) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1821)}}, {{A, B, C, X(6), X(95)}}, {{A, B, C, X(9), X(56196)}}, {{A, B, C, X(10), X(3061)}}, {{A, B, C, X(37), X(42711)}}, {{A, B, C, X(72), X(56186)}}, {{A, B, C, X(213), X(56254)}}, {{A, B, C, X(405), X(458)}}, {{A, B, C, X(518), X(23878)}}, {{A, B, C, X(1743), X(18793)}}, {{A, B, C, X(3230), X(3288)}}, {{A, B, C, X(3954), X(41013)}}, {{A, B, C, X(4222), X(14096)}}, {{A, B, C, X(5283), X(20023)}}, {{A, B, C, X(10477), X(44144)}}, {{A, B, C, X(16975), X(38955)}}, {{A, B, C, X(21384), X(56195)}}, {{A, B, C, X(39680), X(45913)}}, {{A, B, C, X(40718), X(56533)}}
X(60723) = barycentric product X(i)*X(j) for these (i, j): {1, 60737}, {10, 52134}, {100, 23878}, {182, 321}, {183, 37}, {228, 44144}, {306, 60685}, {458, 72}, {2321, 60716}, {3288, 668}, {3403, 42}, {3682, 51315}, {4601, 6784}, {10311, 20336}, {14096, 56186}, {14994, 18098}, {20023, 213}, {27801, 34396}, {33971, 3998}, {42701, 56401}, {42703, 51542}, {42711, 6}, {56189, 59208}, {56254, 59197}, {60726, 75}
X(60723) = barycentric quotient X(i)/X(j) for these (i, j): {1, 60679}, {37, 262}, {42, 2186}, {72, 42313}, {182, 81}, {183, 274}, {213, 263}, {228, 43718}, {321, 327}, {458, 286}, {692, 26714}, {1918, 3402}, {2205, 46319}, {3288, 513}, {3403, 310}, {3990, 54032}, {3998, 59257}, {5360, 51543}, {6784, 3125}, {10311, 28}, {14096, 16696}, {14994, 16703}, {15819, 16740}, {18098, 42299}, {20023, 6385}, {23878, 693}, {34396, 1333}, {42711, 76}, {44144, 57796}, {50487, 52631}, {52134, 86}, {56254, 42300}, {59208, 18180}, {60685, 27}, {60716, 1434}, {60726, 1}, {60737, 75}
X(60723) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7081, 11688, 37619}

X(60724) = X(1)X(39)∩X(2)X(594)

Barycentrics    a*(b+c)*(a^2+b*c+2*a*(b+c)) : :

X(60724) lies on these lines: {1, 39}, {2, 594}, {6, 1621}, {9, 42042}, {12, 23903}, {37, 42}, {43, 3247}, {45, 37657}, {75, 17032}, {81, 17735}, {86, 17759}, {100, 40750}, {172, 37573}, {190, 40721}, {192, 24330}, {213, 59301}, {319, 49717}, {350, 3963}, {672, 1100}, {894, 49749}, {940, 31477}, {966, 20012}, {1002, 42316}, {1213, 4651}, {1215, 4037}, {1575, 3720}, {1791, 19765}, {1914, 3750}, {2092, 59315}, {2171, 15377}, {2176, 19767}, {2177, 4386}, {2321, 43223}, {2594, 20616}, {3125, 4868}, {3178, 16886}, {3240, 16672}, {3293, 16589}, {3294, 20970}, {3571, 40796}, {3666, 3726}, {3678, 21816}, {3690, 16972}, {3721, 3931}, {3727, 37548}, {3743, 3954}, {3780, 5283}, {3807, 31308}, {3842, 59218}, {3879, 24690}, {3943, 29822}, {3993, 21101}, {4007, 59312}, {4021, 20335}, {4033, 30963}, {4065, 22011}, {4075, 24051}, {4199, 22021}, {4210, 21773}, {4441, 17318}, {4465, 37678}, {4478, 50158}, {4646, 21951}, {4649, 40774}, {4653, 5291}, {4664, 24514}, {4685, 5257}, {4727, 30970}, {4754, 25264}, {4852, 24592}, {5277, 33771}, {6155, 16600}, {6542, 30966}, {6683, 29750}, {7227, 50180}, {7230, 24049}, {7277, 50257}, {14624, 39967}, {16587, 17600}, {16673, 42043}, {16826, 60706}, {17027, 17393}, {17056, 21956}, {17135, 17388}, {17246, 20347}, {17299, 31330}, {17301, 30949}, {17315, 31027}, {17316, 30945}, {17320, 31004}, {17362, 20011}, {17390, 25349}, {17499, 32026}, {17592, 41269}, {17756, 29814}, {20483, 29653}, {20654, 27567}, {20691, 59305}, {20692, 21808}, {20963, 25092}, {21024, 26115}, {21070, 52538}, {24059, 24067}, {25426, 39252}, {25427, 51296}, {25499, 40006}, {28594, 58380}, {28606, 37676}, {29580, 41142}, {29585, 30962}, {30571, 60688}, {30950, 39260}, {30985, 50068}, {31136, 50123}, {31443, 37520}, {31451, 37522}, {35309, 44304}, {37317, 54416}, {37554, 39255}, {40747, 60677}, {52959, 56191}

X(60724) = isogonal conjugate of X(60680)
X(60724) = perspector of circumconic {{A, B, C, X(660), X(1018)}}
X(60724) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 60680}, {58, 27483}, {81, 30571}, {86, 25426}, {274, 60671}, {593, 59261}, {757, 60676}, {1014, 60675}, {1125, 59194}, {1333, 60678}, {1509, 59272}, {7192, 28841}, {40748, 40773}, {51443, 56658}
X(60724) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 60680}, {10, 27483}, {37, 60678}, {3842, 20913}, {40586, 30571}, {40600, 25426}, {40607, 60676}
X(60724) = X(i)-Ceva conjugate of X(j) for these {i, j}: {16826, 3842}
X(60724) = pole of line {6373, 58288} with respect to the Brocard inellipse
X(60724) = pole of line {3925, 41809} with respect to the Kiepert hyperbola
X(60724) = pole of line {757, 18166} with respect to the Stammler hyperbola
X(60724) = pole of line {665, 4977} with respect to the Steiner inellipse
X(60724) = pole of line {873, 8025} with respect to the Wallace hyperbola
X(60724) = pole of line {3634, 20335} with respect to the dual conic of Yff parabola
X(60724) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2238)}}, {{A, B, C, X(2), X(1962)}}, {{A, B, C, X(6), X(2667)}}, {{A, B, C, X(37), X(291)}}, {{A, B, C, X(39), X(4093)}}, {{A, B, C, X(42), X(292)}}, {{A, B, C, X(210), X(4102)}}, {{A, B, C, X(756), X(6539)}}, {{A, B, C, X(872), X(52555)}}, {{A, B, C, X(941), X(3728)}}, {{A, B, C, X(1500), X(52205)}}, {{A, B, C, X(2276), X(59272)}}, {{A, B, C, X(2318), X(15377)}}, {{A, B, C, X(3725), X(39967)}}, {{A, B, C, X(3864), X(34475)}}, {{A, B, C, X(3930), X(4824)}}, {{A, B, C, X(4204), X(31904)}}, {{A, B, C, X(4272), X(59243)}}, {{A, B, C, X(4360), X(5625)}}, {{A, B, C, X(8818), X(17233)}}, {{A, B, C, X(16606), X(37593)}}, {{A, B, C, X(20142), X(24512)}}, {{A, B, C, X(20693), X(40794)}}, {{A, B, C, X(21805), X(31011)}}, {{A, B, C, X(21904), X(40718)}}, {{A, B, C, X(28840), X(39974)}}, {{A, B, C, X(40747), X(59207)}}
X(60724) = barycentric product X(i)*X(j) for these (i, j): {1, 3842}, {6, 60736}, {10, 4649}, {42, 60706}, {100, 4824}, {210, 60717}, {213, 60719}, {226, 60711}, {321, 60697}, {1018, 28840}, {1089, 59243}, {1255, 59218}, {1334, 60732}, {1400, 60730}, {1441, 60713}, {1500, 51314}, {1824, 60729}, {1826, 60701}, {2321, 60715}, {3952, 4784}, {4551, 4913}, {4674, 4753}, {16369, 335}, {16826, 37}, {27495, 40747}, {28615, 59203}, {31904, 3949}, {40433, 59219}, {40718, 40774}, {41013, 60703}, {51311, 594}, {51356, 756}, {60699, 72}, {60731, 65}
X(60724) = barycentric quotient X(i)/X(j) for these (i, j): {6, 60680}, {10, 60678}, {37, 27483}, {42, 30571}, {213, 25426}, {756, 59261}, {872, 59272}, {1334, 60675}, {1500, 60676}, {1918, 60671}, {3842, 75}, {4649, 86}, {4753, 30939}, {4784, 7192}, {4824, 693}, {4913, 18155}, {5625, 16709}, {16369, 239}, {16826, 274}, {20142, 30940}, {28615, 59194}, {28840, 7199}, {40774, 30966}, {51311, 1509}, {51356, 873}, {59207, 56658}, {59218, 4359}, {59219, 20888}, {59243, 757}, {60697, 81}, {60699, 286}, {60701, 17206}, {60703, 1444}, {60706, 310}, {60711, 333}, {60713, 21}, {60715, 1434}, {60717, 57785}, {60719, 6385}, {60730, 28660}, {60731, 314}, {60736, 76}
X(60724) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1500, 2295}, {1, 2276, 24512}, {37, 20693, 756}, {37, 21904, 59207}, {42, 59207, 21904}, {192, 37632, 24330}, {1575, 3723, 3720}, {1962, 3930, 37}, {2276, 24512, 20331}, {4649, 60711, 60697}, {16777, 52555, 594}, {17390, 25349, 30941}, {17592, 51058, 41269}, {21904, 59207, 2238}, {40750, 59238, 100}

X(60725) = X(1)X(24482)∩X(37)X(513)

Barycentrics    a*(2*a^2*b*c+2*b^2*c^2+a*(b+c)*(b^2-4*b*c+c^2)) : :

X(60725) lies on these lines: {1, 24482}, {2, 19945}, {10, 24004}, {37, 513}, {38, 49742}, {42, 23343}, {45, 899}, {190, 291}, {244, 545}, {519, 751}, {551, 36872}, {750, 38530}, {756, 49737}, {982, 49748}, {1001, 1149}, {1083, 36267}, {1125, 24399}, {1739, 28542}, {2228, 2325}, {2292, 24433}, {3123, 4422}, {3242, 9039}, {3616, 24397}, {3622, 24418}, {3720, 24405}, {3821, 49993}, {4389, 4871}, {4446, 25269}, {4448, 24457}, {4681, 23659}, {4941, 17352}, {4947, 27191}, {7227, 22174}, {10582, 24422}, {14839, 42083}, {16482, 27846}, {16826, 24423}, {17063, 49722}, {17261, 21035}, {17332, 22167}, {17334, 21330}, {17351, 22172}, {17354, 24456}, {17768, 22220}, {19957, 25036}, {21936, 32936}, {21963, 33115}, {24406, 24495}, {30950, 43922}, {31855, 51294}

X(60725) = pole of line {17759, 47775} with respect to the Steiner circumellipse
X(60725) = pole of line {1575, 47778} with respect to the Steiner inellipse
X(60725) = isogonal conjugate of the bicevian chordal perspector of X(81) and X(100)
X(60725) = intersection, other than A, B, C, of circumconics {{A, B, C, X(256), X(21143)}}, {{A, B, C, X(751), X(3572)}}, {{A, B, C, X(876), X(4492)}}, {{A, B, C, X(14437), X(30571)}}
X(60725) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 24338, 19945}, {2, 53340, 25382}, {16482, 57023, 27846}, {24004, 24517, 10}

X(60726) = X(6)X(31)∩X(10)X(98)

Barycentrics    a^2*(b+c)*(a^4-2*b^2*c^2-a^2*(b^2+c^2)) : :

X(60726) lies on these lines: {6, 31}, {10, 98}, {41, 3214}, {48, 1376}, {65, 22061}, {72, 23621}, {95, 306}, {183, 52134}, {190, 43664}, {284, 60714}, {910, 22278}, {1155, 22099}, {1755, 37619}, {1826, 2201}, {2174, 53128}, {2304, 5687}, {2333, 14486}, {2594, 20727}, {2980, 21011}, {3293, 54329}, {3684, 4685}, {3753, 42669}, {4028, 45857}, {4251, 50587}, {4386, 9454}, {4456, 14495}, {5275, 51949}, {8804, 57408}, {15523, 21012}, {21801, 21840}, {41526, 59305}

X(60726) = isogonal conjugate of X(60679)
X(60726) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 60679}, {28, 42313}, {81, 262}, {86, 2186}, {263, 274}, {286, 43718}, {310, 3402}, {327, 1333}, {693, 26714}, {4623, 52631}, {5317, 59257}, {6385, 46319}, {16696, 42299}, {16703, 42288}, {18180, 42300}
X(60726) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 60679}, {37, 327}, {38997, 514}, {40586, 262}, {40591, 42313}, {40600, 2186}, {51580, 310}, {55051, 16892}
X(60726) = X(i)-Ceva conjugate of X(j) for these {i, j}: {2344, 37}, {52134, 60723}
X(60726) = pole of line {649, 53258} with respect to the circumcircle
X(60726) = pole of line {16892, 46107} with respect to the polar circle
X(60726) = pole of line {3136, 53424} with respect to the Kiepert hyperbola
X(60726) = pole of line {86, 17209} with respect to the Stammler hyperbola
X(60726) = pole of line {310, 17167} with respect to the Wallace hyperbola
X(60726) = pole of line {2140, 24160} with respect to the dual conic of Yff parabola
X(60726) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(95)}}, {{A, B, C, X(31), X(1910)}}, {{A, B, C, X(37), X(3056)}}, {{A, B, C, X(42), X(56246)}}, {{A, B, C, X(55), X(15628)}}, {{A, B, C, X(71), X(18082)}}, {{A, B, C, X(212), X(56245)}}, {{A, B, C, X(458), X(1011)}}, {{A, B, C, X(674), X(23878)}}, {{A, B, C, X(902), X(3288)}}, {{A, B, C, X(1826), X(21035)}}, {{A, B, C, X(2276), X(42711)}}, {{A, B, C, X(14004), X(14096)}}, {{A, B, C, X(14829), X(59208)}}
X(60726) = barycentric product X(i)*X(j) for these (i, j): {1, 60723}, {6, 60737}, {10, 182}, {31, 42711}, {37, 52134}, {101, 23878}, {183, 42}, {190, 3288}, {210, 60716}, {213, 3403}, {313, 34396}, {458, 71}, {1918, 20023}, {2200, 44144}, {3990, 51315}, {4600, 6784}, {10311, 306}, {14096, 18082}, {33971, 3682}, {56246, 59208}, {60685, 72}
X(60726) = barycentric quotient X(i)/X(j) for these (i, j): {6, 60679}, {10, 327}, {42, 262}, {71, 42313}, {182, 86}, {183, 310}, {213, 2186}, {458, 44129}, {1918, 263}, {2200, 43718}, {2205, 3402}, {3288, 514}, {3403, 6385}, {3682, 59257}, {4055, 54032}, {6784, 3120}, {9420, 53521}, {10311, 27}, {14096, 16887}, {23878, 3261}, {32739, 26714}, {34396, 58}, {42711, 561}, {52134, 274}, {53581, 52631}, {59208, 17167}, {60685, 286}, {60716, 57785}, {60723, 75}, {60737, 76}

X(60727) = X(2)X(32)∩X(76)X(419)

Barycentrics    a^8-2*b^4*c^4-a^4*(b^4+c^4) : :

X(60727) lies on these lines: {2, 32}, {76, 419}, {99, 56377}, {110, 20023}, {182, 8920}, {184, 3978}, {206, 1502}, {316, 5117}, {458, 39266}, {1691, 11333}, {1915, 11338}, {1974, 9230}, {2056, 7754}, {3098, 40708}, {3225, 35136}, {3734, 33336}, {5651, 60707}, {6374, 19126}, {6620, 11185}, {6697, 33797}, {7782, 19599}, {7802, 56376}, {18878, 53197}, {19127, 30736}, {34396, 56442}, {38907, 42671}, {40146, 40421}

X(60727) = pole of line {141, 19602} with respect to the Wallace hyperbola
X(60727) = isotomic conjugate of the bicevian chordal perspector of X(2) and X(66)
X(60727) = intersection, other than A, B, C, of circumconics {{A, B, C, X(32), X(42826)}}, {{A, B, C, X(315), X(44165)}}, {{A, B, C, X(626), X(40421)}}, {{A, B, C, X(1502), X(40876)}}, {{A, B, C, X(8023), X(40146)}}, {{A, B, C, X(20065), X(42486)}}
X(60727) = barycentric product X(i)*X(j) for these (i, j): {1502, 42826}, {38830, 59204}, {59248, 6}, {60694, 76}
X(60727) = barycentric quotient X(i)/X(j) for these (i, j): {42826, 32}, {59204, 20859}, {59248, 76}, {60694, 6}
X(60727) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 16985, 32}, {2, 315, 40876}, {419, 37894, 76}

X(60728) = X(2)X(6)∩X(99)X(6292)

Barycentrics    a^4+3*b^4+7*b^2*c^2+3*c^4+5*a^2*(b^2+c^2) : :

X(60728) lies on these lines: {2, 6}, {99, 6292}, {140, 5984}, {2896, 7804}, {3096, 7825}, {3818, 60652}, {3934, 8782}, {4027, 31274}, {6179, 60278}, {6704, 32027}, {6722, 7944}, {7760, 55743}, {7767, 16896}, {7771, 7822}, {7794, 31268}, {7800, 19689}, {7831, 33265}, {7836, 15482}, {7879, 14535}, {7890, 55767}, {7904, 19692}, {7929, 16045}, {7938, 33020}, {10007, 42006}, {14712, 31168}, {14929, 20088}, {17128, 35369}, {18840, 20081}, {24206, 40236}, {33706, 42786}, {35540, 55081}, {39784, 51860}, {39998, 39999}, {40425, 59180}, {40484, 40870}, {54901, 60643}, {59213, 60707}

X(60728) = isotomic conjugate of the bicevian chordal perspector of X(2) and X(83)
X(60728) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(40042)}}, {{A, B, C, X(1031), X(3763)}}, {{A, B, C, X(3589), X(11606)}}, {{A, B, C, X(7779), X(10159)}}, {{A, B, C, X(9477), X(50248)}}, {{A, B, C, X(20582), X(43098)}}, {{A, B, C, X(34573), X(40425)}}
X(60728) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 141, 7779}, {2, 50248, 3589}, {141, 16988, 2}, {6292, 10159, 46226}, {6292, 46226, 33021}, {37671, 51128, 16987}

X(60729) = X(63)X(69)∩X(72)X(295)

Barycentrics    (a^2-b^2-c^2)*(a^2+b*c+2*a*(b+c)) : :

X(60729) lies on these lines: {9, 30962}, {63, 69}, {72, 295}, {75, 4042}, {86, 4641}, {228, 1444}, {304, 3927}, {319, 4046}, {320, 37664}, {325, 33066}, {846, 3879}, {894, 24690}, {1999, 17731}, {3219, 30941}, {3509, 4416}, {3980, 17270}, {4357, 32913}, {5220, 30758}, {6629, 30115}, {7283, 33297}, {10025, 17347}, {16369, 16826}, {16827, 18827}, {17746, 29473}, {20336, 57854}, {20769, 22099}, {21281, 57279}, {22163, 23151}, {24627, 37678}, {32853, 49518}, {37632, 38000}, {40131, 54280}, {45962, 56517}, {60699, 60719}, {60706, 60717}

X(60729) = X(i)-isoconjugate-of-X(j) for these {i, j}: {4, 60671}, {19, 25426}, {25, 30571}, {28, 59272}, {608, 60675}, {1474, 60676}, {1973, 27483}, {1974, 60678}, {2203, 59261}, {2333, 60680}, {6591, 28841}
X(60729) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 25426}, {6337, 27483}, {6505, 30571}, {36033, 60671}, {40591, 59272}, {51574, 60676}, {56696, 31909}
X(60729) = X(i)-Ceva conjugate of X(j) for these {i, j}: {60719, 16826}
X(60729) = X(i)-cross conjugate of X(j) for these {i, j}: {60703, 16826}
X(60729) = pole of line {1474, 25426} with respect to the Stammler hyperbola
X(60729) = pole of line {27, 242} with respect to the Wallace hyperbola
X(60729) = pole of line {514, 4010} with respect to the dual conic of polar circle
X(60729) = isotomic conjugate of the bicevian chordal perspector of X(4) and X(92)
X(60729) = intersection, other than A, B, C, of circumconics {{A, B, C, X(63), X(51311)}}, {{A, B, C, X(69), X(51356)}}, {{A, B, C, X(71), X(295)}}, {{A, B, C, X(72), X(16369)}}, {{A, B, C, X(306), X(337)}}, {{A, B, C, X(464), X(31904)}}, {{A, B, C, X(1791), X(60724)}}, {{A, B, C, X(4649), X(5227)}}, {{A, B, C, X(9028), X(28840)}}, {{A, B, C, X(10319), X(60715)}}, {{A, B, C, X(20336), X(59218)}}
X(60729) = barycentric product X(i)*X(j) for these (i, j): {3, 60719}, {304, 4649}, {305, 60697}, {306, 51356}, {345, 60717}, {348, 60731}, {1444, 60736}, {3718, 60715}, {3926, 60699}, {4563, 4824}, {16369, 57987}, {16826, 69}, {17206, 3842}, {20142, 337}, {20336, 51311}, {28840, 4561}, {31904, 52396}, {40071, 59243}, {51314, 72}, {57685, 59203}, {57854, 59218}, {57918, 60713}, {60701, 75}, {60703, 76}, {60706, 63}, {60711, 7182}, {60730, 77}, {60732, 78}
X(60729) = barycentric quotient X(i)/X(j) for these (i, j): {3, 25426}, {48, 60671}, {63, 30571}, {69, 27483}, {71, 59272}, {72, 60676}, {78, 60675}, {304, 60678}, {306, 59261}, {1331, 28841}, {1444, 60680}, {3842, 1826}, {4649, 19}, {4753, 8756}, {4784, 6591}, {4824, 2501}, {4913, 3064}, {5625, 1839}, {16369, 862}, {16826, 4}, {20142, 242}, {28840, 7649}, {31904, 8747}, {51311, 28}, {51314, 286}, {51356, 27}, {57685, 59194}, {59203, 44143}, {59218, 430}, {59243, 1474}, {60697, 25}, {60699, 393}, {60701, 1}, {60703, 6}, {60706, 92}, {60711, 33}, {60713, 607}, {60715, 34}, {60717, 278}, {60719, 264}, {60724, 1824}, {60730, 318}, {60731, 281}, {60732, 273}, {60736, 41013}
X(60729) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {60717, 60731, 60706}

X(60730) = X(2)X(17144)∩X(8)X(210)

Barycentrics    b*c*(-a+b+c)*(a^2+b*c+2*a*(b+c)) : :

X(60730) lies on these lines: {2, 17144}, {8, 210}, {37, 26045}, {75, 4648}, {76, 17294}, {274, 29574}, {314, 646}, {319, 4043}, {321, 1909}, {333, 1334}, {350, 3661}, {668, 4044}, {740, 40790}, {1269, 17295}, {1574, 25510}, {1654, 22016}, {1655, 3175}, {1999, 2295}, {2340, 3996}, {3208, 11679}, {3596, 4007}, {3679, 30830}, {3729, 34282}, {3765, 4671}, {3770, 17372}, {3780, 27064}, {3886, 40739}, {3912, 17050}, {3948, 25280}, {3969, 19810}, {4102, 28660}, {4359, 29569}, {4377, 50084}, {4433, 7081}, {4441, 20917}, {4447, 32932}, {4489, 59511}, {4595, 60737}, {5308, 17158}, {5564, 18137}, {7146, 49507}, {16826, 60706}, {17243, 20174}, {17310, 20913}, {17389, 25303}, {17759, 37596}, {17786, 44140}, {18147, 48630}, {19787, 32858}, {19796, 26978}, {20888, 49765}, {20923, 42696}, {21281, 34255}, {21605, 34284}, {21868, 26048}, {24524, 42034}, {24598, 41142}, {27424, 56086}, {27523, 42032}, {28797, 32851}, {29573, 32104}, {29585, 31997}, {29602, 32092}, {30090, 32087}, {32864, 58287}, {34064, 59305}, {34258, 59311}, {50156, 50634}, {51353, 59212}, {60719, 60732}

X(60730) = X(i)-isoconjugate-of-X(j) for these {i, j}: {56, 25426}, {57, 60671}, {604, 30571}, {1106, 60675}, {1397, 27483}, {1402, 60680}, {1408, 60676}, {1412, 59272}, {16947, 59261}, {28841, 43924}, {40748, 56556}
X(60730) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 25426}, {3161, 30571}, {5452, 60671}, {6552, 60675}, {40599, 59272}, {40605, 60680}, {59577, 60676}
X(60730) = X(i)-Ceva conjugate of X(j) for these {i, j}: {60719, 60706}
X(60730) = X(i)-cross conjugate of X(j) for these {i, j}: {60731, 60706}
X(60730) = pole of line {2533, 4462} with respect to the Steiner circumellipse
X(60730) = pole of line {20317, 29198} with respect to the Steiner inellipse
X(60730) = pole of line {1014, 1429} with respect to the Wallace hyperbola
X(60730) = isotomic conjugate of the bicevian chordal perspector of X(7) and X(57)
X(60730) = intersection, other than A, B, C, of circumconics {{A, B, C, X(8), X(6625)}}, {{A, B, C, X(210), X(4102)}}, {{A, B, C, X(312), X(51865)}}, {{A, B, C, X(314), X(3975)}}, {{A, B, C, X(333), X(3706)}}, {{A, B, C, X(960), X(4649)}}, {{A, B, C, X(2478), X(31904)}}, {{A, B, C, X(3057), X(60715)}}, {{A, B, C, X(3702), X(28660)}}, {{A, B, C, X(3714), X(3842)}}, {{A, B, C, X(3877), X(51311)}}, {{A, B, C, X(3880), X(28840)}}, {{A, B, C, X(4009), X(4913)}}, {{A, B, C, X(4124), X(17197)}}, {{A, B, C, X(4519), X(4997)}}, {{A, B, C, X(4673), X(27424)}}, {{A, B, C, X(14555), X(51356)}}, {{A, B, C, X(27538), X(56086)}}, {{A, B, C, X(28809), X(52652)}}
X(60730) = barycentric product X(i)*X(j) for these (i, j): {314, 3842}, {318, 60729}, {333, 60736}, {341, 60717}, {346, 60732}, {561, 60713}, {2321, 51314}, {3596, 4649}, {3701, 51356}, {3718, 60699}, {4824, 7257}, {4913, 668}, {16826, 312}, {27495, 52652}, {28659, 60697}, {28660, 60724}, {28840, 646}, {30713, 51311}, {59761, 60715}, {60701, 7017}, {60706, 8}, {60711, 76}, {60719, 9}, {60731, 75}
X(60730) = barycentric quotient X(i)/X(j) for these (i, j): {8, 30571}, {9, 25426}, {55, 60671}, {210, 59272}, {312, 27483}, {333, 60680}, {346, 60675}, {644, 28841}, {2321, 60676}, {3596, 60678}, {3701, 59261}, {3842, 65}, {4649, 56}, {4753, 1319}, {4784, 43924}, {4824, 4017}, {4913, 513}, {5625, 32636}, {16826, 57}, {20142, 1429}, {27495, 7146}, {28809, 56658}, {28840, 3669}, {31904, 1396}, {40774, 1469}, {51311, 1412}, {51314, 1434}, {51356, 1014}, {52133, 40748}, {59219, 39793}, {59243, 1408}, {60697, 604}, {60699, 34}, {60701, 222}, {60703, 603}, {60706, 7}, {60711, 6}, {60713, 31}, {60715, 1407}, {60717, 269}, {60719, 85}, {60724, 1400}, {60729, 77}, {60731, 1}, {60732, 279}, {60736, 226}
X(60730) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 312, 3975}, {314, 2321, 17787}, {321, 6542, 1909}, {3948, 29615, 25280}, {4441, 29616, 20917}, {4671, 20055, 3765}, {16826, 60736, 60706}

X(60731) = X(1)X(4991)∩X(8)X(9)

Barycentrics    (a-b-c)*(a^2+b*c+2*a*(b+c)) : :

X(60731) lies on these lines: {1, 4991}, {2, 3751}, {6, 16830}, {8, 9}, {10, 894}, {43, 38000}, {44, 5263}, {45, 49470}, {57, 26038}, {63, 37109}, {69, 38057}, {72, 16824}, {75, 5220}, {85, 41712}, {86, 4663}, {190, 3696}, {210, 333}, {238, 49457}, {239, 984}, {312, 3715}, {314, 3701}, {319, 3932}, {320, 3826}, {321, 4756}, {518, 16823}, {612, 37652}, {726, 17117}, {740, 17261}, {756, 1999}, {846, 4685}, {899, 24627}, {966, 59406}, {968, 20012}, {1001, 17335}, {1043, 5302}, {1045, 3214}, {1150, 5205}, {1211, 33118}, {1351, 44430}, {1386, 51034}, {1698, 17238}, {1738, 6646}, {1966, 25280}, {2550, 54280}, {2663, 59305}, {3006, 37656}, {3219, 4427}, {3242, 50075}, {3305, 10453}, {3416, 17346}, {3578, 33078}, {3616, 37681}, {3617, 17350}, {3679, 3923}, {3681, 3757}, {3683, 3996}, {3703, 4886}, {3705, 14555}, {3731, 49495}, {3740, 14829}, {3755, 9791}, {3773, 6651}, {3775, 17292}, {3821, 17254}, {3823, 17344}, {3836, 17288}, {3842, 4649}, {3844, 17271}, {3876, 35628}, {3896, 33761}, {3920, 19742}, {3925, 33066}, {3967, 55095}, {3993, 50016}, {4023, 32851}, {4026, 17256}, {4046, 42033}, {4061, 56078}, {4078, 6542}, {4085, 24697}, {4134, 54335}, {4353, 41140}, {4361, 49447}, {4384, 5223}, {4388, 25006}, {4407, 29630}, {4429, 4643}, {4514, 41002}, {4551, 60705}, {4646, 4835}, {4664, 49486}, {4676, 16885}, {4682, 41629}, {4684, 6666}, {4690, 24358}, {4703, 32865}, {4716, 49456}, {4866, 7155}, {4966, 17263}, {4981, 32911}, {5224, 38047}, {5232, 9780}, {5235, 46897}, {5247, 20964}, {5268, 37683}, {5271, 32937}, {5297, 16704}, {5692, 16821}, {5695, 17336}, {5739, 29641}, {5743, 33121}, {5850, 24199}, {5852, 7321}, {5880, 17347}, {5904, 16817}, {6172, 24280}, {6734, 27420}, {7064, 35104}, {7080, 26059}, {7290, 36534}, {9534, 41229}, {11679, 27538}, {12717, 59417}, {15485, 49458}, {15492, 49484}, {16468, 36480}, {16814, 28581}, {16815, 24325}, {16816, 31302}, {16825, 49448}, {16828, 27270}, {16833, 49446}, {17116, 32935}, {17120, 50302}, {17135, 27065}, {17156, 41839}, {17160, 49523}, {17252, 32784}, {17266, 33087}, {17268, 49560}, {17287, 29674}, {17300, 34379}, {17308, 26083}, {17319, 49488}, {17326, 29633}, {17330, 49524}, {17331, 50295}, {17332, 24723}, {17333, 24248}, {17348, 32922}, {17379, 39586}, {17594, 59295}, {17738, 50095}, {17794, 24592}, {19843, 27254}, {20131, 31322}, {20156, 27475}, {21020, 32938}, {21039, 44694}, {21075, 29967}, {21077, 25446}, {21085, 33164}, {21371, 57279}, {21805, 32917}, {24058, 56318}, {24331, 49498}, {24821, 50117}, {26037, 32912}, {26103, 51780}, {26580, 33139}, {27064, 31330}, {28058, 41228}, {29580, 50283}, {29584, 49489}, {29824, 35595}, {29873, 31037}, {30393, 30567}, {30564, 54309}, {30867, 33140}, {31143, 48647}, {32924, 42039}, {32928, 42041}, {33076, 49693}, {33165, 50308}, {33166, 56810}, {33682, 36531}, {36404, 37654}, {36798, 56115}, {37658, 40739}, {37680, 46909}, {49449, 49675}, {49466, 49707}, {49474, 51297}, {49527, 50015}, {49536, 50305}, {50119, 50834}, {50127, 53620}, {50291, 51196}, {52923, 60723}, {59624, 60714}, {60699, 60736}, {60706, 60717}

X(60731) = reflection of X(i) in X(j) for these {i,j}: {16823, 17277}
X(60731) = X(i)-isoconjugate-of-X(j) for these {i, j}: {7, 60671}, {56, 30571}, {57, 25426}, {604, 27483}, {1014, 59272}, {1397, 60678}, {1400, 60680}, {1407, 60675}, {1408, 59261}, {1412, 60676}, {1469, 40748}, {3669, 28841}
X(60731) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 30571}, {3161, 27483}, {5452, 25426}, {24771, 60675}, {40582, 60680}, {40599, 60676}, {59577, 59261}
X(60731) = X(i)-Ceva conjugate of X(j) for these {i, j}: {60706, 16826}
X(60731) = X(i)-cross conjugate of X(j) for these {i, j}: {60711, 16826}
X(60731) = pole of line {4498, 17166} with respect to the Bevan circle
X(60731) = pole of line {210, 3685} with respect to the Feuerbach hyperbola
X(60731) = pole of line {1412, 1428} with respect to the Stammler hyperbola
X(60731) = pole of line {4024, 4468} with respect to the Steiner circumellipse
X(60731) = pole of line {99, 644} with respect to the Yff parabola
X(60731) = pole of line {1434, 1447} with respect to the Wallace hyperbola
X(60731) = pole of line {4859, 16831} with respect to the dual conic of Yff parabola
X(60731) = isotomic conjugate of the bicevian chordal perspector of X(7) and X(85)
X(60731) = intersection, other than A, B, C, of circumconics {{A, B, C, X(8), X(6625)}}, {{A, B, C, X(9), X(4649)}}, {{A, B, C, X(21), X(3691)}}, {{A, B, C, X(314), X(3686)}}, {{A, B, C, X(333), X(3685)}}, {{A, B, C, X(391), X(7155)}}, {{A, B, C, X(452), X(31904)}}, {{A, B, C, X(1334), X(7077)}}, {{A, B, C, X(1697), X(60715)}}, {{A, B, C, X(2321), X(3842)}}, {{A, B, C, X(2325), X(4753)}}, {{A, B, C, X(3208), X(4866)}}, {{A, B, C, X(3707), X(36798)}}, {{A, B, C, X(3786), X(60675)}}, {{A, B, C, X(3790), X(27495)}}, {{A, B, C, X(3886), X(51314)}}, {{A, B, C, X(4034), X(56087)}}, {{A, B, C, X(4266), X(59243)}}, {{A, B, C, X(5250), X(51311)}}, {{A, B, C, X(5853), X(28840)}}
X(60731) = barycentric product X(i)*X(j) for these (i, j): {1, 60730}, {21, 60736}, {55, 60719}, {190, 4913}, {200, 60732}, {210, 51314}, {281, 60729}, {312, 4649}, {314, 60724}, {318, 60701}, {333, 3842}, {341, 60715}, {345, 60699}, {346, 60717}, {2321, 51356}, {3596, 60697}, {3701, 51311}, {4102, 5625}, {4753, 4997}, {4784, 646}, {4824, 645}, {16826, 8}, {20142, 4518}, {27495, 52133}, {28840, 3699}, {30713, 59243}, {31904, 3710}, {40774, 52652}, {60703, 7017}, {60706, 9}, {60711, 75}, {60713, 76}
X(60731) = barycentric quotient X(i)/X(j) for these (i, j): {8, 27483}, {9, 30571}, {21, 60680}, {41, 60671}, {55, 25426}, {200, 60675}, {210, 60676}, {312, 60678}, {1334, 59272}, {2321, 59261}, {2344, 40748}, {3842, 226}, {3886, 56658}, {3939, 28841}, {4649, 57}, {4753, 3911}, {4784, 3669}, {4824, 7178}, {4913, 514}, {4948, 43052}, {5625, 553}, {16369, 1284}, {16826, 7}, {20142, 1447}, {27495, 7179}, {28840, 3676}, {40774, 7146}, {51311, 1014}, {51314, 57785}, {51356, 1434}, {59218, 3649}, {59243, 1412}, {60697, 56}, {60699, 278}, {60701, 77}, {60703, 222}, {60706, 85}, {60711, 1}, {60713, 6}, {60715, 269}, {60717, 279}, {60719, 6063}, {60724, 65}, {60729, 348}, {60730, 75}, {60732, 1088}, {60736, 1441}
X(60731) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 27549, 3790}, {8, 9, 3685}, {10, 1757, 894}, {10, 4416, 4645}, {210, 333, 7081}, {518, 17277, 16823}, {756, 32864, 1999}, {3617, 17350, 50314}, {3681, 5278, 3757}, {3686, 3717, 8}, {3696, 15481, 190}, {3707, 24393, 3883}, {3755, 50093, 9791}, {3773, 42334, 29615}, {3773, 50309, 42334}, {3775, 33159, 17292}, {3842, 4753, 4649}, {4384, 5223, 24349}, {17335, 49450, 1001}, {17348, 49515, 32922}, {20142, 27495, 16826}, {50016, 51294, 3993}, {60706, 60729, 60717}

X(60732) = X(7)X(8)∩X(226)X(4554)

Barycentrics    b*(a+b-c)*c*(a-b+c)*(a^2+b*c+2*a*(b+c)) : :

X(60732) lies on these lines: {7, 8}, {76, 17298}, {226, 4554}, {256, 24215}, {274, 4416}, {279, 39738}, {348, 26125}, {664, 42289}, {1284, 7176}, {1400, 1434}, {1446, 6625}, {1458, 55082}, {2481, 5542}, {4334, 40718}, {4654, 6063}, {5223, 59255}, {7209, 57826}, {16708, 33066}, {26563, 26806}, {30063, 30097}, {31225, 42290}, {51194, 55946}, {51314, 60715}, {60706, 60717}, {60719, 60730}

X(60732) = isotomic conjugate of X(60675)
X(60732) = X(i)-isoconjugate-of-X(j) for these {i, j}: {9, 60671}, {31, 60675}, {41, 30571}, {55, 25426}, {284, 59272}, {663, 28841}, {2175, 27483}, {2194, 60676}, {9447, 60678}, {57657, 59261}
X(60732) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 60675}, {223, 25426}, {478, 60671}, {1214, 60676}, {3160, 30571}, {40590, 59272}, {40593, 27483}, {56696, 3786}
X(60732) = X(i)-cross conjugate of X(j) for these {i, j}: {16826, 60706}
X(60732) = pole of line {21, 3684} with respect to the Wallace hyperbola
X(60732) = intersection, other than A, B, C, of circumconics {{A, B, C, X(8), X(6625)}}, {{A, B, C, X(65), X(60715)}}, {{A, B, C, X(69), X(51356)}}, {{A, B, C, X(75), X(40017)}}, {{A, B, C, X(226), X(7235)}}, {{A, B, C, X(377), X(31904)}}, {{A, B, C, X(518), X(4649)}}, {{A, B, C, X(1434), X(4059)}}, {{A, B, C, X(3212), X(57826)}}, {{A, B, C, X(3696), X(3842)}}, {{A, B, C, X(3868), X(51311)}}, {{A, B, C, X(4259), X(59243)}}, {{A, B, C, X(4753), X(49702)}}, {{A, B, C, X(10030), X(57785)}}
X(60732) = barycentric product X(i)*X(j) for these (i, j): {57, 60719}, {226, 51314}, {273, 60729}, {279, 60730}, {331, 60701}, {349, 51311}, {1088, 60731}, {1231, 31904}, {1434, 60736}, {1441, 51356}, {3842, 57785}, {4569, 4913}, {4572, 4784}, {4625, 4824}, {4649, 6063}, {16826, 85}, {20567, 60697}, {28840, 4554}, {57787, 60703}, {57792, 60711}, {60699, 7182}, {60706, 7}, {60715, 76}, {60717, 75}
X(60732) = barycentric quotient X(i)/X(j) for these (i, j): {2, 60675}, {7, 30571}, {56, 60671}, {57, 25426}, {65, 59272}, {85, 27483}, {226, 60676}, {651, 28841}, {1434, 60680}, {1441, 59261}, {3842, 210}, {4649, 55}, {4753, 3689}, {4784, 663}, {4824, 4041}, {4913, 3900}, {4948, 4814}, {5625, 3683}, {6063, 60678}, {16826, 9}, {20142, 3684}, {28840, 650}, {31904, 1172}, {40774, 4517}, {51311, 284}, {51314, 333}, {51356, 21}, {59219, 4111}, {59243, 2194}, {60697, 41}, {60699, 33}, {60701, 219}, {60703, 212}, {60706, 8}, {60711, 220}, {60713, 1253}, {60715, 6}, {60717, 1}, {60719, 312}, {60720, 56658}, {60724, 1334}, {60729, 78}, {60730, 346}, {60731, 200}, {60736, 2321}
X(60732) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 85, 10030}, {226, 57785, 7196}, {1463, 4059, 7}

X(60733) = X(1)X(7)∩X(354)X(658)

Barycentrics    (a+b-c)*(a-b+c)*(a^4-b*(b-c)^2*c-4*a^3*(b+c)-2*a*(b-c)^2*(b+c)+a^2*(5*b^2+3*b*c+5*c^2)) : :

X(60733) lies on these lines: {1, 7}, {85, 42871}, {354, 658}, {518, 55082}, {664, 15570}, {1447, 7672}, {3212, 11526}, {3243, 40719}, {3748, 33765}, {5226, 24600}, {5228, 27475}, {5728, 24203}, {6604, 38053}, {8732, 27253}, {10012, 60709}, {10390, 43750}, {14151, 34018}, {21617, 56928}, {26125, 51194}, {31526, 44841}, {37703, 37757}, {38250, 45834}, {41246, 51058}, {42311, 53242}, {49478, 56783}

X(60733) = pole of line {354, 14189} with respect to the Feuerbach hyperbola
X(60733) = pole of line {4025, 57252} with respect to the Steiner circumellipse
X(60733) = isotomic conjugate of the bicevian chordal perspector of X(8) and X(75)
X(60733) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1742), X(10390)}}, {{A, B, C, X(2293), X(52001)}}, {{A, B, C, X(5543), X(38250)}}, {{A, B, C, X(10012), X(10481)}}, {{A, B, C, X(14189), X(21453)}}
X(60733) = barycentric product X(i)*X(j) for these (i, j): {10012, 21453}, {60709, 7}
X(60733) = barycentric quotient X(i)/X(j) for these (i, j): {10012, 4847}, {60709, 8}
X(60733) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 7, 14189}, {354, 21453, 9446}

X(60734) = X(7)X(7243)∩X(10)X(349)

Barycentrics    b*(a+b-c)*c*(a-b+c)*(b+c)*(a^2-2*b*c-a*(b+c)) : :

X(60734) lies on these lines: {7, 7243}, {10, 349}, {75, 1088}, {85, 3671}, {226, 306}, {313, 4082}, {347, 27339}, {348, 32092}, {946, 17866}, {1042, 9312}, {1231, 4647}, {1362, 49483}, {1447, 26237}, {1909, 25719}, {3006, 7179}, {3760, 52422}, {3886, 4441}, {3944, 17885}, {4554, 60706}, {6604, 32104}, {7244, 55096}, {12609, 52565}, {17858, 21436}, {17861, 24210}, {17880, 20880}, {17881, 42005}, {20894, 38468}, {21075, 21403}, {21264, 43063}, {24209, 24241}, {25002, 41006}, {25723, 31997}, {34388, 56253}

X(60734) = X(i)-isoconjugate-of-X(j) for these {i, j}: {41, 42302}, {55, 51443}, {58, 60673}, {284, 2279}, {1002, 2194}, {1333, 40779}, {1408, 59269}, {2150, 60677}, {2206, 60668}, {7252, 8693}, {27475, 57657}
X(60734) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 60673}, {37, 40779}, {223, 51443}, {1214, 1002}, {3160, 42302}, {40590, 2279}, {40603, 60668}, {55059, 663}, {56325, 60677}, {59577, 59269}, {59608, 42290}
X(60734) = X(i)-cross conjugate of X(j) for these {i, j}: {3696, 4044}
X(60734) = pole of line {2185, 2328} with respect to the Wallace hyperbola
X(60734) = pole of line {4163, 17899} with respect to the dual conic of Bevan circle
X(60734) = pole of line {4858, 17059} with respect to the dual conic of Stammler hyperbola
X(60734) = pole of line {3670, 3673} with respect to the dual conic of Yff parabola
X(60734) = isotomic conjugate of the bicevian chordal perspector of X(21) and X(81)
X(60734) = intersection, other than A, B, C, of circumconics {{A, B, C, X(10), X(3930)}}, {{A, B, C, X(75), X(2321)}}, {{A, B, C, X(226), X(1088)}}, {{A, B, C, X(306), X(4384)}}, {{A, B, C, X(321), X(4044)}}, {{A, B, C, X(1001), X(22021)}}, {{A, B, C, X(1441), X(57792)}}, {{A, B, C, X(2171), X(3668)}}, {{A, B, C, X(3963), X(7205)}}, {{A, B, C, X(3969), X(52421)}}, {{A, B, C, X(4082), X(4847)}}, {{A, B, C, X(28809), X(34258)}}, {{A, B, C, X(37658), X(58024)}}
X(60734) = barycentric product X(i)*X(j) for these (i, j): {10, 60720}, {12, 60735}, {226, 4441}, {313, 5228}, {321, 40719}, {1001, 349}, {1441, 4384}, {1446, 3886}, {1471, 27801}, {1893, 304}, {3696, 85}, {3701, 42309}, {4044, 7}, {4554, 4804}, {21615, 65}, {23151, 57809}, {28809, 3668}, {30713, 59242}, {31926, 57807}, {34388, 60721}, {42289, 76}, {59202, 60229}, {59207, 6063}
X(60734) = barycentric quotient X(i)/X(j) for these (i, j): {7, 42302}, {10, 40779}, {12, 60677}, {37, 60673}, {57, 51443}, {65, 2279}, {226, 1002}, {321, 60668}, {349, 59255}, {1001, 284}, {1441, 27475}, {1471, 1333}, {1893, 19}, {2280, 2194}, {2321, 59269}, {3668, 42290}, {3696, 9}, {3886, 2287}, {4044, 8}, {4384, 21}, {4441, 333}, {4551, 8693}, {4552, 37138}, {4554, 51563}, {4724, 7252}, {4762, 3737}, {4804, 650}, {5228, 58}, {21615, 314}, {23151, 283}, {27474, 3786}, {28044, 2332}, {28809, 1043}, {30713, 59260}, {31926, 270}, {37658, 2328}, {40718, 40757}, {40719, 81}, {40784, 3736}, {42289, 6}, {42309, 1014}, {45755, 21789}, {54440, 5546}, {59202, 16713}, {59207, 55}, {59242, 1412}, {60229, 59193}, {60720, 86}, {60721, 60}, {60722, 57657}, {60735, 261}
X(60734) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 35517, 4847}, {75, 6063, 9436}, {4441, 60720, 40719}

X(60735) = X(1)X(75)∩X(6)X(4754)

Barycentrics    b*(a+b)*c*(a+c)*(-a^2+2*b*c+a*(b+c)) : :

X(60735) lies on these lines: {1, 75}, {6, 4754}, {76, 17277}, {81, 16748}, {190, 60719}, {238, 20888}, {305, 19792}, {310, 333}, {873, 42028}, {1001, 4441}, {1434, 10030}, {1738, 16887}, {1920, 55095}, {2345, 25508}, {2550, 30941}, {4000, 16705}, {4384, 21615}, {4429, 30966}, {5132, 37670}, {5228, 60720}, {6385, 55946}, {8033, 41629}, {14377, 14964}, {16707, 30599}, {16712, 37756}, {16738, 18600}, {16739, 16750}, {16930, 17379}, {17259, 18135}, {18140, 29484}, {18166, 20181}, {20156, 28809}, {20174, 20911}, {26582, 30965}, {28660, 32008}, {32850, 33297}, {42302, 52652}

X(60735) = isotomic conjugate of X(60677)
X(60735) = perspector of circumconic {{A, B, C, X(799), X(35565)}}
X(60735) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 60677}, {42, 2279}, {213, 1002}, {669, 32041}, {798, 37138}, {872, 42302}, {1400, 60673}, {1402, 40779}, {1500, 51443}, {1918, 27475}, {2205, 59255}, {24290, 32724}, {51563, 53581}
X(60735) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 60677}, {6626, 1002}, {31998, 37138}, {34021, 27475}, {39054, 8693}, {40582, 60673}, {40592, 2279}, {40605, 40779}, {55059, 4079}
X(60735) = pole of line {31, 9454} with respect to the Stammler hyperbola
X(60735) = pole of line {1, 672} with respect to the Wallace hyperbola
X(60735) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(673)}}, {{A, B, C, X(75), X(4441)}}, {{A, B, C, X(76), X(33933)}}, {{A, B, C, X(310), X(18157)}}, {{A, B, C, X(740), X(3696)}}, {{A, B, C, X(1010), X(31926)}}, {{A, B, C, X(1043), X(52379)}}, {{A, B, C, X(1471), X(2274)}}, {{A, B, C, X(2234), X(4724)}}, {{A, B, C, X(2667), X(59207)}}, {{A, B, C, X(3736), X(42302)}}, {{A, B, C, X(3875), X(56705)}}, {{A, B, C, X(3886), X(52652)}}, {{A, B, C, X(4044), X(4647)}}, {{A, B, C, X(4673), X(28809)}}, {{A, B, C, X(4804), X(57040)}}, {{A, B, C, X(10436), X(40719)}}, {{A, B, C, X(17394), X(55970)}}, {{A, B, C, X(20156), X(42028)}}, {{A, B, C, X(33935), X(40005)}}, {{A, B, C, X(36289), X(37129)}}, {{A, B, C, X(39721), X(42358)}}, {{A, B, C, X(57537), X(57815)}}
X(60735) = barycentric product X(i)*X(j) for these (i, j): {261, 60734}, {274, 4384}, {304, 31926}, {314, 40719}, {333, 60720}, {1001, 310}, {1434, 28809}, {1471, 40072}, {1509, 4044}, {2280, 6385}, {3696, 873}, {3886, 57785}, {4441, 86}, {4623, 4804}, {4724, 670}, {4762, 799}, {18021, 42289}, {21615, 81}, {23151, 44129}, {28660, 5228}, {51314, 56658}, {52619, 54440}, {60721, 76}
X(60735) = barycentric quotient X(i)/X(j) for these (i, j): {2, 60677}, {21, 60673}, {81, 2279}, {86, 1002}, {99, 37138}, {274, 27475}, {310, 59255}, {314, 60668}, {333, 40779}, {662, 8693}, {757, 51443}, {799, 32041}, {1001, 42}, {1043, 59269}, {1434, 42290}, {1471, 1402}, {1509, 42302}, {2280, 213}, {3696, 756}, {3886, 210}, {4044, 594}, {4384, 37}, {4441, 10}, {4623, 51563}, {4702, 21805}, {4724, 512}, {4762, 661}, {4804, 4705}, {5228, 1400}, {21615, 321}, {23151, 71}, {28809, 2321}, {31926, 19}, {37658, 1334}, {40719, 65}, {42289, 181}, {42309, 1427}, {45755, 3709}, {54440, 4557}, {56658, 60676}, {59202, 3925}, {59207, 1500}, {59217, 52020}, {59242, 1042}, {60720, 226}, {60721, 6}, {60722, 1918}, {60734, 12}
X(60735) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {274, 30940, 86}, {274, 314, 18157}

X(60736) = X(2)X(1500)∩X(10)X(321)

Barycentrics    b*c*(b+c)*(a^2+b*c+2*a*(b+c)) : :

X(60736) lies on these lines: {2, 1500}, {8, 52245}, {10, 321}, {75, 141}, {76, 6539}, {239, 2295}, {274, 6542}, {312, 29576}, {314, 28604}, {350, 29610}, {668, 51353}, {1018, 4384}, {1213, 4043}, {1268, 25660}, {1269, 17239}, {1573, 31036}, {1909, 29615}, {3187, 17750}, {3501, 5271}, {3626, 25298}, {3679, 3765}, {3690, 59296}, {3730, 5278}, {3770, 32025}, {3842, 59219}, {3912, 3969}, {3934, 27044}, {3995, 16589}, {4358, 24603}, {4472, 30939}, {4651, 20683}, {4671, 30830}, {4967, 20891}, {4980, 20888}, {5257, 22016}, {6376, 42029}, {7237, 23944}, {10009, 31329}, {12782, 31330}, {15668, 52555}, {16349, 31477}, {16709, 17390}, {16752, 26759}, {16826, 60706}, {17144, 17397}, {17244, 19804}, {17289, 20174}, {17294, 32092}, {17308, 32104}, {17389, 31997}, {17759, 40773}, {18139, 40006}, {19963, 25741}, {20432, 20911}, {20691, 31993}, {21858, 27042}, {21956, 26601}, {22034, 25614}, {24190, 33172}, {24589, 29571}, {25002, 48381}, {27076, 31026}, {27495, 60719}, {27797, 60288}, {28612, 29674}, {29605, 52716}, {29616, 59255}, {29756, 34573}, {30566, 60097}, {30599, 33297}, {31025, 52959}, {34258, 60230}, {53478, 56249}, {56210, 60264}, {60244, 60267}, {60699, 60731}

X(60736) = isotomic conjugate of X(60680)
X(60736) = perspector of circumconic {{A, B, C, X(4033), X(4583)}}
X(60736) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 60680}, {58, 25426}, {81, 60671}, {593, 59272}, {849, 60676}, {1333, 30571}, {1408, 60675}, {2206, 27483}, {2308, 59194}, {3733, 28841}
X(60736) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 60680}, {10, 25426}, {37, 30571}, {3842, 24512}, {4075, 60676}, {40586, 60671}, {40603, 27483}, {59577, 60675}
X(60736) = X(i)-Ceva conjugate of X(j) for these {i, j}: {60706, 3842}
X(60736) = pole of line {594, 3948} with respect to the Kiepert hyperbola
X(60736) = pole of line {6372, 46403} with respect to the Steiner circumellipse
X(60736) = pole of line {3837, 4129} with respect to the Steiner inellipse
X(60736) = pole of line {757, 18166} with respect to the Wallace hyperbola
X(60736) = pole of line {918, 58361} with respect to the dual conic of circumcircle
X(60736) = pole of line {726, 756} with respect to the dual conic of Yff parabola
X(60736) = pole of line {244, 39786} with respect to the dual conic of Wallace hyperbola
X(60736) = isotomic conjugate of the bicevian chordal perspector of X(81) and X(86)
X(60736) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(21020)}}, {{A, B, C, X(10), X(335)}}, {{A, B, C, X(75), X(3948)}}, {{A, B, C, X(76), X(4647)}}, {{A, B, C, X(141), X(20142)}}, {{A, B, C, X(321), X(334)}}, {{A, B, C, X(523), X(4665)}}, {{A, B, C, X(594), X(40098)}}, {{A, B, C, X(756), X(6539)}}, {{A, B, C, X(2292), X(51311)}}, {{A, B, C, X(3661), X(59261)}}, {{A, B, C, X(3862), X(27495)}}, {{A, B, C, X(3971), X(40848)}}, {{A, B, C, X(3994), X(4824)}}, {{A, B, C, X(4424), X(60715)}}, {{A, B, C, X(5051), X(31904)}}, {{A, B, C, X(16369), X(49509)}}, {{A, B, C, X(20913), X(40024)}}, {{A, B, C, X(28605), X(59218)}}, {{A, B, C, X(41809), X(51356)}}
X(60736) = barycentric product X(i)*X(j) for these (i, j): {10, 60706}, {37, 60719}, {226, 60730}, {313, 4649}, {349, 60711}, {1089, 51356}, {1255, 59203}, {1441, 60731}, {2321, 60732}, {3701, 60717}, {3842, 75}, {4824, 668}, {16369, 18895}, {16826, 321}, {20336, 60699}, {27801, 60697}, {27808, 4784}, {28654, 51311}, {28840, 4033}, {30713, 60715}, {31904, 52369}, {32018, 59218}, {41013, 60729}, {51314, 594}, {60724, 76}
X(60736) = barycentric quotient X(i)/X(j) for these (i, j): {2, 60680}, {10, 30571}, {37, 25426}, {42, 60671}, {313, 60678}, {321, 27483}, {594, 60676}, {756, 59272}, {1018, 28841}, {1089, 59261}, {1255, 59194}, {2321, 60675}, {3842, 1}, {4044, 56658}, {4649, 58}, {4753, 52680}, {4784, 3733}, {4824, 513}, {4913, 3737}, {4948, 4833}, {4963, 4840}, {16369, 1914}, {16826, 81}, {27495, 40773}, {28840, 1019}, {40718, 40748}, {40774, 3736}, {51311, 593}, {51314, 1509}, {51356, 757}, {59203, 4359}, {59218, 1100}, {59219, 3720}, {59243, 849}, {60697, 1333}, {60699, 28}, {60701, 1790}, {60703, 1437}, {60706, 86}, {60711, 284}, {60713, 2194}, {60715, 1412}, {60717, 1014}, {60719, 274}, {60724, 6}, {60729, 1444}, {60730, 333}, {60731, 21}, {60732, 1434}
X(60736) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 321, 3948}, {10, 4044, 59212}, {75, 3661, 20913}, {75, 594, 3963}, {321, 59212, 4044}, {4980, 52043, 20888}, {6539, 28605, 28654}, {28605, 29593, 76}, {60706, 60730, 16826}

X(60737) = X(1)X(2)∩X(71)X(190)

Barycentrics    (b+c)*(-a^4+2*b^2*c^2+a^2*(b^2+c^2)) : :

X(60737) lies on these lines: {1, 2}, {9, 56253}, {69, 30035}, {71, 190}, {75, 28402}, {183, 52134}, {321, 4095}, {333, 25280}, {458, 60685}, {672, 3765}, {902, 11320}, {1018, 4044}, {1334, 3948}, {1400, 3963}, {1423, 4659}, {1441, 4019}, {1918, 21022}, {2245, 4377}, {2293, 21278}, {2329, 26243}, {2333, 46104}, {3219, 17739}, {3230, 30819}, {3403, 20023}, {3596, 28287}, {3934, 54282}, {3936, 16603}, {3969, 4136}, {4150, 21011}, {4456, 44176}, {4555, 53194}, {4595, 60730}, {4642, 19791}, {4670, 28369}, {15983, 20258}, {16583, 21327}, {16605, 21345}, {17062, 18139}, {17318, 56926}, {17335, 56249}, {19807, 22097}, {19811, 34384}, {20336, 21231}, {20892, 28351}, {21238, 40934}, {21281, 30985}, {21858, 28358}, {22356, 30882}, {25102, 37676}, {25425, 59207}, {33736, 37716}, {52043, 56509}

X(60737) = isotomic conjugate of X(60679)
X(60737) = X(i)-isoconjugate-of-X(j) for these {i, j}: {28, 43718}, {31, 60679}, {58, 2186}, {81, 263}, {86, 3402}, {262, 1333}, {274, 46319}, {513, 26714}, {2203, 42313}, {5317, 54032}, {16696, 42288}, {36132, 53521}, {52631, 52935}
X(60737) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 60679}, {10, 2186}, {37, 262}, {16603, 7146}, {38997, 649}, {39009, 53521}, {39026, 26714}, {40586, 263}, {40591, 43718}, {40600, 3402}, {51580, 86}, {55051, 21123}
X(60737) = X(i)-Ceva conjugate of X(j) for these {i, j}: {183, 60723}, {3403, 42711}, {52652, 321}
X(60737) = pole of line {7649, 21123} with respect to the polar circle
X(60737) = pole of line {514, 53336} with respect to the Steiner circumellipse
X(60737) = pole of line {86, 17209} with respect to the Wallace hyperbola
X(60737) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1821)}}, {{A, B, C, X(2), X(183)}}, {{A, B, C, X(42), X(56246)}}, {{A, B, C, X(145), X(27809)}}, {{A, B, C, X(182), X(386)}}, {{A, B, C, X(226), X(24239)}}, {{A, B, C, X(306), X(56251)}}, {{A, B, C, X(321), X(3705)}}, {{A, B, C, X(387), X(33971)}}, {{A, B, C, X(519), X(23878)}}, {{A, B, C, X(995), X(60135)}}, {{A, B, C, X(2333), X(41267)}}, {{A, B, C, X(3009), X(3288)}}, {{A, B, C, X(3017), X(54834)}}, {{A, B, C, X(4052), X(49554)}}, {{A, B, C, X(10311), X(54426)}}, {{A, B, C, X(10449), X(44144)}}, {{A, B, C, X(16609), X(56805)}}, {{A, B, C, X(17749), X(60075)}}, {{A, B, C, X(39680), X(45905)}}
X(60737) = barycentric product X(i)*X(j) for these (i, j): {1, 42711}, {10, 183}, {182, 313}, {190, 23878}, {306, 458}, {321, 52134}, {1978, 3288}, {3403, 37}, {3701, 60716}, {3998, 51315}, {4039, 8842}, {10311, 40071}, {14096, 56251}, {14994, 18082}, {20023, 42}, {20336, 60685}, {33971, 52396}, {44144, 71}, {56246, 59197}, {60723, 75}, {60726, 76}
X(60737) = barycentric quotient X(i)/X(j) for these (i, j): {2, 60679}, {10, 262}, {37, 2186}, {42, 263}, {71, 43718}, {101, 26714}, {182, 58}, {183, 86}, {213, 3402}, {306, 42313}, {313, 327}, {458, 27}, {1918, 46319}, {3288, 649}, {3403, 274}, {3682, 54032}, {4079, 52631}, {6784, 3122}, {10311, 1474}, {14096, 17187}, {14994, 16887}, {18082, 42299}, {20023, 310}, {23878, 514}, {33971, 8747}, {34396, 2206}, {42711, 75}, {44144, 44129}, {51372, 18653}, {51373, 51370}, {52134, 81}, {52396, 59257}, {56246, 42300}, {59197, 17167}, {60685, 28}, {60716, 1014}, {60723, 1}, {60726, 6}
X(60737) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 40886, 1201}, {10, 4039, 42}, {4095, 16609, 321}, {29456, 29699, 29574}

X(60738) = TRILINEAR PRODUCT OF PU(215)

Barycentrics    b*c*(3*a^8 - 3*a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + b^8 - 3*a^6*c^2 + 7*a^4*b^2*c^2 - a^2*b^4*c^2 - 4*b^6*c^2 - 2*a^4*c^4 - a^2*b^2*c^4 + 6*b^4*c^4 + a^2*c^6 - 4*b^2*c^6 + c^8) : :

X(60738) lies on these lines: {1, 564}, {79, 12904}, {80, 12903}, {158, 35201}, {162, 1784}, {1895, 36063}, {2962, 36119}, {2964, 36053}, {5728, 10073}

X(60738) = barycentric product X(i)*X(j) for these {i,j}: {92, 12121}, {662, 18039}, {1577, 60605}, {14206, 14989}
X(60738) = barycentric quotient X(i)/X(j) for these {i,j}: {12121, 63}, {14989, 2349}, {18039, 1577}, {60605, 662}

X(60739) = BARYCENTRIC PRODUCT OF PU(215)

Barycentrics    3*a^8 - 3*a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + b^8 - 3*a^6*c^2 + 7*a^4*b^2*c^2 - a^2*b^4*c^2 - 4*b^6*c^2 - 2*a^4*c^4 - a^2*b^2*c^4 + 6*b^4*c^4 + a^2*c^6 - 4*b^2*c^6 + c^8 : :

X(60739) lies on these lines: {6, 13}, {50, 112}, {99, 45331}, {111, 5306}, {230, 53136}, {393, 39176}, {395, 43092}, {396, 43091}, {523, 51894}, {566, 18580}, {800, 47226}, {1033, 8553}, {1249, 46262}, {2079, 14702}, {2493, 7735}, {2963, 8749}, {2965, 14910}, {3815, 30789}, {5467, 38730}, {5913, 16306}, {6103, 37637}, {7737, 52951}, {12042, 50149}, {13337, 14482}, {14579, 40136}, {14836, 30537}, {15356, 51431}, {15860, 39601}, {16303, 18579}, {16310, 33505}, {18365, 52945}, {18487, 47275}, {30685, 37644}, {35282, 47284}, {36825, 48453}, {38739, 46127}, {38872, 59657}, {39602, 41358}

X(60739) = (7*J^2 - 9)*R^2*SW*X[6] + 6*S^2*X[381]

X(60739) = polar conjugate of the isotomic conjugate of X(12121)
X(60739) = crossdifference of every pair of points on line {526, 12041}
X(60739) = barycentric product X(i)*X(j) for these {i,j}: {4, 12121}, {30, 14989}, {110, 18039}, {523, 60605}
X(60739) = barycentric quotient X(i)/X(j) for these {i,j}: {12121, 69}, {14989, 1494}, {18039, 850}, {60605, 99}
X(60739) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 3018, 1989}, {50, 1990, 19656}, {3018, 3163, 6}, {18487, 58267, 47275}

X(60740) = CEVAPOINT OF PU(215)

Barycentrics    (3*a^8 + 2*a^6*b^2 - 10*a^4*b^4 + 2*a^2*b^6 + 3*b^8 - 8*a^6*c^2 + 7*a^4*b^2*c^2 + 7*a^2*b^4*c^2 - 8*b^6*c^2 + 6*a^4*c^4 - 9*a^2*b^2*c^4 + 6*b^4*c^4 - c^8)*(3*a^8 - 8*a^6*b^2 + 6*a^4*b^4 - b^8 + 2*a^6*c^2 + 7*a^4*b^2*c^2 - 9*a^2*b^4*c^2 - 10*a^4*c^4 + 7*a^2*b^2*c^4 + 6*b^4*c^4 + 2*a^2*c^6 - 8*b^2*c^6 + 3*c^8) : :
X(60740) = 5 X[20] - 2 X[52056], 3 X[376] - 2 X[60603], 2 X[1657] + X[60008], X[10620] - 4 X[13471], 5 X[15081] - 8 X[36164]

X(60740) lies on these lines: {20, 14254}, {30, 32609}, {376, 60603}, {523, 12244}, {1138, 2777}, {1657, 3471}, {1990, 18365}, {3529, 15454}, {3543, 14851}, {5189, 45821}, {9214, 11001}, {10620, 13471}, {13619, 52661}, {15081, 36164}, {16111, 60604}, {35906, 43619}

X(60740) = reflection of X(i) in X(j) for these {i,j}: {3543, 14851}, {60604, 16111}
X(60740) = isogonal conjugate of X(10620)

X(60741) = CROSSPOINT OF PU(215)

Barycentrics    (a^8 - 6*a^4*b^4 + 8*a^2*b^6 - 3*b^8 + 9*a^4*b^2*c^2 - 7*a^2*b^4*c^2 - 2*b^6*c^2 - 6*a^4*c^4 - 7*a^2*b^2*c^4 + 10*b^4*c^4 + 8*a^2*c^6 - 2*b^2*c^6 - 3*c^8)*(3*a^8 - 3*a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + b^8 - 3*a^6*c^2 + 7*a^4*b^2*c^2 - a^2*b^4*c^2 - 4*b^6*c^2 - 2*a^4*c^4 - a^2*b^2*c^4 + 6*b^4*c^4 + a^2*c^6 - 4*b^2*c^6 + c^8) : :
X(60741) = 7 X[4] - X[60008], 3 X[15061] - 4 X[21315], X[265] + 2 X[36172], 2 X[382] + X[52056], 2 X[1539] + X[34193], 4 X[1553] - X[23236], X[10721] + 2 X[18319], X[12121] + 2 X[14989], 2 X[13202] + X[38580], 2 X[14508] - 5 X[15027], X[14508] - 4 X[21316], 5 X[15027] - 8 X[21316], 5 X[14643] - 4 X[31378], X[20127] - 4 X[25641], 8 X[36169] - 5 X[38794], X[38581] - 4 X[46686]

X(60741) lies on these lines: {4, 47055}, {30, 14644}, {265, 36172}, {381, 14851}, {382, 39170}, {523, 7728}, {1539, 34193}, {1553, 23236}, {2777, 14993}, {3003, 18325}, {10721, 18319}, {12121, 14989}, {13202, 38580}, {14508, 15027}, {14643, 31378}, {14980, 22337}, {18507, 30716}, {20127, 25641}, {32423, 57471}, {36169, 38794}, {38581, 46686}

X(60741) = midpoint of X(i) and X(j) for these {i,j}: {10721, 60604}, {14989, 60605}
X(60741) = reflection of X(i) in X(j) for these {i,j}: {12121, 60605}, {14851, 381}, {38788, 57305}, {60604, 18319}
X(60741) = complement of the isogonal conjugate of X(10620)
X(60741) = X(10620)-complementary conjugate of X(10)
X(60741) = {X(14508),X(21316)}-harmonic conjugate of X(15027)



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leftri  Centers of coaxial circles: X(60742) - X(60773)  rightri

This preamble and centers X(60742)-X(60773) were contributed by César Eliud Lozada, November 25, 2023.

Given two non-concentric circles 𝒞1 and 𝒞2 and a point P, neither on any of the given circles nor on their radical axis, there exists an unique circle through P and coaxial with the given circles. (A simple proof and a method for determining this circle can be seen here.)

Such circle is denoted here as Ωx(𝒞1, 𝒞2, P).

underbar

X(60742) = CENTER OF Ωx( CIRCUMCIRCLE, INCIRCLE, X(2) )

Barycentrics    a*(9*a^5-10*(b+c)*a^4+2*b*c*a^3+2*(b+c)*(3*b^2-4*b*c+3*c^2)*a^2-(9*b^2-14*b*c+9*c^2)*(b^2+c^2)*a+4*(b^4-c^4)*(b-c)) : :

X(60742) lies on these lines: {1, 3}, {2, 60767}, {376, 60752}, {381, 60756}, {3679, 60748}, {4881, 21539}, {7611, 38031}, {11194, 37807}, {31189, 59387}, {37817, 60747}

X(60742) = anticomplement of X(60767)
X(60742) = X(60767)-Dao conjugate of-X(60767)

X(60743) = CENTER OF Ωx( CIRCUMCIRCLE, INCIRCLE, X(3) )

Barycentrics    a^2*(a^8-2*(b+c)*a^7-2*(b^2-b*c+c^2)*a^6+2*(b+c)*(3*b^2-2*b*c+3*c^2)*a^5-2*(b+c)^2*b*c*a^4-2*(b+c)*(3*b^4+3*c^4-4*b*c*(b^2-b*c+c^2))*a^3+2*(b^2-b*c+c^2)*(b^2+c^2)^2*a^2+2*(b^2-c^2)*(b-c)*(b^4+c^4)*a-(b^4-c^4)*(b^2-c^2)*(b-c)^2) : :

X(60743) lies on these lines: {1, 3}, {2, 60769}, {24, 1851}, {104, 37300}, {355, 37282}, {944, 37301}, {1004, 37820}, {1012, 38761}, {2834, 6644}, {3149, 26492}, {3433, 47391}, {3560, 31936}, {5249, 37287}, {5450, 12617}, {6642, 23850}, {6713, 6911}, {7502, 60753}, {9956, 16410}, {10785, 35979}, {12116, 35976}, {20818, 34544}, {22758, 37249}, {25875, 37821}, {36003, 37000}, {37284, 41012}, {37292, 49107}

X(60743) = midpoint of X(3) and X(1617)
X(60743) = anticomplement of X(60769)
X(60743) = X(60769)-Dao conjugate of-X(60769)
X(60743) = X(1617)-of-anti-X3-ABC reflections triangle
X(60743) = X(39538)-of-intouch triangle, when ABC is acute
X(60743) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (36, 15931, 40), (36152, 37561, 3), (37578, 37579, 36), (59332, 59334, 3)

X(60744) = CENTER OF Ωx( CIRCUMCIRCLE, INCIRCLE, X(4) )

Barycentrics    a*(-a^2+b^2+c^2)*(a^7-2*(b+c)*a^6-(b-c)^2*a^5-(b-c)^4*a^3+2*(b^2-c^2)*(b-c)*(3*b^2+2*b*c+3*c^2)*a^2+(b^2-6*b*c+c^2)*(b^2-c^2)^2*a-4*(b^2-c^2)^3*(b-c)) : :

X(60744) lies on these lines: {1, 3}, {2, 60768}, {5, 7046}, {381, 21664}, {971, 15237}, {2968, 5603}, {3241, 38554}, {10746, 26333}, {11396, 37252}, {18531, 60754}, {37260, 41722}

X(60744) = reflection of X(7046) in X(5)
X(60744) = anticomplement of X(60768)
X(60744) = X(60768)-Dao conjugate of-X(60768)
X(60744) = X(31516)-reciprocal conjugate of-X(92)
X(60744) = barycentric product X(63)*X(31516)
X(60744) = trilinear product X(3)*X(31516)
X(60744) = trilinear quotient X(31516)/X(4)
X(60744) = X(7046)-of-Johnson triangle

X(60745) = CENTER OF Ωx( CIRCUMCIRCLE, INCIRCLE, X(5) )

Barycentrics    a*(a^9-(b+c)*a^8-2*(b^2+c^2)*a^7+2*(b+c)*(b^2+c^2)*a^6+2*(b-c)^2*b*c*a^5-(b+c)*(2*b^2-3*b*c+2*c^2)*b*c*a^4+2*(b^2-b*c+c^2)*(b^4+c^4-b*c*(b^2-b*c+c^2))*a^3-(b^2-c^2)*(b-c)*(2*b^4+3*b^2*c^2+2*c^4)*a^2-(b^4-c^4)*(b^2-c^2)*(b-c)^2*a+(b^4-c^4)*(b^2-c^2)^2*(b-c)) : :

X(60745) lies on these lines: {1, 3}, {5101, 52295}, {24042, 44288}, {39504, 60759}, {60749, 60755}

X(60746) = CENTER OF Ωx( CIRCUMCIRCLE, NINE-POINT CIRCLE, X(20) )

Barycentrics    (-a^2+b^2+c^2)*(9*a^8-7*(b^2+c^2)*a^6-(11*b^4-30*b^2*c^2+11*c^4)*a^4+7*(b^4-c^4)*(b^2-c^2)*a^2+2*(b^2-c^2)^4) : :
X(60746) = 2*X(3)-X(30771)

As a point on the Euler line, X(60746) has Shinagawa coefficients (-7*S^2+(4*(28*R*r+7*r^2+8*E))*r^2, 11*S^2-(4*(44*R*r+11*r^2+12*E))*r^2)

X(60746) lies on these lines: {2, 3}, {99, 40995}, {112, 59655}, {216, 44541}, {1578, 51911}, {1579, 51910}, {3184, 34810}, {8780, 15311}, {10605, 16163}, {10606, 18440}, {12121, 32263}, {13416, 15305}, {16111, 18451}, {18438, 36987}, {18445, 38723}, {18550, 56073}, {21968, 48378}, {26944, 43604}, {29012, 58762}, {30549, 38749}, {38726, 47391}, {38736, 52874}

X(60746) = midpoint of X(20) and X(6353)
X(60746) = reflection of X(i) in X(j) for these (i, j): (20850, 37460), (30771, 3)
X(60746) = pole of the line {523, 44928} with respect to the orthocentroidal circle
X(60746) = pole of the line {523, 44928} with respect to the Yff hyperbola
X(60746) = X(30771)-of-ABC-X3 reflections triangle
X(60746) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (2, 47114, 3), (20, 44247, 3), (376, 44241, 3), (3522, 31829, 3), (3528, 6823, 3), (3547, 33923, 3), (6676, 10304, 3), (18533, 54992, 382)

X(60747) = CENTER OF Ωx( CIRCUMCIRCLE, SPIEKER CIRCLE, X(1) )

Barycentrics    a*(3*a^6-7*(b+c)*a^5-2*(5*b^2-17*b*c+5*c^2)*a^4+2*(b+c)*(5*b^2-9*b*c+5*c^2)*a^3+(7*b^4+7*c^4-2*b*c*(13*b^2-15*b*c+13*c^2))*a^2-(b+c)*(3*b^4+3*c^4-2*b*c*(9*b^2-11*b*c+9*c^2))*a-8*(b^2-c^2)^2*b*c) : :

X(60747) lies on these lines: {3, 10}, {1012, 60766}, {37817, 60742}, {49128, 60770}

X(60748) = CENTER OF Ωx( CIRCUMCIRCLE, SPIEKER CIRCLE, X(2) )

Barycentrics    5*a^6+2*(b+c)*a^5-2*(4*b^2+11*b*c+4*c^2)*a^4+2*(b+c)*(3*b^2+8*b*c+3*c^2)*a^3-(5*b^4+5*c^4+2*(5*b^2+21*b*c+5*c^2)*b*c)*a^2-8*(b^4-c^4)*(b-c)*a+8*(b^4-c^4)*(b^2-c^2) : :

X(60748) lies on these lines: {2, 60752}, {3, 10}, {376, 60771}, {381, 60767}, {3679, 60742}

X(60748) = complement of X(60752)

X(60749) = CENTER OF Ωx( CIRCUMCIRCLE, ANTICOMPLEMENTARY CIRCLE, X(5) )

Barycentrics    2*a^10-3*(b^2+c^2)*a^8-2*(b^4+5*b^2*c^2+c^4)*a^6+(b^2+c^2)*(2*b^2-b*c+2*c^2)*(2*b^2+b*c+2*c^2)*a^4-(b^2-c^2)^2*b^2*c^2*a^2-(b^4-c^4)*(b^2-c^2)^3 : :
X(60749) = 5*X(3)-X(18559) = 4*X(3)-X(45971) = 5*X(140)-2*X(6756) = 3*X(140)-2*X(10127) = X(140)-2*X(10691) = 3*X(376)+X(18564) = X(6243)-4*X(50476) = X(11591)+2*X(17712) = 4*X(11592)-X(45286) = 2*X(13348)+X(13470) = 2*X(15606)+X(45732) = 2*X(15644)+X(45970) = 2*X(32165)-X(41628) = X(34633)-3*X(38083) = X(34657)-3*X(38022) = X(34668)-3*X(38081)

As a point on the Euler line, X(60749) has Shinagawa coefficients (2*S^2-(32*R*r+8*r^2-7*E)*r^2, -6*S^2+(3*(32*R*r+8*r^2+E))*r^2)

X(60749) lies on these lines: {2, 3}, {511, 45969}, {539, 10627}, {1503, 44324}, {2979, 50708}, {6101, 21660}, {6243, 50476}, {10272, 48892}, {11591, 17712}, {11592, 45286}, {11703, 45838}, {13348, 13470}, {13364, 29317}, {13451, 29181}, {15606, 45732}, {15644, 45970}, {18400, 54044}, {19924, 32191}, {32165, 41628}, {32423, 54042}, {34633, 38083}, {34657, 38022}, {34668, 38081}, {43598, 54036}, {60745, 60755}

X(60749) = midpoint of X(i) and X(j) for these (i, j): {5, 52397}, {15686, 52069}
X(60749) = reflection of X(i) in X(j) for these (i, j): (140, 10691), (428, 3628), (13490, 10124), (23410, 7734), (41628, 32165)
X(60749) = pole of the line {6103, 14577} with respect to the Dao-Moses-Telv circle
X(60749) = (X(3), X(60462))-harmonic conjugate of X(2)

X(60750) = CENTER OF Ωx( CIRCUMCIRCLE, ANTICOMPLEMENTARY CIRCLE, X(6) )

Barycentrics    a^2*(a^8+4*b^2*c^2*a^4-3*(b^2+c^2)*b^2*c^2*a^2-(b^4+6*b^2*c^2+c^4)*(b^4-b^2*c^2+c^4)) : :
X(60750) = 2*X(576)-3*X(39524) = X(11477)-3*X(44415)

X(60750) lies on these lines: {2, 3}, {576, 39524}, {5663, 13355}, {5969, 13233}, {11477, 44415}, {11511, 52951}, {43619, 50669}

X(60750) = pole of the line {8723, 9012} with respect to the 1st Brocard circle
X(60750) = pole of the line {1974, 44467} with respect to the Moses-Parry circle

X(60751) = CENTER OF Ωx( INCIRCLE, ANTICOMPLEMENTARY CIRCLE, X(1) )

Barycentrics    3*a^4+4*b*c*a^2+4*(b^3+c^3)*a+(b^2-c^2)^2 : :

X(60751) lies on these lines: {1, 4}, {2, 54315}, {3, 11043}, {8, 33133}, {376, 24248}, {387, 12635}, {496, 36561}, {551, 3923}, {631, 986}, {758, 37642}, {846, 50739}, {941, 39768}, {962, 5266}, {966, 54335}, {975, 28629}, {976, 5082}, {987, 3296}, {993, 4419}, {997, 4000}, {999, 4310}, {1000, 17725}, {1125, 5573}, {1284, 19262}, {1386, 34647}, {1387, 60762}, {2099, 17602}, {2292, 6857}, {2550, 30115}, {3085, 17783}, {3086, 37549}, {3241, 33070}, {3242, 34625}, {3295, 19548}, {3421, 49487}, {3524, 17596}, {3529, 24851}, {3545, 37717}, {3576, 3663}, {3616, 6051}, {3618, 18061}, {3622, 4195}, {3649, 4340}, {3670, 7288}, {3671, 37554}, {3672, 24203}, {3677, 44675}, {3735, 7735}, {3744, 30305}, {3782, 4293}, {3871, 36578}, {3877, 26228}, {3924, 5084}, {3931, 5703}, {4234, 24280}, {4295, 37539}, {4305, 50065}, {4307, 39542}, {4339, 12699}, {4424, 5218}, {4511, 19785}, {4642, 59591}, {4870, 17723}, {5226, 5725}, {5289, 17061}, {5429, 24695}, {5698, 37817}, {5724, 10590}, {5739, 39766}, {6361, 37552}, {8164, 17719}, {9778, 37589}, {10176, 37650}, {11269, 49454}, {11529, 39595}, {13742, 19582}, {14039, 17738}, {15170, 36512}, {15950, 17599}, {16485, 40998}, {16519, 31405}, {17024, 26096}, {17526, 25253}, {17567, 24443}, {17720, 18391}, {24291, 52713}, {26105, 30117}, {26728, 38053}, {32776, 51665}, {32817, 49518}, {32930, 51673}, {36573, 37598}, {36574, 47743}, {37599, 54445}, {37716, 59388}, {38314, 48817}, {50615, 50636}

X(60751) = pole of the line {14837, 29126} with respect to the Steiner inellipse
X(60751) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 13161, 944), (1, 24210, 3488), (1, 33144, 1056), (999, 39544, 4310)

X(60752) = CENTER OF Ωx( INCIRCLE, ANTICOMPLEMENTARY CIRCLE, X(2) )

Barycentrics    11*a^6-10*(b+c)*a^5-(5*b^2-38*b*c+5*c^2)*a^4-32*(b+c)*b*c*a^3-(11*b^2-10*b*c+11*c^2)*(b-c)^2*a^2+2*(b^2-c^2)*(b-c)*(5*b^2-6*b*c+5*c^2)*a+(5*b^2-6*b*c+5*c^2)*(b^2-c^2)^2 : :

X(60752) lies on these lines: {1, 4}, {2, 60748}, {376, 60742}, {3679, 60771}, {5071, 24808}, {5844, 36682}, {26446, 31189}, {49455, 60770}

X(60752) = anticomplement of X(60748)
X(60752) = X(60748)-Dao conjugate of-X(60748)

X(60753) = CENTER OF Ωx( INCIRCLE, ANTICOMPLEMENTARY CIRCLE, X(3) )

Barycentrics    3*a^10-2*(b+c)*a^9-(7*b^2-6*b*c+7*c^2)*a^8+4*(b^3+c^3)*a^7+2*(b^2+c^2)*(b^2-4*b*c+c^2)*a^6+4*(b+c)*(b^2+b*c+c^2)*b*c*a^5+2*(3*b^4+3*c^4+4*b*c*(b+c)^2)*(b-c)^2*a^4-4*(b^2-c^2)*(b-c)*(b^4+c^4+b*c*(b^2+3*b*c+c^2))*a^3-(b^4-c^4)*(b^2-c^2)*(5*b^2-8*b*c+5*c^2)*a^2+2*(b^4-c^4)*(b^2-c^2)^2*(b-c)*a+(b^2-c^2)^4*(b-c)^2 : :

X(60753) lies on these lines: {1, 4}, {7502, 60743}, {60757, 60763}, {60760, 60772}

X(60754) = CENTER OF Ωx( INCIRCLE, ANTICOMPLEMENTARY CIRCLE, X(4) )

Barycentrics    3*a^10-2*(b+c)*a^9-3*(b-c)^2*a^8+4*(b^2-c^2)*(b-c)*a^7-2*(3*b^2-4*b*c+3*c^2)*(b+c)^2*a^6+8*(b+c)*(b^2+c^2)*b*c*a^5+2*(b^2+c^2)*(3*b^2+2*b*c+3*c^2)*(b-c)^2*a^4-4*(b^4-c^4)*(b^2+c^2)*(b-c)*a^3+(b^2-c^2)^2*(b-c)^2*(b+3*c)*(3*b+c)*a^2+2*(b^2-c^2)^3*(b-c)^3*a-(3*b^2-2*b*c+3*c^2)*(b^2-c^2)^4 : :

X(60754) lies on these lines: {1, 4}, {10743, 18537}, {18531, 60744}

X(60755) = CENTER OF Ωx( INCIRCLE, ANTICOMPLEMENTARY CIRCLE, X(5) )

Barycentrics    a*(a^9-(b+c)*a^8-2*(b-c)^2*a^7+2*(b^2-c^2)*(b-c)*a^6-2*(2*b^2+3*b*c+2*c^2)*b*c*a^5+(b+c)*(4*b^2+7*b*c+4*c^2)*b*c*a^4+(b-c)^2*(2*b^4+11*b^2*c^2+2*c^4)*a^3-(b^2-c^2)*(b-c)*(2*b^4+11*b^2*c^2+2*c^4)*a^2-(b^2-c^2)^2*(b^4+c^4-b*c*(4*b^2-7*b*c+4*c^2))*a+(b^2-c^2)^3*(b-c)^3) : :

X(60755) lies on these lines: {1, 4}, {60745, 60749}, {60759, 60764}, {60761, 60773}

X(60756) = CENTER OF Ωx( INCIRCLE, NINE-POINT CIRCLE, X(2) )

Barycentrics    2*a^5-4*(b+c)*a^4-(b^2-12*b*c+c^2)*a^3+(b+c)*(7*b^2-16*b*c+7*c^2)*a^2-3*(3*b^2+2*b*c+3*c^2)*(b-c)^2*a+(b^2-c^2)*(b-c)*(5*b^2-6*b*c+5*c^2) : :
X(60756) = 2*X(5)+X(15251) = 5*X(5071)-X(24808)

X(60756) lies on these lines: {1, 5}, {2, 28915}, {100, 51530}, {381, 60742}, {516, 19512}, {2789, 5461}, {2826, 45310}, {3679, 60767}, {5071, 24808}, {9779, 31189}, {10171, 28850}, {28893, 50802}

X(60756) = pole of the line {6084, 44433} with respect to the orthoptic circle of Steiner inellipse

X(60757) = CENTER OF Ωx( INCIRCLE, NINE-POINT CIRCLE, X(3) )

Barycentrics    2*a^10-2*(b+c)*a^9-(5*b^2-4*b*c+5*c^2)*a^8+2*(b+c)*(3*b^2-2*b*c+3*c^2)*a^7+2*(b^2-b*c+c^2)*(b-c)^2*a^6-2*(b+c)*(b^2+c^2)*(3*b^2-4*b*c+3*c^2)*a^5+2*(2*b^6+2*c^6-(b^2-c^2)^2*b*c)*a^4+2*(b^4-c^4)*(b^2+c^2)*(b-c)*a^3-2*(b^4-c^4)*(b^2-c^2)*(2*b^2-3*b*c+2*c^2)*a^2+(b^2-c^2)^4*(b-c)^2 : :

X(60757) lies on these lines: {1, 5}, {2, 34332}, {3, 915}, {2834, 6644}, {5020, 9058}, {6642, 20999}, {6678, 52831}, {6711, 34840}, {6713, 44815}, {6911, 37800}, {44452, 47149}, {60753, 60763}, {60760, 60768}

X(60757) = midpoint of X(3) and X(2969)
X(60757) = complement of X(34332)
X(60757) = X(36052)-complementary conjugate of-X(42423)
X(60757) = center of the central inconic through X(3) and X(2969)
X(60757) = pole of the line {517, 59809} with respect to the Feuerbach circumhyperbola
X(60757) = pole of the line {2990, 10015} with respect to the Steiner inellipse
X(60757) = X(2969)-of-anti-X3-ABC reflections triangle
X(60757) = center of circle {{X(3), X(11), X(2969)}}

X(60758) = CENTER OF Ωx( INCIRCLE, NINE-POINT CIRCLE, X(4) )

Barycentrics    2*a^10-2*(b+c)*a^9-(b^2-4*b*c+c^2)*a^8+2*(b^2-c^2)*(b-c)*a^7-2*(3*b^2+5*b*c+3*c^2)*(b-c)^2*a^6+2*(b^2-c^2)*(b-c)*(3*b^2+4*b*c+3*c^2)*a^5+2*(2*b^4+2*c^4-3*b*c*(b+c)^2)*(b-c)^2*a^4-2*(b^2-c^2)*(b-c)*(5*b^4-2*b^2*c^2+5*c^4)*a^3+2*(b^2-c^2)^2*(2*b^4+2*c^4+3*b*c*(b-c)^2)*a^2+4*(b^2-c^2)^2*(b-c)^2*(b^3+c^3)*a-(3*b^2-2*b*c+3*c^2)*(b^2-c^2)^4 : :
X(60758) = 2*X(5)-X(15252) = 3*X(381)-X(21664) = X(1897)-5*X(3091) = X(51565)+3*X(59387)

X(60758) lies on these lines: {1, 5}, {2, 38554}, {4, 280}, {104, 38606}, {282, 5514}, {381, 21664}, {515, 6711}, {517, 1542}, {522, 44927}, {867, 12138}, {1596, 53991}, {1897, 3091}, {2804, 44929}, {3679, 60768}, {5972, 52260}, {6717, 20418}, {6827, 42018}, {10265, 40535}, {10743, 18537}, {12114, 49207}, {18339, 38357}, {20262, 51755}, {51565, 59387}, {57302, 60356}

X(60758) = midpoint of X(i) and X(j) for these (i, j): {4, 2968}, {18339, 38357}
X(60758) = reflection of X(15252) in X(5)
X(60758) = complement of X(38554)
X(60758) = X(36121)-complementary conjugate of-X(117)
X(60758) = center of the central inconic through X(4) and X(2968)
X(60758) = pole of the line {6087, 44428} with respect to the polar circle
X(60758) = pole of the line {2399, 10015} with respect to the Steiner inellipse
X(60758) = X(2968)-of-Euler triangle
X(60758) = X(15252)-of-Johnson triangle
X(60758) = X(21664)-of-Ehrmann-mid triangle
X(60758) = X(27087)-of-Fuhrmann triangle, when ABC is acute
X(60758) = center of circle {{X(4), X(11), X(2968)}}

X(60759) = CENTER OF Ωx( INCIRCLE, NINE-POINT CIRCLE, X(5) )

Barycentrics    2*(b^2-b*c+c^2)*a^5-2*(b^3+c^3)*a^4-(4*b^4+4*c^4-b*c*(7*b^2-4*b*c+7*c^2))*a^3+2*(b^2-c^2)*(b-c)*(2*b^2+b*c+2*c^2)*a^2+(b^2-c^2)^2*(2*b-c)*(b-2*c)*a-2*(b^2-c^2)^3*(b-c) : :
X(60759) = X(1)-3*X(38044) = 3*X(2)+X(10738) = 9*X(2)-X(13199) = X(2)-3*X(38084) = 9*X(2)-5*X(38762) = 3*X(3)+X(10724) = X(3)-5*X(31272) = X(3)-3*X(34126) = X(3)+3*X(59391) = X(4)-3*X(38141) = 3*X(4)+X(38753) = X(4)+3*X(57298) = 3*X(5)-X(119) = 3*X(5)+X(1484) = 5*X(5)-X(11698) = X(5)-3*X(23513) = 7*X(5)-X(37725) = 5*X(5)+X(37726) = 3*X(11)+X(119) = 3*X(11)-X(1484) = 5*X(11)+X(11698) = X(11)+3*X(23513) = 7*X(11)+X(37725) = 5*X(11)-X(37726) = X(12)-3*X(38184) = X(80)+3*X(5886) = 5*X(119)-3*X(11698) = X(119)-9*X(23513) = 7*X(119)-3*X(37725) = 5*X(119)+3*X(37726) = X(355)+3*X(16173) = X(1317)-3*X(10283) = 5*X(1484)+3*X(11698) = X(1484)+9*X(23513) = 7*X(1484)+3*X(37725) = 5*X(1484)-3*X(37726) = X(10724)-3*X(22938) = X(10724)+9*X(34126) = X(10724)-9*X(59391) = 3*X(10738)+X(13199) = X(10738)+9*X(38084) = 3*X(10738)+5*X(38762) = X(13199)-3*X(33814) = X(13199)-5*X(38762) = X(22938)+5*X(31272) = X(22938)+3*X(34126) = X(22938)-3*X(59391) = 5*X(31272)-3*X(34126) = 5*X(31272)+3*X(59391) = X(33814)-9*X(38084)

X(60759) lies on these lines: {1, 5}, {2, 10738}, {3, 10724}, {4, 38141}, {6, 38168}, {7, 38173}, {8, 38177}, {9, 38180}, {10, 38182}, {30, 6713}, {100, 1656}, {104, 381}, {140, 3825}, {143, 58475}, {149, 3090}, {153, 3545}, {214, 11230}, {382, 38693}, {403, 12138}, {498, 13274}, {499, 13273}, {513, 46174}, {515, 33709}, {517, 6702}, {528, 547}, {546, 2829}, {549, 24466}, {550, 21154}, {567, 58056}, {632, 38760}, {900, 59854}, {912, 58587}, {944, 32558}, {946, 12619}, {1145, 11680}, {1156, 38107}, {1320, 5790}, {1385, 6246}, {1482, 5154}, {1532, 28186}, {1537, 6830}, {1539, 53715}, {1594, 1862}, {1621, 38114}, {1699, 12515}, {2320, 6980}, {2476, 34123}, {2771, 46028}, {2800, 9955}, {2801, 58604}, {2802, 9956}, {2805, 40340}, {3035, 3628}, {3036, 3814}, {3045, 18350}, {3091, 10742}, {3146, 38754}, {3254, 38108}, {3526, 34474}, {3579, 38133}, {3627, 38761}, {3817, 10265}, {3832, 12248}, {3841, 48154}, {3843, 10728}, {3845, 38077}, {3850, 20418}, {3851, 12773}, {4193, 5690}, {4996, 7489}, {5055, 10707}, {5072, 38669}, {5079, 38665}, {5083, 58561}, {5087, 18254}, {5141, 12747}, {5330, 38215}, {5541, 54447}, {5603, 19914}, {5848, 18583}, {5854, 24387}, {5948, 10281}, {6154, 38763}, {6174, 15699}, {6564, 48701}, {6565, 48700}, {6594, 38318}, {6829, 12690}, {6841, 13226}, {6859, 45043}, {6881, 9945}, {6882, 28174}, {6911, 38722}, {6914, 10090}, {6918, 47744}, {6923, 10584}, {6924, 10058}, {6929, 10589}, {6941, 34773}, {6949, 38135}, {6958, 10598}, {6959, 10591}, {6971, 22791}, {6990, 13257}, {7393, 13222}, {7486, 20095}, {7681, 40273}, {7697, 32454}, {7704, 25413}, {7743, 15558}, {8674, 20304}, {8703, 38069}, {8976, 19113}, {9024, 24206}, {9669, 32141}, {10074, 10895}, {10113, 53753}, {10175, 21630}, {10222, 15863}, {10247, 12531}, {10276, 32161}, {10427, 38171}, {10576, 48714}, {10577, 48715}, {10698, 18493}, {10711, 19709}, {10767, 15061}, {10768, 38224}, {10769, 15561}, {10770, 38764}, {10771, 38776}, {10772, 57297}, {10773, 57299}, {10774, 57300}, {10775, 57301}, {10776, 57302}, {10777, 57303}, {10778, 14643}, {10779, 38796}, {10780, 57304}, {10781, 57322}, {10782, 57323}, {10993, 31235}, {11219, 16128}, {11235, 25438}, {11570, 17605}, {11715, 18480}, {11793, 58539}, {12047, 20118}, {12736, 14988}, {12767, 30308}, {12811, 38631}, {12812, 20400}, {12832, 39542}, {13253, 38021}, {13364, 58522}, {13374, 58683}, {13665, 19081}, {13743, 18861}, {13754, 58508}, {13785, 19082}, {13861, 54065}, {13913, 42215}, {13951, 19112}, {13977, 42216}, {14217, 26446}, {14740, 58632}, {16125, 33856}, {17100, 45976}, {19163, 53755}, {21850, 38147}, {22505, 53722}, {22515, 53733}, {22765, 37375}, {22793, 46684}, {24465, 34753}, {25485, 51709}, {28182, 37374}, {31512, 57313}, {31649, 56790}, {31657, 38205}, {34127, 53720}, {34128, 53711}, {36175, 57325}, {38022, 50843}, {38026, 50824}, {38055, 40269}, {38079, 51008}, {38081, 50842}, {38083, 50841}, {38090, 50979}, {38099, 50823}, {38104, 50821}, {38119, 48906}, {38317, 51157}, {38636, 55866}, {39504, 60745}, {41859, 55861}, {47399, 53809}, {51198, 59399}, {58611, 58631}, {60755, 60764}, {60761, 60769}

X(60759) = midpoint of X(i) and X(j) for these (i, j): {3, 22938}, {4, 38602}, {5, 11}, {80, 19907}, {104, 22799}, {119, 1484}, {149, 51525}, {946, 12619}, {1385, 6246}, {1539, 53715}, {3627, 38761}, {6702, 16174}, {10113, 53753}, {10222, 15863}, {10265, 12611}, {10738, 33814}, {10742, 51529}, {11698, 37726}, {11715, 18480}, {11729, 12019}, {11793, 58539}, {13374, 58683}, {16125, 33856}, {19163, 53755}, {22505, 53722}, {22515, 53733}, {22793, 46684}, {23961, 24042}, {31649, 56790}, {34126, 59391}, {38141, 57298}, {58611, 58631}
X(60759) = reflection of X(i) in X(j) for these (i, j): (140, 6667), (143, 58475), (3035, 3628), (5083, 58561), (14740, 58632), (32161, 10276)
X(60759) = complement of X(33814)
X(60759) = inverse of X(1484) in nine-point circle
X(60759) = pole of the line {900, 1484} with respect to the nine-point circle
X(60759) = X(1511)-of-3rd Euler triangle, when ABC is acute
X(60759) = X(12041)-of-4th Euler triangle, when ABC is acute
X(60759) = X(20304)-of-Wasat triangle, when ABC is acute
X(60759) = X(22799)-of-Ehrmann-mid triangle
X(60759) = X(22938)-of-anti-X3-ABC reflections triangle
X(60759) = X(38602)-of-Euler triangle
X(60759) = X(46031)-of-Fuhrmann triangle, when ABC is acute
X(60759) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {3, 18342, 22938}, {4, 18341, 38602}, {5, 11, 47399}, {946, 12619, 25437}
X(60759) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (2, 10738, 33814), (2, 13199, 38762), (3, 31272, 34126), (3, 59391, 22938), (4, 57298, 38602), (5, 1484, 119), (5, 10283, 7951), (11, 12, 5533), (11, 119, 1484), (11, 8068, 1387), (11, 23513, 5), (104, 381, 22799), (149, 3090, 38752), (149, 38752, 51525), (946, 59419, 12619), (1656, 51517, 100), (3035, 38319, 3628), (3526, 48680, 34474), (3817, 10265, 12611), (6246, 32557, 1385), (8227, 37718, 6265), (10738, 38762, 13199), (11715, 38161, 18480), (13199, 38762, 33814), (20107, 26086, 140), (22938, 34126, 3), (23477, 23517, 1483), (31272, 59391, 3), (38141, 38602, 4), (38761, 59390, 3627)

X(60760) = CENTER OF Ωx( INCIRCLE, SPIEKER CIRCLE, X(3) )

Barycentrics    3*a^7-(7*b^2+2*b*c+7*c^2)*a^5+2*(b^2-c^2)*(b-c)*a^4+(5*b^4+5*c^4+2*(2*b^2+7*b*c+2*c^2)*b*c)*a^3-4*(b+c)*(b^4+c^4-2*b*c*(b-c)^2)*a^2-(b^2-c^2)^2*(b+c)^2*a+2*(b^2-c^2)^3*(b-c) : :

X(60760) lies on these lines: {1, 2}, {40, 60383}, {60753, 60772}, {60757, 60768}

X(60761) = CENTER OF Ωx( INCIRCLE, SPIEKER CIRCLE, X(5) )

Barycentrics    a*(a^6-2*(b+c)*a^5-(b-c)^2*a^4+4*(b+c)*(b^2+c^2)*a^3-(b^4+c^4+2*b*c*(b+2*c)*(2*b+c))*a^2-2*(b^4-3*b^2*c^2+c^4)*(b+c)*a+(b^2-c^2)^2*(b+c)^2) : :
X(60761) = 7*X(200)+X(6765)

X(60761) lies on these lines: {1, 2}, {355, 60384}, {34717, 35459}, {60755, 60773}, {60759, 60769}

X(60762) = CENTER OF Ωx( NINE-POINT CIRCLE, ANTICOMPLEMENTARY CIRCLE, X(1) )

Barycentrics    a^7-(b+c)*a^6-(3*b^2-4*b*c+3*c^2)*a^5+(b^2-c^2)*(b-c)*a^4+(b^4+c^4-2*b*c*(b^2+b*c+c^2))*a^3-(b+c)*(b^4+c^4-2*b*c*(b^2-3*b*c+c^2))*a^2+(b^2-c^2)^2*(b-c)^2*a+(b^4-c^4)*(b^2-c^2)*(b+c) : :

As a point on the Euler line, X(60762) has Shinagawa coefficients (S^2-(4*(4*R+3*r))*r^3, S^2-(4*(8*R-r))*r^3)

X(60762) lies on these lines: {2, 3}, {517, 33163}, {1064, 49530}, {1387, 60751}, {3744, 5252}, {3944, 23708}, {5603, 20430}, {5818, 60367}, {29856, 52857}, {60766, 60770}

X(60763) = CENTER OF Ωx( NINE-POINT CIRCLE, ANTICOMPLEMENTARY CIRCLE, X(3) )

Barycentrics    a^10-3*(b^2+c^2)*a^8+2*(b^2+c^2)^2*a^6+2*(b^4+b^2*c^2+c^4)*(b^2+c^2)*a^4-(b^2-c^2)^2*(3*b^4+8*b^2*c^2+3*c^4)*a^2+(b^4-c^4)*(b^2-c^2)^3 : :
X(60763) = X(4)-4*X(50138) = 2*X(5)+X(7526) = 2*X(140)+X(1595)

As a point on the Euler line, X(60763) has Shinagawa coefficients (2*S^2-(32*R*r+8*r^2+5*E)*r^2, 3*E*r^2)

X(60763) lies on these lines: {2, 3}, {343, 39522}, {539, 578}, {542, 12228}, {567, 11442}, {569, 32140}, {1209, 11424}, {1263, 8797}, {1493, 9936}, {1989, 13351}, {3582, 37696}, {3584, 37697}, {3618, 10264}, {3818, 18475}, {4550, 18388}, {4846, 12379}, {5476, 58471}, {5480, 44201}, {5654, 15060}, {5892, 23329}, {5946, 14561}, {6689, 6759}, {7880, 14767}, {9827, 10263}, {9833, 10610}, {9971, 54042}, {10072, 37729}, {10516, 47391}, {10984, 18488}, {11426, 32358}, {11457, 13353}, {11550, 37513}, {12006, 26937}, {12242, 15083}, {12824, 15061}, {13336, 44078}, {13391, 43653}, {13434, 25738}, {14389, 18445}, {14708, 20126}, {14826, 40111}, {15028, 43608}, {15038, 37644}, {15068, 23292}, {15321, 46264}, {15805, 40686}, {19153, 38110}, {20410, 57332}, {34826, 39571}, {36749, 41628}, {37584, 56464}, {46261, 58447}, {60753, 60757}, {60768, 60772}

X(60763) = midpoint of X(i) and X(j) for these (i, j): {3, 5064}, {381, 54994}
X(60763) = pole of the line {6103, 13345} with respect to the Dao-Moses-Telv circle
X(60763) = X(5064)-of-anti-X3-ABC reflections triangle
X(60763) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (381, 18564, 4), (381, 48411, 2), (3541, 14786, 140), (5133, 7576, 381), (15765, 18585, 26), (23329, 38317, 5892)

X(60764) = CENTER OF Ωx( NINE-POINT CIRCLE, ANTICOMPLEMENTARY CIRCLE, X(5) )

Barycentrics    (b^2+c^2)*a^8-2*(b^4-b^2*c^2+c^4)*a^6-15*(b^2+c^2)*b^2*c^2*a^4+(2*b^4+13*b^2*c^2+2*c^4)*(b^2-c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)^3 : :
X(60764) = 2*X(5)-X(50134)

As a point on the Euler line, X(60764) has Shinagawa coefficients (2*S^2-(32*R*r+8*r^2-7*E)*r^2, 2*S^2-(32*R*r+8*r^2-3*E)*r^2)

X(60764) lies on these lines: {2, 3}, {141, 13451}, {1352, 45969}, {5480, 44324}, {7605, 15087}, {13364, 24206}, {60755, 60759}, {60769, 60773}

X(60764) = midpoint of X(5) and X(37439)
X(60764) = reflection of X(50134) in X(5)
X(60764) = pole of the line {6, 44832} with respect to the Evans conic
X(60764) = pole of the line {6, 54047} with respect to the Kiepert circumhyperbola
X(60764) = X(50134)-of-Johnson triangle
X(60764) = (X(1656), X(5899))-harmonic conjugate of X(2)

X(60765) = CENTER OF Ωx( NINE-POINT CIRCLE, ANTICOMPLEMENTARY CIRCLE, X(20) )

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(9*a^6-17*(b^2+c^2)*a^4+(7*b^4+26*b^2*c^2+7*c^4)*a^2+(b^4-c^4)*(b^2-c^2)) : :
X(60765) = 2*X(3)-X(10565) = X(4)-2*X(8889)

As a point on the Euler line, X(60765) has Shinagawa coefficients (-4*S^2+(16*(4*R*r+r^2+E))*r^2, 5*S^2-(4*(20*R*r+5*r^2+6*E))*r^2)

X(60765) lies on these lines: {2, 3}, {53, 44541}, {74, 17040}, {99, 32000}, {112, 5065}, {184, 54050}, {800, 1285}, {1300, 58093}, {3357, 18925}, {3431, 35512}, {3618, 37853}, {5894, 32601}, {5907, 53050}, {6225, 13367}, {6403, 36987}, {6515, 11454}, {6696, 18945}, {6776, 10606}, {8541, 54170}, {8567, 18913}, {10249, 18919}, {10605, 14912}, {11204, 18931}, {11270, 45011}, {11405, 51028}, {11433, 21663}, {11468, 18916}, {11473, 42637}, {11474, 42638}, {12041, 18947}, {12250, 19357}, {12828, 15055}, {13399, 19467}, {14907, 32001}, {15152, 17821}, {15153, 40686}, {18852, 36611}, {18918, 23329}, {18933, 25564}, {18935, 44883}, {18951, 32210}, {19119, 34778}, {20421, 45088}, {20774, 38749}, {23291, 23328}, {29180, 30247}, {31859, 56013}, {31884, 41585}, {43660, 58950}, {44882, 58762}

X(60765) = reflection of X(i) in X(j) for these (i, j): (4, 8889), (10565, 3)
X(60765) = pole of the line {185, 35260} with respect to the Jerabek circumhyperbola
X(60765) = X(8889)-of-anti-Euler triangle
X(60765) = X(10565)-of-ABC-X3 reflections triangle
X(60765) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (4, 19708, 186), (376, 378, 4), (376, 35483, 378), (378, 35485, 376), (427, 6823, 403), (1594, 33703, 4), (1597, 7714, 4), (1885, 6622, 4), (3090, 18560, 4), (3516, 54992, 378), (3529, 3541, 4), (3855, 35490, 4), (30100, 59346, 4), (35483, 35485, 4), (41099, 57584, 4)

X(60766) = CENTER OF Ωx( NINE-POINT CIRCLE, SPIEKER CIRCLE, X(1) )

Barycentrics    4*(b+c)*a^6-(5*b^2+16*b*c+5*c^2)*a^5-(b+c)*(11*b^2-32*b*c+11*c^2)*a^4+2*(3*b^4+3*c^4+b*c*(13*b^2-28*b*c+13*c^2))*a^3+2*(b+c)*(3*b^4+3*c^4-b*c*(17*b^2-24*b*c+17*c^2))*a^2-(b^2-c^2)^2*(b^2+10*b*c+c^2)*a+(b^2-c^2)^2*(b+c)^3 : :

X(60766) lies on these lines: {5, 10}, {1012, 60747}, {60762, 60770}

X(60767) = CENTER OF Ωx( NINE-POINT CIRCLE, SPIEKER CIRCLE, X(2) )

Barycentrics    4*(b+c)*a^5-(9*b^2+8*b*c+9*c^2)*a^4+2*(b+c)*(3*b^2+4*b*c+3*c^2)*a^3-2*(b^2+18*b*c+c^2)*b*c*a^2-2*(b^2-c^2)*(b-c)*(5*b^2+6*b*c+5*c^2)*a+3*(3*b^2-2*b*c+3*c^2)*(b^2-c^2)^2 : :

X(60767) lies on these lines: {2, 60742}, {5, 10}, {381, 60748}, {3679, 60756}, {5071, 60771}, {19512, 59387}

X(60767) = complement of X(60742)

X(60768) = CENTER OF Ωx( NINE-POINT CIRCLE, SPIEKER CIRCLE, X(3) )

Barycentrics    4*(b+c)*a^9-(b^2+8*b*c+c^2)*a^8-2*(b+c)*(5*b^2-4*b*c+5*c^2)*a^7+2*(b^4+c^4+7*b*c*(b^2+c^2))*a^6+2*(b^2-c^2)*(b-c)*(3*b^2-2*b*c+3*c^2)*a^5-2*(b-c)^4*b*c*a^4+2*(b^4-c^4)*(b-c)*(b^2+6*b*c+c^2)*a^3-2*(b^2-c^2)*(b+c)^3*(b^3-c^3)*a^2-2*(b^2-c^2)^4*(b+c)*a+(b^2-c^2)^4*(b+c)^2 : :

X(60768) lies on these lines: {2, 60744}, {3, 280}, {5, 10}, {3679, 60758}, {15252, 26446}, {59657, 59680}, {60757, 60760}, {60763, 60772}

X(60768) = midpoint of X(3) and X(7046)
X(60768) = complement of X(60744)
X(60768) = X(7046)-of-anti-X3-ABC reflections triangle
X(60768) = center of circle {{X(3), X(7046), X(31847)}}

X(60769) = CENTER OF Ωx( NINE-POINT CIRCLE, SPIEKER CIRCLE, X(5) )

Barycentrics    (b^2+c^2)*a^8-2*(b+c)*(b^2+c^2)*a^7-2*(b^3-c^3)*(b-c)*a^6+2*(b+c)*(3*b^4+3*c^4-2*b*c*(b-c)^2)*a^5-2*(b^2+c^2)*(b^2+4*b*c+c^2)*b*c*a^4-2*(b^2-c^2)*(b-c)*(3*b^4+3*c^4+2*b*c*(b+c)^2)*a^3+2*(b^2-c^2)^2*(b^4+c^4-b*c*(b^2-4*b*c+c^2))*a^2+2*(b^4-c^4)*(b^2-c^2)^2*(b-c)*a-(b^2-c^2)^4*(b-c)^2 : :
X(60769) = X(1617)-5*X(1656)

X(60769) lies on these lines: {2, 60743}, {5, 10}, {119, 18446}, {1385, 50206}, {1478, 6881}, {1594, 1851}, {1617, 1656}, {4187, 26487}, {4193, 12116}, {6882, 18491}, {6991, 10532}, {11499, 37359}, {12511, 37406}, {14022, 32613}, {22758, 50208}, {25962, 37821}, {37820, 52254}, {52769, 58421}, {60759, 60761}, {60764, 60773}

X(60769) = complement of X(60743)
X(60769) = X(39538)-of-2nd Zaniah triangle, when ABC is acute

X(60770) = CENTER OF Ωx( ANTICOMPLEMENTARY CIRCLE, SPIEKER CIRCLE, X(1) )

Barycentrics    3*a^5-5*(b+c)*a^4-8*(b^2-4*b*c+c^2)*a^3+8*(2*b-c)*(b-2*c)*(b+c)*a^2-11*(b^2-c^2)^2*a+(b^2-c^2)*(b-c)*(5*b^2+2*b*c+5*c^2) : :

X(60770) lies on these lines: {4, 9}, {49128, 60747}, {49455, 60752}, {60762, 60766}

X(60771) = CENTER OF Ωx( ANTICOMPLEMENTARY CIRCLE, SPIEKER CIRCLE, X(2) )

Barycentrics    5*a^6-38*(b+c)*a^5+(37*b^2+58*b*c+37*c^2)*a^4-64*(b+c)*b*c*a^3-(5*b^2-74*b*c+5*c^2)*(b+c)^2*a^2+2*(b^2-c^2)*(b-c)*(19*b^2+6*b*c+19*c^2)*a-(37*b^2-6*b*c+37*c^2)*(b^2-c^2)^2 : :

X(60771) lies on these lines: {4, 9}, {376, 60748}, {3679, 60752}, {5071, 60767}, {15702, 24808}

X(60772) = CENTER OF Ωx( ANTICOMPLEMENTARY CIRCLE, SPIEKER CIRCLE, X(3) )

Barycentrics    3*a^9+3*(b+c)*a^8-2*(7*b^2+8*b*c+7*c^2)*a^7+2*(b+c)*(b^2+12*b*c+c^2)*a^6+8*(b^4+c^4-2*b*c*(b+c)^2)*a^5-8*(b+c)*(b^4+c^4-b*c*(b^2+3*b*c+c^2))*a^4+2*(b^2-c^2)^2*(7*b^2+8*b*c+7*c^2)*a^3-2*(b^2-c^2)*(b-c)*(b^4+c^4+14*b*c*(b^2+b*c+c^2))*a^2-(b^2-c^2)^2*(b-c)^2*(11*b^2+6*b*c+11*c^2)*a+(b^2-c^2)^3*(b-c)*(5*b^2+2*b*c+5*c^2) : :

X(60772) lies on these lines: {4, 9}, {60753, 60760}, {60763, 60768}

X(60773) = CENTER OF Ωx( ANTICOMPLEMENTARY CIRCLE, SPIEKER CIRCLE, X(5) )

Barycentrics    a^9-5*(b+c)*a^8+2*(3*b^2+8*b*c+3*c^2)*a^7+2*(b+c)*(b^2-12*b*c+c^2)*a^6-4*(2*b^4+2*c^4-b*c*(4*b^2+11*b*c+4*c^2))*a^5+2*(b+c)*(4*b^4+4*c^4-b*c*(4*b^2+15*b*c+4*c^2))*a^4-2*(b^2-c^2)^2*(3*b^2+8*b*c+3*c^2)*a^3-2*(b^2-c^2)*(b-c)*(b^4+c^4-b*c*(10*b^2+7*b*c+10*c^2))*a^2+(b^2-c^2)^2*(b-c)^2*(7*b^2-2*b*c+7*c^2)*a+(b^2-c^2)^3*(b-c)*(-3*b^2+2*b*c-3*c^2) : :

X(60773) lies on these lines: {4, 9}, {60755, 60761}, {60764, 60769}

X(60774) = X(4)X(51)∩X(125)X(511)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^6*b^2 - a^4*b^4 - a^2*b^6 + b^8 + a^6*c^2 + a^2*b^4*c^2 - 6*b^6*c^2 - a^4*c^4 + a^2*b^2*c^4 + 10*b^4*c^4 - a^2*c^6 - 6*b^2*c^6 + c^8) : :

X(60774) lies on these lines: {2, 15073}, {3, 58496}, {4, 51}, {6, 14580}, {23, 5622}, {25, 8549}, {30, 16270}, {125, 511}, {184, 575}, {217, 13410}, {235, 15125}, {287, 13137}, {343, 1216}, {373, 3618}, {394, 8538}, {427, 15126}, {428, 58483}, {468, 2393}, {569, 6642}, {852, 20975}, {895, 3292}, {924, 2501}, {974, 14915}, {1112, 34146}, {1204, 13598}, {1316, 2386}, {1495, 13198}, {1503, 11746}, {1692, 46243}, {1885, 58492}, {2072, 15123}, {3003, 44886}, {3060, 23291}, {3260, 60518}, {3269, 20977}, {3284, 51458}, {3546, 43653}, {3574, 46363}, {3917, 16051}, {5094, 50649}, {5159, 14984}, {5462, 6146}, {5640, 6776}, {5651, 14913}, {6403, 37643}, {6689, 11577}, {7387, 19360}, {7464, 21663}, {7529, 10540}, {9027, 47277}, {9729, 21659}, {9730, 18396}, {9786, 15138}, {9967, 37638}, {10095, 18914}, {10263, 23335}, {10297, 13754}, {10602, 11284}, {11064, 34382}, {11245, 58550}, {11645, 58481}, {11695, 13367}, {12006, 30522}, {12085, 33586}, {12283, 35260}, {12828, 40949}, {13414, 44126}, {13415, 44125}, {13419, 58482}, {13567, 47328}, {15024, 18925}, {15026, 31804}, {15043, 18945}, {15316, 38260}, {15465, 37984}, {16621, 58559}, {17928, 43650}, {19161, 23049}, {19457, 32110}, {21849, 31133}, {22530, 32393}, {26283, 44470}, {26926, 58471}, {26937, 45186}, {26958, 34751}, {31383, 44079}, {32251, 53777}, {32377, 58489}, {34137, 39024}, {35901, 40350}, {37490, 47527}, {37981, 41603}, {39562, 41615}, {41257, 52520}, {44668, 47296}, {45279, 58909}, {45732, 58546}

X(60774) = midpoint of X(25739) and X(52000)
X(60774) = reflection of X(i) in X(j) for these {i,j}: {35370, 58495}, {35371, 15118}, {37984, 15465}, {44084, 11746}
X(60774) = X(91)-complementary conjugate of X(15116)
X(60774) = crossdifference of every pair of points on line {155, 32320}
X(60774) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {852, 20975, 47195}, {5943, 43130, 1995}, {11188, 18919, 6467}

X(60775) = X(4)X(51)∩X(125)X(511)

Barycentrics    a^2*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - 3*a^4*c^2 + 2*a^2*b^2*c^2 - 3*b^4*c^2 + 3*a^2*c^4 + 3*b^2*c^4 - c^6)*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 - a^4*c^2 + 2*a^2*b^2*c^2 + 3*b^4*c^2 - a^2*c^4 - 3*b^2*c^4 + c^6) : :

X(60775) lies on the circumconic {{A,B,C,X(2),X(6)}} and these lines: {2, 6503}, {3, 2165}, {6, 1147}, {24, 254}, {25, 571}, {37, 921}, {96, 52582}, {111, 13398}, {155, 50647}, {159, 1976}, {230, 13854}, {231, 3515}, {232, 40144}, {251, 15355}, {454, 54467}, {493, 51905}, {494, 51946}, {577, 44527}, {1033, 3018}, {1300, 39416}, {1593, 1879}, {1880, 2178}, {1989, 2079}, {2351, 59189}, {2395, 47125}, {2493, 8746}, {2963, 7393}, {2987, 20806}, {3003, 41489}, {3053, 34818}, {5421, 39951}, {5523, 59162}, {7488, 51316}, {7509, 43448}, {8573, 34288}, {8576, 8911}, {8577, 26920}, {8770, 36748}, {8882, 34756}, {12309, 56891}, {14533, 41271}, {14910, 15905}, {15109, 52154}, {16081, 31635}, {16172, 21397}, {20998, 41373}, {37917, 47168}, {37954, 47192}, {40347, 44533}, {44665, 47731}, {44802, 52223}, {47421, 55549}

X(60775) = isogonal conjugate of X(6515)
X(60775) = isogonal conjugate of the anticomplement of X(394)
X(60775) = isogonal conjugate of the isotomic conjugate of X(6504)
X(60775) = isotomic conjugate of the polar conjugate of X(39109)
X(60775) = isogonal conjugate of the polar conjugate of X(254)
X(60775) = polar conjugate of the isotomic conjugate of X(15316)
X(60775) = X(i)-Ceva conjugate of X(j) for these (i,j): {254, 39109}, {6504, 15316}, {57484, 3}
X(60775) = X(i)-isoconjugate of X(j) for these (i,j): {1, 6515}, {2, 920}, {6, 33808}, {19, 40697}, {47, 39116}, {63, 3542}, {75, 1609}, {92, 155}, {158, 6503}, {664, 58888}, {1748, 34853}, {2167, 41587}, {2349, 51425}, {8883, 14213}, {32680, 44816}, {44179, 47731}
X(60775) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 6515}, {6, 40697}, {9, 33808}, {135, 57070}, {206, 1609}, {577, 59155}, {1147, 6503}, {3162, 3542}, {22391, 155}, {32664, 920}, {34853, 39116}, {37864, 47731}, {39025, 58888}, {40588, 41587}
X(60775) = cevapoint of X(i) and X(j) for these (i,j): {647, 47421}, {3124, 39201}
X(60775) = trilinear pole of line {512, 30451}
X(60775) = crossdifference of every pair of points on line {27087, 44816}
X(60775) = barycentric product X(i)*X(j) for these {i,j}: {1, 921}, {3, 254}, {4, 15316}, {6, 6504}, {24, 32132}, {31, 57998}, {54, 8800}, {68, 34756}, {69, 39109}, {96, 40678}, {97, 41536}, {136, 57638}, {155, 57697}, {184, 46746}, {523, 13398}, {1147, 52582}, {2165, 57484}, {5504, 16172}, {9723, 59189}, {10419, 59497}, {39114, 57703}, {39416, 52584}, {47732, 57875}
X(60775) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 33808}, {3, 40697}, {6, 6515}, {25, 3542}, {31, 920}, {32, 1609}, {51, 41587}, {184, 155}, {254, 264}, {577, 6503}, {921, 75}, {1147, 59155}, {1495, 51425}, {2165, 39116}, {2351, 34853}, {3063, 58888}, {6504, 76}, {6753, 57070}, {8800, 311}, {13398, 99}, {14270, 44816}, {15316, 69}, {16172, 44138}, {32132, 20563}, {34428, 39115}, {34756, 317}, {39109, 4}, {39416, 30450}, {40678, 39113}, {41536, 324}, {44077, 35603}, {46746, 18022}, {47732, 467}, {52582, 55553}, {54034, 8883}, {57484, 7763}, {57638, 57763}, {57697, 46746}, {57998, 561}, {59189, 847}, {60501, 47731}
X(60775) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8276, 8277, 9937}, {8939, 8943, 6503}

X(60776) = X(3)X(49)∩X(6)X(2351)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(3*a^8 - 6*a^6*b^2 + 4*a^4*b^4 - 2*a^2*b^6 + b^8 - 6*a^6*c^2 + 2*a^2*b^4*c^2 - 4*b^6*c^2 + 4*a^4*c^4 + 2*a^2*b^2*c^4 + 6*b^4*c^4 - 2*a^2*c^6 - 4*b^2*c^6 + c^8) : :

X(60776) lies on these lines: {3, 49}, {6, 2351}, {24, 8883}, {25, 571}, {50, 161}, {52, 15512}, {154, 3135}, {237, 20993}, {427, 9756}, {570, 11402}, {933, 59228}, {1184, 22391}, {1495, 1661}, {1609, 44077}, {3564, 52350}, {6193, 8905}, {6289, 56504}, {6290, 56506}, {6641, 14575}, {7499, 7778}, {10608, 41169}, {11090, 49322}, {11091, 49321}, {13558, 33586}, {14593, 16310}, {18494, 53386}, {19165, 21213}, {23195, 36748}, {23606, 40947}, {39111, 41523}

X(60776) = isogonal conjugate of X(55031)
X(60776) = isogonal conjugate of the isotomic conjugate of X(6193)
X(60776) = X(i)-Ceva conjugate of X(j) for these (i,j): {24, 6}, {8883, 571}, {57638, 32661}
X(60776) = X(i)-isoconjugate of X(j) for these (i,j): {1, 55031}, {75, 34428}, {304, 41525}, {921, 39115}, {14518, 18695}, {20571, 39110}, {57998, 58251}
X(60776) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 55031}, {68, 20563}, {206, 34428}
X(60776) = barycentric product X(i)*X(j) for these {i,j}: {6, 6193}, {54, 41523}, {571, 40698}, {1993, 39111}, {8882, 8905}
X(60776) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 55031}, {32, 34428}, {1609, 39115}, {1974, 41525}, {6193, 76}, {8905, 28706}, {39111, 5392}, {40698, 57904}, {41523, 311}, {52436, 39110}
X(60776) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3167, 52032}, {2351, 52435, 6}, {10132, 10133, 155}

X(60777) = X(6)X(523)∩X(50)X(526)

Barycentrics    a^2*(b^2 - c^2)*(a^2 - b^2 - b*c - c^2)*(a^2 - b^2 + b*c - c^2)*(a^4 + b^4 - a^2*c^2 - b^2*c^2)*(a^4 - a^2*b^2 - b^2*c^2 + c^4) : :

X(60777) lies on the cubic 1356 and these lines: {6, 523}, {50, 526}, {98, 5996}, {110, 647}, {248, 15453}, {323, 3268}, {512, 1976}, {686, 46243}, {878, 17414}, {1691, 3569}, {2065, 8430}, {2623, 8901}, {2698, 53700}, {2966, 53192}, {6137, 34394}, {6138, 34395}, {7578, 43665}, {9213, 14355}, {15470, 52557}, {34397, 47230}, {35912, 51456}, {47635, 54085}

X(60777) = X(i)-isoconjugate of X(j) for these (i,j): {94, 23997}, {240, 60053}, {297, 36061}, {325, 32678}, {476, 1959}, {511, 32680}, {662, 14356}, {1755, 35139}, {2166, 2421}, {3405, 46155}, {14560, 46238}, {32662, 40703}, {36129, 36212}
X(60777) = X(i)-Dao conjugate of X(j) for these (i,j): {1084, 14356}, {11597, 2421}, {16221, 297}, {17433, 60524}, {18334, 325}, {36899, 35139}, {39085, 60053}, {40604, 2396}, {55071, 36790}, {60342, 2799}
X(60777) = cevapoint of X(526) and X(39495)
X(60777) = trilinear pole of line {2088, 14270}
X(60777) = crossdifference of every pair of points on line {511, 868}
X(60777) = barycentric product X(i)*X(j) for these {i,j}: {50, 43665}, {98, 526}, {186, 879}, {248, 44427}, {287, 47230}, {290, 14270}, {323, 2395}, {340, 878}, {523, 14355}, {685, 16186}, {1821, 2624}, {1910, 32679}, {1976, 3268}, {2088, 2966}, {2422, 7799}, {5967, 9213}, {6531, 8552}, {9154, 44814}, {10411, 51441}, {14590, 51404}, {15470, 52451}, {35235, 43754}, {36897, 39495}, {45792, 57260}, {52418, 53173}, {52437, 53149}, {53132, 53691}
X(60777) = barycentric quotient X(i)/X(j) for these {i,j}: {50, 2421}, {98, 35139}, {186, 877}, {248, 60053}, {323, 2396}, {512, 14356}, {526, 325}, {878, 265}, {879, 328}, {1910, 32680}, {1976, 476}, {2081, 60524}, {2088, 2799}, {2395, 94}, {2422, 1989}, {2624, 1959}, {2715, 39295}, {6531, 46456}, {8552, 6393}, {9126, 51438}, {14270, 511}, {14355, 99}, {14600, 32662}, {14601, 14560}, {15630, 15475}, {16186, 6333}, {19627, 14966}, {32679, 46238}, {34397, 4230}, {39495, 5976}, {43665, 20573}, {44427, 44132}, {44808, 51439}, {44809, 51440}, {44814, 50567}, {47230, 297}, {51404, 14592}, {51441, 10412}, {51869, 46155}, {52038, 43084}, {52743, 51389}, {53149, 6344}

X(60778) = X(5)X(6)∩X(25)X(59189)

Barycentrics    (a^4 - 2*a^2*b^2 + b^4 - 2*b^2*c^2 + c^4)*(a^4 + b^4 - 2*a^2*c^2 - 2*b^2*c^2 + c^4)*(3*a^8 - 6*a^6*b^2 + 4*a^4*b^4 - 2*a^2*b^6 + b^8 - 6*a^6*c^2 + 2*a^2*b^4*c^2 - 4*b^6*c^2 + 4*a^4*c^4 + 2*a^2*b^2*c^4 + 6*b^4*c^4 - 2*a^2*c^6 - 4*b^2*c^6 + c^8) : :

X(60778) lies on the cubic 1357 and these lines: {5, 6}, {25, 59189}, {32, 14593}, {230, 34853}, {847, 7735}, {1609, 41524}, {39116, 51481}

X(60778) = polar conjugate of the isotomic conjugate of X(39111)
X(60778) = X(393)-Ceva conjugate of X(14593)
X(60778) = X(304)-isoconjugate of X(39110)
X(60778) = X(68)-Dao conjugate of X(3926)
X(60778) = barycentric product X(i)*X(j) for these {i,j}: {4, 39111}, {25, 40698}, {847, 60776}, {6193, 14593}
X(60778) = barycentric quotient X(i)/X(j) for these {i,j}: {1974, 39110}, {14593, 55031}, {39111, 69}, {40698, 305}, {60776, 9723}
X(60778) = {X(2165),X(56891)}-harmonic conjugate of X(5)

X(60779) = X(6)X(39110)∩X(24)X(254)

Barycentrics    a^2*(a^2 + b^2 - c^2)^2*(a^2 - b^2 + c^2)^2*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - 3*a^4*c^2 + 2*a^2*b^2*c^2 - 3*b^4*c^2 + 3*a^2*c^4 + 3*b^2*c^4 - c^6)*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 - a^4*c^2 + 2*a^2*b^2*c^2 + 3*b^4*c^2 - a^2*c^4 - 3*b^2*c^4 + c^6) : :

X(60779) lies on the cubic 1357 and these lines: {6, 39110}, {24, 254}, {25, 59189}, {232, 40678}, {847, 39416}, {2207, 39109}, {6504, 37174}, {8743, 34756}, {8800, 27376}, {35296, 57484}

X(60779) = polar conjugate of the isotomic conjugate of X(39109)
X(60779) = X(39416)-Ceva conjugate of X(58757)
X(60779) = X(i)-isoconjugate of X(j) for these (i,j): {63, 40697}, {75, 6503}, {155, 304}, {326, 6515}, {394, 33808}, {920, 3926}, {1102, 3542}
X(60779) = X(i)-Dao conjugate of X(j) for these (i,j): {206, 6503}, {3162, 40697}, {15259, 6515}
X(60779) = barycentric product X(i)*X(j) for these {i,j}: {4, 39109}, {24, 59189}, {25, 254}, {393, 60775}, {921, 1096}, {1974, 46746}, {2207, 6504}, {6524, 15316}, {6753, 39416}, {8882, 41536}, {13398, 58757}, {14593, 34756}, {44077, 52582}
X(60779) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 40697}, {32, 6503}, {254, 305}, {1096, 33808}, {1974, 155}, {2207, 6515}, {15316, 4176}, {36417, 1609}, {39109, 69}, {41536, 28706}, {44077, 59155}, {46746, 40050}, {52439, 3542}, {59189, 20563}, {60775, 3926}

X(60780) = X(2)X(3)∩X(125)X(156)

Barycentrics    a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - 3*a^8*c^2 + 4*a^6*b^2*c^2 - 3*a^4*b^4*c^2 + 5*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 - 3*a^4*b^2*c^4 - 4*a^2*b^4*c^4 + 2*b^6*c^4 + 2*a^4*c^6 + 5*a^2*b^2*c^6 + 2*b^4*c^6 - 3*a^2*c^8 - 3*b^2*c^8 + c^10 : :
X(60780) = 3 X[2] + X[7505], 5 X[1656] + X[32534], 7 X[3090] + X[35503]

X(60780) lies on these lines: {2, 3}, {49, 26917}, {68, 40111}, {110, 18356}, {113, 32138}, {125, 156}, {184, 58435}, {265, 11449}, {569, 58407}, {1511, 9927}, {1614, 15059}, {5012, 43866}, {5422, 8254}, {5448, 44673}, {5449, 5972}, {5876, 14708}, {5889, 32329}, {5895, 14677}, {6241, 15061}, {6247, 46817}, {7592, 15806}, {7728, 11468}, {9306, 34826}, {9704, 43808}, {9820, 47296}, {9826, 11591}, {10264, 32139}, {10272, 11441}, {10539, 13561}, {10540, 23294}, {11456, 40685}, {11663, 47450}, {12041, 22802}, {12111, 14643}, {12161, 26958}, {12293, 34153}, {12900, 20191}, {13491, 34128}, {14516, 59648}, {14627, 59771}, {16665, 43821}, {18114, 45847}, {18350, 23293}, {18390, 43394}, {18439, 43608}, {20304, 32171}, {21230, 37638}, {21659, 23515}, {25739, 45622}, {26882, 40241}, {26937, 45957}, {28408, 34380}, {32046, 43817}, {32358, 59553}, {32767, 34514}, {34573, 44493}, {34780, 40920}, {34799, 38724}, {43839, 58806}, {46730, 51391}, {54073, 59279}, {54384, 58546}

X(60780) = midpoint of X(i) and X(j) for these {i,j}: {3, 35488}, {6640, 7505}
X(60780) = complement of X(6640)
X(60780) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6639, 140}, {2, 7505, 6640}, {2, 14940, 3}, {3, 16868, 44279}, {4, 631, 35493}, {5, 140, 18570}, {5, 549, 52070}, {5, 550, 23323}, {5, 15646, 4}, {5, 37814, 44263}, {5, 44452, 37814}, {24, 10224, 44288}, {140, 10020, 44907}, {140, 13406, 3}, {140, 31829, 549}, {140, 34330, 6639}, {140, 44911, 5}, {140, 46031, 10226}, {140, 50140, 7503}, {186, 10255, 18377}, {403, 11250, 44271}, {468, 13371, 37440}, {546, 34331, 37119}, {546, 37119, 44287}, {547, 31833, 5}, {631, 50009, 3}, {1656, 6644, 5}, {1656, 7503, 50140}, {2072, 10018, 1658}, {3147, 18569, 7575}, {3542, 18281, 3627}, {3548, 10201, 550}, {3627, 44282, 3542}, {3628, 10125, 49673}, {3628, 16238, 5}, {3628, 37911, 16238}, {5094, 13861, 33332}, {5498, 15350, 44235}, {5498, 44235, 378}, {7506, 7566, 13163}, {7506, 52296, 39504}, {10020, 11585, 7502}, {10125, 49673, 3}, {10224, 44234, 24}, {10226, 46031, 4}, {11449, 11704, 265}, {11468, 18504, 7728}, {11585, 52297, 10020}, {13163, 39504, 7566}, {14782, 14783, 35473}, {16239, 58465, 52262}, {18567, 18571, 35471}, {42807, 42808, 35491}, {52262, 58465, 5}

X(60781) = X(2)X(3)∩X(54)X(14843)

Barycentrics    7*a^4 - 16*a^2*b^2 + 9*b^4 - 16*a^2*c^2 - 18*b^2*c^2 + 9*c^4 : :
X(60781) = 27 X[2] - 2 X[3], 24 X[2] + X[4], 21 X[2] + 4 X[5], 51 X[2] - X[20], 33 X[2] - 8 X[140], 26 X[2] - X[376], 23 X[2] + 2 X[381], 123 X[2] + 2 X[382], 117 X[2] + 8 X[546], 17 X[2] + 8 X[547], 183 X[2] - 8 X[548], 29 X[2] - 4 X[549], 129 X[2] - 4 X[550], 6 X[2] - X[631], 9 X[2] - 4 X[632], 3 X[2] + 2 X[1656], 177 X[2] - 2 X[1657], 18 X[2] + 7 X[3090], and many others

X(60781) lies on these lines: {2, 3}, {54, 14843}, {61, 43005}, {62, 43004}, {69, 22330}, {141, 53858}, {325, 32883}, {355, 58232}, {371, 43374}, {372, 43375}, {373, 7999}, {395, 42610}, {396, 42611}, {485, 60316}, {486, 60315}, {515, 58229}, {576, 3619}, {590, 3317}, {615, 3316}, {944, 10172}, {1199, 17825}, {1285, 7749}, {1352, 55704}, {1482, 46931}, {1614, 22112}, {1698, 10595}, {1975, 32884}, {3054, 31404}, {3070, 17852}, {3292, 13472}, {3303, 47743}, {3304, 8164}, {3592, 32789}, {3594, 32790}, {3618, 5965}, {3620, 11482}, {3624, 7967}, {3634, 7982}, {3646, 48363}, {3734, 39142}, {3746, 10589}, {3933, 32897}, {5048, 7317}, {5237, 42142}, {5238, 42139}, {5326, 10591}, {5343, 42490}, {5344, 42491}, {5346, 7736}, {5349, 42475}, {5350, 42474}, {5351, 42114}, {5352, 42111}, {5446, 44299}, {5485, 59546}, {5550, 15178}, {5562, 10219}, {5563, 10588}, {5603, 58245}, {5650, 9781}, {5657, 51073}, {5690, 46930}, {5818, 19862}, {5844, 58236}, {5890, 40247}, {5901, 46932}, {5921, 55701}, {6361, 10171}, {6390, 32898}, {6419, 13939}, {6420, 13886}, {6425, 23273}, {6426, 23267}, {6427, 8972}, {6428, 13941}, {6429, 42566}, {6430, 42567}, {6447, 18762}, {6448, 18538}, {6453, 42561}, {6454, 31412}, {6667, 38665}, {6688, 11412}, {6699, 15029}, {6721, 38664}, {6722, 23235}, {6723, 14094}, {7294, 10590}, {7581, 8252}, {7582, 8253}, {7607, 60616}, {7608, 60629}, {7739, 12815}, {7769, 52713}, {7828, 15850}, {7858, 23055}, {7991, 19872}, {8227, 28228}, {8797, 57927}, {8888, 40664}, {9168, 10280}, {9540, 43505}, {9624, 34631}, {9780, 10222}, {10095, 33884}, {10147, 23275}, {10148, 23269}, {10155, 18840}, {10170, 15028}, {10175, 30389}, {10187, 16267}, {10188, 16268}, {10194, 19053}, {10195, 19054}, {10519, 51128}, {10541, 39874}, {10625, 33879}, {11002, 32142}, {11230, 12245}, {11423, 18950}, {11459, 12045}, {11465, 11793}, {11477, 34573}, {11488, 16961}, {11489, 16960}, {11695, 45187}, {12295, 15023}, {12317, 38632}, {12383, 15025}, {12900, 15054}, {13199, 38319}, {13464, 19876}, {13935, 43506}, {14061, 38751}, {14482, 31467}, {14494, 60183}, {14561, 55721}, {14651, 20399}, {14912, 47355}, {14924, 43841}, {14927, 55681}, {15020, 23515}, {15024, 16625}, {15032, 59777}, {15034, 15081}, {15044, 38793}, {15059, 20125}, {16254, 22333}, {16261, 17704}, {16774, 19123}, {18841, 53103}, {19130, 55611}, {19878, 54447}, {20104, 26105}, {20190, 42786}, {21356, 25555}, {22235, 42913}, {22236, 43463}, {22237, 42912}, {22238, 43464}, {24206, 55708}, {26878, 51780}, {26929, 56467}, {30315, 38074}, {31272, 38763}, {31273, 38775}, {31425, 50802}, {31447, 50809}, {31652, 43620}, {31670, 55617}, {32001, 52712}, {32064, 50414}, {32767, 35260}, {32817, 32839}, {32818, 32838}, {32821, 32885}, {32823, 37688}, {33416, 42162}, {33417, 42159}, {33630, 52703}, {34126, 38631}, {34127, 38627}, {34128, 38626}, {35820, 42601}, {35821, 42600}, {36752, 54434}, {36996, 38318}, {37640, 42489}, {37641, 42488}, {38042, 46934}, {38079, 51179}, {38083, 50818}, {38136, 55602}, {38317, 55718}, {38666, 58418}, {38667, 58419}, {38668, 58420}, {38669, 58421}, {38670, 58422}, {38671, 58423}, {38672, 58424}, {38673, 58425}, {38674, 58426}, {38675, 58427}, {38676, 58428}, {38681, 58432}, {38683, 58429}, {38686, 58431}, {38689, 58430}, {39785, 60144}, {40330, 51126}, {41139, 54616}, {41347, 56203}, {42089, 42581}, {42092, 42580}, {42149, 42517}, {42152, 42516}, {42160, 42914}, {42161, 42915}, {42164, 52079}, {42165, 52080}, {42262, 43509}, {42265, 43510}, {42522, 45385}, {42523, 45384}, {42590, 42987}, {42591, 42986}, {42598, 43028}, {42599, 43029}, {42602, 43386}, {42603, 43387}, {42612, 43442}, {42613, 43443}, {42777, 42998}, {42778, 42999}, {42910, 42936}, {42911, 42937}, {42944, 43481}, {42945, 43482}, {42950, 42982}, {42951, 42983}, {42978, 49861}, {42979, 49862}, {43100, 49874}, {43107, 49873}, {43226, 43642}, {43227, 43641}, {43238, 43404}, {43239, 43403}, {43444, 43542}, {43445, 43543}, {43536, 43565}, {43564, 54597}, {43621, 55652}, {51212, 55597}, {51538, 55631}, {53098, 60143}, {55694, 58445}, {60163, 60237}

X(60781) = midpoint of X(1656) and X(55866)
X(60781) = reflection of X(i) in X(j) for these {i,j}: {58192, 15712}, {58195, 3}
X(60781) = anticomplement of X(55866)
X(60781) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5, 3533}, {2, 20, 46219}, {2, 547, 15709}, {2, 1656, 631}, {2, 3090, 3525}, {2, 3091, 632}, {2, 3523, 16239}, {2, 3543, 47598}, {2, 3628, 3090}, {2, 3839, 15723}, {2, 5056, 3526}, {2, 5067, 4}, {2, 7486, 140}, {2, 7504, 17567}, {2, 10303, 55858}, {2, 15699, 376}, {2, 15703, 3545}, {2, 16921, 32977}, {2, 16922, 14001}, {2, 32957, 32952}, {2, 32958, 32953}, {2, 32967, 32978}, {2, 32968, 32959}, {2, 32969, 32960}, {2, 32975, 14069}, {2, 32976, 32951}, {2, 32992, 33189}, {2, 32998, 16043}, {2, 32999, 32970}, {2, 33009, 16923}, {2, 33048, 33027}, {2, 33052, 33049}, {2, 33249, 32956}, {2, 33270, 33015}, {2, 46935, 5}, {2, 46936, 3}, {2, 55864, 55859}, {3, 5, 50689}, {3, 382, 58196}, {3, 546, 49140}, {3, 1656, 12812}, {3, 3090, 3544}, {3, 3544, 4}, {3, 3628, 46936}, {3, 3857, 3146}, {3, 5072, 12102}, {3, 5079, 3857}, {3, 12102, 20}, {3, 12103, 58193}, {3, 12811, 50688}, {3, 12812, 3091}, {3, 46936, 3090}, {3, 49140, 376}, {3, 50689, 3529}, {3, 55857, 55861}, {3, 55861, 2}, {4, 631, 19708}, {4, 15715, 20}, {5, 140, 3534}, {5, 3522, 41099}, {5, 3524, 4}, {5, 3533, 3524}, {5, 5076, 3091}, {5, 10303, 3529}, {5, 11812, 5073}, {5, 15694, 3522}, {5, 15720, 3543}, {5, 47598, 15720}, {5, 50692, 3855}, {5, 55858, 10303}, {5, 55860, 2}, {20, 41106, 4}, {20, 45760, 631}, {20, 46219, 15709}, {140, 3545, 3528}, {140, 3843, 15692}, {140, 3857, 3}, {140, 5079, 3146}, {140, 7486, 3545}, {140, 15692, 631}, {140, 15703, 7486}, {140, 18586, 52401}, {140, 18587, 52402}, {140, 49139, 3523}, {325, 32883, 52718}, {376, 631, 15712}, {376, 11812, 3524}, {376, 15682, 58202}, {381, 10299, 49138}, {381, 12108, 50693}, {381, 41985, 2}, {381, 46853, 50691}, {381, 49138, 4}, {381, 55859, 55864}, {381, 55864, 10299}, {546, 3628, 15699}, {546, 19709, 3091}, {546, 41992, 3526}, {547, 14869, 5072}, {547, 15709, 41106}, {547, 45760, 3858}, {547, 46219, 20}, {549, 5068, 33703}, {549, 58203, 3}, {631, 632, 3525}, {631, 1656, 5071}, {631, 3090, 3091}, {631, 3091, 17538}, {631, 3522, 3524}, {631, 3533, 15694}, {631, 3843, 3528}, {631, 3855, 15696}, {631, 5071, 4}, {631, 41099, 3522}, {632, 1656, 3091}, {632, 3090, 17538}, {632, 3091, 631}, {632, 3627, 15713}, {632, 3628, 1656}, {632, 3858, 14869}, {632, 5076, 10303}, {632, 5079, 15692}, {632, 12812, 3}, {632, 14869, 45760}, {1656, 3091, 3090}, {1656, 3526, 19709}, {1656, 15694, 5}, {1656, 15696, 5055}, {1656, 15712, 5056}, {1656, 46219, 3858}, {1656, 48154, 2}, {1656, 55858, 5076}, {1656, 55859, 50691}, {2045, 2046, 3854}, {3090, 3091, 5071}, {3090, 3525, 4}, {3090, 3529, 5}, {3090, 3533, 3529}, {3090, 3545, 5079}, {3090, 3628, 5067}, {3090, 14869, 41106}, {3090, 55858, 3524}, {3091, 3146, 3843}, {3091, 3522, 5076}, {3091, 5076, 41099}, {3091, 10303, 3522}, {3091, 15692, 3146}, {3091, 15717, 35407}, {3091, 17538, 4}, {3091, 17578, 546}, {3091, 41989, 3545}, {3146, 3534, 3529}, {3146, 5079, 3545}, {3146, 7486, 5079}, {3522, 3529, 17538}, {3522, 5076, 3529}, {3522, 15694, 631}, {3522, 46935, 1656}, {3523, 3855, 11001}, {3523, 5055, 3855}, {3523, 15713, 631}, {3523, 50692, 34200}, {3524, 3525, 10303}, {3524, 5071, 41099}, {3524, 11001, 34200}, {3525, 3544, 3}, {3525, 5067, 3090}, {3525, 5071, 17538}, {3525, 5072, 15715}, {3525, 17538, 631}, {3525, 49138, 12108}, {3526, 5056, 376}, {3526, 5073, 11812}, {3526, 15699, 5056}, {3526, 15707, 140}, {3526, 17578, 631}, {3526, 19709, 15712}, {3528, 3545, 4}, {3528, 5067, 7486}, {3529, 3533, 10303}, {3529, 10303, 3524}, {3529, 41099, 5076}, {3529, 55858, 3525}, {3533, 10303, 3525}, {3533, 41099, 631}, {3543, 44245, 3529}, {3545, 15709, 45759}, {3545, 15719, 35400}, {3627, 49139, 3146}, {3628, 41985, 12108}, {3628, 48154, 632}, {3628, 55856, 55857}, {3628, 55857, 2}, {3628, 55860, 10303}, {3628, 55861, 3}, {3832, 5054, 21735}, {3843, 5079, 41989}, {3843, 15703, 1656}, {3843, 41989, 3091}, {3850, 55863, 10304}, {3851, 11539, 15717}, {3851, 15717, 15682}, {3854, 15721, 548}, {3855, 11001, 4}, {3856, 15688, 50690}, {3858, 5072, 3091}, {3858, 15693, 20}, {3858, 45760, 15693}, {3860, 16239, 140}, {5054, 35018, 3832}, {5055, 16239, 3523}, {5056, 15716, 3855}, {5056, 17578, 19709}, {5059, 35381, 631}, {5067, 5071, 1656}, {5070, 55856, 2}, {5070, 55857, 3628}, {5071, 17538, 3091}, {5072, 14869, 20}, {5072, 46219, 14869}, {5073, 15712, 3522}, {5076, 55858, 15694}, {5079, 7486, 3090}, {5079, 15707, 546}, {7375, 7376, 32971}, {7505, 52299, 4}, {9540, 43505, 43517}, {10172, 34595, 944}, {10303, 50689, 3}, {10303, 55858, 3533}, {11230, 19877, 12245}, {12101, 35018, 5}, {12102, 14869, 3}, {12108, 50693, 10299}, {13935, 43506, 43518}, {14093, 35407, 12103}, {14269, 15694, 15693}, {14269, 15709, 3524}, {14782, 14783, 8703}, {15022, 50688, 12811}, {15693, 19709, 33699}, {15693, 35382, 14269}, {15693, 45759, 15692}, {15693, 46219, 45760}, {15694, 41099, 3524}, {15694, 55858, 632}, {15696, 15713, 3523}, {15696, 34200, 3522}, {15699, 33699, 547}, {15699, 41992, 546}, {15709, 41106, 15715}, {15711, 47598, 15694}, {15712, 17578, 376}, {15712, 19709, 17578}, {15712, 41992, 632}, {15717, 58193, 3}, {16842, 16862, 37244}, {16921, 32977, 14039}, {16923, 33009, 14033}, {21492, 21553, 11340}, {21546, 21549, 37269}, {32838, 37647, 32818}, {32967, 32978, 33285}, {33015, 33270, 16041}, {35382, 45760, 3522}, {35732, 42282, 3851}, {37177, 37178, 32985}, {42490, 43101, 5343}, {42491, 43104, 5344}, {42610, 43446, 43554}, {42611, 43447, 43555}, {46853, 55864, 631}, {46935, 55858, 3090}, {46935, 55860, 3533}, {47599, 55856, 5070}, {50693, 55864, 12108}, {55857, 55858, 55860}, {55866, 58192, 3526}

X(60782) = X(1)X(6946)∩X(2)X(11)

Barycentrics    a*(a - b - c)*(a^4 - a^3*b - a^2*b^2 + a*b^3 - a^3*c + 3*a^2*b*c - a*b^2*c - 3*b^3*c - a^2*c^2 - a*b*c^2 + 6*b^2*c^2 + a*c^3 - 3*b*c^3) : :
X(60782) = 4 X[3816] - 5 X[31272], X[3586] - 3 X[37718], 2 X[26333] - 3 X[59391]

X(60782) lies on these lines: {1, 6946}, {2, 11}, {3, 12019}, {4, 55966}, {7, 12831}, {8, 13279}, {10, 48713}, {21, 17606}, {36, 80}, {56, 38669}, {57, 2801}, {65, 6915}, {88, 14191}, {109, 5400}, {119, 6826}, {165, 41166}, {212, 16569}, {214, 13384}, {226, 5660}, {243, 37805}, {294, 650}, {354, 14151}, {388, 37725}, {404, 1837}, {411, 24914}, {474, 3486}, {499, 11491}, {651, 45885}, {899, 1936}, {900, 9511}, {942, 12738}, {952, 999}, {997, 2802}, {1006, 3586}, {1054, 7004}, {1155, 1156}, {1210, 49176}, {1308, 60579}, {1318, 1320}, {1329, 13272}, {1387, 6767}, {1466, 5229}, {1470, 59387}, {1478, 10711}, {1479, 6963}, {1633, 52242}, {1708, 1750}, {1739, 45272}, {1788, 3149}, {1857, 35994}, {1864, 35990}, {2093, 2800}, {2316, 3738}, {2346, 52638}, {2361, 37680}, {2475, 10958}, {2481, 4998}, {2635, 9364}, {2646, 17531}, {2829, 50701}, {2932, 12690}, {2982, 35320}, {3036, 22560}, {3086, 6970}, {3090, 11507}, {3091, 11509}, {3196, 51406}, {3254, 6745}, {3256, 3817}, {3295, 51525}, {3474, 19541}, {3475, 38055}, {3485, 6918}, {3617, 10966}, {3651, 10395}, {3658, 24624}, {3699, 28956}, {3812, 45230}, {3871, 11376}, {3887, 4845}, {3935, 18839}, {4188, 22760}, {4293, 18491}, {4294, 10993}, {4551, 44858}, {4674, 10703}, {5083, 5531}, {5183, 17638}, {5193, 28236}, {5205, 37788}, {5225, 10310}, {5253, 10950}, {5260, 37564}, {5348, 32911}, {5541, 9819}, {5704, 37579}, {5723, 51408}, {5818, 8071}, {5840, 6827}, {5851, 12848}, {5854, 8168}, {5856, 52457}, {6246, 48695}, {6265, 6797}, {6326, 11529}, {6702, 37306}, {6713, 6954}, {6829, 8068}, {6830, 12775}, {6839, 13273}, {6840, 10724}, {6844, 12332}, {6854, 8164}, {6858, 58421}, {6859, 23513}, {6881, 38752}, {6882, 10738}, {6883, 33814}, {6906, 10826}, {6940, 10572}, {6947, 13199}, {6978, 10591}, {6987, 24466}, {7069, 17596}, {7081, 28930}, {7173, 14882}, {7288, 11500}, {7972, 37602}, {7993, 41554}, {8540, 9025}, {8715, 50443}, {9581, 25440}, {9780, 26357}, {9803, 12832}, {9897, 10074}, {9963, 12743}, {10031, 37740}, {10087, 16173}, {10427, 37240}, {10573, 12776}, {10588, 20400}, {10593, 11849}, {10698, 25415}, {10742, 28452}, {10860, 46684}, {10965, 18220}, {11501, 14986}, {11508, 47743}, {11545, 22765}, {11604, 45393}, {12531, 38455}, {12737, 25405}, {12739, 44840}, {13143, 56040}, {13257, 24465}, {14115, 14513}, {14204, 18815}, {14439, 16561}, {14547, 17122}, {15015, 53054}, {15325, 18524}, {15737, 34930}, {16141, 35982}, {16371, 51636}, {16610, 51361}, {17100, 37300}, {17572, 22768}, {17603, 35985}, {18240, 37736}, {18483, 59329}, {21161, 46816}, {21630, 25438}, {21669, 59327}, {22767, 59388}, {24715, 35015}, {26476, 52367}, {37708, 50907}, {37730, 45976}, {37771, 45946}, {46694, 55869}, {48696, 50891}, {50890, 54391}, {52428, 56010}

X(60782) = midpoint of X(i) and X(j) for these {i,j}: {149, 17784}, {1750, 1768}
X(60782) = reflection of X(i) in X(j) for these {i,j}: {100, 1376}, {497, 11}, {10860, 46684}
X(60782) = crossdifference of every pair of points on line {665, 53046}
X(60782) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 45043, 11}, {11, 55, 53055}, {80, 10090, 104}, {100, 53055, 55}, {100, 59377, 1621}, {165, 51768, 41166}, {354, 41701, 14151}, {12740, 17636, 1320}, {24646, 24647, 5218}

X(60783) = X(2)X(311)∩X(4)X(47731)

Barycentrics    b^2*c^2*(a^4 - 2*a^2*b^2 + b^4 - 2*b^2*c^2 + c^4)*(a^4 + b^4 - 2*a^2*c^2 - 2*b^2*c^2 + c^4)*(3*a^8 - 6*a^6*b^2 + 4*a^4*b^4 - 2*a^2*b^6 + b^8 - 6*a^6*c^2 + 2*a^2*b^4*c^2 - 4*b^6*c^2 + 4*a^4*c^4 + 2*a^2*b^2*c^4 + 6*b^4*c^4 - 2*a^2*c^6 - 4*b^2*c^6 + c^8) : :

X(60783) lies on the cubic K621 and these lines: {2, 311}, {4, 47731}, {6, 847}, {393, 41524}, {925, 1609}, {6193, 39117}, {8573, 46200}, {39416, 58702}, {40698, 60778}, {40814, 55553}, {56017, 59155}

X(60783) = isotomic conjugate of the isogonal conjugate of X(60778)
X(60783) = polar conjugate of the isotomic conjugate of X(40698)
X(60783) = polar conjugate of the isogonal conjugate of X(39111)
X(60783) = X(2052)-Ceva conjugate of X(847)
X(60783) = X(i)-isoconjugate of X(j) for these (i,j): {63, 39110}, {563, 55031}
X(60783) = X(i)-Dao conjugate of X(j) for these (i,j): {68, 394}, {3162, 39110}
X(60783) = cevapoint of X(i) and X(j) for these (i,j): {39111, 60778}, {41524, 47731}
X(60783) = barycentric product X(i)*X(j) for these {i,j}: {4, 40698}, {76, 60778}, {264, 39111}, {847, 6193}, {55553, 60776}
X(60783) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 39110}, {847, 55031}, {6193, 9723}, {14593, 34428}, {39111, 3}, {40698, 69}, {41523, 52032}, {60776, 1147}, {60778, 6}

X(60784) = X(1)X(1436)∩X(19)X(57)

Barycentrics    a*(a^7 + a^6*b - 3*a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 + 3*a^2*b^5 - a*b^6 - b^7 + a^6*c + 10*a^5*b*c - a^4*b^2*c - 4*a^3*b^3*c - a^2*b^4*c - 6*a*b^5*c + b^6*c - 3*a^5*c^2 - a^4*b*c^2 + 2*a^3*b^2*c^2 - 2*a^2*b^3*c^2 + a*b^4*c^2 + 3*b^5*c^2 - 3*a^4*c^3 - 4*a^3*b*c^3 - 2*a^2*b^2*c^3 + 12*a*b^3*c^3 - 3*b^4*c^3 + 3*a^3*c^4 - a^2*b*c^4 + a*b^2*c^4 - 3*b^3*c^4 + 3*a^2*c^5 - 6*a*b*c^5 + 3*b^2*c^5 - a*c^6 + b*c^6 - c^7) : :

X(60784) lies on these lines: {1, 1436}, {3, 17831}, {6, 2122}, {9, 1158}, {19, 57}, {37, 14522}, {40, 219}, {46, 1743}, {48, 1697}, {63, 28616}, {84, 281}, {165, 198}, {223, 34047}, {282, 6001}, {1073, 10319}, {1394, 2331}, {1604, 2324}, {1710, 1720}, {1723, 59336}, {1903, 7992}, {2173, 5128}, {2262, 3339}, {3079, 8802}, {3358, 59483}, {3359, 59681}, {7291, 56544}, {7330, 59671}, {8804, 10860}, {12705, 40942}, {14647, 20262}, {16554, 54420}, {17438, 51779}, {20818, 49163}, {37526, 40937}, {40117, 47851}

X(60784) = excentral-isogonal conjugate of X(1750)
X(60784) = X(329)-Ceva conjugate of X(1)
X(60784) = X(2)-isoconjugate of X(34432)
X(60784) = X(i)-Dao conjugate of X(j) for these (i,j): {84, 189}, {32664, 34432}
X(60784) = barycentric product X(1)*X(6223)
X(60784) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 34432}, {6223, 75}
X(60784) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {46, 18594, 2270}, {1158, 59644, 9}

X(60785) = X(1)X(142)∩X(43)X(165)

Barycentrics    a*(a^3*b - 2*a^2*b^2 + a*b^3 + a^3*c - 2*a^2*b*c - b^3*c - 2*a^2*c^2 + 2*b^2*c^2 + a*c^3 - b*c^3) : :

X(60785) lies on these lines: {1, 142}, {6, 35338}, {8, 27170}, {10, 27514}, {35, 238}, {41, 24309}, {42, 3664}, {43, 165}, {46, 3293}, {55, 40505}, {192, 1026}, {200, 17272}, {218, 11495}, {386, 4307}, {527, 4878}, {1045, 1781}, {1086, 41548}, {1740, 16779}, {2293, 3008}, {2340, 3663}, {3059, 37597}, {3339, 4334}, {3672, 41276}, {3731, 4335}, {3752, 14523}, {3779, 20367}, {3870, 17298}, {3935, 17288}, {3950, 56714}, {3973, 24708}, {3987, 13750}, {4006, 58653}, {4069, 17262}, {4343, 29571}, {4551, 6180}, {4674, 5902}, {7676, 47487}, {8769, 60677}, {9440, 60714}, {10310, 37732}, {13576, 24220}, {16601, 58634}, {17278, 55340}, {18252, 21078}, {18726, 21867}, {37560, 37699}, {41566, 57022}, {49997, 59337}

X(60785) = X(1174)-Ceva conjugate of X(1)
X(60785) = X(i)-Dao conjugate of X(j) for these (i,j): {20880, 1233}, {40474, 24225}
X(60785) = barycentric product X(i)*X(j) for these {i,j}: {1, 25237}, {100, 40474}
X(60785) = barycentric quotient X(i)/X(j) for these {i,j}: {25237, 75}, {40474, 693}
X(60785) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {43, 1742, 1743}, {1818, 3755, 1}

X(60786) = X(1)X(3)∩X(42)X(77)

Barycentrics    a*(a + b - c)*(a - b + c)*(a^3 - a^2*b + a*b^2 - b^3 - a^2*c + 4*a*b*c - b^2*c + a*c^2 - b*c^2 - c^3) : :

X(60786) lies on these lines: {1, 3}, {2, 2263}, {7, 612}, {8, 4320}, {10, 1448}, {25, 1041}, {31, 1445}, {33, 1721}, {34, 1722}, {42, 77}, {43, 223}, {63, 9316}, {69, 200}, {78, 1042}, {100, 8897}, {109, 1395}, {197, 7289}, {210, 6180}, {221, 54386}, {222, 3751}, {226, 5268}, {240, 1767}, {278, 1738}, {279, 28043}, {291, 1422}, {307, 26034}, {478, 1743}, {497, 12652}, {515, 26929}, {518, 1407}, {614, 4318}, {653, 1096}, {756, 8545}, {948, 26040}, {969, 40443}, {975, 3671}, {1044, 1490}, {1125, 56460}, {1211, 8580}, {1254, 54289}, {1376, 1427}, {1394, 5247}, {1406, 41538}, {1456, 4383}, {1458, 3870}, {1698, 56366}, {1706, 7273}, {1709, 1736}, {1716, 55023}, {1728, 1777}, {1742, 10382}, {1745, 18915}, {1750, 5928}, {1836, 9817}, {2000, 4331}, {2285, 5276}, {2324, 3509}, {2340, 4350}, {2362, 7347}, {2550, 7365}, {2647, 24570}, {2900, 35338}, {2947, 18921}, {3158, 8271}, {3186, 7093}, {3190, 4341}, {3624, 56444}, {3811, 4306}, {3911, 5272}, {3914, 57477}, {3920, 4327}, {3961, 4334}, {4296, 37666}, {4319, 9778}, {4332, 54392}, {4348, 5262}, {4551, 56848}, {4641, 41712}, {4646, 15832}, {4848, 21147}, {4849, 6610}, {4882, 10371}, {5265, 28011}, {5287, 42289}, {5311, 7190}, {5880, 6354}, {6762, 9363}, {7182, 9312}, {7271, 10401}, {7348, 16232}, {7672, 17074}, {10369, 50581}, {12560, 17022}, {16475, 52424}, {16496, 17625}, {19372, 24914}, {23511, 26007}, {28774, 29857}, {29828, 52358}, {32926, 39126}, {32937, 40862}, {33131, 37798}, {33137, 34050}, {34041, 43035}, {34488, 52089}, {34595, 56451}, {51194, 52635}, {55472, 56909}

X(60786) = X(1041)-Ceva conjugate of X(1)
X(60786) = X(i)-isoconjugate of X(j) for these (i,j): {2082, 30676}, {7347, 7348}
X(60786) = cevapoint of X(1721) and X(1722)
X(60786) = barycentric product X(i)*X(j) for these {i,j}: {6203, 57266}, {6204, 57267}, {8817, 30677}
X(60786) = barycentric quotient X(i)/X(j) for these {i,j}: {1037, 30676}, {6203, 57270}, {6204, 57269}, {30677, 497}
X(60786) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {33, 3474, 1721}, {34, 1788, 1722}, {43, 5018, 223}, {57, 8270, 1}, {65, 1038, 1}, {109, 1708, 1707}, {222, 41539, 3751}, {1214, 37541, 17594}, {3911, 34036, 5272}, {3920, 21454, 4327}, {4318, 5435, 614}, {17093, 56359, 269}

X(60787) = X(1)X(5)∩X(43)X(1709)

Barycentrics    a*(a^7*b - 2*a^6*b^2 - a^5*b^3 + 4*a^4*b^4 - a^3*b^5 - 2*a^2*b^6 + a*b^7 + a^7*c - 4*a^6*b*c + 8*a^5*b^2*c - 3*a^4*b^3*c - 9*a^3*b^4*c + 8*a^2*b^5*c - b^7*c - 2*a^6*c^2 + 8*a^5*b*c^2 - 14*a^4*b^2*c^2 + 12*a^3*b^3*c^2 + 6*a^2*b^4*c^2 - 12*a*b^5*c^2 + 2*b^6*c^2 - a^5*c^3 - 3*a^4*b*c^3 + 12*a^3*b^2*c^3 - 24*a^2*b^3*c^3 + 11*a*b^4*c^3 + b^5*c^3 + 4*a^4*c^4 - 9*a^3*b*c^4 + 6*a^2*b^2*c^4 + 11*a*b^3*c^4 - 4*b^4*c^4 - a^3*c^5 + 8*a^2*b*c^5 - 12*a*b^2*c^5 + b^3*c^5 - 2*a^2*c^6 + 2*b^2*c^6 + a*c^7 - b*c^7) : :

X(60787) lies on these lines: {1, 5}, {43, 1709}, {44, 17613}, {515, 14554}, {1376, 35338}, {1742, 9324}, {3216, 12114}, {3293, 12672}, {4674, 17654}, {6745, 43672}, {34051, 60782}, {48883, 59326}

X(60787) = {X(52005),X(56426)}-harmonic conjugate of X(32486)






leftri  Chordal perspectors of bicevian conics and pedal circles: X(60788) - X(60843)  rightri

This preamble and centers X(60788)-X(60843) were contributed by César Eliud Lozada, December 3, 2023.

Let ABC be a triangle, P', P" two distinc points, none on their sidelines, and A'B'C', A"B"C" their respective cevian triangles with respect to ABC. Call 𝒞 the bicevian conic of P' and P".

Let P be a point on the line P'P" and denote A1, B1, C1 the second intersections of 𝒞 and the lines PA', PB', PC', respectively. Similarly, denote A2, B2, C2 the second intersections of 𝒞 and the lines PA", PB", PC", respectively. Then the lines AA1, BB1, CC1 concur in a point Q1 and the lines AA2, BB2, CC2 concur in a point Q2.

The point Q1 is denoted here the (P', P")-bicevian conic chordal perspector of-P whilst the point Q2 is denoted as the (P", P')-bicevian conic chordal perspector of-P.

⬥ Pedal triangles version

Let ABC be a triangle, P' a point not on their sidelines, P" the isogonal conjugate of P' and A'B'C', A"B"C" their respective pedal triangles with respect to ABC. Call 𝒞 the circle through A', B', C', A", B", C".

Let P be a point on the line P'P" and denote A1, B1, C1 the second intersections of 𝒞 and the lines PA', PB', PC', respectively. Similarly, denote A2, B2, C2 the second intersections of 𝒞 and the lines PA", PB", PC", respectively. Then the lines AA1, BB1, CC1 concur in a point Q1 and the lines AA2, BB2, CC2 concur in a point Q2.

In this case, the point Q1 is denoted here the P'-pedal circle chordal perspector of-P and, naturally, the point Q2 is denoted as the P"-pedal circle chordal perspector of-P. In this notation, the term "pedal circle" may be replaced with the name of the circle, if it has a given name. Therefore, the (X(2), X(4))-bicevian conic chordal perspector of-P coincides with the X(3)-nine-point circle chordal perspector of-P and the (X(4), X(2))-bicevian conic chordal perspector of-P coincides with the X(4)-nine-point circle chordal perspector of-P.

underbar

X(60788) = ( X(1), X(2) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(8)

Barycentrics    ((2*b-c)*a-b*c-c^2)*((b-2*c)*a+b^2+b*c)*((b-c)*a^2+(b^2+b*c-c^2)*a-b*c*(b+c))*((b-c)*a^2+(b^2-b*c-c^2)*a+b*c*(b+c)) : :

X(60788) lies on these lines: {2, 39701}, {8, 39956}, {56, 55988}, {312, 3976}, {333, 979}, {6557, 56276}, {28660, 58019}, {39694, 56086}, {40012, 46827}

X(60788) = X(i)-isoconjugate of-X(j) for these {i, j}: {978, 3915}, {3210, 16946}, {4186, 20805}, {4383, 21769}
X(60788) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (979, 4383), (34860, 3210), (39694, 3875), (39956, 978), (56192, 21857), (56276, 30568), (56279, 3913), (58019, 18135), (60807, 1)
X(60788) = barycentric product X(i)*X(j) for these {i, j}: {75, 60807}, {979, 40012}, {34860, 39694}, {39956, 58019}, {42304, 56276}
X(60788) = trilinear product X(i)*X(j) for these {i, j}: {2, 60807}, {979, 34860}, {39694, 39956}, {39701, 60789}, {42304, 56279}, {56155, 56276}
X(60788) = trilinear quotient X(i)/X(j) for these (i, j): (979, 3915), (34860, 978), (39694, 4383), (39956, 21769), (40012, 3210), (56123, 21857), (56276, 3913), (56279, 3217), (58019, 3875)

X(60789) = ( X(2), X(1) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(8)

Barycentrics    a*(a+b-3*c)*(a-3*b+c)*((2*b-c)*a-b*c-c^2)*((b-2*c)*a+b^2+b*c) : :

X(60789) lies on the Feuerbach hyperbola and these lines: {1, 14261}, {8, 21342}, {9, 23649}, {21, 3445}, {314, 4373}, {983, 16945}, {3999, 7319}, {4866, 8056}, {5560, 53619}, {6557, 56276}, {7320, 42304}, {27818, 41527}

X(60789) = X(31343)-beth conjugate of-X(17749)
X(60789) = X(1015)-cross conjugate of-X(58794)
X(60789) = X(24151)-Dao conjugate of-X(3875)
X(60789) = X(i)-isoconjugate of-X(j) for these {i, j}: {145, 3915}, {1420, 3913}, {1743, 4383}, {3052, 3875}, {3175, 33628}, {3214, 16948}, {3217, 5435}, {4186, 4855}, {4498, 57192}, {16946, 18743}, {17477, 44724}
X(60789) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (3445, 4383), (3680, 30568), (4052, 56253), (4373, 18135), (8056, 3875), (34860, 18743), (38266, 3915), (39956, 145), (42304, 39126), (56123, 52353), (56155, 5435), (56174, 3175), (56192, 3950), (58794, 4106), (60806, 1), (60807, 39701)
X(60789) = barycentric product X(i)*X(j) for these {i, j}: {75, 60806}, {3445, 40012}, {3680, 42304}, {4373, 39956}, {6557, 56155}, {8056, 34860}, {27835, 60807}
X(60789) = trilinear product X(i)*X(j) for these {i, j}: {2, 60806}, {3445, 34860}, {3680, 56155}, {8056, 39956}, {38266, 40012}
X(60789) = trilinear quotient X(i)/X(j) for these (i, j): (3445, 3915), (3680, 3913), (4052, 3175), (4373, 3875), (6557, 30568), (8056, 4383), (34860, 145), (38266, 16946), (39956, 1743), (40012, 18743), (40014, 18135), (42304, 5435), (56123, 3950), (56155, 1420), (56174, 3214), (56192, 4849), (58794, 4498)

X(60790) = ( X(1), X(2) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(10)

Barycentrics    ((b-c)*a+b^2+b*c)*((b-c)*a-b*c-c^2)*((b-c)*a^2+(b^2-c^2)*a+b*c*(b+c))*((b-c)*a^2+(b^2-c^2)*a-b*c*(b+c)) : :

X(60790) lies on the Kiepert hyperbola and these lines: {2, 39748}, {10, 39798}, {76, 40010}, {226, 20615}, {321, 596}, {2051, 5482}, {6539, 35058}, {39747, 50605}

X(60790) = cevapoint of X(244) and X(40086)
X(60790) = X(40010)-Ceva conjugate of-X(40013)
X(60790) = X(i)-isoconjugate of-X(j) for these {i, j}: {595, 3216}, {2220, 17147}, {4057, 57151}, {4222, 22458}, {16685, 32911}
X(60790) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (596, 17147), (35058, 4360), (39748, 32911), (39798, 3216), (39964, 595), (40010, 18140), (40013, 18133), (40085, 3159), (40148, 16685), (42471, 3995), (57915, 40034), (60808, 1)
X(60790) = pole of the line {40013, 60808} with respect to the circumhyperbola dual of Yff parabola
X(60790) = barycentric product X(i)*X(j) for these {i, j}: {75, 60808}, {596, 35058}, {39747, 42471}, {39748, 40013}, {39798, 40010}, {39964, 57915}
X(60790) = trilinear product X(i)*X(j) for these {i, j}: {2, 60808}, {596, 39748}, {35058, 39798}, {39949, 42471}, {39964, 40013}, {40010, 40148}, {40086, 53627}
X(60790) = trilinear quotient X(i)/X(j) for these (i, j): (596, 3216), (8050, 57151), (35058, 32911), (39748, 595), (39798, 16685), (39964, 2220), (40010, 4360), (40013, 17147), (40085, 21858), (42471, 3293), (57915, 18133)

X(60791) = ( X(2), X(1) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(42)

Barycentrics    a^2*((b+c)*a+b*c-c^2)*((b+c)*a-b^2+b*c)*((b+c)*a^2+(b^2-c^2)*a+b*c*(b-c))*((b+c)*a^2-(b^2-c^2)*a-b*c*(b-c)) : :

X(60791) lies on these lines: {1, 8049}, {31, 34444}, {42, 13476}, {213, 2350}, {3720, 40515}, {26037, 56190}

X(60791) = X(i)-isoconjugate of-X(j) for these {i, j}: {1621, 17135}, {3294, 29767}, {4251, 18137}, {8053, 17143}, {16552, 17277}, {20954, 57084}
X(60791) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (2350, 17135), (8049, 18152), (13476, 18137), (34444, 17277), (39735, 40088), (39797, 17143), (40147, 4651), (40504, 4043)
X(60791) = barycentric product X(i)*X(j) for these {i, j}: {2350, 8049}, {13476, 39797}, {17758, 34444}, {39734, 40147}, {39950, 40504}
X(60791) = trilinear product X(i)*X(j) for these {i, j}: {2350, 39797}, {13476, 34444}, {39950, 40147}
X(60791) = trilinear quotient X(i)/X(j) for these (i, j): (2350, 16552), (8049, 17143), (13476, 17135), (17758, 18137), (34444, 1621), (39735, 18152), (39797, 17277), (39950, 29767), (40005, 40088), (40147, 3294), (40504, 4651), (40515, 4043)

X(60792) = ( X(1), X(2) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(43)

Barycentrics    a*((3*b-c)*a-b*c)*((b-3*c)*a+b*c)*((b+c)*a+b*c-2*c^2)*((b+c)*a-2*b^2+b*c) : :

X(60792) lies on these lines: {43, 39966}, {192, 39742}, {27644, 36598}, {31008, 40027}, {40171, 60793}

X(60792) = X(i)-isoconjugate of-X(j) for these {i, j}: {8616, 16569}, {16969, 17349}
X(60792) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (36598, 17349), (36614, 8616), (38247, 17144), (39742, 1278), (39966, 16569), (60236, 20943)
X(60792) = barycentric product X(i)*X(j) for these {i, j}: {36598, 60236}, {38247, 39742}, {39966, 40027}
X(60792) = trilinear product X(i)*X(j) for these {i, j}: {36598, 39742}, {36614, 60236}, {38247, 39966}
X(60792) = trilinear quotient X(i)/X(j) for these (i, j): (36598, 8616), (38247, 17349), (39742, 16569), (39966, 16969), (40027, 17144), (60236, 1278)

X(60793) = ( X(2), X(1) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(43)

Barycentrics    a^2*((b+c)*a+b*c-2*c^2)*((b+c)*a-2*b^2+b*c)*((b+c)*a^2+(b^2-b*c-c^2)*a+b*c*(b-c))*((b+c)*a^2-(b^2+b*c-c^2)*a-b*c*(b-c)) : :

X(60793) lies on these lines: {43, 39742}, {2176, 28360}, {33296, 39741}, {34445, 38832}, {40171, 60792}

X(60793) = X(i)-isoconjugate of-X(j) for these {i, j}: {8616, 10453}, {17144, 20992}, {17349, 21384}
X(60793) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (34445, 17349), (39742, 20923), (39966, 10453), (39970, 17144)
X(60793) = barycentric product X(i)*X(j) for these {i, j}: {34445, 60236}, {39741, 39966}, {39742, 39970}
X(60793) = trilinear product X(i)*X(j) for these {i, j}: {34445, 39742}, {39966, 39970}
X(60793) = trilinear quotient X(i)/X(j) for these (i, j): (34445, 8616), (39741, 17144), (39742, 10453), (39966, 21384), (39970, 17349), (60236, 20923)

X(60794) = ( X(1), X(3) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(3)

Barycentrics    a^3*(-a^2+b^2+c^2)^2*(a^3+(b-c)*a^2-(b^2+c^2)*a-(b+c)*(b^2-c^2))*(a^3-(b-c)*a^2-(b^2+c^2)*a+(b+c)*(b^2-c^2)) : :

X(60794) lies on these lines: {3, 1069}, {21, 90}, {284, 46038}, {1259, 6512}, {1295, 36082}, {1813, 58887}, {2164, 37504}, {7040, 7531}, {22382, 55248}, {22768, 36746}, {36626, 56099}

X(60794) = isogonal conjugate of the polar conjugate of X(6513)
X(60794) = X(1069)-Ceva conjugate of-X(255)
X(60794) = X(1092)-cross conjugate of-X(255)
X(60794) = X(i)-Dao conjugate of-X(j) for these (i, j): (1147, 46), (6503, 20930), (22391, 52033), (36033, 1068), (37867, 6505)
X(60794) = X(i)-isoconjugate of-X(j) for these {i, j}: {4, 1068}, {46, 158}, {92, 52033}, {225, 3559}, {393, 5905}, {823, 55214}, {1093, 3157}, {1096, 20930}, {1118, 5552}, {2052, 2178}, {6505, 6520}, {6506, 23984}, {8747, 21077}, {46389, 54240}
X(60794) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (48, 1068), (90, 2052), (184, 52033), (255, 5905), (394, 20930), (577, 46), (1069, 92), (1092, 6505), (2164, 158), (2193, 3559), (2289, 5552), (2638, 6506), (2994, 57806), (3990, 21077), (4055, 21853), (4100, 3157), (6512, 75), (6513, 264), (7040, 6521), (7335, 56848), (20570, 18027), (23090, 57083), (23224, 21188), (36082, 54240), (39201, 55214), (52430, 2178)
X(60794) = pole of the line {46, 3559} with respect to the Stammler hyperbola
X(60794) = barycentric product X(i)*X(j) for these {i, j}: {1, 6512}, {3, 6513}, {63, 1069}, {90, 394}, {255, 2994}, {326, 2164}, {577, 20570}, {2289, 7318}, {6507, 7040}, {6511, 7042}, {7072, 7183}, {7125, 36626}
X(60794) = trilinear product X(i)*X(j) for these {i, j}: {3, 1069}, {6, 6512}, {48, 6513}, {90, 255}, {394, 2164}, {577, 2994}, {1092, 7040}, {1804, 7072}, {6056, 7318}, {7335, 36626}, {20570, 52430}, {36082, 57241}
X(60794) = trilinear quotient X(i)/X(j) for these (i, j): (3, 1068), (48, 52033), (90, 158), (255, 46), (283, 3559), (326, 20930), (394, 5905), (577, 2178), (822, 55214), (1069, 4), (1092, 3157), (1259, 5552), (2164, 393), (2994, 2052), (3682, 21077), (3990, 21853), (4091, 21188), (6507, 6505), (6512, 2), (6513, 92)

X(60795) = ( X(1), X(3) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(35)

Barycentrics    a^3*(-a^2+b^2+c^2)*(a^4-(2*b^2+c^2)*a^2+(b^2-c^2)*b^2)*(a^4-(b^2+2*c^2)*a^2-(b^2-c^2)*c^2)*(a^3+(b-c)*a^2-(b^2+b*c+c^2)*a-(b+c)*(b^2-c^2))*(a^3-(b-c)*a^2-(b^2+b*c+c^2)*a+(b+c)*(b^2-c^2)) : :

X(60795) lies on these lines: {35, 54}, {2169, 52408}, {3467, 11107}

X(60795) = X(i)-isoconjugate of-X(j) for these {i, j}: {53, 17483}, {324, 21773}, {2181, 46749}, {13450, 23070}
X(60795) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (97, 46749), (2169, 17483), (3467, 324), (14533, 3336)
X(60795) = barycentric product X(i)*X(j) for these {i, j}: {97, 3467}, {14533, 46750}
X(60795) = trilinear product X(2169)*X(3467)
X(60795) = trilinear quotient X(i)/X(j) for these (i, j): (97, 17483), (2169, 3336), (14533, 21773), (19210, 23070)

X(60796) = ( X(3), X(1) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(35)

Barycentrics    a^2*(a^4-(2*b^2+c^2)*a^2+(b^2-c^2)*b^2)*(a^4-(b^2+2*c^2)*a^2-(b^2-c^2)*c^2)*(a^6+(b-c)*a^5-(b^2+b*c+c^2)*a^4-2*(b^3-c^3)*a^3-(b^2-c^2)^2*a^2+(b^4-c^4)*(b+c)*a+(b+c)*(b^2-c^2)*(b^3-c^3))*(a^6-(b-c)*a^5-(b^2+b*c+c^2)*a^4+2*(b^3-c^3)*a^3-(b^2-c^2)^2*a^2-(b^4-c^4)*(b+c)*a+(b+c)*(b^2-c^2)*(b^3-c^3)) : :

X(60796) lies on these lines: {1, 3484}, {35, 2169}, {54, 6198}, {3469, 56422}, {11461, 25044}, {15171, 46064}

X(60796) = X(i)-isoconjugate of-X(j) for these {i, j}: {5, 3468}, {51, 46752}
X(60796) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (2148, 3468), (2167, 46752), (3469, 14213)
X(60796) = barycentric product X(2167)*X(3469)
X(60796) = trilinear product X(54)*X(3469)
X(60796) = trilinear quotient X(i)/X(j) for these (i, j): (54, 3468), (95, 46752), (3469, 5), (35196, 15777)

X(60797) = ( X(1), X(3) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(36)

Barycentrics    a^3*(-a^2+b^2+c^2)*(a^4+(b^2-2*c^2)*a^2-(b^2-c^2)*(2*b^2+c^2))*(a^4-(2*b^2-c^2)*a^2+(b^2-c^2)*(b^2+2*c^2))*(a^3+(b-c)*a^2-(b^2-b*c+c^2)*a-(b+c)*(b^2-c^2))*(a^3-(b-c)*a^2-(b^2-b*c+c^2)*a+(b+c)*(b^2-c^2)) : :

X(60797) lies on these lines: {36, 74}, {3065, 17515}, {35200, 52407}

X(60797) = X(i)-isoconjugate of-X(j) for these {i, j}: {484, 1784}, {1990, 17484}, {19297, 46106}, {23071, 52661}
X(60797) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (3065, 46106), (14919, 17791), (18877, 484), (19302, 1784), (35200, 17484)
X(60797) = barycentric product X(i)*X(j) for these {i, j}: {3065, 14919}, {18877, 40716}, {21739, 35200}
X(60797) = trilinear product X(i)*X(j) for these {i, j}: {3065, 35200}, {14919, 19302}, {18877, 21739}
X(60797) = trilinear quotient X(i)/X(j) for these (i, j): (3065, 1784), (14919, 17484), (18877, 19297), (19302, 1990), (21739, 46106), (35200, 484)

X(60798) = ( X(3), X(1) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(36)

Barycentrics    a^2*(a^4+(b^2-2*c^2)*a^2-(b^2-c^2)*(2*b^2+c^2))*(a^4-(2*b^2-c^2)*a^2+(b^2-c^2)*(b^2+2*c^2))*(a^6+(b-c)*a^5-(b^2-b*c+c^2)*a^4-2*(b^3-c^3)*a^3-(b^2-c^2)^2*a^2+(b^4-c^4)*(b+c)*a+(b^2-c^2)*(b-c)*(b^3+c^3))*(a^6-(b-c)*a^5-(b^2-b*c+c^2)*a^4+2*(b^3-c^3)*a^3-(b^2-c^2)^2*a^2-(b^4-c^4)*(b+c)*a+(b^2-c^2)*(b-c)*(b^3+c^3)) : :

X(60798) lies on these lines: {1, 38933}, {36, 35200}, {74, 1870}, {999, 57488}, {2192, 52646}, {3466, 56844}, {3583, 57472}, {15404, 55044}

X(60798) = X(i)-isoconjugate of-X(j) for these {i, j}: {30, 3465}, {14206, 56911}
X(60798) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (2159, 3465), (3466, 14206), (40352, 56911)
X(60798) = barycentric product X(2349)*X(3466)
X(60798) = trilinear product X(74)*X(3466)
X(60798) = trilinear quotient X(i)/X(j) for these (i, j): (74, 3465), (2159, 56911), (3466, 30)

X(60799) = ( X(1), X(3) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(56)

Barycentrics    a^3*(-a^2+b^2+c^2)*(a^3+(b-c)*a^2-(b-c)^2*a-(b+c)*(b^2-c^2))*(a^3-(b-c)*a^2-(b-c)^2*a+(b+c)*(b^2-c^2))*(a^4+2*(b^2-c^2)*a^2-(b^2-c^2)*(3*b^2+c^2))*(a^4-2*(b^2-c^2)*a^2+(b^2-c^2)*(b^2+3*c^2)) : :

X(60799) lies on these lines: {3, 46881}, {28, 84}, {48, 14379}, {56, 64}, {603, 2188}, {1413, 60800}, {1433, 7053}, {1435, 60802}, {1436, 2155}, {34046, 41088}

X(60799) = X(3343)-Dao conjugate of-X(322)
X(60799) = X(i)-isoconjugate of-X(j) for these {i, j}: {20, 7952}, {40, 1895}, {196, 27382}, {198, 15466}, {204, 322}, {208, 52346}, {329, 1249}, {342, 7070}, {347, 44695}, {2324, 44697}, {2331, 18750}, {3194, 52345}, {3195, 14615}, {7078, 14249}, {7080, 44696}, {7156, 40702}, {8804, 41083}, {8822, 53011}, {18623, 55116}, {21075, 44698}, {23984, 55063}, {33673, 40971}, {38357, 44699}, {41088, 52578}
X(60799) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (84, 15466), (268, 52346), (1073, 322), (1413, 44697), (1433, 18750), (1436, 1895), (2155, 7952), (2188, 27382), (2208, 1249), (2638, 55063), (7118, 44695), (7129, 14249), (8809, 40701), (14642, 40), (19614, 329), (33581, 2331), (41081, 14615), (41087, 52345), (41489, 47372), (55117, 33673), (60803, 92)
X(60799) = barycentric product X(i)*X(j) for these {i, j}: {63, 60803}, {64, 41081}, {84, 1073}, {189, 19614}, {268, 8809}, {309, 14642}, {1433, 2184}, {1436, 19611}, {2208, 34403}, {7129, 15394}, {30457, 56972}, {44692, 55117}, {52037, 52158}
X(60799) = trilinear product X(i)*X(j) for these {i, j}: {3, 60803}, {64, 1433}, {84, 19614}, {189, 14642}, {1073, 1436}, {2155, 41081}, {2188, 8809}, {2208, 19611}, {7151, 15394}, {14379, 40836}, {30457, 55117}, {46881, 60800}
X(60799) = trilinear quotient X(i)/X(j) for these (i, j): (64, 7952), (84, 1895), (189, 15466), (268, 27382), (271, 52346), (1073, 329), (1364, 55058), (1413, 44696), (1422, 44697), (1433, 20), (1436, 1249), (2155, 2331), (2188, 7070), (2192, 44695), (2208, 204), (2357, 53011), (7118, 7156), (7151, 6525), (8809, 342), (8886, 6616)

X(60800) = ( X(3), X(1) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(56)

Barycentrics    a^2*(a^4+2*(b^2-c^2)*a^2-(b^2-c^2)*(3*b^2+c^2))*(a^4-2*(b^2-c^2)*a^2+(b^2-c^2)*(b^2+3*c^2))*(a^6+2*(b-c)*a^5-(b-c)^2*a^4-4*(b^3-c^3)*a^3-(b^2-c^2)^2*a^2+2*(b^4-c^4)*(b+c)*a+(b^2-c^2)^2*(b-c)^2)*(a^6-2*(b-c)*a^5-(b-c)^2*a^4+4*(b^3-c^3)*a^3-(b^2-c^2)^2*a^2-2*(b^4-c^4)*(b+c)*a+(b^2-c^2)^2*(b-c)^2) : :

X(60800) lies on these lines: {1, 3342}, {6, 41088}, {34, 64}, {56, 7037}, {86, 47637}, {269, 3345}, {1413, 60799}, {1474, 7152}, {2192, 41085}, {3086, 46065}, {3270, 31942}, {7149, 8747}, {9119, 47850}

X(60800) = X(3345)-beth conjugate of-X(34)
X(60800) = X(14092)-Dao conjugate of-X(56943)
X(60800) = X(i)-isoconjugate of-X(j) for these {i, j}: {20, 1490}, {154, 33672}, {610, 56943}, {1035, 52346}, {3197, 18750}, {5930, 13614}, {5932, 7070}, {27382, 47848}
X(60800) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (64, 56943), (2155, 1490), (2184, 33672), (3345, 18750), (7037, 27382), (7149, 15466), (7152, 20), (33581, 3197), (41489, 3176), (41514, 14615), (47850, 52346), (60802, 92)
X(60800) = barycentric product X(i)*X(j) for these {i, j}: {63, 60802}, {64, 41514}, {253, 7152}, {1073, 7149}, {2155, 56596}, {2184, 3345}, {8809, 47850}
X(60800) = trilinear product X(i)*X(j) for these {i, j}: {3, 60802}, {64, 3345}, {2155, 41514}, {2184, 7152}, {3342, 60803}, {7037, 8809}, {7149, 19614}, {8811, 52158}, {33581, 56596}
X(60800) = trilinear quotient X(i)/X(j) for these (i, j): (64, 1490), (253, 33672), (1034, 52346), (2155, 3197), (2184, 56943), (3345, 20), (7007, 44695), (7037, 7070), (7149, 1895), (7152, 610), (8806, 52345), (8809, 5932), (8811, 5930), (41514, 18750), (47850, 27382), (52158, 13614), (56596, 14615)

X(60801) = ( X(1), X(4) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(4)

Barycentrics    (a^2+b^2-c^2)^2*(a^2-b^2+c^2)^2*((b-c)*a^5+b*c*a^4-2*(b^3-c^3)*a^3+(b^4-c^4)*(b+c)*a-(b^2-c^2)^2*b*c)*((b-c)*a^5-b*c*a^4-2*(b^3-c^3)*a^3+(b^4-c^4)*(b+c)*a+(b^2-c^2)^2*b*c)/a : :

X(60801) lies on these lines: {4, 6285}, {29, 3362}, {90, 41497}, {3560, 56261}, {8761, 53817}

X(60801) = polar conjugate of the isotomic conjugate of X(40165)
X(60801) = X(7049)-Ceva conjugate of-X(158)
X(60801) = X(1093)-cross conjugate of-X(158)
X(60801) = X(i)-Dao conjugate of-X(j) for these (i, j): (6523, 1745), (36103, 20764)
X(60801) = X(i)-isoconjugate of-X(j) for these {i, j}: {3, 20764}, {255, 1745}, {394, 21767}, {577, 6360}, {1092, 1148}, {1816, 22341}, {18604, 21854}, {18749, 52430}
X(60801) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (19, 20764), (158, 6360), (393, 1745), (1096, 21767), (2052, 18749), (3362, 394), (6520, 1148), (7049, 63), (7361, 326), (8748, 1816), (8761, 255), (40165, 69)
X(60801) = pole of the line {158, 56271} with respect to the Feuerbach circumhyperbola
X(60801) = barycentric product X(i)*X(j) for these {i, j}: {4, 40165}, {92, 7049}, {158, 7361}, {2052, 3362}, {8761, 57806}
X(60801) = trilinear product X(i)*X(j) for these {i, j}: {4, 7049}, {19, 40165}, {158, 3362}, {393, 7361}, {2052, 8761}
X(60801) = trilinear quotient X(i)/X(j) for these (i, j): (4, 20764), (158, 1745), (393, 21767), (1093, 1148), (1896, 1816), (2052, 6360), (3362, 255), (7049, 3), (7361, 394), (8761, 577), (40165, 63), (57806, 18749)

X(60802) = ( X(1), X(4) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(34)

Barycentrics    a*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4+2*(b^2-c^2)*a^2-(b^2-c^2)*(3*b^2+c^2))*(a^4-2*(b^2-c^2)*a^2+(b^2-c^2)*(b^2+3*c^2))*(a^6+2*(b-c)*a^5-(b-c)^2*a^4-4*(b^3-c^3)*a^3-(b^2-c^2)^2*a^2+2*(b^4-c^4)*(b+c)*a+(b^2-c^2)^2*(b-c)^2)*(a^6-2*(b-c)*a^5-(b-c)^2*a^4+4*(b^3-c^3)*a^3-(b^2-c^2)^2*a^2-2*(b^4-c^4)*(b+c)*a+(b^2-c^2)^2*(b-c)^2) : :

X(60802) lies on these lines: {4, 8806}, {19, 30457}, {28, 3345}, {34, 64}, {286, 5931}, {1119, 7149}, {1435, 60799}

X(60802) = X(7149)-beth conjugate of-X(1118)
X(60802) = X(40839)-Dao conjugate of-X(33672)
X(60802) = X(i)-isoconjugate of-X(j) for these {i, j}: {3176, 35602}, {3197, 37669}, {15905, 56943}
X(60802) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (459, 33672), (3345, 37669), (7007, 27382), (7149, 18750), (8806, 42699), (40838, 52346), (41489, 1490), (60800, 63)
X(60802) = barycentric product X(i)*X(j) for these {i, j}: {92, 60800}, {459, 3345}, {2184, 7149}, {8809, 40838}, {41489, 56596}
X(60802) = trilinear product X(i)*X(j) for these {i, j}: {4, 60800}, {64, 7149}, {459, 7152}, {7007, 8809}, {41489, 41514}
X(60802) = trilinear quotient X(i)/X(j) for these (i, j): (459, 56943), (6526, 3176), (7007, 7070), (7149, 20), (7152, 15905), (40838, 27382), (41489, 3197), (41514, 37669)

X(60803) = ( X(4), X(1) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(34)

Barycentrics    a^2*(a^3+(b-c)*a^2-(b-c)^2*a-(b+c)*(b^2-c^2))*(a^3-(b-c)*a^2-(b-c)^2*a+(b+c)*(b^2-c^2))*(a^4+2*(b^2-c^2)*a^2-(b^2-c^2)*(3*b^2+c^2))*(a^4-2*(b^2-c^2)*a^2+(b^2-c^2)*(b^2+3*c^2)) : :

X(60803) lies on these lines: {1, 1073}, {6, 7367}, {11, 6526}, {34, 7008}, {55, 14379}, {56, 64}, {58, 1433}, {84, 269}, {86, 5931}, {253, 14986}, {459, 3086}, {937, 2184}, {939, 53012}, {1301, 11398}, {1398, 31942}, {1436, 1474}, {3304, 8798}, {5204, 11589}, {7129, 41489}, {7354, 58758}, {8747, 40836}, {10072, 13157}, {40960, 52078}

X(60803) = cevapoint of X(2310) and X(55242)
X(60803) = X(52158)-beth conjugate of-X(56)
X(60803) = X(7151)-cross conjugate of-X(1436)
X(60803) = X(i)-Dao conjugate of-X(j) for these (i, j): (3341, 52346), (14092, 329)
X(60803) = X(i)-isoconjugate of-X(j) for these {i, j}: {20, 40}, {154, 322}, {198, 18750}, {221, 52346}, {223, 27382}, {329, 610}, {347, 7070}, {1097, 41088}, {1103, 41084}, {1394, 7080}, {1817, 8804}, {1895, 7078}, {2187, 14615}, {2324, 18623}, {2331, 37669}, {2360, 52345}, {3198, 8822}, {3213, 55112}, {7012, 55058}, {7013, 44695}, {7074, 33673}, {7128, 55063}, {27398, 30456}, {35602, 47372}, {36841, 55212}, {44697, 55111}, {44699, 53557}, {57193, 57245}
X(60803) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (64, 329), (84, 18750), (189, 14615), (282, 52346), (1413, 18623), (1422, 33673), (1433, 37669), (1436, 20), (1903, 52345), (2155, 40), (2184, 322), (2192, 27382), (2208, 610), (2357, 8804), (3270, 55063), (7117, 55058), (7118, 7070), (7129, 1895), (7151, 1249), (7154, 44695), (8809, 40702), (14642, 7078), (30457, 7080), (33581, 198), (40836, 15466), (41489, 7952), (52158, 27398), (52389, 42699), (55242, 17898), (60799, 63)
X(60803) = pole of the line {64, 52384} with respect to the Feuerbach circumhyperbola
X(60803) = barycentric product X(i)*X(j) for these {i, j}: {64, 189}, {84, 2184}, {92, 60799}, {253, 1436}, {282, 8809}, {309, 2155}, {459, 1433}, {1073, 40836}, {1422, 44692}, {1440, 30457}, {2208, 57921}, {7129, 19611}, {7151, 34403}, {8808, 52158}, {33581, 44190}
X(60803) = trilinear product X(i)*X(j) for these {i, j}: {4, 60799}, {64, 84}, {189, 2155}, {253, 2208}, {309, 33581}, {1073, 7129}, {1256, 41088}, {1413, 44692}, {1422, 30457}, {1436, 2184}, {2192, 8809}, {3341, 60800}, {7151, 19611}, {19614, 40836}, {41081, 41489}, {46639, 55242}, {46881, 60802}, {52158, 52384}
X(60803) = trilinear quotient X(i)/X(j) for these (i, j): (64, 40), (84, 20), (189, 18750), (253, 322), (280, 52346), (282, 27382), (309, 14615), (1256, 41084), (1413, 1394), (1422, 18623), (1436, 610), (1440, 33673), (1903, 8804), (2155, 198), (2184, 329), (2192, 7070), (2208, 154), (2357, 3198), (6526, 47372), (7004, 55058)
X(60803) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 1073, 41088), (1, 3341, 41086)

X(60804) = ( X(1), X(5) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(11)

Barycentrics    (-a+b+c)*(b-c)^2*((b^2+c^2)*a^2-(b^2-c^2)^2)/a : :

X(60804) lies on these lines: {5, 1087}, {11, 523}, {110, 2596}, {564, 7741}, {1091, 3614}, {2166, 38458}, {2595, 13434}, {2602, 2619}, {2962, 3467}, {4858, 7004}, {5400, 60091}, {7069, 14213}, {8819, 8902}, {56283, 60805}

X(60804) = X(5)-Ceva conjugate of-X(2618)
X(60804) = X(i)-Dao conjugate of-X(j) for these (i, j): (137, 4551), (216, 4564), (522, 44687), (650, 2167), (1577, 95), (2618, 27529), (6615, 54), (14363, 7012), (40588, 2149), (40628, 97), (55067, 18315)
X(60804) = X(i)-isoconjugate of-X(j) for these {i, j}: {12, 14587}, {54, 59}, {97, 7115}, {933, 23067}, {2148, 4564}, {2149, 2167}, {2169, 7012}, {4551, 36134}, {4552, 14586}, {4559, 18315}, {4998, 54034}, {8882, 44717}, {14533, 46102}, {24027, 44687}
X(60804) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (5, 4564), (11, 2167), (51, 2149), (53, 7012), (1146, 44687), (1393, 1262), (1953, 59), (2150, 14587), (2170, 54), (2181, 7115), (2618, 4552), (3271, 2148), (3737, 18315), (4858, 95), (6369, 4585), (7004, 97), (7069, 1252), (7117, 2169), (7252, 36134), (8735, 2190), (12077, 4551), (14213, 4998), (17880, 34386), (18180, 52378), (21044, 56254), (21102, 651), (41218, 34544), (41221, 2171), (44706, 44717), (52325, 3738), (55195, 2616), (56283, 39177), (57215, 18831)
X(60804) = perspector of the circumconic through X(57215) and X(60074)
X(60804) = pole of the line {4242, 4551} with respect to the polar circle
X(60804) = barycentric product X(i)*X(j) for these {i, j}: {5, 4858}, {11, 14213}, {53, 17880}, {311, 2170}, {324, 7004}, {1393, 23978}, {1953, 34387}, {2618, 4560}, {3737, 18314}, {4391, 21102}, {6368, 57215}, {6369, 60074}, {7069, 23989}, {8735, 18695}, {12077, 18155}, {21666, 44708}, {35174, 52325}, {41221, 52379}
X(60804) = trilinear product X(i)*X(j) for these {i, j}: {5, 11}, {51, 34387}, {53, 26932}, {261, 41221}, {311, 3271}, {324, 7117}, {343, 8735}, {522, 21102}, {655, 52325}, {1111, 7069}, {1364, 13450}, {1393, 24026}, {1953, 4858}, {2170, 14213}, {2181, 17880}, {2600, 60074}, {2618, 3737}, {2973, 44707}, {4560, 12077}, {7252, 18314}
X(60804) = trilinear quotient X(i)/X(j) for these (i, j): (5, 59), (11, 54), (53, 7115), (60, 14587), (311, 4998), (324, 46102), (343, 44717), (1364, 19210), (1393, 24027), (1953, 2149), (2170, 2148), (2600, 1983), (2618, 4551), (3271, 54034), (3737, 36134), (4560, 18315), (4858, 2167), (6368, 23067), (7004, 2169), (7069, 1110)
X(60804) = (X(1090), X(1109))-harmonic conjugate of X(11)

X(60805) = ( X(5), X(1) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(11)

Barycentrics    (-a+b+c)*(b-c)^2*((b-c)*a^5-(b-c)*(2*b^2+b*c+2*c^2)*a^3+(b+c)^2*b*c*a^2+(b^3+c^3)*(b^2-c^2)*a-(b^2-c^2)^2*b*c)*((b-c)*a^5-(b-c)*(2*b^2+b*c+2*c^2)*a^3-(b+c)^2*b*c*a^2+(b^3+c^3)*(b^2-c^2)*a+(b^2-c^2)^2*b*c) : :

X(60805) lies on the cubic K672 and these lines: {1, 51879}, {11, 2618}, {389, 18990}, {6369, 44311}, {8901, 41218}, {56283, 60804}

X(60805) = X(1109)-cross conjugate of-X(11)
X(60805) = X(i)-Dao conjugate of-X(j) for these (i, j): (523, 51879), (650, 18662), (6615, 37732)
X(60805) = X(i)-isoconjugate of-X(j) for these {i, j}: {59, 37732}, {1101, 51879}, {2149, 18662}, {4564, 21770}, {7012, 20803}, {21860, 52378}
X(60805) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (11, 18662), (115, 51879), (2170, 37732), (3271, 21770), (4516, 21860), (7117, 20803), (55195, 8819)
X(60805) = trilinear quotient X(i)/X(j) for these (i, j): (11, 37732), (1109, 51879), (2170, 21770), (4858, 18662), (7004, 20803), (21044, 21860)

X(60806) = ( X(1), X(6) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(9)

Barycentrics    a^2*(a+b-3*c)*(a-3*b+c)*((2*b-c)*a-b*c-c^2)*((b-2*c)*a+b^2+b*c) : :

X(60806) lies on these lines: {9, 23649}, {284, 38266}, {333, 8056}, {3445, 34820}, {3680, 56279}, {34860, 52549}

X(60806) = X(24151)-Dao conjugate of-X(18135)
X(60806) = X(i)-isoconjugate of-X(j) for these {i, j}: {145, 4383}, {1420, 30568}, {1743, 3875}, {3052, 18135}, {3175, 16948}, {3214, 41629}, {3217, 39126}, {3913, 5435}, {3915, 18743}, {4106, 57192}, {4498, 43290}, {28387, 52352}, {33628, 56253}
X(60806) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (3445, 3875), (8056, 18135), (38266, 4383), (39956, 18743), (56155, 39126), (56174, 56253), (56192, 52353), (60789, 75)
X(60806) = barycentric product X(i)*X(j) for these {i, j}: {1, 60789}, {3445, 34860}, {3680, 56155}, {8056, 39956}, {38266, 40012}
X(60806) = trilinear product X(i)*X(j) for these {i, j}: {6, 60789}, {3445, 39956}, {34860, 38266}
X(60806) = trilinear quotient X(i)/X(j) for these (i, j): (3445, 4383), (3680, 30568), (4052, 56253), (4373, 18135), (8056, 3875), (34860, 18743), (38266, 3915), (39956, 145), (42304, 39126), (56123, 52353), (56155, 5435), (56174, 3175), (56192, 3950), (58794, 4106)

X(60807) = ( X(6), X(1) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(9)

Barycentrics    a*((2*b-c)*a-b*c-c^2)*((b-2*c)*a+b^2+b*c)*((b-c)*a^2+(b^2+b*c-c^2)*a-b*c*(b+c))*((b-c)*a^2+(b^2-b*c-c^2)*a+b*c*(b+c)) : :

X(60807) lies on the Feuerbach hyperbola and these lines: {8, 39956}, {314, 39694}, {979, 4866}, {3680, 56279}, {7155, 56123}, {45989, 56155}

X(60807) = X(i)-isoconjugate of-X(j) for these {i, j}: {978, 4383}, {3210, 3915}, {3875, 21769}
X(60807) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (979, 3875), (39694, 18135), (39956, 3210), (56279, 30568), (60788, 75), (60789, 27835)
X(60807) = barycentric product X(i)*X(j) for these {i, j}: {1, 60788}, {979, 34860}, {39694, 39956}, {39701, 60789}, {42304, 56279}, {56155, 56276}
X(60807) = trilinear product X(i)*X(j) for these {i, j}: {6, 60788}, {979, 39956}, {39701, 60806}, {56155, 56279}
X(60807) = trilinear quotient X(i)/X(j) for these (i, j): (979, 4383), (34860, 3210), (39694, 3875), (39956, 978), (56192, 21857), (56276, 30568), (56279, 3913), (58019, 18135)

X(60808) = ( X(6), X(1) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(37)

Barycentrics    a*((b-c)*a+b^2+b*c)*((b-c)*a-b*c-c^2)*((b-c)*a^2+(b^2-c^2)*a+b*c*(b+c))*((b-c)*a^2+(b^2-c^2)*a-b*c*(b+c)) : :

X(60808) lies on these lines: {1, 39964}, {10, 39798}, {37, 40148}, {75, 26819}, {8050, 46838}, {16726, 57915}, {40085, 42471}

X(60808) = X(35058)-Ceva conjugate of-X(596)
X(60808) = X(40085)-cross conjugate of-X(39798)
X(60808) = X(i)-isoconjugate of-X(j) for these {i, j}: {595, 17147}, {2220, 18133}, {3216, 32911}, {4063, 57151}, {4360, 16685}
X(60808) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (596, 18133), (35058, 18140), (39748, 4360), (39798, 17147), (39964, 32911), (40010, 40087), (40013, 40034), (40085, 40603), (40148, 3216), (40519, 57151), (42471, 56249), (60790, 75)
X(60808) = barycentric product X(i)*X(j) for these {i, j}: {1, 60790}, {596, 39748}, {35058, 39798}, {39949, 42471}, {39964, 40013}, {40010, 40148}, {40086, 53627}
X(60808) = trilinear product X(i)*X(j) for these {i, j}: {6, 60790}, {596, 39964}, {35058, 40148}, {39748, 39798}
X(60808) = trilinear quotient X(i)/X(j) for these (i, j): (596, 17147), (35058, 4360), (39748, 32911), (39798, 3216), (39964, 595), (40010, 18140), (40013, 18133), (40085, 3159), (40148, 16685), (42471, 3995), (57915, 40034)

X(60809) = ( X(1), X(6) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(44)

Barycentrics    a^2*(a-2*b+c)*(a-2*c+b)*((3*b-c)*a-b*c-c^2)*((b-3*c)*a+b^2+b*c) : :

X(60809) lies on these lines: {1, 60810}, {44, 39982}, {45, 52556}, {88, 16704}, {89, 52206}, {902, 16694}, {1252, 41935}, {3285, 9456}

X(60809) = isogonal conjugate of the anticomplement of X(24183)
X(60809) = cevapoint of X(1015) and X(55263)
X(60809) = crosssum of X(4370) and X(34587)
X(60809) = X(i)-cross conjugate of-X(j) for these (i, j): (42, 106), (3248, 23345), (50512, 901)
X(60809) = X(i)-Dao conjugate of-X(j) for these (i, j): (9460, 40089), (40586, 52872), (40594, 18145), (40595, 17160), (55053, 57051)
X(60809) = X(i)-isoconjugate of-X(j) for these {i, j}: {44, 17160}, {81, 52872}, {190, 57051}, {519, 37680}, {902, 18145}, {1016, 38979}, {1023, 21297}, {2251, 40089}, {3264, 33882}, {4358, 40091}, {4491, 24004}, {16704, 31855}, {17780, 21385}, {21606, 23344}
X(60809) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (42, 52872), (88, 18145), (106, 17160), (667, 57051), (903, 40089), (1022, 21606), (3248, 38979), (9456, 37680), (23345, 21297), (39697, 3264), (39982, 4358), (55263, 59737)
X(60809) = X(30579)-zayin conjugate of-X(44)
X(60809) = barycentric product X(i)*X(j) for these {i, j}: {88, 39982}, {106, 39697}, {9456, 39994}
X(60809) = trilinear product X(i)*X(j) for these {i, j}: {106, 39982}, {9456, 39697}
X(60809) = trilinear quotient X(i)/X(j) for these (i, j): (37, 52872), (88, 17160), (106, 37680), (649, 57051), (903, 18145), (1015, 38979), (1022, 21297), (6548, 21606), (9456, 40091), (20568, 40089), (23345, 21385), (39697, 4358), (39982, 519), (39994, 3264), (40522, 53582), (55244, 59737), (55263, 4145)

X(60810) = ( X(6), X(1) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(44)

Barycentrics    a*((3*b-c)*a-b*c-c^2)*((b-3*c)*a+b^2+b*c)*((b-c)*a^2+(b^2+2*b*c-c^2)*a-b*c*(b+c))*((b-c)*a^2+(b^2-2*b*c-c^2)*a+b*c*(b+c)) : :

X(60810) lies on these lines: {1, 60809}, {44, 58292}, {519, 39982}, {30939, 39698}

X(60810) = cevapoint of X(37) and X(39982)
X(60810) = X(i)-isoconjugate of-X(j) for these {i, j}: {17495, 40091}, {33882, 39995}, {37680, 49997}
X(60810) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (39697, 39995), (39698, 18145), (39982, 17495), (40039, 40089)
X(60810) = barycentric product X(39698)*X(39982)
X(60810) = trilinear quotient X(i)/X(j) for these (i, j): (39697, 17495), (39698, 17160), (39982, 49997), (39994, 39995), (40039, 18145)

X(60811) = ( X(1), X(7) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(7)

Barycentrics    (a+b-c)^2*(a-b+c)^2*((b-c)*a^3-(2*b^2+b*c-2*c^2)*a^2+(b+c)*(b^2-c^2)*a+b*c*(b-c)^2)*((b-c)*a^3-(2*b^2-b*c-2*c^2)*a^2+(b+c)*(b^2-c^2)*a-b*c*(b-c)^2)/a : :

X(60811) lies on the circumhyperbola dual of Yff parabola and these lines: {2, 40593}, {7, 43750}, {675, 53632}, {27475, 50561}

X(60811) = cevapoint of X(2310) and X(24002)
X(60811) = X(43750)-Ceva conjugate of-X(1088)
X(60811) = X(57880)-cross conjugate of-X(1088)
X(60811) = X(i)-Dao conjugate of-X(j) for these (i, j): (17113, 1742), (59608, 21856)
X(60811) = X(i)-isoconjugate of-X(j) for these {i, j}: {220, 20995}, {1253, 1742}, {3177, 14827}, {6602, 34497}, {7071, 20793}, {8012, 38835}
X(60811) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (269, 20995), (279, 1742), (479, 34497), (1088, 3177), (1446, 21084), (3668, 21856), (7177, 20793), (23062, 31526), (43750, 9), (53632, 101), (56265, 200), (57792, 20935), (57880, 40593), (59941, 21195)
X(60811) = touchpoint of circumhyperbola dual of Yff parabola and line {57880, 60811}
X(60811) = barycentric product X(i)*X(j) for these {i, j}: {85, 43750}, {1088, 56265}, {3261, 53632}
X(60811) = trilinear product X(i)*X(j) for these {i, j}: {7, 43750}, {279, 56265}, {693, 53632}
X(60811) = trilinear quotient X(i)/X(j) for these (i, j): (279, 20995), (1088, 1742), (1446, 21856), (7056, 20793), (10509, 38835), (23062, 34497), (43750, 55), (53632, 692), (56265, 220), (57792, 3177), (57880, 31526)

X(60812) = ( X(1), X(8) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(2)

Barycentrics    (-a+b+c)*((b-c)*a+b*c)*((b-c)*a-b*c)*((2*b-c)*a-b*c+c^2)*((b-2*c)*a-b^2+b*c) : :

X(60812) lies on these lines: {2, 9309}, {85, 17063}, {87, 40420}, {257, 9311}, {330, 10405}, {1376, 2053}, {2319, 6169}, {3840, 32023}, {6384, 18031}, {6557, 7155}, {14829, 51845}, {16569, 30610}, {16606, 56164}, {32008, 32916}

X(60812) = X(i)-Dao conjugate of-X(j) for these (i, j): (11, 24749), (38991, 57177), (45252, 43)
X(60812) = X(i)-isoconjugate of-X(j) for these {i, j}: {43, 9316}, {109, 24749}, {651, 57177}, {1376, 1403}, {1423, 9310}, {2176, 6180}, {2209, 9312}, {3729, 41526}
X(60812) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (87, 6180), (330, 9312), (650, 24749), (663, 57177), (2053, 9310), (2162, 9316), (2319, 1376), (7155, 3729), (9309, 1423), (9311, 3212), (9315, 1403), (9439, 2176), (27498, 7), (32023, 30545)
X(60812) = X(21173)-zayin conjugate of-X(24749)
X(60812) = barycentric product X(i)*X(j) for these {i, j}: {8, 27498}, {2319, 32023}, {6383, 9439}, {7155, 9311}, {9309, 27424}
X(60812) = trilinear product X(i)*X(j) for these {i, j}: {9, 27498}, {2053, 32023}, {2319, 9311}, {6384, 9439}, {7155, 9309}, {9315, 27424}
X(60812) = trilinear quotient X(i)/X(j) for these (i, j): (87, 9316), (330, 6180), (522, 24749), (650, 57177), (2319, 9310), (6384, 9312), (7155, 1376), (9309, 1403), (9311, 1423), (9315, 41526), (9439, 2209), (27424, 3729), (27498, 57), (32023, 3212)

X(60813) = ( X(8), X(1) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(2)

Barycentrics    a*((2*b-c)*a-b*c+c^2)*((b-2*c)*a-b^2+b*c)*(a^2+2*(b-c)*a-(3*b+c)*(b-c))*(a^2-2*(b-c)*a+(b+3*c)*(b-c)) : :

X(60813) lies on these lines: {2, 56718}, {57, 9309}, {105, 6169}, {330, 10405}, {516, 45252}, {3062, 8056}, {9311, 56043}, {19605, 39959}, {34018, 36620}, {41339, 56355}

X(60813) = X(i)-isoconjugate of-X(j) for these {i, j}: {144, 9310}, {165, 1376}, {1419, 4513}, {3207, 3729}, {16283, 31627}
X(60813) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (3062, 3729), (9309, 144), (9311, 16284), (9315, 165), (11051, 1376), (56718, 40883)
X(60813) = barycentric product X(i)*X(j) for these {i, j}: {3062, 9311}, {9309, 10405}, {9315, 44186}, {11051, 32023}
X(60813) = trilinear product X(i)*X(j) for these {i, j}: {3062, 9309}, {9311, 11051}, {9315, 10405}, {9439, 36620}, {51845, 56718}
X(60813) = trilinear quotient X(i)/X(j) for these (i, j): (3062, 1376), (9309, 165), (9311, 144), (9315, 3207), (10405, 3729), (11051, 9310), (19605, 4513), (32023, 16284), (36620, 9312), (56718, 56714), (59170, 59573)

X(60814) = ( X(1), X(8) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(8)

Barycentrics    (-a+b+c)^2*((b-c)*a^2+(b^2+b*c-c^2)*a-b*c*(b+c))*((b-c)*a^2+(b^2-b*c-c^2)*a+b*c*(b+c))/a : :

X(60814) lies on these lines: {8, 56276}, {75, 3831}, {646, 6048}, {979, 1222}, {1219, 39694}, {2370, 53625}, {44723, 50608}

X(60814) = X(56276)-Ceva conjugate of-X(341)
X(60814) = X(i)-Dao conjugate of-X(j) for these (i, j): (6552, 978), (24771, 21769)
X(60814) = X(i)-isoconjugate of-X(j) for these {i, j}: {978, 1106}, {1262, 16614}, {1398, 20805}, {1407, 21769}, {3169, 7366}, {3210, 52410}
X(60814) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (200, 21769), (341, 3210), (346, 978), (979, 1407), (2310, 16614), (3692, 20805), (4082, 21857), (5423, 3169), (30693, 19582), (39694, 269), (53625, 1461), (56276, 57), (56279, 56), (58019, 279)
X(60814) = barycentric product X(i)*X(j) for these {i, j}: {312, 56276}, {341, 39694}, {346, 58019}, {979, 59761}, {3596, 56279}, {52622, 53625}
X(60814) = trilinear product X(i)*X(j) for these {i, j}: {8, 56276}, {200, 58019}, {312, 56279}, {341, 979}, {346, 39694}, {4397, 53625}, {6556, 39701}
X(60814) = trilinear quotient X(i)/X(j) for these (i, j): (341, 978), (346, 21769), (979, 1106), (1146, 16614), (1265, 20805), (30693, 3169), (39694, 1407), (56276, 56), (56279, 604), (58019, 269), (59761, 3210)

X(60815) = ( X(1), X(8) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(10)

Barycentrics    (-a+b+c)*((b-c)*a^2+(b+c)*b*a-(b^2-c^2)*c)*((b-c)*a^2+(b^2-c^2)*a+b*c*(b+c))*((b-c)*a^2+(b^2-c^2)*a-b*c*(b+c))*((b-c)*a^2-(b+c)*c*a-(b^2-c^2)*b) : :

X(60815) lies on these lines: {10, 57666}, {3701, 44040}, {39748, 56173}, {41013, 42471}

X(60815) = X(44040)-reciprocal conjugate of-X(17147)
X(60815) = barycentric product X(35058)*X(44040)
X(60815) = trilinear product X(39748)*X(44040)
X(60815) = trilinear quotient X(44040)/X(3216)

X(60816) = ( X(8), X(1) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(10)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*((b-c)*a^2+(b+c)*b*a-(b^2-c^2)*c)*((b-c)*a^2-(b+c)*c*a-(b^2-c^2)*b) : :

X(60816) lies on these lines: {1, 18677}, {4, 4674}, {10, 7069}, {33, 56259}, {37, 8756}, {51, 65}, {92, 34860}, {225, 2181}, {1393, 3668}, {1739, 12616}, {2190, 2299}, {5552, 56248}, {7649, 55244}, {39585, 56136}, {41013, 42471}, {52384, 52541}, {59642, 60415}

X(60816) = polar conjugate of X(32939)
X(60816) = crosssum of X(i) and X(j) for these {i, j}: {255, 22458}, {39006, 57103}
X(60816) = X(i)-cross conjugate of-X(j) for these (i, j): (3271, 3064), (20619, 1877)
X(60816) = X(i)-Dao conjugate of-X(j) for these (i, j): (37, 42705), (1249, 32939), (5190, 47796), (5521, 48281), (20620, 20293), (36103, 404), (38991, 57042), (39025, 57103)
X(60816) = X(i)-isoconjugate of-X(j) for these {i, j}: {3, 404}, {48, 32939}, {69, 44085}, {184, 44139}, {651, 57042}, {664, 57103}, {906, 47796}, {1331, 48281}, {1333, 42705}, {1437, 56318}, {4564, 39006}, {6516, 48387}, {18604, 56319}, {20293, 36059}
X(60816) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (4, 32939), (10, 42705), (19, 404), (92, 44139), (663, 57042), (1826, 56318), (1973, 44085), (3063, 57103), (3064, 20293), (3271, 39006), (6591, 48281), (7649, 47796), (8735, 44311), (40518, 6517), (44040, 345), (56248, 4561), (57666, 63), (57830, 304)
X(60816) = Zosma transform of X(56885)
X(60816) = pole of the line {20293, 47796} with respect to the polar circle
X(60816) = barycentric product X(i)*X(j) for these {i, j}: {19, 57830}, {92, 57666}, {278, 44040}, {7649, 56248}
X(60816) = trilinear product X(i)*X(j) for these {i, j}: {4, 57666}, {25, 57830}, {34, 44040}, {6591, 56248}
X(60816) = trilinear quotient X(i)/X(j) for these (i, j): (4, 404), (25, 44085), (92, 32939), (264, 44139), (321, 42705), (650, 57042), (663, 57103), (2170, 39006), (7649, 48281), (17924, 47796), (18344, 48387), (41013, 56318), (44040, 78), (44426, 20293), (56248, 1332), (57666, 3), (57830, 69)

X(60817) = ( X(1), X(8) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(42)

Barycentrics    a^2*(-a+b+c)*((b+c)*a^2+(b-c)*b*a+(b^2-c^2)*c)*((b+c)*a^2-(b-c)*c*a-(b^2-c^2)*b) : :

X(60817) lies on these lines: {8, 46877}, {42, 51}, {43, 1699}, {65, 1193}, {210, 7069}, {213, 60818}, {1002, 53083}, {1334, 16588}, {1824, 2181}, {2334, 52150}, {3214, 41506}, {7109, 14936}, {9561, 35506}, {20028, 39741}, {28471, 59006}, {34262, 59300}

X(60817) = crosssum of X(i) and X(j) for these {i, j}: {2975, 17074}, {17496, 34589}, {21173, 24237}, {37558, 52358}
X(60817) = X(i)-cross conjugate of-X(j) for these (i, j): (872, 41), (2310, 663)
X(60817) = X(i)-Dao conjugate of-X(j) for these (i, j): (11, 57244), (5452, 14829), (14714, 57091), (17115, 34589), (32664, 17074), (38986, 51662), (38991, 17496), (39025, 21173), (40586, 52358), (40600, 37558), (40607, 52357)
X(60817) = X(i)-isoconjugate of-X(j) for these {i, j}: {2, 17074}, {7, 2975}, {57, 14829}, {77, 11109}, {81, 52358}, {85, 572}, {86, 37558}, {95, 56412}, {99, 51662}, {109, 57244}, {261, 20617}, {274, 55323}, {331, 22118}, {552, 14973}, {651, 17496}, {664, 21173}, {757, 52357}, {934, 57091}, {1014, 17751}, {1262, 40624}, {1275, 11998}, {1434, 21061}, {1509, 56325}, {4564, 24237}, {4566, 57125}, {4626, 58339}, {6063, 20986}, {7045, 34589}, {18026, 23187}, {52139, 57785}
X(60817) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (31, 17074), (41, 2975), (42, 52358), (55, 14829), (213, 37558), (607, 11109), (650, 57244), (657, 57091), (663, 17496), (798, 51662), (872, 56325), (1334, 17751), (1500, 52357), (1918, 55323), (2051, 6063), (2175, 572), (2179, 56412), (2310, 40624), (3063, 21173), (3271, 24237), (9447, 20986), (14936, 34589), (34434, 85), (38365, 26847), (46880, 310), (51870, 349), (52150, 1434), (53083, 57785), (54121, 20567), (56188, 4572), (56194, 4554), (57180, 58339), (57905, 41283), (59006, 4573)
X(60817) = barycentric product X(i)*X(j) for these {i, j}: {9, 34434}, {41, 54121}, {42, 46880}, {55, 2051}, {210, 53083}, {284, 51870}, {650, 56194}, {663, 56188}, {1334, 20028}, {2175, 57905}, {2321, 52150}, {3063, 56252}, {3700, 59006}, {21033, 40453}, {46393, 53702}
X(60817) = trilinear product X(i)*X(j) for these {i, j}: {41, 2051}, {55, 34434}, {210, 52150}, {213, 46880}, {663, 56194}, {1334, 53083}, {2175, 54121}, {2194, 51870}, {3063, 56188}, {4041, 59006}, {9447, 57905}, {40453, 40966}, {53549, 53702}
X(60817) = trilinear quotient X(i)/X(j) for these (i, j): (6, 17074), (9, 14829), (33, 11109), (37, 52358), (41, 572), (42, 37558), (51, 56412), (55, 2975), (181, 20617), (210, 17751), (213, 55323), (512, 51662), (522, 57244), (650, 17496), (663, 21173), (756, 52357), (1146, 40624), (1334, 21061), (1500, 56325), (1946, 23187)

X(60818) = ( X(8), X(1) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(42)

Barycentrics    a^2*((b+c)*a^2+(b-c)*b*a+(b^2-c^2)*c)*((b+c)*a^2-(b-c)*c*a-(b^2-c^2)*b)*((b+c)*a^4+(b^2-c^2)*a^3-(b-c)*(b^2+b*c-c^2)*a^2-(b^4-c^4)*a-(b^2-c^2)*(b+c)*b*c)*((b+c)*a^4-(b^2-c^2)*a^3-(b-c)*(b^2-b*c-c^2)*a^2+(b^4-c^4)*a+(b^2-c^2)*(b+c)*b*c) : :

X(60818) lies on these lines: {1, 46880}, {213, 60817}

X(60818) = X(i)-isoconjugate of-X(j) for these {i, j}: {572, 21596}, {1764, 14829}, {2975, 20245}
X(60818) = X(34434)-reciprocal conjugate of-X(21596)
X(60818) = barycentric product X(34434)*X(43739)
X(60818) = trilinear quotient X(i)/X(j) for these (i, j): (2051, 21596), (34434, 20245), (43739, 14829)

X(60819) = ( X(3), X(2) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(2)

Barycentrics    1/a^2*(a^2-b^2+c^2)*(a^2+b^2-c^2)*((b^2-c^2)*a^6-(2*b^4+b^2*c^2-2*c^4)*a^4+(b^4-c^4)*(b^2+c^2)*a^2+(b^2-c^2)^2*b^2*c^2)*((b^2-c^2)*a^6-(2*b^4-b^2*c^2-2*c^4)*a^4+(b^4-c^4)*(b^2+c^2)*a^2-(b^2-c^2)^2*b^2*c^2) : :

X(60819) lies on these lines: {2, 9291}, {69, 16089}, {76, 57855}, {95, 40800}, {287, 1988}, {850, 23613}, {1972, 2052}, {6528, 38283}, {15466, 42313}, {60199, 60833}

X(60819) = isotomic conjugate of X(6638)
X(60819) = polar conjugate of X(32445)
X(60819) = cevapoint of X(i) and X(j) for these {i, j}: {850, 2972}, {43710, 54114}
X(60819) = X(54114)-Ceva conjugate of-X(264)
X(60819) = X(18027)-cross conjugate of-X(264)
X(60819) = X(i)-Dao conjugate of-X(j) for these (i, j): (2, 6638), (1249, 32445), (6374, 57008)
X(60819) = X(i)-isoconjugate of-X(j) for these {i, j}: {31, 6638}, {48, 32445}, {560, 57008}, {3164, 9247}, {3168, 52430}
X(60819) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (2, 6638), (4, 32445), (76, 57008), (264, 3164), (275, 26887), (324, 42453), (1988, 184), (2052, 3168), (14618, 59745), (40800, 577), (43710, 6), (44828, 32661), (54114, 3), (60833, 51336)
X(60819) = trilinear pole of the line {525, 42331} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(60819) = pole of the the tripolar of X(32445) with respect to the polar circle
X(60819) = barycentric product X(i)*X(j) for these {i, j}: {76, 43710}, {264, 54114}, {1988, 18022}, {18027, 40800}
X(60819) = trilinear product X(i)*X(j) for these {i, j}: {75, 43710}, {92, 54114}, {1969, 1988}, {40800, 57806}
X(60819) = trilinear quotient X(i)/X(j) for these (i, j): (75, 6638), (92, 32445), (561, 57008), (1969, 3164), (1988, 9247), (40440, 26887), (40800, 52430), (43710, 31), (54114, 48), (57806, 3168)

X(60820) = ( X(2), X(3) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(4)

Barycentrics    a^2*(-a^2+b^2+c^2)*(a^4+2*(b^2-c^2)*a^2-(3*b^2+c^2)*(b^2-c^2))*(a^4-2*(b^2-c^2)*a^2+(b^2-c^2)*(b^2+3*c^2))*((2*b^2-c^2)*a^6-(b^2-c^2)*(4*b^2+3*c^2)*a^4+(b^2-c^2)*(2*b^4+3*b^2*c^2+3*c^4)*a^2-(b^2-c^2)^3*c^2)*((b^2-2*c^2)*a^6-(b^2-c^2)*(3*b^2+4*c^2)*a^4+(b^2-c^2)*(3*b^4+3*b^2*c^2+2*c^4)*a^2-(b^2-c^2)^3*b^2) : :

X(60820) lies on the Jerabek hyperbola and these lines: {4, 8798}, {6, 18890}, {54, 14371}, {64, 32319}, {253, 8795}, {459, 56271}, {1073, 3527}, {11270, 11589}, {34403, 43711}

X(60820) = X(32319)-cross conjugate of-X(18890)
X(60820) = X(i)-Dao conjugate of-X(j) for these (i, j): (3343, 20477), (14092, 56296)
X(60820) = X(i)-isoconjugate of-X(j) for these {i, j}: {204, 20477}, {610, 56296}, {1895, 6759}, {18750, 51936}
X(60820) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (64, 56296), (1073, 20477), (14642, 6759), (15318, 15466), (18890, 20), (32319, 1249), (33581, 51936)
X(60820) = barycentric product X(i)*X(j) for these {i, j}: {253, 18890}, {1073, 15318}, {13157, 14371}, {32319, 34403}
X(60820) = trilinear product X(i)*X(j) for these {i, j}: {2184, 18890}, {15318, 19614}, {19611, 32319}
X(60820) = trilinear quotient X(i)/X(j) for these (i, j): (2155, 51936), (2184, 56296), (15318, 1895), (18890, 610), (19611, 20477), (19614, 6759), (32319, 204)

X(60821) = ( X(3), X(2) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(4)

Barycentrics    ((2*b^2-c^2)*a^6-(b^2-c^2)*(4*b^2+3*c^2)*a^4+(b^2-c^2)*(2*b^4+3*b^2*c^2+3*c^4)*a^2-(b^2-c^2)^3*c^2)*((b^2-2*c^2)*a^6-(b^2-c^2)*(3*b^2+4*c^2)*a^4+(b^2-c^2)*(3*b^4+3*b^2*c^2+2*c^4)*a^2-(b^2-c^2)^3*b^2)*((b^2-c^2)*a^10-(4*b^4+b^2*c^2-4*c^4)*a^8+2*(b^2-c^2)*(3*b^4+4*b^2*c^2+3*c^4)*a^6-2*(b^2-c^2)*(2*b^6+2*c^6+(b^2+3*c^2)*b^2*c^2)*a^4+(b^4-c^4)^2*(b^2-c^2)*a^2-(b^2-c^2)^4*b^2*c^2)*((b^2-c^2)*a^10-(4*b^4-b^2*c^2-4*c^4)*a^8+2*(b^2-c^2)*(3*b^4+4*b^2*c^2+3*c^4)*a^6-2*(b^2-c^2)*(2*b^6+2*c^6+b^2*c^2*(3*b^2+c^2))*a^4+(b^4-c^4)^2*(b^2-c^2)*a^2+(b^2-c^2)^4*b^2*c^2) : :

X(60821) lies on the Kiepert hyperbola and these lines: {4, 18890}, {275, 13855}, {459, 56271}, {2052, 15318}, {8796, 34287}

X(60821) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (15318, 46717), (32319, 41373), (34287, 20477), (56271, 56296)
X(60821) = barycentric product X(15318)*X(34287)

X(60822) = ( X(2), X(4) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(20)

Barycentrics    (3*a^4+2*(b^2-3*c^2)*a^2+3*(b^2-c^2)^2)*(3*a^4-2*(3*b^2-c^2)*a^2+3*(b^2-c^2)^2)*(3*a^4+2*(b^2-3*c^2)*a^2-(b^2-c^2)*(5*b^2+3*c^2))*(3*a^4-2*(3*b^2-c^2)*a^2+(b^2-c^2)*(3*b^2+5*c^2)) : :

X(60822) lies on these lines: {20, 3532}, {1249, 51316}, {14615, 35510}, {40170, 60823}

X(60822) = X(18594)-isoconjugate of-X(37672)
X(60822) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (3532, 37672), (35510, 32831), (38253, 32001), (51316, 3146)
X(60822) = X(2)-nine-point circle chordal perspector of X(20)
X(60822) = pole of the line {3532, 51316} with respect to the Kiepert circumhyperbola
X(60822) = barycentric product X(i)*X(j) for these {i, j}: {15077, 38253}, {35510, 51316}
X(60822) = trilinear quotient X(51316)/X(18594)

X(60823) = ( X(4), X(2) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(20)

Barycentrics    (-a^2+b^2+c^2)*(3*a^4+2*(b^2-3*c^2)*a^2+3*(b^2-c^2)^2)*(3*a^4-2*(3*b^2-c^2)*a^2+3*(b^2-c^2)^2)*(3*a^6-(3*b^2+7*c^2)*a^4-(3*b^4-6*b^2*c^2-5*c^4)*a^2+(3*b^2-c^2)*(b^2-c^2)^2)*(3*a^6-(7*b^2+3*c^2)*a^4+(5*b^4+6*b^2*c^2-3*c^4)*a^2-(b^2-3*c^2)*(b^2-c^2)^2) : :

X(60823) lies on these lines: {20, 51316}, {12429, 15077}, {40170, 60822}

X(60823) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (43670, 32001), (51316, 6622)
X(60823) = X(4)-nine-point circle chordal perspector of X(20)
X(60823) = barycentric product X(15077)*X(43670)

X(60824) = ( X(2), X(5) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(3)

Barycentrics    (-a^2+b^2+c^2)^2*((b^2+c^2)*a^2-(b^2-c^2)^2)*(a^4-(2*b^2+c^2)*a^2+(b^2-c^2)^2)*(a^4-(b^2+2*c^2)*a^2+(b^2-c^2)^2) : :

X(60824) lies on the cubic K1324 and these lines: {3, 539}, {5, 25043}, {20, 930}, {93, 264}, {252, 631}, {381, 18370}, {382, 19552}, {394, 60825}, {548, 35888}, {1092, 50463}, {1487, 3090}, {3526, 21975}, {3843, 31392}, {5067, 56738}, {5070, 16762}, {7796, 46139}, {11140, 13599}, {11271, 25044}, {12325, 32637}, {21394, 38444}, {52975, 55549}

X(60824) = X(39019)-cross conjugate of-X(60597)
X(60824) = X(i)-Dao conjugate of-X(j) for these (i, j): (5, 3518), (6, 57489), (1147, 25044), (2972, 1510), (6368, 137), (21975, 8884), (39171, 4), (52032, 32002)
X(60824) = X(i)-isoconjugate of-X(j) for these {i, j}: {19, 57489}, {158, 25044}, {2190, 3518}, {2964, 8884}
X(60824) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (3, 57489), (93, 8794), (216, 3518), (343, 32002), (418, 2965), (577, 25044), (930, 16813), (2439, 53176), (2963, 8884), (3519, 275), (5562, 1994), (11140, 8795), (17434, 1510), (25043, 2052), (34983, 57137), (38342, 52779), (39019, 137), (41212, 47424), (42445, 6152), (43083, 2413), (46139, 42405), (51477, 8882), (52347, 7769), (55217, 54950), (57195, 57211), (57764, 57573), (60597, 41298)
X(60824) = Cundy-Parry-Phi-transform of X(10619)
X(60824) = pole of the line {3518, 25044} with respect to the Stammler hyperbola
X(60824) = pole of the line {49, 32002} with respect to the Steiner-Wallace hyperbola
X(60824) = barycentric product X(i)*X(j) for these {i, j}: {343, 3519}, {394, 25043}, {930, 60597}, {2963, 52347}, {5562, 11140}, {17434, 46139}, {28706, 51477}, {34983, 55283}, {39019, 57764}, {55217, 58305}
X(60824) = trilinear product X(i)*X(j) for these {i, j}: {255, 25043}, {2962, 5562}, {3519, 44706}, {18695, 51477}, {36148, 60597}
X(60824) = trilinear quotient X(i)/X(j) for these (i, j): (63, 57489), (255, 25044), (2962, 8884), (3519, 2190), (5562, 2964), (18695, 32002), (25043, 158), (44706, 3518)

X(60825) = ( X(5), X(2) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(3)

Barycentrics    (-a^2+b^2+c^2)^2*(a^4-(2*b^2+c^2)*a^2+(b^2-c^2)^2)*(a^4-(b^2+2*c^2)*a^2+(b^2-c^2)^2)*(a^8-2*(2*b^2+c^2)*a^6+(6*b^4+b^2*c^2+2*c^4)*a^4-(b^2-c^2)*(4*b^4-b^2*c^2-2*c^4)*a^2+(b^2-c^2)^4)*(a^8-2*(b^2+2*c^2)*a^6+(2*b^4+b^2*c^2+6*c^4)*a^4-(b^2-c^2)*(2*b^4+b^2*c^2-4*c^4)*a^2+(b^2-c^2)^4) : :

X(60825) lies on these lines: {2, 3459}, {3, 34433}, {97, 3519}, {276, 20572}, {394, 60824}, {1297, 39419}, {2963, 22268}, {25738, 56338}

X(60825) = X(1147)-Dao conjugate of-X(15787)
X(60825) = X(158)-isoconjugate of-X(15787)
X(60825) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (577, 15787), (34433, 3518), (37084, 58876), (39419, 107)
X(60825) = barycentric product X(3265)*X(39419)
X(60825) = trilinear product X(24018)*X(39419)
X(60825) = trilinear quotient X(i)/X(j) for these (i, j): (255, 15787), (39419, 24019)

X(60826) = ( X(2), X(5) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(4)

Barycentrics    ((b^2+c^2)*a^2-(b^2-c^2)^2)*(a^4+2*(b^2-c^2)*a^2-(b^2-c^2)*(3*b^2+c^2))*(a^4-2*(b^2-c^2)*a^2+(b^2-c^2)*(b^2+3*c^2))*(a^8-(2*b^2+c^2)*a^6+(b^2-c^2)*(2*b^2+3*c^2)*a^4-(b^2-c^2)*(2*b^4+b^2*c^2+5*c^4)*a^2+(b^2+2*c^2)*(b^2-c^2)^3)*(a^8-(b^2+2*c^2)*a^6-(b^2-c^2)*(3*b^2+2*c^2)*a^4+(b^2-c^2)*(5*b^4+b^2*c^2+2*c^4)*a^2-(2*b^2+c^2)*(b^2-c^2)^3) : :

X(60826) lies on these lines: {4, 15319}, {64, 15619}, {253, 39286}, {459, 60827}

X(60826) = barycentric product X(13157)*X(15319)

X(60827) = ( X(5), X(2) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(4)

Barycentrics    (a^8-(2*b^2+c^2)*a^6+(b^2-c^2)*(2*b^2+3*c^2)*a^4-(b^2-c^2)*(2*b^4+b^2*c^2+5*c^4)*a^2+(b^2+2*c^2)*(b^2-c^2)^3)*(a^8-(b^2+2*c^2)*a^6-(b^2-c^2)*(3*b^2+2*c^2)*a^4+(b^2-c^2)*(5*b^4+b^2*c^2+2*c^4)*a^2-(2*b^2+c^2)*(b^2-c^2)^3)*(a^12-3*(b^2+c^2)*a^10+(3*b^4+5*b^2*c^2+c^4)*a^8-2*(b^2-c^2)*(b^4+2*b^2*c^2+3*c^4)*a^6+(b^2-c^2)*(3*b^6+9*c^6+(b^2+3*c^2)*b^2*c^2)*a^4-(b^2-c^2)^3*(3*b^4+4*b^2*c^2+5*c^4)*a^2+(b^4+b^2*c^2-c^4)*(b^2-c^2)^4)*(a^12-3*(b^2+c^2)*a^10+(b^4+5*b^2*c^2+3*c^4)*a^8+2*(b^2-c^2)*(3*b^4+2*b^2*c^2+c^4)*a^6-(b^2-c^2)*(9*b^6+3*c^6+(3*b^2+c^2)*b^2*c^2)*a^4+(5*b^4+4*b^2*c^2+3*c^4)*(b^2-c^2)^3*a^2-(b^4-b^2*c^2-c^4)*(b^2-c^2)^4) : :

X(60827) lies on the Kiepert hyperbola and these lines: {275, 15319}, {459, 60826}, {3463, 43530}, {33664, 39284}

X(60828) = ( X(2), X(5) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(5)

Barycentrics    ((b^2+c^2)*a^2-(b^2-c^2)^2)^2*(a^2-b^2+c^2)*(a^2+b^2-c^2)/a^2 : :

X(60828) lies on these lines: {2, 14938}, {3, 2052}, {4, 94}, {5, 324}, {25, 847}, {30, 44732}, {49, 436}, {52, 8887}, {53, 41587}, {93, 37943}, {107, 13621}, {140, 46106}, {195, 648}, {250, 10688}, {264, 1656}, {275, 14627}, {339, 18027}, {381, 1093}, {382, 52578}, {393, 3549}, {546, 52661}, {567, 37127}, {1075, 37481}, {1105, 18859}, {1154, 56303}, {1209, 39569}, {1625, 27359}, {1629, 18378}, {1941, 37495}, {2070, 8884}, {2972, 6662}, {2974, 34853}, {3526, 15466}, {3628, 40684}, {3843, 14249}, {4994, 53863}, {5446, 42400}, {5449, 6747}, {5576, 6530}, {5943, 59650}, {6524, 7528}, {6528, 58732}, {6639, 11547}, {6761, 43821}, {7489, 59482}, {7517, 33971}, {7529, 52439}, {10095, 30506}, {14129, 53028}, {14363, 39530}, {15226, 23290}, {18121, 32351}, {19210, 41202}, {20975, 45195}, {21841, 44145}, {35717, 58806}, {36753, 56296}, {45793, 59164}, {46025, 56302}, {46219, 52147}, {46924, 58805}

X(60828) = polar conjugate of the isogonal conjugate of X(36412)
X(60828) = polar conjugate of the isotomic conjugate of X(45793)
X(60828) = isogonal conjugate of X(46089)
X(60828) = cevapoint of X(41212) and X(57195)
X(60828) = crosspoint of X(5) and X(42466)
X(60828) = crosssum of X(34980) and X(46088)
X(60828) = X(i)-Ceva conjugate of-X(j) for these (i, j): (324, 36412), (35360, 23290)
X(60828) = X(i)-cross conjugate of-X(j) for these (i, j): (23607, 36412), (36412, 45793), (39019, 18314), (41212, 57195)
X(60828) = X(i)-Dao conjugate of-X(j) for these (i, j): (5, 19210), (137, 23286), (216, 97), (6368, 2972), (6663, 3), (14363, 54), (15450, 46088), (40588, 14533)
X(60828) = X(i)-isoconjugate of-X(j) for these {i, j}: {54, 2169}, {97, 2148}, {2167, 14533}, {2190, 19210}, {2616, 15958}, {23286, 36134}
X(60828) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (5, 97), (51, 14533), (53, 54), (216, 19210), (311, 34386), (324, 95), (1087, 63), (1625, 15958), (1953, 2169), (2181, 2148), (3078, 22052), (3199, 54034), (6528, 52939), (6750, 19170), (12077, 23286), (13450, 275), (14569, 8882), (14577, 25044), (14978, 59183), (15451, 46088), (23290, 15412), (23607, 216), (24862, 3269), (27358, 19209), (27371, 16030), (34983, 32320), (35360, 18315), (36412, 3), (39019, 2972), (39284, 59143), (41212, 35071), (41279, 222), (42441, 59184), (45793, 69), (46394, 23606), (51513, 2623), (52604, 14586), (55132, 8552), (55219, 58308), (56272, 57875), (57195, 520), (59142, 20574)
X(60828) = pole of the line {526, 23286} with respect to the polar circle
X(60828) = pole of the line {19210, 22115} with respect to the Stammler hyperbola
X(60828) = pole of the line {46089, 52437} with respect to the Steiner-Wallace hyperbola
X(60828) = barycentric product X(i)*X(j) for these {i, j}: {4, 45793}, {5, 324}, {53, 311}, {92, 1087}, {264, 36412}, {276, 23607}, {343, 13450}, {467, 56272}, {6528, 57195}, {7017, 41279}, {14129, 25043}, {14569, 28706}, {14570, 23290}, {14978, 31610}, {15415, 52604}, {18314, 35360}, {39284, 59164}, {39569, 53245}, {41212, 57556}, {46456, 55132}
X(60828) = trilinear product X(i)*X(j) for these {i, j}: {4, 1087}, {19, 45793}, {53, 14213}, {92, 36412}, {311, 2181}, {318, 41279}, {324, 1953}, {823, 57195}, {2617, 23290}, {2618, 35360}, {13450, 44706}, {14569, 18695}, {23607, 40440}, {23999, 24862}, {36129, 55132}
X(60828) = trilinear quotient X(i)/X(j) for these (i, j): (5, 2169), (53, 2148), (324, 2167), (1087, 3), (1953, 14533), (2181, 54034), (2617, 15958), (2618, 23286), (13450, 2190), (14213, 97), (23290, 2616), (35360, 36134), (36129, 46966), (36412, 48), (39019, 37754), (41212, 42080), (41279, 603), (44706, 19210), (45793, 63), (57195, 822)
X(60828) = X(37732)-of-orthic triangle, when ABC is acute
X(60828) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (4, 35360, 143), (5, 324, 14978), (5, 15912, 42441), (324, 13450, 5), (10095, 35719, 30506), (37127, 56298, 567)

X(60829) = ( X(2), X(6) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(69)

Barycentrics    a^2*(a^2+b^2-3*c^2)*(a^2-3*b^2+c^2)*((2*b^2-c^2)*a^2-b^2*c^2-c^4)*((b^2-2*c^2)*a^2+b^4+b^2*c^2) : :

X(60829) lies on the Jerabek hyperbola and these lines: {1176, 53059}, {6340, 60830}, {8770, 34817}, {17040, 47847}, {19222, 34208}

X(60829) = X(i)-isoconjugate of-X(j) for these {i, j}: {1707, 7754}, {3053, 18056}
X(60829) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (8769, 18056), (8770, 7754), (40319, 52016), (47847, 54412)
X(60829) = barycentric product X(6391)*X(47847)
X(60829) = trilinear quotient X(i)/X(j) for these (i, j): (2996, 18056), (8769, 7754)

X(60830) = ( X(6), X(2) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(69)

Barycentrics    ((2*b^2-c^2)*a^2-b^2*c^2-c^4)*((b^2-2*c^2)*a^2+b^4+b^2*c^2)*((b^2-c^2)*a^4+(b^4+b^2*c^2-c^4)*a^2-b^2*c^2*(b^2+c^2))*((b^2-c^2)*a^4+(b^4-b^2*c^2-c^4)*a^2+b^2*c^2*(b^2+c^2)) : :

X(60830) lies on these lines: {6340, 60829}

X(60831) = ( X(2), X(7) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(7)

Barycentrics    (a+b-c)^2*(a-b+c)^2*(a^2+2*(b-c)*a-(3*b+c)*(b-c))*(a^2-2*(b-c)*a+(b+3*c)*(b-c)) : :
X(60831) = 2*X(7)+X(58836)

X(60831) lies on these lines: {2, 23618}, {7, 1699}, {85, 10004}, {142, 19605}, {658, 20059}, {1119, 42069}, {1434, 26818}, {2369, 53622}, {3945, 56873}, {4569, 4869}, {8581, 56870}, {8732, 43762}, {10509, 11051}, {13609, 42483}, {14256, 57826}, {31527, 43182}, {31995, 56264}, {35160, 53640}, {42462, 58817}

X(60831) = cevapoint of X(1086) and X(58817)
X(60831) = X(36620)-Ceva conjugate of-X(279)
X(60831) = X(i)-cross conjugate of-X(j) for these (i, j): (11, 59941), (479, 279)
X(60831) = X(i)-Dao conjugate of-X(j) for these (i, j): (514, 13609), (1015, 58835), (1086, 57064), (6609, 3207), (17113, 144), (36908, 21872), (59608, 21060)
X(60831) = X(i)-isoconjugate of-X(j) for these {i, j}: {101, 58835}, {144, 1253}, {165, 220}, {200, 3207}, {480, 1419}, {692, 57064}, {1110, 13609}, {2328, 21872}, {3059, 33634}, {3160, 6602}, {7079, 22117}, {14827, 16284}
X(60831) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (269, 165), (279, 144), (479, 3160), (513, 58835), (514, 57064), (738, 1419), (1086, 13609), (1088, 16284), (1407, 3207), (1427, 21872), (3062, 200), (3668, 21060), (7053, 22117), (10405, 346), (11051, 220), (19605, 728), (23062, 31627), (30682, 50559), (36620, 8), (42872, 2324), (44186, 341), (53622, 3939), (53640, 3699), (55284, 7256), (57880, 50560), (58817, 7658)
X(60831) = pole of the line {279, 3062} with respect to the circumhyperbola dual of Yff parabola
X(60831) = barycentric product X(i)*X(j) for these {i, j}: {7, 36620}, {269, 44186}, {279, 10405}, {1088, 3062}, {3676, 53640}, {11051, 57792}, {19605, 23062}, {52621, 53622}
X(60831) = trilinear product X(i)*X(j) for these {i, j}: {57, 36620}, {269, 10405}, {279, 3062}, {479, 19605}, {1088, 11051}, {1407, 44186}, {1440, 42872}, {3669, 53640}, {7216, 55284}, {24002, 53622}
X(60831) = trilinear quotient X(i)/X(j) for these (i, j): (269, 3207), (279, 165), (479, 1419), (514, 58835), (693, 57064), (1088, 144), (1111, 13609), (1446, 21060), (3062, 220), (3668, 21872), (7177, 22117), (10405, 200), (11051, 1253), (19605, 480), (23062, 3160), (36620, 9), (42872, 7074), (44186, 346), (53640, 644), (55284, 7259)
X(60831) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (7, 17113, 9533), (7, 36620, 3062)

X(60832) = ( X(7), X(2) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(9)

Barycentrics    (-a+b+c)*(a^2-2*b*a+(b-c)^2)*(a^2-2*c*a+(b-c)^2)*(a^3-(3*b+c)*a^2+(b+c)*(3*b-c)*a-(b-c)^3)*(a^3-(b+3*c)*a^2-(b+c)*(b-3*c)*a+(b-c)^3) : :

X(60832) lies on these lines: {9, 277}, {200, 6601}, {480, 55013}, {6605, 42361}, {21617, 34525}

X(60832) = X(i)-isoconjugate of-X(j) for these {i, j}: {1445, 21002}, {1617, 16572}, {8732, 21059}
X(60832) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (277, 8732), (6601, 36845), (42361, 6604), (42470, 3870)
X(60832) = barycentric product X(6601)*X(42361)
X(60832) = trilinear product X(277)*X(42470)
X(60832) = trilinear quotient X(i)/X(j) for these (i, j): (6601, 16572), (42361, 1445), (42470, 218)

X(60833) = ( X(3), X(4) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(2)

Barycentrics    ((2*b^2-c^2)*a^2-b^2*c^2+c^4)*((b^2-2*c^2)*a^2-b^4+b^2*c^2)*((b^2-c^2)*a^6-(2*b^4+b^2*c^2-2*c^4)*a^4+(b^4-c^4)*(b^2+c^2)*a^2+(b^2-c^2)^2*b^2*c^2)*((b^2-c^2)*a^6-(2*b^4-b^2*c^2-2*c^4)*a^4+(b^4-c^4)*(b^2+c^2)*a^2-(b^2-c^2)^2*b^2*c^2) : :

X(60833) lies on the Kiepert hyperbola and these lines: {4, 51336}, {98, 1988}, {459, 43710}, {801, 40800}, {2052, 9307}, {2996, 54114}, {9289, 9290}, {38283, 43188}, {60199, 60819}

X(60833) = X(i)-isoconjugate of-X(j) for these {i, j}: {1957, 6638}, {1958, 32445}
X(60833) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (1988, 9306), (9289, 57008), (9292, 32445), (9307, 3164), (43710, 9308), (51336, 6638), (54114, 1975)
X(60833) = barycentric product X(i)*X(j) for these {i, j}: {9289, 43710}, {9307, 54114}, {51336, 60819}
X(60833) = trilinear product X(i)*X(j) for these {i, j}: {9255, 43710}, {9258, 54114}
X(60833) = trilinear quotient X(i)/X(j) for these (i, j): (9255, 6638), (9258, 32445), (43710, 1957), (54114, 1958)

X(60834) = ( X(4), X(3) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(2)

Barycentrics    a^2*(a^2+b^2-3*c^2)*(a^2-3*b^2+c^2)*(-a^2+b^2+c^2)^2*((2*b^2-c^2)*a^2-b^2*c^2+c^4)*((b^2-2*c^2)*a^2-b^4+b^2*c^2) : :

X(60834) lies on these lines: {2, 9307}, {3, 51336}, {1073, 6391}, {2996, 54114}, {6340, 57799}, {8770, 40801}, {9289, 56339}, {9292, 9306}, {17811, 43727}, {22152, 36609}, {38282, 43188}, {52144, 56362}

X(60834) = X(6)-Dao conjugate of-X(37199)
X(60834) = X(i)-isoconjugate of-X(j) for these {i, j}: {19, 37199}, {1957, 6353}
X(60834) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (3, 37199), (6391, 9308), (9289, 54412), (9307, 21447), (40319, 1968), (51336, 6353), (60839, 1975)
X(60834) = barycentric product X(i)*X(j) for these {i, j}: {6340, 51336}, {6391, 9289}, {9307, 60839}
X(60834) = trilinear product X(i)*X(j) for these {i, j}: {6391, 9255}, {9258, 60839}
X(60834) = trilinear quotient X(i)/X(j) for these (i, j): (63, 37199), (6391, 1957), (9255, 6353)

X(60835) = ( X(4), X(3) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(3)

Barycentrics    a^4*(-a^2+b^2+c^2)^3*(a^6-(3*b^2+c^2)*a^4+(3*b^2-c^2)*(b^2+c^2)*a^2-(b^2-c^2)^3)*(a^6-(b^2+3*c^2)*a^4-(b^2-3*c^2)*(b^2+c^2)*a^2+(b^2-c^2)^3) : :

X(60835) lies on these lines: {3, 15316}, {254, 1105}, {1294, 13398}, {3147, 4558}, {5063, 60775}, {6504, 6816}, {34756, 56307}

X(60835) = X(15316)-Ceva conjugate of-X(1092)
X(60835) = X(i)-Dao conjugate of-X(j) for these (i, j): (1147, 3542), (37867, 6515)
X(60835) = X(i)-isoconjugate of-X(j) for these {i, j}: {158, 3542}, {920, 1093}, {1609, 6521}, {6515, 6520}, {6524, 33808}
X(60835) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (577, 3542), (921, 6521), (1092, 6515), (4100, 920), (6507, 33808), (13398, 15352), (15316, 2052), (16391, 39116), (23606, 1609), (57484, 59139), (59176, 47731), (60775, 1093)
X(60835) = barycentric product X(i)*X(j) for these {i, j}: {394, 15316}, {921, 6507}, {1092, 6504}, {3964, 60775}, {4100, 57998}, {13398, 52613}, {16391, 57484}
X(60835) = trilinear product X(i)*X(j) for these {i, j}: {255, 15316}, {921, 1092}, {4100, 6504}, {6507, 60775}, {23606, 57998}
X(60835) = trilinear quotient X(i)/X(j) for these (i, j): (255, 3542), (921, 1093), (1092, 920), (3964, 33808), (4100, 1609), (6504, 6521), (6507, 6515), (13398, 36126), (15316, 158), (60775, 6520)

X(60836) = ( X(3), X(4) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(4)

Barycentrics    ((b^2-c^2)*a^10-(4*b^4-b^2*c^2-4*c^4)*a^8+2*(b^2-c^2)*(3*b^4+4*b^2*c^2+3*c^4)*a^6-2*(b^2-c^2)*(2*b^6+2*c^6+(3*b^2+c^2)*b^2*c^2)*a^4+(b^4-c^4)^2*(b^2-c^2)*a^2+(b^2-c^2)^4*b^2*c^2)*((b^2-c^2)*a^10-(4*b^4+b^2*c^2-4*c^4)*a^8+2*(b^2-c^2)*(3*b^4+4*b^2*c^2+3*c^4)*a^6-2*(b^2-c^2)*(2*b^6+2*c^6+(b^2+3*c^2)*b^2*c^2)*a^4+(b^4-c^4)^2*(b^2-c^2)*a^2-(b^2-c^2)^4*b^2*c^2)*(a^2+b^2-c^2)^3*(a^2-b^2+c^2)^3/a^2 : :

X(60836) lies on these lines: {4, 56271}, {264, 14059}, {1105, 13855}, {1217, 34287}, {15352, 38281}

X(60836) = X(56271)-Ceva conjugate of-X(1093)
X(60836) = X(i)-isoconjugate of-X(j) for these {i, j}: {4100, 46717}, {6507, 41373}
X(60836) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (1093, 46717), (6524, 41373), (34287, 3964), (56271, 394)
X(60836) = barycentric product X(i)*X(j) for these {i, j}: {1093, 34287}, {2052, 56271}
X(60836) = trilinear product X(i)*X(j) for these {i, j}: {158, 56271}, {6520, 34287}
X(60836) = trilinear quotient X(i)/X(j) for these (i, j): (6520, 41373), (6521, 46717), (34287, 6507), (56271, 255)

X(60837) = ( X(3), X(4) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(5)

Barycentrics    ((b^2-c^2)*a^6-(2*b^4+3*b^2*c^2-3*c^4)*a^4+(b^2-c^2)*(b^4-2*b^2*c^2+3*c^4)*a^2-(b^2-c^2)^3*c^2)*((b^2-c^2)*a^6-(3*b^4-3*b^2*c^2-2*c^4)*a^4+(b^2-c^2)*(3*b^4-2*b^2*c^2+c^4)*a^2-(b^2-c^2)^3*b^2)*((b^2-c^2)*a^10-4*(b^4-c^4)*a^8+(6*b^6-6*c^6+b^2*c^2*(3*b^2-c^2))*a^6-(b^2-c^2)*(4*b^6+4*c^6+b^2*c^2*(5*b^2+3*c^2))*a^4+(b^4-c^4)*(b^2-c^2)*(b^4-b^2*c^2-c^4)*a^2+(b^2-c^2)^4*b^2*c^2)*((b^2-c^2)*a^10-4*(b^4-c^4)*a^8+(6*b^6-6*c^6+b^2*c^2*(b^2-3*c^2))*a^6-(b^2-c^2)*(4*b^6+4*c^6+b^2*c^2*(3*b^2+5*c^2))*a^4+(b^4-c^4)*(b^2-c^2)*(b^4+b^2*c^2-c^4)*a^2-(b^2-c^2)^4*b^2*c^2) : :

X(60837) lies on these lines: {13450, 45195}, {42466, 56272}

X(60837) = X(45195)-reciprocal conjugate of-X(43988)
X(60837) = barycentric quotient X(45195)/X(43988)

X(60838) = ( X(4), X(3) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(5)

Barycentrics    (-a^2+b^2+c^2)^2*(a^4-2*b^2*a^2+(b^2-c^2)^2)*(a^4-2*c^2*a^2+(b^2-c^2)^2)*((b^2-c^2)*a^6-(2*b^4+3*b^2*c^2-3*c^4)*a^4+(b^2-c^2)*(b^4-2*b^2*c^2+3*c^4)*a^2-(b^2-c^2)^3*c^2)*((b^2-c^2)*a^6-(3*b^4-3*b^2*c^2-2*c^4)*a^4+(b^2-c^2)*(3*b^4-2*b^2*c^2+c^4)*a^2-(b^2-c^2)^3*b^2) : :

X(60838) lies on these lines: {5, 45195}, {68, 44715}, {5392, 15318}, {42466, 56272}

X(60838) = X(45195)-reciprocal conjugate of-X(11547)
X(60838) = barycentric product X(45195)*X(52350)
X(60838) = barycentric quotient X(45195)/X(11547)

X(60839) = ( X(6), X(3) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(3)

Barycentrics    a^2*(a^2+b^2-3*c^2)*(a^2-3*b^2+c^2)*(-a^2+b^2+c^2)^2 : :

X(60839) lies on these lines: {2, 1975}, {3, 6391}, {39, 53059}, {64, 56437}, {69, 56339}, {235, 5203}, {394, 22401}, {683, 57518}, {1073, 36212}, {1217, 34208}, {1297, 3565}, {1593, 9737}, {2936, 20993}, {3053, 5866}, {4558, 5023}, {6390, 14376}, {6464, 47421}, {8681, 40321}, {9723, 15815}, {11479, 14489}, {14961, 52041}, {17974, 35602}, {18876, 23115}, {20580, 53173}, {35136, 54973}, {40322, 47430}, {40697, 59546}, {43705, 57688}

X(60839) = isogonal conjugate of the polar conjugate of X(6340)
X(60839) = isotomic conjugate of X(21447)
X(60839) = cevapoint of X(3269) and X(52613)
X(60839) = cross-difference of every pair of points on the line X(8651)X(57071)
X(60839) = crosssum of X(6388) and X(57071)
X(60839) = X(i)-Ceva conjugate of-X(j) for these (i, j): (6340, 6391), (6391, 394)
X(60839) = X(i)-cross conjugate of-X(j) for these (i, j): (3964, 394), (20975, 3265)
X(60839) = X(i)-Dao conjugate of-X(j) for these (i, j): (2, 21447), (6, 6353), (125, 57071), (1147, 3053), (6337, 54412), (6338, 57518), (6503, 193), (15261, 2207), (22391, 19118), (35071, 3566), (37867, 3167)
X(60839) = X(i)-isoconjugate of-X(j) for these {i, j}: {19, 6353}, {31, 21447}, {92, 19118}, {158, 3053}, {162, 57071}, {193, 1096}, {393, 1707}, {823, 8651}, {1973, 54412}, {2207, 18156}, {3167, 6520}, {3566, 24019}, {4028, 5317}, {6388, 24000}, {8747, 21874}, {17876, 23964}, {23999, 47430}
X(60839) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (2, 21447), (3, 6353), (69, 54412), (184, 19118), (255, 1707), (326, 18156), (394, 193), (520, 3566), (577, 3053), (647, 57071), (1092, 3167), (1804, 17081), (2632, 17876), (2996, 2052), (3269, 6388), (3565, 107), (3682, 4028), (3917, 41584), (3926, 57518), (3964, 6337), (3990, 21874), (4091, 3798), (5562, 41588), (6340, 264), (6391, 4), (8769, 158), (8770, 393), (10607, 439), (14248, 6524), (20975, 5139), (22401, 40326), (26922, 8940), (27364, 13450), (34208, 1093), (35136, 6528), (38252, 1096), (39201, 8651), (40319, 25), (45199, 235), (51386, 51374), (53059, 2207), (55549, 56891), (60834, 9307)
X(60839) = pole of the line {394, 40319} with respect to the Jerabek circumhyperbola
X(60839) = pole of the line {3053, 6353} with respect to the Stammler hyperbola
X(60839) = pole of the line {193, 21447} with respect to the Steiner-Wallace hyperbola
X(60839) = barycentric product X(i)*X(j) for these {i, j}: {3, 6340}, {69, 6391}, {305, 40319}, {326, 8769}, {394, 2996}, {520, 35136}, {1975, 60834}, {3265, 3565}, {3926, 8770}, {3964, 34208}, {4176, 14248}, {10607, 57857}, {45199, 57800}
X(60839) = trilinear product X(i)*X(j) for these {i, j}: {48, 6340}, {63, 6391}, {255, 2996}, {304, 40319}, {326, 8770}, {394, 8769}, {822, 35136}, {1102, 14248}, {1958, 60834}, {3565, 24018}, {3926, 38252}, {6507, 34208}
X(60839) = trilinear quotient X(i)/X(j) for these (i, j): (48, 19118), (63, 6353), (75, 21447), (255, 3053), (304, 54412), (326, 193), (394, 1707), (656, 57071), (822, 8651), (1102, 6337), (2632, 6388), (2996, 158), (3565, 24019), (3682, 21874), (3708, 5139), (3926, 18156), (3998, 4028), (4131, 3798), (6340, 92), (6391, 19)
X(60839) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (3, 6391, 40319), (3, 6461, 10607), (5013, 6337, 59211)

X(60840) = ( X(3), X(6) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(32)

Barycentrics    a^2*(a^4+b^4-c^4)*(a^4-b^4+c^4)*(a^6+(b^2-c^2)*a^4-(b^2-c^2)^2*a^2-(b^4-c^4)*(b^2+c^2))*(a^6-(b^2-c^2)*a^4-(b^2-c^2)^2*a^2+(b^4-c^4)*(b^2+c^2)) : :

X(60840) lies on these lines: {6, 14376}, {32, 60495}, {83, 26209}, {1974, 2353}, {2207, 13854}, {13575, 56344}, {34207, 46288}

X(60840) = X(i)-isoconjugate of-X(j) for these {i, j}: {22, 21582}, {159, 20641}, {315, 18596}, {1370, 1760}, {4123, 18629}
X(60840) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (2156, 21582), (2353, 1370), (13575, 40073), (20975, 53822), (34207, 315), (40144, 17907), (40146, 159), (52041, 34254), (56008, 55225), (60495, 28419)
X(60840) = barycentric product X(i)*X(j) for these {i, j}: {66, 34207}, {2353, 13575}, {13854, 52041}, {14376, 40144}, {40009, 40146}, {52583, 60495}
X(60840) = trilinear product X(i)*X(j) for these {i, j}: {2156, 34207}, {39733, 40146}
X(60840) = trilinear quotient X(i)/X(j) for these (i, j): (66, 21582), (2156, 1370), (2353, 18596), (3708, 53822), (13575, 20641), (34207, 1760), (39733, 40073)

X(60841) = ( X(6), X(4) )-BICEVIAN CONIC CHORDAL PERSPECTOR OF-X(4)

Barycentrics    ((b^2-c^2)*a^6-(2*b^4-b^2*c^2-2*c^4)*a^4+(b^4-c^4)*(b^2+c^2)*a^2-(b^2-c^2)^2*b^2*c^2)*((b^2-c^2)*a^6-(2*b^4+b^2*c^2-2*c^4)*a^4+(b^4-c^4)*(b^2+c^2)*a^2+(b^2-c^2)^2*b^2*c^2)*(a^2+b^2-c^2)^2*(a^2-b^2+c^2)^2/a^2 : :

X(60841) lies on the Kiepert hyperbola and these lines: {2, 9291}, {4, 35709}, {262, 14249}, {264, 9290}, {275, 1988}, {13380, 21447}, {13599, 30258}, {15352, 38297}, {40448, 40800}

X(60841) = cevapoint of X(3269) and X(14618)
X(60841) = X(43710)-Ceva conjugate of-X(2052)
X(60841) = X(i)-cross conjugate of-X(j) for these (i, j): (43710, 60819), (52249, 264)
X(60841) = X(i)-Dao conjugate of-X(j) for these (i, j): (1249, 6638), (6523, 32445)
X(60841) = X(i)-isoconjugate of-X(j) for these {i, j}: {48, 6638}, {255, 32445}, {3164, 52430}, {3168, 4100}, {9247, 57008}
X(60841) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (4, 6638), (264, 57008), (393, 32445), (1093, 3168), (1988, 577), (2052, 3164), (8884, 26887), (13450, 42453), (40800, 1092), (43710, 3), (54114, 394), (60819, 69)
X(60841) = touchpoint of Kiepert circumhyperbola and line {27360, 60841}
X(60841) = pole of the the tripolar of X(6638) with respect to the polar circle
X(60841) = barycentric product X(i)*X(j) for these {i, j}: {4, 60819}, {264, 43710}, {1988, 18027}, {2052, 54114}
X(60841) = trilinear product X(i)*X(j) for these {i, j}: {19, 60819}, {92, 43710}, {158, 54114}, {1988, 57806}, {6521, 40800}
X(60841) = trilinear quotient X(i)/X(j) for these (i, j): (92, 6638), (158, 32445), (1969, 57008), (1988, 52430), (6521, 3168), (40800, 4100), (43710, 48), (54114, 255), (57806, 3164)

X(60842) = X(55)-PEDAL CIRCLE CHORDAL PERSPECTOR OF-X(55)

Barycentrics    (-a+b+c)^2*(a^4+2*(b-c)*a^3-4*b*c*a^2+2*(b-c)*(b^2-b*c-c^2)*a+(b^2-c^2)*(b-c)^2)*(a^4-2*(b-c)*a^3-4*b*c*a^2+2*(b-c)*(b^2+b*c-c^2)*a-(b^2-c^2)*(b-c)^2) : :

X(60842) lies on these lines: {942, 5880}, {14547, 28125}, {38007, 42447}

X(60842) = isogonal conjugate of X(38900)
X(60842) = cevapoint of X(6607) and X(43959)

X(60843) = X(56)-PEDAL CIRCLE CHORDAL PERSPECTOR OF-X(56)

Barycentrics    (a^5-(b+c)*a^4-2*(b-c)^2*a^3+2*(b^3-c^3)*a^2+(b^2-c^2)*(b^2-4*b*c+c^2)*a-(b^2-c^2)^2*(b-c))*(a^5-(b+c)*a^4-2*(b-c)^2*a^3-2*(b^3-c^3)*a^2-(b^2-c^2)*(b^2-4*b*c+c^2)*a+(b^2-c^2)^2*(b-c)) : :

X(60843) lies on these lines: {517, 6256}, {859, 40293}, {945, 2829}, {953, 37002}, {3086, 10428}, {38008, 42448}

X(60843) = isotomic conjugate of the anticomplement of X(34543)
X(60843) = isogonal conjugate of X(38901)
X(60843) = X(34543)-cross conjugate of-X(2)
X(60843) = perspector of the inconic with center X(34543)

X(60844) = X(11)X(660)∩X(80)X(4876)

Barycentrics    (b^2 - a*c)*(a*b - c^2)*(a^5 - a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - a^4*c - a^3*b*c + b^4*c + 2*a^3*c^2 + 2*a*b^2*c^2 - b^3*c^2 - 2*a^2*c^3 - b^2*c^3 + b*c^4) : :

X(60844) lies on the cubic KI051 and these lines: {11, 660}, {80, 4876}, {83, 14665}, {291, 32857}, {295, 9470}, {516, 14200}, {908, 7077}, {1916, 5992}, {4518, 32850}, {9599, 52656}, {17777, 36801}

X(60845) = X(7)X(3025)∩X(11)X(655)

Barycentrics    (a^2 - a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^5 - a^3*b^2 - a^2*b^3 + b^5 - a^3*b*c + 2*a^2*b^2*c + 2*a*b^3*c - 3*b^4*c - a^3*c^2 + 2*a^2*b*c^2 - 4*a*b^2*c^2 + 2*b^3*c^2 - a^2*c^3 + 2*a*b*c^3 + 2*b^2*c^3 - 3*b*c^4 + c^5) : :

X(60845) lies on the cubic KI051 and these lines: {7, 3025}, {11, 655}, {55, 2222}, {80, 517}, {516, 14204}, {528, 51562}, {672, 2161}, {901, 19628}, {953, 5397}, {1155, 2006}, {1807, 9629}, {1836, 14628}, {2099, 34232}, {3245, 56419}, {5057, 18359}, {5087, 52351}, {5172, 5961}, {5219, 34464}, {5719, 53809}, {7982, 58739}, {12701, 59283}, {13756, 30305}, {17777, 36804}, {19642, 47318}, {37798, 51881}

X(60845) = {X(51886),X(56691)}-harmonic conjugate of X(38954)

X(60846) = X(1)X(6)∩X(105)X(165)

Barycentrics    a*(5*a^2 - 2*a*b + b^2 - 2*a*c - 6*b*c + c^2) : :
X(60846) = X[1] + 4 X[8692], 3 X[1] - 2 X[15600], X[1] + 2 X[15601], X[3973] - 4 X[8692], 3 X[3973] + 2 X[15600], X[3973] + 2 X[35227], 6 X[8692] + X[15600], 2 X[8692] + X[35227], X[15600] + 3 X[15601], X[15600] - 3 X[35227], 3 X[4859] - 2 X[7613], X[7613] - 3 X[16020]

Source: HG251023

X(60846) lies on these lines: {1, 6}, {3, 11506}, {10, 37024}, {31, 10582}, {55, 23511}, {56, 5666}, {63, 3315}, {100, 54390}, {105, 165}, {145, 25101}, {200, 748}, {269, 7677}, {387, 51724}, {390, 3008}, {516, 4859}, {519, 10005}, {614, 4414}, {1125, 4307}, {1420, 6180}, {1471, 12560}, {1621, 2999}, {1707, 10980}, {1721, 24644}, {1722, 53053}, {1742, 7963}, {2263, 51302}, {2550, 31183}, {2725, 59117}, {2975, 25731}, {3052, 5437}, {3158, 37679}, {3161, 39567}, {3241, 4924}, {3361, 28017}, {3576, 46943}, {3616, 3664}, {3646, 5266}, {3663, 52653}, {3677, 3683}, {3685, 17151}, {3744, 7308}, {3749, 8580}, {3755, 47357}, {3811, 8951}, {3883, 17284}, {3886, 16833}, {3923, 51060}, {3929, 17597}, {3961, 30393}, {4310, 51090}, {4328, 8543}, {4334, 13462}, {4344, 29571}, {4383, 10389}, {4402, 4779}, {4422, 4901}, {4423, 5269}, {4640, 5573}, {4641, 44841}, {4666, 17127}, {4862, 5698}, {4888, 38053}, {4902, 17768}, {4929, 27549}, {5211, 59779}, {5250, 54315}, {5263, 16832}, {5281, 45204}, {5284, 9347}, {5853, 37650}, {7292, 35258}, {8236, 37681}, {8245, 30389}, {8299, 16569}, {8583, 25880}, {9580, 24789}, {9623, 40091}, {9778, 24175}, {9819, 60353}, {11512, 16192}, {11712, 51766}, {12526, 28082}, {13329, 43166}, {13576, 31200}, {15803, 51687}, {16602, 21000}, {16610, 35445}, {16688, 20470}, {16823, 25590}, {16948, 17207}, {17063, 53056}, {17265, 28566}, {17337, 38200}, {17338, 49704}, {17349, 49451}, {17716, 39958}, {17724, 31142}, {17889, 50865}, {18229, 32942}, {19875, 48810}, {24248, 50836}, {24295, 48851}, {24695, 59372}, {25055, 50092}, {25072, 39587}, {26685, 49466}, {29573, 51192}, {30282, 49997}, {30350, 32913}, {30392, 47623}, {31312, 50302}, {32922, 55998}, {38025, 50294}, {39251, 40131}, {41313, 51147}

X(60846) = midpoint of X(i) and X(j) for these {i,j}: {1, 3973}, {3161, 39567}, {4402, 4779}, {15601, 35227}
X(60846) = reflection of X(i) in X(j) for these {i,j}: {1, 35227}, {3973, 15601}, {4859, 16020}, {15601, 8692}
X(60846) = X(60666)-Ceva conjugate of X(1)
X(60846) = barycentric product X(1)*X(24599)
X(60846) = barycentric quotient X(24599)/X(75)
X(60846) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 238, 1743}, {1, 16469, 16667}, {6, 38316, 1}, {9, 1279, 1}, {165, 5272, 8056}, {392, 16485, 1}, {1001, 3246, 7290}, {1001, 7290, 1}, {1191, 5436, 1}, {1707, 29820, 10980}, {3247, 38315, 1}, {3749, 17123, 8580}, {5272, 8616, 165}, {7987, 21214, 7963}, {8692, 35227, 3973}, {15485, 16487, 3731}, {16475, 16484, 1}, {27549, 49771, 4929}

X(60847) = X(1)X(6)∩X(105)X(165)

Barycentrics    a^2*(a^2 - b^2 - 2*b*c - c^2 + 2*S)^2 : :
X(60847) = (1 + Cos[A] - Sin[A])^2 : :

X(60847) lies on these lines: {1, 19000}, {3, 6213}, {9, 55}, {21, 13454}, {37, 44590}, {44, 44591}, {100, 30413}, {218, 5416}, {219, 5414}, {255, 606}, {405, 7090}, {1295, 6135}, {1486, 45417}, {1584, 55397}, {1617, 6203}, {1621, 30412}, {1743, 18999}, {1804, 3084}, {2066, 55432}, {2323, 19037}, {3271, 45471}, {3295, 30556}, {3688, 45470}, {4640, 13360}, {5248, 31595}, {5393, 13887}, {5584, 51957}, {5687, 14121}, {6204, 37541}, {6212, 10306}, {7133, 40937}, {8715, 31594}, {10310, 32556}, {11398, 55430}, {11496, 31562}, {11497, 40910}, {11500, 31561}, {13389, 55577}

X(60847) = isogonal conjugate of X(13459)
X(60847) = isogonal conjugate of the isotomic conjugate of X(13458)
X(60847) = X(3084)-Ceva conjugate of X(1335)
X(60847) = X(i)-isoconjugate of X(j) for these (i,j): {1, 13459}, {2, 13460}, {34, 13386}, {57, 1336}, {269, 13426}, {273, 34125}, {278, 6212}, {279, 13427}, {393, 52419}, {608, 46744}, {1096, 13453}, {1118, 3083}, {3676, 6136}, {6364, 36127}, {13390, 16232}, {13424, 13438}
X(60847) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 13459}, {5452, 1336}, {6503, 13453}, {6600, 13426}, {11517, 13386}, {32664, 13460}, {54017, 23989}
X(60847) = barycentric product X(i)*X(j) for these {i,j}: {6, 13458}, {8, 1335}, {9, 3084}, {33, 55387}, {55, 5391}, {78, 6213}, {200, 52420}, {212, 46745}, {219, 13387}, {220, 13436}, {312, 606}, {326, 13456}, {345, 34121}, {394, 13454}, {644, 6365}, {1123, 1259}, {5414, 56386}, {6065, 22106}, {30557, 30557}
X(60847) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 13459}, {31, 13460}, {55, 1336}, {78, 46744}, {212, 6212}, {219, 13386}, {220, 13426}, {255, 52419}, {394, 13453}, {606, 57}, {1253, 13427}, {1259, 1267}, {1335, 7}, {1364, 22107}, {2289, 3083}, {3084, 85}, {5391, 6063}, {5414, 13390}, {6056, 1124}, {6135, 54240}, {6213, 273}, {6365, 24002}, {13387, 331}, {13436, 57792}, {13454, 2052}, {13456, 158}, {13458, 76}, {34121, 278}, {36054, 6364}, {46745, 57787}, {52420, 1088}, {52425, 34125}, {53066, 16232}, {55387, 7182}

X(60848) = X(1)X(18999)∩X(9)X(55)

Barycentrics    a^2*(a^2 - b^2 - 2*b*c - c^2 - 2*S)^2 : :
X(60848) = (1 + Cos[A] + Sin[A])^2 : :

X(60848) lies on these lines: {1, 18999}, {3, 6212}, {9, 55}, {21, 13426}, {37, 44591}, {44, 44590}, {100, 30412}, {218, 5415}, {219, 2066}, {255, 605}, {405, 14121}, {1295, 6136}, {1486, 45416}, {1583, 55398}, {1617, 6204}, {1621, 30413}, {1743, 19000}, {1804, 3083}, {2323, 19038}, {3271, 45470}, {3295, 30557}, {3688, 45471}, {4640, 13359}, {5248, 31594}, {5405, 13940}, {5414, 55432}, {5584, 51955}, {5687, 7090}, {6203, 37541}, {6213, 10306}, {6913, 44038}, {8715, 31595}, {10310, 32555}, {11398, 55431}, {11496, 31561}, {11498, 40910}, {11500, 31562}, {13388, 55579}, {31438, 54322}, {40937, 42013}

X(60848) = isogonal conjugate of X(13437)
X(60848) = isogonal conjugate of the isotomic conjugate of X(13425)
X(60848) = X(3083)-Ceva conjugate of X(1124)
X(60848) = X(i)-isoconjugate of X(j) for these (i,j): {1, 13437}, {2, 13438}, {34, 13387}, {57, 1123}, {269, 13454}, {273, 34121}, {278, 6213}, {279, 13456}, {393, 52420}, {608, 46745}, {1096, 13436}, {1118, 3084}, {1659, 2362}, {3676, 6135}, {6365, 36127}, {13435, 13460}
X(60848) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 13437}, {5452, 1123}, {6503, 13436}, {6600, 13454}, {11517, 13387}, {32664, 13438}, {54019, 23989}
X(60848) = barycentric product X(i)*X(j) for these {i,j}: {6, 13425}, {8, 1124}, {9, 3083}, {33, 55388}, {55, 1267}, {78, 6212}, {200, 52419}, {212, 46744}, {219, 13386}, {220, 13453}, {312, 605}, {326, 13427}, {345, 34125}, {394, 13426}, {644, 6364}, {1259, 1336}, {2066, 56385}, {6065, 22107}, {30556, 30556}
X(60848) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 13437}, {31, 13438}, {55, 1123}, {78, 46745}, {212, 6213}, {219, 13387}, {220, 13454}, {255, 52420}, {394, 13436}, {605, 57}, {1124, 7}, {1253, 13456}, {1259, 5391}, {1267, 6063}, {1364, 22106}, {2066, 1659}, {2289, 3084}, {3083, 85}, {6056, 1335}, {6136, 54240}, {6212, 273}, {6364, 24002}, {13386, 331}, {13425, 76}, {13426, 2052}, {13427, 158}, {13453, 57792}, {34125, 278}, {36054, 6365}, {46744, 57787}, {52419, 1088}, {52425, 34121}, {53065, 2362}, {55388, 7182}

X(60849) = X(1)X(371)∩X(25)X(31)

Barycentrics    a^2*(a^2 + 2*a*b + b^2 - c^2 - 2*S)*(a^2 - b^2 + 2*a*c + c^2 - 2*S) : :
X(60849) = Sin[A]^2/(-1 + Cot[A/2]) : :

X(60849) lies on the conic {{A,B,C,X(1),X(6)}} and these lines: {1, 371}, {6, 34125}, {19, 5412}, {25, 31}, {34, 13460}, {56, 53064}, {58, 6502}, {86, 13390}, {106, 54016}, {198, 53066}, {573, 5414}, {605, 2260}, {606, 2183}, {607, 5410}, {1220, 14121}, {1707, 6203}, {1880, 8576}, {1950, 3156}, {1973, 6424}, {2297, 31438}, {2334, 18996}, {2362, 7713}, {5413, 52413}, {6213, 35764}, {8736, 52286}, {13389, 56328}, {24220, 30380}, {58838, 60580}

X(60849) = isogonal conjugate of X(56386)
X(60849) =isogonal conjugate of the anticomplement of X(5405)
X(60849) =isogonal conjugate of the isotomic conjugate of X(13390)
X(60849) =polar conjugate of the isotomic conjugate of X(6502)
X(60849) =X(13390)-Ceva conjugate of X(6502)
X(60849) =X(i)-isoconjugate of X(j) for these (i,j): {1, 56386}, {2, 30557}, {8, 13388}, {63, 7090}, {69, 7133}, {75, 5414}, {76, 53066}, {78, 1659}, {100, 54017}, {312, 2067}, {321, 1805}, {345, 2362}, {1332, 58840}, {2066, 46745}, {3084, 14121}, {3596, 53063}, {5391, 42013}, {6213, 56385}, {13387, 30556}, {13458, 16232}, {15889, 31534}, {15892, 31548}, {34907, 46421}, {35518, 54018}
X(60849) =X(i)-Dao conjugate of X(j) for these (i,j): {3, 56386}, {206, 5414}, {3162, 7090}, {8054, 54017}, {13388, 304}, {32664, 30557}
X(60849) =crossdifference of every pair of points on line {6332, 54017}
X(60849) =barycentric product X(i)*X(j) for these {i,j}: {1, 16232}, {4, 6502}, {6, 13390}, {19, 13389}, {34, 30556}, {56, 14121}, {57, 42013}, {92, 53064}, {109, 58838}, {225, 1806}, {273, 53065}, {278, 2066}, {514, 54016}, {608, 56385}, {1336, 2067}, {1659, 34125}, {2362, 6212}, {5414, 13459}, {13460, 30557}, {32674, 54019}
X(60849) =barycentric quotient X(i)/X(j) for these {i,j}: {6, 56386}, {25, 7090}, {31, 30557}, {32, 5414}, {560, 53066}, {604, 13388}, {608, 1659}, {649, 54017}, {1395, 2362}, {1397, 2067}, {1806, 332}, {1973, 7133}, {2066, 345}, {2067, 5391}, {2206, 1805}, {2362, 46745}, {5414, 13458}, {6502, 69}, {13389, 304}, {13390, 76}, {14121, 3596}, {16232, 75}, {30556, 3718}, {34125, 56385}, {42013, 312}, {53063, 3084}, {53064, 63}, {53065, 78}, {54016, 190}, {56385, 57919}, {58838, 35519}

X(60850) = X(1)X(372)∩X(25)X(31)

Barycentrics    a^2*(a^2 + 2*a*b + b^2 - c^2 + 2*S)*(a^2 - b^2 + 2*a*c + c^2 + 2*S) : :
X(60850) = Sin[A]^2/(1 + Cot[A/2]) : :

X(60850) lies on the conic {{A,B,C,X(1),X(6)}} and these lines: {1, 372}, {6, 34121}, {19, 5413}, {25, 31}, {34, 13438}, {56, 53063}, {58, 2067}, {86, 1659}, {106, 54018}, {198, 53065}, {573, 2066}, {605, 2183}, {606, 2260}, {607, 5411}, {1220, 7090}, {1707, 6204}, {1880, 8577}, {1950, 3155}, {1973, 6423}, {2334, 18995}, {5412, 52413}, {6212, 35765}, {7713, 16232}, {8736, 52287}, {13388, 56328}, {24220, 30381}, {58840, 60580}

X(60850) = isogonal conjugate of X(56385)
on ABCIK
X(60850) = isogonal conjugate of the anticomplement of X(5393)
X(60850) = isogonal conjugate of the isotomic conjugate of X(1659)
X(60850) = polar conjugate of the isotomic conjugate of X(2067)
X(60850) = X(1659)-Ceva conjugate of X(2067)
X(60850) = X(i)-isoconjugate of X(j) for these (i,j): {1, 56385}, {2, 30556}, {8, 13389}, {63, 14121}, {69, 42013}, {75, 2066}, {76, 53065}, {78, 13390}, {100, 54019}, {312, 6502}, {321, 1806}, {345, 16232}, {1267, 7133}, {1332, 58838}, {2362, 13425}, {3083, 7090}, {3596, 53064}, {5414, 46744}, {6212, 56386}, {13386, 30557}, {15890, 31535}, {15891, 31547}, {34908, 46422}, {35518, 54016}
X(60850) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 56385}, {206, 2066}, {3162, 14121}, {8054, 54019}, {13389, 304}, {32664, 30556}
X(60850) = crossdifference of every pair of points on line {6332, 54019}
X(60850) = barycentric product X(i)*X(j) for these {i,j}: {1, 2362}, {4, 2067}, {6, 1659}, {19, 13388}, {34, 30557}, {56, 7090}, {57, 7133}, {92, 53063}, {109, 58840}, {225, 1805}, {273, 53066}, {278, 5414}, {514, 54018}, {608, 56386}, {1123, 6502}, {2066, 13437}, {6213, 16232}, {13390, 34121}, {13438, 30556}, {32674, 54017}
X(60850) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 56385}, {25, 14121}, {31, 30556}, {32, 2066}, {560, 53065}, {604, 13389}, {608, 13390}, {649, 54019}, {1395, 16232}, {1397, 6502}, {1659, 76}, {1805, 332}, {1973, 42013}, {2066, 13425}, {2067, 69}, {2206, 1806}, {2362, 75}, {5414, 345}, {6502, 1267}, {7090, 3596}, {7133, 312}, {13388, 304}, {16232, 46744}, {30557, 3718}, {34121, 56386}, {53063, 63}, {53064, 3083}, {53066, 78}, {54018, 190}, {56386, 57919}, {58840, 35519}

X(60851) = X(1)X(7348)∩X(25)X(41)

Barycentrics    a^2*((a - b - c)*(a + b - c) - 2*S)*((a - b - c)*(a - b + c) - 2*S) : :
X(60851) = (1 + Cos[A])*Sin[A]/(1 + Cot[A/2]) : :

X(60851) lies on these lines: {1, 7348}, {6, 34121}, {9, 2066}, {19, 5412}, {25, 41}, {31, 6424}, {33, 13427}, {55, 53065}, {57, 2067}, {284, 5414}, {333, 7090}, {371, 1707}, {608, 5410}, {673, 1659}, {1436, 19000}, {1951, 3156}, {2164, 44590}, {2259, 5416}, {2291, 54018}, {2339, 30557}, {6212, 35764}, {8576, 40974}, {8735, 52286}, {13388, 39273}, {58840, 60573}

X(60851) = isogonal conjugate of the isotomic conjugate of X(7090)
X(60851) = polar conjugate of the isotomic conjugate of X(5414)
X(60851) = X(7090)-Ceva conjugate of X(5414)
X(60851) = X(i)-isoconjugate of X(j) for these (i,j): {2, 13389}, {7, 30556}, {57, 56385}, {63, 13390}, {69, 16232}, {75, 6502}, {76, 53064}, {77, 14121}, {85, 2066}, {348, 42013}, {651, 54019}, {1267, 2362}, {1441, 1806}, {1659, 3083}, {2067, 46744}, {6063, 53065}, {6516, 58838}, {7090, 52419}, {7133, 13453}, {13386, 13388}, {15413, 54016}, {31535, 34216}
X(60851) = X(i)-Dao conjugate of X(j) for these (i,j): {206, 6502}, {3162, 13390}, {5452, 56385}, {13389, 7182}, {32664, 13389}, {38991, 54019}
X(60851) = crossdifference of every pair of points on line {4025, 30193}
X(60851) = barycentric product X(i)*X(j) for these {i,j}: {1, 7133}, {4, 5414}, {6, 7090}, {9, 2362}, {19, 30557}, {25, 56386}, {33, 13388}, {55, 1659}, {92, 53066}, {101, 58840}, {281, 2067}, {318, 53063}, {522, 54018}, {1123, 2066}, {1805, 1826}, {6213, 42013}, {6502, 13454}, {8750, 54017}, {13389, 13456}, {14121, 34121}, {15891, 46378}, {34909, 48308}
X(60851) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 13390}, {31, 13389}, {32, 6502}, {41, 30556}, {55, 56385}, {560, 53064}, {607, 14121}, {663, 54019}, {1659, 6063}, {1805, 17206}, {1973, 16232}, {2066, 1267}, {2067, 348}, {2175, 2066}, {2212, 42013}, {2362, 85}, {5414, 69}, {6502, 13453}, {7090, 76}, {7133, 75}, {9447, 53065}, {13388, 7182}, {30557, 304}, {42013, 46744}, {53063, 77}, {53064, 52419}, {53065, 3083}, {53066, 63}, {54018, 664}, {56386, 305}, {57657, 1806}, {58840, 3261}

X(60852) = X(1)X(7347)∩X(25)X(41)

Barycentrics    a^2*((a - b - c)*(a + b - c) + 2*S)*((a - b - c)*(a - b + c) + 2*S) : :
X(60852) = (1 + Cos[A])*Sin[A]/(1 - Cot[A/2]) : :

X(60852) lies on these lines: {1, 7347}, {6, 34125}, {9, 5414}, {19, 5413}, {25, 41}, {31, 6423}, {33, 13456}, {55, 53066}, {57, 6502}, {284, 2066}, {333, 14121}, {372, 1707}, {608, 5411}, {673, 13390}, {1436, 18999}, {1951, 3155}, {2164, 44591}, {2259, 5415}, {2291, 54016}, {2339, 30556}, {6213, 35765}, {8577, 40974}, {8735, 52287}, {13389, 39273}, {58838, 60573}

X(60852) = isogonal conjugate of the isotomic conjugate of X(14121)
X(60852) = polar conjugate of the isotomic conjugate of X(2066)
X(60852) = X(14121)-Ceva conjugate of X(2066)
X(60852) = X(i)-isoconjugate of X(j) for these (i,j): {2, 13388}, {7, 30557}, {57, 56386}, {63, 1659}, {69, 2362}, {75, 2067}, {76, 53063}, {77, 7090}, {85, 5414}, {348, 7133}, {651, 54017}, {1441, 1805}, {3084, 13390}, {5391, 16232}, {6063, 53066}, {6502, 46745}, {6516, 58840}, {13387, 13389}, {13436, 42013}, {14121, 52420}, {15413, 54018}, {31534, 34215}
X(60852) = X(i)-Dao conjugate of X(j) for these (i,j): {206, 2067}, {3162, 1659}, {5452, 56386}, {13388, 7182}, {32664, 13388}, {38991, 54017}
X(60852) = crossdifference of every pair of points on line {4025, 54017}
X(60852) = barycentric product X(i)*X(j) for these {i,j}: {1, 42013}, {4, 2066}, {6, 14121}, {9, 16232}, {19, 30556}, {25, 56385}, {33, 13389}, {55, 13390}, {92, 53065}, {101, 58838}, {281, 6502}, {318, 53064}, {522, 54016}, {1336, 5414}, {1806, 1826}, {2067, 13426}, {6212, 7133}, {7090, 34125}, {8750, 54019}, {13388, 13427}, {15892, 46379}, {34910, 48309}
X(60852) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 1659}, {31, 13388}, {32, 2067}, {41, 30557}, {55, 56386}, {560, 53063}, {607, 7090}, {663, 54017}, {1806, 17206}, {1973, 2362}, {2066, 69}, {2067, 13436}, {2175, 5414}, {2212, 7133}, {5414, 5391}, {6502, 348}, {7133, 46745}, {9447, 53066}, {13389, 7182}, {13390, 6063}, {14121, 76}, {16232, 85}, {30556, 304}, {42013, 75}, {53063, 52420}, {53064, 77}, {53065, 63}, {53066, 3084}, {54016, 664}, {56385, 305}, {57657, 1805}, {58838, 3261}

X(60853) = X(2)X(585)∩X(4)X(8)

Barycentrics    b*c*((a - b - c)*(a + b - c) + 2*S)*((a - b - c)*(a - b + c) + 2*S) : :
X(60853) = 1/(1 - Cos[A] - Sin[A]) : :

X(60853) lies on these lines: {2, 585}, {4, 8}, {75, 492}, {312, 14121}, {314, 42013}, {491, 20570}, {3706, 58896}, {6212, 11679}, {13389, 18816}, {13426, 57270}, {13459, 57266}, {16232, 30710}, {18750, 31547}, {30556, 31623}

X(60853) = isogonal conjugate of X(53063)
X(60853) = isotomic conjugate of X(13388)
X(60853) = polar conjugate of X(2362)
X(60853) = isotomic conjugate of the complement of X(13386)
X(60853) = isotomic conjugate of the isogonal conjugate of X(42013)
X(60853) = polar conjugate of the isogonal conjugate of X(30556)
X(60853) = X(i)-isoconjugate of X(j) for these (i,j): {1, 53063}, {6, 2067}, {31, 13388}, {48, 2362}, {56, 5414}, {57, 53066}, {184, 1659}, {603, 7133}, {604, 30557}, {606, 16232}, {1397, 56386}, {1400, 1805}, {1459, 54018}, {6213, 53064}, {6502, 34121}, {7090, 52411}, {32660, 58840}
X(60853) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 5414}, {2, 13388}, {3, 53063}, {9, 2067}, {1249, 2362}, {3161, 30557}, {5452, 53066}, {7952, 7133}, {13388, 222}, {14121, 51841}, {40582, 1805}, {40624, 54017}
X(60853) = cevapoint of X(i) and X(j) for these (i,j): {2, 13386}, {30556, 42013}
X(60853) = trilinear pole of line {4391, 54017}
X(60853) = barycentric product X(i)*X(j) for these {i,j}: {75, 14121}, {76, 42013}, {92, 56385}, {264, 30556}, {312, 13390}, {668, 58838}, {1969, 2066}, {3596, 16232}, {6335, 54019}, {7017, 13389}, {7090, 46744}, {18022, 53065}
X(60853) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2067}, {2, 13388}, {4, 2362}, {6, 53063}, {8, 30557}, {9, 5414}, {21, 1805}, {55, 53066}, {92, 1659}, {281, 7133}, {312, 56386}, {318, 7090}, {1336, 16232}, {1783, 54018}, {1806, 1437}, {2066, 48}, {4391, 54017}, {5414, 606}, {6136, 54016}, {6212, 6502}, {6502, 603}, {7090, 6213}, {7133, 34121}, {13386, 13389}, {13389, 222}, {13390, 57}, {13426, 42013}, {14121, 1}, {15892, 46377}, {16232, 56}, {30556, 3}, {30557, 1335}, {31534, 10253}, {34125, 53064}, {34910, 32556}, {42013, 6}, {44426, 58840}, {53064, 52411}, {53065, 184}, {54016, 1415}, {54017, 6365}, {54019, 905}, {56385, 63}, {56386, 3084}, {58838, 513}

X(60854) = X(2)X(586)∩X(4)X(8)

Barycentrics    b*c*((a - b - c)*(a + b - c) - 2*S)*((a - b - c)*(a - b + c) - 2*S) : :
X(60854) = 1/(1 - Cos[A] + Sin[A]) : :

X(60854) lies on these lines: {2, 586}, {4, 8}, {75, 491}, {312, 7090}, {314, 7133}, {492, 20570}, {2362, 30710}, {3706, 58897}, {6213, 11679}, {13388, 18816}, {13437, 57267}, {13454, 54464}, {18750, 31548}, {30557, 31623}

X(60854) = isogonal conjugate of X(53064)
X(60854) = isotomic conjugate of X(13389)
X(60854) = polar conjugate of X(16232)
X(60854) = isotomic conjugate of the complement of X(13387)
X(60854) = isotomic conjugate of the isogonal conjugate of X(7133)
X(60854) = polar conjugate of the isogonal conjugate of X(30557)
X(60854) = X(i)-isoconjugate of X(j) for these (i,j): {1, 53064}, {6, 6502}, {31, 13389}, {48, 16232}, {56, 2066}, {57, 53065}, {184, 13390}, {603, 42013}, {604, 30556}, {605, 2362}, {1397, 56385}, {1400, 1806}, {1459, 54016}, {2067, 34125}, {6212, 53063}, {14121, 52411}, {32660, 58838}
X(60854) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 2066}, {2, 13389}, {3, 53064}, {9, 6502}, {1249, 16232}, {3161, 30556}, {5452, 53065}, {7090, 51842}, {7952, 42013}, {13389, 222}, {40582, 1806}, {40624, 54019}
X(60854) = cevapoint of X(i) and X(j) for these (i,j): {2, 13387}, {7133, 30557}
X(60854) = trilinear pole of line {4391, 54019}
X(60854) = barycentric product X(i)*X(j) for these {i,j}: {75, 7090}, {76, 7133}, {92, 56386}, {264, 30557}, {312, 1659}, {668, 58840}, {1969, 5414}, {2362, 3596}, {6335, 54017}, {7017, 13388}, {14121, 46745}, {18022, 53066}
X(60854) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 6502}, {2, 13389}, {4, 16232}, {6, 53064}, {8, 30556}, {9, 2066}, {21, 1806}, {55, 53065}, {92, 13390}, {281, 42013}, {312, 56385}, {318, 14121}, {1123, 2362}, {1659, 57}, {1783, 54016}, {1805, 1437}, {2066, 605}, {2067, 603}, {2362, 56}, {4391, 54019}, {5414, 48}, {6135, 54018}, {6213, 2067}, {7090, 1}, {7133, 6}, {13387, 13388}, {13388, 222}, {13454, 7133}, {14121, 6212}, {15891, 46376}, {30556, 1124}, {30557, 3}, {31535, 10252}, {34121, 53063}, {34909, 32555}, {42013, 34125}, {44426, 58838}, {53063, 52411}, {53066, 184}, {54017, 905}, {54018, 1415}, {54019, 6364}, {56385, 3083}, {56386, 63}, {58840, 513}

X(60855) = X(2)X(187)∩X(6)X(76)

Barycentrics    3*b^2*c^2 + 2*a^2*(a^2 + b^2 + c^2) : :

X(60855) lies on these lines: {2, 187}, {4, 5092}, {5, 7846}, {6, 76}, {39, 15301}, {99, 5024}, {115, 7875}, {141, 7812}, {183, 12150}, {262, 35002}, {264, 8744}, {315, 3619}, {373, 35060}, {381, 7919}, {382, 49112}, {384, 574}, {458, 52147}, {597, 47286}, {620, 14036}, {626, 16895}, {671, 5026}, {729, 35566}, {754, 16986}, {1003, 53095}, {1078, 1384}, {1506, 7892}, {1975, 55085}, {2030, 39266}, {2548, 7814}, {2896, 55738}, {3054, 7857}, {3055, 7807}, {3090, 13335}, {3096, 7745}, {3098, 10358}, {3111, 46512}, {3114, 54413}, {3314, 7753}, {3329, 3734}, {3545, 58849}, {3552, 6683}, {3589, 7790}, {3618, 7827}, {3620, 7768}, {3630, 7877}, {3631, 7762}, {3763, 7883}, {3767, 33269}, {3788, 19689}, {3815, 6661}, {3934, 5008}, {4045, 11361}, {4256, 37100}, {5007, 31276}, {5025, 7889}, {5041, 20081}, {5050, 38664}, {5055, 12042}, {5140, 6688}, {5149, 14931}, {5167, 34236}, {5210, 11285}, {5276, 18146}, {5354, 40022}, {5395, 60278}, {5476, 43453}, {5485, 60287}, {5640, 14962}, {5939, 9166}, {6248, 10359}, {6292, 7823}, {6656, 51126}, {6680, 16921}, {6704, 7747}, {7388, 42277}, {7389, 42274}, {7470, 55672}, {7736, 7799}, {7746, 10583}, {7751, 14075}, {7752, 7819}, {7756, 14034}, {7759, 46226}, {7763, 33198}, {7766, 9466}, {7769, 14001}, {7772, 17128}, {7773, 7944}, {7775, 7931}, {7777, 7820}, {7785, 7822}, {7791, 43618}, {7792, 43291}, {7793, 31239}, {7794, 7921}, {7795, 7858}, {7802, 8362}, {7803, 32971}, {7809, 7868}, {7811, 18907}, {7824, 8588}, {7825, 7948}, {7828, 16924}, {7834, 16044}, {7839, 17130}, {7841, 47355}, {7842, 39784}, {7843, 7938}, {7844, 33013}, {7847, 14035}, {7849, 7900}, {7851, 15031}, {7852, 32966}, {7854, 20088}, {7856, 59635}, {7861, 33018}, {7862, 14043}, {7865, 16988}, {7867, 19694}, {7869, 7941}, {7872, 14042}, {7879, 10159}, {7885, 7914}, {7886, 33002}, {7887, 18584}, {7891, 9698}, {7899, 33217}, {7912, 7915}, {7913, 14041}, {7932, 39565}, {7933, 39590}, {7935, 16897}, {8290, 60129}, {8352, 48310}, {8367, 37688}, {8368, 37647}, {8586, 22486}, {8627, 33734}, {9301, 10347}, {9463, 60707}, {9734, 35950}, {10302, 15533}, {10630, 14608}, {10788, 15819}, {10979, 28723}, {10987, 27020}, {11054, 52713}, {11055, 22246}, {11147, 55794}, {11149, 55801}, {11170, 22677}, {11289, 16967}, {11290, 16966}, {11303, 16809}, {11304, 16808}, {11646, 52088}, {12017, 12203}, {12215, 42852}, {12251, 55716}, {13586, 15482}, {14037, 31401}, {14061, 44543}, {14568, 16989}, {14930, 32836}, {15018, 40814}, {15302, 31128}, {15491, 35297}, {15602, 32456}, {15655, 43459}, {16932, 39668}, {17503, 60238}, {17541, 37675}, {18840, 60649}, {18841, 53105}, {18842, 21356}, {19690, 55759}, {22052, 37186}, {22676, 37455}, {31455, 33225}, {31489, 33220}, {32135, 43532}, {32459, 35954}, {32832, 37689}, {32833, 37665}, {36794, 58782}, {39646, 55705}, {40332, 42421}, {41134, 42849}, {41231, 41254}, {41235, 59777}, {42786, 54393}, {44173, 59933}, {52289, 60428}, {53107, 60100}, {53109, 60644}, {54493, 60616}, {54494, 60645}, {54616, 60228}, {54639, 60286}, {60072, 60096}, {60131, 60282}, {60145, 60642}, {60209, 60647}

X(60855) = crossdifference of every pair of points on line {688, 17414}
X(60855) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 316, 7937}, {2, 3972, 7771}, {2, 5475, 7934}, {2, 7737, 7831}, {2, 7804, 3972}, {4, 7859, 7918}, {5, 7846, 7942}, {76, 83, 7878}, {76, 7878, 7894}, {83, 7770, 76}, {115, 7875, 7884}, {141, 7812, 7850}, {141, 53489, 7812}, {384, 7786, 7782}, {384, 7808, 7786}, {598, 7937, 316}, {1506, 7892, 7940}, {2548, 7832, 7814}, {2548, 16898, 7832}, {3096, 7745, 7860}, {3314, 7753, 7926}, {3329, 3734, 7757}, {3589, 8370, 7790}, {3618, 11185, 7827}, {3815, 6661, 7835}, {3934, 7787, 6179}, {5025, 7889, 7943}, {5475, 7934, 48913}, {6292, 7823, 7936}, {6704, 7747, 7876}, {7737, 7831, 11057}, {7747, 7876, 7910}, {7752, 7819, 7930}, {7777, 7820, 7870}, {7785, 7822, 7922}, {7794, 7921, 7949}, {7795, 7858, 7871}, {7868, 15484, 7809}, {7885, 16896, 7914}, {7918, 43527, 7859}, {7926, 47005, 3314}, {10583, 33020, 7746}, {11174, 11286, 99}, {11286, 14535, 11174}, {14041, 16987, 7913}, {51126, 53418, 6656}

X(60856) = X(2)X(7)∩X(6)X(664)

Barycentrics    (a + b - c)*(a - b + c)*(2*a^3 - 3*a^2*b + a*b^2 - 3*a^2*c + a*b*c - b^2*c + a*c^2 - b*c^2) : :

X(60856) lies on the cubic K1359 and these lines: {2, 7}, {6, 664}, {44, 85}, {45, 55082}, {65, 4676}, {77, 17120}, {190, 5228}, {241, 3758}, {347, 51171}, {458, 653}, {1170, 25242}, {1319, 51055}, {1405, 3212}, {1441, 17349}, {1442, 37677}, {1471, 24349}, {1737, 45305}, {2182, 4209}, {2245, 27021}, {2267, 27472}, {2982, 39694}, {3177, 55432}, {3210, 52424}, {3618, 17086}, {3834, 14564}, {4328, 25728}, {4393, 4552}, {4572, 41259}, {4670, 31225}, {4700, 25719}, {4704, 7269}, {5263, 41712}, {5422, 6360}, {5729, 13727}, {6604, 54389}, {7176, 54377}, {7190, 17261}, {9312, 16670}, {11345, 37541}, {17259, 55096}, {17280, 56927}, {17351, 39126}, {17367, 22464}, {17369, 33298}, {17825, 54107}, {20569, 31618}, {28957, 32939}, {34361, 35157}, {37543, 41839}, {37550, 59299}, {40663, 49720}, {51170, 53997}, {52663, 56265}

X(60856) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12848, 17950}, {9, 41246, 26125}, {57, 50127, 40862}, {1944, 8257, 2}

X(60857) = X(2)X(11)∩X(6)X(666)

Barycentrics    (a^2 + b^2 - a*c - b*c)*(a^2 - a*b - b*c + c^2)*(a^3*b - a^2*b^2 + a^3*c + 2*a^2*b*c - a^2*c^2 - 2*b^2*c^2) : :

X(60857) lies on the cubic K1359 and these lines: {1, 46798}, {2, 11}, {6, 666}, {239, 2284}, {2481, 4363}, {3758, 51929}, {5228, 34085}, {14621, 43929}, {36803, 41259}, {36816, 50127}

X(60857) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 56850, 56855}, {673, 6654, 52902}

X(60858) = X(2)X(13)∩X(6)X(23895)

Barycentrics    (3*a^2 + 3*b^2 - 3*c^2 + 2*Sqrt[3]*S)*(3*a^2 - 3*b^2 + 3*c^2 + 2*Sqrt[3]*S)*(a^4 - a^2*b^2 - a^2*c^2 - 2*b^2*c^2 - 2*Sqrt[3]*a^2*S) : :

X(60858) lies on the cubic K1359 and these lines: {2, 13}, {6, 23895}, {62, 43085}, {110, 25233}, {300, 11083}, {458, 36306}, {476, 1316}, {597, 11537}, {598, 36316}, {3972, 41477}, {5611, 14185}, {7804, 54472}, {8836, 14356}, {11092, 56395}, {11119, 16645}, {11127, 35314}, {14389, 32461}, {16030, 51275}, {23896, 43084}, {25234, 35930}

X(60858) = X(2151)-isoconjugate of X(43538)
X(60858) = X(40578)-Dao conjugate of X(43538)
X(60858) = barycentric product X(300)*X(36759)
X(60858) = barycentric quotient X(i)/X(j) for these {i,j}: {13, 43538}, {36759, 15}
X(60858) = {X(2),X(21466)}-harmonic conjugate of X(11078)

X(60859) = X(2)X(14)∩X(6)X(23896)

Barycentrics    (3*a^2 + 3*b^2 - 3*c^2 - 2*Sqrt[3]*S)*(3*a^2 - 3*b^2 + 3*c^2 - 2*Sqrt[3]*S)*(a^4 - a^2*b^2 - a^2*c^2 - 2*b^2*c^2 + 2*Sqrt[3]*a^2*S) : :

X(60859) lies on the cubic K1359 and these lines: {2, 14}, {6, 23896}, {61, 43086}, {110, 25234}, {301, 11088}, {458, 36309}, {476, 1316}, {597, 11549}, {598, 36317}, {3972, 41478}, {5615, 14187}, {7804, 54473}, {8838, 14356}, {11078, 56395}, {11120, 16644}, {11126, 35315}, {14389, 32460}, {16030, 51268}, {23895, 43084}, {25233, 35930}

X(60859) = X(2152)-isoconjugate of X(43539)
X(60859) = X(40579)-Dao conjugate of X(43539)
X(60859) = barycentric product X(301)*X(36760)
X(60859) = barycentric quotient X(i)/X(j) for these {i,j}: {14, 43539}, {36760, 16}
X(60859) = {X(2),X(21467)}-harmonic conjugate of X(11092)

X(60860) = X(2)X(14)∩X(6)X(23896)

Barycentrics    (a^2 + b^2)*(a^2 + c^2)*(a^4 + 2*a^2*b^2 + 2*a^2*c^2 + b^2*c^2) : :

X(60860) lies on the cubics K1013 and K1359 and these lines: {2, 32}, {4, 40163}, {6, 4577}, {69, 40000}, {76, 57421}, {82, 983}, {237, 38908}, {458, 42396}, {597, 52979}, {689, 41259}, {733, 3117}, {827, 34396}, {1501, 7878}, {3329, 41295}, {3618, 41884}, {3763, 40425}, {5012, 14247}, {7760, 33798}, {8928, 14853}, {12212, 59249}, {13519, 52936}, {21010, 36081}, {21512, 51862}, {37184, 39557}, {42299, 43722}

X(60860) = isogonal conjugate of X(59262)
X(60860) = isotomic conjugate of the isogonal conjugate of X(41295)
X(60860) = isogonal conjugate of the isotomic conjugate of X(59249)
X(60860) = X(i)-isoconjugate of X(j) for these (i,j): {1, 59262}, {38, 60667}, {39, 60664}, {75, 59273}, {1930, 60672}, {1964, 42006}, {8061, 43357}
X(60860) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 59262}, {206, 59273}, {41884, 42006}
X(60860) = cevapoint of X(3329) and X(12212)
X(60860) = barycentric product X(i)*X(j) for these {i,j}: {6, 59249}, {75, 51312}, {76, 41295}, {82, 60683}, {83, 3329}, {251, 60707}, {308, 12212}, {689, 14318}, {3112, 60686}, {10007, 52395}, {32085, 60702}, {39685, 51862}
X(60860) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 59262}, {32, 59273}, {82, 60664}, {83, 42006}, {251, 60667}, {827, 43357}, {3329, 141}, {10007, 7794}, {12212, 39}, {14318, 3005}, {41295, 6}, {46288, 60672}, {51312, 1}, {59249, 76}, {60683, 1930}, {60686, 38}, {60702, 3933}, {60707, 8024}
X(60860) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {83, 251, 56976}, {83, 40850, 2}, {20022, 59180, 83}

X(60861) = X(2)X(37)∩X(6)X(668)

Barycentrics    b*c*(-2*a^3 - a*b^2 - a*b*c + b^2*c - a*c^2 + b*c^2) : :

X(60861) lies on the cubic K1359 and these lines: {2, 37}, {6, 668}, {44, 6376}, {45, 18140}, {76, 17369}, {313, 17368}, {314, 17293}, {458, 6335}, {598, 60288}, {646, 17318}, {889, 24289}, {894, 18044}, {995, 49472}, {1100, 17786}, {3264, 17367}, {3589, 3596}, {3758, 52043}, {3770, 5749}, {3809, 46898}, {3948, 17354}, {3963, 17381}, {4033, 4393}, {4110, 4852}, {4266, 29400}, {4277, 26752}, {4370, 18146}, {4422, 30830}, {4494, 29598}, {4670, 20917}, {6381, 50115}, {6386, 41259}, {16525, 40859}, {16666, 24524}, {16669, 59514}, {16777, 30112}, {17053, 40479}, {17230, 30939}, {17313, 30866}, {17335, 59212}, {17349, 56249}, {17350, 18133}, {17379, 18040}, {18135, 54389}, {20174, 59772}, {20331, 30964}, {23659, 31337}, {25101, 58410}, {26039, 34284}, {34282, 48635}, {35544, 53037}

X(60861) = X(649)-isoconjugate of X(59029)
X(60861) = X(5375)-Dao conjugate of X(59029)
X(60861) = crossdifference of every pair of points on line {667, 9297}
X(60861) = barycentric quotient X(100)/X(59029)
X(60861) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 41316, 17790}, {894, 18044, 18144}, {4506, 17382, 75}, {16666, 59519, 24524}, {18046, 29423, 192}, {29388, 29484, 4699}, {29705, 29764, 1278}

X(60862) = X(2)X(98)∩X(6)X(2966)

Barycentrics    (a^4 + b^4 - a^2*c^2 - b^2*c^2)*(a^4 - a^2*b^2 - b^2*c^2 + c^4)*(a^6 - 3*a^4*b^2 + 2*a^2*b^4 - 3*a^4*c^2 - a^2*b^2*c^2 + b^4*c^2 + 2*a^2*c^4 + b^2*c^4) : :

X(60862) lies on the cubic K1359 and these lines: {2, 98}, {6, 2966}, {249, 7771}, {297, 53499}, {458, 685}, {575, 32545}, {597, 34369}, {2080, 53865}, {2395, 30535}, {3329, 47737}, {3618, 52081}, {5034, 39941}, {5038, 14382}, {5050, 47388}, {11174, 41932}, {16989, 36899}, {31489, 40428}, {34396, 43754}, {35906, 59373}, {41259, 43187}, {51171, 51963}, {51224, 58347}

X(60862) = X(i)-isoconjugate of X(j) for these (i,j): {1755, 43532}, {1959, 46316}
X(60862) = X(i)-Dao conjugate of X(j) for these (i,j): {36899, 43532}, {39100, 325}
X(60862) = trilinear pole of line {2080, 59775}
X(60862) = crossdifference of every pair of points on line {3569, 55143}
X(60862) = barycentric product X(i)*X(j) for these {i,j}: {98, 39099}, {183, 53865}, {290, 2080}, {2966, 59775}, {14382, 45146}, {21460, 52145}
X(60862) = barycentric quotient X(i)/X(j) for these {i,j}: {98, 43532}, {1976, 46316}, {2080, 511}, {2966, 53199}, {21460, 5968}, {39099, 325}, {45146, 40810}, {53865, 262}, {59775, 2799}
X(60862) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5967, 287}, {1976, 5967, 40820}

X(60863) = X(2)X(99)∩X(6)X(892)

Barycentrics    (a^2 - b*c)*(a^2 + b*c)*(a^2 + b^2 - 2*c^2)*(a^2 - 2*b^2 + c^2) : :

X(60863) lies on the cubics K553 and K1359 and these lines: {2, 99}, {6, 892}, {32, 40871}, {76, 5108}, {83, 5466}, {182, 48983}, {316, 1648}, {385, 17941}, {597, 17948}, {598, 843}, {691, 1316}, {880, 3978}, {895, 19222}, {1215, 18047}, {1641, 11054}, {3114, 18023}, {3589, 52551}, {3618, 9214}, {4369, 17103}, {5027, 47646}, {5967, 52035}, {5968, 9154}, {6792, 7812}, {7606, 18818}, {7708, 54413}, {7770, 14263}, {7792, 16092}, {7803, 59422}, {7804, 17964}, {7827, 41939}, {7828, 15000}, {7841, 40877}, {8370, 32525}, {9178, 46778}, {10302, 54607}, {10630, 14608}, {10754, 53375}, {11053, 22254}, {11284, 44182}, {11286, 45143}, {11338, 36821}, {17277, 52747}, {22486, 52198}, {24284, 57452}, {32971, 59423}, {34473, 57617}, {37649, 52767}, {39061, 59373}, {40820, 51430}, {41238, 60498}, {41259, 53080}, {41520, 51980}, {45327, 52038}, {47352, 57539}, {51258, 57588}, {57612, 58769}

X(60863) = isogonal conjugate of X(18872)
X(60863) = X(9154)-Ceva conjugate of X(671)
X(60863) = X(i)-isoconjugate of X(j) for these (i,j): {1, 18872}, {187, 1581}, {351, 37134}, {524, 1967}, {694, 896}, {805, 2642}, {881, 24039}, {882, 23889}, {922, 1916}, {1927, 3266}, {1934, 14567}, {9468, 14210}
X(60863) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 18872}, {325, 50567}, {8290, 524}, {8623, 9155}, {15477, 9468}, {15899, 694}, {19576, 187}, {35078, 690}, {39031, 922}, {39043, 896}, {39044, 14210}, {39061, 1916}
X(60863) = cevapoint of X(i) and X(j) for these (i,j): {385, 5026}, {5968, 36821}
X(60863) = trilinear pole of line {385, 804}
X(60863) = barycentric product X(i)*X(j) for these {i,j}: {111, 3978}, {385, 671}, {419, 30786}, {691, 14295}, {804, 892}, {880, 9178}, {895, 17984}, {897, 1966}, {923, 1926}, {1580, 46277}, {1691, 18023}, {1933, 57999}, {5026, 57539}, {5027, 53080}, {5380, 14296}, {5466, 17941}, {5968, 14382}, {5976, 9154}, {12215, 17983}, {14603, 32740}, {16092, 57452}, {18901, 19626}, {31125, 56976}, {36820, 52551}, {46154, 56979}, {51510, 52756}, {52632, 56980}
X(60863) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 18872}, {111, 694}, {385, 524}, {419, 468}, {671, 1916}, {691, 805}, {732, 7813}, {804, 690}, {892, 18829}, {895, 36214}, {897, 1581}, {923, 1967}, {1580, 896}, {1691, 187}, {1933, 922}, {1966, 14210}, {2086, 21906}, {3978, 3266}, {4027, 5026}, {4039, 4062}, {4107, 4750}, {4164, 14419}, {5026, 2482}, {5027, 351}, {5968, 40810}, {5976, 50567}, {8753, 17980}, {9154, 36897}, {9178, 882}, {11183, 1649}, {12215, 6390}, {12829, 5477}, {14295, 35522}, {14382, 52145}, {14602, 14567}, {14908, 17970}, {17941, 5468}, {17964, 52700}, {17984, 44146}, {18023, 18896}, {19626, 8789}, {21460, 45146}, {24284, 14417}, {27982, 7267}, {30786, 40708}, {31125, 56977}, {32729, 17938}, {32740, 9468}, {36085, 37134}, {36213, 9155}, {36820, 14357}, {36821, 47648}, {36827, 46161}, {39495, 44814}, {40820, 5967}, {44089, 44102}, {46154, 56978}, {46277, 1934}, {48983, 38947}, {51430, 5642}, {51510, 14608}, {51980, 14251}, {52450, 47734}, {52632, 56981}, {52940, 39292}, {53681, 4760}, {56976, 52898}, {56980, 5467}, {56982, 23889}, {57452, 52094}
X(60863) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 35606, 99}, {6, 52756, 892}, {11053, 47286, 22254}

X(60864) = X(2)X(353)∩X(6)X(18823)

Barycentrics    (2*a^2 - b^2 - c^2)*(2*a^4 + a^2*b^2 + 2*b^4 - 2*a^2*c^2 - 2*b^2*c^2 - c^4)*(2*a^4 - 2*a^2*b^2 - b^4 + a^2*c^2 - 2*b^2*c^2 + 2*c^4) : :

X(60864) lies on the cubic K1359 and these lines: {2, 353}, {6, 18823}, {141, 9164}, {338, 40826}, {351, 34763}, {523, 597}, {599, 4590}, {1641, 3266}, {1648, 51541}, {1992, 35511}, {2770, 9169}, {5967, 8787}, {10415, 36820}, {20582, 36953}, {46275, 59373}, {47352, 57539}

X(60864) = X(i)-isoconjugate of X(j) for these (i,j): {897, 5104}, {923, 7840}, {9208, 36085}
X(60864) = X(i)-Dao conjugate of X(j) for these (i,j): {2482, 7840}, {6593, 5104}, {38988, 9208}
X(60864) = crossdifference of every pair of points on line {5104, 9208}
X(60864) = barycentric product X(i)*X(j) for these {i,j}: {524, 43535}, {32694, 35522}
X(60864) = barycentric quotient X(i)/X(j) for these {i,j}: {187, 5104}, {351, 9208}, {524, 7840}, {32694, 691}, {43535, 671}

X(60865) = X(2)X(649)∩X(6)X(190)

Barycentrics    (2*a - b - c)*(a^2*b + a*b^2 - a^2*c - b^2*c)*(a^2*b - a^2*c - a*c^2 + b*c^2) : :

X(60865) lies on the cubic K1359 and these lines: {2, 649}, {6, 190}, {44, 24004}, {89, 30964}, {727, 9059}, {902, 4759}, {1252, 6632}, {2384, 8709}, {3240, 18793}, {3758, 57023}, {4672, 24429}, {8851, 11345}, {16704, 55262}, {26685, 27136}, {27494, 35172}, {36872, 57051}, {52900, 60809}

X(60865) = X(i)-isoconjugate of X(j) for these (i,j): {6, 36814}, {88, 3009}, {106, 1575}, {726, 9456}, {903, 21760}, {1463, 2316}, {3257, 6373}, {3837, 32665}, {5376, 52633}, {6336, 20777}, {20785, 36125}, {20908, 32719}
X(60865) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 36814}, {214, 1575}, {4370, 726}, {6544, 21140}, {33678, 903}, {35092, 3837}, {52659, 43040}, {52877, 21830}, {55055, 6373}
X(60865) = cevapoint of X(44) and X(4432)
X(60865) = trilinear pole of line {519, 1960}
X(60865) = crossdifference of every pair of points on line {3009, 6373}
X(60865) = barycentric product X(i)*X(j) for these {i,j}: {44, 32020}, {519, 3226}, {727, 3264}, {900, 8709}, {1960, 54985}, {3911, 36799}, {4358, 20332}, {16704, 27809}, {18793, 30939}
X(60865) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 36814}, {44, 1575}, {519, 726}, {727, 106}, {900, 3837}, {902, 3009}, {1317, 24816}, {1319, 1463}, {1647, 21140}, {1960, 6373}, {2251, 21760}, {3226, 903}, {3253, 27922}, {3264, 35538}, {3762, 20908}, {3911, 43040}, {4120, 21053}, {4358, 52043}, {4432, 17793}, {8709, 4555}, {8851, 1320}, {17780, 23354}, {18793, 4674}, {20332, 88}, {22086, 22092}, {22356, 20785}, {23202, 20777}, {23355, 23345}, {23757, 42766}, {24816, 59806}, {27809, 4080}, {32020, 20568}, {34077, 9456}, {36799, 4997}, {52680, 18792}, {52963, 21830}
X(60865) = {X(20332),X(36799)}-harmonic conjugate of X(27809)

X(60866) = X(2)X(2418)∩X(6)X(35179)

Barycentrics    (a^2 + b^2 - 5*c^2)*(a^2 - 5*b^2 + c^2)*(3*a^4 + a^2*b^2 + a^2*c^2 - 2*b^2*c^2) : :

X(60866) lies on the cubic K1359 and these lines: {2, 2418}, {6, 35179}, {183, 17968}, {458, 14608}, {1003, 1296}, {6656, 34165}, {7770, 14262}, {7841, 38951}, {8370, 52484}, {11331, 52477}, {32130, 54616}

X(60866) = barycentric product X(i)*X(j) for these {i,j}: {5485, 14614}, {32472, 35179}
X(60866) = barycentric quotient X(i)/X(j) for these {i,j}: {1296, 39639}, {5485, 60180}, {14614, 1992}, {32472, 1499}, {39238, 51918}, {41412, 1384}

X(60867) = X(2)X(523)∩X(6)X(598)

Barycentrics    (a^2 + b^2 - 2*c^2)*(a^2 - 2*b^2 + c^2)*(4*a^4 - a^2*b^2 - 2*b^4 - a^2*c^2 + 2*b^2*c^2 - 2*c^4) : :

X(60867) lies on the cubic K1359 and these lines: {2, 523}, {6, 598}, {111, 9100}, {381, 48983}, {458, 17983}, {599, 892}, {691, 35955}, {3363, 51258}, {5467, 9855}, {6032, 11163}, {7827, 14263}, {7841, 14246}, {8352, 52483}, {8370, 59422}, {8598, 45331}, {11159, 23348}, {11161, 52035}, {11184, 30786}, {11628, 59227}, {18023, 41259}, {21358, 39061}, {47352, 57539}, {52450, 59373}

X(60867) = X(896)-isoconjugate of X(6323)
X(60867) = X(15899)-Dao conjugate of X(6323)
X(60867) = barycentric product X(671)*X(3849)
X(60867) = barycentric quotient X(i)/X(j) for these {i,j}: {111, 6323}, {3849, 524}
X(60867) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 9214, 17948}, {2, 17948, 52756}, {9214, 52758, 52756}, {17948, 52758, 2}, {52748, 52749, 5968}

X(60868) = X(2)X(514)∩X(6)X(903)

Barycentrics    (a + b - 2*c)*(a - 2*b + c)*(4*a^3 - 2*a^2*b + a*b^2 - 2*b^3 - 2*a^2*c + b^2*c + a*c^2 + b*c^2 - 2*c^3) : :

X(60868) lies on the cubic K1359 and these lines: {2, 514}, {6, 903}, {458, 6336}, {598, 4080}, {4555, 17230}, {4945, 31179}, {4997, 29572}, {6549, 17367}, {41259, 57995}, {50128, 60578}

X(60868) = X(44)-isoconjugate of X(28563)
X(60868) = X(40595)-Dao conjugate of X(28563)
X(60868) = crossdifference of every pair of points on line {902, 9461}
X(60868) = barycentric product X(903)*X(28562)
X(60868) = barycentric quotient X(i)/X(j) for these {i,j}: {106, 28563}, {28562, 519}

X(60869) = X(2)X(647)∩X(6)X(264)

Barycentrics    b^2*c^2*(a^4 + b^4 - a^2*c^2 - b^2*c^2)*(-a^4 + a^2*b^2 + b^2*c^2 - c^4)*(-2*a^4 + a^2*b^2 + b^4 + a^2*c^2 - 2*b^2*c^2 + c^4) : :

X(60869) lies on the cubic K1359 and these lines: {2, 647}, {6, 264}, {76, 6035}, {94, 23968}, {98, 1302}, {401, 14966}, {575, 5967}, {685, 52641}, {1495, 4240}, {1821, 38340}, {2052, 23964}, {2407, 3260}, {2966, 30528}, {3818, 20021}, {5050, 60594}, {7578, 60520}, {9211, 18024}, {9214, 58263}, {11059, 57799}, {11079, 39290}, {14254, 53866}, {14355, 40427}, {14920, 60496}, {17974, 58943}, {18911, 51943}, {22456, 52147}, {32000, 56571}, {32545, 43754}, {34359, 42313}, {34810, 51430}, {36823, 41231}, {36893, 52710}, {37648, 51404}, {40705, 52712}, {41079, 51228}, {43530, 60199}, {51257, 52289}, {57803, 57991}

X(60869) = isotomic conjugate of X(35910)
X(60869) = polar conjugate of X(35908)
X(60869) = isotomic conjugate of the isogonal conjugate of X(35906)
X(60869) = polar conjugate of the isogonal conjugate of X(35912)
X(60869) = X(i)-isoconjugate of X(j) for these (i,j): {31, 35910}, {48, 35908}, {74, 1755}, {163, 32112}, {232, 35200}, {237, 2349}, {240, 18877}, {511, 2159}, {684, 36131}, {1494, 9417}, {1959, 40352}, {2433, 23997}, {3289, 36119}, {3569, 36034}, {9418, 33805}, {14919, 57653}, {15627, 51651}
X(60869) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 35910}, {115, 32112}, {133, 232}, {1249, 35908}, {1511, 3289}, {3163, 511}, {3258, 3569}, {6739, 59734}, {36899, 74}, {39008, 684}, {39058, 1494}, {39085, 18877}, {57295, 41172}
X(60869) = cevapoint of X(35906) and X(35912)
X(60869) = trilinear pole of line {30, 9409}
X(60869) = crossdifference of every pair of points on line {237, 39469}
X(60869) = barycentric product X(i)*X(j) for these {i,j}: {30, 290}, {76, 35906}, {98, 3260}, {264, 35912}, {287, 46106}, {336, 1784}, {1495, 18024}, {1637, 43187}, {1821, 14206}, {1910, 46234}, {1990, 57799}, {2173, 46273}, {2407, 43665}, {2966, 41079}, {3284, 60199}, {6394, 52661}, {9033, 22456}, {9214, 52145}, {11064, 16081}, {14265, 36891}, {34536, 51389}, {36035, 36036}, {36893, 58085}, {43752, 53174}, {43768, 53245}, {46786, 51228}, {51257, 51937}, {52451, 52552}, {57991, 58261}
X(60869) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 35910}, {4, 35908}, {30, 511}, {98, 74}, {248, 18877}, {287, 14919}, {290, 1494}, {293, 35200}, {523, 32112}, {685, 1304}, {879, 14380}, {1495, 237}, {1568, 44716}, {1637, 3569}, {1784, 240}, {1821, 2349}, {1910, 2159}, {1976, 40352}, {1990, 232}, {2173, 1755}, {2395, 2433}, {2407, 2421}, {2420, 14966}, {2715, 32640}, {2966, 44769}, {3081, 58343}, {3260, 325}, {3284, 3289}, {4240, 4230}, {5642, 9155}, {5967, 9717}, {6148, 51383}, {6357, 43034}, {6531, 8749}, {6793, 9475}, {7359, 59734}, {9033, 684}, {9154, 9139}, {9214, 5968}, {9406, 9417}, {9407, 9418}, {9409, 39469}, {11064, 36212}, {11125, 53521}, {14206, 1959}, {14254, 14356}, {14265, 36875}, {14355, 14385}, {14398, 2491}, {14581, 2211}, {15628, 15627}, {16081, 16080}, {18653, 17209}, {20021, 46147}, {20031, 32695}, {22456, 16077}, {32696, 32715}, {34369, 48451}, {34761, 51262}, {34810, 47049}, {35906, 6}, {35912, 3}, {36084, 36034}, {36104, 36131}, {36120, 36119}, {36789, 51389}, {36891, 52091}, {41079, 2799}, {42716, 42717}, {42750, 42751}, {43665, 2394}, {46106, 297}, {46234, 46238}, {46273, 33805}, {46786, 51227}, {48453, 52199}, {51228, 46787}, {51389, 36790}, {51430, 36213}, {51431, 51335}, {51457, 40083}, {51654, 51651}, {52145, 36890}, {52451, 14264}, {52485, 39265}, {52491, 17986}, {52661, 6530}, {52672, 60499}, {52752, 52765}, {53174, 44715}, {53866, 842}, {57260, 40354}, {58085, 56605}, {58261, 868}
X(60869) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 46786, 52145}, {287, 16081, 53245}, {52145, 57490, 46786}

X(60870) = X(2)X(525)∩X(6)X(1494)

Barycentrics    (a^4 - 2*a^2*b^2 + b^4 + a^2*c^2 + b^2*c^2 - 2*c^4)*(a^4 + a^2*b^2 - 2*b^4 - 2*a^2*c^2 + b^2*c^2 + c^4)*(4*a^6 - a^4*b^2 - a^2*b^4 - 2*b^6 - a^4*c^2 + 2*b^4*c^2 - a^2*c^4 + 2*b^2*c^4 - 2*c^6) : :

X(60870) lies on the cubic K1359 and these lines: {2, 525}, {6, 1494}, {74, 381}, {458, 598}, {597, 58875}, {599, 44769}, {2420, 44575}, {5476, 35908}, {11179, 17986}, {11331, 16077}, {12079, 34094}, {32112, 45321}, {40477, 56399}, {40884, 58347}
on K1359

X(60870) = X(2173)-isoconjugate of X(14388)
X(60870) = X(36896)-Dao conjugate of X(14388)
X(60870) = crossdifference of every pair of points on line {1495, 9411}
X(60870) = barycentric product X(i)*X(j) for these {i,j}: {1494, 11645}, {36890, 51926}
X(60870) = barycentric quotient X(i)/X(j) for these {i,j}: {74, 14388}, {11645, 30}, {41358, 1990}, {51926, 9214}
X(60870) = {X(2),X(51227)}-harmonic conjugate of X(35910)

X(60871) = ISOGONAL CONJUGATE OF X(16985)

Barycentrics    a*(a^2*b + a*b^2 + a^2*c - a*b*c + b^2*c)*(a^2*b + a^2*c - a*b*c + a*c^2 + b*c^2) : :

X(60871) llies on the circumconic {A,B,C,X(1),X(2)}, the cubic K1359, and these lines: {1, 19238}, {2, 3230}, {6, 3227}, {81, 2242}, {105, 10800}, {213, 330}, {274, 2176}, {291, 995}, {458, 16082}, {667, 17126}, {4383, 30710}, {4393, 39698}, {8616, 56329}, {16834, 55952}, {16969, 32009}, {20963, 38247}, {30114, 32020}, {30116, 30571}, {32911, 55953}, {36871, 50127}, {37687, 56058}, {49997, 52654}

X(60871) = isogonal conjugate of X(16975)
X(60871) = isogonal conjugate of the isotomic conjugate of X(56129)
X(60871) = X(i)-isoconjugate of X(j) for these (i,j): {1, 16975}, {6, 30942}
X(60871) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 16975}, {9, 30942}
X(60871) = cevapoint of X(i) and X(j) for these (i,j): {1, 54981}, {6, 37540}
X(60871) = trilinear pole of line {513, 890}
X(60871) = barycentric product X(i)*X(j) for these {i,j}: {1, 56166}, {6, 56129}
X(60871) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 30942}, {6, 16975}, {56129, 76}, {56166, 75}

X(60872) = ISOTOMIC CONJUGATE OF X(11331)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^4 + 2*a^2*b^2 + 2*b^4 - a^2*c^2 - b^2*c^2 - c^4)*(2*a^4 - a^2*b^2 - b^4 + 2*a^2*c^2 - b^2*c^2 + 2*c^4) : :

X(60872) llies on the cubic K1359 and these lines: {2, 1495}, {6, 1494}, {69, 3284}, {95, 3763}, {141, 44578}, {253, 51171}, {264, 1990}, {287, 39899}, {305, 11064}, +{328, 56399}, {394, 57852}, {401, 48879}, {441, 42313}, {458, 6330}, {647, 34767}, {1441, 17368}, {1799, 37638}, {2373, 59136}, {3098, 44575}, {3618, 36889}, {3629, 57823}, {9211, 18024}, {11331, 48905}, {11348, 42352}, {14389, 18018}, {18019, 59771}, {23964, 42308}, {35510, 51170}, {40884, 48881}, {44579, 48884}, {47355, 55958}, {57984, 60861}, {60866, 60867}

X(60872) = isotomic conjugate of X(11331)
X(60872) = isotomic conjugate of the isogonal conjugate of X(43706)
X(60872) = isotomic conjugate of the polar conjugate of X(14458)
X(60872) = isogonal conjugate of the polar conjugate of X(14387)
X(60872) = X(14387)-Ceva conjugate of X(14458)
X(60872) = X(i)-isoconjugate of X(j) for these (i,j): {19, 3098}, {31, 11331}, {162, 9210}, {1973, 7788}
X(60872) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 11331}, {6, 3098}, {125, 9210}, {6337, 7788}
X(60872) = cevapoint of X(6) and X(44883)
X(60872) = trilinear pole of line {525, 9409}
X(60872) = crossdifference of every pair of points on line {9210, 9411}
X(60872) = barycentric product X(i)*X(j) for these {i,j}: {3, 14387}, {69, 14458}, {76, 43706}, {647, 9211}, {3267, 59136}
X(60872) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 11331}, {3, 3098}, {69, 7788}, {647, 9210}, {9211, 6331}, {9409, 9411}, {14387, 264}, {14458, 4}, {43706, 6}, {59136, 112}

X(60873) = ISOTOMIC CONJUGATE OF X(17230)

Barycentrics    (2*a^2 + a*b + 2*b^2 - a*c - b*c)*(2*a^2 - a*b + a*c - b*c + 2*c^2) : :

X(60873) llies on the circumconic {A,B,C,X(2),X(7)}, the cubic K1359, and these lines: {2, 902}, {6, 903}, {7, 1404}, {44, 75}, {86, 3285}, {239, 27494}, {310, 16704}, {335, 4393}, {458, 52781}, {649, 6548}, {675, 30554}, {1268, 17259}, {3875, 56124}, {4366, 29572}, {4373, 31300}, {4402, 36588}, {5222, 6650}, {5235, 56052}, {5936, 26685}, {6384, 37684}, {6542, 39749}, {14953, 60679}, {17230, 32941}, {17236, 20179}, {17277, 55955}, {17379, 17382}, {17384, 30598}, {17385, 28650}, {18815, 60856}, {20172, 29593}, {26860, 39734}, {27475, 29570}, {29590, 39721}, {40039, 60861}, {41259, 60865}

X(60873) = isotomic conjugate of X(17230)
X(60873) = isotomic conjugate of the anticomplement of X(17367)
X(60873) = X(i)-isoconjugate of X(j) for these (i,j): {6, 49448}, {31, 17230}, {101, 50335}, {228, 31916}, {692, 30519}, {3257, 9461}
X(60873) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 17230}, {9, 49448}, {1015, 50335}, {1086, 30519}, {55055, 9461}
X(60873) = cevapoint of X(1086) and X(28882)
X(60873) = trilinear pole of line {514, 1960}
X(60873) = barycentric product X(i)*X(j) for these {i,j}: {86, 60624}, {3261, 30554}
X(60873) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 49448}, {2, 17230}, {27, 31916}, {513, 50335}, {514, 30519}, {1960, 9461}, {30554, 101}, {60624, 10}

X(60874) = MIDPOINT OF X(2) AND X(17037)

Barycentrics    13*a^8 - 8*a^6*b^2 - 22*a^4*b^4 + 16*a^2*b^6 + b^8 - 8*a^6*c^2 + 44*a^4*b^2*c^2 - 16*a^2*b^4*c^2 - 20*b^6*c^2 - 22*a^4*c^4 - 16*a^2*b^2*c^4 + 38*b^4*c^4 + 16*a^2*c^6 - 20*b^2*c^6 + c^8 : :
X(60874) = 11 X[2] - 10 X[20200], 7 X[2] - 8 X[20204], 5 X[2] - 4 X[20208], 5 X[2] - X[20218], X[253] - 4 X[1249], X[253] + 2 X[17037], 11 X[253] - 20 X[20200], 7 X[253] - 16 X[20204], 5 X[253] - 8 X[20208], 5 X[253] - 2 X[20218], 2 X[1249] + X[17037], 11 X[1249] - 5 X[20200], 7 X[1249] - 4 X[20204], 5 X[1249] - 2 X[20208], and many others

X(60874) lies on the cubic K1360 and these lines: {2, 253}, {20, 648}, {30, 41374}, {376, 15312}, {597, 42287}, {1503, 1992}, {3091, 15274}, {3839, 10002}, {6527, 45245}, {10304, 15576}, {10718, 41361}, {11160, 39358}, {11348, 40138}, {15692, 47383}, {52283, 52711}

X(60874) = midpoint of X(2) and X(17037)
X(60874) = reflection of X(i) in X(j) for these {i,j}: {2, 1249}, {253, 2}
X(60874) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1249, 17037, 253}, {20208, 20218, 253}

X(60875) = MIDPOINT OF X(2) AND X(20213)

Barycentrics    5*a^12 - 8*a^10*b^2 - 19*a^8*b^4 + 56*a^6*b^6 - 49*a^4*b^8 + 16*a^2*b^10 - b^12 - 8*a^10*c^2 + 46*a^8*b^2*c^2 - 56*a^6*b^4*c^2 + 4*a^4*b^6*c^2 + 16*a^2*b^8*c^2 - 2*b^10*c^2 - 19*a^8*c^4 - 56*a^6*b^2*c^4 + 90*a^4*b^4*c^4 - 32*a^2*b^6*c^4 + 17*b^8*c^4 + 56*a^6*c^6 + 4*a^4*b^2*c^6 - 32*a^2*b^4*c^6 - 28*b^6*c^6 - 49*a^4*c^8 + 16*a^2*b^2*c^8 + 17*b^4*c^8 + 16*a^2*c^10 - 2*b^2*c^10 - c^12 : :
X(60875) = 11 X[2] - 10 X[20199], 7 X[2] - 8 X[20203], 5 X[2] - 4 X[20207], 5 X[2] - X[20217], 4 X[1073] - X[14361], 11 X[1073] - 5 X[20199], 7 X[1073] - 4 X[20203], 5 X[1073] - 2 X[20207], 2 X[1073] + X[20213], 10 X[1073] - X[20217], 11 X[14361] - 20 X[20199], 7 X[14361] - 16 X[20203], 5 X[14361] - 8 X[20207], X[14361] + 2 X[20213], and many others

X(60875) lies on the cubic K1360 and these lines: {2, 253}, {376, 3917}, {394, 13509}, {1032, 54975}, {2394, 54784}, {3524, 26898}, {3545, 36876}, {10152, 15682}, {10714, 32064}, {15258, 33924}, {38918, 44210}, {44436, 56013}

X(60875) = midpoint of X(2) and X(20213)
X(60875) = reflection of X(i) in X(j) for these {i,j}: {2, 1073}, {14361, 2}
X(60875) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1073, 20213, 14361}, {20207, 20217, 14361}

X(60876) = MIDPOINT OF X(2) AND X(20211)

Barycentrics    5*a^6 + 4*a^5*b - 11*a^4*b^2 - 8*a^3*b^3 + 7*a^2*b^4 + 4*a*b^5 - b^6 + 4*a^5*c + 6*a^4*b*c + 8*a^3*b^2*c - 4*a^2*b^3*c - 12*a*b^4*c - 2*b^5*c - 11*a^4*c^2 + 8*a^3*b*c^2 - 6*a^2*b^2*c^2 + 8*a*b^3*c^2 + b^4*c^2 - 8*a^3*c^3 - 4*a^2*b*c^3 + 8*a*b^2*c^3 + 4*b^3*c^3 + 7*a^2*c^4 - 12*a*b*c^4 + b^2*c^4 + 4*a*c^5 - 2*b*c^5 - c^6 : :
X(60876) = 11 X[2] - 10 X[20197], 7 X[2] - 8 X[20201], 5 X[2] - 4 X[20205], 5 X[2] - X[20215], X[189] - 4 X[223], 11 X[189] - 20 X[20197], 7 X[189] - 16 X[20201], 5 X[189] - 8 X[20205], X[189] + 2 X[20211], 5 X[189] - 2 X[20215], 11 X[223] - 5 X[20197], 7 X[223] - 4 X[20201], 5 X[223] - 2 X[20205], 2 X[223] + X[20211], and many others

X(60876) lies on the cubic K1360 and these lines: {2, 77}, {329, 664}, {376, 54054}, {515, 3241}, {1992, 2094}, {15933, 34231}, {31143, 31155}, {41823, 50101}

X(60876) = midpoint of X(2) and X(20211)
X(60876) = reflection of X(i) in X(j) for these {i,j}: {2, 223}, {189, 2}
X(60876) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {223, 20211, 189}, {20205, 20215, 189}



leftri

Points related to the Aguilera triangle: X(60877)-X(61035)

rightri

This preamble and centers X(60877)-X(61035) were contributed by Ivan Pavlov on Dec 11, 2023.

In a scalene acute triangle ABC, let MaMbMc be its medial triangle. Let ωa be the circle centered at Ma and passing through B and C, and define ωb and ωc cyclically. Inside ABC, let Oa be center of the circle, closest to A, which is externally tangent to ωa and is inscribed in angle BAC. Define Ob and Oc cyclically. The triangle OaObOc is called the (1st) Aguilera triangle of ABC and has the following barycentrics of the A-vertex, derived by Manuel Aguilera: a*(-a + b + c)*(a + b + c) + 2*(b + c)*S : b*((-a + b + c)*(a + b + c) - 2*S) : c*((-a + b + c)*(a + b + c) - 2*S)

If a point P lies on line X(1)X(3), the pedal triangle of P is orthologic to the Aguilera triangle and the orthology center lies on line X(2)X(7).

The triangle inverse-in-incircle of the Aguilera triangle is called here the (1st) Aguilera-Pavlov triangle.
Its A-vertex has the following barycentrics: S (b + c) + 2 a b c : b (-S + 2 b c ) : c (-S + 2 b c )

The centroid of the Aguilera-Pavlov triangle coincides with the incenter of ABC.
If a point P lies on line X(1)X(6), the pedal triangle of P is orthologic to the Aguilera-Pavlov triangle.

X(60877) = ORTHOCENTER OF THE AGUILERA TRIANGLE

Barycentrics    a*(a+b+c)*(a^2-2*a*b+b^2-2*a*c-2*b*c+c^2)-(4*a^2-2*(b-c)^2-2*a*(b+c))*S : :

X(60877) lies on circumconic {{A, B, C, X(13390), X(34919)}} and on these lines: {1, 527}, {7, 13389}, {9, 3068}, {144, 55398}, {175, 60975}, {176, 60998}, {481, 6459}, {482, 60953}, {1659, 8545}, {5405, 6173}, {5851, 52809}, {9814, 51764}, {12848, 13388}, {15726, 52805}, {15733, 60902}, {30557, 60997}, {38454, 52808}

X(60877) = pole of line {17603, 30277} wrt Feuerbach hyperbola
X(60877) = pole of line {481, 6173} wrt dual conic of Yff parabola

X(60878) = CIRCUMCENTER OF THE AGUILERA TRIANGLE

Barycentrics    -a*(a^3*(b+c)+3*a*(b-c)^2*(b+c)+a^2*(-3*b^2+4*b*c-3*c^2)-(b-c)^2*(b^2+4*b*c+c^2))+a*(2*a^2+2*(b-c)^2-4*a*(b+c))*S : :

X(60878) lies on these lines: {1, 6610}, {7, 34215}, {55, 60930}, {527, 45713}, {1659, 8255}, {5851, 52809}, {11495, 30355}, {15733, 45714}, {38454, 52805}, {42014, 55397}, {51764, 60982}

X(60878) = pole of line {4860, 52419} wrt Feuerbach hyperbola

X(60879) = ORTHOLOGY CENTER OF ANTI-ARA WRT AGUILERA TRIANGLE

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(2*a^4-2*a^3*(b+c)-a^2*(b^2+c^2)+(b-c)^2*(b^2+c^2)) : :

X(60879) lies on these lines: {4, 144}, {7, 25}, {9, 427}, {24, 31657}, {33, 60919}, {34, 60883}, {142, 468}, {235, 5805}, {390, 11396}, {428, 527}, {516, 1829}, {518, 12135}, {971, 3575}, {1001, 22479}, {1445, 37432}, {1593, 5759}, {1598, 60922}, {1824, 38454}, {1828, 1890}, {1843, 5845}, {1851, 1889}, {1862, 5856}, {1876, 52819}, {1892, 60937}, {1902, 12139}, {1906, 5735}, {1974, 51150}, {2801, 12137}, {3088, 21168}, {3089, 59386}, {3515, 21151}, {3516, 59418}, {3517, 59380}, {3541, 59381}, {3542, 38107}, {3867, 51144}, {4000, 44100}, {4312, 7713}, {5064, 6172}, {5090, 5223}, {5094, 18230}, {5220, 11391}, {5338, 11246}, {5410, 60887}, {5412, 60913}, {5413, 60914}, {5542, 11363}, {5698, 57530}, {5817, 7507}, {5843, 6756}, {5850, 49542}, {6646, 14004}, {6995, 20059}, {7378, 61006}, {7487, 36996}, {7505, 38171}, {7547, 38139}, {7714, 60984}, {10151, 18482}, {10301, 60933}, {11380, 60882}, {11383, 11495}, {11384, 60898}, {11385, 60899}, {11386, 60900}, {11388, 60907}, {11389, 60908}, {11390, 16112}, {11392, 60909}, {11393, 60910}, {11394, 60917}, {11395, 60918}, {11398, 60923}, {11399, 60924}, {11400, 60925}, {11401, 60926}, {11832, 60906}, {12167, 51190}, {12173, 36991}, {13884, 60920}, {13937, 60921}, {15587, 41611}, {17562, 24470}, {18494, 60884}, {19118, 59405}, {20195, 52297}, {25985, 60969}, {26020, 61012}, {26371, 60880}, {26372, 60881}, {26373, 60892}, {26374, 60893}, {26375, 60894}, {26377, 60895}, {26378, 60896}, {28121, 41007}, {35764, 60915}, {35765, 60916}, {37119, 38113}, {37197, 59385}, {37362, 60970}, {37394, 60939}, {37453, 60996}, {38137, 44960}, {41584, 47595}, {44084, 58472}, {45400, 60888}, {45401, 60889}, {45502, 60890}, {45503, 60891}, {46444, 51194}, {52285, 60942}

X(60879) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 7717, 25}

X(60880) = ORTHOLOGY CENTER OF 1ST ANTI-AURIGA WRT AGUILERA TRIANGLE

Barycentrics    (a+b+c)*(2*a^5-4*a^4*(b+c)+a^2*(b-c)^2*(b+c)-(b-c)^4*(b+c)+a*(b-c)^2*(b^2+c^2)+a^3*(b^2+4*b*c+c^2))+4*a*(a^2-2*a*b+b^2-2*a*c-2*b*c+c^2)*sqrt(R*(r+4*R))*S : :

X(60880) lies on these lines: {1, 34917}, {7, 5597}, {9, 26359}, {144, 26394}, {390, 26395}, {516, 45711}, {518, 48493}, {527, 45696}, {528, 48494}, {971, 48454}, {1001, 26319}, {2801, 48501}, {4312, 26296}, {5220, 26389}, {5223, 26382}, {5542, 26365}, {5598, 36976}, {5759, 26290}, {5762, 48460}, {5779, 26386}, {5805, 26326}, {5843, 48519}, {5845, 45724}, {5850, 48511}, {5856, 48533}, {8186, 8255}, {11366, 36971}, {11495, 26393}, {16112, 26390}, {18496, 60884}, {26302, 60897}, {26310, 60900}, {26334, 60907}, {26344, 60908}, {26351, 60919}, {26371, 60879}, {26379, 60882}, {26380, 60883}, {26381, 36996}, {26383, 60906}, {26385, 60887}, {26387, 60910}, {26388, 60909}, {26391, 60892}, {26392, 60893}, {26396, 60894}, {26398, 31657}, {26399, 60895}, {26400, 60896}, {26401, 60926}, {26402, 60925}, {44582, 60913}, {44583, 60914}, {45345, 60888}, {45348, 60889}, {45349, 60890}, {45352, 60891}, {45354, 60899}, {45355, 60901}, {45357, 60915}, {45360, 60916}, {45361, 60918}, {45362, 60917}, {45365, 60920}, {45366, 60921}, {45369, 60922}, {45371, 60923}, {45373, 60924}, {48487, 48509}

X(60880) = reflection of X(i) in X(j) for these {i,j}: {60881, 1}

X(60881) = ORTHOLOGY CENTER OF 2ND ANTI-AURIGA WRT AGUILERA TRIANGLE

Barycentrics    (a+b+c)*(2*a^5-4*a^4*(b+c)+a^2*(b-c)^2*(b+c)-(b-c)^4*(b+c)+a*(b-c)^2*(b^2+c^2)+a^3*(b^2+4*b*c+c^2))-4*a*(a^2-2*a*b+b^2-2*a*c-2*b*c+c^2)*sqrt(R*(r+4*R))*S : :

X(60881) lies on these lines: {1, 34917}, {7, 5598}, {9, 26360}, {144, 26418}, {390, 26419}, {516, 45712}, {518, 48494}, {527, 45697}, {528, 48493}, {971, 48455}, {1001, 26320}, {2801, 48502}, {4312, 26297}, {5220, 26413}, {5223, 26406}, {5542, 26366}, {5597, 36976}, {5759, 26291}, {5762, 48461}, {5779, 26410}, {5805, 26327}, {5843, 48520}, {5845, 45725}, {5850, 48512}, {5856, 48534}, {8187, 8255}, {11367, 36971}, {11495, 26417}, {16112, 26414}, {18498, 60884}, {26303, 60897}, {26311, 60900}, {26335, 60907}, {26345, 60908}, {26352, 60919}, {26372, 60879}, {26403, 60882}, {26404, 60883}, {26405, 36996}, {26407, 60906}, {26409, 60887}, {26411, 60910}, {26412, 60909}, {26415, 60892}, {26416, 60893}, {26420, 60894}, {26422, 31657}, {26423, 60895}, {26424, 60896}, {26425, 60926}, {26426, 60925}, {44584, 60913}, {44585, 60914}, {45346, 60889}, {45347, 60888}, {45350, 60891}, {45351, 60890}, {45353, 60898}, {45356, 60901}, {45358, 60916}, {45359, 60915}, {45363, 60918}, {45364, 60917}, {45367, 60921}, {45368, 60920}, {45370, 60922}, {45372, 60923}, {45374, 60924}, {48488, 48510}

X(60881) = reflection of X(i) in X(j) for these {i,j}: {60880, 1}
X(60881) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 38454, 60880}

X(60882) = ORTHOLOGY CENTER OF 5TH ANTI-BROCARD WRT AGUILERA TRIANGLE

Barycentrics    a^6-2*a^4*b*c+b^2*(b-c)^2*c^2-2*a^5*(b+c)+a^2*(b^4-2*b^3*c+b^2*c^2-2*b*c^3+c^4) : :

X(60882) lies on these lines: {7, 32}, {9, 83}, {98, 5805}, {142, 1078}, {144, 7787}, {182, 5759}, {239, 24269}, {390, 10800}, {516, 12194}, {518, 12195}, {527, 12150}, {673, 4279}, {971, 12110}, {1001, 22520}, {1691, 51150}, {2080, 31657}, {2801, 12198}, {3398, 5762}, {4312, 10789}, {5039, 51190}, {5171, 21151}, {5182, 51002}, {5220, 10795}, {5223, 10791}, {5542, 11364}, {5779, 10796}, {5817, 10358}, {5843, 32134}, {5845, 12212}, {5850, 49545}, {5856, 13194}, {7808, 18230}, {7815, 60996}, {10104, 38107}, {10359, 21168}, {10788, 36996}, {10790, 60897}, {10792, 60907}, {10793, 60908}, {10794, 16112}, {10797, 60909}, {10798, 60910}, {10799, 60919}, {10801, 60923}, {10802, 60924}, {10803, 60925}, {10804, 60926}, {11380, 60879}, {11490, 11495}, {11837, 60898}, {11838, 60899}, {11839, 60906}, {11840, 60917}, {11841, 60918}, {11842, 60922}, {12197, 12200}, {12835, 60883}, {13885, 60920}, {13938, 60921}, {14880, 31671}, {18501, 60884}, {18502, 60901}, {18994, 60887}, {26379, 60880}, {26403, 60881}, {26427, 60892}, {26428, 60893}, {26429, 60894}, {26431, 60895}, {26432, 60896}, {35766, 60915}, {35767, 60916}, {37479, 59418}, {42534, 50995}, {44586, 60913}, {44587, 60914}, {45402, 60888}, {45403, 60889}, {45504, 60890}, {45505, 60891}

X(60883) = ORTHOLOGY CENTER OF 2ND ANTI-CIRCUMPERP-TANGENTIAL WRT AGUILERA TRIANGLE

Barycentrics    (a+b-c)*(a-b+c)*(2*a^4-2*a^3*(b+c)-a^2*(b+c)^2+(b^2-c^2)^2) : :

X(60883) lies on these lines: {1, 5762}, {3, 60923}, {4, 60910}, {5, 15932}, {6, 4331}, {7, 21}, {9, 12}, {10, 61014}, {11, 57}, {31, 6354}, {34, 60879}, {36, 31657}, {55, 5759}, {65, 516}, {142, 5433}, {144, 388}, {226, 3683}, {241, 50307}, {390, 2099}, {392, 4298}, {480, 11501}, {496, 49177}, {498, 59381}, {499, 38107}, {518, 10944}, {527, 5434}, {528, 7672}, {673, 24836}, {954, 37579}, {960, 60979}, {971, 1858}, {999, 60922}, {1086, 1471}, {1118, 8748}, {1156, 13273}, {1317, 3243}, {1319, 5542}, {1329, 61012}, {1358, 42309}, {1361, 33966}, {1386, 22464}, {1388, 11038}, {1420, 59372}, {1427, 41011}, {1428, 51150}, {1445, 1454}, {1456, 3668}, {1458, 17365}, {1469, 5845}, {1470, 60896}, {1478, 5779}, {1479, 31671}, {1708, 3925}, {1758, 5718}, {1770, 37544}, {1788, 59412}, {1837, 10398}, {1839, 1893}, {1875, 1890}, {1882, 47345}, {2067, 60913}, {2078, 37703}, {2262, 2385}, {2263, 53529}, {2550, 12848}, {2551, 61009}, {2801, 18976}, {3057, 18979}, {3058, 5173}, {3059, 41538}, {3062, 9579}, {3085, 21168}, {3086, 59386}, {3339, 5722}, {3361, 5886}, {3585, 60901}, {3600, 5289}, {3614, 38108}, {3826, 37787}, {3962, 5850}, {4292, 12688}, {4293, 36996}, {4295, 57278}, {4321, 60933}, {4327, 17276}, {4854, 37543}, {5172, 8255}, {5204, 21151}, {5217, 59418}, {5220, 18962}, {5221, 5225}, {5223, 5252}, {5228, 24248}, {5261, 61006}, {5263, 17950}, {5298, 6173}, {5432, 31658}, {5443, 38043}, {5693, 5843}, {5695, 56927}, {5723, 16468}, {5732, 15326}, {5735, 37722}, {5817, 10895}, {5832, 6067}, {6068, 10956}, {6172, 11237}, {6180, 24695}, {6253, 44547}, {6502, 60914}, {6604, 24280}, {7098, 15844}, {7173, 38150}, {7294, 20195}, {7676, 14882}, {7679, 60954}, {8614, 34028}, {9654, 51516}, {9655, 60884}, {10177, 37566}, {10384, 12701}, {10404, 60905}, {10593, 38137}, {10896, 59385}, {10950, 18412}, {11011, 30331}, {11376, 38036}, {11495, 11509}, {11681, 61026}, {12560, 60982}, {12588, 50995}, {12835, 60882}, {12943, 36991}, {14564, 49478}, {15185, 41537}, {15254, 21617}, {15298, 15888}, {15481, 50573}, {16112, 18961}, {16686, 59247}, {17717, 43056}, {18391, 36999}, {18421, 28174}, {18838, 28534}, {18954, 60897}, {18955, 60898}, {18956, 60899}, {18957, 60900}, {18958, 60906}, {18959, 60907}, {18960, 60908}, {18963, 60917}, {18964, 60918}, {18965, 60920}, {18966, 60921}, {18967, 60926}, {18996, 60887}, {21153, 52793}, {24723, 41246}, {24796, 52511}, {24914, 38052}, {25466, 60969}, {25973, 55871}, {26380, 60880}, {26404, 60881}, {26433, 60892}, {26434, 60893}, {26435, 60894}, {26437, 42884}, {26481, 41697}, {28774, 59574}, {28915, 52510}, {30424, 32636}, {34612, 41539}, {35514, 37567}, {35768, 60915}, {35769, 60916}, {36589, 48810}, {37618, 38030}, {37717, 51305}, {45404, 60888}, {45405, 60889}, {45506, 60890}, {45507, 60891}, {47007, 59808}, {50031, 59335}, {50195, 51489}, {54370, 57285}

X(60883) = reflection of X(i) in X(j) for these {i,j}: {10950, 18412}, {31391, 4292}, {65, 52819}, {6284, 14100}, {60919, 1}, {60961, 4298}, {60979, 960}, {8581, 12573}
X(60883) = inverse of X(8727) in Feuerbach hyperbola
X(60883) = pole of line {663, 676} wrt incircle
X(60883) = pole of line {226, 971} wrt Feuerbach hyperbola
X(60883) = pole of line {4040, 10015} wrt Suppa-Cucoanes circle
X(60883) = pole of line {3664, 43035} wrt dual conic of Yff parabola
X(60883) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(8822), X(48357)}}, {{A, B, C, X(16705), X(26592)}}
X(60883) = barycentric product X(i)*X(j) for these (i, j): {26592, 56}
X(60883) = barycentric quotient X(i)/X(j) for these (i, j): {26592, 3596}
X(60883) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 52653, 3485}, {7, 7677, 25557}, {144, 388, 60909}, {516, 14100, 6284}, {516, 52819, 65}, {527, 12573, 8581}, {999, 60922, 60924}, {1836, 30223, 7965}, {2550, 12848, 41712}, {2550, 41712, 40663}, {4312, 11372, 1836}, {4312, 15299, 5805}, {5805, 15299, 11}, {8581, 12573, 5434}, {39144, 39145, 8727}, {59412, 60941, 1788}

X(60884) = ORTHOLOGY CENTER OF ANTI-EHRMANN-MID WRT AGUILERA TRIANGLE

Barycentrics    a*(a^5+2*a^4*(b+c)-4*(b-c)^2*(b+c)^3+a^3*(-8*b^2+6*b*c-8*c^2)+2*a^2*(b+c)*(b^2+c^2)+a*(b-c)^2*(7*b^2+8*b*c+7*c^2)) : :
X(60884) = -3*X[3]+4*X[9], -2*X[7]+3*X[381], -X[40]+3*X[52665], -8*X[142]+9*X[5055], -3*X[376]+5*X[61006], -4*X[546]+3*X[59386], -2*X[550]+3*X[21168], -5*X[1656]+6*X[5817], -7*X[3090]+6*X[38111], -7*X[3526]+6*X[21151], -7*X[3832]+6*X[38137], -5*X[3843]+4*X[5805]

X(60884) lies on these lines: {3, 9}, {4, 5843}, {5, 36996}, {7, 381}, {30, 144}, {40, 52665}, {142, 5055}, {355, 48664}, {376, 61006}, {382, 5762}, {390, 18526}, {480, 35000}, {516, 4701}, {517, 3062}, {518, 8148}, {527, 3830}, {546, 59386}, {550, 21168}, {954, 13743}, {990, 16669}, {991, 16675}, {999, 60910}, {1001, 26321}, {1156, 12773}, {1159, 2771}, {1482, 11372}, {1656, 5817}, {1657, 5759}, {1709, 3689}, {2095, 54135}, {2550, 47032}, {2801, 10247}, {2951, 18528}, {3036, 33898}, {3065, 8069}, {3090, 38111}, {3218, 19541}, {3295, 60909}, {3306, 5927}, {3339, 31507}, {3526, 21151}, {3534, 6172}, {3711, 6244}, {3832, 38137}, {3843, 5805}, {3845, 60984}, {3851, 38107}, {3940, 60966}, {4312, 18480}, {5054, 18230}, {5066, 59375}, {5070, 38108}, {5072, 38139}, {5079, 38171}, {5220, 16139}, {5223, 12702}, {5289, 31803}, {5542, 18493}, {5691, 41705}, {5696, 35448}, {5708, 10398}, {5722, 60961}, {5729, 60948}, {5789, 6260}, {5845, 18440}, {5850, 12699}, {5851, 10742}, {5856, 48680}, {6001, 40587}, {6173, 19709}, {6646, 36721}, {6666, 15694}, {6767, 14100}, {7373, 8581}, {7989, 38172}, {7992, 9947}, {8158, 12688}, {8171, 30223}, {9654, 60923}, {9655, 60883}, {9668, 60919}, {9669, 60924}, {9730, 58534}, {9952, 59387}, {9955, 59372}, {10157, 30304}, {10222, 24644}, {10394, 37234}, {10861, 16408}, {10864, 31821}, {11220, 35595}, {11227, 30326}, {11495, 18524}, {12848, 28452}, {13369, 16853}, {13665, 60913}, {13785, 60914}, {14269, 18482}, {15481, 43178}, {15681, 60942}, {15684, 60977}, {15688, 60983}, {15689, 61000}, {15693, 61023}, {15696, 59418}, {15701, 60986}, {15703, 20195}, {15718, 38067}, {15720, 38113}, {15723, 38082}, {15733, 44455}, {15934, 18540}, {16370, 61025}, {16371, 61026}, {16411, 17616}, {16417, 61012}, {16418, 60969}, {18243, 31493}, {18357, 59412}, {18407, 36971}, {18481, 51090}, {18491, 41700}, {18494, 60879}, {18496, 60880}, {18498, 60881}, {18499, 38454}, {18501, 60882}, {18503, 60900}, {18508, 60906}, {18512, 60887}, {18515, 52769}, {18521, 60892}, {18523, 60893}, {18539, 60894}, {18541, 52819}, {18542, 60896}, {18543, 60926}, {18544, 60895}, {18545, 60925}, {18761, 41694}, {19914, 38756}, {22770, 31828}, {23251, 60915}, {23261, 60916}, {26336, 60907}, {26346, 60908}, {26446, 43182}, {28444, 29007}, {28453, 61004}, {31391, 36279}, {33878, 50995}, {34773, 52653}, {35514, 59503}, {37624, 42819}, {38031, 60911}, {38117, 55692}, {38122, 46219}, {38130, 43181}, {38318, 55860}, {38335, 60976}, {39899, 51190}, {45375, 60888}, {45376, 60889}, {45377, 60890}, {45378, 60891}, {45379, 60898}, {45380, 60899}, {45381, 60917}, {45382, 60918}, {45384, 60920}, {45385, 60921}, {45834, 50192}, {46264, 51144}, {48661, 48671}

X(60884) = midpoint of X(i) and X(j) for these {i,j}: {5691, 41705}
X(60884) = reflection of X(i) in X(j) for these {i,j}: {1482, 11372}, {1657, 5759}, {12702, 5223}, {12773, 1156}, {15934, 18540}, {18481, 51090}, {18508, 60906}, {18526, 390}, {2095, 54135}, {3, 5779}, {382, 36991}, {3534, 6172}, {31671, 31672}, {33878, 50995}, {36971, 18407}, {36996, 5}, {39899, 51190}, {4312, 18480}, {43178, 15481}, {46264, 51144}, {60922, 4}, {60933, 18482}, {60984, 3845}, {7, 60901}, {8581, 31937}
X(60884) = inverse of X(32625) in Stammler circle
X(60884) = pole of line {667, 3900} wrt Stammler circle
X(60884) = pole of line {30223, 53056} wrt Feuerbach hyperbola
X(60884) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 5779, 51516}, {4, 5843, 60922}, {7, 60901, 381}, {527, 31672, 31671}, {3843, 51514, 5805}, {5762, 36991, 382}, {5817, 31657, 1656}, {31671, 31672, 3830}, {35454, 38902, 3}

X(60885) = ORTHOLOGY CENTER OF ANTI-INNER-GARCIA WRT AGUILERA TRIANGLE

Barycentrics    a*(a^5+3*a^3*b*c-2*a^4*(b+c)-2*b*(b-c)^2*c*(b+c)+2*a^2*(b+c)*(b^2+c^2)-a*(b^4+b^3*c+4*b^2*c^2+b*c^3+c^4)) : :
X(60885) = -X[3245]+4*X[6594], -3*X[3582]+2*X[41555]

X(60885) lies on these lines: {1, 6}, {3, 44785}, {10, 8543}, {35, 5698}, {36, 527}, {55, 31142}, {56, 61007}, {78, 5696}, {80, 5853}, {100, 516}, {142, 37701}, {144, 52769}, {214, 18450}, {329, 15931}, {390, 25439}, {404, 30424}, {480, 5587}, {519, 53055}, {528, 3583}, {758, 37787}, {971, 6326}, {993, 6172}, {997, 8545}, {1156, 56117}, {1259, 5735}, {1260, 1699}, {1621, 21060}, {2077, 61035}, {2550, 7951}, {2801, 4511}, {2951, 52026}, {3245, 6594}, {3421, 47357}, {3434, 41858}, {3576, 36973}, {3582, 41555}, {3586, 47387}, {3746, 21075}, {3748, 9954}, {3814, 45043}, {3832, 7080}, {3841, 40333}, {3869, 60912}, {3940, 42014}, {4130, 14077}, {4413, 5219}, {4855, 43178}, {4880, 60989}, {5119, 47375}, {5178, 6736}, {5253, 43180}, {5440, 15726}, {5720, 11372}, {5775, 18230}, {5843, 38602}, {5850, 7677}, {5851, 51636}, {5902, 8257}, {6700, 11263}, {8715, 30332}, {10176, 60981}, {10306, 18491}, {10394, 22836}, {10427, 17768}, {10980, 25893}, {12773, 45391}, {13370, 41572}, {15175, 34919}, {15507, 40910}, {15733, 51768}, {17057, 38200}, {18254, 45395}, {26725, 60978}, {27383, 45392}, {30329, 61012}, {31018, 52653}, {37249, 60982}, {37602, 51099}, {38059, 54357}, {38211, 41684}, {38454, 51409}, {41228, 60911}, {43177, 60979}, {48697, 54192}

X(60885) = midpoint of X(i) and X(j) for these {i,j}: {18450, 56551}, {4511, 60935}, {4867, 41700}
X(60885) = reflection of X(i) in X(j) for these {i,j}: {18450, 214}, {4880, 60989}, {41684, 38211}, {41700, 9}, {45043, 3814}
X(60885) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(2717)}}, {{A, B, C, X(80), X(43065)}}, {{A, B, C, X(1108), X(15909)}}, {{A, B, C, X(2323), X(34894)}}, {{A, B, C, X(2801), X(5660)}}, {{A, B, C, X(6603), X(56117)}}, {{A, B, C, X(36101), X(41700)}}
X(60885) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 1001, 5251}, {9, 518, 41700}, {78, 54370, 5696}, {908, 6745, 5660}, {4511, 60935, 2801}, {4867, 41700, 518}, {5537, 5660, 44425}

X(60886) = ORTHOLOGY CENTER OF AGUILERA WRT ANTI-INNER-GARCIA TRIANGLE

Barycentrics    -a*(-2*a^3*b^2-2*a^3*c^2+a^4*(b+c)-b^2*(b-c)^2*(b+c)+a^2*b*c*(b+c)-b*(b-c)^2*c*(b+c)-(b-c)^2*c^2*(b+c)+2*a*(b-c)^2*(b^2+b*c+c^2))+2*a*(a^3-a^2*b-a*b^2+b^3-a^2*c+3*a*b*c-b^2*c-a*c^2-b*c^2+c^3)*S : :

X(60886) lies on these lines: {1, 651}, {11, 13390}, {80, 31539}, {100, 55398}, {104, 18460}, {175, 45043}, {516, 60904}, {528, 45713}, {952, 52806}, {1659, 12831}, {5393, 5660}, {5405, 11219}, {5851, 52809}, {12730, 30431}, {13388, 60782}, {30342, 38055}

X(60887) = ORTHOLOGY CENTER OF ANTI-OUTER-GREBE WRT AGUILERA TRIANGLE

Barycentrics    a^2*(r+4*R)+2*sb*sc*s : :

X(60887) lies on these lines: {2, 60920}, {6, 7}, {9, 3068}, {142, 3069}, {144, 7585}, {176, 40133}, {371, 5759}, {372, 21151}, {390, 7969}, {485, 5817}, {516, 6459}, {518, 19066}, {527, 19054}, {590, 18230}, {615, 60996}, {971, 1587}, {1001, 13902}, {1151, 59418}, {1588, 5805}, {1702, 19086}, {2346, 44591}, {2550, 19065}, {2801, 19078}, {3070, 36991}, {3071, 59385}, {3299, 60924}, {3301, 60923}, {3311, 5762}, {3312, 31657}, {4312, 19004}, {5220, 19026}, {5223, 13883}, {5410, 60879}, {5412, 7717}, {5542, 18992}, {5686, 13911}, {5732, 6460}, {5779, 7583}, {5843, 19117}, {5850, 49548}, {5856, 19113}, {6172, 32787}, {6173, 19053}, {6417, 60922}, {6418, 59380}, {6419, 60915}, {6500, 51514}, {6666, 32785}, {7581, 36996}, {7582, 59386}, {7584, 38107}, {7586, 60921}, {7676, 44590}, {7677, 44606}, {7968, 11038}, {8236, 44635}, {8581, 31408}, {8981, 59381}, {9540, 31658}, {10427, 19112}, {11495, 19000}, {13159, 19079}, {13665, 60901}, {13846, 61023}, {13935, 38122}, {13936, 38052}, {13947, 38204}, {13951, 38171}, {13959, 38053}, {13973, 40333}, {15587, 31413}, {16112, 19024}, {16593, 24818}, {18482, 23259}, {18512, 60884}, {18994, 60882}, {18996, 60883}, {19003, 59372}, {19006, 60897}, {19008, 60898}, {19010, 60899}, {19012, 60900}, {19018, 60906}, {19028, 60909}, {19030, 60910}, {19032, 60917}, {19034, 60918}, {19038, 60919}, {19048, 60925}, {19050, 60926}, {20195, 32786}, {23249, 31672}, {26385, 60880}, {26409, 60881}, {26460, 60892}, {26461, 60893}, {26462, 60894}, {26464, 60895}, {26465, 60896}, {31671, 42215}, {32788, 59374}, {35514, 35774}, {35771, 60916}, {35823, 38073}, {38149, 49602}, {38150, 42561}, {45043, 49241}, {45513, 60891}, {45515, 60890}, {49233, 59413}, {51841, 52819}, {51842, 60992}

X(60887) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 51190, 60908}, {51150, 60889, 7}

X(60888) = ORTHOLOGY CENTER OF 1ST ANTI-KENMOTU CENTERS WRT AGUILERA TRIANGLE

Barycentrics    2*a^4+a^2*b^2-b^2*(b-c)^2+a^2*c^2-(b-c)^2*c^2-2*a^3*(b+c)+2*(a^2-(b-c)^2)*S : :

X(60888) lies on these lines: {3, 60890}, {6, 7}, {9, 45472}, {144, 492}, {390, 45476}, {516, 45713}, {518, 49078}, {527, 591}, {971, 13748}, {1001, 45436}, {2801, 49337}, {3102, 60916}, {4312, 45426}, {5220, 45456}, {5223, 45444}, {5542, 45398}, {5759, 12305}, {5762, 9733}, {5779, 6289}, {5805, 45440}, {5843, 49355}, {5850, 49347}, {5856, 48703}, {11495, 45416}, {16112, 45454}, {31657, 43119}, {36996, 45406}, {45345, 60880}, {45347, 60881}, {45375, 60884}, {45400, 60879}, {45402, 60882}, {45404, 60883}, {45411, 59380}, {45412, 60893}, {45415, 60892}, {45421, 60984}, {45422, 60895}, {45424, 60896}, {45428, 60897}, {45430, 60898}, {45432, 60899}, {45434, 60900}, {45438, 60901}, {45446, 60906}, {45458, 60909}, {45460, 60910}, {45462, 60915}, {45464, 60918}, {45467, 60917}, {45470, 60919}, {45484, 60920}, {45487, 60921}, {45488, 60922}, {45490, 60923}, {45492, 60924}, {45494, 60925}, {45496, 60926}, {49323, 49345}

X(60888) = midpoint of X(i) and X(j) for these {i,j}: {144, 60894}, {7, 60908}
X(60888) = reflection of X(i) in X(j) for these {i,j}: {3, 60890}, {60889, 7}
X(60888) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 51190, 60913}, {7, 5845, 60889}, {7, 60908, 5845}

X(60889) = ORTHOLOGY CENTER OF 2ND ANTI-KENMOTU CENTERS WRT AGUILERA TRIANGLE

Barycentrics    2*a^4+a^2*b^2-b^2*(b-c)^2+a^2*c^2-(b-c)^2*c^2-2*a^3*(b+c)-2*(a^2-(b-c)^2)*S : :

X(60889) lies on these lines: {3, 60891}, {6, 7}, {9, 45473}, {144, 491}, {390, 45477}, {516, 45714}, {518, 49079}, {527, 1991}, {971, 13749}, {1001, 45437}, {2801, 49338}, {3103, 60915}, {4312, 45427}, {5220, 45457}, {5223, 45445}, {5542, 45399}, {5759, 12306}, {5762, 9732}, {5779, 6290}, {5805, 45441}, {5843, 49356}, {5850, 49348}, {5856, 48704}, {11495, 45417}, {16112, 45455}, {31657, 43118}, {36996, 45407}, {45346, 60881}, {45348, 60880}, {45376, 60884}, {45401, 60879}, {45403, 60882}, {45405, 60883}, {45410, 59380}, {45413, 60892}, {45414, 60893}, {45420, 60894}, {45423, 60895}, {45425, 60896}, {45429, 60897}, {45431, 60898}, {45433, 60899}, {45435, 60900}, {45439, 60901}, {45447, 60906}, {45459, 60909}, {45461, 60910}, {45463, 60916}, {45465, 60917}, {45466, 60918}, {45471, 60919}, {45485, 60921}, {45486, 60920}, {45489, 60922}, {45491, 60923}, {45493, 60924}, {45495, 60925}, {45497, 60926}, {49324, 49346}

X(60889) = midpoint of X(i) and X(j) for these {i,j}: {7, 60907}
X(60889) = reflection of X(i) in X(j) for these {i,j}: {3, 60891}, {60888, 7}
X(60889) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 51190, 60914}, {7, 5845, 60888}, {7, 60887, 51150}, {7, 60907, 5845}

X(60890) = ORTHOLOGY CENTER OF 1ST ANTI-KENMOTU-FREE-VERTICES WRT AGUILERA TRIANGLE

Barycentrics    -3*a^4*b^2-b^4*(b-c)^2+4*a^4*b*c-3*a^4*c^2+2*b^2*(b-c)^2*c^2-(b-c)^2*c^4+2*a^5*(b+c)-2*a^3*b^2*(b+c)-2*a^3*c^2*(b+c)+2*a^2*(b-c)^2*(2*b^2+b*c+2*c^2)-(4*a^4+2*a^2*b^2-2*b^2*(b-c)^2+2*a^2*c^2-2*(b-c)^2*c^2-4*a^3*(b+c))*S : :

X(60890) lies on these lines: {3, 60888}, {7, 372}, {9, 641}, {39, 60914}, {144, 45508}, {182, 5845}, {390, 45572}, {516, 45715}, {518, 48746}, {527, 41490}, {971, 48466}, {1001, 45540}, {2801, 48754}, {4312, 45530}, {5062, 60913}, {5220, 45558}, {5223, 45546}, {5542, 45500}, {5759, 45498}, {5762, 9739}, {5779, 45554}, {5805, 45544}, {5843, 48772}, {5850, 48764}, {5856, 48705}, {11495, 45520}, {16112, 45556}, {21151, 45553}, {21168, 45522}, {36996, 45510}, {45349, 60880}, {45351, 60881}, {45377, 60884}, {45410, 59380}, {45502, 60879}, {45504, 60882}, {45506, 60883}, {45515, 60887}, {45516, 60893}, {45519, 60892}, {45526, 60895}, {45528, 60896}, {45532, 60897}, {45534, 60898}, {45536, 60899}, {45538, 60900}, {45542, 60901}, {45548, 60906}, {45550, 60907}, {45560, 60909}, {45562, 60910}, {45565, 60916}, {45566, 60918}, {45569, 60917}, {45570, 60919}, {45574, 60920}, {45577, 60921}, {45578, 60922}, {45580, 60923}, {45582, 60924}, {45584, 60925}, {45586, 60926}, {48740, 48762}

X(60890) = midpoint of X(i) and X(j) for these {i,j}: {3, 60888}
X(60890) = reflection of X(i) in X(j) for these {i,j}: {60891, 31657}
X(60890) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5845, 31657, 60891}

X(60891) = ORTHOLOGY CENTER OF 2ND ANTI-KENMOTU-FREE-VERTICES WRT AGUILERA TRIANGLE

Barycentrics    3*a^4*b^2+b^4*(b-c)^2-4*a^4*b*c+3*a^4*c^2-2*b^2*(b-c)^2*c^2+(b-c)^2*c^4-2*a^5*(b+c)+2*a^3*b^2*(b+c)+2*a^3*c^2*(b+c)-2*a^2*(b-c)^2*(2*b^2+b*c+2*c^2)-(4*a^4+2*a^2*b^2-2*b^2*(b-c)^2+2*a^2*c^2-2*(b-c)^2*c^2-4*a^3*(b+c))*S : :

X(60891) lies on these lines: {3, 60889}, {7, 371}, {9, 642}, {39, 60913}, {144, 45509}, {182, 5845}, {390, 45573}, {516, 45716}, {518, 48747}, {527, 41491}, {971, 48467}, {1001, 45541}, {2801, 48755}, {4312, 45531}, {5058, 60914}, {5220, 45559}, {5223, 45547}, {5542, 45501}, {5759, 45499}, {5762, 9738}, {5779, 45555}, {5805, 45545}, {5843, 48773}, {5850, 48765}, {5856, 48706}, {11495, 45521}, {16112, 45557}, {21151, 45552}, {21168, 45523}, {36996, 45511}, {45350, 60881}, {45352, 60880}, {45378, 60884}, {45411, 59380}, {45503, 60879}, {45505, 60882}, {45507, 60883}, {45513, 60887}, {45517, 60892}, {45518, 60893}, {45524, 60894}, {45527, 60895}, {45529, 60896}, {45533, 60897}, {45535, 60898}, {45537, 60899}, {45539, 60900}, {45543, 60901}, {45549, 60906}, {45551, 60908}, {45561, 60909}, {45563, 60910}, {45564, 60915}, {45567, 60917}, {45568, 60918}, {45571, 60919}, {45575, 60921}, {45576, 60920}, {45579, 60922}, {45581, 60923}, {45583, 60924}, {45585, 60925}, {45587, 60926}, {48741, 48763}

X(60891) = midpoint of X(i) and X(j) for these {i,j}: {3, 60889}
X(60891) = reflection of X(i) in X(j) for these {i,j}: {60890, 31657}

X(60892) = ORTHOLOGY CENTER OF ANTI-LUCAS(+1) HOMOTHETIC WRT AGUILERA TRIANGLE

Barycentrics    -a^11+7*a^10*(b+c)+a^9*(13*b^2-10*b*c+13*c^2)-a^8*(15*b^3+17*b^2*c+17*b*c^2+15*c^3)+a^7*(-30*b^4+4*b^3*c-64*b^2*c^2+4*b*c^3-30*c^4)+(b-c)^4*(b+c)^3*(b^4-4*b^3*c-6*b^2*c^2-4*b*c^3+c^4)-a*(b-c)^4*(b+c)^2*(3*b^4+4*b^3*c+14*b^2*c^2+4*b*c^3+3*c^4)+2*a^6*(b^5+11*b^4*c-14*b^3*c^2-14*b^2*c^3+11*b*c^4+c^5)+2*a^5*(11*b^6+12*b^5*c+19*b^4*c^2+68*b^3*c^3+19*b^2*c^4+12*b*c^5+11*c^6)+2*a^4*(7*b^7-13*b^6*c+11*b^5*c^2+3*b^4*c^3+3*b^3*c^4+11*b^2*c^5-13*b*c^6+7*c^7)-a^2*(b-c)^2*(9*b^7-b^6*c-39*b^5*c^2-65*b^4*c^3-65*b^3*c^4-39*b^2*c^5-b*c^6+9*c^7)-a^3*(b^8+20*b^7*c-16*b^6*c^2-4*b^5*c^3-130*b^4*c^4-4*b^3*c^5-16*b^2*c^6+20*b*c^7+c^8)+4*(2*a^9+a^8*(b+c)-a^7*(4*b^2+3*b*c+4*c^2)+a^5*b*c*(17*b^2-14*b*c+17*c^2)-a^6*(10*b^3+7*b^2*c+7*b*c^2+10*c^3)+a^4*(8*b^5+3*b^4*c+5*b^3*c^2+5*b^2*c^3+3*b*c^4+8*c^5)-a*(b-c)^2*(2*b^6+b^5*c-6*b^4*c^2-6*b^3*c^3-6*b^2*c^4+b*c^5+2*c^6)+a^3*(4*b^6-b^5*c+28*b^4*c^2+22*b^3*c^3+28*b^2*c^4-b*c^5+4*c^6)-(b-c)^2*(b^7+2*b^6*c-7*b^4*c^3-7*b^3*c^4+2*b*c^6+c^7)+a^2*(2*b^7+3*b^6*c+7*b^5*c^2-16*b^4*c^3-16*b^3*c^4+7*b^2*c^5+3*b*c^6+2*c^7))*S : :
Barycentrics    (b^2 + S)*(c^2 + S)*(2*a^3*(a - b - c) + (a + b - c)*(a - b + c)*S) (Peter Moses, December 14, 2023)

X(60892) lies on these lines: {7, 493}, {9, 5490}, {144, 26494}, {390, 26495}, {516, 45718}, {518, 49402}, {527, 45699}, {971, 48468}, {1001, 26322}, {2801, 49410}, {4312, 26298}, {5220, 26483}, {5223, 26442}, {5542, 26367}, {5759, 26292}, {5762, 49378}, {5779, 26466}, {5805, 26328}, {5843, 49428}, {5845, 45727}, {5850, 49420}, {5856, 48707}, {6464, 60893}, {7717, 8948}, {11495, 26493}, {16112, 26488}, {18521, 60884}, {26304, 60897}, {26312, 60900}, {26337, 60907}, {26347, 60908}, {26353, 60919}, {26373, 60879}, {26391, 60880}, {26415, 60881}, {26427, 60882}, {26433, 60883}, {26439, 36996}, {26447, 60906}, {26460, 60887}, {26471, 60910}, {26477, 60909}, {26496, 60894}, {26498, 31657}, {26499, 60895}, {26500, 60896}, {26501, 60926}, {45413, 60889}, {45415, 60888}, {45517, 60891}, {45519, 60890}, {45589, 60898}, {45591, 60899}, {45593, 60901}, {45596, 60914}, {45597, 60913}, {45600, 60916}, {45601, 60915}, {45603, 60918}, {45606, 60921}, {45607, 60920}, {45610, 60922}, {45612, 60923}, {45614, 60924}, {45615, 60925}, {49396, 49418}

X(60893) = ORTHOLOGY CENTER OF ANTI-LUCAS(-1) HOMOTHETIC WRT AGUILERA TRIANGLE

Barycentrics    a^11-13*a^9*b^2+30*a^7*b^4-22*a^5*b^6+a^3*b^8+3*a*b^8*(b-c)^2+10*a^9*b*c-4*a^7*b^3*c-24*a^5*b^5*c+20*a^3*b^7*c+4*a*b^7*(b-c)^2*c-13*a^9*c^2+64*a^7*b^2*c^2-38*a^5*b^4*c^2-16*a^3*b^6*c^2+8*a*b^6*(b-c)^2*c^2-4*a^7*b*c^3-136*a^5*b^3*c^3-4*a^3*b^5*c^3-4*a*b^5*(b-c)^2*c^3+30*a^7*c^4-38*a^5*b^2*c^4-130*a^3*b^4*c^4-22*a*b^4*(b-c)^2*c^4-24*a^5*b*c^5-4*a^3*b^3*c^5-4*a*b^3*(b-c)^2*c^5-22*a^5*c^6-16*a^3*b^2*c^6+8*a*b^2*(b-c)^2*c^6+20*a^3*b*c^7+4*a*b*(b-c)^2*c^7+a^3*c^8+3*a*(b-c)^2*c^8-7*a^10*(b+c)+15*a^8*b^2*(b+c)-2*a^6*b^4*(b+c)-14*a^4*b^6*(b+c)+9*a^2*b^8*(b+c)-b^8*(b-c)^2*(b+c)+2*a^8*b*c*(b+c)-20*a^6*b^3*c*(b+c)+40*a^4*b^5*c*(b+c)-28*a^2*b^7*c*(b+c)+4*b^7*(b-c)^2*c*(b+c)+15*a^8*c^2*(b+c)+48*a^6*b^2*c^2*(b+c)-62*a^4*b^4*c^2*(b+c)+8*b^6*(b-c)^2*c^2*(b+c)-20*a^6*b*c^3*(b+c)+56*a^4*b^3*c^3*(b+c)+12*a^2*b^5*c^3*(b+c)-4*b^5*(b-c)^2*c^3*(b+c)-2*a^6*c^4*(b+c)-62*a^4*b^2*c^4*(b+c)+14*a^2*b^4*c^4*(b+c)-14*b^4*(b-c)^2*c^4*(b+c)+40*a^4*b*c^5*(b+c)+12*a^2*b^3*c^5*(b+c)-4*b^3*(b-c)^2*c^5*(b+c)-14*a^4*c^6*(b+c)+8*b^2*(b-c)^2*c^6*(b+c)-28*a^2*b*c^7*(b+c)+4*b*(b-c)^2*c^7*(b+c)+9*a^2*c^8*(b+c)-(b-c)^2*c^8*(b+c)+(8*a^9-16*a^7*b^2+16*a^3*b^6-8*a*b^6*(b-c)^2-12*a^7*b*c+68*a^5*b^3*c-4*a^3*b^5*c-4*a*b^5*(b-c)^2*c-16*a^7*c^2-56*a^5*b^2*c^2+112*a^3*b^4*c^2+24*a*b^4*(b-c)^2*c^2+68*a^5*b*c^3+88*a^3*b^3*c^3+24*a*b^3*(b-c)^2*c^3+112*a^3*b^2*c^4+24*a*b^2*(b-c)^2*c^4-4*a^3*b*c^5-4*a*b*(b-c)^2*c^5+16*a^3*c^6-8*a*(b-c)^2*c^6+4*a^8*(b+c)-40*a^6*b^2*(b+c)+32*a^4*b^4*(b+c)+8*a^2*b^6*(b+c)-4*b^6*(b-c)^2*(b+c)+12*a^6*b*c*(b+c)-20*a^4*b^3*c*(b+c)+4*a^2*b^5*c*(b+c)-4*b^5*(b-c)^2*c*(b+c)-40*a^6*c^2*(b+c)+40*a^4*b^2*c^2*(b+c)+24*a^2*b^4*c^2*(b+c)+4*b^4*(b-c)^2*c^2*(b+c)-20*a^4*b*c^3*(b+c)-88*a^2*b^3*c^3*(b+c)+24*b^3*(b-c)^2*c^3*(b+c)+32*a^4*c^4*(b+c)+24*a^2*b^2*c^4*(b+c)+4*b^2*(b-c)^2*c^4*(b+c)+4*a^2*b*c^5*(b+c)-4*b*(b-c)^2*c^5*(b+c)+8*a^2*c^6*(b+c)-4*(b-c)^2*c^6*(b+c))*S : :
Barycentrics    (b^2 - S)*(c^2 - S)*(2*a^3*(a - b - c) - (a + b - c)*(a - b + c)*S) (Peter Moses, December 14, 2023)

X(60893) lies on these lines: {7, 494}, {9, 5491}, {144, 26503}, {390, 26504}, {516, 45717}, {518, 49401}, {527, 45698}, {971, 48469}, {1001, 26323}, {2801, 49409}, {4312, 26299}, {5220, 26484}, {5223, 26443}, {5542, 26368}, {5759, 26293}, {5762, 49377}, {5779, 26467}, {5805, 26329}, {5843, 49427}, {5845, 45726}, {5850, 49419}, {5856, 48708}, {6464, 60892}, {7717, 8946}, {11495, 26502}, {16112, 26489}, {18523, 60884}, {26305, 60897}, {26313, 60900}, {26338, 60908}, {26354, 60919}, {26374, 60879}, {26392, 60880}, {26416, 60881}, {26428, 60882}, {26434, 60883}, {26440, 36996}, {26448, 60906}, {26461, 60887}, {26472, 60910}, {26478, 60909}, {26505, 60894}, {26507, 31657}, {26508, 60895}, {26509, 60896}, {26510, 60926}, {26511, 60925}, {45412, 60888}, {45414, 60889}, {45516, 60890}, {45518, 60891}, {45588, 60898}, {45590, 60899}, {45592, 60901}, {45594, 60907}, {45595, 60913}, {45598, 60914}, {45599, 60915}, {45602, 60916}, {45604, 60917}, {45605, 60920}, {45608, 60921}, {45609, 60922}, {45611, 60923}, {45613, 60924}, {49395, 49417}

X(60894) = ORTHOLOGY CENTER OF 3RD ANTI-TRI-SQUARES-CENTRAL WRT AGUILERA TRIANGLE

Barycentrics    2*a^4+a^2*b^2-b^2*(b-c)^2+a^2*c^2-(b-c)^2*c^2-2*a^3*(b+c)+(5*a^2-3*(b-c)^2-2*a*(b+c))*S : :

X(60894) lies on these lines: {7, 3068}, {9, 26361}, {144, 492}, {193, 4440}, {390, 26514}, {516, 45719}, {518, 49060}, {527, 5860}, {971, 48476}, {1001, 26324}, {2801, 49068}, {4312, 26300}, {5220, 26485}, {5223, 26444}, {5542, 26369}, {5759, 26294}, {5762, 49038}, {5779, 26468}, {5805, 26330}, {5843, 49086}, {5850, 49078}, {5856, 48711}, {11495, 26512}, {16112, 26490}, {18539, 60884}, {21168, 45522}, {26306, 60897}, {26314, 60900}, {26339, 60907}, {26355, 60919}, {26375, 60879}, {26396, 60880}, {26420, 60881}, {26429, 60882}, {26435, 60883}, {26441, 36996}, {26449, 60906}, {26462, 60887}, {26473, 60910}, {26479, 60909}, {26496, 60892}, {26505, 60893}, {26516, 31657}, {26517, 60895}, {26518, 60896}, {26519, 60926}, {26520, 60925}, {44594, 60913}, {44595, 60914}, {45420, 60889}, {45524, 60891}, {49012, 60898}, {49014, 60899}, {49016, 60901}, {49018, 60915}, {49020, 60917}, {49022, 60918}, {49026, 60921}, {49028, 60922}, {49030, 60923}, {49032, 60924}, {49054, 49076}

X(60894) = reflection of X(i) in X(j) for these {i,j}: {144, 60888}, {60907, 60933}

X(60895) = ORTHOLOGY CENTER OF ANTI-INNER-YFF WRT AGUILERA TRIANGLE

Barycentrics    a^6+2*a^3*b*c*(b+c)+2*a*b*(b-c)^2*c*(b+c)-(b-c)^4*(b+c)^2-a^4*(3*b^2+2*b*c+3*c^2)+a^2*(b-c)^2*(3*b^2+2*b*c+3*c^2) : :
X(60895) = -X[40]+3*X[6173], -X[944]+3*X[51099], -2*X[1483]+3*X[42871], -2*X[3826]+3*X[38107], -5*X[5818]+9*X[38073], -3*X[5886]+2*X[15254], -5*X[7987]+9*X[38024], -7*X[10248]+3*X[36991], -X[12512]+3*X[51098], -2*X[15481]+3*X[38108], -X[20070]+9*X[59375], -7*X[31423]+9*X[38093] and many others

X(60895) lies on these lines: {1, 7}, {2, 5536}, {3, 25557}, {4, 2801}, {5, 5220}, {9, 6832}, {10, 52457}, {11, 5729}, {35, 36976}, {40, 6173}, {46, 30379}, {56, 36971}, {142, 5709}, {144, 10527}, {219, 5829}, {226, 54408}, {329, 3817}, {355, 518}, {498, 61008}, {499, 37787}, {517, 5880}, {527, 946}, {528, 1482}, {942, 38007}, {944, 51099}, {954, 26357}, {971, 16127}, {993, 5603}, {1001, 5762}, {1125, 5758}, {1479, 10394}, {1483, 42871}, {1699, 5905}, {1836, 10947}, {2078, 3474}, {2095, 7680}, {2323, 5819}, {2550, 6901}, {3062, 45648}, {3085, 30275}, {3086, 12848}, {3090, 51573}, {3295, 8255}, {3296, 34917}, {3333, 60982}, {3336, 18223}, {3337, 6890}, {3338, 60932}, {3434, 5696}, {3656, 28534}, {3678, 6864}, {3746, 10044}, {3751, 53599}, {3826, 38107}, {4860, 37374}, {4973, 6935}, {5045, 16134}, {5178, 41228}, {5223, 6734}, {5249, 41338}, {5572, 45654}, {5687, 61035}, {5715, 5811}, {5751, 13476}, {5759, 11012}, {5763, 25524}, {5779, 5852}, {5812, 13374}, {5818, 38073}, {5840, 25558}, {5843, 10943}, {5845, 45728}, {5851, 37726}, {5856, 22753}, {5886, 15254}, {5903, 10043}, {5904, 6835}, {6361, 34486}, {6594, 6970}, {6763, 6837}, {6831, 41555}, {6833, 60989}, {6836, 18398}, {6851, 12005}, {6865, 58565}, {6889, 24468}, {6962, 37731}, {7741, 41700}, {7982, 17647}, {7987, 38024}, {7988, 31018}, {8257, 10200}, {8545, 12047}, {8581, 45634}, {9535, 29657}, {9612, 54159}, {9776, 10164}, {9778, 26842}, {9779, 17484}, {9812, 17483}, {10072, 60951}, {10171, 18228}, {10248, 36991}, {10267, 11495}, {10268, 43151}, {10529, 20059}, {10573, 45043}, {10595, 16113}, {10597, 35514}, {10680, 13743}, {10902, 21151}, {11240, 14450}, {11246, 33925}, {11372, 45632}, {11376, 11662}, {11415, 11522}, {11813, 60940}, {12001, 51514}, {12053, 61021}, {12114, 22791}, {12116, 16116}, {12436, 54205}, {12512, 51098}, {12608, 52684}, {12617, 54422}, {12649, 59385}, {12675, 12699}, {13408, 29181}, {14100, 45638}, {14986, 60975}, {15298, 21617}, {15299, 41572}, {15481, 38108}, {15909, 43740}, {16202, 59380}, {18393, 60946}, {18412, 37702}, {18544, 60884}, {19049, 60914}, {19050, 60913}, {19854, 60981}, {20070, 59375}, {23708, 50573}, {24299, 38030}, {24390, 42014}, {24987, 38052}, {25466, 33558}, {26308, 60897}, {26317, 60900}, {26333, 37826}, {26342, 60907}, {26349, 60908}, {26377, 60879}, {26399, 60880}, {26423, 60881}, {26431, 60882}, {26437, 42884}, {26452, 60906}, {26464, 60887}, {26475, 60910}, {26481, 60909}, {26499, 60892}, {26508, 60893}, {26517, 60894}, {30318, 45287}, {31162, 60963}, {31423, 38093}, {34485, 34919}, {35252, 38031}, {37022, 52783}, {37550, 60992}, {37692, 61015}, {38059, 60959}, {38130, 58433}, {45422, 60888}, {45423, 60889}, {45526, 60890}, {45527, 60891}, {45625, 60898}, {45626, 60899}, {45630, 60901}, {45640, 60915}, {45641, 60916}, {45644, 60918}, {45645, 60917}, {45650, 60920}, {45651, 60921}, {47375, 59719}, {49170, 60962}, {50443, 61007}, {51489, 58564}, {55104, 60978}

X(60895) = midpoint of X(i) and X(j) for these {i,j}: {1, 5735}, {1482, 52682}, {11372, 60933}, {31162, 60963}, {4301, 30424}, {4312, 43166}
X(60895) = reflection of X(i) in X(j) for these {i,j}: {1001, 20330}, {144, 60911}, {11495, 31657}, {3, 25557}, {43177, 43180}, {43178, 43177}, {5220, 5}, {5759, 52769}, {5779, 42356}, {51489, 58564}, {52684, 12608}, {54370, 946}, {60896, 7}
X(60895) = anticomplement of X(60912)
X(60895) = X(i)-Dao conjugate of X(j) for these {i, j}: {60912, 60912}
X(60895) = pole of line {44408, 44811} wrt circumcircle
X(60895) = pole of line {7, 3553} wrt dual conic of Yff parabola
X(60895) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(38007)}}, {{A, B, C, X(4), X(38459)}}, {{A, B, C, X(77), X(3254)}}, {{A, B, C, X(4341), X(15909)}}, {{A, B, C, X(7190), X(34917)}}
X(60895) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5735, 516}, {7, 390, 60923}, {7, 4295, 30424}, {7, 516, 60896}, {7, 55109, 5735}, {7, 60926, 1}, {144, 38037, 60911}, {516, 43177, 43178}, {516, 43180, 43177}, {527, 946, 54370}, {1482, 52682, 528}, {5542, 30424, 4298}, {5759, 38053, 52769}, {5762, 20330, 1001}, {5852, 42356, 5779}, {24474, 26332, 49168}, {25557, 38454, 3}

X(60896) = ORTHOLOGY CENTER OF ANTI-OUTER-YFF WRT AGUILERA TRIANGLE

Barycentrics    a^6-3*a^4*(b-c)^2-2*a^3*b*c*(b+c)-2*a*b*(b-c)^2*c*(b+c)-(b-c)^4*(b+c)^2+a^2*(b-c)^2*(3*b^2+2*b*c+3*c^2) : :
X(60896) = -2*X[6666]+3*X[38123], -2*X[15254]+3*X[38122], -2*X[15481]+3*X[26446], -9*X[15708]+5*X[50840], -3*X[38036]+5*X[61020], -3*X[38107]+2*X[42356], -3*X[38130]+2*X[61000]

X(60896) lies on these lines: {1, 7}, {2, 1768}, {3, 17768}, {4, 3255}, {5, 16112}, {9, 2252}, {35, 10052}, {40, 60933}, {46, 41572}, {79, 6836}, {84, 12609}, {119, 3826}, {142, 3358}, {144, 5552}, {165, 5905}, {191, 37112}, {329, 10164}, {377, 15071}, {443, 31803}, {497, 18240}, {498, 29007}, {499, 60988}, {518, 37562}, {527, 3359}, {631, 3647}, {758, 6916}, {946, 7171}, {971, 5880}, {993, 2096}, {1001, 6914}, {1071, 5832}, {1125, 52027}, {1156, 39692}, {1158, 10198}, {1470, 60883}, {1519, 6173}, {1633, 39475}, {1709, 5249}, {1836, 10167}, {2077, 5759}, {2550, 2801}, {2949, 6908}, {3062, 6870}, {3085, 60934}, {3256, 3474}, {3336, 6838}, {3337, 18224}, {3522, 14450}, {3634, 5811}, {3649, 37022}, {3753, 12678}, {3754, 12667}, {3812, 6259}, {3817, 9776}, {3822, 14647}, {3832, 9782}, {3833, 6939}, {4413, 13257}, {4654, 10860}, {4655, 59620}, {4857, 18223}, {5218, 46684}, {5220, 5843}, {5223, 6735}, {5439, 12679}, {5554, 59412}, {5572, 45655}, {5693, 6897}, {5698, 6875}, {5728, 18838}, {5729, 10958}, {5758, 12512}, {5762, 11248}, {5805, 10202}, {5845, 45729}, {5850, 10915}, {5856, 25438}, {5884, 6850}, {5902, 6925}, {5927, 41706}, {6223, 19925}, {6326, 6955}, {6666, 38123}, {6684, 60942}, {6701, 6855}, {6825, 60994}, {6832, 7701}, {6843, 60987}, {6847, 11263}, {6862, 49107}, {6864, 31871}, {6865, 45084}, {6909, 16133}, {6918, 18243}, {6928, 49194}, {6934, 16132}, {6962, 37524}, {6964, 16009}, {6965, 47034}, {6966, 37701}, {6974, 26725}, {6982, 10265}, {7580, 11246}, {7951, 41694}, {7967, 12119}, {7987, 11415}, {7989, 41690}, {7992, 12617}, {8581, 45635}, {9778, 17483}, {9812, 26842}, {9843, 10309}, {9943, 57282}, {10246, 38761}, {10270, 43151}, {10310, 41548}, {10528, 20059}, {10531, 59386}, {10573, 40269}, {10679, 38454}, {10805, 35514}, {10940, 24982}, {11220, 20292}, {11227, 24703}, {11239, 60984}, {11571, 12647}, {12000, 51514}, {12246, 28629}, {12436, 54227}, {12514, 61002}, {12699, 58567}, {12703, 54158}, {12705, 51706}, {13243, 33108}, {13329, 24695}, {13369, 48482}, {14100, 45639}, {15064, 26040}, {15254, 38122}, {15298, 60936}, {15299, 30379}, {15481, 26446}, {15708, 50840}, {15931, 44447}, {16143, 50695}, {16203, 25557}, {16209, 21153}, {17613, 17718}, {17860, 26871}, {18228, 58441}, {18542, 60884}, {18545, 38121}, {19047, 60914}, {19048, 60913}, {21077, 37560}, {21164, 51090}, {21616, 37526}, {24927, 38030}, {26309, 60897}, {26318, 60900}, {26343, 60907}, {26350, 60908}, {26358, 60919}, {26378, 60879}, {26400, 60880}, {26424, 60881}, {26432, 60882}, {26453, 60906}, {26465, 60887}, {26476, 60910}, {26482, 60909}, {26500, 60892}, {26509, 60893}, {26518, 60894}, {28628, 34862}, {29301, 36674}, {31658, 37713}, {34919, 46435}, {35010, 38037}, {36991, 41698}, {37606, 38759}, {38036, 61020}, {38107, 42356}, {38130, 61000}, {38204, 60959}, {41389, 44785}, {41707, 50573}, {45424, 60888}, {45425, 60889}, {45528, 60890}, {45529, 60891}, {45627, 60898}, {45628, 60899}, {45631, 60901}, {45642, 60915}, {45643, 60916}, {45646, 60918}, {45647, 60917}, {45652, 60920}, {45653, 60921}, {49163, 49184}, {51366, 59600}

X(60896) = midpoint of X(i) and X(j) for these {i,j}: {1071, 17668}, {2550, 36996}, {2951, 5735}, {3255, 49178}, {30424, 43182}, {40, 60933}, {4312, 5732}
X(60896) = reflection of X(i) in X(j) for these {i,j}: {1001, 31657}, {144, 60912}, {16112, 5}, {43175, 43176}, {43178, 43182}, {5698, 52769}, {5779, 3826}, {54370, 142}, {60895, 7}, {60942, 6684}, {60965, 21077}, {946, 60980}
X(60896) = anticomplement of X(60911)
X(60896) = X(i)-Dao conjugate of X(j) for these {i, j}: {60911, 60911}
X(60896) = pole of line {28473, 44408} wrt circumcircle
X(60896) = pole of line {7, 3554} wrt dual conic of Yff parabola
X(60896) = intersection, other than A, B, C, of circumconics {{A, B, C, X(77), X(3255)}}, {{A, B, C, X(279), X(5553)}}
X(60896) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 390, 60924}, {7, 516, 60895}, {7, 60925, 1}, {516, 43176, 43175}, {516, 43182, 43178}, {2550, 36996, 2801}, {2951, 5735, 516}, {3826, 5851, 5779}, {5698, 21151, 52769}, {11495, 42885, 11248}, {12608, 37534, 10200}, {15016, 49178, 4}, {43175, 43177, 43176}

X(60897) = ORTHOLOGY CENTER OF ARA WRT AGUILERA TRIANGLE

Barycentrics    a^2*(a^6+a^4*(b-c)^2-2*a^5*(b+c)+2*a*(b-c)^2*(b+c)^3-(b-c)^2*(b^2+c^2)^2-a^2*(b^4-6*b^2*c^2+c^4)) : :

X(60897) lies on these lines: {3, 9}, {7, 25}, {22, 144}, {23, 20059}, {24, 36996}, {26, 5843}, {105, 28015}, {142, 5020}, {159, 5845}, {182, 58534}, {197, 11495}, {222, 2212}, {390, 8192}, {480, 37577}, {516, 9798}, {518, 3556}, {527, 9909}, {954, 13730}, {1001, 22654}, {1400, 3423}, {1423, 1617}, {1445, 1473}, {1486, 24328}, {1593, 36991}, {1597, 31672}, {1598, 5805}, {2354, 37492}, {2801, 9912}, {2808, 3197}, {4224, 8232}, {4312, 8185}, {4343, 54312}, {4357, 13615}, {5198, 59385}, {5220, 10830}, {5223, 8193}, {5542, 11365}, {5572, 22769}, {5594, 60908}, {5595, 60907}, {5759, 11414}, {5762, 7387}, {5817, 7395}, {5850, 49553}, {5851, 54065}, {5856, 13222}, {6600, 20760}, {6636, 61006}, {6642, 31657}, {6666, 16419}, {7071, 7291}, {7085, 60949}, {7484, 18230}, {7506, 59380}, {7517, 60922}, {7529, 38107}, {7580, 27509}, {7677, 28376}, {8190, 60898}, {8191, 60899}, {8194, 60917}, {8195, 60918}, {8732, 33849}, {9626, 41705}, {9818, 60901}, {9911, 12411}, {10037, 60923}, {10046, 60924}, {10323, 21168}, {10594, 59386}, {10790, 60882}, {10828, 60900}, {10829, 16112}, {10831, 60909}, {10832, 60910}, {10833, 60919}, {10834, 60925}, {10835, 60926}, {11284, 60996}, {11853, 60906}, {13889, 60920}, {13943, 60921}, {14100, 16541}, {15804, 56547}, {17257, 20835}, {17810, 58472}, {18378, 51514}, {18482, 18535}, {18534, 31671}, {18621, 34371}, {18954, 60883}, {19006, 60887}, {19459, 51190}, {19541, 56445}, {20834, 45705}, {20850, 60933}, {21279, 28044}, {26302, 60880}, {26303, 60881}, {26304, 60892}, {26305, 60893}, {26306, 60894}, {26308, 60895}, {26309, 60896}, {26685, 37309}, {26866, 60948}, {26939, 37426}, {35776, 60915}, {35777, 60916}, {37198, 59418}, {37366, 61019}, {37485, 50995}, {37581, 60990}, {44598, 60913}, {44599, 60914}, {45428, 60888}, {45429, 60889}, {45532, 60890}, {45533, 60891}

X(60897) = reflection of X(i) in X(j) for these {i,j}: {42460, 18621}
X(60897) = pole of line {3900, 17069} wrt circumcircle
X(60897) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {18621, 34371, 42460}

X(60898) = ORTHOLOGY CENTER OF 1ST AURIGA WRT AGUILERA TRIANGLE

Barycentrics    a^2*(-a+b+c)*r+(4*a^3-3*a^2*b-b^3-3*a^2*c+b^2*c+b*c^2-c^3)*(-2*R+sqrt(R*(r+4*R))) : :

X(60898) lies on these lines: {7, 5597}, {9, 5599}, {55, 226}, {144, 5601}, {390, 5598}, {518, 12454}, {527, 11207}, {528, 11208}, {971, 9834}, {1001, 11493}, {2550, 5600}, {2801, 12460}, {3485, 26401}, {4312, 8186}, {5220, 11867}, {5223, 8197}, {5542, 11366}, {5759, 11822}, {5762, 11252}, {5779, 8200}, {5805, 8196}, {5843, 32146}, {5845, 12452}, {5850, 49555}, {5853, 12455}, {5856, 13228}, {6147, 26399}, {8190, 60897}, {8198, 60907}, {8199, 60908}, {8201, 60917}, {8202, 60918}, {10386, 26423}, {11367, 30331}, {11384, 60879}, {11492, 11495}, {11823, 35514}, {11837, 60882}, {11843, 36996}, {11861, 60900}, {11863, 60906}, {11865, 16112}, {11869, 60909}, {11871, 60910}, {11873, 60919}, {11875, 60922}, {11877, 60923}, {11879, 60924}, {11881, 60925}, {11883, 60926}, {12458, 12464}, {13890, 60920}, {13944, 60921}, {15171, 26389}, {18495, 60901}, {18955, 60883}, {19008, 60887}, {35778, 60915}, {35781, 60916}, {44600, 60913}, {44601, 60914}, {45353, 60881}, {45379, 60884}, {45430, 60888}, {45431, 60889}, {45534, 60890}, {45535, 60891}, {45588, 60893}, {45589, 60892}, {45625, 60895}, {45627, 60896}, {49012, 60894}

X(60898) = reflection of X(i) in X(j) for these {i,j}: {60899, 55}
X(60898) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {55, 516, 60899}

X(60899) = ORTHOLOGY CENTER OF 2ND AURIGA WRT AGUILERA TRIANGLE

Barycentrics    a^2*(-a+b+c)*r-(4*a^3-3*a^2*b-b^3-3*a^2*c+b^2*c+b*c^2-c^3)*(2*R+sqrt(R*(r+4*R))) : :

X(60899) lies on these lines: {7, 5598}, {9, 5600}, {55, 226}, {144, 5602}, {390, 5597}, {518, 12455}, {527, 11208}, {528, 11207}, {971, 9835}, {1001, 11492}, {2550, 5599}, {2801, 12461}, {3485, 26425}, {4312, 8187}, {5220, 11868}, {5223, 8204}, {5542, 11367}, {5759, 11823}, {5762, 11253}, {5779, 8207}, {5805, 8203}, {5843, 32147}, {5845, 12453}, {5850, 49556}, {5853, 12454}, {5856, 13230}, {6147, 26423}, {8191, 60897}, {8205, 60907}, {8206, 60908}, {8208, 60917}, {8209, 60918}, {10386, 26399}, {11366, 30331}, {11385, 60879}, {11493, 11495}, {11822, 35514}, {11838, 60882}, {11844, 36996}, {11862, 60900}, {11864, 60906}, {11866, 16112}, {11870, 60909}, {11872, 60910}, {11874, 60919}, {11876, 60922}, {11878, 60923}, {11880, 60924}, {11882, 60925}, {11884, 60926}, {12459, 12465}, {13891, 60920}, {13945, 60921}, {15171, 26413}, {18497, 60901}, {18956, 60883}, {19010, 60887}, {35779, 60916}, {35780, 60915}, {44602, 60913}, {44603, 60914}, {45354, 60880}, {45380, 60884}, {45432, 60888}, {45433, 60889}, {45536, 60890}, {45537, 60891}, {45590, 60893}, {45591, 60892}, {45626, 60895}, {45628, 60896}, {49014, 60894}

X(60899) = reflection of X(i) in X(j) for these {i,j}: {60898, 55}
X(60899) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {55, 516, 60898}

X(60900) = ORTHOLOGY CENTER OF 5TH BROCARD WRT AGUILERA TRIANGLE

Barycentrics    2*a^6-2*a^5*(b+c)+a^4*(b^2+c^2)+a^2*b*c*(2*b^2-b*c+2*c^2)-(b-c)^2*(b^4+b^2*c^2+c^4) : :

X(60900) lies on these lines: {7, 32}, {9, 3096}, {142, 7846}, {144, 2896}, {390, 9997}, {516, 9941}, {518, 12495}, {527, 7811}, {971, 9873}, {1001, 22744}, {2801, 12498}, {3094, 5845}, {3098, 5759}, {3099, 4312}, {5220, 10872}, {5223, 9857}, {5542, 11368}, {5762, 9821}, {5779, 9996}, {5805, 9993}, {5817, 10356}, {5843, 32151}, {5850, 49561}, {5856, 13235}, {6172, 7865}, {7914, 18230}, {9301, 60922}, {9862, 36996}, {9994, 60907}, {9995, 60908}, {10038, 60923}, {10047, 60924}, {10357, 21168}, {10828, 60897}, {10871, 16112}, {10873, 60909}, {10874, 60910}, {10875, 60917}, {10876, 60918}, {10877, 60919}, {10878, 60925}, {10879, 60926}, {11386, 60879}, {11494, 11495}, {11861, 60898}, {11862, 60899}, {11885, 60906}, {12497, 12500}, {13892, 60920}, {13946, 60921}, {18500, 60901}, {18503, 60884}, {18957, 60883}, {19012, 60887}, {26310, 60880}, {26311, 60881}, {26312, 60892}, {26313, 60893}, {26314, 60894}, {26316, 31657}, {26317, 60895}, {26318, 60896}, {35782, 60915}, {35783, 60916}, {44604, 60913}, {44605, 60914}, {45434, 60888}, {45435, 60889}, {45538, 60890}, {45539, 60891}

X(60901) = ORTHOLOGY CENTER OF EHRMANN-MID WRT AGUILERA TRIANGLE

Barycentrics    2*a^5*(b+c)+(b-c)^4*(b+c)^2-4*a*(b-c)^2*(b+c)^3+a^4*(-5*b^2+4*b*c-5*c^2)+2*a^3*(b+c)*(b^2+c^2)+2*a^2*(b-c)^2*(2*b^2+3*b*c+2*c^2) : :
X(60901) = -X[3]+3*X[5817], 3*X[4]+X[144], -3*X[5]+2*X[142], -X[7]+3*X[381], -X[20]+3*X[59381], -2*X[182]+3*X[38166], X[355]+X[11372], -6*X[547]+5*X[20195], -2*X[548]+3*X[21153], -3*X[549]+4*X[6666], -5*X[632]+6*X[38318], -2*X[1385]+3*X[38043] and many others

X(60901) lies on these lines: {3, 5817}, {4, 144}, {5, 142}, {7, 381}, {9, 30}, {20, 59381}, {33, 59613}, {140, 5732}, {182, 38166}, {355, 11372}, {382, 5759}, {390, 18525}, {495, 14100}, {496, 8581}, {516, 3627}, {518, 21850}, {527, 3845}, {546, 5805}, {547, 20195}, {548, 21153}, {549, 6666}, {550, 31658}, {632, 38318}, {894, 36722}, {908, 5927}, {942, 10392}, {954, 37234}, {1001, 18761}, {1012, 9945}, {1145, 10724}, {1156, 10742}, {1385, 38043}, {1478, 60910}, {1479, 60909}, {1484, 2801}, {1656, 21151}, {1657, 59418}, {1699, 51463}, {1737, 31391}, {2550, 18357}, {2771, 30329}, {2951, 18529}, {3062, 5587}, {3091, 36996}, {3146, 21168}, {3358, 37281}, {3419, 60966}, {3534, 61023}, {3543, 61006}, {3583, 60919}, {3585, 60883}, {3628, 38122}, {3817, 17051}, {3818, 5845}, {3820, 15587}, {3826, 5499}, {3830, 6172}, {3832, 59386}, {3839, 20059}, {3843, 59385}, {3850, 38150}, {3851, 59380}, {3853, 52835}, {3858, 38137}, {3860, 60963}, {3861, 5735}, {4187, 10861}, {4312, 18492}, {4326, 18528}, {5055, 60996}, {5066, 6173}, {5071, 38065}, {5220, 18517}, {5223, 12699}, {5316, 10157}, {5542, 9955}, {5686, 12702}, {5719, 8232}, {5722, 60937}, {5728, 6147}, {5729, 44229}, {5744, 19541}, {5763, 5777}, {5781, 59594}, {5784, 37356}, {5790, 35514}, {5809, 12433}, {5818, 38121}, {5844, 43166}, {5850, 18483}, {5853, 37705}, {5856, 22938}, {5881, 24644}, {5901, 38037}, {5946, 58473}, {6000, 58534}, {6564, 60913}, {6565, 60914}, {6684, 38179}, {6713, 38180}, {6841, 10394}, {6849, 24470}, {6864, 12684}, {6990, 41543}, {7672, 40266}, {7676, 18524}, {7677, 26321}, {7678, 38055}, {7717, 18494}, {8226, 31019}, {8227, 38030}, {8236, 18526}, {8703, 60986}, {9818, 60897}, {9947, 21628}, {9956, 38158}, {10109, 38093}, {10175, 43182}, {10398, 57282}, {10883, 13257}, {10895, 60923}, {10896, 60924}, {11038, 18493}, {11112, 61012}, {11113, 60969}, {11114, 61025}, {11231, 43151}, {11495, 18491}, {11539, 61001}, {12618, 17239}, {12761, 16112}, {13624, 38059}, {13665, 60887}, {14269, 60957}, {14893, 60977}, {15008, 21620}, {15171, 15298}, {15296, 34352}, {15299, 18990}, {15687, 60942}, {15699, 58433}, {15726, 38042}, {17233, 48878}, {17236, 36652}, {17257, 36721}, {17528, 60959}, {17579, 61026}, {17757, 25722}, {18358, 47595}, {18406, 41700}, {18407, 38454}, {18412, 39542}, {18440, 51190}, {18481, 50243}, {18495, 60898}, {18497, 60899}, {18499, 36976}, {18500, 60900}, {18502, 60882}, {18507, 60906}, {18509, 60907}, {18511, 60908}, {18519, 42884}, {18520, 60917}, {18522, 60918}, {18538, 60920}, {18541, 60939}, {18542, 60925}, {18544, 60926}, {18583, 38145}, {18762, 60921}, {19130, 51150}, {19709, 59374}, {19875, 58834}, {19925, 22792}, {22793, 22801}, {23046, 60962}, {24828, 48938}, {25561, 51151}, {28186, 43161}, {28204, 30331}, {28452, 37787}, {28459, 60981}, {30311, 40269}, {31659, 38181}, {31663, 38130}, {31670, 50995}, {31673, 51090}, {34200, 38067}, {34697, 51768}, {35786, 60915}, {35787, 60916}, {37424, 51489}, {37447, 41228}, {37584, 60949}, {37822, 54135}, {38071, 60980}, {38159, 60759}, {40663, 51790}, {41099, 60984}, {41106, 59375}, {41854, 50205}, {42819, 50824}, {45355, 60880}, {45356, 60881}, {45438, 60888}, {45439, 60889}, {45542, 60890}, {45543, 60891}, {45592, 60893}, {45593, 60892}, {45630, 60895}, {45631, 60896}, {49016, 60894}

X(60901) = midpoint of X(i) and X(j) for these {i,j}: {144, 31671}, {1156, 10742}, {18440, 51190}, {18499, 36976}, {18507, 60906}, {3, 36991}, {355, 11372}, {382, 5759}, {390, 18525}, {3830, 6172}, {31670, 50995}, {31673, 51090}, {37822, 54135}, {4, 5779}, {5223, 12699}, {5728, 40263}, {7, 60884}, {7672, 40266}, {9, 31672}
X(60901) = reflection of X(i) in X(j) for these {i,j}: {20330, 42356}, {2550, 18357}, {31657, 5}, {34773, 1001}, {38113, 5817}, {38171, 38139}, {47595, 18358}, {550, 31658}, {5542, 9955}, {5732, 140}, {5805, 546}, {51150, 19130}, {51151, 25561}, {52835, 3853}, {6173, 5066}, {8703, 60986}
X(60901) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 144, 31671}, {5, 31657, 38171}, {9, 31672, 30}, {144, 31671, 5762}, {381, 60884, 7}, {382, 51516, 5759}, {546, 5843, 5805}, {2801, 42356, 20330}, {3091, 36996, 38107}, {3843, 60922, 59385}, {5779, 31671, 144}, {5805, 59389, 546}, {5817, 36991, 3}, {20330, 42356, 38034}, {31657, 38139, 5}, {38111, 43177, 31657}

X(60902) = ORTHOLOGY CENTER OF AGUILERA WRT EXCENTERS-MIDPOINTS TRIANGLE

Barycentrics    (-a+b+c)*(-2*a^2-(b-c)^2+a*(b+c))+2*a*S : :

X(60902) lies on these lines: {1, 142}, {8, 14121}, {9, 31567}, {145, 176}, {390, 30556}, {482, 3243}, {516, 3640}, {518, 52805}, {519, 3641}, {528, 45713}, {944, 31564}, {1659, 3870}, {3158, 5393}, {3244, 31570}, {3434, 13390}, {3996, 56386}, {4514, 56385}, {5405, 24392}, {5880, 30342}, {7090, 14942}, {12628, 49592}, {12630, 17805}, {13388, 17784}, {13389, 36845}, {15733, 60877}, {20075, 55398}, {30341, 42871}, {31563, 35514}, {45714, 52809}

X(60902) = reflection of X(i) in X(j) for these {i,j}: {12628, 49592}, {52808, 45713}
X(60902) = intersection, other than A, B, C, of circumconics {{A, B, C, X(277), X(14121)}}, {{A, B, C, X(2191), X(42013)}}
X(60902) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 30334, 30557}, {528, 45713, 52808}

X(60903) = ORTHOLOGY CENTER OF AGUILERA WRT EXTOUCH TRIANGLE

Barycentrics    a*(a+b+c)*(a^4*b-2*a^3*b^2+2*a*b^4-b^5+a^4*c+2*a^3*b*c-2*a*b^3*c-b^4*c-2*a^3*c^2+2*b^3*c^2-2*a*b*c^3+2*b^2*c^3+2*a*c^4-b*c^4-c^5)+4*a*S^3 : :

X(60903) lies on these lines: {1, 971}, {4, 481}, {9, 31563}, {40, 31573}, {57, 58896}, {84, 6502}, {103, 6136}, {175, 36991}, {482, 36996}, {515, 52808}, {516, 3640}, {910, 32555}, {944, 31568}, {946, 30342}, {990, 18992}, {1372, 31672}, {1374, 5805}, {1490, 51841}, {1659, 41561}, {1721, 45426}, {1750, 13388}, {2801, 3641}, {3083, 11220}, {3207, 32556}, {5393, 5658}, {5691, 51763}, {5732, 30556}, {10697, 31560}, {13389, 30304}, {15726, 45713}

X(60904) = ORTHOLOGY CENTER OF AGUILERA WRT FUHRMANN TRIANGLE

Barycentrics    -(a*(a+b+c)*(a^3-a^2*b-a*b^2+b^3-a^2*c+3*a*b*c-b^2*c-a*c^2-b*c^2+c^3))+2*(2*a^3-2*a^2*b+a*b^2-b^3-2*a^2*c+b^2*c+a*c^2+b*c^2-c^3)*S : :

X(60904) lies on these lines: {1, 528}, {80, 30432}, {100, 5393}, {482, 14151}, {516, 60886}, {1317, 1371}, {1659, 41553}, {2801, 52805}, {5405, 10707}, {12730, 31538}, {30334, 45043}, {31567, 53055}

X(60905) = ORTHOLOGY CENTER OF INNER-GARCIA WRT AGUILERA TRIANGLE

Barycentrics    5*a^3-2*(b-c)^2*(b+c)-a*(3*b^2+2*b*c+3*c^2) : :
X(60905) = -3*X[2]+2*X[30424], -3*X[7]+4*X[1125], -X[8]+3*X[144], -2*X[10]+3*X[6172], -12*X[142]+13*X[34595], -3*X[390]+2*X[3244], -6*X[551]+5*X[30340], -5*X[3522]+4*X[43181], -10*X[3616]+9*X[38024], -2*X[3621]+3*X[50838], -7*X[3622]+6*X[5542], -5*X[3623]+6*X[30331] and many others

X(60905) lies on these lines: {1, 527}, {2, 30424}, {3, 44785}, {7, 1125}, {8, 144}, {9, 46}, {10, 6172}, {40, 6068}, {57, 4679}, {63, 1699}, {65, 61007}, {72, 5696}, {78, 3648}, {90, 3254}, {142, 34595}, {165, 329}, {200, 17781}, {210, 41866}, {224, 5732}, {238, 4862}, {390, 3244}, {405, 60982}, {518, 3633}, {519, 30332}, {528, 3632}, {551, 30340}, {758, 10394}, {936, 30353}, {954, 28645}, {958, 11662}, {960, 30290}, {971, 5693}, {993, 8543}, {997, 8544}, {1001, 5563}, {1086, 15601}, {1155, 31142}, {1260, 41853}, {1490, 2951}, {1707, 29658}, {1738, 3973}, {1743, 24248}, {1763, 2941}, {1770, 45039}, {1836, 3929}, {2093, 60940}, {2325, 41325}, {2550, 3585}, {2801, 3869}, {3000, 56809}, {3059, 40263}, {3243, 5852}, {3245, 3679}, {3336, 8257}, {3339, 12572}, {3452, 53056}, {3474, 8580}, {3485, 61021}, {3522, 43181}, {3616, 38024}, {3621, 50838}, {3622, 5542}, {3623, 30331}, {3624, 3916}, {3625, 50835}, {3626, 50834}, {3634, 50837}, {3646, 24470}, {3663, 16469}, {3671, 60975}, {3683, 4654}, {3687, 44446}, {3707, 5819}, {3731, 50307}, {3814, 30312}, {3874, 7671}, {3876, 16120}, {3886, 17347}, {3923, 17272}, {3927, 41869}, {3928, 24703}, {3944, 16570}, {4292, 9814}, {4295, 5234}, {4298, 60998}, {4310, 16487}, {4321, 60936}, {4355, 31435}, {4384, 60927}, {4512, 5905}, {4640, 28609}, {4645, 25728}, {4655, 17284}, {4663, 50997}, {4672, 29598}, {4676, 17274}, {4691, 5686}, {4847, 50865}, {4859, 32857}, {4873, 50995}, {4882, 6361}, {4887, 16020}, {4915, 28194}, {4929, 17766}, {5290, 8545}, {5303, 52769}, {5493, 5815}, {5550, 59375}, {5586, 60932}, {5587, 52682}, {5692, 5784}, {5744, 7988}, {5762, 7330}, {5779, 18480}, {5833, 61024}, {5839, 28557}, {5843, 34773}, {5847, 55998}, {5851, 10609}, {5857, 15298}, {5904, 15733}, {6256, 35514}, {6327, 25734}, {6765, 36976}, {7174, 17334}, {7288, 60993}, {7290, 17276}, {7308, 11246}, {7987, 43177}, {8666, 53055}, {9588, 56288}, {9589, 38454}, {9746, 56555}, {9778, 21060}, {9780, 51100}, {9965, 10980}, {10177, 18398}, {10198, 61027}, {10384, 60919}, {10398, 60950}, {10404, 60883}, {11019, 28610}, {11038, 60976}, {11106, 12563}, {11112, 55922}, {11415, 11522}, {11525, 28212}, {12560, 41572}, {12573, 60934}, {12666, 31806}, {13411, 51576}, {13462, 60956}, {14100, 41864}, {14803, 42843}, {15297, 60989}, {15299, 54432}, {15481, 38200}, {15803, 52457}, {15808, 51098}, {16112, 52835}, {16209, 21153}, {17151, 28526}, {17262, 28570}, {17484, 35258}, {18230, 51073}, {18412, 41707}, {18450, 30144}, {18493, 38036}, {19862, 50840}, {20072, 49495}, {20073, 49476}, {20347, 52155}, {21031, 41348}, {21616, 30379}, {23681, 33098}, {24723, 50127}, {25055, 25557}, {25440, 30295}, {25568, 31508}, {25639, 30311}, {28160, 36922}, {28558, 29573}, {29827, 56509}, {30286, 34744}, {30556, 51764}, {30557, 51763}, {31253, 38094}, {33151, 36277}, {35242, 61035}, {37720, 41555}, {38053, 60962}, {38101, 46932}, {38150, 60911}, {39878, 43216}, {40333, 60983}, {41865, 50726}, {43182, 59418}, {46873, 58441}, {46933, 59412}, {47375, 59316}, {49456, 51052}, {51118, 54398}, {54318, 60951}, {60923, 61010}

X(60905) = midpoint of X(i) and X(j) for these {i,j}: {390, 60957}
X(60905) = reflection of X(i) in X(j) for these {i,j}: {1, 5698}, {20059, 5542}, {2093, 60940}, {2550, 60942}, {2951, 5759}, {4312, 9}, {5223, 144}, {5696, 72}, {5735, 54370}, {52835, 16112}, {60933, 1001}, {60971, 551}, {7, 51090}
X(60905) = anticomplement of X(30424)
X(60905) = X(i)-Dao conjugate of X(j) for these {i, j}: {30424, 30424}
X(60905) = pole of line {1019, 6366} wrt Bevan circle
X(60905) = pole of line {28292, 34958} wrt incircle
X(60905) = pole of line {10855, 17603} wrt Feuerbach hyperbola
X(60905) = pole of line {3239, 27115} wrt Steiner circumellipse
X(60905) = pole of line {3700, 46919} wrt Steiner inellipse
X(60905) = pole of line {664, 23890} wrt Yff parabola
X(60905) = pole of line {4162, 7178} wrt Suppa-Cucoanes circle
X(60905) = pole of line {3945, 3946} wrt dual conic of Yff parabola
X(60905) = intersection, other than A, B, C, of circumconics {{A, B, C, X(79), X(10405)}}, {{A, B, C, X(2160), X(3062)}}, {{A, B, C, X(7110), X(28626)}}
X(60905) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5698, 50836}, {9, 17768, 4312}, {63, 5057, 5231}, {72, 15726, 5696}, {144, 516, 5223}, {390, 60957, 5850}, {527, 5698, 1}, {1001, 60933, 59372}, {1698, 4312, 5880}, {1698, 5880, 38052}, {3616, 43180, 38024}, {3616, 60984, 43180}, {3650, 58798, 54290}, {5057, 5231, 1699}, {6173, 15254, 3624}, {9965, 40998, 10980}, {20059, 52653, 5542}, {54290, 58798, 1698}, {56288, 60935, 60912}

X(60906) = ORTHOLOGY CENTER OF GOSSARD WRT AGUILERA TRIANGLE

Barycentrics    (2*a^4-(b^2-c^2)^2-a^2*(b^2+c^2))*(2*a^10-2*a^9*(b+c)+2*a^5*(b+c)*(b^2-2*c^2)*(2*b^2-c^2)-2*a^8*(b^2+c^2)+2*a^7*(b+c)*(b^2+c^2)-6*a^3*(b-c)^2*(b+c)^3*(b^2+c^2)+(b-c)^4*(b+c)^2*(b^2+c^2)^2+a^4*(b^2-c^2)^2*(9*b^2-2*b*c+9*c^2)+a^6*(-5*b^4+12*b^2*c^2-5*c^4)+2*a*(b-c)^2*(b+c)^3*(b^4+3*b^2*c^2+c^4)-a^2*(b^2-c^2)^2*(5*b^4-4*b^3*c+12*b^2*c^2-4*b*c^3+5*c^4)) : :
X(60906) = -4*X[142]+5*X[15183], -2*X[2550]+3*X[16210], -2*X[3243]+3*X[16211], -X[4312]+3*X[11852], -2*X[5542]+3*X[11831], -2*X[5732]+3*X[16190], -2*X[5805]+3*X[11897], -3*X[11038]+4*X[51712], -2*X[11049]+3*X[61023], -3*X[11845]+X[36996], -3*X[11911]+X[60922], -4*X[15184]+5*X[18230] and many others

X(60906) lies on these lines: {7, 402}, {9, 1650}, {30, 5759}, {142, 15183}, {144, 4240}, {390, 11910}, {516, 12438}, {518, 12626}, {527, 1651}, {971, 12113}, {1001, 22755}, {2550, 16210}, {2801, 12729}, {3243, 16211}, {4312, 11852}, {5220, 11904}, {5223, 11900}, {5542, 11831}, {5732, 16190}, {5762, 11251}, {5805, 11897}, {5843, 32162}, {5845, 12583}, {5850, 49585}, {5856, 13268}, {11038, 51712}, {11049, 61023}, {11495, 11848}, {11832, 60879}, {11839, 60882}, {11845, 36996}, {11853, 60897}, {11863, 60898}, {11864, 60899}, {11885, 60900}, {11901, 60907}, {11902, 60908}, {11903, 16112}, {11905, 60909}, {11906, 60910}, {11907, 60917}, {11908, 60918}, {11909, 60919}, {11911, 60922}, {11912, 60923}, {11913, 60924}, {11914, 60925}, {11915, 60926}, {12696, 12789}, {13894, 60920}, {13948, 60921}, {15184, 18230}, {18507, 60901}, {18508, 60884}, {18958, 60883}, {19018, 60887}, {26383, 60880}, {26407, 60881}, {26447, 60892}, {26448, 60893}, {26449, 60894}, {26451, 31657}, {26452, 60895}, {26453, 60896}, {35790, 60915}, {35791, 60916}, {44610, 60913}, {44611, 60914}, {45289, 61006}, {45446, 60888}, {45447, 60889}, {45548, 60890}, {45549, 60891}, {51741, 59405}

X(60906) = midpoint of X(i) and X(j) for these {i,j}: {144, 4240}, {18508, 60884}
X(60906) = reflection of X(i) in X(j) for these {i,j}: {1650, 9}, {18507, 60901}, {7, 402}

X(60907) = ORTHOLOGY CENTER OF INNER-GREBE WRT AGUILERA TRIANGLE

Barycentrics    (b-c)^2*(b^2+c^2)-a^2*(2*a^2+b^2+c^2-2*a*(b+c))+(a^2-(b-c)^2)*S : :

X(60907) lies on these lines: {6, 7}, {9, 5591}, {144, 1271}, {390, 5605}, {516, 3641}, {518, 12627}, {527, 5861}, {971, 5871}, {1001, 22756}, {1161, 5762}, {2801, 6263}, {4312, 5589}, {5220, 10921}, {5223, 5689}, {5542, 11370}, {5595, 60897}, {5759, 11824}, {5779, 6215}, {5805, 6202}, {5817, 10514}, {5843, 5875}, {5850, 49586}, {5856, 13269}, {8198, 60898}, {8205, 60899}, {8216, 60917}, {8217, 60918}, {8974, 60920}, {9994, 60900}, {10040, 60923}, {10048, 60924}, {10517, 21168}, {10783, 36996}, {10792, 60882}, {10919, 16112}, {10923, 60909}, {10925, 60910}, {10927, 60919}, {10929, 60925}, {10931, 60926}, {11388, 60879}, {11495, 11497}, {11901, 60906}, {11916, 60922}, {12697, 12801}, {13949, 60921}, {18509, 60901}, {18959, 60883}, {21151, 45552}, {26334, 60880}, {26335, 60881}, {26336, 60884}, {26337, 60892}, {26339, 60894}, {26341, 31657}, {26342, 60895}, {26343, 60896}, {35792, 60915}, {35795, 60916}, {45550, 60890}, {45594, 60893}

X(60907) = reflection of X(i) in X(j) for these {i,j}: {60894, 60933}, {60908, 7}, {7, 60889}
X(60907) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 5845, 60908}, {5845, 60889, 7}

X(60908) = ORTHOLOGY CENTER OF OUTER-GREBE WRT AGUILERA TRIANGLE

Barycentrics    (b-c)^2*(b^2+c^2)-a^2*(2*a^2+b^2+c^2-2*a*(b+c))-(a^2-(b-c)^2)*S : :

X(60908) lies on these lines: {6, 7}, {9, 5590}, {144, 1270}, {390, 5604}, {516, 3640}, {518, 12628}, {527, 5860}, {971, 5870}, {1001, 22757}, {1160, 5762}, {2801, 6262}, {4312, 5588}, {5220, 10922}, {5223, 5688}, {5542, 11371}, {5594, 60897}, {5759, 11825}, {5779, 6214}, {5805, 6201}, {5817, 10515}, {5843, 5874}, {5850, 49587}, {5856, 13270}, {8199, 60898}, {8206, 60899}, {8218, 60917}, {8219, 60918}, {8975, 60920}, {9995, 60900}, {10041, 60923}, {10049, 60924}, {10518, 21168}, {10784, 36996}, {10793, 60882}, {10920, 16112}, {10924, 60909}, {10926, 60910}, {10928, 60919}, {10930, 60925}, {10932, 60926}, {11389, 60879}, {11495, 11498}, {11902, 60906}, {11917, 60922}, {12698, 12802}, {13950, 60921}, {18511, 60901}, {18960, 60883}, {21151, 45553}, {26338, 60893}, {26340, 60933}, {26344, 60880}, {26345, 60881}, {26346, 60884}, {26347, 60892}, {26348, 31657}, {26349, 60895}, {26350, 60896}, {35793, 60916}, {35794, 60915}, {45551, 60891}

X(60908) = reflection of X(i) in X(j) for these {i,j}: {60907, 7}, {7, 60888}
X(60908) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 51190, 60887}, {7, 5845, 60907}, {5845, 60888, 7}

X(60909) = ORTHOLOGY CENTER OF 1ST JOHNSON-YFF WRT AGUILERA TRIANGLE

Barycentrics    a*(a+b-c)*(a-b+c)*(a^3+2*(b+c)^3-a*(3*b^2+2*b*c+3*c^2)) : :

X(60909) lies on circumconic {{A, B, C, X(1268), X(2297)}} and on these lines: {1, 5779}, {4, 60919}, {5, 60924}, {7, 12}, {9, 56}, {10, 60961}, {11, 5817}, {36, 59381}, {40, 31391}, {44, 4327}, {45, 1458}, {55, 971}, {57, 3715}, {65, 5223}, {144, 388}, {210, 5785}, {226, 5850}, {354, 10398}, {390, 10944}, {480, 2057}, {495, 5843}, {498, 31657}, {516, 5252}, {518, 2099}, {527, 11237}, {553, 50834}, {673, 24816}, {756, 1407}, {954, 2801}, {958, 60969}, {960, 60966}, {984, 5018}, {999, 51516}, {1001, 1388}, {1156, 1317}, {1376, 10861}, {1445, 15481}, {1454, 60990}, {1456, 7174}, {1469, 50995}, {1471, 16885}, {1478, 5762}, {1479, 60901}, {1697, 3062}, {1757, 5228}, {1836, 12859}, {2263, 49515}, {2550, 18961}, {2951, 37568}, {2975, 61025}, {3057, 11372}, {3085, 36996}, {3295, 60884}, {3303, 14100}, {3304, 15299}, {3476, 52653}, {3585, 31671}, {3600, 61006}, {3711, 37541}, {3913, 25722}, {3927, 5290}, {4293, 21168}, {4298, 61014}, {4312, 9578}, {4331, 17334}, {4423, 17625}, {4663, 7190}, {4860, 5219}, {5172, 15296}, {5183, 9814}, {5204, 31658}, {5217, 5732}, {5253, 61026}, {5261, 20059}, {5298, 61023}, {5432, 21151}, {5433, 18230}, {5434, 6172}, {5542, 5729}, {5686, 40663}, {5726, 36279}, {5735, 9656}, {5759, 7354}, {5805, 10895}, {5845, 12588}, {5851, 10956}, {5856, 13273}, {5880, 60936}, {5919, 10384}, {6284, 36991}, {6600, 14882}, {7672, 45288}, {7677, 60944}, {7951, 38107}, {7962, 24644}, {8273, 51489}, {8543, 42871}, {9654, 60922}, {9850, 31435}, {10106, 51090}, {10404, 52819}, {10590, 59386}, {10797, 60882}, {10831, 60897}, {10873, 60900}, {10923, 60907}, {10924, 60908}, {10957, 42356}, {11038, 15950}, {11392, 60879}, {11495, 11501}, {11869, 60898}, {11870, 60899}, {11905, 60906}, {11930, 60917}, {11931, 60918}, {12059, 19520}, {12573, 60942}, {12678, 31397}, {12953, 31672}, {13897, 60920}, {13954, 60921}, {15326, 59418}, {15346, 38200}, {17599, 34048}, {17604, 30326}, {17605, 38036}, {17609, 30330}, {17622, 54370}, {17642, 54135}, {17768, 60946}, {19028, 60887}, {24914, 60992}, {25524, 61012}, {25557, 60943}, {26388, 60880}, {26412, 60881}, {26477, 60892}, {26478, 60893}, {26479, 60894}, {26481, 60895}, {26482, 60896}, {30318, 42819}, {30331, 37738}, {31472, 60913}, {31479, 59380}, {35800, 60915}, {35801, 60916}, {37709, 41694}, {38053, 60995}, {38204, 60993}, {39126, 60731}, {39897, 51190}, {42884, 60911}, {44622, 60914}, {45458, 60888}, {45459, 60889}, {45560, 60890}, {45561, 60891}, {52783, 60939}

X(60909) = reflection of X(i) in X(j) for these {i,j}: {55, 15298}, {60923, 495}
X(60909) = pole of line {165, 15299} wrt Feuerbach hyperbola
X(60909) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5779, 60910}, {7, 41712, 5221}, {7, 5220, 41712}, {9, 8581, 56}, {144, 388, 60883}, {495, 5843, 60923}, {971, 15298, 55}, {5223, 60937, 65}, {5732, 15837, 5217}

X(60910) = ORTHOLOGY CENTER OF 2ND JOHNSON-YFF WRT AGUILERA TRIANGLE

Barycentrics    a*(a-b-c)*(a^3-3*a*(b-c)^2+2*(b-c)^2*(b+c)) : :
X(60910) = -3*X[17728]+2*X[60992]

X(60910) lies on these lines: {1, 5779}, {2, 59600}, {4, 60883}, {5, 60923}, {6, 2310}, {7, 11}, {9, 55}, {12, 5817}, {35, 59381}, {44, 4319}, {45, 2293}, {56, 971}, {57, 3062}, {65, 7995}, {100, 61026}, {144, 497}, {279, 58836}, {354, 30330}, {390, 3621}, {479, 15913}, {496, 5843}, {499, 31657}, {516, 1837}, {518, 2098}, {527, 11238}, {528, 18802}, {673, 24840}, {950, 51090}, {954, 60911}, {999, 60884}, {1001, 10394}, {1155, 2951}, {1210, 12679}, {1253, 16885}, {1376, 25722}, {1445, 15726}, {1466, 3358}, {1478, 60901}, {1479, 5762}, {1621, 61025}, {1697, 17632}, {1728, 5584}, {1743, 4907}, {1776, 60970}, {1836, 52819}, {1858, 5728}, {1859, 2358}, {2099, 13253}, {2257, 58906}, {2340, 34524}, {2346, 60944}, {2550, 61009}, {2801, 12740}, {2875, 42447}, {3056, 50995}, {3057, 5223}, {3058, 6172}, {3086, 36996}, {3295, 51516}, {3303, 15298}, {3304, 8581}, {3340, 24644}, {3361, 12684}, {3474, 60941}, {3486, 52653}, {3583, 31671}, {3826, 10958}, {3911, 43182}, {3925, 60959}, {4081, 53994}, {4294, 21168}, {4312, 5221}, {4413, 15587}, {4423, 10391}, {4995, 61023}, {5204, 5732}, {5217, 31658}, {5274, 20059}, {5432, 18230}, {5433, 21151}, {5542, 11376}, {5572, 8545}, {5698, 5809}, {5727, 36920}, {5735, 9671}, {5759, 6284}, {5784, 22768}, {5785, 25917}, {5805, 10896}, {5825, 38057}, {5845, 12589}, {5850, 12053}, {5852, 10959}, {5856, 13274}, {6180, 9355}, {6601, 10947}, {6762, 8163}, {7354, 36991}, {7671, 29007}, {7675, 15254}, {7676, 60954}, {7741, 38107}, {8236, 37734}, {8255, 60943}, {8257, 17668}, {9309, 36101}, {9657, 12573}, {9669, 60922}, {9844, 12514}, {9848, 57279}, {10177, 60964}, {10396, 12688}, {10591, 59386}, {10798, 60882}, {10832, 60897}, {10861, 25524}, {10874, 60900}, {10925, 60907}, {10926, 60908}, {11019, 60961}, {11246, 60939}, {11393, 60879}, {11495, 11502}, {11871, 60898}, {11872, 60899}, {11906, 60906}, {11932, 60917}, {11933, 60918}, {12680, 51773}, {12701, 12860}, {12764, 12832}, {12943, 31672}, {13898, 60920}, {13955, 60921}, {14942, 17350}, {15006, 61000}, {15185, 60973}, {15338, 59418}, {15346, 20195}, {16141, 41547}, {17599, 24430}, {17606, 38052}, {17642, 36973}, {17728, 60992}, {17768, 41574}, {18395, 38121}, {18839, 60965}, {19030, 60887}, {21010, 40528}, {23351, 42462}, {24703, 60979}, {26387, 60880}, {26411, 60881}, {26471, 60892}, {26472, 60893}, {26473, 60894}, {26475, 60895}, {26476, 60896}, {28071, 55989}, {30331, 37740}, {30628, 41711}, {35514, 40663}, {35802, 60915}, {35803, 60916}, {36971, 41572}, {37271, 41866}, {38454, 41563}, {39873, 51190}, {40269, 42871}, {41694, 50443}, {44623, 60913}, {44624, 60914}, {45460, 60888}, {45461, 60889}, {45562, 60890}, {45563, 60891}, {53056, 58834}, {54361, 59412}

X(60910) = reflection of X(i) in X(j) for these {i,j}: {1837, 10392}, {37567, 41712}, {480, 9}, {41712, 5729}, {56, 15299}, {60924, 496}
X(60910) = inverse of X(16112) in Feuerbach hyperbola
X(60910) = perspector of circumconic {{A, B, C, X(644), X(60487)}}
X(60910) = X(i)-isoconjugate-of-X(j) for these {i, j}: {57, 56355}
X(60910) = X(i)-Dao conjugate of X(j) for these {i, j}: {5452, 56355}
X(60910) = pole of line {1638, 17427} wrt incircle
X(60910) = pole of line {9, 165} wrt Feuerbach hyperbola
X(60910) = pole of line {1323, 24181} wrt dual conic of Yff parabola
X(60910) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(480), X(1156)}}, {{A, B, C, X(1538), X(51380)}}, {{A, B, C, X(3689), X(45824)}}, {{A, B, C, X(3693), X(55989)}}
X(60910) = barycentric product X(i)*X(j) for these (i, j): {1538, 52663}
X(60910) = barycentric quotient X(i)/X(j) for these (i, j): {55, 56355}
X(60910) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5779, 60909}, {7, 1156, 16112}, {9, 15733, 480}, {9, 4326, 15837}, {57, 3062, 31391}, {144, 497, 60919}, {496, 5843, 60924}, {516, 10392, 1837}, {516, 41712, 37567}, {516, 5729, 41712}, {971, 15299, 56}, {1743, 41339, 38293}, {1743, 4907, 41339}, {1864, 30223, 55}, {5223, 10384, 3057}, {6762, 10866, 8163}, {10398, 11372, 65}, {14100, 15837, 4326}, {25722, 61012, 1376}, {30330, 60937, 354}, {40269, 53055, 42871}

X(60911) = ORTHOLOGY CENTER OF K798E WRT AGUILERA TRIANGLE

Barycentrics    a*(a^5-a^4*(b+c)+a*(b^2-c^2)^2-2*a^3*(b^2-b*c+c^2)-(b-c)^2*(b+c)*(b^2+3*b*c+c^2)+a^2*(b+c)*(2*b^2-b*c+2*c^2)) : :
X(60911) = X[3]+X[16112], X[946]+X[60942], X[962]+7*X[60983], X[3062]+3*X[21153], 3*X[3839]+5*X[50840], 5*X[5220]+X[8148], -X[5880]+3*X[38108], 3*X[6173]+X[41705], -5*X[8227]+X[60933], -X[11495]+3*X[59381], 3*X[38031]+X[60884], 3*X[38036]+X[60977] and many others

X(60911) lies on circumconic {{A, B, C, X(3467), X(7079)}} and on these lines: {1, 29007}, {2, 1768}, {3, 16112}, {4, 9}, {5, 17768}, {7, 499}, {36, 41694}, {46, 60947}, {55, 15064}, {57, 10171}, {63, 3817}, {79, 6991}, {90, 13411}, {140, 18243}, {142, 6861}, {144, 10527}, {165, 27065}, {191, 3091}, {226, 7082}, {390, 9897}, {405, 31803}, {498, 60925}, {517, 15481}, {518, 576}, {527, 25362}, {631, 7701}, {758, 6913}, {946, 60942}, {954, 60910}, {962, 60983}, {971, 5450}, {991, 9355}, {1001, 2801}, {1012, 10176}, {1125, 7330}, {1156, 10058}, {1158, 3634}, {1445, 30424}, {1482, 4127}, {1656, 3652}, {1699, 3219}, {1709, 3305}, {1728, 3671}, {1776, 5219}, {1898, 54430}, {3062, 21153}, {3073, 30142}, {3086, 60934}, {3149, 3647}, {3218, 7988}, {3336, 5056}, {3359, 3828}, {3523, 5506}, {3545, 5535}, {3560, 20117}, {3587, 28158}, {3678, 11496}, {3683, 5927}, {3822, 37822}, {3839, 50840}, {3843, 16139}, {3872, 5223}, {3929, 50802}, {4015, 10306}, {4134, 37569}, {4301, 41229}, {4312, 37787}, {4413, 46684}, {4414, 5400}, {4512, 30326}, {4640, 10157}, {4669, 12703}, {5047, 15071}, {5119, 38155}, {5220, 8148}, {5248, 5777}, {5259, 12528}, {5302, 9856}, {5536, 9779}, {5542, 8545}, {5692, 6912}, {5693, 6920}, {5709, 12571}, {5728, 44840}, {5729, 30329}, {5732, 37106}, {5735, 61024}, {5762, 42356}, {5790, 6246}, {5811, 10198}, {5812, 12558}, {5825, 18391}, {5832, 18232}, {5843, 25557}, {5850, 60973}, {5851, 6713}, {5852, 20330}, {5880, 38108}, {5887, 30147}, {5902, 16133}, {6173, 41705}, {6763, 60957}, {6825, 58449}, {6832, 11263}, {6846, 60950}, {6858, 8257}, {6914, 22935}, {6924, 22936}, {6972, 13089}, {6986, 41872}, {6989, 16127}, {7308, 58441}, {7672, 41700}, {7966, 28236}, {7989, 56288}, {8227, 60933}, {8543, 18412}, {8715, 58631}, {9956, 40256}, {10320, 60923}, {10396, 12563}, {11495, 59381}, {12047, 41572}, {13405, 30223}, {15298, 30331}, {15726, 31658}, {15866, 60936}, {15868, 60926}, {16120, 37282}, {16865, 19861}, {17561, 43176}, {17668, 25440}, {18483, 26921}, {18540, 28164}, {18908, 25439}, {19878, 37534}, {21060, 42012}, {21616, 61002}, {24467, 60980}, {27784, 36746}, {28444, 54192}, {29097, 36661}, {31156, 43175}, {31806, 37234}, {33108, 34789}, {36865, 37251}, {38031, 60884}, {38036, 60977}, {38052, 61012}, {38059, 43177}, {38068, 60986}, {38123, 61001}, {38150, 60905}, {41228, 60885}, {42884, 60909}, {43166, 58245}, {43179, 51779}, {43180, 60937}, {43182, 60958}, {47357, 50818}, {51073, 59333}, {52653, 61025}, {59412, 61026}, {60924, 60946}

X(60911) = midpoint of X(i) and X(j) for these {i,j}: {1001, 5779}, {144, 60895}, {3, 16112}, {3062, 43178}, {7330, 60964}, {9, 54370}, {946, 60942}
X(60911) = reflection of X(i) in X(j) for these {i,j}: {22836, 42843}, {52769, 15254}, {60912, 9}
X(60911) = complement of X(60896)
X(60911) = pole of line {48387, 52726} wrt circumcircle
X(60911) = pole of line {28473, 48288} wrt excentral-hexyl ellipse
X(60911) = pole of line {1442, 4000} wrt dual conic of Yff parabola
X(60911) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 516, 60912}, {9, 54370, 516}, {144, 38037, 60895}, {971, 15254, 52769}, {1001, 5779, 2801}, {1709, 3305, 10164}, {3062, 21153, 43178}, {8545, 15299, 5542}

X(60912) = ORTHOLOGY CENTER OF K798I WRT AGUILERA TRIANGLE

Barycentrics    a*((a-b)^3*(a+b)^2-a^2*(a-b)*(a+3*b)*c-(a-b)*(2*a^2-a*b+b^2)*c^2+(2*a^2+b^2)*c^3+a*c^4-c^5) : :
X(60912) = -X[946]+3*X[60986], -X[962]+9*X[61023], -3*X[1001]+X[1482], -5*X[1698]+X[5735], -X[3811]+3*X[47375], 3*X[5686]+X[43161], -3*X[5732]+7*X[16192], -3*X[6173]+7*X[31423], -5*X[10595]+9*X[38025], X[12245]+3*X[47357], -X[16112]+3*X[51516], -X[18482]+3*X[38179] and many others

X(60912) lies on these lines: {1, 37787}, {2, 5536}, {3, 2801}, {4, 9}, {5, 38454}, {7, 498}, {35, 10394}, {46, 3947}, {55, 5729}, {57, 43180}, {63, 6745}, {78, 5223}, {100, 5696}, {140, 25557}, {142, 15296}, {144, 5552}, {165, 3219}, {182, 518}, {191, 6172}, {220, 28345}, {390, 10573}, {411, 55160}, {480, 11517}, {484, 10590}, {499, 60926}, {517, 15254}, {527, 6684}, {528, 5690}, {580, 30142}, {602, 30145}, {611, 25065}, {631, 60989}, {756, 1754}, {946, 60986}, {954, 15556}, {962, 61023}, {971, 6796}, {984, 13329}, {991, 1757}, {993, 50371}, {1001, 1482}, {1125, 5761}, {1158, 52684}, {1253, 1736}, {1376, 58699}, {1445, 3338}, {1454, 61021}, {1479, 36976}, {1621, 15104}, {1698, 5735}, {1699, 27065}, {1708, 13405}, {1709, 50808}, {1728, 4314}, {1776, 35445}, {2095, 3833}, {2346, 41861}, {2949, 10198}, {2954, 3190}, {3074, 4347}, {3085, 12848}, {3090, 24468}, {3254, 6963}, {3305, 3817}, {3337, 10303}, {3428, 10176}, {3523, 6763}, {3579, 15726}, {3584, 60951}, {3587, 28164}, {3634, 5709}, {3647, 10310}, {3652, 5779}, {3681, 15931}, {3715, 7580}, {3746, 7671}, {3811, 47375}, {3813, 22992}, {3822, 5880}, {3826, 5762}, {3841, 5812}, {3869, 60885}, {3876, 59320}, {3928, 50829}, {3929, 43181}, {4015, 11500}, {4134, 18446}, {4295, 60995}, {4297, 41229}, {4312, 29007}, {4640, 15813}, {5302, 31793}, {5433, 38055}, {5445, 30312}, {5499, 17768}, {5506, 18230}, {5554, 52653}, {5584, 31803}, {5659, 11680}, {5686, 43161}, {5687, 42014}, {5697, 53055}, {5728, 15837}, {5732, 16192}, {5766, 18391}, {5771, 5856}, {5777, 12511}, {5784, 25440}, {5850, 37534}, {5852, 31657}, {5903, 8543}, {5904, 6986}, {5927, 7964}, {6173, 31423}, {6668, 33558}, {6737, 43175}, {6889, 61011}, {7098, 61007}, {7280, 18450}, {7308, 10171}, {7330, 12512}, {7988, 35595}, {8544, 58887}, {8715, 15733}, {9588, 56288}, {10175, 37584}, {10267, 61030}, {10320, 60924}, {10595, 38025}, {10894, 16125}, {11010, 30332}, {11025, 36946}, {11362, 15297}, {11531, 16859}, {12047, 61015}, {12245, 47357}, {12329, 39475}, {12704, 19862}, {12776, 30144}, {13227, 46684}, {13407, 60932}, {14151, 21842}, {15299, 30331}, {15865, 41572}, {15867, 60925}, {15932, 60975}, {16112, 51516}, {17556, 38216}, {18242, 40256}, {18395, 45043}, {18412, 37571}, {18482, 38179}, {18540, 28158}, {20103, 55869}, {20117, 35239}, {20330, 38113}, {21635, 31018}, {22837, 42842}, {24393, 47745}, {25558, 38760}, {26364, 52457}, {28534, 50821}, {29105, 36661}, {29828, 43169}, {30295, 37572}, {30318, 37618}, {31259, 38059}, {31445, 58637}, {32188, 51525}, {33179, 42819}, {36973, 54290}, {37556, 43179}, {37624, 38031}, {38052, 60969}, {38054, 60985}, {38123, 60962}, {40131, 49631}, {40273, 42356}, {40659, 51489}, {41563, 60923}, {43151, 61005}, {43182, 60949}, {49183, 59722}, {59372, 60948}, {59412, 61025}

X(60912) = midpoint of X(i) and X(j) for these {i,j}: {144, 60896}, {1158, 52684}, {3, 5220}, {40, 54370}, {40659, 51489}, {5779, 11495}
X(60912) = reflection of X(i) in X(j) for these {i,j}: {22837, 42842}, {25557, 140}, {52769, 31658}, {60911, 9}
X(60912) = complement of X(60895)
X(60912) = pole of line {3887, 48387} wrt circumcircle
X(60912) = pole of line {1790, 33325} wrt Stammler hyperbola
X(60912) = pole of line {3239, 26641} wrt Steiner inellipse
X(60912) = pole of line {4000, 7269} wrt dual conic of Yff parabola
X(60912) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(5011)}}, {{A, B, C, X(4), X(55986)}}, {{A, B, C, X(63), X(54370)}}, {{A, B, C, X(78), X(23058)}}, {{A, B, C, X(281), X(55920)}}, {{A, B, C, X(7079), X(7161)}}
X(60912) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 5220, 2801}, {9, 40, 54370}, {9, 516, 60911}, {35, 41700, 10394}, {40, 54370, 516}, {46, 8545, 30424}, {518, 31658, 52769}, {954, 41712, 30329}, {1445, 15298, 5542}, {3305, 41338, 3817}, {3715, 7580, 15064}, {6191, 6192, 3730}, {11010, 51768, 30332}, {56288, 60935, 60905}

X(60913) = ORTHOLOGY CENTER OF 1ST KENMOTU-CENTERS WRT AGUILERA TRIANGLE

Barycentrics    a^2*(-a^2-(b-c)^2+2*a*(b+c))+2*(a^2-(b-c)^2)*S : :

X(60913) lies on these lines: {6, 7}, {9, 590}, {39, 60891}, {142, 615}, {144, 3068}, {371, 5762}, {372, 31657}, {390, 44635}, {482, 40133}, {485, 5779}, {486, 38107}, {516, 7969}, {518, 26300}, {527, 32787}, {971, 3070}, {1001, 44606}, {1124, 60924}, {1151, 5759}, {1152, 21151}, {1335, 60923}, {1587, 36996}, {1588, 59386}, {2066, 60919}, {2067, 60883}, {2550, 49233}, {2801, 49240}, {3071, 5805}, {3311, 60922}, {3312, 59380}, {4312, 18991}, {5062, 60890}, {5220, 44620}, {5223, 13911}, {5412, 60879}, {5418, 59381}, {5542, 7968}, {5732, 42259}, {5817, 42265}, {5843, 7583}, {5850, 13883}, {5856, 48714}, {6068, 13922}, {6172, 13846}, {6173, 32788}, {6409, 59418}, {6417, 51514}, {6419, 60916}, {6561, 31671}, {6564, 60901}, {6666, 32789}, {7585, 20059}, {8252, 60996}, {8253, 18230}, {8972, 61006}, {8976, 51516}, {8983, 51090}, {9540, 21168}, {10427, 48715}, {10577, 38171}, {11038, 44636}, {11495, 44590}, {13159, 49243}, {13665, 60884}, {13847, 59374}, {13902, 52653}, {13910, 51144}, {13966, 38111}, {13971, 38054}, {13973, 38052}, {13975, 38123}, {13976, 38207}, {13977, 38124}, {16112, 44618}, {18482, 42283}, {18992, 59372}, {19048, 60896}, {19050, 60895}, {19053, 59375}, {19054, 60984}, {19065, 59412}, {19146, 38115}, {20195, 32790}, {23251, 36991}, {23261, 59385}, {31472, 60909}, {31672, 42284}, {38108, 42582}, {38150, 42270}, {42271, 52835}, {44582, 60880}, {44584, 60881}, {44586, 60882}, {44594, 60894}, {44598, 60897}, {44600, 60898}, {44602, 60899}, {44604, 60900}, {44610, 60906}, {44623, 60910}, {44627, 60917}, {44629, 60918}, {44643, 60925}, {44645, 60926}, {45595, 60893}, {45597, 60892}, {49226, 49248}

X(60913) = midpoint of X(i) and X(j) for these {i,j}: {371, 60915}
X(60913) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 7, 60914}, {7, 51190, 60888}, {7, 60887, 6}, {9, 60920, 590}, {371, 60915, 5762}

X(60914) = ORTHOLOGY CENTER OF 2ND KENMOTU-CENTERS WRT AGUILERA TRIANGLE

Barycentrics    a^2*(a^2+(b-c)^2-2*a*(b+c))+(2*a^2-2*(b-c)^2)*S : :

X(60914) lies on these lines: {6, 7}, {9, 615}, {39, 60890}, {142, 590}, {144, 3069}, {371, 31657}, {372, 5762}, {390, 44636}, {481, 40133}, {485, 38107}, {486, 5779}, {516, 7968}, {518, 26301}, {527, 32788}, {971, 3071}, {1001, 44607}, {1124, 60923}, {1151, 21151}, {1152, 5759}, {1335, 60924}, {1587, 59386}, {1588, 36996}, {2550, 49232}, {2801, 49241}, {3070, 5805}, {3311, 59380}, {3312, 60922}, {4312, 18992}, {5058, 60891}, {5220, 44621}, {5223, 13973}, {5413, 60879}, {5414, 60919}, {5420, 59381}, {5542, 7969}, {5732, 42258}, {5817, 42262}, {5843, 7584}, {5850, 13936}, {5856, 48715}, {6068, 13991}, {6172, 13847}, {6173, 32787}, {6410, 59418}, {6418, 51514}, {6420, 60915}, {6502, 60883}, {6560, 31671}, {6565, 60901}, {6666, 32790}, {7586, 20059}, {8252, 18230}, {8253, 60996}, {8981, 38111}, {8983, 38054}, {8988, 38207}, {10427, 48714}, {10576, 38171}, {11038, 44635}, {11495, 44591}, {13159, 49242}, {13785, 60884}, {13846, 59374}, {13911, 38052}, {13912, 38123}, {13913, 38124}, {13935, 21168}, {13941, 61006}, {13951, 51516}, {13959, 52653}, {13971, 51090}, {13972, 51144}, {16112, 44619}, {18482, 42284}, {18991, 59372}, {19047, 60896}, {19049, 60895}, {19053, 60984}, {19054, 59375}, {19066, 59412}, {19145, 38115}, {20195, 32789}, {23251, 59385}, {23261, 36991}, {31672, 42283}, {38108, 42583}, {38150, 42273}, {42272, 52835}, {44583, 60880}, {44585, 60881}, {44587, 60882}, {44595, 60894}, {44599, 60897}, {44601, 60898}, {44603, 60899}, {44605, 60900}, {44611, 60906}, {44622, 60909}, {44624, 60910}, {44628, 60917}, {44630, 60918}, {44644, 60925}, {44646, 60926}, {45596, 60892}, {45598, 60893}, {49227, 49249}

X(60914) = midpoint of X(i) and X(j) for these {i,j}: {372, 60916}
X(60914) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 7, 60913}, {7, 51190, 60889}, {9, 60921, 615}, {372, 60916, 5762}

X(60915) = ORTHOLOGY CENTER OF 1ST KENMOTU-FREE-VERTICES WRT AGUILERA TRIANGLE

Barycentrics    3*a^6-2*a^5*(b+c)-2*(b-c)^4*(b+c)^2+a^4*(-6*b^2+2*b*c-6*c^2)+2*a^3*(b+c)*(b^2+c^2)+a^2*(b-c)^2*(5*b^2+4*b*c+5*c^2)+2*a^2*(a^2-2*a*b+b^2-2*a*c-2*b*c+c^2)*S : :

X(60915) lies on these lines: {6, 60916}, {7, 372}, {9, 10576}, {144, 485}, {371, 5762}, {390, 35810}, {486, 59386}, {516, 35641}, {518, 35842}, {527, 35822}, {971, 35820}, {1001, 35784}, {1152, 59380}, {1587, 20059}, {2801, 35852}, {3070, 5843}, {3103, 60889}, {3312, 51514}, {4312, 35774}, {5220, 35798}, {5223, 35788}, {5418, 21168}, {5542, 35762}, {5759, 6200}, {5779, 6564}, {5805, 6565}, {5845, 35840}, {5850, 49601}, {5856, 35882}, {6396, 31657}, {6419, 60887}, {6420, 60914}, {6560, 36996}, {10577, 38107}, {11495, 35772}, {16112, 35796}, {23251, 60884}, {31671, 35821}, {35610, 35862}, {35764, 60879}, {35766, 60882}, {35768, 60883}, {35769, 60924}, {35776, 60897}, {35778, 60898}, {35780, 60899}, {35782, 60900}, {35786, 60901}, {35787, 59385}, {35790, 60906}, {35792, 60907}, {35794, 60908}, {35800, 60909}, {35802, 60910}, {35804, 60917}, {35806, 60918}, {35808, 60919}, {35809, 60923}, {35812, 60920}, {35814, 60921}, {35816, 60925}, {35818, 60926}, {38137, 42270}, {42265, 51516}, {45357, 60880}, {45359, 60881}, {45462, 60888}, {45564, 60891}, {45599, 60893}, {45601, 60892}, {45640, 60895}, {45642, 60896}, {49018, 60894}

X(60915) = reflection of X(i) in X(j) for these {i,j}: {371, 60913}
X(60915) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5762, 60913, 371}

X(60916) = ORTHOLOGY CENTER OF 2ND KENMOTU-FREE-VERTICES WRT AGUILERA TRIANGLE

Barycentrics    3*a^6-2*a^5*(b+c)-2*(b-c)^4*(b+c)^2+a^4*(-6*b^2+2*b*c-6*c^2)+2*a^3*(b+c)*(b^2+c^2)+a^2*(b-c)^2*(5*b^2+4*b*c+5*c^2)-2*a^2*(a^2-2*a*b+b^2-2*a*c-2*b*c+c^2)*S : :

X(60916) lies on these lines: {6, 60915}, {7, 371}, {9, 10577}, {144, 486}, {372, 5762}, {390, 35811}, {485, 59386}, {516, 35642}, {518, 35843}, {527, 35823}, {971, 35821}, {1001, 35785}, {1151, 59380}, {1588, 20059}, {2801, 35853}, {3071, 5843}, {3102, 60888}, {3311, 51514}, {4312, 35775}, {5220, 35799}, {5223, 35789}, {5420, 21168}, {5542, 35763}, {5759, 6396}, {5779, 6565}, {5805, 6564}, {5845, 35841}, {5850, 49602}, {5856, 35883}, {6200, 31657}, {6419, 60913}, {6561, 36996}, {10576, 38107}, {11495, 35773}, {16112, 35797}, {23261, 60884}, {31671, 35820}, {35611, 35863}, {35765, 60879}, {35767, 60882}, {35768, 60924}, {35769, 60883}, {35771, 60887}, {35777, 60897}, {35779, 60899}, {35781, 60898}, {35783, 60900}, {35786, 59385}, {35787, 60901}, {35791, 60906}, {35793, 60908}, {35795, 60907}, {35801, 60909}, {35803, 60910}, {35805, 60918}, {35807, 60917}, {35808, 60923}, {35809, 60919}, {35813, 60921}, {35815, 60920}, {35817, 60925}, {35819, 60926}, {38137, 42273}, {42262, 51516}, {45358, 60881}, {45360, 60880}, {45463, 60889}, {45565, 60890}, {45600, 60892}, {45602, 60893}, {45641, 60895}, {45643, 60896}

X(60916) = reflection of X(i) in X(j) for these {i,j}: {372, 60914}
X(60916) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 60922, 60915}, {5762, 60914, 372}

X(60917) = ORTHOLOGY CENTER OF LUCAS HOMOTHETIC WRT AGUILERA TRIANGLE

Barycentrics    a^11+5*a^10*(b+c)-a*(b-c)^4*(b+c)^2*(b^2+c^2)^2-(b-c)^4*(b+c)^3*(b^2+c^2)^2-a^9*(b^2+10*b*c+c^2)+a^2*(b-c)^2*(b+c)^3*(b^2+c^2)*(5*b^2-4*b*c+5*c^2)-a^8*(b+c)*(17*b^2+10*b*c+17*c^2)-2*a^7*(b^4+6*b^3*c+16*b^2*c^2+6*b*c^3+c^4)+2*a^6*(b+c)*(11*b^4+10*b^3*c-16*b^2*c^2+10*b*c^3+11*c^4)+2*a^5*(b^6+28*b^5*c+17*b^4*c^2+84*b^3*c^3+17*b^2*c^4+28*b*c^5+c^6)-2*a^4*(b+c)*(7*b^6+4*b^5*c-25*b^4*c^2+12*b^3*c^3-25*b^2*c^4+4*b*c^5+7*c^6)+a^3*(b^8-36*b^7*c+36*b^5*c^3+126*b^4*c^4+36*b^3*c^5-36*b*c^7+c^8)+4*(a^9-2*a^8*(b+c)-a^7*(4*b^2+7*b*c+4*c^2)+b*c*(b+c)*(b^3-b^2*c+b*c^2-c^3)^2+a*(b^2+b*c+c^2)*(b^3-b^2*c+b*c^2-c^3)^2-a^6*(2*b^3+7*b^2*c+7*b*c^2+2*c^3)+3*a^5*(2*b^4+7*b^3*c-2*b^2*c^2+7*b*c^3+2*c^4)+a^4*(2*b^5+13*b^4*c+13*b^3*c^2+13*b^2*c^3+13*b*c^4+2*c^5)+a^3*(-4*b^6+3*b^5*c+24*b^4*c^2+38*b^3*c^3+24*b^2*c^4+3*b*c^5-4*c^6)+a^2*(2*b^7-5*b^6*c+3*b^5*c^2-4*b^4*c^3-4*b^3*c^4+3*b^2*c^5-5*b*c^6+2*c^7))*S : :

X(60917) lies on these lines: {7, 493}, {9, 8222}, {144, 6462}, {390, 8210}, {516, 12440}, {518, 12636}, {527, 12152}, {971, 9838}, {1001, 22761}, {2801, 12741}, {4312, 8188}, {5220, 10951}, {5223, 8214}, {5542, 11377}, {5759, 11828}, {5762, 10669}, {5779, 8220}, {5805, 8212}, {5843, 32177}, {5845, 12590}, {5850, 49606}, {5856, 13275}, {6461, 60918}, {8194, 60897}, {8201, 60898}, {8208, 60899}, {8216, 60907}, {8218, 60908}, {10875, 60900}, {10945, 16112}, {11394, 60879}, {11495, 11503}, {11840, 60882}, {11846, 36996}, {11907, 60906}, {11930, 60909}, {11932, 60910}, {11947, 60919}, {11949, 60922}, {11951, 60923}, {11953, 60924}, {11955, 60925}, {11957, 60926}, {12861, 22841}, {13899, 60920}, {13956, 60921}, {18520, 60901}, {18963, 60883}, {19032, 60887}, {31657, 45623}, {35804, 60915}, {35807, 60916}, {44627, 60913}, {44628, 60914}, {45362, 60880}, {45364, 60881}, {45381, 60884}, {45465, 60889}, {45467, 60888}, {45567, 60891}, {45569, 60890}, {45604, 60893}, {45645, 60895}, {45647, 60896}, {49020, 60894}

X(60918) = ORTHOLOGY CENTER OF LUCAS(-1) HOMOTHETIC WRT AGUILERA TRIANGLE

Barycentrics    a^11+5*a^10*(b+c)-a*(b-c)^4*(b+c)^2*(b^2+c^2)^2-(b-c)^4*(b+c)^3*(b^2+c^2)^2-a^9*(b^2+10*b*c+c^2)+a^2*(b-c)^2*(b+c)^3*(b^2+c^2)*(5*b^2-4*b*c+5*c^2)-a^8*(b+c)*(17*b^2+10*b*c+17*c^2)-2*a^7*(b^4+6*b^3*c+16*b^2*c^2+6*b*c^3+c^4)+2*a^6*(b+c)*(11*b^4+10*b^3*c-16*b^2*c^2+10*b*c^3+11*c^4)+2*a^5*(b^6+28*b^5*c+17*b^4*c^2+84*b^3*c^3+17*b^2*c^4+28*b*c^5+c^6)-2*a^4*(b+c)*(7*b^6+4*b^5*c-25*b^4*c^2+12*b^3*c^3-25*b^2*c^4+4*b*c^5+7*c^6)+a^3*(b^8-36*b^7*c+36*b^5*c^3+126*b^4*c^4+36*b^3*c^5-36*b*c^7+c^8)-4*(a^9-2*a^8*(b+c)-a^7*(4*b^2+7*b*c+4*c^2)+b*c*(b+c)*(b^3-b^2*c+b*c^2-c^3)^2+a*(b^2+b*c+c^2)*(b^3-b^2*c+b*c^2-c^3)^2-a^6*(2*b^3+7*b^2*c+7*b*c^2+2*c^3)+3*a^5*(2*b^4+7*b^3*c-2*b^2*c^2+7*b*c^3+2*c^4)+a^4*(2*b^5+13*b^4*c+13*b^3*c^2+13*b^2*c^3+13*b*c^4+2*c^5)+a^3*(-4*b^6+3*b^5*c+24*b^4*c^2+38*b^3*c^3+24*b^2*c^4+3*b*c^5-4*c^6)+a^2*(2*b^7-5*b^6*c+3*b^5*c^2-4*b^4*c^3-4*b^3*c^4+3*b^2*c^5-5*b*c^6+2*c^7))*S : :

X(60918) lies on these lines: {7, 494}, {9, 8223}, {144, 6463}, {390, 8211}, {516, 12441}, {518, 12637}, {527, 12153}, {971, 9839}, {1001, 22762}, {2801, 12742}, {4312, 8189}, {5220, 10952}, {5223, 8215}, {5542, 11378}, {5759, 11829}, {5762, 10673}, {5779, 8221}, {5805, 8213}, {5843, 32178}, {5845, 12591}, {5850, 49607}, {5856, 13276}, {6461, 60917}, {8195, 60897}, {8202, 60898}, {8209, 60899}, {8217, 60907}, {8219, 60908}, {10876, 60900}, {10946, 16112}, {11395, 60879}, {11495, 11504}, {11841, 60882}, {11847, 36996}, {11908, 60906}, {11931, 60909}, {11933, 60910}, {11948, 60919}, {11950, 60922}, {11952, 60923}, {11954, 60924}, {11956, 60925}, {11958, 60926}, {12862, 22842}, {13900, 60920}, {13957, 60921}, {18522, 60901}, {18964, 60883}, {19034, 60887}, {31657, 45624}, {35805, 60916}, {35806, 60915}, {44629, 60913}, {44630, 60914}, {45361, 60880}, {45363, 60881}, {45382, 60884}, {45464, 60888}, {45466, 60889}, {45566, 60890}, {45568, 60891}, {45603, 60892}, {45644, 60895}, {45646, 60896}, {49022, 60894}

X(60919) = ORTHOLOGY CENTER OF MANDART-INCIRCLE WRT AGUILERA TRIANGLE

Barycentrics    (a-b-c)*(2*a^4-a^2*(b-c)^2+(b-c)^4-2*a^3*(b+c)) : :
X(60919) = -3*X[354]+2*X[52819], -X[3059]+2*X[61002], -5*X[11025]+3*X[60951], -4*X[15587]+3*X[34612], -4*X[58563]+3*X[60932]

X(60919) lies on circumconic {{A, B, C, X(3254), X(10509)}} and on these lines: {1, 5762}, {3, 60924}, {4, 60909}, {7, 55}, {9, 11}, {12, 5805}, {33, 60879}, {35, 31657}, {56, 5759}, {65, 12863}, {142, 5432}, {144, 497}, {354, 52819}, {390, 2098}, {480, 8730}, {498, 38107}, {499, 59381}, {516, 3057}, {518, 10950}, {527, 3058}, {528, 25722}, {673, 24837}, {950, 5850}, {954, 26357}, {971, 6284}, {1001, 10966}, {1086, 1253}, {1155, 60992}, {1156, 13274}, {1317, 7962}, {1364, 6025}, {1478, 31671}, {1479, 5779}, {1697, 4312}, {1836, 60937}, {1837, 5223}, {1864, 61003}, {1936, 17602}, {2066, 60913}, {2293, 17365}, {2310, 17334}, {2330, 51150}, {2646, 5542}, {2801, 12743}, {2886, 60969}, {2951, 10388}, {3056, 5845}, {3059, 61002}, {3062, 9580}, {3085, 59386}, {3086, 21168}, {3243, 5857}, {3295, 60922}, {3583, 60901}, {3601, 52783}, {3612, 38030}, {3614, 38150}, {3663, 41339}, {3748, 61021}, {3816, 61012}, {4294, 36996}, {4319, 17276}, {4326, 60933}, {4336, 17246}, {4423, 60959}, {4860, 60939}, {4995, 6173}, {5048, 30331}, {5204, 59418}, {5217, 21151}, {5220, 10953}, {5222, 38293}, {5274, 61006}, {5326, 20195}, {5414, 60914}, {5433, 31658}, {5572, 18839}, {5698, 22760}, {5732, 15338}, {5735, 15888}, {5766, 38053}, {5817, 10896}, {5843, 15171}, {5851, 27778}, {5852, 10394}, {6172, 11238}, {6600, 61035}, {6601, 42014}, {6646, 14942}, {7082, 60949}, {7173, 38108}, {7678, 60944}, {8163, 9785}, {9668, 60884}, {9669, 51516}, {9819, 28174}, {10384, 60905}, {10385, 60984}, {10592, 38137}, {10624, 12680}, {10799, 60882}, {10833, 60897}, {10877, 60900}, {10895, 59385}, {10927, 60907}, {10928, 60908}, {10947, 16112}, {10965, 60925}, {11019, 61014}, {11025, 60951}, {11038, 34471}, {11372, 12701}, {11375, 38036}, {11680, 61025}, {11873, 60898}, {11874, 60899}, {11909, 60906}, {11947, 60917}, {11948, 60918}, {12053, 51090}, {12589, 50995}, {12953, 36991}, {13606, 31507}, {13901, 60920}, {13958, 60921}, {15299, 37722}, {15587, 34612}, {15726, 17620}, {15845, 60935}, {15950, 20330}, {17603, 60945}, {19038, 60887}, {22464, 30621}, {24465, 35445}, {24470, 41870}, {24703, 60966}, {25557, 37564}, {26105, 61009}, {26351, 60880}, {26352, 60881}, {26353, 60892}, {26354, 60893}, {26355, 60894}, {26358, 60896}, {26651, 50441}, {28194, 39779}, {29007, 42356}, {30330, 61007}, {33176, 43179}, {35808, 60915}, {35809, 60916}, {37735, 38043}, {38055, 52769}, {38122, 52793}, {41555, 60994}, {43151, 60993}, {44043, 59807}, {45081, 52682}, {45470, 60888}, {45471, 60889}, {45570, 60890}, {45571, 60891}, {50196, 51489}, {58563, 60932}, {59476, 61008}

X(60919) = reflection of X(i) in X(j) for these {i,j}: {3059, 61002}, {31391, 60961}, {41572, 5572}, {60883, 1}, {7354, 8581}
X(60919) = pole of line {4449, 21104} wrt incircle
X(60919) = pole of line {142, 2886} wrt Feuerbach hyperbola
X(60919) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5762, 60883}, {7, 2346, 8255}, {7, 36976, 11495}, {142, 15837, 5432}, {144, 497, 60910}, {516, 60961, 31391}, {516, 8581, 7354}, {3295, 60922, 60923}, {5805, 15298, 12}

X(60920) = ORTHOLOGY CENTER OF 3RD TRI-SQUARES-CENTRAL WRT AGUILERA TRIANGLE

Barycentrics    a^2*(-a^2-(b-c)^2+2*a*(b+c))+2*(-(b-c)^2+a*(b+c))*S : :

X(60920) lies on these lines: {2, 60887}, {6, 142}, {7, 3068}, {9, 590}, {144, 8972}, {371, 5805}, {372, 38122}, {390, 13902}, {485, 971}, {516, 1151}, {518, 10068}, {527, 13846}, {615, 20195}, {910, 30277}, {1001, 22763}, {1587, 21151}, {1702, 38036}, {2550, 7969}, {2801, 8988}, {3069, 60996}, {3070, 5732}, {3071, 38150}, {3243, 49232}, {3254, 48714}, {3311, 38107}, {3826, 13973}, {4258, 31540}, {4312, 13888}, {5022, 31541}, {5220, 13896}, {5223, 13893}, {5418, 31658}, {5542, 13883}, {5735, 31454}, {5759, 9540}, {5762, 8981}, {5779, 8976}, {5843, 13925}, {5845, 13910}, {5850, 49618}, {5853, 44635}, {5856, 13922}, {6173, 32787}, {6221, 31671}, {6459, 59385}, {6561, 18482}, {6564, 31672}, {6666, 8253}, {7583, 31657}, {7584, 38171}, {7968, 38053}, {8252, 58433}, {8581, 31472}, {8974, 60907}, {8975, 60908}, {9646, 15298}, {9661, 15299}, {10576, 38108}, {11038, 19066}, {11495, 13887}, {13847, 60999}, {13884, 60879}, {13885, 60882}, {13886, 36996}, {13889, 60897}, {13890, 60898}, {13891, 60899}, {13892, 60900}, {13894, 60906}, {13895, 16112}, {13897, 60909}, {13898, 60910}, {13899, 60917}, {13900, 60918}, {13901, 60919}, {13903, 60922}, {13904, 60923}, {13905, 60924}, {13906, 60925}, {13907, 60926}, {13912, 13914}, {13936, 38204}, {14100, 44623}, {15587, 31484}, {17668, 44618}, {18230, 32785}, {18538, 60901}, {18965, 60883}, {18991, 38052}, {19054, 59374}, {19065, 40333}, {19117, 38111}, {20330, 35775}, {31412, 36991}, {32788, 38093}, {35812, 60915}, {35815, 60916}, {38054, 49548}, {38200, 49233}, {42258, 52835}, {42273, 59389}, {45365, 60880}, {45368, 60881}, {45384, 60884}, {45484, 60888}, {45486, 60889}, {45574, 60890}, {45576, 60891}, {45605, 60893}, {45607, 60892}, {45650, 60895}, {45652, 60896}

X(60920) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 142, 60921}

X(60921) = ORTHOLOGY CENTER OF 4TH TRI-SQUARES-CENTRAL WRT AGUILERA TRIANGLE

Barycentrics    a^2*(a^2+(b-c)^2-2*a*(b+c))+2*(-(b-c)^2+a*(b+c))*S : :

X(60921) lies on these lines: {6, 142}, {7, 3069}, {9, 615}, {144, 13941}, {371, 38122}, {372, 5805}, {390, 13959}, {486, 971}, {516, 1152}, {518, 10067}, {527, 13847}, {590, 20195}, {910, 30276}, {1001, 22764}, {1588, 21151}, {1703, 38036}, {2550, 7968}, {2801, 13976}, {3068, 60996}, {3070, 38150}, {3071, 5732}, {3243, 49233}, {3254, 48715}, {3312, 38107}, {3826, 13911}, {4258, 31541}, {4312, 13942}, {5022, 31540}, {5220, 13953}, {5223, 13947}, {5420, 31658}, {5542, 13936}, {5759, 13935}, {5762, 13966}, {5779, 13951}, {5843, 13993}, {5845, 13972}, {5850, 49619}, {5853, 44636}, {5856, 13991}, {6173, 32788}, {6398, 31671}, {6460, 59385}, {6560, 18482}, {6565, 31672}, {6666, 8252}, {7583, 38171}, {7584, 31657}, {7586, 60887}, {7969, 38053}, {8253, 58433}, {8581, 44622}, {10577, 38108}, {11038, 19065}, {11495, 13940}, {13846, 60999}, {13883, 38204}, {13937, 60879}, {13938, 60882}, {13939, 36996}, {13943, 60897}, {13944, 60898}, {13945, 60899}, {13946, 60900}, {13948, 60906}, {13949, 60907}, {13950, 60908}, {13952, 16112}, {13954, 60909}, {13955, 60910}, {13956, 60917}, {13957, 60918}, {13958, 60919}, {13961, 60922}, {13962, 60923}, {13963, 60924}, {13964, 60925}, {13965, 60926}, {13975, 13978}, {14100, 44624}, {17668, 44619}, {18230, 32786}, {18762, 60901}, {18966, 60883}, {18992, 38052}, {19053, 59374}, {19066, 40333}, {19116, 38111}, {20330, 35774}, {32787, 38093}, {35813, 60916}, {35814, 60915}, {36991, 42561}, {38054, 49547}, {38200, 49232}, {42259, 52835}, {42270, 59389}, {45366, 60880}, {45367, 60881}, {45385, 60884}, {45485, 60889}, {45487, 60888}, {45575, 60891}, {45577, 60890}, {45606, 60892}, {45608, 60893}, {45651, 60895}, {45653, 60896}, {49026, 60894}

X(60921) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 142, 60920}, {615, 60914, 9}

X(60922) = ORTHOLOGY CENTER OF X3-ABC REFLECTIONS WRT AGUILERA TRIANGLE

Barycentrics    3*a^6-2*a^5*(b+c)-2*(b-c)^4*(b+c)^2+a^4*(-6*b^2+2*b*c-6*c^2)+2*a^3*(b+c)*(b^2+c^2)+a^2*(b-c)^2*(5*b^2+4*b*c+5*c^2) : :
X(60922) = -5*X[2]+6*X[38080], -4*X[9]+5*X[1656], -4*X[140]+3*X[21168], -8*X[142]+7*X[3526], -2*X[390]+3*X[10247], -2*X[549]+3*X[59375], -5*X[631]+6*X[38111], -2*X[1156]+3*X[51517], -2*X[1385]+3*X[59372], -5*X[1698]+6*X[38172], -3*X[1699]+X[41705], -4*X[2550]+3*X[59503] and many others

X(60922) lies on these lines: {2, 38080}, {3, 7}, {4, 5843}, {5, 144}, {6, 60915}, {9, 1656}, {30, 36996}, {140, 21168}, {142, 3526}, {355, 5850}, {381, 527}, {382, 971}, {390, 10247}, {516, 1482}, {517, 4312}, {518, 11898}, {528, 50805}, {549, 59375}, {631, 38111}, {962, 30283}, {999, 60883}, {1001, 22765}, {1156, 51517}, {1351, 5845}, {1385, 59372}, {1445, 11662}, {1454, 15518}, {1598, 60879}, {1698, 38172}, {1699, 41705}, {2094, 13226}, {2550, 59503}, {2801, 12747}, {3062, 22793}, {3090, 61006}, {3091, 38137}, {3295, 60919}, {3311, 60913}, {3312, 60914}, {3534, 5732}, {3616, 38041}, {3617, 38170}, {3618, 38164}, {3653, 51098}, {3830, 36991}, {3843, 59385}, {3851, 5817}, {3894, 36999}, {3927, 60979}, {4295, 8158}, {5050, 51150}, {5054, 6173}, {5055, 6172}, {5070, 18230}, {5072, 38150}, {5076, 31672}, {5079, 38108}, {5093, 51190}, {5220, 11929}, {5223, 5790}, {5535, 31479}, {5542, 10246}, {5690, 59412}, {5698, 20330}, {5708, 5812}, {5709, 60937}, {5715, 5789}, {5733, 17246}, {5771, 50740}, {5851, 10738}, {5856, 12331}, {5880, 38121}, {5886, 51090}, {5901, 52653}, {5905, 13257}, {6068, 38752}, {6244, 11246}, {6417, 60887}, {6583, 41861}, {6666, 55857}, {6827, 60975}, {6842, 60934}, {6863, 8232}, {6882, 12848}, {6907, 60998}, {6922, 60939}, {6923, 60956}, {6958, 8732}, {6971, 41563}, {6980, 60946}, {7517, 60897}, {7580, 17483}, {8226, 20078}, {8727, 9965}, {9301, 60900}, {9654, 60909}, {9655, 37625}, {9669, 60910}, {10202, 51489}, {10679, 38454}, {10680, 13743}, {11038, 37624}, {11495, 11849}, {11842, 60882}, {11875, 60898}, {11876, 60899}, {11911, 60906}, {11916, 60907}, {11917, 60908}, {11928, 16112}, {11949, 60917}, {11950, 60918}, {12000, 60925}, {12001, 60926}, {12017, 38115}, {12245, 50240}, {12617, 28646}, {12619, 41712}, {12684, 12699}, {12702, 12872}, {13903, 60920}, {13961, 60921}, {14561, 51144}, {14848, 50997}, {15008, 18530}, {15298, 59318}, {15693, 38065}, {15694, 59374}, {15696, 43177}, {15703, 61023}, {15720, 38122}, {15723, 38093}, {15934, 61021}, {16853, 60959}, {17527, 61009}, {17662, 37567}, {18492, 52665}, {18493, 38036}, {19709, 38073}, {20195, 55858}, {21153, 61020}, {21454, 37364}, {25557, 38031}, {26921, 50726}, {31272, 38173}, {31300, 36652}, {33558, 54175}, {34753, 60941}, {37545, 60992}, {37584, 60953}, {37612, 60955}, {38030, 43180}, {38064, 51195}, {38066, 51100}, {38113, 46219}, {44455, 54158}, {45369, 60880}, {45370, 60881}, {45488, 60888}, {45489, 60889}, {45578, 60890}, {45579, 60891}, {45609, 60893}, {45610, 60892}, {49028, 60894}, {53091, 59405}, {57282, 60961}

X(60922) = midpoint of X(i) and X(j) for these {i,j}: {36971, 54133}, {4, 20059}, {5735, 60933}
X(60922) = reflection of X(i) in X(j) for these {i,j}: {144, 5}, {3, 7}, {3062, 22793}, {382, 31671}, {31671, 5735}, {44455, 54158}, {5698, 20330}, {5759, 31657}, {5779, 5805}, {51516, 59386}, {54175, 33558}, {59380, 51514}, {60884, 4}
X(60922) = pole of line {39476, 44811} wrt circumcircle
X(60922) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 51514, 7}, {3, 7, 59380}, {4, 20059, 5843}, {4, 5843, 60884}, {5, 144, 51516}, {7, 5759, 31657}, {9, 38107, 1656}, {142, 59381, 3526}, {144, 59386, 5}, {527, 5805, 5779}, {971, 31671, 382}, {971, 5735, 31671}, {2095, 37826, 381}, {5735, 60933, 971}, {5758, 24470, 3}, {5762, 31657, 5759}, {18230, 38171, 5070}, {36971, 54133, 517}, {38113, 60996, 46219}, {59385, 60901, 3843}, {60883, 60924, 999}, {60915, 60916, 6}, {60919, 60923, 3295}

X(60923) = ORTHOLOGY CENTER OF INNER-YFF WRT AGUILERA TRIANGLE

Barycentrics    a^6-4*a^3*b*c*(b+c)-(b-c)^4*(b+c)^2+a^4*(-3*b^2+4*b*c-3*c^2)+a^2*(b-c)^2*(3*b^2+4*b*c+3*c^2) : :

X(60923) lies on these lines: {1, 7}, {3, 60883}, {5, 60910}, {9, 498}, {11, 38107}, {12, 5779}, {35, 5759}, {36, 21151}, {46, 52819}, {55, 5762}, {56, 31657}, {80, 38149}, {142, 499}, {144, 191}, {226, 1709}, {354, 10947}, {388, 15071}, {484, 60975}, {495, 5843}, {497, 59386}, {518, 12647}, {527, 10056}, {611, 5845}, {613, 51150}, {954, 8069}, {971, 1478}, {999, 59380}, {1001, 22766}, {1056, 2800}, {1124, 60914}, {1156, 8068}, {1319, 38030}, {1335, 60913}, {1387, 38041}, {1428, 38115}, {1445, 17700}, {1479, 5805}, {1698, 60959}, {1733, 2550}, {1737, 10398}, {1836, 11018}, {2801, 10057}, {3062, 9612}, {3295, 60919}, {3301, 60887}, {3336, 60939}, {3338, 60992}, {3474, 41853}, {3582, 59374}, {3583, 59385}, {3584, 6172}, {3585, 36991}, {3826, 5729}, {3911, 38123}, {5010, 59418}, {5119, 10059}, {5218, 21168}, {5220, 10954}, {5223, 10039}, {5290, 7992}, {5298, 38065}, {5432, 59381}, {5572, 18223}, {5714, 16127}, {5726, 52665}, {5728, 5880}, {5817, 7951}, {5832, 15733}, {5840, 15934}, {5850, 31397}, {5856, 10087}, {5903, 35514}, {5905, 13405}, {6173, 10072}, {6284, 31671}, {6684, 61014}, {6767, 51514}, {6908, 15932}, {7952, 37559}, {8232, 10321}, {8545, 15518}, {8581, 10043}, {9654, 60884}, {10037, 60897}, {10038, 60900}, {10040, 60907}, {10041, 60908}, {10042, 11372}, {10090, 10427}, {10198, 60969}, {10320, 60911}, {10384, 30384}, {10392, 10826}, {10523, 16112}, {10531, 58566}, {10578, 17483}, {10580, 26842}, {10801, 60882}, {10895, 60901}, {11020, 20292}, {11045, 16193}, {11398, 60879}, {11495, 11507}, {11545, 38170}, {11877, 60898}, {11878, 60899}, {11912, 60906}, {11951, 60917}, {11952, 60918}, {12514, 60979}, {12850, 18244}, {13159, 16153}, {13407, 60937}, {13411, 51090}, {13904, 60920}, {13962, 60921}, {14548, 24014}, {15325, 38111}, {15587, 44547}, {15837, 31452}, {16593, 24846}, {17010, 52653}, {17437, 60938}, {18391, 59412}, {18395, 40333}, {21077, 60966}, {21617, 54370}, {21620, 60961}, {25557, 42884}, {26364, 61012}, {27529, 61026}, {30274, 41861}, {30275, 38037}, {31391, 57282}, {31434, 60997}, {31479, 51516}, {35808, 60916}, {35809, 60915}, {38054, 44675}, {38057, 41700}, {38121, 40663}, {41563, 60912}, {41684, 59413}, {41707, 60942}, {43151, 58887}, {45043, 53616}, {45371, 60880}, {45372, 60881}, {45490, 60888}, {45491, 60889}, {45580, 60890}, {45581, 60891}, {45611, 60893}, {45612, 60892}, {49030, 60894}, {51816, 60993}, {60905, 61010}

X(60923) = midpoint of X(i) and X(j) for these {i,j}: {7, 60925}
X(60923) = reflection of X(i) in X(j) for these {i,j}: {60909, 495}, {954, 8255}
X(60923) = pole of line {514, 38324} wrt incircle
X(60923) = pole of line {354, 60924} wrt Feuerbach hyperbola
X(60923) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 7, 60924}, {7, 390, 60895}, {7, 60925, 516}, {142, 15299, 499}, {495, 5843, 60909}, {2550, 18412, 10573}, {2951, 4312, 1770}, {5805, 14100, 1479}, {8255, 17768, 954}, {10384, 38036, 30384}, {10398, 38052, 1737}

X(60924) = ORTHOLOGY CENTER OF OUTER-YFF WRT AGUILERA TRIANGLE

Barycentrics    a^6+4*a^3*b*c*(b+c)-(b-c)^4*(b+c)^2-3*a^4*(b^2+c^2)+3*a^2*(b-c)^2*(b^2+c^2) : :

X(60924) lies on these lines: {1, 7}, {3, 60919}, {5, 60909}, {9, 499}, {11, 5779}, {12, 38107}, {35, 21151}, {36, 5759}, {46, 10075}, {55, 24465}, {56, 5762}, {142, 498}, {144, 3086}, {388, 59386}, {496, 5843}, {497, 5083}, {518, 10573}, {527, 10072}, {611, 51150}, {613, 5845}, {920, 60990}, {946, 60961}, {954, 8071}, {971, 1479}, {999, 60883}, {1001, 22767}, {1124, 60913}, {1156, 5533}, {1210, 5850}, {1335, 60914}, {1445, 15518}, {1478, 5805}, {1496, 24159}, {1698, 11023}, {1728, 61003}, {1737, 5223}, {1836, 12915}, {2330, 38115}, {2550, 12647}, {2646, 38030}, {2801, 10073}, {3062, 9614}, {3295, 59380}, {3299, 60887}, {3337, 60939}, {3338, 52819}, {3361, 5758}, {3582, 6172}, {3583, 36991}, {3584, 59374}, {3585, 59385}, {3624, 60959}, {3660, 51489}, {3894, 18391}, {4995, 38065}, {5119, 60993}, {5220, 10523}, {5433, 59381}, {5536, 54366}, {5570, 5728}, {5572, 18224}, {5686, 18395}, {5696, 6601}, {5697, 35514}, {5729, 5852}, {5811, 52665}, {5817, 7741}, {5841, 15934}, {5856, 10090}, {5905, 11019}, {6173, 10056}, {7280, 59418}, {7288, 21168}, {7354, 31671}, {7373, 51514}, {7672, 53615}, {7717, 54428}, {8069, 38454}, {8732, 10321}, {9669, 60884}, {10039, 38052}, {10046, 60897}, {10047, 60900}, {10048, 60907}, {10049, 60908}, {10050, 11372}, {10052, 14100}, {10085, 12053}, {10087, 10427}, {10200, 61012}, {10320, 60912}, {10398, 61010}, {10578, 26842}, {10580, 17483}, {10629, 18412}, {10802, 60882}, {10896, 60901}, {10948, 16112}, {11399, 60879}, {11495, 11508}, {11879, 60898}, {11880, 60899}, {11913, 60906}, {11953, 60917}, {11954, 60918}, {12047, 38036}, {12699, 31391}, {12701, 16215}, {13159, 16152}, {13411, 38054}, {13905, 60920}, {13963, 60921}, {14986, 20059}, {15837, 38122}, {16593, 24845}, {17626, 24703}, {17700, 60938}, {17768, 42884}, {18393, 60998}, {21616, 60966}, {25415, 54158}, {26363, 60969}, {32760, 36976}, {35768, 60916}, {35769, 60915}, {37704, 41705}, {37710, 38149}, {37737, 38041}, {38037, 60934}, {39599, 54370}, {43151, 59316}, {44675, 51090}, {45373, 60880}, {45374, 60881}, {45492, 60888}, {45493, 60889}, {45582, 60890}, {45583, 60891}, {45613, 60893}, {45614, 60892}, {49032, 60894}, {51768, 60956}, {51816, 61021}, {59335, 60955}, {60911, 60946}

X(60924) = midpoint of X(i) and X(j) for these {i,j}: {7, 60926}
X(60924) = reflection of X(i) in X(j) for these {i,j}: {46, 60992}, {60910, 496}, {60966, 21616}
X(60924) = pole of line {354, 10947} wrt Feuerbach hyperbola
X(60924) = pole of line {7, 53996} wrt dual conic of Yff parabola
X(60924) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 7, 60923}, {7, 390, 60896}, {7, 60926, 516}, {142, 15298, 498}, {496, 5843, 60910}, {999, 60922, 60883}, {5805, 8581, 1478}, {15518, 17437, 1445}, {38036, 60937, 12047}

X(60925) = ORTHOLOGY CENTER OF INNER-YFF TANGENTS WRT AGUILERA TRIANGLE

Barycentrics    (a-b-c)*(a^5+a^4*(b+c)-2*a^2*(b-c)^2*(b+c)+(b-c)^4*(b+c)+a*(b-c)^2*(b^2+c^2)-2*a^3*(b^2-5*b*c+c^2)) : :

X(60925) lies on these lines: {1, 7}, {2, 30223}, {8, 3255}, {9, 1195}, {12, 16112}, {40, 41572}, {55, 5905}, {119, 1156}, {144, 10528}, {329, 5281}, {377, 12711}, {388, 9961}, {497, 20292}, {498, 60911}, {518, 12648}, {527, 11239}, {938, 15016}, {954, 12775}, {971, 12115}, {1001, 22768}, {1071, 17620}, {1253, 24695}, {1445, 59333}, {1478, 16154}, {1519, 30275}, {1697, 60933}, {2077, 59418}, {2346, 5553}, {2550, 5086}, {2801, 12749}, {3062, 10970}, {3085, 29007}, {3086, 60988}, {3256, 9778}, {3359, 12848}, {3434, 5832}, {3487, 16133}, {3488, 5840}, {3601, 11415}, {3826, 10958}, {5218, 31018}, {5220, 10955}, {5223, 10915}, {5250, 61002}, {5261, 6223}, {5274, 9776}, {5572, 18225}, {5686, 6735}, {5698, 20846}, {5728, 34339}, {5759, 7676}, {5762, 10679}, {5766, 61010}, {5779, 10942}, {5805, 10531}, {5809, 45043}, {5825, 9780}, {5843, 32213}, {5845, 12594}, {5850, 49626}, {5851, 10956}, {5856, 13278}, {5880, 10940}, {6008, 59977}, {6172, 45701}, {6173, 10384}, {6256, 36991}, {6684, 60947}, {6838, 59335}, {6925, 50195}, {7671, 10202}, {7672, 35514}, {7673, 23340}, {7677, 10269}, {7717, 26378}, {8545, 12686}, {8581, 10935}, {8732, 37534}, {9809, 41166}, {10200, 60996}, {10596, 59386}, {10803, 60882}, {10805, 36996}, {10834, 60897}, {10878, 60900}, {10929, 60907}, {10930, 60908}, {10941, 26357}, {10965, 60919}, {11047, 13373}, {11372, 11919}, {11400, 60879}, {11495, 11509}, {11881, 60898}, {11882, 60899}, {11914, 60906}, {11955, 60917}, {11956, 60918}, {12000, 60922}, {12053, 60980}, {12703, 12874}, {13906, 60920}, {13964, 60921}, {14803, 52769}, {15298, 60946}, {15299, 61019}, {15867, 60912}, {16203, 31657}, {16209, 43151}, {17010, 54445}, {18224, 58887}, {18230, 26364}, {18542, 60901}, {18545, 60884}, {19048, 60887}, {24982, 40333}, {26065, 27521}, {26228, 52428}, {26333, 59385}, {26402, 60880}, {26426, 60881}, {26511, 60893}, {26520, 60894}, {30513, 34919}, {35816, 60915}, {35817, 60916}, {37719, 41694}, {38037, 61008}, {38053, 53055}, {38055, 59380}, {44643, 60913}, {44644, 60914}, {45494, 60888}, {45495, 60889}, {45584, 60890}, {45585, 60891}, {45615, 60892}, {45729, 51190}, {51090, 59719}, {52457, 52653}, {54370, 60943}, {56288, 60950}

X(60925) = reflection of X(i) in X(j) for these {i,j}: {390, 7675}, {3434, 5832}, {60946, 15298}, {7, 60923}
X(60925) = pole of line {354, 5905} wrt Feuerbach hyperbola
X(60925) = intersection, other than A, B, C, of circumconics {{A, B, C, X(269), X(3255)}}, {{A, B, C, X(5553), X(10481)}}
X(60925) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 60896, 7}, {7, 390, 60926}, {516, 7675, 390}, {1156, 7679, 5817}, {5809, 59412, 45043}, {12573, 43182, 8544}

X(60926) = ORTHOLOGY CENTER OF OUTER-YFF TANGENTS WRT AGUILERA TRIANGLE

Barycentrics    (a-b-c)*(a^5+a^4*(b+c)-2*a^2*(b-c)^2*(b+c)+(b-c)^4*(b+c)+a*(b-c)^2*(b^2-4*b*c+c^2)-2*a^3*(b^2+b*c+c^2)) : :

X(60926) lies on these lines: {1, 7}, {2, 54408}, {3, 36976}, {8, 3254}, {9, 10527}, {11, 5220}, {40, 30379}, {55, 25557}, {56, 38454}, {144, 10529}, {329, 5274}, {496, 5729}, {497, 3873}, {499, 60912}, {515, 30318}, {518, 1837}, {527, 11240}, {528, 2098}, {944, 14151}, {946, 8545}, {950, 61011}, {954, 20330}, {971, 12116}, {1001, 10966}, {1058, 7671}, {1156, 37726}, {1445, 12704}, {1479, 2801}, {1482, 54158}, {1519, 52684}, {1697, 6173}, {1936, 26228}, {2078, 9778}, {2256, 5829}, {2323, 5838}, {2550, 14923}, {2975, 5698}, {3057, 5880}, {3062, 10971}, {3085, 61008}, {3086, 37787}, {3303, 8255}, {3304, 36971}, {3333, 60932}, {3434, 5784}, {3474, 33925}, {3486, 34605}, {3488, 5841}, {3616, 5766}, {3813, 42014}, {3913, 61035}, {5223, 10916}, {5231, 18228}, {5253, 26357}, {5281, 9776}, {5435, 5536}, {5558, 34917}, {5572, 18226}, {5603, 8543}, {5657, 30312}, {5686, 6734}, {5709, 8732}, {5728, 5812}, {5758, 12848}, {5759, 7677}, {5762, 10680}, {5768, 12755}, {5779, 10943}, {5805, 10532}, {5809, 40269}, {5815, 50835}, {5817, 7678}, {5843, 32214}, {5845, 12595}, {5850, 49627}, {5852, 10959}, {5856, 13279}, {6172, 45700}, {6361, 30295}, {6601, 41228}, {6836, 50196}, {7672, 24474}, {7673, 35514}, {7676, 10267}, {7717, 26377}, {8163, 13463}, {8227, 61015}, {8581, 10936}, {8609, 41325}, {10198, 60996}, {10384, 60933}, {10431, 17625}, {10597, 59386}, {10804, 60882}, {10806, 36996}, {10835, 60897}, {10879, 60900}, {10931, 60907}, {10932, 60908}, {10940, 26358}, {10941, 14100}, {10949, 16112}, {10957, 42356}, {11012, 59418}, {11372, 11920}, {11376, 15254}, {11401, 60879}, {11495, 11510}, {11883, 60898}, {11884, 60899}, {11915, 60906}, {11957, 60917}, {11958, 60918}, {12001, 60922}, {12047, 61027}, {12701, 15726}, {13907, 60920}, {13965, 60921}, {15298, 37692}, {15299, 41563}, {15868, 60911}, {16202, 31657}, {16208, 43151}, {17768, 42886}, {18220, 60997}, {18223, 59316}, {18230, 26363}, {18543, 60884}, {18544, 60901}, {18967, 60883}, {19050, 60887}, {19843, 60981}, {20078, 30223}, {21617, 38036}, {24460, 36547}, {24541, 60959}, {24987, 40333}, {26332, 59385}, {26401, 60880}, {26425, 60881}, {26501, 60892}, {26510, 60893}, {26519, 60894}, {27385, 47375}, {29007, 38037}, {30384, 54370}, {31162, 60952}, {35818, 60915}, {35819, 60916}, {36579, 40950}, {36991, 48482}, {37704, 50573}, {37720, 41700}, {37734, 42871}, {44645, 60913}, {44646, 60914}, {45496, 60888}, {45497, 60889}, {45586, 60890}, {45587, 60891}, {45728, 51190}, {47386, 56929}

X(60926) = reflection of X(i) in X(j) for these {i,j}: {41563, 15299}, {5729, 496}, {7, 60924}
X(60926) = pole of line {514, 59977} wrt incircle
X(60926) = pole of line {354, 3434} wrt Feuerbach hyperbola
X(60926) = intersection, other than A, B, C, of circumconics {{A, B, C, X(8), X(38459)}}, {{A, B, C, X(269), X(3254)}}, {{A, B, C, X(4328), X(34917)}}, {{A, B, C, X(4341), X(6601)}}, {{A, B, C, X(4350), X(43740)}}
X(60926) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 60895, 7}, {7, 390, 60925}, {175, 176, 38459}, {390, 11038, 30284}

X(60927) = ORTHOLOGY CENTER OF GEMINI 63 WRT AGUILERA TRIANGLE

Barycentrics    2*a^4+4*a^3*(b+c)-(b-c)^2*(b^2+b*c+c^2)-2*a*(b+c)*(b^2+b*c+c^2)-a^2*(3*b^2+b*c+3*c^2) : :
X(60927) = -5*X[29622]+4*X[51057]

X(60927) lies on circumconic {{A, B, C, X(17248), X(23618)}} and on these lines: {2, 7}, {239, 5698}, {390, 50129}, {516, 27484}, {518, 17389}, {528, 29617}, {2796, 16833}, {3573, 51002}, {3661, 5220}, {3790, 5223}, {3797, 17363}, {4370, 51191}, {4384, 60905}, {5735, 7384}, {5762, 36728}, {5779, 36731}, {5851, 27489}, {5852, 27475}, {5880, 29576}, {7321, 20156}, {11684, 26531}, {15254, 17397}, {16468, 50114}, {16475, 52653}, {16834, 50836}, {17264, 50995}, {17310, 50996}, {17399, 51150}, {17768, 27483}, {20154, 48627}, {24603, 30424}, {25557, 29612}, {29580, 51099}, {29584, 47357}, {29594, 50834}, {29622, 51057}, {41325, 50107}, {50079, 50835}

X(60927) = reflection of X(i) in X(j) for these {i,j}: {17333, 6172}, {29617, 51053}, {60984, 50116}
X(60927) = pole of line {14100, 17248} wrt Feuerbach hyperbola
X(60927) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 9, 17248}, {527, 50116, 60984}, {527, 6172, 17333}, {528, 51053, 29617}

X(60928) = ORTHOCENTER OF AGUILERA-PAVLOV TRIANGLE

Barycentrics    a*(a+b+c)*(a*(a^2+3*(b-c)^2)*(b+c)+a^2*(-3*b^2+4*b*c-3*c^2)-(b-c)^2*(b^2+4*b*c+c^2))+12*a^2*b*c*S : :

X(60928) lies on these lines: {1, 6610}, {176, 7671}, {354, 482}, {517, 52805}, {971, 52809}, {1371, 5572}, {5049, 30341}, {5902, 51764}, {5919, 31567}, {8965, 54474}, {11025, 17804}, {14100, 31538}, {30557, 61028}, {31391, 31539}

X(60928) = reflection of X(i) in X(j) for these {i,j}: {60931, 5049}
X(60928) = pole of line {481, 4860} wrt Feuerbach hyperbola

X(60929) = ORTHOLOGY CENTER OF ANTI-ARTZT WRT AGUILERA-PAVLOV TRIANGLE

Barycentrics    a*(2*b*c*(b^2-b*c+c^2)-a*(b+c)*(2*b^2-3*b*c+2*c^2)+a^2*(2*b^2-b*c+2*c^2)) : :
X(60929) = -2*X[3056]+5*X[17304], 2*X[3663]+X[25304], -X[3729]+4*X[17792]

X(60929) lies on these lines: {1, 3123}, {2, 29353}, {513, 50127}, {674, 17274}, {2801, 37712}, {3056, 17304}, {3663, 25304}, {3729, 17792}, {3731, 25279}, {6007, 17294}, {9024, 17301}, {9025, 16834}, {9037, 48829}, {15988, 24309}, {17298, 21746}, {17579, 29046}, {51152, 61030}

X(60930) = ORTHOLOGY CENTER OF 1ST MOSES-MIYAMOTO-APOLLONIUS TRIANGLE WRT AGUILERA-PAVLOV TRIANGLE

Barycentrics    a*(a^3*b-3*a^2*b^2+3*a*b^3-b^4+a^3*c+4*a^2*b*c-3*a*b^2*c-2*b^3*c-3*a^2*c^2-3*a*b*c^2+6*b^2*c^2+3*a*c^3-2*b*c^3-c^4)+2*a*(a*b-b^2+a*c+2*b*c-c^2)*S : :

X(60930) lies on these lines: {7, 354}, {55, 60878}, {165, 6204}, {176, 31588}, {517, 52805}, {1373, 31571}, {3576, 30386}, {3740, 30413}, {3817, 30307}, {5049, 30342}, {5902, 30426}, {5919, 30334}, {5927, 30289}, {10175, 30314}, {10246, 18460}, {11192, 30369}, {11195, 30407}, {11203, 30361}, {11217, 30419}, {11224, 30320}, {11227, 30277}

X(60930) = reflection of X(i) in X(j) for these {i,j}: {60931, 354}
X(60930) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 30376, 30347}, {354, 15726, 60931}, {6204, 30355, 30297}, {30355, 30397, 6204}

X(60931) = ORTHOLOGY CENTER OF 2ND MOSES-MIYAMOTO-APOLLONIUS TRIANGLE WRT AGUILERA-PAVLOV TRIANGLE

Barycentrics    a*(a^3*b-3*a^2*b^2+3*a*b^3-b^4+a^3*c+4*a^2*b*c-3*a*b^2*c-2*b^3*c-3*a^2*c^2-3*a*b*c^2+6*b^2*c^2+3*a*c^3-2*b*c^3-c^4)-2*a*(a*b-b^2+a*c+2*b*c-c^2)*S : :

X(60931) lies on these lines: {7, 354}, {165, 6203}, {175, 31589}, {517, 52808}, {1374, 31572}, {3576, 30385}, {3740, 30412}, {3817, 30306}, {5049, 30341}, {5902, 30425}, {5919, 30333}, {5927, 30288}, {7133, 11211}, {10175, 30313}, {10246, 18458}, {11192, 30368}, {11195, 30406}, {11203, 30360}, {11217, 30418}, {11224, 30319}, {11227, 30276}

X(60931) = reflection of X(i) in X(j) for these {i,j}: {60928, 5049}, {60930, 354}
X(60931) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 30375, 30346}, {354, 15726, 60930}, {6203, 30354, 30296}, {30354, 30396, 6203}

X(60932) = X(2)X(7)∩X(65)X(528)

Barycentrics    (a+b-c)*(a-b+c)*(2*a^3-2*a*b*c-3*a^2*(b+c)+(b-c)^2*(b+c)) : :
X(60932) = -4*X[58563]+X[60919]

X(60932) lies on these lines: {1, 36976}, {2, 7}, {30, 5728}, {36, 5542}, {65, 528}, {79, 1156}, {85, 17346}, {100, 41570}, {190, 32007}, {241, 17392}, {273, 1839}, {354, 38454}, {376, 7675}, {390, 11529}, {411, 43177}, {516, 5902}, {518, 5434}, {519, 7672}, {551, 7677}, {651, 1170}, {653, 1855}, {662, 1434}, {938, 41869}, {942, 37428}, {1001, 51423}, {1004, 47387}, {1155, 8255}, {1441, 50095}, {1443, 4667}, {1446, 60094}, {1470, 42885}, {1835, 1890}, {1992, 17079}, {2263, 50303}, {2346, 15931}, {3058, 5572}, {3059, 49732}, {3241, 11526}, {3333, 60926}, {3338, 60895}, {3359, 54158}, {3361, 38024}, {3485, 38025}, {3543, 5809}, {3576, 11038}, {3583, 4312}, {3600, 30318}, {3649, 15254}, {3656, 42884}, {3664, 17092}, {3668, 50114}, {3671, 5259}, {3674, 16783}, {3828, 7679}, {3947, 38101}, {3970, 22003}, {4134, 5850}, {4292, 10394}, {4298, 5904}, {4315, 14151}, {4318, 50294}, {4331, 50080}, {4552, 50110}, {4860, 36971}, {5220, 10404}, {5221, 5880}, {5228, 17301}, {5425, 30331}, {5586, 60905}, {5698, 54392}, {5703, 30340}, {5729, 57282}, {5735, 6836}, {5759, 18443}, {5762, 10202}, {5766, 11036}, {5784, 31938}, {6068, 27385}, {6354, 50103}, {6604, 50107}, {6925, 54159}, {7670, 58707}, {7676, 50808}, {7678, 50802}, {8544, 41854}, {8808, 54648}, {9440, 47487}, {9578, 38097}, {9612, 38075}, {11112, 14054}, {11237, 41712}, {11246, 15726}, {11374, 38067}, {11552, 51768}, {12560, 50836}, {13407, 60912}, {13411, 43180}, {15008, 28202}, {16133, 51090}, {16666, 43066}, {17023, 41804}, {17078, 46922}, {17294, 56927}, {17620, 34612}, {18406, 45043}, {18838, 28534}, {21153, 59372}, {24470, 40263}, {25557, 32636}, {26723, 55010}, {26725, 38059}, {30284, 51705}, {30287, 41866}, {30295, 41853}, {30311, 41858}, {30312, 41859}, {30330, 50865}, {30332, 41864}, {30353, 41860}, {30359, 41856}, {30404, 41855}, {30628, 49719}, {35617, 42057}, {36731, 41004}, {37545, 38065}, {39126, 49722}, {41803, 50109}, {50844, 57283}, {58563, 60919}

X(60932) = midpoint of X(i) and X(j) for these {i,j}: {30628, 49719}, {41572, 60952}, {553, 52819}, {7, 60951}
X(60932) = reflection of X(i) in X(j) for these {i,j}: {17781, 9}, {3058, 5572}, {3059, 49732}, {41572, 60951}, {553, 60945}, {6172, 60972}, {60936, 60952}, {60951, 52819}, {60952, 7}, {7, 553}
X(60932) = pole of line {3676, 4794} wrt incircle
X(60932) = pole of line {14100, 41857} wrt Feuerbach hyperbola
X(60932) = pole of line {4724, 30574} wrt Suppa-Cucoanes circle
X(60932) = orthology center of the pedal triangle of X(354) wrt Aguilera triangle
X(60932) = intersection, other than A, B, C, of circumconics {{A, B, C, X(9), X(60094)}}, {{A, B, C, X(79), X(527)}}, {{A, B, C, X(142), X(34578)}}, {{A, B, C, X(226), X(43762)}}, {{A, B, C, X(279), X(30275)}}, {{A, B, C, X(329), X(54648)}}, {{A, B, C, X(673), X(54357)}}, {{A, B, C, X(1156), X(3219)}}, {{A, B, C, X(1170), X(37787)}}, {{A, B, C, X(1434), X(30379)}}, {{A, B, C, X(10509), X(21617)}}, {{A, B, C, X(23618), X(41857)}}, {{A, B, C, X(38340), X(56543)}}, {{A, B, C, X(39980), X(55869)}}
X(60932) = barycentric quotient X(i)/X(j) for these (i, j): {109, 20219}
X(60932) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 1445, 21617}, {7, 37787, 226}, {7, 41563, 60937}, {7, 5435, 30275}, {7, 57, 30379}, {7, 6172, 60967}, {7, 60941, 8232}, {7, 60946, 60953}, {7, 60948, 142}, {7, 61027, 4654}, {9, 4654, 61027}, {9, 527, 17781}, {57, 60989, 60948}, {142, 60989, 59491}, {226, 37787, 61015}, {527, 52819, 60951}, {527, 60945, 553}, {527, 60951, 41572}, {527, 60952, 60936}, {553, 60951, 60952}, {1445, 21617, 61016}, {4031, 61021, 61022}, {4654, 61027, 41857}, {6172, 60967, 8545}, {8232, 60941, 60947}, {8257, 61011, 908}, {8545, 12848, 50573}, {12848, 60967, 6172}, {21454, 60975, 7}, {30379, 41857, 5249}, {41572, 60952, 527}, {60948, 60970, 1445}, {60953, 61007, 60946}

X(60933) = X(1)X(3255)∩X(2)X(7)

Barycentrics    3*a^2-2*(b-c)^2-a*(b+c) : :
X(60933) = -3*X[2]+5*X[7], -X[40]+2*X[60896], -5*X[390]+7*X[20057], -4*X[546]+5*X[5805], -4*X[550]+5*X[5732], -5*X[1698]+4*X[15481], -3*X[1699]+2*X[16112], -5*X[2550]+4*X[3626], -7*X[3528]+5*X[5759], -16*X[3530]+15*X[21153], -17*X[3544]+15*X[5817], -4*X[3631]+5*X[47595] and many others

X(60933) lies on these lines: {1, 3255}, {2, 7}, {6, 4862}, {10, 7222}, {30, 36867}, {35, 42885}, {36, 42843}, {37, 4888}, {40, 60896}, {44, 4859}, {69, 4007}, {72, 56997}, {75, 4034}, {145, 23766}, {165, 41548}, {190, 17241}, {192, 29619}, {193, 1266}, {200, 11246}, {284, 58786}, {319, 49722}, {320, 3729}, {344, 4480}, {382, 971}, {390, 20057}, {480, 44785}, {516, 944}, {518, 3632}, {522, 23730}, {524, 17151}, {528, 26726}, {529, 18421}, {545, 4851}, {546, 5805}, {550, 5732}, {673, 39707}, {758, 36922}, {903, 3759}, {936, 24470}, {954, 19535}, {960, 4355}, {1001, 5563}, {1086, 1743}, {1100, 49747}, {1145, 2093}, {1373, 30556}, {1374, 30557}, {1419, 22464}, {1449, 3663}, {1697, 60925}, {1698, 15481}, {1699, 16112}, {1707, 33103}, {1721, 8271}, {1770, 41863}, {1836, 24392}, {2099, 34716}, {2321, 4454}, {2323, 6180}, {2324, 7271}, {2325, 4488}, {2345, 53598}, {2550, 3626}, {2801, 41577}, {2951, 38454}, {2975, 16133}, {3062, 3254}, {3158, 3474}, {3174, 5528}, {3247, 3664}, {3337, 25522}, {3528, 5759}, {3530, 21153}, {3544, 5817}, {3586, 24473}, {3629, 5845}, {3631, 47595}, {3636, 5542}, {3640, 30426}, {3641, 30425}, {3644, 29605}, {3667, 23760}, {3672, 4667}, {3677, 41011}, {3679, 17118}, {3686, 31995}, {3731, 4675}, {3751, 32857}, {3758, 17304}, {3779, 4014}, {3812, 5586}, {3824, 31446}, {3841, 41865}, {3851, 5779}, {3855, 59386}, {3868, 9579}, {3873, 9580}, {3874, 41869}, {3875, 4440}, {3941, 24405}, {3946, 4346}, {3973, 17278}, {4000, 4887}, {4050, 36854}, {4084, 5881}, {4292, 11523}, {4295, 6762}, {4298, 15829}, {4301, 12246}, {4321, 60883}, {4326, 60919}, {4361, 4715}, {4363, 17239}, {4364, 28640}, {4384, 7321}, {4398, 16834}, {4402, 4700}, {4409, 17388}, {4416, 42697}, {4494, 44139}, {4641, 23681}, {4643, 7228}, {4645, 4901}, {4648, 4896}, {4670, 17255}, {4681, 29602}, {4684, 24280}, {4718, 4898}, {4741, 17116}, {4795, 17045}, {4796, 16503}, {4858, 39126}, {4880, 17057}, {4912, 17262}, {5053, 7225}, {5079, 38107}, {5220, 38052}, {5223, 5852}, {5248, 41870}, {5537, 11495}, {5727, 40269}, {5758, 9841}, {5785, 50238}, {5832, 54422}, {5839, 53594}, {5853, 20050}, {5857, 12560}, {6006, 48398}, {6147, 31424}, {6329, 51150}, {6601, 55922}, {6603, 21314}, {6938, 16200}, {7174, 50307}, {7201, 18726}, {7232, 17284}, {7238, 17279}, {7263, 16833}, {7277, 16667}, {7289, 16548}, {7290, 24231}, {7671, 61033}, {8227, 60911}, {8583, 52783}, {9317, 53240}, {9589, 34791}, {10177, 11034}, {10299, 21151}, {10301, 60879}, {10384, 60926}, {10389, 44447}, {10390, 34919}, {10404, 12526}, {10427, 35023}, {10528, 41348}, {10980, 17051}, {11008, 49770}, {11372, 45632}, {11662, 19537}, {11737, 38075}, {12531, 21139}, {12737, 43166}, {13407, 54290}, {13462, 34647}, {14100, 18839}, {14269, 18482}, {14564, 55432}, {14869, 38122}, {15185, 15726}, {15687, 31672}, {15720, 31658}, {15733, 31391}, {15808, 38053}, {16118, 41709}, {16570, 33130}, {16578, 17092}, {16673, 17392}, {16831, 17258}, {16832, 17332}, {16885, 31183}, {17067, 37681}, {17132, 17314}, {17139, 18164}, {17231, 49721}, {17234, 25728}, {17235, 29598}, {17249, 29603}, {17267, 31138}, {17273, 17308}, {17275, 49727}, {17286, 17288}, {17294, 17361}, {17300, 29623}, {17312, 25269}, {17313, 36911}, {17317, 49748}, {17336, 31333}, {17373, 50089}, {18139, 25734}, {18193, 33096}, {18412, 53615}, {20072, 48627}, {20533, 29618}, {20583, 51002}, {20850, 60897}, {20881, 20930}, {21255, 54389}, {21630, 31162}, {24199, 54280}, {24393, 59412}, {24441, 28639}, {24708, 55340}, {24856, 53640}, {25466, 28646}, {25524, 28645}, {25722, 61030}, {26339, 60894}, {26340, 60908}, {28534, 42871}, {29606, 41325}, {30331, 51099}, {30340, 52653}, {30350, 49736}, {30625, 32007}, {32098, 41006}, {33148, 36277}, {34641, 51102}, {34744, 51782}, {35018, 38108}, {36279, 51362}, {36991, 50688}, {38025, 51098}, {38036, 41705}, {38088, 51195}, {38097, 51100}, {38186, 51144}, {39709, 55937}, {41555, 42356}, {41570, 43182}, {42696, 50119}, {42819, 50836}, {45713, 51764}, {45714, 51763}, {53665, 59579}, {55863, 59381}

X(60933) = midpoint of X(i) and X(j) for these {i,j}: {144, 60976}, {60894, 60907}, {60971, 60984}, {7, 20059}
X(60933) = reflection of X(i) in X(j) for these {i,j}: {144, 142}, {11372, 60895}, {17262, 17376}, {2550, 30424}, {38150, 51514}, {40, 60896}, {41705, 54370}, {5223, 5880}, {5698, 5542}, {5735, 60922}, {5759, 43177}, {5839, 53594}, {51090, 43180}, {52835, 5735}, {55998, 4851}, {6173, 60963}, {60884, 18482}, {60905, 1001}, {60940, 61022}, {60942, 60980}, {60957, 60942}, {60963, 60984}, {60977, 9}, {7, 60962}, {9, 7}
X(60933) = complement of X(60957)
X(60933) = anticomplement of X(60942)
X(60933) = X(i)-Dao conjugate of X(j) for these {i, j}: {60942, 60942}
X(60933) = pole of line {3004, 28473} wrt Conway circle
X(60933) = pole of line {3676, 28473} wrt incircle
X(60933) = pole of line {3064, 39532} wrt polar circle
X(60933) = pole of line {6173, 11238} wrt Feuerbach hyperbola
X(60933) = pole of line {522, 26985} wrt Steiner circumellipse
X(60933) = pole of line {522, 31250} wrt Steiner inellipse
X(60933) = pole of line {3669, 28473} wrt Suppa-Cucoanes circle
X(60933) = pole of line {1, 57000} wrt dual conic of Yff parabola
X(60933) = orthology center of the pedal triangle of X(1482) wrt Aguilera triangle
X(60933) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(29007)}}, {{A, B, C, X(2), X(3255)}}, {{A, B, C, X(144), X(3254)}}, {{A, B, C, X(673), X(31231)}}, {{A, B, C, X(1445), X(55922)}}, {{A, B, C, X(3062), X(37787)}}, {{A, B, C, X(6172), X(6601)}}, {{A, B, C, X(6173), X(23618)}}, {{A, B, C, X(8232), X(34917)}}, {{A, B, C, X(8545), X(10390)}}, {{A, B, C, X(9436), X(39707)}}, {{A, B, C, X(15909), X(41563)}}, {{A, B, C, X(18230), X(34919)}}, {{A, B, C, X(21446), X(27003)}}, {{A, B, C, X(27065), X(56354)}}
X(60933) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 144, 60983}, {2, 7, 60980}, {7, 12848, 60992}, {7, 144, 142}, {7, 41563, 30379}, {7, 41572, 57}, {7, 52819, 60955}, {7, 60934, 226}, {7, 60936, 60937}, {7, 60939, 61022}, {7, 60946, 21617}, {7, 60951, 60938}, {7, 60956, 60961}, {7, 60971, 20059}, {7, 60975, 60945}, {7, 60977, 20195}, {7, 60984, 60962}, {7, 60996, 59375}, {7, 8732, 60993}, {9, 38093, 6666}, {9, 60955, 60985}, {9, 60968, 60989}, {57, 28609, 30827}, {57, 5905, 28609}, {57, 908, 31190}, {63, 17483, 4654}, {63, 4654, 25525}, {69, 4659, 4007}, {142, 144, 9}, {142, 527, 144}, {142, 61000, 18230}, {142, 61020, 6173}, {144, 18230, 61000}, {144, 20059, 60976}, {144, 60976, 527}, {144, 60983, 60942}, {226, 9965, 3928}, {320, 3729, 17296}, {329, 553, 5437}, {527, 60942, 60957}, {527, 60984, 60963}, {527, 61022, 60940}, {545, 4851, 55998}, {894, 17274, 17306}, {971, 5735, 52835}, {971, 60922, 5735}, {1743, 4902, 1086}, {3218, 29007, 60994}, {3218, 31164, 5219}, {3306, 17484, 31142}, {3662, 31300, 50127}, {3663, 4644, 1449}, {3664, 4419, 3247}, {3729, 17296, 4873}, {4114, 20214, 51780}, {4363, 17272, 59772}, {4363, 17345, 17272}, {4440, 17364, 3875}, {4643, 7228, 25590}, {4675, 17334, 3731}, {4686, 40341, 3632}, {4741, 17116, 17270}, {4912, 17376, 17262}, {5223, 5880, 38200}, {5249, 20078, 3929}, {5542, 5698, 38316}, {5749, 45789, 50092}, {5850, 30424, 2550}, {5852, 5880, 5223}, {5905, 41572, 60965}, {6646, 50128, 10436}, {7232, 17351, 17284}, {7277, 17301, 16667}, {7321, 17347, 4384}, {9965, 60934, 60950}, {17118, 17344, 3679}, {17262, 17376, 29573}, {17276, 17365, 1}, {20059, 60963, 60977}, {20059, 60984, 7}, {23958, 29552, 41264}, {24231, 24695, 7290}, {28609, 31190, 908}, {38036, 41705, 54370}, {43180, 51090, 38053}, {59372, 60905, 1001}, {59375, 61006, 60996}, {60938, 60966, 8257}, {60942, 60980, 2}, {60947, 60988, 31231}, {60956, 61021, 60953}, {60962, 60976, 61020}, {60993, 61014, 8732}, {60996, 61006, 60986}

X(60934) = X(2)X(7)∩X(30)X(1000)

Barycentrics    (a+b-c)*(a-b+c)*(3*a^3-5*a^2*(b+c)+(b-c)^2*(b+c)+a*(b^2+10*b*c+c^2)) : :

X(60934) lies on these lines: {2, 7}, {30, 1000}, {85, 28974}, {192, 53997}, {281, 56869}, {347, 2256}, {348, 17258}, {388, 17768}, {390, 944}, {392, 3600}, {497, 16112}, {516, 9613}, {651, 3672}, {912, 40269}, {948, 17276}, {954, 6906}, {956, 16133}, {1108, 4644}, {1210, 5825}, {1436, 24328}, {1441, 4454}, {1479, 41694}, {1788, 15481}, {2346, 10307}, {2550, 18961}, {3085, 60896}, {3086, 60911}, {3255, 41546}, {3560, 5843}, {3663, 54425}, {4018, 7672}, {4312, 10039}, {4321, 51090}, {4346, 37800}, {5177, 5832}, {5252, 34711}, {5261, 5657}, {5265, 31445}, {5281, 17613}, {5698, 8581}, {5703, 52027}, {5729, 6898}, {5732, 5766}, {5762, 6850}, {5779, 6893}, {5850, 12560}, {6604, 17347}, {6842, 60922}, {6940, 21168}, {6941, 59386}, {6961, 31657}, {6981, 38107}, {7330, 14986}, {7674, 25722}, {8236, 30318}, {8544, 59418}, {9579, 20070}, {10865, 36976}, {11036, 57278}, {12573, 60905}, {14151, 48667}, {17668, 17784}, {18662, 20211}, {28606, 43058}, {28965, 28981}, {29624, 43047}, {36975, 43161}, {38037, 60924}, {39126, 54280}

X(60934) = reflection of X(i) in X(j) for these {i,j}: {7, 60937}
X(60934) = pole of line {8732, 14100} wrt Feuerbach hyperbola
X(60934) = orthology center of the pedal triangle of X(1697) wrt Aguilera triangle
X(60934) = intersection, other than A, B, C, of circumconics {{A, B, C, X(142), X(10307)}}, {{A, B, C, X(5748), X(27475)}}, {{A, B, C, X(8732), X(23618)}}, {{A, B, C, X(27003), X(55937)}}, {{A, B, C, X(56028), X(56551)}}
X(60934) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 18230, 30379}, {7, 29007, 2}, {7, 41563, 60939}, {7, 6172, 1445}, {7, 60936, 60956}, {7, 60937, 60967}, {7, 60941, 60938}, {7, 60944, 61019}, {7, 60946, 144}, {7, 60957, 41572}, {7, 60983, 5435}, {7, 60995, 142}, {7, 8232, 30275}, {7, 8545, 8232}, {7, 9, 8732}, {142, 60940, 61009}, {144, 60939, 41563}, {144, 60998, 7}, {144, 61009, 60940}, {144, 9965, 60950}, {4419, 6180, 347}, {5435, 60983, 60947}, {41563, 60939, 12848}, {50573, 60938, 60941}, {60933, 60950, 9965}, {60953, 60977, 52819}, {60965, 61002, 329}

X(60935) = X(2)X(7)∩X(40)X(5828)

Barycentrics    a*(a^4+7*a^2*b*c-2*a^3*(b+c)+2*a*(b+c)*(b^2-3*b*c+c^2)-(b-c)^2*(b^2+3*b*c+c^2)) : :
X(60935) = 2*X[1156]+X[3935], -X[4564]+2*X[51418], -3*X[4881]+2*X[18450], X[5057]+2*X[6068]

X(60935) lies on these lines: {2, 7}, {8, 54370}, {20, 52684}, {40, 5828}, {45, 24635}, {55, 11678}, {72, 6912}, {100, 15726}, {190, 3262}, {346, 5942}, {390, 12648}, {480, 16112}, {514, 40872}, {516, 5080}, {518, 5048}, {519, 51768}, {528, 5176}, {651, 6510}, {728, 10405}, {758, 41700}, {971, 5440}, {1012, 3940}, {1156, 3935}, {1443, 16578}, {1532, 5762}, {2340, 9355}, {2801, 4511}, {2975, 15254}, {3100, 23693}, {3257, 36101}, {3303, 12125}, {3436, 5698}, {3681, 42014}, {3868, 5729}, {3869, 5220}, {3872, 5223}, {3912, 37781}, {3957, 7671}, {4188, 8544}, {4420, 5696}, {4564, 51418}, {4881, 18450}, {5057, 6068}, {5734, 57279}, {5759, 6925}, {5766, 6872}, {5804, 54398}, {5805, 6945}, {5817, 6957}, {5850, 44675}, {5851, 61035}, {5880, 11681}, {6180, 26669}, {6603, 34056}, {6913, 51516}, {6916, 21168}, {6932, 58798}, {7291, 21362}, {9588, 56288}, {9812, 20588}, {10177, 29817}, {10394, 34772}, {10590, 59412}, {10711, 51362}, {11372, 59387}, {15298, 52653}, {15587, 41695}, {15845, 60919}, {16561, 20533}, {17019, 55400}, {17336, 20930}, {17776, 54113}, {20921, 32933}, {25268, 40863}, {25728, 45738}, {27385, 43177}, {27834, 37131}, {30284, 42843}, {30625, 56244}, {30628, 41711}, {30695, 55337}, {30806, 60366}, {31397, 51090}, {38459, 60419}, {46685, 61030}, {54051, 58808}

X(60935) = midpoint of X(i) and X(j) for these {i,j}: {37787, 56551}
X(60935) = reflection of X(i) in X(j) for these {i,j}: {3218, 37787}, {37787, 9}, {38460, 53055}, {4511, 60885}, {4564, 51418}
X(60935) = anticomplement of X(30379)
X(60935) = perspector of circumconic {{A, B, C, X(664), X(31628)}}
X(60935) = X(i)-Dao conjugate of X(j) for these {i, j}: {30379, 30379}
X(60935) = X(i)-Ceva conjugate of X(j) for these {i, j}: {30806, 3935}
X(60935) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {2742, 693}, {15728, 6604}, {34894, 69}, {51567, 21285}, {60483, 21293}
X(60935) = pole of line {100, 14100} wrt Feuerbach hyperbola
X(60935) = pole of line {200, 522} wrt Steiner circumellipse
X(60935) = pole of line {522, 20103} wrt Steiner inellipse
X(60935) = pole of line {100, 3900} wrt Yff parabola
X(60935) = pole of line {650, 651} wrt Hutson-Moses hyperbola
X(60935) = pole of line {3729, 6332} wrt dual conic of incircle
X(60935) = orthology center of the pedal triangle of X(2077) wrt Aguilera triangle
X(60935) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(35164)}}, {{A, B, C, X(57), X(5537)}}, {{A, B, C, X(144), X(4564)}}, {{A, B, C, X(527), X(34894)}}, {{A, B, C, X(673), X(37789)}}, {{A, B, C, X(1156), X(30379)}}, {{A, B, C, X(3911), X(36101)}}, {{A, B, C, X(5435), X(37131)}}, {{A, B, C, X(6172), X(55986)}}, {{A, B, C, X(8568), X(23617)}}, {{A, B, C, X(8732), X(42483)}}, {{A, B, C, X(21446), X(31190)}}, {{A, B, C, X(45203), X(57064)}}
X(60935) = barycentric product X(i)*X(j) for these (i, j): {5537, 75}
X(60935) = barycentric quotient X(i)/X(j) for these (i, j): {5537, 1}
X(60935) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 6172, 60940}, {7, 9, 61012}, {9, 144, 60970}, {9, 1445, 61026}, {9, 36973, 63}, {9, 527, 37787}, {9, 6172, 3219}, {9, 60942, 61024}, {9, 60964, 18230}, {9, 60973, 7}, {9, 60974, 60954}, {9, 60977, 60994}, {9, 60981, 27065}, {9, 60990, 60947}, {63, 5748, 27003}, {63, 60966, 36973}, {144, 46873, 60984}, {329, 6172, 144}, {480, 16112, 25722}, {518, 53055, 38460}, {527, 37787, 3218}, {908, 60966, 56551}, {1445, 60965, 20059}, {3218, 60969, 60363}, {3306, 60953, 59375}, {6172, 60944, 9}, {6172, 60995, 60997}, {6180, 34524, 26669}, {17484, 61006, 50573}, {20059, 61026, 1445}, {27003, 61012, 8257}, {27065, 60969, 60981}, {29007, 60981, 61004}, {37787, 56551, 527}, {60905, 60912, 56288}, {60954, 60957, 60974}, {60981, 61004, 60969}, {60987, 61027, 31019}, {60995, 60997, 2}

X(60936) = X(2)X(7)∩X(77)X(4419)

Barycentrics    (a+b-c)*(a-b+c)*(2*a^3+6*a*b*c-3*a^2*(b+c)+(b-c)^2*(b+c)) : :

X(60936) lies on these lines: {2, 7}, {65, 5852}, {77, 4419}, {241, 17334}, {390, 5882}, {516, 5697}, {518, 45288}, {651, 3663}, {909, 18162}, {1441, 20881}, {2951, 36976}, {3338, 41707}, {3554, 4644}, {3671, 5258}, {3947, 5445}, {4084, 5850}, {4312, 5270}, {4321, 60905}, {4327, 24695}, {4346, 54425}, {4656, 17074}, {4667, 7269}, {4862, 37800}, {5542, 8543}, {5728, 5843}, {5759, 8544}, {5762, 31775}, {5851, 14100}, {5856, 17668}, {5857, 12709}, {5880, 60909}, {6180, 17276}, {7675, 36996}, {7676, 43182}, {7677, 51090}, {8581, 17768}, {8609, 17365}, {11372, 11920}, {14151, 30331}, {15298, 60896}, {15726, 17620}, {15866, 60911}, {17329, 33298}, {17347, 39126}, {18967, 42842}, {23529, 24411}, {23618, 43762}, {24352, 51364}, {31295, 37709}, {31391, 38454}, {33151, 34050}, {39599, 54370}, {41801, 50090}, {49465, 53529}

X(60936) = reflection of X(i) in X(j) for these {i,j}: {144, 61002}, {41572, 7}, {60932, 60952}, {60957, 61003}, {7, 60961}
X(60936) = pole of line {3676, 48287} wrt incircle
X(60936) = pole of line {14100, 15845} wrt Feuerbach hyperbola
X(60936) = orthology center of the pedal triangle of X(3057) wrt Aguilera triangle
X(60936) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2167), X(56545)}}, {{A, B, C, X(3062), X(8257)}}, {{A, B, C, X(23618), X(30379)}}, {{A, B, C, X(27475), X(30852)}}
X(60936) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 12848, 60938}, {7, 144, 1445}, {7, 29007, 142}, {7, 37787, 60992}, {7, 41563, 57}, {7, 527, 41572}, {7, 6172, 8732}, {7, 60934, 8545}, {7, 60937, 41857}, {7, 60943, 6173}, {7, 60946, 9}, {7, 60948, 61022}, {7, 60951, 60945}, {7, 60957, 12848}, {7, 60961, 60952}, {7, 60988, 60993}, {7, 61008, 60980}, {7, 8545, 21617}, {7, 9, 30379}, {9, 30379, 61016}, {57, 60977, 41563}, {142, 29007, 61015}, {144, 1445, 50573}, {527, 60952, 60932}, {527, 61002, 144}, {527, 61003, 60957}, {3911, 61000, 60954}, {6172, 8732, 60947}, {6180, 17276, 22464}, {6646, 40862, 307}, {6666, 60993, 60988}, {20059, 60998, 7}, {60942, 60992, 37787}, {60944, 60988, 6666}, {61014, 61022, 60948}

X(60937) = X(1)X(971)∩X(2)X(7)

Barycentrics    a*(a+b-c)*(a-b+c)*(a^2+b^2+6*b*c+c^2-2*a*(b+c)) : :
X(60937) = -2*X[4326]+3*X[10389]

X(60937) lies on these lines: {1, 971}, {2, 7}, {6, 4328}, {12, 38052}, {30, 31393}, {37, 269}, {40, 495}, {45, 1418}, {55, 2951}, {65, 5223}, {72, 5785}, {77, 3247}, {78, 10861}, {84, 3487}, {85, 728}, {165, 15837}, {192, 9312}, {200, 15587}, {241, 3731}, {354, 30330}, {388, 516}, {390, 10106}, {442, 5833}, {480, 37541}, {518, 3340}, {610, 24328}, {651, 1449}, {738, 10004}, {912, 11529}, {938, 10392}, {942, 5779}, {948, 3663}, {950, 36991}, {954, 3601}, {1001, 1420}, {1014, 4877}, {1020, 47299}, {1156, 5083}, {1210, 5817}, {1387, 50908}, {1407, 17022}, {1441, 4659}, {1471, 15601}, {1706, 5261}, {1709, 11218}, {1721, 9440}, {1743, 5228}, {1836, 60919}, {1892, 60879}, {2003, 54358}, {2137, 7153}, {2257, 4644}, {2263, 7174}, {2270, 10400}, {2292, 7273}, {2297, 25887}, {2310, 18216}, {2346, 55922}, {2550, 6736}, {3174, 17668}, {3243, 16133}, {3255, 56262}, {3256, 6600}, {3333, 5843}, {3339, 3927}, {3361, 3646}, {3476, 30331}, {3485, 5542}, {3586, 31672}, {3587, 18541}, {3600, 52653}, {3616, 7091}, {3666, 34991}, {3667, 58323}, {3668, 4419}, {3671, 5850}, {3672, 43035}, {3677, 52089}, {3692, 4454}, {3745, 34033}, {3868, 5665}, {3870, 10865}, {3946, 54425}, {4032, 42309}, {4059, 52511}, {4073, 39959}, {4292, 5759}, {4298, 31435}, {4315, 11111}, {4326, 10389}, {4327, 7290}, {4335, 37553}, {4384, 39126}, {4416, 6604}, {4461, 31994}, {4488, 32086}, {4656, 7365}, {4848, 5686}, {4870, 38024}, {5128, 30424}, {5173, 42014}, {5218, 43151}, {5252, 34720}, {5434, 50836}, {5572, 16112}, {5698, 12573}, {5703, 9841}, {5708, 51516}, {5709, 60922}, {5714, 59386}, {5719, 7171}, {5722, 60901}, {5726, 17528}, {5728, 11518}, {5805, 9612}, {5809, 37723}, {5853, 37709}, {6006, 58324}, {6068, 24465}, {6361, 7160}, {6610, 16777}, {7225, 54377}, {7288, 38059}, {7322, 60786}, {7962, 43166}, {8543, 38316}, {8557, 17365}, {8726, 51489}, {10404, 60883}, {10509, 56255}, {10582, 58608}, {10588, 38204}, {10860, 13405}, {11018, 30304}, {11038, 34497}, {11374, 31657}, {11495, 30353}, {11523, 41228}, {12047, 38036}, {12705, 21620}, {13407, 60923}, {13411, 21151}, {13462, 16418}, {15346, 40659}, {15518, 59335}, {15803, 31658}, {15844, 38150}, {15934, 18540}, {16572, 58816}, {17079, 50090}, {17276, 52023}, {17319, 25716}, {18421, 40587}, {19604, 21446}, {24471, 50995}, {24929, 58808}, {31397, 35514}, {31507, 31508}, {36971, 41338}, {37532, 51514}, {37534, 59380}, {37582, 59381}, {37737, 38030}, {38037, 50443}, {38158, 54361}, {39273, 41441}, {41554, 53055}, {41694, 41861}, {43180, 60911}

X(60937) = midpoint of X(i) and X(j) for these {i,j}: {7, 60934}
X(60937) = reflection of X(i) in X(j) for these {i,j}: {3340, 12560}, {4312, 57282}, {4654, 60967}, {9, 60964}
X(60937) = X(i)-isoconjugate-of-X(j) for these {i, j}: {41, 56074}, {55, 56043}
X(60937) = X(i)-Dao conjugate of X(j) for these {i, j}: {223, 56043}, {3160, 56074}
X(60937) = X(i)-Ceva conjugate of X(j) for these {i, j}: {7091, 57}, {31994, 8580}, {56331, 1}
X(60937) = pole of line {3676, 3900} wrt incircle
X(60937) = pole of line {57, 2951} wrt Feuerbach hyperbola
X(60937) = pole of line {1, 21151} wrt dual conic of Yff parabola
X(60937) = orthology center of the pedal triangle of X(3295) wrt Aguilera triangle
X(60937) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(144)}}, {{A, B, C, X(2), X(3062)}}, {{A, B, C, X(7), X(31994)}}, {{A, B, C, X(57), X(23618)}}, {{A, B, C, X(142), X(55922)}}, {{A, B, C, X(527), X(10390)}}, {{A, B, C, X(673), X(5437)}}, {{A, B, C, X(1156), X(18230)}}, {{A, B, C, X(1423), X(2137)}}, {{A, B, C, X(2346), X(6172)}}, {{A, B, C, X(3255), X(52457)}}, {{A, B, C, X(3452), X(27475)}}, {{A, B, C, X(3598), X(19604)}}, {{A, B, C, X(3928), X(39273)}}, {{A, B, C, X(5273), X(57661)}}, {{A, B, C, X(5435), X(21446)}}, {{A, B, C, X(5665), X(52819)}}, {{A, B, C, X(14100), X(19605)}}, {{A, B, C, X(17257), X(43751)}}, {{A, B, C, X(18228), X(25430)}}, {{A, B, C, X(20059), X(45834)}}, {{A, B, C, X(28610), X(39948)}}, {{A, B, C, X(29007), X(56262)}}, {{A, B, C, X(31507), X(57826)}}, {{A, B, C, X(40131), X(41441)}}
X(60937) = barycentric product X(i)*X(j) for these (i, j): {1, 31994}, {7, 8580}, {226, 24557}, {4461, 57}
X(60937) = barycentric quotient X(i)/X(j) for these (i, j): {7, 56074}, {57, 56043}, {4461, 312}, {8580, 8}, {24557, 333}, {31994, 75}
X(60937) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 11372, 10384}, {1, 3062, 14100}, {1, 6180, 1419}, {2, 7, 60992}, {7, 12848, 60945}, {7, 144, 52819}, {7, 1445, 60955}, {7, 20059, 61021}, {7, 29007, 1445}, {7, 30275, 60980}, {7, 37787, 60938}, {7, 41563, 60932}, {7, 41572, 60982}, {7, 60934, 527}, {7, 60936, 60933}, {7, 60939, 553}, {7, 60941, 21454}, {7, 60943, 30379}, {7, 60944, 60948}, {7, 60956, 60962}, {7, 60957, 60975}, {7, 60998, 60961}, {7, 61027, 21617}, {7, 8232, 142}, {7, 8732, 61022}, {9, 3928, 60970}, {9, 60933, 60990}, {9, 60963, 60968}, {9, 60965, 36973}, {9, 61020, 60985}, {37, 269, 59215}, {55, 31391, 2951}, {142, 60973, 9}, {142, 8232, 5219}, {144, 52819, 61007}, {354, 60910, 30330}, {518, 12560, 3340}, {527, 60967, 4654}, {553, 61014, 60939}, {651, 7190, 1449}, {942, 5779, 10398}, {954, 5732, 3601}, {1001, 4321, 1420}, {1445, 60955, 57}, {1445, 8545, 29007}, {1743, 7274, 5228}, {2951, 9814, 31391}, {3731, 7271, 241}, {4312, 15298, 40}, {5762, 57282, 4312}, {6172, 60939, 61014}, {6666, 61022, 8732}, {8732, 60995, 6666}, {12047, 60924, 38036}, {15299, 59372, 3333}, {20059, 60969, 63}, {21454, 61006, 60941}, {21617, 60952, 7}, {26125, 40862, 10436}, {30379, 60943, 20195}, {41572, 60946, 60977}, {60942, 60945, 12848}, {60944, 60948, 60947}, {60952, 61027, 6173}, {60957, 60981, 60949}, {60962, 61004, 60974}, {60975, 60981, 1708}, {60977, 60982, 41572}, {60995, 61022, 31231}

X(60938) = X(1)X(7673)∩X(2)X(7)

Barycentrics    a*(a+b-c)*(a-b+c)*((a-b)^2-2*(a+2*b)*c+c^2) : :

X(60938) lies on these lines: {1, 7673}, {2, 7}, {40, 11038}, {46, 5542}, {55, 58563}, {56, 42819}, {65, 3895}, {77, 1100}, {84, 59385}, {165, 2346}, {173, 8388}, {241, 7190}, {258, 8389}, {269, 16667}, {354, 11495}, {390, 3333}, {516, 3338}, {518, 5221}, {651, 7271}, {942, 7675}, {954, 37582}, {1001, 4652}, {1004, 8730}, {1014, 17207}, {1156, 31507}, {1158, 38036}, {1434, 17107}, {1443, 1449}, {1721, 21346}, {2160, 39273}, {2951, 7671}, {3174, 3873}, {3336, 59372}, {3337, 4312}, {3339, 3874}, {3358, 26877}, {3361, 5248}, {3434, 41573}, {3522, 8236}, {3600, 6764}, {3647, 16133}, {3692, 17298}, {3826, 10404}, {4015, 5223}, {4189, 38316}, {4190, 5853}, {4326, 10980}, {4328, 16673}, {4355, 30312}, {4606, 43760}, {4860, 5572}, {5250, 38053}, {5290, 7679}, {5541, 14151}, {5586, 12514}, {5708, 5728}, {5709, 21151}, {5732, 10122}, {5759, 37534}, {5762, 37612}, {5805, 37447}, {5880, 6067}, {6180, 16669}, {6762, 56999}, {6909, 43166}, {7131, 7198}, {7177, 14377}, {7263, 36595}, {7269, 59215}, {7289, 24590}, {10123, 52835}, {10389, 10390}, {10481, 37800}, {10509, 50561}, {11529, 30284}, {12515, 38055}, {13156, 56972}, {13159, 54370}, {14953, 18164}, {15298, 43180}, {15299, 30424}, {17078, 17380}, {17234, 32007}, {17304, 41804}, {17437, 60923}, {17700, 60924}, {17728, 42356}, {23062, 33765}, {24467, 38107}, {26892, 58472}, {30330, 30353}, {30331, 51816}, {31657, 37532}, {34522, 45227}, {37526, 59418}, {38030, 59318}, {38122, 55104}, {38204, 41229}, {39156, 52509}, {40333, 57279}, {41338, 43151}, {41861, 43178}

X(60938) = X(i)-isoconjugate-of-X(j) for these {i, j}: {55, 56217}
X(60938) = X(i)-Dao conjugate of X(j) for these {i, j}: {223, 56217}
X(60938) = pole of line {333, 55337} wrt Wallace hyperbola
X(60938) = pole of line {1, 41857} wrt dual conic of Yff parabola
X(60938) = orthology center of the pedal triangle of X(3304) wrt Aguilera triangle
X(60938) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6666)}}, {{A, B, C, X(2), X(4666)}}, {{A, B, C, X(9), X(14377)}}, {{A, B, C, X(85), X(41857)}}, {{A, B, C, X(142), X(45834)}}, {{A, B, C, X(279), X(8232)}}, {{A, B, C, X(527), X(31507)}}, {{A, B, C, X(553), X(21446)}}, {{A, B, C, X(673), X(3305)}}, {{A, B, C, X(1400), X(17107)}}, {{A, B, C, X(1434), X(1445)}}, {{A, B, C, X(2160), X(40131)}}, {{A, B, C, X(3219), X(39273)}}, {{A, B, C, X(4606), X(53337)}}, {{A, B, C, X(5325), X(39980)}}, {{A, B, C, X(8545), X(10509)}}, {{A, B, C, X(10390), X(20195)}}, {{A, B, C, X(18230), X(56028)}}, {{A, B, C, X(21454), X(43760)}}, {{A, B, C, X(21617), X(23062)}}
X(60938) = barycentric product X(i)*X(j) for these (i, j): {4666, 7}
X(60938) = barycentric quotient X(i)/X(j) for these (i, j): {57, 56217}, {4666, 8}
X(60938) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 60990, 60949}, {2, 7, 41857}, {7, 12848, 60936}, {7, 144, 60952}, {7, 18230, 60967}, {7, 29007, 60953}, {7, 37787, 60937}, {7, 41563, 60961}, {7, 5435, 8232}, {7, 57, 1445}, {7, 60939, 41572}, {7, 60941, 60934}, {7, 60948, 9}, {7, 60951, 60933}, {7, 61013, 4654}, {7, 61019, 226}, {7, 8732, 21617}, {9, 57, 60948}, {63, 142, 60958}, {142, 553, 7}, {142, 60968, 63}, {1418, 5228, 77}, {1445, 8545, 60947}, {1652, 1653, 40131}, {3339, 4321, 7672}, {3361, 12560, 7677}, {4031, 60992, 60945}, {4321, 7672, 30318}, {4326, 10980, 11025}, {4654, 20195, 61013}, {5435, 8232, 61016}, {8257, 60933, 60966}, {20195, 61005, 3305}, {26877, 59386, 3358}, {41857, 60949, 8545}, {60934, 60941, 50573}, {60955, 60968, 553}, {60984, 61012, 60965}, {60989, 61020, 60964}

X(60939) = X(2)X(7)∩X(6)X(279)

Barycentrics    (a+b-c)*(a-b+c)*(3*a^3+a*(b-c)^2-5*a^2*(b+c)+(b-c)^2*(b+c)) : :

X(60939) lies on these lines: {1, 59418}, {2, 7}, {6, 279}, {8, 12573}, {20, 5728}, {37, 45227}, {56, 11038}, {65, 390}, {78, 4321}, {85, 391}, {145, 7672}, {198, 38859}, {241, 3945}, {273, 55937}, {282, 42483}, {346, 6604}, {347, 17014}, {388, 5686}, {516, 938}, {518, 3600}, {936, 5850}, {942, 5759}, {948, 37681}, {949, 41356}, {954, 6986}, {971, 50700}, {1119, 37389}, {1156, 24465}, {1210, 4312}, {1229, 4454}, {1323, 16667}, {1418, 4644}, {1434, 2287}, {1446, 5819}, {1449, 3160}, {1467, 5766}, {1617, 2346}, {1743, 10481}, {1788, 40333}, {1876, 7717}, {2262, 23839}, {2321, 32003}, {3146, 5809}, {3149, 36996}, {3161, 32098}, {3243, 4308}, {3247, 5543}, {3336, 60923}, {3337, 60924}, {3340, 8236}, {3358, 37434}, {3361, 5542}, {3474, 14100}, {3475, 15837}, {3487, 31658}, {3522, 7675}, {3553, 38459}, {3622, 7677}, {3623, 11526}, {3664, 51302}, {3668, 5222}, {3672, 5228}, {3686, 31994}, {3731, 58816}, {3946, 36640}, {4005, 8581}, {4292, 10398}, {4293, 18412}, {4294, 41861}, {4295, 15299}, {4298, 5223}, {4323, 38316}, {4326, 9778}, {4848, 59413}, {4860, 60919}, {5173, 11025}, {5221, 5225}, {5261, 38057}, {5265, 38053}, {5434, 50835}, {5698, 58608}, {5704, 30424}, {5708, 5762}, {5714, 38108}, {5729, 6835}, {5779, 6864}, {5785, 12436}, {5817, 57282}, {5838, 42309}, {5843, 6918}, {5853, 20008}, {6147, 59381}, {6734, 59412}, {6831, 59386}, {6855, 34753}, {6904, 41228}, {6922, 60922}, {6988, 31657}, {6994, 44697}, {7176, 51194}, {7365, 37666}, {7670, 58706}, {7673, 13601}, {7676, 37541}, {7679, 46932}, {8814, 14021}, {9533, 23062}, {9579, 10392}, {10394, 50695}, {10405, 53994}, {10521, 52511}, {10865, 40659}, {11246, 60910}, {12560, 52653}, {12649, 41824}, {12669, 44547}, {12832, 45043}, {13411, 59372}, {15006, 30332}, {15933, 18421}, {16133, 31888}, {16662, 51842}, {16663, 51841}, {17113, 47386}, {17784, 30628}, {18541, 60901}, {21151, 37582}, {24471, 51190}, {26827, 40979}, {29616, 56927}, {30329, 43161}, {30340, 32636}, {30813, 59595}, {32093, 43760}, {34784, 41539}, {35514, 36279}, {36118, 40065}, {37394, 60879}, {37650, 52023}, {40154, 56348}, {43151, 53056}, {43215, 45744}, {52265, 59380}, {52783, 60909}, {55989, 60832}

X(60939) = reflection of X(i) in X(j) for these {i,j}: {7, 60955}
X(60939) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 42015}, {9, 10579}, {650, 6575}
X(60939) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 42015}, {478, 10579}
X(60939) = pole of line {3475, 14100} wrt Feuerbach hyperbola
X(60939) = pole of line {284, 1190} wrt Stammler hyperbola
X(60939) = pole of line {522, 43049} wrt Steiner circumellipse
X(60939) = pole of line {1, 59385} wrt dual conic of Yff parabola
X(60939) = orthology center of the pedal triangle of X(3333) wrt Aguilera triangle
X(60939) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(10509)}}, {{A, B, C, X(6), X(8012)}}, {{A, B, C, X(9), X(1170)}}, {{A, B, C, X(63), X(55937)}}, {{A, B, C, X(142), X(279)}}, {{A, B, C, X(278), X(41867)}}, {{A, B, C, X(329), X(42483)}}, {{A, B, C, X(527), X(8713)}}, {{A, B, C, X(673), X(5273)}}, {{A, B, C, X(959), X(27626)}}, {{A, B, C, X(5745), X(44794)}}, {{A, B, C, X(8232), X(43762)}}, {{A, B, C, X(14282), X(40869)}}
X(60939) = barycentric product X(i)*X(j) for these (i, j): {664, 8713}, {10578, 7}, {14282, 658}, {14324, 4573}
X(60939) = barycentric quotient X(i)/X(j) for these (i, j): {1, 42015}, {56, 10579}, {109, 6575}, {8713, 522}, {10578, 8}, {14282, 3239}, {14324, 3700}
X(60939) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 1445, 2}, {7, 18230, 226}, {7, 29007, 60967}, {7, 37787, 8232}, {7, 41563, 60934}, {7, 41572, 20059}, {7, 52819, 60975}, {7, 5435, 142}, {7, 60941, 9}, {7, 60948, 8732}, {7, 60954, 61027}, {7, 60957, 60961}, {7, 60995, 41857}, {7, 61019, 30275}, {142, 60982, 7}, {553, 61014, 60937}, {1210, 4312, 59385}, {1400, 28079, 3598}, {4292, 10398, 36991}, {5542, 21153, 5703}, {7674, 15185, 145}, {12848, 21454, 60998}, {12848, 60934, 41563}, {20078, 61006, 144}, {41857, 60947, 60995}, {60937, 61014, 6172}, {60961, 61007, 60957}

X(60940) = X(2)X(7)∩X(6)X(7961)

Barycentrics    (a-b-c)*(3*a^4+(b-c)^4-2*a^3*(b+c)+2*a*(b-c)^2*(b+c)-4*a^2*(b^2-3*b*c+c^2)) : :
X(60940) = -3*X[10177]+2*X[12915], -3*X[21153]+2*X[54178], -3*X[21164]+2*X[43177], -3*X[51099]+4*X[51788], -X[54179]+3*X[59418], -4*X[58650]+3*X[61028]

X(60940) lies on these lines: {2, 7}, {6, 7961}, {37, 53020}, {55, 6068}, {220, 7960}, {281, 17351}, {497, 5856}, {513, 60483}, {516, 54135}, {517, 5698}, {522, 28124}, {971, 6948}, {1146, 49721}, {1156, 3434}, {1376, 5851}, {2093, 60905}, {2096, 5784}, {2397, 51190}, {2550, 5779}, {2551, 36279}, {3086, 15297}, {3254, 5274}, {3262, 54280}, {3359, 52684}, {3421, 5220}, {3729, 53994}, {4419, 55432}, {4454, 4858}, {4715, 36916}, {5123, 5880}, {5223, 12647}, {5735, 7682}, {5759, 6938}, {5761, 31445}, {5762, 6929}, {5804, 12572}, {5805, 6973}, {5817, 5832}, {6601, 10947}, {6950, 21168}, {6980, 51516}, {6982, 37822}, {10177, 12915}, {10427, 59572}, {11495, 15813}, {11662, 58798}, {11813, 60895}, {15346, 26040}, {15733, 17658}, {17365, 34524}, {21153, 54178}, {21164, 43177}, {26932, 54389}, {34522, 49742}, {51099, 51788}, {54179, 59418}, {58650, 61028}

X(60940) = midpoint of X(i) and X(j) for these {i,j}: {144, 12848}, {2093, 60905}, {36973, 61007}
X(60940) = reflection of X(i) in X(j) for these {i,j}: {3421, 5220}, {36973, 60942}, {5735, 7682}, {52457, 9}, {60933, 61022}, {7, 8257}
X(60940) = complement of X(60956)
X(60940) = orthology center of the pedal triangle of X(3359) wrt Aguilera triangle
X(60940) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2316), X(56546)}}, {{A, B, C, X(8545), X(34894)}}, {{A, B, C, X(30379), X(34919)}}
X(60940) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 144, 60946}, {7, 6172, 60935}, {9, 527, 52457}, {9, 60963, 30827}, {9, 60977, 61002}, {144, 12848, 527}, {144, 41563, 60950}, {144, 61009, 60934}, {329, 5273, 3452}, {527, 60942, 36973}, {527, 61022, 60933}, {527, 8257, 7}, {6172, 60997, 9}, {41572, 60966, 61010}, {56551, 60951, 5905}, {60934, 61009, 142}

X(60941) = X(2)X(7)∩X(6)X(3160)

Barycentrics    (a+b-c)*(a-b+c)*(5*a^3-9*a^2*(b+c)+(b-c)^2*(b+c)+a*(3*b^2+2*b*c+3*c^2)) : :

X(60941) lies on these lines: {2, 7}, {6, 3160}, {8, 41712}, {20, 10398}, {37, 5543}, {65, 52653}, {210, 10865}, {279, 1743}, {346, 32003}, {390, 6738}, {391, 31994}, {518, 4308}, {938, 5759}, {942, 21168}, {962, 15299}, {1001, 4323}, {1100, 31721}, {1449, 56043}, {1788, 59412}, {3057, 5572}, {3091, 4312}, {3146, 10392}, {3161, 6604}, {3212, 5838}, {3243, 6049}, {3304, 7677}, {3339, 5129}, {3361, 5850}, {3474, 60910}, {3487, 59381}, {3600, 5223}, {3668, 37681}, {3671, 17554}, {3876, 8581}, {3973, 10481}, {4032, 27484}, {4313, 5728}, {4345, 42884}, {4460, 4552}, {4488, 39126}, {5222, 36640}, {5265, 5542}, {5686, 12573}, {5703, 31658}, {5704, 5805}, {5729, 12246}, {5731, 18412}, {5785, 17580}, {5843, 37545}, {6766, 9785}, {7674, 12630}, {7679, 50038}, {9778, 14100}, {10177, 13601}, {10384, 20070}, {10509, 27818}, {10578, 15837}, {11037, 15298}, {12432, 41861}, {18802, 25606}, {23618, 50559}, {24470, 51516}, {30287, 31391}, {30332, 37567}, {30628, 41539}, {31722, 32007}, {34753, 60922}, {36996, 37582}, {43182, 53056}

X(60941) = pole of line {10578, 10865} wrt Feuerbach hyperbola
X(60941) = pole of line {1, 38151} wrt dual conic of Yff parabola
X(60941) = orthology center of the pedal triangle of X(3361) wrt Aguilera triangle
X(60941) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(142), X(27818)}}, {{A, B, C, X(5435), X(10509)}}, {{A, B, C, X(5437), X(43760)}}, {{A, B, C, X(5745), X(42318)}}, {{A, B, C, X(18230), X(43762)}}
X(60941) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 1445, 5435}, {7, 18230, 5226}, {7, 37787, 18230}, {7, 41563, 60957}, {7, 60954, 60995}, {7, 60983, 8545}, {7, 61019, 59374}, {57, 61014, 144}, {142, 60975, 7}, {1445, 41572, 8732}, {5728, 59418, 4313}, {8232, 60947, 61023}, {8732, 12848, 41572}, {8732, 60943, 37797}, {21454, 61006, 60937}, {50573, 60938, 60934}, {60932, 60947, 8232}, {60942, 60955, 60998}, {60959, 60970, 5273}, {60992, 61007, 20059}

X(60942) = X(2)X(7)∩X(6)X(4021)

Barycentrics    4*a^2-(b-c)^2-3*a*(b+c) : :
X(60942) = -9*X[2]+5*X[7], -3*X[210]+X[17668], -5*X[390]+X[20050], -5*X[1001]+4*X[3636], -X[3241]+5*X[50840], -5*X[3243]+7*X[20057], -7*X[3528]+5*X[5732], -X[3529]+5*X[5759], -17*X[3544]+15*X[38150], -X[3632]+5*X[5223], -7*X[3851]+5*X[5805], -11*X[3855]+5*X[5735] and many others

X(60942) lies on these lines: {2, 7}, {6, 4021}, {10, 7227}, {37, 4667}, {44, 3663}, {45, 3664}, {69, 2325}, {71, 21362}, {72, 4304}, {75, 3707}, {141, 59579}, {190, 319}, {191, 21075}, {192, 4464}, {210, 17668}, {220, 1323}, {320, 25101}, {355, 382}, {390, 20050}, {391, 4488}, {518, 3244}, {519, 17262}, {522, 21084}, {524, 3950}, {528, 34641}, {545, 17348}, {546, 5762}, {550, 971}, {551, 58813}, {594, 50118}, {651, 52405}, {673, 39710}, {758, 14563}, {946, 60911}, {950, 3951}, {954, 19526}, {960, 4315}, {993, 42843}, {1001, 3636}, {1086, 15492}, {1100, 49742}, {1266, 17349}, {1268, 17256}, {1317, 31165}, {1743, 3946}, {1757, 3755}, {1770, 41694}, {1836, 61031}, {2550, 3585}, {3008, 16885}, {3059, 6068}, {3161, 17296}, {3241, 50840}, {3243, 20057}, {3528, 5732}, {3529, 5759}, {3530, 5843}, {3544, 38150}, {3631, 5845}, {3632, 5223}, {3644, 49759}, {3650, 3697}, {3671, 5302}, {3672, 16670}, {3678, 31730}, {3683, 37703}, {3686, 3729}, {3731, 4644}, {3739, 7231}, {3759, 49748}, {3826, 10592}, {3851, 5805}, {3855, 5735}, {3875, 4700}, {3879, 4029}, {3912, 17336}, {3927, 5722}, {3945, 16676}, {3947, 18253}, {3973, 4000}, {3986, 4670}, {4034, 4461}, {4035, 33066}, {4058, 4690}, {4060, 50107}, {4072, 17372}, {4078, 17770}, {4098, 17390}, {4134, 47320}, {4292, 56997}, {4310, 15601}, {4312, 38057}, {4356, 4663}, {4360, 50090}, {4361, 17132}, {4370, 17231}, {4398, 41140}, {4422, 15828}, {4431, 17346}, {4432, 49505}, {4473, 17288}, {4557, 41430}, {4640, 21060}, {4641, 4656}, {4643, 17293}, {4662, 5493}, {4675, 25072}, {4715, 17243}, {4718, 4969}, {4741, 17339}, {4753, 4780}, {4848, 11684}, {4851, 59585}, {4856, 17318}, {4862, 17067}, {4873, 32099}, {4877, 56020}, {4887, 17278}, {4896, 17245}, {4909, 16672}, {4912, 7263}, {4923, 5695}, {4930, 42871}, {4967, 17331}, {4982, 51170}, {5079, 38108}, {5248, 42885}, {5252, 5837}, {5260, 16133}, {5536, 10863}, {5542, 5852}, {5692, 21578}, {5709, 9842}, {5714, 31446}, {5719, 31445}, {5739, 25734}, {5795, 12526}, {5825, 9581}, {5832, 58798}, {5839, 17133}, {5851, 6594}, {5856, 24389}, {6006, 11068}, {6007, 22312}, {6259, 43174}, {6260, 26921}, {6684, 60896}, {6687, 48631}, {6923, 38127}, {6930, 28234}, {7064, 49537}, {7222, 16832}, {7262, 17725}, {7491, 47745}, {10175, 37826}, {10177, 61033}, {10299, 21153}, {11008, 29605}, {12573, 60909}, {14100, 61030}, {14269, 31671}, {14869, 31657}, {15064, 58651}, {15587, 58635}, {15681, 60884}, {15687, 60901}, {15720, 59381}, {15726, 40659}, {16552, 20257}, {16669, 17246}, {16671, 17395}, {16814, 17365}, {17023, 17258}, {17151, 28301}, {17235, 31191}, {17239, 49726}, {17253, 29604}, {17272, 54389}, {17273, 29596}, {17275, 49721}, {17279, 53598}, {17329, 17354}, {17335, 24199}, {17340, 17344}, {17363, 25269}, {17364, 29623}, {17376, 28333}, {17487, 50099}, {18540, 28194}, {21061, 22031}, {21627, 30305}, {21873, 22003}, {22214, 60725}, {24386, 24703}, {25557, 38059}, {28345, 35024}, {28534, 38098}, {28639, 49737}, {30556, 31538}, {30557, 31539}, {31391, 58677}, {32024, 41006}, {32938, 53663}, {34606, 36920}, {34632, 51781}, {34747, 50836}, {36522, 50081}, {36866, 38130}, {36991, 49135}, {38122, 55863}, {40256, 52684}, {40341, 49752}, {41548, 52638}, {41707, 60923}, {45305, 55076}, {49501, 49771}, {49502, 49783}, {49517, 50017}, {50688, 52835}, {50796, 54288}, {52285, 60879}, {57000, 57284}

X(60942) = midpoint of X(i) and X(j) for these {i,j}: {2550, 60905}, {36973, 60940}, {5223, 5698}, {5839, 55998}, {60933, 60957}, {60950, 60965}, {7, 60977}, {9, 144}
X(60942) = reflection of X(i) in X(j) for these {i,j}: {10, 15481}, {142, 9}, {15587, 58635}, {24393, 5220}, {30424, 3826}, {40659, 58678}, {4851, 59585}, {43177, 31658}, {5542, 15254}, {53594, 17348}, {60896, 6684}, {60933, 60980}, {60962, 142}, {60963, 60999}, {7, 6666}, {9, 61000}, {946, 60911}
X(60942) = complement of X(60933)
X(60942) = anticomplement of X(60980)
X(60942) = X(i)-Dao conjugate of X(j) for these {i, j}: {60980, 60980}
X(60942) = pole of line {23865, 48386} wrt circumcircle
X(60942) = pole of line {4521, 28473} wrt Spieker circle
X(60942) = pole of line {5432, 6666} wrt Feuerbach hyperbola
X(60942) = pole of line {522, 26777} wrt Steiner circumellipse
X(60942) = pole of line {522, 31209} wrt Steiner inellipse
X(60942) = pole of line {100, 45674} wrt Yff parabola
X(60942) = pole of line {1, 56997} wrt dual conic of Yff parabola
X(60942) = orthology center of the pedal triangle of X(3579) wrt Aguilera triangle
X(60942) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(35141)}}, {{A, B, C, X(80), X(41572)}}, {{A, B, C, X(2349), X(3306)}}, {{A, B, C, X(6173), X(43971)}}, {{A, B, C, X(6601), X(20059)}}, {{A, B, C, X(6666), X(23618)}}, {{A, B, C, X(9436), X(39710)}}, {{A, B, C, X(27003), X(36101)}}, {{A, B, C, X(35595), X(55995)}}
X(60942) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 144, 60957}, {2, 60933, 60980}, {7, 144, 60977}, {7, 50573, 61014}, {7, 6172, 61006}, {9, 142, 60986}, {9, 36973, 60973}, {9, 6172, 61000}, {9, 6173, 18230}, {9, 63, 60994}, {9, 60965, 60964}, {9, 60973, 61004}, {9, 60989, 61012}, {9, 60990, 8257}, {44, 17334, 3663}, {63, 31018, 3911}, {142, 527, 60962}, {142, 60986, 61001}, {144, 3219, 41572}, {144, 6172, 9}, {144, 60935, 60979}, {144, 60966, 61003}, {144, 60983, 60933}, {144, 61000, 142}, {144, 61006, 7}, {190, 4416, 2321}, {226, 3219, 5325}, {329, 3929, 5745}, {391, 4488, 4659}, {527, 60999, 60963}, {894, 50093, 5257}, {1445, 60946, 60961}, {1445, 60961, 61022}, {1743, 4419, 3946}, {3219, 17484, 54357}, {3305, 20078, 553}, {3629, 4681, 3244}, {3729, 54280, 3686}, {3879, 17261, 4029}, {3911, 31018, 3452}, {3927, 12572, 24391}, {3928, 18228, 6692}, {4357, 17350, 50115}, {4640, 21060, 59584}, {4862, 37650, 17067}, {5223, 5698, 5853}, {5273, 28609, 58463}, {5839, 55998, 17133}, {5843, 31658, 43177}, {5852, 15254, 5542}, {6172, 60957, 60983}, {6173, 18230, 58433}, {6646, 17353, 50092}, {8545, 41563, 52819}, {12848, 60937, 60945}, {15481, 17768, 10}, {15828, 21255, 4422}, {16669, 17246, 50114}, {16814, 17365, 29571}, {16885, 17276, 3008}, {17257, 50127, 5750}, {17260, 31300, 50116}, {17261, 20072, 3879}, {17333, 17350, 4357}, {17340, 17344, 29594}, {17484, 54357, 226}, {17781, 54357, 17484}, {18230, 20059, 6173}, {33066, 56078, 4035}, {36973, 60940, 527}, {37787, 60936, 60992}, {49520, 49710, 49684}, {60941, 60998, 60955}, {60957, 60983, 2}, {60963, 61023, 60999}, {60977, 61006, 6666}, {60984, 60996, 61020}

X(60943) = X(2)X(7)∩X(5)X(954)

Barycentrics    (a+b-c)*(a-b+c)*(a^3-3*a^2*(b+c)-(b-c)^2*(b+c)+a*(3*b^2+4*b*c+3*c^2)) : :

X(60943) lies on these lines: {1, 6886}, {2, 7}, {5, 954}, {12, 1001}, {37, 37800}, {55, 42356}, {56, 31259}, {77, 29571}, {80, 56028}, {85, 17263}, {119, 6939}, {344, 1441}, {346, 20236}, {388, 5047}, {390, 1479}, {480, 2886}, {495, 42884}, {497, 2346}, {498, 516}, {499, 5542}, {518, 10527}, {651, 4648}, {857, 50036}, {942, 38318}, {943, 6849}, {971, 6833}, {1442, 5308}, {1478, 6992}, {1532, 31479}, {1698, 12560}, {1996, 53242}, {2476, 2550}, {2911, 37650}, {3008, 7190}, {3086, 11038}, {3243, 10529}, {3434, 6600}, {3475, 11025}, {3485, 3876}, {3487, 6887}, {3553, 5222}, {3600, 5251}, {3601, 59389}, {3624, 4321}, {3668, 25072}, {3672, 37771}, {3678, 5686}, {3731, 22464}, {3841, 40333}, {3870, 24389}, {3947, 12573}, {3984, 11526}, {4328, 31183}, {4917, 5853}, {5129, 5261}, {5173, 58635}, {5179, 14189}, {5218, 7676}, {5223, 26363}, {5228, 17337}, {5252, 42819}, {5281, 44425}, {5432, 11495}, {5572, 17718}, {5587, 8236}, {5692, 12432}, {5703, 5720}, {5714, 6989}, {5723, 16777}, {5728, 6832}, {5729, 6861}, {5732, 6890}, {5736, 5778}, {5759, 6825}, {5762, 6863}, {5766, 6848}, {5779, 6862}, {5805, 6834}, {5817, 6824}, {6180, 17245}, {6601, 11680}, {6837, 7675}, {6840, 10590}, {6847, 36991}, {6853, 21168}, {6889, 31658}, {6891, 21151}, {6908, 59418}, {6949, 59386}, {6952, 36996}, {6953, 38150}, {6958, 31657}, {6959, 38107}, {6967, 38122}, {7080, 59413}, {7282, 37382}, {7318, 27475}, {8068, 45043}, {8255, 60910}, {9578, 10587}, {9612, 21153}, {9654, 38031}, {10056, 30331}, {10177, 17620}, {10320, 60911}, {10586, 30318}, {10592, 10786}, {11036, 18397}, {11240, 15950}, {15298, 37692}, {15837, 17605}, {15909, 55920}, {16133, 30312}, {16845, 57283}, {17014, 18261}, {17084, 28740}, {17086, 27268}, {17277, 56927}, {17352, 55082}, {17354, 55096}, {17728, 58563}, {18483, 30332}, {24553, 36949}, {25557, 60909}, {25568, 34784}, {26364, 38052}, {26492, 38030}, {27529, 59412}, {28748, 28753}, {28809, 34388}, {29621, 53997}, {30340, 41700}, {31434, 43166}, {33116, 56085}, {37375, 47357}, {37434, 52026}, {37731, 41861}, {38109, 38149}, {41785, 56746}, {44307, 57477}, {50695, 54430}, {54370, 60925}, {60155, 60188}

X(60943) = pole of line {14100, 36976} wrt Feuerbach hyperbola
X(60943) = pole of line {5228, 17056} wrt Kiepert hyperbola
X(60943) = pole of line {1, 61019} wrt dual conic of Yff parabola
X(60943) = orthology center of the pedal triangle of X(3612) wrt Aguilera triangle
X(60943) = intersection, other than A, B, C, of circumconics {{A, B, C, X(80), X(20195)}}, {{A, B, C, X(142), X(60075)}}, {{A, B, C, X(3218), X(56028)}}, {{A, B, C, X(5249), X(60155)}}, {{A, B, C, X(5905), X(27475)}}, {{A, B, C, X(6173), X(15909)}}, {{A, B, C, X(7318), X(40719)}}, {{A, B, C, X(9776), X(42318)}}, {{A, B, C, X(23618), X(41563)}}, {{A, B, C, X(26842), X(55937)}}
X(60943) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 7, 61019}, {7, 18230, 37787}, {7, 5226, 61013}, {7, 60944, 144}, {7, 60954, 12848}, {7, 60995, 29007}, {7, 60996, 60988}, {7, 61017, 2}, {7, 8232, 61027}, {7, 9, 41563}, {9, 5219, 21617}, {9, 60979, 6172}, {142, 8545, 7}, {226, 6666, 1445}, {908, 3305, 31018}, {908, 5219, 5226}, {2550, 10588, 7679}, {3085, 38037, 390}, {3305, 6666, 18230}, {3485, 38057, 7672}, {3947, 38059, 12573}, {7679, 8543, 2550}, {11374, 38108, 5728}, {20195, 60937, 30379}, {21617, 61015, 9}, {31053, 60970, 61010}, {37797, 60941, 8732}, {41857, 61016, 57}, {52819, 60986, 60947}, {60995, 61008, 60946}

X(60944) = X(2)X(7)∩X(45)X(651)

Barycentrics    a*(a+b-c)*(a-b+c)*(2*a^2-4*a*(b+c)+(2*b+c)*(b+2*c)) : :

X(60944) lies on these lines: {2, 7}, {45, 651}, {55, 1156}, {109, 9330}, {198, 7279}, {390, 9897}, {484, 10590}, {516, 18513}, {657, 60479}, {954, 7489}, {971, 6950}, {1001, 14151}, {1319, 15254}, {1388, 17543}, {1441, 17336}, {1442, 3731}, {1743, 7269}, {2099, 5220}, {2346, 60910}, {2801, 37525}, {2886, 6068}, {3616, 15297}, {3748, 7671}, {3973, 7190}, {4323, 41229}, {4419, 37771}, {4525, 5223}, {4552, 25251}, {5080, 5698}, {5119, 30332}, {5251, 18467}, {5425, 41700}, {5432, 5851}, {5723, 49742}, {5729, 15934}, {5759, 6923}, {5762, 6980}, {5766, 6930}, {5779, 6914}, {5790, 20119}, {5809, 6976}, {5817, 6929}, {5856, 11680}, {6049, 31435}, {6610, 16814}, {6938, 36991}, {6948, 59418}, {6951, 21168}, {6968, 59385}, {6982, 37584}, {7082, 10578}, {7672, 15481}, {7676, 16112}, {7677, 60909}, {7678, 60919}, {7679, 17768}, {8236, 15298}, {10394, 24929}, {11010, 50688}, {15296, 52653}, {16133, 41712}, {25057, 36914}, {30311, 38454}, {31994, 56244}, {33761, 34048}, {37579, 56203}, {52682, 59392}, {52684, 54051}

X(60944) = reflection of X(i) in X(j) for these {i,j}: {61008, 61015}, {7, 61008}
X(60944) = pole of line {14100, 60954} wrt Feuerbach hyperbola
X(60944) = pole of line {100, 28536} wrt Yff parabola
X(60944) = orthology center of the pedal triangle of X(5010) wrt Aguilera triangle
X(60944) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(527), X(55920)}}, {{A, B, C, X(1156), X(6173)}}, {{A, B, C, X(1255), X(31164)}}, {{A, B, C, X(3306), X(43757)}}
X(60944) = barycentric quotient X(i)/X(j) for these (i, j): {109, 32630}
X(60944) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 9, 60954}, {9, 142, 61026}, {9, 60935, 6172}, {9, 60937, 60947}, {9, 60964, 61012}, {9, 60966, 61024}, {9, 60969, 18230}, {9, 60973, 60970}, {9, 60981, 61023}, {9, 61004, 2}, {9, 8545, 37787}, {226, 50573, 60951}, {527, 61015, 61008}, {1445, 8545, 60953}, {3219, 3305, 5273}, {6172, 18230, 60997}, {6666, 60936, 60988}, {8232, 61006, 41563}, {12848, 61027, 7}, {17257, 28966, 28780}, {29007, 37787, 8545}, {60937, 60947, 60948}, {60964, 61012, 60996}, {60970, 60973, 60957}

X(60945) = X(2)X(7)∩X(3)X(5542)

Barycentrics    (a+b-c)*(a-b+c)*(2*a^3-4*a*b*c-3*a^2*(b+c)+(b-c)^2*(b+c)) : :
X(60945) = X[1770]+3*X[41861], 3*X[11246]+X[14100]

X(60945) lies on these lines: {2, 7}, {3, 5542}, {6, 10481}, {37, 58816}, {65, 5853}, {85, 3686}, {269, 4667}, {277, 1743}, {279, 1449}, {284, 1434}, {346, 32098}, {388, 24393}, {390, 11518}, {391, 32086}, {443, 4355}, {480, 37270}, {515, 30329}, {516, 942}, {518, 4298}, {938, 52835}, {946, 3358}, {971, 24470}, {1001, 3671}, {1100, 1323}, {1418, 3664}, {1462, 16470}, {1467, 12560}, {1479, 4312}, {1723, 24181}, {1770, 41861}, {1839, 53237}, {2262, 2391}, {2321, 6604}, {2325, 32007}, {2550, 3339}, {3008, 52023}, {3243, 3600}, {3361, 38053}, {3474, 4326}, {3487, 21153}, {3601, 11038}, {3660, 58607}, {3668, 3946}, {3674, 16503}, {3678, 5850}, {3827, 13572}, {4007, 32003}, {4034, 31994}, {4254, 59242}, {4292, 5728}, {4315, 42871}, {4419, 7274}, {4644, 7271}, {4648, 51302}, {5173, 61033}, {5290, 38057}, {5586, 5698}, {5708, 5805}, {5759, 8726}, {5762, 9940}, {5791, 38204}, {5809, 9579}, {5819, 52511}, {5852, 58678}, {6067, 37363}, {6147, 31658}, {6841, 13159}, {6847, 38036}, {6989, 38130}, {7672, 10106}, {8255, 43151}, {8581, 41538}, {8729, 45707}, {8734, 45708}, {8814, 21446}, {10177, 37566}, {10404, 41712}, {11018, 38454}, {11036, 59418}, {11037, 37551}, {11246, 14100}, {11529, 43161}, {12577, 31793}, {15803, 59372}, {15934, 28194}, {16133, 41551}, {16667, 21314}, {17603, 60919}, {17768, 58608}, {18541, 31672}, {21060, 37271}, {21258, 59646}, {24929, 58813}, {31657, 37623}, {34028, 43035}, {37545, 38122}, {37582, 43180}, {40937, 45227}

X(60945) = midpoint of X(i) and X(j) for these {i,j}: {16133, 41551}, {4292, 5728}, {41572, 60961}, {553, 60932}, {65, 12573}, {7, 52819}, {7672, 10106}
X(60945) = reflection of X(i) in X(j) for these {i,j}: {15006, 5572}
X(60945) = complement of X(61003)
X(60945) = pole of line {8713, 23865} wrt circumcircle
X(60945) = pole of line {3676, 4040} wrt incircle
X(60945) = pole of line {284, 8012} wrt Stammler hyperbola
X(60945) = pole of line {333, 51972} wrt Wallace hyperbola
X(60945) = pole of line {1, 52023} wrt dual conic of Yff parabola
X(60945) = orthology center of the pedal triangle of X(5045) wrt Aguilera triangle
X(60945) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(142), X(1434)}}, {{A, B, C, X(226), X(10509)}}, {{A, B, C, X(284), X(8012)}}, {{A, B, C, X(3598), X(8814)}}, {{A, B, C, X(18230), X(60075)}}, {{A, B, C, X(27475), X(41867)}}, {{A, B, C, X(41857), X(43762)}}
X(60945) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 12848, 60937}, {7, 144, 60953}, {7, 1445, 226}, {7, 21454, 60955}, {7, 37787, 41857}, {7, 41572, 60961}, {7, 41857, 3982}, {7, 57, 142}, {7, 60932, 52819}, {7, 60938, 60992}, {7, 60939, 9}, {7, 60948, 21617}, {7, 60951, 60936}, {7, 60975, 60933}, {7, 60992, 60980}, {7, 8232, 4654}, {142, 60974, 5745}, {226, 1445, 6666}, {516, 5572, 15006}, {553, 52819, 7}, {3911, 21617, 58433}, {4031, 60992, 60938}, {4298, 37544, 57284}, {8545, 61014, 61000}, {9436, 41246, 5750}, {12848, 60937, 60942}, {21454, 60982, 61022}, {21617, 60948, 3911}, {41572, 60961, 527}, {52819, 60961, 41572}

X(60946) = X(2)X(7)∩X(55)X(5851)

Barycentrics    (a+b-c)*(a-b+c)*(3*a^3-5*a^2*(b+c)+(b-c)^2*(b+c)+a*(b^2+8*b*c+c^2)) : :
X(60946) = -9*X[5686]+8*X[54288]

X(60946) lies on circumconic {{A, B, C, X(1156), X(8257)}} and on these lines: {2, 7}, {55, 5851}, {390, 2801}, {480, 15813}, {497, 1156}, {515, 30332}, {516, 12647}, {651, 4419}, {664, 49748}, {912, 3488}, {954, 5843}, {971, 6938}, {1376, 6068}, {1478, 3245}, {1621, 34919}, {2550, 59416}, {3434, 5856}, {3476, 3877}, {3554, 7269}, {4346, 37771}, {4454, 20881}, {4552, 20073}, {4644, 8609}, {5218, 12831}, {5220, 40663}, {5252, 28534}, {5281, 55920}, {5559, 49135}, {5686, 54288}, {5723, 49747}, {5728, 6976}, {5759, 6948}, {5762, 6923}, {5766, 18446}, {5779, 6929}, {5784, 51379}, {5805, 6968}, {5817, 6973}, {6180, 17334}, {6950, 36996}, {6980, 60922}, {6982, 37826}, {8543, 42842}, {10944, 50244}, {10947, 16112}, {11038, 37602}, {11200, 34931}, {11662, 57282}, {14151, 47357}, {15298, 60925}, {15726, 36976}, {17276, 37800}, {17347, 56927}, {17768, 60909}, {18393, 60895}, {20119, 59388}, {22758, 53055}, {24411, 28118}, {30287, 58651}, {30384, 54370}, {31526, 56933}, {60911, 60924}

X(60946) = reflection of X(i) in X(j) for these {i,j}: {20059, 61011}, {60925, 15298}, {60971, 31164}, {7, 8545}
X(60946) = pole of line {14100, 61019} wrt Feuerbach hyperbola
X(60946) = pole of line {4895, 47887} wrt Suppa-Cucoanes circle
X(60946) = orthology center of the pedal triangle of X(5119) wrt Aguilera triangle
X(60946) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 144, 60940}, {7, 144, 41563}, {7, 18230, 60988}, {7, 6172, 37787}, {7, 60944, 2}, {7, 60954, 8732}, {7, 60995, 61008}, {7, 8545, 61027}, {7, 9, 61019}, {63, 226, 5435}, {144, 20059, 60950}, {144, 60998, 12848}, {527, 31164, 60971}, {527, 61011, 20059}, {8732, 61006, 60954}, {12848, 60934, 60998}, {12848, 60998, 7}, {29007, 61008, 60995}, {50573, 60952, 57}, {60937, 60977, 41572}, {60942, 60961, 1445}, {60953, 61007, 60932}, {60992, 61000, 60947}, {60995, 61008, 60943}

X(60947) = X(2)X(7)∩X(44)X(77)

Barycentrics    a*(a+b-c)*(a-b+c)*(3*a^2+3*b^2+4*b*c+3*c^2-6*a*(b+c)) : :

X(60947) lies on these lines: {2, 7}, {20, 5825}, {44, 77}, {45, 7190}, {46, 60911}, {56, 15481}, {210, 17620}, {241, 16885}, {390, 11362}, {516, 10826}, {518, 1388}, {651, 3973}, {1001, 11011}, {1155, 16112}, {1156, 2951}, {1442, 16670}, {1728, 4304}, {2346, 30330}, {3062, 30295}, {3339, 16133}, {3340, 16859}, {3576, 40269}, {3832, 5128}, {3878, 7672}, {3895, 36920}, {3988, 5223}, {4312, 30312}, {4315, 41229}, {4318, 15601}, {5228, 16814}, {5722, 55104}, {5728, 31837}, {5729, 7675}, {5779, 8544}, {6180, 15492}, {6684, 60925}, {7131, 7181}, {7269, 16676}, {7548, 54370}, {10394, 21153}, {11372, 40256}, {11662, 38107}, {14740, 34784}, {15254, 41712}, {15299, 30331}, {17768, 24914}, {22464, 37650}, {25101, 56927}, {30628, 47375}, {31672, 37468}, {33557, 38271}, {37524, 41694}

X(60947) = orthology center of the pedal triangle of X(5204) wrt Aguilera triangle
X(60947) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1156), X(20059)}}, {{A, B, C, X(5748), X(36101)}}, {{A, B, C, X(7131), X(29007)}}, {{A, B, C, X(27003), X(39273)}}
X(60947) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 1445, 8545}, {9, 37787, 1445}, {9, 3929, 60983}, {9, 57, 29007}, {9, 60937, 60944}, {9, 60970, 60949}, {9, 60974, 60966}, {9, 60985, 61004}, {9, 60989, 60973}, {9, 60990, 60935}, {9, 60994, 63}, {1445, 8545, 60938}, {5223, 7677, 30318}, {5435, 60983, 60934}, {5729, 31658, 7675}, {6172, 8732, 60936}, {8232, 60941, 60932}, {12848, 18230, 21617}, {20195, 61007, 7}, {31231, 60933, 60988}, {37787, 60954, 9}, {52819, 60986, 60943}, {60939, 60995, 41857}, {60941, 61023, 8232}, {60944, 60948, 60937}, {60992, 61000, 60946}

X(60948) = X(2)X(7)∩X(6)X(1443)

Barycentrics    a*(a+b-c)*(a-b+c)*((a-b)^2-(2*a+b)*c+c^2) : :

X(60948) lies on these lines: {1, 56028}, {2, 7}, {6, 1443}, {35, 20116}, {36, 30284}, {40, 8236}, {46, 390}, {55, 11025}, {56, 3889}, {65, 7677}, {77, 16667}, {100, 15185}, {191, 38059}, {241, 1100}, {354, 2346}, {404, 518}, {484, 30331}, {516, 3336}, {651, 1418}, {658, 10509}, {662, 1014}, {673, 2160}, {954, 5708}, {971, 26877}, {1001, 5221}, {1155, 5572}, {1156, 31391}, {1210, 37433}, {1250, 37773}, {1376, 34784}, {1402, 35617}, {1405, 41777}, {1420, 11526}, {1465, 34028}, {1466, 37285}, {1471, 4318}, {1621, 58564}, {1776, 30311}, {1836, 7678}, {3149, 12669}, {3243, 4855}, {3337, 5542}, {3338, 3523}, {3358, 59385}, {3361, 3811}, {3587, 15933}, {3651, 5728}, {3668, 37771}, {3674, 56532}, {3873, 6600}, {3957, 61033}, {4326, 53056}, {4343, 17596}, {4850, 54358}, {5011, 14189}, {5228, 7269}, {5686, 17580}, {5709, 59418}, {5729, 60884}, {5759, 37532}, {5805, 6845}, {5809, 7171}, {5817, 24467}, {5902, 52769}, {6603, 45227}, {6841, 34753}, {6910, 38053}, {6985, 10394}, {7045, 57183}, {7098, 8543}, {7176, 45751}, {7190, 16673}, {7671, 11495}, {7673, 37567}, {7675, 15803}, {7679, 24914}, {8544, 10398}, {9352, 30628}, {9441, 21346}, {10090, 12755}, {10638, 37772}, {10916, 15932}, {11010, 43179}, {11219, 15909}, {11246, 42356}, {12515, 53055}, {14100, 30295}, {14151, 41541}, {15254, 16133}, {15298, 30340}, {15837, 58563}, {16706, 41804}, {17012, 18593}, {17023, 41808}, {17075, 17367}, {17263, 32007}, {18221, 59340}, {18412, 18450}, {18625, 26723}, {21151, 37612}, {24580, 59405}, {26724, 55010}, {26866, 60897}, {36279, 42884}, {37462, 38057}, {37524, 41861}, {45834, 55920}, {59372, 60912}

X(60948) = X(i)-isoconjugate-of-X(j) for these {i, j}: {55, 42326}
X(60948) = X(i)-Dao conjugate of X(j) for these {i, j}: {223, 42326}
X(60948) = X(i)-Ceva conjugate of X(j) for these {i, j}: {32007, 3957}
X(60948) = X(i)-cross conjugate of X(j) for these {i, j}: {17745, 3957}
X(60948) = pole of line {284, 2348} wrt Stammler hyperbola
X(60948) = pole of line {1, 61013} wrt dual conic of Yff parabola
X(60948) = orthology center of the pedal triangle of X(5563) wrt Aguilera triangle
X(60948) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(20195)}}, {{A, B, C, X(2), X(3957)}}, {{A, B, C, X(7), X(32007)}}, {{A, B, C, X(9), X(17745)}}, {{A, B, C, X(57), X(41431)}}, {{A, B, C, X(88), X(54357)}}, {{A, B, C, X(226), X(43760)}}, {{A, B, C, X(527), X(42325)}}, {{A, B, C, X(662), X(53337)}}, {{A, B, C, X(672), X(2160)}}, {{A, B, C, X(673), X(3219)}}, {{A, B, C, X(1025), X(38340)}}, {{A, B, C, X(1170), X(21617)}}, {{A, B, C, X(2346), X(6666)}}, {{A, B, C, X(3305), X(39273)}}, {{A, B, C, X(4654), X(21446)}}, {{A, B, C, X(6173), X(45834)}}, {{A, B, C, X(10509), X(37787)}}, {{A, B, C, X(17484), X(37131)}}, {{A, B, C, X(17781), X(36101)}}, {{A, B, C, X(20078), X(55937)}}, {{A, B, C, X(26745), X(55868)}}, {{A, B, C, X(27186), X(27475)}}, {{A, B, C, X(29007), X(43762)}}
X(60948) = barycentric product X(i)*X(j) for these (i, j): {1, 32007}, {279, 56244}, {3957, 7}, {17263, 57}, {17745, 85}, {21453, 61033}, {42325, 664}
X(60948) = barycentric quotient X(i)/X(j) for these (i, j): {57, 42326}, {3957, 8}, {17263, 312}, {17745, 9}, {32007, 75}, {42325, 522}, {56244, 346}, {61033, 4847}
X(60948) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 60974, 61024}, {2, 7, 61013}, {6, 17092, 1443}, {7, 1445, 37787}, {7, 18230, 61027}, {7, 5435, 61019}, {7, 60941, 41563}, {7, 60944, 60937}, {7, 60954, 8545}, {7, 61017, 226}, {7, 61019, 61008}, {7, 8732, 60988}, {9, 20059, 56551}, {9, 3306, 60996}, {9, 57, 60938}, {9, 61001, 35595}, {57, 1708, 21454}, {57, 60989, 60932}, {142, 60932, 7}, {142, 60970, 60981}, {142, 60989, 60970}, {144, 23958, 60968}, {226, 61016, 61017}, {553, 6666, 41857}, {658, 10509, 53242}, {1445, 60938, 9}, {1445, 60955, 60954}, {1652, 1653, 672}, {3911, 60945, 21617}, {6173, 60994, 60969}, {8257, 60968, 144}, {27003, 60970, 142}, {60937, 60947, 60944}, {60974, 60985, 2}, {60984, 61026, 60973}, {61013, 61024, 29007}, {61014, 61022, 60936}

X(60949) = X(2)X(7)∩X(77)X(220)

Barycentrics    a*(a^4-6*a^2*b*c-2*a^3*(b+c)+2*a*(b+c)^3-(b-c)^2*(b^2+c^2)) : :

X(60949) lies on these lines: {2, 7}, {40, 5686}, {69, 55337}, {72, 7675}, {75, 32024}, {77, 220}, {84, 59418}, {191, 2938}, {200, 7676}, {210, 11495}, {390, 6764}, {480, 4640}, {516, 41229}, {518, 3303}, {728, 32099}, {954, 31445}, {960, 51773}, {971, 37426}, {1001, 17609}, {1156, 42015}, {1212, 7190}, {1441, 30625}, {1721, 21039}, {1757, 4335}, {2324, 24635}, {2346, 4512}, {2475, 38200}, {3059, 5220}, {3146, 59413}, {3174, 3681}, {3338, 38059}, {3358, 21168}, {3672, 16572}, {3692, 4416}, {3715, 58634}, {3751, 4343}, {3869, 11526}, {3875, 25237}, {3927, 5728}, {4326, 5223}, {4360, 31169}, {4423, 58563}, {4853, 7673}, {5227, 51190}, {5231, 7678}, {5234, 12560}, {5709, 5817}, {5732, 12528}, {5759, 7330}, {5779, 26921}, {5809, 54398}, {5853, 6872}, {6067, 24703}, {6600, 35258}, {6762, 8236}, {6912, 43166}, {7079, 7282}, {7082, 60919}, {7085, 60897}, {7672, 12526}, {10884, 45120}, {10889, 21061}, {11038, 31435}, {14829, 56085}, {15481, 15587}, {16865, 38316}, {21296, 56244}, {24467, 59381}, {26878, 36996}, {31165, 42871}, {32100, 39126}, {34820, 39273}, {35986, 46917}, {36976, 42012}, {37584, 60901}, {37612, 38113}, {38130, 59333}, {41561, 43151}, {43182, 60912}

X(60949) = pole of line {14100, 60958} wrt Feuerbach hyperbola
X(60949) = orthology center of the pedal triangle of X(5584) wrt Aguilera triangle
X(60949) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(527), X(42015)}}, {{A, B, C, X(1223), X(3305)}}, {{A, B, C, X(1445), X(55965)}}, {{A, B, C, X(7131), X(18230)}}, {{A, B, C, X(9776), X(36101)}}, {{A, B, C, X(21454), X(39273)}}, {{A, B, C, X(34820), X(40131)}}
X(60949) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 60990, 60938}, {7, 9, 60958}, {9, 142, 3305}, {9, 36973, 29007}, {9, 3929, 61024}, {9, 57, 18230}, {9, 63, 1445}, {9, 60937, 60981}, {9, 60942, 60966}, {9, 60955, 7308}, {9, 60965, 60969}, {9, 60968, 6666}, {9, 60970, 60947}, {9, 60977, 60964}, {9, 60985, 60986}, {9, 60990, 2}, {9, 61005, 63}, {144, 3219, 9}, {144, 60969, 60965}, {144, 60975, 60957}, {144, 60997, 41572}, {4326, 5223, 34784}, {6666, 60968, 3306}, {7308, 60955, 60996}, {8545, 60938, 41857}, {56545, 60997, 8545}, {60957, 60981, 60937}

X(60950) = X(2)X(7)∩X(4)X(16112)

Barycentrics    3*a^5-2*a^3*(b-c)^2-5*a^4*(b+c)-(b-c)^4*(b+c)-a*(b^2-c^2)^2+2*a^2*(b+c)*(3*b^2-4*b*c+3*c^2) : :

X(60950) lies on circumconic {{A, B, C, X(4), X(41572)}} and on these lines: {2, 7}, {4, 16112}, {72, 4293}, {193, 25241}, {347, 2323}, {452, 18221}, {516, 49168}, {518, 944}, {758, 6987}, {943, 42885}, {971, 6869}, {1006, 42843}, {1444, 56020}, {2324, 4341}, {2550, 5857}, {2900, 9778}, {2949, 6908}, {3419, 34744}, {3474, 17668}, {3488, 44663}, {4018, 5698}, {4292, 45039}, {4294, 14054}, {4552, 20110}, {5218, 41548}, {5223, 9613}, {5686, 56880}, {5731, 11523}, {5766, 30284}, {5768, 54422}, {5770, 5812}, {5779, 44229}, {5805, 6866}, {5825, 10395}, {5850, 22836}, {5852, 21168}, {6067, 36971}, {6601, 38454}, {6846, 60911}, {6847, 54302}, {6873, 59386}, {6876, 36996}, {6904, 40661}, {7674, 61030}, {10398, 60905}, {11495, 47387}, {12625, 20070}, {26668, 41804}, {30143, 51090}, {30628, 36976}, {34032, 55405}, {45738, 53994}, {56288, 60925}

X(60950) = reflection of X(i) in X(j) for these {i,j}: {60965, 60942}, {61010, 9}, {7, 60974}
X(60950) = pole of line {3064, 28473} wrt polar circle
X(60950) = pole of line {522, 26641} wrt Steiner circumellipse
X(60950) = orthology center of the pedal triangle of X(5709) wrt Aguilera triangle
X(60950) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 6172, 60969}, {9, 527, 61010}, {9, 52819, 60987}, {9, 60933, 226}, {9, 60977, 61003}, {9, 60978, 18230}, {9, 60982, 142}, {9, 61011, 8232}, {144, 12848, 9}, {144, 20059, 60946}, {144, 20078, 60957}, {144, 41563, 60940}, {144, 9965, 60934}, {329, 3218, 54366}, {527, 60942, 60965}, {527, 60974, 7}, {1445, 60979, 52457}, {8232, 20059, 61011}, {9965, 60934, 60933}

X(60951) = X(2)X(7)∩X(30)X(10394)

Barycentrics    (a+b-c)*(a-b+c)*(2*a^3+a*b*c-3*a^2*(b+c)+(b-c)^2*(b+c)) : :
X(60951) = -2*X[3058]+3*X[7671], -5*X[11025]+2*X[60919]

X(60951) lies on these lines: {2, 7}, {30, 10394}, {65, 11114}, {241, 14564}, {381, 5729}, {390, 25415}, {528, 7672}, {942, 11662}, {954, 28466}, {1156, 1836}, {1441, 17346}, {1443, 4644}, {1737, 30424}, {3058, 7671}, {3543, 18391}, {3584, 60912}, {3656, 53055}, {3758, 41804}, {3873, 5856}, {4312, 18513}, {4318, 50303}, {4331, 50282}, {4525, 5850}, {4552, 17389}, {4870, 15254}, {4995, 8255}, {5220, 11237}, {5228, 49747}, {5298, 25557}, {5542, 37587}, {5698, 31156}, {5735, 6840}, {5759, 37533}, {5762, 28459}, {5851, 11246}, {5880, 6175}, {6180, 56534}, {6987, 15933}, {8236, 16200}, {8543, 16858}, {9352, 10427}, {10072, 60895}, {10385, 36976}, {11025, 60919}, {11238, 36971}, {13405, 55920}, {15733, 49719}, {16833, 36595}, {16834, 41803}, {17075, 17120}, {17092, 17365}, {20084, 41551}, {22464, 50114}, {28194, 30332}, {34919, 44447}, {40149, 54735}, {50107, 56927}, {54318, 60905}

X(60951) = midpoint of X(i) and X(j) for these {i,j}: {41572, 60932}
X(60951) = reflection of X(i) in X(j) for these {i,j}: {60932, 52819}, {60952, 553}, {7, 60932}
X(60951) = pole of line {14100, 30311} wrt Feuerbach hyperbola
X(60951) = pole of line {4794, 47800} wrt Suppa-Cucoanes circle
X(60951) = orthology center of the pedal triangle of X(5902) wrt Aguilera triangle
X(60951) = intersection, other than A, B, C, of circumconics {{A, B, C, X(63), X(54735)}}, {{A, B, C, X(37761), X(56358)}}
X(60951) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 12848, 37787}, {7, 1445, 60988}, {7, 37787, 61008}, {7, 6172, 61027}, {7, 60941, 61019}, {7, 60944, 226}, {7, 60954, 21617}, {7, 9, 61013}, {144, 60987, 60981}, {226, 50573, 60944}, {527, 52819, 60932}, {527, 553, 60952}, {1708, 4654, 2}, {5905, 60940, 56551}, {6172, 61027, 29007}, {12848, 60975, 7}, {21617, 61014, 60954}, {41563, 61027, 6172}, {41572, 60932, 527}, {60932, 60952, 553}, {60982, 61007, 8545}

X(60952) = X(2)X(7)∩X(354)X(5851)

Barycentrics    (a+b-c)*(a-b+c)*(2*a^3+10*a*b*c-3*a^2*(b+c)+(b-c)^2*(b+c)) : :
X(60952) = -X[11662]+4*X[24470]

X(60952) lies on these lines: {2, 7}, {85, 49722}, {241, 49742}, {354, 5851}, {376, 8544}, {388, 34711}, {390, 50811}, {519, 5696}, {528, 8581}, {551, 8543}, {651, 50114}, {1156, 11019}, {1441, 50119}, {2346, 43182}, {3058, 15726}, {3241, 30318}, {3245, 30424}, {3671, 5288}, {3828, 30312}, {3919, 5850}, {4308, 50738}, {4321, 50836}, {4327, 50303}, {4666, 34919}, {4870, 25557}, {5298, 15254}, {5434, 28534}, {5542, 10074}, {5735, 6925}, {5766, 10304}, {5880, 6735}, {6180, 17301}, {6909, 43177}, {9580, 55922}, {9814, 50865}, {10072, 54370}, {11662, 24470}, {14151, 51071}, {15346, 25006}, {15683, 30332}, {17346, 39126}, {17625, 36868}, {18450, 51705}, {22464, 49747}, {29574, 41801}, {30295, 50808}, {30311, 50802}, {30353, 36976}, {31162, 60926}, {38055, 51709}, {43180, 44675}, {45043, 50796}

X(60952) = midpoint of X(i) and X(j) for these {i,j}: {60932, 60936}
X(60952) = reflection of X(i) in X(j) for these {i,j}: {41572, 60932}, {60932, 7}, {60951, 553}
X(60952) = orthology center of the pedal triangle of X(5919) wrt Aguilera triangle
X(60952) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 144, 60938}, {7, 29007, 60992}, {7, 37787, 61022}, {7, 41563, 60955}, {7, 60934, 1445}, {7, 60946, 57}, {7, 60951, 553}, {7, 60961, 60936}, {7, 60998, 8545}, {7, 61008, 60993}, {7, 61013, 60980}, {7, 61027, 6173}, {7, 8545, 30379}, {57, 60946, 50573}, {527, 553, 60951}, {527, 60932, 41572}, {553, 60951, 60932}, {4654, 60963, 7}, {6173, 60937, 61027}, {6173, 61027, 21617}, {8545, 30379, 61015}, {17254, 40892, 307}, {29007, 60992, 61016}, {60932, 60936, 527}, {60953, 60963, 4654}

X(60953) = X(1)X(6610)∩X(2)X(7)

Barycentrics    a*(a+b-c)*(a-b+c)*(a^2+b^2+10*b*c+c^2-2*a*(b+c)) : :

X(60953) lies on these lines: {1, 6610}, {2, 7}, {6, 7274}, {37, 7271}, {40, 30424}, {45, 51302}, {55, 30353}, {65, 11530}, {84, 6147}, {85, 4659}, {241, 16676}, {269, 3247}, {388, 2136}, {390, 51779}, {482, 60877}, {484, 15298}, {516, 1056}, {518, 4915}, {528, 51767}, {728, 4454}, {738, 33949}, {954, 30282}, {971, 15934}, {1001, 13462}, {1319, 4321}, {1418, 3731}, {1419, 7190}, {1420, 8543}, {1442, 33633}, {1449, 4328}, {1519, 38036}, {1706, 5290}, {2099, 3243}, {2124, 5543}, {2257, 17365}, {2550, 51781}, {2801, 11529}, {3062, 5572}, {3333, 43180}, {3339, 5220}, {3340, 61030}, {3361, 15254}, {3485, 7091}, {3487, 9841}, {3587, 5762}, {3601, 8544}, {3671, 6762}, {3748, 4326}, {3753, 5223}, {4298, 5698}, {4312, 5119}, {4315, 47357}, {4355, 31435}, {4419, 10481}, {4644, 58816}, {4862, 52023}, {5122, 21153}, {5228, 16670}, {5252, 51102}, {5528, 41553}, {5542, 5603}, {5696, 41863}, {5732, 24929}, {5735, 57282}, {5784, 11523}, {5851, 16173}, {5856, 10956}, {7671, 44841}, {8255, 10860}, {10384, 11038}, {10394, 11518}, {10864, 12563}, {11191, 45706}, {11495, 31508}, {11545, 38154}, {12246, 12577}, {13384, 18450}, {16112, 17626}, {16133, 51653}, {17757, 38052}, {18220, 30340}, {18766, 43166}, {30295, 35445}, {30331, 50811}, {30332, 37556}, {37584, 60922}, {38097, 40663}, {56255, 58809}

X(60953) = midpoint of X(i) and X(j) for these {i,j}: {1, 9814}, {7, 60998}
X(60953) = reflection of X(i) in X(j) for these {i,j}: {55922, 9814}, {60982, 7}, {60997, 142}
X(60953) = pole of line {14077, 36920} wrt Adams circle
X(60953) = pole of line {3676, 14077} wrt incircle
X(60953) = pole of line {4860, 14100} wrt Feuerbach hyperbola
X(60953) = pole of line {14077, 21104} wrt Suppa-Cucoanes circle
X(60953) = pole of line {1, 61022} wrt dual conic of Yff parabola
X(60953) = orthology center of the pedal triangle of X(6767) wrt Aguilera triangle
X(60953) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6172)}}, {{A, B, C, X(2), X(55922)}}, {{A, B, C, X(7), X(52715)}}, {{A, B, C, X(144), X(10390)}}, {{A, B, C, X(329), X(34917)}}, {{A, B, C, X(3062), X(18230)}}, {{A, B, C, X(5316), X(27475)}}, {{A, B, C, X(5665), X(12848)}}, {{A, B, C, X(7091), X(8545)}}, {{A, B, C, X(18228), X(34919)}}
X(60953) = barycentric product X(i)*X(j) for these (i, j): {1, 52715}
X(60953) = barycentric quotient X(i)/X(j) for these (i, j): {52715, 75}
X(60953) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 9814, 15726}, {2, 7, 61022}, {7, 12848, 553}, {7, 144, 60945}, {7, 29007, 60938}, {7, 30275, 60993}, {7, 527, 60982}, {7, 6172, 21454}, {7, 60934, 52819}, {7, 60946, 60932}, {7, 60967, 226}, {7, 60998, 527}, {7, 61027, 30379}, {7, 8232, 60992}, {7, 8545, 57}, {7, 9, 60955}, {9, 6173, 5437}, {57, 60937, 8545}, {142, 527, 60997}, {142, 60965, 9}, {144, 9776, 60972}, {226, 60993, 30275}, {1445, 8545, 60944}, {3982, 60961, 61021}, {3982, 61021, 7}, {4654, 60952, 60963}, {5219, 30379, 38093}, {6173, 30827, 142}, {8232, 60992, 20195}, {8581, 12560, 3243}, {9814, 15726, 55922}, {16112, 58563, 30330}, {30275, 60975, 60987}, {30275, 60993, 6173}, {30379, 61027, 5219}, {43180, 54370, 3333}, {51768, 59372, 51816}, {52819, 60934, 60977}, {59375, 60935, 3306}, {60932, 60946, 61007}, {60956, 61021, 60933}, {60961, 61021, 60956}, {60962, 60964, 60990}

X(60954) = X(2)X(7)∩X(77)X(3973)

Barycentrics    a*(a+b-c)*(a-b+c)*(2*a^2+2*b^2+3*b*c+2*c^2-4*a*(b+c)) : :

X(60954) lies on these lines: {2, 7}, {77, 3973}, {241, 15492}, {390, 10573}, {484, 3839}, {516, 18395}, {651, 16885}, {938, 26878}, {971, 6942}, {1001, 5330}, {1156, 11495}, {1441, 17335}, {1442, 1743}, {1728, 4313}, {2099, 16861}, {2346, 55920}, {3616, 15296}, {3731, 7269}, {4308, 41229}, {4537, 5223}, {4552, 17349}, {5220, 7677}, {5433, 5852}, {5692, 18467}, {5704, 26921}, {5729, 59381}, {5759, 6928}, {5762, 6971}, {5779, 6924}, {5809, 6936}, {5817, 6917}, {5825, 6868}, {5857, 11681}, {6049, 57279}, {6874, 38108}, {6875, 10394}, {6902, 21168}, {6934, 36991}, {7082, 9778}, {7098, 19877}, {7279, 54322}, {7671, 15837}, {7672, 15254}, {7676, 60910}, {7678, 38454}, {7679, 60883}, {8236, 15299}, {8543, 41712}, {10303, 54432}, {12432, 41872}, {15297, 52653}, {15556, 16859}, {16112, 30295}, {17354, 40999}, {17620, 58635}, {17768, 30312}, {32003, 56244}, {33761, 52424}, {37650, 37771}, {40269, 41700}, {44009, 58324}, {45976, 51516}

X(60954) = reflection of X(i) in X(j) for these {i,j}: {60988, 61016}, {7, 60988}
X(60954) = pole of line {14100, 60944} wrt Feuerbach hyperbola
X(60954) = orthology center of the pedal triangle of X(7280) wrt Aguilera triangle
X(60954) = intersection, other than A, B, C, of circumconics {{A, B, C, X(142), X(55920)}}, {{A, B, C, X(673), X(23958)}}, {{A, B, C, X(2346), X(6173)}}, {{A, B, C, X(30852), X(36101)}}
X(60954) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 18230, 61017}, {7, 9, 60944}, {9, 142, 61025}, {9, 1445, 29007}, {9, 60947, 37787}, {9, 60970, 6172}, {9, 60974, 60935}, {9, 60994, 144}, {9, 61012, 18230}, {9, 61024, 60983}, {9, 8257, 60969}, {527, 61016, 60988}, {1445, 60955, 60948}, {1445, 8545, 60955}, {1708, 27065, 5226}, {3218, 60973, 60976}, {3911, 61000, 60936}, {6666, 41572, 61008}, {8257, 60969, 60996}, {8732, 61006, 60946}, {12848, 60943, 7}, {21617, 61014, 60951}, {29007, 37787, 1445}, {41700, 52769, 40269}, {52819, 61015, 61013}, {60935, 60974, 60957}, {60986, 61014, 21617}

X(60955) = X(1)X(1418)∩X(2)X(7)

Barycentrics    a*(a+b-c)*(a-b+c)*((a-b)^2-2*(a+3*b)*c+c^2) : :

X(60955) lies on these lines: {1, 1418}, {2, 7}, {6, 7271}, {37, 7274}, {40, 5542}, {46, 59372}, {56, 12560}, {65, 2136}, {84, 5805}, {173, 45707}, {241, 3247}, {258, 45708}, {269, 1449}, {279, 3946}, {354, 4326}, {376, 30331}, {388, 38200}, {516, 1058}, {518, 1706}, {728, 4869}, {738, 1434}, {942, 5732}, {954, 15803}, {971, 5708}, {999, 43166}, {1001, 3361}, {1086, 2257}, {1159, 7966}, {1210, 59389}, {1407, 54358}, {1420, 7225}, {1467, 5665}, {1697, 11038}, {1721, 18216}, {2346, 35445}, {2550, 4298}, {2951, 5572}, {3062, 55922}, {3254, 24465}, {3336, 15298}, {3337, 15299}, {3338, 4312}, {3600, 5853}, {3671, 38053}, {3697, 5223}, {3826, 5290}, {4000, 10481}, {4292, 52835}, {4315, 34701}, {4355, 38052}, {4402, 43983}, {4648, 58816}, {4659, 39126}, {4848, 59414}, {4859, 16572}, {4860, 14100}, {4907, 21346}, {5083, 5528}, {5128, 30340}, {5221, 8581}, {5434, 51102}, {5575, 24471}, {5586, 25557}, {5709, 31657}, {5759, 37526}, {5762, 37534}, {6147, 38122}, {6180, 16670}, {6601, 7091}, {6604, 17296}, {6610, 16667}, {6766, 12577}, {7171, 31671}, {7177, 17113}, {7190, 17092}, {7289, 51150}, {7330, 38107}, {7675, 11518}, {7676, 10389}, {7701, 13159}, {8255, 41338}, {9814, 16112}, {10509, 47374}, {10580, 15006}, {11036, 37551}, {11372, 30424}, {11523, 37544}, {12514, 38054}, {12705, 38036}, {13462, 42819}, {15228, 51816}, {15726, 30330}, {16133, 41547}, {17207, 35935}, {18421, 42871}, {18482, 18541}, {20116, 43178}, {21153, 37582}, {24392, 41573}, {26921, 38111}, {30295, 44841}, {31658, 37545}, {33765, 50561}, {34494, 45704}, {34753, 38108}, {37532, 59380}, {37612, 60922}, {38150, 57282}, {41325, 47299}, {59335, 60924}

X(60955) = midpoint of X(i) and X(j) for these {i,j}: {7, 60939}
X(60955) = X(i)-Ceva conjugate of X(j) for these {i, j}: {32086, 10582}
X(60955) = pole of line {14100, 60953} wrt Feuerbach hyperbola
X(60955) = pole of line {284, 6602} wrt Stammler hyperbola
X(60955) = pole of line {333, 728} wrt Wallace hyperbola
X(60955) = pole of line {1, 15006} wrt dual conic of Yff parabola
X(60955) = orthology center of the pedal triangle of X(7373) wrt Aguilera triangle
X(60955) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(18230)}}, {{A, B, C, X(2), X(10390)}}, {{A, B, C, X(7), X(32086)}}, {{A, B, C, X(9), X(1434)}}, {{A, B, C, X(57), X(34821)}}, {{A, B, C, X(144), X(55922)}}, {{A, B, C, X(226), X(23062)}}, {{A, B, C, X(673), X(7308)}}, {{A, B, C, X(738), X(1400)}}, {{A, B, C, X(1445), X(7091)}}, {{A, B, C, X(3062), X(6172)}}, {{A, B, C, X(3929), X(39273)}}, {{A, B, C, X(5665), X(8232)}}, {{A, B, C, X(6601), X(18228)}}, {{A, B, C, X(8012), X(18164)}}, {{A, B, C, X(21446), X(21454)}}, {{A, B, C, X(42309), X(59207)}}
X(60955) = barycentric product X(i)*X(j) for these (i, j): {1, 32086}, {10582, 7}
X(60955) = barycentric quotient X(i)/X(j) for these (i, j): {10582, 8}, {32086, 75}
X(60955) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 58563, 10390}, {7, 12848, 60961}, {7, 1445, 60937}, {7, 21454, 60945}, {7, 21617, 4654}, {7, 41563, 60952}, {7, 52819, 60933}, {7, 60938, 57}, {7, 60939, 527}, {7, 60941, 60998}, {7, 60948, 8545}, {7, 60975, 60962}, {7, 60992, 6173}, {7, 61019, 41857}, {7, 8732, 226}, {7, 9, 60953}, {9, 20195, 51780}, {9, 60968, 3928}, {56, 12560, 38316}, {57, 60937, 1445}, {65, 4321, 3243}, {142, 60990, 9}, {226, 8732, 20195}, {553, 60938, 60968}, {553, 60992, 7}, {1445, 8545, 60954}, {2951, 10980, 5572}, {7190, 17092, 59215}, {8257, 60962, 60965}, {11495, 58563, 1}, {12848, 60961, 60977}, {21454, 61022, 60982}, {41857, 61019, 5219}, {60941, 60998, 60942}, {60949, 60996, 7308}

X(60956) = X(2)X(7)∩X(347)X(6610)

Barycentrics    (a+b-c)*(a-b+c)*(5*a^3-7*a^2*(b+c)+3*(b-c)^2*(b+c)-a*(b^2-14*b*c+c^2)) : :
X(60956) = -3*X[7671]+4*X[12915], -9*X[11038]+8*X[51788], -2*X[54135]+3*X[59385], -4*X[54178]+3*X[59418]

X(60956) lies on these lines: {2, 7}, {347, 6610}, {390, 6938}, {497, 5851}, {516, 54179}, {651, 4346}, {954, 6950}, {999, 8543}, {1156, 5274}, {1319, 5698}, {2093, 30424}, {2095, 6982}, {2096, 24929}, {3476, 28534}, {3672, 53020}, {3820, 30312}, {3945, 7961}, {4312, 12647}, {4862, 54425}, {5261, 36279}, {5762, 6948}, {5766, 30282}, {5779, 6973}, {5843, 6929}, {5856, 17784}, {6068, 59572}, {6244, 30295}, {6282, 8544}, {6923, 60922}, {6930, 15934}, {6968, 59386}, {6980, 51514}, {7671, 12915}, {7956, 30311}, {7962, 30318}, {7994, 30353}, {8101, 30367}, {8102, 30405}, {9954, 30287}, {11038, 51788}, {13097, 30359}, {13098, 30404}, {13462, 60905}, {15726, 17642}, {18450, 37611}, {24248, 51766}, {25568, 44785}, {38058, 40333}, {51768, 60924}, {54135, 59385}, {54178, 59418}

X(60956) = reflection of X(i) in X(j) for these {i,j}: {144, 52457}, {12848, 7}, {2093, 30424}, {2094, 60963}, {30332, 7962}, {60957, 36973}, {61007, 61022}
X(60956) = anticomplement of X(60940)
X(60956) = X(i)-Dao conjugate of X(j) for these {i, j}: {60940, 60940}
X(60956) = orthology center of the pedal triangle of X(7962) wrt Aguilera triangle
X(60956) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 144, 8732}, {7, 527, 12848}, {7, 6172, 30379}, {7, 60934, 8232}, {7, 60936, 60934}, {7, 60946, 2}, {7, 60951, 21454}, {7, 60957, 1445}, {7, 60976, 41572}, {7, 60995, 6173}, {7, 60998, 60967}, {7, 61008, 59375}, {7, 8545, 30275}, {226, 60963, 7}, {527, 36973, 60957}, {527, 52457, 144}, {527, 60963, 2094}, {527, 61022, 61007}, {30275, 60934, 8545}, {60933, 60953, 61021}, {60961, 61021, 60953}

X(60957) = X(2)X(7)∩X(8)X(12943)

Barycentrics    7*a^2-3*(b-c)^2-4*a*(b+c) : :
X(60957) = -6*X[2]+5*X[7], -5*X[390]+4*X[3244], -4*X[546]+5*X[5779], -4*X[550]+5*X[5759], -4*X[551]+5*X[50840], -16*X[3530]+15*X[21151], -17*X[3544]+15*X[59386], -4*X[3626]+5*X[5223], -4*X[3629]+5*X[51190], -4*X[3631]+5*X[50995], -16*X[3636]+15*X[11038], -3*X[3681]+2*X[17668] and many others

X(60957) lies on these lines: {2, 7}, {8, 12943}, {69, 4488}, {72, 57000}, {190, 21296}, {193, 4460}, {320, 3161}, {346, 4480}, {382, 5762}, {390, 3244}, {391, 52709}, {480, 30295}, {516, 3632}, {518, 3644}, {545, 5839}, {546, 5779}, {550, 5759}, {551, 50840}, {651, 36640}, {673, 39709}, {758, 40269}, {954, 17571}, {958, 16133}, {971, 3529}, {1100, 4419}, {1443, 2324}, {1743, 4346}, {2550, 56880}, {2551, 28646}, {3036, 34744}, {3160, 6603}, {3474, 3711}, {3528, 33597}, {3530, 21151}, {3544, 59386}, {3616, 17258}, {3626, 5223}, {3629, 51190}, {3631, 50995}, {3636, 11038}, {3672, 16667}, {3681, 17668}, {3689, 9778}, {3729, 32099}, {3851, 5817}, {3855, 5805}, {3869, 17620}, {3897, 42819}, {3945, 16673}, {3973, 4887}, {4060, 4461}, {4308, 5289}, {4312, 5686}, {4313, 57002}, {4344, 24695}, {4363, 5936}, {4402, 4440}, {4416, 4454}, {4643, 7229}, {4644, 16777}, {4670, 28626}, {4681, 51052}, {4715, 17314}, {4862, 37681}, {4867, 5731}, {4869, 25728}, {4900, 28228}, {5079, 51516}, {5220, 59412}, {5222, 16669}, {5308, 16675}, {5525, 17170}, {5541, 34632}, {5543, 34522}, {5698, 5852}, {5772, 32935}, {5815, 54286}, {5825, 58798}, {5845, 40341}, {5851, 6154}, {5853, 20054}, {6006, 47663}, {6067, 30311}, {6068, 35023}, {6329, 51144}, {6763, 60911}, {7222, 17332}, {7717, 10301}, {9780, 15481}, {9812, 16112}, {10299, 21168}, {10307, 56114}, {11034, 45834}, {11737, 38073}, {14269, 60901}, {14869, 59381}, {15687, 31671}, {15720, 31657}, {15726, 34784}, {15808, 30340}, {15913, 56933}, {17261, 29623}, {17262, 28333}, {17263, 31722}, {17328, 53620}, {17336, 29627}, {17345, 54389}, {17351, 29611}, {17364, 20073}, {17373, 17487}, {20111, 25718}, {20583, 50997}, {28645, 30478}, {30424, 40333}, {30556, 31601}, {30557, 31602}, {30625, 32003}, {31189, 48629}, {31721, 42050}, {31995, 54280}, {32024, 32098}, {32088, 56054}, {34641, 50835}, {34747, 50839}, {34919, 56028}, {35018, 38107}, {36588, 37654}, {38024, 50837}, {38092, 50834}, {39707, 42318}, {55863, 59380}

X(60957) = reflection of X(i) in X(j) for these {i,j}: {144, 60977}, {12630, 30332}, {20059, 9}, {390, 60905}, {60933, 60942}, {60936, 61003}, {60956, 36973}, {60971, 6172}, {60976, 7}, {7, 144}
X(60957) = anticomplement of X(60933)
X(60957) = X(i)-Dao conjugate of X(j) for these {i, j}: {60933, 60933}
X(60957) = pole of line {10589, 14100} wrt Feuerbach hyperbola
X(60957) = pole of line {522, 31209} wrt Steiner circumellipse
X(60957) = orthology center of the pedal triangle of X(7991) wrt Aguilera triangle
X(60957) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(8545), X(56028)}}, {{A, B, C, X(9436), X(39709)}}, {{A, B, C, X(20195), X(34919)}}, {{A, B, C, X(31231), X(42318)}}, {{A, B, C, X(39707), X(51351)}}
X(60957) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 144, 60942}, {7, 29007, 5226}, {7, 41563, 60941}, {7, 527, 60976}, {7, 9, 60996}, {9, 527, 20059}, {9, 6173, 61001}, {9, 60933, 60980}, {63, 60965, 29007}, {142, 61006, 61023}, {144, 20059, 9}, {144, 20078, 60950}, {144, 20214, 60965}, {144, 60933, 60983}, {144, 60975, 60949}, {144, 60976, 18230}, {144, 60984, 61006}, {329, 20078, 28610}, {329, 3218, 5328}, {518, 30332, 12630}, {527, 36973, 60956}, {527, 6172, 60971}, {527, 60942, 60933}, {527, 60977, 144}, {527, 61003, 60936}, {3218, 5328, 5435}, {3644, 11008, 20050}, {4416, 4454, 32087}, {5328, 28610, 3218}, {5850, 60905, 390}, {6172, 60971, 59374}, {9965, 17781, 18228}, {12848, 60936, 7}, {17257, 31300, 35578}, {60933, 60942, 2}, {60935, 60974, 60954}, {60937, 60949, 60981}, {60942, 60983, 6172}, {60961, 61007, 60939}, {60966, 60990, 37787}, {60970, 60973, 60944}, {60984, 61006, 142}

X(60958) = X(1)X(21039)∩X(2)X(7)

Barycentrics    a*(a^4-2*a^2*b*c-2*a^3*(b+c)+2*a*(b+c)^3-(b-c)^2*(b^2+4*b*c+c^2)) : :

X(60958) lies on these lines: {1, 21039}, {2, 7}, {10, 50399}, {40, 40333}, {46, 38204}, {55, 58634}, {71, 24590}, {75, 32008}, {77, 1212}, {78, 1001}, {86, 31269}, {141, 39273}, {191, 13159}, {200, 2346}, {220, 7190}, {273, 1223}, {390, 31435}, {405, 7675}, {411, 2951}, {480, 3740}, {516, 6835}, {518, 54392}, {631, 3358}, {728, 32087}, {936, 4326}, {938, 5686}, {954, 5044}, {958, 9850}, {1170, 4328}, {1210, 15298}, {1229, 3692}, {1621, 3174}, {1697, 59413}, {1698, 6991}, {1709, 43151}, {1723, 29571}, {2257, 5308}, {2287, 60721}, {2324, 24554}, {2550, 5250}, {3149, 31658}, {3646, 5703}, {3647, 30353}, {3683, 11495}, {3870, 40659}, {3874, 5223}, {3895, 34720}, {3945, 16572}, {4321, 5234}, {4423, 5572}, {4512, 7676}, {4666, 15185}, {4679, 42356}, {5047, 41228}, {5129, 5809}, {5217, 11344}, {5227, 59405}, {5260, 30318}, {5284, 30628}, {5287, 54358}, {5542, 41229}, {5728, 11108}, {5732, 6986}, {5759, 6864}, {5779, 13369}, {5785, 10394}, {5805, 55104}, {5817, 6865}, {6601, 25006}, {6734, 38057}, {6831, 38108}, {6894, 52835}, {6895, 59389}, {6918, 59381}, {7330, 21151}, {7677, 8583}, {8236, 20007}, {8544, 16410}, {8726, 12669}, {10122, 10398}, {10396, 17554}, {10582, 11025}, {11038, 57279}, {11372, 31730}, {11517, 16293}, {11526, 19860}, {12514, 38052}, {12630, 37556}, {12649, 24393}, {13411, 15299}, {17277, 20946}, {17620, 25893}, {17682, 18655}, {17687, 28627}, {25542, 41861}, {25930, 40937}, {26878, 59386}, {26893, 58472}, {26921, 38107}, {31211, 59682}, {31445, 50203}, {31672, 37428}, {31995, 56244}, {32088, 39126}, {33597, 38031}, {34772, 38316}, {36991, 37423}, {37532, 38171}, {38113, 52265}, {39244, 42449}, {41872, 43178}, {42014, 58608}, {43182, 60911}

X(60958) = pole of line {14100, 60949} wrt Feuerbach hyperbola
X(60958) = pole of line {6332, 56322} wrt dual conic of incircle
X(60958) = orthology center of the pedal triangle of X(8273) wrt Aguilera triangle
X(60958) = intersection, other than A, B, C, of circumconics {{A, B, C, X(57), X(3477)}}, {{A, B, C, X(63), X(1223)}}, {{A, B, C, X(142), X(42015)}}, {{A, B, C, X(1445), X(32008)}}
X(60958) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 9, 1445}, {7, 9, 60949}, {9, 142, 63}, {9, 20195, 60974}, {9, 36973, 60983}, {9, 57, 61024}, {9, 6173, 61005}, {9, 60937, 6172}, {9, 60955, 3929}, {9, 60964, 60966}, {9, 60965, 61006}, {9, 60990, 3219}, {9, 7308, 18230}, {63, 142, 60938}, {142, 61003, 7}, {144, 27065, 9}, {1212, 25878, 77}, {20195, 60974, 3306}, {60964, 60966, 8545}, {60996, 61024, 57}

X(60959) = X(2)X(7)∩X(4)X(11024)

Barycentrics    a^5-a^4*(b+c)-(b-c)^4*(b+c)+a*(b^2-c^2)^2+2*a^2*(b+c)*(b^2-6*b*c+c^2)-2*a^3*(b^2-4*b*c+c^2) : :

X(60959) lies on these lines: {2, 7}, {4, 11024}, {8, 5728}, {10, 10398}, {21, 59418}, {72, 11037}, {218, 37659}, {346, 25935}, {377, 36991}, {390, 19860}, {405, 962}, {442, 5817}, {443, 971}, {452, 516}, {474, 21151}, {495, 5815}, {497, 58608}, {954, 3616}, {1001, 5766}, {1005, 11495}, {1210, 5833}, {1260, 10578}, {1490, 17580}, {1698, 60923}, {1728, 19855}, {1750, 43182}, {1837, 2550}, {1864, 15587}, {2345, 25964}, {2478, 59385}, {2951, 50696}, {3062, 5177}, {3160, 34492}, {3488, 40587}, {3624, 60924}, {3729, 56937}, {3753, 35514}, {3826, 5825}, {3925, 60910}, {3945, 25930}, {4208, 6223}, {4295, 51090}, {4312, 12572}, {4326, 17784}, {4423, 60919}, {4461, 51972}, {4644, 25878}, {4648, 25067}, {4847, 30330}, {5084, 5805}, {5308, 26669}, {5436, 9785}, {5542, 8583}, {5554, 59413}, {5572, 36845}, {5686, 24987}, {5729, 9780}, {5732, 6904}, {5758, 5886}, {5762, 11108}, {5777, 17582}, {5779, 8728}, {5812, 17559}, {5942, 31994}, {6601, 10177}, {6675, 59381}, {6856, 38108}, {6857, 31658}, {6919, 38150}, {7367, 23618}, {9778, 13615}, {9779, 14022}, {10861, 37462}, {11038, 19861}, {15299, 19843}, {16053, 17183}, {16112, 25973}, {16408, 31657}, {16601, 24554}, {16853, 60922}, {16863, 59380}, {17169, 24557}, {17379, 26658}, {17527, 38107}, {17528, 60901}, {17554, 55109}, {17567, 38122}, {17668, 34919}, {20905, 31995}, {21031, 38057}, {24541, 60926}, {24982, 40333}, {25584, 26668}, {26540, 29611}, {27396, 58002}, {28827, 55096}, {34028, 55400}, {37249, 54445}, {37313, 52769}, {38059, 60895}, {38204, 60896}, {41228, 44547}, {50726, 51516}, {54425, 55432}

X(60959) = pole of line {329, 14100} wrt Feuerbach hyperbola
X(60959) = orthology center of the pedal triangle of X(8726) wrt Aguilera triangle
X(60959) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(329), X(23618)}}, {{A, B, C, X(1223), X(8232)}}
X(60959) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 61009, 9}, {2, 61012, 18230}, {7, 9, 329}, {9, 142, 8232}, {9, 52819, 144}, {9, 60950, 6172}, {9, 60972, 61009}, {9, 60982, 61003}, {9, 60987, 7}, {405, 5759, 52653}, {2550, 5809, 5175}, {5273, 60941, 60970}, {18230, 60996, 61017}, {60982, 61003, 20059}

X(60960) = X(2)X(7)∩X(44)X(673)

Barycentrics    a^4+b*(b-c)^2*c-4*a^3*(b+c)+a^2*(3*b^2+b*c+3*c^2) : :
X(60960) = -2*X[24692]+3*X[38052]

X(60960) lies on these lines: {2, 7}, {6, 51052}, {44, 673}, {45, 27475}, {65, 32024}, {190, 518}, {192, 51194}, {220, 7176}, {320, 16593}, {390, 3751}, {516, 1757}, {651, 14189}, {1001, 3758}, {1121, 36920}, {1156, 14197}, {1743, 53602}, {2099, 31169}, {2310, 52507}, {2550, 54280}, {2663, 4343}, {3000, 39341}, {3212, 30625}, {3243, 31302}, {3826, 17256}, {3923, 5223}, {4059, 32008}, {4389, 38186}, {4419, 36404}, {4480, 17738}, {4664, 42871}, {4724, 6006}, {5088, 5526}, {5686, 50314}, {5762, 36654}, {5850, 49768}, {16503, 17120}, {17261, 51058}, {17332, 24699}, {17334, 51150}, {17347, 47595}, {20072, 20533}, {24692, 38052}, {35102, 40872}, {36854, 55337}, {41325, 51190}, {42819, 46922}, {49704, 49783}, {49721, 51053}, {49748, 51002}, {50126, 50835}

X(60960) = midpoint of X(i) and X(j) for these {i,j}: {20072, 20533}
X(60960) = reflection of X(i) in X(j) for these {i,j}: {320, 16593}, {673, 44}
X(60960) = pole of line {100, 47762} wrt Yff parabola
X(60960) = orthology center of the pedal triangle of X(9441) wrt Aguilera triangle
X(60960) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(35167)}}, {{A, B, C, X(1223), X(17260)}}
X(60960) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 10436, 18230}, {9, 142, 17260}, {9, 44421, 1445}, {9, 60990, 21371}, {144, 17350, 9}, {672, 10025, 1447}

X(60961) = X(1)X(7955)∩X(2)X(7)

Barycentrics    (a+b-c)*(a-b+c)*(2*a^3+8*a*b*c-3*a^2*(b+c)+(b-c)^2*(b+c)) : :
X(60961) = -3*X[10861]+2*X[57284]

X(60961) lies on these lines: {1, 7955}, {2, 7}, {10, 60909}, {12, 38208}, {55, 43182}, {56, 51090}, {65, 5850}, {269, 4419}, {388, 4312}, {392, 4298}, {497, 3062}, {498, 38123}, {516, 3057}, {518, 13601}, {651, 3946}, {942, 5843}, {946, 60924}, {948, 4862}, {950, 971}, {954, 43177}, {956, 3671}, {1000, 28194}, {1001, 41426}, {1108, 17365}, {1145, 51782}, {1210, 5779}, {1278, 25719}, {1407, 4656}, {1418, 17334}, {1419, 3672}, {1420, 52653}, {1429, 3451}, {1456, 4353}, {1604, 24328}, {2256, 3668}, {2646, 43176}, {2801, 41558}, {3160, 33633}, {3304, 5542}, {3333, 41705}, {3476, 34628}, {3485, 59372}, {3487, 52027}, {3660, 58608}, {3663, 6180}, {3664, 43047}, {3674, 56530}, {4292, 5762}, {4295, 6766}, {4301, 8163}, {4321, 5698}, {4328, 4644}, {4416, 39126}, {4667, 7190}, {4848, 5223}, {4870, 51098}, {5083, 5572}, {5290, 5657}, {5543, 56043}, {5722, 60884}, {5853, 25722}, {6610, 17246}, {7175, 38855}, {7962, 54179}, {7988, 33994}, {9578, 59412}, {9612, 59386}, {9850, 12575}, {10592, 38172}, {10861, 57284}, {10895, 38151}, {11019, 60910}, {11372, 12053}, {11374, 59380}, {11375, 38054}, {12573, 17768}, {13405, 17613}, {13411, 31657}, {14100, 17625}, {14749, 43058}, {15803, 21168}, {15837, 43151}, {21446, 52803}, {21620, 60923}, {30424, 37567}, {30621, 45275}, {34867, 38859}, {43065, 58816}, {57282, 60922}

X(60961) = midpoint of X(i) and X(j) for these {i,j}: {20059, 60979}, {31391, 60919}, {7, 60936}
X(60961) = reflection of X(i) in X(j) for these {i,j}: {10106, 8581}, {41572, 60945}, {52819, 7}, {60883, 4298}, {61003, 61002}
X(60961) = X(i)-Dao conjugate of X(j) for these {i, j}: {20103, 41006}
X(60961) = pole of line {3676, 4105} wrt incircle
X(60961) = pole of line {10167, 11019} wrt Feuerbach hyperbola
X(60961) = pole of line {1, 31657} wrt dual conic of Yff parabola
X(60961) = orthology center of the pedal triangle of X(9957) wrt Aguilera triangle
X(60961) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(10307)}}, {{A, B, C, X(673), X(6692)}}, {{A, B, C, X(3306), X(31507)}}, {{A, B, C, X(3598), X(52803)}}, {{A, B, C, X(20059), X(56043)}}, {{A, B, C, X(27475), X(30827)}}
X(60961) = barycentric product X(i)*X(j) for these (i, j): {20103, 7}
X(60961) = barycentric quotient X(i)/X(j) for these (i, j): {20103, 8}
X(60961) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 12848, 60955}, {7, 142, 60993}, {7, 144, 57}, {7, 1445, 61022}, {7, 21617, 60980}, {7, 29007, 30379}, {7, 30275, 61020}, {7, 41563, 60938}, {7, 41572, 60945}, {7, 52819, 553}, {7, 60934, 9}, {7, 60937, 226}, {7, 60956, 60933}, {7, 60957, 60939}, {7, 60976, 60975}, {7, 60998, 60937}, {7, 61007, 4031}, {7, 8232, 6173}, {7, 8545, 142}, {7, 9, 60992}, {57, 144, 61014}, {57, 5316, 3911}, {516, 8581, 10106}, {527, 60945, 41572}, {527, 61002, 61003}, {1445, 60946, 60942}, {3663, 6180, 43035}, {20059, 60979, 527}, {29007, 30379, 6666}, {31391, 60919, 516}, {41572, 60945, 52819}, {60933, 60953, 7}, {60939, 60957, 61007}, {60942, 61022, 1445}, {60953, 60956, 61021}, {60953, 61021, 3982}, {60955, 60977, 12848}, {60988, 61015, 58433}

X(60962) = X(2)X(7)∩X(6)X(4887)

Barycentrics    4*a^2-3*(b-c)^2-a*(b+c) : :
X(60962) = -3*X[2]+7*X[7], -7*X[2550]+5*X[4668], X[3633]+7*X[4312], -5*X[3843]+7*X[5805], -11*X[5072]+7*X[5779], -X[5698]+3*X[59372], -7*X[5732]+5*X[17538], -7*X[5735]+X[33703], -7*X[5759]+11*X[21735], -3*X[10177]+4*X[58607], -8*X[12108]+7*X[31658], -X[14100]+2*X[61033] and many others

X(60962) lies on these lines: {2, 7}, {6, 4887}, {10, 5852}, {37, 4896}, {69, 4060}, {319, 50119}, {320, 2321}, {499, 41707}, {516, 1482}, {518, 3625}, {519, 18541}, {524, 53594}, {528, 34637}, {535, 14563}, {545, 3950}, {548, 5762}, {971, 3627}, {1001, 43180}, {1086, 16669}, {1100, 3663}, {1125, 17255}, {1266, 17364}, {1418, 16578}, {1449, 4346}, {1743, 17067}, {2325, 17298}, {2550, 4668}, {2551, 5586}, {3631, 4058}, {3633, 4312}, {3664, 16777}, {3671, 5857}, {3686, 42697}, {3689, 11246}, {3707, 17347}, {3755, 32857}, {3834, 59579}, {3843, 5805}, {3850, 5843}, {3879, 4440}, {3946, 4644}, {4000, 4902}, {4021, 49747}, {4029, 17300}, {4034, 52709}, {4035, 32939}, {4292, 12437}, {4295, 21627}, {4298, 5289}, {4363, 53598}, {4398, 50109}, {4409, 4718}, {4416, 7321}, {4419, 4888}, {4431, 17361}, {4454, 17296}, {4464, 50133}, {4480, 17234}, {4659, 21296}, {4675, 16675}, {4691, 5850}, {4715, 7263}, {4741, 4967}, {4757, 47745}, {4764, 49761}, {4795, 17323}, {4851, 17132}, {4912, 17243}, {5072, 5779}, {5542, 5625}, {5698, 59372}, {5732, 17538}, {5735, 33703}, {5759, 21735}, {5837, 10404}, {5845, 32455}, {6144, 50019}, {6601, 31507}, {6603, 10481}, {7222, 17272}, {7231, 17239}, {7232, 17355}, {7238, 17351}, {7271, 53996}, {7277, 50114}, {8581, 45288}, {10177, 58607}, {12053, 14450}, {12108, 31658}, {12690, 24473}, {14100, 61033}, {14893, 18482}, {15185, 17660}, {15254, 38054}, {15684, 31671}, {15712, 31657}, {17139, 17207}, {17231, 50118}, {17246, 46845}, {17313, 59585}, {17314, 28301}, {17317, 50090}, {17329, 24603}, {17334, 29571}, {17340, 31138}, {17344, 49727}, {17348, 28333}, {17668, 61030}, {18249, 28646}, {20257, 45751}, {21171, 30556}, {22312, 22327}, {23046, 60901}, {24391, 57282}, {24692, 49529}, {25557, 51090}, {28534, 30331}, {30340, 38316}, {31191, 48631}, {31672, 38335}, {32007, 41006}, {33067, 53663}, {34522, 58816}, {34919, 45834}, {35251, 42885}, {38037, 41705}, {38053, 60905}, {38123, 60912}, {38454, 43182}, {49163, 49184}, {49170, 60895}, {49684, 53601}, {50691, 52835}, {58188, 59418}

X(60962) = midpoint of X(i) and X(j) for these {i,j}: {15185, 31391}, {5735, 36996}, {6173, 60971}, {60963, 60984}, {60976, 60977}, {7, 60933}, {9, 20059}
X(60962) = reflection of X(i) in X(j) for these {i,j}: {1001, 43180}, {142, 7}, {144, 6666}, {14100, 61033}, {24393, 5880}, {3950, 17376}, {51090, 25557}, {60942, 142}, {60977, 61000}, {9, 60980}
X(60962) = complement of X(60977)
X(60962) = anticomplement of X(61000)
X(60962) = X(i)-Dao conjugate of X(j) for these {i, j}: {61000, 61000}
X(60962) = pole of line {23865, 39476} wrt circumcircle
X(60962) = pole of line {14100, 60980} wrt Feuerbach hyperbola
X(60962) = pole of line {1, 56998} wrt dual conic of Yff parabola
X(60962) = orthology center of the pedal triangle of X(10222) wrt Aguilera triangle
X(60962) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1445), X(31507)}}, {{A, B, C, X(3255), X(6666)}}, {{A, B, C, X(8545), X(45834)}}, {{A, B, C, X(15909), X(50573)}}, {{A, B, C, X(35595), X(56234)}}
X(60962) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4654, 56523}, {2, 60976, 60977}, {2, 60977, 61000}, {2, 7, 61020}, {7, 144, 6173}, {7, 1445, 60993}, {7, 18230, 59375}, {7, 41572, 60992}, {7, 52819, 61022}, {7, 60936, 226}, {7, 60956, 60937}, {7, 60975, 60955}, {7, 60984, 60933}, {7, 9, 60980}, {9, 142, 61001}, {9, 6173, 60996}, {9, 60933, 20059}, {142, 527, 60942}, {142, 60942, 60986}, {144, 6173, 6666}, {144, 60996, 9}, {527, 6666, 144}, {545, 17376, 3950}, {553, 5905, 3452}, {3630, 4726, 3625}, {3663, 17365, 4667}, {4644, 4862, 3946}, {4654, 9965, 5745}, {5745, 56523, 26065}, {6173, 60971, 527}, {6173, 6666, 142}, {6646, 50116, 5257}, {7228, 17345, 10}, {8545, 60968, 60994}, {17347, 24199, 3707}, {17361, 49722, 4431}, {18230, 27130, 60995}, {21454, 28609, 6692}, {26685, 59491, 2}, {35578, 45789, 17306}, {60933, 60963, 7}, {60933, 61020, 60976}, {60937, 60974, 61004}, {60953, 60990, 60964}, {60955, 60965, 8257}

X(60963) = X(1)X(28534)∩X(2)X(7)

Barycentrics    5*a^2-4*(b-c)^2-a*(b+c) : :
X(60963) = -X[2]+3*X[7], -X[376]+2*X[43177], -3*X[2550]+2*X[4669], -2*X[3534]+3*X[5732], -2*X[3845]+3*X[5805], -4*X[3860]+3*X[60901], -2*X[5223]+3*X[38097], -3*X[5759]+5*X[19708], -3*X[5779]+5*X[19709], -3*X[10177]+4*X[58560], -8*X[11812]+9*X[38122], -2*X[12100]+3*X[31657] and many others

X(60963) lies on these lines: {1, 28534}, {2, 7}, {6, 4902}, {30, 5735}, {69, 50119}, {200, 44785}, {320, 4659}, {376, 43177}, {516, 7967}, {518, 4677}, {519, 30424}, {528, 3243}, {535, 11529}, {545, 29573}, {551, 5698}, {903, 16834}, {954, 19704}, {971, 3830}, {1001, 37587}, {1022, 6008}, {1086, 16670}, {1266, 50129}, {1449, 4862}, {1699, 5851}, {1836, 3254}, {2550, 4669}, {3158, 5856}, {3247, 4888}, {3255, 10390}, {3337, 15297}, {3339, 11236}, {3340, 34605}, {3534, 5732}, {3671, 34610}, {3679, 5880}, {3680, 34749}, {3729, 17240}, {3829, 41555}, {3845, 5805}, {3860, 60901}, {3870, 5528}, {3875, 50133}, {4007, 21296}, {4034, 31995}, {4292, 34701}, {4310, 50294}, {4338, 34719}, {4346, 4667}, {4355, 15829}, {4364, 36834}, {4403, 53115}, {4419, 4896}, {4440, 17389}, {4454, 4873}, {4643, 49733}, {4644, 4887}, {4655, 48851}, {4675, 16676}, {4700, 52714}, {4715, 16833}, {4725, 17151}, {4745, 5850}, {4795, 49741}, {4851, 28297}, {4880, 5220}, {4912, 17313}, {5066, 5843}, {5223, 38097}, {5426, 17525}, {5438, 24470}, {5542, 47357}, {5759, 19708}, {5762, 8703}, {5779, 19709}, {5845, 8584}, {5852, 38052}, {6006, 6545}, {6594, 9352}, {6603, 20121}, {7174, 50301}, {7222, 53598}, {7228, 17272}, {7232, 17359}, {7238, 17284}, {7321, 17346}, {7982, 37430}, {8544, 36005}, {9814, 11235}, {10177, 58560}, {11112, 11523}, {11114, 11518}, {11160, 50099}, {11662, 15803}, {11812, 38122}, {12100, 31657}, {12101, 31672}, {12703, 54158}, {15534, 51194}, {15682, 36996}, {15693, 21153}, {15698, 21151}, {15701, 31658}, {15713, 38067}, {15726, 50865}, {16593, 36522}, {17251, 17345}, {17264, 17298}, {17296, 50107}, {17376, 28322}, {17487, 29582}, {17528, 54422}, {21314, 35110}, {22165, 47595}, {24231, 50303}, {24391, 50736}, {24393, 38092}, {25055, 25557}, {28204, 52682}, {29597, 31332}, {29600, 36911}, {30331, 51107}, {30340, 38314}, {30353, 36971}, {31138, 49721}, {31162, 60895}, {32857, 50080}, {34607, 41570}, {34638, 43181}, {38021, 54370}, {38025, 51090}, {38053, 51098}, {38057, 50834}, {38059, 50837}, {38073, 41106}, {38088, 51144}, {38186, 51195}, {40341, 50085}, {41099, 59386}, {42050, 58816}, {42697, 50095}, {42762, 44551}, {42871, 51097}, {50835, 51072}, {50839, 51092}, {50990, 50996}, {50991, 51151}, {50993, 50995}, {50997, 51185}, {51058, 53546}

X(60963) = midpoint of X(i) and X(j) for these {i,j}: {2, 60971}, {2094, 60956}, {6172, 20059}, {6173, 60933}, {7, 60984}
X(60963) = reflection of X(i) in X(j) for these {i,j}: {144, 60986}, {21153, 59380}, {376, 43177}, {3679, 5880}, {31162, 60895}, {34638, 43181}, {38316, 59372}, {47357, 5542}, {551, 43180}, {5698, 551}, {59389, 59386}, {59414, 59412}, {6172, 142}, {6173, 7}, {60933, 60984}, {60942, 60999}, {60977, 6172}, {60984, 60962}, {60986, 60980}, {9, 6173}
X(60963) = pole of line {3676, 28537} wrt incircle
X(60963) = pole of line {14100, 61020} wrt Feuerbach hyperbola
X(60963) = pole of line {28537, 30725} wrt Suppa-Cucoanes circle
X(60963) = orthology center of the pedal triangle of X(10247) wrt Aguilera triangle
X(60963) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3254), X(6172)}}, {{A, B, C, X(3255), X(18230)}}, {{A, B, C, X(10390), X(29007)}}, {{A, B, C, X(37787), X(55922)}}
X(60963) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 60971, 527}, {2, 60984, 60971}, {7, 12848, 60993}, {7, 144, 60980}, {7, 6172, 59375}, {7, 60952, 4654}, {7, 60956, 226}, {7, 60971, 2}, {7, 60975, 61022}, {7, 61021, 60982}, {7, 9, 61020}, {9, 6173, 38093}, {142, 20059, 60977}, {142, 527, 6172}, {142, 59375, 6173}, {142, 60977, 9}, {144, 59374, 60986}, {144, 60980, 20195}, {527, 60962, 60984}, {527, 60984, 60933}, {527, 60986, 144}, {527, 60999, 60942}, {3982, 9965, 25525}, {4654, 60952, 60953}, {4862, 17365, 1449}, {4888, 17276, 3247}, {6172, 59375, 142}, {6173, 20195, 59374}, {7222, 53598, 59772}, {17294, 49722, 4659}, {17768, 59372, 38316}, {18230, 50127, 60996}, {59375, 60984, 20059}, {60942, 60999, 61023}

X(60964) = X(2)X(7)∩X(55)X(17668)

Barycentrics    a*(a^4+4*a^2*b*c-2*a^3*(b+c)-(b-c)^2*(b^2+4*b*c+c^2)+2*a*(b^3+c^3)) : :

X(60964) lies on these lines: {2, 7}, {37, 53996}, {55, 17668}, {75, 28980}, {169, 17062}, {223, 16579}, {442, 5832}, {480, 61028}, {516, 6850}, {518, 12559}, {651, 24554}, {912, 54318}, {954, 5784}, {971, 1001}, {997, 42843}, {1125, 7330}, {1158, 10198}, {1444, 4877}, {1723, 4644}, {2257, 4667}, {2323, 7190}, {2346, 25722}, {2550, 10039}, {3243, 4861}, {3358, 6892}, {3475, 42012}, {3664, 8557}, {3692, 4659}, {3729, 28974}, {3731, 16578}, {3811, 42885}, {3812, 3927}, {3824, 11231}, {3869, 16133}, {3901, 5223}, {3925, 20588}, {3986, 58412}, {4293, 31435}, {4341, 6180}, {4364, 17073}, {4643, 16608}, {4657, 36949}, {5220, 31794}, {5248, 41854}, {5250, 9579}, {5259, 41694}, {5436, 18444}, {5542, 45636}, {5732, 6906}, {5735, 6937}, {5759, 6897}, {5762, 5880}, {5770, 9843}, {5805, 6842}, {5817, 6898}, {5843, 15297}, {6147, 28628}, {6510, 16777}, {6600, 15346}, {6706, 17351}, {6893, 52684}, {6940, 21153}, {6941, 38150}, {6977, 21151}, {7079, 38461}, {7284, 17561}, {8167, 58623}, {8581, 22759}, {9440, 24341}, {10177, 60910}, {11111, 21578}, {11372, 43161}, {11551, 28629}, {12514, 17768}, {13729, 59389}, {15185, 42014}, {15299, 38053}, {17043, 41312}, {17332, 21258}, {17528, 54286}, {17718, 41548}, {23058, 38948}, {23140, 37595}, {24328, 59681}, {25524, 31445}, {26635, 56418}, {28965, 51058}, {30284, 38316}, {37437, 52835}, {43173, 47042}

X(60964) = midpoint of X(i) and X(j) for these {i,j}: {9, 60937}
X(60964) = reflection of X(i) in X(j) for these {i,j}: {3927, 15481}, {61005, 9}, {7330, 60911}
X(60964) = pole of line {14100, 60974} wrt Feuerbach hyperbola
X(60964) = orthology center of the pedal triangle of X(10267) wrt Aguilera triangle
X(60964) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(41572)}}, {{A, B, C, X(1223), X(8257)}}, {{A, B, C, X(2346), X(41563)}}, {{A, B, C, X(3062), X(21617)}}, {{A, B, C, X(36101), X(55868)}}
X(60964) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 60970, 60968}, {9, 142, 8257}, {9, 36973, 61000}, {9, 527, 61005}, {9, 57, 60994}, {9, 6173, 1445}, {9, 60933, 63}, {9, 60937, 527}, {9, 60953, 60990}, {9, 60965, 60942}, {9, 60968, 60970}, {9, 60977, 60949}, {9, 60985, 37787}, {9, 61002, 55869}, {9, 61020, 60989}, {9, 8545, 60973}, {142, 61004, 9}, {6600, 15346, 15587}, {8545, 60958, 60966}, {41857, 60979, 61011}, {58463, 60980, 142}, {60944, 60996, 61012}, {60953, 60990, 60962}, {60968, 60970, 60974}, {60980, 60994, 57}, {60989, 61020, 60938}

X(60965) = X(2)X(7)∩X(40)X(12607)

Barycentrics    a*(a^4+12*a^2*b*c-2*a^3*(b+c)+2*a*(b+c)*(b^2-4*b*c+c^2)-(b-c)^2*(b^2+6*b*c+c^2)) : :
X(60965) = -3*X[3576]+4*X[42843], -2*X[11495]+3*X[47375]

X(60965) lies on these lines: {2, 7}, {40, 12607}, {200, 17668}, {322, 3729}, {480, 31391}, {516, 12667}, {518, 5693}, {529, 31393}, {728, 30806}, {758, 3577}, {971, 37531}, {1418, 34524}, {2136, 3146}, {2270, 21362}, {2324, 6180}, {2951, 5537}, {3062, 15733}, {3174, 15726}, {3243, 10384}, {3255, 41571}, {3358, 5843}, {3576, 42843}, {3692, 4488}, {3897, 38316}, {3951, 11530}, {4328, 55432}, {4659, 20895}, {4907, 8271}, {5223, 5903}, {5732, 33597}, {5762, 52684}, {5779, 24474}, {5832, 9612}, {5850, 54370}, {5853, 36991}, {5856, 34789}, {5857, 15298}, {5904, 41694}, {6769, 18239}, {6872, 37556}, {10860, 25568}, {10864, 12635}, {11495, 47375}, {11523, 12528}, {11531, 15347}, {15346, 58635}, {16133, 19860}, {17262, 44664}, {18839, 60910}, {21077, 37560}, {34690, 50836}, {34716, 51779}, {40979, 56020}, {41441, 53408}, {41562, 41863}

X(60965) = reflection of X(i) in X(j) for these {i,j}: {2951, 6600}, {60896, 21077}, {60950, 60942}, {60990, 9}, {9, 60973}
X(60965) = pole of line {649, 28473} wrt Bevan circle
X(60965) = orthology center of the pedal triangle of X(10306) wrt Aguilera triangle
X(60965) = intersection, other than A, B, C, of circumconics {{A, B, C, X(144), X(42470)}}, {{A, B, C, X(3062), X(8732)}}, {{A, B, C, X(3577), X(41572)}}
X(60965) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 56551, 60966}, {7, 6172, 61009}, {9, 3928, 60994}, {9, 527, 60990}, {9, 60953, 142}, {9, 60955, 8257}, {9, 60963, 60985}, {144, 20214, 60957}, {144, 5905, 41572}, {144, 60969, 60949}, {144, 8545, 9}, {329, 60934, 61002}, {527, 60942, 60950}, {5905, 41572, 60933}, {5905, 56545, 57}, {8257, 60962, 60955}, {8545, 60949, 60969}, {20059, 60935, 1445}, {29007, 60957, 63}, {60984, 61012, 60938}

X(60966) = X(2)X(7)∩X(190)X(322)

Barycentrics    a*(a^4+10*a^2*b*c-2*a^3*(b+c)+2*a*(b+c)*(b^2-4*b*c+c^2)-(b-c)^2*(b^2+4*b*c+c^2)) : :

X(60966) lies on these lines: {2, 7}, {8, 11372}, {72, 5779}, {78, 971}, {100, 2951}, {145, 10384}, {190, 322}, {200, 3062}, {241, 34524}, {269, 26669}, {306, 54113}, {480, 15726}, {516, 3436}, {518, 2098}, {651, 2324}, {728, 30695}, {936, 10861}, {960, 60909}, {1001, 20323}, {1088, 23618}, {1156, 34784}, {1158, 41705}, {1320, 51768}, {1376, 31391}, {1709, 21060}, {1766, 21362}, {2321, 5942}, {2476, 5833}, {3059, 16112}, {3177, 17261}, {3419, 60901}, {3729, 20895}, {3731, 24635}, {3868, 10398}, {3869, 4853}, {3870, 14100}, {3873, 30330}, {3876, 5785}, {3895, 11114}, {3916, 59381}, {3927, 51516}, {3940, 60884}, {3984, 41228}, {4345, 6762}, {4652, 31658}, {4666, 58608}, {4855, 5732}, {5250, 12527}, {5287, 55406}, {5728, 11520}, {5759, 52684}, {5762, 58798}, {5815, 12705}, {5817, 6734}, {5850, 15299}, {5852, 15297}, {6180, 25930}, {6735, 35514}, {6745, 43182}, {7190, 55432}, {7676, 47375}, {8581, 19861}, {9312, 25243}, {10392, 12649}, {10884, 51489}, {11681, 38052}, {12514, 51784}, {15657, 51567}, {15837, 35258}, {17296, 37781}, {18750, 56082}, {21077, 60923}, {21151, 27385}, {21616, 60924}, {22370, 41325}, {24703, 60919}, {25728, 30625}, {25734, 54107}, {27834, 36101}, {34035, 54414}, {36991, 57287}, {37424, 55104}, {43216, 50995}, {54358, 54444}

X(60966) = reflection of X(i) in X(j) for these {i,j}: {1445, 9}, {12649, 10392}, {60924, 21616}
X(60966) = anticomplement of X(60992)
X(60966) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 10307}
X(60966) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 10307}, {60992, 60992}
X(60966) = X(i)-Ceva conjugate of X(j) for these {i, j}: {16284, 200}
X(60966) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {14493, 56927}, {56026, 21285}
X(60966) = pole of line {1376, 14100} wrt Feuerbach hyperbola
X(60966) = pole of line {100, 53622} wrt Yff parabola
X(60966) = pole of line {651, 46392} wrt Hutson-Moses hyperbola
X(60966) = orthology center of the pedal triangle of X(10310) wrt Aguilera triangle
X(60966) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(46137)}}, {{A, B, C, X(57), X(6244)}}, {{A, B, C, X(144), X(56355)}}, {{A, B, C, X(200), X(45203)}}, {{A, B, C, X(527), X(42470)}}, {{A, B, C, X(1156), X(8732)}}, {{A, B, C, X(1320), X(20059)}}, {{A, B, C, X(3911), X(45824)}}, {{A, B, C, X(5435), X(36101)}}, {{A, B, C, X(6692), X(21446)}}
X(60966) = barycentric product X(i)*X(j) for these (i, j): {6244, 75}
X(60966) = barycentric quotient X(i)/X(j) for these (i, j): {1, 10307}, {6244, 1}
X(60966) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 56551, 60965}, {9, 527, 1445}, {9, 57, 61012}, {9, 60933, 8257}, {9, 60937, 2}, {9, 60942, 60949}, {9, 60964, 60958}, {9, 60965, 7}, {9, 60973, 8545}, {9, 60974, 60947}, {9, 60977, 60974}, {9, 60990, 37787}, {63, 908, 3306}, {144, 329, 60979}, {144, 60935, 9}, {200, 3062, 25722}, {329, 56545, 63}, {5223, 24644, 4853}, {8257, 60933, 60938}, {8545, 60958, 60964}, {15298, 51090, 5250}, {20059, 61012, 57}, {37787, 60957, 60990}, {56551, 60935, 908}, {60940, 61010, 41572}, {60942, 61003, 144}

X(60967) = X(2)X(7)∩X(30)X(390)

Barycentrics    (a+b-c)*(a-b+c)*(a^3-3*a^2*(b+c)-(b-c)^2*(b+c)+a*(3*b^2+14*b*c+3*c^2)) : :
X(60967) = 2*X[9579]+X[30332]

X(60967) lies on these lines: {2, 7}, {30, 390}, {56, 38025}, {85, 50107}, {376, 954}, {388, 528}, {519, 12560}, {551, 4321}, {948, 17301}, {971, 5049}, {1156, 3296}, {1210, 38075}, {1443, 29624}, {1996, 47374}, {2263, 48856}, {2550, 11237}, {2894, 50736}, {3085, 30424}, {3086, 43180}, {3475, 15726}, {3600, 8543}, {3649, 42014}, {3753, 5686}, {4292, 5766}, {4312, 10056}, {4323, 30318}, {4328, 50114}, {4552, 43983}, {4606, 43762}, {4664, 17079}, {4848, 38097}, {4870, 38053}, {5261, 17528}, {5274, 30311}, {5281, 30295}, {5290, 34619}, {5434, 47357}, {5698, 10404}, {5703, 8544}, {5714, 38073}, {5735, 37421}, {5880, 7080}, {6361, 36976}, {6604, 17346}, {7672, 50835}, {7674, 49719}, {7677, 16418}, {8581, 51099}, {9312, 50110}, {9579, 30332}, {10072, 38037}, {10394, 11036}, {10569, 11025}, {10587, 20084}, {10711, 45043}, {12573, 50836}, {13405, 30353}, {15933, 36991}, {17389, 53997}, {17757, 40333}, {24328, 24604}, {32007, 54280}, {34753, 38082}, {37582, 38067}, {49747, 52023}, {54831, 58809}

X(60967) = midpoint of X(i) and X(j) for these {i,j}: {4654, 60937}
X(60967) = reflection of X(i) in X(j) for these {i,j}: {7, 4654}
X(60967) = orthology center of the pedal triangle of X(10389) wrt Aguilera triangle
X(60967) = intersection, other than A, B, C, of circumconics {{A, B, C, X(142), X(54831)}}, {{A, B, C, X(527), X(3296)}}, {{A, B, C, X(1156), X(3305)}}, {{A, B, C, X(21454), X(43762)}}, {{A, B, C, X(30379), X(57826)}}
X(60967) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 61027, 8232}, {7, 18230, 60938}, {7, 226, 30275}, {7, 29007, 60939}, {7, 37787, 21454}, {7, 5226, 30379}, {7, 6172, 60932}, {7, 60937, 60934}, {7, 60946, 60975}, {7, 60995, 57}, {7, 60998, 60956}, {7, 8232, 8732}, {226, 60953, 7}, {4654, 60937, 527}, {6172, 60932, 12848}, {8545, 60932, 6172}, {26125, 40892, 2}

X(60968) = X(2)X(7)∩X(46)X(518)

Barycentrics    a*(a^4-(b-c)^4-2*a^2*b*c-2*a^3*(b+c)+2*a*(b^3+c^3)) : :

X(60968) lies on these lines: {2, 7}, {40, 3243}, {46, 518}, {84, 52835}, {219, 1418}, {269, 2323}, {516, 12116}, {920, 18223}, {971, 37532}, {1001, 3338}, {1086, 1723}, {1155, 6600}, {1444, 18164}, {1454, 8581}, {1697, 30284}, {1706, 59414}, {1709, 41555}, {1721, 57022}, {1768, 3254}, {2324, 51302}, {2900, 8730}, {2951, 5536}, {3333, 5248}, {3336, 5223}, {3358, 5735}, {3433, 40910}, {3474, 6601}, {3826, 41229}, {3873, 7676}, {4293, 6762}, {4321, 37550}, {4326, 54408}, {4413, 58635}, {4640, 58563}, {4666, 58607}, {4860, 58564}, {4862, 8557}, {4973, 21165}, {5119, 24473}, {5128, 18450}, {5709, 5732}, {5759, 26877}, {5770, 59389}, {5805, 24467}, {6067, 11246}, {6763, 38052}, {7183, 42309}, {7289, 20367}, {7330, 38150}, {8271, 9441}, {9841, 31730}, {10167, 11495}, {11038, 56288}, {11517, 15803}, {11551, 31435}, {12514, 38053}, {15298, 17700}, {15299, 16153}, {16370, 42819}, {17092, 53996}, {18444, 37551}, {21151, 59333}, {21153, 37534}, {21578, 34701}, {26921, 38122}, {30295, 30628}, {31658, 37612}, {38200, 57279}, {41570, 43151}, {43166, 52027}, {54370, 59386}, {55399, 56848}, {55437, 56418}

X(60968) = reflection of X(i) in X(j) for these {i,j}: {9, 1445}
X(60968) = pole of line {649, 42325} wrt Bevan circle
X(60968) = orthology center of the pedal triangle of X(10680) wrt Aguilera triangle
X(60968) = intersection, other than A, B, C, of circumconics {{A, B, C, X(57), X(38269)}}, {{A, B, C, X(1445), X(14377)}}, {{A, B, C, X(3062), X(41563)}}, {{A, B, C, X(10390), X(21617)}}, {{A, B, C, X(20078), X(36101)}}, {{A, B, C, X(41572), X(55922)}}
X(60968) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 3218, 60974}, {7, 60970, 60964}, {9, 57, 60985}, {9, 60955, 6173}, {9, 60963, 60937}, {63, 60938, 142}, {144, 23958, 60948}, {144, 60948, 8257}, {144, 8257, 9}, {553, 60938, 60955}, {3306, 60949, 6666}, {7289, 20367, 54420}, {8732, 9965, 61010}, {20059, 37787, 60973}, {60962, 60994, 8545}, {60964, 60974, 60970}

X(60969) = X(2)X(7)∩X(21)X(971)

Barycentrics    a*(a^4+3*a^2*b*c-2*a^3*(b+c)-(b-c)^2*(b^2+3*b*c+c^2)+2*a*(b^3+c^3)) : :

X(60969) lies on these lines: {2, 7}, {3, 10861}, {6, 24554}, {8, 15298}, {21, 971}, {37, 37659}, {40, 37161}, {45, 25878}, {55, 25722}, {78, 5785}, {100, 15587}, {190, 25001}, {377, 5759}, {392, 6912}, {394, 17019}, {404, 31658}, {405, 5779}, {442, 5762}, {443, 21168}, {452, 52684}, {474, 59381}, {516, 2475}, {518, 15988}, {651, 40937}, {673, 26538}, {954, 34772}, {958, 60909}, {1001, 10394}, {1212, 38459}, {1253, 24341}, {1444, 24557}, {1621, 14100}, {1654, 48381}, {1993, 54358}, {2269, 41845}, {2277, 26636}, {2323, 7269}, {2346, 15733}, {2476, 5805}, {2478, 5817}, {2550, 15296}, {2801, 39778}, {2886, 60919}, {2951, 35258}, {2975, 8581}, {3059, 3935}, {3062, 4512}, {3085, 15518}, {3146, 5250}, {3262, 28980}, {3294, 5088}, {3616, 15299}, {3692, 4461}, {3731, 25930}, {3868, 37224}, {3876, 19520}, {3945, 8557}, {3957, 30628}, {4188, 21153}, {4189, 5732}, {4190, 59418}, {4193, 38108}, {4208, 55104}, {4312, 56288}, {4416, 25935}, {4640, 31391}, {4643, 26540}, {4666, 30330}, {4881, 52769}, {5129, 5768}, {5141, 38150}, {5223, 19860}, {5235, 26011}, {5259, 41562}, {5284, 58608}, {5542, 24541}, {5554, 5686}, {5572, 29817}, {5731, 10864}, {5770, 17559}, {5819, 26998}, {5843, 6675}, {5845, 26543}, {6180, 24635}, {6224, 51768}, {6856, 59386}, {6857, 36996}, {6871, 59385}, {6872, 36991}, {6910, 21151}, {6986, 51489}, {6994, 55472}, {7191, 25885}, {7330, 17558}, {7483, 31657}, {7676, 17668}, {8728, 26878}, {10198, 60923}, {10398, 54392}, {10578, 42012}, {11108, 51516}, {11113, 60901}, {11114, 31672}, {13747, 38113}, {15254, 18450}, {15726, 35989}, {15823, 57283}, {16418, 60884}, {16503, 26639}, {16814, 25067}, {16865, 19861}, {17012, 26635}, {17256, 25000}, {17261, 25237}, {17277, 20905}, {17321, 26668}, {17331, 26531}, {17332, 25964}, {17532, 31671}, {17577, 18482}, {17619, 38179}, {20533, 26581}, {21061, 24050}, {24993, 26671}, {25005, 38057}, {25024, 25903}, {25091, 33761}, {25466, 60883}, {25728, 56244}, {25924, 47755}, {25985, 60879}, {26363, 60924}, {26877, 59380}, {32008, 38468}, {37584, 50741}, {38052, 60912}, {59476, 61035}

X(60969) = reflection of X(i) in X(j) for these {i,j}: {61024, 9}, {7, 60991}
X(60969) = pole of line {4640, 14100} wrt Feuerbach hyperbola
X(60969) = pole of line {100, 43344} wrt Yff parabola
X(60969) = orthology center of the pedal triangle of X(10902) wrt Aguilera triangle
X(60969) = intersection, other than A, B, C, of circumconics {{A, B, C, X(57), X(39391)}}, {{A, B, C, X(1156), X(21617)}}, {{A, B, C, X(1223), X(37787)}}, {{A, B, C, X(2320), X(20059)}}, {{A, B, C, X(2346), X(41572)}}, {{A, B, C, X(5745), X(36101)}}, {{A, B, C, X(41563), X(55920)}}
X(60969) = barycentric product X(i)*X(j) for these (i, j): {58699, 86}
X(60969) = barycentric quotient X(i)/X(j) for these (i, j): {58699, 10}
X(60969) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 61006, 61009}, {2, 9, 61012}, {7, 6172, 60950}, {7, 9, 60970}, {9, 142, 37787}, {9, 144, 3219}, {9, 527, 61024}, {9, 6173, 60994}, {9, 60937, 63}, {9, 60965, 60949}, {9, 60966, 61006}, {9, 60973, 6172}, {9, 61004, 29007}, {9, 8257, 60954}, {45, 25878, 26669}, {63, 60937, 20059}, {527, 60991, 7}, {954, 41228, 34772}, {3219, 27003, 55873}, {3219, 31019, 3218}, {6173, 60994, 60948}, {8545, 60949, 60965}, {15587, 15837, 100}, {18230, 60944, 9}, {36991, 52653, 6872}, {60935, 60981, 27065}, {60949, 60965, 144}, {60954, 60996, 8257}, {60981, 61004, 60935}

X(60970) = X(2)X(7)∩X(20)X(3358)

Barycentrics    a*(a^4+a^2*b*c-2*a^3*(b+c)-(b-c)^2*(b^2+b*c+c^2)+2*a*(b^3+c^3)) : :

X(60970) lies on these lines: {2, 7}, {3, 41228}, {6, 24635}, {8, 43161}, {20, 3358}, {21, 5728}, {40, 5775}, {46, 59412}, {55, 30628}, {71, 16560}, {72, 6986}, {78, 5223}, {100, 3059}, {149, 24389}, {190, 1229}, {191, 1210}, {193, 39273}, {220, 26669}, {239, 25241}, {241, 37659}, {348, 26668}, {390, 12649}, {391, 5942}, {411, 971}, {480, 3681}, {516, 6734}, {518, 2330}, {573, 7291}, {662, 911}, {673, 11683}, {938, 12514}, {954, 3868}, {958, 41712}, {993, 18412}, {1001, 3869}, {1155, 15587}, {1170, 1212}, {1442, 2323}, {1602, 12329}, {1621, 5572}, {1697, 20008}, {1713, 37076}, {1723, 5222}, {1760, 5819}, {1768, 43182}, {1776, 60910}, {1959, 16503}, {1998, 4326}, {2257, 17014}, {2346, 3957}, {2550, 27059}, {2801, 4996}, {2949, 6245}, {3101, 21367}, {3149, 5779}, {3177, 15657}, {3337, 38054}, {3436, 38057}, {3672, 8557}, {3683, 58608}, {3692, 29616}, {3715, 11678}, {3719, 37655}, {3876, 37282}, {3877, 42884}, {3927, 26878}, {3935, 6600}, {3939, 47487}, {4189, 7675}, {4293, 41229}, {4312, 5705}, {4335, 4414}, {4341, 25930}, {4359, 54107}, {4384, 45738}, {4416, 37781}, {4511, 52769}, {4512, 30330}, {4640, 14100}, {4652, 5732}, {4661, 47375}, {5057, 42356}, {5088, 16552}, {5204, 5220}, {5228, 24554}, {5248, 41861}, {5278, 18750}, {5703, 15298}, {5729, 11344}, {5730, 38031}, {5731, 9845}, {5759, 6836}, {5762, 6831}, {5768, 37423}, {5770, 6865}, {5773, 21061}, {5784, 35979}, {5785, 15803}, {5805, 6828}, {5809, 6872}, {5817, 6835}, {5843, 52265}, {5850, 6763}, {6067, 38454}, {6350, 33077}, {6594, 46685}, {6601, 36976}, {6855, 37532}, {6870, 54370}, {6918, 51516}, {6988, 24467}, {6991, 38108}, {7098, 15844}, {7183, 10004}, {7330, 50700}, {7676, 15733}, {8261, 11684}, {8581, 57283}, {9778, 42012}, {10394, 20846}, {10396, 11106}, {10398, 31424}, {10509, 59181}, {10861, 37229}, {11025, 29817}, {11349, 59681}, {11372, 54290}, {11415, 38037}, {11495, 25722}, {11682, 38316}, {12526, 54392}, {12573, 24987}, {12755, 39778}, {15829, 18467}, {16578, 52405}, {17011, 54358}, {17134, 24435}, {17277, 30807}, {17284, 59682}, {17316, 20110}, {17336, 20946}, {17615, 58635}, {17668, 30295}, {18231, 37550}, {18259, 30424}, {18482, 52269}, {18607, 34028}, {20171, 51052}, {21075, 38130}, {21390, 38379}, {25000, 37774}, {25101, 56244}, {25252, 28916}, {26001, 59646}, {26563, 26671}, {26635, 55437}, {26872, 32858}, {26877, 31657}, {27385, 35010}, {27396, 50995}, {28606, 55405}, {32024, 38468}, {35514, 54203}, {36991, 50695}, {37362, 60879}, {37555, 40968}, {38150, 60905}, {51058, 52134}

X(60970) = reflection of X(i) in X(j) for these {i,j}: {29007, 9}
X(60970) = anticomplement of X(21617)
X(60970) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 15909}
X(60970) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 15909}, {21617, 21617}
X(60970) = X(i)-Ceva conjugate of X(j) for these {i, j}: {20880, 3957}
X(60970) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {58974, 693}
X(60970) = pole of line {1621, 14100} wrt Feuerbach hyperbola
X(60970) = pole of line {284, 910} wrt Stammler hyperbola
X(60970) = pole of line {100, 53243} wrt Yff parabola
X(60970) = pole of line {333, 30807} wrt Wallace hyperbola
X(60970) = orthology center of the pedal triangle of X(11012) wrt Aguilera triangle
X(60970) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(55986)}}, {{A, B, C, X(57), X(3449)}}, {{A, B, C, X(144), X(55965)}}, {{A, B, C, X(226), X(36101)}}, {{A, B, C, X(911), X(1400)}}, {{A, B, C, X(1156), X(41572)}}, {{A, B, C, X(1170), X(52819)}}, {{A, B, C, X(2287), X(40869)}}, {{A, B, C, X(2346), X(21617)}}, {{A, B, C, X(5249), X(55987)}}, {{A, B, C, X(8232), X(42483)}}, {{A, B, C, X(21446), X(25525)}}, {{A, B, C, X(36100), X(54357)}}, {{A, B, C, X(37131), X(37797)}}
X(60970) = barycentric product X(i)*X(j) for these (i, j): {15931, 75}
X(60970) = barycentric quotient X(i)/X(j) for these (i, j): {1, 15909}, {15931, 1}
X(60970) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 9, 60969}, {9, 142, 60981}, {9, 144, 60935}, {9, 1445, 2}, {9, 18230, 27065}, {9, 3928, 60937}, {9, 527, 29007}, {9, 63, 144}, {9, 60933, 61004}, {9, 60947, 61026}, {9, 60949, 61006}, {9, 60968, 60964}, {9, 60973, 60944}, {9, 60994, 37787}, {9, 61005, 6172}, {9, 61024, 3219}, {9, 8257, 18230}, {9, 8545, 61025}, {63, 5744, 3218}, {142, 60948, 27003}, {142, 60989, 60948}, {573, 16551, 7291}, {2346, 15185, 3957}, {3218, 27065, 31019}, {3218, 60969, 7}, {3219, 61012, 9}, {5223, 21153, 78}, {5273, 60941, 60959}, {6600, 34784, 3935}, {6666, 61003, 908}, {8545, 60990, 20059}, {11495, 42014, 25722}, {12514, 15299, 52653}, {20059, 61025, 8545}, {59491, 60979, 142}, {60943, 61010, 31053}, {60944, 60957, 60973}, {60964, 60974, 60968}, {60994, 61024, 61012}

X(60971) = X(2)X(7)∩X(8)X(49722)

Barycentrics    11*a^2-7*(b-c)^2-4*a*(b+c) : :
X(60971) = -2*X[2]+3*X[7], -3*X[390]+4*X[51071], -4*X[551]+5*X[30340], -3*X[673]+4*X[36525], -6*X[2550]+5*X[51072], -6*X[3243]+5*X[51092], -4*X[3830]+3*X[36991], -3*X[4312]+X[4677], -4*X[4745]+3*X[5223], -4*X[5066]+3*X[5779], -6*X[5542]+5*X[51105], -9*X[5686]+10*X[51066] and many others

X(60971) lies on these lines: {2, 7}, {8, 49722}, {390, 51071}, {516, 50839}, {518, 50789}, {528, 12630}, {551, 30340}, {673, 36525}, {971, 15682}, {2550, 51072}, {2801, 50864}, {3241, 28534}, {3243, 51092}, {3534, 5762}, {3543, 5735}, {3679, 30424}, {3829, 30311}, {3830, 36991}, {3845, 5843}, {4312, 4677}, {4313, 57006}, {4323, 34610}, {4346, 50114}, {4421, 30295}, {4440, 50129}, {4454, 17294}, {4460, 17364}, {4488, 17264}, {4644, 17395}, {4669, 5850}, {4715, 36588}, {4745, 5223}, {4902, 37681}, {5066, 5779}, {5308, 49742}, {5542, 51105}, {5543, 42050}, {5686, 51066}, {5698, 38314}, {5732, 15697}, {5759, 8703}, {5805, 41099}, {5817, 19709}, {5845, 15534}, {5851, 9812}, {5880, 53620}, {5936, 7222}, {7229, 17345}, {8236, 15678}, {8543, 11194}, {8584, 51190}, {10109, 38107}, {10304, 43177}, {10394, 24473}, {11001, 36996}, {11038, 50836}, {11540, 38111}, {11812, 38065}, {12100, 21151}, {15693, 31657}, {15701, 59380}, {15713, 59381}, {15719, 21168}, {16668, 17301}, {16674, 17392}, {17295, 21296}, {17314, 28322}, {17346, 31995}, {19708, 59418}, {20073, 29575}, {22165, 50996}, {25055, 43180}, {31671, 33699}, {32087, 50119}, {34627, 52682}, {36620, 56933}, {37429, 54206}, {38024, 51090}, {38052, 50834}, {38054, 50837}, {38086, 51144}, {41106, 59386}, {47595, 50990}, {50095, 52709}, {50736, 54422}, {50840, 51098}, {50991, 50995}, {50993, 51151}, {50997, 59405}, {51110, 59372}, {51143, 51191}, {51150, 51185}

X(60971) = midpoint of X(i) and X(j) for these {i,j}: {20059, 60984}, {6172, 60976}
X(60971) = reflection of X(i) in X(j) for these {i,j}: {144, 6173}, {10394, 24473}, {2, 60963}, {30332, 3241}, {3543, 5735}, {3679, 30424}, {34627, 52682}, {5817, 51514}, {6172, 7}, {6173, 60962}, {60905, 551}, {60946, 31164}, {60957, 6172}, {60977, 60986}, {60984, 60933}, {7, 60984}
X(60971) = orthology center of the pedal triangle of X(11224) wrt Aguilera triangle
X(60971) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 60984, 60963}, {7, 20059, 60976}, {7, 60946, 5226}, {144, 6173, 61023}, {144, 60962, 7}, {144, 61023, 6172}, {527, 31164, 60946}, {527, 6172, 60957}, {527, 6173, 144}, {527, 60933, 60984}, {527, 60962, 6173}, {527, 60963, 2}, {527, 60986, 60977}, {6172, 59374, 18230}, {6173, 60996, 59374}, {6173, 61023, 60996}, {20059, 60984, 527}

X(60972) = X(2)X(7)∩X(10)X(5729)

Barycentrics    2*a^5-3*a^4*(b+c)-(b-c)^4*(b+c)-2*a^3*(b^2-6*b*c+c^2)+4*a^2*(b+c)*(b^2-4*b*c+c^2) : :
X(60972) = -3*X[46916]+2*X[61028]

X(60972) lies on these lines: {2, 7}, {10, 5729}, {30, 51489}, {72, 12577}, {405, 4301}, {442, 38216}, {474, 43177}, {516, 3753}, {519, 5728}, {528, 950}, {529, 12573}, {551, 954}, {1056, 5223}, {1125, 6068}, {1156, 24982}, {2325, 25935}, {2550, 10392}, {3487, 38024}, {3664, 25067}, {3679, 10398}, {3686, 25001}, {4326, 34607}, {4667, 25930}, {4679, 36971}, {5084, 5735}, {5087, 33558}, {5436, 5766}, {5603, 21168}, {5715, 38073}, {5759, 28194}, {5817, 10175}, {5825, 40333}, {5850, 10176}, {5853, 7671}, {5880, 8582}, {6259, 17528}, {6745, 8255}, {6916, 54135}, {9711, 47510}, {9859, 10394}, {14100, 34612}, {15006, 34611}, {16284, 17346}, {17355, 25964}, {17532, 38076}, {19860, 36976}, {20103, 61035}, {25606, 41166}, {30424, 58798}, {37271, 41561}, {38454, 40998}, {43035, 55432}, {46916, 61028}, {49736, 58608}, {50107, 51972}, {50742, 59418}, {59389, 59412}

X(60972) = midpoint of X(i) and X(j) for these {i,j}: {14100, 34612}, {6172, 60932}
X(60972) = reflection of X(i) in X(j) for these {i,j}: {34611, 15006}, {49736, 58608}
X(60972) = pole of line {1, 61035} wrt dual conic of Yff parabola
X(60972) = orthology center of the pedal triangle of X(11227) wrt Aguilera triangle
X(60972) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 25525, 60995}, {9, 52819, 61003}, {9, 60982, 329}, {9, 60987, 226}, {144, 9776, 60953}, {5316, 61021, 52457}, {6172, 60932, 527}, {18230, 30275, 30827}, {60959, 61009, 9}

X(60973) = X(2)X(7)∩X(19)X(21362)

Barycentrics    a*(a^4+8*a^2*b*c-2*a^3*(b+c)+2*a*(b+c)*(b^2-3*b*c+c^2)-(b-c)^2*(b^2+4*b*c+c^2)) : :
X(60973) = -X[2951]+3*X[47375]

X(60973) lies on these lines: {2, 7}, {19, 21362}, {119, 37826}, {190, 20930}, {269, 16578}, {390, 10935}, {480, 17668}, {495, 5857}, {516, 6256}, {518, 1351}, {519, 18540}, {528, 31672}, {651, 34492}, {920, 41707}, {971, 37700}, {990, 23693}, {1001, 24928}, {1156, 30628}, {1158, 21077}, {1387, 34647}, {1706, 5828}, {1709, 25568}, {1721, 3939}, {1836, 20588}, {2310, 8271}, {2550, 10827}, {2951, 47375}, {3062, 3174}, {3243, 40269}, {3257, 18041}, {3262, 3729}, {3811, 40263}, {5220, 50193}, {5696, 41694}, {5698, 15298}, {5732, 37403}, {5734, 6762}, {5761, 7330}, {5762, 37406}, {5804, 24391}, {5850, 60911}, {5852, 5886}, {5853, 5881}, {6180, 53996}, {6259, 12607}, {6594, 30353}, {6600, 15726}, {10860, 59584}, {11236, 51362}, {12665, 37569}, {15185, 60910}, {15346, 58634}, {15733, 16112}, {16139, 17768}, {20085, 51786}, {28534, 35460}, {30330, 61033}, {31844, 35341}, {35251, 43178}, {40587, 44663}, {42843, 59787}, {43166, 54135}, {45206, 54113}

X(60973) = midpoint of X(i) and X(j) for these {i,j}: {144, 61010}, {3062, 3174}, {9, 60965}
X(60973) = reflection of X(i) in X(j) for these {i,j}: {60974, 9}, {60990, 60994}
X(60973) = pole of line {23865, 39227} wrt circumcircle
X(60973) = pole of line {8257, 11502} wrt Feuerbach hyperbola
X(60973) = orthology center of the pedal triangle of X(11248) wrt Aguilera triangle
X(60973) = intersection, other than A, B, C, of circumconics {{A, B, C, X(144), X(34894)}}, {{A, B, C, X(3062), X(30379)}}, {{A, B, C, X(3306), X(37203)}}, {{A, B, C, X(8257), X(23618)}}, {{A, B, C, X(31018), X(56234)}}
X(60973) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 61012, 60985}, {9, 144, 61005}, {9, 36973, 60942}, {9, 60933, 1445}, {9, 60937, 142}, {9, 60968, 37787}, {9, 60977, 63}, {9, 60985, 61012}, {9, 60989, 60947}, {9, 60990, 60994}, {9, 8545, 60964}, {144, 29007, 9}, {144, 61010, 527}, {144, 61025, 61024}, {527, 60994, 60990}, {20059, 37787, 60968}, {29007, 56551, 144}, {29007, 61024, 61025}, {60944, 60957, 60970}, {60954, 60976, 3218}, {60984, 61026, 60948}, {60985, 61012, 8257}, {60990, 60994, 60974}

X(60974) = X(2)X(7)∩X(3)X(518)

Barycentrics    a*(a^4-2*a^3*(b+c)-(b-c)^2*(b^2+c^2)+2*a*(b^3+c^3)) : :
X(60974) = -3*X[165]+X[3174], -X[6601]+3*X[24477]

X(60974) lies on these lines: {1, 21059}, {2, 7}, {3, 518}, {6, 37597}, {19, 16551}, {40, 5768}, {46, 2550}, {55, 15185}, {77, 2323}, {100, 34784}, {104, 6282}, {165, 3174}, {210, 37270}, {219, 241}, {277, 37650}, {284, 1444}, {390, 10936}, {411, 12669}, {443, 38057}, {480, 20588}, {516, 1158}, {519, 3587}, {528, 12515}, {573, 7289}, {583, 38186}, {673, 1760}, {758, 18443}, {920, 5698}, {942, 1001}, {958, 37544}, {971, 6985}, {993, 30329}, {1155, 3059}, {1214, 55405}, {1253, 8271}, {1376, 40659}, {1466, 41712}, {1467, 12526}, {1602, 40910}, {1621, 11025}, {1706, 5775}, {1723, 4000}, {1766, 16560}, {1768, 2951}, {2245, 47595}, {2257, 3946}, {2324, 16578}, {2346, 3873}, {2900, 7411}, {2975, 7672}, {2999, 4284}, {3243, 3601}, {3336, 38052}, {3338, 6857}, {3419, 34695}, {3474, 42012}, {3553, 25065}, {3640, 18460}, {3641, 18458}, {3651, 5732}, {3652, 5805}, {3663, 8557}, {3666, 54358}, {3681, 35977}, {3692, 17296}, {3740, 37271}, {3826, 5791}, {3869, 7677}, {3875, 25241}, {3916, 5728}, {4293, 24393}, {4319, 57022}, {4343, 4414}, {4420, 18450}, {4640, 5572}, {4652, 7675}, {4858, 45738}, {4880, 30274}, {4996, 12755}, {5057, 7678}, {5088, 21384}, {5119, 34744}, {5220, 37582}, {5223, 6763}, {5228, 40937}, {5248, 20116}, {5250, 11518}, {5686, 6904}, {5708, 15254}, {5731, 6762}, {5735, 6845}, {5755, 5845}, {5759, 6899}, {5762, 37356}, {5773, 17134}, {5817, 6896}, {5850, 37534}, {5852, 37612}, {5856, 13226}, {5857, 5880}, {6224, 34716}, {6601, 24477}, {6847, 12704}, {6849, 7330}, {6989, 21077}, {6990, 38150}, {7291, 54420}, {7676, 30628}, {8580, 58677}, {8666, 37531}, {8726, 21153}, {8730, 11495}, {9940, 26921}, {10167, 47387}, {10202, 42843}, {10398, 54432}, {10857, 47375}, {10980, 58607}, {11194, 24929}, {11523, 18444}, {12443, 52797}, {12513, 31793}, {12573, 37550}, {12610, 24316}, {14523, 21002}, {15348, 43182}, {15481, 37545}, {15487, 36808}, {15837, 17603}, {15934, 42819}, {16410, 45120}, {16547, 24590}, {16572, 52542}, {17080, 34028}, {17092, 37659}, {17348, 44664}, {17668, 42014}, {18607, 45126}, {20875, 37581}, {21151, 26877}, {21255, 59682}, {21370, 24310}, {21578, 34610}, {24474, 42842}, {24609, 59405}, {25722, 30295}, {25930, 52405}, {27174, 46885}, {27484, 37274}, {28534, 31671}, {30625, 38468}, {31926, 46884}, {32578, 42449}, {35976, 41228}, {37433, 52835}, {37500, 50995}, {41573, 54408}

X(60974) = midpoint of X(i) and X(j) for these {i,j}: {3358, 5709}, {7, 60950}, {9, 60990}
X(60974) = reflection of X(i) in X(j) for these {i,j}: {60973, 9}, {9, 60994}
X(60974) = complement of X(61010)
X(60974) = X(i)-Dao conjugate of X(j) for these {i, j}: {218, 3870}
X(60974) = pole of line {3309, 23865} wrt circumcircle
X(60974) = pole of line {14100, 60964} wrt Feuerbach hyperbola
X(60974) = pole of line {284, 4228} wrt Stammler hyperbola
X(60974) = pole of line {522, 24562} wrt Steiner inellipse
X(60974) = pole of line {333, 32024} wrt Wallace hyperbola
X(60974) = pole of line {1, 60991} wrt dual conic of Yff parabola
X(60974) = orthology center of the pedal triangle of X(11249) wrt Aguilera triangle
X(60974) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(21617)}}, {{A, B, C, X(7), X(44178)}}, {{A, B, C, X(57), X(3433)}}, {{A, B, C, X(104), X(8732)}}, {{A, B, C, X(142), X(7131)}}, {{A, B, C, X(226), X(39273)}}, {{A, B, C, X(284), X(40131)}}, {{A, B, C, X(672), X(39943)}}, {{A, B, C, X(673), X(1708)}}, {{A, B, C, X(908), X(42470)}}, {{A, B, C, X(1156), X(41563)}}, {{A, B, C, X(1445), X(54236)}}, {{A, B, C, X(3062), X(41572)}}, {{A, B, C, X(5249), X(21446)}}, {{A, B, C, X(5905), X(36101)}}, {{A, B, C, X(24029), X(53888)}}
X(60974) = barycentric product X(i)*X(j) for these (i, j): {37578, 75}
X(60974) = barycentric quotient X(i)/X(j) for these (i, j): {37578, 1}
X(60974) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 60948, 60985}, {2, 7, 60991}, {7, 3218, 60968}, {7, 60950, 527}, {9, 20195, 60958}, {9, 3928, 60990}, {9, 63, 61005}, {9, 60933, 8545}, {9, 60937, 61004}, {9, 60977, 60966}, {9, 60989, 1445}, {57, 63, 55869}, {63, 55871, 3219}, {63, 60989, 8257}, {144, 37787, 9}, {144, 8732, 52457}, {219, 241, 53996}, {3218, 5744, 57}, {3218, 60970, 7}, {3306, 60958, 20195}, {3358, 5709, 516}, {5745, 60945, 142}, {6762, 37551, 12437}, {16551, 20367, 19}, {18607, 55399, 45126}, {60948, 61024, 2}, {60954, 60957, 60935}, {60962, 61004, 60937}, {60968, 60970, 60964}, {60990, 60994, 60973}

X(60975) = X(2)X(7)∩X(65)X(3146)

Barycentrics    (a+b-c)*(a-b+c)*(5*a^3-a*(b-c)^2-7*a^2*(b+c)+3*(b-c)^2*(b+c)) : :

X(60975) lies on these lines: {2, 7}, {56, 30340}, {65, 3146}, {175, 60877}, {196, 6994}, {279, 4644}, {348, 4747}, {390, 2099}, {484, 60923}, {497, 36971}, {516, 18421}, {938, 5735}, {954, 37106}, {1319, 11038}, {1449, 36640}, {1737, 38158}, {3091, 5729}, {3160, 4667}, {3339, 9814}, {3340, 30332}, {3361, 43180}, {3600, 12635}, {3621, 61030}, {3671, 60905}, {4312, 18391}, {4321, 4511}, {4346, 5228}, {4454, 6604}, {4461, 56927}, {4659, 32003}, {4896, 51302}, {5122, 21151}, {5173, 7671}, {5220, 5261}, {5223, 51782}, {5252, 50835}, {5265, 25557}, {5281, 8255}, {5542, 13462}, {5696, 12432}, {5698, 11106}, {5759, 24929}, {5762, 6987}, {5779, 6843}, {5784, 56999}, {5843, 6826}, {5851, 13273}, {5856, 14151}, {5880, 37161}, {6354, 37666}, {6827, 60922}, {6844, 59386}, {6858, 51516}, {6872, 17097}, {6882, 51514}, {6954, 59380}, {7319, 55922}, {7672, 15733}, {8543, 16865}, {9533, 47386}, {10392, 51792}, {10398, 59385}, {10590, 41700}, {11036, 11662}, {11545, 38149}, {12528, 37544}, {14986, 60895}, {15932, 60912}, {17014, 22464}, {23839, 34371}, {24328, 38859}, {24712, 56933}, {29353, 52510}, {30282, 59418}, {30295, 35986}, {36996, 50701}, {38092, 40663}, {40333, 41712}, {47374, 50562}, {51423, 52653}

X(60975) = reflection of X(i) in X(j) for these {i,j}: {144, 60997}, {60998, 7}, {7, 60982}, {9814, 30424}
X(60975) = orthology center of the pedal triangle of X(11529) wrt Aguilera triangle
X(60975) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(279), X(6173)}}, {{A, B, C, X(2982), X(3929)}}, {{A, B, C, X(3928), X(55922)}}, {{A, B, C, X(5744), X(55937)}}, {{A, B, C, X(5745), X(34919)}}, {{A, B, C, X(6172), X(7319)}}, {{A, B, C, X(8545), X(17097)}}, {{A, B, C, X(25525), X(34917)}}, {{A, B, C, X(30275), X(43762)}}
X(60975) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 30379, 59375}, {7, 41563, 8232}, {7, 527, 60998}, {7, 52819, 60939}, {7, 5435, 6173}, {7, 6172, 226}, {7, 60932, 21454}, {7, 60941, 142}, {7, 60946, 60967}, {7, 60951, 12848}, {7, 60957, 60937}, {7, 60976, 60961}, {9, 6173, 58463}, {144, 60984, 5905}, {226, 61007, 6172}, {527, 60997, 144}, {1708, 60937, 60981}, {8232, 41563, 61006}, {12848, 30275, 37787}, {21454, 60984, 7}, {30275, 37787, 2}, {52819, 61021, 57}, {60953, 60987, 30275}

X(60976) = X(2)X(7)∩X(8)X(5852)

Barycentrics    9*a^2-5*(b-c)^2-4*a*(b+c) : :
X(60976) = -6*X[2]+7*X[7], -7*X[390]+8*X[3635], -8*X[548]+7*X[5759], -20*X[3843]+21*X[59385], -8*X[3850]+7*X[5779], -7*X[4312]+5*X[4668], -8*X[4361]+9*X[36588], -8*X[4691]+7*X[5223], -22*X[5072]+21*X[5817], -3*X[5686]+4*X[30424], -15*X[8236]+16*X[15570], -3*X[11038]+2*X[60905] and many others

X(60976) lies on circumconic {{A, B, C, X(3255), X(38093)}} and on these lines: {2, 7}, {8, 5852}, {320, 4488}, {390, 3635}, {516, 3633}, {518, 4764}, {548, 5759}, {971, 33703}, {1657, 5762}, {3086, 41707}, {3161, 17241}, {3625, 5850}, {3627, 5843}, {3723, 4419}, {3843, 59385}, {3850, 5779}, {4312, 4668}, {4361, 36588}, {4364, 28626}, {4402, 20072}, {4409, 5845}, {4416, 52709}, {4431, 4454}, {4440, 32108}, {4480, 4869}, {4643, 5936}, {4644, 16884}, {4655, 5772}, {4691, 5223}, {4887, 37681}, {4912, 17314}, {5072, 5817}, {5222, 16671}, {5308, 16677}, {5686, 30424}, {5839, 28333}, {7229, 17239}, {8236, 15570}, {9780, 17329}, {9812, 51463}, {11038, 60905}, {12812, 38107}, {15712, 21151}, {16593, 52885}, {16666, 17276}, {16672, 17365}, {17233, 21296}, {17345, 29611}, {17347, 31995}, {17538, 36996}, {17768, 30332}, {21735, 59418}, {30340, 51090}, {31391, 34784}, {32455, 51190}, {38024, 50840}, {38111, 45760}, {38335, 60884}, {43177, 58188}

X(60976) = reflection of X(i) in X(j) for these {i,j}: {144, 60933}, {34784, 31391}, {6172, 60971}, {60957, 7}, {60977, 60962}, {7, 20059}
X(60976) = anticomplement of X(60977)
X(60976) = X(i)-Dao conjugate of X(j) for these {i, j}: {60977, 60977}
X(60976) = pole of line {14100, 59374} wrt Feuerbach hyperbola
X(60976) = orthology center of the pedal triangle of X(11531) wrt Aguilera triangle
X(60976) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 144, 61000}, {2, 17236, 56522}, {2, 17350, 31266}, {2, 27065, 30867}, {2, 5273, 27184}, {2, 55868, 3662}, {2, 56520, 894}, {2, 5745, 24627}, {2, 59491, 27002}, {7, 20059, 60971}, {7, 41563, 5435}, {7, 527, 60957}, {7, 6172, 60996}, {7, 60983, 142}, {7, 9, 59374}, {142, 144, 60983}, {142, 60983, 18230}, {144, 18230, 6172}, {144, 20059, 60933}, {144, 60933, 7}, {527, 60962, 60977}, {2094, 17484, 5328}, {3218, 60973, 60954}, {5435, 26840, 31224}, {5435, 61023, 61020}, {5905, 28610, 5226}, {18230, 60957, 144}, {30379, 60983, 59375}, {33116, 35466, 1999}, {59374, 60971, 60984}, {60933, 61020, 60962}, {60942, 60999, 9}, {60962, 60977, 2}

X(60977) = X(1)X(5852)∩X(2)X(7)

Barycentrics    5*a^2-2*(b-c)^2-3*a*(b+c) : :
X(60977) = -9*X[2]+7*X[7], -8*X[548]+7*X[5732], -7*X[2550]+8*X[4691], -7*X[3243]+8*X[3635], -10*X[3843]+7*X[5735], -8*X[3850]+7*X[5805], -5*X[4668]+7*X[5223], -22*X[5072]+21*X[38150], -7*X[5759]+5*X[17538], -8*X[12108]+7*X[31657], -20*X[12812]+21*X[38108], -6*X[14893]+7*X[60901] and many others

X(60977) lies on these lines: {1, 5852}, {2, 7}, {44, 4862}, {45, 4888}, {69, 4480}, {72, 56998}, {190, 17240}, {191, 15296}, {193, 4464}, {220, 21314}, {319, 3729}, {320, 25728}, {516, 3625}, {518, 3633}, {524, 55998}, {528, 50838}, {535, 36922}, {545, 17151}, {548, 5732}, {971, 1657}, {1001, 19538}, {1086, 3973}, {1317, 34716}, {1371, 30556}, {1372, 30557}, {1449, 4021}, {1707, 17725}, {1743, 17276}, {1836, 61032}, {2321, 4488}, {2325, 21296}, {2550, 4691}, {2951, 5528}, {3062, 38454}, {3243, 3635}, {3247, 4644}, {3339, 28646}, {3627, 5762}, {3630, 5845}, {3640, 30432}, {3641, 30431}, {3663, 16670}, {3664, 16676}, {3671, 28647}, {3678, 41852}, {3686, 4454}, {3707, 31995}, {3731, 17365}, {3843, 5735}, {3850, 5805}, {3875, 20072}, {3879, 20073}, {3951, 9579}, {3986, 36834}, {4034, 4416}, {4304, 11523}, {4312, 5220}, {4315, 15829}, {4361, 4912}, {4363, 28633}, {4452, 4700}, {4512, 37703}, {4643, 7227}, {4668, 5223}, {4715, 17262}, {4741, 17286}, {4851, 28333}, {4859, 16885}, {4887, 37650}, {4902, 17278}, {4929, 28566}, {5072, 38150}, {5252, 5857}, {5719, 31424}, {5722, 54422}, {5759, 17538}, {5839, 17132}, {6006, 48082}, {6180, 52405}, {6762, 30305}, {6763, 23708}, {7174, 24695}, {7228, 16832}, {7231, 17332}, {9578, 11684}, {11552, 41229}, {12108, 31657}, {12812, 38108}, {14893, 60901}, {15254, 59372}, {15481, 38052}, {15492, 31183}, {15601, 24231}, {15684, 60884}, {15712, 21153}, {16236, 44663}, {16570, 33101}, {16667, 17246}, {16669, 49747}, {16673, 49742}, {16688, 21320}, {17243, 36911}, {17255, 29598}, {17272, 17293}, {17284, 17345}, {17298, 17336}, {17308, 17329}, {17328, 32101}, {17344, 49721}, {17394, 31332}, {21168, 43177}, {21735, 36996}, {25734, 32859}, {30424, 38057}, {31391, 40659}, {31671, 38335}, {32455, 51194}, {36991, 50691}, {37654, 53594}, {38025, 50837}, {38036, 60911}, {38097, 50834}, {38113, 45760}, {38154, 52682}, {38316, 51090}, {42871, 50836}, {53598, 54389}, {58678, 61028}

X(60977) = midpoint of X(i) and X(j) for these {i,j}: {144, 60957}
X(60977) = reflection of X(i) in X(j) for these {i,j}: {20059, 142}, {3243, 5698}, {31391, 40659}, {4312, 5220}, {5735, 5779}, {60933, 9}, {60962, 61000}, {60963, 6172}, {60971, 60986}, {60976, 60962}, {7, 60942}, {9, 144}
X(60977) = complement of X(60976)
X(60977) = anticomplement of X(60962)
X(60977) = pole of line {14100, 20195} wrt Feuerbach hyperbola
X(60977) = pole of line {522, 27115} wrt Steiner circumellipse
X(60977) = pole of line {100, 21115} wrt Yff parabola
X(60977) = pole of line {4162, 34958} wrt Suppa-Cucoanes circle
X(60977) = orthology center of the pedal triangle of X(12702) wrt Aguilera triangle
X(60977) = intersection, other than A, B, C, of circumconics {{A, B, C, X(80), X(41563)}}, {{A, B, C, X(3254), X(20059)}}, {{A, B, C, X(20195), X(23618)}}, {{A, B, C, X(23958), X(36101)}}, {{A, B, C, X(42470), X(56551)}}
X(60977) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 31266, 17353}, {2, 60962, 61020}, {2, 60976, 60962}, {7, 144, 60942}, {7, 20195, 6173}, {7, 61006, 6666}, {7, 9, 20195}, {9, 38093, 18230}, {9, 60990, 60989}, {63, 17484, 5219}, {142, 20059, 60963}, {142, 527, 20059}, {142, 6172, 9}, {144, 20059, 6172}, {144, 20078, 41563}, {144, 60957, 527}, {144, 60976, 61000}, {144, 60979, 36973}, {329, 3928, 30827}, {527, 60962, 60976}, {527, 60986, 60971}, {3218, 31142, 31190}, {3929, 5905, 25525}, {4312, 5220, 38200}, {4718, 6144, 3633}, {5219, 17484, 28609}, {5325, 56523, 2}, {5698, 5850, 3243}, {5735, 5779, 59389}, {6172, 20059, 142}, {6646, 50127, 17306}, {6666, 60942, 61006}, {12848, 60961, 60955}, {17333, 31300, 10436}, {17781, 20078, 57}, {18230, 60980, 38093}, {18230, 60984, 60980}, {20059, 60963, 60933}, {20195, 60933, 7}, {33800, 59375, 144}, {41572, 60937, 60982}, {41572, 60946, 60937}, {52819, 60934, 60953}

X(60978) = X(2)X(7)∩X(4)X(43178)

Barycentrics    a^4*(b+c)-(b-c)^4*(b+c)-6*a^2*b*c*(b+c)+2*a*(b^2-c^2)^2-2*a^3*(b^2-b*c+c^2) : :

X(60978) lies on these lines: {2, 7}, {4, 43178}, {10, 41570}, {72, 25557}, {218, 4675}, {405, 1770}, {442, 8287}, {516, 1006}, {943, 1125}, {950, 5528}, {971, 6881}, {997, 38053}, {1001, 30384}, {1086, 16601}, {1737, 3826}, {2550, 3488}, {2886, 10177}, {2900, 26040}, {3586, 38052}, {3742, 41555}, {3925, 15733}, {4197, 10394}, {4294, 5436}, {4413, 47387}, {5220, 13407}, {5550, 5766}, {5696, 41859}, {5698, 12609}, {5732, 6826}, {5735, 55108}, {5759, 6878}, {5784, 8728}, {5805, 6883}, {5817, 6877}, {5832, 50204}, {6067, 58564}, {6706, 26932}, {6827, 38150}, {6832, 54370}, {6843, 38123}, {6854, 21151}, {6882, 51489}, {6911, 38122}, {6987, 28150}, {6992, 59385}, {6993, 36991}, {7671, 33108}, {8164, 38057}, {8226, 15726}, {10393, 37462}, {12047, 15254}, {15556, 24564}, {17197, 17201}, {17529, 44547}, {18391, 38200}, {18482, 28459}, {20291, 36023}, {20328, 23840}, {24199, 37788}, {25006, 61030}, {25076, 29571}, {25375, 45281}, {25993, 37805}, {26725, 60885}, {30329, 54288}, {41548, 58634}, {55104, 60895}

X(60978) = midpoint of X(i) and X(j) for these {i,j}: {7, 3219}
X(60978) = reflection of X(i) in X(j) for these {i,j}: {5249, 142}
X(60978) = complement of X(60981)
X(60978) = X(i)-complementary conjugate of X(j) for these {i, j}: {34917, 141}
X(60978) = pole of line {17056, 43065} wrt Kiepert hyperbola
X(60978) = pole of line {1, 61030} wrt dual conic of Yff parabola
X(60978) = orthology center of the pedal triangle of X(13151) wrt Aguilera triangle
X(60978) = intersection, other than A, B, C, of circumconics {{A, B, C, X(943), X(37787)}}, {{A, B, C, X(3254), X(5249)}}
X(60978) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 37787, 6666}, {7, 3219, 527}, {9, 142, 60991}, {9, 38093, 25525}, {9, 6173, 61011}, {142, 527, 5249}, {142, 6666, 21617}, {3826, 8255, 61028}, {12848, 61008, 226}, {18230, 60950, 9}

X(60979) = X(2)X(7)∩X(72)X(5762)

Barycentrics    2*a^5-2*a*b*(b-c)^2*c-3*a^4*(b+c)-(b-c)^4*(b+c)-2*a^3*(b^2-b*c+c^2)+4*a^2*(b^3+c^3) : :

X(60979) lies on these lines: {2, 7}, {20, 54228}, {21, 51090}, {69, 45738}, {72, 5762}, {78, 5759}, {84, 41705}, {219, 22464}, {224, 5732}, {306, 54107}, {377, 4312}, {390, 11682}, {516, 3869}, {518, 10950}, {662, 2327}, {960, 60883}, {1071, 5843}, {1847, 60431}, {2346, 41570}, {2478, 10398}, {2894, 18406}, {2911, 17276}, {2951, 44447}, {2975, 5542}, {3059, 38454}, {3062, 10431}, {3174, 36976}, {3177, 17364}, {3419, 31671}, {3436, 5223}, {3553, 4419}, {3664, 24635}, {3668, 37659}, {3868, 5850}, {3875, 20110}, {3916, 31657}, {3927, 60922}, {4001, 18750}, {4292, 5692}, {4304, 4867}, {4350, 34526}, {4416, 20236}, {4652, 21151}, {4847, 15909}, {4855, 59418}, {5046, 10392}, {5220, 5832}, {5587, 54398}, {5698, 7675}, {5728, 39772}, {5779, 58798}, {5784, 17768}, {5805, 6734}, {5845, 43216}, {5856, 46685}, {7411, 43182}, {10307, 56101}, {10527, 38036}, {10884, 36996}, {11020, 40998}, {11372, 11415}, {11684, 30424}, {12514, 60923}, {14100, 16465}, {15254, 38061}, {15299, 41012}, {17347, 20927}, {18655, 24435}, {20223, 26872}, {21060, 44425}, {21078, 22003}, {21616, 54302}, {22128, 34028}, {22768, 42843}, {24703, 60910}, {24982, 41712}, {25006, 36971}, {25719, 40903}, {26540, 59646}, {27385, 31658}, {27529, 38130}, {28194, 36922}, {37112, 54290}, {43177, 60885}, {55109, 57279}, {56382, 58325}

X(60979) = reflection of X(i) in X(j) for these {i,j}: {144, 61003}, {20059, 60961}, {41572, 9}, {57287, 41228}, {60883, 960}, {7, 61002}
X(60979) = anticomplement of X(52819)
X(60979) = X(i)-Dao conjugate of X(j) for these {i, j}: {52819, 52819}
X(60979) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {13404, 7}, {43344, 693}
X(60979) = pole of line {2886, 14100} wrt Feuerbach hyperbola
X(60979) = pole of line {284, 2272} wrt Stammler hyperbola
X(60979) = orthology center of the pedal triangle of X(14110) wrt Aguilera triangle
X(60979) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(10307), X(54366)}}, {{A, B, C, X(15909), X(52819)}}
X(60979) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 144, 63}, {7, 60981, 142}, {9, 527, 41572}, {63, 908, 54357}, {142, 60970, 59491}, {144, 329, 60966}, {144, 60935, 60942}, {144, 61003, 17781}, {516, 41228, 57287}, {527, 60961, 20059}, {527, 61002, 7}, {3452, 61014, 61012}, {4312, 5785, 377}, {6172, 60943, 9}, {17950, 27420, 25019}, {26651, 40905, 9436}, {36973, 60977, 144}, {52457, 60950, 1445}, {60964, 61011, 41857}

X(60980) = X(2)X(7)∩X(6)X(4896)

Barycentrics    2*a^2-3*(b-c)^2+a*(b+c) : :
X(60980) = 3*X[2]+5*X[7], 3*X[354]+X[17668], -X[382]+5*X[5805], -5*X[2550]+X[3632], 7*X[3528]+5*X[5735], -X[3529]+5*X[5732], -3*X[3817]+X[16112], -7*X[3851]+15*X[38107], 11*X[3855]+5*X[36996], -X[3950]+3*X[17313], X[4312]+3*X[38053], -13*X[5079]+5*X[5779] and many others

X(60980) lies on these lines: {1, 57000}, {2, 7}, {6, 4896}, {10, 7232}, {37, 4887}, {75, 4060}, {192, 29623}, {320, 3686}, {354, 17668}, {382, 5805}, {516, 550}, {518, 3626}, {519, 7263}, {528, 33812}, {545, 59585}, {546, 971}, {551, 17323}, {594, 31138}, {903, 17317}, {946, 7171}, {954, 19537}, {1001, 5267}, {1086, 1100}, {1125, 17235}, {1266, 17300}, {2321, 17298}, {2325, 17234}, {2550, 3632}, {3000, 55340}, {3008, 16669}, {3036, 51782}, {3244, 4780}, {3247, 4346}, {3528, 5735}, {3529, 5732}, {3530, 5762}, {3629, 50013}, {3634, 15481}, {3644, 29601}, {3663, 4675}, {3671, 5289}, {3689, 41548}, {3739, 7238}, {3817, 16112}, {3826, 5850}, {3834, 7228}, {3851, 38107}, {3855, 36996}, {3879, 48627}, {3912, 7321}, {3950, 17313}, {3986, 17255}, {4000, 4667}, {4007, 52709}, {4021, 17392}, {4292, 57002}, {4295, 51723}, {4312, 38053}, {4328, 53996}, {4355, 28629}, {4363, 21255}, {4395, 4856}, {4398, 29574}, {4402, 32093}, {4419, 4902}, {4431, 17297}, {4480, 17263}, {4545, 17360}, {4644, 4859}, {4648, 4862}, {4657, 4758}, {4659, 4869}, {4670, 48631}, {4681, 29606}, {4686, 49765}, {4700, 17364}, {4796, 5845}, {4851, 17133}, {4867, 11551}, {4909, 17395}, {4967, 17288}, {4982, 20090}, {5079, 5779}, {5083, 17620}, {5199, 21258}, {5220, 38204}, {5253, 16133}, {5572, 18240}, {5575, 54424}, {5759, 10299}, {5795, 10404}, {5832, 56997}, {5843, 35018}, {5856, 35023}, {6006, 59630}, {6067, 44785}, {6147, 12436}, {6154, 10427}, {6601, 45834}, {6603, 58816}, {7222, 17284}, {7231, 17359}, {8544, 50244}, {10177, 31391}, {10481, 34522}, {10521, 17062}, {10980, 24386}, {11008, 51194}, {11036, 12437}, {11037, 21627}, {11038, 20057}, {12053, 60925}, {12611, 33709}, {13369, 18483}, {14269, 31672}, {14869, 31658}, {15587, 61030}, {15681, 31671}, {15687, 18482}, {15700, 38065}, {15720, 38122}, {15726, 58564}, {15733, 33558}, {15841, 24389}, {16675, 17276}, {17023, 48629}, {17050, 45751}, {17118, 29594}, {17132, 17243}, {17197, 17207}, {17231, 49727}, {17233, 50119}, {17239, 49733}, {17241, 49722}, {17262, 29600}, {17265, 59579}, {17267, 50118}, {17273, 24603}, {17275, 31139}, {17296, 31995}, {17332, 31211}, {17334, 25072}, {17340, 41141}, {17345, 34824}, {17361, 50095}, {17373, 50099}, {17380, 39704}, {17396, 31313}, {17443, 53546}, {18726, 53538}, {20121, 42050}, {20533, 29625}, {20583, 51195}, {21171, 30557}, {21620, 54286}, {24237, 34830}, {24467, 60911}, {24475, 33815}, {24693, 49505}, {25440, 42885}, {27475, 39707}, {28358, 53543}, {28639, 49741}, {29604, 48632}, {31418, 41865}, {31507, 34919}, {34641, 51100}, {34747, 51099}, {38030, 43175}, {38071, 60901}, {38454, 43151}, {40341, 47595}, {49135, 52835}, {50688, 59385}, {51514, 55863}, {52553, 60578}, {58587, 59746}

X(60980) = midpoint of X(i) and X(j) for these {i,j}: {1001, 30424}, {4851, 53594}, {43175, 52682}, {5542, 5880}, {5805, 43177}, {60933, 60942}, {60963, 60986}, {61004, 61021}, {7, 142}, {7263, 17376}, {9, 60962}, {946, 60896}
X(60980) = reflection of X(i) in X(j) for these {i,j}: {15481, 3634}, {5572, 58607}, {6666, 142}, {61000, 6666}, {61033, 58563}, {9, 58433}
X(60980) = complement of X(60942)
X(60980) = pole of line {23865, 48343} wrt circumcircle
X(60980) = pole of line {14100, 60962} wrt Feuerbach hyperbola
X(60980) = pole of line {522, 26985} wrt Steiner inellipse
X(60980) = pole of line {1, 3255} wrt dual conic of Yff parabola
X(60980) = orthology center of the pedal triangle of X(15178) wrt Aguilera triangle
X(60980) = intersection, other than A, B, C, of circumconics {{A, B, C, X(144), X(43971)}}, {{A, B, C, X(1445), X(45834)}}, {{A, B, C, X(2185), X(3929)}}, {{A, B, C, X(3254), X(6666)}}, {{A, B, C, X(5435), X(55090)}}, {{A, B, C, X(8545), X(31507)}}, {{A, B, C, X(27475), X(31231)}}, {{A, B, C, X(39707), X(40719)}}
X(60980) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 60933, 60942}, {2, 7, 60933}, {7, 144, 60963}, {7, 1445, 61021}, {7, 18230, 60984}, {7, 21617, 60961}, {7, 30275, 60937}, {7, 30379, 52819}, {7, 5249, 61002}, {7, 59375, 61020}, {7, 60988, 41572}, {7, 60992, 60945}, {7, 60996, 20059}, {7, 61008, 60936}, {7, 61013, 60952}, {7, 9, 60962}, {9, 60933, 60957}, {9, 60996, 61001}, {57, 60964, 60994}, {142, 527, 6666}, {142, 60942, 2}, {142, 60962, 9}, {142, 60964, 58463}, {142, 60986, 20195}, {142, 61001, 60996}, {142, 6666, 60999}, {144, 20195, 60986}, {527, 6666, 61000}, {553, 5249, 5745}, {1086, 3664, 3946}, {3631, 4739, 3626}, {3662, 50116, 5750}, {3739, 7238, 53598}, {3834, 7228, 17355}, {4000, 4888, 4667}, {4654, 9776, 3452}, {4851, 53594, 17133}, {5249, 26842, 553}, {5542, 5880, 5853}, {5805, 59380, 43177}, {6173, 60963, 59374}, {6173, 61020, 7}, {7263, 17376, 519}, {9965, 41867, 5325}, {15733, 58563, 61033}, {18230, 60984, 60977}, {20195, 59374, 142}, {20195, 60963, 144}, {30340, 59412, 3243}, {30424, 38054, 1001}, {38030, 52682, 43175}, {38093, 60977, 18230}, {41572, 60988, 3911}, {60933, 60942, 527}, {60993, 60996, 33800}, {60996, 61001, 58433}

X(60981) = X(2)X(7)∩X(21)X(662)

Barycentrics    a*(a^4+a^2*b*c-2*a^3*(b+c)+2*a*(b+c)*(b^2+c^2)-(b-c)^2*(b^2+3*b*c+c^2)) : :

X(60981) lies on these lines: {2, 7}, {10, 2894}, {20, 54370}, {21, 662}, {100, 61028}, {190, 20880}, {191, 30424}, {219, 7269}, {224, 16865}, {377, 5698}, {392, 53055}, {405, 10394}, {484, 51100}, {516, 6839}, {518, 8539}, {651, 1212}, {954, 3940}, {960, 8543}, {971, 1006}, {993, 18450}, {997, 5785}, {1001, 4511}, {1004, 15346}, {1213, 5829}, {1332, 4861}, {1442, 6510}, {1443, 24635}, {1621, 15733}, {1698, 5735}, {1723, 3945}, {1728, 17554}, {2346, 3059}, {2550, 36976}, {2801, 5251}, {3294, 22003}, {3683, 7411}, {3692, 32087}, {3758, 31269}, {3868, 5220}, {3925, 38454}, {3957, 61030}, {4197, 5880}, {4208, 12514}, {4304, 51768}, {4313, 31435}, {4423, 11020}, {4640, 30295}, {4679, 10883}, {5223, 54318}, {5248, 5696}, {5250, 30332}, {5284, 10177}, {5308, 8557}, {5440, 37306}, {5506, 43177}, {5603, 54203}, {5686, 15298}, {5729, 11108}, {5732, 37106}, {5759, 6826}, {5762, 6881}, {5779, 6883}, {5805, 6829}, {5817, 6827}, {6690, 61035}, {6763, 43180}, {6830, 38108}, {6843, 59385}, {6854, 21168}, {6877, 59386}, {6878, 36996}, {6905, 31658}, {6911, 59381}, {6987, 18540}, {6993, 40333}, {7291, 54324}, {7676, 15587}, {8544, 31424}, {9440, 21039}, {9799, 52684}, {10122, 25542}, {10176, 60885}, {10861, 37300}, {11031, 17123}, {11036, 41229}, {11372, 28150}, {15296, 38057}, {15837, 58634}, {17277, 37788}, {17862, 40435}, {18389, 41700}, {19843, 60926}, {19854, 60895}, {19855, 55109}, {19862, 54302}, {24703, 30311}, {24953, 25557}, {25590, 59682}, {26066, 30312}, {26563, 43762}, {28459, 60901}, {31144, 31640}, {31391, 41695}, {31393, 50839}, {34784, 41711}, {34919, 55960}, {37105, 43178}, {38092, 54286}, {47375, 55920}, {50701, 59418}

X(60981) = midpoint of X(i) and X(j) for these {i,j}: {144, 17483}
X(60981) = reflection of X(i) in X(j) for these {i,j}: {3219, 9}, {7, 5249}
X(60981) = anticomplement of X(60978)
X(60981) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 34917}
X(60981) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 34917}, {60978, 60978}
X(60981) = pole of line {1776, 14100} wrt Feuerbach hyperbola
X(60981) = pole of line {284, 1155} wrt Stammler hyperbola
X(60981) = pole of line {100, 20219} wrt Yff parabola
X(60981) = pole of line {333, 30806} wrt Wallace hyperbola
X(60981) = orthology center of the pedal triangle of X(15931) wrt Aguilera triangle
X(60981) = intersection, other than A, B, C, of circumconics {{A, B, C, X(21), X(527)}}, {{A, B, C, X(226), X(1156)}}, {{A, B, C, X(662), X(56543)}}, {{A, B, C, X(1400), X(34068)}}, {{A, B, C, X(2346), X(52819)}}, {{A, B, C, X(8545), X(55960)}}, {{A, B, C, X(12848), X(55920)}}, {{A, B, C, X(32008), X(37787)}}, {{A, B, C, X(36101), X(54357)}}
X(60981) = barycentric quotient X(i)/X(j) for these (i, j): {1, 34917}
X(60981) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 144, 60987}, {2, 30275, 60996}, {2, 52457, 61008}, {2, 9, 37787}, {7, 61023, 5273}, {7, 9, 61024}, {9, 142, 60970}, {9, 20195, 60994}, {9, 3305, 61023}, {9, 527, 3219}, {9, 60937, 60949}, {9, 60953, 3929}, {9, 60958, 18230}, {9, 60964, 144}, {9, 60966, 60983}, {9, 60973, 61006}, {9, 6666, 61012}, {9, 8545, 6172}, {142, 60970, 60948}, {142, 60979, 7}, {142, 60989, 27003}, {144, 17483, 527}, {144, 60987, 60951}, {219, 24554, 7269}, {1001, 42014, 7671}, {1708, 60937, 60975}, {5784, 15254, 21}, {6172, 8545, 56551}, {8257, 36973, 12848}, {27003, 60970, 60989}, {27065, 60935, 9}, {27065, 60969, 60935}, {37659, 40937, 1442}, {60935, 60969, 61004}, {60935, 61004, 29007}, {60937, 60949, 60957}

X(60982) = X(2)X(7)∩X(36)X(954)

Barycentrics    (a+b-c)*(a-b+c)*(3*a^3-4*a^2*(b+c)+2*(b-c)^2*(b+c)-a*(b+c)^2) : :

X(60982) lies on these lines: {1, 34917}, {2, 7}, {4, 30424}, {36, 954}, {40, 54158}, {65, 12625}, {72, 4355}, {165, 8255}, {218, 14564}, {279, 4667}, {354, 36971}, {405, 60905}, {481, 6459}, {482, 6460}, {516, 3488}, {528, 18421}, {674, 52510}, {942, 5735}, {943, 41870}, {948, 16670}, {950, 18221}, {971, 18541}, {1174, 58809}, {1418, 4888}, {1441, 4034}, {1449, 3668}, {1490, 24470}, {1743, 52023}, {3158, 41570}, {3243, 3476}, {3254, 41556}, {3333, 60895}, {3339, 5880}, {3361, 25557}, {3487, 43180}, {3576, 5542}, {3586, 4312}, {3671, 5436}, {4007, 56927}, {4298, 11523}, {4315, 51099}, {4321, 5856}, {4419, 58816}, {4454, 32098}, {4644, 10481}, {4659, 6604}, {4675, 51302}, {5220, 5290}, {5221, 15346}, {5528, 18801}, {5665, 34919}, {5696, 14054}, {5708, 5715}, {5729, 9612}, {5762, 18443}, {5766, 30340}, {5784, 37544}, {5845, 52511}, {5851, 9814}, {6610, 21314}, {7271, 17365}, {7274, 17276}, {7671, 9580}, {7672, 61030}, {8544, 10393}, {9579, 10394}, {10202, 51489}, {10382, 11246}, {10389, 36976}, {10521, 26036}, {11038, 13384}, {12560, 60883}, {15299, 18393}, {16554, 39063}, {20121, 34578}, {31794, 52682}, {37240, 44785}, {37249, 60885}, {38200, 40663}, {51764, 60878}

X(60982) = midpoint of X(i) and X(j) for these {i,j}: {7, 60975}
X(60982) = reflection of X(i) in X(j) for these {i,j}: {60953, 7}, {9, 60987}
X(60982) = pole of line {5427, 43042} wrt Adams circle
X(60982) = pole of line {284, 32578} wrt Stammler hyperbola
X(60982) = orthology center of the pedal triangle of X(15934) wrt Aguilera triangle
X(60982) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(34917)}}, {{A, B, C, X(4), X(6172)}}, {{A, B, C, X(63), X(55922)}}, {{A, B, C, X(1434), X(6173)}}, {{A, B, C, X(5273), X(34919)}}, {{A, B, C, X(5665), X(8545)}}
X(60982) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 12848, 226}, {7, 21454, 61022}, {7, 41563, 41857}, {7, 41572, 60937}, {7, 527, 60953}, {7, 57, 6173}, {7, 60932, 57}, {7, 60939, 142}, {7, 60967, 3982}, {7, 60975, 527}, {7, 60992, 61020}, {7, 61021, 60963}, {7, 8545, 4654}, {9, 6173, 25525}, {9, 60963, 61011}, {9, 61011, 28609}, {9, 61020, 60991}, {142, 60950, 9}, {226, 52819, 12848}, {553, 61021, 7}, {1445, 61008, 31231}, {3911, 30275, 38093}, {4312, 5728, 52835}, {4654, 61007, 8545}, {8545, 60951, 61007}, {20059, 60959, 61003}, {21454, 61022, 60955}, {31231, 61008, 20195}, {41572, 60937, 60977}, {60945, 61022, 21454}

X(60983) = X(2)X(7)∩X(8)X(15481)

Barycentrics    9*a^2-(b-c)^2-8*a*(b+c) : :
X(60983) = -12*X[2]+5*X[7], -X[8]+8*X[15481], 2*X[382]+5*X[5759], 5*X[390]+2*X[3632], -8*X[546]+15*X[5817], 2*X[550]+5*X[5779], -X[962]+8*X[60911], 5*X[1156]+2*X[6154], 2*X[3244]+5*X[5223], -X[3529]+15*X[21168], -8*X[3530]+15*X[59381], -17*X[3544]+10*X[5805] and many others

X(60983) lies on circumconic {{A, B, C, X(39709), X(51351)}} and on these lines: {2, 7}, {8, 15481}, {190, 32087}, {193, 29619}, {344, 31722}, {382, 5759}, {390, 3632}, {391, 4431}, {516, 50688}, {518, 20057}, {546, 5817}, {550, 5779}, {954, 16866}, {960, 6049}, {962, 60911}, {971, 3528}, {1001, 17543}, {1156, 6154}, {3161, 17233}, {3244, 5223}, {3529, 21168}, {3530, 59381}, {3544, 5805}, {3626, 5686}, {3629, 50995}, {3631, 51144}, {3672, 3973}, {3679, 50840}, {3707, 4461}, {3715, 9778}, {3851, 5762}, {3855, 59385}, {3986, 28626}, {4323, 5234}, {4402, 20073}, {4419, 15492}, {4488, 17277}, {4686, 51052}, {5220, 20050}, {5222, 16885}, {5232, 59579}, {5308, 16814}, {5692, 40269}, {5698, 59413}, {5766, 50241}, {5843, 14869}, {5850, 15808}, {6223, 26878}, {7064, 9309}, {7319, 21677}, {9780, 17768}, {9785, 41229}, {10299, 31658}, {12630, 20054}, {15688, 60884}, {15720, 21151}, {15828, 17272}, {17239, 54389}, {17241, 21296}, {17332, 29611}, {17335, 31995}, {17347, 29627}, {18516, 35514}, {20583, 51191}, {25722, 58635}, {30331, 34747}, {30340, 38059}, {31657, 55863}, {31994, 32024}, {32086, 32088}, {34641, 50836}, {34784, 58678}, {38130, 41705}, {39709, 42318}, {40333, 60905}, {40341, 51190}

X(60983) = reflection of X(i) in X(j) for these {i,j}: {7, 60996}
X(60983) = pole of line {14100, 61023} wrt Feuerbach hyperbola
X(60983) = pole of line {333, 41926} wrt Wallace hyperbola
X(60983) = orthology center of the pedal triangle of X(16192) wrt Aguilera triangle
X(60983) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 144, 60933}, {7, 9, 61023}, {9, 144, 18230}, {9, 36973, 60958}, {9, 3929, 60947}, {9, 60942, 2}, {9, 60949, 37787}, {9, 60964, 27065}, {9, 60965, 3305}, {9, 60966, 60981}, {9, 60977, 60986}, {9, 61005, 61012}, {9, 61024, 60954}, {142, 144, 60976}, {142, 60976, 7}, {144, 60933, 60957}, {144, 61000, 6172}, {144, 61006, 61000}, {3161, 54280, 32099}, {4488, 17277, 52709}, {5686, 51090, 30332}, {6172, 18230, 144}, {6172, 60957, 60942}, {6666, 20059, 59374}, {18230, 60976, 142}, {45789, 61000, 20059}, {59375, 60976, 30379}, {60934, 60947, 5435}

X(60984) = X(1)X(50738)∩X(2)X(7)

Barycentrics    7*a^2-5*(b-c)^2-2*a*(b+c) : :
X(60984) = -X[8]+4*X[30424], -4*X[547]+3*X[51516], -4*X[549]+3*X[21168], -4*X[551]+3*X[52653], -5*X[631]+6*X[38065], -5*X[1656]+6*X[38080], -5*X[1698]+6*X[38094], -5*X[3091]+6*X[38073], -X[3146]+4*X[5735], -5*X[3522]+8*X[43177], -3*X[3524]+4*X[31657], -3*X[3545]+2*X[5779] and many others

X(60984) lies on these lines: {1, 50738}, {2, 7}, {8, 30424}, {30, 36996}, {65, 12125}, {69, 49722}, {145, 528}, {192, 32093}, {193, 4373}, {279, 35110}, {320, 4454}, {346, 17297}, {376, 5762}, {381, 5843}, {390, 5048}, {391, 7321}, {516, 3241}, {518, 4740}, {519, 4312}, {545, 20533}, {547, 51516}, {549, 21168}, {551, 52653}, {631, 38065}, {903, 1992}, {954, 17549}, {962, 9845}, {966, 49733}, {971, 3543}, {1121, 6604}, {1656, 38080}, {1698, 38094}, {2550, 50835}, {3091, 38073}, {3146, 5735}, {3243, 50839}, {3522, 43177}, {3524, 31657}, {3545, 5779}, {3616, 38024}, {3617, 4741}, {3618, 38086}, {3622, 5698}, {3623, 30332}, {3672, 16884}, {3679, 5850}, {3723, 3945}, {3839, 5805}, {3845, 60884}, {3870, 30353}, {3873, 15726}, {4000, 16671}, {4310, 50303}, {4346, 4644}, {4389, 4747}, {4419, 16672}, {4430, 15733}, {4452, 17364}, {4461, 17294}, {4480, 29627}, {4488, 17298}, {4545, 32087}, {4648, 16677}, {4688, 27484}, {4851, 28322}, {4862, 50114}, {4869, 17264}, {4887, 5222}, {4896, 5308}, {4955, 27288}, {5032, 51002}, {5059, 11520}, {5067, 38082}, {5068, 38075}, {5071, 38107}, {5220, 46933}, {5223, 51100}, {5232, 7222}, {5542, 38314}, {5686, 5852}, {5759, 10304}, {5819, 37756}, {5851, 10707}, {6006, 53361}, {6147, 50739}, {7228, 17251}, {7229, 53598}, {7232, 49726}, {7238, 54389}, {7714, 60879}, {7966, 28194}, {8544, 34772}, {8581, 44663}, {9579, 20008}, {9812, 31146}, {10004, 17078}, {10303, 38067}, {10385, 60919}, {11036, 11111}, {11038, 15677}, {11112, 20007}, {11239, 60896}, {11240, 14450}, {15682, 31671}, {15692, 21151}, {15694, 38111}, {15702, 59381}, {15708, 31658}, {15721, 38122}, {17121, 36606}, {17314, 28297}, {17346, 42697}, {17528, 54398}, {19053, 60914}, {19054, 60913}, {19875, 50834}, {19877, 38101}, {19883, 50837}, {20072, 24599}, {20073, 29621}, {21170, 30556}, {21356, 50995}, {21358, 51191}, {25055, 51090}, {25557, 38025}, {28333, 37654}, {30287, 41539}, {30311, 41555}, {30628, 31391}, {30695, 32098}, {31272, 38095}, {31995, 50095}, {32857, 50282}, {32863, 56086}, {35935, 58786}, {36240, 39353}, {36991, 50687}, {37161, 54422}, {37666, 50103}, {37780, 47374}, {38021, 41705}, {38151, 52665}, {39587, 50301}, {41099, 60901}, {41325, 49748}, {45420, 60889}, {45421, 60888}, {47352, 51144}, {47595, 50996}, {48856, 50307}, {50088, 50992}, {50736, 57282}, {50997, 51150}, {51052, 51057}

X(60984) = midpoint of X(i) and X(j) for these {i,j}: {2, 20059}, {60933, 60963}, {7, 60971}
X(60984) = reflection of X(i) in X(j) for these {i,j}: {144, 2}, {15682, 31671}, {2, 7}, {20059, 60971}, {21168, 59380}, {390, 51099}, {5223, 51100}, {50835, 2550}, {50836, 5542}, {50839, 3243}, {50995, 51151}, {50996, 47595}, {50997, 51150}, {51052, 51057}, {51090, 51098}, {51144, 51195}, {51190, 51002}, {52653, 59372}, {52665, 38151}, {59386, 51514}, {6172, 6173}, {60884, 3845}, {60927, 50116}, {60963, 60962}, {60971, 60933}, {7, 60963}
X(60984) = anticomplement of X(6172)
X(60984) = anticomplement of isotomic conjugate of X(55948)
X(60984) = X(i)-Dao conjugate of X(j) for these {i, j}: {6172, 6172}
X(60984) = X(i)-Ceva conjugate of X(j) for these {i, j}: {55948, 2}
X(60984) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {55922, 69}, {55948, 6327}, {56274, 21285}, {58109, 693}
X(60984) = pole of line {522, 1638} wrt Steiner circumellipse
X(60984) = pole of line {522, 44563} wrt Steiner inellipse
X(60984) = pole of line {1, 51098} wrt dual conic of Yff parabola
X(60984) = orthology center of the pedal triangle of X(16200) wrt Aguilera triangle
X(60984) = intersection, other than A, B, C, of circumconics {{A, B, C, X(144), X(1121)}}, {{A, B, C, X(527), X(10405)}}, {{A, B, C, X(673), X(31188)}}, {{A, B, C, X(3911), X(55937)}}, {{A, B, C, X(40869), X(53212)}}, {{A, B, C, X(53640), X(56543)}}
X(60984) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20059, 527}, {2, 527, 144}, {2, 61006, 61023}, {2, 7, 59375}, {7, 18230, 60980}, {7, 5435, 60993}, {7, 6172, 6173}, {7, 60946, 30275}, {7, 60957, 142}, {7, 60975, 21454}, {7, 60976, 9}, {7, 60987, 26842}, {7, 60996, 61020}, {9, 6173, 60999}, {142, 60957, 61006}, {142, 61023, 2}, {144, 46873, 60935}, {320, 4454, 29616}, {527, 50116, 60927}, {527, 6173, 6172}, {527, 60933, 60971}, {527, 60962, 60963}, {527, 60963, 7}, {527, 60971, 20059}, {4346, 4644, 17014}, {4740, 11160, 31145}, {5223, 51100, 53620}, {5542, 50836, 38314}, {5698, 30340, 3622}, {5843, 51514, 59386}, {6173, 60999, 59374}, {7222, 17345, 5232}, {17483, 20059, 60998}, {20059, 61000, 30852}, {28534, 51099, 390}, {43180, 60905, 3616}, {50995, 51151, 21356}, {50997, 51150, 59373}, {51002, 51190, 5032}, {51090, 51098, 25055}, {51144, 51195, 47352}, {59374, 60971, 60976}, {60938, 60965, 61012}, {60942, 61020, 60996}, {60948, 60973, 61026}, {60977, 60980, 18230}, {60993, 61007, 5435}

X(60985) = X(2)X(7)∩X(46)X(1001)

Barycentrics    a*(a^4-(b-c)^4+2*a^2*b*c-2*a^3*(b+c)+2*a*(b+c)*(b^2-3*b*c+c^2)) : :

X(60985) lies on these lines: {2, 7}, {40, 5883}, {46, 1001}, {55, 58564}, {84, 6849}, {100, 11025}, {354, 6600}, {474, 518}, {480, 4860}, {516, 6899}, {528, 17699}, {631, 12704}, {971, 37612}, {1158, 38037}, {1375, 38186}, {1376, 15185}, {1418, 55432}, {1709, 42356}, {1723, 17278}, {2257, 24779}, {2550, 10916}, {2900, 37270}, {3243, 3333}, {3247, 25065}, {3337, 5223}, {3358, 6841}, {3359, 43166}, {3651, 37526}, {3742, 41338}, {3752, 54358}, {3870, 61033}, {3919, 12703}, {4384, 20930}, {4413, 40659}, {4859, 8557}, {5119, 42819}, {5253, 7672}, {5440, 40726}, {5542, 11047}, {5709, 21153}, {5732, 6985}, {5805, 37356}, {5817, 26877}, {5880, 15299}, {6762, 59414}, {6845, 11372}, {6851, 52835}, {6915, 12669}, {7190, 16578}, {7675, 35976}, {7676, 9352}, {7678, 20292}, {10177, 11495}, {10390, 34894}, {10601, 56848}, {12515, 38060}, {15298, 17437}, {15348, 34917}, {15803, 37284}, {16503, 54420}, {17529, 41229}, {17582, 38057}, {18164, 41610}, {20116, 25440}, {24467, 38108}, {26892, 58473}, {31658, 37532}, {38031, 59318}, {38054, 60912}

X(60985) = pole of line {649, 47977} wrt Bevan circle
X(60985) = orthology center of the pedal triangle of X(16203) wrt Aguilera triangle
X(60985) = intersection, other than A, B, C, of circumconics {{A, B, C, X(5905), X(21446)}}, {{A, B, C, X(10390), X(30379)}}, {{A, B, C, X(18230), X(34894)}}
X(60985) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 60948, 60974}, {7, 61012, 60973}, {9, 5437, 20195}, {9, 57, 60968}, {9, 60955, 60933}, {9, 60963, 60965}, {9, 61020, 60937}, {142, 1445, 9}, {1445, 3306, 142}, {3218, 18230, 61005}, {3306, 3911, 5437}, {8257, 60973, 61012}

X(60986) = X(2)X(7)∩X(10)X(528)

Barycentrics    4*a^2+(b-c)^2-5*a*(b+c) : :
X(60986) = -X[1]+3*X[38025], -5*X[2]+X[7], -X[3]+3*X[38067], -X[4]+3*X[38075], -X[5]+3*X[38082], -X[8]+3*X[38097], -X[11]+3*X[38102], -X[12]+3*X[38103], -4*X[140]+X[43177], X[376]+3*X[5817], X[673]+3*X[41138], X[946]+2*X[60912] and many others

X(60986) lies on these lines: {1, 38025}, {2, 7}, {3, 38067}, {4, 38075}, {5, 38082}, {6, 4909}, {8, 38097}, {10, 528}, {11, 38102}, {12, 38103}, {30, 31658}, {37, 50114}, {44, 4667}, {45, 3008}, {140, 43177}, {190, 50119}, {210, 10177}, {238, 50291}, {239, 4029}, {319, 31333}, {344, 3686}, {376, 5817}, {381, 516}, {390, 51102}, {392, 38060}, {405, 12437}, {518, 551}, {519, 1001}, {522, 45322}, {524, 29600}, {544, 28345}, {547, 5762}, {549, 971}, {599, 41141}, {673, 41138}, {936, 50739}, {946, 60912}, {954, 17542}, {1121, 6606}, {1125, 5220}, {1212, 16578}, {1266, 29628}, {1334, 53391}, {1698, 5698}, {2321, 5564}, {2325, 4384}, {2550, 3583}, {2801, 10165}, {3058, 15837}, {3059, 58677}, {3090, 5735}, {3241, 5686}, {3243, 38314}, {3247, 37681}, {3254, 59377}, {3294, 20257}, {3524, 5732}, {3526, 38065}, {3534, 31672}, {3543, 59389}, {3545, 5759}, {3589, 3986}, {3624, 38024}, {3626, 17269}, {3634, 5880}, {3652, 58449}, {3655, 38031}, {3663, 16814}, {3664, 16885}, {3679, 5853}, {3707, 3912}, {3717, 50310}, {3731, 3946}, {3739, 49726}, {3740, 15733}, {3814, 3826}, {3817, 38454}, {3839, 52835}, {3879, 29575}, {3943, 50085}, {3950, 4971}, {3973, 4648}, {3984, 50398}, {4021, 16675}, {4072, 4399}, {4098, 4852}, {4292, 57005}, {4361, 28313}, {4363, 31211}, {4364, 6687}, {4370, 4688}, {4416, 17263}, {4419, 17067}, {4428, 6600}, {4448, 6006}, {4454, 31722}, {4473, 16815}, {4656, 50103}, {4664, 41140}, {4669, 30331}, {4670, 31285}, {4700, 17316}, {4725, 17243}, {4759, 25352}, {4848, 8543}, {4877, 35935}, {4908, 50098}, {4967, 17339}, {4982, 29585}, {4995, 14100}, {5054, 5779}, {5055, 5805}, {5066, 18482}, {5071, 21168}, {5222, 16676}, {5223, 25055}, {5234, 34610}, {5298, 8581}, {5308, 16670}, {5542, 15325}, {5559, 34894}, {5572, 58635}, {5696, 59587}, {5729, 13411}, {5766, 9581}, {5784, 37298}, {5837, 41687}, {5843, 10124}, {5845, 20582}, {5852, 38054}, {5856, 45310}, {6068, 59376}, {6174, 61028}, {6684, 9842}, {6705, 52684}, {6745, 42014}, {6928, 31399}, {6935, 54135}, {7263, 28322}, {7290, 48856}, {8236, 31145}, {8703, 60901}, {9342, 30295}, {9780, 38092}, {10056, 15299}, {10072, 15298}, {10157, 10164}, {10304, 36991}, {10385, 15006}, {10392, 16858}, {10445, 36728}, {11108, 24391}, {11111, 57284}, {11179, 38117}, {11236, 18250}, {11237, 12573}, {11523, 17554}, {11539, 31657}, {12572, 17528}, {15492, 17245}, {15570, 51101}, {15687, 38139}, {15694, 38122}, {15701, 60884}, {15702, 21151}, {15703, 38107}, {15709, 36996}, {15723, 59380}, {16112, 43151}, {16503, 29574}, {16590, 16593}, {16832, 54389}, {16833, 17133}, {17244, 50133}, {17251, 17279}, {17256, 29596}, {17259, 17355}, {17265, 53598}, {17278, 49747}, {17330, 29594}, {17332, 21255}, {17336, 24199}, {17349, 17389}, {17352, 17399}, {17354, 24603}, {17382, 49737}, {17559, 31446}, {17768, 38204}, {19709, 31671}, {19862, 25557}, {19876, 38052}, {19878, 43180}, {20072, 29626}, {21356, 51152}, {21358, 47595}, {21627, 31435}, {21849, 58473}, {22758, 51705}, {24389, 49736}, {24564, 34605}, {25558, 58453}, {28204, 43175}, {28292, 59840}, {28297, 53594}, {28459, 50796}, {28653, 31311}, {29573, 37654}, {29582, 50074}, {29597, 50996}, {30332, 46933}, {30424, 38094}, {31140, 40998}, {31144, 31175}, {31162, 38037}, {34627, 38154}, {34641, 38210}, {34648, 38158}, {34718, 38126}, {35258, 46916}, {36949, 58458}, {37756, 50090}, {38048, 47356}, {38068, 60911}, {38080, 55856}, {38086, 47355}, {38145, 54131}, {38200, 52653}, {40659, 58608}, {41229, 51723}, {42029, 56085}, {42819, 50124}, {42871, 51103}, {43166, 50810}, {47352, 50995}, {47508, 47593}, {48310, 51150}, {49511, 49775}, {49543, 50113}, {51053, 51058}, {51144, 51151}, {51572, 59722}, {54648, 60243}, {57721, 60267}, {58410, 59644}, {58560, 58678}

X(60986) = midpoint of X(i) and X(j) for these {i,j}: {144, 60963}, {2, 9}, {210, 10177}, {2550, 50836}, {21168, 38150}, {29573, 37654}, {390, 51102}, {3243, 50835}, {3534, 31672}, {3679, 47357}, {38108, 59381}, {38122, 51516}, {38200, 52653}, {4669, 30331}, {43166, 50810}, {47508, 47593}, {47595, 50997}, {5223, 51099}, {5542, 50834}, {5686, 38316}, {5817, 21153}, {50995, 51002}, {50996, 51194}, {51053, 51058}, {51090, 51100}, {51144, 51151}, {51150, 51191}, {51152, 51190}, {58560, 58678}, {58608, 58629}, {59389, 59418}, {6172, 6173}, {60971, 60977}, {8236, 59414}, {8703, 60901}
X(60986) = reflection of X(i) in X(j) for these {i,j}: {142, 2}, {18482, 5066}, {2, 6666}, {21849, 58473}, {40659, 58629}, {42871, 51103}, {43151, 50829}, {50834, 15481}, {51071, 42819}, {51100, 3826}, {51101, 15570}, {51705, 52769}, {6173, 60999}, {60963, 60980}
X(60986) = complement of X(6173)
X(60986) = anticomplement of X(60999)
X(60986) = complement of isotomic conjugate of X(55954)
X(60986) = X(i)-Dao conjugate of X(j) for these {i, j}: {60999, 60999}
X(60986) = X(i)-complementary conjugate of X(j) for these {i, j}: {55920, 141}, {55954, 2887}, {58105, 4885}
X(60986) = pole of line {28292, 47771} wrt orthoptic circle of the Steiner inellipse
X(60986) = pole of line {2826, 4521} wrt Spieker circle
X(60986) = pole of line {14100, 61000} wrt Feuerbach hyperbola
X(60986) = pole of line {17056, 50114} wrt Kiepert hyperbola
X(60986) = pole of line {522, 14392} wrt Steiner inellipse
X(60986) = pole of line {1, 38093} wrt dual conic of Yff parabola
X(60986) = orthology center of the pedal triangle of X(17502) wrt Aguilera triangle
X(60986) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(60094)}}, {{A, B, C, X(85), X(38093)}}, {{A, B, C, X(142), X(1121)}}, {{A, B, C, X(527), X(32008)}}, {{A, B, C, X(673), X(4031)}}, {{A, B, C, X(5559), X(30379)}}, {{A, B, C, X(6173), X(55954)}}, {{A, B, C, X(6606), X(56543)}}, {{A, B, C, X(9436), X(55955)}}, {{A, B, C, X(20195), X(43971)}}, {{A, B, C, X(21454), X(57721)}}, {{A, B, C, X(27003), X(34894)}}, {{A, B, C, X(30275), X(43734)}}, {{A, B, C, X(35595), X(36101)}}, {{A, B, C, X(40868), X(53212)}}
X(60986) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 144, 59374}, {2, 38093, 58433}, {2, 50093, 50092}, {2, 527, 142}, {2, 59374, 20195}, {2, 59375, 60996}, {2, 6172, 6173}, {2, 6173, 60999}, {2, 61006, 59375}, {2, 61023, 9}, {2, 7, 38093}, {7, 9, 61000}, {9, 142, 60942}, {9, 18230, 6666}, {9, 20195, 144}, {9, 6173, 6172}, {9, 60933, 61006}, {9, 60977, 60983}, {9, 60985, 60949}, {9, 60989, 3219}, {44, 29571, 4667}, {142, 60942, 60962}, {142, 6666, 61001}, {144, 20195, 60980}, {144, 59374, 60963}, {144, 60963, 527}, {210, 10177, 61030}, {238, 50291, 50294}, {597, 4755, 551}, {1445, 61027, 553}, {3679, 47357, 5853}, {3731, 37650, 3946}, {3826, 28534, 51100}, {3911, 8545, 61022}, {3912, 17335, 3707}, {4364, 6687, 31191}, {4370, 4688, 50118}, {4419, 31183, 17067}, {4422, 49731, 17359}, {4664, 41140, 50109}, {4908, 50098, 50100}, {5223, 25055, 51099}, {5273, 51780, 6692}, {16814, 17337, 3663}, {17260, 17353, 5257}, {17264, 17277, 50095}, {17264, 50095, 2321}, {17282, 50127, 20196}, {17330, 41310, 29594}, {17359, 49731, 10}, {18230, 61023, 2}, {19875, 50836, 2550}, {19883, 50834, 5542}, {21617, 60954, 61014}, {29007, 61016, 60992}, {35595, 54357, 5316}, {37787, 61015, 226}, {38057, 47357, 3679}, {38108, 59381, 516}, {38314, 50835, 3243}, {47352, 50995, 51002}, {48310, 51191, 51150}, {50573, 61008, 61021}, {50996, 59373, 51194}, {51053, 51488, 51058}, {51090, 51100, 28534}, {58433, 61000, 7}, {60943, 60947, 52819}, {60996, 61006, 60933}

X(60987) = X(2)X(7)∩X(4)X(3812)

Barycentrics    a^5-2*a^3*(b-c)^2-a^4*(b+c)-(b-c)^4*(b+c)+a*(b^2-c^2)^2+2*a^2*(b+c)*(b^2-4*b*c+c^2) : :

X(60987) lies on these lines: {2, 7}, {4, 3812}, {8, 34917}, {72, 45085}, {200, 41570}, {218, 4644}, {281, 25964}, {377, 10394}, {405, 4295}, {442, 5729}, {443, 5784}, {497, 10177}, {516, 6987}, {518, 1056}, {528, 3488}, {938, 2894}, {948, 55432}, {954, 5856}, {962, 5436}, {971, 6826}, {997, 5542}, {1001, 1006}, {1005, 30295}, {1125, 5758}, {1156, 52255}, {1260, 3475}, {1376, 8255}, {1441, 53994}, {1490, 12436}, {1519, 38037}, {1621, 36976}, {1737, 10398}, {1788, 47510}, {2345, 16608}, {2550, 3419}, {2949, 10198}, {3035, 33993}, {3434, 7671}, {3474, 13615}, {3485, 37244}, {3487, 25524}, {3616, 5766}, {3816, 33558}, {3925, 42014}, {3945, 53996}, {4329, 36023}, {4363, 21258}, {4413, 61035}, {4419, 16601}, {4423, 36971}, {4454, 56937}, {4511, 11038}, {4643, 6706}, {4659, 51972}, {5177, 10395}, {5180, 52653}, {5220, 25466}, {5308, 16578}, {5439, 11023}, {5572, 6601}, {5657, 54158}, {5696, 10399}, {5715, 9843}, {5732, 50701}, {5762, 6883}, {5779, 6881}, {5805, 6827}, {5809, 45043}, {5817, 5851}, {5819, 36019}, {6356, 55118}, {6832, 15297}, {6839, 36991}, {6840, 59385}, {6843, 60896}, {6844, 38150}, {6846, 12609}, {6854, 36996}, {6858, 38108}, {6864, 12664}, {6878, 21168}, {6882, 38107}, {6904, 10393}, {6905, 21151}, {6911, 31657}, {6947, 59386}, {6954, 38122}, {9612, 9814}, {10427, 37240}, {11037, 11523}, {12572, 30424}, {13405, 47375}, {15254, 16845}, {16053, 17139}, {17170, 41239}, {17626, 58564}, {17757, 38057}, {17825, 34032}, {23840, 34371}, {24389, 30330}, {25001, 56927}, {26040, 61028}, {28459, 31671}, {30305, 47357}, {31789, 52682}, {37106, 59418}, {37788, 42697}, {39063, 52663}

X(60987) = midpoint of X(i) and X(j) for these {i,j}: {7, 60997}, {9, 60982}
X(60987) = pole of line {3676, 30235} wrt incircle
X(60987) = pole of line {3064, 14077} wrt polar circle
X(60987) = pole of line {14100, 61010} wrt Feuerbach hyperbola
X(60987) = pole of line {17056, 34522} wrt Kiepert hyperbola
X(60987) = pole of line {1, 41570} wrt dual conic of Yff parabola
X(60987) = orthology center of the pedal triangle of X(18443) wrt Aguilera triangle
X(60987) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(8545)}}, {{A, B, C, X(57), X(34917)}}, {{A, B, C, X(63), X(34919)}}, {{A, B, C, X(85), X(52457)}}, {{A, B, C, X(27475), X(54366)}}
X(60987) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12848, 9}, {2, 144, 60981}, {2, 7, 52457}, {7, 329, 61011}, {7, 6172, 5905}, {7, 60997, 527}, {7, 9776, 6173}, {9, 52819, 60950}, {9, 6173, 226}, {9, 60933, 61003}, {9, 60991, 8232}, {9, 61011, 329}, {142, 60986, 58463}, {142, 8257, 2}, {329, 61011, 61010}, {443, 44547, 45039}, {1708, 52819, 12848}, {5437, 6173, 142}, {26842, 60984, 7}, {30275, 60975, 60953}, {31019, 60935, 61027}, {60951, 60981, 144}

X(60988) = X(2)X(7)∩X(77)X(4859)

Barycentrics    (a+b-c)*(a-b+c)*(a^2*(b+c)+(b-c)^2*(b+c)+a*(-2*b^2+b*c-2*c^2)) : :

X(60988) lies on these lines: {2, 7}, {77, 4859}, {222, 26724}, {390, 3612}, {404, 5832}, {499, 60896}, {516, 7280}, {518, 30312}, {651, 17278}, {971, 6941}, {1442, 4000}, {1443, 37800}, {1737, 40269}, {2550, 4861}, {3086, 60925}, {3160, 24181}, {3560, 38107}, {3660, 17620}, {3873, 41548}, {4197, 37566}, {4530, 17090}, {4552, 48627}, {4648, 7269}, {5265, 12609}, {5433, 17768}, {5542, 10039}, {5728, 6937}, {5729, 59380}, {5732, 37437}, {5759, 6961}, {5805, 6906}, {5817, 6981}, {5880, 7677}, {6842, 10394}, {6850, 21151}, {6940, 38122}, {6977, 59386}, {7672, 25557}, {7675, 37163}, {7676, 34879}, {7678, 15726}, {7679, 8581}, {8236, 38123}, {8255, 11025}, {8544, 13729}, {9782, 37550}, {10304, 30384}, {10427, 25722}, {11023, 37112}, {11375, 16133}, {11680, 17668}, {15485, 60718}, {16593, 28978}, {17074, 24789}, {17080, 40688}, {17227, 40999}, {17234, 28974}, {21195, 42462}, {30311, 31391}, {30318, 38200}, {30628, 41555}, {31225, 48629}, {34028, 34051}, {34784, 61035}, {37438, 38111}

X(60988) = midpoint of X(i) and X(j) for these {i,j}: {7, 60954}
X(60988) = reflection of X(i) in X(j) for these {i,j}: {60954, 61016}
X(60988) = pole of line {1, 29007} wrt dual conic of Yff parabola
X(60988) = orthology center of the pedal triangle of X(21842) wrt Aguilera triangle
X(60988) = intersection, other than A, B, C, of circumconics {{A, B, C, X(85), X(29007)}}, {{A, B, C, X(673), X(31053)}}, {{A, B, C, X(5748), X(42318)}}, {{A, B, C, X(27003), X(27475)}}, {{A, B, C, X(33864), X(55967)}}
X(60988) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 7, 29007}, {7, 142, 61008}, {7, 1445, 60951}, {7, 18230, 60946}, {7, 60954, 527}, {7, 60996, 60943}, {7, 61008, 61013}, {7, 61017, 8545}, {7, 61019, 37787}, {7, 8732, 60948}, {77, 4859, 37771}, {142, 30379, 7}, {142, 60992, 21617}, {527, 61016, 60954}, {3911, 60980, 41572}, {6666, 60936, 60944}, {6666, 60993, 60936}, {8545, 20195, 61017}, {21617, 30379, 60992}, {31231, 60933, 60947}, {58433, 60961, 61015}

X(60989) = X(2)X(7)∩X(36)X(518)

Barycentrics    a*(a^4+a^2*b*c-2*a^3*(b+c)-(b-c)^2*(b^2+c^2)+a*(b+c)*(2*b^2-3*b*c+2*c^2)) : :
X(60989) = -4*X[1155]+X[5528]

X(60989) lies on these lines: {1, 19624}, {2, 7}, {36, 518}, {100, 61030}, {191, 5439}, {241, 2323}, {474, 5220}, {484, 528}, {514, 53396}, {516, 5535}, {529, 38211}, {631, 60912}, {662, 18206}, {673, 16568}, {954, 30274}, {1001, 5902}, {1155, 5528}, {1470, 41712}, {1727, 28534}, {1749, 14527}, {1768, 15726}, {2346, 61033}, {2364, 39273}, {2801, 4973}, {2949, 9940}, {3243, 3576}, {3254, 5536}, {3336, 5880}, {3337, 7483}, {3358, 52835}, {4317, 57279}, {4640, 10177}, {4880, 60885}, {5425, 42819}, {5696, 37524}, {5697, 42886}, {5728, 37286}, {5729, 54432}, {5735, 37532}, {5784, 37582}, {5852, 34324}, {5903, 42842}, {6600, 37578}, {6833, 60895}, {6899, 24468}, {7677, 45234}, {8680, 24618}, {9441, 57022}, {10164, 41570}, {10202, 31658}, {11529, 38316}, {14793, 18412}, {15185, 15931}, {15296, 59372}, {15297, 60905}, {16547, 16551}, {16548, 16560}, {18443, 21153}, {18540, 59389}, {18607, 52423}, {26877, 43177}, {37525, 42871}, {45630, 52682}, {51102, 54286}, {52027, 54159}, {53665, 59682}

X(60989) = midpoint of X(i) and X(j) for these {i,j}: {3218, 37787}, {4880, 60885}
X(60989) = reflection of X(i) in X(j) for these {i,j}: {3254, 41555}, {9, 37787}
X(60989) = X(i)-Dao conjugate of X(j) for these {i, j}: {5526, 3935}
X(60989) = pole of line {169, 649} wrt Bevan circle
X(60989) = pole of line {6161, 23865} wrt circumcircle
X(60989) = pole of line {284, 2246} wrt Stammler hyperbola
X(60989) = pole of line {522, 3957} wrt Steiner circumellipse
X(60989) = pole of line {100, 42325} wrt Yff parabola
X(60989) = orthology center of the pedal triangle of X(22765) wrt Aguilera triangle
X(60989) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(57), X(3446)}}, {{A, B, C, X(142), X(4564)}}, {{A, B, C, X(226), X(37131)}}, {{A, B, C, X(514), X(21617)}}, {{A, B, C, X(2364), X(40131)}}, {{A, B, C, X(5219), X(39273)}}, {{A, B, C, X(6173), X(7131)}}, {{A, B, C, X(8545), X(44178)}}, {{A, B, C, X(17484), X(36101)}}, {{A, B, C, X(21446), X(31019)}}, {{A, B, C, X(37797), X(43760)}}
X(60989) = barycentric product X(i)*X(j) for these (i, j): {41341, 75}
X(60989) = barycentric quotient X(i)/X(j) for these (i, j): {41341, 1}
X(60989) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 57, 6173}, {9, 60963, 8545}, {9, 60968, 60933}, {9, 60985, 20195}, {9, 60990, 60977}, {9, 61020, 60964}, {63, 1445, 8257}, {142, 60970, 9}, {3218, 3219, 35596}, {3218, 37787, 527}, {3218, 50573, 60990}, {8257, 60974, 63}, {16560, 20367, 16548}, {27003, 60970, 60981}, {27003, 60981, 142}, {38454, 41555, 3254}, {60932, 60948, 57}, {60938, 60964, 61020}, {60948, 60981, 27003}

X(60990) = X(2)X(7)∩X(40)X(518)

Barycentrics    a*(a^4-(b-c)^4-4*a^2*b*c-2*a^3*(b+c)+2*a*(b+c)*(b^2+c^2)) : :
X(60990) = -3*X[165]+2*X[6600], -X[7674]+3*X[9778], -3*X[11194]+2*X[42819], -2*X[24389]+3*X[24477], 2*X[25557]+X[28646], -X[30331]+3*X[34646]

X(60990) lies on these lines: {1, 21002}, {2, 7}, {20, 5853}, {21, 10390}, {40, 518}, {46, 5223}, {84, 516}, {165, 6600}, {191, 59372}, {219, 269}, {220, 1418}, {223, 55405}, {241, 2324}, {277, 15662}, {377, 38200}, {480, 1155}, {497, 41573}, {517, 18725}, {528, 58808}, {728, 17296}, {920, 60924}, {954, 3916}, {971, 5709}, {1001, 3333}, {1004, 46917}, {1012, 43166}, {1419, 2323}, {1454, 60909}, {1697, 3243}, {1706, 24393}, {1723, 4862}, {1768, 5856}, {1836, 6067}, {2096, 35514}, {2097, 21866}, {2257, 3663}, {2270, 5781}, {2346, 35258}, {2550, 4292}, {2951, 15733}, {3062, 5536}, {3158, 7411}, {3340, 18726}, {3358, 5762}, {3576, 18162}, {3586, 34695}, {3640, 30401}, {3641, 30400}, {3692, 21296}, {3870, 7676}, {4000, 16572}, {4304, 34610}, {4312, 5832}, {4321, 12526}, {4326, 10391}, {4328, 40937}, {4335, 32913}, {4350, 53996}, {4361, 44664}, {4869, 55337}, {4880, 18412}, {4907, 57022}, {5128, 8544}, {5220, 5785}, {5227, 47595}, {5250, 11038}, {5542, 12514}, {5735, 7701}, {5779, 37532}, {5805, 7330}, {5833, 5880}, {5843, 52684}, {5850, 37560}, {5852, 59333}, {6766, 12513}, {7183, 23062}, {7190, 24635}, {7580, 8730}, {7673, 36846}, {7674, 9778}, {7982, 18161}, {7994, 42470}, {8236, 17576}, {8557, 17276}, {8580, 58635}, {8581, 37550}, {8822, 18206}, {9799, 24391}, {10389, 20835}, {10431, 24392}, {10884, 11523}, {10980, 58564}, {11020, 61033}, {11194, 42819}, {11220, 61030}, {11520, 37556}, {12669, 33557}, {14100, 54408}, {15298, 59335}, {15299, 54432}, {15841, 51090}, {17092, 25930}, {17579, 51102}, {17668, 30353}, {18482, 18540}, {21151, 55104}, {21153, 37526}, {21168, 26877}, {21384, 41787}, {24389, 24477}, {24771, 51384}, {25557, 28646}, {26921, 31657}, {30295, 34784}, {30331, 34646}, {31391, 42014}, {31393, 42871}, {31435, 38053}, {31658, 37534}, {34894, 46684}, {36101, 36629}, {37435, 59413}, {37555, 51194}, {37581, 60897}, {37612, 59381}, {38052, 41229}, {43175, 59345}, {51058, 54344}

X(60990) = midpoint of X(i) and X(j) for these {i,j}: {5732, 54422}
X(60990) = reflection of X(i) in X(j) for these {i,j}: {3174, 11495}, {3358, 24467}, {34894, 46684}, {60965, 9}, {60973, 60994}, {61010, 142}, {9, 60974}
X(60990) = X(i)-Dao conjugate of X(j) for these {i, j}: {16572, 36845}
X(60990) = X(i)-Ceva conjugate of X(j) for these {i, j}: {42361, 1}
X(60990) = pole of line {649, 3309} wrt Bevan circle
X(60990) = pole of line {284, 10389} wrt Stammler hyperbola
X(60990) = pole of line {522, 25925} wrt Steiner inellipse
X(60990) = orthology center of the pedal triangle of X(22770) wrt Aguilera triangle
X(60990) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(8232)}}, {{A, B, C, X(7), X(41790)}}, {{A, B, C, X(21), X(18230)}}, {{A, B, C, X(84), X(1445)}}, {{A, B, C, X(226), X(10390)}}, {{A, B, C, X(329), X(6601)}}, {{A, B, C, X(3062), X(12848)}}, {{A, B, C, X(9776), X(21446)}}, {{A, B, C, X(9965), X(36101)}}, {{A, B, C, X(36629), X(40869)}}, {{A, B, C, X(52819), X(55922)}}
X(60990) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 144, 61002}, {9, 20195, 7308}, {9, 3928, 60974}, {9, 527, 60965}, {9, 5437, 6666}, {9, 60933, 60937}, {9, 60953, 60964}, {9, 60955, 142}, {9, 60968, 57}, {9, 60977, 36973}, {142, 527, 61010}, {142, 61005, 9}, {144, 3218, 1445}, {518, 11495, 3174}, {527, 60994, 60973}, {3218, 50573, 60989}, {3868, 7675, 3243}, {5732, 54422, 518}, {5762, 24467, 3358}, {8822, 18206, 40979}, {9436, 27509, 18634}, {20059, 60970, 8545}, {37787, 60957, 60966}, {60938, 60949, 2}, {60962, 60964, 60953}, {60973, 60974, 60994}, {60992, 61003, 52457}

X(60991) = X(2)X(7)∩X(4)X(38053)

Barycentrics    a^4*(b+c)-(b-c)^4*(b+c)-2*a^2*b*c*(b+c)+2*a*(b^2-c^2)^2-2*a^3*(b^2+b*c+c^2) : :

X(60991) lies on these lines: {2, 7}, {4, 38053}, {11, 58564}, {72, 3826}, {218, 17278}, {442, 518}, {516, 3651}, {528, 33593}, {946, 38316}, {948, 4341}, {950, 30284}, {954, 5880}, {971, 6841}, {1001, 7742}, {1490, 6849}, {1602, 52015}, {2346, 35990}, {2550, 3487}, {2886, 15185}, {2900, 3475}, {3120, 4343}, {3243, 21620}, {3419, 42871}, {3553, 24779}, {3742, 8226}, {3772, 54358}, {3822, 30329}, {3838, 5572}, {3925, 40659}, {4293, 5436}, {5177, 11038}, {5542, 10916}, {5715, 5732}, {5728, 25557}, {5731, 51723}, {5805, 6985}, {5812, 38122}, {6260, 59389}, {6600, 17718}, {6828, 12669}, {6845, 43177}, {6899, 21151}, {6907, 20330}, {6990, 38054}, {7676, 20292}, {7678, 10129}, {8255, 17668}, {10177, 27869}, {10404, 37224}, {11025, 11680}, {11036, 45039}, {11523, 38200}, {12608, 38037}, {12611, 38060}, {13257, 38205}, {15587, 41548}, {16503, 34830}, {16601, 17245}, {17529, 45120}, {17758, 60265}, {20116, 25639}, {21077, 38057}, {22021, 24050}, {26015, 61033}, {27475, 37445}, {30384, 42819}, {31657, 37356}, {33108, 34784}, {40465, 59936}, {40937, 52023}, {41555, 58563}, {50741, 51099}

X(60991) = midpoint of X(i) and X(j) for these {i,j}: {7, 60969}
X(60991) = complement of X(61024)
X(60991) = pole of line {16601, 17056} wrt Kiepert hyperbola
X(60991) = pole of line {1, 21059} wrt dual conic of Yff parabola
X(60991) = orthology center of the pedal triangle of X(24299) wrt Aguilera triangle
X(60991) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1445), X(17758)}}, {{A, B, C, X(1708), X(27475)}}, {{A, B, C, X(34917), X(41572)}}
X(60991) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 7, 60974}, {7, 60969, 527}, {9, 142, 60978}, {9, 61020, 60982}, {142, 226, 9}, {142, 60980, 30379}, {27186, 60996, 142}

X(60992) = X(1)X(21151)∩X(2)X(7)

Barycentrics    (a+b-c)*(a-b+c)*(-2*a*(b-c)^2+a^2*(b+c)+(b-c)^2*(b+c)) : :
X(60992) = -3*X[17728]+X[60910]

X(60992) lies on these lines: {1, 21151}, {2, 7}, {10, 8581}, {11, 31391}, {12, 38204}, {46, 10075}, {55, 43151}, {56, 516}, {65, 5542}, {77, 3946}, {85, 24199}, {104, 15909}, {241, 3663}, {269, 4000}, {279, 60831}, {348, 17304}, {354, 15841}, {376, 13462}, {388, 38052}, {390, 1420}, {392, 3671}, {443, 5833}, {479, 17113}, {497, 2951}, {518, 4848}, {528, 41554}, {673, 3451}, {942, 31657}, {946, 3361}, {948, 4859}, {950, 1467}, {954, 1466}, {956, 4298}, {971, 1210}, {1000, 18421}, {1014, 17197}, {1086, 1108}, {1122, 14524}, {1145, 24473}, {1155, 60919}, {1319, 30331}, {1362, 61034}, {1388, 43179}, {1407, 40940}, {1419, 5222}, {1427, 24177}, {1429, 38855}, {1458, 3755}, {1470, 52769}, {1512, 18412}, {1617, 11495}, {1738, 4334}, {1788, 5223}, {2078, 7676}, {2256, 4675}, {2291, 10509}, {2346, 3256}, {2550, 4321}, {2801, 12832}, {3008, 6180}, {3059, 17625}, {3062, 8166}, {3086, 11372}, {3338, 60923}, {3339, 5657}, {3340, 11038}, {3600, 59412}, {3660, 5572}, {3664, 5228}, {3672, 59215}, {3912, 39126}, {3916, 51090}, {4292, 5805}, {4295, 38036}, {4308, 21627}, {4315, 11112}, {4328, 4648}, {4350, 52542}, {4847, 15587}, {4862, 51302}, {4904, 28344}, {5083, 10427}, {5173, 8255}, {5221, 43180}, {5265, 52653}, {5303, 7677}, {5433, 38059}, {5434, 51100}, {5575, 7195}, {5704, 9842}, {5708, 59380}, {5728, 37566}, {5759, 15803}, {5762, 37582}, {5843, 34753}, {5850, 21075}, {5853, 36846}, {5880, 12573}, {6147, 38111}, {6260, 10398}, {6604, 17298}, {6610, 17366}, {6684, 15298}, {6734, 10861}, {6738, 43176}, {6906, 13370}, {7176, 20257}, {7201, 27475}, {7365, 23681}, {7675, 34489}, {8074, 10521}, {9311, 41777}, {9578, 40333}, {9579, 59385}, {9581, 36991}, {9613, 38149}, {9814, 10589}, {9841, 10384}, {10164, 15837}, {10167, 11019}, {10481, 24181}, {10865, 25006}, {12560, 38053}, {12575, 51773}, {12610, 24237}, {13411, 38122}, {14330, 21195}, {15558, 38055}, {15733, 41573}, {17067, 37800}, {17092, 22464}, {17117, 25719}, {17396, 25723}, {17606, 38158}, {17668, 24389}, {17728, 60910}, {17768, 41547}, {18838, 30329}, {20236, 38468}, {20905, 41006}, {24391, 41228}, {24465, 41166}, {24470, 55108}, {24471, 51150}, {24914, 60909}, {25722, 26015}, {30424, 32636}, {32625, 38859}, {34710, 42871}, {37545, 60922}, {37550, 60895}, {37709, 59413}, {38107, 57282}, {40615, 52870}, {41539, 61035}, {43036, 50103}, {44217, 51782}, {51842, 60887}

X(60992) = midpoint of X(i) and X(j) for these {i,j}: {46, 60924}, {7, 1445}
X(60992) = reflection of X(i) in X(j) for these {i,j}: {10392, 1210}, {61014, 1445}
X(60992) = complement of X(60966)
X(60992) = X(i)-isoconjugate-of-X(j) for these {i, j}: {41, 56026}, {219, 14493}, {1253, 23618}
X(60992) = X(i)-Dao conjugate of X(j) for these {i, j}: {2310, 4130}, {3160, 56026}, {11019, 728}, {17113, 23618}, {43182, 9}, {59573, 346}
X(60992) = X(i)-Ceva conjugate of X(j) for these {i, j}: {7, 14100}, {21453, 55368}, {30610, 30719}, {36838, 3676}
X(60992) = X(i)-complementary conjugate of X(j) for these {i, j}: {10307, 141}
X(60992) = X(i)-cross conjugate of X(j) for these {i, j}: {40133, 11019}
X(60992) = pole of line {3676, 30804} wrt incircle
X(60992) = pole of line {14100, 17625} wrt Feuerbach hyperbola
X(60992) = pole of line {522, 29005} wrt Steiner inellipse
X(60992) = pole of line {1, 971} wrt dual conic of Yff parabola
X(60992) = orthology center of the pedal triangle of X(24928) wrt Aguilera triangle
X(60992) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(11019)}}, {{A, B, C, X(9), X(9311)}}, {{A, B, C, X(63), X(10167)}}, {{A, B, C, X(144), X(279)}}, {{A, B, C, X(278), X(18228)}}, {{A, B, C, X(479), X(3599)}}, {{A, B, C, X(527), X(10509)}}, {{A, B, C, X(672), X(3451)}}, {{A, B, C, X(673), X(3452)}}, {{A, B, C, X(908), X(15909)}}, {{A, B, C, X(1200), X(2291)}}, {{A, B, C, X(1434), X(52819)}}, {{A, B, C, X(2006), X(5316)}}, {{A, B, C, X(2051), X(46873)}}, {{A, B, C, X(3306), X(45834)}}, {{A, B, C, X(5257), X(21049)}}, {{A, B, C, X(5328), X(14554)}}, {{A, B, C, X(5437), X(27475)}}, {{A, B, C, X(36620), X(50560)}}
X(60992) = barycentric product X(i)*X(j) for these (i, j): {226, 26818}, {279, 41006}, {1088, 14100}, {1200, 57792}, {1434, 21049}, {3160, 59170}, {10167, 273}, {11019, 7}, {20905, 57}, {20978, 6063}, {22088, 331}, {36620, 43182}, {40133, 85}, {45203, 60831}
X(60992) = barycentric quotient X(i)/X(j) for these (i, j): {7, 56026}, {34, 14493}, {279, 23618}, {1200, 220}, {10167, 78}, {11019, 8}, {14100, 200}, {20905, 312}, {20978, 55}, {21049, 2321}, {22088, 219}, {26818, 333}, {40133, 9}, {41006, 346}
X(60992) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 7, 60937}, {7, 12848, 60933}, {7, 1445, 527}, {7, 18230, 60998}, {7, 29007, 60952}, {7, 37787, 60936}, {7, 41572, 60962}, {7, 5435, 144}, {7, 57, 52819}, {7, 60938, 60945}, {7, 60941, 20059}, {7, 60948, 41572}, {7, 60955, 553}, {7, 60988, 21617}, {7, 61008, 41857}, {7, 61019, 8545}, {7, 8232, 60953}, {7, 9, 60961}, {57, 60993, 61021}, {142, 61022, 7}, {226, 3911, 5316}, {269, 4000, 43035}, {527, 1445, 61014}, {1086, 1418, 3668}, {2550, 4321, 10106}, {3911, 60961, 9}, {4859, 7271, 948}, {5435, 31190, 3911}, {8545, 61019, 6666}, {11019, 43182, 14100}, {20059, 60941, 61007}, {20195, 60953, 8232}, {21617, 30379, 60988}, {21617, 60988, 142}, {29007, 61016, 60986}, {30379, 61022, 226}, {37787, 60936, 60942}, {52457, 60990, 61003}, {60938, 60945, 4031}, {60946, 60947, 61000}, {60952, 61016, 29007}

X(60993) = X(2)X(7)∩X(516)X(1319)

Barycentrics    (a+b-c)*(a-b+c)*(2*a^3-4*a*(b-c)^2-a^2*(b+c)+3*(b-c)^2*(b+c)) : :

X(60993) lies on these lines: {2, 7}, {56, 30424}, {65, 43180}, {77, 18261}, {241, 4887}, {516, 1319}, {651, 17067}, {950, 43177}, {1056, 18421}, {1086, 6610}, {1519, 51768}, {1738, 51766}, {2078, 30295}, {2099, 5542}, {2801, 18838}, {3340, 30340}, {3660, 15726}, {3753, 8581}, {3873, 30287}, {4311, 52682}, {4312, 5603}, {4346, 59215}, {4896, 5228}, {5083, 15733}, {5119, 60924}, {5122, 5762}, {5193, 53055}, {5252, 51100}, {5850, 17757}, {5853, 14151}, {5880, 10106}, {6284, 43181}, {7288, 60905}, {8544, 34489}, {10004, 60692}, {10392, 36996}, {10427, 41553}, {14100, 17626}, {15298, 38123}, {15934, 59380}, {21151, 30282}, {24465, 38454}, {24929, 31657}, {25558, 41558}, {36991, 51792}, {38204, 60909}, {43151, 60919}, {43182, 51783}, {51790, 59385}, {51816, 60923}, {56049, 60578}

X(60993) = midpoint of X(i) and X(j) for these {i,j}: {7, 30379}
X(60993) = reflection of X(i) in X(j) for these {i,j}: {3911, 30379}
X(60993) = perspector of circumconic {{A, B, C, X(664), X(36620)}}
X(60993) = X(i)-Ceva conjugate of X(j) for these {i, j}: {60487, 3676}
X(60993) = pole of line {279, 3676} wrt incircle
X(60993) = pole of line {5083, 14100} wrt Feuerbach hyperbola
X(60993) = pole of line {1, 53529} wrt dual conic of Yff parabola
X(60993) = orthology center of the pedal triangle of X(25405) wrt Aguilera triangle
X(60993) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(144), X(514)}}, {{A, B, C, X(3928), X(37131)}}, {{A, B, C, X(27475), X(31190)}}
X(60993) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 12848, 60963}, {7, 142, 60961}, {7, 1445, 60962}, {7, 30275, 60953}, {7, 30379, 527}, {7, 5435, 60984}, {7, 57, 61021}, {7, 59374, 60998}, {7, 60988, 60936}, {7, 61008, 60952}, {7, 61022, 553}, {7, 8732, 60933}, {57, 61021, 52819}, {527, 30379, 3911}, {5435, 60984, 61007}, {6173, 60953, 30275}, {8732, 60933, 61014}, {30275, 60953, 226}, {33800, 60980, 60996}, {59374, 60998, 5219}, {60936, 60988, 6666}, {60992, 61021, 57}

X(60994) = X(2)X(7)∩X(5)X(17768)

Barycentrics    a*((a-b)^3*(a+b)-(a-b)*(2*a^2+b^2)*c-a*b*c^2+(2*a+b)*c^3-c^4) : :

X(60994) lies on these lines: {2, 7}, {5, 17768}, {6, 25065}, {55, 41577}, {182, 518}, {191, 5084}, {214, 3940}, {219, 16578}, {480, 6594}, {516, 10525}, {573, 16560}, {631, 54302}, {758, 6883}, {1001, 3878}, {1155, 17668}, {1253, 57022}, {1405, 18726}, {2183, 16551}, {2245, 17052}, {2949, 6865}, {3336, 6856}, {3358, 6869}, {3826, 5857}, {3874, 42885}, {3946, 8557}, {4317, 41229}, {5044, 15481}, {5422, 16585}, {5432, 41548}, {5535, 6844}, {5542, 15296}, {5722, 34741}, {5732, 6876}, {5759, 6903}, {5779, 37251}, {5817, 6900}, {5852, 38113}, {5853, 11362}, {5883, 11108}, {6600, 61030}, {6825, 60896}, {6827, 10265}, {6866, 54370}, {6873, 38150}, {7614, 53391}, {8609, 18261}, {9581, 56288}, {10176, 50204}, {11263, 18233}, {11495, 46684}, {14100, 41566}, {15185, 15837}, {15254, 31794}, {15297, 51090}, {16112, 19541}, {16577, 55399}, {16579, 52424}, {17279, 59682}, {18482, 28534}, {21363, 26934}, {24386, 41338}, {24391, 55104}, {24393, 37708}, {24779, 37650}, {26669, 52405}, {26878, 54422}, {37282, 40661}, {41555, 60919}

X(60994) = midpoint of X(i) and X(j) for these {i,j}: {60973, 60990}, {9, 60974}
X(60994) = pole of line {23865, 48345} wrt circumcircle
X(60994) = pole of line {14100, 61004} wrt Feuerbach hyperbola
X(60994) = pole of line {522, 26641} wrt Steiner inellipse
X(60994) = orthology center of the pedal triangle of X(26286) wrt Aguilera triangle
X(60994) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(21446), X(31266)}}, {{A, B, C, X(21617), X(43971)}}, {{A, B, C, X(31019), X(55995)}}, {{A, B, C, X(31053), X(36101)}}
X(60994) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 9, 61004}, {9, 20195, 60981}, {9, 3928, 60965}, {9, 57, 60964}, {9, 6173, 60969}, {9, 63, 60942}, {9, 60933, 29007}, {9, 60968, 8545}, {9, 60977, 60935}, {9, 60989, 7}, {9, 60990, 60973}, {9, 61005, 61000}, {9, 8257, 6666}, {57, 60964, 60980}, {142, 60942, 61002}, {144, 60954, 9}, {3218, 29007, 60933}, {3911, 61002, 142}, {6666, 60980, 58463}, {8545, 60968, 60962}, {37787, 61024, 61012}, {60948, 60969, 6173}, {60970, 61012, 61024}, {60973, 60974, 60990}, {60973, 60990, 527}

X(60995) = X(2)X(7)∩X(4)X(5766)

Barycentrics    (a+b-c)*(a-b+c)*(3*a^3-7*a^2*(b+c)-(b-c)^2*(b+c)+5*a*(b+c)^2) : :

X(60995) lies on these lines: {2, 7}, {4, 5766}, {8, 8543}, {12, 5698}, {37, 54425}, {45, 948}, {72, 4323}, {150, 34926}, {218, 5543}, {269, 25072}, {347, 3731}, {388, 15254}, {390, 3586}, {405, 4308}, {516, 10590}, {651, 5308}, {952, 954}, {971, 6935}, {1001, 3476}, {1012, 36991}, {1156, 18801}, {1319, 38025}, {1441, 3161}, {1532, 59385}, {1728, 11037}, {1750, 5281}, {1864, 7671}, {3085, 54370}, {3160, 16601}, {3485, 5220}, {3487, 5729}, {3523, 8544}, {3622, 30318}, {4295, 60912}, {4313, 6912}, {4321, 38059}, {5049, 5728}, {5080, 52653}, {5122, 38067}, {5218, 15726}, {5252, 47357}, {5261, 12572}, {5287, 54414}, {5436, 6049}, {5686, 9623}, {5703, 5777}, {5726, 50836}, {5759, 6907}, {5784, 27383}, {5805, 6969}, {5880, 10588}, {6604, 17335}, {6735, 59413}, {6847, 52684}, {6916, 59418}, {7190, 37681}, {7678, 15845}, {7679, 59412}, {8164, 37822}, {9812, 30311}, {10056, 51768}, {10164, 30353}, {10398, 11038}, {10592, 52682}, {12630, 12648}, {13257, 33993}, {13405, 30326}, {14151, 38060}, {15298, 30384}, {15950, 51099}, {16112, 59476}, {16676, 43035}, {17354, 52422}, {17784, 47375}, {18450, 54445}, {18541, 59381}, {19877, 30312}, {25568, 42014}, {31721, 34056}, {31994, 56937}, {38053, 60909}, {38057, 40663}

X(60995) = reflection of X(i) in X(j) for these {i,j}: {30275, 5219}, {7, 30275}
X(60995) = pole of line {6332, 30181} wrt dual conic of incircle
X(60995) = orthology center of the pedal triangle of X(30282) wrt Aguilera triangle
X(60995) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(6173)}}, {{A, B, C, X(63), X(55920)}}, {{A, B, C, X(3306), X(42318)}}, {{A, B, C, X(9776), X(60168)}}
X(60995) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 60935, 60997}, {2, 60998, 30379}, {4, 5766, 30332}, {7, 60954, 60941}, {7, 60983, 41563}, {7, 61017, 60996}, {7, 61023, 37787}, {9, 142, 61009}, {9, 226, 12848}, {9, 25525, 60972}, {142, 60934, 7}, {527, 5219, 30275}, {954, 5809, 8236}, {954, 5817, 5809}, {954, 6913, 53055}, {6172, 18230, 5273}, {6666, 61022, 31231}, {8232, 12848, 226}, {8545, 30379, 60998}, {8545, 61015, 2}, {18230, 27130, 60962}, {29007, 61008, 60946}, {30311, 36976, 9812}, {31231, 60937, 61022}, {31231, 61022, 8732}, {41857, 60947, 60939}, {60935, 60997, 6172}, {60943, 60946, 61008}

X(60996) = X(1)X(12630)∩X(2)X(7)

Barycentrics    a^2+3*(b-c)^2-4*a*(b+c) : :
X(60996) = -8*X[1]+X[12630], 6*X[2]+X[7], X[3]+6*X[38171], X[4]+6*X[38122], 4*X[5]+3*X[21151], -X[8]+8*X[3826], 4*X[10]+3*X[11038], X[20]+6*X[38150], X[69]+6*X[38186], X[100]+6*X[38205], -8*X[140]+X[5759], 4*X[141]+3*X[59405] and many others

X(60996) lies on these lines: {1, 12630}, {2, 7}, {3, 38171}, {4, 38122}, {5, 21151}, {8, 3826}, {10, 11038}, {20, 38150}, {69, 38186}, {75, 29627}, {85, 34019}, {86, 42318}, {100, 38205}, {140, 5759}, {141, 59405}, {145, 38200}, {193, 29628}, {210, 58563}, {214, 45043}, {236, 8388}, {279, 52705}, {344, 31995}, {346, 24199}, {354, 34784}, {376, 18482}, {390, 1125}, {391, 17298}, {404, 1001}, {442, 5809}, {443, 4313}, {468, 7717}, {516, 3523}, {518, 3619}, {547, 38065}, {549, 31671}, {551, 38092}, {615, 60887}, {631, 5805}, {632, 59381}, {673, 15668}, {938, 8728}, {954, 16408}, {966, 3834}, {971, 3090}, {1086, 16675}, {1100, 4648}, {1156, 6667}, {1212, 17092}, {1213, 31244}, {1223, 56331}, {1376, 2346}, {1385, 38149}, {1656, 5817}, {1698, 5542}, {1699, 43151}, {2345, 17265}, {2550, 3616}, {2932, 53055}, {2951, 3817}, {2975, 38206}, {3008, 3945}, {3036, 14151}, {3059, 3742}, {3068, 60921}, {3069, 60920}, {3091, 5732}, {3160, 34522}, {3161, 17263}, {3174, 4666}, {3177, 10012}, {3241, 17317}, {3243, 3617}, {3247, 17067}, {3475, 3711}, {3522, 52835}, {3525, 31658}, {3526, 5762}, {3530, 38137}, {3533, 21168}, {3545, 31672}, {3589, 51190}, {3618, 31189}, {3620, 16815}, {3628, 5779}, {3634, 5223}, {3636, 38201}, {3664, 31183}, {3672, 4859}, {3679, 51101}, {3689, 10578}, {3731, 4346}, {3739, 5936}, {3763, 51150}, {3812, 7672}, {3816, 7678}, {3824, 17559}, {3828, 38024}, {3836, 39581}, {3844, 38046}, {3848, 7671}, {3873, 40659}, {3875, 29621}, {3879, 24599}, {3912, 32087}, {3917, 58472}, {3925, 10580}, {3946, 29624}, {3973, 4896}, {4000, 5308}, {4060, 29616}, {4208, 7675}, {4292, 17554}, {4312, 34595}, {4321, 5261}, {4323, 5289}, {4326, 5274}, {4335, 25502}, {4343, 26102}, {4344, 16020}, {4371, 17311}, {4383, 41825}, {4384, 4869}, {4402, 4460}, {4422, 7222}, {4423, 9812}, {4454, 25101}, {4470, 17357}, {4488, 7321}, {4644, 17337}, {4675, 16669}, {4698, 51052}, {4699, 29579}, {4748, 48632}, {4855, 38316}, {4862, 25072}, {5055, 60901}, {5067, 36996}, {5068, 59389}, {5070, 59380}, {5079, 38139}, {5175, 50237}, {5232, 16832}, {5265, 12573}, {5284, 37309}, {5436, 56999}, {5543, 6603}, {5657, 20330}, {5703, 17582}, {5704, 5728}, {5708, 50394}, {5714, 16853}, {5735, 55864}, {5766, 17567}, {5772, 24325}, {5775, 5883}, {5815, 51706}, {5819, 17398}, {5833, 6700}, {5838, 17356}, {5839, 17313}, {5843, 55856}, {5845, 47355}, {5850, 51073}, {5880, 6910}, {5886, 35514}, {5901, 38121}, {6006, 27138}, {6557, 56085}, {6601, 56028}, {6684, 38036}, {6690, 36976}, {6846, 7171}, {6854, 54051}, {6856, 10394}, {6890, 38037}, {6933, 10861}, {7028, 8389}, {7229, 17279}, {7263, 36588}, {7269, 25930}, {7486, 43177}, {7670, 58444}, {7673, 58679}, {7677, 25524}, {7679, 25466}, {7815, 60882}, {7988, 58834}, {8167, 30295}, {8252, 60913}, {8253, 60914}, {8255, 31245}, {8581, 10588}, {9710, 9797}, {9940, 12669}, {9956, 38030}, {10124, 38080}, {10171, 43182}, {10177, 25722}, {10198, 60926}, {10200, 60925}, {10303, 21153}, {10427, 31272}, {10582, 61029}, {10584, 17668}, {10589, 14100}, {11024, 54286}, {11037, 19855}, {11284, 60897}, {11372, 38123}, {11451, 58473}, {12436, 17558}, {12690, 44217}, {12730, 38202}, {15570, 20050}, {15841, 45834}, {16593, 17321}, {16713, 17207}, {17073, 25932}, {17117, 29583}, {17151, 29600}, {17170, 56532}, {17228, 53620}, {17241, 42696}, {17255, 31285}, {17272, 31211}, {17277, 21296}, {17286, 30833}, {17303, 31243}, {17307, 19877}, {17340, 31139}, {17376, 37654}, {17380, 38314}, {17383, 20533}, {17384, 24580}, {17386, 20053}, {19521, 57283}, {19872, 43180}, {19878, 51090}, {20119, 34123}, {20582, 38086}, {20880, 20946}, {21020, 58385}, {24206, 38115}, {24393, 46933}, {25006, 41573}, {25055, 30331}, {26104, 41325}, {27818, 27826}, {28635, 48635}, {29607, 51171}, {29626, 48627}, {30284, 54318}, {30556, 31602}, {30557, 31601}, {30628, 58564}, {31333, 49722}, {32003, 60733}, {32008, 32098}, {32105, 50110}, {32858, 41915}, {34573, 50995}, {36620, 56310}, {37436, 54392}, {37453, 60879}, {37633, 54358}, {38094, 50836}, {38113, 46219}, {38124, 58421}, {38170, 51700}, {38207, 58453}, {39716, 55967}, {40537, 56933}, {43161, 54445}, {45755, 46399}, {51127, 51144}, {51514, 55866}, {51516, 55857}

X(60996) = midpoint of X(i) and X(j) for these {i,j}: {7, 60983}
X(60996) = X(i)-complementary conjugate of X(j) for these {i, j}: {45834, 141}
X(60996) = pole of line {14100, 60957} wrt Feuerbach hyperbola
X(60996) = pole of line {333, 17201} wrt Wallace hyperbola
X(60996) = pole of line {1, 4924} wrt dual conic of Yff parabola
X(60996) = orthology center of the pedal triangle of X(30389) wrt Aguilera triangle
X(60996) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(32015)}}, {{A, B, C, X(8), X(6666)}}, {{A, B, C, X(9), X(56054)}}, {{A, B, C, X(57), X(44841)}}, {{A, B, C, X(85), X(18230)}}, {{A, B, C, X(86), X(51351)}}, {{A, B, C, X(226), X(42318)}}, {{A, B, C, X(1445), X(27818)}}, {{A, B, C, X(3929), X(21446)}}, {{A, B, C, X(5936), X(40719)}}, {{A, B, C, X(6557), X(51780)}}, {{A, B, C, X(6601), X(20195)}}, {{A, B, C, X(9436), X(28626)}}, {{A, B, C, X(17338), X(56044)}}, {{A, B, C, X(21454), X(27475)}}
X(60996) = barycentric product X(i)*X(j) for these (i, j): {44841, 75}
X(60996) = barycentric quotient X(i)/X(j) for these (i, j): {44841, 1}
X(60996) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 38204, 40333}, {1, 40333, 59413}, {1, 59413, 12630}, {2, 144, 6666}, {2, 26806, 26685}, {2, 27186, 329}, {2, 30275, 60981}, {2, 3662, 5296}, {2, 5249, 18228}, {2, 59374, 6172}, {2, 59375, 60986}, {2, 7, 18230}, {2, 9776, 5273}, {5, 21151, 36991}, {7, 142, 59374}, {7, 6172, 60976}, {7, 60983, 527}, {7, 61017, 60995}, {7, 61019, 5435}, {7, 9, 60957}, {9, 20195, 58433}, {9, 3306, 60948}, {9, 6173, 60962}, {9, 60980, 20059}, {57, 60958, 61024}, {140, 38107, 5759}, {142, 20195, 2}, {142, 58433, 9}, {142, 60991, 27186}, {142, 60999, 20195}, {142, 61001, 60980}, {142, 6666, 6173}, {144, 6173, 7}, {144, 6666, 61023}, {346, 24199, 52709}, {551, 38092, 50839}, {631, 5805, 59418}, {1001, 59412, 30332}, {1125, 38052, 390}, {1656, 31657, 5817}, {2550, 3616, 8236}, {3059, 3742, 11025}, {3525, 59386, 31658}, {3619, 4751, 9780}, {3628, 38111, 5779}, {3664, 31183, 37681}, {3739, 29611, 5936}, {3739, 53665, 29611}, {3826, 38053, 8}, {4000, 17245, 5308}, {4312, 34595, 38059}, {4402, 17316, 4460}, {4648, 17278, 5222}, {4859, 29571, 3672}, {5067, 36996, 38108}, {5223, 38054, 30340}, {5550, 59412, 1001}, {6173, 61023, 60971}, {6173, 6666, 144}, {7308, 60955, 60949}, {8257, 60969, 60954}, {16832, 21255, 5232}, {17263, 42697, 3161}, {17265, 34824, 2345}, {18230, 50127, 60963}, {20195, 38093, 142}, {26685, 26806, 35578}, {33800, 60980, 60993}, {58433, 60980, 61001}, {58564, 61028, 30628}, {59375, 61006, 60933}, {60933, 60986, 61006}, {60942, 61020, 60984}, {60964, 61012, 60944}

X(60997) = X(2)X(7)∩X(10)X(6223)

Barycentrics    (a-b-c)*(a^4+(b-c)^4-2*a^2*(b^2-6*b*c+c^2)) : :
X(60997) = -7*X[9780]+4*X[15346]

X(60997) lies on these lines: {2, 7}, {8, 10394}, {10, 6223}, {21, 5766}, {220, 4644}, {281, 7229}, {390, 3872}, {516, 9623}, {936, 43177}, {958, 962}, {960, 11037}, {971, 6916}, {1012, 5759}, {1212, 4419}, {1532, 5817}, {2324, 3945}, {2550, 6925}, {2551, 5880}, {3036, 45116}, {3146, 5795}, {4295, 5234}, {4326, 7674}, {4363, 6554}, {4470, 46835}, {4659, 41006}, {4858, 52709}, {4863, 14100}, {5080, 59412}, {5220, 5815}, {5222, 55432}, {5223, 31397}, {5281, 47375}, {5289, 51099}, {5686, 6735}, {5696, 41562}, {5732, 54051}, {5735, 12572}, {5758, 31445}, {5762, 6913}, {5779, 6907}, {5784, 12528}, {5791, 5811}, {5805, 6939}, {5832, 6957}, {5851, 38057}, {5856, 52653}, {6067, 15845}, {6872, 30332}, {6904, 8544}, {6908, 52684}, {6909, 59418}, {6935, 21168}, {7282, 55116}, {7671, 36845}, {7961, 43065}, {8236, 38460}, {8255, 25568}, {8580, 41561}, {9780, 15346}, {9785, 11106}, {9814, 10590}, {9874, 10624}, {10177, 10580}, {12648, 61030}, {15254, 30478}, {17316, 25251}, {18220, 60926}, {18250, 30424}, {18251, 54228}, {18623, 55406}, {19843, 54370}, {26932, 29611}, {30305, 50836}, {30557, 60877}, {30854, 42697}, {31434, 60923}, {31627, 47386}, {32087, 53994}, {36888, 50562}, {37161, 55922}, {38211, 53620}

X(60997) = midpoint of X(i) and X(j) for these {i,j}: {144, 60975}
X(60997) = reflection of X(i) in X(j) for these {i,j}: {60953, 142}, {7, 60987}
X(60997) = complement of X(60998)
X(60997) = pole of line {4679, 14100} wrt Feuerbach hyperbola
X(60997) = orthology center of the pedal triangle of X(30503) wrt Aguilera triangle
X(60997) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(55984)}}, {{A, B, C, X(8), X(8545)}}, {{A, B, C, X(57), X(34919)}}
X(60997) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 144, 8545}, {2, 60935, 60995}, {7, 18228, 52457}, {7, 6172, 329}, {9, 52457, 18228}, {9, 6173, 3452}, {142, 527, 60953}, {144, 3219, 6172}, {144, 60975, 527}, {144, 60984, 20214}, {527, 60987, 7}, {5273, 6172, 9}, {6172, 18230, 60944}, {6172, 60995, 60935}, {8545, 60949, 56545}, {41572, 60949, 144}

X(60998) = X(1)X(54228)∩X(2)X(7)

Barycentrics    (a+b-c)*(a-b+c)*(3*a^3-5*a^2*(b+c)+(b-c)^2*(b+c)+a*(b^2+14*b*c+c^2)) : :
X(60998) = -5*X[3617]+8*X[15346]

X(60998) lies on these lines: {1, 54228}, {2, 7}, {85, 4454}, {145, 12529}, {176, 60877}, {279, 4419}, {388, 20070}, {390, 3476}, {391, 39126}, {516, 9814}, {651, 17014}, {948, 4346}, {954, 6909}, {971, 3488}, {1012, 36996}, {1156, 41556}, {1476, 3622}, {1532, 59386}, {3485, 30340}, {3487, 34862}, {3522, 5766}, {3586, 36991}, {3600, 5698}, {3617, 15346}, {3623, 30318}, {3672, 6180}, {3872, 12560}, {4298, 60905}, {4312, 31397}, {4315, 50836}, {4321, 52653}, {4644, 40133}, {4659, 31994}, {4667, 5543}, {4747, 55082}, {5059, 7320}, {5261, 5880}, {5265, 15254}, {5290, 30424}, {5686, 40663}, {5703, 43177}, {5726, 51100}, {5762, 6916}, {5779, 6939}, {5784, 20007}, {5843, 6913}, {5850, 9623}, {5851, 11038}, {6735, 59412}, {6907, 60922}, {6912, 11036}, {7671, 17625}, {7674, 10865}, {9533, 47374}, {9778, 30353}, {12640, 50725}, {14986, 54370}, {18393, 60924}, {20096, 34926}, {24352, 47386}, {30287, 58696}, {30312, 46932}, {38053, 51772}, {44675, 59372}, {45043, 54448}

X(60998) = reflection of X(i) in X(j) for these {i,j}: {60975, 7}, {7, 60953}
X(60998) = anticomplement of X(60997)
X(60998) = X(i)-Dao conjugate of X(j) for these {i, j}: {60997, 60997}
X(60998) = pole of line {21183, 53357} wrt Adams circle
X(60998) = orthology center of the pedal triangle of X(31393) wrt Aguilera triangle
X(60998) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(36973)}}, {{A, B, C, X(2), X(56263)}}, {{A, B, C, X(1476), X(8545)}}, {{A, B, C, X(3306), X(55937)}}, {{A, B, C, X(3452), X(34919)}}, {{A, B, C, X(5328), X(27475)}}, {{A, B, C, X(5437), X(55922)}}, {{A, B, C, X(6172), X(7320)}}, {{A, B, C, X(6173), X(57826)}}, {{A, B, C, X(28609), X(34917)}}
X(60998) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 12848, 21454}, {7, 18230, 60992}, {7, 29007, 8732}, {7, 30275, 59375}, {7, 5226, 6173}, {7, 527, 60975}, {7, 5435, 61022}, {7, 59374, 60993}, {7, 6172, 57}, {7, 60936, 20059}, {7, 60941, 60955}, {7, 60957, 52819}, {7, 60971, 61021}, {7, 60995, 30379}, {7, 61027, 30275}, {9, 6173, 6692}, {9, 61022, 5435}, {144, 21454, 12848}, {144, 60984, 9965}, {4654, 61021, 7}, {5219, 60993, 59374}, {5766, 8544, 3522}, {8545, 30379, 60995}, {12848, 21454, 60939}, {12848, 60934, 60946}, {12848, 60946, 144}, {17483, 20059, 60984}, {30379, 60995, 2}, {60942, 60955, 60941}

X(60999) = X(2)X(7)∩X(516)X(549)

Barycentrics    2*a^2+5*(b-c)^2-7*a*(b+c) : :
X(60999) = 7*X[2]+X[7], X[376]+3*X[38150], X[381]+3*X[38122], X[599]+3*X[38186], 5*X[631]+3*X[38073], 5*X[632]+3*X[38080], 5*X[1656]+3*X[38065], 5*X[1698]+3*X[38024], X[2550]+3*X[25055], -7*X[3090]+3*X[38075], X[3241]+3*X[38200], X[3243]+3*X[53620] and many others

X(60999) lies on these lines: {2, 7}, {376, 38150}, {381, 38122}, {516, 549}, {518, 3828}, {519, 3826}, {528, 1125}, {547, 971}, {551, 5853}, {599, 38186}, {631, 38073}, {632, 38080}, {1001, 16417}, {1121, 32015}, {1266, 29626}, {1656, 38065}, {1698, 38024}, {2325, 50119}, {2550, 25055}, {2801, 10172}, {3008, 16666}, {3090, 38075}, {3241, 38200}, {3243, 53620}, {3525, 5735}, {3526, 38067}, {3545, 5732}, {3616, 38092}, {3624, 38025}, {3634, 4407}, {3653, 43175}, {3663, 16677}, {3664, 16671}, {3679, 38053}, {3686, 17297}, {3723, 3946}, {3742, 61030}, {3763, 38086}, {3834, 31211}, {3848, 15733}, {4060, 17241}, {4395, 29606}, {4545, 17234}, {4667, 31183}, {4669, 42871}, {4688, 41141}, {4700, 29628}, {4758, 31191}, {4982, 29590}, {5054, 5805}, {5071, 21151}, {5220, 38101}, {5298, 12573}, {5542, 31479}, {5698, 34595}, {5759, 15709}, {5762, 10124}, {5880, 19862}, {6006, 45339}, {6174, 38205}, {6681, 28534}, {8703, 18482}, {9780, 38097}, {9843, 50740}, {10012, 44664}, {10156, 10171}, {10304, 52835}, {10427, 59376}, {11238, 15006}, {11539, 31658}, {13846, 60921}, {13847, 60920}, {15254, 19878}, {15692, 59385}, {15694, 38107}, {15699, 31657}, {15701, 31671}, {15702, 21153}, {15703, 38108}, {15721, 59418}, {15723, 59381}, {16593, 41311}, {16672, 17067}, {16884, 17278}, {17133, 29600}, {17243, 28313}, {17244, 50110}, {17251, 21255}, {17264, 24199}, {17355, 49733}, {17359, 34824}, {19709, 31672}, {19875, 24393}, {19876, 38057}, {20330, 50821}, {21356, 51194}, {21358, 51002}, {25072, 49742}, {25101, 49722}, {28297, 59585}, {28301, 41313}, {29582, 50099}, {29604, 31243}, {30331, 51109}, {31139, 50118}, {31140, 61029}, {31146, 61031}, {31157, 38206}, {31235, 38095}, {31253, 34753}, {31260, 38096}, {38052, 47357}, {38082, 55856}, {38088, 47355}, {38111, 38318}, {38314, 40333}, {38454, 58441}, {40659, 58607}, {42819, 51108}, {43151, 50802}, {47352, 47595}, {48310, 51151}, {49765, 50085}, {51152, 59373}, {57005, 57284}, {58560, 58634}, {58563, 58629}

X(60999) = midpoint of X(i) and X(j) for these {i,j}: {1001, 51100}, {2, 142}, {20330, 50821}, {24393, 51099}, {38111, 38318}, {4669, 42871}, {43151, 50802}, {58560, 58634}, {58563, 58629}, {6173, 60986}, {60942, 60963}, {8703, 18482}
X(60999) = reflection of X(i) in X(j) for these {i,j}: {2, 58433}, {42819, 51108}, {6666, 2}, {61033, 58560}
X(60999) = complement of X(60986)
X(60999) = pole of line {28292, 48156} wrt orthoptic circle of the Steiner inellipse
X(60999) = pole of line {522, 47869} wrt Steiner inellipse
X(60999) = pole of line {1, 50838} wrt dual conic of Yff parabola
X(60999) = orthology center of the pedal triangle of X(31662) wrt Aguilera triangle
X(60999) = intersection, other than A, B, C, of circumconics {{A, B, C, X(527), X(32015)}}, {{A, B, C, X(1121), X(6666)}}
X(60999) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 142, 527}, {2, 38093, 142}, {2, 59374, 9}, {2, 59375, 18230}, {2, 6173, 60986}, {2, 60996, 38093}, {9, 6173, 60984}, {142, 20195, 58433}, {142, 58433, 6666}, {142, 60986, 6173}, {142, 61001, 7}, {142, 6666, 60980}, {6666, 60980, 61000}, {20195, 38093, 2}, {24627, 27130, 17338}, {60963, 61023, 60942}

X(61000) = X(2)X(7)∩X(44)X(3946)

Barycentrics    6*a^2-(b-c)^2-5*a*(b+c) : :
X(61000) = -15*X[2]+7*X[7], 7*X[390]+X[20053], X[1657]+7*X[5779], X[3630]+7*X[51144], X[3633]+7*X[5223], -15*X[3843]+7*X[31671], 5*X[4668]+7*X[5698], X[4764]+7*X[51052], -11*X[5072]+7*X[5805], -7*X[5732]+11*X[21735], 7*X[5759]+X[33703], X[6144]+7*X[50995] and many others

X(61000) lies on these lines: {2, 7}, {37, 4909}, {44, 3946}, {72, 57003}, {190, 3686}, {192, 4700}, {193, 4029}, {320, 31333}, {390, 20053}, {498, 41707}, {516, 3627}, {518, 3635}, {524, 59585}, {528, 50837}, {548, 971}, {954, 19538}, {1125, 5852}, {1657, 5779}, {2321, 25728}, {2325, 4416}, {3008, 15492}, {3625, 4133}, {3630, 51144}, {3633, 5223}, {3663, 16885}, {3664, 16814}, {3707, 3729}, {3731, 4667}, {3759, 50090}, {3843, 31671}, {3850, 5762}, {3973, 4419}, {3986, 4758}, {4021, 16669}, {4060, 17346}, {4361, 28301}, {4370, 17344}, {4422, 53598}, {4478, 36522}, {4480, 17277}, {4643, 59579}, {4668, 5698}, {4681, 4856}, {4718, 50019}, {4764, 51052}, {4869, 31722}, {4887, 17337}, {4946, 22312}, {4982, 17319}, {5072, 5805}, {5732, 21735}, {5759, 33703}, {5795, 41687}, {5843, 12108}, {5850, 14150}, {5851, 43151}, {5857, 18249}, {6144, 50995}, {7228, 31211}, {15006, 60910}, {15587, 58677}, {15684, 31672}, {15689, 60884}, {15712, 31658}, {15726, 58635}, {15733, 58678}, {15828, 17279}, {17067, 17276}, {17132, 17348}, {17133, 17262}, {17239, 17332}, {17241, 17347}, {17255, 31191}, {17275, 50118}, {17329, 29596}, {17365, 25072}, {17538, 21168}, {18482, 23046}, {30331, 50834}, {36991, 49140}, {37654, 55998}, {38130, 60896}, {40998, 51463}, {43177, 59381}, {49716, 59576}, {51790, 53620}, {56998, 57284}, {58608, 61033}

X(61000) = midpoint of X(i) and X(j) for these {i,j}: {142, 144}, {5220, 51090}, {5698, 24393}, {60962, 60977}, {9, 60942}
X(61000) = reflection of X(i) in X(j) for these {i,j}: {15587, 58677}, {6666, 9}, {60980, 6666}, {61033, 58608}, {7, 58433}
X(61000) = complement of X(60962)
X(61000) = pole of line {4995, 14100} wrt Feuerbach hyperbola
X(61000) = pole of line {522, 27115} wrt Steiner inellipse
X(61000) = orthology center of the pedal triangle of X(31663) wrt Aguilera triangle
X(61000) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(9328)}}, {{A, B, C, X(57), X(9343)}}
X(61000) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 144, 60976}, {2, 226, 26065}, {2, 31053, 26685}, {2, 60977, 60962}, {7, 60986, 58433}, {7, 9, 60986}, {9, 20195, 61023}, {9, 36973, 60964}, {9, 6172, 60942}, {9, 60933, 18230}, {9, 60957, 61001}, {9, 60966, 61004}, {9, 61005, 60994}, {142, 144, 527}, {142, 60942, 144}, {142, 60962, 61020}, {144, 18230, 60933}, {144, 60976, 60977}, {144, 60983, 9}, {144, 61006, 60983}, {329, 5325, 58463}, {527, 58433, 7}, {527, 6666, 60980}, {5220, 51090, 5853}, {6666, 60980, 60999}, {8545, 61014, 60945}, {15492, 17334, 3008}, {16669, 49742, 4021}, {17350, 50093, 5750}, {18230, 60933, 142}, {20059, 60983, 45789}, {20059, 61023, 20195}, {25527, 58463, 2}, {25728, 54280, 2321}, {29007, 50573, 52819}, {30852, 60984, 20059}, {58433, 60986, 6666}, {60936, 60954, 3911}, {60946, 60947, 60992}

X(61001) = X(2)X(7)∩X(10)X(42819)

Barycentrics    4*a^2+3*(b-c)^2-7*a*(b+c) : :
X(61001) = -21*X[2]+X[7], 3*X[10]+2*X[42819], 2*X[140]+3*X[38318], 3*X[210]+2*X[61033], -6*X[547]+X[18482], X[1001]+4*X[3634], 4*X[1125]+X[24393], 7*X[3090]+3*X[21153], -X[3243]+11*X[5550], 7*X[3523]+3*X[59389], -11*X[3525]+X[5732], 7*X[3526]+3*X[38108] and many others

X(61001) lies on these lines: {2, 7}, {10, 42819}, {37, 25077}, {140, 38318}, {210, 61033}, {516, 1656}, {518, 19862}, {547, 18482}, {632, 971}, {673, 56061}, {954, 16856}, {1001, 3634}, {1100, 17337}, {1125, 24393}, {1698, 5853}, {2321, 17263}, {2550, 4857}, {3008, 16777}, {3090, 21153}, {3243, 5550}, {3523, 59389}, {3525, 5732}, {3526, 38108}, {3533, 5817}, {3622, 59414}, {3624, 38057}, {3628, 31658}, {3707, 17234}, {3731, 17067}, {3740, 58564}, {3742, 58635}, {3819, 58473}, {3826, 3847}, {3879, 29626}, {3946, 16673}, {3950, 28309}, {3986, 17356}, {4044, 29446}, {4060, 4384}, {4098, 4395}, {4423, 61031}, {4667, 16669}, {4698, 31191}, {4896, 15492}, {5054, 31672}, {5056, 52835}, {5067, 38150}, {5070, 5805}, {5218, 15006}, {5326, 14100}, {5762, 48154}, {5779, 55858}, {6594, 6667}, {6600, 8167}, {6989, 9842}, {7228, 15828}, {7294, 8581}, {7486, 59418}, {8236, 46932}, {9780, 38316}, {9956, 43175}, {10164, 42356}, {10175, 52769}, {10219, 58472}, {11019, 59476}, {11495, 58441}, {11539, 60901}, {12437, 17590}, {13411, 50795}, {14869, 38139}, {15185, 58677}, {15254, 38204}, {15481, 38054}, {15570, 15808}, {15702, 38075}, {15703, 31671}, {16239, 43177}, {16503, 29596}, {16667, 37650}, {16675, 17278}, {17243, 28329}, {17275, 41141}, {17279, 31211}, {17341, 24603}, {17348, 28337}, {17552, 57284}, {19855, 21627}, {19876, 38025}, {19877, 38200}, {24389, 59584}, {28345, 58418}, {31248, 31278}, {31423, 38037}, {31657, 55859}, {34522, 59610}, {34595, 38053}, {34824, 59579}, {36991, 55864}, {38107, 55860}, {38111, 41992}, {38113, 55856}, {38122, 46219}, {38123, 60911}, {38171, 55861}, {40659, 58451}, {43161, 54447}, {46845, 50114}, {46931, 59413}, {46936, 59385}, {55857, 59381}

X(61001) = midpoint of X(i) and X(j) for these {i,j}: {18230, 20195}, {61006, 61020}
X(61001) = reflection of X(i) in X(j) for these {i,j}: {142, 20195}, {18230, 6666}
X(61001) = complement of X(20195)
X(61001) = complement of isotomic conjugate of X(56060)
X(61001) = X(i)-complementary conjugate of X(j) for these {i, j}: {56028, 141}, {56060, 2887}, {56350, 1329}, {58107, 4885}
X(61001) = pole of line {522, 47664} wrt Steiner inellipse
X(61001) = orthology center of the pedal triangle of X(31666) wrt Aguilera triangle
X(61001) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(673), X(4114)}}, {{A, B, C, X(9436), X(56061)}}, {{A, B, C, X(20195), X(56060)}}
X(61001) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 18230, 20195}, {2, 51780, 58463}, {2, 6666, 142}, {2, 9, 58433}, {9, 142, 60962}, {9, 6173, 60957}, {9, 60957, 61000}, {9, 60996, 60980}, {142, 60986, 60942}, {142, 6666, 60986}, {527, 6666, 18230}, {15808, 38210, 15570}, {17356, 31285, 3986}, {18230, 20195, 527}, {35595, 60948, 9}, {38059, 51073, 3826}, {58433, 60980, 60996}, {61016, 61017, 226}

X(61002) = X(2)X(7)∩X(10)X(5832)

Barycentrics    (a-b-c)*(2*a^4+(b-c)^4-a^3*(b+c)+a*(b-c)^2*(b+c)+a^2*(-3*b^2+2*b*c-3*c^2)) : :

X(61002) lies on these lines: {2, 7}, {10, 5832}, {20, 15829}, {21, 3255}, {219, 3663}, {220, 17276}, {281, 17272}, {377, 5837}, {516, 3878}, {518, 14454}, {960, 4292}, {971, 31789}, {1071, 12572}, {1125, 15823}, {1146, 17344}, {1212, 17365}, {1329, 15481}, {2323, 3946}, {2324, 4419}, {2550, 5735}, {2551, 54422}, {3059, 60919}, {3664, 40937}, {3686, 4858}, {3868, 5795}, {3885, 5853}, {4304, 5289}, {4643, 20262}, {4862, 24779}, {5223, 10629}, {5250, 60925}, {5267, 43177}, {5542, 8666}, {5698, 5732}, {5762, 31837}, {5825, 6919}, {5833, 38057}, {5850, 30329}, {5856, 14740}, {5857, 12573}, {5883, 18250}, {6603, 17246}, {7675, 56387}, {10165, 31424}, {10391, 40998}, {10427, 43151}, {10444, 24705}, {12514, 60896}, {13405, 41548}, {15296, 15865}, {15587, 38454}, {15837, 61035}, {16112, 24703}, {17183, 40979}, {17253, 46835}, {17273, 37774}, {17332, 34852}, {17347, 30854}, {21616, 60911}, {22464, 37659}, {24389, 42014}, {26932, 53598}, {41551, 44256}

X(61002) = midpoint of X(i) and X(j) for these {i,j}: {144, 60936}, {3059, 60919}, {60961, 61003}, {7, 60979}
X(61002) = reflection of X(i) in X(j) for these {i,j}: {52819, 142}
X(61002) = complement of X(41572)
X(61002) = pole of line {6067, 14100} wrt Feuerbach hyperbola
X(61002) = pole of line {284, 3256} wrt Stammler hyperbola
X(61002) = pole of line {522, 28834} wrt Steiner inellipse
X(61002) = pole of line {1, 5832} wrt dual conic of Yff parabola
X(61002) = orthology center of the pedal triangle of X(31786) wrt Aguilera triangle
X(61002) = intersection, other than A, B, C, of circumconics {{A, B, C, X(21), X(29007)}}, {{A, B, C, X(226), X(3255)}}, {{A, B, C, X(3254), X(52819)}}, {{A, B, C, X(6601), X(12848)}}, {{A, B, C, X(8232), X(34919)}}, {{A, B, C, X(9965), X(60114)}}
X(61002) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 144, 60990}, {7, 5249, 60980}, {7, 60957, 9965}, {9, 60977, 60940}, {142, 527, 52819}, {142, 60942, 60994}, {142, 60994, 3911}, {144, 60936, 527}, {144, 61012, 50573}, {307, 26651, 44356}, {329, 60934, 60965}, {1944, 4357, 40942}, {3452, 60942, 9}, {5735, 5785, 2550}, {6646, 27420, 40880}, {53598, 59646, 26932}

X(61003) = X(2)X(7)∩X(4)X(5223)

Barycentrics    2*a^5-3*a^4*(b+c)-(b-c)^4*(b+c)-2*a^3*(b+c)^2+4*a^2*(b+c)*(b^2+c^2) : :
X(61003) = -2*X[5572]+3*X[40998]

X(61003) lies on these lines: {2, 7}, {4, 5223}, {8, 52835}, {69, 30625}, {72, 516}, {218, 3663}, {219, 43035}, {220, 3668}, {390, 11523}, {405, 5542}, {442, 13159}, {480, 7580}, {518, 950}, {954, 5248}, {960, 12573}, {1260, 11495}, {1490, 2951}, {1728, 60924}, {1864, 60919}, {2321, 45738}, {2550, 12526}, {2900, 36976}, {3177, 3879}, {3419, 34648}, {3436, 24393}, {3664, 16601}, {3686, 30807}, {3869, 5853}, {3874, 5728}, {3875, 20111}, {3927, 5805}, {4292, 45120}, {4326, 5698}, {4341, 34526}, {5436, 11038}, {5572, 40998}, {5715, 5817}, {5730, 43175}, {5758, 11372}, {5762, 5777}, {5779, 5812}, {5795, 7672}, {5843, 13369}, {6067, 8226}, {6068, 13257}, {6356, 51418}, {6846, 38036}, {6889, 38130}, {8804, 50995}, {10123, 15587}, {10481, 25878}, {10889, 24705}, {11517, 43182}, {14189, 59605}, {15006, 30628}, {17270, 30694}, {21068, 24316}, {21084, 28849}, {21296, 56937}, {30695, 32099}, {41006, 56927}, {43151, 61035}, {43216, 49757}, {54398, 59385}, {56020, 60721}

X(61003) = midpoint of X(i) and X(j) for these {i,j}: {144, 60979}, {60936, 60957}
X(61003) = reflection of X(i) in X(j) for these {i,j}: {12573, 960}, {30628, 15006}, {5728, 12572}, {52819, 9}, {60961, 61002}, {7672, 5795}
X(61003) = anticomplement of X(60945)
X(61003) = X(i)-Dao conjugate of X(j) for these {i, j}: {60945, 60945}
X(61003) = pole of line {3064, 8713} wrt polar circle
X(61003) = pole of line {3925, 14100} wrt Feuerbach hyperbola
X(61003) = orthology center of the pedal triangle of X(31793) wrt Aguilera triangle
X(61003) = intersection, other than A, B, C, of circumconics {{A, B, C, X(57), X(7964)}}, {{A, B, C, X(63), X(42015)}}
X(61003) = barycentric product X(i)*X(j) for these (i, j): {75, 7964}
X(61003) = barycentric quotient X(i)/X(j) for these (i, j): {7964, 1}
X(61003) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 60958, 142}, {9, 25525, 18230}, {9, 28609, 8232}, {9, 527, 52819}, {9, 52819, 60972}, {9, 60933, 60987}, {9, 60950, 61014}, {9, 60977, 60950}, {9, 60982, 60959}, {9, 60990, 1708}, {9, 60991, 6666}, {9, 61010, 226}, {144, 329, 9}, {144, 60966, 60942}, {144, 60979, 527}, {527, 61002, 60961}, {5850, 12572, 5728}, {17781, 60979, 144}, {20059, 60959, 60982}, {21617, 61024, 5745}, {52457, 60990, 60992}

X(61004) = X(2)X(7)∩X(37)X(6510)

Barycentrics    a*(a^4+4*a^2*b*c-2*a^3*(b+c)-(b-c)^2*(b^2+3*b*c+c^2)+a*(b+c)*(2*b^2-3*b*c+2*c^2)) : :
X(61004) = X[41711]+3*X[42014]

X(61004) lies on circumconic {{A, B, C, X(6504), X(26842)}} and on these lines: {2, 7}, {37, 6510}, {45, 16578}, {515, 6930}, {516, 6923}, {518, 50194}, {758, 1159}, {971, 6914}, {993, 5126}, {1001, 2801}, {1125, 15297}, {1156, 1621}, {1376, 6594}, {1478, 5698}, {2550, 24402}, {2886, 5856}, {3254, 11680}, {3731, 53996}, {3822, 5880}, {3884, 37234}, {3925, 6068}, {3939, 24341}, {4364, 36949}, {4585, 51058}, {4667, 8557}, {5248, 40263}, {5432, 10427}, {5440, 5784}, {5528, 55920}, {5729, 18389}, {5732, 6950}, {5759, 6951}, {5805, 6980}, {5817, 6965}, {5851, 6690}, {5853, 12647}, {15325, 25557}, {15587, 15813}, {15730, 34522}, {15733, 42869}, {15837, 17668}, {16120, 37601}, {16579, 34048}, {16608, 17332}, {17044, 49737}, {17351, 59682}, {20119, 59416}, {20588, 61031}, {21362, 54324}, {28453, 60884}, {41711, 42014}, {47357, 51768}

X(61004) = midpoint of X(i) and X(j) for these {i,j}: {144, 61011}, {1478, 5698}, {9, 8545}
X(61004) = reflection of X(i) in X(j) for these {i,j}: {5880, 3822}, {61021, 60980}, {993, 15254}
X(61004) = pole of line {23865, 52726} wrt circumcircle
X(61004) = pole of line {14100, 41566} wrt Feuerbach hyperbola
X(61004) = orthology center of the pedal triangle of X(32613) wrt Aguilera triangle
X(61004) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 60944, 9}, {7, 9, 60994}, {9, 20195, 61012}, {9, 6173, 37787}, {9, 60933, 60970}, {9, 60937, 60974}, {9, 60964, 142}, {9, 60965, 61005}, {9, 60966, 61000}, {9, 60973, 60942}, {9, 60977, 61024}, {9, 60985, 60947}, {63, 31266, 27003}, {63, 7308, 5745}, {144, 61011, 527}, {144, 61027, 61011}, {527, 60980, 61021}, {29007, 60981, 60935}, {60935, 60969, 60981}, {60937, 60974, 60962}

X(61005) = X(2)X(7)∩X(90)X(5698)

Barycentrics    a*(a^4-4*a^2*b*c-2*a^3*(b+c)-(b-c)^2*(b^2+c^2)+2*a*(b+c)*(b^2+b*c+c^2)) : :
X(61005) = -X[9579]+3*X[38200], -3*X[16418]+2*X[42819]

X(61005) lies on these lines: {2, 7}, {40, 24393}, {46, 38057}, {77, 52405}, {90, 5698}, {191, 3174}, {220, 53996}, {516, 7330}, {518, 3295}, {920, 15298}, {943, 31424}, {971, 1158}, {1001, 5045}, {1376, 58635}, {1723, 4419}, {1768, 6594}, {1770, 2550}, {3059, 20588}, {3243, 5250}, {3678, 41854}, {3681, 7676}, {3730, 7289}, {3826, 57282}, {3946, 16572}, {3951, 7675}, {4294, 5853}, {4326, 61030}, {4343, 32912}, {4640, 6600}, {4641, 54358}, {4648, 56217}, {4869, 56244}, {4877, 18206}, {5686, 56288}, {5732, 55104}, {5762, 40273}, {7672, 11684}, {9579, 38200}, {10390, 56203}, {10582, 58607}, {12704, 38037}, {15254, 58563}, {15481, 58634}, {15662, 52542}, {16418, 42819}, {17201, 18164}, {17296, 55337}, {17561, 51816}, {21151, 26878}, {24467, 31658}, {31672, 37584}, {33635, 39273}, {37532, 38108}, {40998, 41573}, {43151, 60912}, {45126, 55466}, {49627, 51090}

X(61005) = reflection of X(i) in X(j) for these {i,j}: {1001, 31445}, {57282, 3826}, {60964, 9}
X(61005) = orthology center of the pedal triangle of X(35239) wrt Aguilera triangle
X(61005) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(41857)}}, {{A, B, C, X(90), X(1445)}}, {{A, B, C, X(553), X(39273)}}, {{A, B, C, X(943), X(8232)}}, {{A, B, C, X(4654), X(10390)}}, {{A, B, C, X(5905), X(6601)}}, {{A, B, C, X(6666), X(7131)}}, {{A, B, C, X(18230), X(56203)}}, {{A, B, C, X(33635), X(40131)}}
X(61005) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 144, 60973}, {9, 20195, 3305}, {9, 527, 60964}, {9, 57, 6666}, {9, 6173, 60958}, {9, 63, 60974}, {9, 60965, 61004}, {9, 60968, 2}, {9, 60974, 8257}, {9, 60977, 8545}, {9, 60985, 18230}, {9, 60990, 142}, {63, 3219, 1708}, {144, 61024, 9}, {144, 61025, 56551}, {3218, 18230, 60985}, {3305, 60938, 20195}, {5220, 11495, 40659}

X(61006) = X(2)X(7)∩X(190)X(391)

Barycentrics    7*a^2-(b-c)^2-6*a*(b+c) : :
X(61006) = -9*X[2]+4*X[7], -X[4]+6*X[51516], X[20]+4*X[5779], X[69]+4*X[51144], X[145]+4*X[5223], X[149]+4*X[6068], X[193]+4*X[50995], -6*X[210]+X[25722], 3*X[376]+2*X[60884], 4*X[390]+X[3621], 4*X[1156]+X[20095], -X[1278]+6*X[27484] and many others

X(61006) lies on these lines: {2, 7}, {4, 51516}, {8, 25728}, {20, 5779}, {44, 3672}, {45, 3945}, {69, 51144}, {72, 11106}, {145, 5223}, {149, 6068}, {190, 391}, {193, 50995}, {210, 25722}, {319, 346}, {344, 17361}, {376, 60884}, {390, 3621}, {452, 20008}, {516, 3617}, {518, 3623}, {528, 50840}, {631, 5843}, {954, 16865}, {966, 7227}, {971, 3522}, {1001, 37677}, {1156, 20095}, {1278, 27484}, {1654, 41325}, {1743, 4021}, {1992, 51191}, {2325, 32099}, {3060, 58534}, {3062, 9778}, {3090, 60922}, {3091, 5762}, {3146, 5759}, {3161, 4416}, {3177, 25243}, {3240, 4335}, {3241, 50834}, {3523, 36996}, {3525, 59380}, {3533, 38111}, {3543, 60901}, {3544, 38137}, {3600, 60909}, {3616, 5850}, {3620, 4473}, {3622, 17120}, {3628, 51514}, {3679, 50837}, {3681, 14100}, {3707, 32087}, {3731, 29624}, {3740, 31391}, {3832, 5817}, {3839, 31671}, {3854, 59385}, {3873, 58608}, {3927, 5129}, {3935, 4326}, {3940, 50742}, {3951, 10398}, {3973, 5222}, {4000, 15492}, {4297, 52665}, {4304, 20007}, {4312, 9780}, {4346, 17334}, {4384, 4488}, {4419, 16885}, {4430, 5572}, {4452, 17349}, {4454, 17277}, {4460, 4700}, {4480, 31995}, {4517, 9309}, {4644, 16814}, {4661, 30628}, {4678, 5086}, {4687, 4747}, {4779, 49450}, {4869, 17347}, {5044, 10861}, {5056, 59386}, {5059, 36991}, {5068, 5805}, {5232, 17293}, {5261, 60883}, {5274, 60919}, {5542, 46934}, {5550, 59372}, {5719, 17558}, {5722, 54398}, {5726, 18249}, {5732, 21734}, {5766, 20013}, {5838, 25269}, {5839, 28329}, {5852, 30340}, {5853, 20052}, {6605, 42483}, {6636, 60897}, {6684, 41705}, {7231, 17259}, {7268, 27340}, {7378, 60879}, {7408, 7717}, {7486, 38107}, {8972, 60913}, {9802, 51768}, {10303, 31657}, {11038, 15254}, {11160, 50997}, {11372, 20070}, {11552, 19855}, {11684, 41712}, {12528, 51489}, {13941, 60914}, {15022, 38108}, {15717, 31658}, {15828, 17284}, {15913, 56309}, {17244, 32093}, {17262, 28309}, {17288, 30833}, {17314, 28337}, {17343, 20533}, {17364, 29621}, {17576, 41228}, {17768, 40333}, {20049, 50835}, {20075, 42014}, {20080, 51190}, {21296, 25101}, {24393, 30332}, {26878, 37108}, {27804, 58398}, {29611, 59579}, {30305, 41229}, {30424, 46931}, {30625, 52715}, {30695, 32024}, {31145, 50836}, {31302, 39567}, {34632, 45116}, {36101, 56200}, {37685, 55438}, {38052, 46932}, {38113, 55864}, {38171, 46935}, {38204, 46930}, {43983, 43984}, {45289, 60906}, {46872, 54120}, {46933, 59412}, {50693, 59418}, {50808, 58834}

X(61006) = reflection of X(i) in X(j) for these {i,j}: {18230, 9}, {56518, 45789}, {61020, 61001}, {7, 20195}
X(61006) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 31507}
X(61006) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 31507}
X(61006) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {56331, 21285}, {58106, 693}
X(61006) = pole of line {3740, 5281} wrt Feuerbach hyperbola
X(61006) = pole of line {522, 58835} wrt Steiner circumellipse
X(61006) = orthology center of the pedal triangle of X(35242) wrt Aguilera triangle
X(61006) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(36625)}}, {{A, B, C, X(7), X(36605)}}, {{A, B, C, X(8), X(20059)}}, {{A, B, C, X(57), X(31508)}}, {{A, B, C, X(142), X(42483)}}, {{A, B, C, X(5437), X(36101)}}, {{A, B, C, X(6646), X(46872)}}, {{A, B, C, X(40869), X(56200)}}
X(61006) = barycentric product X(i)*X(j) for these (i, j): {31508, 75}
X(61006) = barycentric quotient X(i)/X(j) for these (i, j): {1, 31507}, {31508, 1}
X(61006) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 144, 20059}, {7, 18230, 20195}, {7, 6172, 60942}, {9, 142, 61023}, {9, 527, 18230}, {9, 63, 61012}, {9, 60933, 60986}, {9, 60935, 61025}, {9, 60937, 3305}, {9, 60949, 60970}, {9, 60965, 60958}, {9, 60966, 60969}, {9, 60970, 61026}, {9, 60973, 60981}, {9, 60977, 6666}, {9, 61000, 6172}, {9, 61005, 37787}, {9, 61007, 54357}, {142, 60957, 60984}, {144, 60939, 20078}, {144, 60984, 60957}, {190, 391, 4461}, {527, 20195, 7}, {527, 45789, 56518}, {527, 61001, 61020}, {3161, 4416, 29616}, {3305, 21454, 2}, {4419, 16885, 37681}, {4704, 51170, 3623}, {5223, 52653, 145}, {5698, 15481, 5686}, {5779, 21168, 20}, {6172, 60983, 9}, {6666, 60942, 60977}, {8232, 41563, 60975}, {14100, 58678, 3681}, {17332, 54389, 5232}, {17334, 37650, 4346}, {17349, 20073, 4452}, {21296, 31722, 25101}, {36996, 59381, 3523}, {41563, 60944, 8232}, {50573, 60935, 17484}, {60933, 60986, 60996}, {60933, 60996, 59375}, {60937, 60941, 21454}, {60946, 60954, 8732}, {60957, 61023, 142}, {60983, 61000, 144}

X(61007) = X(2)X(7)∩X(80)X(2093)

Barycentrics    (a+b-c)*(a-b+c)*(5*a^3-8*a^2*(b+c)+2*(b-c)^2*(b+c)+a*(b^2+6*b*c+c^2)) : :
X(61007) = -3*X[7962]+4*X[30331], -3*X[10384]+2*X[30305]

X(61007) lies on these lines: {2, 7}, {45, 14564}, {46, 52684}, {56, 60885}, {65, 60905}, {80, 2093}, {516, 5727}, {517, 14100}, {971, 18397}, {1323, 1419}, {1699, 36971}, {1743, 5723}, {1788, 30424}, {2099, 50836}, {3340, 5698}, {3553, 7277}, {4021, 7961}, {4304, 5759}, {4312, 5587}, {4315, 5850}, {4321, 5852}, {4328, 17334}, {4480, 6604}, {4644, 59215}, {5193, 42843}, {5220, 9578}, {5223, 5252}, {5526, 6180}, {5692, 8581}, {5696, 41538}, {5720, 5843}, {5722, 5762}, {5729, 5735}, {5851, 30353}, {7098, 60912}, {7288, 43180}, {7962, 30331}, {9312, 20072}, {9580, 38454}, {9814, 11246}, {10384, 30305}, {10394, 15556}, {12730, 30628}, {15299, 37704}, {15726, 41539}, {16670, 22464}, {23708, 38036}, {30330, 60919}, {31162, 51768}, {36996, 52026}, {50443, 60895}, {50834, 51782}

X(61007) = reflection of X(i) in X(j) for these {i,j}: {36973, 60940}, {4312, 36279}, {57, 12848}, {60956, 61022}
X(61007) = pole of line {5219, 14100} wrt Feuerbach hyperbola
X(61007) = orthology center of the pedal triangle of X(36279) wrt Aguilera triangle
X(61007) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(80), X(144)}}, {{A, B, C, X(3062), X(3218)}}, {{A, B, C, X(5219), X(23618)}}, {{A, B, C, X(15909), X(20059)}}
X(61007) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 41563, 50573}, {7, 60939, 4031}, {7, 60947, 20195}, {7, 9, 5219}, {144, 52819, 60937}, {527, 12848, 57}, {527, 60940, 36973}, {527, 61022, 60956}, {4031, 60961, 7}, {4312, 41700, 5587}, {4312, 41707, 41705}, {5435, 60984, 60993}, {5729, 11662, 5735}, {6172, 60975, 226}, {6173, 37787, 31231}, {8545, 60951, 60982}, {8545, 60982, 4654}, {20059, 60941, 60992}, {41563, 41572, 9}, {60932, 60946, 60953}, {60939, 60957, 60961}

X(61008) = X(1)X(37771)∩X(2)X(7)

Barycentrics    (a+b-c)*(a-b+c)*(a^2*(b+c)+(b-c)^2*(b+c)-a*(2*b^2+b*c+2*c^2)) : :

X(61008) lies on these lines: {1, 37771}, {2, 7}, {5, 10394}, {11, 7671}, {12, 7705}, {65, 30312}, {85, 18151}, {390, 30384}, {404, 5880}, {495, 38055}, {498, 60895}, {516, 5010}, {518, 7679}, {528, 15950}, {651, 4675}, {946, 30332}, {948, 1443}, {954, 6911}, {971, 6830}, {997, 38052}, {1001, 5172}, {1006, 38122}, {1441, 17234}, {1442, 4648}, {1478, 18450}, {1656, 5729}, {1737, 5542}, {1788, 50393}, {1836, 30295}, {2476, 5784}, {2550, 4511}, {2801, 7951}, {2886, 61035}, {3035, 33558}, {3085, 60926}, {3476, 38053}, {3485, 37462}, {3488, 6826}, {3523, 12047}, {3586, 6839}, {3826, 7672}, {3873, 41555}, {4000, 7269}, {4312, 5131}, {4552, 17244}, {4751, 40999}, {4859, 7190}, {5218, 36976}, {5228, 17796}, {5252, 14151}, {5261, 51706}, {5432, 38454}, {5444, 52769}, {5543, 24181}, {5696, 25639}, {5698, 6910}, {5703, 55108}, {5723, 17392}, {5726, 38024}, {5728, 6829}, {5732, 6840}, {5759, 6954}, {5805, 6905}, {5809, 6843}, {5817, 6859}, {5886, 53055}, {6049, 51723}, {6067, 34784}, {6827, 21151}, {6844, 36991}, {6879, 36996}, {6880, 59386}, {6881, 38171}, {6882, 31657}, {6883, 18541}, {6888, 37692}, {6946, 11374}, {7678, 14100}, {8544, 9612}, {9347, 15253}, {9578, 30318}, {10129, 10427}, {10883, 17603}, {11038, 18391}, {11526, 38200}, {11680, 15733}, {11813, 50836}, {12609, 17580}, {13407, 30340}, {15726, 17605}, {17092, 52023}, {17283, 55096}, {17620, 58564}, {17718, 60782}, {18134, 28930}, {18815, 27475}, {19372, 26131}, {20292, 37309}, {20328, 23839}, {20923, 28931}, {22464, 29571}, {26015, 41570}, {26724, 37543}, {26738, 52659}, {27191, 55082}, {30628, 41548}, {31225, 41804}, {33108, 61028}, {37633, 37695}, {37635, 56418}, {37701, 38209}, {38037, 60925}, {38205, 41556}, {40474, 57167}, {50701, 59385}, {59476, 60919}

X(61008) = midpoint of X(i) and X(j) for these {i,j}: {7, 60944}
X(61008) = reflection of X(i) in X(j) for these {i,j}: {30311, 17605}, {60944, 61015}
X(61008) = pole of line {1, 37787} wrt dual conic of Yff parabola
X(61008) = orthology center of the pedal triangle of X(37525) wrt Aguilera triangle
X(61008) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(85), X(37787)}}, {{A, B, C, X(527), X(17758)}}, {{A, B, C, X(673), X(31019)}}, {{A, B, C, X(3218), X(27475)}}, {{A, B, C, X(18815), X(40719)}}, {{A, B, C, X(31164), X(57722)}}, {{A, B, C, X(31266), X(60087)}}
X(61008) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 52457, 60981}, {2, 7, 37787}, {7, 142, 60988}, {7, 18230, 41563}, {7, 21617, 61013}, {7, 37787, 60951}, {7, 5226, 61027}, {7, 60944, 527}, {7, 60954, 41572}, {7, 60995, 60946}, {7, 60996, 61019}, {7, 61017, 9}, {7, 61019, 60948}, {11, 8255, 7671}, {142, 21617, 7}, {142, 226, 30379}, {142, 5249, 59374}, {226, 60978, 12848}, {527, 61015, 60944}, {5219, 6173, 8545}, {5880, 11375, 8543}, {6666, 41572, 60954}, {15726, 17605, 30311}, {20195, 60982, 31231}, {21617, 30379, 226}, {31231, 60982, 1445}, {52819, 58433, 61016}, {60943, 60946, 60995}, {60946, 60995, 29007}, {60986, 61021, 50573}

X(61009) = X(2)X(7)∩X(8)X(10398)

Barycentrics    3*a^5-5*a^4*(b+c)-(b-c)^4*(b+c)+2*a^2*(b-3*c)*(3*b-c)*(b+c)-a*(b^2-c^2)^2-2*a^3*(b^2-8*b*c+c^2) : :

X(61009) lies on these lines: {2, 7}, {8, 10398}, {20, 51489}, {72, 11035}, {145, 5728}, {322, 391}, {347, 55432}, {390, 14923}, {405, 8158}, {443, 5779}, {452, 5759}, {474, 36996}, {954, 3622}, {971, 6904}, {1864, 25722}, {1901, 25004}, {2550, 60910}, {2551, 60883}, {3161, 25935}, {3617, 5729}, {3922, 5698}, {3945, 26669}, {4187, 59386}, {4312, 8582}, {4345, 5436}, {4454, 20905}, {4644, 25067}, {5084, 5762}, {5175, 10392}, {5177, 5817}, {5554, 5809}, {5686, 56879}, {5732, 37267}, {5777, 10861}, {5805, 6919}, {5825, 25005}, {5843, 16408}, {5850, 8583}, {6857, 59381}, {7056, 23618}, {7229, 26001}, {7671, 7674}, {8728, 51516}, {10865, 17615}, {11038, 24558}, {14100, 17784}, {15266, 27340}, {15831, 25932}, {17120, 26658}, {17527, 60922}, {17567, 31657}, {17576, 59418}, {19860, 43166}, {20007, 44547}, {20015, 30628}, {24982, 59412}, {25964, 54389}, {26105, 60919}, {26129, 38036}, {30315, 38052}, {30330, 36845}, {30513, 54448}, {36991, 37435}, {52264, 59380}

X(61009) = pole of line {14100, 25568} wrt Feuerbach hyperbola
X(61009) = orthology center of the pedal triangle of X(37526) wrt Aguilera triangle
X(61009) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 61006, 60969}, {7, 6172, 60965}, {9, 142, 60995}, {9, 52819, 329}, {9, 60972, 60959}, {9, 60987, 8232}, {142, 60940, 60934}, {144, 21454, 20059}, {144, 60939, 9965}, {5749, 25019, 2}, {60934, 60940, 144}

X(61010) = X(2)X(7)∩X(4)X(518)

Barycentrics    a^5-a^4*(b+c)-(b-c)^4*(b+c)-2*a^3*(b+c)^2+a*(b^2-c^2)^2+2*a^2*(b+c)*(b^2+c^2) : :
X(61010) = -3*X[1699]+2*X[24389], X[5880]+2*X[28645], -3*X[34647]+2*X[42819], -3*X[38150]+X[54422]

X(61010) lies on these lines: {2, 7}, {4, 518}, {72, 2550}, {218, 4000}, {219, 948}, {220, 52023}, {277, 35599}, {279, 53996}, {390, 10393}, {405, 38053}, {442, 38057}, {443, 45120}, {452, 11038}, {497, 15185}, {516, 1490}, {529, 3488}, {950, 3243}, {954, 5698}, {962, 5853}, {971, 5812}, {1001, 3487}, {1005, 2346}, {1260, 3474}, {1264, 17789}, {1699, 24389}, {1836, 3059}, {1901, 50995}, {2323, 54425}, {2324, 3668}, {2900, 7674}, {3434, 34784}, {3436, 7672}, {3475, 13615}, {3651, 5759}, {4326, 41570}, {4329, 22021}, {4335, 33099}, {4648, 16601}, {4851, 44664}, {4869, 56937}, {5057, 30628}, {5177, 5686}, {5220, 5714}, {5223, 9612}, {5436, 11037}, {5526, 24779}, {5542, 12572}, {5572, 24703}, {5658, 38454}, {5665, 5795}, {5715, 5811}, {5728, 50196}, {5729, 37359}, {5762, 6985}, {5766, 60925}, {5776, 5845}, {5777, 5805}, {5779, 6841}, {5802, 51194}, {5809, 40269}, {5813, 17220}, {5815, 24393}, {5817, 5852}, {5843, 37356}, {5856, 13257}, {5880, 28645}, {6554, 16608}, {6600, 7580}, {6836, 12669}, {6896, 59386}, {6899, 36996}, {6908, 21077}, {6913, 20330}, {7676, 44447}, {8226, 24477}, {9812, 61030}, {10270, 43151}, {10398, 60924}, {10402, 56873}, {10580, 61033}, {11113, 51099}, {12532, 45043}, {14450, 40661}, {15662, 24181}, {17139, 41610}, {17296, 51972}, {17481, 20533}, {18391, 53510}, {18446, 43161}, {21068, 41010}, {23062, 34401}, {26105, 58564}, {27475, 37169}, {30807, 53994}, {33993, 59476}, {34028, 57477}, {34647, 42819}, {36991, 37433}, {37086, 59405}, {37105, 59418}, {38150, 54422}, {41712, 57285}, {42884, 51409}, {53056, 59614}, {55109, 59385}, {60905, 60923}

X(61010) = midpoint of X(i) and X(j) for these {i,j}: {11523, 52835}
X(61010) = reflection of X(i) in X(j) for these {i,j}: {144, 60973}, {60950, 9}, {60990, 142}
X(61010) = anticomplement of X(60974)
X(61010) = X(i)-Dao conjugate of X(j) for these {i, j}: {60974, 60974}
X(61010) = pole of line {3064, 3309} wrt polar circle
X(61010) = pole of line {14100, 60987} wrt Feuerbach hyperbola
X(61010) = pole of line {522, 26546} wrt Steiner circumellipse
X(61010) = orthology center of the pedal triangle of X(37531) wrt Aguilera triangle
X(61010) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(1445)}}, {{A, B, C, X(9), X(34401)}}, {{A, B, C, X(63), X(6601)}}, {{A, B, C, X(20347), X(55024)}}
X(61010) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 144, 61024}, {9, 25525, 6666}, {9, 527, 60950}, {9, 60933, 52819}, {9, 60968, 1708}, {9, 61011, 7}, {142, 527, 60990}, {144, 61025, 6172}, {144, 8232, 9}, {329, 61011, 60987}, {527, 60973, 144}, {8732, 9965, 60968}, {30807, 56927, 53994}, {31053, 60970, 60943}, {41572, 60966, 60940}, {61013, 61024, 2}

X(61011) = X(2)X(7)∩X(4)X(2801)

Barycentrics    a^5-a^4*(b+c)-(b-c)^4*(b+c)+a*(b^2-c^2)^2-2*a^3*(b^2+b*c+c^2)+2*a^2*(b^3+c^3) : :
X(61011) = -2*X[993]+3*X[38053], -4*X[3822]+3*X[38057], -2*X[20330]+X[22758], -3*X[38150]+2*X[51755]

X(61011) lies on these lines: {2, 7}, {4, 2801}, {72, 5880}, {79, 5696}, {218, 1086}, {219, 52023}, {390, 5180}, {405, 25557}, {442, 5220}, {452, 30340}, {515, 3243}, {516, 18446}, {518, 1478}, {535, 3488}, {758, 2550}, {912, 5805}, {948, 2323}, {950, 60926}, {954, 8069}, {971, 37826}, {993, 38053}, {1001, 51409}, {1260, 11246}, {1490, 5735}, {1836, 15733}, {2077, 5759}, {2911, 24779}, {3434, 61030}, {3487, 5248}, {3822, 38057}, {4295, 11523}, {4675, 16601}, {4858, 6604}, {4860, 14022}, {4973, 6878}, {5057, 7671}, {5176, 7672}, {5229, 6598}, {5528, 10123}, {5570, 5728}, {5729, 18223}, {5758, 31730}, {5784, 57282}, {5812, 13369}, {5852, 33558}, {5856, 12831}, {6889, 60912}, {7580, 38454}, {8226, 41555}, {8680, 51058}, {9028, 51194}, {10052, 10427}, {10177, 24703}, {10573, 16732}, {11236, 38211}, {11495, 41548}, {12572, 43180}, {14151, 34605}, {17139, 60721}, {20330, 22758}, {24630, 59405}, {34377, 47595}, {34917, 34919}, {37244, 52783}, {38055, 57278}, {38150, 51755}

X(61011) = midpoint of X(i) and X(j) for these {i,j}: {20059, 60946}, {7, 5905}
X(61011) = reflection of X(i) in X(j) for these {i,j}: {144, 61004}, {22758, 20330}, {63, 142}, {9, 226}
X(61011) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 55960}
X(61011) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 55960}
X(61011) = pole of line {3064, 3887} wrt polar circle
X(61011) = orthology center of the pedal triangle of X(37533) wrt Aguilera triangle
X(61011) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(37787)}}, {{A, B, C, X(63), X(3254)}}, {{A, B, C, X(8545), X(34917)}}, {{A, B, C, X(14377), X(30379)}}
X(61011) = barycentric quotient X(i)/X(j) for these (i, j): {1, 55960}
X(61011) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 329, 60987}, {7, 52457, 6173}, {7, 59374, 26842}, {9, 6173, 60978}, {9, 60963, 60982}, {142, 527, 63}, {142, 61003, 9}, {144, 61027, 61004}, {527, 61004, 144}, {908, 60932, 8257}, {8232, 20059, 60950}, {20059, 60946, 527}, {41857, 60979, 60964}, {60987, 61010, 329}

X(61012) = X(1)X(56355)∩X(2)X(7)

Barycentrics    a*((a-b)^3*(a+b)-(a-b)^2*(2*a-b)*c-4*a*b*c^2+(2*a+b)*c^3-c^4) : :

X(61012) lies on these lines: {1, 56355}, {2, 7}, {6, 26669}, {8, 15299}, {21, 31658}, {44, 25067}, {45, 24554}, {78, 10398}, {100, 14100}, {190, 20905}, {239, 25243}, {377, 5817}, {390, 5554}, {404, 971}, {405, 59381}, {411, 51489}, {474, 5779}, {480, 3935}, {516, 5046}, {518, 20323}, {573, 31049}, {658, 23618}, {673, 26665}, {954, 25875}, {1001, 2098}, {1156, 17668}, {1329, 60883}, {1376, 25722}, {1442, 16578}, {1621, 15837}, {1743, 25930}, {1776, 4413}, {2245, 25004}, {2346, 10177}, {2476, 38108}, {2478, 5759}, {2550, 15297}, {3086, 15518}, {3262, 17277}, {3358, 6904}, {3616, 15298}, {3816, 60919}, {3832, 11372}, {3869, 41712}, {3870, 30330}, {3873, 25893}, {3876, 37244}, {3897, 38031}, {3957, 5572}, {4187, 5762}, {4188, 5732}, {4189, 21153}, {4190, 36991}, {4193, 5805}, {4422, 25964}, {4511, 18412}, {5084, 21168}, {5129, 5804}, {5154, 38150}, {5187, 59385}, {5223, 19861}, {5228, 34524}, {5253, 8581}, {5422, 54358}, {5728, 34772}, {5729, 37248}, {5734, 31435}, {5761, 16845}, {5819, 27059}, {5843, 26877}, {6600, 7671}, {6871, 54370}, {6872, 59418}, {6921, 21151}, {7082, 26040}, {7330, 17580}, {7483, 38113}, {7504, 38318}, {7548, 17619}, {7614, 37555}, {8165, 37550}, {8557, 37681}, {8582, 51090}, {10200, 60924}, {10392, 57287}, {10396, 20007}, {10580, 20588}, {10601, 17011}, {11108, 26878}, {11112, 60901}, {11433, 32858}, {11531, 16859}, {12528, 16410}, {12573, 20060}, {13243, 17612}, {13567, 33157}, {13747, 31657}, {16408, 51516}, {16417, 60884}, {16885, 25878}, {17261, 55330}, {17279, 26540}, {17280, 48381}, {17289, 25000}, {17335, 20930}, {17339, 26531}, {17355, 26001}, {17556, 31671}, {17559, 26921}, {17566, 38122}, {17567, 36996}, {17579, 31672}, {17768, 27197}, {17776, 18928}, {17825, 28606}, {18482, 37375}, {20292, 25973}, {20533, 26575}, {21446, 55989}, {23617, 36101}, {24541, 38059}, {25003, 27052}, {25091, 32911}, {25101, 25935}, {25524, 60909}, {25939, 37680}, {26005, 32779}, {26011, 41242}, {26020, 60879}, {26364, 60923}, {26621, 27484}, {26639, 51058}, {26653, 41792}, {30329, 60885}, {38052, 60911}, {38460, 42884}

X(61012) = pole of line {14100, 60935} wrt Feuerbach hyperbola
X(61012) = pole of line {284, 11227} wrt Stammler hyperbola
X(61012) = orthology center of the pedal triangle of X(37561) wrt Aguilera triangle
X(61012) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(56355)}}, {{A, B, C, X(142), X(34894)}}, {{A, B, C, X(1223), X(29007)}}, {{A, B, C, X(2346), X(30379)}}, {{A, B, C, X(3452), X(36101)}}, {{A, B, C, X(17743), X(26651)}}, {{A, B, C, X(21446), X(30827)}}, {{A, B, C, X(23617), X(40869)}}
X(61012) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17350, 26651}, {2, 9, 60969}, {7, 9, 60935}, {9, 142, 29007}, {9, 20195, 61004}, {9, 57, 60966}, {9, 63, 61006}, {9, 60964, 60944}, {9, 60970, 3219}, {9, 60974, 6172}, {9, 60985, 60973}, {9, 60989, 60942}, {9, 60994, 61024}, {9, 61005, 60983}, {9, 6666, 60981}, {44, 25067, 37659}, {57, 60966, 20059}, {144, 1445, 3218}, {474, 5779, 10861}, {480, 30628, 3935}, {1376, 60910, 25722}, {3218, 27065, 31018}, {3452, 61014, 60979}, {8257, 60935, 27003}, {8257, 60973, 60985}, {15837, 58608, 1621}, {17353, 25019, 2}, {18230, 60954, 9}, {37787, 61024, 60994}, {50573, 61002, 144}, {60938, 60965, 60984}, {60944, 60996, 60964}, {60973, 60985, 7}, {60994, 61024, 60970}

X(61013) = X(2)X(7)∩X(12)X(7672)

Barycentrics    (a+b-c)*(a-b+c)*(a^2*(b+c)+(b-c)^2*(b+c)-a*(2*b^2+3*b*c+2*c^2)) : :

X(61013) lies on these lines: {2, 7}, {11, 11025}, {12, 7672}, {65, 7679}, {85, 17241}, {390, 12047}, {518, 2476}, {857, 8818}, {946, 8236}, {948, 1442}, {954, 6985}, {971, 6845}, {1441, 17233}, {1443, 4648}, {1478, 30284}, {1532, 20330}, {1836, 7676}, {2346, 17718}, {2478, 38053}, {2550, 4420}, {2886, 34784}, {3059, 3838}, {3091, 11038}, {3487, 6849}, {3649, 3826}, {3651, 11374}, {3944, 4343}, {3984, 38200}, {4687, 41804}, {4870, 42819}, {5047, 10404}, {5074, 14189}, {5129, 51706}, {5228, 56534}, {5287, 18625}, {5542, 40269}, {5572, 7678}, {5686, 21077}, {5714, 6851}, {5728, 6990}, {5880, 16133}, {6831, 12669}, {6841, 10394}, {7190, 37771}, {7269, 37800}, {7671, 42356}, {7675, 9612}, {7677, 11375}, {7741, 20116}, {7951, 30329}, {8068, 12755}, {8581, 13751}, {9578, 11526}, {10129, 30628}, {11237, 42871}, {11263, 38052}, {11680, 15185}, {12609, 40333}, {12611, 53055}, {13411, 37105}, {14100, 30311}, {14526, 43178}, {16826, 17075}, {16831, 41808}, {17092, 17245}, {18393, 30331}, {18492, 21620}, {25722, 41548}, {33108, 40659}, {33133, 54358}, {33593, 45043}, {36595, 55998}, {37701, 52769}

X(61013) = pole of line {14100, 60951} wrt Feuerbach hyperbola
X(61013) = pole of line {1, 56028} wrt dual conic of Yff parabola
X(61013) = orthology center of the pedal triangle of X(37571) wrt Aguilera triangle
X(61013) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(673), X(27186)}}, {{A, B, C, X(3219), X(27475)}}, {{A, B, C, X(3305), X(57722)}}, {{A, B, C, X(6666), X(17758)}}, {{A, B, C, X(8818), X(59207)}}
X(61013) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 61010, 61024}, {2, 7, 60948}, {7, 21617, 61008}, {7, 5226, 60943}, {7, 60943, 37787}, {7, 60944, 41572}, {7, 60954, 52819}, {7, 60995, 41563}, {7, 61008, 60988}, {7, 61017, 1445}, {7, 8232, 29007}, {7, 9, 60951}, {142, 226, 41857}, {142, 41857, 7}, {142, 908, 18230}, {1445, 5219, 61017}, {4654, 20195, 60938}, {5226, 37797, 5219}, {5572, 17605, 7678}, {21617, 41857, 142}, {30382, 30383, 30949}, {52819, 61015, 60954}

X(61014) = X(1)X(21168)∩X(2)X(7)

Barycentrics    (a+b-c)*(a-b+c)*(4*a^3-7*a^2*(b+c)+(b-c)^2*(b+c)+2*a*(b+c)^2) : :

X(61014) lies on these lines: {1, 21168}, {2, 7}, {10, 60883}, {44, 3668}, {56, 5850}, {65, 51090}, {72, 4315}, {218, 1323}, {347, 16670}, {516, 1837}, {948, 3973}, {950, 5759}, {954, 3304}, {1155, 43182}, {1210, 5762}, {1441, 3707}, {1743, 43035}, {1788, 4312}, {2325, 56927}, {3057, 5728}, {3062, 3474}, {3340, 52653}, {3488, 16236}, {3614, 30424}, {4292, 5779}, {4298, 60909}, {4304, 31793}, {4480, 39126}, {4641, 43036}, {5083, 6068}, {5173, 58608}, {5204, 43176}, {5220, 12573}, {5223, 10106}, {5433, 38054}, {5434, 50834}, {5493, 9844}, {5658, 53056}, {5714, 10172}, {5758, 37704}, {5811, 41705}, {5825, 59389}, {5843, 37582}, {5856, 41573}, {5927, 31391}, {6604, 25728}, {6684, 60923}, {6766, 10396}, {7288, 59372}, {10395, 18482}, {11019, 60919}, {12053, 15299}, {13411, 59381}, {14100, 41539}, {14564, 17245}, {15006, 36976}, {15492, 52023}, {15803, 36996}, {17606, 38151}, {18397, 21578}, {18645, 56020}, {21620, 26878}, {24471, 51144}, {25716, 51170}, {25723, 37677}, {31721, 56043}, {34720, 36920}, {50195, 54175}, {51516, 57282}

X(61014) = midpoint of X(i) and X(j) for these {i,j}: {1445, 41563}
X(61014) = reflection of X(i) in X(j) for these {i,j}: {10392, 5729}, {12053, 15299}, {4848, 41712}, {60992, 1445}
X(61014) = pole of line {3676, 59980} wrt incircle
X(61014) = pole of line {5927, 13405} wrt Feuerbach hyperbola
X(61014) = pole of line {1, 38107} wrt dual conic of Yff parabola
X(61014) = orthology center of the pedal triangle of X(37582) wrt Aguilera triangle
X(61014) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(20059)}}, {{A, B, C, X(28610), X(54676)}}
X(61014) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 37787, 61016}, {7, 50573, 60942}, {7, 60947, 6666}, {9, 12848, 52819}, {9, 52819, 226}, {9, 60950, 61003}, {9, 60982, 8232}, {57, 144, 60961}, {142, 41572, 61021}, {144, 60941, 57}, {516, 41712, 4848}, {516, 5729, 10392}, {527, 1445, 60992}, {1445, 41563, 527}, {5759, 10398, 950}, {6172, 60939, 60937}, {8732, 60933, 60993}, {21617, 60954, 60986}, {37787, 41572, 142}, {41572, 61016, 7}, {60936, 60948, 61022}, {60937, 60939, 553}, {60945, 61000, 8545}, {60951, 60954, 21617}, {60979, 61012, 3452}

X(61015) = X(2)X(7)∩X(10)X(8543)

Barycentrics    (a+b-c)*(a-b+c)*(2*a^3-5*a^2*(b+c)-(b-c)^2*(b+c)+a*(4*b^2+6*b*c+4*c^2)) : :

X(61015) lies on these lines: {2, 7}, {10, 8543}, {12, 15254}, {37, 5723}, {45, 22464}, {80, 2346}, {390, 5587}, {480, 6735}, {498, 54370}, {516, 6932}, {518, 15950}, {551, 14151}, {631, 8544}, {651, 29571}, {954, 5722}, {1001, 5252}, {1012, 31672}, {1156, 5660}, {1317, 38060}, {1323, 25072}, {1420, 50398}, {1441, 25101}, {1532, 18482}, {1699, 36976}, {3091, 5766}, {3434, 47375}, {3476, 38025}, {3583, 6957}, {3584, 51768}, {3586, 38075}, {3616, 30318}, {3634, 30312}, {3731, 37800}, {3832, 30332}, {4304, 6912}, {4315, 5251}, {5220, 11375}, {5432, 15726}, {5542, 37701}, {5572, 37703}, {5686, 11526}, {5692, 7672}, {5696, 59719}, {5698, 10588}, {5719, 5728}, {5720, 5817}, {5727, 8236}, {5729, 11374}, {5732, 6966}, {5779, 37713}, {5784, 27385}, {6326, 30284}, {6833, 52684}, {7190, 37650}, {7671, 13405}, {7676, 44425}, {8227, 60926}, {9623, 16236}, {10106, 16859}, {10164, 30295}, {10165, 18450}, {10175, 45043}, {10394, 13411}, {10708, 34926}, {11025, 18412}, {11230, 38055}, {12047, 60912}, {14100, 52638}, {15298, 23708}, {15837, 42356}, {17605, 38454}, {17620, 58608}, {20927, 56085}, {21578, 52769}, {25067, 60419}, {27471, 51052}, {30305, 38037}, {36991, 52026}, {37692, 60895}, {38102, 41556}

X(61015) = midpoint of X(i) and X(j) for these {i,j}: {60944, 61008}
X(61015) = pole of line {14100, 50573} wrt Feuerbach hyperbola
X(61015) = pole of line {1, 30312} wrt dual conic of Yff parabola
X(61015) = orthology center of the pedal triangle of X(37600) wrt Aguilera triangle
X(61015) = intersection, other than A, B, C, of circumconics {{A, B, C, X(80), X(142)}}, {{A, B, C, X(2346), X(3218)}}, {{A, B, C, X(6173), X(60094)}}, {{A, B, C, X(9776), X(57721)}}, {{A, B, C, X(23618), X(50573)}}, {{A, B, C, X(27475), X(31164)}}
X(61015) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 60995, 8545}, {2, 8545, 30379}, {7, 31188, 8732}, {7, 50573, 41572}, {7, 5219, 21617}, {7, 60943, 5219}, {7, 60948, 4031}, {7, 6666, 61016}, {7, 9, 50573}, {9, 6666, 54357}, {142, 29007, 60936}, {226, 37787, 60932}, {226, 60986, 37787}, {1445, 8232, 41857}, {5226, 61023, 12848}, {8232, 18230, 1445}, {8545, 30379, 60952}, {21617, 50573, 7}, {29007, 61017, 142}, {37701, 41700, 5542}, {58433, 60961, 60988}, {60944, 61008, 527}, {60954, 61013, 52819}

X(61016) = X(2)X(7)∩X(10)X(7677)

Barycentrics    (a+b-c)*(a-b+c)*(2*a^3-5*a^2*(b+c)-(b-c)^2*(b+c)+2*a*(2*b^2+b*c+2*c^2)) : :

X(61016) lies on circumconic {{A, B, C, X(28610), X(42318)}} and on these lines: {2, 7}, {10, 7677}, {77, 37650}, {100, 24389}, {140, 5728}, {241, 17337}, {273, 8756}, {349, 29446}, {354, 59476}, {390, 5704}, {516, 6943}, {518, 5433}, {631, 7675}, {1001, 24914}, {1125, 7672}, {1155, 42356}, {1156, 43182}, {1210, 3746}, {1229, 20881}, {1737, 52769}, {2287, 18645}, {2346, 5659}, {3035, 3059}, {3149, 31672}, {3358, 6834}, {3523, 5809}, {3616, 11526}, {3634, 7679}, {3660, 58635}, {3826, 26481}, {4304, 6986}, {4315, 5258}, {4857, 21153}, {5432, 5572}, {5542, 37731}, {5686, 30318}, {5729, 38122}, {5732, 6962}, {5817, 8544}, {6600, 26015}, {6705, 36991}, {6734, 11510}, {6745, 34784}, {6831, 18482}, {6860, 38150}, {7288, 38057}, {7670, 58440}, {7671, 58441}, {7673, 43174}, {7676, 10164}, {8543, 38059}, {8609, 17366}, {10165, 30284}, {11025, 13405}, {13411, 50190}, {16133, 58449}, {17086, 29607}, {17278, 22464}, {17341, 33298}, {17352, 31225}, {17566, 41228}, {17590, 37544}, {17620, 58634}, {26446, 42884}, {29596, 40999}, {31183, 37800}, {31197, 43056}, {34028, 37687}, {35617, 43223}, {37582, 38318}, {38052, 58405}, {40663, 42819}, {42309, 58442}

X(61016) = midpoint of X(i) and X(j) for these {i,j}: {60954, 60988}
X(61016) = pole of line {1, 7679} wrt dual conic of Yff parabola
X(61016) = orthology center of the pedal triangle of X(37605) wrt Aguilera triangle
X(61016) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1445, 21617}, {7, 37787, 61014}, {7, 60947, 50573}, {7, 6666, 61015}, {9, 30379, 60936}, {9, 31231, 61019}, {9, 61019, 30379}, {57, 60943, 41857}, {142, 37787, 41572}, {142, 61014, 7}, {226, 61001, 61017}, {1445, 21617, 60932}, {3634, 12573, 7679}, {5435, 8232, 60938}, {8732, 18230, 8545}, {29007, 60992, 60952}, {52819, 58433, 61008}, {60948, 61017, 226}, {60954, 60988, 527}, {60986, 60992, 29007}

X(61017) = X(2)X(7)∩X(11)X(2346)

Barycentrics    (a+b-c)*(a-b+c)*(a^3-3*a^2*(b+c)-(b-c)^2*(b+c)+3*a*(b^2+b*c+c^2)) : :

X(61017) lies on these lines: {2, 7}, {11, 2346}, {12, 7677}, {37, 37771}, {55, 7678}, {390, 498}, {499, 11038}, {516, 6960}, {651, 17245}, {673, 7332}, {954, 1656}, {971, 6952}, {1001, 4193}, {1441, 17263}, {1442, 29571}, {2550, 6933}, {3008, 7269}, {3085, 8236}, {3584, 30331}, {3826, 8543}, {4313, 6886}, {4321, 34595}, {4323, 19855}, {5326, 30295}, {5432, 7676}, {5552, 59413}, {5686, 26363}, {5703, 6887}, {5728, 38318}, {5732, 6972}, {5759, 6863}, {5766, 6944}, {5805, 6949}, {5809, 6832}, {5817, 6862}, {6600, 11680}, {6825, 59418}, {6833, 36991}, {6834, 59385}, {6852, 10394}, {6853, 31658}, {6884, 7675}, {6953, 30332}, {6958, 21151}, {6979, 38150}, {7190, 31183}, {7279, 11349}, {7672, 11375}, {7951, 52769}, {10528, 12630}, {11025, 17718}, {11495, 30311}, {15844, 17534}, {16593, 30839}, {17337, 17796}, {20104, 51090}, {20107, 38054}, {20116, 37731}, {20119, 38752}, {22464, 25072}, {26364, 40333}, {28748, 28757}, {30329, 37701}, {31479, 42884}, {50205, 57283}

X(61017) = orthology center of the pedal triangle of X(37616) wrt Aguilera triangle
X(61017) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(673), X(26842)}}, {{A, B, C, X(17483), X(27475)}}
X(61017) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 28741, 28780}, {2, 5219, 37797}, {2, 8232, 61019}, {7, 18230, 60954}, {11, 59476, 2346}, {142, 29007, 7}, {142, 61015, 29007}, {226, 61001, 61016}, {226, 61016, 60948}, {1445, 5219, 61013}, {5432, 42356, 7676}, {6666, 21617, 37787}, {8545, 20195, 60988}, {18230, 60996, 60959}, {60943, 61019, 8232}

X(61018) = X(2)X(7)∩X(241)X(1107)

Barycentrics    (a+b-c)*(a-b+c)*(a^3-a^2*(b+c)+b*c*(b+c)+a*(2*b^2+b*c+2*c^2)) : :

X(61018) lies on these lines: {2, 7}, {56, 16830}, {65, 16823}, {171, 51329}, {239, 4051}, {241, 1107}, {390, 17594}, {516, 17596}, {518, 7081}, {673, 893}, {799, 43760}, {942, 21554}, {948, 7185}, {954, 16434}, {999, 44430}, {1001, 1403}, {1210, 7379}, {1402, 7677}, {1429, 16826}, {1466, 19310}, {1469, 60731}, {1699, 24283}, {1758, 29639}, {1781, 24778}, {2176, 5228}, {2550, 3705}, {3008, 3674}, {3212, 4384}, {3361, 39586}, {3476, 50286}, {3757, 7672}, {3912, 56928}, {4090, 5223}, {4292, 7385}, {4308, 39587}, {4315, 50291}, {4321, 5268}, {4417, 47595}, {4518, 8581}, {5122, 13634}, {5222, 9575}, {5272, 12560}, {5274, 44431}, {5276, 17074}, {5704, 7407}, {5728, 7413}, {5819, 7736}, {5838, 37665}, {5845, 37662}, {5853, 29840}, {6996, 37597}, {6998, 37582}, {8236, 37553}, {9746, 53056}, {10521, 31211}, {13462, 48854}, {13635, 24929}, {14189, 17080}, {16593, 33116}, {16603, 17292}, {16609, 16815}, {16706, 41003}, {17023, 17084}, {17095, 43053}, {17277, 24471}, {23544, 27000}, {25940, 27399}, {26241, 37541}, {27475, 37674}, {29634, 38053}, {36528, 41346}, {37642, 59405}, {37646, 51150}, {37661, 43056}, {37683, 51194}, {39954, 44794}, {44733, 55967}

X(61018) = pole of line {333, 2348} wrt Wallace hyperbola
X(61018) = pole of line {1, 7385} wrt dual conic of Yff parabola
X(61018) = orthology center of the pedal triangle of X(37617) wrt Aguilera triangle
X(61018) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(672), X(893)}}, {{A, B, C, X(673), X(894)}}, {{A, B, C, X(799), X(53337)}}, {{A, B, C, X(1025), X(37137)}}, {{A, B, C, X(1400), X(43760)}}, {{A, B, C, X(1423), X(21446)}}, {{A, B, C, X(1447), X(40420)}}, {{A, B, C, X(3452), X(4518)}}, {{A, B, C, X(3662), X(27475)}}, {{A, B, C, X(5437), X(39954)}}, {{A, B, C, X(5749), X(42318)}}, {{A, B, C, X(7249), X(9436)}}, {{A, B, C, X(8056), X(17754)}}, {{A, B, C, X(10436), X(55967)}}, {{A, B, C, X(13478), X(24333)}}, {{A, B, C, X(21371), X(39273)}}, {{A, B, C, X(36538), X(60085)}}, {{A, B, C, X(40719), X(56358)}}
X(61018) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 56555, 3452}, {2, 57, 1447}, {57, 5219, 36538}, {241, 41245, 7176}, {30097, 56547, 894}

X(61019) = X(2)X(7)∩X(35)X(390)

Barycentrics    (a+b-c)*(a-b+c)*(a^3-3*a^2*(b+c)-(b-c)^2*(b+c)+3*a*(b^2+c^2)) : :

X(61019) lies on these lines: {2, 7}, {11, 11495}, {12, 50393}, {35, 390}, {56, 3826}, {77, 3008}, {100, 6601}, {140, 954}, {214, 34625}, {241, 17278}, {269, 31183}, {273, 37382}, {278, 26724}, {279, 42326}, {346, 20881}, {347, 24779}, {388, 7679}, {404, 2550}, {480, 3035}, {497, 7676}, {498, 5542}, {499, 516}, {518, 5552}, {651, 37650}, {673, 2164}, {938, 37407}, {948, 17092}, {971, 6834}, {1001, 5433}, {1210, 7675}, {1376, 6067}, {1420, 38200}, {1440, 42318}, {1442, 3554}, {1443, 54425}, {1698, 4321}, {1788, 7672}, {2346, 5218}, {3085, 5445}, {3174, 26015}, {3243, 10528}, {3434, 37309}, {3600, 5258}, {3619, 40999}, {3624, 12560}, {3660, 40659}, {3672, 25065}, {3870, 41573}, {4000, 8609}, {4015, 5686}, {4292, 6886}, {4318, 16020}, {4848, 10587}, {4855, 5853}, {4859, 22464}, {5122, 18482}, {5223, 26364}, {5228, 17245}, {5265, 17580}, {5308, 7269}, {5572, 17728}, {5704, 5809}, {5728, 6889}, {5729, 6863}, {5732, 6838}, {5759, 6891}, {5762, 6958}, {5779, 6959}, {5805, 6833}, {5817, 6944}, {6180, 17337}, {6600, 41555}, {6713, 35238}, {6825, 10394}, {6832, 37582}, {6837, 15803}, {6847, 59385}, {6848, 36991}, {6861, 38171}, {6862, 38107}, {6888, 37524}, {6926, 59418}, {6949, 36996}, {6952, 59386}, {6953, 8544}, {6967, 31658}, {6983, 38108}, {7190, 29571}, {7678, 10589}, {8236, 10165}, {8692, 53529}, {9710, 51773}, {10072, 30331}, {10090, 43161}, {10320, 60912}, {10586, 38316}, {11239, 40663}, {12573, 19854}, {12736, 59417}, {12832, 14151}, {13370, 31458}, {14189, 51775}, {15299, 60925}, {15325, 42884}, {15570, 41687}, {16593, 28420}, {16706, 31225}, {17093, 53242}, {17095, 17370}, {17234, 56927}, {17263, 39126}, {17283, 33298}, {17582, 57283}, {17620, 61028}, {17718, 58563}, {18391, 30284}, {23062, 37757}, {24393, 30318}, {24477, 34784}, {24599, 53997}, {24789, 57477}, {25557, 41712}, {26363, 38052}, {26487, 38030}, {30332, 35242}, {30628, 41566}, {31145, 41558}, {31185, 56873}, {35262, 59413}, {37366, 60897}, {37758, 56085}

X(61019) = X(i)-Dao conjugate of X(j) for these {i, j}: {3870, 55337}
X(61019) = pole of line {14100, 60946} wrt Feuerbach hyperbola
X(61019) = pole of line {1, 6886} wrt dual conic of Yff parabola
X(61019) = orthology center of the pedal triangle of X(37618) wrt Aguilera triangle
X(61019) = intersection, other than A, B, C, of circumconics {{A, B, C, X(9), X(42326)}}, {{A, B, C, X(329), X(42318)}}, {{A, B, C, X(672), X(2164)}}, {{A, B, C, X(673), X(5905)}}, {{A, B, C, X(1440), X(51351)}}, {{A, B, C, X(1708), X(43760)}}, {{A, B, C, X(2346), X(8257)}}, {{A, B, C, X(7318), X(9436)}}, {{A, B, C, X(17483), X(55937)}}, {{A, B, C, X(39273), X(55871)}}, {{A, B, C, X(41563), X(43762)}}
X(61019) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 7, 60943}, {2, 8232, 61017}, {7, 18230, 29007}, {7, 37787, 41563}, {7, 5435, 60948}, {7, 60941, 60951}, {7, 60943, 61027}, {7, 60944, 60934}, {7, 60954, 144}, {7, 60996, 61008}, {7, 61017, 8232}, {7, 9, 60946}, {9, 31231, 61016}, {57, 20195, 21617}, {142, 1445, 7}, {142, 3911, 1445}, {241, 17278, 37800}, {1788, 38053, 7672}, {2550, 7288, 7677}, {3306, 3911, 5435}, {5219, 60955, 41857}, {6666, 60992, 8545}, {7677, 30312, 2550}, {17338, 40862, 28966}, {30379, 61016, 9}, {31188, 37797, 2}, {55870, 59491, 55868}

X(61020) = X(1)X(56998)∩X(2)X(7)

Barycentrics    3*a^2-4*(b-c)^2+a*(b+c) : :
X(61020) = 3*X[2]+7*X[7], 8*X[548]+7*X[5735], -2*X[1657]+7*X[5732], -7*X[2550]+2*X[3625], -7*X[3243]+2*X[3633], -2*X[3627]+7*X[5805], -2*X[3630]+7*X[47595], -2*X[3635]+7*X[5542], -16*X[3850]+21*X[38150], X[4312]+4*X[25557], -2*X[4718]+7*X[51058], -11*X[5072]+21*X[38107] and many others

X(61020) lies on these lines: {1, 56998}, {2, 7}, {37, 4902}, {516, 10595}, {518, 4004}, {548, 5735}, {971, 3843}, {1086, 1449}, {1657, 5732}, {1698, 5852}, {1699, 17051}, {2550, 3625}, {3243, 3633}, {3247, 4675}, {3254, 10390}, {3255, 55922}, {3336, 15296}, {3627, 5805}, {3630, 47595}, {3635, 5542}, {3729, 17241}, {3850, 38150}, {4000, 4896}, {4007, 31995}, {4029, 52714}, {4034, 21296}, {4312, 25557}, {4431, 17296}, {4648, 4887}, {4659, 7321}, {4718, 51058}, {4851, 28309}, {4859, 16670}, {4869, 4873}, {5072, 38107}, {5436, 57003}, {5438, 6147}, {5573, 33097}, {5586, 25466}, {5698, 38054}, {5762, 15712}, {5843, 12812}, {5857, 52783}, {5902, 41566}, {6144, 51194}, {7222, 21255}, {7228, 17284}, {7232, 17239}, {7238, 17272}, {7263, 28337}, {7671, 58607}, {10916, 41865}, {12108, 38122}, {14893, 31672}, {15718, 38065}, {16673, 49747}, {16676, 17276}, {16832, 17345}, {17118, 31138}, {17151, 17376}, {17313, 55998}, {17344, 31139}, {17668, 58563}, {18482, 38335}, {20121, 34522}, {20292, 44841}, {21151, 21735}, {21153, 60922}, {25722, 61033}, {25728, 31333}, {28640, 36834}, {29598, 48631}, {30331, 51098}, {30424, 38053}, {31391, 58564}, {31658, 51514}, {32455, 51150}, {33703, 43177}, {36996, 59389}, {38024, 42819}, {38036, 60896}, {41702, 42871}

X(61020) = reflection of X(i) in X(j) for these {i,j}: {18230, 142}, {61006, 61001}, {9, 20195}
X(61020) = pole of line {14100, 60963} wrt Feuerbach hyperbola
X(61020) = pole of line {1, 60962} wrt dual conic of Yff parabola
X(61020) = orthology center of the pedal triangle of X(37624) wrt Aguilera triangle
X(61020) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3254), X(18230)}}, {{A, B, C, X(3255), X(6172)}}, {{A, B, C, X(10390), X(37787)}}, {{A, B, C, X(21446), X(23958)}}, {{A, B, C, X(29007), X(55922)}}
X(61020) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 60962, 60977}, {2, 7, 60962}, {7, 30275, 60961}, {7, 59374, 20059}, {7, 59375, 60980}, {7, 60980, 6173}, {7, 60992, 60982}, {7, 60996, 60984}, {7, 8732, 61021}, {7, 9, 60963}, {142, 18230, 20195}, {142, 527, 18230}, {142, 60933, 9}, {142, 60962, 61000}, {142, 61000, 2}, {144, 6666, 45789}, {527, 61001, 61006}, {1086, 4888, 1449}, {3982, 9776, 28609}, {4312, 25557, 38316}, {4675, 4862, 3247}, {4859, 17365, 16670}, {5435, 61023, 60976}, {5880, 59372, 3243}, {6173, 60933, 142}, {6173, 60963, 38093}, {7321, 17298, 4659}, {20059, 59374, 6666}, {37646, 59769, 56078}, {43177, 59386, 52835}, {56520, 59491, 17353}, {60938, 60964, 60989}, {60957, 61023, 17338}, {60962, 60976, 60933}, {60984, 60996, 60942}

X(61021) = X(2)X(7)∩X(65)X(2801)

Barycentrics    (a+b-c)*(a-b+c)*(4*a^3-2*a*(b-c)^2-5*a^2*(b+c)+3*(b-c)^2*(b+c)) : :
X(61021) = -X[37826]+3*X[51514]

X(61021) lies on these lines: {2, 7}, {56, 43180}, {65, 2801}, {241, 4896}, {515, 4312}, {516, 2099}, {758, 8581}, {946, 51768}, {950, 5735}, {971, 18389}, {1086, 14564}, {1319, 5542}, {1420, 30340}, {1434, 18645}, {1454, 60912}, {1478, 30286}, {3256, 30295}, {3339, 5818}, {3485, 60905}, {3668, 6610}, {3748, 60919}, {4295, 10864}, {4298, 5730}, {4315, 50843}, {4644, 43035}, {4667, 22464}, {4848, 5880}, {4887, 5228}, {5119, 10059}, {5122, 31657}, {5173, 15726}, {5759, 30282}, {5762, 24929}, {5784, 15556}, {5805, 10392}, {5843, 51755}, {5850, 51782}, {5856, 41553}, {10175, 41700}, {10398, 59386}, {10481, 15730}, {12053, 60895}, {13462, 59372}, {14100, 51783}, {14151, 34195}, {15934, 60922}, {36991, 51790}, {37826, 51514}, {40663, 51100}, {51090, 51409}, {51792, 59385}, {51816, 60924}

X(61021) = midpoint of X(i) and X(j) for these {i,j}: {63, 20059}
X(61021) = reflection of X(i) in X(j) for these {i,j}: {144, 5745}, {226, 7}, {61004, 60980}
X(61021) = pole of line {3676, 14413} wrt incircle
X(61021) = pole of line {1, 11661} wrt dual conic of Yff parabola
X(61021) = orthology center of the pedal triangle of X(50194) wrt Aguilera triangle
X(61021) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 12848, 6173}, {7, 1445, 60980}, {7, 20059, 60937}, {7, 41572, 142}, {7, 527, 226}, {7, 5435, 59375}, {7, 57, 60993}, {7, 60932, 61022}, {7, 60951, 30379}, {7, 60953, 3982}, {7, 60971, 60998}, {7, 60982, 553}, {7, 60998, 4654}, {7, 8732, 61020}, {57, 60975, 52819}, {57, 60993, 60992}, {63, 20059, 527}, {142, 41572, 61014}, {527, 5745, 144}, {527, 60980, 61004}, {3982, 60961, 60953}, {6173, 12848, 3911}, {50573, 61008, 60986}, {52457, 60972, 5316}, {52819, 60993, 57}, {60932, 61022, 4031}, {60933, 60953, 60956}, {60953, 60956, 60961}, {60963, 60982, 7}

X(61022) = X(2)X(7)∩X(516)X(999)

Barycentrics    (a+b-c)*(a-b+c)*(a^2*(b+c)+(b-c)^2*(b+c)-2*a*(b^2-4*b*c+c^2)) : :
X(61022) = X[497]+X[30353], X[2093]+3*X[59372], X[2095]+3*X[59380], X[2096]+3*X[59386], -X[3421]+3*X[38052], -X[3476]+3*X[4321], -2*X[3820]+3*X[38204], -X[5759]+3*X[21164], -X[6282]+3*X[21151], -X[7962]+3*X[11038], -X[37822]+3*X[38107]

X(61022) lies on these lines: {2, 7}, {65, 10427}, {269, 3946}, {279, 36888}, {497, 30353}, {516, 999}, {517, 5542}, {528, 4315}, {664, 50109}, {942, 43177}, {946, 20418}, {948, 17067}, {950, 8544}, {971, 7682}, {1086, 10481}, {1323, 17301}, {1418, 3663}, {1434, 4616}, {1476, 3254}, {2093, 59372}, {2095, 59380}, {2096, 59386}, {2321, 39126}, {2550, 4915}, {2951, 15006}, {3361, 5698}, {3421, 38052}, {3476, 4321}, {3488, 5732}, {3600, 21627}, {3671, 25557}, {3755, 4334}, {3820, 38204}, {4000, 7271}, {4298, 5880}, {4312, 30384}, {4419, 51302}, {4648, 7274}, {4667, 5228}, {4675, 58816}, {4862, 7961}, {4888, 53020}, {4973, 51090}, {5083, 18801}, {5572, 15841}, {5708, 6260}, {5759, 21164}, {5784, 24391}, {5805, 18541}, {6244, 43151}, {6282, 21151}, {6610, 50114}, {6744, 43181}, {7960, 24181}, {7962, 11038}, {8102, 45708}, {8581, 24393}, {9954, 58634}, {11019, 15726}, {12915, 58563}, {13098, 45707}, {13462, 47357}, {14151, 50894}, {17625, 61030}, {17668, 41573}, {18421, 51099}, {21620, 36279}, {21625, 31805}, {24386, 41555}, {26932, 32446}, {30331, 51705}, {34371, 51150}, {36996, 54135}, {37822, 38107}, {42309, 47386}, {52563, 53538}, {55922, 56263}

X(61022) = midpoint of X(i) and X(j) for these {i,j}: {36996, 54135}, {497, 30353}, {60933, 60940}, {60956, 61007}, {7, 57}
X(61022) = reflection of X(i) in X(j) for these {i,j}: {12915, 58563}, {30331, 51788}, {3452, 142}, {5572, 58577}, {54178, 31657}, {6244, 43151}, {9, 6692}, {9954, 58634}
X(61022) = complement of X(36973)
X(61022) = X(i)-complementary conjugate of X(j) for these {i, j}: {56263, 141}
X(61022) = pole of line {1, 6610} wrt dual conic of Yff parabola
X(61022) = orthology center of the pedal triangle of X(51788) wrt Aguilera triangle
X(61022) = intersection, other than A, B, C, of circumconics {{A, B, C, X(514), X(56551)}}, {{A, B, C, X(527), X(1434)}}, {{A, B, C, X(673), X(5316)}}, {{A, B, C, X(1476), X(37787)}}, {{A, B, C, X(3254), X(3452)}}, {{A, B, C, X(4616), X(56543)}}, {{A, B, C, X(6172), X(56263)}}, {{A, B, C, X(17197), X(33573)}}, {{A, B, C, X(18230), X(38009)}}, {{A, B, C, X(36973), X(55922)}}
X(61022) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 7, 60953}, {7, 1445, 60961}, {7, 21454, 60982}, {7, 30275, 4654}, {7, 30379, 226}, {7, 37787, 60952}, {7, 52819, 60962}, {7, 5435, 60998}, {7, 60932, 61021}, {7, 60938, 52819}, {7, 60939, 60933}, {7, 60948, 60936}, {7, 60975, 60963}, {7, 60988, 41857}, {7, 8732, 60937}, {142, 527, 3452}, {226, 30379, 142}, {226, 60992, 30379}, {517, 31657, 54178}, {527, 6692, 9}, {553, 60993, 7}, {1445, 60961, 60942}, {3911, 8545, 60986}, {4031, 61021, 60932}, {8732, 60995, 31231}, {15841, 43182, 5572}, {21454, 60982, 60945}, {31231, 60937, 60995}, {31231, 60995, 6666}, {60933, 60940, 527}, {60936, 60948, 61014}, {60955, 60982, 21454}

X(61023) = X(2)X(7)∩X(8)X(4702)

Barycentrics    7*a^2+(b-c)^2-8*a*(b+c) : :
X(61023) = 2*X[1]+X[50835], -4*X[2]+X[7], 2*X[6]+X[50996], 8*X[10]+X[30332], 2*X[37]+X[51053], 2*X[141]+X[50997], 2*X[210]+X[7671], -X[376]+4*X[31658], 2*X[381]+X[5759], X[390]+2*X[3679], 2*X[549]+X[5779], 2*X[551]+X[5223] and many others

X(61023) lies on these lines: {1, 50835}, {2, 7}, {6, 50996}, {8, 4702}, {10, 30332}, {30, 5817}, {37, 51053}, {44, 5308}, {45, 5222}, {141, 50997}, {190, 31722}, {193, 29575}, {210, 7671}, {238, 48856}, {344, 17295}, {346, 50095}, {376, 31658}, {381, 5759}, {390, 3679}, {391, 17294}, {480, 4428}, {516, 3839}, {518, 38023}, {519, 5686}, {528, 38057}, {549, 5779}, {551, 5223}, {597, 50995}, {599, 51190}, {673, 4370}, {954, 15933}, {958, 6049}, {962, 60912}, {966, 17359}, {971, 3524}, {1001, 3241}, {1125, 50834}, {1156, 6174}, {1698, 50840}, {1997, 56201}, {2345, 49731}, {2801, 54445}, {3059, 58629}, {3161, 17277}, {3244, 50838}, {3534, 60901}, {3545, 21168}, {3589, 51191}, {3616, 5220}, {3617, 51102}, {3618, 51002}, {3620, 51152}, {3624, 30340}, {3634, 50837}, {3681, 10177}, {3707, 29616}, {3715, 10578}, {3731, 37681}, {3763, 51151}, {3826, 44847}, {3828, 40333}, {3925, 30311}, {3945, 3973}, {4000, 49742}, {4308, 5234}, {4312, 19876}, {4335, 36634}, {4343, 42043}, {4344, 50291}, {4346, 31183}, {4389, 31189}, {4402, 17261}, {4413, 30295}, {4422, 17251}, {4460, 50110}, {4488, 49722}, {4648, 15492}, {4677, 30331}, {4687, 51057}, {4688, 51052}, {4725, 37654}, {4995, 60910}, {5044, 10394}, {5054, 21151}, {5055, 5762}, {5056, 5735}, {5064, 7717}, {5066, 31671}, {5071, 5805}, {5281, 30393}, {5298, 60909}, {5302, 34610}, {5541, 45116}, {5698, 9780}, {5703, 5729}, {5732, 15692}, {5772, 48851}, {5825, 16418}, {5838, 17330}, {5843, 11539}, {5845, 21358}, {5850, 19883}, {5853, 38097}, {5856, 38102}, {5857, 38103}, {5880, 19877}, {5936, 17355}, {6068, 45310}, {6966, 54179}, {7229, 17259}, {7672, 31165}, {9708, 53055}, {9779, 38454}, {9814, 36835}, {10303, 43177}, {10304, 21153}, {10385, 15837}, {11001, 31672}, {11038, 25055}, {11049, 60906}, {11106, 34701}, {11160, 29582}, {12572, 50736}, {12630, 24393}, {13846, 60887}, {14269, 38139}, {14848, 38166}, {15601, 39587}, {15693, 60884}, {15694, 31657}, {15699, 38107}, {15702, 36996}, {15703, 60922}, {15709, 38122}, {15828, 25590}, {16670, 29624}, {16676, 17014}, {16814, 17301}, {16833, 28313}, {16885, 17392}, {17132, 36588}, {17133, 36911}, {17263, 21296}, {17297, 29627}, {17336, 31995}, {17337, 49747}, {17349, 50129}, {18482, 41106}, {19862, 51098}, {20073, 29628}, {20582, 51144}, {25728, 50119}, {27549, 50310}, {28534, 41848}, {29580, 51194}, {30628, 58635}, {31140, 36976}, {31721, 52705}, {31994, 32008}, {32086, 32100}, {34595, 43180}, {34747, 43179}, {34784, 58608}, {35514, 50821}, {38080, 47599}, {38086, 48310}, {38111, 47598}, {38137, 47478}, {38149, 38179}, {38216, 45043}, {38318, 59386}, {39581, 50313}, {42034, 56085}, {43161, 50864}, {43182, 50829}, {47352, 59405}, {50687, 59389}, {50738, 57284}, {51126, 51195}, {52746, 57565}

X(61023) = midpoint of X(i) and X(j) for these {i,j}: {3545, 21168}, {5054, 51516}, {52653, 53620}, {6172, 59374}
X(61023) = reflection of X(i) in X(j) for these {i,j}: {10304, 21153}, {11038, 25055}, {14269, 38139}, {14848, 38166}, {19875, 38101}, {21151, 5054}, {25055, 38059}, {3524, 38067}, {3545, 38108}, {3839, 38075}, {38024, 19883}, {38065, 11539}, {38073, 5055}, {38080, 47599}, {38086, 48310}, {38092, 19875}, {38107, 15699}, {38111, 47598}, {38137, 47478}, {38314, 38025}, {5054, 38113}, {5055, 38082}, {50687, 59389}, {53620, 38057}, {59373, 38088}, {59374, 2}, {59375, 38093}, {59377, 38102}, {59385, 3545}, {59405, 47352}, {59413, 53620}, {7, 59374}
X(61023) = complement of X(59375)
X(61023) = anticomplement of X(38093)
X(61023) = X(i)-Dao conjugate of X(j) for these {i, j}: {38093, 38093}
X(61023) = pole of line {14100, 60983} wrt Feuerbach hyperbola
X(61023) = pole of line {1, 38092} wrt dual conic of Yff parabola
X(61023) = orthology center of the pedal triangle of X(58221) wrt Aguilera triangle
X(61023) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(54622)}}, {{A, B, C, X(8), X(6173)}}, {{A, B, C, X(57), X(55920)}}, {{A, B, C, X(142), X(55948)}}, {{A, B, C, X(2094), X(40435)}}, {{A, B, C, X(6172), X(32008)}}, {{A, B, C, X(9436), X(57565)}}, {{A, B, C, X(9776), X(55956)}}, {{A, B, C, X(36588), X(51351)}}
X(61023) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 144, 6173}, {2, 3219, 2094}, {2, 527, 59374}, {2, 59375, 38093}, {2, 60984, 142}, {2, 60986, 18230}, {2, 61006, 60984}, {2, 9, 6172}, {7, 9, 60983}, {8, 47357, 50839}, {9, 142, 61006}, {9, 20195, 61000}, {9, 3305, 60981}, {9, 51780, 36973}, {9, 60958, 29007}, {9, 60981, 60944}, {9, 7308, 8545}, {9, 8257, 3219}, {142, 60957, 7}, {142, 61006, 60957}, {144, 6173, 60971}, {144, 6666, 60996}, {516, 19875, 38092}, {516, 38075, 3839}, {516, 38101, 19875}, {518, 38088, 59373}, {527, 38093, 59375}, {528, 38057, 53620}, {971, 38067, 3524}, {3161, 17277, 32087}, {3973, 25072, 3945}, {5055, 5762, 38073}, {5762, 38082, 5055}, {5817, 59381, 59418}, {5843, 11539, 38065}, {5850, 19883, 38024}, {5856, 38102, 59377}, {6172, 59374, 527}, {6172, 60971, 144}, {8232, 60947, 60941}, {12848, 61015, 5226}, {17254, 17338, 2}, {18230, 60996, 6666}, {20195, 61000, 20059}, {21168, 38108, 59385}, {38113, 51516, 21151}, {51488, 59373, 38314}, {52653, 53620, 528}, {60942, 60999, 60963}, {60976, 61020, 5435}

X(61024) = X(2)X(7)∩X(21)X(518)

Barycentrics    a*(a^4-a^2*b*c-2*a^3*(b+c)+2*a*(b+c)*(b^2+c^2)-(b-c)^2*(b^2+b*c+c^2)) : :

X(61024) lies on these lines: {2, 7}, {3, 12669}, {20, 5686}, {21, 518}, {40, 59413}, {46, 40333}, {55, 34784}, {71, 7291}, {100, 40659}, {191, 516}, {210, 7411}, {219, 1442}, {220, 23144}, {344, 56244}, {377, 38057}, {390, 12514}, {480, 1259}, {846, 4343}, {954, 3927}, {958, 7672}, {960, 7677}, {971, 3651}, {993, 30284}, {1001, 3868}, {1071, 26878}, {1155, 58634}, {1214, 34028}, {1443, 37659}, {1621, 15185}, {1697, 12630}, {1723, 3672}, {1760, 2550}, {1768, 43151}, {1776, 14100}, {2287, 25083}, {2801, 35204}, {3059, 4640}, {3174, 35258}, {3294, 24050}, {3336, 38204}, {3358, 9799}, {3681, 6600}, {3683, 5572}, {3692, 32099}, {3730, 16551}, {3759, 31169}, {3811, 5223}, {4313, 57279}, {5227, 39273}, {5250, 8236}, {5251, 30329}, {5259, 20116}, {5284, 58564}, {5526, 25065}, {5542, 6763}, {5692, 18444}, {5709, 59385}, {5728, 31445}, {5732, 16192}, {5735, 60911}, {5759, 6851}, {5762, 6841}, {5779, 6985}, {5784, 15481}, {5785, 8544}, {5805, 6990}, {5817, 6849}, {5832, 30311}, {5833, 60905}, {5850, 54302}, {6601, 55960}, {6899, 21168}, {6986, 45120}, {7269, 40937}, {7330, 36991}, {7678, 24703}, {7679, 26066}, {9441, 21039}, {10391, 15837}, {10394, 37284}, {10884, 21153}, {10916, 51090}, {11038, 17558}, {11520, 38316}, {12573, 18249}, {12755, 51506}, {15587, 30295}, {17092, 25878}, {17272, 59682}, {17277, 20880}, {17336, 56085}, {17768, 18259}, {21151, 24467}, {23151, 27396}, {24393, 57287}, {26006, 41808}, {26877, 38122}, {28606, 54358}, {29817, 61033}, {31165, 42819}, {31446, 38052}, {37774, 40999}, {38037, 55109}, {38149, 59318}, {50742, 50835}, {51058, 54419}, {56934, 56948}

X(61024) = reflection of X(i) in X(j) for these {i,j}: {60969, 9}
X(61024) = anticomplement of X(60991)
X(61024) = X(i)-Dao conjugate of X(j) for these {i, j}: {60991, 60991}
X(61024) = pole of line {23865, 50355} wrt circumcircle
X(61024) = pole of line {14100, 60981} wrt Feuerbach hyperbola
X(61024) = pole of line {284, 354} wrt Stammler hyperbola
X(61024) = pole of line {100, 58974} wrt Yff parabola
X(61024) = pole of line {333, 20880} wrt Wallace hyperbola
X(61024) = orthology center of the pedal triangle of X(59320) wrt Aguilera triangle
X(61024) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(55965)}}, {{A, B, C, X(21), X(142)}}, {{A, B, C, X(57), X(37741)}}, {{A, B, C, X(226), X(2346)}}, {{A, B, C, X(1156), X(52819)}}, {{A, B, C, X(1445), X(55960)}}, {{A, B, C, X(5249), X(36101)}}, {{A, B, C, X(8232), X(55920)}}, {{A, B, C, X(21446), X(41867)}}
X(61024) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 144, 61010}, {2, 60974, 60948}, {2, 61010, 61013}, {7, 9, 60981}, {9, 1445, 18230}, {9, 3929, 60949}, {9, 527, 60969}, {9, 57, 60958}, {9, 63, 7}, {9, 60942, 60935}, {9, 60949, 6172}, {9, 60966, 60944}, {9, 60973, 61025}, {9, 60974, 2}, {9, 60977, 61004}, {9, 60989, 6666}, {9, 60994, 61012}, {9, 61005, 144}, {9, 6666, 27065}, {57, 60958, 60996}, {63, 54357, 3218}, {144, 29007, 56551}, {144, 61025, 60973}, {219, 24635, 1442}, {3059, 4640, 7676}, {3219, 60970, 9}, {3358, 55104, 59418}, {5223, 31424, 7675}, {5745, 61003, 21617}, {60970, 61012, 60994}, {60973, 61025, 29007}, {60994, 61012, 37787}

X(61025) = X(2)X(7)∩X(21)X(5779)

Barycentrics    a*(2*(a-b)^3*(a+b)-(a-b)^2*(4*a+b)*c-2*(a-3*b)*b*c^2+(4*a-b)*c^3-2*c^4) : :

X(61025) lies on these lines: {2, 7}, {21, 5779}, {44, 24554}, {45, 37659}, {145, 15298}, {377, 21168}, {390, 15296}, {404, 59381}, {405, 51516}, {971, 4189}, {1001, 40269}, {1255, 37672}, {1621, 60910}, {1994, 54358}, {2475, 5759}, {2476, 5762}, {2975, 60909}, {3062, 35258}, {3622, 15299}, {4188, 10861}, {4208, 26878}, {5046, 5817}, {5141, 5805}, {5154, 38108}, {5732, 17548}, {5843, 7483}, {5850, 24541}, {6910, 36996}, {6933, 59386}, {7226, 25885}, {7504, 38107}, {7705, 38179}, {11114, 60901}, {11372, 17578}, {11680, 60919}, {14997, 26635}, {15680, 36991}, {15837, 25722}, {15988, 50995}, {16370, 60884}, {16814, 26669}, {17331, 48381}, {17332, 26540}, {17335, 20905}, {17336, 25001}, {17566, 38113}, {17576, 52684}, {17577, 31671}, {20085, 51768}, {20119, 38215}, {21151, 37291}, {21153, 37307}, {21796, 26636}, {24987, 51090}, {26543, 51144}, {29817, 30330}, {37161, 55104}, {37256, 59418}, {52653, 60911}, {59412, 60912}

X(61025) = orthology center of the pedal triangle of X(59331) wrt Aguilera triangle
X(61025) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 9, 61026}, {9, 142, 60954}, {9, 60935, 61006}, {9, 60964, 37787}, {9, 60966, 3219}, {9, 60973, 61024}, {9, 61004, 7}, {9, 8545, 60970}, {8545, 60970, 20059}, {10861, 31658, 4188}, {17260, 26651, 2}, {29007, 61024, 60973}, {56551, 61005, 144}

X(61026) = X(2)X(7)∩X(44)X(26669)

Barycentrics    a*(2*(a-b)^3*(a+b)-(a-b)^2*(4*a-b)*c+2*b*(-3*a+b)*c^2+(4*a+b)*c^3-2*c^4) : :

X(61026) lies on these lines: {2, 7}, {21, 59381}, {44, 26669}, {100, 60910}, {145, 15299}, {390, 15297}, {404, 5779}, {474, 51516}, {516, 25005}, {971, 4188}, {1728, 20007}, {2475, 5817}, {2478, 21168}, {3358, 37267}, {3622, 15298}, {3957, 30330}, {3973, 25930}, {4189, 31658}, {4193, 5762}, {4422, 26540}, {4661, 54348}, {5046, 5759}, {5129, 26878}, {5141, 38108}, {5154, 5805}, {5253, 60909}, {5554, 52653}, {5732, 37307}, {5843, 13747}, {6548, 25924}, {6921, 36996}, {6931, 59386}, {9352, 31391}, {10398, 34772}, {10861, 17572}, {11372, 50689}, {11681, 60883}, {14986, 15518}, {15492, 25067}, {15680, 59418}, {16189, 17544}, {16371, 60884}, {16814, 24554}, {16885, 37659}, {17335, 25001}, {17336, 20905}, {17339, 48381}, {17349, 25243}, {17354, 25000}, {17548, 21153}, {17566, 31657}, {17579, 60901}, {17825, 33761}, {20533, 26610}, {24982, 51090}, {26001, 59579}, {27529, 60923}, {31671, 37375}, {34545, 54358}, {36101, 55989}, {36991, 37256}, {59412, 60911}

X(61026) = orthology center of the pedal triangle of X(59332) wrt Aguilera triangle
X(61026) = intersection, other than A, B, C, of circumconics {{A, B, C, X(30827), X(36101)}}, {{A, B, C, X(40869), X(55989)}}
X(61026) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 9, 61025}, {9, 142, 60944}, {9, 1445, 60935}, {9, 37787, 144}, {9, 60947, 60970}, {9, 60970, 61006}, {9, 60994, 6172}, {9, 61012, 2}, {9, 8257, 29007}, {1445, 20059, 23958}, {1445, 60935, 20059}, {60948, 60973, 60984}

X(61027) = X(2)X(7)∩X(30)X(954)

Barycentrics    (a+b-c)*(a-b+c)*(a^3-3*a^2*(b+c)-(b-c)^2*(b+c)+a*(3*b^2+8*b*c+3*c^2)) : :
X(61027) = X[390]+2*X[1478], X[1156]+2*X[12831], 2*X[1836]+X[36976], -8*X[3822]+5*X[40333], X[5759]+2*X[37826], 2*X[18446]+X[36991]

X(61027) lies on these lines: {2, 7}, {30, 954}, {79, 3085}, {85, 17264}, {388, 8543}, {390, 1478}, {480, 49732}, {497, 30311}, {498, 30424}, {499, 43180}, {515, 8236}, {516, 10056}, {528, 10956}, {758, 5686}, {912, 5817}, {1001, 5434}, {1056, 53055}, {1156, 12831}, {1441, 50107}, {1443, 5308}, {1836, 36976}, {2263, 50291}, {2346, 10385}, {2550, 6175}, {2801, 11038}, {3086, 30340}, {3475, 7671}, {3485, 3889}, {3487, 10394}, {3582, 59372}, {3584, 4312}, {3600, 5259}, {3649, 5220}, {3679, 12560}, {3822, 40333}, {3947, 51100}, {4318, 48856}, {4321, 25055}, {4323, 41863}, {4870, 8581}, {4995, 11495}, {5218, 30295}, {5261, 34619}, {5274, 41858}, {5281, 41853}, {5290, 50836}, {5542, 10072}, {5552, 5880}, {5703, 41854}, {5729, 6147}, {5735, 6838}, {5759, 37826}, {5766, 37427}, {5809, 15933}, {5904, 50835}, {6180, 17392}, {6890, 43177}, {7190, 50114}, {7269, 54425}, {7677, 16858}, {8544, 13411}, {9578, 51102}, {10198, 60905}, {10199, 51098}, {10399, 11036}, {10404, 15254}, {10588, 30312}, {10590, 45043}, {10786, 52682}, {11238, 42356}, {12047, 60926}, {13405, 41860}, {13407, 54370}, {14986, 41870}, {15726, 17718}, {16672, 43066}, {17078, 51488}, {17132, 36595}, {17301, 37800}, {17335, 32007}, {17346, 56927}, {17577, 43740}, {17732, 60083}, {18446, 36991}, {21279, 36728}, {30332, 41869}, {42289, 50282}, {49742, 52023}, {50739, 57283}

X(61027) = orthology center of the pedal triangle of X(59337) wrt Aguilera triangle
X(61027) = intersection, other than A, B, C, of circumconics {{A, B, C, X(79), X(6173)}}, {{A, B, C, X(142), X(60083)}}, {{A, B, C, X(3219), X(55920)}}, {{A, B, C, X(27475), X(31018)}}
X(61027) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 60967, 7}, {7, 18230, 60948}, {7, 5226, 61008}, {7, 6172, 60951}, {7, 60943, 61019}, {7, 60944, 12848}, {7, 60954, 60939}, {7, 60995, 37787}, {7, 61017, 8732}, {7, 8232, 60943}, {7, 8545, 60946}, {9, 4654, 60932}, {553, 60986, 1445}, {5219, 60953, 30379}, {6172, 60951, 41563}, {6173, 60937, 60952}, {8232, 60967, 2}, {17781, 31164, 5905}, {21617, 60952, 6173}, {29007, 60951, 6172}, {31019, 60935, 60987}, {41857, 60932, 4654}, {61004, 61011, 144}

X(61028) = X(9)X(165)∩X(10)X(1071)

Barycentrics    a*(a^2+b^2+4*b*c+c^2-2*a*(b+c))*(-(b-c)^2+a*(b+c)) : :
X(61028) = -3*X[2]+X[7671], X[72]+2*X[5880], -X[144]+4*X[58635], 5*X[1698]+X[5696], 2*X[3678]+X[30424], -2*X[3742]+3*X[38093], -2*X[3833]+3*X[38204], -X[3873]+3*X[59374], X[4661]+3*X[59375], -4*X[5044]+X[5698], X[8581]+2*X[24393], -7*X[9780]+X[10394] and many others

X(61028) lies on these lines: {2, 7671}, {7, 3681}, {9, 165}, {10, 1071}, {35, 5506}, {37, 60785}, {46, 3697}, {72, 5880}, {100, 60981}, {142, 354}, {144, 58635}, {210, 527}, {374, 29353}, {392, 528}, {480, 60964}, {516, 10176}, {517, 2550}, {518, 599}, {758, 51100}, {936, 11496}, {960, 9589}, {971, 14647}, {1001, 5440}, {1212, 35338}, {1698, 5696}, {1737, 3826}, {3174, 10389}, {3219, 30295}, {3243, 4915}, {3254, 4553}, {3339, 4662}, {3452, 7965}, {3555, 9710}, {3652, 58658}, {3678, 30424}, {3742, 38093}, {3833, 38204}, {3848, 5572}, {3873, 59374}, {3880, 51102}, {4002, 13750}, {4413, 8257}, {4430, 34784}, {4661, 59375}, {4880, 5223}, {5044, 5698}, {5049, 34625}, {5173, 30275}, {5325, 5918}, {5432, 6666}, {5439, 41859}, {5686, 10861}, {5729, 59335}, {5853, 5919}, {6174, 60986}, {6253, 57284}, {6510, 28125}, {6854, 54158}, {6911, 54203}, {7064, 17635}, {8545, 15346}, {8581, 24393}, {9004, 47595}, {9709, 26921}, {9780, 10394}, {9856, 45085}, {9858, 30478}, {10310, 54370}, {10855, 24477}, {14523, 17278}, {17614, 42842}, {17620, 61019}, {17625, 25006}, {18230, 25722}, {25606, 46694}, {26040, 60987}, {27131, 30311}, {30287, 58696}, {30557, 60928}, {30628, 58564}, {31391, 58677}, {31837, 52682}, {33108, 61008}, {37560, 58631}, {38202, 50842}, {38316, 56177}, {38454, 49732}, {40333, 41228}, {40937, 54474}, {44671, 51057}, {46916, 60972}, {46917, 47375}, {58650, 60940}, {58678, 60977}

X(61028) = midpoint of X(i) and X(j) for these {i,j}: {354, 3059}, {3740, 15587}, {4430, 34784}, {5686, 10861}, {7, 3681}
X(61028) = reflection of X(i) in X(j) for these {i,j}: {10177, 2}, {15185, 354}, {354, 142}, {3681, 40659}, {3740, 58634}, {5572, 3848}, {9, 3740}
X(61028) = complement of X(7671)
X(61028) = X(i)-isoconjugate-of-X(j) for these {i, j}: {14074, 58322}
X(61028) = X(i)-Dao conjugate of X(j) for these {i, j}: {142, 34919}
X(61028) = pole of line {3887, 4885} wrt Spieker circle
X(61028) = pole of line {60910, 60942} wrt Feuerbach hyperbola
X(61028) = pole of line {4130, 45320} wrt Steiner inellipse
X(61028) = orthology center of the pedal triangle of X(9) wrt Aguilera-Pavlov triangle
X(61028) = intersection, other than A, B, C, of circumconics {{A, B, C, X(142), X(3062)}}, {{A, B, C, X(354), X(11051)}}, {{A, B, C, X(4847), X(19605)}}, {{A, B, C, X(5559), X(14077)}}, {{A, B, C, X(20880), X(41555)}}, {{A, B, C, X(51384), X(56718)}}
X(61028) = barycentric product X(i)*X(j) for these (i, j): {354, 50107}, {1229, 37541}, {1996, 3059}, {4847, 8545}, {30181, 35341}, {35338, 47787}, {45791, 47386}, {46644, 61035}
X(61028) = barycentric quotient X(i)/X(j) for these (i, j): {1212, 34919}, {1996, 42311}, {4847, 55984}, {8545, 21453}, {14077, 56322}, {35326, 14074}, {37541, 1170}, {50107, 57815}
X(61028) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15733, 10177}, {9, 15587, 17668}, {142, 3059, 15185}, {142, 4847, 41555}, {142, 61030, 354}, {354, 3059, 61030}, {3740, 15587, 15726}, {3826, 8255, 60978}, {3925, 61035, 142}, {4413, 42014, 8257}, {15587, 58634, 9}, {15726, 58634, 3740}, {30628, 60996, 58564}

X(61029) = X(2)X(165)∩X(10)X(3681)

Barycentrics    a*b*c*(a+b+c)*(a+3*(b+c))*(-(b-c)^2+a*(b+c)) : :
X(61029) = -7*X[3624]+X[4309], -X[5250]+7*X[50393]

X(61029) lies on these lines: {1, 37436}, {2, 165}, {10, 3681}, {21, 59420}, {35, 5284}, {46, 3305}, {142, 354}, {200, 40333}, {226, 3740}, {329, 1698}, {377, 28164}, {405, 28150}, {442, 5927}, {443, 3576}, {497, 20195}, {515, 44217}, {517, 8728}, {519, 50793}, {912, 38042}, {946, 17529}, {1125, 3434}, {1210, 3833}, {1738, 17592}, {1836, 6666}, {2550, 10389}, {2886, 3848}, {3090, 37560}, {3219, 30424}, {3339, 3947}, {3475, 38200}, {3624, 4309}, {3663, 3989}, {3698, 17658}, {3720, 60785}, {3753, 38127}, {3823, 53663}, {3824, 21075}, {3828, 31164}, {3838, 5316}, {3873, 38054}, {3914, 29571}, {3950, 29854}, {3982, 5220}, {3986, 32776}, {4061, 18134}, {4208, 10884}, {4301, 24564}, {4349, 26723}, {4356, 33131}, {4413, 58463}, {4423, 58433}, {4430, 5542}, {4654, 38057}, {4656, 17889}, {4661, 38210}, {4699, 39597}, {4896, 32912}, {5047, 51118}, {5049, 31419}, {5057, 31263}, {5250, 50393}, {5260, 59323}, {5325, 11246}, {5657, 50727}, {6692, 31245}, {6736, 25466}, {6737, 28629}, {6745, 25525}, {6904, 58221}, {6991, 21628}, {10167, 38123}, {10176, 12609}, {10180, 50091}, {10310, 16862}, {10431, 43151}, {10582, 60996}, {10855, 58615}, {11019, 33108}, {11024, 55109}, {12436, 19854}, {12527, 19855}, {14647, 54447}, {15931, 35985}, {16408, 25893}, {16842, 18483}, {17067, 17599}, {17245, 21949}, {17552, 41869}, {17591, 24177}, {19860, 28236}, {20103, 31266}, {20292, 51090}, {20347, 59306}, {21020, 29594}, {21060, 31019}, {21255, 31330}, {23812, 59408}, {24175, 29639}, {24199, 29641}, {24392, 38093}, {24693, 59692}, {25972, 48888}, {28146, 50202}, {28158, 31156}, {28160, 50396}, {28172, 50397}, {28174, 50395}, {28178, 50205}, {28186, 50238}, {28216, 50394}, {28232, 50207}, {29600, 32915}, {30331, 33110}, {31140, 60999}, {31191, 32772}, {33105, 45204}, {33118, 50116}, {33147, 50291}, {37097, 54474}, {37319, 41430}

X(61029) = midpoint of X(i) and X(j) for these {i,j}: {10884, 59387}
X(61029) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1174, 39948}, {28148, 58322}
X(61029) = X(i)-Dao conjugate of X(j) for these {i, j}: {1212, 28626}, {40606, 39948}
X(61029) = pole of line {5222, 16601} wrt dual conic of Yff parabola
X(61029) = orthology center of the pedal triangle of X(405) wrt Aguilera-Pavlov triangle
X(61029) = intersection, other than A, B, C, of circumconics {{A, B, C, X(142), X(55937)}}, {{A, B, C, X(3247), X(15185)}}, {{A, B, C, X(3925), X(3947)}}, {{A, B, C, X(4847), X(9780)}}, {{A, B, C, X(25507), X(51384)}}
X(61029) = barycentric product X(i)*X(j) for these (i, j): {142, 9780}, {354, 42029}, {1229, 3339}, {16713, 3947}, {20880, 3247}, {25507, 3925}
X(61029) = barycentric quotient X(i)/X(j) for these (i, j): {142, 28626}, {354, 39948}, {3247, 2346}, {3339, 1170}, {3925, 60243}, {3947, 60229}, {4847, 30711}, {9780, 32008}, {28147, 56322}, {35326, 28148}, {42029, 57815}, {48026, 58322}
X(61029) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 59412, 4512}, {142, 3925, 4847}, {142, 61031, 354}, {354, 3925, 61031}, {19862, 51783, 5284}, {25006, 27186, 5542}

X(61030) = X(9)X(1174)∩X(30)X(511)

Barycentrics    a*(a^2+b^2+b*c+c^2-2*a*(b+c))*(-(b-c)^2+a*(b+c)) : :
X(61030) = -X[7]+X[2890], -X[8]+X[34917], -X[9]+X[1174], -X[100]+X[60989], -X[142]+X[354], -X[165]+X[3174], -X[200]+X[8257], -X[210]+X[10177], -X[1001]+X[3940], -X[1389]+X[12629], -X[1697]+X[3951], -X[2078]+X[3935] and many others

X(61030) lies on these lines: {7, 2890}, {8, 34917}, {9, 1174}, {30, 511}, {100, 60989}, {142, 354}, {165, 3174}, {200, 8257}, {210, 10177}, {1001, 3940}, {1389, 12629}, {1697, 3951}, {2078, 3935}, {2340, 16578}, {2550, 5902}, {3243, 3872}, {3295, 5220}, {3340, 60953}, {3434, 61011}, {3555, 5784}, {3621, 60975}, {3632, 13375}, {3634, 16216}, {3678, 15254}, {3740, 5572}, {3742, 60999}, {3817, 24389}, {3826, 3833}, {3848, 58433}, {3873, 6173}, {3874, 5880}, {3881, 25557}, {3957, 60981}, {3989, 4343}, {4028, 22312}, {4309, 5698}, {4326, 61005}, {4362, 35892}, {4661, 6172}, {4662, 16201}, {5082, 5696}, {5083, 30379}, {5528, 30295}, {5559, 34919}, {5659, 24477}, {5686, 11239}, {5692, 47357}, {5728, 24393}, {5837, 45081}, {6600, 60994}, {6601, 15909}, {6762, 10884}, {6764, 55109}, {6765, 55104}, {7672, 60982}, {7674, 60950}, {9812, 61010}, {9814, 11524}, {10056, 38057}, {10267, 60912}, {11025, 20195}, {11218, 25568}, {11220, 60990}, {12647, 18412}, {12648, 60997}, {12848, 20015}, {14100, 60942}, {15587, 60980}, {17389, 31346}, {17620, 52819}, {17625, 61022}, {17668, 60962}, {21039, 55340}, {22836, 42842}, {25006, 60978}, {25722, 60933}, {30144, 42886}, {36845, 52457}, {41711, 42014}, {46685, 60935}, {51152, 60929}, {55922, 56091}, {56095, 56263}, {58608, 58635}

X(61030) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1174, 34578}, {1308, 58322}
X(61030) = X(i)-Dao conjugate of X(j) for these {i, j}: {142, 3254}, {35125, 56322}, {40606, 34578}
X(61030) = X(i)-Ceva conjugate of X(j) for these {i, j}: {9, 6594}
X(61030) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {34578, 2890}
X(61030) = pole of line {11, 6594} wrt Feuerbach hyperbola
X(61030) = pole of line {110, 18164} wrt Stammler hyperbola
X(61030) = pole of line {2, 56322} wrt Steiner circumellipse
X(61030) = pole of line {2, 56322} wrt Steiner inellipse
X(61030) = pole of line {3939, 5375} wrt Hutson-Moses hyperbola
X(61030) = pole of line {99, 16708} wrt Wallace hyperbola
X(61030) = pole of line {1086, 16601} wrt dual conic of Yff parabola
X(61030) = orthology center of the pedal triangle of X(518) wrt Aguilera-Pavlov triangle
X(61030) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(7), X(42325)}}, {{A, B, C, X(9), X(6067)}}, {{A, B, C, X(142), X(514)}}, {{A, B, C, X(354), X(513)}}, {{A, B, C, X(512), X(52020)}}, {{A, B, C, X(522), X(3935)}}, {{A, B, C, X(523), X(3925)}}, {{A, B, C, X(528), X(35338)}}, {{A, B, C, X(900), X(41553)}}, {{A, B, C, X(918), X(51384)}}, {{A, B, C, X(1389), X(28292)}}, {{A, B, C, X(2804), X(51416)}}, {{A, B, C, X(2826), X(41555)}}, {{A, B, C, X(3059), X(3900)}}, {{A, B, C, X(3309), X(5526)}}, {{A, B, C, X(4762), X(17264)}}, {{A, B, C, X(5559), X(14077)}}, {{A, B, C, X(5856), X(35341)}}, {{A, B, C, X(6366), X(6594)}}, {{A, B, C, X(6602), X(6607)}}, {{A, B, C, X(8713), X(38459)}}, {{A, B, C, X(28217), X(55922)}}, {{A, B, C, X(28345), X(55123)}}, {{A, B, C, X(28473), X(41548)}}
X(61030) = barycentric product X(i)*X(j) for these (i, j): {142, 3935}, {1229, 2078}, {1233, 19624}, {3059, 37757}, {17264, 354}, {20880, 5526}, {30565, 35338}, {37787, 4847}, {38459, 51972}
X(61030) = barycentric quotient X(i)/X(j) for these (i, j): {354, 34578}, {1212, 3254}, {2078, 1170}, {3887, 56322}, {3935, 32008}, {5526, 2346}, {6362, 60489}, {8012, 42064}, {17264, 57815}, {19624, 1174}, {22108, 58322}, {35326, 1308}, {35338, 37143}, {35341, 60488}, {37757, 42311}, {37787, 21453}, {38459, 10509}
X(61030) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {142, 15185, 61033}, {142, 61033, 58607}, {210, 10177, 60986}, {354, 3059, 61028}, {518, 15733, 527}, {518, 528, 758}, {2340, 57022, 16578}, {3059, 15185, 142}, {3681, 30628, 7671}, {5572, 40659, 6666}, {6666, 40659, 58677}, {7671, 34784, 3681}, {15185, 41566, 41573}, {15185, 61028, 354}, {30628, 34784, 9}, {51463, 61035, 41555}, {58564, 58634, 58433}

X(61031) = X(2)X(3158)∩X(5)X(10)

Barycentrics    (a-3*(b+c))*(-(b-c)^2+a*(b+c)) : :
X(61031) = 5*X[1698]+X[5082], -X[3295]+4*X[3634], X[3340]+5*X[3617], -4*X[3841]+X[21620], 2*X[18517]+X[31730], -13*X[19877]+X[56936], X[31673]+2*X[35239]

X(61031) lies on these lines: {2, 3158}, {5, 10}, {8, 4035}, {9, 9812}, {142, 354}, {165, 2550}, {200, 58463}, {226, 3681}, {306, 4923}, {497, 6666}, {516, 5325}, {551, 50395}, {958, 12511}, {1376, 52769}, {1697, 5274}, {1698, 5082}, {1699, 38057}, {1738, 17591}, {1836, 60942}, {2321, 29641}, {2900, 19860}, {3295, 3634}, {3340, 3617}, {3576, 19843}, {3663, 21949}, {3677, 17067}, {3679, 25568}, {3707, 4388}, {3742, 38204}, {3755, 17592}, {3826, 3848}, {3829, 58451}, {3833, 10916}, {3838, 21060}, {3841, 21620}, {3914, 3989}, {3921, 17530}, {3928, 59412}, {3947, 4662}, {4104, 21241}, {4138, 49457}, {4208, 6762}, {4423, 61001}, {4430, 5249}, {4884, 53594}, {4891, 29600}, {4967, 7179}, {5049, 8728}, {5231, 6692}, {5257, 32773}, {5302, 51118}, {5316, 11680}, {5437, 40333}, {5493, 18253}, {5658, 38154}, {5686, 28609}, {5705, 12116}, {5794, 28236}, {5795, 37421}, {5902, 24391}, {5919, 21627}, {6361, 31446}, {6700, 31493}, {6743, 28628}, {6745, 31245}, {9623, 18446}, {9842, 15908}, {10164, 38201}, {10388, 10589}, {10580, 20195}, {10582, 58433}, {11522, 45085}, {12514, 28232}, {12640, 24987}, {15254, 51783}, {18481, 31494}, {18517, 31730}, {19854, 59337}, {19877, 56936}, {20335, 31330}, {20588, 61004}, {20935, 59255}, {24477, 38052}, {27798, 44661}, {28178, 31445}, {30478, 58221}, {31140, 40998}, {31146, 60999}, {31420, 41869}, {31673, 35239}, {33110, 54357}, {33111, 49772}, {33117, 53663}, {33118, 50115}, {33135, 50291}, {36845, 41867}, {38059, 49736}, {50205, 51724}, {50841, 59419}

X(61031) = complement of X(10389)
X(61031) = complement of isogonal conjugate of X(10390)
X(61031) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1174, 39980}, {28162, 58322}
X(61031) = X(i)-Dao conjugate of X(j) for these {i, j}: {1212, 30712}, {11530, 2346}, {40606, 39980}
X(61031) = X(i)-complementary conjugate of X(j) for these {i, j}: {10390, 10}, {34821, 1}, {56054, 141}, {56348, 2886}, {58103, 522}
X(61031) = pole of line {3752, 16601} wrt dual conic of Yff parabola
X(61031) = orthology center of the pedal triangle of X(958) wrt Aguilera-Pavlov triangle
X(61031) = intersection, other than A, B, C, of circumconics {{A, B, C, X(142), X(2051)}}, {{A, B, C, X(354), X(3340)}}, {{A, B, C, X(3617), X(4847)}}, {{A, B, C, X(3731), X(15185)}}, {{A, B, C, X(3925), X(51870)}}
X(61031) = barycentric product X(i)*X(j) for these (i, j): {142, 3617}, {354, 42034}, {1229, 3340}, {4847, 5226}, {17169, 4058}, {20880, 3731}
X(61031) = barycentric quotient X(i)/X(j) for these (i, j): {142, 30712}, {354, 39980}, {3340, 1170}, {3617, 32008}, {3731, 2346}, {3925, 56226}, {4058, 56157}, {4847, 56201}, {5226, 21453}, {21808, 31503}, {28161, 56322}, {35326, 28162}, {42034, 57815}
X(61031) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 59413, 3158}, {10, 2886, 3452}, {10, 3817, 3740}, {226, 25006, 24393}, {354, 3925, 61029}, {354, 61029, 142}, {354, 61032, 4847}, {2886, 3740, 3817}, {3925, 61032, 354}, {5231, 26040, 6692}, {5274, 9780, 51780}, {10164, 38201, 49732}, {25006, 33108, 226}

X(61032) = X(10)X(3893)∩X(11)X(3740)

Barycentrics    (2*a-3*(b+c))*(-(b-c)^2+a*(b+c)) : :
X(61032) = -X[165]+3*X[5659], -4*X[4691]+X[15862], 2*X[5178]+X[10543]

X(61032) lies on these lines: {8, 31245}, {10, 3893}, {11, 3740}, {142, 354}, {165, 5659}, {191, 28216}, {210, 3817}, {517, 6841}, {523, 6545}, {547, 3679}, {1699, 38139}, {1836, 60977}, {2098, 3617}, {2346, 4423}, {2886, 3681}, {3006, 4046}, {3614, 4662}, {3626, 11011}, {3697, 7173}, {3848, 26015}, {3921, 44847}, {3956, 17533}, {3989, 4854}, {4430, 33108}, {4669, 38058}, {4691, 15862}, {4745, 34122}, {4819, 29671}, {4863, 10389}, {5178, 10543}, {5258, 28186}, {5559, 20196}, {5745, 6154}, {5902, 31419}, {6172, 9812}, {6174, 58441}, {7958, 10175}, {8168, 9780}, {10176, 24390}, {10943, 38112}, {11238, 38057}, {17240, 29641}, {17502, 31157}, {17591, 32865}, {17605, 24393}, {17728, 38200}, {17774, 26038}, {24392, 47375}, {24953, 59337}, {28224, 47033}, {28634, 30742}, {31330, 31337}, {42438, 52818}

X(61032) = X(i)-isoconjugate-of-X(j) for these {i, j}: {28184, 58322}
X(61032) = orthology center of the pedal triangle of X(5258) wrt Aguilera-Pavlov triangle
X(61032) = intersection, other than A, B, C, of circumconics {{A, B, C, X(354), X(11011)}}, {{A, B, C, X(3626), X(4847)}}, {{A, B, C, X(15185), X(16814)}}
X(61032) = barycentric product X(i)*X(j) for these (i, j): {142, 3626}, {11011, 1229}, {16814, 20880}
X(61032) = barycentric quotient X(i)/X(j) for these (i, j): {3626, 32008}, {11011, 1170}, {16814, 2346}, {28183, 56322}, {35326, 28184}
X(61032) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {354, 61031, 3925}, {3925, 4847, 51463}, {4847, 61031, 354}

X(61033) = X(1)X(21059)∩X(7)X(149)

Barycentrics    a*((a-b)^2-(2*a+b)*c+c^2)*(-(b-c)^2+a*(b+c)) : :
X(61033) = -3*X[2]+2*X[58677], X[9]+3*X[3873], -X[142]+3*X[354], -3*X[210]+5*X[61001], -X[2550]+5*X[18398], X[3555]+X[24393], -3*X[3742]+X[40659], X[3868]+3*X[38316], 3*X[4430]+5*X[18230], 3*X[6173]+X[30628], 3*X[7671]+X[60933], -3*X[10177]+X[60942] and many others

X(61033) lies on these lines: {1, 21059}, {2, 58677}, {7, 149}, {9, 3873}, {78, 3243}, {142, 354}, {210, 61001}, {214, 999}, {516, 12005}, {518, 1125}, {527, 5572}, {758, 42819}, {942, 5853}, {971, 40273}, {1001, 3874}, {1385, 15570}, {1420, 7672}, {1484, 2801}, {2346, 60989}, {2550, 18398}, {2810, 58473}, {3174, 10980}, {3555, 24393}, {3650, 10122}, {3742, 40659}, {3826, 58565}, {3868, 38316}, {3870, 60985}, {3957, 60948}, {4343, 17449}, {4430, 18230}, {4667, 14523}, {5173, 60945}, {5223, 5506}, {5542, 11263}, {6173, 30628}, {6583, 40249}, {6743, 34791}, {7671, 60933}, {7677, 15556}, {10072, 18412}, {10177, 60942}, {10391, 15006}, {10527, 11038}, {10580, 61010}, {11020, 60990}, {14100, 60962}, {15179, 42470}, {15733, 33558}, {16578, 21346}, {17597, 54358}, {18389, 42884}, {19854, 38053}, {20195, 34784}, {24474, 43175}, {25722, 61020}, {26015, 60991}, {29652, 35892}, {29817, 61024}, {30330, 60973}, {58560, 58634}, {58608, 61000}

X(61033) = midpoint of X(i) and X(j) for these {i,j}: {1001, 3874}, {142, 15185}, {14100, 60962}, {24474, 43175}, {30329, 42871}, {3555, 24393}, {3881, 20116}
X(61033) = reflection of X(i) in X(j) for these {i,j}: {142, 58607}, {3826, 58565}, {40659, 58433}, {6666, 58564}, {60980, 58563}, {60999, 58560}, {61000, 58608}
X(61033) = anticomplement of X(58677)
X(61033) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1174, 42326}
X(61033) = X(i)-Dao conjugate of X(j) for these {i, j}: {21104, 1111}, {40606, 42326}, {58677, 58677}
X(61033) = X(i)-Ceva conjugate of X(j) for these {i, j}: {765, 35338}
X(61033) = pole of line {16601, 17245} wrt dual conic of Yff parabola
X(61033) = orthology center of the pedal triangle of X(15570) wrt Aguilera-Pavlov triangle
X(61033) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(42325)}}, {{A, B, C, X(3059), X(3254)}}, {{A, B, C, X(3957), X(4847)}}, {{A, B, C, X(5284), X(6666)}}, {{A, B, C, X(15179), X(41573)}}, {{A, B, C, X(15185), X(17745)}}
X(61033) = barycentric product X(i)*X(j) for these (i, j): {142, 3957}, {1212, 32007}, {4847, 60948}, {10481, 56244}, {17263, 354}, {17745, 20880}
X(61033) = barycentric quotient X(i)/X(j) for these (i, j): {354, 42326}, {3957, 32008}, {17263, 57815}, {17745, 2346}, {32007, 31618}, {42325, 56322}, {56244, 56118}, {60948, 21453}
X(61033) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {142, 15185, 61030}, {142, 354, 58607}, {354, 15185, 142}, {518, 58564, 6666}, {3742, 40659, 58433}, {3873, 11025, 9}, {3881, 20116, 518}, {3892, 30329, 42871}, {15185, 41555, 41577}, {15733, 58563, 60980}

X(61034) = X(43)X(1403)∩X(142)X(354)

Barycentrics    a*(-(b-c)^2+a*(b+c))*(-(b*c)+a*(b+c)) : :

X(61034) lies on these lines: {6, 49537}, {42, 28351}, {43, 1403}, {55, 27626}, {65, 1738}, {72, 3821}, {100, 27678}, {142, 354}, {210, 4357}, {226, 53005}, {239, 17792}, {513, 16669}, {518, 3662}, {579, 1155}, {584, 52086}, {674, 17366}, {869, 28358}, {899, 21892}, {1086, 22277}, {1122, 20455}, {1362, 60992}, {1463, 3751}, {1716, 4383}, {1742, 36635}, {2110, 27633}, {2223, 60785}, {2228, 21857}, {2664, 28366}, {3008, 21746}, {3056, 5222}, {3057, 3755}, {3094, 41015}, {3555, 49676}, {3661, 25144}, {3663, 20683}, {3672, 4517}, {3681, 17236}, {3688, 3946}, {3713, 4413}, {3740, 17248}, {3742, 27147}, {3752, 3778}, {3759, 9025}, {3779, 4000}, {3888, 17121}, {4255, 28275}, {4393, 25279}, {4553, 4852}, {4686, 21865}, {4688, 22279}, {4718, 40521}, {4878, 21320}, {4890, 29571}, {4941, 53676}, {5224, 58655}, {6007, 17353}, {12723, 53600}, {15310, 16468}, {16583, 20861}, {16610, 17065}, {16690, 27637}, {17231, 44671}, {17237, 22271}, {17244, 25108}, {17247, 58693}, {17282, 35892}, {17304, 56542}, {17356, 57024}, {17382, 56537}, {17718, 25521}, {20359, 40940}, {21257, 25106}, {22312, 50092}, {24309, 60722}, {24575, 37596}, {25277, 52043}, {25917, 50290}, {27349, 33121}, {31165, 50091}, {50591, 54418}, {54338, 59406}

X(61034) = X(i)-isoconjugate-of-X(j) for these {i, j}: {87, 2346}, {330, 1174}, {932, 58322}, {1170, 2319}, {2053, 21453}, {2162, 32008}, {6605, 7153}, {7121, 57815}, {7209, 59141}, {31618, 57264}, {34071, 56322}
X(61034) = X(i)-Dao conjugate of X(j) for these {i, j}: {142, 7155}, {1212, 6384}, {40598, 57815}, {40606, 330}, {40610, 56322}
X(61034) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1475, 354}
X(61034) = orthology center of the pedal triangle of X(16468) wrt Aguilera-Pavlov triangle
X(61034) = intersection, other than A, B, C, of circumconics {{A, B, C, X(43), X(4847)}}, {{A, B, C, X(142), X(1423)}}, {{A, B, C, X(354), X(1403)}}, {{A, B, C, X(1212), X(51902)}}, {{A, B, C, X(2176), X(15185)}}, {{A, B, C, X(3059), X(3212)}}, {{A, B, C, X(27644), X(51384)}}
X(61034) = barycentric product X(i)*X(j) for these (i, j): {142, 43}, {192, 354}, {1212, 3212}, {1229, 1403}, {1233, 2209}, {1418, 27538}, {1423, 4847}, {1475, 6376}, {2293, 30545}, {4595, 48151}, {10481, 3208}, {17169, 20691}, {17217, 35310}, {18107, 35335}, {18164, 3971}, {20880, 2176}, {20906, 35326}, {21104, 52923}, {21808, 33296}, {27644, 3925}, {31008, 52020}, {35338, 3835}, {52023, 56181}, {52964, 53240}
X(61034) = barycentric quotient X(i)/X(j) for these (i, j): {43, 32008}, {142, 6384}, {192, 57815}, {354, 330}, {1212, 7155}, {1403, 1170}, {1423, 21453}, {1475, 87}, {2176, 2346}, {2209, 1174}, {2293, 2319}, {3208, 56118}, {3212, 31618}, {3925, 60244}, {3971, 56127}, {4083, 56322}, {4847, 27424}, {10481, 7209}, {20229, 2053}, {20691, 56157}, {20880, 6383}, {20979, 58322}, {21808, 42027}, {35326, 932}, {35338, 4598}, {52020, 16606}
X(61034) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {142, 52020, 354}, {1738, 4260, 65}, {25108, 58620, 17244}

X(61035) = X(2)X(8255)∩X(7)X(480)

Barycentrics    (a-b-c)*(2*a^2-(b-c)^2-a*(b+c))*(-(b-c)^2+a*(b+c)) : :

X(61035) lies on these lines: {2, 8255}, {5, 5696}, {7, 480}, {8, 17297}, {9, 3255}, {11, 15733}, {12, 5784}, {55, 52457}, {78, 3649}, {100, 38454}, {142, 354}, {200, 6173}, {320, 28058}, {390, 56177}, {516, 5440}, {518, 6735}, {519, 38055}, {527, 1155}, {528, 4511}, {529, 18450}, {599, 28118}, {908, 15726}, {1086, 2340}, {1260, 11246}, {1329, 10394}, {2077, 60885}, {2099, 2550}, {2801, 17757}, {2886, 61008}, {3035, 37787}, {3753, 5542}, {3816, 7671}, {3826, 37796}, {3838, 15587}, {3912, 4081}, {3913, 60926}, {4012, 4869}, {4413, 60987}, {4421, 36976}, {4675, 28043}, {4915, 38024}, {5048, 5853}, {5217, 5698}, {5220, 5552}, {5221, 7080}, {5223, 26446}, {5231, 38093}, {5687, 60895}, {5729, 26364}, {5732, 12678}, {5805, 37569}, {5829, 54316}, {5851, 60935}, {6362, 14283}, {6600, 60919}, {6603, 60417}, {6690, 60981}, {11495, 44447}, {11502, 47387}, {11529, 38052}, {12848, 59572}, {13995, 27529}, {14151, 38455}, {15254, 27385}, {15837, 61002}, {16200, 20330}, {16465, 25973}, {17231, 23529}, {17298, 30620}, {17392, 28125}, {17768, 30295}, {20103, 60972}, {21075, 43177}, {21155, 31658}, {22753, 54158}, {25558, 55016}, {25722, 42356}, {28609, 30353}, {28739, 59600}, {29353, 51419}, {30318, 32049}, {33558, 49732}, {34784, 60988}, {35242, 60905}, {38056, 38201}, {41539, 60992}, {43151, 61003}, {43178, 58798}, {44669, 45043}, {59476, 60969}

X(61035) = reflection of X(i) in X(j) for these {i,j}: {37787, 3035}, {41555, 142}, {51463, 41555}
X(61035) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1170, 2291}, {1174, 34056}, {10509, 18889}, {14733, 58322}, {21453, 34068}, {35348, 53243}, {36141, 56322}
X(61035) = X(i)-Dao conjugate of X(j) for these {i, j}: {142, 1156}, {3119, 23893}, {6594, 2346}, {35091, 56322}, {35110, 21453}, {40606, 34056}, {52870, 10509}, {52880, 40443}
X(61035) = pole of line {16601, 60972} wrt dual conic of Yff parabola
X(61035) = orthology center of the pedal triangle of X(60885) wrt Aguilera-Pavlov triangle
X(61035) = intersection, other than A, B, C, of circumconics {{A, B, C, X(142), X(527)}}, {{A, B, C, X(354), X(1155)}}, {{A, B, C, X(1323), X(14283)}}, {{A, B, C, X(1855), X(41570)}}, {{A, B, C, X(3059), X(30806)}}, {{A, B, C, X(4847), X(6745)}}, {{A, B, C, X(6174), X(51463)}}, {{A, B, C, X(6366), X(6594)}}, {{A, B, C, X(6603), X(15185)}}, {{A, B, C, X(10427), X(41555)}}, {{A, B, C, X(20880), X(44785)}}
X(61035) = barycentric product X(i)*X(j) for these (i, j): {142, 6745}, {1155, 1229}, {1212, 30806}, {1323, 51972}, {3059, 37780}, {4847, 527}, {20880, 6603}
X(61035) = barycentric quotient X(i)/X(j) for these (i, j): {354, 34056}, {527, 21453}, {1155, 1170}, {1212, 1156}, {1323, 10509}, {2293, 2291}, {3059, 41798}, {4847, 1121}, {6362, 60479}, {6366, 56322}, {6510, 40443}, {6603, 2346}, {6608, 23893}, {6745, 32008}, {8012, 4845}, {10581, 23351}, {20229, 34068}, {21127, 35348}, {30806, 31618}, {35312, 60487}, {35326, 14733}, {35338, 37139}, {37780, 42311}, {52334, 56284}, {61028, 46644}
X(61035) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {142, 3059, 6067}, {142, 41570, 354}, {142, 61028, 3925}, {142, 61030, 41555}, {6745, 44785, 6068}, {41555, 61030, 51463}

X(61036) = X(1)X(6)∩X(42)X(7064)

Barycentrics    a^2*(b + c)*(a^2 + a*b + a*c - 2*b*c) : :

X(61036) lies on these lines: {1, 6}, {42, 7064}, {71, 21796}, {101, 33628}, {198, 14974}, {228, 902}, {239, 22016}, {321, 17117}, {527, 28350}, {583, 8610}, {672, 17053}, {893, 33635}, {992, 17355}, {1018, 21857}, {1055, 23222}, {1213, 19870}, {1334, 2092}, {1824, 40987}, {1953, 49758}, {2238, 2321}, {2251, 3204}, {2277, 3730}, {2295, 5257}, {2318, 40984}, {3008, 22019}, {3125, 21853}, {3175, 3875}, {3217, 3915}, {3231, 53129}, {3288, 3709}, {3729, 27623}, {3778, 58287}, {3930, 21750}, {3950, 50590}, {3977, 28289}, {3986, 3997}, {3995, 14997}, {4016, 46902}, {4255, 34820}, {4503, 17257}, {4849, 55372}, {5019, 9310}, {5042, 9351}, {7109, 59207}, {8693, 35108}, {16549, 28244}, {16583, 21871}, {17261, 27644}, {17277, 54282}, {17319, 32911}, {17351, 52897}, {17781, 28368}, {20683, 40934}, {21779, 60711}, {21809, 40977}, {21814, 41423}, {22277, 39688}, {25269, 56185}, {25589, 41877}, {28365, 50127}, {28369, 50093}, {28370, 39956}, {33589, 56556}, {37633, 38000}, {37673, 59772}

X(61036) = isogonal conjugate of the isotomic conjugate of X(3175)
X(61036) = X(i)-Ceva conjugate of X(j) for these (i,j): {56, 42}, {4383, 3214}, {55988, 10}
X(61036) = X(i)-isoconjugate of X(j) for these (i,j): {21, 42304}, {58, 40012}, {81, 34860}, {86, 39956}, {333, 56155}, {514, 8690}, {757, 56123}, {1509, 56192}
X(61036) = X(i)-Dao conjugate of X(j) for these (i,j): {10, 40012}, {2321, 3596}, {20317, 16727}, {40586, 34860}, {40600, 39956}, {40607, 56123}, {40611, 42304}
X(61036) = crossdifference of every pair of points on line {513, 26144}
X(61036) = barycentric product X(i)*X(j) for these {i,j}: {1, 3214}, {6, 3175}, {9, 28387}, {10, 3915}, {31, 56253}, {37, 4383}, {42, 3875}, {56, 59577}, {65, 3913}, {72, 4186}, {100, 4139}, {213, 18135}, {226, 3217}, {321, 16946}, {765, 21963}, {1018, 4498}, {1400, 30568}, {2176, 27432}, {4106, 4557}, {4551, 42312}, {4559, 20317}, {4566, 58334}
X(61036) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 40012}, {42, 34860}, {213, 39956}, {692, 8690}, {872, 56192}, {1400, 42304}, {1402, 56155}, {1500, 56123}, {3175, 76}, {3214, 75}, {3217, 333}, {3875, 310}, {3913, 314}, {3915, 86}, {4106, 52619}, {4139, 693}, {4186, 286}, {4383, 274}, {4498, 7199}, {16946, 81}, {17477, 17205}, {18135, 6385}, {21963, 1111}, {27432, 6383}, {28387, 85}, {30568, 28660}, {42312, 18155}, {56253, 561}, {58334, 7253}, {59577, 3596}
X(61036) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 3723, 16971}, {9, 2176, 2300}, {44, 16685, 20228}, {2324, 16970, 5336}, {3204, 5301, 2251}, {3217, 3915, 16946}, {3731, 54981, 6}, {3973, 41418, 6}, {21796, 52963, 71}

X(61037) = X(3)X(3973)∩X(9)X(55)

Barycentrics    a^2*(a - b - c)*(a^2 + 2*a*b + b^2 + 2*a*c - 6*b*c + c^2) : :

X(61037) lies on these lines: {3, 3973}, {6, 1201}, {9, 55}, {11, 27508}, {44, 198}, {56, 1743}, {101, 38855}, {220, 2347}, {259, 60554}, {374, 3553}, {651, 7023}, {672, 1615}, {1030, 16885}, {1423, 4383}, {1436, 2265}, {1466, 59681}, {1616, 53090}, {2098, 2324}, {2110, 36635}, {2178, 3196}, {2183, 3197}, {2270, 37567}, {3021, 7674}, {3161, 3913}, {3303, 3731}, {4413, 5749}, {4423, 5296}, {4534, 17314}, {4557, 21002}, {5687, 59579}, {5839, 59221}, {7368, 34524}, {8162, 16673}, {8715, 15828}, {12513, 38869}, {15492, 36744}, {15519, 56076}, {16572, 51773}, {16814, 37503}, {20818, 38296}, {23089, 23511}, {24328, 37650}, {28351, 37679}, {38293, 58368}

X(61037) = isogonal conjugate of X(8051)
X(61037) = isogonal conjugate of the anticomplement of X(24151)
X(61037) = isogonal conjugate of the isotomic conjugate of X(8055)
X(61037) = X(i)-Ceva conjugate of X(j) for these (i,j): {56, 55}, {1743, 6}, {23511, 1616}
X(61037) = X(i)-isoconjugate of X(j) for these (i,j): {1, 8051}, {2, 2137}, {57, 6553}, {269, 56076}, {3676, 53630}, {8056, 44301}, {19604, 24150}, {23511, 46356}
X(61037) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 8051}, {346, 3596}, {5452, 6553}, {6600, 56076}, {8056, 40014}, {17071, 4391}, {32664, 2137}
X(61037) = crossdifference of every pair of points on line {3667, 3669}
X(61037) = barycentric product X(i)*X(j) for these {i,j}: {1, 2136}, {6, 8055}, {8, 1616}, {9, 23511}, {21, 21896}, {41, 33780}, {55, 4452}, {56, 6552}, {281, 23089}, {1743, 24151}, {3158, 47636}, {4076, 17071}
X(61037) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 8051}, {31, 2137}, {55, 6553}, {220, 56076}, {1616, 7}, {2136, 75}, {3052, 44301}, {4452, 6063}, {6552, 3596}, {8055, 76}, {17071, 1358}, {21896, 1441}, {23089, 348}, {23511, 85}, {24151, 40014}, {33780, 20567}
X(61037) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 1696, 3304}, {480, 7083, 55}

X(61038) = X(3)X(4497)∩X(39)X(42)

Barycentrics    a^4*(b + c)*(a*b - b^2 + a*c + b*c - c^2) : :

X(61038) lies on these lines: {3, 4497}, {10, 24735}, {32, 560}, {39, 42}, {187, 18758}, {386, 15624}, {1125, 20990}, {1193, 40638}, {3778, 22425}, {3941, 4253}, {4097, 50590}, {5299, 16693}, {8053, 25092}, {9447, 40370}, {12329, 19762}, {16687, 17023}, {16691, 16784}, {22271, 25066}, {22297, 43065}

X(61038) = isogonal conjugate of the isotomic conjugate of X(22277)
X(61038) = X(56)-Ceva conjugate of X(213)
X(61038) = X(274)-isoconjugate of X(60075)
X(61038) = X(210)-Dao conjugate of X(3596)
X(61038) = crossdifference of every pair of points on line {3261, 17494}
X(61038) = barycentric product X(i)*X(j) for these {i,j}: {6, 22277}, {31, 3970}, {37, 3941}, {42, 4253}, {56, 40599}, {213, 3873}, {1402, 25082}, {1918, 17234}, {2205, 33933}, {52594, 53321}
X(61038) = barycentric quotient X(i)/X(j) for these {i,j}: {1918, 60075}, {3873, 6385}, {3941, 274}, {3970, 561}, {4253, 310}, {22277, 76}, {25082, 40072}, {40599, 3596}

X(61039) = X(11)X(523)∩X(72)X(521)

Barycentrics    (b - c)*(a^2 - a*b + b^2 - c^2)*(-a^2 + b^2 + a*c - c^2)*(-a^2 + b^2 + c^2)*(a^3*b - a^2*b^2 - a*b^3 + b^4 + a^3*c + a*b^2*c - a^2*c^2 + a*b*c^2 - 2*b^2*c^2 - a*c^3 + c^4) : :

X(61039) lies on these lines: {11, 523}, {72, 521}, {522, 10058}, {759, 53921}, {2006, 7649}, {18359, 20294}, {20315, 52351}

X(61039) = X(i)-isoconjugate of X(j) for these (i,j): {36, 36106}, {913, 4585}, {1870, 6099}, {1983, 37203}, {3218, 32698}, {4242, 36052}
X(61039) = X(i)-Dao conjugate of X(j) for these (i,j): {119, 4242}, {15898, 36106}, {39002, 36}
X(61039) = crossdifference of every pair of points on line {1983, 52413}
X(61039) = barycentric product X(i)*X(j) for these {i,j}: {912, 60074}, {52351, 55126}
X(61039) = barycentric quotient X(i)/X(j) for these {i,j}: {912, 4585}, {2161, 36106}, {6187, 32698}, {8609, 4242}, {42769, 16586}, {52431, 6099}, {55126, 17923}, {60074, 46133}

X(61040) = X(84)X(513)∩X(521)X(4091)

Barycentrics    a*(a - b - c)*(b - c)*(a^2 - b^2 - c^2)*(a^3 - a^2*b - a*b^2 + b^3 + a^2*c + 2*a*b*c + b^2*c - a*c^2 - b*c^2 - c^3)*(a^3 + a^2*b - a*b^2 - b^3 - a^2*c + 2*a*b*c - b^2*c - a*c^2 + b*c^2 + c^3) : :

X(61040) lies on these lines: {84, 513}, {521, 4091}, {522, 905}, {1021, 23189}, {1422, 48281}, {1433, 37628}, {1440, 24002}, {2765, 8059}, {3900, 23224}, {10397, 46391}, {13138, 36037}, {39471, 57101}, {40836, 44426}, {52389, 59973}, {53211, 53642}

X(61040) = X(i)-Ceva conjugate of X(j) for these (i,j): {1440, 26932}, {13138, 1433}, {37141, 282}, {46355, 1364}, {53642, 52037}
X(61040) = X(i)-isoconjugate of X(j) for these (i,j): {4, 57118}, {40, 108}, {59, 54239}, {100, 208}, {101, 196}, {109, 7952}, {162, 227}, {190, 3209}, {198, 653}, {221, 1897}, {223, 1783}, {329, 32674}, {342, 692}, {347, 8750}, {651, 2331}, {664, 3195}, {934, 40971}, {1461, 55116}, {2149, 59935}, {2187, 18026}, {2199, 6335}, {2324, 32714}, {3194, 4551}, {3342, 57117}, {4559, 41083}, {4565, 53009}, {6129, 7012}, {7074, 36118}, {7078, 36127}, {7115, 14837}, {7128, 14298}, {10397, 23984}, {15501, 23706}, {23985, 57245}, {24033, 57101}, {32676, 57810}, {32739, 40701}, {36059, 47372}, {36067, 51375}, {40117, 40212}
X(61040) = X(i)-Dao conjugate of X(j) for these (i,j): {11, 7952}, {125, 227}, {521, 57101}, {650, 59935}, {656, 8058}, {905, 17896}, {1015, 196}, {1086, 342}, {3341, 1897}, {6615, 54239}, {7004, 6260}, {7358, 7080}, {8054, 208}, {14714, 40971}, {15526, 57810}, {20620, 47372}, {26932, 347}, {34467, 221}, {35072, 329}, {35508, 55116}, {36033, 57118}, {38983, 40}, {38991, 2331}, {39006, 223}, {39025, 3195}, {40618, 40702}, {40619, 40701}, {40626, 322}, {40628, 14837}, {55053, 3209}, {55064, 53009}, {55067, 41083}
X(61040) = trilinear pole of line {1364, 34591}
X(61040) = crossdifference of every pair of points on line {198, 208}
X(61040) = barycentric product X(i)*X(j) for these {i,j}: {84, 6332}, {189, 521}, {268, 693}, {271, 514}, {280, 905}, {282, 4025}, {285, 525}, {309, 652}, {332, 55242}, {513, 44189}, {522, 41081}, {647, 57795}, {649, 57783}, {1256, 57245}, {1413, 15416}, {1433, 4391}, {1436, 35518}, {1440, 57055}, {1459, 34404}, {1946, 44190}, {2188, 3261}, {2192, 15413}, {2968, 37141}, {3239, 56972}, {3737, 56944}, {3900, 34400}, {4091, 7020}, {4131, 7003}, {4397, 55117}, {4560, 52389}, {7004, 44327}, {7008, 30805}, {7129, 52616}, {7253, 52037}, {8808, 57081}, {13138, 26932}, {15411, 52384}, {15419, 53013}, {17880, 36049}, {18155, 41087}, {22383, 57793}, {34591, 53642}
X(61040) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 59935}, {48, 57118}, {84, 653}, {189, 18026}, {268, 100}, {271, 190}, {280, 6335}, {282, 1897}, {285, 648}, {309, 46404}, {332, 55241}, {513, 196}, {514, 342}, {521, 329}, {525, 57810}, {647, 227}, {649, 208}, {650, 7952}, {652, 40}, {657, 40971}, {663, 2331}, {667, 3209}, {693, 40701}, {905, 347}, {1413, 32714}, {1422, 36118}, {1433, 651}, {1436, 108}, {1440, 13149}, {1459, 223}, {1946, 198}, {2170, 54239}, {2188, 101}, {2192, 1783}, {2208, 32674}, {2638, 10397}, {3063, 3195}, {3064, 47372}, {3270, 14298}, {3737, 41083}, {3900, 55116}, {4025, 40702}, {4041, 53009}, {4091, 7013}, {6332, 322}, {7004, 14837}, {7117, 6129}, {7118, 8750}, {7129, 36127}, {7252, 3194}, {7367, 56183}, {8059, 7128}, {8611, 21075}, {10397, 1103}, {13138, 46102}, {22383, 221}, {23189, 1817}, {23224, 7011}, {24031, 57245}, {26932, 17896}, {32652, 7115}, {34400, 4569}, {34591, 8058}, {35072, 57101}, {36049, 7012}, {36054, 7078}, {37141, 55346}, {40628, 6260}, {40836, 54240}, {41081, 664}, {41087, 4551}, {44189, 668}, {46391, 51375}, {52037, 4566}, {52384, 52607}, {52389, 4552}, {55117, 934}, {55242, 225}, {56972, 658}, {57055, 7080}, {57081, 27398}, {57108, 2324}, {57783, 1978}, {57795, 6331}, {58340, 55111}

X(61041) = X(65)X(513)∩X(80)X(21186)

Barycentrics    (b - c)*(a^2 - a*b + b^2 - c^2)*(-a^2 + b^2 + a*c - c^2)*(-a^2 + b^2 + c^2)*(-2*a^4 + a^3*b + a^2*b^2 - a*b^3 + b^4 + a^3*c - 2*a^2*b*c + a*b^2*c + a^2*c^2 + a*b*c^2 - 2*b^2*c^2 - a*c^3 + c^4) : :

X(61041) lies on these lines: {65, 513}, {80, 21186}, {125, 656}, {522, 40437}, {1807, 57241}, {2006, 21172}, {2906, 40396}, {44426, 60074}, {51421, 53522}, {52389, 59973}

X(61041) = X(i)-isoconjugate of X(j) for these (i,j): {102, 4242}, {1897, 58741}, {1983, 52780}, {4511, 36067}, {5081, 36040}, {32667, 32851}
X(61041) = X(i)-Dao conjugate of X(j) for these (i,j): {10017, 5081}, {34467, 58741}
X(61041) = barycentric product X(i)*X(j) for these {i,j}: {905, 59283}, {2006, 39471}, {10017, 53811}, {18815, 46391}, {46974, 60074}, {52351, 53522}
X(61041) = barycentric quotient X(i)/X(j) for these {i,j}: {2182, 4242}, {10017, 53045}, {22383, 58741}, {39471, 32851}, {46391, 4511}, {46974, 4585}, {53522, 17923}, {59283, 6335}

X(61042) = X(1)X(521)∩X(59)X(1331)

Barycentrics    a^2*(a - b - c)*(b - c)*(a^2 - b^2 + b*c - c^2)*(a^4 - 2*a^2*b^2 + b^4 - a^3*c + a^2*b*c + a*b^2*c - b^3*c + a^2*c^2 - 2*a*b*c^2 + b^2*c^2 + a*c^3 + b*c^3 - 2*c^4)*(a^4 - a^3*b + a^2*b^2 + a*b^3 - 2*b^4 + a^2*b*c - 2*a*b^2*c + b^3*c - 2*a^2*c^2 + a*b*c^2 + b^2*c^2 - b*c^3 + c^4) : :

X(61042) = lies on these lines: {1, 521}, {59, 1331}, {102, 953}, {513, 47645}, {522, 40437}, {1870, 3738}, {2364, 2432}, {2399, 57091}, {7649, 36121}

X(61042) = X(i)-isoconjugate of X(j) for these (i,j): {109, 59283}, {515, 2222}, {655, 2182}, {1455, 51562}, {1807, 23987}, {2161, 2406}, {2425, 18359}, {7452, 52391}, {24035, 52431}, {52377, 53522}
X(61042) = X(i)-Dao conjugate of X(j) for these (i,j): {11, 59283}, {38984, 515}, {40584, 2406}
X(61042) = cevapoint of X(53046) and X(53285)
X(61042) = barycentric product X(i)*X(j) for these {i,j}: {36, 2399}, {102, 3904}, {320, 2432}, {654, 34393}, {3738, 36100}, {4391, 58741}, {4453, 15629}, {22128, 53152}
X(61042) = barycentric quotient X(i)/X(j) for these {i,j}: {36, 2406}, {102, 655}, {650, 59283}, {654, 515}, {1870, 24035}, {2399, 20566}, {2432, 80}, {3904, 35516}, {4511, 42718}, {8648, 2182}, {15629, 51562}, {21758, 1455}, {21828, 51421}, {32677, 2222}, {34393, 46405}, {36100, 35174}, {52413, 23987}, {52434, 2425}, {53314, 34050}, {55255, 52383}, {57174, 11700}, {58313, 8755}, {58741, 651}

X(61043) = X(3)X(513)∩X(109)X(6099)

Barycentrics    a^2*(a - b - c)*(b - c)*(a^2 - b^2 + b*c - c^2)*(a^4 - 2*a^2*b^2 + b^4 - a^3*c + a^2*b*c + a*b^2*c - b^3*c - a^2*c^2 - b^2*c^2 + a*c^3 + b*c^3)*(a^4 - a^3*b - a^2*b^2 + a*b^3 + a^2*b*c + b^3*c - 2*a^2*c^2 + a*b*c^2 - b^2*c^2 - b*c^3 + c^4) : :

X(61043) lies on these lines: {3, 513}, {109, 6099}, {522, 10058}, {915, 2716}, {18191, 23189}, {30212, 45390}, {52407, 53314}

X(61043) = X(i)-isoconjugate of X(j) for these (i,j): {655, 8609}, {1411, 56881}, {1737, 2222}, {3658, 52383}, {18838, 51562}, {32675, 48380}, {52377, 55126}
X(61043) = X(i)-Dao conjugate of X(j) for these (i,j): {35128, 48380}, {35204, 56881}, {38984, 1737}
X(61043) = cevapoint of X(8648) and X(53046)
X(61043) = barycentric product X(i)*X(j) for these {i,j}: {2990, 3738}, {3904, 36052}, {3960, 45393}, {15381, 53045}, {53046, 57753}
X(61043) = barycentric quotient X(i)/X(j) for these {i,j}: {654, 1737}, {2323, 56881}, {2990, 35174}, {3657, 60091}, {3738, 48380}, {4282, 3658}, {8648, 8609}, {15381, 53811}, {21758, 18838}, {32655, 2222}, {36052, 655}, {45393, 36804}, {53046, 119}, {57174, 11570}

X(61044) = X(2)X(1350)∩X(20)X(185)

Barycentrics    3*a^6 + 9*a^4*b^2 - 11*a^2*b^4 - b^6 + 9*a^4*c^2 - 2*a^2*b^2*c^2 + b^4*c^2 - 11*a^2*c^4 + b^2*c^4 - c^6 : :
X(61044) = 3 X[2] - 4 X[1350], 9 X[2] - 8 X[5480], 13 X[2] - 12 X[38072], 5 X[2] - 4 X[54131], 7 X[2] - 8 X[54169], 3 X[1350] - 2 X[5480], 13 X[1350] - 9 X[38072], 5 X[1350] - 3 X[54131], 7 X[1350] - 6 X[54169], 2 X[1350] - 3 X[54170], 26 X[5480] - 27 X[38072], 4 X[5480] - 3 X[51212], 10 X[5480] - 9 X[54131], 7 X[5480] - 9 X[54169], 4 X[5480] - 9 X[54170], and many others

Source: HG251023

X(61044) lies on these lines: {2, 1350}, {3, 51171}, {4, 3620}, {5, 55593}, {6, 3522}, {20, 185}, {30, 5921}, {69, 3146}, {125, 7396}, {140, 55604}, {141, 3832}, {159, 12087}, {182, 10304}, {316, 10008}, {323, 19149}, {376, 1351}, {390, 1469}, {516, 49451}, {518, 9961}, {524, 14927}, {542, 55581}, {548, 5093}, {549, 50966}, {550, 14912}, {575, 33750}, {576, 33748}, {597, 15705}, {599, 50687}, {631, 21850}, {1352, 3543}, {1353, 3534}, {1503, 5059}, {1657, 34380}, {1992, 44882}, {1993, 59343}, {2071, 37488}, {2781, 14683}, {2979, 6995}, {3056, 3600}, {3060, 52520}, {3088, 37486}, {3090, 55595}, {3091, 7938}, {3094, 37665}, {3098, 3523}, {3399, 5395}, {3424, 43688}, {3524, 18583}, {3525, 55602}, {3528, 5050}, {3529, 3564}, {3530, 55624}, {3589, 55614}, {3618, 15717}, {3619, 5068}, {3629, 59411}, {3751, 9778}, {3763, 15022}, {3818, 50688}, {3839, 25561}, {3917, 7398}, {4232, 15107}, {4549, 6403}, {5017, 5304}, {5052, 22676}, {5056, 42786}, {5067, 38136}, {5085, 21734}, {5104, 37689}, {5188, 32990}, {5476, 15708}, {5969, 5984}, {5999, 37667}, {6225, 9924}, {6329, 55673}, {7406, 48878}, {7409, 37636}, {7411, 37492}, {7470, 50685}, {7486, 19130}, {7487, 10625}, {7500, 41716}, {8703, 53091}, {9019, 53021}, {9530, 40867}, {9541, 35840}, {9589, 49505}, {9812, 49511}, {10124, 51173}, {10168, 55633}, {10299, 38110}, {10303, 14561}, {10477, 50696}, {10516, 50689}, {10996, 15741}, {11179, 15697}, {11180, 15640}, {11413, 18919}, {11477, 12007}, {11645, 51215}, {11821, 13598}, {12017, 21735}, {12244, 14984}, {13346, 19121}, {13736, 48883}, {14118, 37485}, {14810, 15692}, {14848, 15698}, {15066, 52301}, {15069, 50692}, {15431, 31133}, {15448, 37669}, {15516, 50969}, {15577, 37913}, {15589, 18906}, {15681, 50974}, {15682, 39884}, {15684, 50978}, {15686, 50962}, {15687, 51213}, {15691, 51177}, {15704, 39899}, {15712, 55632}, {15721, 51141}, {15988, 17576}, {16051, 47582}, {16163, 25321}, {16192, 59408}, {16386, 47277}, {17508, 58188}, {17538, 48906}, {17578, 48910}, {17834, 18931}, {18440, 33703}, {18788, 27549}, {18860, 35287}, {19154, 37477}, {19459, 33524}, {19877, 38146}, {20007, 43216}, {21167, 55607}, {21356, 51024}, {21358, 50970}, {22234, 58193}, {26543, 37161}, {29012, 49140}, {29317, 49135}, {30270, 32973}, {30769, 51360}, {31305, 37484}, {32006, 51374}, {32111, 34621}, {32113, 52403}, {32522, 35439}, {32841, 59548}, {33014, 47619}, {33923, 55705}, {34200, 55692}, {34507, 43621}, {34628, 51001}, {34638, 50952}, {34815, 37188}, {35927, 39141}, {37200, 43981}, {37460, 37483}, {37655, 50636}, {37668, 40236}, {37941, 47457}, {37952, 47571}, {38035, 46934}, {38064, 55655}, {38317, 55601}, {40107, 55589}, {41374, 56021}, {41465, 49670}, {46853, 55697}, {46935, 55598}, {46936, 55597}, {47114, 47461}, {47352, 51139}, {48892, 55721}, {50965, 53094}, {50977, 51211}, {50982, 51029}, {55603, 55864}, {55666, 58184}, {55670, 58186}, {55718, 58195}

X(61044) = midpoint of X(5059) and X(20080)
X(61044) = reflection of X(i) in X(j) for these {i,j}: {2, 54170}, {4, 33878}, {69, 53097}, {193, 20}, {1351, 48874}, {1352, 55587}, {3146, 69}, {3543, 50967}, {3818, 55588}, {6225, 9924}, {6776, 48873}, {9589, 49505}, {11160, 54174}, {11477, 48881}, {14927, 48872}, {15640, 11180}, {15684, 50978}, {31670, 52987}, {33703, 18440}, {34507, 55586}, {39874, 1657}, {39899, 15704}, {43621, 34507}, {44456, 550}, {48901, 55590}, {49670, 41465}, {50952, 34638}, {50962, 15686}, {50974, 15681}, {51001, 34628}, {51028, 376}, {51212, 1350}, {51538, 55591}, {55720, 48885}, {55721, 48892}, {55722, 44882}, {55724, 48906}
X(61044) = anticomplement of X(51212)
X(61044) = X(42373)-anticomplementary conjugate of X(21270)
X(61044) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {141, 51538, 3832}, {376, 51028, 5032}, {550, 44456, 14912}, {599, 51163, 51537}, {1350, 51212, 2}, {1351, 48874, 376}, {1352, 55587, 50967}, {3098, 14853, 3523}, {3618, 31884, 15717}, {3619, 53023, 5068}, {6776, 48873, 20}, {10519, 31670, 3091}, {11477, 25406, 51170}, {11477, 48881, 25406}, {14927, 48872, 15683}, {18583, 55629, 3524}, {21850, 55610, 631}, {25406, 48881, 50693}, {31670, 52987, 10519}, {38110, 55639, 10299}, {40330, 48901, 3839}, {44882, 55722, 1992}, {46264, 48873, 48920}, {48885, 55720, 11179}, {48901, 54173, 40330}, {48901, 55590, 54173}, {50693, 51170, 25406}, {51163, 51537, 50687}, {51212, 54170, 1350}

X(61045) = X(2)X(2854)∩X(140)X(143)

Barycentrics    a^2*(a^4*b^2 - b^6 + a^4*c^2 - 16*a^2*b^2*c^2 - 10*b^4*c^2 - 10*b^2*c^4 - c^6) : :
X(61045) = X[6] + 3 X[33879], 11 X[3589] - 2 X[58471], X[373] - 3 X[48310], 3 X[5085] + X[16261], X[7998] + 3 X[47352], X[12220] + 5 X[16776], X[12220] + 35 X[47355], X[16776] - 7 X[47355], X[41579] - 10 X[51126], 7 X[44299] + 5 X[51185], X[54334] + 2 X[58532]

Source: HG251023

X(61045) lies on these lines: {2, 2854}, {6, 33879}, {110, 38402}, {140, 143}, {182, 5609}, {206, 55693}, {373, 9019}, {524, 15082}, {597, 5650}, {2393, 12045}, {4045, 33962}, {5085, 16261}, {5663, 10168}, {6593, 52171}, {7998, 47352}, {8546, 16187}, {8705, 40670}, {9027, 20582}, {11413, 55673}, {12220, 16776}, {14915, 50983}, {19137, 55685}, {20113, 30739}, {20396, 24206}, {22112, 32154}, {25711, 40280}, {31521, 55682}, {38317, 44262}, {41579, 51126}, {44299, 51185}, {54334, 58532}

X(61045) = midpoint of X(597) and X(5650)

X(61046) = X(2)X(3108)∩X(6)X(543)

Barycentrics    10*a^4 + 14*a^2*b^2 + b^4 + 14*a^2*c^2 - 4*b^2*c^2 + c^4 : :
X(61046) = 9 X[6] - X[11159], X[7798] + 3 X[59373]

Source: HG251023

X(61046)lies on these lines: {2, 3108}, {6, 543}, {30, 22330}, {381, 41154}, {754, 8584}, {1992, 4045}, {3849, 20583}, {5007, 8598}, {5041, 59635}, {5304, 7622}, {5355, 5461}, {6722, 11163}, {7610, 22246}, {7615, 14930}, {7617, 37665}, {7619, 7735}, {7753, 36523}, {7757, 36521}, {7765, 8597}, {7798, 59373}, {7810, 7894}, {7827, 7838}, {8182, 14482}, {8352, 39593}, {8370, 41940}, {9605, 34506}, {11317, 41147}, {12150, 15300}, {12156, 40246}, {13357, 27088}, {34504, 43136}, {35955, 43183}

X(61046) = midpoint of X(1992) and X(4045)
X(61046) = crossdifference of every pair of points on line {8664, 9023}

X(61047) = X(31)X(51)∩X(56)X(106)

Barycentrics    a^2*(2*a - b - c)^2*(a + b - c)*(a - b + c) : :

X(61047) lies on these lines: {12, 60078}, {31, 51}, {35, 1682}, {55, 20958}, {56, 106}, {678, 22371}, {692, 1397}, {902, 1404}, {1362, 2078}, {1460, 16686}, {2175, 34446}, {2342, 3022}, {3884, 5083}, {4542, 42070}, {10473, 30652}

X(61047) = isogonal conjugate of the isotomic conjugate of X(1317)
X(61047) = X(56)-Ceva conjugate of X(1404)
X(61047) = X(i)-isoconjugate of X(j) for these (i,j): {8, 679}, {9, 54974}, {55, 57929}, {75, 1318}, {88, 4997}, {312, 2226}, {333, 30575}, {522, 4618}, {903, 1320}, {1022, 4582}, {2170, 57564}, {2316, 20568}, {2320, 36594}, {3257, 60480}, {4391, 4638}, {4555, 23838}, {4723, 59150}, {4768, 39414}, {5376, 60578}, {28659, 41935}, {36590, 52553}
X(61047) = X(i)-Dao conjugate of X(j) for these (i,j): {206, 1318}, {223, 57929}, {478, 54974}, {519, 3596}, {900, 34387}, {1647, 35519}, {52659, 57995}, {55055, 60480}
X(61047) = crossdifference of every pair of points on line {1639, 3904}
X(61047) = barycentric product X(i)*X(j) for these {i,j}: {6, 1317}, {7, 1017}, {44, 1319}, {56, 4370}, {57, 678}, {59, 35092}, {101, 39771}, {109, 6544}, {222, 42070}, {278, 22371}, {519, 1404}, {604, 4738}, {651, 3251}, {902, 3911}, {1014, 21821}, {1023, 53528}, {1252, 14027}, {1262, 4542}, {1397, 36791}, {1402, 16729}, {1407, 4152}, {1461, 4543}, {1635, 23703}, {1877, 22356}, {3285, 40663}, {4564, 42084}, {14584, 17455}, {20972, 56642}, {23202, 37790}, {23344, 30725}, {43924, 53582}, {45144, 53529}
X(61047) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 1318}, {56, 54974}, {57, 57929}, {59, 57564}, {604, 679}, {678, 312}, {902, 4997}, {1017, 8}, {1317, 76}, {1319, 20568}, {1397, 2226}, {1402, 30575}, {1404, 903}, {1405, 36594}, {1415, 4618}, {1960, 60480}, {2251, 1320}, {3251, 4391}, {3911, 57995}, {4152, 59761}, {4370, 3596}, {4542, 23978}, {4543, 52622}, {4738, 28659}, {6544, 35519}, {9459, 2316}, {14027, 23989}, {14637, 52338}, {16729, 40072}, {21821, 3701}, {22371, 345}, {23344, 4582}, {35092, 34387}, {36791, 40363}, {39771, 3261}, {41280, 41935}, {42070, 7017}, {42084, 4858}

X(61048) = X(7)X(3253)∩X(56)X(651)

Barycentrics    a^4*(b - c)^2*(a + b - c)*(a - b + c) : :

X(61048) lies no these lines: {7, 3253}, {56, 651}, {181, 23644}, {604, 1911}, {1259, 15375}, {1357, 8650}, {1460, 23858}, {3248, 8660}, {4565, 12835}, {39956, 56012}, {41280, 52410}

X(61048) = isogonal conjugate of the isotomic conjugate of X(1357)
X(61048) = X(i)-Ceva conjugate of X(j) for these (i,j): {56, 57181}, {15375, 22383}
X(61048) = X(i)-isoconjugate of X(j) for these (i,j): {8, 7035}, {9, 31625}, {75, 4076}, {190, 646}, {312, 1016}, {341, 4998}, {522, 57950}, {561, 6065}, {643, 27808}, {644, 1978}, {645, 4033}, {668, 3699}, {670, 4069}, {765, 3596}, {799, 30730}, {874, 36801}, {1089, 6064}, {1110, 40363}, {1252, 28659}, {1275, 30693}, {1928, 6066}, {2321, 4601}, {3701, 4600}, {3718, 15742}, {3939, 6386}, {3952, 7257}, {4087, 5378}, {4103, 4631}, {4110, 5383}, {4391, 6632}, {4552, 7258}, {4554, 6558}, {4564, 59761}, {4567, 30713}, {4572, 4578}, {4582, 24004}, {4768, 6635}, {5382, 44723}, {6057, 24037}, {31615, 52622}, {35519, 57731}, {46102, 52406}
X(61048) = X(i)-Dao conjugate of X(j) for these (i,j): {206, 4076}, {478, 31625}, {512, 6057}, {513, 3596}, {514, 40363}, {661, 28659}, {798, 4110}, {38996, 30730}, {40368, 6065}, {40369, 6066}, {40617, 6386}, {40627, 30713}, {50497, 3701}, {55053, 646}, {55060, 27808}
X(61048) = crossdifference of every pair of points on line {646, 4526}
X(61048) = barycentric product X(i)*X(j) for these {i,j}: {6, 1357}, {7, 1977}, {11, 52410}, {31, 53538}, {32, 1358}, {56, 1015}, {57, 3248}, {109, 21143}, {115, 7342}, {222, 42067}, {244, 604}, {278, 22096}, {513, 57181}, {552, 1084}, {608, 3937}, {649, 43924}, {651, 8027}, {664, 3249}, {667, 3669}, {669, 17096}, {764, 1415}, {798, 7203}, {1014, 3121}, {1019, 51641}, {1086, 1397}, {1106, 2170}, {1333, 53540}, {1356, 1509}, {1395, 3942}, {1398, 7117}, {1402, 16726}, {1404, 43922}, {1407, 3271}, {1408, 3125}, {1412, 3122}, {1417, 2087}, {1919, 3676}, {1980, 24002}, {2206, 53545}, {2310, 7366}, {2969, 52411}, {3063, 43932}, {3120, 16947}, {3124, 7341}, {3733, 7180}, {4017, 57129}, {4565, 8034}, {7023, 14936}, {7153, 38986}, {7250, 7252}, {7336, 23979}, {14027, 41935}, {14827, 41292}, {22383, 43923}, {23989, 41280}, {43921, 52635}, {43929, 53539}
X(61048) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 4076}, {56, 31625}, {244, 28659}, {552, 44168}, {604, 7035}, {667, 646}, {669, 30730}, {1015, 3596}, {1084, 6057}, {1086, 40363}, {1356, 594}, {1357, 76}, {1358, 1502}, {1397, 1016}, {1408, 4601}, {1415, 57950}, {1501, 6065}, {1919, 3699}, {1924, 4069}, {1977, 8}, {1980, 644}, {3121, 3701}, {3122, 30713}, {3248, 312}, {3249, 522}, {3271, 59761}, {3669, 6386}, {3937, 57919}, {7180, 27808}, {7203, 4602}, {7341, 34537}, {7342, 4590}, {8027, 4391}, {9233, 6066}, {9427, 7064}, {16726, 40072}, {16947, 4600}, {17096, 4609}, {21143, 35519}, {21762, 27538}, {22096, 345}, {23560, 4903}, {23989, 44159}, {38986, 4110}, {41280, 1252}, {41281, 23990}, {42067, 7017}, {42336, 21580}, {43924, 1978}, {51641, 4033}, {52410, 4998}, {53538, 561}, {53540, 27801}, {57129, 7257}, {57181, 668}

X(61049) = X(8)X(21320)∩X(56)X(651)

Barycentrics    a^2*(a + b - c)*(a - b + c)*(a*b + a*c - 2*b*c)^2 : :

X(61049) lies on these lines: {8, 21320}, {56, 651}, {899, 52896}, {978, 21362}, {1201, 3271}, {1284, 1317}, {1357, 1400}, {1423, 4551}, {6049, 28386}, {7083, 20999}

X(61049) = X(i)-isoconjugate of X(j) for these (i,j): {9, 57542}, {36798, 37129}
X(61049) = X(i)-Dao conjugate of X(j) for these (i,j): {478, 57542}, {536, 3596}, {891, 11}, {1646, 4391}
X(61049) = crossdifference of every pair of points on line {4526, 36798}
X(61049) = barycentric product X(i)*X(j) for these {i,j}: {7, 59797}, {56, 13466}, {57, 42083}, {651, 14434}, {899, 52896}, {1016, 47016}, {3230, 43037}, {4998, 39011}
X(61049) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 57542}, {3230, 36798}, {4998, 57572}, {13466, 3596}, {14434, 4391}, {39011, 11}, {42083, 312}, {47016, 1086}, {52896, 31002}, {59797, 8}

X(61050) = X(11)X(28834)∩X(55)X(6169)

Barycentrics    a^4*(a - b - c)^3*(b - c)^2 : :

X(61050) lies on these lines: {11, 28834}, {55, 6169}, {56, 4617}, {2175, 32739}, {3271, 8645}, {3937, 8642}, {7083, 20999}, {8641, 14936}

X(61050) = isogonal conjugate of the isotomic conjugate of X(3022)
X(61050) = X(i)-Ceva conjugate of X(j) for these (i,j): {56, 3063}, {480, 57180}
X(61050) = X(i)-isoconjugate of X(j) for these (i,j): {8, 24011}, {9, 57581}, {75, 59457}, {85, 1275}, {100, 52937}, {190, 36838}, {312, 23586}, {479, 7035}, {561, 7339}, {651, 46406}, {658, 4554}, {664, 4569}, {668, 4626}, {738, 31625}, {765, 57880}, {934, 4572}, {1016, 23062}, {1088, 4998}, {1262, 20567}, {1446, 4620}, {1978, 4617}, {3596, 24013}, {4552, 4635}, {4564, 57792}, {4566, 4625}, {6046, 24037}, {6063, 7045}, {6386, 6614}, {7055, 24032}, {7128, 57918}, {7147, 34537}, {7182, 55346}, {7183, 57538}, {20618, 46254}, {23971, 28659}, {24027, 41283}, {40495, 59151}, {41353, 46135}, {52607, 55205}, {53321, 55213}
X(61050) = X(i)-Dao conjugate of X(j) for these (i,j): {206, 59457}, {478, 57581}, {512, 6046}, {513, 57880}, {522, 41283}, {3900, 3596}, {6608, 561}, {8054, 52937}, {14714, 4572}, {17115, 6063}, {38991, 46406}, {39025, 4569}, {40368, 7339}, {55053, 36838}, {55068, 55213}
X(61050) = crossdifference of every pair of points on line {4554, 36838}
X(61050) = barycentric product X(i)*X(j) for these {i,j}: {6, 3022}, {11, 14827}, {31, 3119}, {32, 4081}, {41, 2310}, {55, 14936}, {56, 35508}, {57, 24012}, {220, 3271}, {244, 6602}, {269, 52064}, {480, 1015}, {513, 57180}, {604, 24010}, {607, 3270}, {649, 4105}, {650, 8641}, {657, 663}, {667, 4130}, {728, 3248}, {798, 58329}, {884, 52614}, {1146, 2175}, {1253, 2170}, {1397, 23970}, {1857, 39687}, {1919, 4163}, {1977, 5423}, {2194, 36197}, {2212, 34591}, {2489, 58338}, {3063, 3900}, {3121, 56182}, {3124, 6061}, {3709, 21789}, {4524, 7252}, {5532, 23990}, {6059, 35072}, {7058, 7063}, {7071, 7117}, {7154, 47432}, {8638, 28132}, {9447, 24026}, {9448, 23978}, {14935, 30706}, {21833, 23609}, {23615, 32739}, {42069, 52425}, {52335, 57657}, {55206, 57134}
X(61050) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 59457}, {56, 57581}, {480, 31625}, {604, 24011}, {649, 52937}, {657, 4572}, {663, 46406}, {667, 36838}, {1015, 57880}, {1021, 55213}, {1084, 6046}, {1146, 41283}, {1397, 23586}, {1501, 7339}, {1919, 4626}, {1977, 479}, {1980, 4617}, {2175, 1275}, {2310, 20567}, {3022, 76}, {3063, 4569}, {3119, 561}, {3248, 23062}, {3270, 57918}, {3271, 57792}, {4081, 1502}, {4105, 1978}, {4117, 7147}, {4130, 6386}, {6059, 57538}, {6061, 34537}, {6602, 7035}, {7063, 6354}, {8641, 4554}, {9427, 7143}, {9447, 7045}, {9448, 1262}, {14827, 4998}, {14936, 6063}, {22096, 30682}, {23970, 40363}, {23978, 41287}, {24010, 28659}, {24012, 312}, {35508, 3596}, {39687, 7055}, {41280, 23971}, {52064, 341}, {57134, 55205}, {57180, 668}, {58329, 4602}, {58338, 52608}

X(61051) = X(11)X(40624)∩X(56)X(52928)

Barycentrics    a^2*(a - b - c)*(b - c)^2*(a*b + b^2 + a*c + c^2)^2 : :

X(61051) lies on these lines: {11, 40624}, {56, 52928}, {244, 55060}, {3120, 3259}, {3271, 8054}, {14412, 39015}, {17420, 38992}, {38364, 52326}

X(61051) = isotomic conjugate of the isogonal conjugate of X(41224)
X(61051) = X(55991)-complementary conjugate of X(6371)
X(61051) = X(i)-Ceva conjugate of X(j) for these (i,j): {56, 6371}, {3596, 3910}
X(61051) = X(i)-isoconjugate of X(j) for these (i,j): {6648, 36147}, {8707, 36098}
X(61051) = X(i)-Dao conjugate of X(j) for these (i,j): {3910, 3596}, {6371, 56}, {38992, 8707}, {39015, 6648}
X(61051) = crossdifference of every pair of points on line {8687, 8707}
X(61051) = barycentric product X(i)*X(j) for these {i,j}: {7, 35506}, {76, 41224}, {1086, 1682}, {3004, 52326}, {3596, 39015}, {3910, 6371}, {17420, 48131}
X(61051) = barycentric quotient X(i)/X(j) for these {i,j}: {1682, 1016}, {6371, 6648}, {35506, 8}, {39015, 56}, {41224, 6}, {52326, 8707}, {57157, 8687}

X(61052) = X(7)X(18827)∩X(56)X(4565)

Barycentrics    a^2*(b - c)^2*(a + b - c)*(a - b + c)*(b + c)^2 : :

X(61052) lies on these lines: {7, 18827}, {8, 35176}, {56, 4565}, {65, 57680}, {244, 55060}, {608, 41280}, {1284, 4318}, {1356, 3122}, {1365, 2611}, {1400, 2054}, {2643, 20975}, {3027, 4552}, {3123, 4017}, {3124, 21823}, {3248, 51641}, {3649, 24816}, {3675, 4934}, {17058, 50330}, {23772, 34387}

X(61052) = isogonal conjugate of X(6064)
X(61052) = isotomic conjugate of the isogonal conjugate of X(1356)
X(61052) = isogonal conjugate of the isotomic conjugate of X(1365)
X(61052) = X(i)-Ceva conjugate of X(j) for these (i,j): {12, 57185}, {56, 7180}, {6063, 7178}, {51641, 8034}
X(61052) = X(i)-isoconjugate of X(j) for these (i,j): {1, 6064}, {8, 24041}, {9, 4590}, {21, 4600}, {33, 47389}, {41, 34537}, {55, 24037}, {60, 7035}, {78, 18020}, {99, 643}, {101, 4631}, {110, 7257}, {112, 55207}, {190, 4612}, {200, 7340}, {219, 46254}, {249, 312}, {250, 3718}, {261, 765}, {284, 4601}, {314, 4570}, {332, 5379}, {333, 4567}, {644, 4610}, {645, 662}, {646, 4556}, {668, 4636}, {757, 4076}, {799, 5546}, {873, 6065}, {906, 55233}, {1016, 2185}, {1018, 55196}, {1021, 55194}, {1098, 4998}, {1101, 3596}, {1110, 18021}, {1252, 52379}, {1259, 23999}, {1264, 24000}, {1414, 7256}, {2150, 31625}, {2287, 4620}, {3699, 52935}, {3719, 23582}, {3939, 4623}, {4041, 31614}, {4086, 59152}, {4561, 52914}, {4564, 7058}, {4565, 7258}, {4573, 7259}, {4587, 55231}, {4592, 36797}, {5376, 30606}, {6066, 57992}, {8611, 55270}, {9447, 44168}, {23357, 28659}, {23995, 40363}, {44694, 57991}
X(61052) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 6064}, {223, 24037}, {244, 7257}, {478, 4590}, {512, 55}, {513, 261}, {514, 18021}, {523, 3596}, {647, 57919}, {661, 52379}, {1015, 4631}, {1084, 645}, {3005, 8}, {3160, 34537}, {4988, 28660}, {5139, 36797}, {5190, 55233}, {6609, 7340}, {15267, 4998}, {18314, 40363}, {21905, 3712}, {34591, 55207}, {38986, 643}, {38996, 5546}, {40590, 4601}, {40607, 4076}, {40608, 7256}, {40611, 4600}, {40615, 52612}, {40617, 4623}, {40622, 670}, {40627, 333}, {50330, 314}, {50497, 21}, {55053, 4612}, {55060, 99}, {55064, 7258}, {56325, 31625}
X(61052) = cevapoint of X(16592) and X(16613)
X(61052) = crossdifference of every pair of points on line {645, 4612}
X(61052) = barycentric product X(i)*X(j) for these {i,j}: {6, 1365}, {7, 3124}, {12, 1015}, {34, 3708}, {37, 53540}, {42, 53545}, {56, 115}, {57, 2643}, {65, 3125}, {76, 1356}, {109, 21131}, {125, 608}, {181, 1086}, {222, 8754}, {226, 3122}, {244, 2171}, {278, 20975}, {338, 1397}, {348, 2971}, {512, 7178}, {513, 57185}, {523, 7180}, {594, 1357}, {604, 1109}, {656, 55208}, {661, 4017}, {756, 53538}, {764, 21859}, {798, 4077}, {1014, 21833}, {1042, 21044}, {1084, 6063}, {1118, 3269}, {1146, 7143}, {1254, 2170}, {1358, 1500}, {1367, 2207}, {1395, 20902}, {1400, 3120}, {1401, 34294}, {1402, 16732}, {1407, 4092}, {1412, 21043}, {1425, 8735}, {1426, 53560}, {1427, 4516}, {1432, 21725}, {1441, 3121}, {1577, 51641}, {1648, 7316}, {1880, 18210}, {1977, 34388}, {2197, 2969}, {2310, 7147}, {2489, 17094}, {2970, 52411}, {3248, 6358}, {3271, 6354}, {3665, 51906}, {3669, 4705}, {3676, 4079}, {3700, 7250}, {3733, 55197}, {3937, 8736}, {4024, 43924}, {4036, 57181}, {4041, 7216}, {4117, 20567}, {4128, 60245}, {4466, 57652}, {4552, 8034}, {4565, 8029}, {4573, 22260}, {6046, 14936}, {7063, 57792}, {7249, 21823}, {7337, 15526}, {7649, 55234}, {9427, 41283}, {17085, 19610}, {17096, 58289}, {20982, 52382}, {21134, 32674}, {21824, 52372}, {23962, 41280}, {24002, 50487}, {26942, 42067}, {30572, 55263}, {42068, 57918}, {43034, 51441}, {43923, 55232}, {52621, 53581}, {53321, 55195}, {53551, 55261}
X(61052) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 6064}, {7, 34537}, {12, 31625}, {34, 46254}, {56, 4590}, {57, 24037}, {65, 4601}, {115, 3596}, {125, 57919}, {181, 1016}, {222, 47389}, {244, 52379}, {338, 40363}, {512, 645}, {513, 4631}, {604, 24041}, {608, 18020}, {656, 55207}, {661, 7257}, {667, 4612}, {669, 5546}, {798, 643}, {876, 36806}, {1015, 261}, {1042, 4620}, {1084, 55}, {1086, 18021}, {1109, 28659}, {1356, 6}, {1357, 1509}, {1365, 76}, {1397, 249}, {1400, 4600}, {1402, 4567}, {1407, 7340}, {1500, 4076}, {1919, 4636}, {1977, 60}, {2171, 7035}, {2489, 36797}, {2643, 312}, {2971, 281}, {3120, 28660}, {3121, 21}, {3122, 333}, {3124, 8}, {3125, 314}, {3248, 2185}, {3269, 1264}, {3271, 7058}, {3669, 4623}, {3676, 52612}, {3708, 3718}, {3709, 7256}, {3733, 55196}, {4017, 799}, {4041, 7258}, {4077, 4602}, {4079, 3699}, {4092, 59761}, {4117, 41}, {4128, 27958}, {4565, 31614}, {4705, 646}, {6063, 44168}, {7063, 220}, {7109, 6065}, {7143, 1275}, {7178, 670}, {7180, 99}, {7216, 4625}, {7250, 4573}, {7316, 52940}, {7337, 23582}, {7649, 55233}, {8034, 4560}, {8663, 30729}, {8754, 7017}, {9427, 2175}, {15630, 15628}, {16732, 40072}, {17094, 52608}, {20975, 345}, {21043, 30713}, {21131, 35519}, {21725, 17787}, {21823, 7081}, {21833, 3701}, {21835, 56181}, {21859, 57950}, {21906, 3712}, {22260, 3700}, {23099, 3709}, {23216, 52425}, {23962, 44159}, {30572, 55262}, {41280, 23357}, {41281, 23963}, {42067, 46103}, {42068, 607}, {43923, 55231}, {43924, 4610}, {50487, 644}, {51641, 662}, {51664, 55202}, {53321, 55194}, {53538, 873}, {53540, 274}, {53545, 310}, {53551, 55260}, {53581, 3939}, {55197, 27808}, {55208, 811}, {55234, 4561}, {57181, 52935}, {57185, 668}, {58260, 59734}, {58289, 30730}, {59801, 7067}

X(61053) = X(110)X(2175)∩X(171)X(36213)

Barycentrics    a^2*(a - b - c)*(b - c)^2*(a^2 + b*c)^2 : :

X(61053) lies on these lines: {110, 2175}, {171, 36213}, {181, 51335}, {694, 2162}, {1365, 43920}, {1397, 1976}, {1460, 52162}, {1977, 3124}, {4128, 5027}, {7063, 7252}, {7083, 20998}, {16592, 56242}

X(61053) = isogonal conjugate of the isotomic conjugate of X(3023)
X(61053) = X(i)-Ceva conjugate of X(j) for these (i,j): {56, 20981}, {40770, 3063}
X(61053) = X(i)-isoconjugate of X(j) for these (i,j): {75, 55018}, {4564, 40099}, {27805, 37137}, {29055, 56241}
X(61053) = X(i)-Dao conjugate of X(j) for these (i,j): {206, 55018}, {3907, 3596}
X(61053) = crossdifference of every pair of points on line {27133, 27805}
X(61053) = barycentric product X(i)*X(j) for these {i,j}: {6, 3023}, {9, 7207}, {172, 4459}, {1086, 10799}, {2329, 53541}, {2330, 7200}, {3271, 6645}, {3287, 4367}, {3907, 20981}, {4128, 27958}
X(61053) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 55018}, {3023, 76}, {3271, 40099}, {3287, 56241}, {4128, 60245}, {4459, 44187}, {7207, 85}, {10799, 1016}, {56242, 37137}

X(61054) = X(56)X(32714)∩X(418)X(52430)

Barycentrics    a^4*(a - b - c)*(b - c)^2*(a^2 - b^2 - c^2)^2 : :

X(61054) lies on these lines: {56, 32714}, {418, 52430}, {692, 14578}, {1436, 6059}, {1946, 3270}, {2175, 52411}, {3271, 7117}, {22084, 23226}, {22096, 22386}, {23189, 26932}, {23198, 32656}

X(61054) = isogonal conjugate of the isotomic conjugate of X(1364)
X(61054) = isogonal conjugate of the polar conjugate of X(7117)
X(61054) = X(i)-Ceva conjugate of X(j) for these (i,j): {56, 22383}, {1259, 36054}, {1436, 3063}, {52430, 39201}
X(61054) = X(i)-isoconjugate of X(j) for these (i,j): {8, 24032}, {9, 57538}, {12, 23999}, {59, 57806}, {92, 46102}, {100, 52938}, {158, 4998}, {190, 54240}, {264, 7012}, {273, 15742}, {312, 23984}, {318, 55346}, {653, 6335}, {668, 36127}, {823, 4552}, {1118, 7035}, {1783, 46404}, {1897, 18026}, {1969, 7115}, {2052, 4564}, {2149, 18027}, {3596, 24033}, {4551, 6528}, {4559, 57973}, {5379, 57809}, {6358, 23582}, {6521, 44717}, {7017, 7128}, {8736, 46254}, {18020, 56285}, {23985, 28659}, {24000, 34388}, {32230, 57807}, {35307, 42405}
X(61054) = X(i)-Dao conjugate of X(j) for these (i,j): {478, 57538}, {521, 3596}, {650, 18027}, {905, 18022}, {1147, 4998}, {6615, 57806}, {8054, 52938}, {22391, 46102}, {34467, 18026}, {39006, 46404}, {40628, 1969}, {55053, 54240}, {55067, 57973}
X(61054) = crossdifference of every pair of points on line {4552, 6335}
X(61054) = barycentric product X(i)*X(j) for these {i,j}: {3, 7117}, {6, 1364}, {7, 39687}, {11, 577}, {48, 7004}, {56, 35072}, {57, 2638}, {60, 3269}, {184, 26932}, {212, 3942}, {219, 3937}, {222, 3270}, {244, 2289}, {255, 2170}, {270, 37754}, {345, 22096}, {394, 3271}, {513, 36054}, {520, 7252}, {521, 22383}, {603, 34591}, {604, 24031}, {607, 7215}, {647, 23189}, {649, 57241}, {650, 23224}, {652, 1459}, {663, 4091}, {822, 3737}, {905, 1946}, {1015, 1259}, {1021, 51640}, {1086, 6056}, {1092, 8735}, {1146, 7335}, {1264, 1977}, {1363, 36421}, {1397, 23983}, {1402, 16731}, {1436, 55044}, {1437, 53560}, {1565, 52425}, {1804, 14936}, {1919, 52616}, {2150, 2632}, {2189, 2972}, {2193, 18210}, {2200, 17219}, {2310, 7125}, {2968, 52411}, {3063, 4131}, {3122, 6514}, {3248, 3719}, {3435, 47410}, {3669, 58340}, {3990, 18191}, {4055, 17197}, {4516, 18604}, {4560, 39201}, {4858, 52430}, {7065, 36419}, {9247, 17880}, {14578, 35014}, {14585, 34387}, {17216, 57657}, {23204, 40527}, {23614, 32714}, {34980, 46103}, {41220, 59196}, {43924, 57057}, {47432, 55117}, {51664, 57134}
X(61054) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 18027}, {56, 57538}, {184, 46102}, {577, 4998}, {604, 24032}, {649, 52938}, {667, 54240}, {1259, 31625}, {1364, 76}, {1397, 23984}, {1459, 46404}, {1919, 36127}, {1946, 6335}, {1977, 1118}, {2150, 23999}, {2170, 57806}, {2289, 7035}, {2638, 312}, {3269, 34388}, {3270, 7017}, {3271, 2052}, {3737, 57973}, {3937, 331}, {3942, 57787}, {4091, 4572}, {6056, 1016}, {7004, 1969}, {7117, 264}, {7215, 57918}, {7252, 6528}, {7335, 1275}, {9247, 7012}, {14575, 7115}, {14585, 59}, {16731, 40072}, {18210, 52575}, {22096, 278}, {22383, 18026}, {23189, 6331}, {23224, 4554}, {23606, 44717}, {23614, 15416}, {23983, 40363}, {24031, 28659}, {26932, 18022}, {34980, 26942}, {35072, 3596}, {36054, 668}, {37754, 57807}, {39201, 4552}, {39687, 8}, {41220, 26611}, {41280, 23985}, {52411, 55346}, {52425, 15742}, {52430, 4564}, {57241, 1978}, {58310, 4559}, {58340, 646}

X(61055) = X(55)X(17074)∩X(56)X(1462)

Barycentrics    a^4*(a + b - c)*(a - b + c)*(a*b - b^2 + a*c - c^2)^2 : :

X(61055) lies on these lines: {7, 21010}, {55, 17074}, {56, 1462}, {181, 2350}, {604, 1911}, {651, 2110}, {1284, 53529}, {1357, 1402}, {1397, 32739}, {1400, 3271}, {1458, 2223}, {1460, 20999}, {2175, 52411}, {2283, 34253}, {8638, 23225}, {20776, 42079}

X(61055) = isogonal conjugate of the isotomic conjugate of X(1362)
X(61055) = X(56)-Ceva conjugate of X(52635)
X(61055) = X(i)-isoconjugate of X(j) for these (i,j): {9, 57537}, {294, 18031}, {312, 6185}, {673, 36796}, {885, 51560}, {1024, 36803}, {2481, 14942}, {3596, 51838}, {4858, 57536}, {6559, 34018}, {28132, 34085}, {28659, 41934}
X(61055) = X(i)-Dao conjugate of X(j) for these (i,j): {478, 57537}, {518, 3596}, {926, 4081}
X(61055) = crossdifference of every pair of points on line {28132, 36796}
X(61055) = barycentric product X(i)*X(j) for these {i,j}: {6, 1362}, {7, 39686}, {56, 6184}, {57, 42079}, {59, 35505}, {222, 42071}, {241, 2223}, {278, 20776}, {518, 52635}, {604, 4712}, {665, 2283}, {672, 1458}, {1275, 15615}, {1397, 4437}, {1402, 16728}, {1415, 3126}, {1462, 23612}, {1876, 20752}, {2284, 53539}, {3252, 51329}, {3323, 23990}, {9436, 9454}, {9455, 40704}, {20662, 56643}, {34253, 40730}, {34337, 52411}, {39014, 59457}, {41353, 46388}, {53544, 54325}
X(61055) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 57537}, {1362, 76}, {1397, 6185}, {1458, 18031}, {2223, 36796}, {2283, 36803}, {4437, 40363}, {4712, 28659}, {6184, 3596}, {8638, 28132}, {9454, 14942}, {9455, 294}, {15615, 1146}, {16728, 40072}, {20776, 345}, {35505, 34387}, {39014, 4081}, {39686, 8}, {41280, 41934}, {42071, 7017}, {42079, 312}, {52635, 2481}

X(61056) = X(56)X(32735)∩X(649)X(1357)

Barycentrics    a^2*(b - c)^2*(a + b - c)*(a - b + c)*(a*b - b^2 + a*c - c^2)^2 : :

X(61056) lies on these lines: {56, 32735}, {649, 1357}, {1458, 2223}, {3025, 41341}, {3123, 4017}, {3271, 43924}, {3669, 43921}, {3937, 8642}, {7336, 53545}, {38989, 53544}

X(61056) = isogonal conjugate of the isotomic conjugate of X(3323)
X(61056) = X(56)-Ceva conjugate of X(53539)
X(61056) = X(i)-isoconjugate of X(j) for these (i,j): {9, 57536}, {4076, 51838}, {5377, 14942}, {28071, 39293}, {36086, 36802}, {51560, 52927}
X(61056) = X(i)-Dao conjugate of X(j) for these (i,j): {478, 57536}, {518, 4076}, {918, 3596}, {926, 480}, {17435, 646}, {38989, 36802}
X(61056) = crossdifference of every pair of points on line {28132, 36802}
X(61056) = barycentric product X(i)*X(j) for these {i,j}: {6, 3323}, {7, 35505}, {56, 35094}, {241, 3675}, {665, 43042}, {918, 53539}, {1086, 1362}, {1262, 52304}, {1357, 4437}, {1358, 6184}, {2254, 53544}, {3126, 3669}, {4712, 53538}, {15615, 57792}, {16728, 53540}, {17435, 34855}, {39014, 57880}, {43924, 53583}
X(61056) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 57536}, {665, 36802}, {1357, 6185}, {1358, 57537}, {1362, 1016}, {3126, 646}, {3323, 76}, {3675, 36796}, {6184, 4076}, {15615, 220}, {35094, 3596}, {35505, 8}, {39014, 480}, {39686, 6065}, {43042, 36803}, {52304, 23978}, {52635, 5377}, {53539, 666}, {53544, 51560}

X(61057) = X(12)X(1846)∩X(31)X(61054)

Barycentrics    a^4*(a + b - c)*(a - b + c)*(a^2*b - b^3 + a^2*c - 2*a*b*c + b^2*c + b*c^2 - c^3)^2 : :

X(61057) lies on these lines: {12, 1846}, {31, 61054}, {56, 957}, {181, 60817}, {1042, 1357}, {1397, 61048}, {1402, 3271}, {7337, 20991}, {8648, 61047}, {15507, 23981}, {53551, 61049}

X(61057) = isogonal conjugate of the isotomic conjugate of X(1361)
X(61057) = X(i)-isoconjugate of X(j) for these (i,j): {9, 57550}, {312, 59196}, {18816, 51565}, {28659, 41933}, {34234, 36795}
X(61057) = X(i)-Dao conjugate of X(j) for these (i,j): {478, 57550}, {517, 3596}, {57293, 35518}
X(61057) = barycentric product X(i)*X(j) for these {i,j}: {6, 1361}, {7, 59800}, {56, 23980}, {57, 42078}, {222, 42072}, {604, 24028}, {1397, 26611}, {1415, 42757}, {1457, 2183}, {3310, 23981}, {3326, 23979}, {7115, 35012}, {15632, 57181}, {21664, 52411}, {23984, 41220}, {51987, 53548}, {52410, 55016}
X(61057) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 57550}, {1361, 76}, {1397, 59196}, {23980, 3596}, {24028, 28659}, {26611, 40363}, {41220, 23983}, {41280, 41933}, {42072, 7017}, {42078, 312}, {59800, 8}

X(61058) = X(73)X(43693)∩X(1357)X(7117)

Barycentrics    a^2*(b - c)^2*(a + b - c)*(a - b + c)*(b + c)^2*(a^2 - b^2 - c^2)^2 : :

X(61058) lies on these lines: {73, 43693}, {1357, 7117}, {1365, 2611}, {1367, 17216}, {1439, 57683}, {2632, 2972}, {3028, 43692}, {3269, 37754}, {3937, 61054}, {7004, 51664}

X(61058) = isogonal conjugate of the isotomic conjugate of X(1367)
X(61058) = X(13853)-Ceva conjugate of X(57185)
X(61058) = X(i)-isoconjugate of X(j) for these (i,j): {8, 24000}, {9, 23582}, {29, 5379}, {33, 18020}, {55, 23999}, {78, 32230}, {100, 52921}, {107, 643}, {162, 36797}, {250, 318}, {270, 15742}, {312, 23964}, {607, 46254}, {644, 52919}, {645, 24019}, {823, 5546}, {1096, 6064}, {1259, 24021}, {1264, 24022}, {1857, 24041}, {1896, 4570}, {1897, 52914}, {2289, 34538}, {2326, 46102}, {3699, 52920}, {3719, 23590}, {4564, 36421}, {4567, 8748}, {6059, 24037}, {6061, 24032}, {7012, 59482}, {7070, 44181}, {7257, 32713}, {15384, 52346}, {28659, 41937}, {55206, 55270}
X(61058) = X(i)-Dao conjugate of X(j) for these (i,j): {125, 36797}, {223, 23999}, {478, 23582}, {512, 6059}, {520, 1259}, {525, 3596}, {647, 7017}, {3005, 1857}, {6503, 6064}, {8054, 52921}, {17434, 345}, {34467, 52914}, {35071, 645}, {38985, 643}, {40618, 55233}, {40622, 6528}, {40627, 8748}, {50330, 1896}, {55060, 107}
X(61058) = crossdifference of every pair of points on line {5546, 36797}
X(61058) = barycentric product X(i)*X(j) for these {i,j}: {6, 1367}, {7, 3269}, {56, 15526}, {57, 2632}, {73, 4466}, {77, 3708}, {115, 1804}, {125, 222}, {201, 3942}, {273, 37754}, {278, 2972}, {331, 34980}, {338, 7335}, {339, 52411}, {348, 20975}, {394, 1365}, {520, 7178}, {603, 20902}, {604, 17879}, {647, 17094}, {656, 51664}, {822, 4077}, {1086, 7066}, {1109, 7125}, {1214, 18210}, {1358, 52386}, {1363, 2052}, {1364, 6354}, {1397, 36793}, {1400, 17216}, {1407, 7068}, {1425, 26932}, {1439, 53560}, {1459, 57243}, {1565, 2197}, {1577, 51640}, {1813, 21134}, {2643, 7183}, {3120, 40152}, {3122, 52565}, {3124, 7055}, {3125, 52385}, {3265, 7180}, {3270, 20618}, {3669, 57109}, {3682, 53545}, {3926, 61052}, {3937, 26942}, {3998, 53540}, {4017, 24018}, {4025, 55234}, {4131, 57185}, {4565, 5489}, {4858, 7138}, {6046, 35072}, {6356, 7117}, {6517, 21131}, {7004, 37755}, {7143, 23983}, {7147, 24031}, {7215, 8736}, {7337, 23974}, {13853, 55044}, {16732, 22341}, {30493, 53576}, {52387, 53538}
X(61058) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 23582}, {57, 23999}, {77, 46254}, {125, 7017}, {222, 18020}, {394, 6064}, {520, 645}, {604, 24000}, {608, 32230}, {647, 36797}, {649, 52921}, {822, 643}, {1084, 6059}, {1118, 34538}, {1356, 2207}, {1357, 36419}, {1363, 394}, {1364, 7058}, {1365, 2052}, {1367, 76}, {1397, 23964}, {1409, 5379}, {1425, 46102}, {1804, 4590}, {2197, 15742}, {2632, 312}, {2972, 345}, {3122, 8748}, {3124, 1857}, {3125, 1896}, {3269, 8}, {3271, 36421}, {3708, 318}, {3937, 46103}, {3942, 57779}, {4017, 823}, {4025, 55233}, {4077, 57973}, {4131, 4631}, {4466, 44130}, {6046, 57538}, {7055, 34537}, {7066, 1016}, {7068, 59761}, {7117, 59482}, {7125, 24041}, {7138, 4564}, {7143, 23984}, {7147, 24032}, {7178, 6528}, {7180, 107}, {7183, 24037}, {7335, 249}, {7337, 23590}, {15526, 3596}, {17094, 6331}, {17216, 28660}, {17879, 28659}, {18210, 31623}, {20975, 281}, {21134, 46110}, {22096, 2189}, {22341, 4567}, {22383, 52914}, {23224, 4612}, {24018, 7257}, {34980, 219}, {35071, 1259}, {36793, 40363}, {37754, 78}, {39201, 5546}, {39687, 6061}, {40152, 4600}, {41280, 41937}, {42080, 2289}, {43924, 52919}, {51640, 662}, {51641, 24019}, {51664, 811}, {52385, 4601}, {52386, 4076}, {52411, 250}, {55208, 36126}, {55234, 1897}, {57109, 646}, {57181, 52920}, {61048, 36420}, {61052, 393}, {61054, 7054}

X(61059) = X(31)X(61053)∩X(56)X(51867)

Barycentrics    a^2*(a + b - c)*(a - b + c)*(b + c)^2*(a^2 - b*c)^2 : :

X(61059) lies on these lines: {31, 61053}, {56, 51867}, {110, 1397}, {181, 3124}, {238, 1284}, {694, 2176}, {1356, 4559}, {1357, 28360}, {1400, 2054}, {1402, 2107}, {1460, 20998}, {1976, 2175}, {2300, 3271}, {3027, 4154}, {4455, 5027}, {5029, 61055}, {5040, 61047}, {5168, 61048}, {7083, 52162}, {42655, 51641}, {51318, 51328}

X(61059) = isogonal conjugate of the isotomic conjugate of X(3027)
X(61059) = X(i)-isoconjugate of X(j) for these (i,j): {9, 57554}, {261, 30663}, {2185, 40098}, {2311, 40017}, {3572, 36806}, {18827, 56154}, {36066, 60577}, {36800, 37128}, {52205, 52379}
X(61059) = X(i)-Dao conjugate of X(j) for these (i,j): {478, 57554}, {740, 3596}, {4155, 4092}, {38978, 60577}
X(61059) = crossdifference of every pair of points on line {28828, 36800}
X(61059) = barycentric product X(i)*X(j) for these {i,j}: {6, 3027}, {12, 51328}, {56, 35068}, {57, 4094}, {181, 4366}, {594, 12835}, {1284, 2238}, {1400, 4368}, {1428, 4037}, {1914, 7235}, {2171, 8300}, {3747, 16609}, {35078, 55018}
X(61059) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 57554}, {181, 40098}, {1284, 40017}, {3027, 76}, {3573, 36806}, {3747, 36800}, {4094, 312}, {4366, 18021}, {4368, 28660}, {7235, 18895}, {8300, 52379}, {12835, 1509}, {35068, 3596}, {41333, 56154}, {46390, 60577}, {51328, 261}, {55018, 57558}

X(61060) = X(181)X(20975)∩X(1365)X(53321)

Barycentrics    a^4*(a + b - c)*(a - b + c)*(b + c)^2*(a^2 - b^2 + b*c - c^2)^2 : :

X(61060) lies on these lines: {181, 20975}, {1365, 53321}, {1397, 1576}, {1402, 61052}, {1460, 7669}, {2175, 40352}, {3271, 40956}, {5191, 61053}, {42670, 61047}

X(61060) = isogonal conjugate of the isotomic conjugate of X(3028)
X(61060) = X(i)-isoconjugate of X(j) for these (i,j): {9, 57555}, {1098, 57645}, {6740, 14616}, {7058, 34535}, {20566, 52380}, {36804, 60571}
X(61060) = X(i)-Dao conjugate of X(j) for these (i,j): {478, 57555}, {758, 3596}, {15267, 57645}
X(61060) = barycentric product X(i)*X(j) for these {i,j}: {6, 3028}, {12, 52059}, {56, 35069}, {215, 6354}, {594, 41282}, {604, 4736}, {1254, 34544}, {1464, 2245}, {1983, 51663}, {3724, 18593}, {4053, 52440}, {18334, 55017}
X(61060) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 57555}, {215, 7058}, {3028, 76}, {4736, 28659}, {6354, 57789}, {35069, 3596}, {41282, 1509}, {52059, 261}, {55017, 57546}

X(61061) = X(238)X(1284)∩X(244)X(61053)

Barycentrics    a^2*(b - c)^2*(a + b - c)*(a - b + c)*(a^2 - b*c)^2 : :

X(61062) lies on these lines: {238, 1284}, {244, 61053}, {1357, 1977}, {1397, 32735}, {1404, 61049}, {5061, 5211}, {7336, 43920}, {43924, 61048}, {51329, 61047}, {51650, 61052}

X(61061) = X(i)-isoconjugate of X(j) for these (i,j): {9, 57566}, {660, 36801}, {4076, 30663}, {4518, 5378}
X(61061) = X(i)-Dao conjugate of X(j) for these (i,j): {478, 57566}, {812, 3596}
X(61061) = barycentric product X(i)*X(j) for these {i,j}: {56, 35119}, {1086, 12835}, {1357, 4366}, {1358, 51328}, {1428, 27918}, {1429, 27846}, {4375, 43924}, {8300, 53538}, {8632, 43041}, {27855, 57181}, {56660, 61048}
X(61061) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 57566}, {1357, 40098}, {8632, 36801}, {12835, 1016}, {35119, 3596}, {51328, 4076}, {61048, 52205}

X(61062) = X(667)X(61048)∩X(902)X(1404)

Barycentrics    a^2*(2*a - b - c)^2*(b - c)^2*(a + b - c)*(a - b + c) : :

X(61062) lies on these lines: {667, 61048}, {902, 1404}, {1357, 8054}, {1458, 61049}, {3248, 51641}, {3271, 8643}, {20962, 23539}, {53542, 61051}

X(61062) = isogonal conjugate of the isotomic conjugate of X(14027)
X(61062) = X(i)-isoconjugate of X(j) for these (i,j): {9, 57564}, {646, 4638}, {679, 4076}, {1318, 7035}, {3257, 4582}, {3699, 4618}, {4997, 5376}, {6065, 57929}, {6635, 23838}
X(61062) = X(i)-Dao conjugate of X(j) for these (i,j): {478, 57564}, {900, 3596}, {55055, 4582}
X(61062) = crossdifference of every pair of points on line {4582, 30731}
X(61062) = barycentric product X(i)*X(j) for these {i,j}: {6, 14027}, {56, 35092}, {57, 42084}, {109, 14442}, {649, 39771}, {678, 53538}, {1015, 1317}, {1017, 1358}, {1086, 61047}, {1262, 52337}, {1319, 2087}, {1357, 4370}, {1404, 1647}, {1407, 4542}, {1635, 53528}, {1960, 30725}, {3251, 3669}, {6544, 43924}, {36791, 61048}
X(61062) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 57564}, {1017, 4076}, {1317, 31625}, {1357, 54974}, {1960, 4582}, {1977, 1318}, {3251, 646}, {4542, 59761}, {8661, 60480}, {14027, 76}, {14442, 35519}, {14637, 1639}, {35092, 3596}, {39771, 1978}, {42084, 312}, {52337, 23978}, {53538, 57929}, {57181, 4618}, {61047, 1016}, {61048, 2226}

X(61063) = COMPLEMENT OF X(14970)

Barycentrics    (a^2 - b*c)^2*(a^2 + b*c)^2*(b^2 + c^2)^2 : :

X(61063) lies on the Steiner inellipse and these lines: {2, 14970}, {39, 55050}, {115, 3934}, {141, 15449}, {325, 15573}, {385, 3978}, {1015, 59509}, {1084, 3589}, {1086, 51575}, {3005, 35077}, {3229, 9496}, {4576, 56978}, {4577, 9480}, {6665, 59994}, {7794, 52042}, {7813, 52876}, {11574, 15526}, {19563, 35119}, {21536, 35088}, {23992, 39079}, {28664, 52532}

X(61063) = complement of X(14970)
X(61063) = complement of the isogonal conjugate of X(8623)
X(61063) = complement of the isotomic conjugate of X(732)
X(61063) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 732}, {38, 5031}, {163, 5113}, {385, 21238}, {732, 2887}, {1580, 3934}, {1691, 1215}, {1923, 3229}, {1933, 3589}, {1964, 325}, {2236, 141}, {3051, 18904}, {4093, 46826}, {4164, 44312}, {8623, 10}, {14602, 16600}, {35540, 21235}, {41178, 24040}, {56828, 5943}, {56915, 37}, {56980, 8060}
X(61063) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 732}, {689, 782}
X(61063) = X(733)-isoconjugate of X(43763)
X(61063) = X(i)-Dao conjugate of X(j) for these (i,j): {732, 2}, {36213, 733}, {41178, 58784}
X(61063) = crossdifference of every pair of points on line {733, 881}
X(61063) = barycentric product X(i)*X(j) for these {i,j}: {732, 732}, {2528, 46294}, {4027, 7794}, {8623, 35540}, {51318, 59995}
X(61063) = barycentric quotient X(i)/X(j) for these {i,j}: {732, 14970}, {2236, 43763}, {4027, 52395}, {8041, 41517}, {8623, 733}, {17941, 59026}, {46294, 52936}, {51318, 59996}

X(61064) = COMPLEMENT OF X(430998)

Barycentrics    (2*a^4 - b^4 - c^4)^2 : :
X(61064) = 5 X[2] - X[39346], 2 X[4577] + X[15449], 5 X[4577] + X[39346], 3 X[4577] + X[43098], 5 X[15449] - 2 X[39346], 3 X[15449] - 2 X[43098], 3 X[39346] - 5 X[43098], 3 X[3524] - X[14718], X[15588] + 3 X[47352], X[17949] - 3 X[48310]

X(61064) lies on the Steiner inellipse and these lines: {2, 4577}, {115, 3589}, {206, 7818}, {385, 7664}, {754, 52958}, {1084, 1194}, {1086, 4697}, {2482, 9479}, {3524, 14718}, {5642, 35073}, {6676, 15526}, {8265, 55050}, {14403, 14420}, {15013, 39008}, {15527, 16950}, {15588, 47352}, {17949, 48310}, {18374, 35088}, {19571, 55152}, {31168, 41884}

X(61064) = midpoint of X(2) and X(4577)
X(61064) = reflection of X(15449) in X(2)
X(61064) = complement of X(43098)
X(61064) = complement of the isogonal conjugate of X(8627)
X(61064) = complement of the isotomic conjugate of X(754)
X(61064) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 754}, {754, 2887}, {2244, 141}, {4156, 21245}, {4157, 21244}, {7214, 17046}, {8627, 10}, {14420, 21253}, {14428, 8287}, {34072, 33907}, {35549, 21235}, {46543, 21259}, {52758, 21256}, {52958, 37}, {52979, 21238}
X(61064) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 754}, {4577, 33907}
X(61064) = X(i)-Dao conjugate of X(j) for these (i,j): {754, 2}, {33907, 15449}
X(61064) = barycentric product X(i)*X(j) for these {i,j}: {754, 754}, {4157, 7214}, {8627, 35549}, {52906, 52979}
X(61064) = barycentric quotient X(i)/X(j) for these {i,j}: {754, 43098}, {8627, 755}

X(61065) = COMPLEMENT OF X(4586)

Barycentrics    (b - c)^2*(b^2 + b*c + c^2)^2 : :
X(61065) = 3 X[2] + X[39345], X[4586] + 3 X[43097], X[39345] - 3 X[43097]

X(61065) lies on the Steiner inellipse and these lines: {2, 4586}, {11, 35119}, {115, 21138}, {116, 1015}, {561, 40379}, {716, 30877}, {794, 55049}, {1084, 8287}, {1086, 21210}, {1211, 35068}, {1501, 7357}, {1921, 5031}, {4370, 17359}, {4475, 33904}, {6184, 20540}, {7261, 51328}, {16893, 28654}, {17757, 35120}, {23972, 37662}, {23989, 39691}, {35110, 50291}

X(61065) = midpoint of X(i) and X(j) for these {i,j}: {2, 43097}, {4586, 39345}
X(61065) = complement of X(4586)
X(61065) = complement of the isogonal conjugate of X(3250)
X(61065) = complement of the isotomic conjugate of X(824)
X(61065) = X(i)-complementary conjugate of X(j) for these (i,j): {2, 788}, {6, 4874}, {31, 824}, {292, 30665}, {513, 21264}, {649, 24325}, {667, 17023}, {788, 2}, {824, 2887}, {869, 514}, {893, 3805}, {984, 3835}, {1469, 4885}, {1491, 141}, {2276, 513}, {3250, 10}, {3661, 21260}, {3736, 4369}, {3774, 661}, {3783, 27854}, {3799, 27076}, {3862, 3837}, {3864, 21261}, {4122, 21245}, {4475, 116}, {4481, 3741}, {4486, 20542}, {4517, 20317}, {4522, 21244}, {7146, 17072}, {7204, 46399}, {8630, 39}, {14436, 4370}, {14945, 794}, {18900, 6586}, {29956, 518}, {30654, 19563}, {30665, 20333}, {30671, 3836}, {30870, 40379}, {30966, 42327}, {31909, 21259}, {33931, 21262}, {40728, 650}, {40736, 21348}, {40773, 512}, {45782, 21191}, {45882, 51575}, {46386, 37}, {46503, 525}, {52655, 4083}, {52957, 33568}, {56556, 522}, {58862, 59509}, {58864, 17755}
X(61065) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 824}, {7224, 3805}, {7261, 30665}, {7357, 788}, {40362, 30870}, {43097, 33904}
X(61065) = X(i)-isoconjugate of X(j) for these (i,j): {825, 1492}, {4586, 34069}, {5384, 40746}
X(61065) = X(i)-Dao conjugate of X(j) for these (i,j): {788, 1501}, {824, 2}, {19584, 5384}, {30665, 51328}, {33568, 752}, {38995, 825}, {55049, 34069}
X(61065) = barycentric product X(i)*X(j) for these {i,j}: {788, 30870}, {824, 824}, {4469, 16732}, {4475, 33931}, {4476, 21207}, {4486, 23596}, {12837, 34387}, {40362, 55049}
X(61065) = barycentric quotient X(i)/X(j) for these {i,j}: {788, 34069}, {824, 4586}, {984, 5384}, {1491, 1492}, {3250, 825}, {4122, 4613}, {4469, 4567}, {4475, 985}, {4476, 4570}, {12837, 59}, {23596, 37207}, {30870, 46132}, {55049, 1501}
X(61065) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 39345, 4586}, {4586, 43097, 39345}

X(61066) = COMPLEMENT OF X(46136)

Barycentrics    (2*a^4 - 2*a^3*b - a^2*b^2 + 2*a*b^3 - b^4 - 2*a^3*c + 4*a^2*b*c - 2*a*b^2*c - a^2*c^2 - 2*a*b*c^2 + 2*b^2*c^2 + 2*a*c^3 - c^4)^2 : :

X(61066) lies on the Steiner inellipse and these lines: {2, 46136}, {6, 34232}, {9, 55153}, {37, 35128}, {44, 1146}, {45, 35091}, {115, 2245}, {577, 32641}, {650, 23980}, {655, 23593}, {1015, 8609}, {1086, 3911}, {3239, 4370}, {3936, 15526}, {4675, 35094}, {17355, 35122}, {35088, 50773}

X(61066) = complement of X(46136)
X(61066) = complement of the isotomic conjugate of X(952)
X(61066) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 952}, {32, 43048}, {952, 2887}, {1110, 55317}, {2265, 141}, {43043, 17046}, {52478, 21241}
X(61066) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 952}, {655, 35013}
X(61066) = X(i)-Dao conjugate of X(j) for these (i,j): {952, 2}, {35587, 50943}, {45950, 3904}
X(61066) = barycentric product X(i)*X(j) for these {i,j}: {8, 3319}, {952, 952}
X(61066) = barycentric quotient X(i)/X(j) for these {i,j}: {952, 46136}, {3319, 7}

X(61067) = COMPLEMENT OF X(46140)

Barycentrics    a^4*(a^4*b^2 - b^6 + a^4*c^2 - 2*a^2*b^2*c^2 + b^4*c^2 + b^2*c^4 - c^6)^2 : :

X(61067) lies on the Steiner inellipse and these lines: {2, 46140}, {3, 55047}, {32, 1084}, {39, 15526}, {115, 427}, {187, 55048}, {574, 35071}, {800, 35133}, {1015, 40959}, {6793, 52588}, {14581, 56794}, {15116, 15449}, {16315, 35078}, {17416, 59994}, {21248, 26159}, {42665, 47426}

X(61067) = complement of X(46140)
X(61067) = complement of the isotomic conjugate of X(2393)
X(61067) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 2393}, {560, 468}, {858, 21235}, {1924, 52628}, {2393, 2887}, {9247, 54075}, {14580, 20305}, {18669, 626}, {20884, 40379}, {46592, 21259}, {51962, 4892}, {57485, 21256}
X(61067) = X(2)-Ceva conjugate of X(2393)
X(61067) = X(2373)-isoconjugate of X(37220)
X(61067) = X(2393)-Dao conjugate of X(2)
X(61067) = crossdifference of every pair of points on line {2373, 35522}
X(61067) = barycentric product X(i)*X(j) for these {i,j}: {1560, 34158}, {2393, 2393}, {5181, 51962}, {14580, 14961}, {42665, 46592}, {47426, 57485}
X(61067) = barycentric quotient X(2393)/X(46140)

X(61068) = COMPLEMENT OF X(43091)

Barycentrics    (Sqrt[3]*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4) + 2*(2*a^2 - b^2 - c^2)*S)^2 : :
X(61068) = 3 X[23895] + X[43091], 2 X[23895] + X[43961], 2 X[43091] - 3 X[43961]

X(61068) lies on the Steiner inellipse and these lines: {2, 18777}, {115, 396}, {395, 23992}, {523, 5642}, {524, 41888}, {530, 11537}, {2482, 23871}, {5463, 40578}, {9200, 45331}, {11080, 51482}, {11127, 37786}, {18334, 40696}, {18776, 52748}, {30454, 30468}, {30467, 30469}, {40581, 50858}

X(61068) = midpoint of X(2) and X(23895)
X(61068) = reflection of X(43961) in X(2)
X(61068) = complement of X(43091)
X(61068) = complement of the isotomic conjugate of X(530)
X(61068) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 530}, {530, 2887}, {9200, 21253}, {23712, 20305}, {52748, 21256}
X(61068) = X(2)-Ceva conjugate of X(530)
X(61068) = X(530)-Dao conjugate of X(2)
X(61068) = barycentric product X(i)*X(j) for these {i,j}: {298, 42001}, {299, 30469}, {530, 530}
X(61068) = barycentric quotient X(i)/X(j) for these {i,j}: {530, 43091}, {11537, 36316}, {30467, 30465}, {30469, 14}, {42001, 13}

X(61069) = COMPLEMENT OF X(43092)

Barycentrics    (Sqrt[3]*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4) - 2*(2*a^2 - b^2 - c^2)*S)^2 : :
X(61069) =3 X[23896] + X[43092], 2 X[23896] + X[43962], 2 X[43092] - 3 X[43962]

X(61069) lies on the Steiner inellipse and these lines: {2, 18776}, {115, 395}, {396, 23992}, {523, 5642}, {524, 41887}, {531, 11549}, {2482, 23870}, {5464, 40579}, {9201, 45331}, {11085, 51483}, {11126, 37785}, {18334, 40695}, {18777, 52749}, {30455, 30465}, {30466, 30470}, {40580, 50855}

X(61069) =midpoint of X(2) and X(23896)
X(61069) =reflection of X(43962) in X(2)
X(61069) =complement of X(43092)
X(61069) =complement of the isotomic conjugate of X(531)
X(61069) =X(i)-complementary conjugate of X(j) for these (i,j): {31, 531}, {531, 2887}, {9201, 21253}, {23713, 20305}, {52749, 21256}
X(61069) =X(2)-Ceva conjugate of X(531)
X(61069) =X(531)-Dao conjugate of X(2)
X(61069) =barycentric product X(i)*X(j) for these {i,j}: {298, 30466}, {299, 42002}, {531, 531}
X(61069) =barycentric quotient X(i)/X(j) for these {i,j}: {531, 43092}, {11549, 36317}, {30466, 13}, {30470, 30468}, {42002, 14}

X(61070) = COMPLEMENT OF X(46142)

Barycentrics    (a^6*b^2 - a^4*b^4 + a^6*c^2 - 2*a^4*b^2*c^2 + a^2*b^4*c^2 - b^6*c^2 - a^4*c^4 + a^2*b^2*c^4 + 2*b^4*c^4 - b^2*c^6)^2 : :
X(61070) = X[46142] + 3 X[53199]

X(61070) lies on the Steiner inellipse and these lines: {2, 46142}, {6, 35078}, {115, 511}, {141, 35088}, {230, 1084}, {325, 15526}, {523, 11672}, {577, 2966}, {2482, 23878}, {3163, 47229}, {3734, 44155}, {3815, 23992}, {5661, 18334}, {15819, 39009}, {34359, 50977}, {36207, 40805}, {48316, 59561}

X(61070) = midpoint of X(2) and X(53199)
X(61070) = complement of X(46142)
X(61070) = complement of the isotomic conjugate of X(2782)
X(61070) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 2782}, {2782, 2887}, {6071, 24040}, {24041, 55312}, {36084, 55143}
X(61070) = X(2)-Ceva conjugate of X(2782)
X(61070) = X(2782)-Dao conjugate of X(2)
X(61070) = barycentric product X(2782)*X(2782)
X(61070) = barycentric quotient X(2782)/X(46142)

X(61071) = COMPLEMENT OF X(46144)

Barycentrics    (b - c)^2*(b + c)^2*(4*a^4 - a^2*b^2 + b^4 - a^2*c^2 - 4*b^2*c^2 + c^4)^2 : :
X(61071) = 3 X[9487] + X[46144]

X(61071) lies on the Steiner inellipse and these lines: {2, 9487}, {6, 35087}, {115, 1499}, {230, 2482}, {523, 35133}, {1648, 35088}, {3291, 11672}, {3815, 35077}, {6791, 47587}, {7735, 23967}, {7753, 34103}, {15526, 44398}, {15993, 35073}, {17416, 23991}, {17952, 17968}, {23976, 47242}

X(61071) = midpoint of X(i) and X(j) for these {i,j}: {2, 9487}, {17952, 22329}
X(61071) = complement of X(46144)
X(61071) = complement of the isogonal conjugate of X(9135)
X(61071) = complement of the isotomic conjugate of X(2793)
X(61071) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 2793}, {798, 22110}, {2030, 4369}, {2793, 2887}, {9135, 10}, {22329, 42327}
X(61071) = X(2)-Ceva conjugate of X(2793)
X(61071) = X(2793)-Dao conjugate of X(2)
X(61071) = barycentric product X(2793)*X(2793)
X(61071) = barycentric quotient X(i)/X(j) for these {i,j}: {2793, 46144}, {9135, 2709}

X(61072) = X(6)X(173)∩X(37)X(236)

Barycentrics    a*(a + b - c)*(a - b + c)*(-a + b + c)*(a*b + b^2 + a*c - 2*b*c + c^2 - 2*Sqrt[b*c*(a + b - c)*(a - b + c)]) : :

X(61072) lies on the Steiner inellipse and these lines: {6, 173}, {37, 236}, {42, 10502}, {115, 45304}, {174, 3752}, {244, 10494}, {386, 12491}, {536, 40893}, {1086, 21623}, {1279, 8076}, {3666, 8126}, {4255, 7590}, {4646, 8351}, {5573, 8090}, {7028, 16602}, {8082, 17054}, {8083, 49478}, {8092, 52541}, {8100, 24046}, {8125, 16610}, {8128, 37528}, {21624, 37662}

X(61072) = X(32)-complementary conjugate of X(10492)
X(61072) = X(i)-Ceva conjugate of X(j) for these (i,j): {174, 513}, {8056, 10495}
X(61072) = X(i)-isoconjugate of X(j) for these (i,j): {6, 59443}, {3659, 55331}, {45874, 55332}, {45875, 55363}
X(61072) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 59443}, {6728, 556}
X(61072) = crossdifference of every pair of points on line {3659, 55363}
X(61072) = barycentric product X(i)*X(j) for these {i,j}: {1, 10504}, {8, 12809}, {11, 59469}, {173, 21623}, {244, 59465}, {505, 21618}, {2089, 6732}, {7022, 10501}, {10491, 52999}
X(61072) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 59443}, {6732, 53123}, {10504, 75}, {12809, 7}, {45877, 55332}, {45878, 55363}, {59465, 7035}, {59469, 4998}

X(61073) = COMPLEMENT OF X(4597)

Barycentrics    (a - 2*b - 2*c)^2*(b - c)^2 : :
X(61073) = 3 X[2] + X[39364], 2 X[4597] - 3 X[35124], X[4597] + 3 X[35170], X[35124] + 2 X[35170], 3 X[35124] + 2 X[39364], 3 X[35170] - X[39364]

X(61073) lies on the Steiner inellipse and these lines: {2, 4597}, {10, 4370}, {11, 35092}, {80, 1017}, {115, 15614}, {867, 38963}, {1015, 1647}, {1500, 23980}, {2482, 24603}, {3125, 53167}, {3661, 13466}, {3679, 52966}, {3912, 27751}, {4791, 4957}, {4997, 34362}, {6184, 17057}, {14936, 35090}, {16589, 35069}, {20532, 21251}, {28603, 30605}, {29571, 35110}, {35085, 49764}, {35113, 49772}, {35123, 49769}, {35129, 52959}

X(61073) = midpoint of X(i) and X(j) for these {i,j}: {2, 35170}, {4597, 39364}
X(61073) = reflection of X(35124) in X(2)
X(61073) = complement of X(4597)
X(61073) = complement of the isogonal conjugate of X(4775)
X(61073) = complement of the isotomic conjugate of X(4777)
X(61073) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 47779}, {31, 4777}, {45, 3835}, {513, 21242}, {649, 34824}, {667, 551}, {904, 48289}, {1405, 4885}, {1911, 48229}, {1919, 4850}, {2099, 17072}, {2177, 513}, {3679, 21260}, {3711, 59971}, {4273, 4369}, {4653, 512}, {4671, 21262}, {4752, 27076}, {4770, 3454}, {4775, 10}, {4777, 2887}, {4791, 626}, {4792, 53571}, {4800, 20542}, {4814, 1329}, {4825, 21251}, {4833, 3741}, {4893, 141}, {4931, 21245}, {4944, 21244}, {5235, 42327}, {23352, 21241}, {43052, 17046}, {43924, 17051}, {47683, 21240}
X(61073) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 4777}, {39705, 523}
X(61073) = X(i)-isoconjugate of X(j) for these (i,j): {59, 30607}, {2163, 5385}, {4588, 4604}, {4597, 34073}
X(61073) = X(i)-Dao conjugate of X(j) for these (i,j): {4777, 2}, {6615, 30607}, {40587, 5385}, {55045, 4604}
X(61073) = barycentric product X(i)*X(j) for these {i,j}: {45, 4957}, {514, 53584}, {693, 4825}, {3120, 4803}, {4777, 4777}, {4791, 4893}, {4931, 47683}, {4944, 43052}
X(61073) = barycentric quotient X(i)/X(j) for these {i,j}: {45, 5385}, {2170, 30607}, {4775, 4588}, {4777, 4597}, {4803, 4600}, {4825, 100}, {4893, 4604}, {4957, 20569}, {53584, 190}
X(61073) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 39364, 4597}, {4597, 35170, 39364}

X(61074) = X(2)-CEVA CONJUGATE OF X(6084)

Barycentrics    (b - c)^2*(2*a^2 - a*b + b^2 - a*c - 2*b*c + c^2)^2 : :

X(61074) lies on the Steiner inellipse and these lines: {32, 32644}, {115, 5519}, {514, 40621}, {1015, 1358}, {1086, 3667}, {1146, 6547}, {1281, 2482}, {3008, 35111}, {3241, 24281}, {3290, 6184}, {4000, 40540}, {4370, 17132}, {5516, 45677}, {7263, 40487}, {13466, 40609}, {21129, 35092}, {27918, 35094}, {29600, 35123}, {35130, 50025}, {39012, 39786}

X(61074) = complement of the isogonal conjugate of X(8659)
X(61074) = complement of the isotomic conjugate of X(6084)
X(61074) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 6084}, {604, 4925}, {649, 3823}, {1279, 3835}, {1919, 3693}, {2348, 59971}, {3008, 21260}, {6084, 2887}, {8647, 20317}, {8659, 10}, {23704, 3038}, {38266, 2505}, {48032, 141}, {53523, 21244}, {53558, 21245}, {57181, 5853}
X(61074) = X(2)-Ceva conjugate of X(6084)
X(61074) = X(6084)-Dao conjugate of X(2)
X(61074) = barycentric product X(i)*X(j) for these {i,j}: {1358, 3021}, {6084, 6084}, {56793, 56796}
X(61074) = barycentric quotient X(i)/X(j) for these {i,j}: {3021, 4076}, {8659, 6078}

X(61075) = COMPLEMENT OF X(53642)

Barycentrics    (a - b - c)^2*(b - c)^2*(a^3 + a^2*b - a*b^2 - b^3 + a^2*c - 2*a*b*c + b^2*c - a*c^2 + b*c^2 - c^3)^2 : :

X(61075) lies on the Steiner inellipse and these lines: {2, 53642}, {9, 23986}, {115, 46663}, {220, 1783}, {223, 31142}, {1086, 6506}, {1146, 7358}, {1212, 20264}, {1528, 17747}, {3239, 40616}, {4370, 34524}, {5514, 13612}, {6184, 6260}, {13609, 35072}, {20209, 46830}, {23980, 40943}, {34591, 57291}, {35081, 58325}, {35116, 60419}, {53824, 53833}

X(61075) = complement of X(53642)
X(61075) = complement of the isotomic conjugate of X(8058)
X(61075) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 8058}, {40, 17072}, {198, 4885}, {213, 24018}, {220, 20318}, {221, 3900}, {223, 46399}, {650, 21239}, {657, 20205}, {663, 946}, {667, 3086}, {1402, 17898}, {1415, 40555}, {1817, 17066}, {2175, 57055}, {2187, 522}, {2199, 7658}, {2212, 14331}, {2324, 3835}, {2331, 46396}, {3063, 57}, {3195, 521}, {3900, 20306}, {6129, 2886}, {7074, 513}, {7080, 21260}, {7368, 20317}, {8058, 2887}, {8641, 281}, {10397, 18589}, {14298, 141}, {14837, 17046}, {17896, 17047}, {22383, 55118}, {27398, 42327}, {38357, 21252}, {40971, 20316}, {47432, 123}, {55212, 17052}, {57049, 21244}, {57101, 1368}, {57180, 56857}
X(61075) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 8058}, {1034, 3900}
X(61075) = X(i)-isoconjugate of X(j) for these (i,j): {1256, 1262}, {8059, 37141}
X(61075) = X(i)-Dao conjugate of X(j) for these (i,j): {6129, 189}, {8058, 2}, {14837, 34400}, {55044, 37141}
X(61075) = barycentric product X(i)*X(j) for these {i,j}: {8, 3318}, {329, 5514}, {1034, 13612}, {1103, 24026}, {4081, 55015}, {7080, 38357}, {7358, 7952}, {8058, 8058}, {14837, 57049}, {16596, 55116}
X(61075) = barycentric quotient X(i)/X(j) for these {i,j}: {1103, 7045}, {2310, 1256}, {3318, 7}, {4081, 46355}, {4092, 7157}, {5514, 189}, {8058, 53642}, {13612, 5932}, {14298, 37141}, {16596, 34400}, {38357, 1440}, {47432, 1433}, {53557, 56972}, {55015, 59457}, {57049, 44327}

X(61076) = COMPLEMENT OF X(32041)

Barycentrics    (b - c)^2*(-a^2 + a*b + a*c + 2*b*c)^2 : :
X(61076) = 5 X[2] - X[39350], 2 X[2481] + X[6184], 3 X[2481] + X[32041], 5 X[2481] + X[39350], 3 X[6184] - 2 X[32041], 5 X[6184] - 2 X[39350], 5 X[32041] - 3 X[39350], X[14947] - 3 X[59377]

X(61076) lies on the Steiner inellipse and these lines: {2, 2481}, {11, 35094}, {115, 4904}, {381, 2808}, {519, 35120}, {524, 35084}, {551, 28850}, {1015, 1111}, {1086, 23821}, {1146, 17761}, {2482, 2795}, {3679, 3789}, {4370, 4688}, {4762, 39012}, {4858, 35508}, {4957, 35125}, {14936, 31150}, {14947, 59377}, {17301, 23980}, {20532, 29594}, {23972, 50114}, {23989, 47869}, {35066, 39775}, {35069, 41311}, {35113, 41140}, {35123, 41141}, {39014, 44567}, {45322, 45338}

X(61076) = midpoint of X(2) and X(2481)
X(61076) = reflection of X(6184) in X(2)
X(61076) = complement of X(32041)
X(61076) = complement of the isotomic conjugate of X(4762)
X(61076) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 24720}, {31, 4762}, {56, 54264}, {649, 3826}, {667, 29571}, {1001, 3835}, {1333, 4913}, {1471, 4885}, {1919, 2276}, {2280, 513}, {4384, 21260}, {4441, 21262}, {4724, 141}, {4762, 2887}, {4804, 21245}, {5228, 17072}, {9454, 33570}, {9456, 45328}, {31926, 21259}, {37658, 59971}, {45755, 1329}, {54440, 27076}, {57129, 15569}, {57181, 3755}, {59207, 31946}, {59242, 46399}, {60721, 512}, {60722, 514}, {60735, 23301}
X(61076) = X(2)-Ceva conjugate of X(4762)
X(61076) = X(8693)-isoconjugate of X(37138)
X(61076) = X(i)-Dao conjugate of X(j) for these (i,j): {4762, 2}, {33570, 518}
X(61076) = barycentric product X(i)*X(j) for these {i,j}: {4762, 4762}, {39012, 57537}
X(61076) = barycentric quotient X(i)/X(j) for these {i,j}: {4724, 37138}, {4762, 32041}, {39012, 6184}

X(61077) = COMPLEMENT OF X(53202)

Barycentrics    (b - c)^2*(b + c)^2*(-a^6 + a^4*b^2 + a^4*c^2 - 3*a^2*b^2*c^2 + b^4*c^2 + b^2*c^4)^2 : :
X(61077) = X[53202] + 3 X[53221]

X(61077) lies on the Steiner inellipse and these lines: {2, 53202}, {30, 35073}, {115, 30476}, {512, 15526}, {525, 1084}, {538, 3163}, {2482, 59707}, {3143, 35088}, {3734, 44155}, {6390, 11672}, {7801, 34364}, {8369, 23967}, {11328, 34360}, {15014, 16084}, {35078, 52628}, {35087, 59780}

X(61077) = midpoint of X(i) and X(j) for these {i,j}: {2, 53221}, {15014, 16084}
X(61077) = complement of X(53202)
X(61077) = complement of the isotomic conjugate of X(9035)
X(61077) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 9035}, {865, 8287}, {9035, 2887}, {15014, 21259}, {16084, 21263}, {47206, 20305}, {56430, 42327}
X(61077) = X(2)-Ceva conjugate of X(9035)
X(61077) = X(9035)-Dao conjugate of X(2)
X(61077) = barycentric product X(i)*X(j) for these {i,j}: {865, 16084}, {9035, 9035}
X(61077) = barycentric quotient X(i)/X(j) for these {i,j}: {865, 16098}, {9035, 53202}, {16084, 57988}, {56430, 57739}

X(61078) = X(7)X(1357)&cap:X(11)X(3663)

Barycentrics    (a + b - c)*(a - b + c)*(a*b + a*c - 2*b*c)^2 : :

X(61078) lies on the incircle and these lines: {7, 1357}, {11, 3663}, {55, 29352}, {56, 29351}, {65, 47015}, {150, 497}, {181, 18057}, {226, 1358}, {354, 5581}, {1317, 43041}, {1356, 39793}, {1364, 41004}, {1365, 41003}, {3023, 15903}, {3596, 21404}, {3676, 24816}, {4009, 6381}, {4415, 41285}, {4526, 4728}, {5219, 40784}, {5252, 47006}, {9436, 14027}, {15950, 33966}, {23813, 53534}, {36920, 47022}, {40614, 52896}

X(61078) = isotomic conjugate of the isogonal conjugate of X(61049)
X(61078) = X(7)-Ceva conjugate of X(43037)
X(61078) = X(41)-isoconjugate of X(57542)
X(61078) = X(i)-Dao conjugate of X(j) for these (i,j): {536, 8}, {891, 3271}, {1646, 650}, {3160, 57542}, {13466, 36798}
X(61078) = barycentric product X(i)*X(j) for these {i,j}: {7, 13466}, {76, 61049}, {85, 42083}, {536, 43037}, {4554, 14434}, {6063, 59797}, {6381, 52896}, {31625, 47016}
X(61078) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 57542}, {536, 36798}, {8031, 4009}, {13466, 8}, {14434, 650}, {39011, 3271}, {42083, 9}, {43037, 3227}, {47016, 1015}, {52896, 37129}, {59797, 55}, {61049, 6}

X(61079) = X(7)X(31316)&cap:X(56)X(100)

Barycentrics    (b - c)^2*(-a + b - c)*(a + b - c)*(-3*a + b + c)^2 : :

X(61079) lies on the incircle and these lines: {7, 31316}, {8, 44301}, {11, 38384}, {55, 30236}, {56, 100}, {57, 3021}, {65, 6018}, {244, 1358}, {1319, 37743}, {1357, 58893}, {1361, 37566}, {1362, 45204}, {2976, 3756}, {3318, 53525}, {3660, 59807}, {3667, 16185}, {3669, 17071}, {3911, 52907}, {5435, 15519}, {13756, 18838}, {14027, 14112}, {15637, 58858}, {32636, 34194}

X(61079) = reflection of X(16185) in the Nagel line
X(61079) = X(i)-Ceva conjugate of X(j) for these (i,j): {7, 30719}, {145, 51656}, {5435, 31182}, {6049, 58858}, {44301, 3667}
X(61079) = X(i)-isoconjugate of X(j) for these (i,j): {41, 57578}, {765, 33963}, {1293, 31343}
X(61079) = X(i)-Dao conjugate of X(j) for these (i,j): {513, 33963}, {3160, 57578}, {3667, 8}, {3669, 4373}, {4521, 6557}, {31182, 8055}
X(61079) = barycentric product X(i)*X(j) for these {i,j}: {7, 40621}, {145, 40617}, {514, 58858}, {1086, 6049}, {3667, 30719}, {3676, 31182}, {3756, 5435}, {3911, 15637}, {4462, 51656}, {4943, 58817}, {56323, 58811}
X(61079) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 57578}, {1015, 33963}, {1420, 5382}, {3756, 6557}, {4394, 31343}, {4534, 6556}, {4943, 6558}, {6049, 1016}, {15637, 4997}, {30719, 53647}, {31182, 3699}, {40617, 4373}, {40621, 8}, {51656, 27834}, {58811, 21272}, {58858, 190}

X(61080) = X(11)X(971)&cap:X(56)X(840)

Barycentrics    a^2*(a + b - c)*(a - b + c)*(a^4*b - 2*a^3*b^2 + 2*a*b^4 - b^5 + a^4*c + a^2*b^2*c - 2*a*b^3*c - 2*a^3*c^2 + a^2*b*c^2 + b^3*c^2 - 2*a*b*c^3 + b^2*c^3 + 2*a*c^4 - c^5)^2 : :

X(61080) lies on the incircle and these lines: {11, 971}, {12, 46415}, {55, 2720}, {56, 840}, {57, 3025}, {65, 3328}, {103, 35604}, {354, 3326}, {513, 1360}, {1155, 1364}, {1317, 3900}, {1319, 3022}, {1358, 18838}, {2078, 3024}, {3028, 51664}, {3318, 18839}, {5173, 31522}

X(61080) = reflection of X(1360) in the OI line
X(61080) = X(7)-Ceva conjugate of X(43047)
X(61080) = X(2801)-Dao conjugate of X(8)
X(61080) = barycentric product X(i)*X(j) for these {i,j}: {7, 35116}, {2801, 43047}
X(61080) = barycentric quotient X(i)/X(j) for these {i,j}: {35116, 8}, {43047, 35164}

X(61081) = X(2)X(3)&cap:X(511)X(60068)

Barycentrics    (S^2 - 4*SB*SC)*SW + S*Sqrt[SA*SB*SC*SW] : :
X(61081) = 3 X[2] - 4 X[5001], 9 X[2] - 8 X[47613], 7 X[3523] - 8 X[31664], 4 X[5000] - 5 X[37760], 3 X[5001] - 2 X[47613], 3 X[5003] - 4 X[47613]

X(61081) lies on these lines: {2, 3}, {511, 60068}, {12384, 34239}, {29012, 32619}, {29181, 41199}, {31670, 32618}, {36990, 41198}

X(61081) = reflection of X(i) in X(j) for these {i,j}: {20, 40895}, {5003, 5001}, {5189, 5002}
X(61081) = anticomplement of X(5003)
X(61081) = orthoptic-circle-of-the-Steiner-circumellipse-inverse of X(5000)
X(61081) = anticomplement of the isogonal conjugate of X(34135)
X(61081) = X(34135)-anticomplementary conjugate of X(8)
X(61081) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 5002, 2}, {5001, 5003, 2}

X(61082) = X(2)X(3)&cap:X(511)X(60067)

Barycentrics    (S^2 - 4*SB*SC)*SW + S*Sqrt[SA*SB*SC*SW] : :
X(61082) = 3 X[2] - 4 X[5000], 9 X[2] - 8 X[47612], 7 X[3523] - 8 X[31665], 3 X[5000] - 2 X[47612], 4 X[5001] - 5 X[37760], 3 X[5002] - 4 X[47612]

X(61082) lies on these lines: {2, 3}, {511, 60067}, {12384, 34240}, {29012, 32618}, {29181, 41198}, {31670, 32619}, {36990, 41199}

X(61082) = reflection of X(i) in X(j) for these {i,j}: {20, 40894}, {5002, 5000}, {5189, 5003}
X(61082) = anticomplement of X(5002)
X(61082) = orthoptic-circle-of-the-Steiner-circumellipse-inverse of X(5001)
X(61082) = anticomplement of the isogonal conjugate of X(34136)
X(61082) = X(34136)-anticomplementary conjugate of X(8)
X(61082) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 5003, 2}, {5000, 5002, 2}

X(61083) = ISOGONAL CONJUGATE OF X(61084)

Barycentrics    (SB + SC)*(SA*SB - S*Sqrt[SA*SB])*(SA*SC - S*Sqrt[SA*SC]) : :

See Costas Vittas, Antreas Hatzipolakis and Peter Moses, euclid 6066.

X(61083) lies on the cubic K006, the curves Q039 and Q117 and this line: {4, 61084}

X(61083) = isogonal conjugate of X(61084)

X(61084) = ISOGONAL CONJUGATE OF X(61083)

Barycentrics    (SB + SC)*(SA*SB + S*Sqrt[SA*SB])*(SA*SC + S*Sqrt[SA*SC]) : :

See Costas Vittas, Antreas Hatzipolakis and Peter Moses, euclid 6066.

X(61084) lies on the cubic K006, the curves Q039 and Q117 and this line: {4, 61083}

X(61084) = isogonal conjugate of X(61083)

X(61085) = MIDPOINT OF X(61083) AND X(61084)

Barycentrics    Sqrt[SB] + Sqrt[SC] : :

X(61085) lies on the Kiepert circumhyperbola, the cubic K858, and this line: X(4)X(61083)

X(61085) = midpoint of X(61083) and X(61084)
X(61085) = X(i)-complementary conjugate of X(j) for these (i,j): {5374, 1368}, {20034, 141}

X(61086) = X(1)X(7)∩X(6)X(517)

Barycentrics    a*(a^5 - a^4*b - a*b^4 + b^5 - a^4*c + 6*a^3*b*c - 4*a^2*b^2*c + 2*a*b^3*c - 3*b^4*c - 4*a^2*b*c^2 - 2*a*b^2*c^2 + 2*b^3*c^2 + 2*a*b*c^3 + 2*b^2*c^3 - a*c^4 - 3*b*c^4 + c^5) : :
X(61086) = 3 X[1] - X[1721], 3 X[990] - 2 X[1721], X[990] + 2 X[12652], X[1721] + 3 X[12652], 3 X[3576] - 2 X[24309], 3 X[3241] + X[9801], 3 X[5603] - 2 X[12610], X[7996] + 3 X[11224]

X(61086) lies on the cubic K1361 and these lines: {1, 7}, {3, 1279}, {4, 23050}, {6, 517}, {8, 12618}, {10, 56466}, {30, 50130}, {31, 41338}, {33, 9580}, {34, 1697}, {38, 1709}, {40, 595}, {46, 1471}, {55, 1465}, {57, 52428}, {106, 1292}, {109, 54408}, {149, 2000}, {165, 614}, {222, 17642}, {223, 10388}, {241, 42884}, {386, 6769}, {392, 25878}, {497, 8270}, {519, 21629}, {573, 16970}, {601, 12704}, {612, 1699}, {919, 2717}, {946, 975}, {971, 3242}, {984, 54370}, {995, 6282}, {997, 4660}, {999, 1418}, {1038, 12053}, {1064, 37569}, {1191, 31793}, {1253, 1718}, {1295, 58967}, {1385, 50677}, {1407, 12915}, {1419, 2823}, {1421, 35445}, {1456, 3057}, {1482, 49478}, {1722, 43174}, {2098, 12721}, {2099, 12723}, {2114, 37555}, {2550, 53599}, {2801, 16496}, {2807, 3056}, {2835, 7289}, {2999, 7994}, {3241, 9801}, {3295, 15852}, {3333, 35658}, {3340, 32118}, {3428, 21002}, {3656, 17392}, {3677, 10860}, {3729, 3872}, {3744, 7580}, {3752, 6244}, {3811, 17766}, {3817, 5268}, {3870, 31034}, {3877, 37659}, {3886, 29016}, {3915, 59340}, {3920, 9812}, {4000, 35514}, {4648, 5603}, {4675, 20330}, {4861, 24280}, {4906, 10178}, {5045, 37501}, {5048, 17635}, {5082, 54305}, {5262, 20070}, {5272, 10164}, {5289, 18252}, {5297, 9779}, {5657, 37650}, {5697, 41733}, {5779, 49515}, {5886, 17245}, {6610, 8147}, {7174, 11372}, {7191, 9778}, {7957, 16466}, {7982, 12717}, {7987, 28011}, {7991, 16469}, {7996, 11224}, {9355, 49448}, {9623, 17355}, {9944, 15934}, {10167, 17597}, {10445, 30116}, {11019, 60786}, {11319, 19860}, {12512, 30148}, {12650, 50637}, {14942, 56139}, {15251, 17278}, {15726, 49465}, {16484, 54474}, {17054, 31787}, {17337, 26446}, {17595, 17613}, {17721, 37374}, {18446, 20281}, {18481, 29291}, {19861, 56782}, {20978, 49487}, {21153, 60846}, {22837, 28526}, {24046, 37560}, {24928, 42314}, {28194, 50294}, {28849, 49684}, {28850, 32941}, {29024, 41869}, {30117, 30503}, {30145, 51118}, {32850, 36652}, {36480, 45305}, {36846, 49446}, {37681, 59417}, {39148, 47645}, {49482, 54318}, {53529, 60919}, {56309, 56359}

X(61086) = midpoint of X(i) and X(j) for these {i,j}: {1, 12652}, {7982, 12717}
X(61086) = reflection of X(i) in X(j) for these {i,j}: {8, 12618}, {990, 1}
X(61086) = crossdifference of every pair of points on line {657, 9001}
X(61086) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 4312, 4327}, {40, 7290, 13329}, {390, 4318, 1}, {962, 4344, 3332}, {4296, 9785, 1}, {4347, 12575, 1}

X(61087) = X(1)X(7225)∩X(4)X(9)

Barycentrics    a*(a^5 + a^4*b - a*b^4 - b^5 + a^4*c - 6*a^3*b*c + 4*a^2*b^2*c - 2*a*b^3*c + 3*b^4*c + 4*a^2*b*c^2 - 2*a*b^2*c^2 - 2*b^3*c^2 - 2*a*b*c^3 - 2*b^2*c^3 - a*c^4 + 3*b*c^4 - c^5) : :
X(61087) = 3 X[40] - X[12717], 3 X[1766] - 2 X[12717], 3 X[5657] - 2 X[12618], 3 X[165] - X[12652]

X(61087) lies on the cubic K1361 and these lines: {1, 7225}, {3, 1279}, {4, 9}, {20, 1219}, {46, 36574}, {55, 40961}, {63, 4450}, {105, 165}, {108, 8270}, {277, 37551}, {355, 29291}, {517, 990}, {962, 12610}, {1308, 28838}, {1448, 12410}, {1697, 3663}, {1721, 7991}, {1763, 17784}, {2093, 32118}, {2263, 40910}, {2328, 4211}, {2955, 8915}, {3430, 6769}, {3434, 21370}, {3729, 4696}, {3751, 29353}, {3895, 49446}, {4202, 5250}, {4353, 31393}, {5119, 24248}, {5691, 29050}, {5853, 7289}, {9778, 50699}, {10005, 59417}, {10444, 20880}, {12702, 49515}, {12722, 36279}, {12723, 37567}, {12912, 41340}, {15487, 20344}, {15829, 35667}, {20070, 41826}, {20368, 29668}, {28194, 48803}, {28351, 59340}, {29043, 39885}, {30269, 37569}, {30272, 50528}, {34036, 37577}

X(61087) = midpoint of X(1721) and X(7991)
X(61087) = reflection of X(i) in X(j) for these {i,j}: {1, 24309}, {962, 12610}, {1766, 40}, {21629, 43174}

X(61088) = X(20)X(64)∩X(66)X(74)

Barycentrics    3*a^12 - 2*a^10*b^2 - 7*a^8*b^4 + 4*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 - b^12 - 2*a^10*c^2 + 18*a^8*b^2*c^2 - 4*a^6*b^4*c^2 - 4*a^4*b^6*c^2 - 10*a^2*b^8*c^2 + 2*b^10*c^2 - 7*a^8*c^4 - 4*a^6*b^2*c^4 - 2*a^4*b^4*c^4 + 12*a^2*b^6*c^4 + b^8*c^4 + 4*a^6*c^6 - 4*a^4*b^2*c^6 + 12*a^2*b^4*c^6 - 4*b^6*c^6 + 5*a^4*c^8 - 10*a^2*b^2*c^8 + b^4*c^8 - 2*a^2*c^10 + 2*b^2*c^10 - c^12 : :
X(61088) = 3 X[2] - 4 X[44883], 3 X[4] - 4 X[23300], X[69] - 3 X[54050], 2 X[34778] - 3 X[54050], 2 X[141] - 3 X[10606], 2 X[159] - 3 X[376], 4 X[206] - 3 X[5656], 2 X[2883] - 3 X[5085], 5 X[3091] - 8 X[15579], 5 X[3522] - 4 X[15577], 7 X[3523] - 8 X[15578], 9 X[3524] - 8 X[58437], 3 X[3543] - 4 X[18382], 3 X[32064] - 2 X[34775], 5 X[3618] - 6 X[10249], 5 X[3763] - 6 X[23328], 7 X[3832] - 8 X[20300], 3 X[5050] - X[48672], 2 X[5480] - 3 X[52028], X[5895] - 3 X[52028], 3 X[5596] - 4 X[34776], 2 X[34776] - 3 X[46264], X[6225] - 3 X[25406], 2 X[19149] - 3 X[25406], 4 X[6696] - 3 X[10516], X[18440] - 3 X[35450], 6 X[10192] - 7 X[55676], 9 X[10304] - 8 X[35228], 3 X[11179] - 2 X[34779], 3 X[14561] - 2 X[22802], 9 X[15045] - 8 X[58547], 4 X[15581] - 7 X[50693], 4 X[15585] - 5 X[55646], 4 X[16252] - 5 X[53094], 5 X[19132] - 6 X[51737], X[19588] - 3 X[34622], 4 X[34117] - X[54211], 2 X[34774] - 3 X[43273], 2 X[34782] - 3 X[59411], 3 X[41719] - 4 X[48906], 2 X[51491] - 3 X[53023]

X(61088) lies on the cubic K1361 and these lines: {2, 32125}, {3, 35219}, {4, 9914}, {6, 15311}, {20, 64}, {30, 36851}, {66, 74}, {141, 10606}, {159, 376}, {161, 59343}, {182, 5878}, {193, 2781}, {206, 5656}, {511, 20427}, {550, 39879}, {1192, 6247}, {1297, 56570}, {1352, 3357}, {1428, 12950}, {1498, 44882}, {1619, 7386}, {1853, 6995}, {2071, 28419}, {2330, 12940}, {2777, 11579}, {2883, 5085}, {3091, 15579}, {3522, 15577}, {3523, 15578}, {3524, 58437}, {3543, 18382}, {3546, 32321}, {3556, 26939}, {3580, 7500}, {3618, 10249}, {3763, 23328}, {3827, 6361}, {3832, 20300}, {4232, 10117}, {5050, 48672}, {5480, 5895}, {5596, 6000}, {5621, 6623}, {5925, 29181}, {6225, 19149}, {6241, 6776}, {6696, 10516}, {7169, 26929}, {7398, 23332}, {7494, 41602}, {8263, 18440}, {8549, 40318}, {9833, 13348}, {10192, 55676}, {10304, 35228}, {11179, 34779}, {11206, 15066}, {11459, 11821}, {11598, 14982}, {11745, 17822}, {12294, 30443}, {12412, 44441}, {13203, 31099}, {14216, 29012}, {14561, 22802}, {14853, 43599}, {15045, 58547}, {15581, 50693}, {15583, 48910}, {15585, 55646}, {16111, 38885}, {16252, 53094}, {19132, 51737}, {19161, 31978}, {19588, 34622}, {20987, 37460}, {23315, 30769}, {33582, 44248}, {34117, 54211}, {34774, 43273}, {34782, 59411}, {35481, 39874}, {35513, 37485}, {37122, 51756}, {41256, 52069}, {41719, 48906}, {43695, 57388}, {44668, 61044}, {51491, 53023}, {58258, 59363}

X(61088) = midpoint of X(i) and X(j) for these {i,j}: {6776, 12250}, {12294, 30443}, {12324, 14927}
X(61088) = reflection of X(i) in X(j) for these {i,j}: {69, 34778}, {1350, 5894}, {1352, 3357}, {1498, 44882}, {5596, 46264}, {5878, 182}, {5895, 5480}, {6225, 19149}, {9833, 48898}, {9924, 48881}, {14982, 11598}, {19161, 31978}, {34781, 36989}, {36990, 6247}, {38885, 16111}, {39879, 550}, {41735, 3}, {48910, 15583}, {51212, 8549}
X(61088) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 54050, 34778}, {5895, 52028, 5480}, {6225, 25406, 19149}

X(61089) = X(20)X(200)∩X(84)X(103)

Barycentrics    a*(a^11 - 3*a^10*b + a^9*b^2 + 5*a^8*b^3 - 6*a^7*b^4 + 2*a^6*b^5 + 2*a^5*b^6 - 6*a^4*b^7 + 5*a^3*b^8 + a^2*b^9 - 3*a*b^10 + b^11 - 3*a^10*c - a^8*b^2*c + 18*a^6*b^4*c - 18*a^4*b^6*c + a^2*b^8*c + 3*b^10*c + a^9*c^2 - a^8*b*c^2 + 4*a^7*b^2*c^2 - 20*a^6*b^3*c^2 + 22*a^5*b^4*c^2 + 10*a^4*b^5*c^2 - 28*a^3*b^6*c^2 + 12*a^2*b^7*c^2 + a*b^8*c^2 - b^9*c^2 + 5*a^8*c^3 - 20*a^6*b^2*c^3 - 48*a^5*b^3*c^3 + 14*a^4*b^4*c^3 + 32*a^3*b^5*c^3 + 12*a^2*b^6*c^3 + 16*a*b^7*c^3 - 11*b^8*c^3 - 6*a^7*c^4 + 18*a^6*b*c^4 + 22*a^5*b^2*c^4 + 14*a^4*b^3*c^4 - 18*a^3*b^4*c^4 - 26*a^2*b^5*c^4 + 2*a*b^6*c^4 - 6*b^7*c^4 + 2*a^6*c^5 + 10*a^4*b^2*c^5 + 32*a^3*b^3*c^5 - 26*a^2*b^4*c^5 - 32*a*b^5*c^5 + 14*b^6*c^5 + 2*a^5*c^6 - 18*a^4*b*c^6 - 28*a^3*b^2*c^6 + 12*a^2*b^3*c^6 + 2*a*b^4*c^6 + 14*b^5*c^6 - 6*a^4*c^7 + 12*a^2*b^2*c^7 + 16*a*b^3*c^7 - 6*b^4*c^7 + 5*a^3*c^8 + a^2*b*c^8 + a*b^2*c^8 - 11*b^3*c^8 + a^2*c^9 - b^2*c^9 - 3*a*c^10 + 3*b*c^10 + c^11) : :

X(61089) = lies on the cubic K1361 and these lines: {4, 1448}, {20, 200}, {84, 103}, {971, 1350}, {990, 42458}, {1490, 56809}, {5732, 59646}, {7291, 7992}, {17170, 54227}

X(61090) = REFLECTION OF X(61089) IN X(3)

Barycentrics    a*(a^11 - a^10*b - 3*a^9*b^2 + 3*a^8*b^3 + 2*a^7*b^4 - 2*a^6*b^5 + 2*a^5*b^6 - 2*a^4*b^7 - 3*a^3*b^8 + 3*a^2*b^9 + a*b^10 - b^11 - a^10*c + 12*a^9*b*c - 7*a^8*b^2*c - 8*a^7*b^3*c - 2*a^6*b^4*c - 16*a^5*b^5*c + 26*a^4*b^6*c + 8*a^3*b^7*c - 13*a^2*b^8*c + 4*a*b^9*c - 3*b^10*c - 3*a^9*c^2 - 7*a^8*b*c^2 + 12*a^7*b^2*c^2 + 20*a^6*b^3*c^2 - 18*a^5*b^4*c^2 - 18*a^4*b^5*c^2 + 12*a^3*b^6*c^2 + 4*a^2*b^7*c^2 - 3*a*b^8*c^2 + b^9*c^2 + 3*a^8*c^3 - 8*a^7*b*c^3 + 20*a^6*b^2*c^3 + 32*a^5*b^3*c^3 - 6*a^4*b^4*c^3 - 8*a^3*b^5*c^3 - 28*a^2*b^6*c^3 - 16*a*b^7*c^3 + 11*b^8*c^3 + 2*a^7*c^4 - 2*a^6*b*c^4 - 18*a^5*b^2*c^4 - 6*a^4*b^3*c^4 - 18*a^3*b^4*c^4 + 34*a^2*b^5*c^4 + 2*a*b^6*c^4 + 6*b^7*c^4 - 2*a^6*c^5 - 16*a^5*b*c^5 - 18*a^4*b^2*c^5 - 8*a^3*b^3*c^5 + 34*a^2*b^4*c^5 + 24*a*b^5*c^5 - 14*b^6*c^5 + 2*a^5*c^6 + 26*a^4*b*c^6 + 12*a^3*b^2*c^6 - 28*a^2*b^3*c^6 + 2*a*b^4*c^6 - 14*b^5*c^6 - 2*a^4*c^7 + 8*a^3*b*c^7 + 4*a^2*b^2*c^7 - 16*a*b^3*c^7 + 6*b^4*c^7 - 3*a^3*c^8 - 13*a^2*b*c^8 - 3*a*b^2*c^8 + 11*b^3*c^8 + 3*a^2*c^9 + 4*a*b*c^9 + b^2*c^9 + a*c^10 - 3*b*c^10 - c^11) : :

X(61090) lies on the cubicf K1361 and these lines: {3, 61089}, {4, 1435}, {6, 971}, {20, 1763}, {84, 169}, {101, 1490}, {6554, 9841}, {61087, 61088}

X(61090) = reflection of X(61089) in X(3)

X(61091) = REFLECTION OF X(42458) IN X(3)

Barycentrics    5*a^18 - 5*a^16*b^2 - 24*a^14*b^4 + 32*a^12*b^6 + 26*a^10*b^8 - 50*a^8*b^10 + 24*a^4*b^14 - 7*a^2*b^16 - b^18 - 5*a^16*c^2 + 56*a^14*b^2*c^2 - 32*a^12*b^4*c^2 - 64*a^10*b^6*c^2 - 106*a^8*b^8*c^2 + 280*a^6*b^10*c^2 - 120*a^4*b^12*c^2 - 16*a^2*b^14*c^2 + 7*b^16*c^2 - 24*a^14*c^4 - 32*a^12*b^2*c^4 + 76*a^10*b^4*c^4 + 156*a^8*b^6*c^4 - 224*a^6*b^8*c^4 - 40*a^4*b^10*c^4 + 108*a^2*b^12*c^4 - 20*b^14*c^4 + 32*a^12*c^6 - 64*a^10*b^2*c^6 + 156*a^8*b^4*c^6 - 112*a^6*b^6*c^6 + 136*a^4*b^8*c^6 - 176*a^2*b^10*c^6 + 28*b^12*c^6 + 26*a^10*c^8 - 106*a^8*b^2*c^8 - 224*a^6*b^4*c^8 + 136*a^4*b^6*c^8 + 182*a^2*b^8*c^8 - 14*b^10*c^8 - 50*a^8*c^10 + 280*a^6*b^2*c^10 - 40*a^4*b^4*c^10 - 176*a^2*b^6*c^10 - 14*b^8*c^10 - 120*a^4*b^2*c^12 + 108*a^2*b^4*c^12 + 28*b^6*c^12 + 24*a^4*c^14 - 16*a^2*b^2*c^14 - 20*b^4*c^14 - 7*a^2*c^16 + 7*b^2*c^16 - c^18 : :

X(61091) lies on the cubicf K1361 and these lines: {3, 1033}, {4, 31367}, {20, 17808}, {376, 44073}, {1297, 6353}, {1350, 15311}, {3089, 33546}, {6523, 6804}

X(61091) = reflection of X(42458) in X(3)

X(61092) = X(1)X(34216)∩X(4)X(9)

Barycentrics    a*(b*c*(2*a^3 - a^2*b - b^3 - a^2*c + b^2*c + b*c^2 - c^3) + (a^3 + a^2*b - a*b^2 - b^3 + a^2*c - 2*a*b*c + b^2*c - a*c^2 + b*c^2 - c^3)*S) : :

X(61092) lies on the cubicf K1362 and these lines: {1, 34216}, {4, 9}, {46, 52808}, {103, 31563}, {165, 16440}, {517, 9732}, {1158, 61087}, {3338, 52806}, {5119, 52805}, {8978, 35808}, {51763, 52420}

X(61092) = {X(40),X(11372)}-harmonic conjugate of X(51957)

X(61093) = X(1)X(34215)∩X(4)X(9)

Barycentrics    a*(b*c*(2*a^3 - a^2*b - b^3 - a^2*c + b^2*c + b*c^2 - c^3) - (a^3 + a^2*b - a*b^2 - b^3 + a^2*c - 2*a*b*c + b^2*c - a*c^2 + b*c^2 - c^3)*S) : :

X(61092) lies on the cubicf K1362 and these lines: {1, 34215}, {4, 9}, {46, 52805}, {103, 31564}, {165, 16441}, {517, 9733}, {1158, 61086}, {3338, 52809}, {5119, 52808}, {51764, 52419}the

X(61093) = {X(40),X(11372)}-harmonic conjugate of X(51955)

X(61094) = X(1)X(7)∩X(4)X(55497)

Barycentrics    a*((a - b - c)*(a + b - c)*(a - b + c)*(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8 - 2*a^6*b*c + 6*a^5*b^2*c + 8*a^4*b^3*c - 6*a^2*b^5*c - 6*a*b^6*c - 4*a^6*c^2 + 6*a^5*b*c^2 + 12*a^4*b^2*c^2 - 6*a*b^5*c^2 - 8*b^6*c^2 + 8*a^4*b*c^3 + 4*a^2*b^3*c^3 + 12*a*b^4*c^3 + 6*a^4*c^4 + 12*a*b^3*c^4 + 14*b^4*c^4 - 6*a^2*b*c^5 - 6*a*b^2*c^5 - 4*a^2*c^6 - 6*a*b*c^6 - 8*b^2*c^6 + c^8) + 4*(a^8*b - a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 + 3*a^4*b^5 - 3*a^3*b^6 - a^2*b^7 + a*b^8 + a^8*c - 4*a^7*b*c + a^6*b^2*c + 6*a^5*b^3*c - 3*a^4*b^4*c - a^2*b^6*c - 2*a*b^7*c + 2*b^8*c - a^7*c^2 + a^6*b*c^2 + 2*a^5*b^2*c^2 + 2*a^4*b^3*c^2 + a^3*b^4*c^2 - a^2*b^5*c^2 - 2*a*b^6*c^2 - 2*b^7*c^2 - 3*a^6*c^3 + 6*a^5*b*c^3 + 2*a^4*b^2*c^3 - 4*a^3*b^3*c^3 + 3*a^2*b^4*c^3 + 2*a*b^5*c^3 - 6*b^6*c^3 + 3*a^5*c^4 - 3*a^4*b*c^4 + a^3*b^2*c^4 + 3*a^2*b^3*c^4 + 2*a*b^4*c^4 + 6*b^5*c^4 + 3*a^4*c^5 - a^2*b^2*c^5 + 2*a*b^3*c^5 + 6*b^4*c^5 - 3*a^3*c^6 - a^2*b*c^6 - 2*a*b^2*c^6 - 6*b^3*c^6 - a^2*c^7 - 2*a*b*c^7 - 2*b^2*c^7 + a*c^8 + 2*b*c^8)*S) : :

X(61094) lies on the cubic K1362 and these lines: {1, 7}, {4, 55497}, {101, 6213}, {165, 3084}, {517, 9732}, {971, 45713}, {1699, 3083}, {1709, 55398}, {2801, 3640}, {6261, 61087}, {9778, 56427}, {9812, 56384}, {10695, 31559}, {30556, 54370}, {39531, 55425}, {41338, 55397}, {45704, 53996}

X(61094) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 31574, 31563}, {31563, 31574, 43178}, {31564, 56380, 43178}

X(61095) = X(1)X(7)∩X(4)X(55498)

Barycentrics    a*((a - b - c)*(a + b - c)*(a - b + c)*(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8 - 2*a^6*b*c + 6*a^5*b^2*c + 8*a^4*b^3*c - 6*a^2*b^5*c - 6*a*b^6*c - 4*a^6*c^2 + 6*a^5*b*c^2 + 12*a^4*b^2*c^2 - 6*a*b^5*c^2 - 8*b^6*c^2 + 8*a^4*b*c^3 + 4*a^2*b^3*c^3 + 12*a*b^4*c^3 + 6*a^4*c^4 + 12*a*b^3*c^4 + 14*b^4*c^4 - 6*a^2*b*c^5 - 6*a*b^2*c^5 - 4*a^2*c^6 - 6*a*b*c^6 - 8*b^2*c^6 + c^8) - 4*(a^8*b - a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 + 3*a^4*b^5 - 3*a^3*b^6 - a^2*b^7 + a*b^8 + a^8*c - 4*a^7*b*c + a^6*b^2*c + 6*a^5*b^3*c - 3*a^4*b^4*c - a^2*b^6*c - 2*a*b^7*c + 2*b^8*c - a^7*c^2 + a^6*b*c^2 + 2*a^5*b^2*c^2 + 2*a^4*b^3*c^2 + a^3*b^4*c^2 - a^2*b^5*c^2 - 2*a*b^6*c^2 - 2*b^7*c^2 - 3*a^6*c^3 + 6*a^5*b*c^3 + 2*a^4*b^2*c^3 - 4*a^3*b^3*c^3 + 3*a^2*b^4*c^3 + 2*a*b^5*c^3 - 6*b^6*c^3 + 3*a^5*c^4 - 3*a^4*b*c^4 + a^3*b^2*c^4 + 3*a^2*b^3*c^4 + 2*a*b^4*c^4 + 6*b^5*c^4 + 3*a^4*c^5 - a^2*b^2*c^5 + 2*a*b^3*c^5 + 6*b^4*c^5 - 3*a^3*c^6 - a^2*b*c^6 - 2*a*b^2*c^6 - 6*b^3*c^6 - a^2*c^7 - 2*a*b*c^7 - 2*b^2*c^7 + a*c^8 + 2*b*c^8)*S) : :

X(61095) lies on the cubic K1362 and these lines: {1, 7}, {4, 55498}, {101, 6212}, {165, 3083}, {517, 9733}, {971, 45714}, {1699, 3084}, {1709, 55397}, {2801, 3641}, {6261, 61086}, {9778, 56384}, {9812, 56427}, {10695, 31560}, {30557, 54370}, {39531, 55454}, {41338, 55398}

X(61095) = midpoint of X(3641) and X(60903)
X(61095) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 31573, 31564}, {31563, 56380, 43178}, {31564, 31573, 43178}

X(61096) = COMPLEMENT OF X(5870)

Barycentrics    2*a^6 - a^4*b^2 - b^6 - a^4*c^2 + b^4*c^2 + b^2*c^4 - c^6 + 2*a^2*(a^2 - b^2 - c^2)*S : :
X(61096) = 3 X[4] - X[48476], 6 X[48467] - X[48476], 3 X[376] + X[14242], 3 X[381] - 2 X[14233], 3 X[591] - 2 X[5874], 5 X[631] - X[14227], 4 X[642] - 3 X[9758], 3 X[3830] - 4 X[14235], 5 X[3843] - 4 X[14239], 2 X[6289] - 3 X[9757], 3 X[25406] - X[39887], 3 X[25406] - 2 X[48743]

X(61096) lies on the cubic K1362 and these lines: {2, 5870}, {3, 66}, {4, 371}, {5, 13748}, {6, 36714}, {20, 487}, {22, 11091}, {30, 1991}, {69, 11825}, {76, 489}, {98, 486}, {99, 490}, {147, 8294}, {154, 55890}, {182, 37342}, {230, 10845}, {372, 6776}, {376, 13835}, {381, 14233}, {382, 12313}, {427, 10132}, {488, 5921}, {492, 6278}, {511, 6314}, {516, 49625}, {524, 1160}, {542, 9739}, {590, 36656}, {591, 5874}, {631, 14227}, {639, 53015}, {640, 22718}, {642, 7710}, {1131, 45106}, {1151, 36709}, {1158, 61093}, {1161, 29181}, {1327, 14245}, {1370, 5409}, {1498, 1579}, {1505, 5477}, {1585, 1629}, {1587, 45512}, {1588, 5304}, {1589, 32064}, {1590, 11206}, {1853, 55885}, {1885, 6465}, {1899, 3156}, {2041, 33394}, {2042, 33393}, {2043, 6307}, {2044, 6306}, {2549, 3070}, {2794, 6230}, {3069, 10784}, {3071, 3767}, {3103, 6560}, {3127, 8968}, {3155, 31383}, {3311, 5480}, {3312, 8550}, {3365, 41021}, {3390, 41020}, {3529, 48477}, {3564, 9733}, {3589, 26348}, {3592, 53023}, {3618, 45551}, {3629, 11917}, {3631, 35247}, {3796, 56504}, {3818, 37343}, {3830, 14235}, {3843, 14239}, {5418, 6811}, {5420, 45510}, {5591, 36701}, {5596, 11514}, {5868, 14813}, {5869, 14814}, {6200, 21736}, {6201, 7585}, {6214, 45472}, {6221, 36711}, {6228, 35945}, {6251, 13711}, {6261, 61095}, {6279, 22699}, {6289, 9756}, {6313, 9738}, {6396, 12256}, {6418, 12007}, {6419, 14853}, {6420, 14912}, {6421, 49229}, {6423, 49228}, {6454, 49057}, {6460, 10783}, {6462, 12297}, {7374, 9540}, {7388, 10514}, {7389, 12203}, {7391, 55566}, {7583, 45440}, {7694, 45378}, {8316, 48727}, {8375, 42283}, {8414, 42265}, {8976, 45861}, {8981, 36658}, {8982, 40275}, {9754, 10847}, {9873, 42260}, {10195, 54935}, {10841, 60132}, {11090, 11442}, {11179, 45410}, {11291, 25406}, {11513, 36851}, {11645, 43144}, {12162, 12603}, {12305, 15069}, {12306, 48905}, {12314, 39899}, {12963, 53475}, {12968, 53499}, {13617, 37636}, {13665, 45862}, {13785, 45860}, {13830, 41490}, {13935, 48734}, {14244, 35830}, {14561, 45411}, {14927, 45499}, {15294, 49103}, {18382, 18457}, {18511, 45871}, {22883, 44667}, {22928, 44666}, {23275, 26331}, {31670, 45489}, {32421, 49038}, {32471, 33431}, {33370, 33430}, {34624, 35948}, {35730, 41024}, {36657, 42215}, {39646, 39661}, {39875, 45513}, {41018, 42174}, {41038, 42281}, {41039, 42280}, {42258, 53479}, {42270, 53514}, {42271, 50680}, {43118, 48906}, {43127, 50977}, {45385, 45868}, {45522, 55041}, {49028, 49318}, {54127, 54876}, {54874, 60274}, {55040, 55177}

X(61096) = midpoint of X(i) and X(j) for these {i,j}: {20, 5871}, {69, 39888}, {3529, 48477}
X(61096) = reflection of X(i) in X(j) for these {i,j}: {4, 48467}, {382, 14230}, {5870, 48466}, {6776, 48742}, {13748, 5}, {33430, 48726}, {39887, 48743}, {49326, 48906}, {61097, 3}
X(61096) = complement of X(5870)
X(61096) = anticomplement of X(48466)
X(61096) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5870, 48466}, {4, 6459, 45545}, {4, 12257, 371}, {4, 26441, 6561}, {4, 31412, 6250}, {4, 45511, 485}, {20, 487, 11824}, {485, 6561, 39660}, {490, 35947, 12124}, {1151, 36990, 36709}, {1352, 59363, 61097}, {3071, 53497, 3767}, {3311, 36712, 5480}, {3818, 43120, 37343}, {6813, 45406, 486}, {8721, 46264, 61097}, {10515, 14232, 48466}, {11291, 25406, 45552}, {25406, 39887, 48743}, {36657, 42215, 45441}

X(61097) = COMPLEMENT OF X(5871)

Barycentrics    2*a^6 - a^4*b^2 - b^6 - a^4*c^2 + b^4*c^2 + b^2*c^4 - c^6 - 2*a^2*(a^2 - b^2 - c^2)*S : :
X(61097) = 3 X[4] - X[48477], 6 X[48466] - X[48477], 3 X[376] + X[14227], 3 X[381] - 2 X[14230], 5 X[631] - X[14242], 4 X[641] - 3 X[9757], 3 X[1991] - 2 X[5875], 3 X[3830] - 4 X[14239], 5 X[3843] - 4 X[14235], 2 X[6290] - 3 X[9758], 3 X[25406] - X[39888], 3 X[25406] - 2 X[48742]

X(61097) lies on the cubic K1362 and these lines: {2, 5871}, {3, 66}, {4, 372}, {5, 13749}, {6, 36709}, {20, 488}, {22, 11090}, {30, 591}, {69, 11824}, {76, 490}, {98, 485}, {99, 489}, {147, 8293}, {154, 55885}, {182, 37343}, {230, 10846}, {371, 6776}, {376, 13712}, {381, 14230}, {382, 12314}, {427, 10133}, {487, 5921}, {491, 6281}, {511, 6318}, {516, 49624}, {524, 1161}, {542, 9738}, {615, 36655}, {631, 14242}, {639, 21737}, {640, 53015}, {641, 7710}, {1132, 45107}, {1152, 36714}, {1158, 61092}, {1160, 29181}, {1328, 14231}, {1370, 5408}, {1498, 1578}, {1504, 5477}, {1586, 1629}, {1587, 5304}, {1588, 45513}, {1589, 11206}, {1590, 32064}, {1853, 55890}, {1885, 6466}, {1899, 3155}, {1991, 5875}, {2041, 33395}, {2042, 33392}, {2043, 6302}, {2044, 6303}, {2549, 3071}, {2794, 6231}, {3068, 10783}, {3070, 3767}, {3102, 6561}, {3156, 31383}, {3311, 8550}, {3312, 5480}, {3364, 41021}, {3389, 41020}, {3529, 48476}, {3564, 9732}, {3589, 26341}, {3594, 53023}, {3618, 45550}, {3629, 11916}, {3631, 35246}, {3796, 56506}, {3818, 37342}, {3830, 14239}, {3843, 14235}, {5418, 45511}, {5420, 6813}, {5590, 36703}, {5596, 11513}, {5868, 14814}, {5869, 14813}, {6200, 12257}, {6202, 7586}, {6215, 45473}, {6229, 35944}, {6250, 13834}, {6261, 61094}, {6280, 22700}, {6290, 9756}, {6317, 9739}, {6398, 36712}, {6417, 12007}, {6419, 14912}, {6420, 14853}, {6422, 49228}, {6424, 49229}, {6453, 49056}, {6459, 10784}, {6463, 12296}, {7000, 13935}, {7388, 12203}, {7389, 10515}, {7391, 55567}, {7584, 45441}, {7694, 45377}, {8317, 48726}, {8376, 42284}, {8406, 42262}, {9540, 48735}, {9754, 10848}, {9873, 42261}, {10194, 54936}, {10842, 60132}, {11091, 11442}, {11179, 45411}, {11292, 25406}, {11514, 36851}, {11645, 43141}, {12162, 12604}, {12305, 48905}, {12306, 15069}, {12313, 39899}, {12963, 53499}, {12968, 53475}, {13616, 37636}, {13665, 45861}, {13710, 41491}, {13785, 45863}, {13951, 45860}, {13966, 36657}, {14229, 35831}, {14561, 45410}, {14927, 45498}, {15293, 49104}, {18382, 18459}, {18509, 45872}, {18510, 45870}, {22882, 44667}, {22927, 44666}, {23269, 26330}, {26441, 40274}, {31411, 53502}, {31670, 45488}, {32419, 49039}, {32470, 33430}, {33371, 33431}, {34624, 35949}, {36658, 42216}, {39646, 39660}, {39876, 45512}, {41018, 42245}, {41038, 42280}, {41039, 42281}, {42259, 53480}, {42272, 50681}, {42273, 53511}, {43119, 48906}, {43126, 50977}, {45384, 45869}, {45523, 55040}, {49029, 49317}, {54126, 54874}, {54876, 60275}, {55041, 55177}

X(61097) = midpoint of X(i) and X(j) for these {i,j}: {20, 5870}, {69, 39887}, {3529, 48476}
X(61097) = reflection of X(i) in X(j) for these {i,j}: {4, 48466}, {382, 14233}, {5871, 48467}, {6776, 48743}, {13749, 5}, {33431, 48727}, {39888, 48742}, {49325, 48906}, {61096, 3}
X(61097) = complement of X(5871)
X(61097) = anticomplement of X(48467)
X(61097) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5871, 48467}, {4, 6460, 45544}, {4, 8982, 6560}, {4, 12256, 372}, {4, 42561, 6251}, {4, 45510, 486}, {20, 488, 11825}, {486, 6560, 39661}, {489, 35946, 12123}, {1152, 36990, 36714}, {1352, 59363, 61096}, {3070, 53498, 3767}, {3312, 36711, 5480}, {3818, 43121, 37342}, {6776, 21736, 371}, {6811, 45407, 485}, {8721, 46264, 61096}, {10514, 14237, 48467}, {11292, 25406, 45553}, {25406, 39888, 48742}, {36658, 42216, 45440}

X(61098) = X(237)X(385)∩X(1691)X(9418)

Barycentrics    a^2*(a^6*b^4 - a^4*b^6 + a^6*b^2*c^2 + a^4*b^4*c^2 - a^2*b^6*c^2 - a^6*c^4 - a^4*b^2*c^4 + a^2*b^4*c^4 - b^6*c^4 - a^4*c^6 + a^2*b^2*c^6 + b^4*c^6)*(a^6*b^4 + a^4*b^6 - a^6*b^2*c^2 + a^4*b^4*c^2 - a^2*b^6*c^2 - a^6*c^4 - a^4*b^2*c^4 - a^2*b^4*c^4 - b^6*c^4 + a^4*c^6 + a^2*b^2*c^6 + b^4*c^6) : :

X(61098) lies on the cubics K789 and K1363 and these lines: {237, 385}, {1691, 9418}, {5989, 24729}, {5999, 39927}, {11174, 51510}, {32540, 46319}, {51928, 51931}

X(61098) = isogonal conjugate of X(25332)
X(61098) = isogonal conjugate of the anticomplement of X(694)
X(61098) = isogonal conjugate of the isotomic conjugate of X(41520)
X(61098) = X(i)-isoconjugate of X(j) for these (i,j): {1, 25332}, {75, 3511}, {1959, 39941}, {1966, 39092}, {46238, 51327}
X(61098) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 25332}, {206, 3511}, {9467, 39092}
X(61098) = barycentric product X(i)*X(j) for these {i,j}: {6, 41520}, {98, 52009}
X(61098) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 25332}, {32, 3511}, {1976, 39941}, {9468, 39092}, {14601, 51327}, {41520, 76}, {52009, 325}

X(61099) = X(3)X(39092)∩X(25)X(32542)

Barycentrics    a^2*(a^8*b^4 - 2*a^6*b^6 + a^4*b^8 + a^8*b^2*c^2 - a^6*b^4*c^2 - a^4*b^6*c^2 + a^2*b^8*c^2 - a^8*c^4 - a^6*b^2*c^4 - a^4*b^4*c^4 - a^2*b^6*c^4 - b^8*c^4 + 2*a^6*c^6 + 3*a^4*b^2*c^6 + 3*a^2*b^4*c^6 + 2*b^6*c^6 - a^4*c^8 - 3*a^2*b^2*c^8 - b^4*c^8)*(a^8*b^4 - 2*a^6*b^6 + a^4*b^8 - a^8*b^2*c^2 + a^6*b^4*c^2 - 3*a^4*b^6*c^2 + 3*a^2*b^8*c^2 - a^8*c^4 + a^6*b^2*c^4 + a^4*b^4*c^4 - 3*a^2*b^6*c^4 + b^8*c^4 + 2*a^6*c^6 + a^4*b^2*c^6 + a^2*b^4*c^6 - 2*b^6*c^6 - a^4*c^8 - a^2*b^2*c^8 + b^4*c^8) : :

X(61099) lies on the cubic K1363 and these lines: {3, 39092}, {25, 32542}, {237, 46272}, {401, 12215}, {458, 14382}, {1316, 60497}, {1691, 58311}, {1971, 3511}, {34396, 51327}

X(61099) = isogonal conjugate of X(39355)
X(61099) = isogonal conjugate of the anticomplement of X(290)
X(61099) = isogonal conjugate of the isotomic conjugate of X(46271)
X(61099) = X(i)-isoconjugate of X(j) for these (i,j): {1, 39355}, {2, 39342}, {75, 46272}, {1755, 39058}
X(61099) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 39355}, {206, 46272}, {32664, 39342}, {36899, 39058}
X(61099) = cevapoint of X(512) and X(47418)
X(61099) = barycentric product X(6)*X(46271)
X(61099) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 39355}, {31, 39342}, {32, 46272}, {98, 39058}, {46271, 76}

X(61100) = X(6)X(1987)∩X(25)X(98)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^12*b^4 - 4*a^10*b^6 + 6*a^8*b^8 - 4*a^6*b^10 + a^4*b^12 + a^12*b^2*c^2 - 3*a^10*b^4*c^2 + 2*a^8*b^6*c^2 + 2*a^6*b^8*c^2 - 3*a^4*b^10*c^2 + a^2*b^12*c^2 + a^12*c^4 - 3*a^10*b^2*c^4 + 3*a^8*b^4*c^4 - 2*a^6*b^6*c^4 + a^4*b^8*c^4 + a^2*b^10*c^4 - b^12*c^4 - 4*a^10*c^6 + 2*a^8*b^2*c^6 - 2*a^6*b^4*c^6 + 2*a^4*b^6*c^6 - 2*a^2*b^8*c^6 + 4*b^10*c^6 + 6*a^8*c^8 + 2*a^6*b^2*c^8 + a^4*b^4*c^8 - 2*a^2*b^6*c^8 - 6*b^8*c^8 - 4*a^6*c^10 - 3*a^4*b^2*c^10 + a^2*b^4*c^10 + 4*b^6*c^10 + a^4*c^12 + a^2*b^2*c^12 - b^4*c^12) : :

X(61100) lies on the cubic K1363 and these lines: {6, 1987}, {25, 98}, {237, 41204}, {1033, 52277}, {1691, 58311}, {3162, 20885}, {5667, 35236}, {19189, 54091}, {37918, 39081}

X(61100) = polar conjugate of the isotomic conjugate of X(57012)
X(61100) = X(i)-Ceva conjugate of X(j) for these (i,j): {237, 25}, {41204, 6}
X(61100) = X(16081)-Dao conjugate of X(18024)
X(61100) = barycentric product X(4)*X(57012)
X(61100) = barycentric quotient X(57012)/X(69)

X(61101) = X(2)X(51427)∩X(66)X(69)

Barycentrics    a^2*(a^4*b^4 - a^2*b^6 + a^4*b^2*c^2 - a^2*b^4*c^2 + a^4*c^4 - a^2*b^2*c^4 + b^4*c^4 - a^2*c^6) : :
X(61101) = 3 X[2] - 4 X[51427], 3 X[2979] - 4 X[51439], 4 X[230] - 3 X[46303], 4 X[325] - 3 X[33873], 2 X[385] - 3 X[11673], 6 X[6786] - 5 X[7925], 5 X[7925] - 3 X[13207], 3 X[7799] - 2 X[14962]

X(61101) lies on these lines: {2, 51427}, {20, 32547}, {22, 56923}, {66, 69}, {99, 2387}, {110, 1971}, {147, 511}, {148, 5167}, {211, 7760}, {230, 46303}, {237, 36214}, {325, 33873}, {384, 4173}, {385, 11673}, {577, 2001}, {670, 18901}, {694, 32748}, {924, 11450}, {1993, 20794}, {2421, 60514}, {2782, 11674}, {2871, 51440}, {3044, 19627}, {3060, 7774}, {3221, 9493}, {3491, 6655}, {3852, 32529}, {5012, 20775}, {5640, 7736}, {5969, 49122}, {6786, 7925}, {7783, 40951}, {7796, 41262}, {7799, 14962}, {7839, 27374}, {7858, 27375}, {7998, 16990}, {8569, 56978}, {9292, 33244}, {10997, 17970}, {14907, 35704}, {14917, 39836}, {15589, 34095}, {18322, 51872}, {25332, 35524}, {33755, 39097}

X(61101) = reflection of X(i) in X(j) for these {i,j}: {148, 5167}, {13207, 6786}, {18322, 51872}

X(61102) = X(4)X(6)∩X(98)X(187)

Barycentrics    a^8 + 2*a^6*b^2 - a^4*b^4 - 2*a^2*b^6 + 2*a^6*c^2 - 3*a^4*b^2*c^2 + 2*a^2*b^4*c^2 - 3*b^6*c^2 - a^4*c^4 + 2*a^2*b^2*c^4 + 6*b^4*c^4 - 2*a^2*c^6 - 3*b^2*c^6 : :
X(61102) = 3 X[4] - 4 X[53419], 3 X[385] - 2 X[9301], X[9301] - 3 X[12188], 3 X[11177] - X[14712], 3 X[12243] - X[43453], 3 X[12243] - 2 X[47286], 3 X[98] - 2 X[187], 4 X[98] - 3 X[21445], 4 X[187] - 3 X[11676], 8 X[187] - 9 X[21445], 2 X[11676] - 3 X[21445], 4 X[625] - 3 X[6054], 2 X[1513] - 3 X[14651], 3 X[1513] - 4 X[43291], 9 X[14651] - 8 X[43291], 3 X[38294] - 4 X[48540], 3 X[5999] - 2 X[35002], 9 X[3524] - 8 X[32459], 3 X[13207] - 2 X[18322], 2 X[6033] - 3 X[14041], 5 X[7925] - 4 X[51872], 3 X[10753] - 4 X[44496], 4 X[11623] - 3 X[38227], 4 X[12042] - 3 X[13586], 2 X[15301] - 3 X[18860], 4 X[15301] - 3 X[23235], 9 X[23234] - 10 X[31275], 3 X[44375] - 4 X[49006], 2 X[47294] - 3 X[54995]

X(61101) lies on these lines: {2, 54678}, {3, 17128}, {4, 6}, {5, 7923}, {23, 53346}, {30, 148}, {74, 290}, {76, 3098}, {83, 50664}, {98, 187}, {99, 58849}, {115, 39095}, {147, 15980}, {182, 60855}, {183, 376}, {186, 60514}, {316, 542}, {323, 14957}, {338, 12367}, {381, 3329}, {384, 14880}, {401, 5191}, {419, 1495}, {420, 47296}, {458, 26864}, {511, 38664}, {574, 11257}, {598, 54903}, {625, 6054}, {671, 11645}, {690, 52076}, {842, 53875}, {1513, 14651}, {2080, 33689}, {2393, 38294}, {2549, 55008}, {2782, 5999}, {3406, 5033}, {3426, 19222}, {3511, 47620}, {3524, 15271}, {3543, 7766}, {3545, 11174}, {3818, 7790}, {3853, 13111}, {5008, 12110}, {5024, 7709}, {5092, 6248}, {5201, 37946}, {5309, 9993}, {5485, 8667}, {5585, 8719}, {5663, 13207}, {5938, 37930}, {6033, 14041}, {6200, 33371}, {6396, 33370}, {6656, 18358}, {7422, 36822}, {7464, 9149}, {7550, 41328}, {7697, 37455}, {7748, 9873}, {7754, 44456}, {7757, 58851}, {7760, 55716}, {7770, 12017}, {7797, 44230}, {7827, 19130}, {7839, 14881}, {7841, 18440}, {7878, 55712}, {7883, 43150}, {7918, 10356}, {7924, 9996}, {7925, 51872}, {7937, 11178}, {8177, 34505}, {8370, 48906}, {8556, 19708}, {8721, 37446}, {9418, 14157}, {9744, 31415}, {9755, 10788}, {9756, 53095}, {9821, 17129}, {9855, 10810}, {10151, 44090}, {10358, 55710}, {10359, 55705}, {10630, 48983}, {10753, 44496}, {11054, 19924}, {11170, 60115}, {11185, 46264}, {11464, 37124}, {11623, 38227}, {11648, 14458}, {12042, 13586}, {12215, 39266}, {12251, 33878}, {13168, 13492}, {13172, 54996}, {14483, 42299}, {14492, 39593}, {14614, 15682}, {14915, 46303}, {15066, 37190}, {15107, 51481}, {15301, 18860}, {15428, 58883}, {17131, 33706}, {17702, 46298}, {18546, 55177}, {23004, 41022}, {23005, 41023}, {23234, 31275}, {25051, 41617}, {32224, 34150}, {34417, 40814}, {35265, 46512}, {35377, 38734}, {36998, 43618}, {37925, 51862}, {43619, 59363}, {44375, 49006}, {47281, 56021}, {47294, 54995}, {51869, 52279}, {54482, 54869}, {54567, 60189}, {54584, 54713}, {54659, 54723}, {54664, 54685}, {54715, 54718}, {54716, 54904}, {54826, 54856}, {54858, 60633}, {60140, 60176}

X(61102) = reflection of X(i) in X(j) for these {i,j}: {99, 58849}, {147, 15980}, {385, 12188}, {2080, 51523}, {9855, 14830}, {11676, 98}, {13172, 54996}, {23235, 18860}, {43453, 47286}, {43460, 115}
X(61102) = crossdifference of every pair of points on line {520, 10567}
X(61102) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 41377, 41204}, {98, 11676, 21445}, {1495, 41254, 419}, {6776, 46034, 4}, {12243, 43453, 47286}, {39266, 53765, 12215}



leftri  Orthoptic or director circles: X(61103) - X(61138)  rightri

This preamble and centers X(61103)-X(61138) were contributed by César Eliud Lozada, January 11, 2024.

Let 𝒞 be a conic and let ℒ be the locus of points from which the tangent lines to 𝒞 are perpendicular. ℒ is, in general, a circle centered at the center of 𝒞 and named the orthoptic or director circle of 𝒞.

If 𝒞 is a parabola then ℒ degenerates to the directrix of 𝒞, and, if 𝒞 is a rectangular hyperbola, ℒ degenerates to the center of 𝒞.

When 𝒞 is an ellipse with semiaxes 𝒶 and 𝒷 then its orthoptic circle has squared-radius ρ2 = 𝒶2 + 𝒷2. This means that, if 𝒞 is a circle with radius 𝓇, then its orthoptic circle has squared-radius ρ2 = 2*𝓇2.

Finally, if 𝒞 is an hyperbola with semiaxes 𝒶 (focal) and 𝒷 then its orthoptic circle has squared-radius ρ2 = 𝒶2 - 𝒷2. Therefore, the orthoptic circle exists only when 𝒶 ≥ 𝒷.

In S.L. Loney, The Elements of Coordinate Geometry, 1962, pp 365, #390, a general expression is deduced for calculating the equation of the director or orthoptic circle of a conic (in cartesian coordinates). Such expression, when applied to the conic given in barycentric as 𝒞 = ∑(FA*x^2 + 2*GA*y*z) = 0, leads to the following equation for the squared-radius of the orthoptic circle:

  ρ^2 = (∑(FA*GA^2)-FA*FB*FC-2*GA*GB*GC)*∑((FB+FC-2*GA)*SA)/∑(FB*FC-2*FA*GA-GA^2+2*GB*GC)^2   (all sums are cyclic)

underbar

X(61103) = PERSPECTOR OF THE ORTHOPTIC CIRCLE OF BROCARD INELLIPSE

Barycentrics    a^2*((3*b^2+c^2)*a^6-(9*b^4+7*b^2*c^2+2*c^4)*a^4+(7*b^6+c^6-b^2*c^2*(11*b^2+7*c^2))*a^2-(b^2-c^2)*(b^4-6*b^2*c^2+3*c^4)*b^2)*((b^2+3*c^2)*a^6-(2*b^4+7*b^2*c^2+9*c^4)*a^4+(b^6+7*c^6-b^2*c^2*(7*b^2+11*c^2))*a^2+(b^2-c^2)*c^2*(3*b^4-6*b^2*c^2+c^4)) : :

This orthoptic circle has center X(39) and squared-radius ρ^2 = R^2*S^2*(5*S^2+SW^2)/(S^2+SW^2)^2.

X(61103) lies on these lines: {}

X(61103) = isogonal conjugate of X(61104)

X(61104) = ISOGONAL CONJUGATE OF X(61103)

Barycentrics    a^8-7*(b^2+c^2)*a^6+(9*b^4+11*b^2*c^2+9*c^4)*a^4-(b^2-3*c^2)*(3*b^2-c^2)*(b^2+c^2)*a^2-(b^2-c^2)^2*b^2*c^2 : :

X(61104) lies on these lines: {3, 83}, {4, 15482}, {98, 7824}, {99, 140}, {114, 33021}, {182, 33004}, {549, 7827}, {574, 631}, {1078, 11171}, {1352, 33258}, {2080, 55085}, {2996, 10303}, {3098, 15717}, {3398, 43459}, {3522, 58851}, {3523, 9737}, {3524, 30270}, {3525, 3734}, {3530, 35002}, {3934, 15483}, {5013, 22712}, {5206, 10359}, {6054, 8359}, {6337, 60212}, {6683, 11676}, {7709, 7815}, {7783, 15819}, {7791, 43461}, {7833, 11155}, {7847, 14639}, {7859, 37459}, {7944, 15561}, {9744, 32990}, {10983, 33706}, {11257, 11285}, {12054, 34473}, {12251, 52770}, {13335, 33273}, {15515, 35925}, {15815, 44530}, {21163, 37334}, {21166, 37512}, {32516, 38664}, {32830, 40925}, {33215, 36998}, {33225, 58445}, {36997, 57633}, {46941, 47352}

X(61104) = isogonal conjugate of X(61103)
X(61104) = pole of the line {5038, 39884} with respect to the Evans conic
X(61104) = pole of the line {14096, 61103} with respect to the Stammler hyperbola
X(61104) = pole of the line {14994, 61103} with respect to the Steiner-Wallace hyperbola
X(61104) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (3, 7786, 12110), (3, 40108, 83), (1078, 11171, 32467), (7824, 13334, 98), (11285, 52771, 11257), (52770, 53096, 12251)

X(61105) = PERSPECTOR OF THE ORTHOPTIC CIRCLE OF DE LONGCHAMPS ELLIPSE

Barycentrics    (a^5+(b-c)*a^4-(2*b^2+b*c+2*c^2)*a^3-2*(b-c)*(b^2+c^2)*a^2+(b^2-c^2)*(b^2-b*c-c^2)*a+(b^2-c^2)^2*(b-c))*(a^5-(b-c)*a^4-(2*b^2+b*c+2*c^2)*a^3+2*(b-c)*(b^2+c^2)*a^2+(b^2-c^2)*(b^2+b*c-c^2)*a-(b^2-c^2)^2*(b-c)) : :

This orthoptic circle has center X(1) and squared-radius ρ^2 = r*(2*r+R)/2.

X(61105) lies on the Feuerbach hyperbola and these lines: {8, 6901}, {21, 5901}, {79, 12005}, {80, 31870}, {943, 37564}, {946, 3065}, {1389, 37734}, {1484, 6595}, {2320, 10595}, {5603, 15446}, {6583, 11604}, {6597, 23015}, {6881, 32635}, {10266, 16159}, {17097, 18990}, {26842, 37621}

X(61105) = isogonal conjugate of X(37621)
X(61105) = antigonal conjugate of the isogonal conjugate of X(41347)

X(61106) = ISOGONAL CONJUGATE OF X(61107)

Barycentrics    a^2*(a-b)^2*(a-c)^2*(a^4-4*b*c*a^2-(b-c)^4) : :

X(61106) lies on these lines: {3, 1252}, {56, 6066}, {59, 5126}, {631, 4998}, {692, 2742}, {952, 38310}, {953, 38599}, {3523, 43986}, {5375, 8760}, {6951, 31633}

X(61106) = isogonal conjugate of X(61107)
X(61106) = X(26866)-reciprocal conjugate of-X(1086)
X(61106) = pole of the line {46537, 61107} with respect to the Stammler hyperbola
X(61106) = barycentric product X(1016)*X(26866)
X(61106) = trilinear product X(765)*X(26866)
X(61106) = trilinear quotient X(26866)/X(244)

X(61107) = PERSPECTOR OF THE ORTHOPTIC CIRCLE OF THE DUAL OF YFF PARABOLA

Barycentrics    (b-c)^2*(a^4-4*b*a^3+6*b^2*a^2-4*(b^2-c^2)*b*a+b^4-c^4)*(a^4-4*c*a^3+6*c^2*a^2+4*(b^2-c^2)*c*a-b^4+c^4) : :

This orthoptic circle has center X(1086) and squared-radius ρ^2 = 4*(b-c)^2*(c-a)^2*(a-b)^2/(S^2-12*(4*R+r)*r^3)^2*r^4.

X(61107) lies on these lines: {}

X(61107) = isogonal conjugate of X(61106)
X(61107) = X(513)-Dao conjugate of-X(26866)
X(61107) = X(765)-isoconjugate of-X(26866)
X(61107) = X(1015)-reciprocal conjugate of-X(26866)
X(61107) = trilinear quotient X(244)/X(26866)

X(61108) = PERSPECTOR OF THE ORTHOPTIC CIRCLE OF THE EXCENTRAL-HEXYL ELLIPSE

Barycentrics    a*(b*a^5-2*(b+c)*c*a^4-2*(b^3+c^3+b*c*(b+2*c))*a^3-2*(b+c)*(b^2+b*c-c^2)*c*a^2+(b^2-c^2)*(b^3-2*c^3-b*c*(2*b+3*c))*a-2*(b^2-c^2)*(b+c)*b*c^2)*(c*a^5-2*(b+c)*b*a^4-2*(b^3+c^3+b*c*(2*b+c))*a^3+2*(b+c)*(b^2-b*c-c^2)*b*a^2+(b^2-c^2)*(2*b^3-c^3+b*c*(3*b+2*c))*a+2*(b^2-c^2)*(b+c)*b^2*c) : :

This orthoptic circle has center X(3) and squared-radius ρ^2 = R*(4*r^3*(2*R+r)+S^2)/(8*r^3).

X(61108) lies on the Jerabek hyperbola and these lines: {65, 5307}, {71, 958}, {72, 5788}, {73, 940}, {333, 34259}, {1245, 5706}

X(61108) = isogonal conjugate of X(61109)
X(61108) = trilinear pole of the line {647, 17418} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line

X(61109) = ISOGONAL CONJUGATE OF X(61108)

Barycentrics    a*(2*(b+c)*a^5+(2*b^2+3*b*c+2*c^2)*a^4-2*(b^3+c^3)*a^3-2*(b^2+c^2)*(b+c)^2*a^2-2*(b+c)*(b^2+c^2)*b*c*a+(b^2-c^2)^2*b*c) : :

X(61109) lies on these lines: {1, 573}, {2, 3}, {8, 228}, {10, 10434}, {40, 968}, {41, 5247}, {42, 9548}, {56, 5712}, {60, 5320}, {198, 958}, {208, 54320}, {386, 10470}, {387, 19763}, {388, 16678}, {515, 31339}, {572, 1724}, {580, 44119}, {581, 1193}, {943, 37547}, {962, 31394}, {970, 19767}, {978, 7987}, {991, 48883}, {993, 57281}, {1104, 2277}, {1125, 10478}, {1385, 5752}, {1426, 17080}, {1452, 10319}, {1478, 39578}, {1698, 61124}, {1766, 54287}, {1834, 19760}, {2223, 4339}, {2352, 5716}, {2550, 23381}, {2551, 52139}, {2975, 5739}, {3085, 60086}, {3189, 15624}, {3616, 37620}, {3720, 10476}, {3831, 10164}, {3869, 42700}, {4267, 37642}, {4276, 5292}, {4297, 48888}, {4300, 6210}, {5230, 10902}, {5235, 5788}, {5251, 5816}, {5285, 54430}, {5312, 10440}, {5657, 17751}, {5706, 19734}, {5713, 11012}, {5744, 22345}, {5751, 27624}, {5755, 51223}, {5786, 19732}, {6176, 10441}, {7967, 20040}, {8273, 28265}, {8726, 28274}, {8760, 27648}, {10857, 28272}, {10884, 28287}, {15931, 35206}, {17502, 27625}, {19765, 45897}, {20760, 54398}, {22097, 37523}, {23361, 30478}, {24248, 30362}, {27644, 37474}, {28266, 44103}, {29814, 35631}, {32613, 54355}, {34281, 37469}, {37558, 56549}, {48875, 48909}, {48878, 48923}, {48882, 50317}, {48886, 48894}, {48908, 48936}, {48929, 48939}

X(61109) = isogonal conjugate of X(61108)
X(61109) = cross-difference of every pair of points on the line X(647)X(17418)
X(61109) = pole of the line {5214, 6005} with respect to the Conway circle
X(61109) = pole of the line {6005, 44409} with respect to the incircle
X(61109) = pole of the line {1858, 37593} with respect to the Feuerbach circumhyperbola
X(61109) = pole of the line {185, 37400} with respect to the Jerabek circumhyperbola
X(61109) = pole of the line {3, 61108} with respect to the Stammler hyperbola
X(61109) = pole of the line {69, 61108} with respect to the Steiner-Wallace hyperbola
X(61109) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (3, 9840, 20), (3, 13731, 2), (3, 19544, 411), (6176, 35203, 10441), (10470, 21363, 386), (13726, 19256, 405), (13731, 14636, 3), (13738, 37225, 2), (37314, 37419, 4)

X(61110) = PERSPECTOR OF THE ORTHOPTIC CIRCLE OF THE JOHNSON CIRCUMCONIC

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*((b^2+c^2)*a^2-(b^2-c^2)^2)*(3*a^4-2*(3*b^2+c^2)*a^2+(b^2-c^2)*(3*b^2+c^2))*(3*a^4-2*(b^2+3*c^2)*a^2-(b^2+3*c^2)*(b^2-c^2)) : :

This orthoptic circle has center X(5) and squared-radius ρ^2 = (S^2+SB*SC)*(S^2+SC*SA)*(S^2+SA*SB)/(16*SA*SB*SC*S^2).

X(61110) lies on these lines: {4, 154}, {5, 8799}, {53, 3574}, {235, 3613}, {275, 41362}, {327, 54412}, {403, 16837}, {1141, 4994}, {1321, 1322}, {1487, 14111}, {1568, 27356}, {1595, 43917}, {1596, 61133}, {1869, 51870}, {1907, 17703}, {3091, 8797}, {5480, 14249}, {6526, 52518}, {7559, 51500}, {7563, 60032}, {10412, 46371}, {13450, 45089}, {14860, 27377}, {14978, 56272}, {15619, 35717}, {22261, 23047}, {27364, 39530}

X(61110) = midpoint of X(4) and X(45062)
X(61110) = polar conjugate of X(19188)
X(61110) = isogonal conjugate of X(61111)
X(61110) = cevapoint of X(5) and X(31802)
X(61110) = crosssum of X(578) and X(17821)
X(61110) = X(6755)-cross conjugate of-X(53)
X(61110) = X(i)-Dao conjugate of-X(j) for these (i, j): (1249, 19188), (6523, 19169), (14363, 3091)
X(61110) = X(i)-isoconjugate of-X(j) for these {i, j}: {48, 19188}, {255, 19169}, {2169, 3091}, {26880, 40440}
X(61110) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (4, 19188), (53, 3091), (217, 26880), (393, 19169), (3199, 17810), (14528, 97), (31504, 394), (56346, 95)
X(61110) = pole of the the tripolar of X(19188) with respect to the polar circle
X(61110) = pole of the line {3087, 19467} with respect to the Kiepert circumhyperbola
X(61110) = barycentric product X(i)*X(j) for these {i, j}: {5, 56346}, {324, 14528}, {2052, 31504}
X(61110) = trilinear product X(i)*X(j) for these {i, j}: {158, 31504}, {1953, 56346}
X(61110) = trilinear quotient X(i)/X(j) for these (i, j): (92, 19188), (158, 19169), (2181, 17810), (14528, 2169), (31504, 255), (56346, 2167)

X(61111) = ISOGONAL CONJUGATE OF X(61110)

Barycentrics    a^2*(-a^2+b^2+c^2)*(a^4+2*(b^2+c^2)*a^2-3*(b^2-c^2)^2)*(a^4-(2*b^2+c^2)*a^2+(b^2-c^2)*b^2)*(a^4-(b^2+2*c^2)*a^2-(b^2-c^2)*c^2) : :

X(61111) lies on these lines: {2, 8884}, {3, 54}, {4, 4993}, {5, 58785}, {20, 275}, {22, 51887}, {30, 4994}, {95, 253}, {96, 34853}, {140, 19176}, {182, 26902}, {216, 7488}, {276, 5481}, {417, 43975}, {418, 13434}, {569, 26876}, {578, 26874}, {631, 19179}, {1578, 16034}, {1579, 16029}, {1589, 16037}, {1590, 16032}, {2055, 39243}, {2072, 19651}, {3091, 19169}, {3522, 43768}, {3785, 34386}, {6815, 19174}, {6823, 8901}, {7503, 19172}, {9729, 21638}, {9792, 15043}, {10282, 54375}, {12012, 37846}, {13160, 23295}, {14118, 19192}, {14533, 36751}, {15035, 19193}, {15055, 19208}, {15072, 19206}, {15717, 59183}, {17928, 19189}, {18475, 20574}, {18925, 57875}, {19177, 34007}, {19185, 22467}, {19205, 38323}, {19212, 20792}, {19357, 37068}, {21166, 39814}, {26887, 26897}, {32391, 56308}, {34473, 39843}, {36748, 58755}, {37126, 46832}, {40319, 51444}

X(61111) = isogonal conjugate of X(61110)
X(61111) = cevapoint of X(578) and X(17821)
X(61111) = crosssum of X(5) and X(31802)
X(61111) = X(i)-Dao conjugate of-X(j) for these (i, j): (1147, 31504), (33537, 5)
X(61111) = X(i)-isoconjugate of-X(j) for these {i, j}: {158, 31504}, {1953, 56346}
X(61111) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (54, 56346), (577, 31504), (3091, 324), (14533, 14528), (17810, 53), (19169, 2052), (19188, 264), (26880, 216), (33578, 3199)
X(61111) = pole of the line {97, 13367} with respect to the Jerabek circumhyperbola
X(61111) = pole of the line {5, 8799} with respect to the Stammler hyperbola
X(61111) = pole of the line {311, 61110} with respect to the Steiner-Wallace hyperbola
X(61111) = barycentric product X(i)*X(j) for these {i, j}: {3, 19188}, {97, 3091}, {276, 26880}, {394, 19169}, {17810, 34386}
X(61111) = trilinear product X(i)*X(j) for these {i, j}: {48, 19188}, {255, 19169}, {2169, 3091}, {26880, 40440}
X(61111) = trilinear quotient X(i)/X(j) for these (i, j): (255, 31504), (2167, 56346), (2169, 14528), (17810, 2181), (19169, 158), (19188, 92)
X(61111) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (3, 54, 97), (3, 42441, 7691), (10610, 58468, 3), (19169, 19188, 3091)

X(61112) = PERSPECTOR OF THE ORTHOPTIC CIRCLE OF THE MACBEATH CIRCUMCONIC

Barycentrics    a^2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^8+2*(b^2-2*c^2)*a^6-2*(b^2-c^2)*(2*b^2+3*c^2)*a^4-2*(b^6+2*c^6-b^2*c^2*(12*b^2-c^2))*a^2+(b^4-c^4)*(b^2-c^2)*(3*b^2+c^2))*(a^8-2*(2*b^2-c^2)*a^6+2*(b^2-c^2)*(3*b^2+2*c^2)*a^4-2*(2*b^6+c^6+b^2*c^2*(b^2-12*c^2))*a^2+(b^4-c^4)*(b^2-c^2)*(b^2+3*c^2)) : :

This orthoptic circle has center X(6) and squared-radius ρ^2 = 2*R^2*S^4*(6*R^2-SW)/(SA*SB*SC*SW^2).

X(61112) lies on the Jerabek hyperbola and these lines: {4, 17818}, {64, 45045}, {68, 11472}, {1596, 4846}, {1597, 6391}, {3089, 15740}, {9786, 43695}, {10605, 35512}, {11744, 17810}, {16657, 18910}, {37497, 57648}

X(61112) = isogonal conjugate of X(61113)

X(61113) = ISOGONAL CONJUGATE OF X(61112)

Barycentrics    (-a^2+b^2+c^2)*(3*a^8-2*(b^2+c^2)*a^6-4*((b^2-c^2)^2-4*b^2*c^2)*a^4+2*(b^4-c^4)*(b^2-c^2)*a^2+(b^2-c^2)^4) : :
X(61113) = 2*X(3)-X(7386) = 3*X(3)-X(18536) = X(4)-2*X(5020) = X(11433)-2*X(37475)

X(61113) lies on these lines: {2, 3}, {69, 10605}, {74, 3620}, {99, 40680}, {141, 10606}, {193, 5890}, {343, 18931}, {390, 1060}, {1038, 4294}, {1040, 4293}, {1062, 3600}, {1181, 15740}, {1285, 15905}, {1578, 6459}, {1579, 6460}, {2996, 15261}, {4549, 40911}, {5622, 16163}, {5656, 9306}, {5667, 38553}, {5907, 12250}, {6000, 14826}, {6193, 40647}, {6225, 17814}, {6361, 37613}, {6391, 48906}, {6515, 54040}, {6776, 8681}, {9541, 11513}, {9862, 40948}, {9967, 61044}, {10249, 15583}, {10516, 58762}, {10897, 43512}, {10898, 43511}, {11427, 37497}, {11431, 15012}, {11433, 37475}, {11469, 15058}, {11511, 54132}, {11574, 36987}, {11793, 20427}, {12244, 13416}, {12358, 54037}, {12827, 15055}, {14482, 15851}, {14615, 14907}, {14683, 44573}, {14913, 46264}, {14961, 37665}, {15033, 51171}, {15305, 54013}, {15311, 17811}, {15941, 17784}, {16657, 18928}, {18850, 52147}, {19357, 53050}, {21663, 43653}, {25406, 41614}, {31884, 54347}, {32817, 41005}, {33884, 45118}, {34781, 46850}, {36751, 53420}, {43670, 60130}, {45816, 48880}, {51347, 60618}

X(61113) = midpoint of X(20) and X(6995)
X(61113) = reflection of X(i) in X(j) for these (i, j): (4, 5020), (7386, 3), (11433, 37475)
X(61113) = anticomplement of X(18537)
X(61113) = isogonal conjugate of X(61112)
X(61113) = X(18537)-Dao conjugate of-X(18537)
X(61113) = pole of the line {3, 61112} with respect to the Stammler hyperbola
X(61113) = pole of the line {69, 61112} with respect to the Steiner-Wallace hyperbola
X(61113) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (3, 31829, 4), (3, 44241, 376), (376, 3537, 3), (376, 18533, 20), (403, 631, 2), (550, 31305, 20), (26906, 27089, 3), (31304, 50693, 20)

X(61114) = PERSPECTOR OF THE ORTHOPTIC CIRCLE OF THE MANDART INELLIPSE

Barycentrics    (a^8-(2*b+3*c)*a^7-2*(b^2-b*c-c^2)*a^6+(6*b^3+3*c^3+b*c*(5*b-2*c))*a^5-2*(b^3+3*c^3+b*c*(5*b-c))*c*a^4-(b^2-c^2)*(6*b^3+3*c^3+b*c*(b+2*c))*a^3+2*(b^2-c^2)*(b^4-c^4-b*c*(b^2-4*b*c-c^2))*a^2+(b^2-c^2)^2*(b-c)*(2*b^2+b*c+3*c^2)*a-(b^2-c^2)^3*(b-c)^2)*(a^8-(3*b+2*c)*a^7+2*(b^2+b*c-c^2)*a^6+(3*b^3+6*c^3-b*c*(2*b-5*c))*a^5-2*(3*b^3+c^3-b*c*(b-5*c))*b*a^4+(b^2-c^2)*(3*b^3+6*c^3+b*c*(2*b+c))*a^3+2*(b^2-c^2)*(b^4-c^4-b*c*(b^2+4*b*c-c^2))*a^2-(b^2-c^2)^2*(b-c)*(3*b^2+b*c+2*c^2)*a+(b^2-c^2)^3*(b-c)^2) : :

This orthoptic circle has center X(9) and squared-radius ρ^2 = S^2*(2*R^2-2*R*r-r^2)/(2*r^2*(4*R+r)^2).

X(61114) lies on the Feuerbach hyperbola and these lines: {1864, 46435}

X(61114) = isogonal conjugate of X(61115)

X(61115) = ISOGONAL CONJUGATE OF X(61114)

Barycentrics    a^2*(a^8-2*(b+c)*a^7-(2*b^2-b*c+2*c^2)*a^6+2*(b+c)*(3*b^2-2*b*c+3*c^2)*a^5+(b^2-6*b*c+c^2)*b*c*a^4-2*(b+c)*(b^2+c^2)*(3*b^2-4*b*c+3*c^2)*a^3+(2*b^6+2*c^6-(5*b^4+5*c^4-2*b*c*(5*b^2+b*c+5*c^2))*b*c)*a^2+2*(b^4-c^4)*(b^2+c^2)*(b-c)*a-(b^2-c^2)*(b-c)^3*(b^3+c^3)) : :

X(61115) lies on these lines: {1, 3}, {84, 37282}, {404, 6705}, {515, 35977}, {1012, 38150}, {2921, 9626}, {4188, 54051}, {5450, 6904}, {5587, 37270}, {6906, 12436}, {10175, 35985}, {21151, 61011}, {37249, 52027}, {37271, 54447}, {37309, 52026}

X(61115) = isogonal conjugate of X(61114)
X(61115) = pole of the line {21, 61114} with respect to the Stammler hyperbola
X(61115) = pole of the line {314, 61114} with respect to the Steiner-Wallace hyperbola
X(61115) = (X(3), X(9940))-harmonic conjugate of X(35)

X(61116) = PERSPECTOR OF THE ORTHOPTIC CIRCLE OF THE ORTHIC INCONIC

Barycentrics    (a^8+(b^2-2*c^2)*a^6-2*(2*b^2+c^2)*b^2*a^4+(b^4-c^4)*(b^2-2*c^2)*a^2+(b^4-c^4)*(b^2-c^2)^2)*(a^8-(2*b^2-c^2)*a^6-2*(b^2+2*c^2)*c^2*a^4+(b^4-c^4)*(2*b^2-c^2)*a^2-(b^4-c^4)*(b^2-c^2)^2) : :
X(61116) = 4*X(7706)+X(15800) = 3*X(15061)-2*X(45619)

This orthoptic circle has center X(6) and squared-radius ρ^2 = (SW-3*R^2)*S^2/SW^2.

X(61116) lies on the Jerabek hyperbola and these lines: {3, 3574}, {4, 10938}, {6, 18400}, {30, 1176}, {51, 265}, {54, 3575}, {64, 32395}, {67, 10628}, {68, 568}, {69, 1154}, {74, 427}, {195, 15316}, {381, 34801}, {389, 6145}, {539, 6391}, {541, 11559}, {567, 40441}, {578, 32330}, {826, 14380}, {895, 1353}, {1173, 12022}, {1177, 5480}, {1181, 32332}, {1209, 37489}, {1593, 34439}, {1597, 34207}, {1899, 44836}, {1986, 33565}, {2777, 34437}, {3431, 18533}, {3519, 32352}, {3521, 14915}, {3527, 18396}, {3541, 11270}, {3567, 16000}, {3580, 55978}, {3581, 37347}, {4846, 31723}, {5486, 44668}, {5504, 11597}, {5576, 43689}, {5663, 18125}, {5965, 55977}, {6000, 15321}, {6242, 13418}, {6815, 33884}, {7399, 7691}, {7728, 34802}, {9786, 49108}, {10110, 22466}, {10619, 43908}, {11432, 32402}, {11436, 32403}, {11472, 45788}, {11743, 14457}, {11818, 18124}, {12233, 32379}, {12234, 42059}, {12242, 14528}, {12254, 13472}, {14049, 43704}, {14389, 44239}, {14790, 15740}, {14853, 43697}, {15061, 45619}, {15077, 22804}, {15739, 42021}, {16657, 58789}, {18382, 43726}, {18390, 18434}, {18405, 52518}, {18430, 32533}, {19366, 32404}, {20424, 31833}, {22334, 22802}, {32337, 38442}, {32345, 34438}, {32365, 58489}, {32369, 38443}, {34483, 43581}, {34817, 50977}, {38260, 48675}, {41169, 57679}, {44268, 56073}

X(61116) = isogonal conjugate of X(35921)
X(61116) = X(3)-vertex conjugate of-X(15321)
X(61116) = (X(12233), X(52008))-harmonic conjugate of X(32379)

X(61117) = ISOGONAL CONJUGATE OF X(61118)

Barycentrics    a^2*(-8*sqrt(3)*S^3*(2*a^2-3*c^2-3*b^2)+5*a^8-12*(b^2+c^2)*a^6+3*(2*b^4+b^2*c^2+2*c^4)*a^4+4*(b^2+c^2)*(b^4+3*b^2*c^2+c^4)*a^2-(3*b^4+13*b^2*c^2+3*c^4)*(b^2-c^2)^2) : :

X(61117) lies on these lines: {3, 2981}, {74, 5238}, {37512, 61119}

X(61117) = isogonal conjugate of X(61118)

X(61118) = PERSPECTOR OF THE ORTHOPTIC CIRCLE OF THE 1st SIMMONS INCONIC

Barycentrics    (-8*sqrt(3)*S^3*(3*a^2+3*c^2-2*b^2)+3*a^8-(4*b^2-7*c^2)*a^6-2*(3*b^4+8*b^2*c^2+10*c^4)*a^4+(b^2-c^2)*(12*b^4+9*b^2*c^2-7*c^4)*a^2-(5*b^2+3*c^2)*(b^2-c^2)^3)*(-8*sqrt(3)*S^3*(3*a^2+3*b^2-2*c^2)+3*a^8+(7*b^2-4*c^2)*a^6-2*(10*b^4+8*b^2*c^2+3*c^4)*a^4+(b^2-c^2)*(7*b^4-9*b^2*c^2-12*c^4)*a^2+(3*b^2+5*c^2)*(b^2-c^2)^3) : :

This orthoptic circle has center X(396) and squared-radius ρ^2 = (-9*R^2+4*SW+2*sqrt(3)*S)*S^2/(3*(SW+sqrt(3)*S)^2).

X(61118) lies on these lines: {}

X(61118) = isogonal conjugate of X(61117)

X(61119) = ISOGONAL CONJUGATE OF X(61120)

Barycentrics    a^2*(8*sqrt(3)*S^3*(2*a^2-3*c^2-3*b^2)+5*a^8-12*(b^2+c^2)*a^6+3*(2*b^4+b^2*c^2+2*c^4)*a^4+4*(b^2+c^2)*(b^4+3*b^2*c^2+c^4)*a^2-(3*b^4+13*b^2*c^2+3*c^4)*(b^2-c^2)^2) : :

X(61119) lies on these lines: {3, 6151}, {74, 5237}, {37512, 61117}

X(61119) = isogonal conjugate of X(61120)

X(61120) = PERSPECTOR OF THE ORTHOPTIC CIRCLE OF THE 2nd SIMMONS INCONIC

Barycentrics    (8*sqrt(3)*S^3*(3*a^2+3*c^2-2*b^2)+3*a^8-(4*b^2-7*c^2)*a^6-2*(3*b^4+8*b^2*c^2+10*c^4)*a^4+(b^2-c^2)*(12*b^4+9*b^2*c^2-7*c^4)*a^2-(5*b^2+3*c^2)*(b^2-c^2)^3)*(8*sqrt(3)*S^3*(3*a^2+3*b^2-2*c^2)+3*a^8+(7*b^2-4*c^2)*a^6-2*(10*b^4+8*b^2*c^2+3*c^4)*a^4+(b^2-c^2)*(7*b^4-9*b^2*c^2-12*c^4)*a^2+(3*b^2+5*c^2)*(b^2-c^2)^3) : :

This orthoptic circle has center X(395) and squared-radius ρ^2 = (-9*R^2+4*SW-2*sqrt(3)*S)*S^2/(3*(SW-sqrt(3)*S)^2).

X(61120) lies on these lines: {}

X(61120) = isogonal conjugate of X(61119)

X(61121) = PERSPECTOR OF THE ORTHOPTIC CIRCLE OF THE BEVAN CIRCLE

Barycentrics    a*(a^6+2*b*a^5-(b^2+3*c^2)*a^4-4*(b^2+3*c^2)*b*a^3-(b^2-c^2)*(b^2+3*c^2)*a^2+2*(b^2-c^2)*(b^2-5*c^2)*b*a+(b^2-c^2)^3)*(a^6+2*c*a^5-(3*b^2+c^2)*a^4-4*(3*b^2+c^2)*c*a^3+(b^2-c^2)*(3*b^2+c^2)*a^2+2*(b^2-c^2)*(5*b^2-c^2)*c*a-(b^2-c^2)^3) : :

This orthoptic circle has center X(40) and squared-radius ρ^2 = 8*R^2.

X(61121) lies on these lines: {40, 2262}, {223, 3333}, {329, 946}, {1817, 37526}, {7682, 34546}

X(61121) = isogonal conjugate of X(61122)
X(61121) = trilinear pole of the line {6129, 14300} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line

X(61122) = ISOGONAL CONJUGATE OF X(61121)

Barycentrics    a*(a^6-(b+3*c)*(3*b+c)*a^4+(3*b^4+3*c^4+2*b*c*(6*b^2+b*c+6*c^2))*a^2-(b^2-c^2)^2*(b+c)^2) : :

X(61122) lies on these lines: {1, 5920}, {2, 40}, {3, 9}, {4, 7308}, {5, 3587}, {8, 7966}, {10, 6865}, {20, 3305}, {44, 37501}, {46, 37701}, {57, 631}, {63, 3523}, {72, 8726}, {78, 947}, {90, 59325}, {140, 5437}, {142, 5758}, {165, 3149}, {210, 8273}, {226, 37407}, {386, 2257}, {405, 6282}, {411, 10860}, {417, 26901}, {515, 37423}, {516, 6864}, {549, 3928}, {550, 18540}, {580, 37554}, {581, 16572}, {602, 5269}, {620, 24469}, {908, 37112}, {938, 11362}, {960, 7971}, {975, 13329}, {997, 51717}, {1001, 6769}, {1006, 3601}, {1058, 1210}, {1071, 10857}, {1334, 46345}, {1376, 10268}, {1385, 6762}, {1394, 3074}, {1445, 3333}, {1449, 36754}, {1698, 6831}, {1699, 41859}, {1706, 5705}, {1709, 16192}, {1713, 19764}, {1728, 30282}, {1743, 36746}, {1750, 37426}, {1753, 7498}, {1998, 34486}, {2077, 11344}, {2136, 5690}, {2323, 37514}, {2954, 47848}, {2999, 37528}, {3073, 15601}, {3088, 56446}, {3146, 35595}, {3158, 10267}, {3219, 15717}, {3306, 10303}, {3341, 40945}, {3359, 52265}, {3361, 15298}, {3428, 8583}, {3452, 6908}, {3522, 27065}, {3524, 3929}, {3526, 37584}, {3530, 24467}, {3541, 56453}, {3577, 14110}, {3579, 6918}, {3624, 41338}, {3634, 6855}, {3715, 12680}, {3781, 9729}, {3811, 52769}, {3876, 10884}, {3890, 7982}, {3916, 21164}, {3927, 11227}, {3984, 18444}, {4255, 8557}, {4423, 7957}, {4512, 10310}, {4640, 10270}, {4652, 56545}, {4855, 37106}, {5054, 37532}, {5085, 5227}, {5119, 5445}, {5217, 30223}, {5219, 6889}, {5220, 58567}, {5223, 12675}, {5234, 12114}, {5268, 37570}, {5273, 6705}, {5314, 17928}, {5316, 6848}, {5432, 37550}, {5433, 54408}, {5436, 6883}, {5531, 58666}, {5534, 58630}, {5563, 7162}, {5584, 25917}, {5587, 6836}, {5691, 37428}, {5706, 17022}, {5708, 10156}, {5715, 8728}, {5745, 6926}, {5759, 17582}, {5761, 60985}, {5791, 37364}, {5806, 16853}, {5882, 20007}, {6147, 38122}, {6260, 18228}, {6666, 6846}, {6700, 6988}, {6765, 58643}, {6766, 13464}, {6803, 50861}, {6825, 30827}, {6828, 54447}, {6834, 20196}, {6835, 41869}, {6849, 52835}, {6890, 54357}, {6895, 18492}, {6897, 9579}, {6916, 12572}, {6940, 21165}, {6947, 9581}, {6962, 31425}, {6967, 31231}, {6972, 55867}, {6987, 57284}, {6989, 25525}, {6992, 57287}, {7193, 13347}, {7404, 56454}, {7484, 26935}, {7682, 17559}, {7719, 57276}, {7741, 59341}, {7771, 55469}, {7987, 33597}, {8580, 11500}, {9623, 31786}, {9708, 12650}, {9843, 43174}, {9845, 51705}, {9940, 54422}, {9947, 51572}, {10085, 58221}, {10176, 12520}, {10383, 44547}, {10864, 54051}, {11012, 37282}, {11108, 31793}, {11372, 31730}, {11491, 46917}, {11523, 18443}, {11529, 31806}, {12245, 37556}, {12512, 54370}, {12555, 19727}, {12667, 18250}, {12687, 59691}, {12699, 38150}, {14647, 18249}, {14786, 56470}, {15720, 37612}, {15836, 25930}, {15844, 31434}, {15852, 37679}, {15908, 50206}, {16670, 36742}, {17704, 55288}, {18230, 37434}, {18621, 58652}, {18634, 34847}, {20195, 55108}, {21168, 60937}, {22753, 50203}, {24470, 60953}, {26333, 50399}, {26867, 26927}, {26890, 43652}, {27385, 54290}, {27402, 36984}, {30393, 58631}, {31787, 54156}, {31871, 43178}, {37537, 44307}, {37704, 61016}, {38901, 59331}, {40836, 40971}, {42316, 46830}, {43151, 54227}, {49171, 51576}

X(61122) = isogonal conjugate of X(61121)
X(61122) = cross-difference of every pair of points on the line X(6129)X(14300)
X(61122) = X(37054)-zayin conjugate of-X(84)
X(61122) = pole of the line {3303, 30223} with respect to the Feuerbach circumhyperbola
X(61122) = pole of the line {14303, 30201} with respect to the Mandart inellipse
X(61122) = pole of the line {1817, 37526} with respect to the Stammler hyperbola
X(61122) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (3, 9, 84), (3, 5044, 1490), (3, 5777, 5732), (3, 5779, 31805), (3, 7330, 9841), (3, 59381, 31445), (9, 9841, 7330), (40, 3646, 946), (63, 3523, 37526), (78, 6986, 3576), (140, 5709, 5437), (549, 26921, 37534), (631, 55104, 57), (936, 21153, 3), (960, 30503, 7971), (1001, 58637, 6769), (1445, 5703, 3333), (6700, 10164, 6988), (6883, 37531, 5436), (6922, 26446, 5705), (7308, 37551, 4), (7330, 9841, 84), (10164, 12514, 37560), (15601, 35658, 3073), (18228, 37108, 6260), (18443, 31837, 11523), (26921, 37534, 3928), (31445, 33575, 3), (50700, 59418, 31730), (59418, 60958, 11372)

X(61123) = PERSPECTOR OF THE ORTHOPTIC CIRCLE OF THE CONWAY CIRCLE

Barycentrics    ((3*b+4*c)*a^4+(5*b^2+5*b*c+4*c^2)*a^3+(5*b^3-4*c^3+b*c*(6*b+c))*a^2+(b^2-c^2)*(3*b^2+5*b*c+4*c^2)*a+4*(b^2-c^2)*(b+c)*b*c)*((4*b+3*c)*a^4+(4*b^2+5*b*c+5*c^2)*a^3-(4*b^3-5*c^3-b*c*(b+6*c))*a^2-(b^2-c^2)*(4*b^2+5*b*c+3*c^2)*a-4*(b^2-c^2)*(b+c)*b*c) : :
X(61123) = X(1)-2*X(11369)

This orthoptic circle has center X(1) and squared-radius ρ^2 = (S^2+4*r^4)/(2*r^2).

X(61123) lies on the Feuerbach hyperbola and these lines: {1, 11369}, {943, 10888}

X(61123) = reflection of X(1) in X(11369)
X(61123) = isogonal conjugate of X(61124)

X(61124) = ISOGONAL CONJUGATE OF X(61123)

Barycentrics    a^2*(4*(b+c)*a^4+(4*b^2+5*b*c+4*c^2)*a^3-(b+c)*(4*b^2-3*b*c+4*c^2)*a^2-(4*b^4+4*c^4+b*c*(5*b^2+6*b*c+5*c^2))*a-b*c*(b+c)*(3*b^2+2*b*c+3*c^2)) : :

X(61124) lies on these lines: {1, 3}, {30, 10887}, {31, 61130}, {140, 10886}, {573, 5312}, {1698, 61109}, {2951, 37195}, {3523, 19863}, {3651, 10888}, {4512, 16452}, {5234, 52139}, {5259, 16435}, {5587, 48930}, {5691, 19262}, {6684, 10454}, {7988, 19543}, {8666, 12546}, {10164, 10479}, {10304, 10465}, {10444, 37105}, {10455, 37288}, {10478, 31730}, {12512, 43223}, {12550, 38602}, {12551, 46684}, {13244, 33814}, {14636, 19875}, {18229, 25440}, {19513, 34595}, {19517, 25542}, {23511, 35206}, {37264, 38052}, {37320, 44425}, {40600, 51576}

X(61124) = isogonal conjugate of X(61123)
X(61124) = pole of the line {21, 61123} with respect to the Stammler hyperbola
X(61124) = pole of the line {314, 61123} with respect to the Steiner-Wallace hyperbola
X(61124) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (3, 10434, 1), (40, 10470, 1)

X(61125) = PERSPECTOR OF THE ORTHOPTIC CIRCLE OF THE 2nd BROCARD CIRCLE

Barycentrics    a^2*((3*b^2-c^2)*a^6-(8*b^4-b^2*c^2-2*c^4)*a^4+(9*b^6-c^6-b^2*c^2*(3*b^2-c^2))*a^2-(b^2-c^2)*b^2*(4*b^4-5*b^2*c^2+3*c^4))*((b^2-3*c^2)*a^6-(2*b^4+b^2*c^2-8*c^4)*a^4+(b^6-9*c^6-b^2*c^2*(b^2-3*c^2))*a^2-(b^2-c^2)*c^2*(3*b^4-5*b^2*c^2+4*c^4)) : :

This orthoptic circle has center X(3) and squared-radius ρ^2 = -2*R^2*(3*S^2-SW^2)/(S^2+SW^2).

X(61125) lies on the Jerabek hyperbola and these lines: {15740, 40279}

X(61125) = isogonal conjugate of X(61126)

X(61126) = ISOGONAL CONJUGATE OF X(61125)

Barycentrics    4*a^8-9*(b^2+c^2)*a^6+(8*b^4+3*b^2*c^2+8*c^4)*a^4-(b^2+c^2)*(3*b^4-2*b^2*c^2+3*c^4)*a^2+(b^2-c^2)^2*b^2*c^2 : :

X(61126) lies on these lines: {2, 3}, {32, 21166}, {69, 35375}, {76, 47113}, {83, 9734}, {187, 12251}, {194, 33813}, {574, 10359}, {1975, 21445}, {3767, 13172}, {7709, 7782}, {7752, 38748}, {7793, 38225}, {7835, 32152}, {7857, 23698}, {7940, 13449}, {8589, 61132}, {9737, 10788}, {9873, 38747}, {10983, 22521}, {11257, 32456}, {14912, 35424}, {15513, 22712}, {18906, 52992}, {26316, 32522}, {32818, 41400}, {32822, 38907}, {35383, 39141}, {43148, 50977}, {43157, 59373}, {51212, 52995}

X(61126) = isogonal conjugate of X(61125)
X(61126) = pole of the line {3, 61125} with respect to the Stammler hyperbola
X(61126) = pole of the line {69, 61125} with respect to the Steiner-Wallace hyperbola
X(61126) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (3, 3552, 4), (20, 37466, 4), (7782, 13335, 7709)

X(61127) = PERSPECTOR OF THE ORTHOPTIC CIRCLE OF THE 2nd DROZ-FARNY CIRCLE

Barycentrics    (2*a^8-(4*b^2+c^2)*a^6+2*(2*b-c)*(2*b+c)*c^2*a^4+(b^2-c^2)*(4*b^4-7*b^2*c^2+c^4)*a^2-2*(b^4-c^4)*(b^2-c^2)^2)*(2*a^8-(b^2+4*c^2)*a^6-2*(b-2*c)*(b+2*c)*b^2*a^4-(b^2-c^2)*(b^4-7*b^2*c^2+4*c^4)*a^2+2*(b^4-c^4)*(b^2-c^2)^2) : :

This orthoptic circle has center X(3) and squared-radius ρ^2 = 10*R^2-2*SW.

X(61127) lies on the Jerabek hyperbola and these lines: {51, 18550}, {54, 37197}, {74, 44438}, {381, 5504}, {403, 3431}, {895, 10113}, {3426, 13851}, {3843, 15317}, {4846, 16227}, {10982, 15002}, {11270, 18560}, {11744, 18390}, {15077, 18356}, {15321, 18376}, {16657, 55980}, {18383, 22334}, {18394, 57715}, {20421, 35481}, {22979, 57648}, {43697, 47336}

X(61127) = isogonal conjugate of X(61128)

X(61128) = ISOGONAL CONJUGATE OF X(61127)

Barycentrics    a^2*(2*a^8-4*(b^2+c^2)*a^6+11*b^2*c^2*a^4+4*(b^4-3*b^2*c^2+c^4)*(b^2+c^2)*a^2-(2*b^4+3*b^2*c^2+2*c^4)*(b^2-c^2)^2) : :
X(61128) = 4*X(3)+X(47485)

X(61128) lies on these lines: {2, 3}, {49, 38942}, {74, 9306}, {95, 44136}, {182, 15036}, {184, 15035}, {578, 43597}, {1147, 43601}, {1236, 7771}, {1511, 9544}, {1614, 22955}, {1899, 12383}, {2079, 43448}, {2394, 22089}, {2979, 32110}, {3060, 10564}, {3357, 43598}, {3431, 5012}, {5621, 11180}, {5651, 11204}, {5664, 39228}, {5667, 40082}, {5866, 32817}, {5890, 34986}, {5891, 11454}, {5907, 11468}, {6699, 23293}, {9545, 13630}, {9682, 23267}, {9703, 45956}, {10546, 16194}, {10574, 12038}, {11270, 11440}, {11430, 15045}, {11438, 43574}, {11449, 40647}, {11459, 21663}, {12041, 18435}, {12111, 43604}, {12112, 35264}, {12118, 43808}, {12236, 14805}, {12893, 18911}, {12901, 15081}, {13336, 51033}, {13352, 15053}, {13445, 46261}, {13482, 15004}, {13858, 36320}, {13859, 36318}, {14855, 26881}, {15020, 58266}, {15032, 47391}, {15033, 43804}, {15072, 51393}, {15305, 43586}, {15578, 40330}, {17702, 26913}, {17821, 46372}, {18475, 20791}, {18912, 22647}, {18916, 53050}, {21243, 38727}, {21396, 59424}, {23329, 41171}, {26882, 46850}, {32599, 50992}, {35602, 56292}, {41714, 55674}, {43129, 55668}, {48375, 58447}, {51833, 54061}, {54681, 56063}

X(61128) = isogonal conjugate of X(61127)
X(61128) = pole of the line {523, 39508} with respect to the 1st Droz-Farny circle
X(61128) = pole of the line {6, 46031} with respect to the Evans conic
X(61128) = pole of the line {3, 61127} with respect to the Stammler hyperbola
X(61128) = pole of the line {69, 61127} with respect to the Steiner-Wallace hyperbola
X(61128) = pole of the line {5650, 35473} with respect to the Thomson-Gibert-Moses hyperbola
X(61128) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (3, 186, 376), (3, 15078, 186), (3, 22467, 4), (3, 37814, 20), (140, 10254, 2), (378, 37951, 4), (549, 37968, 3), (2071, 6644, 4), (3528, 35513, 376), (7426, 18571, 186), (7506, 12086, 4), (12084, 44802, 4), (15051, 37470, 3431), (22467, 45170, 186), (31074, 38321, 4), (40647, 43898, 11449)

X(61129) = PERSPECTOR OF THE ORTHOPTIC CIRCLE OF THE EXCIRCLES RADICAL CIRCLE

Barycentrics    (3*(b+c)*a^4+(4*b^2+5*b*c+5*c^2)*a^3-(2*b-5*c)*(b+c)^2*a^2-(b^2-c^2)*(4*b^2+5*b*c+3*c^2)*a-(b^2-c^2)*(b+c)*b*(b+3*c))*(3*(b+c)*a^4+(5*b^2+5*b*c+4*c^2)*a^3+(5*b-2*c)*(b+c)^2*a^2+(b^2-c^2)*(3*b^2+5*b*c+4*c^2)*a+(b^2-c^2)*(b+c)*c*(3*b+c)) : :

This orthoptic circle has center X(10) and squared-radius ρ^2 = (S^2+4*r^4)/(8*r^2).

X(61129) lies on the Kiepert hyperbola and these lines: {386, 45100}, {946, 56214}, {9569, 34258}, {31165, 60267}, {40718, 51118}

X(61129) = isogonal conjugate of X(61130)

X(61130) = ISOGONAL CONJUGATE OF X(61129)

Barycentrics    a^2*(a^5+4*(b+c)*a^4+(b+2*c)*(2*b+c)*a^3-(b+c)*(4*b^2-3*b*c+4*c^2)*a^2-(b^2+b*c+c^2)*(3*b^2+2*b*c+3*c^2)*a-b*c*(b+c)*(3*b^2+2*b*c+3*c^2)) : :

X(61130) lies on these lines: {3, 6}, {20, 43531}, {31, 61124}, {595, 10434}, {631, 13478}, {936, 993}, {975, 3576}, {1125, 6996}, {1397, 5217}, {1764, 4658}, {2328, 16452}, {2360, 16287}, {2944, 3743}, {3682, 15931}, {4653, 10470}, {5882, 50606}, {8245, 31871}, {8273, 56809}, {12512, 33682}, {24220, 28620}, {25526, 50702}, {37078, 37537}, {39641, 39642}

X(61130) = isogonal conjugate of X(61129)
X(61130) = pole of the line {2, 61129} with respect to the Stammler hyperbola
X(61130) = pole of the line {76, 61129} with respect to the Steiner-Wallace hyperbola
X(61130) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (3, 572, 58), (10470, 37399, 4653)

X(61131) = PERSPECTOR OF THE ORTHOPTIC CIRCLE OF THE 1st LEMOINE CIRCLE

Barycentrics    a^2*((2*b^2+c^2)*a^6-2*(3*b^4+3*b^2*c^2+c^4)*a^4+(4*b^6+c^6-3*b^2*c^2*(3*b^2+2*c^2))*a^2+2*(b^2-c^2)*b^2*c^2*(2*b^2-c^2))*((b^2+2*c^2)*a^6-2*(b^4+3*b^2*c^2+3*c^4)*a^4+(b^6+4*c^6-3*b^2*c^2*(2*b^2+3*c^2))*a^2+2*(b^2-c^2)*b^2*c^2*(b^2-2*c^2)) : :

This orthoptic circle has center X(182) and squared-radius ρ^2 = R^2*(S^2+SW^2)/(2*SW^2).

X(61131) lies on these lines: {576, 14994}, {5171, 14096}, {10358, 20023}

X(61131) = isogonal conjugate of X(61132)

X(61132) = ISOGONAL CONJUGATE OF X(61131)

Barycentrics    4*(b^2+c^2)*a^6-3*(2*b^4+3*b^2*c^2+2*c^4)*a^4+2*(b^2+c^2)*(b^4-4*b^2*c^2+c^4)*a^2+(b^2-c^2)^2*b^2*c^2 : :
X(61132) = 9*X(2)-2*X(6248) = 6*X(2)+X(11257) = 3*X(2)+4*X(13334) = 4*X(3)+3*X(262) = 2*X(3)+5*X(7786) = 3*X(3)+4*X(11272) = 5*X(3)+2*X(14881) = 10*X(3)-3*X(22676) = X(3)+6*X(40108) = X(4)-8*X(6683) = X(4)+6*X(21163) = 2*X(39)+5*X(631) = 6*X(39)+X(12251) = 4*X(39)+3*X(22712) = X(76)-8*X(140) = X(76)+6*X(11171) = 3*X(76)+4*X(32448) = 4*X(140)+3*X(11171) = 6*X(140)+X(32448) = X(194)+6*X(15819) = 3*X(262)-10*X(7786) = 15*X(262)-8*X(14881) = 5*X(262)+2*X(22676) = 11*X(262)-4*X(22728) = X(262)-8*X(40108) = 6*X(549)+X(3095) = 8*X(549)-X(33706) = 4*X(575)+3*X(22677) = 10*X(631)-3*X(22712) = 10*X(632)-3*X(7697) = 5*X(632)+2*X(32516) = X(1916)+6*X(38748) = 4*X(2023)+3*X(21166) = 4*X(3095)+3*X(33706) = 9*X(3524)-2*X(5188) = 3*X(3524)+4*X(44562) = 4*X(6248)+3*X(11257) = X(6248)+6*X(13334) = 2*X(6248)+5*X(32522) = 4*X(6683)+3*X(21163) = 3*X(7697)+4*X(32516) = 15*X(7786)-8*X(11272) = 13*X(10303)-6*X(15819) = 9*X(11171)-2*X(32448) = X(11257)-8*X(13334) = 3*X(11257)-10*X(32522) = 10*X(11272)-3*X(14881) = 2*X(11272)-9*X(40108) = 2*X(12251)-9*X(22712) = 12*X(13334)-5*X(32522)

X(61132) lies on these lines: {2, 6248}, {3, 83}, {4, 6683}, {5, 7918}, {39, 631}, {76, 140}, {98, 11285}, {114, 7876}, {182, 7824}, {183, 32467}, {187, 10359}, {194, 10303}, {511, 3523}, {538, 15702}, {549, 3095}, {575, 7793}, {632, 7697}, {730, 31423}, {1916, 38748}, {2021, 31401}, {2023, 15815}, {2080, 7878}, {2782, 3526}, {3202, 61134}, {3329, 5171}, {3398, 7771}, {3524, 5188}, {3525, 3934}, {3529, 22682}, {3530, 9821}, {3533, 31239}, {3545, 52854}, {3592, 19063}, {3594, 19064}, {3620, 50654}, {4045, 37446}, {5054, 7757}, {5079, 22681}, {5085, 10007}, {5418, 19090}, {5420, 19089}, {6036, 33015}, {6309, 56791}, {6425, 49231}, {6426, 49230}, {6656, 43461}, {6680, 54152}, {6721, 14065}, {7622, 13085}, {7770, 52771}, {7772, 52770}, {7795, 60099}, {7803, 38227}, {7808, 11676}, {7846, 37459}, {7847, 37348}, {7859, 37466}, {7866, 38642}, {7892, 58445}, {7906, 40107}, {7930, 15561}, {7976, 26446}, {7991, 22475}, {8589, 61126}, {9466, 15709}, {9737, 37455}, {9744, 16043}, {9772, 38751}, {9774, 37345}, {10165, 12782}, {10168, 22486}, {11055, 15713}, {11261, 20190}, {11412, 52042}, {12108, 32521}, {12836, 52793}, {13108, 15694}, {13335, 33004}, {13357, 31400}, {14869, 32515}, {14994, 32831}, {15024, 27375}, {15482, 37334}, {15692, 44422}, {15720, 32447}, {21843, 46305}, {22732, 34486}, {31276, 55864}, {32451, 50652}, {32454, 38760}, {32990, 36998}, {33021, 54393}, {33022, 47113}, {35925, 37512}, {38740, 43532}, {43650, 60700}, {48663, 55857}, {51829, 52987}

X(61132) = isogonal conjugate of X(61131)
X(61132) = pole of the line {5171, 14096} with respect to the Stammler hyperbola
X(61132) = pole of the line {576, 14994} with respect to the Steiner-Wallace hyperbola
X(61132) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (2, 13334, 11257), (2, 32522, 6248), (3, 7786, 262), (3, 11174, 12110), (3, 14881, 22676), (3, 40108, 7786), (39, 631, 22712), (140, 11171, 76), (194, 10303, 15819), (632, 32516, 7697), (3525, 7709, 3934), (6248, 13334, 32522), (6248, 32522, 11257), (6683, 21163, 4), (15482, 37479, 37334)

X(61133) = PERSPECTOR OF THE ORTHOPTIC CIRCLE OF THE NINE-POINT CIRCLE

Barycentrics    ((b^2+c^2)*a^6-(2*b^2+3*c^2)*(b^2+c^2)*a^4+(b^2-c^2)*(b^4-4*b^2*c^2-3*c^4)*a^2+(b^2-c^2)^3*c^2)*((b^2+c^2)*a^6-(3*b^2+2*c^2)*(b^2+c^2)*a^4+(b^2-c^2)*(3*b^4+4*b^2*c^2-c^4)*a^2-(b^2-c^2)^3*b^2) : :
X(61133) = X(5)-2*X(21474)

This orthoptic circle has center X(5) and squared-radius ρ^2 = R^2/2.

X(61133) lies on these lines: {3, 17500}, {4, 16030}, {5, 3917}, {30, 40449}, {39, 53}, {311, 3933}, {427, 13450}, {546, 60035}, {578, 2980}, {1594, 46147}, {1596, 61110}, {1906, 36809}, {3574, 43917}, {5305, 60517}, {11424, 34449}, {11816, 15033}, {13403, 15619}, {17703, 18388}, {22335, 43893}

X(61133) = reflection of X(5) in X(21474)
X(61133) = isogonal conjugate of X(61134)
X(61133) = Cundy-Parry-Phi-transform of X(17500)
X(61133) = Cundy-Parry-Psi-transform of X(16030)
X(61133) = pole of the line {5421, 10110} with respect to the Kiepert circumhyperbola

X(61134) = ISOGONAL CONJUGATE OF X(61133)

Barycentrics    a^2*(a^8-3*(b^2+c^2)*a^6+(3*b^4-b^2*c^2+3*c^4)*a^4-((b^2-c^2)^2-4*b^2*c^2)*(b^2+c^2)*a^2-(b^2-c^2)^2*b^2*c^2) : :
X(61134) = X(74)+2*X(40640) = 2*X(13353)-X(13434) = X(14627)-2*X(36153) = 2*X(35500)-X(43613) = 2*X(37126)+X(43602)

X(61134) lies on these lines: {2, 1614}, {3, 54}, {4, 83}, {5, 14157}, {6, 10323}, {20, 569}, {22, 3567}, {23, 5462}, {24, 3796}, {25, 15024}, {26, 15043}, {30, 13353}, {49, 549}, {51, 12088}, {52, 6636}, {74, 11562}, {104, 55098}, {110, 140}, {143, 13564}, {155, 7485}, {156, 3526}, {184, 631}, {185, 35921}, {186, 9729}, {206, 34781}, {215, 52793}, {251, 43843}, {323, 5447}, {376, 578}, {378, 37476}, {389, 7512}, {399, 14128}, {501, 13329}, {511, 1199}, {546, 46865}, {548, 37472}, {550, 567}, {568, 7525}, {575, 45186}, {597, 34613}, {632, 18350}, {1092, 3524}, {1147, 3523}, {1173, 5446}, {1181, 5085}, {1204, 61136}, {1209, 3448}, {1216, 15246}, {1437, 6940}, {1495, 11695}, {1498, 10249}, {1503, 14788}, {1568, 44862}, {1658, 15053}, {1853, 7569}, {1899, 7558}, {1994, 10625}, {1995, 11465}, {2070, 12006}, {2888, 10116}, {2889, 13431}, {2916, 32191}, {2937, 5946}, {3043, 38727}, {3044, 38748}, {3045, 38760}, {3046, 38772}, {3047, 38793}, {3048, 38804}, {3060, 36753}, {3088, 44077}, {3090, 6759}, {3202, 61132}, {3431, 57648}, {3522, 13352}, {3525, 9306}, {3528, 13346}, {3529, 11424}, {3530, 9706}, {3533, 5651}, {3545, 26883}, {3547, 18912}, {3549, 18911}, {3574, 46450}, {3580, 34002}, {3589, 16655}, {3628, 10540}, {3819, 43844}, {3917, 56292}, {3955, 26877}, {4846, 57389}, {5050, 11414}, {5056, 46261}, {5059, 8717}, {5092, 5562}, {5135, 18178}, {5157, 6776}, {5189, 17712}, {5420, 9677}, {5422, 7387}, {5504, 15036}, {5622, 6146}, {5640, 7517}, {5643, 7545}, {5663, 27866}, {5891, 43605}, {5892, 44802}, {5899, 10095}, {5907, 7550}, {5943, 34484}, {5944, 43809}, {6000, 35500}, {6143, 58447}, {6241, 7503}, {6639, 26913}, {6642, 6800}, {6676, 26879}, {6699, 58881}, {6746, 21284}, {6823, 12022}, {6950, 13323}, {6952, 37527}, {7193, 26878}, {7393, 11441}, {7395, 11456}, {7399, 34224}, {7400, 19131}, {7484, 19347}, {7488, 9730}, {7494, 18916}, {7495, 12359}, {7499, 18914}, {7502, 37481}, {7505, 22750}, {7506, 15028}, {7514, 12111}, {7516, 11444}, {7526, 15072}, {7527, 10575}, {7539, 34780}, {7552, 43836}, {7575, 43579}, {8537, 44480}, {8703, 37495}, {9140, 34826}, {9544, 10303}, {9545, 15717}, {9704, 15720}, {9786, 44837}, {9818, 12290}, {10018, 13394}, {10024, 14644}, {10110, 37925}, {10168, 43811}, {10263, 53863}, {10274, 25563}, {10299, 43652}, {10313, 41334}, {10594, 10601}, {10619, 12383}, {10706, 34664}, {10721, 52070}, {10982, 12082}, {11134, 16772}, {11137, 16773}, {11179, 43812}, {11204, 43813}, {11245, 16197}, {11250, 14805}, {11284, 14530}, {11413, 37506}, {11426, 37198}, {11440, 43806}, {11451, 13861}, {11464, 17928}, {11479, 16261}, {11591, 54006}, {12041, 18364}, {12054, 54004}, {12086, 14855}, {12108, 40111}, {12112, 44870}, {12228, 15055}, {12233, 51737}, {12242, 51360}, {12278, 50008}, {13160, 25739}, {13198, 13367}, {13363, 13621}, {13366, 15644}, {13391, 14627}, {13445, 14130}, {13491, 15062}, {13598, 50664}, {13754, 37126}, {14389, 23335}, {14861, 20127}, {14865, 46850}, {14912, 19126}, {14940, 43866}, {15026, 18378}, {15030, 55695}, {15038, 47748}, {15056, 32139}, {15057, 15132}, {15472, 35491}, {15559, 37649}, {15642, 51887}, {15740, 57387}, {15807, 18325}, {16621, 18374}, {16658, 38110}, {17704, 51394}, {18315, 20574}, {18369, 23060}, {18439, 49671}, {18475, 22467}, {19123, 26206}, {19151, 55978}, {19154, 39568}, {19171, 33971}, {20299, 32379}, {20417, 43578}, {21154, 58056}, {21166, 39834}, {21735, 37480}, {32142, 50461}, {32184, 32391}, {32534, 37475}, {32767, 54000}, {33524, 44413}, {33923, 37477}, {34473, 39805}, {34783, 43596}, {37814, 40280}, {37946, 55704}, {37947, 58531}, {38321, 41482}, {38737, 58058}, {38784, 58060}, {38790, 43585}, {40448, 54547}, {41724, 43588}, {43584, 45735}, {43595, 54040}, {43817, 58805}, {43838, 58806}, {44882, 45089}, {46817, 50139}, {46847, 55700}, {48975, 53495}, {51730, 55703}

X(61134) = midpoint of X(3) and X(43845)
X(61134) = reflection of X(i) in X(j) for these (i, j): (13434, 13353), (14627, 36153), (43613, 35500)
X(61134) = isogonal conjugate of X(61133)
X(61134) = Cundy-Parry-Phi-transform of X(16030)
X(61134) = Cundy-Parry-Psi-transform of X(17500)
X(61134) = perspector of the circumconic through X(18315) and X(42396)
X(61134) = pole of the line {826, 12325} with respect to the 1st Brocard circle
X(61134) = pole of the line {826, 23290} with respect to the polar circle
X(61134) = pole of the line {7512, 13367} with respect to the Jerabek circumhyperbola
X(61134) = pole of the line {7745, 52433} with respect to the Kiepert circumhyperbola
X(61134) = pole of the line {5, 3917} with respect to the Stammler hyperbola
X(61134) = pole of the line {311, 3933} with respect to the Steiner-Wallace hyperbola
X(61134) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (2, 1614, 43598), (3, 195, 10627), (3, 5012, 54), (3, 6102, 7691), (3, 7592, 11412), (3, 12161, 2979), (3, 15087, 6101), (4, 182, 43651), (5, 52525, 14157), (20, 569, 15033), (22, 36752, 3567), (23, 5462, 38848), (24, 37514, 15045), (143, 13564, 15107), (155, 7485, 7999), (182, 1176, 19128), (182, 10984, 4), (184, 37515, 631), (186, 9729, 43597), (195, 10627, 23061), (323, 45308, 5447), (389, 22352, 7512), (1092, 13347, 3524), (1181, 5085, 7509), (1181, 7509, 11459), (1209, 18128, 3448), (1995, 15805, 11465), (3523, 11003, 1147), (3549, 18911, 26917), (3628, 10540, 43614), (3796, 37514, 24), (5422, 7387, 9781), (5446, 34545, 1173), (5899, 15047, 10095), (6101, 15087, 15801), (6642, 6800, 26882), (6759, 43650, 3090), (7395, 11456, 15058), (7399, 34224, 41171), (7399, 48906, 34224), (7516, 18445, 11444), (10095, 15047, 12834), (10984, 43651, 8718), (13564, 15037, 143), (14118, 40647, 74), (15028, 26881, 7506), (15043, 15080, 26), (32046, 34148, 54), (37513, 40647, 14118)

X(61135) = PERSPECTOR OF THE ORTHOPTIC CIRCLE OF THE ORTHOCENTROIDAL CIRCLE

Barycentrics    (2*a^8-(6*b^2+c^2)*a^6+2*(3*b^4+5*b^2*c^2-c^4)*a^4-(b^2-c^2)*(2*b^4+9*b^2*c^2-c^4)*a^2-2*(b^2-c^2)^3*c^2)*(2*a^8-(b^2+6*c^2)*a^6-2*(b^4-5*b^2*c^2-3*c^4)*a^4-(b^2-c^2)*(b^4-9*b^2*c^2-2*c^4)*a^2+2*(b^2-c^2)^3*b^2) : :

This orthoptic circle has center X(381) and squared-radius ρ^2 = 2*R^2-4*SW/9.

X(61135) lies on these lines: {381, 5651}, {5063, 44526}, {18877, 60588}, {31861, 44135}, {32444, 53330}, {44438, 58785}

X(61135) = isogonal conjugate of X(61136)

X(61136) = ISOGONAL CONJUGATE OF X(61135)

Barycentrics    a^2*(2*(b^2+c^2)*a^6-(6*b^4-7*b^2*c^2+6*c^4)*a^4+2*(b^2+c^2)*(3*b^4-8*b^2*c^2+3*c^4)*a^2-(2*b^4+3*b^2*c^2+2*c^4)*(b^2-c^2)^2) : :
X(61136) = 7*X(2)-4*X(15060) = 5*X(2)-2*X(18435) = X(2)-2*X(40280) = 2*X(3)-X(33884) = X(3)+2*X(45956) = X(4)-2*X(5640) = X(4)-4*X(9730) = X(4)-10*X(10574) = 5*X(4)+4*X(10575) = 7*X(4)+2*X(12279) = X(4)+2*X(15072) = X(4)+8*X(40647) = X(20)+2*X(568) = 5*X(20)+4*X(10263) = X(20)+8*X(13630) = 4*X(51)-X(15682) = 5*X(568)-2*X(10263) = X(568)-4*X(13630) = 2*X(568)-X(16981) = 8*X(5462)-7*X(5640) = 4*X(5462)-7*X(9730) = 8*X(5462)+X(12279) = 2*X(5462)+7*X(40647) = X(5640)-2*X(9730) = X(5640)-5*X(10574) = 5*X(5640)+2*X(10575) = 7*X(5640)+X(12279) = 5*X(5640)-7*X(15043) = X(5640)+4*X(40647) = 2*X(9730)-5*X(10574) = 5*X(9730)+X(10575) = 10*X(9730)-7*X(15043) = 2*X(9730)+X(15072) = X(9730)+2*X(40647) = X(10263)-10*X(13630) = 4*X(10263)-5*X(16981) = 5*X(10574)+X(15072) = 5*X(10574)+4*X(40647) = 14*X(10575)-5*X(12279) = 2*X(10575)+7*X(15043) = 2*X(10575)-5*X(15072) = X(10575)-10*X(40647) = 5*X(11002)-6*X(13321) = X(12279)-7*X(15072) = 8*X(13630)-X(16981) = 10*X(15060)-7*X(18435) = 2*X(15060)-7*X(40280) = X(15072)-4*X(40647) = X(18435)-5*X(40280) = X(33884)+4*X(45956)

X(61136) lies on these lines: {2, 5655}, {3, 323}, {4, 4846}, {6, 7464}, {20, 568}, {30, 11002}, {51, 15682}, {52, 17538}, {74, 182}, {110, 37470}, {143, 5059}, {184, 15035}, {185, 631}, {186, 6800}, {373, 3545}, {376, 511}, {378, 5050}, {389, 3529}, {569, 35475}, {576, 43576}, {974, 2854}, {1092, 43602}, {1112, 49670}, {1154, 10304}, {1199, 11413}, {1204, 61134}, {1216, 61138}, {1350, 8546}, {1352, 12317}, {1511, 58266}, {1614, 43804}, {1986, 35485}, {1995, 12112}, {2549, 15544}, {2979, 19708}, {3060, 11001}, {3090, 6241}, {3091, 13363}, {3146, 37481}, {3357, 43651}, {3448, 50008}, {3520, 37506}, {3522, 6102}, {3523, 15067}, {3524, 7998}, {3525, 10170}, {3526, 45957}, {3528, 5889}, {3533, 5907}, {3543, 5946}, {3544, 15028}, {3567, 33703}, {3581, 7492}, {3819, 15719}, {3832, 12006}, {3854, 32137}, {3855, 12290}, {3917, 15698}, {4550, 15054}, {5012, 15055}, {5056, 18439}, {5067, 12162}, {5071, 5892}, {5085, 10605}, {5093, 21312}, {5334, 11626}, {5335, 11624}, {5422, 13596}, {5446, 49138}, {5562, 10299}, {5651, 14094}, {5656, 7729}, {5876, 10303}, {5891, 15702}, {5943, 11455}, {5967, 35925}, {6101, 21734}, {6243, 50693}, {6644, 35265}, {6759, 43597}, {7422, 41330}, {7486, 45959}, {7550, 32620}, {7556, 11438}, {7558, 18913}, {7575, 7712}, {7592, 37497}, {7708, 45723}, {7999, 17704}, {8705, 43273}, {8717, 15107}, {9027, 50974}, {9544, 32609}, {9704, 38942}, {9781, 15012}, {9786, 12088}, {10095, 50688}, {10295, 48906}, {10298, 34513}, {10564, 11422}, {10606, 55703}, {10620, 49671}, {10653, 30439}, {10654, 30440}, {10706, 17853}, {10938, 16270}, {11004, 37477}, {11188, 39874}, {11245, 44458}, {11381, 15024}, {11412, 13382}, {11424, 43600}, {11440, 13336}, {11451, 16194}, {11454, 37513}, {11456, 35259}, {11465, 44870}, {11541, 14641}, {12041, 14805}, {12086, 36753}, {12244, 14708}, {12250, 41589}, {12278, 18128}, {13451, 15684}, {13472, 37472}, {14865, 36752}, {15018, 31861}, {15026, 50689}, {15033, 39561}, {15041, 18570}, {15053, 47485}, {15080, 32110}, {15082, 15709}, {15122, 59771}, {15531, 37511}, {15578, 17835}, {15692, 23039}, {15700, 44324}, {15710, 54041}, {15717, 18436}, {15740, 18916}, {16881, 17800}, {17854, 41670}, {17855, 54012}, {18533, 54184}, {18583, 35484}, {18952, 50009}, {21844, 43601}, {23040, 43604}, {23515, 26913}, {30258, 40948}, {31884, 44832}, {32111, 37648}, {32138, 37471}, {32447, 47620}, {32761, 38702}, {33878, 41463}, {34200, 54048}, {35237, 37946}, {35500, 37514}, {36979, 42091}, {36981, 42090}, {37495, 53860}, {37924, 48912}, {37944, 39522}, {43584, 46261}, {43814, 44491}, {44573, 45237}, {44879, 52525}, {45759, 54047}, {46264, 52989}, {50979, 54995}, {54994, 55697}, {58044, 58046}

X(61136) = midpoint of X(i) and X(j) for these (i, j): {20, 16981}, {185, 5650}, {5640, 15072}
X(61136) = reflection of X(i) in X(j) for these (i, j): (2, 40280), (4, 5640), (3524, 20791), (3545, 15045), (3917, 55166), (5640, 9730), (5650, 16836), (11459, 5650), (16261, 373), (16981, 568), (33884, 3), (54047, 45759)
X(61136) = isogonal conjugate of X(61135)
X(61136) = pole of the line {376, 13857} with respect to the Jerabek circumhyperbola
X(61136) = pole of the line {381, 5651} with respect to the Stammler hyperbola
X(61136) = pole of the line {31861, 44135} with respect to the Steiner-Wallace hyperbola
X(61136) = pole of the line {4, 13857} with respect to the Thomson-Gibert-Moses hyperbola
X(61136) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (3, 11003, 3431), (185, 16836, 11459), (373, 16261, 3545), (3060, 14855, 11001), (3567, 46850, 33703), (4846, 18911, 4), (5012, 15055, 39242), (5446, 52093, 49138), (5462, 12279, 4), (5892, 15305, 5071), (5943, 11455, 41099), (6241, 9729, 3090), (9730, 15072, 4), (9730, 40647, 15072), (10574, 15072, 9730), (10574, 40647, 4), (10575, 15043, 4), (11451, 16194, 41106), (11459, 16836, 631), (15045, 16261, 373), (15055, 39242, 35473), (41518, 41519, 376)

X(61137) = PERSPECTOR OF THE ORTHOPTIC CIRCLE OF THE STAMMLER CIRCLE

Barycentrics    a^2*(a^4-2*(8*b^2+c^2)*a^2+(b^2-c^2)*(15*b^2-c^2))*(a^4-2*(b^2+8*c^2)*a^2+(b^2-c^2)*(b^2-15*c^2)) : :

This orthoptic circle has center X(3) and squared-radius ρ^2 = 8*R^2.

X(61137) lies on the Jerabek hyperbola and these lines: {54, 18535}, {68, 14269}, {69, 3843}, {1593, 20421}, {1597, 11270}, {1598, 3431}, {3521, 35403}, {3830, 15740}, {7529, 56068}, {9781, 46851}, {10110, 14490}, {12315, 52518}, {26883, 43908}, {34817, 55593}

X(61137) = isogonal conjugate of X(61138)

X(61138) = ISOGONAL CONJUGATE OF X(61137)

Barycentrics    15*a^4-16*(b^2+c^2)*a^2+(b^2-c^2)^2 : :
X(61138) = 6*X(2)-7*X(3533) = 12*X(2)-7*X(3544) = 15*X(2)-7*X(3854) = 9*X(2)-7*X(7486) = 4*X(3)+X(3533) = 8*X(3)+X(3544) = 6*X(3)+X(7486) = 5*X(3)+3*X(15722) = 5*X(3)+X(55857) = 3*X(3)+X(55863) = X(4)-4*X(3533) = X(4)-2*X(3544) = 5*X(4)-8*X(3854) = 3*X(4)-8*X(7486) = 4*X(5)-3*X(3854) = 4*X(5)-5*X(7486) = 2*X(5)-9*X(15722) = 2*X(5)-3*X(55857) = 2*X(5)-5*X(55863) = X(20)+3*X(7486) = X(20)+6*X(55863) = 3*X(376)+5*X(3533) = 3*X(376)+2*X(3854) = X(376)+4*X(15722) = 3*X(376)+4*X(55857)

X(61138) lies on these lines: {2, 3}, {8, 31447}, {15, 42436}, {16, 42435}, {17, 43646}, {18, 43645}, {51, 40284}, {61, 43023}, {62, 43022}, {69, 55674}, {165, 10595}, {183, 32878}, {185, 55166}, {187, 31450}, {193, 55682}, {325, 32889}, {355, 58219}, {485, 43374}, {486, 43375}, {597, 55641}, {626, 39142}, {944, 4668}, {1000, 37605}, {1056, 7280}, {1058, 5010}, {1151, 43510}, {1152, 43509}, {1216, 61136}, {1285, 5206}, {1352, 55668}, {1975, 32888}, {1992, 55687}, {3069, 9681}, {3098, 43597}, {3241, 31666}, {3311, 9692}, {3316, 42259}, {3317, 42258}, {3411, 10645}, {3412, 10646}, {3487, 4114}, {3576, 3635}, {3579, 5734}, {3600, 31480}, {3618, 55649}, {3619, 55665}, {3621, 58224}, {3625, 5657}, {3630, 10519}, {3633, 7967}, {3653, 50809}, {3785, 32876}, {4301, 35242}, {4309, 7288}, {4317, 5218}, {4691, 5881}, {4999, 31420}, {5013, 46453}, {5023, 9606}, {5085, 32455}, {5210, 31400}, {5303, 59591}, {5319, 37512}, {5334, 42491}, {5335, 42490}, {5343, 42626}, {5344, 42625}, {5351, 37640}, {5352, 37641}, {5418, 31414}, {5432, 31410}, {5447, 20791}, {5585, 31407}, {5587, 22266}, {5603, 16192}, {5650, 12290}, {5759, 61020}, {5890, 15606}, {6144, 14912}, {6200, 9693}, {6279, 10517}, {6280, 10518}, {6329, 55618}, {6337, 43459}, {6361, 9624}, {6396, 9680}, {6409, 7582}, {6410, 7581}, {6411, 13935}, {6412, 9540}, {6418, 9542}, {6452, 31487}, {6455, 7586}, {6456, 7585}, {6459, 35813}, {6460, 35812}, {6496, 35256}, {6497, 35255}, {6560, 42570}, {6561, 42571}, {6684, 37712}, {6776, 55673}, {7317, 37738}, {7689, 41462}, {7735, 15515}, {7736, 15513}, {7738, 8589}, {7751, 9741}, {7765, 21843}, {7782, 52713}, {7982, 50814}, {8164, 9657}, {8550, 51178}, {8588, 9698}, {8717, 43614}, {9543, 19116}, {9589, 10165}, {9607, 53095}, {9670, 47743}, {9705, 10984}, {9729, 54041}, {10155, 18844}, {10168, 55652}, {10170, 52093}, {10541, 50967}, {11002, 55320}, {11179, 55677}, {11206, 52102}, {11412, 17704}, {11425, 11431}, {11477, 50970}, {11487, 43898}, {11488, 42928}, {11489, 42929}, {11592, 34783}, {12244, 48378}, {12245, 13624}, {12383, 15057}, {13347, 43574}, {13348, 15045}, {13392, 38633}, {13630, 33884}, {13886, 42637}, {13939, 42638}, {14531, 16836}, {14561, 55658}, {14853, 55651}, {15023, 30714}, {15024, 36987}, {15051, 16003}, {15055, 20125}, {15063, 48375}, {15069, 21167}, {15080, 44833}, {15480, 21445}, {15740, 20421}, {17502, 20053}, {18439, 55286}, {18840, 59545}, {19872, 28172}, {19877, 58216}, {20057, 31662}, {20396, 38723}, {20423, 55644}, {21151, 60962}, {21153, 61000}, {21168, 43177}, {23249, 42566}, {23259, 42567}, {25406, 40107}, {28186, 46932}, {30389, 50810}, {31399, 58217}, {31412, 42558}, {31470, 37665}, {31663, 54445}, {31670, 55659}, {31673, 58215}, {32789, 43787}, {32790, 43788}, {32817, 32877}, {32819, 52718}, {33749, 54173}, {33750, 39874}, {34089, 42265}, {34091, 42262}, {34473, 52886}, {37481, 54044}, {37832, 43550}, {37835, 43551}, {38064, 50966}, {38068, 50819}, {38110, 55648}, {41100, 42959}, {41101, 42958}, {42089, 42434}, {42090, 42489}, {42091, 42488}, {42092, 42433}, {42111, 42597}, {42114, 42596}, {42115, 43869}, {42116, 43870}, {42119, 43012}, {42120, 43013}, {42139, 43632}, {42142, 43633}, {42147, 52079}, {42148, 52080}, {42153, 43464}, {42154, 43555}, {42155, 43554}, {42156, 43463}, {42159, 43492}, {42162, 43491}, {42163, 43446}, {42166, 43447}, {42528, 43769}, {42529, 43770}, {42557, 42561}, {42639, 60291}, {42640, 60292}, {42641, 43885}, {42642, 43886}, {42773, 42943}, {42774, 42942}, {42795, 43776}, {42796, 43775}, {42815, 43635}, {42816, 43634}, {42926, 42988}, {42927, 42989}, {42944, 43494}, {42945, 43493}, {42974, 43479}, {42975, 43480}, {43018, 43020}, {43019, 43021}, {43174, 50817}, {43199, 43485}, {43200, 43486}, {43238, 43542}, {43239, 43543}, {43256, 43879}, {43257, 43880}, {43444, 51945}, {43445, 51944}, {43517, 53517}, {43518, 53520}, {43536, 53513}, {46264, 55667}, {47286, 55819}, {48873, 55660}, {50974, 55675}, {50983, 55614}, {51028, 55602}, {51170, 55692}, {51171, 55629}, {51212, 55653}, {51538, 55663}, {51579, 55729}, {51581, 60323}, {51732, 55624}, {53092, 54174}, {53489, 55797}, {53516, 54597}, {54132, 55626}, {54169, 55684}, {54170, 55637}, {54857, 60629}, {55606, 59373}, {55632, 59399}, {55643, 61044}, {60183, 60325}, {60329, 60616}

X(61138) = reflection of X(i) in X(j) for these (i, j): (4, 3544), (3544, 3533), (3854, 55857), (7486, 55863)
X(61138) = isogonal conjugate of X(61137)
X(61138) = pole of the line {44409, 51768} with respect to the incircle
X(61138) = pole of the line {10414, 21734} with respect to the Lester circle
X(61138) = pole of the line {185, 19708} with respect to the Jerabek circumhyperbola
X(61138) = pole of the line {3, 61137} with respect to the Stammler hyperbola
X(61138) = pole of the line {69, 3843} with respect to the Steiner-Wallace hyperbola
X(61138) = pole of the line {5650, 21735} with respect to the Thomson-Gibert-Moses hyperbola
X(61138) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (2, 17538, 4), (2, 45759, 376), (3, 3523, 376), (3, 3524, 4), (3, 3530, 20), (3, 15700, 140), (3, 15712, 2), (4, 15715, 3), (5, 21734, 376), (5, 49138, 4), (20, 5067, 4), (140, 5072, 2), (140, 15711, 3), (140, 58191, 20), (376, 631, 5), (376, 3525, 4), (381, 14890, 2), (382, 46219, 5), (548, 3843, 20), (548, 12108, 5), (549, 15689, 2), (631, 3528, 4), (631, 33703, 2), (1657, 12108, 2), (3090, 11001, 4), (3146, 33923, 376), (3146, 41106, 4), (3147, 60765, 4), (3522, 12103, 376), (3523, 15705, 3), (3523, 21734, 5), (3525, 49138, 5), (3526, 46853, 20), (3526, 49134, 5), (3528, 5067, 20), (3528, 49138, 376), (3529, 5071, 4), (3529, 15719, 140), (3545, 11541, 4), (3830, 10304, 376), (3832, 46936, 5), (3854, 7486, 5), (3861, 47599, 5), (5054, 14893, 2), (7401, 60466, 4), (10299, 15698, 3), (12100, 15705, 376), (12108, 45757, 140), (14093, 41983, 2), (14891, 15706, 2)

X(61139) = X(4)X(54)∩X(24)X(125)

Barycentrics    2*a^10-4*a^8*(b^2+c^2)+a^4*(b^2-c^2)^2*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)+a^6*(b^2+c^2)^2+a^2*(b^4-c^4)^2 : :
X(61139) = -3*X[2]+2*X[44829], -3*X[51]+2*X[6146], -2*X[389]+3*X[7576], -3*X[428]+2*X[12241], -3*X[568]+2*X[10116], -3*X[3060]+2*X[10112], -3*X[3830]+2*X[12897], -2*X[5446]+3*X[7540], -4*X[5480]+5*X[52789], -9*X[5946]+8*X[50476], -X[6241]+3*X[18559], -3*X[9730]+4*X[31830], -4*X[10110]+3*X[12022], -5*X[10574]+X[40241], -3*X[11245]+4*X[11745], -2*X[11565]+3*X[13364], -2*X[12605]+3*X[15030], -4*X[13348]+3*X[52397], -2*X[13474]+3*X[16658], -2*X[13488]+3*X[16654], -2*X[13598]+3*X[34603], -2*X[13630]+3*X[38322], -3*X[16194]+2*X[52070], -4*X[16625]+3*X[45968], -4*X[18128]+5*X[37481], -3*X[38321]+2*X[40647], -4*X[43588]+3*X[45730], -4*X[44870]+3*X[52069]

See Antreas Hatzipolakis and Ivan Pavlov, euclid 6016.

X(61139) lies on these lines: {2, 44829}, {3, 2918}, {4, 54}, {5, 1495}, {20, 1352}, {24, 125}, {26, 18474}, {30, 5562}, {32, 51363}, {51, 6146}, {52, 11819}, {64, 67}, {68, 41586}, {74, 52102}, {113, 18377}, {115, 52436}, {143, 45731}, {154, 7507}, {155, 382}, {156, 44288}, {159, 1593}, {182, 7544}, {185, 1503}, {186, 20299}, {235, 13851}, {265, 18378}, {378, 34785}, {389, 7576}, {403, 18383}, {427, 13367}, {428, 12241}, {511, 14516}, {539, 6243}, {542, 5889}, {568, 10116}, {569, 11818}, {1092, 14790}, {1141, 11816}, {1147, 31723}, {1181, 18494}, {1204, 13399}, {1209, 7502}, {1370, 43652}, {1498, 12173}, {1514, 3853}, {1568, 10539}, {1594, 10282}, {1598, 18396}, {1658, 34514}, {1853, 3515}, {1885, 16621}, {1899, 7487}, {2070, 5449}, {2777, 12281}, {2937, 6288}, {2980, 22261}, {3060, 10112}, {3146, 12278}, {3331, 7747}, {3357, 35471}, {3410, 7691}, {3426, 17800}, {3518, 25739}, {3542, 44082}, {3547, 35268}, {3564, 14531}, {3581, 52104}, {3627, 30522}, {3818, 7503}, {3830, 12897}, {5064, 11425}, {5094, 17821}, {5446, 7540}, {5448, 10540}, {5480, 52789}, {5576, 18475}, {5651, 6643}, {5899, 48675}, {5907, 12225}, {5944, 39504}, {5946, 50476}, {6000, 6240}, {6143, 10182}, {6241, 18559}, {6247, 21663}, {6293, 9973}, {6696, 37931}, {6746, 41589}, {6815, 46264}, {6995, 18945}, {7391, 13346}, {7399, 22352}, {7401, 43650}, {7488, 21243}, {7505, 23325}, {7512, 41171}, {7517, 9927}, {7545, 43821}, {7553, 44665}, {7574, 18350}, {7575, 13561}, {7577, 26882}, {7684, 45256}, {7685, 45257}, {7687, 18394}, {7715, 44106}, {7731, 13423}, {8779, 27376}, {9306, 37444}, {9714, 14852}, {9730, 31830}, {9908, 12293}, {10018, 32767}, {10110, 12022}, {10117, 32357}, {10193, 17506}, {10263, 13417}, {10301, 15873}, {10312, 15340}, {10574, 40241}, {10594, 18390}, {10605, 34780}, {10610, 50138}, {10984, 18420}, {10996, 14927}, {11202, 37119}, {11204, 35503}, {11245, 11745}, {11403, 45015}, {11430, 15559}, {11432, 34564}, {11438, 11457}, {11441, 52842}, {11442, 31304}, {11449, 31074}, {11464, 52295}, {11563, 18379}, {11565, 13364}, {11645, 38323}, {12084, 16163}, {12106, 43817}, {12107, 34826}, {12295, 44271}, {12429, 33586}, {12605, 15030}, {13348, 52397}, {13366, 31804}, {13371, 51393}, {13434, 19130}, {13474, 16658}, {13488, 16654}, {13491, 45971}, {13598, 34603}, {13630, 38322}, {14049, 19504}, {14118, 41482}, {14585, 27371}, {15019, 43838}, {15122, 43898}, {15750, 40686}, {15811, 44438}, {16194, 52070}, {16195, 37638}, {16252, 23047}, {16625, 45968}, {17701, 23315}, {18128, 37481}, {18376, 35488}, {18404, 46261}, {18405, 37197}, {18488, 18570}, {18563, 45118}, {18907, 56866}, {19124, 36989}, {19137, 41257}, {19558, 39604}, {20987, 51756}, {21844, 25563}, {22802, 35480}, {22804, 46029}, {23208, 54003}, {23294, 44673}, {23329, 32534}, {23335, 51394}, {24206, 37126}, {26917, 47485}, {26937, 32064}, {26958, 55578}, {29323, 54040}, {31726, 52863}, {32345, 37954}, {34417, 37122}, {34609, 35602}, {34776, 39588}, {37198, 48905}, {37452, 43586}, {38321, 40647}, {38791, 57271}, {43588, 45730}, {43907, 47335}, {44831, 46728}, {44870, 52069}, {51434, 51509}

X(61139) = midpoint of X(i) and X(j) for these {i,j}: {12290, 34797}, {3146, 12278}, {6240, 16659}
X(61086) = reflection of X(i) in X(j) for these {i,j}: {125, 12140}, {185, 3575}, {1885, 16621}, {11381, 16655}, {11750, 5}, {12225, 5907}, {12289, 13403}, {13491, 45971}, {18560, 13474}, {21659, 4}, {3, 45286}, {3574, 32332}, {34224, 389}, {34799, 10112}, {4, 13419}, {44076, 5446}, {45186, 7553}, {45731, 143}, {52, 11819}, {5562, 12134}, {6146, 6756}
X(61139) = anticomplement of X(44829)
X(61086) = X(i)-Dao conjugate of X(j) for these {i, j}: {44829, 44829}
X(61139) = pole of line {23286, 44808} with respect to the circumcircle
X(61139) = pole of line {389, 427} with respect to the Jerabek hyperbola
X(61139) = pole of line {3049, 12077} with respect to the orthic inconic
X(61139) = pole of line {1614, 5562} with respect to the Stammler hyperbola
X(61139) = pole of line {7750, 46724} with respect to the Wallace hyperbola
X(61139) = intersection, other than A, B, C, of circumconics {{A, B, C, X(67), X(38808)}}, {{A, B, C, X(1614), X(5562)}} and {{A, B, C, X(6662), X(8884)}}
X(61139) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 12254, 15033}, {4, 12289, 13403}, {4, 1614, 18388}, {4, 19467, 11424}, {4, 26883, 51403}, {4, 31383, 26883}, {4, 6759, 43831}, {4, 8884, 6747}, {4, 9833, 184}, {30, 12134, 5562}, {30, 16655, 11381}, {235, 41362, 13851}, {1092, 14790, 51360}, {1204, 14216, 13399}, {1495, 11572, 5}, {1503, 3575, 185}, {1885, 16621, 32062}, {3060, 34799, 10112}, {6146, 6756, 51}, {6240, 16659, 6000}, {7540, 44076, 5446}, {7553, 44665, 45186}, {10539, 18569, 1568}, {10540, 31724, 5448}, {11442, 31304, 46730}, {12289, 13403, 21659}, {12290, 34797, 2777}, {13289, 44795, 125}, {13403, 18400, 12289}, {13419, 18400, 4}, {14216, 18533, 1204}, {16658, 18560, 13474}, {17845, 36990, 1593}, {18388, 45185, 1614}, {18394, 44958, 7687}, {18400, 32332, 3574}, {37122, 39571, 34417}, {44407, 45286, 3}

X(61140) = X(164)X(361)∩X(258)X(259)

Barycentrics    (Cos[A/2]*Cot[A/2] - Cos[B/2]*Cot[B/2] - Cos[C/2]*Cot[C/2])*Sin[A] : :

X(61140) = solution, X, of the isoscelizer equations D(A,X) / (-a + b + c) = D(B,X) / (a - b + c) = D(C,X) / (a + b - c); see the preamble just before X(503).

X(61140) lies on these lines: {1, 6726}, {9, 16015}, {164, 361}, {173, 362}, {174, 16572}, {258, 259}, {5437, 58777}, {8056, 8078}

> X(61140) = X(7371)-Ceva conjugate of X(1)
X(61140) = X(6731)-Dao conjugate of X(7027)

X(61141) = X(40)X(366)∩X(165)X(365)

Barycentrics    a*(Sqrt[a]*(a + b - c)*(a - b + c) + (Sqrt[b] + Sqrt[c])*(a - b - c)*(a + b + c - 2*Sqrt[b*c])) : :

X(61141) = solution, X, of the isoscelizer equations (-a + b + c)^2 T(A,X) = (a - b + c)^2 T(B,X) = (a + b - c)^2 T(C,X); see the preamble just before X(503).

X(61141) lies on these lines: {40, 366}, {84, 4180}, {165, 365}, {4182, 10860}, {11372, 40374}

X(61141) = excentral-isogonal conjugate of X(364)
X(61141) = X(4182)-Ceva conjugate of X(1)

X(61142) = X(1)X(2068)∩X(364)X(510)

Barycentrics    a*(Sqrt[a]*(a - b - c) + (Sqrt[b] + Sqrt[c])*(a - b - c + 2*Sqrt[b*c])) : :

X(61142) = solution, X, of the isoscelizer equations T(A,X) / (-a + b + c)^2 = T(B,X) / (a - b + c)^2 = T(C,X) / (a + b - c)^2; see the preamble just before X(503).

X(61142) lies on these lines: {1, 2068}, {9, 40378}, {364, 510}

X(61142) = barycentric product X(366)*X(56707)
X(61142) = barycentric quotient X(56707)/X(18297)

X(61143) = ISOGONAL CONJUGATE OF X(367)

Barycentrics    a/(Sqrt[b] + Sqrt[c])::

X(61143) lies on these lines: {{1, 6}, {365, 366}, {2068, 55325}}.

X(61143) = isogonal conjugate of X(367). X(61143) = X(i)-isoconjugate of X(j) for these (i,j): {{1, 367}, {2, 20664}, {4, 20751}, {6, 20527}, {56, 4181}, {75, 52865}, {81, 20682}, {365, 40378}, {513, 55325}, {514, 58996}, {649, 55322}, {18297, 52866}, {43924, 55373}}. X(61143) = X(i)-Dao conjugate of X(j) for these (i,j): {{1, 4181}, {3, 367}, {9, 20527}, {206, 52865}, {5375, 55322}, {32664, 20664}, {36033, 20751}, {39026, 55325}, {40586, 20682}}. X(61143) = cevapoint of X(1) and X(365). X(61143) = barycentric product X(i)*X(j) for these {i,j}: {{367, 59459}, {20527, 59461}}. X(61143) = barycentric quotient X(i)/X(j) for these {i,j}: {{1, 20527}, {6, 367}, {9, 4181}, {31, 20664}, {32, 52865}, {42, 20682}, {48, 20751}, {100, 55322}, {101, 55325}, {365, 40378}, {644, 55373}, {692, 58996}, {4166, 4180}}.

X(61144) = ISOTOMIC CONJUGATE OF X(367)

Barycentrics    1/(a*(Sqrt[b] + Sqrt[c]))::

X(61144) lies on these lines: {2, 37}, {4179, 18297}

X(61144) = isogonal conjugate of X(52865). X(61144) = isotomic conjugate of X(367). X(61144) = X(i)-isoconjugate of X(j) for these (i,j): {{1, 52865}, {6, 20664}, {25, 20751}, {31, 367}, {32, 20527}, {365, 52866}, {649, 58996}, {667, 55325}, {1333, 20682}, {1397, 4181}, {1919, 55322}}. X(61144) = X(i)-Dao conjugate of X(j) for these (i,j): {{2, 367}, {3, 52865}, {9, 20664}, {37, 20682}, {5375, 58996}, {6376, 20527}, {6505, 20751}, {6631, 55325}, {9296, 55322}}. X(61144) = cevapoint of X(75) and X(18297). X(61144) = barycentric quotient X(i)/X(j) for these {i,j}: {{1, 20664}, {2, 367}, {6, 52865}, {10, 20682}, {63, 20751}, {75, 20527}, {100, 58996}, {190, 55325}, {312, 4181}, {365, 52866}, {646, 55373}, {668, 55322}, {18297, 40378}}.

X(61145) = ISOGONAL CONJUGATE OF X(20527)

Barycentrics    a^2/(Sqrt[b] + Sqrt[c])::

X(61145) lies on these lines: {{6, 31}, {365, 4166}, {52866, 58996}}.

X(61145) = isogonal conjugate of X(20527). X(61145) = isogonal conjugate of the complement of X(366). X(61145) = X(i)-isoconjugate of X(j) for these (i,j): {{1, 20527}, {2, 367}, {57, 4181}, {75, 20664}, {76, 52865}, {86, 20682}, {92, 20751}, {366, 40378}, {513, 55322}, {514, 55325}, {693, 58996}, {3669, 55373}}. X(61145) = X(i)-Dao conjugate of X(j) for these (i,j): {{3, 20527}, {206, 20664}, {5452, 4181}, {22391, 20751}, {32664, 367}, {39026, 55322}, {40600, 20682}}. X(61145) = cevapoint of X(6) and X(18753). X(61145) = barycentric product X(i)*X(j) for these {i,j}: {{367, 59461}, {20664, 59459}}. X(61145) = barycentric quotient X(i)/X(j) for these {i,j}: {{6, 20527}, {31, 367}, {32, 20664}, {55, 4181}, {101, 55322}, {184, 20751}, {213, 20682}, {560, 52865}, {692, 55325}, {3939, 55373}, {18753, 40378}, {32739, 58996}}.




leftri   POINTS ASSOCIATED WITH CIRCLES: X(61146)-(61151)  rightri

Contributed by Peter Moses and Clark Kimberling, January 16, 2024.

Suppose that n >= 2 and that S = {O(1), O(2), ... , O(n)} is a set of n circles with centers and radii o(1), r(1); o(2), r(2); ...; o(n),r(n), where the centers o(i) are normalized barycentric coorindates.

Definition 1. The centroid of S is the point o(1) + o(2) + ... + o(n), this being a combo as defined in the Introduction (in Part 1 of ETC).

Definition 2. The centroid of circumferences of S is the point r(1)*o(1) + r(2)*o(2) + ... + r(n)*o(n).

Definition 3. The centroid of curvatures of S is the point o(1)/r(1) + o(2)/r(2) + ... + o(n)/r(n).

Definition 4. The centroid of areas of S is the point o(1)*r(1)^2 + o(2)*r(2)^2 + ... + o(n)*r(n)^2.

. Definition 5. The centroid of reciprocal areas of S is the point o(1)/r(1)^2 + o(2)/r(2)^2 + ... + o(n)/r(n)^2.

All five centroids are given by the form o(1)*r(1)^n + o(2)*r(2)^n) + ... + + o(n)*r(n)^n, where n is one of the numbers -2, -1, 0, 1, 2. In the following examples, the centroids are indexed by n, from -2, to 2, with these designations: G(-2), G(-1), G(0), G(1), G(2).

Examp1e 1: S = {incircle, circumcircle}
G(-2) = X(8071)
G(-1) = X(55)
G(0) = X(1385) G(1) = X(61146)
G(2) = X(61147)

Examp1e 2: S = {incircle, nine-point circle}
G(-2) = X(8070)
G(-1) = X(12)
G(0) = X(5091) G(1) = X(61148)
G(2) = X(61149)

Examp1e 3: S = {circumcircle, nine-point circle}
G(-2) = X(1656)
G(-1) = X(2)
G(0) = X(140) G(1) = X(549)
G(2) = X(15712)

Examp1e 4: S = {incircle and the 3 excircles}
G(-2) = X(6)
G(-1) = X(1)
G(0) = X(3) G(1) = X(12565)
G(2) = X(61150)

Examp1e 5: S = {the 3 excircles}
G(-2) = X(1743)
G(-1) = X(1)
G(0) = X(165) G(1) = X(2952)
G(2) = X(61151)

underbar



X(61146) = CENTROID OF CIRCUMFERENCES OF INCIRCLE AND CIRCUMCIRCLE

Barycentrics    a*(a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - a^2*b^4 - 2*a*b^5 + b^6 - 2*a^5*c + 4*a^4*b*c - 4*a^3*b^2*c - 2*a^2*b^3*c + 6*a*b^4*c - 2*b^5*c - a^4*c^2 - 4*a^3*b*c^2 + 10*a^2*b^2*c^2 - 4*a*b^3*c^2 - b^4*c^2 + 4*a^3*c^3 - 2*a^2*b*c^3 - 4*a*b^2*c^3 + 4*b^3*c^3 - a^2*c^4 + 6*a*b*c^4 - b^2*c^4 - 2*a*c^5 - 2*b*c^5 + c^6) : :
3 X[1] - X[37569], 2 X[2099] + X[37584], 3 X[3576] - X[5119], 3 X[3576] - 2 X[32613], 3 X[10202] - 2 X[50195], 3 X[10246] - X[10679], 3 X[10246] - 2 X[24929], X[12703] - 3 X[59337], 3 X[37533] - 2 X[37569], 5 X[37624] - X[44455], 4 X[51787] - 9 X[58230], 3 X[5886] - 2 X[7680], 3 X[5731] - X[37000], 4 X[7508] - 3 X[35258], 2 X[8255] - 3 X[38030], 4 X[9956] - 5 X[31245], 3 X[11038] - X[54158], 3 X[38029] - 2 X[47373]

X(61146) lies on these lines: {1, 3}, {5, 19860}, {8, 6825}, {9, 48667}, {10, 6863}, {63, 14988}, {78, 5690}, {84, 26321}, {140, 19861}, {145, 6908}, {200, 59503}, {355, 2886}, {381, 1538}, {392, 6883}, {515, 6923}, {518, 54203}, {528, 3655}, {549, 19907}, {581, 15955}, {912, 956}, {944, 3434}, {946, 6928}, {952, 3419}, {958, 5887}, {962, 6868}, {971, 18519}, {993, 2800}, {997, 3035}, {1006, 3877}, {1064, 49487}, {1125, 6958}, {1191, 37514}, {1203, 36753}, {1457, 37697}, {1483, 36846}, {1490, 18525}, {1519, 6929}, {1537, 11113}, {1657, 12565}, {1836, 5841}, {2807, 31394}, {2900, 12629}, {2951, 15681}, {2975, 24467}, {3526, 8583}, {3560, 12672}, {3586, 10738}, {3616, 6891}, {3622, 6926}, {3623, 37108}, {3656, 28459}, {3679, 6326}, {3753, 6911}, {3811, 5855}, {3816, 5886}, {3869, 26921}, {3870, 5844}, {3897, 6906}, {3940, 51380}, {4321, 59380}, {4323, 5758}, {4511, 5657}, {4666, 10283}, {4853, 5534}, {4915, 51515}, {5258, 5693}, {5267, 40256}, {5330, 6986}, {5450, 51111}, {5554, 6834}, {5587, 6980}, {5603, 6827}, {5691, 18407}, {5694, 41229}, {5720, 5790}, {5722, 15845}, {5730, 31837}, {5731, 6948}, {5836, 11499}, {5842, 12520}, {5882, 21627}, {5884, 8666}, {5901, 6922}, {6001, 22758}, {6684, 30144}, {6713, 12740}, {6796, 51717}, {6862, 24541}, {6865, 10595}, {6916, 7967}, {6949, 25005}, {6959, 24982}, {6971, 8227}, {6982, 59387}, {6988, 12245}, {7330, 7971}, {7491, 12699}, {7508, 35258}, {7993, 13146}, {8255, 38030}, {9840, 13754}, {9856, 37234}, {9956, 31245}, {10039, 26487}, {10129, 59392}, {10393, 37739}, {10525, 10572}, {10526, 12047}, {10805, 36977}, {10884, 31775}, {10914, 33597}, {10950, 15908}, {10953, 39599}, {11038, 54158}, {11260, 12675}, {11362, 22836}, {11491, 14923}, {11682, 55104}, {11729, 32554}, {12560, 60922}, {12608, 37821}, {12650, 18499}, {12688, 18761}, {12705, 13743}, {13464, 30143}, {14786, 19784}, {15813, 54286}, {15952, 54356}, {16132, 47032}, {16466, 36752}, {17757, 37713}, {18515, 52027}, {18524, 52026}, {20243, 37404}, {22791, 31789}, {25485, 52769}, {28160, 36999}, {28168, 41860}, {28204, 31140}, {29243, 61086}, {30284, 35514}, {31141, 52050}, {31434, 59382}, {33858, 37401}, {34123, 55297}, {34698, 34716}, {37429, 51112}, {37826, 39542}, {38029, 47373}, {44284, 51071}, {52407, 54400}

X(61146) = midpoint of X(i) and X(j) for these {i,j}: {40, 25415}, {944, 3434}, {2099, 3428}, {2900, 12629}, {3872, 18446}, {7982, 41338}
X(61146) = reflection of X(i) in X(j) for these {i,j}: {55, 1385}, {355, 2886}, {1482, 50194}, {5119, 32613}, {5691, 18407}, {10679, 24929}, {24474, 5173}, {37533, 1}, {37584, 3428}, {37826, 39542}
X(61146) = pole of line {1201, 37697} with respect to the circumconic {A,B,C,X(1),X(6)}
X(61146) = pole of line {11499, 59691} with respect to the Feuerbach circumhyperbola of the medial triangle
X(61146) = pole of line {8, 6833} with respect to the Jerabek circumhyperbola of the excentral triangle
X(61146) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 18443, 10246}, {1, 24806, 1060}, {1, 30503, 37611}, {1, 34489, 24928}, {3, 25413, 40}, {8, 21740, 37700}, {10, 40257, 45770}, {40, 3576, 5010}, {40, 3612, 26285}, {56, 34339, 37612}, {65, 11249, 37532}, {1006, 10698, 3877}, {1385, 9957, 16202}, {1385, 18856, 10269}, {1385, 25405, 10246}, {1385, 26285, 3612}, {1385, 31788, 3}, {1420, 37534, 37535}, {1482, 10246, 6767}, {1482, 16202, 9957}, {3359, 3576, 3}, {3576, 5119, 32613}, {3579, 33281, 46920}, {3601, 49163, 11849}, {4853, 5534, 12645}, {5720, 9623, 5790}, {5836, 37837, 11499}, {5903, 11012, 59318}, {6265, 26446, 997}, {7330, 7971, 40266}, {9940, 24928, 16203}, {10246, 10679, 24929}, {11227, 25405, 1385}, {13145, 32612, 59333}, {18443, 37531, 10383}, {18444, 38460, 7967}, {23340, 24299, 3295}, {26286, 35004, 46}, {30503, 37611, 3}, {33281, 46920, 1}, {37618, 59333, 32612}

X(61147) = X(1)X(3)∩X(10)X(55298)

Barycentrics    a*(a^9 - 3*a^8*b + 8*a^6*b^3 - 6*a^5*b^4 - 6*a^4*b^5 + 8*a^3*b^6 - 3*a*b^8 + b^9 - 3*a^8*c + 12*a^7*b*c - 12*a^6*b^2*c - 12*a^5*b^3*c + 30*a^4*b^4*c - 12*a^3*b^5*c - 12*a^2*b^6*c + 12*a*b^7*c - 3*b^8*c - 12*a^6*b*c^2 + 40*a^5*b^2*c^2 - 24*a^4*b^3*c^2 - 28*a^3*b^4*c^2 + 36*a^2*b^5*c^2 - 12*a*b^6*c^2 + 8*a^6*c^3 - 12*a^5*b*c^3 - 24*a^4*b^2*c^3 + 56*a^3*b^3*c^3 - 24*a^2*b^4*c^3 - 12*a*b^5*c^3 + 8*b^6*c^3 - 6*a^5*c^4 + 30*a^4*b*c^4 - 28*a^3*b^2*c^4 - 24*a^2*b^3*c^4 + 30*a*b^4*c^4 - 6*b^5*c^4 - 6*a^4*c^5 - 12*a^3*b*c^5 + 36*a^2*b^2*c^5 - 12*a*b^3*c^5 - 6*b^4*c^5 + 8*a^3*c^6 - 12*a^2*b*c^6 - 12*a*b^2*c^6 + 8*b^3*c^6 + 12*a*b*c^7 - 3*a*c^8 - 3*b*c^8 + c^9) : :

X(61147) lies on these lines: {1, 3}, {10, 55298}, {944, 10522}, {4511, 10786}, {4853, 19914}, {4861, 10785}, {6863, 19861}, {6958, 19860}, {18242, 45770}, {19907, 37424}

X(61147) = midpoint of X(944) and X(10522)
X(61147) = reflection of X(8071) in X(1385)
X(61147) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {40, 3576, 14792}, {1385, 3660, 16203}

X(61148) = CENTROID OF CIRCUMFERENCES OF INCIRCLE AND NINE-POINT CIRCUMCIRCLE

Barycentrics    a*(2*a^6 - 4*a^5*b - 2*a^4*b^2 + 8*a^3*b^3 - 2*a^2*b^4 - 4*a*b^5 + 2*b^6 - 4*a^5*c + 12*a^4*b*c - 8*a^3*b^2*c - 7*a^2*b^3*c + 12*a*b^4*c - 5*b^5*c - 2*a^4*c^2 - 8*a^3*b*c^2 + 20*a^2*b^2*c^2 - 8*a*b^3*c^2 - 2*b^4*c^2 + 8*a^3*c^3 - 7*a^2*b*c^3 - 8*a*b^2*c^3 + 10*b^3*c^3 - 2*a^2*c^4 + 12*a*b*c^4 - 2*b^2*c^4 - 4*a*c^5 - 5*b*c^5 + 2*c^6) : :
X(61148) = 3 X[1] - X[37733], 2 X[12] - 3 X[38045], 3 X[5886] - X[37710], 4 X[5901] - 3 X[38045], 2 X[8068] - 3 X[38044], 3 X[10283] - 2 X[37737], 4 X[1125] - 3 X[38114], 5 X[1656] - 3 X[59416], 5 X[3616] - 3 X[59382], 4 X[3628] - 3 X[38058], 3 X[10246] - X[11491], 2 X[31659] - 3 X[38028], X[6763] + 3 X[16200], 5 X[10595] - X[20060], 4 X[9955] - 3 X[38142], 4 X[9956] - 3 X[38178], 5 X[18493] - 3 X[59392], 5 X[31260] - 3 X[38129], 3 X[38033] - 4 X[51700]

X(61148) lines on these lines: {1, 5}, {10, 11567}, {30, 51112}, {78, 59400}, {145, 6862}, {214, 33657}, {515, 33281}, {517, 5267}, {632, 19860}, {758, 10222}, {946, 26087}, {1125, 38114}, {1385, 3754}, {1389, 22765}, {1482, 2975}, {1656, 59416}, {2099, 32153}, {3244, 19920}, {3560, 4430}, {3616, 59382}, {3622, 6959}, {3623, 6824}, {3628, 38058}, {3742, 15178}, {3897, 7508}, {4861, 5844}, {4996, 11849}, {4999, 5690}, {5057, 37290}, {5253, 6924}, {5330, 7489}, {5841, 22791}, {5842, 34773}, {5855, 22837}, {5882, 11263}, {5884, 51529}, {5885, 11715}, {6690, 34352}, {6691, 30147}, {6763, 16200}, {6911, 37624}, {6917, 7967}, {6929, 10595}, {6952, 19914}, {8583, 55861}, {9955, 38142}, {9956, 38178}, {10107, 18857}, {10698, 13743}, {11011, 14988}, {11014, 28174}, {12565, 15704}, {12702, 32633}, {12919, 38669}, {15712, 37611}, {16202, 52272}, {18493, 59392}, {19861, 55856}, {20323, 58561}, {21740, 28224}, {24475, 50194}, {25485, 33658}, {26287, 33814}, {28186, 52837}, {30144, 38042}, {31260, 38129}, {32141, 34471}, {33179, 34791}, {35004, 38602}, {35597, 54192}, {37621, 51683}, {38033, 51700}, {44257, 51071}, {51788, 58566}

X(61148) = midpoint of X(i) and X(j) for these {i,j}: {1482, 2975}, {26470, 37734}
X(61148) = reflection of X(i) in X(j) for these {i,j}: {12, 5901}, {5690, 4999}
X(61148) = pole of line {4511, 33281} with respect to the Jerabek circumhyperbola of the excentral triangle
X(61148) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5, 19907}, {12, 5901, 38045}

X(61149) = X(1)X(5)∩X(3754)X(33281)

Barycentrics    a*(2*a^9 - 6*a^8*b + 16*a^6*b^3 - 12*a^5*b^4 - 12*a^4*b^5 + 16*a^3*b^6 - 6*a*b^8 + 2*b^9 - 6*a^8*c + 24*a^7*b*c - 24*a^6*b^2*c - 24*a^5*b^3*c + 60*a^4*b^4*c - 24*a^3*b^5*c - 24*a^2*b^6*c + 24*a*b^7*c - 6*b^8*c - 24*a^6*b*c^2 + 72*a^5*b^2*c^2 - 48*a^4*b^3*c^2 - 49*a^3*b^4*c^2 + 72*a^2*b^5*c^2 - 23*a*b^6*c^2 + 16*a^6*c^3 - 24*a^5*b*c^3 - 48*a^4*b^2*c^3 + 112*a^3*b^3*c^3 - 48*a^2*b^4*c^3 - 24*a*b^5*c^3 + 16*b^6*c^3 - 12*a^5*c^4 + 60*a^4*b*c^4 - 49*a^3*b^2*c^4 - 48*a^2*b^3*c^4 + 58*a*b^4*c^4 - 12*b^5*c^4 - 12*a^4*c^5 - 24*a^3*b*c^5 + 72*a^2*b^2*c^5 - 24*a*b^3*c^5 - 12*b^4*c^5 + 16*a^3*c^6 - 24*a^2*b*c^6 - 23*a*b^2*c^6 + 16*b^3*c^6 + 24*a*b*c^7 - 6*a*c^8 - 6*b*c^8 + 2*c^9) : :

X(61149) lies on these lines: {1, 5}, {3754, 33281}, {5330, 6914}

X(61149) = reflection of X(8070) in X(5901)

X(61150) = X(1)X(738)∩X(20)X(64)

Barycentrics    a^2*(a^8 - 6*a^4*b^4 + 8*a^2*b^6 - 3*b^8 + 36*a^4*b^2*c^2 - 24*a^2*b^4*c^2 - 12*b^6*c^2 - 6*a^4*c^4 - 24*a^2*b^2*c^4 + 30*b^4*c^4 + 8*a^2*c^6 - 12*b^2*c^6 - 3*c^8) : :
X(61150) = 4 X[19137] - 5 X[53094]

X(61150) lies on these lines: {1, 738}, {3, 13474}, {6, 46850}, {20, 64}, {22, 8567}, {30, 9786}, {49, 37497}, {154, 11413}, {185, 10602}, {382, 37475}, {394, 12279}, {548, 11472}, {1092, 1498}, {1192, 39568}, {1370, 5895}, {1593, 1974}, {1620, 9909}, {1657, 11750}, {1853, 37201}, {3066, 17578}, {3079, 39268}, {3146, 17810}, {3343, 13155}, {3426, 11793}, {3529, 10605}, {3796, 12086}, {5013, 31952}, {5023, 53500}, {5059, 33586}, {5102, 15072}, {5480, 15740}, {5646, 15717}, {5893, 7396}, {6247, 35513}, {6696, 52404}, {6759, 11820}, {7387, 33534}, {7464, 19357}, {7503, 55676}, {8681, 53097}, {10516, 10996}, {10575, 37498}, {10606, 11414}, {11381, 17811}, {11403, 17825}, {11424, 55711}, {11425, 12085}, {12084, 35237}, {12163, 15704}, {12174, 37672}, {12315, 37480}, {12565, 30271}, {13093, 15644}, {13434, 51739}, {13445, 33524}, {13568, 48910}, {14528, 52525}, {14855, 37514}, {14915, 17814}, {15043, 52518}, {15062, 55641}, {15311, 52398}, {15681, 37486}, {15812, 31829}, {16621, 61113}, {16623, 34801}, {17800, 37489}, {17809, 37944}, {17813, 40928}, {17818, 21659}, {18935, 29181}, {19137, 53094}, {22236, 51900}, {22238, 51901}, {22467, 41424}, {22967, 34777}, {33540, 44682}, {35253, 55651}, {35450, 46728}, {36162, 59231}, {37198, 55646}, {37490, 49139}

X(61150) = midpoint of X(3529) and X(18945)
X(61150) = reflection of X(i) in X(j) for these {i,j}: {15811, 3}, {36990, 15812}
X(61150) = X(32840)-Ceva conjugate of X(9605)
X(61150) = pole of line {154, 3522} with respect to the Feuerbach circumhyperbola of the tangential triangle
X(61150) = pole of line {3198, 28057} with respect to the Jerabek circumhyperbola of the excentral triangle
X(61150) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {20, 64, 1350}, {154, 11413, 41427}, {394, 12279, 58795}, {14855, 47527, 37514}

X(61151) = X(1)X(738)∩X(40)X(971)

Barycentrics    a*(3*a^6 - 6*a^5*b + 9*a^4*b^2 - 20*a^3*b^3 + 21*a^2*b^4 - 6*a*b^5 - b^6 - 6*a^5*c + 6*a^4*b*c + 12*a^3*b^2*c - 12*a^2*b^3*c - 6*a*b^4*c + 6*b^5*c + 9*a^4*c^2 + 12*a^3*b*c^2 - 18*a^2*b^2*c^2 + 12*a*b^3*c^2 - 15*b^4*c^2 - 20*a^3*c^3 - 12*a^2*b*c^3 + 12*a*b^2*c^3 + 20*b^3*c^3 + 21*a^2*c^4 - 6*a*b*c^4 - 15*b^2*c^4 - 6*a*c^5 + 6*b*c^5 - c^6) : :

X(61151) lies on these lines: {1, 738}, {40, 971}, {101, 8835}, {165, 170}, {169, 3062}, {1721, 2955}, {1742, 8915}, {2809, 7991}, {3576, 15856}, {5011, 58834}, {5527, 11531}, {6244, 8917}, {7987, 56380}, {10860, 17742}, {14256, 45275}, {34033, 58326}, {37022, 45765}, {45047, 58034}

X(61151) = excentral-isogonal conjugate of X(16572)
X(61151) = X(728)-Ceva conjugate of X(1)
X(61151) = X(479)-Dao conjugate of X(23062)





leftri   Miyamoto Perspectors: X(61152)-X(61159 and X(61244)-X(61297)  rightri

This preamble, based on notes from Keita Miyamoto, was submitted by Clark Kimberling, January 20, 2024. Barycentrics for Miyamoto perspectors were found by Peter Moses.

Let A'B'C' be a triangle homothetic to ABC at X(2) with ratio k. Let Ab=AB∩B'C', and define Bc and Ca cyclically. Let Ac=CA∩B'C', and define Ba and Cb cyclically. Let (I), (Ia), (Ib), (Ic) be the incircles of ABC, A'BcCb, B'CaAc, C'AbBa, respectively. Then there exists a circle (O(k)) tangent to all four circles, (I), (Ia), (Ib), (Ic). The touchpoint of (I) and (O(k)) is the Feuerbach point, X(11). Further, let Ta be the touchpoint of (Ia) and (O(k)), and define Tb and Tc cyclically. The lines ATa, BTb, CTc concur in a point here named the Miyamoto (k)-perspector.

Likewise, if A'B'C' is homothetic to an arbitrary triangle T = A''B''C'', X(2) with ratio k, then the above construction yields a point here named named the (T,k)-Miyamoto perspector. Fifty-four (Euler triangle, k)-Miyamoto perspectors, found by Peter Moses, are indexed at X(61244)-X(61297).

The points X(61152)-X(61159 lie on the line X(2)X(11), and X(21244)-X(61297) lie on X(1)X(5).

The appearance of (k,X(i)) in the following list means that X(i) = Miyamoto (k)-perspector.

(-3,61152), (-2,61153), (3,61154), (1/2,61155), (-3/2,61156), (3/2,61157), (-2/3, 61158), (2/3,61159)

(-8,61244), (-13/2,61245), (-17/4,61246), (-4,61247), (-16/5,61248), (-11/4,61249), (-13/5,61250), (-5/2,61251), (-17/7,61252), (-19/8,61253), (-5,3,61254), (-13/8,61255), (-11/7,61256), (-4/3,61257), (-8/7,61258), (-7/8,61259)

(-5/6,61260), (-4/5,61261), (-3/4,61262), (-2/3,61263), (-3/5,61264), (-3/7,61265), (-2/5,61266), (-3/8,61267), (-2/7,61268), (-1/4,61269),

(-1/6,61270), (-1/7,61271), (-1/8,61272), (1/6,61273), (1/5,61274), (1/3,61275), (2/5,61276), (4/7,61277), (5/8,61278), (2/3,61279),

(3/4,61280), (11/8,61281), (10/7,61282), (3/2,61283), (8/5,61284), (5/3,61285), (7/4,61286), (2,61287), (11/5,61288), (19/7,61289),

(3/4,61290), (11/8,61291), (10/7,61292), (3/2,61293), (8/5,61294), (5/3,61295), (7/4,61296)

underbar



X(61152) = MIRAMOTO (-3)-PERSPECTOR

Barycentrics    a*(5*a^2 - 5*a*b - 5*a*c + 8*b*c) : :

X(61152) lies on these lines: {2, 11}, {3, 37712}, {10, 19535}, {35, 16866}, {42, 14969}, {56, 3632}, {165, 3715}, {382, 10310}, {404, 20050}, {474, 3636}, {480, 44785}, {550, 11499}, {956, 3626}, {984, 9324}, {999, 34747}, {1155, 3711}, {1319, 11525}, {1466, 17563}, {1486, 30734}, {1698, 16860}, {1706, 34471}, {1837, 44848}, {2098, 5438}, {3052, 9350}, {3243, 3689}, {3244, 3304}, {3306, 15570}, {3528, 11500}, {3529, 44846}, {3530, 8273}, {3544, 11496}, {3851, 11248}, {3913, 20057}, {3983, 35242}, {4649, 56010}, {4686, 34247}, {4731, 30282}, {5217, 5251}, {5541, 35272}, {5790, 12119}, {7080, 9657}, {8715, 15808}, {9332, 42043}, {9337, 16569}, {9671, 31246}, {10267, 55863}, {10896, 47742}, {11358, 19739}, {11495, 60983}, {14269, 35000}, {14869, 32141}, {15015, 40587}, {15681, 35238}, {15688, 18524}, {16371, 34641}, {16417, 48696}, {16468, 37540}, {16857, 51817}, {17601, 51294}, {19820, 37099}, {20850, 37577}, {31508, 36835}, {37602, 51094}, {38052, 52638}

X(61152) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 1376, 4413}, {100, 4413, 55}, {1155, 46917, 3711}, {3626, 25440, 19537}, {3632, 17573, 56}, {4421, 4423, 55}

X(61153) = MIRAMOTO (2)-PERSPECTOR

Barycentrics    a*(5*a^2 - 5*a*b - 5*a*c + 2*b*c) : :
X(61153) = 3 X[2] - 5 X[5218]

X(61153) lies on these lines: {1, 19537}, {2, 11}, {3, 3244}, {6, 55933}, {8, 17574}, {10, 16866}, {35, 956}, {43, 21000}, {56, 20057}, {57, 15570}, {165, 3243}, {197, 20850}, {200, 15481}, {382, 11500}, {480, 60983}, {518, 35445}, {546, 11496}, {550, 11248}, {678, 4414}, {899, 8692}, {958, 3626}, {993, 8168}, {997, 51787}, {1011, 19750}, {1155, 42871}, {1388, 37789}, {1478, 34626}, {2177, 37540}, {2223, 21524}, {2802, 37606}, {2975, 20054}, {3052, 16468}, {3158, 4640}, {3189, 5775}, {3242, 17601}, {3295, 3636}, {3486, 32157}, {3528, 10310}, {3529, 11491}, {3530, 10267}, {3550, 4649}, {3612, 10912}, {3629, 12329}, {3689, 5220}, {3722, 17595}, {3746, 25524}, {3851, 11499}, {3871, 5217}, {3880, 30282}, {3895, 37600}, {4031, 37541}, {4262, 4752}, {4302, 11236}, {4313, 8256}, {4314, 37828}, {4681, 15624}, {5010, 11194}, {5119, 56177}, {5144, 29606}, {5248, 16860}, {5251, 5687}, {5524, 16885}, {5537, 11495}, {6244, 43176}, {6600, 60942}, {6767, 40726}, {7232, 50748}, {7676, 60957}, {7951, 34706}, {8053, 49988}, {8236, 17051}, {9332, 42042}, {9337, 26102}, {9345, 17782}, {9670, 27529}, {9708, 38098}, {10087, 51636}, {10301, 11383}, {10386, 26364}, {10528, 15338}, {10895, 20066}, {11239, 15326}, {11497, 26339}, {11498, 26340}, {11501, 31660}, {12630, 24477}, {12635, 37568}, {12653, 37525}, {13204, 24981}, {14269, 18524}, {14969, 17018}, {15254, 46917}, {15688, 35000}, {15720, 37621}, {15808, 25440}, {16370, 48696}, {17783, 33094}, {19654, 52924}, {19705, 37587}, {19833, 37090}, {21518, 29605}, {21870, 36277}, {22034, 60723}, {22557, 33464}, {22558, 33465}, {24703, 59584}, {25415, 33595}, {29602, 40910}, {30337, 45036}, {34200, 35238}, {34791, 35242}, {36744, 59221}, {49498, 54281}, {53053, 59691}

X(61153) = barycentric product X(100)*X(44567)
X(61153) = barycentric quotient X(44567)/X(693)
X(61153) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {35, 3632, 19535}, {55, 100, 1001}, {55, 1376, 4428}, {55, 4421, 1376}, {100, 1001, 1376}, {1001, 4421, 100}, {1376, 4428, 8167}, {3158, 31508, 4640}, {3295, 17573, 3636}, {3626, 17571, 958}, {3689, 35258, 5220}, {3871, 5217, 12513}, {5281, 34607, 2886}, {5432, 20075, 11235}, {24646, 24647, 45310}, {48696, 51817, 16370}

X(61154) = MIRAMOTO (3)-PERSPECTOR

Barycentrics    a*(7*a^2 - 7*a*b - 7*a*c + 4*b*c) : :

X(61154) lies on these lines: {2, 11}, {3, 3633}, {10, 19538}, {35, 4668}, {56, 3635}, {165, 41711}, {171, 14969}, {210, 31508}, {480, 61000}, {548, 10310}, {678, 3242}, {956, 3625}, {1155, 3243}, {1657, 11248}, {3627, 32141}, {3689, 5223}, {3711, 15481}, {3843, 11849}, {3850, 11499}, {3871, 5204}, {3913, 20053}, {4309, 31246}, {4314, 44848}, {4649, 37540}, {4691, 5687}, {4718, 15624}, {4860, 15570}, {5541, 37606}, {6144, 12329}, {6600, 60977}, {7951, 34707}, {8162, 16371}, {8168, 17549}, {8273, 61138}, {9671, 27529}, {9708, 51817}, {10246, 12653}, {11491, 17538}, {11495, 60976}, {11500, 33703}, {11525, 30282}, {12630, 51463}, {14093, 35238}, {14882, 56998}, {15689, 35000}, {17782, 37674}, {18524, 38335}, {21523, 49761}, {41702, 58230}

X(61154) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {55, 100, 4413}, {4995, 17784, 31245}, {5218, 6154, 31140}, {24646, 24647, 59376}

X(61155) = MIRAMOTO (1/2)-PERSPECTOR

Barycentrics    a*(2*a^2 - 2*a*b - 2*a*c - b*c) : :

X(61155) lies on these lines: {1, 89}, {2, 11}, {3, 3622}, {4, 37621}, {6, 30653}, {7, 2078}, {8, 3746}, {9, 3935}, {10, 16859}, {20, 10267}, {21, 145}, {23, 1486}, {31, 3750}, {35, 3616}, {36, 38314}, {37, 1383}, {38, 17715}, {42, 8616}, {56, 17548}, {57, 29817}, {63, 3243}, {81, 3052}, {144, 2346}, {153, 6930}, {165, 4666}, {171, 9345}, {192, 17002}, {197, 13595}, {200, 27065}, {238, 2177}, {244, 17601}, {344, 60459}, {345, 33090}, {354, 23958}, {377, 20066}, {388, 15680}, {404, 46934}, {405, 3617}, {442, 10386}, {452, 943}, {495, 11114}, {498, 5154}, {516, 31019}, {517, 37106}, {551, 5010}, {595, 19767}, {631, 11849}, {678, 8297}, {692, 11003}, {748, 17782}, {750, 16484}, {846, 3938}, {885, 8641}, {896, 49490}, {898, 2384}, {899, 15485}, {940, 21000}, {954, 1005}, {958, 3621}, {962, 10902}, {968, 3749}, {984, 3722}, {993, 3241}, {999, 17549}, {1006, 10679}, {1011, 19717}, {1056, 20067}, {1058, 6910}, {1125, 17572}, {1155, 42819}, {1201, 37574}, {1252, 5377}, {1279, 4689}, {1283, 9791}, {1308, 38941}, {1385, 17613}, {1386, 17013}, {1479, 5141}, {1482, 6875}, {1617, 21454}, {1776, 40269}, {1962, 17716}, {2077, 54445}, {2098, 51683}, {2099, 5427}, {2223, 21508}, {2280, 60711}, {2292, 36565}, {2308, 42042}, {2475, 4294}, {2476, 15171}, {2646, 3890}, {2887, 29866}, {2975, 3303}, {3011, 33134}, {3085, 5046}, {3086, 37291}, {3090, 32141}, {3091, 11491}, {3120, 29675}, {3146, 11496}, {3158, 3305}, {3161, 53661}, {3219, 3870}, {3231, 16969}, {3256, 5435}, {3286, 26860}, {3304, 5303}, {3306, 35445}, {3315, 17595}, {3421, 31156}, {3474, 26842}, {3475, 17483}, {3523, 10586}, {3524, 35000}, {3545, 18524}, {3550, 3720}, {3583, 10197}, {3600, 11510}, {3636, 7280}, {3666, 17024}, {3681, 3683}, {3685, 4671}, {3689, 15254}, {3712, 33089}, {3724, 27811}, {3742, 9352}, {3744, 28606}, {3748, 3873}, {3753, 51787}, {3757, 28605}, {3771, 25958}, {3821, 29638}, {3832, 11500}, {3869, 37080}, {3877, 24929}, {3883, 33077}, {3884, 37571}, {3889, 3916}, {3895, 11525}, {3897, 9957}, {3898, 12758}, {3913, 4678}, {3914, 29681}, {3915, 37573}, {3961, 51294}, {3977, 49466}, {3979, 32912}, {3995, 60723}, {3996, 5278}, {4015, 41872}, {4030, 32862}, {4184, 8025}, {4199, 31037}, {4232, 11383}, {4233, 11406}, {4293, 37299}, {4295, 14798}, {4307, 37635}, {4309, 10198}, {4314, 24987}, {4323, 37583}, {4326, 60969}, {4393, 23407}, {4416, 50744}, {4418, 29651}, {4425, 29848}, {4427, 24349}, {4432, 32931}, {4450, 18134}, {4511, 59337}, {4514, 33113}, {4571, 10005}, {4645, 29830}, {4653, 37610}, {4660, 25959}, {4676, 46897}, {4752, 16788}, {4760, 24357}, {4881, 30282}, {5014, 33116}, {5047, 5687}, {5056, 11499}, {5057, 17718}, {5080, 10056}, {5087, 52638}, {5144, 16826}, {5217, 5253}, {5225, 10585}, {5250, 34772}, {5258, 20050}, {5259, 8715}, {5265, 11509}, {5269, 17019}, {5273, 12630}, {5311, 60688}, {5361, 17135}, {5372, 10453}, {5422, 7074}, {5426, 12653}, {5428, 8148}, {5531, 60911}, {5537, 52769}, {5550, 25440}, {5552, 37162}, {5554, 54430}, {5603, 32613}, {5640, 51377}, {5697, 35016}, {5698, 17484}, {5731, 34486}, {5734, 11012}, {5744, 8236}, {5775, 12649}, {5853, 54357}, {5901, 6942}, {5905, 10578}, {6327, 29839}, {6361, 37105}, {6679, 29868}, {6767, 16370}, {6839, 37000}, {6872, 11508}, {6876, 22791}, {6888, 12116}, {6892, 10806}, {6906, 16202}, {6913, 54448}, {6914, 7967}, {6950, 10246}, {6954, 10596}, {6960, 10531}, {6986, 10306}, {7191, 17594}, {7288, 14882}, {7290, 17012}, {7373, 19535}, {7465, 19823}, {7483, 15172}, {7489, 59388}, {7492, 20872}, {7504, 9669}, {7508, 10247}, {7518, 41227}, {7585, 44591}, {7586, 44590}, {7676, 36003}, {7677, 37541}, {7688, 34632}, {8053, 17379}, {8162, 11194}, {8225, 21568}, {8273, 21734}, {8645, 47776}, {8666, 20057}, {8690, 28531}, {9335, 29820}, {9347, 15569}, {9463, 21788}, {9540, 35773}, {9544, 20986}, {9580, 31266}, {9668, 17577}, {9708, 16858}, {9709, 17536}, {9778, 15931}, {9779, 44425}, {9802, 35204}, {9965, 20835}, {10179, 37600}, {10310, 15717}, {10387, 15988}, {10448, 37588}, {10582, 31508}, {10786, 13729}, {11002, 56878}, {11010, 30143}, {11036, 37285}, {11038, 33925}, {11108, 46932}, {11322, 19740}, {11343, 29621}, {11507, 14986}, {12329, 51171}, {12410, 59359}, {12575, 24541}, {13405, 31053}, {13464, 59331}, {13935, 35772}, {14002, 20989}, {14100, 61025}, {15246, 37577}, {15624, 27268}, {15674, 19843}, {15692, 35238}, {15837, 61026}, {16133, 35989}, {16367, 17014}, {16418, 31145}, {16503, 41423}, {16842, 46930}, {17011, 37553}, {17015, 37817}, {17025, 46904}, {17125, 56009}, {17242, 50000}, {17302, 29831}, {17314, 59235}, {17316, 45765}, {17349, 19998}, {17469, 17592}, {17495, 56777}, {17522, 39587}, {17558, 56936}, {17576, 20076}, {17591, 29818}, {17724, 33151}, {17766, 29643}, {17768, 37703}, {17776, 33091}, {17778, 20064}, {17889, 29689}, {18515, 50824}, {18519, 28461}, {18526, 31649}, {19526, 20054}, {19742, 20012}, {19789, 37090}, {19860, 53053}, {20011, 37652}, {20101, 37175}, {20965, 53145}, {20992, 37677}, {21161, 50872}, {21218, 40637}, {21511, 29624}, {21514, 30833}, {21537, 29586}, {21565, 31546}, {21793, 60724}, {22753, 59421}, {23865, 26853}, {24169, 29853}, {24210, 29665}, {24248, 33148}, {24331, 24344}, {24392, 55867}, {24723, 33122}, {25055, 51817}, {25101, 49991}, {25568, 26792}, {25957, 29870}, {26015, 30331}, {26034, 33173}, {26127, 26364}, {26228, 33155}, {26626, 40910}, {27086, 40292}, {27131, 40998}, {27152, 27264}, {27529, 31452}, {28184, 29308}, {28443, 34631}, {28453, 50818}, {28463, 50805}, {28466, 44455}, {29640, 33104}, {29642, 32948}, {29656, 32776}, {29661, 33109}, {29667, 59692}, {29670, 32930}, {29672, 33125}, {29678, 33106}, {29832, 49704}, {30147, 37563}, {30295, 59375}, {30950, 56010}, {30957, 59679}, {31018, 52653}, {31035, 33845}, {31393, 38460}, {31477, 33854}, {31479, 37375}, {31567, 55876}, {31568, 55877}, {31888, 37292}, {32848, 49506}, {32916, 32943}, {32917, 32941}, {32920, 32936}, {32923, 32934}, {32950, 33124}, {33065, 50748}, {33070, 49709}, {33074, 33158}, {33076, 33156}, {33083, 33171}, {33094, 33130}, {33095, 33127}, {33100, 33144}, {33170, 36479}, {33172, 44419}, {33175, 50295}, {34879, 38053}, {35596, 51099}, {36263, 49675}, {36500, 56313}, {36845, 55868}, {37297, 37547}, {37540, 37633}, {37568, 51715}, {37572, 58565}, {37587, 51103}, {37606, 51636}, {37720, 58404}, {41553, 60944}, {48696, 53620}, {49469, 50756}, {51300, 59217}, {56983, 59299}, {60685, 60712}

X(61155) = anticomplement of X(33108)
X(61155) = crossdifference of every pair of points on line {665, 4893}
X(61155) = barycentric product X(i)*X(j) for these {i,j}: {1, 17335}, {100, 31150}, {190, 4794}
X(61155) = barycentric quotient X(i)/X(j) for these {i,j}: {4794, 514}, {17335, 75}, {31150, 693}
X(61155) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 902, 17126}, {1, 4414, 4392}, {1, 17126, 14996}, {1, 35258, 3218}, {2, 390, 149}, {2, 20075, 33110}, {2, 20095, 2550}, {8, 5248, 16865}, {21, 3295, 145}, {31, 3750, 17018}, {31, 17018, 37685}, {35, 3616, 4188}, {42, 8616, 17127}, {55, 1001, 100}, {55, 1621, 2}, {55, 4423, 4421}, {55, 4428, 1621}, {55, 23404, 5132}, {63, 3957, 4430}, {63, 10389, 3957}, {81, 3052, 30652}, {100, 1001, 2}, {100, 1621, 1001}, {165, 4666, 27003}, {238, 2177, 3240}, {238, 3240, 14997}, {405, 3871, 3617}, {748, 17782, 60714}, {846, 3938, 7226}, {968, 3749, 3920}, {1006, 10679, 59417}, {1279, 4689, 4850}, {1376, 5284, 2}, {2975, 3303, 3623}, {3058, 6690, 11680}, {3219, 3870, 4661}, {3475, 44447, 17483}, {3685, 26227, 4671}, {3744, 28606, 29815}, {3746, 5248, 8}, {3746, 5251, 25439}, {3748, 4640, 3873}, {3757, 32929, 28605}, {3771, 32947, 25958}, {3870, 4512, 3219}, {3913, 5260, 4678}, {4309, 10198, 52367}, {4429, 24542, 2}, {4660, 29632, 25959}, {5047, 5687, 46933}, {5217, 5253, 37307}, {5248, 25439, 5251}, {5251, 25439, 8}, {5259, 8715, 9780}, {5259, 9780, 17570}, {6690, 11680, 2}, {6767, 16370, 54391}, {8167, 9342, 2}, {9709, 17536, 46931}, {24646, 24647, 10707}, {35445, 38316, 3306}

X(61156) = MIRAMOTO (-3/2)-PERSPECTOR

Barycentrics    a*(2*a^2 - 2*a*b - 2*a*c + 5*b*c) : :

X(61156) lies on these lines: {2, 11}, {3, 38138}, {8, 5563}, {10, 4188}, {20, 18491}, {21, 46932}, {35, 16859}, {36, 53620}, {37, 40103}, {43, 37685}, {56, 4678}, {57, 4661}, {75, 26239}, {88, 3242}, {89, 3751}, {145, 474}, {153, 6955}, {165, 27065}, {171, 9350}, {197, 15246}, {200, 4430}, {210, 9352}, {404, 956}, {405, 46931}, {498, 26060}, {750, 3240}, {851, 27081}, {899, 14997}, {958, 37307}, {999, 31145}, {1054, 4392}, {1155, 15481}, {1191, 27645}, {1320, 35272}, {1486, 16042}, {1698, 16865}, {2078, 31188}, {2308, 36634}, {2320, 15015}, {2476, 47742}, {2551, 37256}, {3052, 37687}, {3158, 29817}, {3218, 5223}, {3219, 8580}, {3243, 3306}, {3295, 17535}, {3304, 20014}, {3474, 26792}, {3523, 11499}, {3524, 18524}, {3525, 32141}, {3533, 37621}, {3543, 35238}, {3545, 35000}, {3616, 25439}, {3621, 5253}, {3622, 5687}, {3623, 25524}, {3634, 17570}, {3681, 23958}, {3689, 15570}, {3724, 27812}, {3752, 29815}, {3820, 17579}, {3828, 5010}, {3832, 10310}, {3870, 30350}, {3871, 16408}, {3897, 4002}, {3921, 5122}, {3923, 9458}, {3938, 9335}, {3957, 5437}, {3968, 37525}, {4015, 37524}, {4189, 5251}, {4209, 27025}, {4383, 30652}, {4414, 9330}, {4512, 36835}, {4604, 51157}, {4651, 5372}, {4669, 37587}, {4671, 5205}, {4772, 34247}, {4881, 9623}, {4998, 60720}, {5047, 46930}, {5056, 11248}, {5067, 11849}, {5084, 20066}, {5141, 26364}, {5144, 17292}, {5255, 27625}, {5260, 17548}, {5265, 11501}, {5269, 17020}, {5361, 59296}, {5537, 9779}, {5550, 8715}, {5775, 26062}, {5790, 38602}, {5836, 33176}, {6745, 31019}, {6904, 20060}, {6909, 54448}, {6911, 59417}, {6915, 20070}, {6950, 38042}, {7492, 20989}, {7998, 51377}, {8165, 31295}, {8168, 20049}, {8617, 21788}, {9345, 17018}, {9347, 17013}, {9511, 47772}, {9708, 13587}, {10267, 55864}, {10303, 11491}, {10528, 17580}, {11115, 26029}, {11358, 19742}, {11383, 52284}, {11496, 15022}, {11500, 15717}, {11525, 38460}, {12245, 45976}, {12773, 59388}, {13595, 37577}, {14002, 20872}, {15587, 61026}, {16133, 37541}, {16417, 54391}, {16569, 17127}, {16704, 35983}, {17124, 29814}, {17297, 27756}, {17566, 31419}, {17616, 58650}, {17740, 60459}, {17780, 24349}, {18193, 26745}, {19284, 59299}, {19825, 37099}, {19998, 37684}, {20045, 24620}, {20103, 27131}, {20965, 21780}, {24174, 36565}, {24280, 30578}, {24593, 49450}, {24616, 60731}, {25005, 44848}, {25568, 26842}, {25946, 29616}, {25961, 29866}, {26037, 59679}, {28604, 52086}, {29579, 45765}, {29665, 59593}, {29864, 58443}, {30653, 37540}, {31025, 60723}, {32929, 46938}, {33125, 59726}, {33884, 56878}, {35258, 35595}, {35986, 36991}, {37462, 59591}, {37639, 59295}, {38314, 48696}, {46916, 54357}, {51636, 59415}, {54389, 59239}, {59412, 60885}

X(61156) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {35, 19877, 16859}, {55, 9342, 2}, {100, 4413, 2}, {200, 27003, 4430}, {404, 9709, 3617}, {750, 3240, 14996}, {750, 56009, 3240}, {899, 17126, 14997}, {899, 56010, 17126}, {1376, 4413, 100}, {3035, 33108, 2}, {3306, 46917, 3935}, {3871, 16408, 46934}, {5687, 17531, 3622}, {9780, 25440, 4189}, {17124, 60714, 29814}, {37540, 37680, 30653}

X(61157) = MIRAMOTO (3/2)-PERSPECTOR

Barycentrics    a*(4*a^2 - 4*a*b - 4*a*c + b*c) : :

X(61157) lies on these lines: {1, 37307}, {2, 11}, {3, 3623}, {10, 54342}, {20, 11849}, {21, 4678}, {35, 145}, {42, 30652}, {89, 49478}, {165, 3957}, {171, 17782}, {519, 51817}, {678, 984}, {902, 3240}, {956, 3621}, {993, 31145}, {1000, 51636}, {1023, 4262}, {1056, 36004}, {1155, 15570}, {1320, 37606}, {1486, 14002}, {1994, 7074}, {2177, 4649}, {2320, 2802}, {2975, 20014}, {3085, 20066}, {3091, 32141}, {3146, 11491}, {3158, 3219}, {3161, 53672}, {3218, 3243}, {3241, 5010}, {3256, 21454}, {3295, 4188}, {3421, 15677}, {3522, 11248}, {3523, 37621}, {3550, 17018}, {3600, 14882}, {3617, 5251}, {3622, 3746}, {3689, 15481}, {3722, 4392}, {3748, 9352}, {3749, 17024}, {3750, 9345}, {3774, 30650}, {3832, 18491}, {3839, 18524}, {3870, 31508}, {3877, 51787}, {3889, 31663}, {3913, 20052}, {3935, 5223}, {3996, 5361}, {4015, 56203}, {4193, 10386}, {4309, 27529}, {4314, 25005}, {4326, 61026}, {4640, 4661}, {4704, 15624}, {4781, 24349}, {4881, 31393}, {5068, 11499}, {5144, 29569}, {5154, 15171}, {5248, 17544}, {5259, 46931}, {5267, 20050}, {5687, 16865}, {5744, 12630}, {6600, 61006}, {6767, 13587}, {6950, 12773}, {7280, 20057}, {7465, 19824}, {7676, 20059}, {7705, 31795}, {7967, 38602}, {8617, 16969}, {9337, 17124}, {9709, 17570}, {9778, 17483}, {10129, 52638}, {10267, 15717}, {10304, 35000}, {10310, 21734}, {10389, 27003}, {10434, 58820}, {10528, 15680}, {10578, 26842}, {10987, 17756}, {11002, 51377}, {11239, 20067}, {11322, 19741}, {11383, 52301}, {11496, 50689}, {11500, 17578}, {12329, 51170}, {14996, 37540}, {15172, 17566}, {16704, 20048}, {16981, 56878}, {17127, 60714}, {17549, 20049}, {17594, 29815}, {18515, 50818}, {20214, 35989}, {21000, 32911}, {24325, 24344}, {24616, 49450}, {25440, 46934}, {27131, 59584}, {27741, 28562}, {29583, 45765}, {29585, 40910}, {29588, 37586}, {29866, 32948}, {30282, 38460}, {31452, 52367}, {32613, 59417}, {35448, 37105}, {35595, 46917}, {37162, 59591}, {54409, 59239}, {56028, 58607}

X(61157) = reflection of X(10129) in X(52638)
X(61157) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {35, 145, 17548}, {55, 4421, 1621}, {100, 1621, 4413}, {149, 5218, 2}, {165, 3957, 23958}, {902, 3240, 30653}, {3722, 17601, 4392}, {3871, 4189, 3621}, {4413, 4421, 100}, {5248, 46933, 17544}, {5281, 20075, 2}, {24646, 24647, 59377}

X(61158) = MIRAMOTO (-2/3)-PERSPECTOR

Barycentrics    a*(a^2 - a*b - a*c + 10*b*c) : :

X(61158) lies on these lines: {1, 16864}, {2, 11}, {3, 10172}, {6, 9332}, {8, 17051}, {9, 36835}, {10, 7373}, {35, 16854}, {43, 37682}, {45, 1054}, {56, 17535}, {57, 15481}, {88, 9330}, {140, 18491}, {200, 3848}, {405, 19872}, {474, 5251}, {547, 35238}, {551, 8168}, {692, 16187}, {750, 21747}, {899, 9345}, {956, 1698}, {958, 3634}, {999, 3828}, {1329, 17582}, {1386, 54390}, {2223, 21527}, {2975, 46930}, {3243, 3742}, {3295, 19878}, {3304, 46933}, {3306, 5220}, {3526, 11500}, {3614, 50237}, {3624, 3913}, {3628, 11496}, {3715, 27003}, {3740, 5223}, {3833, 3940}, {3838, 20196}, {3921, 51816}, {3952, 24594}, {4002, 10912}, {4197, 31246}, {4363, 24003}, {4383, 17124}, {4640, 51780}, {4649, 16569}, {4682, 23511}, {4942, 59506}, {5010, 17542}, {5024, 52708}, {5067, 10310}, {5087, 38052}, {5217, 17536}, {5248, 16855}, {5253, 46931}, {5259, 16856}, {5268, 16602}, {5316, 5880}, {5687, 34595}, {5695, 30829}, {5710, 28257}, {5745, 8169}, {6244, 10171}, {6691, 19855}, {6767, 19883}, {7951, 57005}, {8170, 44848}, {8273, 55864}, {8692, 17125}, {9708, 40726}, {9709, 19862}, {9780, 12513}, {10267, 16239}, {10527, 34501}, {10896, 26060}, {11108, 31253}, {11194, 19876}, {11231, 22753}, {11248, 55856}, {11284, 20872}, {11383, 52293}, {11499, 46219}, {11814, 24693}, {12329, 51128}, {13887, 32789}, {13940, 32790}, {14969, 37633}, {16409, 52139}, {16421, 20470}, {16468, 17122}, {16675, 17593}, {16830, 31233}, {16853, 25440}, {16884, 17779}, {17303, 59221}, {17580, 57288}, {19541, 58441}, {19861, 33176}, {20989, 40916}, {21520, 37586}, {24328, 25341}, {24620, 49453}, {30947, 49460}, {31259, 52793}, {32141, 55862}, {33879, 56878}, {36480, 58467}, {37789, 60909}, {42819, 46917}

X(61158) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1376, 8167}, {2, 4413, 1001}, {2, 9342, 55}, {2, 26040, 3816}, {1001, 4413, 1376}, {1376, 8167, 4428}, {1698, 16862, 25524}, {3634, 16408, 958}, {17125, 37540, 8692}, {17535, 19877, 56}

X(61159) = MIRAMOTO (2/3)-PERSPECTOR

Barycentrics    a*(7*a^2 - 7*a*b - 7*a*c - 2*b*c) : :

X(61159) lies on these lines: {2, 11}, {21, 20053}, {548, 10267}, {956, 3633}, {958, 3625}, {1657, 37621}, {2223, 21523}, {2346, 60976}, {3052, 4649}, {3243, 4640}, {3295, 3635}, {3298, 9688}, {3627, 11496}, {3742, 31508}, {3750, 9332}, {3843, 11500}, {3850, 18491}, {3913, 4668}, {4383, 17782}, {4512, 15481}, {4691, 5248}, {8162, 17549}, {8168, 16418}, {8273, 58188}, {9345, 37540}, {9709, 22266}, {10246, 46684}, {10310, 61138}, {10389, 15570}, {11248, 15712}, {11495, 61020}, {12812, 32141}, {14891, 35238}, {14969, 17126}, {15706, 35000}, {19704, 37602}, {21507, 37586}, {35258, 42871}, {35445, 42819}

X(61159) lies on these lines: {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {55, 1621, 4421}, {55, 4428, 1376}, {1001, 4413, 8167}, {1001, 4421, 4413}, {1621, 4413, 1001}, {1621, 4421, 8167}, {4421, 8167, 1376}, {4428, 8167, 1621}

X(61160) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(1) AND CEVIAN-OF-X(19)

Barycentrics    a*(a-b)*(a^2+(b-c)^2)*(a-c)*(b+c) : :

X(61160) lies on these lines: {1, 20974}, {9, 124}, {19, 5521}, {37, 18210}, {100, 28847}, {101, 13397}, {190, 37215}, {228, 21856}, {513, 35326}, {614, 21813}, {649, 3234}, {650, 23845}, {661, 4551}, {851, 51436}, {1018, 3952}, {3120, 18785}, {3294, 26580}, {3730, 31018}, {4069, 35309}, {4557, 35310}, {5057, 20605}, {9367, 22344}, {15487, 21015}, {15507, 23988}, {16549, 27070}, {17747, 39690}, {21319, 21795}, {21362, 35341}, {22321, 36197}, {24455, 44312}, {32739, 61221}, {35312, 49296}, {42723, 57151}, {48269, 61185}

X(61160) = trilinear pole of line {16583, 40934}
X(61160) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 48070}, {513, 40403}, {1019, 56179}, {1021, 56359}, {1037, 4560}, {1459, 40411}, {3733, 30701}, {3737, 7131}, {4025, 57386}, {4573, 14935}, {7084, 7199}, {7123, 7192}, {7203, 56243}, {7252, 8817}, {16726, 52778}, {21789, 30705}, {57129, 57925}
X(61160) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 48070}, {614, 17498}, {6554, 7199}, {15487, 7192}, {16583, 15413}, {17463, 116}, {18589, 514}, {39026, 40403}
X(61160) = X(i)-Ceva conjugate of X(j) for these {i, j}: {57750, 1}
X(61160) = X(i)-cross conjugate of X(j) for these {i, j}: {50490, 614}
X(61160) = pole of line {19, 25} with respect to the Yff parabola
X(61160) = pole of line {3751, 3868} with respect to the Hutson-Moses hyperbola
X(61160) = pole of line {4568, 61223} with respect to the dual conic of incircle
X(61160) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1018), X(3732)}}, {{A, B, C, X(1633), X(3952)}}, {{A, B, C, X(3700), X(21107)}}, {{A, B, C, X(3914), X(4551)}}, {{A, B, C, X(4169), X(16583)}}, {{A, B, C, X(21832), X(50490)}}, {{A, B, C, X(48403), X(55240)}}
X(61160) = barycentric product X(i)*X(j) for these (i, j): {10, 1633}, {37, 3732}, {100, 3914}, {101, 53510}, {162, 21015}, {1018, 4000}, {1020, 6554}, {1040, 61178}, {1332, 52577}, {1783, 18589}, {1978, 21750}, {2082, 4552}, {3673, 4557}, {3699, 40961}, {3952, 614}, {4069, 7195}, {4319, 4566}, {4551, 497}, {16502, 4033}, {16583, 190}, {17441, 1897}, {20235, 8750}, {21813, 799}, {23620, 6335}, {28017, 30730}, {40934, 668}, {40965, 664}, {48403, 765}, {50490, 7035}
X(61160) = barycentric quotient X(i)/X(j) for these (i, j): {37, 48070}, {101, 40403}, {497, 18155}, {614, 7192}, {1018, 30701}, {1020, 30705}, {1633, 86}, {1783, 40411}, {2082, 4560}, {3673, 52619}, {3732, 274}, {3914, 693}, {3952, 57925}, {4000, 7199}, {4319, 7253}, {4551, 8817}, {4557, 56179}, {4559, 7131}, {7083, 3737}, {7289, 15419}, {8020, 6591}, {15487, 17498}, {16502, 1019}, {16583, 514}, {17441, 4025}, {18589, 15413}, {21015, 14208}, {21750, 649}, {21813, 661}, {22057, 4131}, {22363, 1459}, {23620, 905}, {28017, 17096}, {30706, 1021}, {40934, 513}, {40961, 3676}, {40965, 522}, {48398, 16727}, {48403, 1111}, {50490, 244}, {52577, 17924}, {53321, 56359}, {53510, 3261}
X(61160) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3952, 61173, 1018}, {21362, 35341, 46148}

X(61161) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(1) AND CEVIAN-OF-X(21)

Barycentrics    a*(a-b)*(a-c)*(b+c)*(2*a*b*c+a^2*(b+c)-(b-c)^2*(b+c)) : :

X(61161) lies on these lines: {10, 1146}, {30, 59734}, {37, 115}, {71, 2265}, {72, 57693}, {99, 42717}, {100, 112}, {101, 6011}, {119, 1826}, {306, 51390}, {650, 35342}, {661, 61168}, {905, 17136}, {1018, 4551}, {2247, 3579}, {2276, 5725}, {3002, 44669}, {3178, 3991}, {3293, 17745}, {3501, 37699}, {3694, 21076}, {3939, 21891}, {4515, 21081}, {4552, 52607}, {4557, 61162}, {4705, 22280}, {6335, 6528}, {7117, 10609}, {8678, 53268}, {16578, 24086}, {16601, 21674}, {16669, 20972}, {16699, 47033}, {20691, 20700}, {20729, 35059}, {21675, 40937}, {21872, 56894}, {25068, 27714}, {25082, 27690}, {26796, 54118}, {30730, 61174}, {35338, 61237}, {46102, 54952}, {53323, 61236}, {61197, 61220}, {61212, 61228}

X(61161) = trilinear pole of line {2294, 40952}
X(61161) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 56320}, {514, 1175}, {649, 40412}, {943, 1019}, {1459, 40395}, {1790, 14775}, {1794, 17925}, {2259, 7192}, {2982, 3737}, {3733, 40435}, {4025, 40570}, {7252, 60041}, {15439, 17197}, {23189, 40573}, {40422, 57129}
X(61161) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 56320}, {442, 4560}, {942, 905}, {5249, 16755}, {5375, 40412}, {16585, 7199}, {16732, 23989}, {18591, 7192}, {40937, 693}, {52119, 16732}
X(61161) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1252, 37}, {6335, 61180}, {46102, 72}, {61220, 61169}
X(61161) = pole of line {5279, 10461} with respect to the Yff parabola
X(61161) = pole of line {72, 5260} with respect to the Hutson-Moses hyperbola
X(61161) = intersection, other than A, B, C, of circumconics {{A, B, C, X(72), X(54952)}}, {{A, B, C, X(112), X(4559)}}, {{A, B, C, X(115), X(47235)}}, {{A, B, C, X(162), X(4551)}}, {{A, B, C, X(442), X(4238)}}, {{A, B, C, X(906), X(54970)}}, {{A, B, C, X(1783), X(21859)}}, {{A, B, C, X(3952), X(6528)}}, {{A, B, C, X(4552), X(4574)}}
X(61161) = barycentric product X(i)*X(j) for these (i, j): {10, 61220}, {100, 442}, {107, 59163}, {190, 2294}, {226, 61233}, {306, 61236}, {321, 61197}, {1018, 5249}, {1234, 692}, {1332, 1865}, {1841, 52609}, {1897, 56839}, {1978, 40978}, {2260, 4033}, {3952, 942}, {4551, 6734}, {18591, 6335}, {20336, 53323}, {21675, 662}, {23752, 765}, {27808, 40956}, {36797, 41393}, {40937, 4552}, {40952, 668}, {40967, 664}, {55010, 644}, {59177, 6528}, {61169, 75}, {61180, 72}
X(61161) = barycentric quotient X(i)/X(j) for these (i, j): {37, 56320}, {100, 40412}, {442, 693}, {692, 1175}, {942, 7192}, {1018, 40435}, {1234, 40495}, {1783, 40395}, {1824, 14775}, {1841, 17925}, {1865, 17924}, {2260, 1019}, {2294, 514}, {3952, 40422}, {4551, 60041}, {4557, 943}, {4559, 2982}, {5249, 7199}, {6734, 18155}, {14547, 3737}, {14597, 7254}, {16585, 16755}, {18591, 905}, {18607, 15419}, {21675, 1577}, {21859, 60188}, {23207, 23189}, {23752, 1111}, {40937, 4560}, {40952, 513}, {40956, 3733}, {40967, 522}, {40978, 649}, {41393, 17094}, {50354, 17205}, {53323, 28}, {55010, 24002}, {55378, 50346}, {56193, 57710}, {56839, 4025}, {59163, 3265}, {59177, 520}, {61169, 1}, {61180, 286}, {61197, 81}, {61220, 86}, {61233, 333}, {61236, 27}
X(61161) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1018, 4551, 4574}, {1018, 61167, 61172}, {21859, 35310, 1018}, {61220, 61233, 61197}

X(61162) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(1) AND CEVIAN-OF-X(28)

Barycentrics    a*(a-b)*(a-c)*(b+c)*(a^3*(b+c)+a*(b-c)^2*(b+c)+(b^2-c^2)^2+a^2*(b^2+c^2)) : :

X(61162) lies on these lines: {10, 2835}, {37, 20975}, {71, 22274}, {513, 14543}, {661, 61169}, {692, 1783}, {1826, 22272}, {2393, 7359}, {2809, 24086}, {3952, 4010}, {4069, 61167}, {4557, 61161}, {8678, 35327}, {8804, 22273}, {21063, 22283}, {21064, 22284}, {32736, 57162}, {42716, 53350}

X(61162) = trilinear pole of line {40973, 53387}
X(61162) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1019, 40406}, {4025, 57391}
X(61162) = X(i)-Dao conjugate of X(j) for these {i, j}: {18210, 1565}, {21530, 7192}, {40941, 15413}, {53387, 17498}
X(61162) = X(i)-Ceva conjugate of X(j) for these {i, j}: {15742, 37}
X(61162) = pole of line {3995, 14953} with respect to the Yff parabola
X(61162) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3952), X(32713)}}, {{A, B, C, X(4033), X(24019)}}
X(61162) = barycentric product X(i)*X(j) for these (i, j): {37, 53349}, {100, 53417}, {162, 21678}, {190, 40973}, {321, 53282}, {1018, 23537}, {1783, 21530}, {3952, 40941}, {18674, 1897}, {41013, 61201}, {53387, 668}
X(61162) = barycentric quotient X(i)/X(j) for these (i, j): {4557, 40406}, {18674, 4025}, {18732, 15419}, {21530, 15413}, {21678, 14208}, {23537, 7199}, {40941, 7192}, {40973, 514}, {53282, 81}, {53349, 274}, {53387, 513}, {53417, 693}, {61201, 1444}

X(61163) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(1) AND CEVIAN-OF-X(37)

Barycentrics    a*(a-b)*(a-c)*(b+c)*(2*b*c+a*(b+c)) : :

X(61163) lies on these lines: {11, 24071}, {37, 244}, {42, 2107}, {100, 24052}, {101, 43356}, {190, 670}, {321, 17755}, {649, 4427}, {661, 61172}, {672, 4037}, {899, 52893}, {1018, 3952}, {3121, 14752}, {3294, 16815}, {3691, 52579}, {3720, 21820}, {3730, 4671}, {3909, 4813}, {3994, 39258}, {4253, 24049}, {4387, 36808}, {4432, 38346}, {4584, 4632}, {4750, 22003}, {4781, 61235}, {8054, 17475}, {11680, 24064}, {16549, 31035}, {16552, 24044}, {17355, 55333}, {18206, 24081}, {21879, 21885}, {21897, 58292}, {23829, 54118}, {27812, 46196}, {32930, 56533}, {35309, 35310}, {42363, 42720}, {48141, 53355}

X(61163) = trilinear pole of line {2667, 4111}
X(61163) = X(i)-isoconjugate-of-X(j) for these {i, j}: {81, 50520}, {512, 59147}, {513, 40408}, {649, 40439}, {1019, 40433}, {3733, 32009}, {7192, 57397}, {8708, 16726}
X(61163) = X(i)-Dao conjugate of X(j) for these {i, j}: {2486, 17761}, {3121, 244}, {3720, 17494}, {3739, 514}, {5375, 40439}, {16589, 7199}, {39026, 40408}, {39054, 59147}, {40586, 50520}
X(61163) = X(i)-Ceva conjugate of X(j) for these {i, j}: {7035, 42}
X(61163) = X(i)-cross conjugate of X(j) for these {i, j}: {6372, 37}, {50497, 3720}
X(61163) = pole of line {27804, 33296} with respect to the Kiepert parabola
X(61163) = pole of line {1919, 48064} with respect to the Stammler hyperbola
X(61163) = pole of line {37, 42} with respect to the Yff parabola
X(61163) = pole of line {4649, 27644} with respect to the Hutson-Moses hyperbola
X(61163) = pole of line {649, 18196} with respect to the Wallace hyperbola
X(61163) = pole of line {21131, 23100} with respect to the dual conic of Stammler hyperbola
X(61163) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(244), X(6372)}}, {{A, B, C, X(670), X(3952)}}, {{A, B, C, X(799), X(1018)}}, {{A, B, C, X(1978), X(4103)}}, {{A, B, C, X(4169), X(16589)}}, {{A, B, C, X(21832), X(50497)}}, {{A, B, C, X(40521), X(54118)}}
X(61163) = barycentric product X(i)*X(j) for these (i, j): {10, 4436}, {42, 53363}, {100, 21020}, {101, 53478}, {1018, 3739}, {1978, 21753}, {2667, 668}, {3691, 4552}, {3699, 39793}, {3706, 4551}, {3720, 3952}, {4059, 4069}, {4111, 664}, {4600, 50538}, {4754, 56257}, {16589, 190}, {17175, 40521}, {18089, 35309}, {18166, 4103}, {20888, 4557}, {20963, 4033}, {21699, 99}, {21820, 799}, {40975, 52609}, {48393, 765}, {50497, 7035}, {52579, 662}
X(61163) = barycentric quotient X(i)/X(j) for these (i, j): {42, 50520}, {100, 40439}, {101, 40408}, {662, 59147}, {1018, 32009}, {2667, 513}, {3691, 4560}, {3706, 18155}, {3720, 7192}, {3739, 7199}, {4111, 522}, {4436, 86}, {4557, 40433}, {4754, 16737}, {6372, 17205}, {16589, 514}, {20888, 52619}, {20963, 1019}, {21020, 693}, {21699, 523}, {21753, 649}, {21820, 661}, {22369, 1459}, {39793, 3676}, {40975, 17925}, {47672, 16727}, {48393, 1111}, {50497, 244}, {50538, 3120}, {52579, 1577}, {53363, 310}, {53478, 3261}
X(61163) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1018, 4115, 61168}, {4115, 61165, 3952}, {4427, 61234, 649}, {35310, 40521, 35309}

X(61164) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(1) AND CEVIAN-OF-X(38)

Barycentrics    a*(a-b)*(a-c)*(b+c)*(a^2+b*c) : :

X(61164) lies on these lines: {42, 18098}, {100, 649}, {101, 3699}, {171, 18787}, {213, 21893}, {537, 23622}, {661, 61173}, {756, 5147}, {1018, 4551}, {1215, 4154}, {2284, 61234}, {2295, 16592}, {2329, 21021}, {3508, 5143}, {3684, 20693}, {3835, 29421}, {3952, 4613}, {4095, 22061}, {4107, 18047}, {4586, 4621}, {4610, 6632}, {10330, 50456}, {15621, 21369}, {20723, 23398}, {21101, 60726}, {21383, 61166}, {21897, 56009}, {23404, 24491}, {35326, 61235}

X(61164) = trilinear pole of line {2295, 20964}
X(61164) = X(i)-isoconjugate-of-X(j) for these {i, j}: {244, 4603}, {256, 1019}, {257, 3733}, {513, 40432}, {514, 1178}, {649, 32010}, {661, 7303}, {805, 27918}, {893, 7192}, {904, 7199}, {1015, 4594}, {1431, 4560}, {1432, 3737}, {1581, 50456}, {3248, 7260}, {3863, 7255}, {3903, 16726}, {4481, 40763}, {7015, 17925}, {7018, 57129}, {7019, 43925}, {7104, 52619}, {7249, 7252}, {16695, 27447}, {17197, 29055}, {17212, 59480}, {17217, 51974}, {18191, 37137}, {23824, 58981}, {27846, 37134}, {40835, 50514}
X(61164) = X(i)-Dao conjugate of X(j) for these {i, j}: {1215, 16892}, {3709, 21132}, {4369, 6545}, {5375, 32010}, {16587, 693}, {16592, 16727}, {19564, 3776}, {19576, 50456}, {36830, 7303}, {39026, 40432}, {40597, 7192}
X(61164) = X(i)-cross conjugate of X(j) for these {i, j}: {4140, 2329}, {7234, 171}, {57234, 2295}
X(61164) = pole of line {40521, 61234} with respect to the circumcircle
X(61164) = pole of line {672, 3741} with respect to the Yff parabola
X(61164) = pole of line {238, 5260} with respect to the Hutson-Moses hyperbola
X(61164) = intersection, other than A, B, C, of circumconics {{A, B, C, X(42), X(46148)}}, {{A, B, C, X(99), X(51934)}}, {{A, B, C, X(100), X(171)}}, {{A, B, C, X(649), X(4107)}}, {{A, B, C, X(660), X(4551)}}, {{A, B, C, X(662), X(46286)}}, {{A, B, C, X(804), X(37998)}}, {{A, B, C, X(813), X(4559)}}, {{A, B, C, X(1920), X(54118)}}, {{A, B, C, X(3287), X(21894)}}, {{A, B, C, X(3699), X(56257)}}, {{A, B, C, X(4552), X(7239)}}, {{A, B, C, X(4606), X(24052)}}, {{A, B, C, X(16592), X(57234)}}
X(61164) = barycentric product X(i)*X(j) for these (i, j): {10, 4579}, {100, 1215}, {101, 3963}, {171, 3952}, {172, 4033}, {190, 2295}, {210, 6649}, {643, 7211}, {1016, 57234}, {1018, 894}, {1237, 692}, {1332, 1840}, {1783, 4019}, {1909, 4557}, {2329, 4552}, {2533, 765}, {4032, 644}, {4039, 660}, {4069, 7176}, {4095, 651}, {4128, 57950}, {4140, 4564}, {4551, 7081}, {5378, 804}, {7035, 7234}, {16592, 6632}, {17103, 40521}, {17787, 4559}, {18047, 37}, {18099, 4553}, {18905, 4621}, {20964, 668}, {21021, 662}, {21803, 99}, {21818, 4593}, {21859, 27958}, {22061, 6335}, {27697, 36147}, {27808, 7122}, {30730, 7175}, {40790, 4613}, {52609, 7119}, {53559, 57731}, {56257, 6645}
X(61164) = barycentric quotient X(i)/X(j) for these (i, j): {100, 32010}, {101, 40432}, {110, 7303}, {171, 7192}, {172, 1019}, {692, 1178}, {765, 4594}, {894, 7199}, {1016, 7260}, {1018, 257}, {1215, 693}, {1237, 40495}, {1252, 4603}, {1691, 50456}, {1840, 17924}, {1909, 52619}, {2295, 514}, {2329, 4560}, {2330, 3737}, {2533, 1111}, {3287, 17197}, {3952, 7018}, {3963, 3261}, {4019, 15413}, {4032, 24002}, {4033, 44187}, {4039, 3766}, {4069, 4451}, {4095, 4391}, {4128, 764}, {4140, 4858}, {4154, 27855}, {4367, 17205}, {4369, 16727}, {4447, 23829}, {4551, 7249}, {4557, 256}, {4559, 1432}, {4579, 86}, {4621, 40835}, {5027, 27846}, {5378, 18829}, {6645, 16737}, {6649, 57785}, {7081, 18155}, {7119, 17925}, {7122, 3733}, {7175, 17096}, {7211, 4077}, {7234, 244}, {16587, 16892}, {16592, 6545}, {17741, 18077}, {18047, 274}, {18905, 3776}, {20964, 513}, {20981, 16726}, {21021, 1577}, {21752, 21123}, {21755, 21143}, {21803, 523}, {21818, 8061}, {21859, 60245}, {22061, 905}, {24533, 23824}, {27697, 4509}, {40608, 21132}, {40936, 2530}, {51319, 18197}, {51902, 17217}, {56257, 40099}, {57234, 1086}, {61172, 59191}
X(61164) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1018, 4551, 7239}

X(61165) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(1) AND CEVIAN-OF-X(42)

Barycentrics    (a-b)*(a-c)*(b+c)*(b*c*(b+c)+a*(b^2+c^2)) : :

X(61165) lies on these lines: {10, 3124}, {37, 6377}, {190, 24052}, {306, 20500}, {312, 24060}, {321, 20433}, {514, 53363}, {646, 3807}, {661, 61174}, {726, 52893}, {908, 22038}, {1018, 3952}, {1978, 4568}, {3239, 61223}, {3741, 22206}, {3774, 3971}, {4033, 7239}, {4417, 24056}, {4671, 24044}, {17292, 22011}, {20671, 21877}, {21070, 22032}, {21820, 59517}, {22003, 22033}, {22009, 22020}, {24051, 31035}, {24071, 30566}, {25282, 29708}, {53338, 61234}

X(61165) = trilinear pole of line {3728, 21024}
X(61165) = X(i)-isoconjugate-of-X(j) for these {i, j}: {667, 40409}, {1019, 57399}, {1258, 3733}, {1924, 59148}, {16726, 59102}, {40418, 57129}, {40525, 52935}
X(61165) = X(i)-Dao conjugate of X(j) for these {i, j}: {1107, 17212}, {3122, 1015}, {3741, 649}, {6631, 40409}, {9428, 59148}, {21024, 17217}, {21838, 7192}, {51575, 1019}, {59565, 514}
X(61165) = X(i)-Ceva conjugate of X(j) for these {i, j}: {31625, 10}
X(61165) = X(i)-cross conjugate of X(j) for these {i, j}: {40627, 3728}
X(61165) = pole of line {37, 714} with respect to the Yff parabola
X(61165) = pole of line {1919, 4932} with respect to the Wallace hyperbola
X(61165) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1018), X(4602)}}, {{A, B, C, X(1978), X(56257)}}, {{A, B, C, X(3952), X(4609)}}, {{A, B, C, X(4169), X(21024)}}, {{A, B, C, X(50510), X(58294)}}
X(61165) = barycentric product X(i)*X(j) for these (i, j): {10, 53338}, {190, 21024}, {313, 53268}, {321, 61234}, {1018, 20891}, {1107, 4033}, {1978, 21838}, {2309, 27808}, {3728, 668}, {3741, 3952}, {16738, 4103}, {21700, 670}, {21713, 99}, {22206, 799}, {27880, 56241}, {30097, 30730}, {31625, 40627}, {45208, 646}
X(61165) = barycentric quotient X(i)/X(j) for these (i, j): {190, 40409}, {670, 59148}, {1018, 1258}, {1107, 1019}, {1197, 57129}, {2309, 3733}, {3728, 513}, {3741, 7192}, {3952, 40418}, {4033, 1221}, {4079, 40525}, {4103, 60230}, {4557, 57399}, {20891, 7199}, {21024, 514}, {21700, 512}, {21713, 523}, {21838, 649}, {22065, 7254}, {22206, 661}, {27880, 4367}, {30097, 17096}, {39780, 43924}, {40627, 1015}, {45208, 3669}, {45216, 16695}, {51411, 23788}, {51575, 17212}, {53268, 58}, {53338, 86}, {59565, 17217}, {61234, 81}
X(61165) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3952, 61163, 4115}

X(61166) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(1) AND CEVIAN-OF-X(57)

Barycentrics    a*(a-b)*(a-c)*(b+c)*((b-c)^2+a*(b+c)) : :
X(61166) = -1*X[3937]+3*X[6174], X[5531]+X[34462], X[6154]+X[38389], X[12331]+X[31847], X[48696]+X[56884]

X(61166) lies on these lines: {1, 46187}, {10, 53566}, {12, 8286}, {100, 513}, {181, 55060}, {210, 15523}, {226, 22278}, {373, 37703}, {375, 13405}, {517, 11698}, {518, 38472}, {528, 38390}, {650, 46148}, {661, 35310}, {756, 2611}, {1020, 4551}, {1086, 3030}, {1155, 58285}, {1211, 58644}, {2802, 4013}, {2809, 46694}, {2810, 3035}, {2836, 58663}, {3120, 22313}, {3699, 4553}, {3740, 3775}, {3827, 51380}, {3888, 43290}, {3909, 17780}, {3911, 9026}, {3937, 6174}, {3939, 53279}, {3952, 4010}, {3967, 4710}, {4776, 26795}, {4997, 38478}, {5400, 53397}, {5531, 34462}, {5606, 8701}, {5901, 12046}, {6154, 38389}, {6745, 8679}, {8702, 51562}, {8715, 56885}, {9051, 36059}, {12331, 31847}, {12607, 34434}, {14973, 50440}, {15621, 21361}, {16597, 40607}, {20718, 51377}, {21060, 22276}, {21075, 22299}, {21077, 22300}, {21272, 21580}, {21362, 23845}, {21383, 61164}, {21859, 35307}, {22279, 46897}, {23343, 61223}, {23344, 61221}, {27134, 47760}, {37613, 58657}, {42450, 59722}, {46725, 47962}, {47666, 54118}, {48696, 56884}

X(61166) = midpoint of X(i) and X(j) for these {i,j}: {12331, 31847}, {48696, 56884}, {5531, 34462}, {6154, 38389}
X(61166) = trilinear pole of line {4642, 21796}
X(61166) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 56323}, {110, 40451}, {284, 60482}, {1019, 23617}, {1222, 3733}, {1261, 7203}, {1414, 40528}, {1476, 3737}, {3451, 4560}, {7192, 51476}, {7252, 40420}, {23189, 40446}, {32017, 57129}
X(61166) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 56323}, {244, 40451}, {2170, 17197}, {3452, 7192}, {3752, 18155}, {12640, 7253}, {21796, 17496}, {40590, 60482}, {40608, 40528}, {59507, 7199}
X(61166) = pole of line {23832, 61221} with respect to the circumcircle
X(61166) = pole of line {3218, 3995} with respect to the Yff parabola
X(61166) = pole of line {764, 42455} with respect to the dual conic of Wallace hyperbola
X(61166) = intersection, other than A, B, C, of circumconics {{A, B, C, X(100), X(4642)}}, {{A, B, C, X(523), X(6615)}}, {{A, B, C, X(901), X(3952)}}, {{A, B, C, X(1020), X(3257)}}, {{A, B, C, X(3057), X(57646)}}, {{A, B, C, X(4017), X(46004)}}
X(61166) = barycentric product X(i)*X(j) for these (i, j): {10, 21362}, {100, 4415}, {190, 4642}, {226, 61222}, {1018, 3663}, {1020, 6736}, {1122, 30730}, {1201, 4033}, {1828, 52609}, {3057, 4552}, {3452, 4551}, {3752, 3952}, {4069, 52563}, {17183, 21859}, {17906, 72}, {18600, 40521}, {20228, 27808}, {20895, 4559}, {21031, 651}, {21272, 37}, {21580, 42}, {21796, 668}, {21809, 664}, {23113, 41013}, {23845, 321}, {25268, 65}, {26563, 4557}
X(61166) = barycentric quotient X(i)/X(j) for these (i, j): {37, 56323}, {65, 60482}, {661, 40451}, {1018, 1222}, {1122, 17096}, {1201, 1019}, {1828, 17925}, {2347, 3737}, {3057, 4560}, {3452, 18155}, {3663, 7199}, {3709, 40528}, {3752, 7192}, {3952, 32017}, {4069, 52549}, {4415, 693}, {4551, 40420}, {4557, 23617}, {4559, 1476}, {4642, 514}, {6363, 16726}, {6615, 17197}, {17906, 286}, {20228, 3733}, {21031, 4391}, {21272, 274}, {21362, 86}, {21580, 310}, {21796, 513}, {21809, 522}, {21859, 56173}, {22344, 7254}, {23113, 1444}, {23845, 81}, {25268, 314}, {26563, 52619}, {40521, 56258}, {48334, 17205}, {59173, 7203}, {61222, 333}
X(61166) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3952, 61172, 40521}, {3952, 61177, 61172}, {21362, 61222, 23845}, {61172, 61176, 3952}

X(61167) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(1) AND CEVIAN-OF-X(58)

Barycentrics    a*(a-b)*(a-c)*(b+c)*(b^3+c^3+a*(b^2+c^2)) : :

X(61167) lies on these lines: {10, 2170}, {100, 163}, {101, 9070}, {661, 4115}, {1018, 4551}, {3178, 3970}, {3293, 5299}, {3814, 20659}, {4006, 20495}, {4069, 61162}, {4103, 35309}, {14349, 53332}, {17444, 21689}, {20228, 21858}, {20982, 21711}, {21076, 21078}, {35342, 53290}

X(61167) = trilinear pole of line {4016, 20966}
X(61167) = X(i)-isoconjugate-of-X(j) for these {i, j}: {514, 3453}, {3733, 40394}
X(61167) = X(i)-Dao conjugate of X(j) for these {i, j}: {3454, 1019}, {3670, 47796}
X(61167) = X(i)-Ceva conjugate of X(j) for these {i, j}: {2149, 21078}
X(61167) = intersection, other than A, B, C, of circumconics {{A, B, C, X(163), X(4033)}}, {{A, B, C, X(3909), X(4551)}}, {{A, B, C, X(4559), X(58951)}}
X(61167) = barycentric product X(i)*X(j) for these (i, j): {10, 3909}, {100, 3454}, {101, 20896}, {190, 4016}, {1018, 17184}, {1978, 40986}, {3670, 3952}, {18601, 4103}, {20654, 662}, {20966, 668}, {21121, 765}, {22073, 6335}
X(61167) = barycentric quotient X(i)/X(j) for these (i, j): {692, 3453}, {1018, 40394}, {3454, 693}, {3670, 7192}, {3909, 86}, {4016, 514}, {17184, 7199}, {20654, 1577}, {20896, 3261}, {20966, 513}, {21121, 1111}, {22073, 905}, {40986, 649}
X(61167) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {61161, 61172, 1018}

X(61168) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(1) AND CEVIAN-OF-X(65)

Barycentrics    a^2*(a-b)*(a-c)*(b+c)*(b^2+c^2+a*(b+c)) : :

X(61168) lies on these lines: {37, 374}, {71, 10693}, {72, 4712}, {100, 6010}, {101, 110}, {190, 7257}, {213, 5007}, {321, 51381}, {375, 55378}, {573, 24048}, {644, 3903}, {649, 35342}, {661, 61161}, {663, 53268}, {672, 21839}, {765, 36147}, {919, 29119}, {1018, 3952}, {1055, 20785}, {1334, 2503}, {1400, 28282}, {1730, 24066}, {2183, 4053}, {2198, 21874}, {2269, 21810}, {2340, 5360}, {3219, 31059}, {3294, 33950}, {3588, 21078}, {3882, 53332}, {4041, 22280}, {4551, 52931}, {4557, 4559}, {5106, 53129}, {8694, 26733}, {17136, 48144}, {21033, 52087}, {21362, 22003}, {21859, 35307}, {29038, 59120}, {30729, 61234}

X(61168) = trilinear pole of line {2092, 3725}
X(61168) = X(i)-isoconjugate-of-X(j) for these {i, j}: {28, 15420}, {57, 57161}, {81, 4581}, {513, 14534}, {514, 2363}, {667, 40827}, {693, 1169}, {961, 4560}, {1019, 1220}, {1240, 57129}, {1509, 57162}, {1791, 17925}, {1798, 17924}, {2298, 7192}, {3733, 30710}, {6591, 57853}, {6648, 18191}, {7180, 52550}, {7252, 31643}, {8707, 16726}, {16727, 32736}, {16732, 58982}, {17197, 36098}, {17205, 36147}, {17496, 40453}
X(61168) = X(i)-Dao conjugate of X(j) for these {i, j}: {960, 514}, {1193, 17496}, {1211, 7199}, {2092, 18155}, {3125, 1111}, {3666, 3261}, {5452, 57161}, {6631, 40827}, {38992, 17197}, {39015, 17205}, {39026, 14534}, {40586, 4581}, {40591, 15420}, {52087, 7192}, {53566, 24237}, {56905, 46107}, {59509, 52619}
X(61168) = X(i)-Ceva conjugate of X(j) for these {i, j}: {190, 61223}, {765, 42}, {2149, 71}, {3882, 61172}
X(61168) = X(i)-cross conjugate of X(j) for these {i, j}: {52326, 37}
X(61168) = pole of line {4184, 27804} with respect to the Kiepert parabola
X(61168) = pole of line {514, 18200} with respect to the Stammler hyperbola
X(61168) = pole of line {37, 65} with respect to the Yff parabola
X(61168) = pole of line {21, 42} with respect to the Hutson-Moses hyperbola
X(61168) = pole of line {3261, 16737} with respect to the Wallace hyperbola
X(61168) = pole of line {53338, 61223} with respect to the dual conic of incircle
X(61168) = intersection, other than A, B, C, of circumconics {{A, B, C, X(42), X(36147)}}, {{A, B, C, X(101), X(4103)}}, {{A, B, C, X(110), X(3903)}}, {{A, B, C, X(163), X(1018)}}, {{A, B, C, X(429), X(4243)}}, {{A, B, C, X(831), X(1245)}}, {{A, B, C, X(2092), X(4169)}}, {{A, B, C, X(2170), X(52326)}}, {{A, B, C, X(2292), X(29119)}}, {{A, B, C, X(4120), X(58294)}}, {{A, B, C, X(4551), X(7257)}}, {{A, B, C, X(4557), X(5546)}}, {{A, B, C, X(5029), X(42661)}}, {{A, B, C, X(21859), X(56188)}}
X(61168) = barycentric product X(i)*X(j) for these (i, j): {1, 61172}, {10, 53280}, {37, 3882}, {42, 53332}, {65, 61223}, {100, 2292}, {101, 1211}, {109, 3704}, {110, 20653}, {190, 2092}, {306, 61205}, {1018, 3666}, {1020, 3965}, {1193, 3952}, {1228, 32739}, {1252, 21124}, {1293, 4918}, {1331, 429}, {1848, 4574}, {1897, 22076}, {2269, 4552}, {2300, 4033}, {2354, 52609}, {3687, 4559}, {3725, 668}, {3939, 41003}, {4357, 4557}, {4551, 960}, {4605, 46889}, {17185, 21859}, {18697, 692}, {21033, 651}, {21810, 662}, {23067, 46878}, {24471, 4069}, {27067, 46148}, {28369, 56257}, {40153, 4103}, {40521, 54308}, {40966, 664}, {42661, 4600}, {44092, 4561}, {45197, 52923}, {45218, 4595}, {50330, 765}, {52087, 56188}, {52567, 643}, {59174, 7257}, {61226, 72}
X(61168) = barycentric quotient X(i)/X(j) for these (i, j): {42, 4581}, {55, 57161}, {71, 15420}, {101, 14534}, {190, 40827}, {429, 46107}, {643, 52550}, {692, 2363}, {872, 57162}, {960, 18155}, {1018, 30710}, {1193, 7192}, {1211, 3261}, {1331, 57853}, {2092, 514}, {2269, 4560}, {2292, 693}, {2300, 1019}, {2354, 17925}, {3666, 7199}, {3704, 35519}, {3725, 513}, {3882, 274}, {3952, 1240}, {4103, 60264}, {4357, 52619}, {4551, 31643}, {4557, 1220}, {6371, 17205}, {18697, 40495}, {20653, 850}, {20967, 3737}, {21033, 4391}, {21124, 23989}, {21810, 1577}, {22076, 4025}, {22097, 15419}, {28369, 16737}, {32656, 1798}, {32739, 1169}, {40966, 522}, {41003, 52621}, {42661, 3120}, {44092, 7649}, {48131, 16727}, {50330, 1111}, {52087, 17496}, {52326, 17197}, {52567, 4077}, {53280, 86}, {53332, 310}, {59174, 4017}, {61172, 75}, {61205, 27}, {61223, 314}, {61226, 286}
X(61168) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1018, 4115, 61163}, {2269, 21810, 55333}

X(61169) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(1) AND CEVIAN-OF-X(72)

Barycentrics    a^2*(a-b)*(a-c)*(b+c)*(2*a*b*c+a^2*(b+c)-(b-c)^2*(b+c)) : :

X(61169) lies on these lines: {37, 2293}, {42, 2643}, {71, 57693}, {101, 112}, {213, 52969}, {661, 61162}, {663, 35327}, {692, 46177}, {823, 1897}, {2183, 5360}, {2272, 42702}, {2340, 4053}, {4069, 4115}, {4551, 4605}, {4557, 4559}, {14543, 46385}, {14547, 55378}, {17463, 39046}, {22003, 35338}, {22356, 45932}, {23585, 52823}, {35309, 35310}, {35326, 53288}, {42713, 56714}

X(61169) = trilinear pole of line {40952, 40978}
X(61169) = X(i)-isoconjugate-of-X(j) for these {i, j}: {81, 56320}, {513, 40412}, {693, 1175}, {905, 40395}, {943, 7192}, {1019, 40435}, {1444, 14775}, {2259, 7199}, {2982, 4560}, {3733, 40422}, {3737, 60041}, {7254, 40447}, {15413, 40570}, {18191, 54952}
X(61169) = X(i)-Dao conjugate of X(j) for these {i, j}: {442, 18155}, {942, 4025}, {16585, 52619}, {18591, 7199}, {39007, 17219}, {39026, 40412}, {40586, 56320}, {40937, 3261}, {52119, 21207}
X(61169) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1110, 42}, {1897, 61236}, {7012, 71}, {61220, 61161}
X(61169) = X(i)-cross conjugate of X(j) for these {i, j}: {33525, 37}
X(61169) = pole of line {4025, 16755} with respect to the Stammler hyperbola
X(61169) = pole of line {4456, 22001} with respect to the Yff parabola
X(61169) = intersection, other than A, B, C, of circumconics {{A, B, C, X(101), X(4605)}}, {{A, B, C, X(112), X(4559)}}, {{A, B, C, X(442), X(4249)}}, {{A, B, C, X(823), X(1018)}}, {{A, B, C, X(2310), X(33525)}}
X(61169) = barycentric product X(i)*X(j) for these (i, j): {1, 61161}, {10, 61197}, {37, 61220}, {65, 61233}, {100, 2294}, {101, 442}, {110, 21675}, {190, 40952}, {306, 53323}, {1018, 942}, {1234, 32739}, {1252, 23752}, {1331, 1865}, {1783, 56839}, {1838, 4574}, {2260, 3952}, {3939, 55010}, {4033, 40956}, {4557, 5249}, {4559, 6734}, {4605, 8021}, {14547, 4552}, {16585, 56193}, {18591, 1897}, {21859, 54356}, {24019, 59163}, {40937, 4551}, {40967, 651}, {40978, 668}, {59177, 823}, {61180, 71}, {61236, 72}
X(61169) = barycentric quotient X(i)/X(j) for these (i, j): {42, 56320}, {101, 40412}, {442, 3261}, {500, 16755}, {942, 7199}, {1018, 40422}, {1859, 57215}, {1865, 46107}, {2260, 7192}, {2294, 693}, {2333, 14775}, {4303, 15419}, {4557, 40435}, {4559, 60041}, {5249, 52619}, {8750, 40395}, {14547, 4560}, {18591, 4025}, {21675, 850}, {23752, 23989}, {32739, 1175}, {40937, 18155}, {40952, 514}, {40956, 1019}, {40967, 4391}, {40978, 513}, {50354, 16727}, {52306, 17219}, {53323, 27}, {55010, 52621}, {56839, 15413}, {59177, 24018}, {61161, 75}, {61180, 44129}, {61197, 86}, {61220, 274}, {61233, 314}, {61236, 286}

X(61170) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(1) AND CEVIAN-OF-X(79)

Barycentrics    a*(a-b)*(a-c)*(a+b-c)*(a-b+c)*(b+c)*(2*a+b+c) : :

X(61170) lies on these lines: {37, 3013}, {65, 9278}, {73, 1212}, {100, 26733}, {101, 26700}, {109, 15322}, {226, 544}, {650, 61197}, {651, 662}, {1018, 4551}, {1100, 4870}, {1400, 16669}, {1464, 2238}, {2594, 20616}, {3125, 53537}, {3649, 20970}, {5277, 8614}, {6127, 34460}, {11998, 34586}, {14395, 35326}, {16680, 50508}, {17754, 37694}, {32675, 34076}, {32693, 43356}, {35342, 36075}

X(61170) = trilinear pole of line {1962, 22080}
X(61170) = X(i)-isoconjugate-of-X(j) for these {i, j}: {11, 4629}, {21, 47947}, {60, 31010}, {261, 58294}, {284, 4608}, {333, 50344}, {522, 1171}, {650, 40438}, {663, 32014}, {1019, 32635}, {1126, 4560}, {1255, 3737}, {1268, 7252}, {2170, 4596}, {3064, 57685}, {3271, 4632}, {3700, 52558}, {3733, 4102}, {4913, 59194}, {6578, 21044}, {7192, 33635}, {8701, 17197}, {18155, 28615}, {18191, 37212}, {52379, 58301}
X(61170) = X(i)-Dao conjugate of X(j) for these {i, j}: {1125, 4391}, {1213, 18155}, {3120, 4858}, {3647, 4560}, {40590, 4608}, {40611, 47947}, {56846, 7199}
X(61170) = X(i)-Ceva conjugate of X(j) for these {i, j}: {651, 61225}, {4564, 65}
X(61170) = X(i)-cross conjugate of X(j) for these {i, j}: {4983, 3649}, {4988, 1100}
X(61170) = pole of line {21061, 56288} with respect to the Yff parabola
X(61170) = pole of line {65, 3219} with respect to the Hutson-Moses hyperbola
X(61170) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(651), X(21859)}}, {{A, B, C, X(662), X(1018)}}, {{A, B, C, X(1100), X(34076)}}, {{A, B, C, X(1414), X(4551)}}, {{A, B, C, X(4427), X(43356)}}, {{A, B, C, X(4558), X(4574)}}, {{A, B, C, X(4559), X(4565)}}, {{A, B, C, X(4979), X(21894)}}, {{A, B, C, X(4983), X(24290)}}, {{A, B, C, X(4990), X(34591)}}, {{A, B, C, X(5546), X(30729)}}, {{A, B, C, X(6367), X(9034)}}
X(61170) = barycentric product X(i)*X(j) for these (i, j): {10, 61225}, {56, 61174}, {100, 3649}, {108, 41014}, {109, 4647}, {226, 35342}, {321, 36075}, {430, 6516}, {1018, 553}, {1020, 3686}, {1100, 4552}, {1125, 4551}, {1213, 651}, {1230, 1415}, {1414, 8013}, {1427, 30729}, {1441, 35327}, {1962, 664}, {3683, 4566}, {3702, 53321}, {3916, 61178}, {3958, 653}, {4046, 934}, {4115, 57}, {4359, 4559}, {4427, 65}, {4564, 4988}, {4983, 4998}, {18026, 22080}, {20970, 4554}, {21816, 4573}, {21859, 8025}, {23067, 56875}, {30591, 59}, {32636, 3952}, {35339, 3671}, {36059, 44143}
X(61170) = barycentric quotient X(i)/X(j) for these (i, j): {59, 4596}, {65, 4608}, {109, 40438}, {430, 44426}, {553, 7199}, {651, 32014}, {1018, 4102}, {1100, 4560}, {1125, 18155}, {1213, 4391}, {1400, 47947}, {1402, 50344}, {1415, 1171}, {1839, 57215}, {1962, 522}, {2149, 4629}, {2171, 31010}, {2308, 3737}, {3649, 693}, {3683, 7253}, {3958, 6332}, {4046, 4397}, {4115, 312}, {4427, 314}, {4551, 1268}, {4552, 32018}, {4557, 32635}, {4559, 1255}, {4564, 4632}, {4647, 35519}, {4979, 17197}, {4983, 11}, {4988, 4858}, {6516, 57854}, {8013, 4086}, {8040, 4985}, {8663, 4516}, {20970, 650}, {21816, 3700}, {21859, 6539}, {22080, 521}, {23201, 23189}, {30591, 34387}, {30724, 16727}, {32636, 7192}, {35327, 21}, {35342, 333}, {36059, 57685}, {36075, 81}, {41014, 35518}, {50512, 18191}, {61171, 31011}, {61174, 3596}, {61225, 86}
X(61170) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4551, 4559, 21859}, {4559, 21859, 61171}, {35342, 61225, 36075}

X(61171) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(1) AND CEVIAN-OF-X(80)

Barycentrics    a*(a-b)*(a-c)*(2*a-b-c)*(a+b-c)*(a-b+c)*(b+c) : :

X(61171) lies on these lines: {37, 65}, {44, 4530}, {56, 34877}, {109, 4752}, {644, 1415}, {650, 2427}, {1018, 4551}, {1023, 23703}, {1025, 3669}, {1319, 52964}, {3900, 54325}, {14439, 53530}, {21821, 53537}, {24004, 30731}, {40663, 52963}

X(61171) = X(i)-isoconjugate-of-X(j) for these {i, j}: {11, 4591}, {21, 1022}, {58, 60480}, {60, 4049}, {81, 23838}, {88, 3737}, {106, 4560}, {110, 60578}, {261, 55263}, {284, 6548}, {333, 23345}, {645, 43922}, {757, 61179}, {901, 17197}, {903, 7252}, {1019, 1320}, {1021, 56049}, {2170, 4622}, {2185, 55244}, {2316, 7192}, {3257, 18191}, {3271, 4615}, {3733, 4997}, {5546, 6549}, {5548, 17205}, {6336, 23189}, {9456, 18155}, {36058, 57215}
X(61171) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 60480}, {214, 4560}, {244, 60578}, {4370, 18155}, {20619, 57215}, {38979, 17197}, {40586, 23838}, {40590, 6548}, {40607, 61179}, {40611, 1022}, {52659, 7199}, {52872, 4391}, {52877, 650}, {55055, 18191}
X(61171) = X(i)-cross conjugate of X(j) for these {i, j}: {4120, 44}, {4730, 40663}
X(61171) = pole of line {21061, 61168} with respect to the Yff parabola
X(61171) = pole of line {5260, 12739} with respect to the Hutson-Moses hyperbola
X(61171) = pole of line {25066, 30818} with respect to the dual conic of Feuerbach hyperbola
X(61171) = pole of line {4858, 40166} with respect to the dual conic of Wallace hyperbola
X(61171) = intersection, other than A, B, C, of circumconics {{A, B, C, X(37), X(1018)}}, {{A, B, C, X(44), X(2245)}}, {{A, B, C, X(65), X(4551)}}, {{A, B, C, X(71), X(4574)}}, {{A, B, C, X(519), X(20718)}}, {{A, B, C, X(644), X(21809)}}, {{A, B, C, X(1284), X(1319)}}, {{A, B, C, X(1334), X(30731)}}, {{A, B, C, X(1400), X(4559)}}, {{A, B, C, X(1635), X(21894)}}, {{A, B, C, X(2087), X(55261)}}, {{A, B, C, X(2171), X(21859)}}, {{A, B, C, X(2429), X(4557)}}, {{A, B, C, X(3657), X(53535)}}, {{A, B, C, X(3721), X(7239)}}, {{A, B, C, X(3943), X(21801)}}, {{A, B, C, X(3952), X(52924)}}, {{A, B, C, X(4120), X(4530)}}, {{A, B, C, X(4730), X(24290)}}, {{A, B, C, X(17780), X(59305)}}, {{A, B, C, X(21808), X(35310)}}, {{A, B, C, X(35353), X(39155)}}, {{A, B, C, X(37225), X(46541)}}, {{A, B, C, X(39258), X(52963)}}
X(61171) = barycentric product X(i)*X(j) for these (i, j): {10, 23703}, {44, 4552}, {100, 40663}, {109, 3992}, {181, 55243}, {201, 46541}, {321, 61210}, {1018, 3911}, {1020, 2325}, {1023, 226}, {1319, 3952}, {1400, 24004}, {1404, 4033}, {1427, 30731}, {1441, 23344}, {3689, 4566}, {3943, 651}, {4120, 4564}, {4169, 57}, {4358, 4559}, {4551, 519}, {4554, 52963}, {4723, 53321}, {4730, 4998}, {5440, 61178}, {14429, 7012}, {16704, 21859}, {17780, 65}, {21805, 664}, {21942, 37136}, {23067, 38462}, {30572, 765}, {31011, 61170}, {37790, 4574}, {40988, 655}, {51562, 53537}, {52607, 52978}, {56642, 61176}
X(61171) = barycentric quotient X(i)/X(j) for these (i, j): {37, 60480}, {42, 23838}, {44, 4560}, {59, 4622}, {65, 6548}, {181, 55244}, {519, 18155}, {661, 60578}, {902, 3737}, {1018, 4997}, {1023, 333}, {1319, 7192}, {1400, 1022}, {1402, 23345}, {1404, 1019}, {1500, 61179}, {1635, 17197}, {1960, 18191}, {2149, 4591}, {2171, 4049}, {2251, 7252}, {3689, 7253}, {3911, 7199}, {3943, 4391}, {3992, 35519}, {4017, 6549}, {4120, 4858}, {4169, 312}, {4530, 40213}, {4551, 903}, {4552, 20568}, {4557, 1320}, {4559, 88}, {4564, 4615}, {4730, 11}, {4819, 4811}, {4998, 4634}, {8756, 57215}, {14407, 2170}, {14429, 17880}, {17780, 314}, {21805, 522}, {21821, 1639}, {21859, 4080}, {23202, 23189}, {23344, 21}, {23703, 86}, {24004, 28660}, {30572, 1111}, {30725, 16727}, {40663, 693}, {40988, 3904}, {46541, 57779}, {51641, 43922}, {52963, 650}, {52964, 27527}, {52978, 15411}, {53321, 56049}, {53528, 17205}, {53530, 23788}, {53531, 23829}, {53532, 17219}, {53537, 4453}, {55243, 18021}, {61210, 81}
X(61171) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1018, 4559, 21859}, {1023, 23703, 61210}, {4559, 21859, 61170}

X(61172) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(1) AND CEVIAN-OF-X(81)

Barycentrics    a*(a-b)*(a-c)*(b+c)*(b^2+c^2+a*(b+c)) : :

X(61172) lies on these lines: {10, 11}, {37, 3124}, {42, 1386}, {65, 3178}, {72, 7068}, {100, 110}, {108, 29127}, {190, 54986}, {209, 4028}, {210, 3773}, {306, 4437}, {511, 3712}, {513, 3909}, {518, 4062}, {521, 53388}, {650, 61234}, {661, 61163}, {833, 29030}, {960, 20653}, {1016, 2703}, {1018, 4551}, {1125, 24938}, {1211, 40966}, {3027, 3175}, {3122, 58401}, {3293, 5315}, {3699, 3799}, {3704, 22076}, {3740, 8013}, {3812, 27577}, {3869, 27558}, {3882, 53280}, {3916, 35468}, {3932, 51377}, {3936, 20718}, {3952, 4010}, {3969, 14973}, {3977, 8679}, {4036, 15632}, {4150, 22298}, {4358, 38472}, {4436, 61220}, {4514, 4651}, {4552, 52931}, {4576, 42721}, {4689, 17792}, {5836, 21674}, {6734, 21672}, {8286, 27692}, {8287, 27560}, {8691, 8694}, {9049, 50744}, {14839, 17724}, {14923, 27690}, {15523, 22325}, {17780, 22311}, {19998, 49704}, {20989, 56529}, {21054, 58663}, {21076, 21871}, {21858, 59797}, {21865, 46897}, {22279, 29822}, {22300, 57808}, {22320, 56811}, {24086, 46694}, {26892, 59536}, {27714, 58679}, {32849, 56878}, {32851, 50362}, {33175, 56537}, {35104, 35466}, {40533, 41850}, {43067, 53355}, {45235, 46369}, {46973, 57207}, {53761, 61233}, {61205, 61226}

X(61172) = midpoint of X(i) and X(j) for these {i,j}: {3909, 4427}
X(61172) = trilinear pole of line {2092, 2292}
X(61172) = perspector of circumconic {{A, B, C, X(4567), X(50039)}}
X(61172) = X(i)-isoconjugate-of-X(j) for these {i, j}: {56, 57161}, {58, 4581}, {513, 2363}, {514, 1169}, {649, 14534}, {757, 57162}, {961, 3737}, {1019, 2298}, {1220, 3733}, {1474, 15420}, {1791, 57200}, {1798, 7649}, {1919, 40827}, {2359, 17925}, {3120, 58982}, {8687, 17197}, {16726, 36147}, {17205, 32736}, {18191, 36098}, {21173, 40453}, {30710, 57129}, {51641, 52550}
X(61172) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 57161}, {10, 4581}, {960, 513}, {1193, 21173}, {1211, 7192}, {2092, 4560}, {3125, 1086}, {3666, 693}, {4357, 16737}, {5375, 14534}, {9296, 40827}, {17419, 17197}, {38992, 18191}, {39015, 16726}, {39026, 2363}, {40607, 57162}, {51574, 15420}, {52087, 1019}, {56905, 17924}, {59509, 7199}
X(61172) = X(i)-Ceva conjugate of X(j) for these {i, j}: {59, 72}, {100, 53280}, {249, 21873}, {1016, 37}, {3882, 61168}
X(61172) = X(i)-cross conjugate of X(j) for these {i, j}: {17420, 10}, {42661, 37}, {50330, 2292}
X(61172) = pole of line {21, 39766} with respect to the Kiepert parabola
X(61172) = pole of line {2511, 3762} with respect to the Steiner inellipse
X(61172) = pole of line {1999, 3219} with respect to the Yff parabola
X(61172) = pole of line {37, 5260} with respect to the Hutson-Moses hyperbola
X(61172) = pole of line {693, 17212} with respect to the Wallace hyperbola
X(61172) = pole of line {764, 40166} with respect to the dual conic of Wallace hyperbola
X(61172) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(11), X(17420)}}, {{A, B, C, X(37), X(8707)}}, {{A, B, C, X(100), X(21859)}}, {{A, B, C, X(110), X(3903)}}, {{A, B, C, X(429), X(3658)}}, {{A, B, C, X(643), X(1018)}}, {{A, B, C, X(662), X(3882)}}, {{A, B, C, X(692), X(40521)}}, {{A, B, C, X(3124), X(5040)}}, {{A, B, C, X(3699), X(56257)}}, {{A, B, C, X(4103), X(56194)}}, {{A, B, C, X(4574), X(29127)}}
X(61172) = barycentric product X(i)*X(j) for these (i, j): {10, 3882}, {37, 53332}, {100, 1211}, {101, 18697}, {190, 2292}, {226, 61223}, {306, 61226}, {321, 53280}, {1016, 50330}, {1018, 4357}, {1193, 4033}, {1228, 692}, {1332, 429}, {1829, 52609}, {1978, 3725}, {2092, 668}, {2300, 27808}, {3666, 3952}, {3674, 4069}, {3687, 4551}, {3704, 651}, {3939, 45196}, {3965, 4566}, {4103, 54308}, {4552, 960}, {4574, 54314}, {4605, 46877}, {16705, 40521}, {20336, 61205}, {20653, 662}, {20911, 4557}, {21033, 664}, {21124, 765}, {21810, 99}, {22076, 6335}, {24471, 30730}, {27067, 4553}, {27697, 3903}, {27834, 4918}, {36863, 45218}, {40966, 4554}, {41003, 644}, {42661, 4601}, {45197, 4595}, {52087, 56252}, {52567, 645}, {56257, 59509}, {59191, 61164}, {61168, 75}
X(61172) = barycentric quotient X(i)/X(j) for these (i, j): {9, 57161}, {37, 4581}, {72, 15420}, {100, 14534}, {101, 2363}, {429, 17924}, {645, 52550}, {668, 40827}, {692, 1169}, {906, 1798}, {960, 4560}, {1018, 1220}, {1193, 1019}, {1211, 693}, {1228, 40495}, {1332, 57853}, {1500, 57162}, {1829, 17925}, {2092, 513}, {2269, 3737}, {2292, 514}, {2300, 3733}, {2354, 57200}, {3004, 16727}, {3666, 7192}, {3687, 18155}, {3704, 4391}, {3725, 649}, {3882, 86}, {3952, 30710}, {3965, 7253}, {4033, 1240}, {4357, 7199}, {4552, 31643}, {4557, 2298}, {4559, 961}, {4574, 1791}, {4719, 48580}, {4918, 4462}, {6042, 21124}, {6371, 16726}, {17420, 17197}, {18697, 3261}, {20653, 1577}, {20911, 52619}, {20967, 7252}, {21033, 522}, {21124, 1111}, {21810, 523}, {21859, 60086}, {22074, 23189}, {22076, 905}, {22345, 7254}, {24471, 17096}, {27697, 4374}, {28369, 17212}, {40521, 14624}, {40966, 650}, {41003, 24002}, {41609, 57073}, {42661, 3125}, {44092, 6591}, {45196, 52621}, {45218, 43931}, {46878, 57215}, {46879, 57125}, {48131, 17205}, {50330, 1086}, {52087, 21173}, {52326, 18191}, {52567, 7178}, {53280, 81}, {53332, 274}, {55333, 50346}, {59174, 7180}, {59509, 16737}, {61168, 1}, {61205, 28}, {61223, 333}, {61226, 27}
X(61172) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11, 21676, 10}, {306, 22276, 22275}, {1018, 61167, 61161}, {1018, 7239, 35310}, {3882, 61223, 53280}, {3909, 4427, 513}, {3952, 61166, 61176}, {3952, 61177, 61166}, {21081, 56894, 72}, {40521, 61166, 3952}

X(61173) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(1) AND CEVIAN-OF-X(82)

Barycentrics    a*(a-b)*(a-c)*(b+c)*(a^2+b^2-b*c+c^2) : :

X(61173) lies on these lines: {9, 31079}, {100, 650}, {101, 43348}, {190, 57975}, {321, 18084}, {594, 2503}, {661, 61164}, {693, 29421}, {1018, 3952}, {1334, 26580}, {1500, 21341}, {2284, 3909}, {2295, 3124}, {3219, 30179}, {3882, 53337}, {19593, 28393}, {20605, 21282}, {42723, 53280}

X(61173) = X(i)-isoconjugate-of-X(j) for these {i, j}: {513, 40398}, {16892, 57420}
X(61173) = X(i)-Dao conjugate of X(j) for these {i, j}: {16600, 48084}, {16706, 18077}, {21249, 514}, {39026, 40398}
X(61173) = X(i)-cross conjugate of X(j) for these {i, j}: {50486, 7191}
X(61173) = pole of line {37, 82} with respect to the Yff parabola
X(61173) = pole of line {518, 5262} with respect to the Hutson-Moses hyperbola
X(61173) = intersection, other than A, B, C, of circumconics {{A, B, C, X(100), X(4972)}}, {{A, B, C, X(650), X(27712)}}, {{A, B, C, X(919), X(1018)}}, {{A, B, C, X(3952), X(36086)}}, {{A, B, C, X(4169), X(16600)}}, {{A, B, C, X(21832), X(50486)}}
X(61173) = barycentric product X(i)*X(j) for these (i, j): {100, 4972}, {1018, 16706}, {1252, 27712}, {3952, 7191}, {4033, 5299}, {4514, 4551}, {16600, 190}, {21037, 4599}, {21425, 4628}, {33940, 4557}, {33950, 4552}, {33951, 37}, {33955, 40521}, {47712, 765}, {50486, 7035}
X(61173) = barycentric quotient X(i)/X(j) for these (i, j): {101, 40398}, {4514, 18155}, {4972, 693}, {5299, 1019}, {7191, 7192}, {16600, 514}, {16706, 7199}, {17456, 16892}, {20969, 2530}, {21249, 48084}, {23203, 1459}, {27712, 23989}, {33940, 52619}, {33950, 4560}, {33951, 274}, {47652, 16727}, {47712, 1111}, {50486, 244}
X(61173) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1018, 61160, 3952}

X(61174) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(1) AND CEVIAN-OF-X(86)

Barycentrics    (a-b)*b*(a-c)*c*(b+c)*(2*a+b+c) : :

X(61174) lies on these lines: {8, 39768}, {10, 244}, {42, 17793}, {99, 100}, {321, 1109}, {341, 27558}, {518, 59712}, {646, 4756}, {661, 61165}, {693, 53363}, {1230, 4046}, {3120, 4783}, {3178, 52353}, {3240, 30473}, {3699, 6742}, {3701, 21081}, {3702, 52576}, {3741, 21684}, {3770, 46918}, {3775, 4359}, {3909, 53338}, {3952, 4010}, {4039, 25298}, {4062, 4358}, {4103, 35309}, {4119, 20659}, {4391, 61223}, {4696, 20653}, {5606, 8706}, {9347, 24524}, {15863, 38484}, {16709, 46896}, {17163, 27792}, {21020, 27793}, {26582, 56810}, {27690, 44720}, {29822, 56249}, {30730, 61161}

X(61174) = trilinear pole of line {1213, 4647}
X(61174) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 50344}, {512, 52558}, {593, 58294}, {649, 1171}, {667, 40438}, {757, 58301}, {1015, 4629}, {1019, 28615}, {1126, 3733}, {1255, 57129}, {1333, 47947}, {1796, 43925}, {1919, 32014}, {1977, 4632}, {2206, 4608}, {3122, 6578}, {3248, 4596}
X(61174) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 50344}, {37, 47947}, {1125, 513}, {1213, 1019}, {1962, 58300}, {3120, 244}, {3647, 3733}, {4359, 20295}, {5375, 1171}, {6631, 40438}, {9296, 32014}, {21709, 2643}, {35076, 16726}, {39054, 52558}, {40603, 4608}, {40607, 58301}, {56846, 7203}, {59592, 3737}
X(61174) = X(i)-Ceva conjugate of X(j) for these {i, j}: {7035, 321}, {24037, 27569}
X(61174) = X(i)-cross conjugate of X(j) for these {i, j}: {4977, 10}, {4983, 1213}, {4988, 4359}, {30591, 4647}
X(61174) = pole of line {81, 41813} with respect to the Kiepert parabola
X(61174) = pole of line {894, 3995} with respect to the Yff parabola
X(61174) = pole of line {4358, 24194} with respect to the dual conic of Yff parabola
X(61174) = intersection, other than A, B, C, of circumconics {{A, B, C, X(99), X(3952)}}, {{A, B, C, X(100), X(40521)}}, {{A, B, C, X(244), X(4977)}}, {{A, B, C, X(430), X(4236)}}, {{A, B, C, X(799), X(4033)}}, {{A, B, C, X(1018), X(35339)}}, {{A, B, C, X(1230), X(55260)}}, {{A, B, C, X(2787), X(6367)}}, {{A, B, C, X(4010), X(4988)}}, {{A, B, C, X(4103), X(8050)}}, {{A, B, C, X(4551), X(35342)}}, {{A, B, C, X(4647), X(55243)}}, {{A, B, C, X(4983), X(14404)}}
X(61174) = barycentric product X(i)*X(j) for these (i, j): {100, 1230}, {190, 4647}, {313, 35342}, {321, 4427}, {799, 8013}, {1016, 30591}, {1018, 1269}, {1100, 27808}, {1125, 4033}, {1213, 668}, {1332, 44143}, {1441, 30729}, {1962, 1978}, {3596, 61170}, {3649, 646}, {3702, 4552}, {3952, 4359}, {4046, 4554}, {4115, 75}, {4601, 6367}, {4988, 7035}, {16709, 4103}, {20970, 6386}, {21816, 670}, {27801, 35327}, {30713, 61225}, {31625, 4983}, {40521, 52572}, {41014, 6335}, {52576, 662}, {52609, 56875}
X(61174) = barycentric quotient X(i)/X(j) for these (i, j): {10, 47947}, {37, 50344}, {100, 1171}, {190, 40438}, {321, 4608}, {430, 6591}, {553, 7203}, {662, 52558}, {668, 32014}, {756, 58294}, {765, 4629}, {1016, 4596}, {1018, 1126}, {1089, 31010}, {1100, 3733}, {1125, 1019}, {1213, 513}, {1230, 693}, {1269, 7199}, {1332, 57685}, {1500, 58301}, {1839, 57200}, {1962, 649}, {2308, 57129}, {2355, 43925}, {3649, 3669}, {3683, 7252}, {3686, 3737}, {3702, 4560}, {3775, 4481}, {3916, 7254}, {3952, 1255}, {3958, 1459}, {4033, 1268}, {4046, 650}, {4065, 4063}, {4069, 33635}, {4115, 1}, {4359, 7192}, {4427, 81}, {4557, 28615}, {4567, 6578}, {4647, 514}, {4697, 18200}, {4717, 47683}, {4970, 18197}, {4974, 50456}, {4976, 18191}, {4977, 16726}, {4978, 17205}, {4983, 1015}, {4985, 17197}, {4988, 244}, {4992, 16742}, {6367, 3125}, {7035, 4632}, {8013, 661}, {8040, 4979}, {8663, 3121}, {20970, 667}, {21816, 512}, {22080, 22383}, {27808, 32018}, {30591, 1086}, {30729, 21}, {30730, 32635}, {35327, 1333}, {35342, 58}, {36075, 1408}, {40521, 52555}, {41014, 905}, {42437, 47918}, {42439, 48019}, {44143, 17924}, {52576, 1577}, {56875, 17925}, {59218, 4784}, {61170, 56}, {61225, 1412}
X(61174) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4103, 61175, 35309}

X(61175) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(1) AND CEVIAN-OF-X(87)

Barycentrics    (a-b)*(a-c)*(b+c)*(a*(b-c)^2-b*c*(b+c)) : :

X(61175) lies on these lines: {10, 3121}, {306, 20496}, {594, 16592}, {649, 8050}, {1978, 3835}, {2321, 21093}, {3936, 20501}, {3971, 20690}, {4033, 7239}, {4103, 35309}, {4505, 47996}, {4598, 45313}, {6377, 20532}, {21040, 21827}, {21070, 24071}, {23354, 61234}

X(61175) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3733, 56011}, {55997, 57129}
X(61175) = X(i)-Dao conjugate of X(j) for these {i, j}: {16604, 17217}, {21827, 20295}, {34832, 1019}
X(61175) = pole of line {21757, 22024} with respect to the Yff parabola
X(61175) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1978), X(21827)}}, {{A, B, C, X(21040), X(53648)}}
X(61175) = barycentric product X(i)*X(j) for these (i, j): {1978, 21827}, {16604, 4033}, {16710, 4103}, {21040, 4598}, {24165, 3952}
X(61175) = barycentric quotient X(i)/X(j) for these (i, j): {1018, 56011}, {3952, 55997}, {16604, 1019}, {17459, 18197}, {20971, 16695}, {21040, 3835}, {21128, 23824}, {21757, 57129}, {21827, 649}, {22081, 23092}, {24165, 7192}, {34832, 17217}, {48406, 17205}
X(61175) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4033, 7239, 61165}, {6377, 20532, 36951}, {35309, 61174, 4103}

X(61176) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(1) AND CEVIAN-OF-X(88)

Barycentrics    a*(a-b)*(a-c)*(b+c)*(b^2-4*b*c+c^2+a*(b+c)) : :

X(61176) lies on these lines: {10, 12}, {43, 24399}, {100, 28218}, {354, 25377}, {513, 17780}, {518, 1647}, {764, 1026}, {908, 56893}, {3555, 23869}, {3699, 3888}, {3952, 4010}, {4054, 22295}, {4553, 4767}, {5288, 17123}, {5902, 25025}, {10176, 25031}, {13589, 46973}, {14872, 31679}, {15632, 56881}, {21087, 22306}, {21093, 22313}, {21580, 25310}, {23343, 24457}, {23705, 23832}, {42721, 54099}, {58254, 59586}

X(61176) = X(i)-isoconjugate-of-X(j) for these {i, j}: {21, 37627}, {58, 23836}, {1019, 40400}, {1120, 3733}, {1811, 57200}, {3737, 8686}, {36805, 57129}
X(61176) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 23836}, {16594, 7192}, {40611, 37627}
X(61176) = pole of line {3995, 22003} with respect to the Yff parabola
X(61176) = pole of line {11, 764} with respect to the dual conic of Wallace hyperbola
X(61176) = intersection, other than A, B, C, of circumconics {{A, B, C, X(10), X(23705)}}, {{A, B, C, X(65), X(3952)}}, {{A, B, C, X(181), X(40521)}}, {{A, B, C, X(226), X(4033)}}, {{A, B, C, X(758), X(3880)}}, {{A, B, C, X(4551), X(4848)}}, {{A, B, C, X(4695), X(40663)}}, {{A, B, C, X(4927), X(35353)}}, {{A, B, C, X(16609), X(16610)}}
X(61176) = barycentric product X(i)*X(j) for these (i, j): {37, 61186}, {190, 4695}, {226, 23705}, {1018, 1266}, {1149, 4033}, {1878, 52609}, {3880, 4552}, {16610, 3952}, {16711, 40521}, {21041, 3257}, {23832, 321}
X(61176) = barycentric quotient X(i)/X(j) for these (i, j): {37, 23836}, {1018, 1120}, {1149, 1019}, {1266, 7199}, {1400, 37627}, {1878, 17925}, {3880, 4560}, {3952, 36805}, {4557, 40400}, {4559, 8686}, {4574, 1811}, {4695, 514}, {4927, 16727}, {6085, 16726}, {16610, 7192}, {21041, 3762}, {23205, 7254}, {23705, 333}, {23832, 81}, {61171, 56642}, {61186, 274}
X(61176) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3952, 61166, 61172}, {3952, 61177, 40521}, {40521, 61166, 61177}

X(61177) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(1) AND CEVIAN-OF-X(89)

Barycentrics    a*(a-b)*(a-c)*(b+c)*(b^2-b*c+c^2+a*(b+c)) : :

X(61177) lies on these lines: {12, 10129}, {100, 109}, {181, 3873}, {210, 48648}, {513, 4781}, {660, 37210}, {661, 1018}, {693, 15632}, {1155, 50003}, {2810, 51583}, {3030, 24988}, {3032, 24222}, {3681, 3703}, {3753, 30588}, {3799, 4767}, {3903, 51562}, {3936, 22294}, {3952, 4010}, {4553, 17780}, {7287, 50483}, {21088, 22307}, {22325, 31037}, {25142, 25312}, {29824, 38472}, {31272, 38478}, {40501, 50487}, {57151, 61223}

X(61177) = X(i)-isoconjugate-of-X(j) for these {i, j}: {11, 59124}, {649, 55942}, {996, 3733}, {1019, 40401}, {7252, 60085}
X(61177) = X(i)-Dao conjugate of X(j) for these {i, j}: {5375, 55942}
X(61177) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {46480, 150}
X(61177) = X(i)-cross conjugate of X(j) for these {i, j}: {48350, 4424}
X(61177) = pole of line {4552, 46480} with respect to the Steiner circumellipse
X(61177) = pole of line {63, 3995} with respect to the Yff parabola
X(61177) = intersection, other than A, B, C, of circumconics {{A, B, C, X(109), X(3952)}}, {{A, B, C, X(651), X(4033)}}, {{A, B, C, X(661), X(48350)}}, {{A, B, C, X(1018), X(4424)}}, {{A, B, C, X(1025), X(26580)}}, {{A, B, C, X(3877), X(3903)}}, {{A, B, C, X(4579), X(51562)}}, {{A, B, C, X(4850), X(37210)}}, {{A, B, C, X(43050), X(50453)}}
X(61177) = barycentric product X(i)*X(j) for these (i, j): {37, 61187}, {100, 26580}, {190, 4424}, {1016, 48350}, {1018, 4389}, {3877, 4552}, {3952, 4850}, {4033, 995}, {4551, 5233}, {16712, 40521}, {21042, 4604}, {33934, 4557}, {50453, 765}
X(61177) = barycentric quotient X(i)/X(j) for these (i, j): {100, 55942}, {995, 1019}, {1018, 996}, {2149, 59124}, {3877, 4560}, {4033, 58027}, {4266, 3737}, {4389, 7199}, {4424, 514}, {4551, 60085}, {4557, 40401}, {4850, 7192}, {5233, 18155}, {9002, 16726}, {17461, 47683}, {20973, 4833}, {21042, 4791}, {23206, 7254}, {26580, 693}, {33934, 52619}, {44435, 16727}, {48335, 17205}, {48350, 1086}, {50453, 1111}, {61187, 274}
X(61177) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3936, 51377, 22294}, {40521, 61166, 61176}, {40521, 61176, 3952}, {61172, 61176, 40521}

X(61178) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(1) AND CEVIAN-OF-X(92)

Barycentrics    (a-b)*(a-c)*(a+b-c)*(a-b+c)*(b+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2) : :
X(61178) = -3*X[2]+2*X[34588], -2*X[24030]+X[53557]

X(61178) lies on these lines: {1, 38983}, {2, 34588}, {4, 80}, {7, 20901}, {8, 14257}, {10, 56827}, {33, 56326}, {40, 56327}, {57, 44311}, {65, 17869}, {92, 7672}, {100, 108}, {107, 15439}, {109, 23987}, {158, 15443}, {162, 655}, {196, 2550}, {201, 1148}, {208, 54286}, {225, 4674}, {226, 21911}, {278, 291}, {281, 2171}, {514, 61227}, {523, 53321}, {648, 6648}, {651, 53349}, {668, 18026}, {860, 40663}, {1020, 61229}, {1068, 1772}, {1118, 56876}, {1400, 56319}, {1757, 56822}, {1783, 4559}, {1824, 1893}, {1875, 38462}, {1876, 37790}, {1887, 56875}, {1940, 6198}, {2099, 5136}, {2222, 30250}, {2406, 14544}, {2817, 24034}, {3192, 18676}, {3340, 54396}, {3434, 52489}, {3911, 23710}, {4551, 4605}, {5080, 38949}, {5218, 16577}, {5380, 46102}, {5759, 44695}, {7009, 7095}, {7115, 55197}, {7288, 38295}, {7412, 51879}, {7461, 23845}, {8050, 46152}, {8750, 57218}, {8762, 22342}, {11041, 34231}, {17906, 23706}, {17916, 20616}, {17927, 17985}, {18793, 57652}, {21061, 55324}, {21078, 47345}, {24026, 59816}, {24030, 53557}, {38461, 43037}, {41228, 44697}, {45766, 48363}, {61236, 61239}

X(61178) = reflection of X(i) in X(j) for these {i,j}: {53557, 24030}
X(61178) = isogonal conjugate of X(23189)
X(61178) = anticomplement of X(34588)
X(61178) = trilinear pole of line {12, 37}
X(61178) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 23189}, {3, 3737}, {7, 57134}, {9, 7254}, {11, 4575}, {21, 1459}, {27, 36054}, {28, 57241}, {29, 23224}, {41, 15419}, {48, 4560}, {56, 57081}, {57, 23090}, {58, 521}, {60, 656}, {63, 7252}, {77, 21789}, {78, 3733}, {81, 652}, {86, 1946}, {110, 7004}, {162, 1364}, {163, 26932}, {184, 18155}, {212, 7192}, {216, 39177}, {219, 1019}, {222, 1021}, {261, 810}, {269, 58338}, {270, 520}, {284, 905}, {332, 667}, {333, 22383}, {345, 57129}, {514, 2193}, {522, 1437}, {525, 2150}, {577, 57215}, {593, 8611}, {603, 7253}, {604, 15411}, {643, 3937}, {647, 2185}, {649, 1812}, {650, 1790}, {659, 1808}, {662, 7117}, {663, 1444}, {692, 17219}, {811, 61054}, {822, 46103}, {849, 52355}, {859, 37628}, {906, 17197}, {1014, 57108}, {1172, 4091}, {1259, 57200}, {1260, 7203}, {1331, 18191}, {1333, 6332}, {1396, 57057}, {1412, 57055}, {1414, 3270}, {1436, 57213}, {1576, 17880}, {1789, 2605}, {1792, 43924}, {1793, 53314}, {1798, 17420}, {1802, 17096}, {1977, 55207}, {2170, 4558}, {2189, 24018}, {2194, 4025}, {2203, 52616}, {2204, 30805}, {2206, 35518}, {2289, 17925}, {2299, 4131}, {2319, 23092}, {2327, 3669}, {2360, 61040}, {3049, 52379}, {3063, 17206}, {3064, 18604}, {3271, 4592}, {3286, 23696}, {3500, 23145}, {3615, 23226}, {3719, 43925}, {3738, 57736}, {3942, 5546}, {4556, 53560}, {4565, 34591}, {4587, 16726}, {4636, 18210}, {4858, 32661}, {6514, 6591}, {6740, 22379}, {7053, 58329}, {7054, 51664}, {7125, 17926}, {7199, 52425}, {7255, 20753}, {7257, 22096}, {8648, 57985}, {15373, 27527}, {15413, 57657}, {15416, 16947}, {15958, 60804}, {16731, 32674}, {22345, 57161}, {22384, 56154}, {34588, 59005}, {39201, 57779}, {51640, 59482}
X(61178) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 57081}, {3, 23189}, {10, 521}, {37, 6332}, {115, 26932}, {125, 1364}, {136, 11}, {226, 4131}, {244, 7004}, {478, 7254}, {1084, 7117}, {1086, 17219}, {1214, 4025}, {1249, 4560}, {3160, 15419}, {3161, 15411}, {3162, 7252}, {4075, 52355}, {4858, 17880}, {5139, 3271}, {5190, 17197}, {5375, 1812}, {5452, 23090}, {5521, 18191}, {6600, 58338}, {6631, 332}, {6741, 2968}, {7952, 7253}, {10001, 17206}, {17423, 61054}, {23050, 58329}, {34588, 34588}, {35072, 16731}, {36103, 3737}, {39026, 283}, {39052, 2185}, {39053, 86}, {39060, 274}, {39062, 261}, {40586, 652}, {40590, 905}, {40591, 57241}, {40596, 60}, {40599, 57055}, {40600, 1946}, {40603, 35518}, {40608, 3270}, {40611, 1459}, {40622, 1565}, {40837, 7192}, {47345, 514}, {53982, 3738}, {55060, 3937}, {55064, 34591}, {56325, 525}, {56905, 3910}
X(61178) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1897, 4551}, {7012, 4}, {46102, 8736}
X(61178) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {15386, 20}, {26704, 33650}, {36050, 34188}, {57757, 1370}
X(61178) = X(i)-cross conjugate of X(j) for these {i, j}: {181, 7115}, {523, 41013}, {1825, 7012}, {2501, 40149}, {3700, 226}, {4036, 60086}, {4041, 281}, {4559, 4552}, {8736, 46102}, {14308, 2321}, {24006, 4}, {55208, 278}, {55232, 60188}
X(61178) = pole of line {7461, 53279} with respect to the circumcircle
X(61178) = pole of line {11, 124} with respect to the polar circle
X(61178) = pole of line {651, 24035} with respect to the Steiner circumellipse
X(61178) = pole of line {329, 21078} with respect to the Yff parabola
X(61178) = pole of line {219, 3436} with respect to the Hutson-Moses hyperbola
X(61178) = pole of line {1969, 17913} with respect to the dual conic of Jerabek hyperbola
X(61178) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(162)}}, {{A, B, C, X(7), X(26700)}}, {{A, B, C, X(65), X(23981)}}, {{A, B, C, X(80), X(100)}}, {{A, B, C, X(108), X(18026)}}, {{A, B, C, X(109), X(34242)}}, {{A, B, C, X(523), X(2804)}}, {{A, B, C, X(653), X(36127)}}, {{A, B, C, X(655), X(4552)}}, {{A, B, C, X(758), X(2800)}}, {{A, B, C, X(925), X(6742)}}, {{A, B, C, X(1000), X(55185)}}, {{A, B, C, X(1897), X(26704)}}, {{A, B, C, X(2588), X(53153)}}, {{A, B, C, X(2589), X(53154)}}, {{A, B, C, X(2766), X(52914)}}, {{A, B, C, X(3119), X(4041)}}, {{A, B, C, X(3700), X(17094)}}, {{A, B, C, X(4077), X(47695)}}, {{A, B, C, X(4559), X(15439)}}, {{A, B, C, X(11604), X(53927)}}, {{A, B, C, X(23189), X(38983)}}, {{A, B, C, X(23987), X(56827)}}, {{A, B, C, X(24006), X(44428)}}, {{A, B, C, X(35136), X(56241)}}, {{A, B, C, X(35174), X(36098)}}, {{A, B, C, X(39270), X(56173)}}, {{A, B, C, X(41013), X(53151)}}
X(61178) = barycentric product X(i)*X(j) for these (i, j): {4, 4552}, {10, 653}, {12, 648}, {29, 4605}, {34, 4033}, {42, 46404}, {100, 40149}, {101, 57809}, {107, 26942}, {108, 321}, {112, 34388}, {162, 6358}, {181, 6331}, {190, 225}, {201, 823}, {264, 4559}, {278, 3952}, {281, 4566}, {306, 36127}, {313, 32674}, {331, 4557}, {349, 8750}, {429, 6648}, {655, 860}, {1018, 273}, {1020, 318}, {1118, 52609}, {1119, 30730}, {1426, 646}, {1441, 1783}, {1446, 56183}, {1577, 7012}, {1824, 4554}, {1826, 664}, {1835, 36804}, {1847, 4069}, {1865, 54952}, {1867, 32038}, {1874, 4562}, {1880, 668}, {1882, 54970}, {1893, 32041}, {1897, 226}, {1978, 57652}, {2052, 23067}, {2171, 811}, {2197, 6528}, {2321, 36118}, {2333, 4572}, {2501, 4998}, {3700, 55346}, {4086, 7128}, {4242, 60091}, {4551, 92}, {4565, 7141}, {4573, 7140}, {6335, 65}, {7115, 850}, {8736, 99}, {13149, 210}, {14618, 59}, {15352, 7066}, {15455, 1825}, {15742, 7178}, {17906, 56173}, {18020, 55197}, {18026, 37}, {21859, 286}, {23984, 52355}, {24006, 4564}, {24019, 57807}, {24032, 8611}, {27808, 608}, {32714, 3701}, {34922, 7265}, {35307, 40440}, {36797, 6354}, {40117, 57810}, {40961, 42384}, {41013, 651}, {44113, 46405}, {44699, 58759}, {44765, 56827}, {46102, 523}, {46152, 56186}, {52575, 692}, {52607, 8}, {52938, 71}, {53008, 658}, {53009, 53642}, {53321, 7017}, {54240, 72}, {55194, 8754}, {55208, 7035}, {56285, 662}, {60188, 61180}
X(61178) = barycentric quotient X(i)/X(j) for these (i, j): {4, 4560}, {6, 23189}, {7, 15419}, {8, 15411}, {9, 57081}, {10, 6332}, {12, 525}, {19, 3737}, {25, 7252}, {33, 1021}, {34, 1019}, {37, 521}, {40, 57213}, {41, 57134}, {42, 652}, {55, 23090}, {56, 7254}, {59, 4558}, {65, 905}, {71, 57241}, {73, 4091}, {92, 18155}, {100, 1812}, {101, 283}, {107, 46103}, {108, 81}, {109, 1790}, {112, 60}, {158, 57215}, {162, 2185}, {181, 647}, {190, 332}, {201, 24018}, {210, 57055}, {213, 1946}, {220, 58338}, {225, 514}, {226, 4025}, {228, 36054}, {273, 7199}, {278, 7192}, {281, 7253}, {306, 52616}, {307, 30805}, {321, 35518}, {331, 52619}, {429, 3910}, {430, 4976}, {512, 7117}, {514, 17219}, {521, 16731}, {523, 26932}, {594, 52355}, {607, 21789}, {608, 3733}, {644, 1792}, {647, 1364}, {648, 261}, {651, 1444}, {653, 86}, {655, 57985}, {661, 7004}, {664, 17206}, {692, 2193}, {756, 8611}, {811, 52379}, {813, 1808}, {823, 57779}, {860, 3904}, {862, 4435}, {1018, 78}, {1020, 77}, {1118, 17925}, {1119, 17096}, {1214, 4131}, {1254, 51664}, {1331, 6514}, {1334, 57108}, {1395, 57129}, {1400, 1459}, {1402, 22383}, {1403, 23092}, {1409, 23224}, {1415, 1437}, {1426, 3669}, {1435, 7203}, {1441, 15413}, {1577, 17880}, {1783, 21}, {1824, 650}, {1825, 14838}, {1826, 522}, {1832, 54023}, {1833, 54021}, {1835, 3960}, {1840, 3907}, {1857, 17926}, {1867, 23880}, {1874, 812}, {1880, 513}, {1882, 23882}, {1893, 4762}, {1897, 333}, {1903, 61040}, {2149, 4575}, {2171, 656}, {2190, 39177}, {2197, 520}, {2250, 37628}, {2318, 57057}, {2333, 663}, {2489, 3271}, {2501, 11}, {3049, 61054}, {3700, 2968}, {3701, 15416}, {3709, 3270}, {3939, 2327}, {3952, 345}, {4017, 3942}, {4033, 3718}, {4041, 34591}, {4069, 3692}, {4103, 3710}, {4551, 63}, {4552, 69}, {4557, 219}, {4559, 3}, {4564, 4592}, {4566, 348}, {4574, 1259}, {4605, 307}, {4705, 53560}, {4998, 4563}, {5236, 23829}, {5379, 4612}, {6331, 18021}, {6335, 314}, {6354, 17094}, {6358, 14208}, {6531, 60568}, {6591, 18191}, {6648, 57853}, {7012, 662}, {7035, 55207}, {7066, 52613}, {7079, 58329}, {7115, 110}, {7128, 1414}, {7140, 3700}, {7178, 1565}, {7180, 3937}, {7235, 24459}, {7282, 16755}, {7337, 43925}, {7649, 17197}, {8270, 57144}, {8611, 24031}, {8687, 1798}, {8735, 56283}, {8736, 523}, {8750, 284}, {8754, 55195}, {8898, 51644}, {13149, 57785}, {14308, 40616}, {14618, 34387}, {15742, 645}, {17906, 17183}, {18020, 55196}, {18026, 274}, {18785, 23696}, {21016, 48278}, {21075, 57245}, {21078, 57111}, {21741, 23226}, {21805, 14418}, {21853, 59973}, {21859, 72}, {21871, 57101}, {23067, 394}, {24006, 4858}, {24019, 270}, {26704, 19607}, {26942, 3265}, {27808, 57919}, {30730, 1265}, {32674, 58}, {32675, 57736}, {32676, 2150}, {32713, 2189}, {32714, 1014}, {34247, 23145}, {34388, 3267}, {35307, 44706}, {36059, 18604}, {36118, 1434}, {36127, 27}, {36797, 7058}, {39579, 60492}, {40117, 285}, {40149, 693}, {40521, 3694}, {40952, 52306}, {41013, 4391}, {41539, 24562}, {43923, 16726}, {44092, 52326}, {44113, 654}, {44699, 36841}, {46102, 99}, {46152, 16696}, {46404, 310}, {46541, 30606}, {51377, 52307}, {52355, 23983}, {52370, 58340}, {52575, 40495}, {52607, 7}, {52609, 1264}, {52610, 1804}, {52938, 44129}, {53008, 3239}, {53009, 8058}, {53011, 14331}, {53321, 222}, {53323, 46882}, {53861, 47965}, {54016, 1806}, {54018, 1805}, {54240, 286}, {55194, 47389}, {55197, 125}, {55206, 2310}, {55208, 244}, {55212, 53557}, {55323, 23187}, {55346, 4573}, {56183, 2287}, {56285, 1577}, {56319, 20293}, {57185, 18210}, {57220, 4225}, {57243, 17216}, {57652, 649}, {57809, 3261}, {58757, 8735}, {60086, 15420}, {61160, 1040}, {61170, 3916}, {61171, 5440}, {61205, 4267}, {61226, 17185}, {61229, 41081}, {61236, 54356}
X(61178) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {653, 1897, 108}, {1825, 56285, 4}, {2406, 14544, 36059}, {17927, 17985, 37799}, {53151, 61180, 1897}

X(61179) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(1) AND CEVIAN-OF-X(100)

Barycentrics    a*(a+b-2*c)*(a-b-c)*(b-c)*(a-2*b+c)*(b+c) : :

X(61179) lies on these lines: {9, 650}, {33, 4162}, {37, 661}, {210, 4041}, {226, 4049}, {312, 4391}, {513, 750}, {522, 4023}, {901, 9090}, {903, 35144}, {1022, 14349}, {1826, 2501}, {1903, 55242}, {2250, 21894}, {2316, 2341}, {2321, 3700}, {2441, 4790}, {4009, 60577}, {4120, 24078}, {4530, 35015}, {4582, 60484}, {4674, 24290}, {4776, 6548}, {4983, 57162}, {4997, 36800}, {8818, 55236}, {9456, 47227}, {23345, 48026}, {23352, 42758}, {60575, 60578}

X(61179) = trilinear pole of line {4041, 4516}
X(61179) = perspector of circumconic {{A, B, C, X(1320), X(4674)}}
X(61179) = X(i)-isoconjugate-of-X(j) for these {i, j}: {44, 1414}, {81, 23703}, {86, 61210}, {99, 1404}, {109, 16704}, {110, 3911}, {222, 46541}, {249, 30572}, {519, 4565}, {604, 55243}, {651, 52680}, {662, 1319}, {664, 3285}, {757, 61171}, {900, 52378}, {902, 4573}, {1014, 1023}, {1317, 4591}, {1397, 55262}, {1408, 24004}, {1412, 17780}, {1415, 30939}, {1434, 23344}, {1813, 37168}, {1877, 4558}, {1960, 4620}, {2222, 17191}, {2251, 4625}, {3689, 4637}, {4169, 7341}, {4551, 30576}, {4556, 40663}, {4567, 53528}, {4570, 30725}, {4575, 37790}, {4615, 61047}, {4629, 5298}, {4700, 5545}, {7340, 14407}, {30606, 53321}, {37140, 53537}
X(61179) = X(i)-Dao conjugate of X(j) for these {i, j}: {11, 16704}, {136, 37790}, {244, 3911}, {1084, 1319}, {1146, 30939}, {3161, 55243}, {3709, 4922}, {6741, 4358}, {9460, 4625}, {38984, 17191}, {38986, 1404}, {38991, 52680}, {39025, 3285}, {40586, 23703}, {40594, 4573}, {40595, 1414}, {40599, 17780}, {40600, 61210}, {40607, 61171}, {40608, 44}, {40627, 53528}, {50330, 30725}, {51402, 16729}, {55064, 519}, {55068, 30606}, {59577, 24004}
X(61179) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4049, 55244}
X(61179) = pole of line {16704, 37790} with respect to the polar circle
X(61179) = pole of line {42759, 55244} with respect to the Kiepert hyperbola
X(61179) = pole of line {1639, 3762} with respect to the dual conic of Wallace hyperbola
X(61179) = intersection, other than A, B, C, of circumconics {{A, B, C, X(9), X(33)}}, {{A, B, C, X(11), X(35353)}}, {{A, B, C, X(513), X(4086)}}, {{A, B, C, X(650), X(661)}}, {{A, B, C, X(885), X(3952)}}, {{A, B, C, X(2433), X(27780)}}, {{A, B, C, X(3239), X(4129)}}, {{A, B, C, X(3657), X(35015)}}, {{A, B, C, X(3709), X(4944)}}, {{A, B, C, X(4120), X(4530)}}, {{A, B, C, X(4162), X(8611)}}, {{A, B, C, X(4559), X(55255)}}, {{A, B, C, X(4820), X(48005)}}, {{A, B, C, X(7180), X(17424)}}, {{A, B, C, X(7252), X(58294)}}, {{A, B, C, X(18013), X(42552)}}, {{A, B, C, X(21894), X(46393)}}, {{A, B, C, X(23838), X(55244)}}, {{A, B, C, X(40166), X(55195)}}, {{A, B, C, X(55263), X(60480)}}
X(61179) = barycentric product X(i)*X(j) for these (i, j): {10, 23838}, {37, 60480}, {106, 4086}, {210, 6548}, {312, 55263}, {1018, 60578}, {1022, 2321}, {1320, 523}, {1577, 2316}, {1639, 30575}, {3125, 4582}, {3700, 88}, {3737, 4013}, {4041, 903}, {4049, 9}, {4069, 6549}, {4080, 650}, {4092, 4622}, {4516, 4555}, {4674, 522}, {4997, 661}, {5376, 55195}, {6336, 8611}, {16732, 5548}, {20568, 3709}, {21044, 3257}, {23345, 3701}, {36125, 52355}, {36590, 53527}, {53562, 57788}, {55244, 8}
X(61179) = barycentric quotient X(i)/X(j) for these (i, j): {8, 55243}, {33, 46541}, {42, 23703}, {88, 4573}, {106, 1414}, {210, 17780}, {213, 61210}, {312, 55262}, {512, 1319}, {522, 30939}, {650, 16704}, {654, 17191}, {661, 3911}, {663, 52680}, {798, 1404}, {903, 4625}, {1021, 30606}, {1022, 1434}, {1318, 4622}, {1320, 99}, {1334, 1023}, {1500, 61171}, {1639, 16729}, {2316, 662}, {2321, 24004}, {2501, 37790}, {2643, 30572}, {3063, 3285}, {3122, 53528}, {3125, 30725}, {3257, 4620}, {3700, 4358}, {3709, 44}, {4041, 519}, {4049, 85}, {4080, 4554}, {4086, 3264}, {4171, 2325}, {4515, 30731}, {4516, 900}, {4524, 3689}, {4582, 4601}, {4622, 7340}, {4674, 664}, {4705, 40663}, {4730, 1317}, {4770, 36920}, {4843, 4742}, {4983, 5298}, {4997, 799}, {5376, 55194}, {5548, 4567}, {6548, 57785}, {7252, 30576}, {8611, 3977}, {9456, 4565}, {18344, 37168}, {21044, 3762}, {23345, 1014}, {23838, 86}, {32665, 52378}, {36197, 1639}, {40608, 4922}, {42666, 53537}, {43922, 7203}, {44729, 4487}, {52335, 4768}, {53527, 41801}, {53562, 214}, {55206, 8756}, {55238, 14628}, {55244, 7}, {55259, 40218}, {55263, 57}, {56049, 4616}, {57995, 55213}, {60480, 274}, {60578, 7199}

X(61180) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(2) AND CEVIAN-OF-X(21)

Barycentrics    (a-b)*(a-c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(2*a*b*c+a^2*(b+c)-(b-c)^2*(b+c)) : :

X(61180) lies on these lines: {2, 47212}, {4, 2771}, {8, 1148}, {20, 9528}, {29, 34195}, {92, 3873}, {100, 108}, {107, 110}, {112, 59097}, {149, 52167}, {158, 3868}, {196, 3434}, {243, 3218}, {329, 56299}, {331, 20247}, {425, 37783}, {445, 41571}, {523, 37966}, {651, 36127}, {758, 1784}, {811, 53332}, {877, 55231}, {883, 46404}, {1118, 12649}, {1309, 56321}, {1783, 53358}, {1844, 39772}, {1857, 5905}, {1895, 3869}, {1940, 34772}, {1969, 17141}, {3176, 3436}, {3952, 6335}, {4246, 53280}, {4427, 36797}, {4566, 18026}, {5279, 56300}, {5379, 14775}, {6742, 17914}, {7017, 17165}, {7649, 61226}, {11520, 39585}, {12528, 47372}, {13149, 35312}, {15146, 39767}, {24473, 39529}, {30941, 40703}, {31164, 39531}, {44447, 44695}, {52414, 52891}, {61233, 61236}

X(61180) = trilinear pole of line {442, 1838}
X(61180) = perspector of circumconic {{A, B, C, X(23582), X(46102)}}
X(61180) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 56320}, {255, 14775}, {513, 1794}, {652, 2982}, {656, 1175}, {810, 40412}, {822, 40395}, {905, 2259}, {943, 1459}, {1946, 60041}, {2638, 58993}, {3270, 36048}, {7004, 15439}, {14838, 57691}, {22383, 40435}, {23226, 57710}, {24018, 40570}, {32651, 34591}, {36054, 40573}, {52560, 57134}
X(61180) = X(i)-Dao conjugate of X(j) for these {i, j}: {442, 521}, {942, 520}, {1249, 56320}, {6523, 14775}, {15607, 3270}, {16585, 4025}, {18591, 905}, {39007, 1364}, {39026, 1794}, {39053, 60041}, {39062, 40412}, {40596, 1175}, {40937, 525}, {52119, 125}
X(61180) = X(i)-Ceva conjugate of X(j) for these {i, j}: {5379, 4}, {6335, 61161}
X(61180) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {107, 33650}, {109, 34186}, {162, 34188}, {653, 13219}, {5379, 52366}, {7012, 52364}, {7115, 3151}, {7128, 2897}, {23582, 20245}, {23964, 63}, {23984, 2893}, {23985, 17778}, {24000, 3869}, {24019, 37781}, {24033, 2475}, {32674, 39352}, {32713, 39351}, {36127, 3448}, {52378, 6527}, {54240, 21294}
X(61180) = pole of line {8674, 13203} with respect to the anticomplementary circle
X(61180) = pole of line {1624, 4246} with respect to the circumcircle
X(61180) = pole of line {2845, 34186} with respect to the DeLongchamps circle
X(61180) = pole of line {8674, 19506} with respect to the circumcircle of the Johnson triangle
X(61180) = pole of line {11, 125} with respect to the polar circle
X(61180) = pole of line {20, 3869} with respect to the Kiepert parabola
X(61180) = pole of line {520, 23189} with respect to the Stammler hyperbola
X(61180) = pole of line {648, 651} with respect to the Steiner circumellipse
X(61180) = pole of line {23583, 36949} with respect to the Steiner inellipse
X(61180) = pole of line {329, 3151} with respect to the Yff parabola
X(61180) = pole of line {4, 219} with respect to the Hutson-Moses hyperbola
X(61180) = pole of line {17904, 17907} with respect to the dual conic of Jerabek hyperbola
X(61180) = intersection, other than A, B, C, of circumconics {{A, B, C, X(100), X(11604)}}, {{A, B, C, X(108), X(52920)}}, {{A, B, C, X(110), X(4566)}}, {{A, B, C, X(442), X(4240)}}, {{A, B, C, X(648), X(4552)}}, {{A, B, C, X(653), X(52919)}}, {{A, B, C, X(850), X(53353)}}, {{A, B, C, X(942), X(23981)}}, {{A, B, C, X(1844), X(53176)}}, {{A, B, C, X(1897), X(52921)}}, {{A, B, C, X(2294), X(23353)}}, {{A, B, C, X(2804), X(56321)}}, {{A, B, C, X(3952), X(6528)}}, {{A, B, C, X(4427), X(16077)}}, {{A, B, C, X(4581), X(23752)}}, {{A, B, C, X(32713), X(53323)}}
X(61180) = barycentric product X(i)*X(j) for these (i, j): {112, 1234}, {264, 61197}, {273, 61233}, {286, 61161}, {442, 648}, {445, 6742}, {653, 6734}, {1838, 190}, {1841, 668}, {1859, 4554}, {1865, 99}, {1897, 5249}, {2294, 811}, {4033, 46883}, {6335, 942}, {14547, 46404}, {15455, 1844}, {18026, 40937}, {18591, 6528}, {23595, 765}, {27808, 46890}, {36797, 55010}, {40952, 6331}, {40978, 57968}, {44129, 61169}, {51978, 52607}, {53323, 76}, {56839, 823}, {61220, 92}, {61236, 75}
X(61180) = barycentric quotient X(i)/X(j) for these (i, j): {4, 56320}, {101, 1794}, {107, 40395}, {108, 2982}, {112, 1175}, {393, 14775}, {442, 525}, {445, 4467}, {648, 40412}, {653, 60041}, {942, 905}, {1234, 3267}, {1783, 943}, {1838, 514}, {1841, 513}, {1844, 14838}, {1859, 650}, {1865, 523}, {1897, 40435}, {2260, 1459}, {2294, 656}, {4303, 4091}, {5249, 4025}, {6335, 40422}, {6734, 6332}, {6742, 57860}, {7115, 15439}, {7128, 36048}, {8021, 23090}, {8750, 2259}, {14547, 652}, {14597, 23224}, {18591, 520}, {18607, 4131}, {21675, 4064}, {23207, 36054}, {23595, 1111}, {23752, 4466}, {23984, 58993}, {32713, 40570}, {33525, 3270}, {36127, 40573}, {37993, 52306}, {40937, 521}, {40952, 647}, {40956, 22383}, {40967, 8611}, {40978, 810}, {44095, 2605}, {46102, 54952}, {46882, 23189}, {46883, 1019}, {46884, 3737}, {46890, 3733}, {50354, 3942}, {51978, 15411}, {52306, 1364}, {52607, 52560}, {53323, 6}, {55010, 17094}, {56839, 24018}, {61161, 72}, {61169, 71}, {61178, 60188}, {61197, 3}, {61220, 63}, {61233, 78}, {61236, 1}
X(61180) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {653, 1897, 100}, {1897, 61178, 53151}, {53280, 53317, 4246}

X(61181) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(2) AND CEVIAN-OF-X(23)

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(b^2*(a^4-b^4)+(a^2-b^2)^2*c^2+b^2*c^4-c^6) : :

X(61181) lies on these lines: {4, 69}, {25, 36207}, {99, 39382}, {107, 110}, {112, 59098}, {186, 52772}, {250, 2407}, {297, 32113}, {325, 57632}, {468, 5968}, {523, 4230}, {685, 687}, {691, 935}, {1288, 13398}, {1289, 4611}, {1304, 16167}, {1632, 41679}, {1634, 41677}, {2420, 35907}, {2854, 60502}, {4226, 14590}, {5467, 7473}, {5523, 59422}, {8057, 60512}, {9214, 37765}, {12093, 34336}, {12272, 59156}, {18020, 55226}, {20626, 59039}, {35179, 53639}, {36176, 40879}, {36794, 46512}, {37855, 52483}, {44770, 60053}, {53199, 53205}

X(61181) = reflection of X(i) in X(j) for these {i,j}: {16237, 4230}
X(61181) = trilinear pole of line {858, 1560}
X(61181) = perspector of circumconic {{A, B, C, X(6331), X(23582)}}
X(61181) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 60040}, {656, 1177}, {661, 18876}, {810, 2373}, {822, 60133}, {2632, 10423}, {2642, 41511}, {3049, 37220}, {3269, 36095}
X(61181) = X(i)-Dao conjugate of X(j) for these {i, j}: {468, 690}, {858, 9517}, {1249, 60040}, {5181, 520}, {14961, 14417}, {36830, 18876}, {38971, 125}, {39062, 2373}, {40596, 1177}, {61067, 647}
X(61181) = X(i)-Ceva conjugate of X(j) for these {i, j}: {892, 648}
X(61181) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {24000, 11061}, {58980, 4560}
X(61181) = pole of line {512, 13203} with respect to the anticomplementary circle
X(61181) = pole of line {1624, 7473} with respect to the circumcircle
X(61181) = pole of line {512, 19506} with respect to the circumcircle of the Johnson triangle
X(61181) = pole of line {125, 512} with respect to the polar circle
X(61181) = pole of line {20, 2781} with respect to the Kiepert parabola
X(61181) = pole of line {1625, 35907} with respect to the MacBeath circumconic
X(61181) = pole of line {184, 520} with respect to the Stammler hyperbola
X(61181) = pole of line {648, 850} with respect to the Steiner circumellipse
X(61181) = pole of line {23583, 30476} with respect to the Steiner inellipse
X(61181) = pole of line {3, 3265} with respect to the Wallace hyperbola
X(61181) = pole of line {3267, 41676} with respect to the dual conic of Brocard inellipse
X(61181) = pole of line {1502, 6331} with respect to the dual conic of Jerabek hyperbola
X(61181) = pole of line {45215, 52613} with respect to the dual conic of orthic inconic
X(61181) = pole of line {5489, 20975} with respect to the dual conic of Wallace hyperbola
X(61181) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(32713)}}, {{A, B, C, X(69), X(110)}}, {{A, B, C, X(76), X(648)}}, {{A, B, C, X(107), X(264)}}, {{A, B, C, X(286), X(52920)}}, {{A, B, C, X(311), X(35360)}}, {{A, B, C, X(314), X(52914)}}, {{A, B, C, X(315), X(670)}}, {{A, B, C, X(316), X(691)}}, {{A, B, C, X(317), X(52917)}}, {{A, B, C, X(340), X(44770)}}, {{A, B, C, X(511), X(2393)}}, {{A, B, C, X(685), X(44138)}}, {{A, B, C, X(687), X(44132)}}, {{A, B, C, X(858), X(3260)}}, {{A, B, C, X(892), X(1236)}}, {{A, B, C, X(935), X(5523)}}, {{A, B, C, X(1232), X(35311)}}, {{A, B, C, X(1235), X(39269)}}, {{A, B, C, X(5181), X(53232)}}, {{A, B, C, X(6528), X(11185)}}, {{A, B, C, X(9979), X(14977)}}, {{A, B, C, X(13398), X(44128)}}, {{A, B, C, X(14615), X(35179)}}, {{A, B, C, X(15328), X(16230)}}, {{A, B, C, X(17984), X(21459)}}, {{A, B, C, X(18669), X(23353)}}, {{A, B, C, X(20626), X(44131)}}, {{A, B, C, X(34211), X(60053)}}, {{A, B, C, X(44129), X(52919)}}, {{A, B, C, X(44130), X(52921)}}, {{A, B, C, X(44137), X(53199)}}, {{A, B, C, X(44155), X(52672)}}, {{A, B, C, X(51962), X(52471)}}
X(61181) = barycentric product X(i)*X(j) for these (i, j): {112, 1236}, {162, 20884}, {264, 61198}, {316, 60507}, {648, 858}, {1560, 892}, {2393, 6331}, {4235, 59422}, {5523, 99}, {12827, 687}, {14580, 670}, {14961, 6528}, {17172, 1897}, {18020, 47138}, {18669, 811}, {21459, 4576}, {39269, 52630}, {46592, 76}, {47426, 59762}, {52512, 52915}, {52672, 877}, {52916, 57476}
X(61181) = barycentric quotient X(i)/X(j) for these (i, j): {4, 60040}, {107, 60133}, {110, 18876}, {112, 1177}, {648, 2373}, {691, 41511}, {811, 37220}, {858, 525}, {1236, 3267}, {1560, 690}, {2393, 647}, {4230, 36823}, {5181, 14417}, {5468, 53784}, {5523, 523}, {6331, 46140}, {12827, 6334}, {14580, 512}, {14961, 520}, {17172, 4025}, {18669, 656}, {20410, 2492}, {20884, 14208}, {21017, 4064}, {21109, 4466}, {21459, 58784}, {23964, 10423}, {24000, 36095}, {41676, 46165}, {42665, 3269}, {46592, 6}, {47138, 125}, {52672, 879}, {52915, 52513}, {52916, 60002}, {57485, 10097}, {59422, 14977}, {60499, 14380}, {60507, 67}, {61198, 3}
X(61181) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {523, 4230, 16237}, {2407, 2409, 250}, {14590, 30716, 4226}, {46151, 53350, 648}

X(61182) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(2) AND CEVIAN-OF-X(24)

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*((b^2-c^2)^4+a^6*(b^2+c^2)-a^2*(b^2-c^2)^2*(b^2+c^2)-a^4*(b^2+c^2)^2) : :

X(61182) lies on these lines: {4, 12825}, {68, 39118}, {107, 110}, {136, 32263}, {324, 27365}, {476, 59039}, {523, 23181}, {687, 15958}, {691, 930}, {850, 4576}, {925, 4558}, {2501, 61199}, {2970, 14984}, {3060, 43976}, {4226, 4611}, {6153, 40449}, {12893, 15454}, {14516, 56303}, {14570, 50947}, {36789, 59654}, {44768, 58784}

X(61182) = trilinear pole of line {11585, 40939}
X(61182) = X(i)-isoconjugate-of-X(j) for these {i, j}: {656, 57387}
X(61182) = X(i)-Dao conjugate of X(j) for these {i, j}: {11585, 924}, {40596, 57387}, {40939, 525}
X(61182) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {24000, 6193}, {30450, 21294}, {36145, 39352}
X(61182) = pole of line {1624, 30512} with respect to the circumcircle
X(61182) = pole of line {125, 135} with respect to the polar circle
X(61182) = pole of line {20, 6193} with respect to the Kiepert parabola
X(61182) = pole of line {648, 30450} with respect to the Steiner circumellipse
X(61182) = pole of line {3265, 53263} with respect to the Wallace hyperbola
X(61182) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(4240), X(11585)}}, {{A, B, C, X(13398), X(46134)}}, {{A, B, C, X(18670), X(23353)}}
X(61182) = barycentric product X(i)*X(j) for these (i, j): {11585, 648}, {18647, 1897}, {18670, 811}, {40939, 46134}
X(61182) = barycentric quotient X(i)/X(j) for these (i, j): {112, 57387}, {11585, 525}, {18647, 4025}, {18670, 656}, {40939, 924}
X(61182) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {35360, 53350, 110}

X(61183) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(2) AND CEVIAN-OF-X(43)

Barycentrics    (a-b)*(a-c)*(a*(b-c)^2+b*c*(b+c)) : :
X(61183) = -3*X[2]+2*X[3123]

X(61183) lies on these lines: {2, 3123}, {38, 26769}, {100, 190}, {144, 25291}, {192, 1964}, {256, 26764}, {321, 4459}, {513, 4033}, {646, 3888}, {660, 56323}, {668, 4499}, {670, 889}, {874, 21272}, {894, 25295}, {932, 43360}, {1278, 7155}, {1978, 18830}, {2098, 5695}, {3122, 25382}, {4110, 25292}, {4363, 17140}, {4440, 36222}, {4552, 46153}, {4553, 24004}, {4576, 36860}, {4840, 37205}, {4965, 20900}, {16726, 41683}, {17164, 54331}, {17165, 24351}, {17178, 22167}, {17217, 55239}, {17350, 25277}, {17601, 27538}, {20345, 36216}, {20352, 40875}, {21100, 31061}, {21343, 33946}, {22343, 59676}, {24327, 26976}, {24349, 49473}, {25268, 57091}, {25284, 49537}, {27136, 41886}

X(61183) = anticomplement of X(3123)
X(61183) = trilinear pole of line {3840, 17448}
X(61183) = perspector of circumconic {{A, B, C, X(1016), X(57577)}}
X(61183) = X(i)-isoconjugate-of-X(j) for these {i, j}: {513, 57400}, {667, 32011}, {3733, 56256}, {56197, 57129}
X(61183) = X(i)-Dao conjugate of X(j) for these {i, j}: {3123, 3123}, {3840, 4083}, {6631, 32011}, {17448, 31286}, {39026, 57400}, {59676, 513}
X(61183) = X(i)-Ceva conjugate of X(j) for these {i, j}: {61235, 25312}
X(61183) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {932, 149}, {1110, 41840}, {1252, 21219}, {2053, 17036}, {2149, 36858}, {2162, 54102}, {4564, 20537}, {4567, 17149}, {4590, 34086}, {4598, 150}, {4998, 20350}, {5383, 69}, {6378, 54104}, {18830, 21293}, {34071, 4440}
X(61183) = pole of line {1, 25295} with respect to the Kiepert parabola
X(61183) = pole of line {190, 4598} with respect to the Steiner circumellipse
X(61183) = pole of line {2, 330} with respect to the Yff parabola
X(61183) = pole of line {890, 7192} with respect to the Wallace hyperbola
X(61183) = intersection, other than A, B, C, of circumconics {{A, B, C, X(659), X(56323)}}, {{A, B, C, X(660), X(23845)}}, {{A, B, C, X(670), X(17448)}}, {{A, B, C, X(889), X(4557)}}, {{A, B, C, X(890), X(7192)}}, {{A, B, C, X(3570), X(17178)}}, {{A, B, C, X(3840), X(17780)}}, {{A, B, C, X(3952), X(57994)}}, {{A, B, C, X(18830), X(25312)}}, {{A, B, C, X(20892), X(42720)}}
X(61183) = barycentric product X(i)*X(j) for these (i, j): {100, 20892}, {190, 3840}, {1978, 22343}, {17178, 3952}, {17448, 668}, {18102, 4568}, {18192, 4033}, {21025, 99}, {22167, 799}, {25312, 330}, {32039, 59168}, {61235, 75}
X(61183) = barycentric quotient X(i)/X(j) for these (i, j): {101, 57400}, {190, 32011}, {1018, 56256}, {3840, 514}, {3952, 56197}, {16722, 17217}, {17178, 7192}, {17448, 513}, {18102, 10566}, {18192, 1019}, {20892, 693}, {21025, 523}, {22066, 1459}, {22167, 661}, {22343, 649}, {25312, 192}, {59168, 23886}, {59676, 31286}, {61235, 1}
X(61183) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {190, 53338, 3952}, {646, 3888, 23354}, {21100, 53541, 31061}, {53338, 53340, 190}

X(61184) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(2) AND CEVIAN-OF-X(55)

Barycentrics    (a-b)*(a-c)*(a^2+b^2-(a+b)*c)*(a^2-a*b+c*(-b+c))*(-((b-c)^2*(b+c))+a*(b^2+c^2)) : :

X(61184) lies on these lines: {145, 39362}, {666, 885}, {927, 17136}, {2481, 20347}, {3799, 48172}, {3870, 36816}, {3888, 46402}, {3903, 21272}, {4511, 52480}, {12649, 14267}, {14727, 53227}, {21118, 46177}, {36802, 39185}, {36803, 53338}, {52923, 56188}

X(61184) = trilinear pole of line {2886, 16588}
X(61184) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2254, 3449}
X(61184) = X(i)-Dao conjugate of X(j) for these {i, j}: {2886, 926}, {16588, 918}
X(61184) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {36086, 14732}, {36146, 39353}, {39293, 20344}, {51838, 17036}, {57536, 329}
X(61184) = pole of line {666, 46135} with respect to the Steiner circumellipse
X(61184) = intersection, other than A, B, C, of circumconics {{A, B, C, X(666), X(56188)}}, {{A, B, C, X(885), X(21118)}}, {{A, B, C, X(3903), X(43344)}}, {{A, B, C, X(21302), X(46402)}}
X(61184) = barycentric product X(i)*X(j) for these (i, j): {2886, 666}, {16588, 46135}, {17451, 51560}, {18031, 46177}, {20236, 36086}, {21746, 36803}, {40997, 927}
X(61184) = barycentric quotient X(i)/X(j) for these (i, j): {666, 40419}, {919, 3449}, {2886, 918}, {9449, 8638}, {16588, 926}, {17451, 2254}, {21029, 4088}, {21746, 665}, {21804, 24290}, {22070, 53550}, {40997, 50333}, {46177, 672}, {52562, 52614}

X(61185) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(2) AND CEVIAN-OF-X(78)

Barycentrics    (a-b)*(a-c)*(-(a^2*(b-c)^2)+a^3*(b+c)-a*(b-c)^2*(b+c)+(b^2-c^2)^2) : :
X(61185) = -3*X[2]+2*X[7004], -1*X[145]+2*X[53530], -1*X[3868]+2*X[45022]

X(61185) lies on these lines: {2, 7004}, {4, 15906}, {8, 153}, {63, 33811}, {78, 33810}, {100, 190}, {101, 41906}, {108, 2406}, {110, 1309}, {145, 53530}, {152, 329}, {318, 12528}, {522, 4551}, {651, 1897}, {693, 35312}, {823, 35360}, {835, 58992}, {912, 38462}, {1745, 20222}, {1750, 20223}, {1807, 37043}, {1830, 5905}, {1864, 17862}, {2000, 28968}, {2398, 30626}, {2475, 52391}, {2617, 4560}, {2771, 38955}, {2801, 24026}, {2821, 53358}, {2968, 13257}, {2975, 53292}, {3191, 46419}, {3434, 17165}, {3700, 35326}, {3868, 45022}, {3909, 21272}, {4358, 33883}, {4385, 12529}, {4552, 61220}, {4566, 18026}, {4939, 5083}, {5080, 12368}, {5086, 17164}, {5400, 44311}, {5777, 23661}, {5784, 26591}, {5906, 56876}, {6223, 52366}, {6265, 36944}, {7017, 11445}, {7451, 23067}, {8677, 53151}, {10391, 59575}, {11680, 17140}, {13243, 34234}, {14872, 23528}, {17194, 59638}, {17784, 24280}, {21270, 55394}, {23541, 38357}, {24349, 27479}, {24433, 26031}, {24840, 28353}, {26095, 53524}, {27383, 56940}, {35194, 37154}, {40263, 41013}, {44327, 58991}, {48269, 61160}, {51562, 56323}, {56318, 57287}

X(61185) = reflection of X(i) in X(j) for these {i,j}: {145, 53530}, {3868, 45022}
X(61185) = anticomplement of X(7004)
X(61185) = trilinear pole of line {1108, 1210}
X(61185) = perspector of circumconic {{A, B, C, X(1016), X(57538)}}
X(61185) = X(i)-isoconjugate-of-X(j) for these {i, j}: {513, 1167}, {649, 40399}, {652, 40397}, {667, 40424}, {3733, 56259}, {6129, 57422}, {22383, 40444}, {32674, 40527}, {53557, 58984}
X(61185) = X(i)-Dao conjugate of X(j) for these {i, j}: {1108, 14837}, {1210, 521}, {5375, 40399}, {6260, 513}, {6631, 40424}, {7004, 7004}, {35072, 40527}, {39026, 1167}
X(61185) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {25, 17036}, {59, 20}, {100, 34188}, {108, 149}, {250, 2975}, {608, 54102}, {653, 150}, {765, 52366}, {1252, 56943}, {1262, 347}, {1783, 37781}, {1897, 33650}, {2149, 6360}, {4552, 13219}, {4559, 39352}, {4564, 4329}, {4620, 18659}, {4998, 1370}, {5379, 3869}, {7012, 8}, {7045, 52365}, {7115, 2}, {7128, 7}, {8750, 39351}, {15385, 20076}, {15742, 3436}, {18020, 35614}, {18026, 21293}, {23067, 34186}, {23984, 56927}, {23985, 30699}, {24033, 12649}, {32674, 4440}, {34922, 52367}, {44699, 6225}, {44717, 6527}, {46102, 69}, {52378, 17134}, {55346, 3434}, {57756, 36844}, {59103, 2804}, {59151, 59926}, {61178, 3448}
X(61185) = pole of line {2969, 3270} with respect to the polar circle
X(61185) = pole of line {1, 18662} with respect to the Kiepert parabola
X(61185) = pole of line {3733, 8677} with respect to the Stammler hyperbola
X(61185) = pole of line {190, 653} with respect to the Steiner circumellipse
X(61185) = pole of line {4422, 40535} with respect to the Steiner inellipse
X(61185) = pole of line {2, 92} with respect to the Yff parabola
X(61185) = pole of line {6, 938} with respect to the Hutson-Moses hyperbola
X(61185) = pole of line {644, 1331} with respect to the dual conic of incircle
X(61185) = intersection, other than A, B, C, of circumconics {{A, B, C, X(100), X(46435)}}, {{A, B, C, X(110), X(1071)}}, {{A, B, C, X(190), X(41906)}}, {{A, B, C, X(513), X(53277)}}, {{A, B, C, X(1108), X(23343)}}, {{A, B, C, X(1210), X(17780)}}, {{A, B, C, X(1309), X(3952)}}, {{A, B, C, X(3699), X(52938)}}, {{A, B, C, X(4557), X(14776)}}, {{A, B, C, X(4571), X(13138)}}, {{A, B, C, X(6260), X(23987)}}, {{A, B, C, X(7004), X(40628)}}, {{A, B, C, X(13136), X(52609)}}, {{A, B, C, X(17862), X(42720)}}, {{A, B, C, X(23832), X(37566)}}
X(61185) = barycentric product X(i)*X(j) for these (i, j): {100, 17862}, {101, 1226}, {312, 61227}, {1071, 6335}, {1108, 668}, {1210, 190}, {1864, 4554}, {1978, 40958}, {3596, 61212}, {3611, 6331}, {13136, 1532}, {15455, 41562}, {21933, 99}, {37566, 646}, {44327, 6260}, {53288, 76}, {57285, 645}, {61237, 75}
X(61185) = barycentric quotient X(i)/X(j) for these (i, j): {100, 40399}, {101, 1167}, {108, 40397}, {190, 40424}, {521, 40527}, {1018, 56259}, {1071, 905}, {1108, 513}, {1210, 514}, {1226, 3261}, {1532, 10015}, {1864, 650}, {1897, 40444}, {3611, 647}, {6260, 14837}, {17862, 693}, {21933, 523}, {23204, 22383}, {36049, 57422}, {37566, 3669}, {40628, 7004}, {40958, 649}, {40979, 3737}, {41543, 41800}, {41561, 7658}, {41562, 14838}, {53288, 6}, {57285, 7178}, {61212, 56}, {61227, 57}, {61237, 1}
X(61185) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 9809, 33650}, {100, 56881, 3952}, {651, 1897, 14544}

X(61186) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(2) AND CEVIAN-OF-X(88)

Barycentrics    (a-b)*(a-c)*(b^2-4*b*c+c^2+a*(b+c)) : :
X(61186) = -3*X[2]+2*X[2087]

X(61186) lies on these lines: {2, 2087}, {7, 8}, {10, 23816}, {99, 28218}, {100, 46962}, {190, 6009}, {514, 4169}, {519, 52755}, {664, 31343}, {668, 891}, {874, 53340}, {885, 51560}, {1016, 53337}, {1023, 6633}, {1266, 52574}, {1334, 14951}, {2397, 46779}, {3570, 6631}, {3888, 9032}, {3912, 4530}, {4555, 4618}, {4562, 53226}, {4576, 55245}, {4695, 16711}, {4723, 59513}, {6382, 25290}, {7192, 55243}, {8709, 25575}, {20568, 53381}, {25030, 40878}, {26965, 59524}, {30730, 33946}, {33888, 39360}, {46894, 57038}

X(61186) = reflection of X(i) in X(j) for these {i,j}: {42720, 23891}
X(61186) = isotomic conjugate of X(23836)
X(61186) = anticomplement of X(2087)
X(61186) = trilinear pole of line {1266, 16594}
X(61186) = perspector of circumconic {{A, B, C, X(4554), X(31625)}}
X(61186) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 23836}, {55, 37627}, {649, 40400}, {663, 8686}, {667, 1120}, {1919, 36805}, {3248, 6079}
X(61186) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 23836}, {223, 37627}, {2087, 2087}, {2325, 1639}, {5375, 40400}, {6631, 1120}, {9296, 36805}, {16594, 513}, {16610, 900}, {21129, 23764}
X(61186) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {59, 30577}, {101, 39349}, {106, 54102}, {765, 30578}, {901, 4440}, {1016, 21290}, {1252, 17487}, {2316, 17036}, {3257, 149}, {4555, 150}, {4570, 30579}, {4582, 33650}, {4591, 17154}, {4638, 20042}, {5376, 8}, {5548, 39351}, {6551, 514}, {6635, 20295}, {9268, 2}, {32665, 9263}, {32719, 21224}, {42372, 668}, {53682, 6630}, {57564, 21282}, {59149, 44009}
X(61186) = X(i)-cross conjugate of X(j) for these {i, j}: {4927, 1266}, {6085, 16610}, {21129, 52574}
X(61186) = pole of line {18344, 42067} with respect to the polar circle
X(61186) = pole of line {17147, 30579} with respect to the Kiepert parabola
X(61186) = pole of line {2194, 58150} with respect to the Stammler hyperbola
X(61186) = pole of line {668, 693} with respect to the Steiner circumellipse
X(61186) = pole of line {4885, 27076} with respect to the Steiner inellipse
X(61186) = pole of line {192, 537} with respect to the Yff parabola
X(61186) = pole of line {14997, 30578} with respect to the Hutson-Moses hyperbola
X(61186) = pole of line {21, 3733} with respect to the Wallace hyperbola
X(61186) = pole of line {521, 3937} with respect to the dual conic of polar circle
X(61186) = pole of line {279, 4554} with respect to the dual conic of Feuerbach hyperbola
X(61186) = pole of line {3663, 24191} with respect to the dual conic of Yff parabola
X(61186) = pole of line {4516, 8034} with respect to the dual conic of Wallace hyperbola
X(61186) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(668)}}, {{A, B, C, X(8), X(23705)}}, {{A, B, C, X(65), X(3952)}}, {{A, B, C, X(75), X(53647)}}, {{A, B, C, X(85), X(1978)}}, {{A, B, C, X(518), X(3880)}}, {{A, B, C, X(664), X(39126)}}, {{A, B, C, X(891), X(6085)}}, {{A, B, C, X(1122), X(21272)}}, {{A, B, C, X(1149), X(1463)}}, {{A, B, C, X(1266), X(4555)}}, {{A, B, C, X(1441), X(27808)}}, {{A, B, C, X(1469), X(3799)}}, {{A, B, C, X(1878), X(53358)}}, {{A, B, C, X(2087), X(23836)}}, {{A, B, C, X(3212), X(36863)}}, {{A, B, C, X(4059), X(53363)}}, {{A, B, C, X(4695), X(7235)}}, {{A, B, C, X(4927), X(6548)}}, {{A, B, C, X(5252), X(8050)}}, {{A, B, C, X(6079), X(30731)}}, {{A, B, C, X(10030), X(16711)}}, {{A, B, C, X(16594), X(34762)}}, {{A, B, C, X(16610), X(41314)}}, {{A, B, C, X(24471), X(53332)}}, {{A, B, C, X(36920), X(52925)}}, {{A, B, C, X(42697), X(54987)}}
X(61186) = barycentric product X(i)*X(j) for these (i, j): {274, 61176}, {1016, 4927}, {1149, 1978}, {1266, 190}, {3880, 4554}, {4695, 799}, {16594, 4555}, {16610, 668}, {16711, 3952}, {17780, 52574}, {20900, 3257}, {21041, 4615}, {23705, 85}, {23832, 76}, {31625, 6085}
X(61186) = barycentric quotient X(i)/X(j) for these (i, j): {2, 23836}, {57, 37627}, {100, 40400}, {190, 1120}, {651, 8686}, {668, 36805}, {1016, 6079}, {1149, 649}, {1266, 514}, {1332, 1811}, {1878, 6591}, {3880, 650}, {4695, 661}, {4927, 1086}, {6085, 1015}, {8660, 1977}, {16594, 900}, {16610, 513}, {16711, 7192}, {17460, 1635}, {17780, 52556}, {20900, 3762}, {20972, 1960}, {21041, 4120}, {21129, 1647}, {22082, 22086}, {23205, 22383}, {23705, 9}, {23832, 6}, {52140, 23838}, {52206, 23345}, {52574, 6548}, {52871, 1639}, {61176, 37}
X(61186) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {514, 23891, 42720}, {668, 61187, 3952}, {3952, 21272, 61187}, {3952, 61187, 53332}, {53337, 56797, 1016}

X(61187) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(2) AND CEVIAN-OF-X(89)

Barycentrics    (a-b)*(a-c)*(b^2-b*c+c^2+a*(b+c)) : :
X(61187) = -1*X[320]+2*X[49780], -2*X[4403]+X[4440], -2*X[17755]+X[35957]

X(61187) lies on these lines: {75, 2802}, {99, 109}, {100, 13396}, {190, 514}, {316, 5195}, {320, 49780}, {335, 35103}, {512, 3888}, {517, 20924}, {519, 43287}, {537, 35962}, {644, 33951}, {668, 891}, {712, 10027}, {758, 49779}, {789, 2703}, {835, 29059}, {874, 30665}, {1000, 20569}, {1018, 33946}, {2809, 49450}, {3057, 33940}, {3754, 41875}, {3807, 23891}, {3877, 33934}, {3878, 20955}, {3884, 33944}, {4083, 4553}, {4169, 4568}, {4366, 24281}, {4389, 17461}, {4403, 4440}, {4424, 16712}, {4499, 6372}, {4561, 43290}, {4572, 52619}, {4576, 55243}, {4597, 4781}, {4642, 41805}, {5697, 33930}, {6540, 53647}, {14839, 24282}, {14923, 33933}, {17360, 36923}, {17755, 35957}, {18047, 33952}, {18061, 21232}, {20533, 30225}, {21836, 56257}, {29226, 40521}, {30997, 46894}, {33888, 33908}, {35101, 40859}, {53658, 58130}, {53659, 58128}

X(61187) = reflection of X(i) in X(j) for these {i,j}: {20924, 59513}, {320, 49780}, {335, 36226}, {35957, 17755}, {4440, 4403}
X(61187) = trilinear pole of line {4389, 4850}
X(61187) = perspector of circumconic {{A, B, C, X(4620), X(31625)}}
X(61187) = X(i)-isoconjugate-of-X(j) for these {i, j}: {649, 40401}, {667, 996}, {798, 55942}, {1980, 58027}, {2087, 32686}, {3063, 60085}, {3248, 9059}, {4516, 59124}
X(61187) = X(i)-Dao conjugate of X(j) for these {i, j}: {4389, 47779}, {4850, 4777}, {5375, 40401}, {6631, 996}, {10001, 60085}, {31998, 55942}
X(61187) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {101, 39364}, {1016, 21291}, {1252, 17488}, {2163, 54102}, {2364, 17036}, {4570, 30564}, {4588, 4440}, {4597, 150}, {4604, 149}, {5385, 8}, {5549, 39351}, {34073, 9263}
X(61187) = X(i)-cross conjugate of X(j) for these {i, j}: {9002, 4850}, {44435, 4389}, {48335, 16712}
X(61187) = pole of line {333, 17147} with respect to the Kiepert parabola
X(61187) = pole of line {668, 4597} with respect to the Steiner circumellipse
X(61187) = pole of line {192, 519} with respect to the Yff parabola
X(61187) = pole of line {17367, 37680} with respect to the Hutson-Moses hyperbola
X(61187) = pole of line {522, 3733} with respect to the Wallace hyperbola
X(61187) = pole of line {1978, 2397} with respect to the dual conic of Brocard inellipse
X(61187) = pole of line {17095, 18135} with respect to the dual conic of Feuerbach hyperbola
X(61187) = pole of line {24188, 24191} with respect to the dual conic of Yff parabola
X(61187) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4482)}}, {{A, B, C, X(99), X(4582)}}, {{A, B, C, X(109), X(3952)}}, {{A, B, C, X(190), X(4389)}}, {{A, B, C, X(514), X(23888)}}, {{A, B, C, X(664), X(27808)}}, {{A, B, C, X(668), X(1414)}}, {{A, B, C, X(891), X(9002)}}, {{A, B, C, X(995), X(23354)}}, {{A, B, C, X(1000), X(4752)}}, {{A, B, C, X(1978), X(4555)}}, {{A, B, C, X(2703), X(3799)}}, {{A, B, C, X(3766), X(48335)}}, {{A, B, C, X(3877), X(54353)}}, {{A, B, C, X(4850), X(41314)}}, {{A, B, C, X(9059), X(42285)}}, {{A, B, C, X(16712), X(27853)}}, {{A, B, C, X(18003), X(48350)}}, {{A, B, C, X(29059), X(33948)}}
X(61187) = barycentric product X(i)*X(j) for these (i, j): {100, 33934}, {190, 4389}, {274, 61177}, {1016, 44435}, {1978, 995}, {3877, 4554}, {4266, 4572}, {4424, 799}, {4600, 50453}, {4601, 48350}, {4850, 668}, {5233, 664}, {16712, 3952}, {26580, 99}, {31625, 9002}, {48335, 7035}
X(61187) = barycentric quotient X(i)/X(j) for these (i, j): {99, 55942}, {100, 40401}, {190, 996}, {664, 60085}, {995, 649}, {1016, 9059}, {1978, 58027}, {3877, 650}, {4247, 43925}, {4266, 663}, {4389, 514}, {4424, 661}, {4597, 40426}, {4850, 513}, {5233, 522}, {5376, 36091}, {9002, 1015}, {9268, 32686}, {16712, 7192}, {17196, 47683}, {17461, 4893}, {20973, 4775}, {21042, 4931}, {23206, 22383}, {23888, 1647}, {26580, 523}, {33934, 693}, {44435, 1086}, {48335, 244}, {48350, 3125}, {50453, 3120}, {52378, 59124}, {61177, 37}
X(61187) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {190, 6631, 4482}, {517, 59513, 20924}, {668, 53332, 33948}, {3952, 21272, 61186}, {21272, 53332, 668}, {35103, 36226, 335}, {53332, 61186, 3952}

X(61188) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(2) AND CEVIAN-OF-X(94)

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)-2*a^2*(b^4-b^2*c^2+c^4)) : :
X(61188) = -3*X[2]+2*X[2088]

X(61188) lies on these lines: {2, 2088}, {4, 69}, {99, 110}, {249, 4235}, {325, 57603}, {339, 7723}, {394, 34360}, {512, 53371}, {525, 2421}, {935, 10425}, {1975, 15068}, {2394, 2407}, {2420, 14999}, {3566, 11634}, {3580, 60498}, {4549, 14907}, {5654, 7763}, {6528, 46134}, {7782, 11464}, {7799, 36890}, {11064, 35910}, {13754, 52451}, {15329, 38380}, {15631, 52629}, {16077, 18878}, {16237, 61209}, {17932, 57742}, {18880, 18881}, {23342, 45808}, {32113, 51438}, {32815, 36181}, {34211, 52630}, {35139, 35316}, {35575, 59098}, {38520, 46264}, {55277, 59152}

X(61188) = isotomic conjugate of X(15328)
X(61188) = anticomplement of X(2088)
X(61188) = trilinear pole of line {3003, 3580}
X(61188) = perspector of circumconic {{A, B, C, X(4590), X(6331)}}
X(61188) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 61216}, {31, 15328}, {512, 36053}, {661, 14910}, {798, 2986}, {810, 1300}, {1924, 40832}, {1973, 15421}, {2148, 35361}, {2631, 40388}, {2643, 10420}, {3708, 32708}, {20975, 36114}, {51641, 56103}
X(61188) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 15328}, {6, 61216}, {113, 512}, {216, 35361}, {2088, 2088}, {3003, 1637}, {3580, 526}, {6337, 15421}, {9428, 40832}, {11064, 9033}, {16178, 8754}, {31998, 2986}, {34834, 523}, {36830, 14910}, {39005, 20975}, {39021, 115}, {39054, 36053}, {39062, 1300}, {40604, 15470}, {56399, 14582}
X(61188) = X(i)-Ceva conjugate of X(j) for these {i, j}: {16077, 99}
X(61188) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {476, 21221}, {662, 14731}, {1101, 18301}, {14560, 21220}, {15395, 18668}, {24041, 1272}, {32678, 148}, {32680, 3448}, {35139, 21294}, {36061, 39352}, {39295, 8}, {58979, 4560}
X(61188) = X(i)-cross conjugate of X(j) for these {i, j}: {1986, 249}, {15329, 16237}, {38380, 264}, {55121, 3580}, {60342, 2}
X(61188) = pole of line {512, 8754} with respect to the polar circle
X(61188) = pole of line {5254, 18122} with respect to the Kiepert hyperbola
X(61188) = pole of line {2, 94} with respect to the Kiepert parabola
X(61188) = pole of line {14999, 61199} with respect to the MacBeath circumconic
X(61188) = pole of line {184, 512} with respect to the Stammler hyperbola
X(61188) = pole of line {99, 476} with respect to the Steiner circumellipse
X(61188) = pole of line {620, 22104} with respect to the Steiner inellipse
X(61188) = pole of line {3, 523} with respect to the Wallace hyperbola
X(61188) = pole of line {4576, 14588} with respect to the dual conic of nine-point circle
X(61188) = pole of line {125, 520} with respect to the dual conic of polar circle
X(61188) = pole of line {6331, 7763} with respect to the dual conic of Jerabek hyperbola
X(61188) = pole of line {249, 4558} with respect to the dual conic of orthic inconic
X(61188) = pole of line {125, 23105} with respect to the dual conic of Stammler hyperbola
X(61188) = pole of line {8029, 20975} with respect to the dual conic of Wallace hyperbola
X(61188) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(110)}}, {{A, B, C, X(69), X(46134)}}, {{A, B, C, X(76), X(4563)}}, {{A, B, C, X(99), X(264)}}, {{A, B, C, X(113), X(23968)}}, {{A, B, C, X(249), X(14221)}}, {{A, B, C, X(286), X(52935)}}, {{A, B, C, X(316), X(10425)}}, {{A, B, C, X(317), X(6528)}}, {{A, B, C, X(340), X(10411)}}, {{A, B, C, X(403), X(935)}}, {{A, B, C, X(511), X(13754)}}, {{A, B, C, X(670), X(44134)}}, {{A, B, C, X(690), X(55121)}}, {{A, B, C, X(925), X(60130)}}, {{A, B, C, X(1235), X(4576)}}, {{A, B, C, X(1236), X(17932)}}, {{A, B, C, X(1725), X(3573)}}, {{A, B, C, X(1986), X(14591)}}, {{A, B, C, X(2088), X(15328)}}, {{A, B, C, X(2315), X(44151)}}, {{A, B, C, X(2394), X(3268)}}, {{A, B, C, X(2396), X(44132)}}, {{A, B, C, X(3260), X(18878)}}, {{A, B, C, X(3580), X(5468)}}, {{A, B, C, X(4427), X(44143)}}, {{A, B, C, X(4610), X(44129)}}, {{A, B, C, X(5027), X(21731)}}, {{A, B, C, X(5140), X(44084)}}, {{A, B, C, X(6333), X(6334)}}, {{A, B, C, X(10330), X(44142)}}, {{A, B, C, X(16077), X(44138)}}, {{A, B, C, X(17941), X(17984)}}, {{A, B, C, X(35136), X(44133)}}, {{A, B, C, X(35278), X(43976)}}, {{A, B, C, X(54412), X(57216)}}
X(61188) = barycentric product X(i)*X(j) for these (i, j): {305, 61209}, {403, 4563}, {1725, 799}, {2315, 57968}, {2396, 52451}, {3003, 670}, {3580, 99}, {4590, 55121}, {10411, 57486}, {13754, 6331}, {15329, 76}, {16237, 69}, {18020, 6334}, {18609, 668}, {21731, 34537}, {34104, 55264}, {34333, 57932}, {34834, 35139}, {41512, 7799}, {44084, 52608}, {44138, 4558}, {47236, 47389}
X(61188) = barycentric quotient X(i)/X(j) for these (i, j): {2, 15328}, {3, 61216}, {5, 35361}, {69, 15421}, {99, 2986}, {110, 14910}, {113, 1637}, {249, 10420}, {250, 32708}, {323, 15470}, {403, 2501}, {645, 56103}, {648, 1300}, {662, 36053}, {670, 40832}, {686, 20975}, {1304, 40388}, {1725, 661}, {1986, 47230}, {2315, 810}, {2407, 15454}, {3003, 512}, {3580, 523}, {4240, 51965}, {4558, 5504}, {4563, 57829}, {4590, 18878}, {6334, 125}, {12824, 2492}, {12825, 46425}, {12826, 47227}, {12827, 47138}, {12828, 14273}, {13754, 647}, {14165, 14222}, {14264, 2433}, {14570, 60035}, {14590, 38936}, {14999, 51456}, {15329, 6}, {16237, 4}, {18020, 687}, {18609, 513}, {21731, 3124}, {34104, 55265}, {34333, 686}, {34834, 526}, {35139, 40427}, {39170, 14582}, {41512, 1989}, {44084, 2489}, {44138, 14618}, {44769, 10419}, {47236, 8754}, {47405, 9409}, {52000, 6753}, {52451, 2395}, {52603, 52557}, {55121, 115}, {56403, 15475}, {57486, 10412}, {59152, 18879}, {60053, 12028}, {60342, 2088}, {60498, 9178}, {61209, 25}
X(61188) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {877, 53367, 14221}, {11459, 18304, 1352}

X(61189) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(2) AND CEVIAN-OF-X(107)

Barycentrics    (b-c)*(b+c)*((a^2-b^2)^2*(a^2+b^2)+(a^2+b^2)*c^4-2*c^6)*(-3*a^4+(b^2-c^2)^2+2*a^2*(b^2+c^2))*(-a^6+2*b^6+a^4*c^2-b^4*c^2-c^6+a^2*(-b^4+c^4)) : :
X(61189) = -3*X[2]+2*X[60341]

X(61189) lies on these lines: {2, 60341}, {4, 525}, {20, 14343}, {253, 523}, {850, 59256}, {879, 9476}, {1249, 8057}, {1294, 1297}, {6330, 9033}, {6333, 35140}, {10152, 14944}, {16251, 53016}, {34212, 52223}, {43717, 53345}, {44770, 48373}, {53383, 57606}

X(61189) = anticomplement of X(60341)
X(61189) = trilinear pole of line {122, 6587}
X(61189) = perspector of circumconic {{A, B, C, X(6330), X(14944)}}
X(61189) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1301, 8766}, {2155, 34211}, {2312, 46639}, {2409, 19614}, {2445, 19611}, {14379, 24024}, {16096, 32676}
X(61189) = X(i)-Dao conjugate of X(j) for these {i, j}: {4, 2409}, {122, 1503}, {6587, 39473}, {15526, 16096}, {39020, 441}, {45245, 34211}, {60341, 60341}
X(61189) = X(i)-Ceva conjugate of X(j) for these {i, j}: {2419, 43673}, {9476, 1562}
X(61189) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {36092, 12384}
X(61189) = pole of line {441, 15312} with respect to the DeLongchamps circle
X(61189) = pole of line {297, 35140} with respect to the Steiner circumellipse
X(61189) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(20)}}, {{A, B, C, X(69), X(18337)}}, {{A, B, C, X(122), X(34767)}}, {{A, B, C, X(523), X(44705)}}, {{A, B, C, X(525), X(2416)}}, {{A, B, C, X(850), X(6587)}}, {{A, B, C, X(879), X(1562)}}, {{A, B, C, X(1559), X(57626)}}, {{A, B, C, X(2848), X(55127)}}, {{A, B, C, X(14345), X(47071)}}, {{A, B, C, X(14944), X(52485)}}
X(61189) = barycentric product X(i)*X(j) for these (i, j): {20, 43673}, {1249, 2419}, {6330, 8057}, {14615, 34212}, {14944, 525}, {15466, 2435}, {35140, 6587}
X(61189) = barycentric quotient X(i)/X(j) for these (i, j): {20, 34211}, {122, 39473}, {525, 16096}, {1249, 2409}, {1297, 46639}, {2419, 34403}, {2435, 1073}, {3172, 2445}, {6330, 53639}, {6525, 23977}, {6587, 1503}, {8057, 441}, {14944, 648}, {32687, 15384}, {34212, 64}, {35140, 44326}, {42658, 8779}, {43673, 253}, {43717, 1301}, {44705, 16318}, {57296, 60341}

X(61190) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(2) AND CEVIAN-OF-X(115)

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-2*c^2)*(a^2-2*b^2+c^2)*(2*a^4+b^4+c^4-2*a^2*(b^2+c^2)) : :

X(61190) lies on these lines: {2, 31372}, {99, 44010}, {111, 36849}, {315, 6328}, {691, 2396}, {892, 5466}, {1649, 9182}, {4563, 52035}, {4590, 9168}, {6392, 52450}, {7760, 60863}, {8030, 17948}, {11123, 14588}, {17941, 50941}, {30786, 31127}, {31614, 33799}, {54607, 57539}

X(61190) = trilinear pole of line {620, 14588}
X(61190) = X(i)-isoconjugate-of-X(j) for these {i, j}: {922, 42345}, {2642, 57728}
X(61190) = X(i)-Dao conjugate of X(j) for these {i, j}: {620, 33919}, {23991, 690}, {39061, 42345}, {40469, 1648}
X(61190) = X(i)-Ceva conjugate of X(j) for these {i, j}: {54607, 34760}, {57539, 99}
X(61190) = X(i)-cross conjugate of X(j) for these {i, j}: {33906, 620}
X(61190) = pole of line {892, 42370} with respect to the Steiner circumellipse
X(61190) = pole of line {1649, 11053} with respect to the Wallace hyperbola
X(61190) = intersection, other than A, B, C, of circumconics {{A, B, C, X(620), X(34760)}}, {{A, B, C, X(892), X(2858)}}, {{A, B, C, X(5466), X(6328)}}, {{A, B, C, X(33906), X(33921)}}, {{A, B, C, X(37880), X(52940)}}
X(61190) = barycentric product X(i)*X(j) for these (i, j): {620, 892}, {11123, 52940}, {14588, 671}, {20903, 36085}, {20976, 53080}, {22085, 59762}, {33906, 57552}, {42370, 42553}
X(61190) = barycentric quotient X(i)/X(j) for these (i, j): {620, 690}, {671, 42345}, {691, 57728}, {892, 40429}, {11123, 1648}, {14588, 524}, {17199, 4750}, {17467, 2642}, {20976, 351}, {23991, 33919}, {33906, 23992}, {42553, 42344}, {57552, 14728}
X(61190) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {892, 52940, 5466}, {5466, 52940, 34760}, {5466, 5468, 52940}

X(61191) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(2) AND CEVIAN-OF-X(125)

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^4+b^4-(a^2+b^2)*c^2)*(a^4-a^2*b^2-b^2*c^2+c^4)*(2*a^6-2*a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)-a^2*(b^4-4*b^2*c^2+c^4)) : :

X(61191) lies on these lines: {2, 46250}, {20, 9218}, {98, 10733}, {193, 5967}, {287, 32244}, {685, 53351}, {879, 2966}, {2407, 43113}, {2422, 61198}, {2715, 53895}, {13573, 51963}, {14355, 34148}, {18911, 36830}, {35906, 36163}, {39138, 52451}, {43754, 48373}, {53378, 57991}

X(61191) = X(i)-Dao conjugate of X(j) for these {i, j}: {47628, 16230}
X(61191) = X(i)-Ceva conjugate of X(j) for these {i, j}: {47388, 110}
X(61191) = intersection, other than A, B, C, of circumconics {{A, B, C, X(879), X(13494)}}, {{A, B, C, X(2966), X(12066)}}, {{A, B, C, X(5972), X(34761)}}
X(61191) = barycentric product X(i)*X(j) for these (i, j): {2966, 5972}, {17468, 36036}, {17882, 36084}
X(61191) = barycentric quotient X(i)/X(j) for these (i, j): {2715, 46426}, {5972, 2799}
X(61191) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {879, 57742, 34761}, {2966, 57742, 879}

X(61192) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(2) AND CEVIAN-OF-X(142)

Barycentrics    (a-b)*(a-c)*(a+b-c)*(a-b+c)*(2*a^2+(b-c)^2-3*a*(b+c)) : :

X(61192) lies on these lines: {7, 5528}, {9, 44005}, {100, 658}, {883, 4427}, {927, 4608}, {3306, 25716}, {3689, 37780}, {3870, 42309}, {3935, 14189}, {3957, 60733}, {4552, 46725}, {4554, 17780}, {5744, 25718}, {6602, 43989}, {10004, 17784}, {25719, 54357}, {25721, 56507}

X(61192) = trilinear pole of line {6666, 58816}
X(61192) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2310, 58104}, {3063, 32015}
X(61192) = X(i)-Dao conjugate of X(j) for these {i, j}: {6666, 6362}, {10001, 32015}
X(61192) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {7045, 2890}, {53243, 37781}
X(61192) = pole of line {63, 20244} with respect to the Kiepert parabola
X(61192) = pole of line {664, 3939} with respect to the Steiner circumellipse
X(61192) = pole of line {144, 3434} with respect to the Yff parabola
X(61192) = pole of line {220, 5543} with respect to the Hutson-Moses hyperbola
X(61192) = pole of line {348, 28741} with respect to the dual conic of Feuerbach hyperbola
X(61192) = intersection, other than A, B, C, of circumconics {{A, B, C, X(664), X(43191)}}, {{A, B, C, X(2283), X(3748)}}, {{A, B, C, X(4608), X(43042)}}, {{A, B, C, X(6606), X(35312)}}, {{A, B, C, X(6666), X(56543)}}
X(61192) = barycentric product X(i)*X(j) for these (i, j): {190, 58816}, {664, 6666}, {3748, 4554}, {17201, 4552}, {61232, 85}
X(61192) = barycentric quotient X(i)/X(j) for these (i, j): {664, 32015}, {1262, 58104}, {3748, 650}, {6666, 522}, {17201, 4560}, {42438, 6608}, {58816, 514}, {61232, 9}
X(61192) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 35312, 56543}, {100, 664, 35312}

X(61193) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(3) AND CEVIAN-OF-X(20)

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^4-(b^2-c^2)^2)^2*(-(b^2-c^2)^2+a^2*(b^2+c^2)) : :

X(61193) lies on these lines: {2, 34579}, {4, 1987}, {107, 112}, {133, 1562}, {186, 41368}, {232, 52661}, {393, 1989}, {823, 17906}, {1075, 41367}, {1249, 47433}, {1301, 59086}, {1625, 14391}, {2052, 33885}, {2404, 15352}, {2501, 61204}, {3199, 13450}, {3331, 59533}, {3542, 36434}, {4240, 32661}, {5523, 51385}, {6523, 41361}, {6525, 20410}, {6528, 41676}, {6748, 59142}, {6761, 15340}, {6794, 52011}, {12918, 52485}, {14249, 39575}, {15412, 34538}, {15422, 23964}, {24019, 32675}, {32713, 32734}, {40887, 44146}, {46151, 58070}, {47409, 53803}

X(61193) = isotomic conjugate of X(15414)
X(61193) = trilinear pole of line {51, 53}
X(61193) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 15414}, {54, 24018}, {63, 23286}, {75, 46088}, {95, 822}, {97, 656}, {255, 15412}, {304, 58308}, {326, 2623}, {394, 2616}, {520, 2167}, {525, 2169}, {810, 34386}, {1102, 58756}, {1577, 19210}, {2148, 3265}, {2190, 52613}, {2632, 18315}, {4091, 56254}, {4575, 53576}, {7066, 39177}, {14208, 14533}, {14586, 17879}, {15526, 36134}, {15958, 20902}, {18831, 37754}, {23224, 56246}, {32320, 40440}, {32679, 50463}, {42080, 42405}
X(61193) = X(i)-vertex conjugate of X(j) for these {i, j}: {14586, 16813}, {52604, 61217}
X(61193) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 15414}, {5, 52613}, {130, 35071}, {136, 53576}, {137, 15526}, {206, 46088}, {216, 3265}, {338, 36793}, {3162, 23286}, {6523, 15412}, {6663, 60597}, {14363, 525}, {14920, 45792}, {15259, 2623}, {15450, 2972}, {18402, 8552}, {39062, 34386}, {40588, 520}, {40596, 97}, {45249, 20580}, {52032, 4143}, {52869, 41077}
X(61193) = X(i)-Ceva conjugate of X(j) for these {i, j}: {107, 52604}, {23964, 393}, {34538, 4}
X(61193) = X(i)-cross conjugate of X(j) for these {i, j}: {647, 59142}, {12077, 53}, {14577, 23964}, {15451, 4}, {27359, 34538}, {42293, 51}, {51513, 13450}, {52604, 35360}
X(61193) = pole of line {52604, 61217} with respect to the circumcircle
X(61193) = pole of line {8552, 15526} with respect to the polar circle
X(61193) = pole of line {46088, 52613} with respect to the Stammler hyperbola
X(61193) = pole of line {4143, 15414} with respect to the Wallace hyperbola
X(61193) = pole of line {343, 14361} with respect to the dual conic of Jerabek hyperbola
X(61193) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(5), X(2409)}}, {{A, B, C, X(107), X(6344)}}, {{A, B, C, X(108), X(35320)}}, {{A, B, C, X(112), X(1625)}}, {{A, B, C, X(216), X(2404)}}, {{A, B, C, X(1289), X(35278)}}, {{A, B, C, X(1301), X(23181)}}, {{A, B, C, X(1637), X(12077)}}, {{A, B, C, X(2848), X(6368)}}, {{A, B, C, X(3199), X(34859)}}, {{A, B, C, X(3269), X(15412)}}, {{A, B, C, X(9064), X(36831)}}, {{A, B, C, X(11062), X(47228)}}, {{A, B, C, X(16813), X(35318)}}, {{A, B, C, X(18831), X(23232)}}, {{A, B, C, X(32640), X(41678)}}, {{A, B, C, X(35307), X(52607)}}, {{A, B, C, X(35321), X(40117)}}, {{A, B, C, X(53708), X(61194)}}
X(61193) = barycentric product X(i)*X(j) for these (i, j): {51, 6528}, {53, 648}, {107, 5}, {110, 13450}, {112, 324}, {158, 2617}, {264, 52604}, {311, 32713}, {343, 6529}, {1093, 23181}, {1625, 2052}, {1953, 823}, {2179, 57973}, {2181, 811}, {3199, 6331}, {11062, 46456}, {12077, 23582}, {13157, 57219}, {14213, 24019}, {14569, 99}, {14570, 393}, {14576, 30450}, {14577, 38342}, {15352, 216}, {15415, 41937}, {15459, 52945}, {16813, 36412}, {17434, 34538}, {17500, 46151}, {18020, 51513}, {18027, 61194}, {18314, 23964}, {20031, 60524}, {21011, 52919}, {23290, 250}, {23590, 60597}, {24000, 2618}, {27371, 42396}, {31610, 61217}, {32230, 6368}, {33513, 53386}, {35318, 39284}, {35360, 4}, {36126, 44706}, {36129, 51801}, {36306, 6117}, {36309, 6116}, {36831, 52661}, {39569, 685}, {42293, 57556}, {42401, 46394}, {44715, 58071}, {52917, 56272}, {53245, 58070}, {60828, 933}
X(61193) = barycentric quotient X(i)/X(j) for these (i, j): {2, 15414}, {5, 3265}, {25, 23286}, {32, 46088}, {51, 520}, {53, 525}, {107, 95}, {112, 97}, {216, 52613}, {217, 32320}, {311, 52617}, {324, 3267}, {343, 4143}, {393, 15412}, {648, 34386}, {1096, 2616}, {1576, 19210}, {1625, 394}, {1953, 24018}, {1974, 58308}, {2179, 822}, {2181, 656}, {2207, 2623}, {2501, 53576}, {2617, 326}, {2618, 17879}, {3199, 647}, {6528, 34384}, {6529, 275}, {11062, 8552}, {12077, 15526}, {13157, 14638}, {13450, 850}, {14560, 50463}, {14569, 523}, {14570, 3926}, {14576, 52584}, {14918, 45792}, {15352, 276}, {15451, 2972}, {17167, 30805}, {18180, 4131}, {18314, 36793}, {21102, 17216}, {21807, 57109}, {23181, 3964}, {23290, 339}, {23590, 16813}, {23964, 18315}, {24019, 2167}, {27371, 2525}, {32230, 18831}, {32676, 2169}, {32713, 54}, {32715, 46090}, {33631, 39181}, {34538, 42405}, {34859, 41270}, {35360, 69}, {36126, 40440}, {36412, 60597}, {36434, 15422}, {39569, 6333}, {40981, 39201}, {41219, 23103}, {41221, 5489}, {41937, 14586}, {42293, 35071}, {42459, 20580}, {51363, 39473}, {51513, 125}, {52439, 58756}, {52604, 3}, {52926, 54032}, {52945, 41077}, {55219, 3269}, {57655, 15958}, {58071, 43752}, {58757, 8901}, {60517, 53173}, {60597, 23974}, {61194, 577}, {61204, 19180}, {61206, 14533}, {61217, 59183}
X(61193) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {107, 112, 61217}, {107, 6529, 112}

X(61194) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(3) AND CEVIAN-OF-X(66)

Barycentrics    a^4*(a-b)*(a+b)*(a-c)*(a+c)*(-(b^2-c^2)^2+a^2*(b^2+c^2)) : :

X(61194) lies on these lines: {2, 13236}, {6, 38352}, {32, 3124}, {107, 112}, {110, 14966}, {184, 9419}, {418, 40588}, {571, 2493}, {577, 35268}, {647, 1624}, {933, 23964}, {1576, 2491}, {1625, 2081}, {1968, 27359}, {2966, 42396}, {9475, 38356}, {10684, 46247}, {11672, 23217}, {12077, 35360}, {13417, 41172}, {13558, 57261}, {14673, 35901}, {15329, 45215}, {17409, 22391}, {23357, 60607}, {43925, 53321}, {47200, 51324}, {52433, 59142}, {53701, 58784}

X(61194) = trilinear pole of line {217, 27374}
X(61194) = perspector of circumconic {{A, B, C, X(14560), X(32230)}}
X(61194) = X(i)-isoconjugate-of-X(j) for these {i, j}: {54, 20948}, {75, 15412}, {76, 2616}, {95, 1577}, {158, 15414}, {275, 14208}, {276, 656}, {514, 56189}, {525, 40440}, {561, 2623}, {661, 34384}, {693, 56246}, {799, 8901}, {810, 57790}, {811, 53576}, {822, 57844}, {850, 2167}, {1930, 39182}, {1969, 23286}, {2148, 44173}, {2190, 3267}, {2632, 42405}, {2643, 55218}, {3261, 56254}, {8061, 41488}, {8795, 24018}, {16813, 17879}, {18315, 23994}, {18831, 20902}, {23962, 36134}, {24006, 34386}, {32679, 46138}, {34388, 39177}, {37754, 54950}, {40364, 58756}, {42080, 42369}
X(61194) = X(i)-vertex conjugate of X(j) for these {i, j}: {16813, 42401}
X(61194) = X(i)-Dao conjugate of X(j) for these {i, j}: {5, 3267}, {130, 15526}, {137, 23962}, {206, 15412}, {216, 44173}, {1147, 15414}, {2972, 36793}, {6663, 15415}, {15450, 339}, {17423, 53576}, {36830, 34384}, {38996, 8901}, {39062, 57790}, {40368, 2623}, {40588, 850}, {40596, 276}, {52878, 2799}
X(61194) = X(i)-Ceva conjugate of X(j) for these {i, j}: {112, 52604}, {23963, 32}, {23964, 184}
X(61194) = X(i)-cross conjugate of X(j) for these {i, j}: {42293, 217}, {55219, 32}
X(61194) = pole of line {35325, 52604} with respect to the circumcircle
X(61194) = pole of line {15526, 23962} with respect to the polar circle
X(61194) = pole of line {11206, 15270} with respect to the Kiepert parabola
X(61194) = pole of line {3267, 7799} with respect to the Stammler hyperbola
X(61194) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(51), X(4630)}}, {{A, B, C, X(107), X(1576)}}, {{A, B, C, X(184), X(933)}}, {{A, B, C, X(418), X(2409)}}, {{A, B, C, X(1625), X(6529)}}, {{A, B, C, X(1637), X(42293)}}, {{A, B, C, X(2081), X(3124)}}, {{A, B, C, X(2491), X(12077)}}, {{A, B, C, X(2848), X(58305)}}, {{A, B, C, X(14570), X(35319)}}, {{A, B, C, X(14966), X(42396)}}, {{A, B, C, X(15412), X(38352)}}, {{A, B, C, X(15451), X(42659)}}
X(61194) = barycentric product X(i)*X(j) for these (i, j): {3, 52604}, {107, 418}, {110, 51}, {112, 216}, {143, 32737}, {163, 1953}, {182, 52926}, {184, 35360}, {217, 648}, {249, 55219}, {251, 35319}, {343, 61206}, {577, 61193}, {1154, 14560}, {1495, 36831}, {1568, 32715}, {1576, 5}, {1625, 6}, {2150, 35307}, {2179, 662}, {2180, 36145}, {2181, 4575}, {2290, 32678}, {2617, 31}, {2966, 52967}, {3199, 4558}, {11062, 32662}, {12077, 23357}, {14570, 32}, {14574, 311}, {14586, 36412}, {14966, 60517}, {15451, 250}, {16813, 46394}, {17167, 32739}, {17434, 23964}, {18180, 692}, {18314, 23963}, {23181, 25}, {23347, 44715}, {23582, 42293}, {23995, 2618}, {26714, 59208}, {26907, 58950}, {27372, 52915}, {27374, 4577}, {32230, 58305}, {32640, 52945}, {32661, 53}, {32676, 44706}, {32696, 44716}, {32713, 5562}, {32729, 41586}, {32734, 52}, {32738, 5891}, {35322, 57382}, {35323, 57383}, {35324, 59142}, {40981, 99}, {41937, 60597}, {44088, 6528}, {44709, 8750}, {47390, 51513}, {53701, 60525}, {57153, 8798}, {57655, 6368}
X(61194) = barycentric quotient X(i)/X(j) for these (i, j): {5, 44173}, {32, 15412}, {51, 850}, {107, 57844}, {110, 34384}, {112, 276}, {216, 3267}, {217, 525}, {249, 55218}, {418, 3265}, {560, 2616}, {577, 15414}, {648, 57790}, {669, 8901}, {692, 56189}, {827, 41488}, {1501, 2623}, {1576, 95}, {1625, 76}, {1953, 20948}, {2179, 1577}, {2617, 561}, {3049, 53576}, {3199, 14618}, {4630, 39287}, {5562, 52617}, {12077, 23962}, {14560, 46138}, {14570, 1502}, {14574, 54}, {14575, 23286}, {15451, 339}, {17434, 36793}, {18180, 40495}, {23181, 305}, {23347, 43752}, {23590, 42401}, {23963, 18315}, {23964, 42405}, {27374, 826}, {32230, 54950}, {32661, 34386}, {32676, 40440}, {32713, 8795}, {32734, 34385}, {32737, 57765}, {32739, 56246}, {34538, 42369}, {35319, 8024}, {35360, 18022}, {36412, 15415}, {36417, 15422}, {40373, 58308}, {40981, 523}, {41334, 57082}, {41937, 16813}, {42293, 15526}, {44088, 520}, {44162, 58756}, {46288, 39182}, {46394, 60597}, {52604, 264}, {52926, 327}, {52967, 2799}, {55219, 338}, {57655, 18831}, {61193, 18027}, {61206, 275}
X(61194) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1625, 23181, 35319}

X(61195) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(3) AND CEVIAN-OF-X(97)

Barycentrics    a^2*(a-b)*(a+b)*(a-c)*(a+c)*(-(b^2-c^2)^2+a^2*(b^2+c^2))*(a^6*(b^2+c^2)+3*a^2*(b^2-c^2)^2*(b^2+c^2)-3*a^4*(b^4+c^4)-(b^2-c^2)^2*(b^4+c^4)) : :

X(61195) lies on these lines: {2, 34985}, {4, 34951}, {5, 113}, {51, 129}, {107, 1303}, {110, 933}, {418, 46093}, {467, 36426}, {511, 52887}, {520, 35311}, {1625, 2081}, {3078, 5943}, {5562, 8439}, {6528, 42401}, {7480, 34987}, {44830, 57135}

X(61195) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2616, 40448}
X(61195) = X(i)-Dao conjugate of X(j) for these {i, j}: {389, 520}, {46832, 850}
X(61195) = X(i)-Ceva conjugate of X(j) for these {i, j}: {23582, 216}, {47390, 52}
X(61195) = pole of line {107, 110} with respect to the Johnson circumconic
X(61195) = pole of line {3484, 6368} with respect to the Stammler hyperbola
X(61195) = intersection, other than A, B, C, of circumconics {{A, B, C, X(933), X(1625)}}, {{A, B, C, X(14570), X(42401)}}, {{A, B, C, X(15958), X(35360)}}, {{A, B, C, X(18315), X(23181)}}
X(61195) = barycentric product X(i)*X(j) for these (i, j): {110, 34836}, {1625, 45198}, {2617, 45224}, {4558, 6750}, {14570, 389}, {23181, 52280}, {35360, 46832}, {42441, 648}
X(61195) = barycentric quotient X(i)/X(j) for these (i, j): {389, 15412}, {1625, 40448}, {6750, 14618}, {14570, 42333}, {34836, 850}, {42441, 525}, {52604, 40402}

X(61196) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(3) AND CEVIAN-OF-X(99)

Barycentrics    b^2*(b-c)*c^2*(b+c)*(a^4+b^4-(a^2+b^2)*c^2)*(a^4-a^2*b^2-b^2*c^2+c^4)*(-(b^2-c^2)^2+a^2*(b^2+c^2)) : :

X(61196) lies on these lines: {4, 512}, {5, 15451}, {53, 23290}, {98, 1141}, {290, 60034}, {311, 6368}, {327, 850}, {523, 3613}, {868, 60036}, {878, 34449}, {2165, 2395}, {3569, 53493}, {13450, 51513}, {14592, 57603}, {15412, 37121}, {19912, 43917}, {21525, 53266}, {51441, 60037}, {53174, 60035}, {59741, 59745}

X(61196) = perspector of circumconic {{A, B, C, X(16081), X(53245)}}
X(61196) = X(i)-isoconjugate-of-X(j) for these {i, j}: {54, 23997}, {240, 15958}, {511, 36134}, {662, 41270}, {1755, 18315}, {1959, 14586}, {2148, 2421}, {2167, 14966}, {2169, 4230}, {4575, 19189}, {4592, 58306}
X(61196) = X(i)-Dao conjugate of X(j) for these {i, j}: {136, 19189}, {137, 511}, {216, 2421}, {338, 325}, {1084, 41270}, {5139, 58306}, {14363, 4230}, {15450, 3289}, {36899, 18315}, {39019, 36212}, {39085, 15958}, {40588, 14966}, {60596, 15631}
X(61196) = pole of line {511, 19189} with respect to the polar circle
X(61196) = pole of line {237, 32428} with respect to the MacBeath inconic
X(61196) = pole of line {6333, 51383} with respect to the dual conic of Stammler hyperbola
X(61196) = pole of line {684, 9420} with respect to the dual conic of Wallace hyperbola
X(61196) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(5)}}, {{A, B, C, X(216), X(31850)}}, {{A, B, C, X(512), X(6368)}}, {{A, B, C, X(850), X(12077)}}, {{A, B, C, X(1625), X(35364)}}, {{A, B, C, X(2433), X(23181)}}, {{A, B, C, X(5466), X(35360)}}, {{A, B, C, X(14618), X(15415)}}, {{A, B, C, X(18014), X(35363)}}, {{A, B, C, X(35307), X(35352)}}, {{A, B, C, X(35319), X(35366)}}, {{A, B, C, X(35320), X(35354)}}, {{A, B, C, X(35321), X(35347)}}, {{A, B, C, X(52451), X(53174)}}
X(61196) = barycentric product X(i)*X(j) for these (i, j): {324, 879}, {523, 53245}, {1821, 2618}, {2395, 311}, {2799, 60594}, {12077, 290}, {13450, 53173}, {14618, 53174}, {15415, 1976}, {15451, 60199}, {16081, 6368}, {18024, 55219}, {18314, 98}, {23290, 287}, {28706, 53149}, {41221, 43187}, {43665, 5}, {51513, 57799}, {60517, 850}
X(61196) = barycentric quotient X(i)/X(j) for these (i, j): {5, 2421}, {51, 14966}, {53, 4230}, {98, 18315}, {248, 15958}, {311, 2396}, {324, 877}, {512, 41270}, {878, 14533}, {879, 97}, {1910, 36134}, {1953, 23997}, {1976, 14586}, {2395, 54}, {2422, 54034}, {2489, 58306}, {2501, 19189}, {2618, 1959}, {2715, 14587}, {6368, 36212}, {6531, 933}, {12077, 511}, {14569, 58070}, {15451, 3289}, {16081, 18831}, {18024, 55218}, {18314, 325}, {20577, 51440}, {21102, 17209}, {23290, 297}, {41078, 51383}, {41221, 3569}, {43665, 95}, {51404, 23286}, {51441, 2623}, {51513, 232}, {53149, 8882}, {53174, 4558}, {53245, 99}, {55219, 237}, {57195, 44716}, {60517, 110}, {60524, 15631}, {60594, 2966}, {60597, 51386}

X(61197) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(4) AND CEVIAN-OF-X(21)

Barycentrics    a^2*(a-b)*(a-c)*(2*a*b*c+a^2*(b+c)-(b-c)^2*(b+c)) : :

X(61197) lies on these lines: {3, 57693}, {6, 1718}, {8, 22164}, {100, 4574}, {101, 109}, {110, 112}, {163, 53290}, {191, 220}, {218, 1046}, {219, 1761}, {221, 22131}, {222, 1762}, {394, 21376}, {512, 16680}, {517, 20752}, {601, 9310}, {607, 3157}, {608, 3211}, {610, 22134}, {644, 4427}, {650, 61170}, {651, 653}, {692, 53282}, {766, 20875}, {813, 29052}, {825, 58947}, {846, 54474}, {859, 1755}, {912, 5089}, {919, 58974}, {934, 59064}, {956, 22163}, {1018, 2284}, {1292, 2428}, {1409, 59681}, {1464, 3002}, {1630, 22118}, {1744, 2911}, {1760, 23124}, {1951, 52407}, {2172, 14529}, {2176, 20677}, {2246, 21742}, {2272, 22350}, {2294, 46882}, {2421, 52935}, {2443, 57193}, {2771, 53560}, {2939, 7078}, {3197, 18598}, {3330, 7359}, {3579, 52370}, {3827, 20811}, {3869, 22126}, {4551, 53761}, {4556, 57251}, {4587, 35281}, {4636, 57062}, {4904, 34253}, {5360, 20857}, {5730, 22127}, {7117, 34586}, {7291, 20744}, {12528, 17916}, {14597, 40937}, {15071, 25087}, {19241, 24511}, {21784, 23861}, {21859, 61239}, {22123, 56911}, {22153, 34040}, {23353, 24019}, {25063, 31803}, {28162, 59061}, {29289, 59134}, {32674, 36059}, {35342, 53388}, {43065, 52635}, {45038, 46883}, {50198, 55432}, {53243, 59063}, {53260, 58929}, {58951, 58986}, {61161, 61220}

X(61197) = isogonal conjugate of X(56320)
X(61197) = trilinear pole of line {2260, 14547}
X(61197) = perspector of circumconic {{A, B, C, X(59), X(250)}}
X(61197) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 56320}, {63, 14775}, {514, 943}, {521, 40573}, {522, 2982}, {649, 40422}, {650, 60041}, {656, 40395}, {661, 40412}, {693, 2259}, {1021, 52560}, {1146, 36048}, {1175, 1577}, {1459, 40447}, {1794, 17924}, {2170, 54952}, {3737, 60188}, {4858, 15439}, {14208, 40570}, {14838, 57710}, {17877, 59060}, {17886, 59011}, {24026, 32651}, {34591, 58993}, {54244, 57860}
X(61197) = X(i)-vertex conjugate of X(j) for these {i, j}: {692, 906}
X(61197) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 56320}, {442, 4391}, {942, 525}, {3162, 14775}, {5249, 18160}, {5375, 40422}, {15607, 1146}, {16585, 3261}, {18591, 693}, {36830, 40412}, {39007, 26932}, {39026, 40435}, {40596, 40395}, {40937, 850}, {52119, 338}
X(61197) = X(i)-Ceva conjugate of X(j) for these {i, j}: {59, 37993}, {61180, 53323}
X(61197) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {5379, 40007}
X(61197) = X(i)-cross conjugate of X(j) for these {i, j}: {33525, 14547}, {37993, 59}, {52306, 40937}, {61169, 61220}
X(61197) = pole of line {163, 692} with respect to the circumcircle
X(61197) = pole of line {338, 1146} with respect to the polar circle
X(61197) = pole of line {20958, 42670} with respect to the Brocard inellipse
X(61197) = pole of line {22, 1602} with respect to the Kiepert parabola
X(61197) = pole of line {108, 110} with respect to the MacBeath circumconic
X(61197) = pole of line {448, 525} with respect to the Stammler hyperbola
X(61197) = pole of line {1897, 4238} with respect to the Steiner circumellipse
X(61197) = pole of line {13006, 15252} with respect to the Steiner inellipse
X(61197) = pole of line {20, 391} with respect to the Yff parabola
X(61197) = pole of line {329, 405} with respect to the Hutson-Moses hyperbola
X(61197) = pole of line {3267, 15411} with respect to the Wallace hyperbola
X(61197) = pole of line {2850, 11746} with respect to the dual conic of DeLongchamps circle
X(61197) = pole of line {23983, 36793} with respect to the dual conic of polar circle
X(61197) = intersection, other than A, B, C, of circumconics {{A, B, C, X(101), X(653)}}, {{A, B, C, X(109), X(3466)}}, {{A, B, C, X(110), X(4566)}}, {{A, B, C, X(112), X(4559)}}, {{A, B, C, X(442), X(4230)}}, {{A, B, C, X(648), X(4574)}}, {{A, B, C, X(651), X(906)}}, {{A, B, C, X(942), X(2283)}}, {{A, B, C, X(1414), X(36516)}}, {{A, B, C, X(1415), X(32714)}}, {{A, B, C, X(1981), X(8021)}}, {{A, B, C, X(2260), X(61210)}}, {{A, B, C, X(2420), X(18591)}}, {{A, B, C, X(2427), X(40937)}}, {{A, B, C, X(4303), X(23973)}}, {{A, B, C, X(10015), X(52306)}}, {{A, B, C, X(32661), X(52610)}}, {{A, B, C, X(50344), X(50354)}}
X(61197) = barycentric product X(i)*X(j) for these (i, j): {1, 61220}, {3, 61180}, {57, 61233}, {63, 61236}, {100, 942}, {101, 5249}, {109, 6734}, {110, 442}, {162, 56839}, {190, 2260}, {500, 6742}, {1234, 1576}, {1275, 33525}, {1331, 1838}, {1332, 1841}, {1414, 40967}, {1783, 18607}, {1859, 6516}, {1865, 4558}, {1897, 4303}, {2294, 662}, {3824, 8652}, {4551, 54356}, {4552, 46882}, {4566, 8021}, {13397, 14054}, {14547, 664}, {14597, 6335}, {18026, 23207}, {18591, 648}, {21675, 4556}, {23752, 4570}, {26700, 31938}, {36797, 39791}, {37993, 54952}, {39633, 41550}, {39772, 6011}, {40937, 651}, {40952, 99}, {40956, 668}, {40978, 799}, {41393, 52914}, {41493, 57119}, {46102, 52306}, {46890, 52609}, {50354, 765}, {51978, 53321}, {52920, 59163}, {53323, 69}, {55010, 5546}, {61161, 81}, {61169, 86}
X(61197) = barycentric quotient X(i)/X(j) for these (i, j): {6, 56320}, {25, 14775}, {59, 54952}, {100, 40422}, {101, 40435}, {109, 60041}, {110, 40412}, {112, 40395}, {442, 850}, {500, 4467}, {692, 943}, {942, 693}, {1234, 44173}, {1415, 2982}, {1576, 1175}, {1783, 40447}, {1838, 46107}, {1841, 17924}, {1859, 44426}, {1865, 14618}, {2260, 514}, {2294, 1577}, {4303, 4025}, {4559, 60188}, {5249, 3261}, {6734, 35519}, {6742, 57885}, {8021, 7253}, {14547, 522}, {14597, 905}, {16585, 18160}, {18591, 525}, {18607, 15413}, {21675, 52623}, {23207, 521}, {23752, 21207}, {23979, 32651}, {24027, 36048}, {32656, 1794}, {32674, 40573}, {32739, 2259}, {33525, 1146}, {39791, 17094}, {40937, 4391}, {40952, 523}, {40956, 513}, {40967, 4086}, {40978, 661}, {46882, 4560}, {46884, 57215}, {46890, 17925}, {50354, 1111}, {52306, 26932}, {53321, 52560}, {53323, 4}, {54356, 18155}, {56839, 14208}, {59177, 57109}, {61161, 321}, {61169, 10}, {61180, 264}, {61206, 40570}, {61220, 75}, {61233, 312}, {61236, 92}
X(61197) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {101, 109, 906}, {101, 4559, 2427}, {1755, 42669, 859}, {4559, 35326, 101}, {4559, 61212, 109}, {53290, 53324, 163}, {61220, 61233, 61161}

X(61198) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(4) AND CEVIAN-OF-X(23)

Barycentrics    a^2*(a-b)*(a+b)*(a-c)*(a+c)*(b^2*(a^4-b^4)+(a^2-b^2)^2*c^2+b^2*c^4-c^6) : :

X(61198) lies on these lines: {2, 6}, {22, 35901}, {110, 112}, {647, 14966}, {691, 35188}, {805, 9091}, {858, 52672}, {877, 33294}, {1302, 26714}, {1370, 35902}, {1560, 12827}, {2393, 51962}, {2422, 61191}, {2433, 36831}, {2451, 47259}, {2715, 10420}, {2979, 46128}, {2986, 6531}, {3291, 60498}, {3331, 58347}, {4240, 58070}, {4563, 44766}, {5467, 32583}, {6090, 56961}, {6800, 37918}, {10097, 11634}, {14961, 60499}, {14984, 44467}, {15106, 22146}, {16186, 34349}, {32320, 60505}, {34834, 47406}, {36830, 52603}, {45215, 50947}, {45935, 56395}, {46589, 51980}

X(61198) = isogonal conjugate of X(60040)
X(61198) = trilinear pole of line {14961, 47426}
X(61198) = perspector of circumconic {{A, B, C, X(99), X(250)}}
X(61198) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 60040}, {125, 36095}, {512, 37220}, {656, 60133}, {661, 2373}, {798, 46140}, {1177, 1577}, {10423, 20902}, {18876, 24006}, {46165, 55240}
X(61198) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 60040}, {858, 9979}, {5181, 525}, {14961, 35522}, {31998, 46140}, {36830, 2373}, {38971, 338}, {39054, 37220}, {40596, 60133}, {61067, 523}
X(61198) = X(i)-Ceva conjugate of X(j) for these {i, j}: {52630, 5467}, {58980, 23357}, {61181, 46592}
X(61198) = X(i)-cross conjugate of X(j) for these {i, j}: {42665, 858}
X(61198) = pole of line {669, 1576} with respect to the circumcircle
X(61198) = pole of line {338, 2501} with respect to the polar circle
X(61198) = pole of line {22, 99} with respect to the Kiepert parabola
X(61198) = pole of line {110, 525} with respect to the MacBeath circumconic
X(61198) = pole of line {1112, 3566} with respect to the orthic inconic
X(61198) = pole of line {6, 525} with respect to the Stammler hyperbola
X(61198) = pole of line {523, 7482} with respect to the Steiner circumellipse
X(61198) = pole of line {2, 2485} with respect to the Wallace hyperbola
X(61198) = pole of line {525, 11746} with respect to the dual conic of DeLongchamps circle
X(61198) = pole of line {110, 525} with respect to the dual conic of nine-point circle
X(61198) = pole of line {525, 36793} with respect to the dual conic of polar circle
X(61198) = pole of line {14570, 39575} with respect to the dual conic of Jerabek hyperbola
X(61198) = pole of line {1634, 3265} with respect to the dual conic of orthic inconic
X(61198) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(112)}}, {{A, B, C, X(3), X(53760)}}, {{A, B, C, X(6), X(44766)}}, {{A, B, C, X(22), X(55272)}}, {{A, B, C, X(69), X(110)}}, {{A, B, C, X(141), X(35325)}}, {{A, B, C, X(183), X(1302)}}, {{A, B, C, X(193), X(56008)}}, {{A, B, C, X(230), X(14580)}}, {{A, B, C, X(323), X(14591)}}, {{A, B, C, X(325), X(858)}}, {{A, B, C, X(343), X(1625)}}, {{A, B, C, X(385), X(9091)}}, {{A, B, C, X(394), X(32661)}}, {{A, B, C, X(524), X(2393)}}, {{A, B, C, X(648), X(41614)}}, {{A, B, C, X(805), X(56430)}}, {{A, B, C, X(1641), X(47426)}}, {{A, B, C, X(1992), X(46639)}}, {{A, B, C, X(1993), X(61208)}}, {{A, B, C, X(2420), X(11064)}}, {{A, B, C, X(2696), X(5971)}}, {{A, B, C, X(2715), X(3580)}}, {{A, B, C, X(2986), X(58070)}}, {{A, B, C, X(3569), X(42665)}}, {{A, B, C, X(3936), X(18669)}}, {{A, B, C, X(4563), X(20806)}}, {{A, B, C, X(13567), X(61204)}}, {{A, B, C, X(15066), X(26714)}}, {{A, B, C, X(17708), X(22151)}}, {{A, B, C, X(28754), X(57194)}}, {{A, B, C, X(32729), X(37784)}}, {{A, B, C, X(34212), X(47138)}}, {{A, B, C, X(37636), X(61203)}}, {{A, B, C, X(37643), X(58963)}}, {{A, B, C, X(41617), X(48373)}}
X(61198) = barycentric product X(i)*X(j) for these (i, j): {3, 61181}, {101, 17172}, {110, 858}, {163, 20884}, {249, 47138}, {1236, 1576}, {2393, 99}, {2407, 60499}, {2421, 52672}, {4558, 5523}, {5181, 691}, {5467, 59422}, {5468, 57485}, {10420, 12827}, {11634, 56579}, {11636, 19510}, {14580, 4563}, {14961, 648}, {18020, 42665}, {18669, 662}, {21017, 4556}, {21109, 4570}, {22151, 60507}, {41603, 59039}, {46592, 69}, {47426, 892}
X(61198) = barycentric quotient X(i)/X(j) for these (i, j): {6, 60040}, {99, 46140}, {110, 2373}, {112, 60133}, {662, 37220}, {858, 850}, {1236, 44173}, {1576, 1177}, {1634, 46165}, {2393, 523}, {4230, 52486}, {4235, 58078}, {5181, 35522}, {5523, 14618}, {11634, 56685}, {14580, 2501}, {14961, 525}, {14966, 36823}, {17172, 3261}, {18669, 1577}, {20884, 20948}, {21017, 52623}, {21109, 21207}, {32661, 18876}, {32729, 10422}, {34158, 10097}, {42665, 125}, {46592, 4}, {47138, 338}, {47426, 690}, {51962, 9178}, {52672, 43665}, {57485, 5466}, {57655, 10423}, {59422, 52632}, {60499, 2394}, {60507, 46105}, {61181, 264}, {61207, 51823}
X(61198) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 36828, 1625}, {647, 14966, 15329}, {1625, 35325, 36828}, {3051, 41939, 6}, {35325, 61199, 110}, {36830, 52603, 56389}

X(61199) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(4) AND CEVIAN-OF-X(25)

Barycentrics    a^2*(a-b)*(a+b)*(a-c)*(a+c)*(a^2-b^2-c^2)*((b^2-c^2)^2+a^2*(b^2+c^2)) : :

X(61199) lies on these lines: {6, 5181}, {110, 112}, {394, 4121}, {525, 4576}, {647, 23181}, {1611, 52077}, {1613, 3167}, {1624, 14966}, {1634, 45215}, {1691, 41615}, {2421, 36841}, {2501, 61182}, {2623, 15958}, {2715, 59039}, {3051, 59553}, {3124, 14984}, {3231, 3564}, {3269, 13416}, {3291, 34382}, {4563, 24284}, {5468, 55189}, {6391, 56428}, {7881, 15066}, {11064, 14965}, {12038, 48262}, {12310, 20998}, {26714, 59038}, {34966, 42295}, {38356, 41673}, {52913, 58070}

X(61199) = trilinear pole of line {682, 6467}
X(61199) = perspector of circumconic {{A, B, C, X(250), X(53895)}}
X(61199) = X(i)-isoconjugate-of-X(j) for these {i, j}: {661, 40413}, {683, 798}, {1577, 57388}, {1924, 57931}
X(61199) = X(i)-Dao conjugate of X(j) for these {i, j}: {1196, 850}, {1368, 2501}, {9428, 57931}, {20975, 115}, {31998, 683}, {36830, 40413}, {59561, 14618}
X(61199) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4590, 3}, {41937, 23115}, {53350, 53273}
X(61199) = pole of line {22, 3266} with respect to the Kiepert parabola
X(61199) = pole of line {99, 110} with respect to the MacBeath circumconic
X(61199) = pole of line {525, 2451} with respect to the Stammler hyperbola
X(61199) = pole of line {11634, 41676} with respect to the Steiner circumellipse
X(61199) = pole of line {2489, 3267} with respect to the Wallace hyperbola
X(61199) = pole of line {690, 11746} with respect to the dual conic of DeLongchamps circle
X(61199) = pole of line {3124, 36793} with respect to the dual conic of polar circle
X(61199) = intersection, other than A, B, C, of circumconics {{A, B, C, X(110), X(53350)}}, {{A, B, C, X(112), X(40347)}}, {{A, B, C, X(1368), X(4230)}}, {{A, B, C, X(2420), X(22401)}}, {{A, B, C, X(2623), X(12075)}}, {{A, B, C, X(2715), X(61204)}}
X(61199) = barycentric product X(i)*X(j) for these (i, j): {3, 53350}, {101, 18648}, {110, 1368}, {163, 21406}, {670, 682}, {1196, 4563}, {1332, 16716}, {4558, 5254}, {6467, 99}, {17872, 4592}, {18671, 662}, {22401, 648}, {36841, 45207}, {53273, 69}
X(61199) = barycentric quotient X(i)/X(j) for these (i, j): {99, 683}, {110, 40413}, {670, 57931}, {682, 512}, {1196, 2501}, {1368, 850}, {1576, 57388}, {4558, 40405}, {5254, 14618}, {6467, 523}, {12075, 2970}, {16716, 17924}, {17872, 24006}, {18648, 3261}, {18671, 1577}, {21406, 20948}, {22401, 525}, {40325, 58757}, {45207, 58759}, {53273, 4}, {53350, 264}
X(61199) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 35325, 1625}, {110, 61198, 35325}

X(61200) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(4) AND CEVIAN-OF-X(27)

Barycentrics    a^2*(a-b)*(a-c)*(a^2-b^2-c^2)*(2*a^3+a^2*(b+c)+(b-c)^2*(b+c)) : :

X(61200) lies on these lines: {3, 43693}, {6, 41164}, {55, 22130}, {109, 692}, {110, 112}, {154, 2844}, {521, 53388}, {525, 4427}, {601, 47371}, {902, 916}, {906, 1331}, {1813, 35350}, {1955, 52889}, {3052, 3173}, {3211, 38904}, {3915, 42463}, {4636, 57251}, {6056, 23112}, {23067, 32656}, {23171, 52430}, {59055, 59064}

X(61200) = perspector of circumconic {{A, B, C, X(250), X(1262)}}
X(61200) = X(i)-isoconjugate-of-X(j) for these {i, j}: {513, 40445}, {523, 40431}, {661, 40414}, {951, 44426}, {1257, 7649}, {1577, 57390}, {2983, 17924}, {18344, 58005}, {24026, 59090}
X(61200) = X(i)-Dao conjugate of X(j) for these {i, j}: {440, 46107}, {4466, 21207}, {36830, 40414}, {39026, 40445}, {40940, 850}, {59646, 14618}
X(61200) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4570, 3}, {14543, 53290}
X(61200) = pole of line {109, 1576} with respect to the circumcircle
X(61200) = pole of line {338, 21666} with respect to the polar circle
X(61200) = pole of line {22, 3006} with respect to the Kiepert parabola
X(61200) = pole of line {101, 110} with respect to the MacBeath circumconic
X(61200) = pole of line {447, 525} with respect to the Stammler hyperbola
X(61200) = pole of line {4237, 41676} with respect to the Steiner circumellipse
X(61200) = pole of line {2774, 11746} with respect to the dual conic of DeLongchamps circle
X(61200) = pole of line {23989, 36793} with respect to the dual conic of polar circle
X(61200) = intersection, other than A, B, C, of circumconics {{A, B, C, X(109), X(4587)}}, {{A, B, C, X(110), X(14543)}}, {{A, B, C, X(112), X(4574)}}, {{A, B, C, X(440), X(4230)}}, {{A, B, C, X(1331), X(1461)}}
X(61200) = barycentric product X(i)*X(j) for these (i, j): {63, 61221}, {101, 18650}, {110, 440}, {1104, 1332}, {1331, 40940}, {1813, 950}, {1834, 4558}, {2264, 6516}, {14543, 3}, {17863, 906}, {18673, 662}, {21671, 4556}, {40977, 4592}, {40984, 4563}, {44093, 99}, {53290, 69}
X(61200) = barycentric quotient X(i)/X(j) for these (i, j): {101, 40445}, {110, 40414}, {163, 40431}, {440, 850}, {906, 1257}, {950, 46110}, {1104, 17924}, {1576, 57390}, {1813, 58005}, {1834, 14618}, {2264, 44426}, {14543, 264}, {18650, 3261}, {18673, 1577}, {21671, 52623}, {23979, 59090}, {29162, 2973}, {32656, 2983}, {32660, 951}, {40940, 46107}, {40977, 24006}, {40984, 2501}, {44093, 523}, {53290, 4}, {61221, 92}
X(61200) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {109, 36059, 52610}, {53324, 53325, 109}

X(61201) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(4) AND CEVIAN-OF-X(28)

Barycentrics    a^2*(a-b)*(a-c)*(a^2-b^2-c^2)*(a^3*(b+c)+a*(b-c)^2*(b+c)+(b^2-c^2)^2+a^2*(b^2+c^2)) : :

X(61201) lies on these lines: {101, 58967}, {110, 112}, {525, 53332}, {906, 35350}, {912, 3230}, {934, 36080}, {1332, 4561}, {1783, 14544}, {2176, 3157}, {2427, 57151}, {3211, 21769}, {4115, 23874}, {4559, 36059}, {16685, 37817}, {22131, 52362}

X(61201) = perspector of circumconic {{A, B, C, X(250), X(53952)}}
X(61201) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1577, 57391}, {7649, 40406}
X(61201) = X(i)-Dao conjugate of X(j) for these {i, j}: {18210, 16732}, {21530, 17924}, {40941, 850}
X(61201) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4567, 3}, {53349, 53282}
X(61201) = pole of line {22, 3263} with respect to the Kiepert parabola
X(61201) = pole of line {100, 110} with respect to the MacBeath circumconic
X(61201) = pole of line {525, 17498} with respect to the Stammler hyperbola
X(61201) = pole of line {4236, 41676} with respect to the Steiner circumellipse
X(61201) = pole of line {3, 17776} with respect to the Hutson-Moses hyperbola
X(61201) = pole of line {3267, 17899} with respect to the Wallace hyperbola
X(61201) = pole of line {8674, 11746} with respect to the dual conic of DeLongchamps circle
X(61201) = pole of line {1086, 36793} with respect to the dual conic of polar circle
X(61201) = intersection, other than A, B, C, of circumconics {{A, B, C, X(110), X(53349)}}, {{A, B, C, X(112), X(52609)}}, {{A, B, C, X(4230), X(21530)}}
X(61201) = barycentric product X(i)*X(j) for these (i, j): {3, 53349}, {100, 18732}, {101, 18651}, {110, 21530}, {1331, 23537}, {1332, 40941}, {1444, 61162}, {1634, 18709}, {4558, 53417}, {4563, 53387}, {18674, 662}, {21678, 4556}, {40973, 4592}, {53282, 69}
X(61201) = barycentric quotient X(i)/X(j) for these (i, j): {906, 40406}, {1576, 57391}, {18651, 3261}, {18674, 1577}, {18709, 52618}, {18732, 693}, {21530, 850}, {21678, 52623}, {23537, 46107}, {40941, 17924}, {40973, 24006}, {53282, 4}, {53349, 264}, {53387, 2501}, {53417, 14618}, {61162, 41013}

X(61202) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(4) AND CEVIAN-OF-X(40)

Barycentrics    a^2*(a-b)*(a-c)*(a^2*(b-c)^2+a^3*(b+c)-a*(b-c)^2*(b+c)-(b^2-c^2)^2) : :

X(61202) lies on circumconic {{A, B, C, X(8059), X(8750)}} and on these lines: {6, 2310}, {55, 2638}, {101, 58946}, {109, 8059}, {663, 53288}, {692, 2498}, {1020, 6129}, {1576, 7252}, {2175, 21770}, {2426, 32656}, {2427, 3939}, {3052, 51235}, {4557, 46177}, {16685, 21059}, {21002, 21769}, {23067, 57218}, {23113, 35338}, {23845, 53521}, {32676, 61204}, {40613, 53292}, {53325, 61212}

X(61202) = perspector of circumconic {{A, B, C, X(7115), X(15378)}}
X(61202) = X(i)-isoconjugate-of-X(j) for these {i, j}: {513, 40417}, {514, 55987}, {693, 947}, {4025, 40396}, {4391, 57418}, {7192, 56195}
X(61202) = X(i)-Dao conjugate of X(j) for these {i, j}: {946, 17896}, {17102, 35519}, {20262, 15413}, {39026, 40417}, {40943, 3261}
X(61202) = X(i)-Ceva conjugate of X(j) for these {i, j}: {24027, 6}
X(61202) = pole of line {1415, 21758} with respect to the circumcircle
X(61202) = pole of line {16681, 23381} with respect to the Kiepert parabola
X(61202) = barycentric product X(i)*X(j) for these (i, j): {1, 61224}, {100, 2262}, {101, 946}, {109, 20262}, {1415, 23528}, {1813, 1856}, {1897, 22063}, {13138, 40943}, {17102, 1783}, {40117, 52097}, {40945, 653}, {40957, 664}, {55349, 56188}
X(61202) = barycentric quotient X(i)/X(j) for these (i, j): {101, 40417}, {692, 55987}, {946, 3261}, {1856, 46110}, {2262, 693}, {17102, 15413}, {20262, 35519}, {22063, 4025}, {32739, 947}, {40943, 17896}, {40945, 6332}, {40957, 522}, {55349, 17496}, {61224, 75}
X(61202) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2426, 35327, 32656}

X(61203) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(4) AND CEVIAN-OF-X(54)

Barycentrics    a^2*(a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)-2*a^2*(b^4+b^2*c^2+c^4)) : :

X(61203) lies on these lines: {6, 2914}, {107, 58949}, {110, 112}, {394, 34163}, {403, 45938}, {648, 30450}, {933, 32692}, {1289, 26714}, {1986, 47421}, {2211, 15993}, {2421, 41676}, {2501, 35318}, {2904, 60501}, {3016, 12140}, {3289, 5523}, {3462, 8743}, {3574, 60589}, {9707, 32445}, {11005, 39839}, {11444, 39575}, {14826, 41370}, {46151, 58070}, {52416, 58312}, {60507, 60509}

X(61203) = trilinear pole of line {570, 23195}
X(61203) = perspector of circumconic {{A, B, C, X(250), X(52998)}}
X(61203) = X(i)-isoconjugate-of-X(j) for these {i, j}: {63, 50946}, {525, 2216}, {656, 40393}, {810, 57903}, {1179, 24018}, {1577, 40441}, {20902, 59004}
X(61203) = X(i)-vertex conjugate of X(j) for these {i, j}: {1576, 61208}
X(61203) = X(i)-Dao conjugate of X(j) for these {i, j}: {1209, 525}, {3162, 50946}, {8901, 53576}, {39062, 57903}, {40596, 40393}
X(61203) = X(i)-Ceva conjugate of X(j) for these {i, j}: {41677, 50947}
X(61203) = pole of line {1576, 14586} with respect to the circumcircle
X(61203) = pole of line {338, 24978} with respect to the polar circle
X(61203) = pole of line {22, 1225} with respect to the Kiepert parabola
X(61203) = pole of line {110, 16039} with respect to the MacBeath circumconic
X(61203) = pole of line {1112, 45147} with respect to the orthic inconic
X(61203) = pole of line {525, 30451} with respect to the Stammler hyperbola
X(61203) = pole of line {41676, 61182} with respect to the Steiner circumellipse
X(61203) = pole of line {3267, 52584} with respect to the Wallace hyperbola
X(61203) = pole of line {2052, 39575} with respect to the dual conic of Jerabek hyperbola
X(61203) = intersection, other than A, B, C, of circumconics {{A, B, C, X(110), X(33565)}}, {{A, B, C, X(112), X(30450)}}, {{A, B, C, X(570), X(2420)}}, {{A, B, C, X(648), X(61208)}}, {{A, B, C, X(1594), X(4230)}}, {{A, B, C, X(1625), X(32692)}}, {{A, B, C, X(9517), X(39180)}}, {{A, B, C, X(14586), X(16039)}}, {{A, B, C, X(37636), X(61198)}}
X(61203) = barycentric product X(i)*X(j) for these (i, j): {4, 50947}, {107, 1216}, {110, 1594}, {112, 37636}, {570, 648}, {1209, 933}, {1238, 32713}, {1304, 51392}, {6152, 930}, {10550, 1634}, {16698, 1783}, {16813, 42445}, {20185, 41598}, {20626, 41590}, {23195, 6528}, {30248, 6153}, {35360, 51255}, {41676, 60587}, {41677, 6}, {47328, 99}
X(61203) = barycentric quotient X(i)/X(j) for these (i, j): {25, 50946}, {112, 40393}, {570, 525}, {648, 57903}, {1216, 3265}, {1238, 52617}, {1576, 40441}, {1594, 850}, {6152, 41298}, {10550, 52618}, {16698, 15413}, {23195, 520}, {32676, 2216}, {32713, 1179}, {35360, 59137}, {37636, 3267}, {41677, 76}, {42445, 60597}, {47328, 523}, {50947, 69}, {52604, 40449}, {57655, 59004}, {59172, 23286}, {60587, 4580}
X(61203) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 112, 61208}, {112, 1625, 61209}, {1625, 35325, 112}, {52131, 52132, 14591}

X(61204) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(4) AND CEVIAN-OF-X(64)

Barycentrics    a^2*(a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(-2*a^2*(b^2-c^2)^2+a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)) : :

X(61204) lies on these lines: {6, 1562}, {110, 112}, {525, 39195}, {1033, 41373}, {1301, 58952}, {1498, 2138}, {2442, 6529}, {2501, 61193}, {2623, 32695}, {3162, 41376}, {3172, 32445}, {3331, 16318}, {15639, 57204}, {24019, 24033}, {32676, 61202}, {57219, 58070}

X(61204) = trilinear pole of line {800, 44079}
X(61204) = perspector of circumconic {{A, B, C, X(250), X(22239)}}
X(61204) = X(i)-isoconjugate-of-X(j) for these {i, j}: {525, 775}, {647, 57955}, {656, 801}, {661, 57800}, {810, 40830}, {821, 52613}, {822, 57775}, {1105, 24018}, {1577, 57648}, {14208, 41890}, {20902, 59039}, {32320, 57972}
X(61204) = X(i)-Dao conjugate of X(j) for these {i, j}: {2883, 525}, {6509, 3267}, {13567, 4143}, {14091, 850}, {36830, 57800}, {39052, 57955}, {39062, 40830}, {40596, 801}, {59527, 52617}
X(61204) = X(i)-Ceva conjugate of X(j) for these {i, j}: {32230, 25}, {41678, 1624}
X(61204) = pole of line {110, 30249} with respect to the MacBeath circumconic
X(61204) = pole of line {1112, 9033} with respect to the orthic inconic
X(61204) = intersection, other than A, B, C, of circumconics {{A, B, C, X(110), X(1624)}}, {{A, B, C, X(112), X(41678)}}, {{A, B, C, X(235), X(4230)}}, {{A, B, C, X(800), X(2420)}}, {{A, B, C, X(1625), X(32695)}}, {{A, B, C, X(1636), X(2623)}}, {{A, B, C, X(6529), X(32661)}}, {{A, B, C, X(13567), X(61198)}}
X(61204) = barycentric product X(i)*X(j) for these (i, j): {107, 185}, {110, 235}, {112, 13567}, {162, 774}, {648, 800}, {1289, 41580}, {1301, 2883}, {1304, 51403}, {1576, 44131}, {1624, 4}, {1783, 18603}, {6509, 6529}, {10423, 41603}, {16035, 35360}, {17858, 32676}, {19166, 52604}, {19180, 61193}, {20626, 41589}, {24019, 6508}, {30249, 36982}, {32713, 41005}, {36126, 820}, {39417, 41602}, {40097, 41601}, {41678, 6}, {44079, 99}, {52566, 52913}
X(61204) = barycentric quotient X(i)/X(j) for these (i, j): {107, 57775}, {110, 57800}, {112, 801}, {162, 57955}, {185, 3265}, {235, 850}, {648, 40830}, {774, 14208}, {800, 525}, {1576, 57648}, {1624, 69}, {6509, 4143}, {13567, 3267}, {18603, 15413}, {19180, 15414}, {32676, 775}, {32713, 1105}, {36126, 57972}, {41005, 52617}, {41580, 57069}, {41678, 76}, {44079, 523}, {44131, 44173}, {57655, 59039}, {61206, 41890}
X(61204) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {112, 1625, 35325}, {112, 61208, 2420}, {112, 61209, 1625}

X(61205) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(4) AND CEVIAN-OF-X(65)

Barycentrics    a^2*(a-b)*(a-c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(b^2+c^2+a*(b+c)) : :

X(61205) lies on these lines: {6, 10693}, {19, 16685}, {101, 32691}, {107, 59066}, {108, 32693}, {109, 58945}, {110, 112}, {162, 3573}, {219, 21148}, {607, 2176}, {608, 21769}, {644, 1783}, {692, 2498}, {1332, 36099}, {1415, 2443}, {1973, 3915}, {3125, 47232}, {3230, 5089}, {3747, 37908}, {6591, 61236}, {9107, 32722}, {17903, 23112}, {22074, 56905}, {32676, 35327}, {61172, 61226}

X(61205) = isogonal conjugate of X(15420)
X(61205) = trilinear pole of line {2092, 2354}
X(61205) = perspector of circumconic {{A, B, C, X(250), X(2766)}}
X(61205) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 15420}, {63, 4581}, {514, 1791}, {525, 2363}, {652, 31643}, {656, 14534}, {693, 2359}, {810, 40827}, {905, 1220}, {961, 6332}, {1169, 14208}, {1214, 57161}, {1240, 22383}, {1459, 30710}, {1565, 36147}, {1577, 1798}, {2298, 4025}, {3942, 8707}, {4369, 57690}, {6648, 7004}, {8687, 17880}, {17206, 57162}, {20902, 58982}, {20981, 57859}, {26932, 36098}, {52550, 55234}
X(61205) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 15420}, {960, 525}, {1211, 15413}, {2092, 35518}, {3162, 4581}, {3666, 3267}, {17419, 17880}, {36830, 57853}, {38992, 26932}, {39015, 1565}, {39062, 40827}, {40596, 14534}, {52087, 4025}, {56905, 850}
X(61205) = X(i)-Ceva conjugate of X(j) for these {i, j}: {5379, 25}
X(61205) = X(i)-cross conjugate of X(j) for these {i, j}: {42661, 429}
X(61205) = pole of line {1415, 1576} with respect to the circumcircle
X(61205) = pole of line {338, 1086} with respect to the polar circle
X(61205) = pole of line {22, 23381} with respect to the Kiepert parabola
X(61205) = pole of line {110, 7435} with respect to the MacBeath circumconic
X(61205) = pole of line {1112, 1862} with respect to the orthic inconic
X(61205) = pole of line {525, 7254} with respect to the Stammler hyperbola
X(61205) = pole of line {3732, 4244} with respect to the Steiner circumellipse
X(61205) = pole of line {8, 25} with respect to the Hutson-Moses hyperbola
X(61205) = pole of line {3267, 15419} with respect to the Wallace hyperbola
X(61205) = pole of line {17911, 39575} with respect to the dual conic of Jerabek hyperbola
X(61205) = intersection, other than A, B, C, of circumconics {{A, B, C, X(101), X(3882)}}, {{A, B, C, X(110), X(3903)}}, {{A, B, C, X(429), X(4230)}}, {{A, B, C, X(644), X(692)}}, {{A, B, C, X(1193), X(2398)}}, {{A, B, C, X(1211), X(61198)}}, {{A, B, C, X(1415), X(46640)}}, {{A, B, C, X(1897), X(32674)}}, {{A, B, C, X(2092), X(2420)}}, {{A, B, C, X(2300), X(2427)}}, {{A, B, C, X(2443), X(56905)}}, {{A, B, C, X(3569), X(42661)}}, {{A, B, C, X(4574), X(32661)}}, {{A, B, C, X(4612), X(39412)}}, {{A, B, C, X(52326), X(53549)}}
X(61205) = barycentric product X(i)*X(j) for these (i, j): {1, 61226}, {4, 53280}, {19, 3882}, {25, 53332}, {27, 61168}, {28, 61172}, {34, 61223}, {100, 1829}, {101, 1848}, {107, 22076}, {108, 960}, {109, 46878}, {110, 429}, {112, 1211}, {162, 2292}, {190, 2354}, {1193, 1897}, {1228, 61206}, {1292, 41611}, {1783, 3666}, {2092, 648}, {2269, 653}, {2300, 6335}, {3725, 811}, {3903, 444}, {3910, 7115}, {4267, 61178}, {4357, 8750}, {10101, 41607}, {13397, 41609}, {15742, 6371}, {17420, 7012}, {18020, 42661}, {18026, 20967}, {18697, 32676}, {19608, 57220}, {22074, 54240}, {24471, 56183}, {26706, 41581}, {27067, 35325}, {32674, 3687}, {32702, 51407}, {32714, 3965}, {40097, 41600}, {40976, 664}, {44092, 99}, {46102, 52326}, {46640, 56905}, {46889, 52607}, {50330, 5379}, {52567, 52914}, {54314, 692}
X(61205) = barycentric quotient X(i)/X(j) for these (i, j): {6, 15420}, {25, 4581}, {108, 31643}, {110, 57853}, {112, 14534}, {429, 850}, {444, 4374}, {648, 40827}, {692, 1791}, {960, 35518}, {1193, 4025}, {1211, 3267}, {1576, 1798}, {1783, 30710}, {1829, 693}, {1848, 3261}, {1897, 1240}, {2092, 525}, {2269, 6332}, {2292, 14208}, {2299, 57161}, {2300, 905}, {2354, 514}, {3666, 15413}, {3725, 656}, {3882, 304}, {3903, 57859}, {3965, 15416}, {6371, 1565}, {7115, 6648}, {8750, 1220}, {17420, 17880}, {20967, 521}, {22076, 3265}, {22097, 30805}, {22345, 4131}, {32676, 2363}, {32739, 2359}, {40153, 15419}, {40966, 52355}, {40976, 522}, {42661, 125}, {44092, 523}, {46878, 35519}, {46889, 15411}, {52326, 26932}, {52914, 52550}, {53280, 69}, {53332, 305}, {54314, 40495}, {57157, 3937}, {57655, 58982}, {61168, 306}, {61172, 20336}, {61206, 1169}, {61223, 3718}, {61226, 75}
X(61205) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3747, 57653, 37908}

X(61206) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(4) AND CEVIAN-OF-X(66)

Barycentrics    a^4*(a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2) : :

X(61206) lies on these lines: {6, 1112}, {22, 38652}, {23, 41363}, {25, 1501}, {32, 40351}, {107, 685}, {110, 112}, {115, 46682}, {141, 46242}, {154, 3162}, {162, 1492}, {182, 52905}, {184, 17409}, {249, 57216}, {250, 32717}, {378, 38641}, {427, 1915}, {428, 6034}, {468, 1691}, {525, 15388}, {648, 4577}, {692, 2873}, {933, 26714}, {1176, 56921}, {1289, 58113}, {1301, 58963}, {1304, 59136}, {1495, 14580}, {1503, 46243}, {1560, 5972}, {1576, 2491}, {1619, 22135}, {1692, 44084}, {1843, 46288}, {1968, 44116}, {1971, 16318}, {1974, 32740}, {2204, 34858}, {2207, 52436}, {2211, 14567}, {2421, 41679}, {2445, 14398}, {2489, 14560}, {3049, 32715}, {3172, 9408}, {3199, 11060}, {3269, 13171}, {4235, 4576}, {6090, 8778}, {6759, 51509}, {6800, 8743}, {8627, 21284}, {8791, 39691}, {8879, 11206}, {10330, 41676}, {10423, 59933}, {12292, 45723}, {13854, 31383}, {14574, 34859}, {14581, 19627}, {14601, 23216}, {15080, 39575}, {15448, 47187}, {15647, 28343}, {19127, 36879}, {19504, 20976}, {20998, 44467}, {23347, 32738}, {23357, 58760}, {32237, 56922}, {32696, 32716}, {32729, 57204}, {32734, 52604}, {32735, 43925}, {32741, 44102}, {34211, 41678}, {36417, 44077}, {39805, 45123}, {41512, 60505}, {44090, 56915}, {52917, 58070}, {58312, 60428}, {58780, 60503}

X(61206) = inverse of X(1112) in orthic inconic
X(61206) = isogonal conjugate of X(3267)
X(61206) = trilinear pole of line {32, 682}
X(61206) = perspector of circumconic {{A, B, C, X(250), X(10423)}}
X(61206) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 3267}, {2, 14208}, {3, 20948}, {10, 15413}, {19, 52617}, {48, 44173}, {63, 850}, {69, 1577}, {71, 40495}, {72, 3261}, {75, 525}, {76, 656}, {85, 52355}, {92, 3265}, {99, 20902}, {115, 55202}, {125, 799}, {158, 4143}, {162, 36793}, {226, 35518}, {264, 24018}, {274, 4064}, {304, 523}, {305, 661}, {306, 693}, {307, 4391}, {310, 55232}, {312, 17094}, {313, 905}, {314, 57243}, {321, 4025}, {326, 14618}, {328, 32679}, {334, 24459}, {336, 2799}, {338, 4592}, {339, 662}, {345, 4077}, {348, 4086}, {349, 521}, {513, 40071}, {514, 20336}, {520, 1969}, {522, 1231}, {561, 647}, {648, 17879}, {668, 4466}, {670, 3708}, {684, 46273}, {798, 40050}, {810, 1502}, {811, 15526}, {822, 18022}, {879, 46238}, {897, 45807}, {1089, 15419}, {1109, 4563}, {1111, 52609}, {1214, 35519}, {1332, 21207}, {1365, 55207}, {1439, 52622}, {1441, 6332}, {1444, 52623}, {1459, 27801}, {1565, 4033}, {1821, 6333}, {1895, 14638}, {1924, 40360}, {1928, 3049}, {1930, 4580}, {1934, 24284}, {1978, 18210}, {2166, 45792}, {2169, 15415}, {2525, 3112}, {2582, 22340}, {2583, 22339}, {2616, 28706}, {2618, 34386}, {2632, 6331}, {2643, 52608}, {2972, 57973}, {3269, 57968}, {3596, 51664}, {3668, 15416}, {3694, 52621}, {3695, 7199}, {3700, 7182}, {3710, 24002}, {3718, 7178}, {3926, 24006}, {3933, 18070}, {3942, 27808}, {3949, 52619}, {3998, 46107}, {4017, 57919}, {4036, 17206}, {4041, 57918}, {4092, 55205}, {4397, 56382}, {4552, 17880}, {4558, 23994}, {4560, 57807}, {4561, 16732}, {4572, 53560}, {4575, 23962}, {4601, 21134}, {4602, 20975}, {4623, 21046}, {5489, 46254}, {6063, 8611}, {6335, 17216}, {6385, 55230}, {6587, 57780}, {7192, 52369}, {8057, 57921}, {8673, 46244}, {9033, 33805}, {9289, 17893}, {14206, 34767}, {14210, 14977}, {14380, 46234}, {14417, 46277}, {14429, 20568}, {15352, 24020}, {15412, 18695}, {15420, 18697}, {17896, 56944}, {17898, 34403}, {17924, 52396}, {18155, 26942}, {18160, 52388}, {18895, 53556}, {20235, 48070}, {20571, 52584}, {20910, 43714}, {21107, 57925}, {23107, 24000}, {23285, 34055}, {23616, 23999}, {23874, 60197}, {23974, 36126}, {24039, 51258}, {30805, 41013}, {40072, 55234}, {40149, 52616}, {40440, 60597}, {40703, 53173}, {44129, 57109}, {44426, 52565}, {46110, 52385}, {52575, 57241}, {52613, 57806}
X(61206) = X(i)-vertex conjugate of X(j) for these {i, j}: {648, 4563}, {1576, 35325}, {2966, 6331}, {6528, 17932}, {35178, 55279}, {42396, 43188}, {44766, 44766}
X(61206) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 3267}, {6, 52617}, {32, 57069}, {125, 36793}, {136, 23962}, {206, 525}, {1084, 339}, {1147, 4143}, {1249, 44173}, {3162, 850}, {5139, 338}, {6593, 45807}, {9428, 40360}, {11597, 45792}, {14363, 15415}, {15259, 14618}, {15295, 14592}, {15477, 14977}, {17423, 15526}, {22391, 3265}, {31998, 40050}, {32664, 14208}, {34452, 2525}, {34961, 57919}, {36103, 20948}, {36830, 305}, {38986, 20902}, {38996, 125}, {39026, 40071}, {39052, 561}, {39054, 40364}, {39062, 1502}, {40368, 647}, {40369, 3049}, {40596, 76}, {40601, 6333}, {46093, 23974}, {55066, 17879}
X(61206) = X(i)-Ceva conjugate of X(j) for these {i, j}: {112, 1576}, {249, 19118}, {250, 44162}, {2715, 2445}, {15388, 6}, {23357, 44077}, {23964, 25}, {23975, 3172}, {32708, 23347}, {41937, 32}, {55270, 250}, {57655, 1974}, {60179, 44089}
X(61206) = X(i)-cross conjugate of X(j) for these {i, j}: {32, 41937}, {512, 46288}, {669, 25}, {1974, 57655}, {3049, 32}, {14574, 1576}, {44162, 250}, {52436, 23963}, {57204, 1974}, {57206, 44167}, {58310, 54034}, {58317, 1976}, {61218, 112}
X(61206) = pole of line {1576, 2445} with respect to the circumcircle
X(61206) = pole of line {338, 23962} with respect to the polar circle
X(61206) = pole of line {37981, 44089} with respect to the Kiepert hyperbola
X(61206) = pole of line {22, 7750} with respect to the Kiepert parabola
X(61206) = pole of line {110, 39417} with respect to the MacBeath circumconic
X(61206) = pole of line {1112, 9517} with respect to the orthic inconic
X(61206) = pole of line {525, 3267} with respect to the Stammler hyperbola
X(61206) = pole of line {2525, 3267} with respect to the Wallace hyperbola
X(61206) = pole of line {7832, 18797} with respect to the dual conic of Jerabek hyperbola
X(61206) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(44766)}}, {{A, B, C, X(25), X(107)}}, {{A, B, C, X(32), X(2420)}}, {{A, B, C, X(99), X(41533)}}, {{A, B, C, X(110), X(685)}}, {{A, B, C, X(112), X(20031)}}, {{A, B, C, X(184), X(2445)}}, {{A, B, C, X(512), X(9517)}}, {{A, B, C, X(513), X(2873)}}, {{A, B, C, X(525), X(38356)}}, {{A, B, C, X(648), X(35325)}}, {{A, B, C, X(669), X(2491)}}, {{A, B, C, X(805), X(53654)}}, {{A, B, C, X(809), X(18829)}}, {{A, B, C, X(933), X(32696)}}, {{A, B, C, X(1301), X(32649)}}, {{A, B, C, X(1625), X(6529)}}, {{A, B, C, X(1636), X(3049)}}, {{A, B, C, X(2211), X(35907)}}, {{A, B, C, X(2421), X(42295)}}, {{A, B, C, X(2623), X(58317)}}, {{A, B, C, X(2715), X(14574)}}, {{A, B, C, X(4609), X(53918)}}, {{A, B, C, X(9087), X(11794)}}, {{A, B, C, X(9091), X(43188)}}, {{A, B, C, X(10117), X(34190)}}, {{A, B, C, X(13114), X(14998)}}, {{A, B, C, X(14601), X(46249)}}, {{A, B, C, X(14966), X(40825)}}, {{A, B, C, X(17980), X(53699)}}, {{A, B, C, X(19118), X(57216)}}, {{A, B, C, X(23347), X(44080)}}, {{A, B, C, X(23963), X(23966)}}, {{A, B, C, X(27369), X(46543)}}, {{A, B, C, X(35324), X(59007)}}, {{A, B, C, X(39644), X(53692)}}, {{A, B, C, X(39951), X(44326)}}, {{A, B, C, X(41512), X(44084)}}, {{A, B, C, X(42068), X(57204)}}, {{A, B, C, X(44077), X(61213)}}, {{A, B, C, X(44162), X(55270)}}
X(61206) = barycentric product X(i)*X(j) for these (i, j): {1, 32676}, {3, 32713}, {24, 32734}, {27, 32739}, {28, 692}, {30, 32715}, {32, 648}, {51, 933}, {58, 8750}, {100, 2203}, {101, 1474}, {107, 184}, {108, 2194}, {109, 2299}, {110, 25}, {111, 61207}, {112, 6}, {159, 39417}, {162, 31}, {163, 19}, {228, 52920}, {232, 2715}, {237, 685}, {248, 58070}, {250, 512}, {251, 35325}, {275, 61194}, {284, 32674}, {287, 34859}, {427, 4630}, {523, 57655}, {560, 811}, {577, 6529}, {823, 9247}, {1084, 55270}, {1096, 4575}, {1110, 57200}, {1113, 44124}, {1114, 44123}, {1169, 61205}, {1172, 1415}, {1175, 53323}, {1177, 46592}, {1252, 43925}, {1288, 44078}, {1289, 206}, {1297, 2445}, {1301, 154}, {1302, 44080}, {1304, 1495}, {1333, 1783}, {1395, 643}, {1397, 36797}, {1402, 52914}, {1408, 56183}, {1414, 2212}, {1461, 2332}, {1492, 46503}, {1501, 6331}, {1503, 32649}, {1576, 4}, {1625, 8882}, {1660, 30249}, {1692, 32697}, {1755, 36104}, {1843, 827}, {1897, 2206}, {1917, 57968}, {1924, 46254}, {1971, 53708}, {1973, 662}, {1974, 99}, {1976, 4230}, {1990, 32640}, {2159, 56829}, {2165, 61208}, {2173, 36131}, {2181, 36134}, {2189, 4559}, {2200, 52919}, {2204, 651}, {2205, 55231}, {2207, 4558}, {2211, 2966}, {2312, 36046}, {2333, 4556}, {2351, 52917}, {2353, 52915}, {2407, 40354}, {2420, 8749}, {2421, 57260}, {2442, 59499}, {2489, 249}, {2491, 60179}, {2576, 2577}, {2713, 44096}, {2971, 59152}, {3003, 32708}, {3051, 42396}, {3124, 47443}, {3162, 56008}, {3172, 46639}, {3192, 59005}, {3194, 32652}, {3269, 59153}, {3455, 52916}, {3563, 61213}, {4565, 607}, {4590, 57204}, {4636, 57652}, {5317, 906}, {5379, 667}, {5467, 8753}, {5546, 608}, {5994, 8740}, {5995, 8739}, {7115, 7252}, {10311, 26714}, {10420, 44084}, {10423, 2393}, {10425, 44099}, {10547, 46151}, {10641, 16807}, {10642, 16806}, {10985, 59008}, {11060, 14590}, {11402, 58950}, {11636, 8541}, {12167, 58100}, {13486, 14975}, {14533, 61193}, {14560, 186}, {14569, 15958}, {14574, 264}, {14575, 6528}, {14576, 32692}, {14581, 44769}, {14585, 15352}, {14586, 53}, {14587, 51513}, {14591, 1989}, {14601, 877}, {14618, 23963}, {14642, 57219}, {14776, 859}, {14910, 61209}, {14966, 6531}, {15384, 42658}, {15388, 2485}, {15471, 32648}, {16077, 9407}, {16813, 217}, {17409, 44766}, {17442, 34072}, {17925, 23990}, {17926, 23979}, {17938, 419}, {17980, 56980}, {17994, 57742}, {18020, 669}, {18315, 3199}, {18374, 935}, {18384, 52603}, {18831, 40981}, {19118, 3565}, {19136, 30247}, {19153, 39382}, {19627, 46456}, {20031, 3289}, {22456, 9418}, {23090, 23985}, {23347, 74}, {23357, 2501}, {23582, 3049}, {23590, 32320}, {23964, 647}, {23975, 52613}, {23995, 24006}, {24000, 810}, {24019, 48}, {24033, 57134}, {26864, 9064}, {27369, 4577}, {30450, 52436}, {31614, 42068}, {32230, 39201}, {32656, 8747}, {32660, 8748}, {32661, 393}, {32662, 52418}, {32666, 54407}, {32673, 44661}, {32687, 8779}, {32691, 44119}, {32695, 3284}, {32696, 511}, {32709, 53777}, {32717, 46522}, {32718, 52890}, {32719, 37168}, {32725, 852}, {32727, 52889}, {32728, 52891}, {32729, 468}, {32735, 37908}, {32737, 3518}, {32738, 378}, {32740, 4235}, {32741, 7482}, {33581, 52913}, {33631, 35324}, {33640, 44082}, {34190, 40596}, {34207, 57086}, {34394, 36306}, {34395, 36309}, {34397, 476}, {34417, 58994}, {34568, 9408}, {34854, 43754}, {34858, 4246}, {35329, 51446}, {35330, 51447}, {35360, 54034}, {36069, 44113}, {36071, 39690}, {36077, 5320}, {36084, 57653}, {36126, 52430}, {36417, 4563}, {36420, 4574}, {37538, 59092}, {38534, 53329}, {39383, 5413}, {39384, 5412}, {40097, 52143}, {40114, 53944}, {40352, 4240}, {40570, 61197}, {40938, 58113}, {41293, 53654}, {41676, 46288}, {41679, 60501}, {41890, 61204}, {41937, 525}, {41941, 52132}, {41942, 52131}, {42671, 44770}, {44077, 925}, {44079, 59039}, {44086, 59130}, {44088, 52779}, {44089, 805}, {44090, 46970}, {44091, 7953}, {44092, 58982}, {44095, 59011}, {44097, 59075}, {44100, 5545}, {44102, 691}, {44103, 58951}, {44112, 59041}, {44127, 53699}, {44162, 670}, {45141, 58963}, {47328, 59004}, {47390, 58757}, {51822, 60506}, {52142, 60503}, {52153, 53176}, {52604, 54}, {53273, 57388}, {53282, 57391}, {53290, 57390}, {53325, 57392}, {53962, 56924}, {56920, 58111}, {57153, 64}, {57657, 653}, {58102, 7716}, {61218, 83}
X(61206) = barycentric quotient X(i)/X(j) for these (i, j): {3, 52617}, {4, 44173}, {6, 3267}, {19, 20948}, {25, 850}, {28, 40495}, {31, 14208}, {32, 525}, {50, 45792}, {53, 15415}, {99, 40050}, {101, 40071}, {107, 18022}, {110, 305}, {112, 76}, {162, 561}, {163, 304}, {184, 3265}, {187, 45807}, {206, 57069}, {217, 60597}, {237, 6333}, {249, 52608}, {250, 670}, {512, 339}, {560, 656}, {577, 4143}, {647, 36793}, {648, 1502}, {662, 40364}, {669, 125}, {670, 40360}, {685, 18024}, {692, 20336}, {798, 20902}, {810, 17879}, {811, 1928}, {933, 34384}, {1101, 55202}, {1289, 40421}, {1301, 41530}, {1333, 15413}, {1395, 4077}, {1397, 17094}, {1415, 1231}, {1474, 3261}, {1501, 647}, {1576, 69}, {1625, 28706}, {1783, 27801}, {1843, 23285}, {1917, 810}, {1918, 4064}, {1919, 4466}, {1924, 3708}, {1973, 1577}, {1974, 523}, {1980, 18210}, {2175, 52355}, {2194, 35518}, {2203, 693}, {2204, 4391}, {2205, 55232}, {2206, 4025}, {2207, 14618}, {2211, 2799}, {2212, 4086}, {2299, 35519}, {2332, 52622}, {2333, 52623}, {2445, 30737}, {2489, 338}, {2501, 23962}, {2715, 57799}, {2971, 23105}, {3049, 15526}, {3051, 2525}, {3080, 12075}, {3199, 18314}, {3269, 23107}, {4565, 57918}, {4630, 1799}, {5379, 6386}, {5546, 57919}, {6331, 40362}, {6528, 44161}, {6529, 18027}, {8750, 313}, {8753, 52632}, {9233, 3049}, {9247, 24018}, {9407, 9033}, {9408, 52624}, {9418, 684}, {9426, 20975}, {9447, 8611}, {9459, 14429}, {10312, 57082}, {10423, 46140}, {11060, 14592}, {14533, 15414}, {14560, 328}, {14567, 14417}, {14573, 23286}, {14574, 3}, {14575, 520}, {14581, 41079}, {14585, 52613}, {14586, 34386}, {14591, 7799}, {14599, 24459}, {14600, 53173}, {14601, 879}, {14602, 24284}, {14642, 14638}, {14776, 57984}, {14966, 6393}, {15257, 57146}, {16813, 57790}, {17409, 33294}, {17938, 40708}, {17980, 56981}, {18020, 4609}, {18892, 53556}, {19626, 10097}, {19627, 8552}, {20031, 60199}, {20968, 8673}, {22075, 58359}, {23347, 3260}, {23357, 4563}, {23963, 4558}, {23964, 6331}, {23975, 15352}, {23990, 52609}, {23995, 4592}, {24000, 57968}, {24019, 1969}, {27369, 826}, {32320, 23974}, {32649, 35140}, {32656, 52396}, {32660, 52565}, {32661, 3926}, {32674, 349}, {32676, 75}, {32696, 290}, {32708, 40832}, {32713, 264}, {32715, 1494}, {32725, 57981}, {32729, 30786}, {32734, 20563}, {32738, 57819}, {32739, 306}, {32740, 14977}, {34397, 3268}, {34859, 297}, {35325, 8024}, {36104, 46273}, {36131, 33805}, {36417, 2501}, {36797, 40363}, {39417, 40009}, {40351, 2433}, {40352, 34767}, {40354, 2394}, {40373, 39201}, {40981, 6368}, {41293, 3221}, {41676, 52568}, {41937, 648}, {42068, 8029}, {42396, 40016}, {43925, 23989}, {44077, 6563}, {44080, 30474}, {44089, 14295}, {44102, 35522}, {44123, 22340}, {44124, 22339}, {44162, 512}, {46288, 4580}, {46505, 50549}, {46592, 1236}, {47443, 34537}, {52436, 52584}, {52604, 311}, {52914, 40072}, {52915, 40073}, {52916, 40074}, {52920, 57796}, {53323, 1234}, {53581, 21046}, {55270, 44168}, {56829, 46234}, {57153, 14615}, {57204, 115}, {57260, 43665}, {57655, 99}, {57657, 6332}, {58070, 44132}, {58310, 2972}, {58317, 3150}, {61194, 343}, {61205, 1228}, {61207, 3266}, {61208, 7763}, {61218, 141}
X(61206) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 10117, 38356}, {110, 112, 35325}, {112, 61208, 32661}, {1495, 51437, 14580}, {35325, 61207, 110}

X(61207) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(4) AND CEVIAN-OF-X(67)

Barycentrics    a^2*(a-b)*(a+b)*(a-c)*(a+c)*(2*a^2-b^2-c^2)*(a^2+b^2-c^2)*(a^2-b^2+c^2) : :

X(61207) lies on these lines: {6, 25}, {107, 59007}, {110, 112}, {187, 9717}, {248, 40352}, {427, 41939}, {468, 1648}, {524, 51823}, {647, 5502}, {648, 35138}, {690, 60503}, {877, 46543}, {933, 59008}, {935, 58953}, {1112, 20976}, {1304, 2433}, {1499, 57602}, {1503, 57632}, {1560, 5642}, {1640, 2409}, {2421, 14590}, {2501, 4240}, {2502, 44467}, {4235, 5468}, {5026, 34336}, {5477, 12828}, {6353, 6792}, {6800, 36176}, {8791, 11646}, {10097, 32729}, {10423, 35188}, {11206, 35902}, {12077, 53319}, {13509, 60499}, {14273, 14559}, {14401, 15639}, {14602, 44896}, {14999, 16237}, {15329, 23357}, {15647, 38356}, {23964, 53176}, {26714, 58994}, {30510, 36830}, {34574, 52916}, {35265, 41363}, {35266, 47187}, {35356, 41676}, {37777, 60498}, {39560, 52292}, {41618, 52234}, {51233, 52171}, {52169, 57261}, {61211, 61218}

X(61207) = isogonal conjugate of X(14977)
X(61207) = trilinear pole of line {187, 23200}
X(61207) = perspector of circumconic {{A, B, C, X(112), X(250)}}
X(61207) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 14977}, {48, 52632}, {63, 5466}, {69, 23894}, {75, 10097}, {111, 14208}, {125, 36085}, {304, 9178}, {336, 8430}, {339, 36142}, {525, 897}, {647, 46277}, {656, 671}, {661, 30786}, {662, 51258}, {691, 20902}, {810, 18023}, {822, 46111}, {850, 36060}, {892, 3708}, {895, 1577}, {923, 3267}, {3049, 57999}, {3265, 36128}, {4466, 5380}, {14209, 60317}, {14908, 20948}, {17983, 24018}, {43926, 52369}
X(61207) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 14977}, {206, 10097}, {524, 45807}, {1084, 51258}, {1249, 52632}, {1560, 850}, {2482, 3267}, {3162, 5466}, {6593, 525}, {23992, 339}, {36830, 30786}, {38988, 125}, {39052, 46277}, {39062, 18023}, {40596, 671}, {48317, 338}, {52881, 52617}
X(61207) = X(i)-Ceva conjugate of X(j) for these {i, j}: {249, 41616}, {4235, 5467}, {10423, 1576}, {52916, 46592}
X(61207) = X(i)-cross conjugate of X(j) for these {i, j}: {351, 468}
X(61207) = pole of line {647, 1576} with respect to the circumcircle
X(61207) = pole of line {338, 850} with respect to the polar circle
X(61207) = pole of line {22, 7664} with respect to the Kiepert parabola
X(61207) = pole of line {110, 8673} with respect to the MacBeath circumconic
X(61207) = pole of line {512, 1112} with respect to the orthic inconic
X(61207) = pole of line {69, 525} with respect to the Stammler hyperbola
X(61207) = pole of line {41676, 46619} with respect to the Steiner circumellipse
X(61207) = pole of line {305, 3267} with respect to the Wallace hyperbola
X(61207) = pole of line {8673, 11746} with respect to the dual conic of DeLongchamps circle
X(61207) = pole of line {36793, 52617} with respect to the dual conic of polar circle
X(61207) = pole of line {7870, 39575} with respect to the dual conic of Jerabek hyperbola
X(61207) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(35901)}}, {{A, B, C, X(6), X(110)}}, {{A, B, C, X(25), X(112)}}, {{A, B, C, X(51), X(1625)}}, {{A, B, C, X(99), X(40102)}}, {{A, B, C, X(184), X(32661)}}, {{A, B, C, X(187), X(1495)}}, {{A, B, C, X(232), X(468)}}, {{A, B, C, X(351), X(1648)}}, {{A, B, C, X(524), X(2393)}}, {{A, B, C, X(648), X(8541)}}, {{A, B, C, X(690), X(9517)}}, {{A, B, C, X(896), X(39690)}}, {{A, B, C, X(907), X(2418)}}, {{A, B, C, X(922), X(44112)}}, {{A, B, C, X(933), X(10985)}}, {{A, B, C, X(1194), X(7953)}}, {{A, B, C, X(1576), X(19136)}}, {{A, B, C, X(1843), X(35325)}}, {{A, B, C, X(2623), X(52038)}}, {{A, B, C, X(3292), X(8779)}}, {{A, B, C, X(4558), X(10602)}}, {{A, B, C, X(4630), X(56918)}}, {{A, B, C, X(5203), X(10425)}}, {{A, B, C, X(5649), X(21448)}}, {{A, B, C, X(8770), X(40173)}}, {{A, B, C, X(9064), X(59229)}}, {{A, B, C, X(9418), X(14567)}}, {{A, B, C, X(9971), X(36828)}}, {{A, B, C, X(10098), X(56922)}}, {{A, B, C, X(12828), X(15329)}}, {{A, B, C, X(13114), X(34212)}}, {{A, B, C, X(13366), X(35324)}}, {{A, B, C, X(14273), X(14590)}}, {{A, B, C, X(14591), X(34397)}}, {{A, B, C, X(14966), X(40352)}}, {{A, B, C, X(16806), X(54363)}}, {{A, B, C, X(16807), X(54362)}}, {{A, B, C, X(17813), X(46639)}}, {{A, B, C, X(18315), X(40673)}}, {{A, B, C, X(18374), X(32729)}}, {{A, B, C, X(19153), X(32734)}}, {{A, B, C, X(23889), X(44119)}}, {{A, B, C, X(26714), X(34417)}}, {{A, B, C, X(32640), X(40114)}}, {{A, B, C, X(34777), X(56008)}}, {{A, B, C, X(36890), X(46128)}}, {{A, B, C, X(39413), X(52630)}}, {{A, B, C, X(41424), X(58963)}}, {{A, B, C, X(44077), X(61208)}}, {{A, B, C, X(44079), X(61204)}}, {{A, B, C, X(44084), X(60428)}}, {{A, B, C, X(44125), X(52131)}}, {{A, B, C, X(44126), X(52132)}}, {{A, B, C, X(44127), X(46249)}}, {{A, B, C, X(44769), X(57467)}}, {{A, B, C, X(47328), X(61203)}}, {{A, B, C, X(52898), X(60514)}}
X(61207) = barycentric product X(i)*X(j) for these (i, j): {4, 5467}, {19, 23889}, {23, 60503}, {25, 5468}, {107, 3292}, {110, 468}, {112, 524}, {162, 896}, {187, 648}, {250, 690}, {685, 9155}, {811, 922}, {1296, 15471}, {1304, 5642}, {1576, 44146}, {1648, 47443}, {1973, 24039}, {2203, 42721}, {2434, 4232}, {2696, 41618}, {3266, 61206}, {4230, 5967}, {4235, 6}, {4240, 9717}, {4558, 60428}, {5095, 691}, {6593, 935}, {6629, 8750}, {10098, 15303}, {10101, 41606}, {10420, 12828}, {10423, 5181}, {14210, 32676}, {14273, 249}, {14357, 52916}, {14417, 23964}, {14419, 5379}, {14559, 186}, {14567, 6331}, {14590, 56395}, {14591, 43084}, {16702, 1783}, {18020, 351}, {21906, 55270}, {23200, 6528}, {23347, 36890}, {30247, 53777}, {32225, 58994}, {32661, 37778}, {32696, 50567}, {32697, 5477}, {32713, 6390}, {32729, 34336}, {34568, 58347}, {35282, 44770}, {35325, 52898}, {35522, 57655}, {41586, 933}, {41616, 53895}, {41937, 45807}, {44102, 99}, {51823, 61198}, {52234, 56368}
X(61207) = barycentric quotient X(i)/X(j) for these (i, j): {4, 52632}, {6, 14977}, {25, 5466}, {32, 10097}, {107, 46111}, {110, 30786}, {112, 671}, {162, 46277}, {187, 525}, {250, 892}, {351, 125}, {468, 850}, {512, 51258}, {524, 3267}, {648, 18023}, {690, 339}, {811, 57999}, {896, 14208}, {922, 656}, {1576, 895}, {1973, 23894}, {1974, 9178}, {2211, 8430}, {2482, 45807}, {2642, 20902}, {3292, 3265}, {4235, 76}, {5095, 35522}, {5467, 69}, {5468, 305}, {6390, 52617}, {8541, 23288}, {9155, 6333}, {9717, 34767}, {14273, 338}, {14417, 36793}, {14559, 328}, {14567, 647}, {14574, 14908}, {16702, 15413}, {18020, 53080}, {23200, 520}, {23347, 9214}, {23582, 59762}, {23889, 304}, {24039, 40364}, {32676, 897}, {32696, 9154}, {32713, 17983}, {32715, 9139}, {32729, 15398}, {34397, 9213}, {35325, 31125}, {39689, 14417}, {44102, 523}, {44146, 44173}, {46592, 59422}, {47443, 52940}, {52916, 52551}, {56395, 14592}, {57655, 691}, {58347, 52624}, {58780, 52628}, {60428, 14618}, {60503, 18019}, {61206, 111}, {61218, 46154}
X(61207) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 154, 35901}, {6, 35901, 46128}, {110, 61206, 35325}, {14591, 61209, 2420}, {15329, 23357, 56389}, {23964, 53176, 58070}

X(61208) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(4) AND CEVIAN-OF-X(70)

Barycentrics    a^4*(a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4+b^4+c^4-2*a^2*(b^2+c^2)) : :

X(61208) lies on these lines: {6, 38534}, {24, 47421}, {107, 32692}, {110, 112}, {115, 12140}, {154, 20410}, {232, 19627}, {403, 58312}, {933, 58949}, {1289, 2715}, {1576, 14586}, {1971, 5523}, {1986, 39839}, {6529, 23964}, {8743, 9707}, {12412, 22146}, {14397, 52917}, {15100, 51233}, {38848, 40633}, {46151, 61217}

X(61208) = trilinear pole of line {571, 44077}
X(61208) = perspector of circumconic {{A, B, C, X(250), X(53923)}}
X(61208) = X(i)-isoconjugate-of-X(j) for these {i, j}: {68, 1577}, {69, 55250}, {91, 525}, {339, 36145}, {520, 57716}, {647, 20571}, {656, 5392}, {661, 20563}, {810, 57904}, {822, 55553}, {847, 24018}, {850, 1820}, {925, 20902}, {2165, 14208}, {2351, 20948}, {2618, 57875}, {2632, 30450}, {3708, 46134}, {18695, 55253}, {20975, 55215}, {24006, 52350}, {39201, 57898}
X(61208) = X(i)-vertex conjugate of X(j) for these {i, j}: {1576, 61203}
X(61208) = X(i)-Dao conjugate of X(j) for these {i, j}: {135, 338}, {577, 3265}, {34116, 525}, {36830, 20563}, {39013, 339}, {39052, 20571}, {39062, 57904}, {40596, 5392}
X(61208) = X(i)-Ceva conjugate of X(j) for these {i, j}: {107, 1576}, {249, 35603}, {23964, 8745}
X(61208) = X(i)-cross conjugate of X(j) for these {i, j}: {30451, 571}, {34952, 24}, {58760, 8745}
X(61208) = pole of line {1576, 61203} with respect to the circumcircle
X(61208) = intersection, other than A, B, C, of circumconics {{A, B, C, X(24), X(1289)}}, {{A, B, C, X(110), X(14586)}}, {{A, B, C, X(112), X(41679)}}, {{A, B, C, X(571), X(2420)}}, {{A, B, C, X(648), X(61203)}}, {{A, B, C, X(924), X(9517)}}, {{A, B, C, X(1576), X(1625)}}, {{A, B, C, X(1636), X(14397)}}, {{A, B, C, X(1993), X(61198)}}, {{A, B, C, X(3569), X(34952)}}, {{A, B, C, X(6529), X(8745)}}, {{A, B, C, X(32661), X(32692)}}, {{A, B, C, X(35325), X(55227)}}
X(61208) = barycentric product X(i)*X(j) for these (i, j): {3, 52917}, {32, 55227}, {52, 933}, {107, 1147}, {110, 24}, {112, 1993}, {162, 47}, {163, 1748}, {249, 6753}, {250, 924}, {476, 52416}, {563, 823}, {571, 648}, {1288, 34116}, {1304, 51393}, {1576, 317}, {1783, 18605}, {1973, 55249}, {2904, 46963}, {4558, 8745}, {10420, 52000}, {11547, 32661}, {13398, 35603}, {14576, 18315}, {14586, 467}, {14591, 18883}, {18020, 34952}, {23357, 57065}, {23582, 30451}, {23964, 52584}, {32676, 44179}, {32696, 51439}, {32713, 9723}, {32734, 55551}, {34948, 5379}, {41679, 6}, {44077, 99}, {44769, 52952}, {45780, 53923}, {47421, 47443}, {51776, 58070}, {52415, 52603}, {52432, 925}, {52435, 6528}, {52436, 6331}, {52505, 61209}, {52918, 59162}, {53176, 5961}, {57655, 6563}, {61206, 7763}
X(61208) = barycentric quotient X(i)/X(j) for these (i, j): {24, 850}, {47, 14208}, {107, 55553}, {110, 20563}, {112, 5392}, {162, 20571}, {250, 46134}, {317, 44173}, {467, 15415}, {563, 24018}, {571, 525}, {648, 57904}, {823, 57898}, {924, 339}, {933, 34385}, {1147, 3265}, {1576, 68}, {1748, 20948}, {1973, 55250}, {1993, 3267}, {6753, 338}, {8745, 14618}, {9723, 52617}, {14574, 2351}, {14576, 18314}, {14586, 57875}, {14591, 37802}, {18605, 15413}, {23964, 30450}, {24019, 57716}, {30451, 15526}, {32661, 52350}, {32676, 91}, {32713, 847}, {34952, 125}, {36416, 57065}, {41679, 76}, {44077, 523}, {52416, 3268}, {52432, 6563}, {52435, 520}, {52436, 647}, {52584, 36793}, {52604, 56272}, {52917, 264}, {52952, 41079}, {55216, 20902}, {55227, 1502}, {55249, 40364}, {57065, 23962}, {57655, 925}, {61206, 2165}, {61209, 52504}
X(61208) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 112, 61203}, {112, 14591, 32661}, {2420, 61204, 112}

X(61209) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(4) AND CEVIAN-OF-X(74)

Barycentrics    a^2*(a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)-2*a^2*(b^4-b^2*c^2+c^4)) : :

X(61209) lies on these lines: {4, 6}, {110, 112}, {232, 2088}, {287, 60133}, {378, 15920}, {403, 52451}, {512, 46592}, {1304, 32681}, {1968, 32761}, {2421, 4235}, {2433, 46587}, {2713, 53708}, {2715, 10423}, {3003, 14264}, {3016, 6103}, {3199, 15544}, {3269, 17854}, {5502, 32640}, {6000, 60499}, {12133, 44468}, {14560, 23347}, {15072, 39575}, {15639, 57203}, {16237, 61188}, {18911, 57583}, {26714, 30247}, {32695, 32708}, {32732, 53944}, {41512, 47236}, {44084, 60498}, {52058, 57611}, {57204, 60505}, {57655, 61213}

X(61209) = isogonal conjugate of X(15421)
X(61209) = trilinear pole of line {3003, 44084}
X(61209) = perspector of circumconic {{A, B, C, X(107), X(250)}}
X(61209) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 15421}, {63, 15328}, {75, 61216}, {525, 36053}, {656, 2986}, {661, 57829}, {687, 2632}, {810, 40832}, {1109, 43755}, {1300, 24018}, {1577, 5504}, {2631, 40423}, {3708, 18878}, {10420, 20902}, {12028, 32679}, {14208, 14910}, {15526, 36114}, {17879, 32708}, {51664, 56103}
X(61209) = X(i)-vertex conjugate of X(j) for these {i, j}: {32640, 32715}, {32708, 43755}
X(61209) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 15421}, {113, 525}, {206, 61216}, {3162, 15328}, {3580, 45792}, {16178, 338}, {34834, 3267}, {36830, 57829}, {39005, 15526}, {39021, 339}, {39062, 40832}, {40596, 2986}
X(61209) = X(i)-Ceva conjugate of X(j) for these {i, j}: {16237, 15329}, {32695, 112}, {53176, 23347}, {53923, 1576}, {58979, 57655}
X(61209) = X(i)-cross conjugate of X(j) for these {i, j}: {686, 3003}, {21731, 403}, {55265, 6}
X(61209) = pole of line {1576, 32640} with respect to the circumcircle
X(61209) = pole of line {338, 525} with respect to the polar circle
X(61209) = pole of line {51, 60499} with respect to the Jerabek hyperbola
X(61209) = pole of line {22, 1632} with respect to the Kiepert parabola
X(61209) = pole of line {110, 8057} with respect to the MacBeath circumconic
X(61209) = pole of line {523, 1112} with respect to the orthic inconic
X(61209) = pole of line {394, 525} with respect to the Stammler hyperbola
X(61209) = pole of line {33294, 37937} with respect to the Steiner circumellipse
X(61209) = pole of line {3267, 3926} with respect to the Wallace hyperbola
X(61209) = pole of line {8057, 11746} with respect to the dual conic of DeLongchamps circle
X(61209) = pole of line {4143, 36793} with respect to the dual conic of polar circle
X(61209) = pole of line {39575, 52147} with respect to the dual conic of Jerabek hyperbola
X(61209) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(110)}}, {{A, B, C, X(6), X(32661)}}, {{A, B, C, X(53), X(1625)}}, {{A, B, C, X(112), X(393)}}, {{A, B, C, X(403), X(4230)}}, {{A, B, C, X(686), X(1636)}}, {{A, B, C, X(1503), X(13754)}}, {{A, B, C, X(1990), X(2420)}}, {{A, B, C, X(2315), X(3330)}}, {{A, B, C, X(2421), X(60133)}}, {{A, B, C, X(2713), X(41204)}}, {{A, B, C, X(2715), X(3580)}}, {{A, B, C, X(3569), X(21731)}}, {{A, B, C, X(6529), X(8745)}}, {{A, B, C, X(6748), X(35324)}}, {{A, B, C, X(9160), X(18532)}}, {{A, B, C, X(9517), X(35364)}}, {{A, B, C, X(14591), X(32715)}}, {{A, B, C, X(15262), X(32640)}}, {{A, B, C, X(15388), X(35907)}}, {{A, B, C, X(18121), X(39170)}}, {{A, B, C, X(27376), X(35325)}}, {{A, B, C, X(30247), X(33971)}}, {{A, B, C, X(32662), X(53416)}}, {{A, B, C, X(32711), X(47236)}}, {{A, B, C, X(41368), X(53708)}}, {{A, B, C, X(44084), X(60428)}}
X(61209) = barycentric product X(i)*X(j) for these (i, j): {25, 61188}, {107, 13754}, {110, 403}, {112, 3580}, {113, 1304}, {162, 1725}, {186, 41512}, {249, 47236}, {250, 55121}, {1576, 44138}, {1783, 18609}, {1986, 476}, {2315, 823}, {3003, 648}, {4230, 52451}, {4235, 60498}, {10423, 12827}, {11557, 52998}, {12824, 935}, {12825, 22239}, {12826, 2766}, {12828, 691}, {14264, 4240}, {14590, 56403}, {14591, 57486}, {15329, 4}, {15459, 47405}, {16221, 58979}, {16237, 6}, {18020, 21731}, {23582, 686}, {23964, 6334}, {39170, 53176}, {39985, 7480}, {44084, 99}, {44770, 53568}, {46085, 53923}, {46587, 56683}, {52000, 925}, {52504, 61208}, {53785, 58071}
X(61209) = barycentric quotient X(i)/X(j) for these (i, j): {6, 15421}, {25, 15328}, {32, 61216}, {110, 57829}, {112, 2986}, {250, 18878}, {403, 850}, {648, 40832}, {686, 15526}, {1304, 40423}, {1576, 5504}, {1725, 14208}, {1986, 3268}, {2315, 24018}, {3003, 525}, {3199, 35361}, {3580, 3267}, {4240, 52552}, {6334, 36793}, {7480, 39988}, {12828, 35522}, {13754, 3265}, {14264, 34767}, {14560, 12028}, {15329, 69}, {16237, 76}, {18609, 15413}, {21731, 125}, {23347, 15454}, {23357, 43755}, {23582, 57932}, {23964, 687}, {32676, 36053}, {32713, 1300}, {32715, 10419}, {34397, 15470}, {34834, 45792}, {41512, 328}, {41937, 32708}, {44084, 523}, {44138, 44173}, {46587, 56577}, {47236, 338}, {47405, 41077}, {51821, 14380}, {52000, 6563}, {52604, 60035}, {55121, 339}, {56403, 14592}, {57655, 10420}, {60498, 14977}, {61188, 305}, {61206, 14910}, {61208, 52505}
X(61209) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {112, 14591, 2420}, {112, 1625, 61203}, {1625, 61204, 112}, {2420, 61207, 14591}

X(61210) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(4) AND CEVIAN-OF-X(80)

Barycentrics    a^2*(a-b)*(a-c)*(2*a-b-c)*(a+b-c)*(a-b+c) : :

X(61210) lies on these lines: {6, 41}, {100, 59109}, {101, 109}, {163, 35324}, {651, 4604}, {663, 2426}, {919, 14733}, {1023, 23703}, {1319, 2087}, {2195, 34068}, {2222, 58955}, {2284, 59149}, {2720, 59068}, {3204, 52411}, {3669, 23890}, {8652, 32693}, {8685, 28883}, {8687, 8701}, {8693, 58105}, {21859, 35342}, {23981, 32665}, {28864, 29055}, {29157, 59127}, {32656, 53288}, {32669, 35328}, {32674, 34080}, {46408, 51682}, {51406, 51422}

X(61210) = isogonal conjugate of X(60480)
X(61210) = trilinear pole of line {902, 1404}
X(61210) = perspector of circumconic {{A, B, C, X(59), X(109)}}
X(61210) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 60480}, {2, 23838}, {8, 1022}, {9, 6548}, {11, 3257}, {21, 4049}, {86, 61179}, {88, 522}, {100, 60578}, {106, 4391}, {244, 4582}, {312, 23345}, {314, 55263}, {333, 55244}, {514, 1320}, {521, 6336}, {644, 6549}, {646, 43922}, {650, 903}, {654, 57788}, {663, 20568}, {679, 1639}, {693, 2316}, {901, 4858}, {1111, 5548}, {1168, 3904}, {1318, 3762}, {1417, 52622}, {1797, 44426}, {2170, 4555}, {2226, 4768}, {2320, 23598}, {2403, 3680}, {3063, 57995}, {3239, 56049}, {3737, 4080}, {3960, 36590}, {4516, 4615}, {4530, 4618}, {4560, 4674}, {4622, 21044}, {4814, 40833}, {4895, 54974}, {5376, 21132}, {6332, 36125}, {8752, 35518}, {9268, 40166}, {9456, 35519}, {23352, 30608}, {23836, 52140}, {23893, 36887}, {32665, 34387}, {36058, 46110}, {40215, 52356}, {43728, 52031}
X(61210) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 60480}, {214, 4391}, {478, 6548}, {4370, 35519}, {8054, 60578}, {10001, 57995}, {20619, 46110}, {32664, 23838}, {35092, 34387}, {38979, 4858}, {39026, 4997}, {40600, 61179}, {40611, 4049}, {51402, 23978}, {52659, 3261}, {52871, 52622}, {52877, 3700}, {55055, 11}
X(61210) = X(i)-Ceva conjugate of X(j) for these {i, j}: {59, 61047}, {2720, 692}, {23703, 23344}, {32675, 4559}
X(61210) = X(i)-cross conjugate of X(j) for these {i, j}: {1635, 3285}, {1960, 1319}, {20972, 1252}, {22086, 44}, {61047, 59}
X(61210) = pole of line {663, 692} with respect to the circumcircle
X(61210) = pole of line {663, 20958} with respect to the Brocard inellipse
X(61210) = pole of line {16678, 23360} with respect to the Kiepert parabola
X(61210) = pole of line {333, 4560} with respect to the Stammler hyperbola
X(61210) = pole of line {6589, 13006} with respect to the Steiner inellipse
X(61210) = pole of line {1388, 2975} with respect to the Hutson-Moses hyperbola
X(61210) = pole of line {28660, 60480} with respect to the Wallace hyperbola
X(61210) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(101)}}, {{A, B, C, X(41), X(5549)}}, {{A, B, C, X(44), X(2183)}}, {{A, B, C, X(48), X(906)}}, {{A, B, C, X(56), X(109)}}, {{A, B, C, X(73), X(23067)}}, {{A, B, C, X(110), X(52924)}}, {{A, B, C, X(172), X(28864)}}, {{A, B, C, X(519), X(8679)}}, {{A, B, C, X(604), X(1415)}}, {{A, B, C, X(651), X(1405)}}, {{A, B, C, X(654), X(1635)}}, {{A, B, C, X(665), X(1960)}}, {{A, B, C, X(900), X(928)}}, {{A, B, C, X(902), X(919)}}, {{A, B, C, X(1193), X(8701)}}, {{A, B, C, X(1319), X(1458)}}, {{A, B, C, X(1400), X(4559)}}, {{A, B, C, X(1404), X(32675)}}, {{A, B, C, X(1468), X(8652)}}, {{A, B, C, X(1475), X(35326)}}, {{A, B, C, X(1639), X(22086)}}, {{A, B, C, X(2178), X(32653)}}, {{A, B, C, X(2251), X(9454)}}, {{A, B, C, X(2274), X(55243)}}, {{A, B, C, X(2275), X(28883)}}, {{A, B, C, X(2277), X(24004)}}, {{A, B, C, X(2347), X(5546)}}, {{A, B, C, X(2423), X(21786)}}, {{A, B, C, X(3285), X(7113)}}, {{A, B, C, X(3911), X(43039)}}, {{A, B, C, X(4169), X(4557)}}, {{A, B, C, X(7051), X(54020)}}, {{A, B, C, X(7460), X(37168)}}, {{A, B, C, X(8572), X(58089)}}, {{A, B, C, X(8607), X(8756)}}, {{A, B, C, X(8687), X(36075)}}, {{A, B, C, X(13738), X(46541)}}, {{A, B, C, X(19373), X(54022)}}, {{A, B, C, X(20470), X(52680)}}, {{A, B, C, X(21008), X(28856)}}, {{A, B, C, X(32693), X(36074)}}, {{A, B, C, X(34068), X(54325)}}, {{A, B, C, X(35365), X(39155)}}, {{A, B, C, X(42314), X(58109)}}
X(61210) = barycentric product X(i)*X(j) for these (i, j): {1, 23703}, {44, 651}, {59, 900}, {100, 1319}, {101, 3911}, {108, 5440}, {109, 519}, {110, 40663}, {214, 2222}, {664, 902}, {1023, 57}, {1145, 2720}, {1252, 30725}, {1262, 1639}, {1290, 41541}, {1308, 41553}, {1317, 901}, {1331, 1877}, {1402, 55243}, {1404, 190}, {1407, 30731}, {1412, 4169}, {1414, 21805}, {1415, 4358}, {1461, 2325}, {1635, 4564}, {1813, 8756}, {1960, 4998}, {2087, 31615}, {2099, 52924}, {2149, 3762}, {2251, 4554}, {2427, 40218}, {2429, 5435}, {2742, 41556}, {2743, 41554}, {3285, 4552}, {3689, 934}, {3943, 4565}, {4120, 52378}, {4528, 7339}, {4530, 4619}, {4551, 52680}, {4555, 61047}, {4572, 9459}, {4573, 52963}, {4819, 5545}, {4895, 7045}, {5298, 8701}, {12832, 6099}, {14027, 6551}, {14407, 4620}, {14418, 7128}, {14439, 36146}, {14628, 1983}, {14733, 6174}, {16704, 4559}, {17455, 655}, {17780, 56}, {18026, 23202}, {21859, 30576}, {22086, 46102}, {22356, 653}, {23067, 37168}, {23344, 7}, {23346, 52746}, {23832, 56642}, {23981, 36944}, {24004, 604}, {24027, 4768}, {29055, 4434}, {30572, 4570}, {31011, 36075}, {32641, 52659}, {32660, 46109}, {32674, 3977}, {32675, 51583}, {32714, 52978}, {36037, 53530}, {36059, 38462}, {36086, 53531}, {36668, 54020}, {36669, 54022}, {36913, 58955}, {36920, 4588}, {37790, 906}, {39771, 9268}, {46541, 73}, {51463, 53243}, {52377, 53535}, {53528, 765}, {53529, 677}, {53532, 7012}, {56939, 57118}, {61062, 6635}, {61171, 81}
X(61210) = barycentric quotient X(i)/X(j) for these (i, j): {6, 60480}, {31, 23838}, {44, 4391}, {56, 6548}, {59, 4555}, {101, 4997}, {109, 903}, {213, 61179}, {519, 35519}, {604, 1022}, {649, 60578}, {651, 20568}, {664, 57995}, {678, 4768}, {692, 1320}, {900, 34387}, {902, 522}, {1017, 1639}, {1023, 312}, {1252, 4582}, {1319, 693}, {1397, 23345}, {1400, 4049}, {1402, 55244}, {1404, 514}, {1405, 23598}, {1415, 88}, {1635, 4858}, {1639, 23978}, {1877, 46107}, {1960, 11}, {2087, 40166}, {2149, 3257}, {2222, 57788}, {2251, 650}, {2325, 52622}, {2429, 6557}, {3285, 4560}, {3689, 4397}, {3911, 3261}, {4169, 30713}, {4559, 4080}, {4895, 24026}, {5440, 35518}, {8661, 7336}, {8756, 46110}, {9459, 663}, {14407, 21044}, {14637, 52337}, {17455, 3904}, {17780, 3596}, {21805, 4086}, {22086, 26932}, {22356, 6332}, {23202, 521}, {23344, 8}, {23346, 36887}, {23703, 75}, {23990, 5548}, {24004, 28659}, {30572, 21207}, {30725, 23989}, {30731, 59761}, {32660, 1797}, {32674, 6336}, {32719, 1318}, {32739, 2316}, {40172, 52356}, {40663, 850}, {43924, 6549}, {46541, 44130}, {52378, 4615}, {52680, 18155}, {52963, 3700}, {52978, 15416}, {53528, 1111}, {53530, 36038}, {53532, 17880}, {55243, 40072}, {61047, 900}, {61062, 6550}, {61171, 321}
X(61210) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {101, 1415, 4559}, {101, 1983, 2427}, {1023, 23703, 61171}, {1415, 4559, 36075}

X(61211) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(4) AND CEVIAN-OF-X(83)

Barycentrics    a^2*(a-b)*(a+b)*(a-c)*(a+c)*(2*a^2+b^2+c^2) : :

X(61211) lies on these lines: {3, 34437}, {6, 3506}, {99, 7954}, {110, 351}, {112, 58102}, {163, 2284}, {206, 8266}, {338, 51430}, {524, 9407}, {648, 23347}, {691, 58120}, {827, 17997}, {2916, 22138}, {2930, 22143}, {3001, 42671}, {3014, 23583}, {4577, 17941}, {5013, 9876}, {5191, 34990}, {5201, 18374}, {6593, 20975}, {7473, 41677}, {7669, 46127}, {8623, 52958}, {10330, 61219}, {14559, 43083}, {14570, 53274}, {14966, 35324}, {15462, 53246}, {15526, 56565}, {20806, 33801}, {20987, 23163}, {39180, 43754}, {46512, 59739}, {52604, 52915}, {61207, 61218}

X(61211) = isogonal conjugate of X(31065)
X(61211) = trilinear pole of line {5007, 11205}
X(61211) = perspector of circumconic {{A, B, C, X(249), X(46970)}}
X(61211) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 31065}, {82, 31067}, {661, 10159}, {1109, 7953}, {1577, 3108}, {2643, 35137}, {8061, 40425}, {18070, 52554}, {23894, 31068}, {24006, 41435}
X(61211) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 31065}, {141, 31067}, {3589, 23285}, {6292, 850}, {15527, 338}, {36830, 10159}
X(61211) = X(i)-cross conjugate of X(j) for these {i, j}: {8664, 5007}
X(61211) = pole of line {110, 827} with respect to the circumcircle
X(61211) = pole of line {5113, 20976} with respect to the Brocard inellipse
X(61211) = pole of line {3, 2916} with respect to the Kiepert parabola
X(61211) = pole of line {523, 2528} with respect to the Stammler hyperbola
X(61211) = pole of line {850, 7950} with respect to the Wallace hyperbola
X(61211) = intersection, other than A, B, C, of circumconics {{A, B, C, X(110), X(10330)}}, {{A, B, C, X(351), X(8664)}}, {{A, B, C, X(428), X(15329)}}, {{A, B, C, X(526), X(7927)}}, {{A, B, C, X(684), X(39180)}}, {{A, B, C, X(827), X(19609)}}, {{A, B, C, X(1576), X(7954)}}, {{A, B, C, X(2421), X(3589)}}, {{A, B, C, X(4558), X(57678)}}, {{A, B, C, X(5007), X(5467)}}, {{A, B, C, X(6292), X(52630)}}, {{A, B, C, X(42744), X(48101)}}, {{A, B, C, X(44091), X(61213)}}
X(61211) = barycentric product X(i)*X(j) for these (i, j): {101, 17200}, {110, 3589}, {112, 7767}, {249, 7927}, {251, 61219}, {428, 4558}, {1576, 39998}, {1634, 59180}, {4030, 4565}, {4570, 48101}, {4590, 8664}, {5007, 99}, {5546, 7198}, {6292, 827}, {10330, 6}, {11205, 4577}, {16707, 692}, {17193, 4628}, {17457, 4599}, {17469, 662}, {18062, 31}, {20898, 34072}, {21802, 52935}, {22078, 42396}, {22352, 648}, {28486, 41663}, {32661, 44142}, {39784, 7954}, {41623, 53885}, {42554, 4630}, {44091, 4563}
X(61211) = barycentric quotient X(i)/X(j) for these (i, j): {6, 31065}, {39, 31067}, {110, 10159}, {249, 35137}, {428, 14618}, {827, 40425}, {1576, 3108}, {3589, 850}, {4558, 57852}, {4630, 57421}, {5007, 523}, {5467, 31068}, {6292, 23285}, {7767, 3267}, {7927, 338}, {8664, 115}, {10330, 76}, {11205, 826}, {16707, 40495}, {17200, 3261}, {17469, 1577}, {18062, 561}, {21802, 4036}, {22078, 2525}, {22352, 525}, {23357, 7953}, {32661, 41435}, {39998, 44173}, {44091, 2501}, {48101, 21207}, {59180, 52618}, {61219, 8024}
X(61211) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 1576, 1634}, {110, 35357, 5467}, {1634, 35357, 1576}, {41880, 41881, 56980}, {52605, 52606, 2421}

X(61212) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(4) AND CEVIAN-OF-X(84)

Barycentrics    a^2*(a-b)*(a-c)*(a+b-c)*(a-b+c)*(-(a^2*(b-c)^2)+a^3*(b+c)-a*(b-c)^2*(b+c)+(b^2-c^2)^2) : :

X(61212) lies on these lines: {56, 2179}, {101, 109}, {112, 2720}, {219, 13539}, {221, 7124}, {222, 59813}, {2272, 51660}, {2443, 32674}, {4574, 23703}, {8059, 58957}, {8608, 51649}, {12016, 38345}, {21770, 52411}, {21859, 35338}, {22163, 60689}, {32660, 53290}, {38344, 53292}, {40518, 52610}, {53325, 61202}, {61161, 61228}, {61227, 61237}

X(61212) = trilinear pole of line {23204, 40958}
X(61212) = X(i)-isoconjugate-of-X(j) for these {i, j}: {521, 40444}, {522, 40399}, {1167, 4391}, {1897, 40527}, {4560, 56259}
X(61212) = X(i)-Dao conjugate of X(j) for these {i, j}: {1210, 15416}, {6260, 4391}, {34467, 40527}
X(61212) = X(i)-Ceva conjugate of X(j) for these {i, j}: {7128, 56}, {61227, 53288}
X(61212) = pole of line {692, 32652} with respect to the circumcircle
X(61212) = pole of line {21362, 36059} with respect to the MacBeath circumconic
X(61212) = pole of line {2975, 24558} with respect to the Hutson-Moses hyperbola
X(61212) = intersection, other than A, B, C, of circumconics {{A, B, C, X(101), X(53288)}}, {{A, B, C, X(112), X(1108)}}, {{A, B, C, X(906), X(32714)}}, {{A, B, C, X(2283), X(37566)}}, {{A, B, C, X(2720), X(23067)}}, {{A, B, C, X(4559), X(32702)}}, {{A, B, C, X(7252), X(52307)}}
X(61212) = barycentric product X(i)*X(j) for these (i, j): {1, 61227}, {56, 61185}, {57, 61237}, {100, 37566}, {109, 1210}, {110, 57285}, {1020, 40979}, {1071, 108}, {1108, 651}, {1415, 17862}, {1532, 2720}, {1864, 934}, {6260, 8059}, {18026, 23204}, {18239, 30239}, {21933, 4565}, {26700, 41562}, {40628, 7128}, {40958, 664}, {41561, 53622}, {52571, 57118}, {53288, 7}
X(61212) = barycentric quotient X(i)/X(j) for these (i, j): {109, 40424}, {1071, 35518}, {1108, 4391}, {1210, 35519}, {1415, 40399}, {1864, 4397}, {3611, 52355}, {22383, 40527}, {23204, 521}, {32674, 40444}, {37566, 693}, {40958, 522}, {53288, 8}, {57285, 850}, {61185, 3596}, {61227, 75}, {61237, 312}
X(61212) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {109, 61197, 4559}

X(61213) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(4) AND CEVIAN-OF-X(98)

Barycentrics    a^2*(a-b)*(a+b)*(a-c)*(a+c)*(2*a^4+(b^2-c^2)^2-a^2*(b^2+c^2)) : :

X(61213) lies on these lines: {6, 25}, {110, 351}, {156, 20968}, {230, 51820}, {249, 11634}, {399, 51240}, {512, 2420}, {523, 34211}, {878, 2715}, {1503, 35912}, {1511, 47426}, {1614, 15257}, {1625, 14574}, {1976, 53264}, {1992, 46992}, {2086, 14567}, {3292, 33988}, {3455, 14901}, {3566, 4235}, {4226, 38359}, {4230, 32696}, {4630, 32737}, {5468, 10190}, {5968, 35265}, {6130, 60506}, {6800, 46127}, {7418, 14355}, {9178, 9206}, {11653, 53246}, {14591, 46592}, {14966, 43942}, {14999, 53274}, {17938, 32716}, {19165, 52170}, {19627, 21177}, {22146, 39857}, {26714, 59007}, {32661, 53273}, {32734, 52604}, {32761, 56957}, {33803, 52630}, {34761, 53266}, {34782, 43278}, {35191, 58979}, {39072, 47406}, {40820, 46777}, {57655, 61209}, {59115, 59116}

X(61213) = trilinear pole of line {1692, 51335}
X(61213) = perspector of circumconic {{A, B, C, X(112), X(249)}}
X(61213) = X(i)-isoconjugate-of-X(j) for these {i, j}: {63, 60338}, {75, 35364}, {125, 36105}, {523, 8773}, {656, 35142}, {661, 8781}, {850, 36051}, {1109, 10425}, {1577, 2987}, {3563, 14208}, {4077, 56109}, {20902, 32697}, {20948, 32654}, {24006, 43705}
X(61213) = X(i)-Dao conjugate of X(j) for these {i, j}: {114, 850}, {206, 35364}, {3162, 60338}, {35067, 3267}, {36830, 8781}, {39001, 125}, {39069, 1577}, {39072, 523}, {40596, 35142}, {41181, 36793}, {55152, 338}
X(61213) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4226, 56389}, {32696, 1576}, {57742, 6}
X(61213) = X(i)-cross conjugate of X(j) for these {i, j}: {42663, 1692}
X(61213) = pole of line {110, 647} with respect to the circumcircle
X(61213) = pole of line {850, 2970} with respect to the polar circle
X(61213) = pole of line {647, 20976} with respect to the Brocard inellipse
X(61213) = pole of line {427, 14052} with respect to the Kiepert hyperbola
X(61213) = pole of line {3, 114} with respect to the Kiepert parabola
X(61213) = pole of line {8673, 32661} with respect to the MacBeath circumconic
X(61213) = pole of line {512, 12076} with respect to the orthic inconic
X(61213) = pole of line {69, 523} with respect to the Stammler hyperbola
X(61213) = pole of line {2485, 34990} with respect to the Steiner inellipse
X(61213) = pole of line {305, 850} with respect to the Wallace hyperbola
X(61213) = pole of line {339, 34953} with respect to the dual conic of polar circle
X(61213) = pole of line {339, 23105} with respect to the dual conic of Wallace hyperbola
X(61213) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(4558)}}, {{A, B, C, X(25), X(110)}}, {{A, B, C, X(51), X(23181)}}, {{A, B, C, X(112), X(59229)}}, {{A, B, C, X(230), X(232)}}, {{A, B, C, X(351), X(42663)}}, {{A, B, C, X(460), X(15329)}}, {{A, B, C, X(512), X(34291)}}, {{A, B, C, X(526), X(9178)}}, {{A, B, C, X(684), X(878)}}, {{A, B, C, X(1474), X(4556)}}, {{A, B, C, X(1495), X(52144)}}, {{A, B, C, X(1576), X(1974)}}, {{A, B, C, X(1624), X(44079)}}, {{A, B, C, X(1692), X(5467)}}, {{A, B, C, X(1843), X(32737)}}, {{A, B, C, X(2299), X(4636)}}, {{A, B, C, X(2393), X(3564)}}, {{A, B, C, X(2422), X(53263)}}, {{A, B, C, X(6132), X(38359)}}, {{A, B, C, X(6233), X(54965)}}, {{A, B, C, X(8541), X(9145)}}, {{A, B, C, X(8739), X(9207)}}, {{A, B, C, X(8740), X(9206)}}, {{A, B, C, X(8772), X(44113)}}, {{A, B, C, X(10311), X(59007)}}, {{A, B, C, X(10641), X(52606)}}, {{A, B, C, X(10642), X(52605)}}, {{A, B, C, X(11405), X(34574)}}, {{A, B, C, X(14576), X(52604)}}, {{A, B, C, X(19118), X(32713)}}, {{A, B, C, X(32696), X(44099)}}, {{A, B, C, X(32716), X(44089)}}, {{A, B, C, X(32729), X(34397)}}, {{A, B, C, X(34212), X(55267)}}, {{A, B, C, X(35188), X(56922)}}, {{A, B, C, X(42742), X(51431)}}, {{A, B, C, X(42743), X(51335)}}, {{A, B, C, X(44092), X(53280)}}, {{A, B, C, X(44097), X(57119)}}, {{A, B, C, X(44125), X(53384)}}, {{A, B, C, X(44126), X(53385)}}, {{A, B, C, X(47328), X(50947)}}
X(61213) = barycentric product X(i)*X(j) for these (i, j): {4, 56389}, {110, 230}, {112, 3564}, {114, 2715}, {163, 1733}, {187, 52035}, {249, 55122}, {511, 60504}, {662, 8772}, {1576, 51481}, {1692, 99}, {2030, 54965}, {2420, 36875}, {2421, 51820}, {2966, 51335}, {4226, 6}, {4558, 460}, {5477, 691}, {5994, 6783}, {5995, 6782}, {12829, 805}, {12830, 46970}, {14265, 14966}, {17462, 36084}, {32661, 44145}, {39072, 44767}, {42663, 4590}, {44099, 4563}, {44769, 51431}, {47406, 685}, {47734, 56980}, {52144, 648}, {52450, 5467}, {53783, 58070}, {55267, 57742}
X(61213) = barycentric quotient X(i)/X(j) for these (i, j): {25, 60338}, {32, 35364}, {110, 8781}, {112, 35142}, {163, 8773}, {230, 850}, {460, 14618}, {1576, 2987}, {1692, 523}, {1733, 20948}, {2420, 36891}, {2715, 40428}, {3564, 3267}, {4226, 76}, {4558, 57872}, {5477, 35522}, {8772, 1577}, {12829, 14295}, {14574, 32654}, {14966, 52091}, {23357, 10425}, {32661, 43705}, {42663, 115}, {44099, 2501}, {47406, 6333}, {47734, 56981}, {51335, 2799}, {51431, 41079}, {51481, 44173}, {51820, 43665}, {52035, 18023}, {52144, 525}, {52450, 52632}, {55122, 338}, {56389, 69}, {57655, 32697}, {57742, 55266}, {60504, 290}, {61206, 3563}
X(61213) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 56980, 2421}, {184, 44127, 6}, {2421, 56980, 5467}, {5467, 5502, 34291}, {41880, 41881, 1576}

X(61214) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(4) AND CEVIAN-OF-X(100)

Barycentrics    a^2*(a-b-c)*(b-c)*((a^2-b^2)^2-(a-b)^2*(a+b)*c-(a^2+b^2)*c^2+(a+b)*c^3)*(a^4-a^3*b+(b-c)^2*c*(b+c)+a*b*(b^2+c^2)-a^2*(b^2-b*c+2*c^2)) : :

X(61214) lies on these lines: {6, 3657}, {48, 649}, {212, 663}, {219, 650}, {222, 3669}, {654, 2423}, {913, 32677}, {915, 32726}, {919, 6099}, {1812, 4560}, {1814, 2990}, {2193, 7252}, {2427, 32675}, {3063, 60339}, {32698, 32702}, {36054, 56269}, {46393, 52431}

X(61214) = trilinear pole of line {1946, 3271}
X(61214) = perspector of circumconic {{A, B, C, X(915), X(15381)}}
X(61214) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 61231}, {7, 61239}, {57, 56881}, {92, 56410}, {108, 914}, {109, 48380}, {119, 37136}, {190, 18838}, {226, 3658}, {651, 1737}, {653, 912}, {655, 11570}, {664, 8609}, {1025, 52456}, {2252, 18026}, {3257, 12832}, {4564, 55126}, {6335, 51649}, {12831, 37139}, {14266, 24029}, {39294, 42769}
X(61214) = X(i)-Dao conjugate of X(j) for these {i, j}: {11, 48380}, {5452, 56881}, {22391, 56410}, {32664, 61231}, {38983, 914}, {38991, 1737}, {39025, 8609}, {55053, 18838}, {55055, 12832}
X(61214) = X(i)-Ceva conjugate of X(j) for these {i, j}: {32698, 32655}
X(61214) = X(i)-cross conjugate of X(j) for these {i, j}: {52307, 650}
X(61214) = pole of line {2361, 34858} with respect to the circumcircle
X(61214) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(48)}}, {{A, B, C, X(11), X(35365)}}, {{A, B, C, X(110), X(885)}}, {{A, B, C, X(649), X(650)}}, {{A, B, C, X(652), X(46389)}}, {{A, B, C, X(654), X(2427)}}, {{A, B, C, X(2623), X(3700)}}, {{A, B, C, X(4559), X(55255)}}, {{A, B, C, X(23189), X(23289)}}, {{A, B, C, X(23838), X(27780)}}, {{A, B, C, X(43728), X(53306)}}
X(61214) = barycentric product X(i)*X(j) for these (i, j): {11, 6099}, {21, 3657}, {521, 915}, {1946, 46133}, {2990, 650}, {6332, 913}, {15381, 2804}, {26932, 32698}, {32655, 4391}, {36052, 522}, {36106, 7004}, {37203, 652}, {39173, 43728}, {45393, 513}, {53549, 57753}, {61043, 80}
X(61214) = barycentric quotient X(i)/X(j) for these (i, j): {31, 61231}, {41, 61239}, {55, 56881}, {184, 56410}, {650, 48380}, {652, 914}, {663, 1737}, {667, 18838}, {884, 52456}, {913, 653}, {915, 18026}, {1946, 912}, {1960, 12832}, {2194, 3658}, {2990, 4554}, {3063, 8609}, {3271, 55126}, {3657, 1441}, {6099, 4998}, {6139, 12831}, {8648, 11570}, {15381, 54953}, {32655, 651}, {32698, 46102}, {36052, 664}, {37203, 46404}, {45393, 668}, {53549, 119}, {61043, 320}

X(61215) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(4) AND CEVIAN-OF-X(107)

Barycentrics    a^2*(b-c)*(b+c)*(a^2-b^2-c^2)*((a^2-b^2)^2+(a^2+b^2)*c^2-2*c^4)*(a^4-2*b^4+b^2*c^2+c^4+a^2*(b^2-2*c^2))*(3*a^4-(b^2-c^2)^2-2*a^2*(b^2+c^2)) : :

X(61215) lies on these lines: {6, 647}, {154, 42658}, {1073, 52584}, {1249, 6587}, {1304, 32687}, {1636, 2430}, {2394, 56346}, {2435, 34147}, {5502, 32640}, {8749, 46425}, {15292, 56363}, {15451, 53330}, {15905, 58796}, {20580, 37669}, {34767, 42287}, {40352, 42665}

X(61215) = perspector of circumconic {{A, B, C, X(74), X(10152)}}
X(61215) = X(i)-isoconjugate-of-X(j) for these {i, j}: {64, 24001}, {253, 56829}, {823, 11589}, {1301, 14206}, {1784, 46639}, {2173, 53639}, {2184, 4240}, {2631, 44181}, {23347, 57921}, {52954, 56235}
X(61215) = X(i)-Dao conjugate of X(j) for these {i, j}: {122, 46106}, {36896, 53639}, {39020, 3260}, {45248, 2407}
X(61215) = X(i)-Ceva conjugate of X(j) for these {i, j}: {32695, 18877}
X(61215) = pole of line {1495, 32715} with respect to the circumcircle
X(61215) = pole of line {12096, 13754} with respect to the MacBeath circumconic
X(61215) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(154)}}, {{A, B, C, X(20), X(44889)}}, {{A, B, C, X(647), X(2430)}}, {{A, B, C, X(8057), X(8675)}}, {{A, B, C, X(14345), X(52743)}}, {{A, B, C, X(18877), X(51964)}}, {{A, B, C, X(34212), X(55269)}}, {{A, B, C, X(52584), X(57201)}}
X(61215) = barycentric product X(i)*X(j) for these (i, j): {74, 8057}, {122, 1304}, {154, 34767}, {1494, 42658}, {1562, 44769}, {2433, 37669}, {10152, 520}, {14345, 40384}, {14380, 20}, {14919, 6587}, {15291, 525}, {15404, 55127}, {15459, 47409}, {15905, 2394}, {16080, 58796}, {17898, 35200}, {18808, 35602}, {20580, 8749}, {58352, 59145}
X(61215) = barycentric quotient X(i)/X(j) for these (i, j): {74, 53639}, {154, 4240}, {610, 24001}, {1304, 44181}, {1562, 41079}, {2394, 52581}, {2433, 459}, {6525, 58071}, {6587, 46106}, {8057, 3260}, {9409, 38956}, {10152, 6528}, {14345, 36789}, {14380, 253}, {14919, 44326}, {15291, 648}, {15905, 2407}, {18877, 46639}, {32715, 15384}, {34767, 41530}, {39201, 11589}, {40352, 1301}, {42658, 30}, {44705, 52661}, {47409, 41077}, {58352, 23097}, {58796, 11064}

X(61216) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(4) AND CEVIAN-OF-X(110)

Barycentrics    a^2*(b-c)*(b+c)*(a^2-b^2-c^2)*(a^6-a^4*(2*b^2+c^2)+(-(b^2*c)+c^3)^2+a^2*(b^4+2*b^2*c^2-c^4))*(a^6-a^4*(b^2+2*c^2)+(b^3-b*c^2)^2+a^2*(-b^4+2*b^2*c^2+c^4)) : :

X(61216) lies on these lines: {6, 2501}, {184, 512}, {287, 2986}, {394, 525}, {526, 686}, {577, 647}, {878, 42665}, {1300, 26717}, {1409, 57185}, {1640, 60495}, {2436, 53178}, {2623, 14533}, {2715, 10420}, {3049, 14401}, {3050, 15470}, {3990, 55232}, {4055, 55230}, {5504, 10097}, {9033, 14582}, {13198, 44823}, {18878, 53202}, {32320, 55549}, {32695, 32708}, {35912, 51456}, {38872, 47230}, {45801, 55228}, {51990, 58900}

X(61216) = isogonal conjugate of X(16237)
X(61216) = trilinear pole of line {20975, 34982}
X(61216) = perspector of circumconic {{A, B, C, X(1300), X(5504)}}
X(61216) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 16237}, {19, 61188}, {75, 61209}, {92, 15329}, {162, 3580}, {163, 44138}, {403, 662}, {648, 1725}, {686, 23999}, {799, 44084}, {811, 3003}, {823, 13754}, {1897, 18609}, {1986, 32680}, {2315, 6528}, {6334, 24000}, {12827, 36095}, {12828, 36085}, {14264, 24001}, {21731, 46254}, {24041, 47236}, {34834, 36129}, {41512, 52414}
X(61216) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 16237}, {6, 61188}, {115, 44138}, {125, 3580}, {206, 61209}, {1084, 403}, {3005, 47236}, {17423, 3003}, {22391, 15329}, {34467, 18609}, {38988, 12828}, {38996, 44084}, {55066, 1725}
X(61216) = X(i)-Ceva conjugate of X(j) for these {i, j}: {32708, 14910}, {43755, 5504}
X(61216) = X(i)-cross conjugate of X(j) for these {i, j}: {1636, 647}
X(61216) = pole of line {50, 40352} with respect to the circumcircle
X(61216) = pole of line {3580, 44138} with respect to the polar circle
X(61216) = pole of line {265, 2072} with respect to the MacBeath circumconic
X(61216) = pole of line {30, 974} with respect to the orthic inconic
X(61216) = pole of line {16237, 61188} with respect to the Stammler hyperbola
X(61216) = pole of line {2071, 51456} with respect to the Steiner circumellipse
X(61216) = pole of line {10257, 16310} with respect to the Steiner inellipse
X(61216) = pole of line {9826, 44665} with respect to the dual conic of DeLongchamps circle
X(61216) = pole of line {6334, 47236} with respect to the dual conic of Wallace hyperbola
X(61216) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(9161)}}, {{A, B, C, X(6), X(184)}}, {{A, B, C, X(74), X(35912)}}, {{A, B, C, X(110), X(879)}}, {{A, B, C, X(112), X(53330)}}, {{A, B, C, X(125), X(35364)}}, {{A, B, C, X(512), X(525)}}, {{A, B, C, X(526), X(9033)}}, {{A, B, C, X(686), X(1636)}}, {{A, B, C, X(1637), X(46425)}}, {{A, B, C, X(1640), X(38356)}}, {{A, B, C, X(2435), X(60352)}}, {{A, B, C, X(2436), X(57136)}}, {{A, B, C, X(3569), X(42665)}}, {{A, B, C, X(9409), X(14401)}}, {{A, B, C, X(14910), X(51965)}}, {{A, B, C, X(14977), X(14998)}}, {{A, B, C, X(30451), X(32320)}}, {{A, B, C, X(34767), X(35909)}}, {{A, B, C, X(35901), X(44127)}}, {{A, B, C, X(43083), X(43709)}}
X(61216) = barycentric product X(i)*X(j) for these (i, j): {115, 43755}, {512, 57829}, {523, 5504}, {1300, 520}, {2632, 36114}, {2986, 647}, {3049, 40832}, {3269, 687}, {10419, 9033}, {10420, 125}, {12028, 526}, {14220, 39986}, {14380, 15454}, {14592, 52557}, {14910, 525}, {15328, 3}, {15421, 6}, {15470, 265}, {15526, 32708}, {18878, 20975}, {23286, 60035}, {35361, 97}, {35373, 38401}, {35909, 51456}, {36053, 656}, {38936, 43083}, {40388, 41077}, {40423, 9409}, {43701, 51895}, {43709, 53788}
X(61216) = barycentric quotient X(i)/X(j) for these (i, j): {3, 61188}, {6, 16237}, {32, 61209}, {184, 15329}, {351, 12828}, {512, 403}, {523, 44138}, {647, 3580}, {669, 44084}, {810, 1725}, {878, 52451}, {1300, 6528}, {2986, 6331}, {3049, 3003}, {3124, 47236}, {3269, 6334}, {5504, 99}, {9409, 113}, {10419, 16077}, {10420, 18020}, {12028, 35139}, {14270, 1986}, {14582, 57486}, {14910, 648}, {15328, 264}, {15421, 76}, {15470, 340}, {18879, 55270}, {20975, 55121}, {22383, 18609}, {32708, 23582}, {34952, 52000}, {35361, 324}, {36053, 811}, {36114, 23999}, {39201, 13754}, {40388, 15459}, {42659, 12824}, {42665, 12827}, {43755, 4590}, {52153, 41512}, {52505, 55227}, {52557, 14590}, {57829, 670}

X(61217) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(5) AND CEVIAN-OF-X(20)

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^4-(b^2-c^2)^2)^2*(2*a^4+(b^2-c^2)^2-3*a^2*(b^2+c^2)) : :

X(61217) lies on these lines: {107, 112}, {187, 52661}, {393, 14579}, {1562, 52057}, {1625, 4240}, {2052, 10986}, {2917, 41361}, {2934, 41766}, {4235, 6528}, {6525, 56308}, {13509, 40664}, {14586, 16813}, {32661, 35360}, {35311, 35318}, {38605, 47409}, {46151, 61208}

X(61217) = trilinear pole of line {6748, 13366}
X(61217) = X(i)-isoconjugate-of-X(j) for these {i, j}: {63, 39180}, {255, 39183}, {656, 31626}, {822, 40410}, {1173, 24018}, {33513, 37754}, {39181, 44706}
X(61217) = X(i)-vertex conjugate of X(j) for these {i, j}: {52604, 61193}
X(61217) = X(i)-Dao conjugate of X(j) for these {i, j}: {140, 60597}, {233, 3265}, {1493, 52613}, {3162, 39180}, {6523, 39183}, {11792, 15526}, {33549, 525}, {40596, 31626}
X(61217) = X(i)-cross conjugate of X(j) for these {i, j}: {55280, 6748}
X(61217) = pole of line {52604, 61193} with respect to the circumcircle
X(61217) = pole of line {132, 138} with respect to the orthoptic circle of the Steiner inellipse
X(61217) = pole of line {15526, 39019} with respect to the polar circle
X(61217) = pole of line {11206, 35226} with respect to the Kiepert parabola
X(61217) = pole of line {41361, 57811} with respect to the dual conic of Jerabek hyperbola
X(61217) = intersection, other than A, B, C, of circumconics {{A, B, C, X(107), X(35311)}}, {{A, B, C, X(112), X(14579)}}, {{A, B, C, X(140), X(2409)}}, {{A, B, C, X(1637), X(55280)}}, {{A, B, C, X(14586), X(61194)}}, {{A, B, C, X(16813), X(35318)}}, {{A, B, C, X(35308), X(52607)}}
X(61217) = barycentric product X(i)*X(j) for these (i, j): {107, 140}, {110, 44732}, {112, 40684}, {275, 35318}, {648, 6748}, {1232, 32713}, {2052, 35324}, {13366, 6528}, {14978, 933}, {15352, 22052}, {16813, 233}, {17438, 823}, {18831, 53386}, {20879, 24019}, {21012, 52919}, {23582, 55280}, {32078, 52779}, {35311, 4}, {59183, 61193}
X(61217) = barycentric quotient X(i)/X(j) for these (i, j): {25, 39180}, {107, 40410}, {112, 31626}, {140, 3265}, {233, 60597}, {393, 39183}, {1232, 52617}, {6529, 39284}, {6748, 525}, {8882, 39181}, {13366, 520}, {16813, 31617}, {17168, 30805}, {17438, 24018}, {21103, 17216}, {22052, 52613}, {23582, 55279}, {32230, 33513}, {32713, 1173}, {35311, 69}, {35318, 343}, {35324, 394}, {40684, 3267}, {44732, 850}, {53386, 6368}, {55280, 15526}, {59183, 15414}, {61193, 31610}
X(61217) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {107, 112, 61193}, {35318, 35324, 35311}

X(61218) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(6) AND CEVIAN-OF-X(66)

Barycentrics    a^4*(a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(b^2+c^2) : :

X(61218) lies on these lines: {3, 36879}, {32, 3455}, {99, 112}, {577, 9475}, {1576, 2491}, {1634, 35319}, {1843, 41331}, {1968, 12143}, {1974, 9468}, {2489, 52604}, {5063, 17409}, {11405, 34097}, {16813, 20031}, {27369, 41272}, {32676, 34067}, {32713, 34859}, {33875, 44102}, {37893, 46242}, {41328, 56921}, {61207, 61211}

X(61218) = trilinear pole of line {3051, 14820}
X(61218) = perspector of circumconic {{A, B, C, X(18020), X(57655)}}
X(61218) = X(i)-isoconjugate-of-X(j) for these {i, j}: {63, 52618}, {69, 18070}, {75, 4580}, {82, 3267}, {83, 14208}, {125, 4593}, {304, 58784}, {305, 55240}, {308, 656}, {339, 4599}, {525, 3112}, {647, 18833}, {689, 3708}, {810, 40016}, {850, 34055}, {905, 56251}, {1176, 20948}, {1577, 1799}, {1969, 58353}, {4025, 56186}, {4577, 20902}, {10566, 20336}, {15413, 18082}, {17879, 42396}, {18097, 35518}, {18105, 40364}, {18108, 40071}, {18695, 39182}, {20975, 37204}, {24018, 46104}, {34294, 55202}
X(61218) = X(i)-Dao conjugate of X(j) for these {i, j}: {141, 3267}, {206, 4580}, {3124, 339}, {3162, 52618}, {34452, 525}, {39052, 18833}, {39062, 40016}, {40596, 308}, {40938, 44173}, {52042, 2525}, {53983, 23962}, {55050, 125}, {55070, 127}
X(61218) = X(i)-Ceva conjugate of X(j) for these {i, j}: {112, 35325}, {250, 1974}, {15388, 184}
X(61218) = X(i)-cross conjugate of X(j) for these {i, j}: {688, 1843}, {3005, 32}
X(61218) = pole of line {35325, 53273} with respect to the circumcircle
X(61218) = pole of line {115, 23962} with respect to the polar circle
X(61218) = pole of line {69, 15270} with respect to the Kiepert parabola
X(61218) = pole of line {647, 3267} with respect to the Stammler hyperbola
X(61218) = intersection, other than A, B, C, of circumconics {{A, B, C, X(32), X(52630)}}, {{A, B, C, X(99), X(1576)}}, {{A, B, C, X(648), X(35325)}}, {{A, B, C, X(688), X(2491)}}, {{A, B, C, X(809), X(46161)}}, {{A, B, C, X(877), X(1843)}}, {{A, B, C, X(2407), X(3051)}}, {{A, B, C, X(3005), X(20975)}}, {{A, B, C, X(4235), X(27369)}}, {{A, B, C, X(4576), X(4630)}}, {{A, B, C, X(4611), X(14574)}}, {{A, B, C, X(14570), X(35319)}}, {{A, B, C, X(14966), X(41331)}}, {{A, B, C, X(16813), X(34859)}}
X(61218) = barycentric product X(i)*X(j) for these (i, j): {32, 41676}, {107, 20775}, {110, 1843}, {112, 39}, {141, 61206}, {162, 1964}, {163, 17442}, {184, 46151}, {250, 3005}, {1235, 14574}, {1289, 23208}, {1474, 46148}, {1576, 427}, {1634, 25}, {1923, 811}, {1974, 4576}, {2194, 46152}, {2203, 4553}, {2299, 46153}, {2445, 46164}, {2525, 41937}, {3051, 648}, {4230, 51869}, {14586, 27371}, {16030, 52604}, {17171, 32739}, {17187, 8750}, {18020, 688}, {18831, 27374}, {23347, 46147}, {24019, 4020}, {27369, 99}, {27376, 32661}, {32676, 38}, {32713, 3917}, {32715, 51360}, {34397, 46155}, {35319, 8882}, {35325, 6}, {35362, 58306}, {36827, 44102}, {41272, 4235}, {41331, 6331}, {42396, 59994}, {44089, 46161}, {44123, 46167}, {44124, 46166}, {46154, 61207}, {50521, 5379}, {57655, 826}
X(61218) = barycentric quotient X(i)/X(j) for these (i, j): {25, 52618}, {32, 4580}, {39, 3267}, {112, 308}, {162, 18833}, {250, 689}, {427, 44173}, {648, 40016}, {688, 125}, {933, 41488}, {1576, 1799}, {1634, 305}, {1843, 850}, {1923, 656}, {1964, 14208}, {1973, 18070}, {1974, 58784}, {2084, 20902}, {3005, 339}, {3051, 525}, {3917, 52617}, {4576, 40050}, {8750, 56251}, {9494, 20975}, {14574, 1176}, {14575, 58353}, {17442, 20948}, {18020, 42371}, {20775, 3265}, {23208, 57069}, {27369, 523}, {27371, 15415}, {27374, 6368}, {32676, 3112}, {32713, 46104}, {35319, 28706}, {35325, 76}, {41267, 4064}, {41272, 14977}, {41331, 647}, {41676, 1502}, {41937, 42396}, {44162, 18105}, {46148, 40071}, {46151, 18022}, {56915, 24284}, {57204, 34294}, {57655, 4577}, {59994, 2525}, {61206, 83}

X(61219) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(6) AND CEVIAN-OF-X(141)

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(b^2+c^2)*(2*a^2+b^2+c^2) : :

X(61219) lies on these lines: {39, 597}, {99, 827}, {141, 15449}, {1634, 4576}, {2871, 3313}, {4360, 21295}, {4590, 31067}, {5976, 7668}, {6148, 8024}, {6390, 60463}, {7745, 28674}, {7750, 28677}, {7823, 28691}, {10330, 61211}, {22078, 42554}, {41328, 44180}, {41331, 51322}

X(61219) = trilinear pole of line {6292, 11205}
X(61219) = X(i)-isoconjugate-of-X(j) for these {i, j}: {661, 57421}, {798, 40425}, {3108, 55240}, {31065, 46289}
X(61219) = X(i)-Dao conjugate of X(j) for these {i, j}: {39, 31065}, {3589, 523}, {6292, 58784}, {6665, 31067}, {15527, 34294}, {31998, 40425}, {36830, 57421}, {39691, 115}
X(61219) = X(i)-Ceva conjugate of X(j) for these {i, j}: {99, 10330}, {4590, 141}
X(61219) = X(i)-cross conjugate of X(j) for these {i, j}: {8664, 39}
X(61219) = pole of line {625, 52906} with respect to the Kiepert hyperbola
X(61219) = pole of line {39, 141} with respect to the Kiepert parabola
X(61219) = pole of line {3005, 18105} with respect to the Stammler hyperbola
X(61219) = pole of line {826, 14318} with respect to the Wallace hyperbola
X(61219) = intersection, other than A, B, C, of circumconics {{A, B, C, X(141), X(35137)}}, {{A, B, C, X(827), X(19609)}}, {{A, B, C, X(1084), X(8664)}}, {{A, B, C, X(4576), X(4577)}}, {{A, B, C, X(6292), X(40517)}}, {{A, B, C, X(9479), X(15449)}}, {{A, B, C, X(14424), X(22105)}}
X(61219) = barycentric product X(i)*X(j) for these (i, j): {110, 42554}, {1634, 39998}, {3589, 4576}, {4558, 52787}, {4563, 46026}, {6292, 99}, {10330, 141}, {11205, 670}, {16707, 4553}, {17193, 190}, {17200, 4568}, {17457, 799}, {17469, 55239}, {18062, 38}, {20898, 662}, {21038, 4610}, {21126, 4600}, {21817, 4623}, {22078, 6331}, {41676, 7767}, {61211, 8024}
X(61219) = barycentric quotient X(i)/X(j) for these (i, j): {99, 40425}, {110, 57421}, {141, 31065}, {1634, 3108}, {3589, 58784}, {4576, 10159}, {5007, 18105}, {6292, 523}, {7767, 4580}, {7794, 31067}, {7927, 34294}, {8664, 51906}, {10330, 83}, {11205, 512}, {17193, 514}, {17200, 10566}, {17457, 661}, {17469, 55240}, {18062, 3112}, {20898, 1577}, {21038, 4024}, {21126, 3120}, {21817, 4705}, {22078, 647}, {39998, 52618}, {42554, 850}, {46026, 2501}, {52787, 14618}, {61211, 251}

X(61220) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(7) AND CEVIAN-OF-X(21)

Barycentrics    a*(a-b)*(a-c)*(2*a*b*c+a^2*(b+c)-(b-c)^2*(b+c)) : :
X(61220) = -2*X[34977]+X[53524]

X(61220) lies on these lines: {1, 149}, {2, 991}, {3, 34462}, {5, 5495}, {6, 1004}, {10, 4337}, {20, 33810}, {21, 48897}, {33, 6505}, {34, 224}, {40, 2779}, {42, 50307}, {46, 41329}, {51, 16056}, {58, 35979}, {73, 57287}, {77, 2000}, {78, 1330}, {81, 35990}, {100, 109}, {101, 13397}, {107, 1981}, {108, 1813}, {110, 6011}, {125, 37165}, {152, 2822}, {162, 662}, {184, 49127}, {190, 54970}, {200, 2895}, {269, 1998}, {283, 3651}, {326, 21287}, {329, 56813}, {377, 581}, {386, 4190}, {394, 7580}, {399, 16117}, {404, 37469}, {442, 500}, {511, 851}, {513, 53280}, {514, 53349}, {516, 46519}, {572, 7465}, {573, 35980}, {580, 35976}, {612, 5988}, {643, 4585}, {664, 1897}, {833, 15440}, {835, 29067}, {908, 1818}, {914, 1861}, {936, 26064}, {1005, 37659}, {1018, 57217}, {1019, 36030}, {1026, 3952}, {1042, 41575}, {1079, 56583}, {1254, 20612}, {1290, 39630}, {1308, 8701}, {1375, 32269}, {1376, 55400}, {1427, 16465}, {1458, 26015}, {1464, 44669}, {1490, 52364}, {1495, 46549}, {1503, 46552}, {1715, 5889}, {1724, 37301}, {1730, 3060}, {1742, 35258}, {1754, 1993}, {1756, 3724}, {1764, 2979}, {1790, 4220}, {1800, 7414}, {1819, 30267}, {1936, 22128}, {1983, 2610}, {1985, 48938}, {2222, 43345}, {2245, 15447}, {2263, 3870}, {2284, 35310}, {2318, 17781}, {2328, 35989}, {2340, 53617}, {2701, 38470}, {2900, 56848}, {3035, 45885}, {3066, 37272}, {3142, 48937}, {3190, 5905}, {3216, 4188}, {3240, 60785}, {3271, 27628}, {3430, 16049}, {3448, 5531}, {3580, 46488}, {3666, 17616}, {3743, 16120}, {3917, 4192}, {3977, 23691}, {4069, 4756}, {4210, 21363}, {4214, 19782}, {4225, 48883}, {4300, 24987}, {4303, 6734}, {4306, 12649}, {4383, 37309}, {4427, 61223}, {4436, 61172}, {4552, 61185}, {4666, 26109}, {4855, 37694}, {4881, 49997}, {5086, 37558}, {5125, 52676}, {5249, 14547}, {5271, 26053}, {5396, 11112}, {5492, 17653}, {5972, 46555}, {6127, 15015}, {6264, 24876}, {6326, 36154}, {6675, 48927}, {6985, 37483}, {7004, 16586}, {7460, 23181}, {8757, 11517}, {9070, 59005}, {10601, 37270}, {10609, 34586}, {10861, 26635}, {10884, 26054}, {11064, 33305}, {11345, 26657}, {11347, 33586}, {13257, 26611}, {13329, 36003}, {15107, 33325}, {15368, 17197}, {15507, 38389}, {16438, 17810}, {16585, 40967}, {17018, 41825}, {17484, 56808}, {17524, 48926}, {17532, 50317}, {17677, 18465}, {18180, 48907}, {18446, 37098}, {18666, 45738}, {19767, 37435}, {19860, 26051}, {19861, 26117}, {20918, 51420}, {21891, 53283}, {22053, 59491}, {22076, 37425}, {22935, 52005}, {23067, 24029}, {24504, 39341}, {26723, 40958}, {27086, 52680}, {28258, 48921}, {28291, 58991}, {28368, 40984}, {28850, 46583}, {29012, 46550}, {29016, 48380}, {29181, 46553}, {29317, 46551}, {30944, 48929}, {31018, 56809}, {31938, 56839}, {32223, 46554}, {32682, 43348}, {32911, 35977}, {34977, 53524}, {35312, 41353}, {35997, 37508}, {36746, 37229}, {37138, 37206}, {37154, 48877}, {37225, 48893}, {37371, 54407}, {40576, 57118}, {41571, 55010}, {43356, 59034}, {46484, 51360}, {47057, 56317}, {47522, 48908}, {48909, 58889}, {48916, 57002}, {49745, 52544}, {51432, 51649}, {52427, 54059}, {53393, 53542}, {53406, 53743}, {61161, 61197}

X(61220) = reflection of X(i) in X(j) for these {i,j}: {53524, 34977}
X(61220) = trilinear pole of line {942, 2260}
X(61220) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 14775}, {6, 56320}, {11, 15439}, {512, 40412}, {513, 943}, {514, 2259}, {523, 1175}, {525, 40570}, {647, 40395}, {649, 40435}, {652, 40573}, {663, 60041}, {667, 40422}, {1146, 32651}, {1794, 7649}, {2310, 36048}, {2605, 57710}, {3270, 58993}, {3271, 54952}, {7252, 60188}, {8287, 59011}, {21789, 52560}, {22383, 40447}
X(61220) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 56320}, {442, 522}, {942, 656}, {5249, 4467}, {5375, 40435}, {6631, 40422}, {15607, 2310}, {16585, 693}, {16732, 21207}, {18591, 514}, {36103, 14775}, {39007, 7004}, {39026, 943}, {39052, 40395}, {39054, 40412}, {40937, 1577}, {52119, 1109}
X(61220) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4570, 1}
X(61220) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {59, 3869}, {1020, 150}, {1110, 45738}, {1252, 18750}, {1262, 75}, {1275, 17137}, {1402, 17036}, {2149, 63}, {4551, 33650}, {4559, 37781}, {4564, 20245}, {4566, 21293}, {4567, 54109}, {4605, 21294}, {4619, 7192}, {7045, 17135}, {7115, 92}, {7128, 17220}, {7339, 3873}, {23067, 34188}, {23971, 17158}, {23979, 17147}, {24027, 1}, {52378, 21273}, {53321, 149}, {55346, 20242}
X(61220) = X(i)-cross conjugate of X(j) for these {i, j}: {23752, 1}, {50354, 942}, {61169, 61197}
X(61220) = pole of line {35649, 38480} with respect to the Conway circle
X(61220) = pole of line {1109, 2310} with respect to the polar circle
X(61220) = pole of line {2975, 11101} with respect to the Kiepert parabola
X(61220) = pole of line {656, 3737} with respect to the Stammler hyperbola
X(61220) = pole of line {1018, 1020} with respect to the Steiner circumellipse
X(61220) = pole of line {16578, 16599} with respect to the Steiner inellipse
X(61220) = pole of line {19, 27} with respect to the Yff parabola
X(61220) = pole of line {9, 3868} with respect to the Hutson-Moses hyperbola
X(61220) = pole of line {14208, 18155} with respect to the Wallace hyperbola
X(61220) = pole of line {4115, 35341} with respect to the dual conic of incircle
X(61220) = pole of line {17879, 17880} with respect to the dual conic of polar circle
X(61220) = pole of line {18721, 28742} with respect to the dual conic of Feuerbach hyperbola
X(61220) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(39630)}}, {{A, B, C, X(100), X(11604)}}, {{A, B, C, X(109), X(3466)}}, {{A, B, C, X(162), X(4551)}}, {{A, B, C, X(442), X(4242)}}, {{A, B, C, X(445), X(53160)}}, {{A, B, C, X(651), X(13149)}}, {{A, B, C, X(664), X(1331)}}, {{A, B, C, X(942), X(23703)}}, {{A, B, C, X(1025), X(5249)}}, {{A, B, C, X(1897), X(3939)}}, {{A, B, C, X(3120), X(23752)}}, {{A, B, C, X(3738), X(43974)}}, {{A, B, C, X(4575), X(36516)}}, {{A, B, C, X(5546), X(6742)}}, {{A, B, C, X(18607), X(24015)}}, {{A, B, C, X(36037), X(53388)}}, {{A, B, C, X(43050), X(47947)}}, {{A, B, C, X(43345), X(54356)}}, {{A, B, C, X(50354), X(53528)}}
X(61220) = barycentric product X(i)*X(j) for these (i, j): {63, 61180}, {100, 5249}, {190, 942}, {274, 61169}, {304, 53323}, {442, 662}, {651, 6734}, {1016, 50354}, {1020, 51978}, {1234, 163}, {1332, 1838}, {1841, 4561}, {1865, 4592}, {1978, 40956}, {2260, 668}, {2294, 99}, {4303, 6335}, {4552, 54356}, {4585, 45926}, {14547, 4554}, {15455, 500}, {16585, 6742}, {18591, 811}, {18607, 1897}, {21675, 52935}, {23207, 46404}, {23752, 4567}, {31938, 38340}, {37211, 3824}, {40937, 664}, {40952, 799}, {40967, 4573}, {40978, 670}, {46883, 52609}, {52919, 59163}, {55010, 643}, {56839, 648}, {61161, 86}, {61197, 75}, {61233, 7}, {61236, 69}
X(61220) = barycentric quotient X(i)/X(j) for these (i, j): {1, 56320}, {19, 14775}, {100, 40435}, {101, 943}, {108, 40573}, {109, 2982}, {162, 40395}, {163, 1175}, {190, 40422}, {442, 1577}, {500, 14838}, {651, 60041}, {662, 40412}, {692, 2259}, {906, 1794}, {942, 514}, {1020, 52560}, {1234, 20948}, {1262, 36048}, {1838, 17924}, {1841, 7649}, {1859, 3064}, {1865, 24006}, {1897, 40447}, {2149, 15439}, {2260, 513}, {2294, 523}, {3824, 4823}, {4303, 905}, {4551, 60188}, {4564, 54952}, {5249, 693}, {6734, 4391}, {7128, 58993}, {8021, 1021}, {14547, 650}, {14597, 1459}, {15455, 57885}, {16585, 4467}, {18591, 656}, {18607, 4025}, {21675, 4036}, {23207, 652}, {23595, 2973}, {23752, 16732}, {24027, 32651}, {31938, 57066}, {32676, 40570}, {33525, 2310}, {39791, 51664}, {40937, 522}, {40952, 661}, {40956, 649}, {40967, 3700}, {40978, 512}, {41393, 57243}, {44095, 54244}, {45926, 60074}, {46882, 3737}, {46883, 17925}, {46890, 57200}, {50354, 1086}, {52306, 7004}, {53323, 19}, {54356, 4560}, {55010, 4077}, {56839, 525}, {61161, 10}, {61169, 37}, {61180, 92}, {61197, 1}, {61233, 8}, {61236, 4}
X(61220) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 3909, 3882}, {100, 651, 1331}, {110, 13589, 61221}, {442, 500, 54356}, {1818, 2635, 908}, {4551, 35338, 100}, {4551, 61227, 651}, {4551, 61228, 109}

X(61221) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(7) AND CEVIAN-OF-X(27)

Barycentrics    a*(a-b)*(a-c)*(2*a^3+a^2*(b+c)+(b-c)^2*(b+c)) : :

X(61221) lies on these lines: {1, 1283}, {3, 25934}, {22, 1764}, {24, 1715}, {25, 1730}, {33, 1726}, {40, 2778}, {46, 20832}, {55, 20853}, {58, 28029}, {100, 101}, {108, 109}, {110, 6011}, {125, 46555}, {154, 7580}, {162, 163}, {165, 199}, {171, 20852}, {212, 21361}, {283, 48883}, {511, 46549}, {513, 53324}, {514, 14544}, {517, 20918}, {572, 1005}, {573, 35988}, {580, 4222}, {643, 3882}, {692, 4551}, {851, 1495}, {855, 52680}, {1004, 35259}, {1013, 1765}, {1030, 35445}, {1293, 58991}, {1331, 21362}, {1375, 15448}, {1437, 48897}, {1503, 33305}, {1618, 2222}, {1624, 7460}, {1697, 54371}, {1710, 1717}, {1714, 28076}, {1724, 4186}, {1746, 14004}, {1762, 56317}, {1763, 7070}, {1771, 11399}, {1782, 6198}, {1790, 35989}, {1936, 3220}, {1981, 52913}, {2000, 16551}, {2328, 4220}, {2360, 3651}, {3216, 28077}, {3570, 7256}, {3576, 22775}, {3911, 20780}, {4123, 56524}, {4242, 54442}, {4427, 22003}, {4512, 37327}, {5264, 27802}, {5292, 28104}, {5400, 52242}, {5535, 54095}, {5972, 37165}, {7413, 17188}, {7538, 10454}, {7991, 20851}, {9306, 49127}, {9441, 20857}, {9978, 35258}, {10434, 20848}, {10470, 20846}, {11064, 46552}, {13329, 33849}, {13558, 56411}, {13730, 37530}, {16117, 32609}, {17126, 46923}, {17194, 20834}, {17821, 37413}, {18180, 20840}, {18653, 46519}, {20836, 46623}, {20841, 37521}, {20855, 37619}, {20998, 36274}, {21363, 35996}, {23067, 23703}, {23344, 61166}, {24220, 50404}, {24436, 53393}, {24880, 28098}, {29012, 46484}, {32237, 46548}, {32739, 61160}, {33302, 35466}, {36059, 61227}, {36086, 36098}, {37227, 52524}, {46550, 51360}, {46588, 61226}, {53280, 53388}, {53390, 53743}, {53404, 53524}

X(61221) = reflection of X(i) in X(j) for these {i,j}: {61225, 53324}
X(61221) = trilinear pole of line {1104, 2264}
X(61221) = perspector of circumconic {{A, B, C, X(765), X(7128)}}
X(61221) = X(i)-isoconjugate-of-X(j) for these {i, j}: {513, 1257}, {514, 2983}, {522, 951}, {525, 57390}, {647, 40414}, {656, 40431}, {663, 58005}, {1086, 29163}, {1459, 40445}, {2968, 59090}, {17925, 52561}
X(61221) = X(i)-vertex conjugate of X(j) for these {i, j}: {1020, 53321}, {4551, 23067}
X(61221) = X(i)-Dao conjugate of X(j) for these {i, j}: {440, 693}, {1834, 4397}, {39026, 1257}, {39052, 40414}, {40596, 40431}, {40940, 14208}, {40984, 23687}, {59646, 1577}
X(61221) = X(i)-Ceva conjugate of X(j) for these {i, j}: {5379, 1}
X(61221) = pole of line {1020, 4551} with respect to the circumcircle
X(61221) = pole of line {20902, 24026} with respect to the polar circle
X(61221) = pole of line {5083, 8674} with respect to the DeLongchamps ellipse
X(61221) = pole of line {1610, 1621} with respect to the Kiepert parabola
X(61221) = pole of line {1019, 6003} with respect to the Stammler hyperbola
X(61221) = pole of line {9, 440} with respect to the Yff parabola
X(61221) = intersection, other than A, B, C, of circumconics {{A, B, C, X(100), X(14543)}}, {{A, B, C, X(101), X(53290)}}, {{A, B, C, X(108), X(644)}}, {{A, B, C, X(109), X(4587)}}, {{A, B, C, X(162), X(1020)}}, {{A, B, C, X(950), X(23706)}}, {{A, B, C, X(1018), X(6011)}}, {{A, B, C, X(1023), X(1104)}}, {{A, B, C, X(1026), X(36098)}}, {{A, B, C, X(3887), X(29162)}}, {{A, B, C, X(7437), X(59186)}}, {{A, B, C, X(17863), X(42723)}}, {{A, B, C, X(18673), X(56829)}}, {{A, B, C, X(46588), X(48890)}}
X(61221) = barycentric product X(i)*X(j) for these (i, j): {1, 14543}, {100, 40940}, {101, 17863}, {162, 440}, {651, 950}, {1104, 190}, {1332, 1842}, {1783, 18650}, {1834, 662}, {2264, 664}, {18673, 648}, {29162, 765}, {36037, 51410}, {40977, 99}, {40984, 799}, {44093, 811}, {53290, 75}, {59646, 934}, {61200, 92}
X(61221) = barycentric quotient X(i)/X(j) for these (i, j): {101, 1257}, {112, 40431}, {162, 40414}, {440, 14208}, {651, 58005}, {692, 2983}, {950, 4391}, {1104, 514}, {1110, 29163}, {1415, 951}, {1783, 40445}, {1834, 1577}, {1842, 17924}, {2264, 522}, {14543, 75}, {17863, 3261}, {18650, 15413}, {18673, 525}, {29162, 1111}, {32676, 57390}, {40940, 693}, {40977, 523}, {40984, 661}, {44093, 656}, {51410, 36038}, {53290, 1}, {59646, 4397}, {61200, 63}
X(61221) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {25, 1754, 1730}, {100, 3573, 61223}, {108, 109, 1020}, {110, 13589, 61220}, {513, 53324, 61225}, {692, 53279, 4551}, {20834, 37527, 17194}, {23845, 53288, 23067}

X(61222) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(7) AND CEVIAN-OF-X(57)

Barycentrics    a*(a-b)*(a-c)*(a-b-c)*((b-c)^2+a*(b+c)) : :
X(61222) = -1*X[4939]+2*X[24003]

X(61222) lies on these lines: {1, 1145}, {8, 34589}, {9, 9365}, {10, 26095}, {40, 2841}, {42, 59584}, {43, 3158}, {78, 27380}, {100, 109}, {200, 1040}, {210, 53524}, {513, 8683}, {522, 3952}, {528, 5400}, {643, 3737}, {644, 31343}, {646, 3699}, {650, 35341}, {899, 5853}, {978, 2136}, {1016, 8706}, {1018, 2427}, {1026, 4595}, {1066, 59675}, {1201, 12640}, {1293, 30236}, {1698, 25493}, {1897, 51564}, {2057, 54295}, {2310, 46694}, {2742, 6011}, {2743, 39628}, {2802, 32486}, {2810, 53389}, {3030, 28353}, {3169, 59797}, {3214, 12437}, {3216, 3913}, {3293, 56176}, {3680, 13541}, {3880, 49997}, {4383, 52804}, {4468, 25266}, {4574, 61237}, {4939, 24003}, {4995, 17194}, {5537, 23693}, {6048, 12625}, {6154, 45885}, {6736, 22072}, {7004, 14740}, {8694, 58991}, {8715, 37732}, {9371, 51380}, {12541, 27625}, {13205, 60787}, {14074, 28226}, {15621, 21363}, {16569, 24392}, {17059, 24988}, {17780, 56248}, {21362, 23845}, {21627, 27627}, {23067, 57101}, {24433, 58663}, {25096, 38375}, {27805, 36802}, {31855, 44669}, {33810, 37725}, {34465, 51525}, {44416, 56190}, {45269, 51379}, {55372, 56078}, {56183, 61226}, {56280, 56422}

X(61222) = reflection of X(i) in X(j) for these {i,j}: {4939, 24003}
X(61222) = trilinear pole of line {2347, 3057}
X(61222) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 60482}, {11, 59123}, {56, 56323}, {109, 40451}, {513, 1476}, {514, 3451}, {649, 40420}, {934, 40528}, {1222, 43924}, {1261, 43932}, {1357, 8706}, {1459, 40446}, {3271, 6613}, {3669, 23617}, {3676, 51476}, {3733, 56173}, {6363, 59478}, {7203, 56190}, {32017, 57181}, {40617, 59095}
X(61222) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 56323}, {9, 60482}, {11, 40451}, {2170, 1086}, {3452, 3676}, {3752, 693}, {5375, 40420}, {12640, 522}, {14714, 40528}, {39026, 1476}, {59507, 24002}
X(61222) = X(i)-Ceva conjugate of X(j) for these {i, j}: {100, 23845}, {1016, 9}, {1262, 2324}, {21272, 21362}
X(61222) = X(i)-cross conjugate of X(j) for these {i, j}: {6615, 3057}, {14284, 1}
X(61222) = pole of line {3737, 53528} with respect to the Stammler hyperbola
X(61222) = pole of line {16578, 30725} with respect to the Steiner inellipse
X(61222) = pole of line {63, 4358} with respect to the Yff parabola
X(61222) = pole of line {9, 3890} with respect to the Hutson-Moses hyperbola
X(61222) = pole of line {7203, 17218} with respect to the Wallace hyperbola
X(61222) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(39628)}}, {{A, B, C, X(9), X(8706)}}, {{A, B, C, X(100), X(12641)}}, {{A, B, C, X(109), X(3699)}}, {{A, B, C, X(643), X(3057)}}, {{A, B, C, X(644), X(30236)}}, {{A, B, C, X(646), X(651)}}, {{A, B, C, X(1025), X(3452)}}, {{A, B, C, X(1201), X(23705)}}, {{A, B, C, X(1331), X(51564)}}, {{A, B, C, X(1897), X(35281)}}, {{A, B, C, X(3663), X(6011)}}, {{A, B, C, X(3737), X(4768)}}, {{A, B, C, X(3756), X(14284)}}, {{A, B, C, X(4579), X(36802)}}, {{A, B, C, X(21120), X(43050)}}
X(61222) = barycentric product X(i)*X(j) for these (i, j): {1, 25268}, {100, 3452}, {101, 20895}, {190, 3057}, {333, 61166}, {651, 6736}, {1016, 6615}, {1018, 17183}, {1122, 6558}, {1201, 646}, {2347, 668}, {3663, 644}, {3699, 3752}, {4076, 48334}, {4415, 643}, {4578, 52563}, {4595, 52195}, {4642, 645}, {12640, 27834}, {14284, 5382}, {17906, 78}, {18086, 4553}, {18163, 3952}, {18600, 4069}, {21031, 662}, {21120, 765}, {21272, 9}, {21362, 8}, {21580, 55}, {21796, 7257}, {21809, 99}, {22072, 6335}, {23113, 318}, {23845, 312}, {26563, 3939}, {31343, 45204}, {42337, 4564}
X(61222) = barycentric quotient X(i)/X(j) for these (i, j): {1, 60482}, {9, 56323}, {100, 40420}, {101, 1476}, {644, 1222}, {650, 40451}, {657, 40528}, {692, 3451}, {1018, 56173}, {1122, 58817}, {1201, 3669}, {1783, 40446}, {2149, 59123}, {2347, 513}, {3057, 514}, {3452, 693}, {3663, 24002}, {3699, 32017}, {3752, 3676}, {3939, 23617}, {4069, 56258}, {4415, 4077}, {4564, 6613}, {4578, 52549}, {4642, 7178}, {6363, 53538}, {6615, 1086}, {6736, 4391}, {12640, 4462}, {17183, 7199}, {17906, 273}, {18163, 7192}, {20228, 43924}, {20895, 3261}, {21031, 1577}, {21120, 1111}, {21272, 85}, {21362, 7}, {21580, 6063}, {21796, 4017}, {21809, 523}, {22072, 905}, {23113, 77}, {23845, 57}, {25268, 75}, {26563, 52621}, {40982, 6591}, {42337, 4858}, {45219, 30719}, {48334, 1358}, {52563, 59941}, {59173, 43932}, {61166, 226}
X(61222) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 1331, 23703}, {100, 3939, 53388}, {100, 4551, 35338}, {3030, 28353, 53391}, {3699, 61223, 4069}, {4551, 23703, 61227}, {23705, 61223, 3699}, {23845, 61166, 21362}

X(61223) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(7) AND CEVIAN-OF-X(65)

Barycentrics    a*(a-b)*(a-c)*(a-b-c)*(b^2+c^2+a*(b+c)) : :

X(61223) lies on these lines: {1, 8258}, {9, 11609}, {42, 56078}, {43, 4368}, {63, 23155}, {78, 52500}, {100, 101}, {109, 1332}, {190, 4551}, {200, 3790}, {516, 23691}, {643, 4612}, {646, 3699}, {1025, 53321}, {1293, 53629}, {1331, 46640}, {3161, 3240}, {3216, 19582}, {3239, 61165}, {3293, 56311}, {3704, 46877}, {3811, 5497}, {3870, 4929}, {3872, 8275}, {3882, 53280}, {3939, 4571}, {3952, 25268}, {4391, 61174}, {4427, 61220}, {4553, 23845}, {4585, 61225}, {5400, 17777}, {8834, 28370}, {14839, 28353}, {17185, 18235}, {23343, 61166}, {25882, 51390}, {27625, 28661}, {31855, 36926}, {57151, 61177}

X(61223) = trilinear pole of line {960, 2269}
X(61223) = X(i)-isoconjugate-of-X(j) for these {i, j}: {11, 52928}, {56, 4581}, {244, 36098}, {513, 961}, {608, 15420}, {667, 31643}, {1014, 57162}, {1015, 6648}, {1042, 57161}, {1086, 8687}, {1169, 7178}, {1220, 43924}, {1357, 8707}, {1358, 32736}, {1365, 58982}, {1791, 43923}, {2298, 3669}, {2363, 4017}, {3733, 60086}, {7180, 14534}, {30710, 57181}, {36147, 53538}, {40453, 51662}
X(61223) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 4581}, {960, 4017}, {1193, 51662}, {1211, 3676}, {2092, 514}, {3125, 53545}, {3666, 4077}, {6631, 31643}, {17197, 17205}, {17419, 1086}, {34961, 2363}, {38992, 244}, {39015, 53538}, {39026, 961}, {52087, 3669}, {59509, 24002}
X(61223) = X(i)-Ceva conjugate of X(j) for these {i, j}: {190, 61168}, {4570, 78}, {53332, 3882}
X(61223) = X(i)-cross conjugate of X(j) for these {i, j}: {17420, 960}, {52326, 17185}, {57158, 46877}
X(61223) = pole of line {1621, 56946} with respect to the Kiepert parabola
X(61223) = pole of line {1019, 4017} with respect to the Stammler hyperbola
X(61223) = pole of line {21362, 22003} with respect to the Steiner circumellipse
X(61223) = pole of line {9, 312} with respect to the Yff parabola
X(61223) = pole of line {4077, 7199} with respect to the Wallace hyperbola
X(61223) = pole of line {1018, 3952} with respect to the dual conic of incircle
X(61223) = pole of line {4687, 16705} with respect to the dual conic of Feuerbach hyperbola
X(61223) = pole of line {2786, 17755} with respect to the dual conic of Suppa-Cucoanes circle
X(61223) = intersection, other than A, B, C, of circumconics {{A, B, C, X(100), X(646)}}, {{A, B, C, X(101), X(3699)}}, {{A, B, C, X(643), X(1018)}}, {{A, B, C, X(644), X(53332)}}, {{A, B, C, X(960), X(1023)}}, {{A, B, C, X(1026), X(3687)}}, {{A, B, C, X(1193), X(23705)}}, {{A, B, C, X(1635), X(4768)}}, {{A, B, C, X(3573), X(17185)}}, {{A, B, C, X(3716), X(8632)}}, {{A, B, C, X(3887), X(3910)}}, {{A, B, C, X(4551), X(7257)}}
X(61223) = barycentric product X(i)*X(j) for these (i, j): {100, 3687}, {190, 960}, {312, 53280}, {314, 61168}, {333, 61172}, {345, 61226}, {1016, 17420}, {1193, 646}, {1211, 643}, {1332, 46878}, {1848, 4571}, {1978, 20967}, {2092, 7257}, {2269, 668}, {2292, 645}, {3666, 3699}, {3674, 4578}, {3704, 662}, {3718, 61205}, {3882, 8}, {3910, 765}, {3965, 664}, {4033, 4267}, {4076, 48131}, {4357, 644}, {4509, 6065}, {4552, 46877}, {4564, 57158}, {4587, 54314}, {16705, 4069}, {17185, 3952}, {18235, 27805}, {18697, 5546}, {20653, 4612}, {20911, 3939}, {21033, 99}, {24471, 6558}, {30730, 54308}, {36037, 51407}, {40966, 799}, {41003, 7259}, {44092, 55207}, {46879, 56252}, {52326, 7035}, {53332, 9}
X(61223) = barycentric quotient X(i)/X(j) for these (i, j): {9, 4581}, {78, 15420}, {101, 961}, {190, 31643}, {643, 14534}, {644, 1220}, {646, 1240}, {765, 6648}, {960, 514}, {1018, 60086}, {1110, 8687}, {1193, 3669}, {1211, 4077}, {1252, 36098}, {1334, 57162}, {1682, 48131}, {2092, 4017}, {2149, 52928}, {2269, 513}, {2287, 57161}, {2292, 7178}, {2300, 43924}, {2354, 43923}, {3666, 3676}, {3674, 59941}, {3687, 693}, {3699, 30710}, {3704, 1577}, {3725, 7180}, {3882, 7}, {3910, 1111}, {3939, 2298}, {3965, 522}, {4069, 14624}, {4267, 1019}, {4357, 24002}, {4587, 1791}, {4719, 30723}, {5546, 2363}, {6065, 36147}, {6371, 53538}, {7257, 40827}, {17185, 7192}, {17420, 1086}, {18235, 4369}, {20911, 52621}, {20967, 649}, {21033, 523}, {22074, 1459}, {22076, 51664}, {24471, 58817}, {40153, 7203}, {40966, 661}, {40976, 6591}, {41609, 57230}, {44092, 55208}, {46877, 4560}, {46878, 17924}, {46879, 21173}, {46889, 3737}, {48131, 1358}, {50330, 53545}, {51407, 36038}, {52087, 51662}, {52326, 244}, {53280, 57}, {53332, 85}, {54308, 17096}, {57158, 4858}, {61168, 65}, {61172, 226}, {61205, 34}, {61226, 278}
X(61223) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 3573, 61221}, {3699, 61222, 23705}, {4069, 61222, 3699}, {18235, 40966, 17185}, {53280, 61172, 3882}

X(61224) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(7) AND CEVIAN-OF-X(77)

Barycentrics    a*(a-b)*(a-c)*(a^2*(b-c)^2+a^3*(b+c)-a*(b-c)^2*(b+c)-(b^2-c^2)^2) : :

X(61224) lies on these lines: {1, 1146}, {9, 216}, {41, 37732}, {43, 58034}, {100, 58946}, {101, 108}, {163, 3737}, {218, 3216}, {223, 39050}, {583, 1743}, {650, 4559}, {651, 36049}, {906, 35338}, {946, 40957}, {978, 16572}, {1018, 2427}, {1021, 1625}, {1415, 61227}, {1457, 8074}, {1490, 60017}, {1983, 2600}, {2170, 32486}, {2324, 20224}, {2617, 5546}, {4566, 14837}, {4574, 35341}, {4605, 17906}, {7117, 58036}, {14395, 35326}, {20262, 22063}, {22350, 40869}, {33811, 34457}, {34048, 38902}, {43065, 49997}, {46974, 54079}

X(61224) = trilinear pole of line {2262, 40945}
X(61224) = X(i)-isoconjugate-of-X(j) for these {i, j}: {513, 55987}, {514, 947}, {522, 57418}, {649, 40417}, {905, 40396}, {1019, 56195}
X(61224) = X(i)-Dao conjugate of X(j) for these {i, j}: {946, 14837}, {5375, 40417}, {17102, 4391}, {20262, 4025}, {24026, 23978}, {39026, 55987}, {40943, 693}
X(61224) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1262, 1}
X(61224) = pole of line {1759, 1766} with respect to the Yff parabola
X(61224) = pole of line {3869, 3872} with respect to the Hutson-Moses hyperbola
X(61224) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(108), X(56194)}}, {{A, B, C, X(1783), X(37141)}}, {{A, B, C, X(1897), X(57118)}}
X(61224) = barycentric product X(i)*X(j) for these (i, j): {100, 946}, {109, 23528}, {190, 2262}, {1856, 6516}, {17102, 1897}, {18026, 40945}, {20262, 651}, {22063, 6335}, {40943, 44327}, {40957, 4554}, {55349, 56252}, {61202, 75}
X(61224) = barycentric quotient X(i)/X(j) for these (i, j): {100, 40417}, {101, 55987}, {692, 947}, {946, 693}, {1415, 57418}, {1856, 44426}, {2262, 514}, {4557, 56195}, {8750, 40396}, {17102, 4025}, {20262, 4391}, {22063, 905}, {23528, 35519}, {40943, 14837}, {40945, 521}, {40957, 650}, {55349, 21173}, {61202, 1}
X(61224) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 4559, 61237}

X(61225) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(7) AND CEVIAN-OF-X(79)

Barycentrics    a*(a-b)*(a-c)*(a+b-c)*(a-b+c)*(2*a+b+c) : :

X(61225) lies on these lines: {1, 399}, {40, 38579}, {57, 1929}, {81, 16133}, {100, 109}, {108, 28162}, {110, 9811}, {221, 956}, {222, 1001}, {226, 29683}, {513, 53324}, {522, 14544}, {553, 2308}, {664, 32042}, {758, 51654}, {846, 47057}, {896, 18593}, {934, 28148}, {1018, 36074}, {1023, 4559}, {1308, 15439}, {1406, 1724}, {1414, 4636}, {1464, 5427}, {1707, 56848}, {1749, 56844}, {1771, 8757}, {1777, 3157}, {1935, 5251}, {1962, 41546}, {2003, 4649}, {2222, 28184}, {2956, 54295}, {3257, 36098}, {3293, 18360}, {3652, 7100}, {4413, 34048}, {4565, 57119}, {4573, 57060}, {4585, 61223}, {5223, 8270}, {5399, 5495}, {5586, 56343}, {5723, 24465}, {6357, 17768}, {6667, 43043}, {7073, 41695}, {8059, 14074}, {8690, 29055}, {8691, 59069}, {13257, 51408}, {13396, 59015}, {18210, 53404}, {24542, 41801}, {28230, 59125}, {31235, 52659}, {34586, 38602}, {35342, 36075}, {37736, 51766}, {41166, 42082}, {41697, 52372}, {49997, 52440}

X(61225) = reflection of X(i) in X(j) for these {i,j}: {61221, 53324}
X(61225) = trilinear pole of line {1100, 17454}
X(61225) = perspector of circumconic {{A, B, C, X(4564), X(35049)}}
X(61225) = X(i)-isoconjugate-of-X(j) for these {i, j}: {8, 50344}, {9, 47947}, {11, 8701}, {55, 4608}, {284, 31010}, {314, 58301}, {333, 58294}, {513, 32635}, {514, 33635}, {522, 1126}, {649, 4102}, {650, 1255}, {663, 1268}, {1171, 3700}, {1796, 3064}, {2170, 37212}, {3063, 32018}, {3271, 6540}, {3709, 32014}, {4041, 40438}, {4092, 6578}, {4391, 28615}, {4516, 4596}, {4560, 52555}, {4629, 21044}, {6539, 7252}, {9404, 60139}, {35057, 57419}
X(61225) = X(i)-vertex conjugate of X(j) for these {i, j}: {163, 55185}
X(61225) = X(i)-Dao conjugate of X(j) for these {i, j}: {223, 4608}, {478, 47947}, {553, 55186}, {1100, 57066}, {1125, 4086}, {1213, 4391}, {3647, 522}, {5375, 4102}, {10001, 32018}, {35076, 4858}, {39026, 32635}, {40590, 31010}, {56846, 693}, {59592, 4397}
X(61225) = X(i)-Ceva conjugate of X(j) for these {i, j}: {651, 61170}
X(61225) = X(i)-cross conjugate of X(j) for these {i, j}: {4979, 553}, {35327, 35342}
X(61225) = pole of line {8674, 35649} with respect to the Conway circle
X(61225) = pole of line {5083, 8674} with respect to the incircle
X(61225) = pole of line {2975, 37405} with respect to the Kiepert parabola
X(61225) = pole of line {14395, 35326} with respect to the MacBeath circumconic
X(61225) = pole of line {3737, 4041} with respect to the Stammler hyperbola
X(61225) = pole of line {63, 3578} with respect to the Yff parabola
X(61225) = pole of line {9, 5253} with respect to the Hutson-Moses hyperbola
X(61225) = pole of line {4086, 4913} with respect to the Wallace hyperbola
X(61225) = pole of line {8674, 11570} with respect to the Suppa-Cucoanes circle
X(61225) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(100), X(1929)}}, {{A, B, C, X(109), X(36075)}}, {{A, B, C, X(110), X(7343)}}, {{A, B, C, X(553), X(1025)}}, {{A, B, C, X(1331), X(17972)}}, {{A, B, C, X(1414), X(4551)}}, {{A, B, C, X(2254), X(4979)}}, {{A, B, C, X(2308), X(54325)}}, {{A, B, C, X(3257), X(3882)}}, {{A, B, C, X(3738), X(4977)}}, {{A, B, C, X(3939), X(4636)}}, {{A, B, C, X(4115), X(8691)}}, {{A, B, C, X(4579), X(8690)}}, {{A, B, C, X(7451), X(31900)}}, {{A, B, C, X(8699), X(35281)}}, {{A, B, C, X(23703), X(32636)}}, {{A, B, C, X(30724), X(43050)}}, {{A, B, C, X(35055), X(53524)}}
X(61225) = barycentric product X(i)*X(j) for these (i, j): {100, 553}, {108, 4001}, {109, 4359}, {190, 32636}, {269, 30729}, {1014, 4115}, {1100, 664}, {1125, 651}, {1213, 1414}, {1262, 4985}, {1269, 1415}, {1412, 61174}, {1461, 3702}, {1813, 56875}, {1839, 6516}, {1962, 4573}, {2308, 4554}, {3257, 5298}, {3647, 38340}, {3649, 662}, {3683, 658}, {3686, 934}, {3916, 653}, {4046, 4637}, {4427, 57}, {4551, 8025}, {4564, 4977}, {4565, 4647}, {4604, 4870}, {4620, 4983}, {4973, 655}, {4976, 7045}, {4978, 59}, {4979, 4998}, {16709, 4559}, {18026, 22054}, {20970, 4625}, {21454, 35339}, {21859, 30593}, {23201, 46404}, {26700, 3578}, {30591, 52378}, {30724, 765}, {35327, 85}, {35342, 7}, {36075, 75}, {36146, 4966}, {37136, 51409}, {37137, 4697}, {55185, 56846}, {61170, 86}
X(61225) = barycentric quotient X(i)/X(j) for these (i, j): {56, 47947}, {57, 4608}, {59, 37212}, {65, 31010}, {100, 4102}, {101, 32635}, {109, 1255}, {553, 693}, {604, 50344}, {651, 1268}, {664, 32018}, {692, 33635}, {1100, 522}, {1125, 4391}, {1213, 4086}, {1402, 58294}, {1414, 32014}, {1415, 1126}, {1839, 44426}, {1962, 3700}, {2149, 8701}, {2308, 650}, {2355, 3064}, {3647, 57066}, {3649, 1577}, {3683, 3239}, {3686, 4397}, {3702, 52622}, {3916, 6332}, {3958, 52355}, {4001, 35518}, {4115, 3701}, {4359, 35519}, {4427, 312}, {4551, 6539}, {4564, 6540}, {4565, 40438}, {4870, 4791}, {4969, 4768}, {4973, 3904}, {4976, 24026}, {4977, 4858}, {4978, 34387}, {4979, 11}, {4983, 21044}, {4985, 23978}, {5298, 3762}, {8025, 18155}, {17454, 35057}, {20970, 4041}, {21859, 6538}, {22054, 521}, {22080, 8611}, {23201, 652}, {23703, 31011}, {26700, 60139}, {30724, 1111}, {30729, 341}, {31900, 57215}, {32636, 514}, {35327, 9}, {35339, 56086}, {35342, 8}, {36059, 1796}, {36075, 1}, {50512, 2170}, {52378, 4596}, {56846, 55186}, {56875, 46110}, {61170, 10}, {61174, 30713}
X(61225) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {109, 4551, 23703}, {109, 651, 4551}, {513, 53324, 61221}, {1935, 34043, 37558}

X(61226) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(7) AND CEVIAN-OF-X(81)

Barycentrics    a*(a-b)*(a-c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(b^2+c^2+a*(b+c)) : :

X(61226) lies on these lines: {1, 451}, {2, 3192}, {4, 3216}, {19, 17981}, {24, 1724}, {25, 4383}, {33, 43}, {34, 978}, {78, 36103}, {100, 8750}, {101, 108}, {109, 40097}, {112, 35342}, {162, 662}, {186, 52680}, {200, 18687}, {208, 37694}, {232, 2238}, {238, 52427}, {386, 406}, {427, 37663}, {444, 44092}, {468, 35466}, {475, 17749}, {648, 3570}, {650, 53761}, {811, 55233}, {899, 1861}, {1193, 46878}, {1376, 3195}, {1452, 54386}, {1474, 7438}, {1714, 3542}, {1780, 31384}, {1788, 56818}, {1848, 40976}, {1870, 49997}, {1876, 16610}, {1897, 3699}, {2299, 4231}, {2324, 18685}, {3293, 6198}, {3306, 42856}, {4183, 55068}, {4232, 37681}, {5233, 17555}, {6011, 59092}, {7412, 37732}, {7649, 61180}, {16552, 39575}, {17906, 23706}, {19504, 44097}, {22350, 51359}, {25985, 37662}, {26020, 51415}, {27805, 36797}, {30250, 58986}, {31855, 56877}, {32911, 35973}, {37289, 48897}, {37658, 45141}, {46588, 61221}, {56183, 61222}, {61172, 61205}

X(61226) = trilinear pole of line {1829, 2269}
X(61226) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 4581}, {6, 15420}, {73, 57161}, {123, 58997}, {125, 58982}, {512, 57853}, {513, 1791}, {514, 2359}, {521, 961}, {523, 1798}, {525, 1169}, {647, 14534}, {656, 2363}, {905, 2298}, {1220, 1459}, {1444, 57162}, {1565, 32736}, {1946, 31643}, {2968, 52928}, {3049, 40827}, {3937, 8707}, {3942, 36147}, {4367, 57690}, {6648, 7117}, {7004, 36098}, {7254, 14624}, {8687, 26932}, {22383, 30710}, {23189, 60086}, {56242, 57859}
X(61226) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 15420}, {429, 21186}, {960, 656}, {1211, 4025}, {2092, 6332}, {3125, 4466}, {3666, 14208}, {17197, 17219}, {17419, 26932}, {36103, 4581}, {38992, 7004}, {39015, 3942}, {39026, 1791}, {39052, 14534}, {39053, 31643}, {39054, 57853}, {40596, 2363}, {52087, 905}, {56905, 1577}, {59509, 15413}
X(61226) = X(i)-cross conjugate of X(j) for these {i, j}: {17420, 46878}
X(61226) = pole of line {244, 1109} with respect to the polar circle
X(61226) = pole of line {656, 22093} with respect to the Stammler hyperbola
X(61226) = pole of line {1766, 21376} with respect to the Yff parabola
X(61226) = pole of line {3869, 5227} with respect to the Hutson-Moses hyperbola
X(61226) = pole of line {14208, 24560} with respect to the Wallace hyperbola
X(61226) = intersection, other than A, B, C, of circumconics {{A, B, C, X(100), X(53332)}}, {{A, B, C, X(101), X(3699)}}, {{A, B, C, X(108), X(6335)}}, {{A, B, C, X(109), X(57061)}}, {{A, B, C, X(429), X(4242)}}, {{A, B, C, X(653), X(55233)}}, {{A, B, C, X(662), X(3882)}}, {{A, B, C, X(1783), X(40097)}}, {{A, B, C, X(1897), X(32674)}}, {{A, B, C, X(2617), X(35307)}}, {{A, B, C, X(2812), X(3910)}}, {{A, B, C, X(3666), X(42719)}}, {{A, B, C, X(17420), X(46393)}}
X(61226) = barycentric product X(i)*X(j) for these (i, j): {19, 53332}, {27, 61172}, {100, 1848}, {101, 54314}, {108, 3687}, {112, 18697}, {278, 61223}, {286, 61168}, {429, 662}, {653, 960}, {1193, 6335}, {1211, 162}, {1228, 32676}, {1783, 4357}, {1829, 190}, {1897, 3666}, {2092, 811}, {2292, 648}, {2354, 668}, {3674, 56183}, {3725, 6331}, {3882, 4}, {3910, 7012}, {14594, 56841}, {15742, 48131}, {17185, 61178}, {17420, 46102}, {18026, 2269}, {20911, 8750}, {20967, 46404}, {21124, 5379}, {22074, 52938}, {22076, 823}, {27805, 444}, {36110, 51407}, {36118, 3965}, {37206, 41611}, {40976, 4554}, {42661, 46254}, {44092, 799}, {46877, 52607}, {46878, 651}, {53280, 92}, {55233, 59174}, {57158, 7128}, {61205, 75}
X(61226) = barycentric quotient X(i)/X(j) for these (i, j): {1, 15420}, {19, 4581}, {101, 1791}, {112, 2363}, {162, 14534}, {163, 1798}, {429, 1577}, {444, 4369}, {653, 31643}, {662, 57853}, {692, 2359}, {811, 40827}, {960, 6332}, {1172, 57161}, {1193, 905}, {1211, 14208}, {1783, 1220}, {1829, 514}, {1848, 693}, {1897, 30710}, {2092, 656}, {2269, 521}, {2292, 525}, {2300, 1459}, {2333, 57162}, {2354, 513}, {3666, 4025}, {3687, 35518}, {3725, 647}, {3882, 69}, {3910, 17880}, {4357, 15413}, {6335, 1240}, {6371, 3942}, {7012, 6648}, {7115, 36098}, {8750, 2298}, {17420, 26932}, {18697, 3267}, {20967, 652}, {21033, 52355}, {21810, 4064}, {22074, 57241}, {22076, 24018}, {22097, 4131}, {22345, 4091}, {27805, 57859}, {32674, 961}, {32676, 1169}, {40966, 8611}, {40976, 650}, {41611, 4468}, {42661, 3708}, {44092, 661}, {46877, 15411}, {46878, 4391}, {46889, 57081}, {48131, 1565}, {50330, 4466}, {52326, 7004}, {52567, 57243}, {53280, 63}, {53332, 304}, {54308, 15419}, {54314, 3261}, {56905, 21186}, {59174, 55234}, {61168, 72}, {61172, 306}, {61205, 1}, {61223, 345}
X(61226) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {468, 44113, 54407}

X(61227) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(7) AND CEVIAN-OF-X(84)

Barycentrics    a*(a-b)*(a-c)*(a+b-c)*(a-b+c)*(-(a^2*(b-c)^2)+a^3*(b+c)-a*(b-c)^2*(b+c)+(b^2-c^2)^2) : :

X(61227) lies on these lines: {1, 1537}, {33, 34052}, {51, 57}, {73, 4304}, {100, 109}, {108, 1461}, {162, 3737}, {223, 1040}, {226, 15368}, {269, 40615}, {513, 53321}, {514, 61178}, {515, 51660}, {603, 37732}, {971, 43058}, {1020, 56410}, {1364, 33811}, {1394, 1745}, {1413, 3149}, {1415, 61224}, {1419, 56904}, {1422, 1750}, {1433, 56889}, {1490, 38554}, {1633, 57118}, {1877, 51649}, {2122, 11500}, {2222, 59123}, {2617, 4565}, {2635, 34050}, {2823, 53557}, {2947, 47848}, {5400, 43043}, {5731, 10571}, {14733, 26700}, {21362, 23067}, {32714, 57117}, {34049, 51361}, {35320, 36048}, {36059, 61221}, {36118, 36127}, {53761, 61229}, {61212, 61237}

X(61227) = trilinear pole of line {1108, 37566}
X(61227) = X(i)-isoconjugate-of-X(j) for these {i, j}: {522, 1167}, {650, 40399}, {652, 40444}, {663, 40424}, {1783, 40527}, {3737, 56259}, {7358, 58984}, {8058, 57422}, {40397, 57055}
X(61227) = X(i)-Dao conjugate of X(j) for these {i, j}: {6260, 522}, {7004, 2968}, {39006, 40527}
X(61227) = X(i)-Ceva conjugate of X(j) for these {i, j}: {55346, 57}
X(61227) = X(i)-cross conjugate of X(j) for these {i, j}: {53288, 61237}
X(61227) = pole of line {2804, 35649} with respect to the Conway circle
X(61227) = pole of line {2804, 5083} with respect to the incircle
X(61227) = pole of line {63, 20895} with respect to the Yff parabola
X(61227) = pole of line {2804, 11570} with respect to the Suppa-Cucoanes circle
X(61227) = intersection, other than A, B, C, of circumconics {{A, B, C, X(100), X(46435)}}, {{A, B, C, X(162), X(1210)}}, {{A, B, C, X(1108), X(26700)}}, {{A, B, C, X(1331), X(8059)}}, {{A, B, C, X(3939), X(36127)}}, {{A, B, C, X(4551), X(36110)}}, {{A, B, C, X(23703), X(37566)}}, {{A, B, C, X(40958), X(54325)}}
X(61227) = barycentric product X(i)*X(j) for these (i, j): {57, 61185}, {109, 17862}, {190, 37566}, {1071, 653}, {1108, 664}, {1210, 651}, {1226, 1415}, {1414, 21933}, {1532, 37136}, {1864, 658}, {23204, 46404}, {37141, 6260}, {38340, 41562}, {40628, 55346}, {40958, 4554}, {40979, 4566}, {41561, 61240}, {53288, 85}, {57285, 662}, {61212, 75}, {61237, 7}
X(61227) = barycentric quotient X(i)/X(j) for these (i, j): {108, 40444}, {109, 40399}, {651, 40424}, {1071, 6332}, {1108, 522}, {1210, 4391}, {1415, 1167}, {1459, 40527}, {1864, 3239}, {3611, 8611}, {4559, 56259}, {17862, 35519}, {21933, 4086}, {23204, 652}, {37566, 514}, {40628, 2968}, {40958, 650}, {40979, 7253}, {41562, 57066}, {53288, 9}, {57285, 1577}, {61185, 312}, {61212, 1}, {61237, 8}
X(61227) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {109, 61231, 4551}, {4551, 23703, 61222}, {4551, 61228, 35338}

X(61228) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(7) AND CEVIAN-OF-X(90)

Barycentrics    a*(a-b)*(a-c)*(a+b-c)*(a-b+c)*(-(a^2*(b-c)^2)+a^3*(b+c)+(b^2-c^2)^2-a*(b+c)*(b^2+c^2)) : :

X(61228) lies on circumconic {{A, B, C, X(6011), X(10916)}} and on these lines: {1, 5840}, {46, 52}, {65, 48907}, {100, 109}, {497, 991}, {513, 23067}, {1214, 53524}, {1813, 13397}, {1983, 2600}, {2720, 6011}, {3737, 4575}, {4337, 10572}, {28291, 30239}, {56422, 56590}, {61161, 61212}

X(61228) = X(i)-Dao conjugate of X(j) for these {i, j}: {41540, 522}
X(61228) = pole of line {35649, 55126} with respect to the Conway circle
X(61228) = pole of line {5083, 55126} with respect to the incircle
X(61228) = pole of line {11570, 55126} with respect to the Suppa-Cucoanes circle
X(61228) = barycentric product X(i)*X(j) for these (i, j): {10916, 651}
X(61228) = barycentric quotient X(i)/X(j) for these (i, j): {10916, 4391}
X(61228) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 61231, 4551}

X(61229) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(7) AND CEVIAN-OF-X(92)

Barycentrics    a*(a-b)*(a-c)*(a+b-c)*(a-b+c)*(b+c)*((a-b)^2*(a+b)+(a+b)^2*c-(a+b)*c^2-c^3)*(a^3+a^2*(b-c)-a*(b-c)^2-(b-c)*(b+c)^2) : :

X(61229) lies on these lines: {1, 53844}, {10, 52078}, {40, 3341}, {46, 80}, {57, 2968}, {65, 52389}, {100, 1813}, {109, 1783}, {268, 37541}, {282, 296}, {291, 1422}, {579, 7003}, {653, 14304}, {668, 53642}, {1018, 23067}, {1020, 61178}, {1214, 41086}, {1433, 1771}, {1436, 33848}, {1708, 7008}, {1715, 1788}, {1754, 2192}, {2357, 8808}, {4551, 52610}, {4674, 52384}, {4848, 38955}, {8886, 10310}, {11500, 46881}, {20225, 47848}, {23703, 32652}, {41539, 52037}, {53761, 61227}, {56549, 57492}

X(61229) = trilinear pole of line {37, 73}
X(61229) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 57213}, {21, 6129}, {27, 10397}, {28, 57101}, {40, 3737}, {58, 8058}, {81, 14298}, {107, 55044}, {110, 38357}, {112, 16596}, {162, 53557}, {196, 23090}, {198, 4560}, {208, 57081}, {221, 7253}, {223, 1021}, {283, 54239}, {284, 14837}, {329, 7252}, {342, 57134}, {347, 21789}, {521, 3194}, {522, 2360}, {649, 27398}, {650, 1817}, {652, 41083}, {663, 8822}, {1019, 2324}, {1301, 55058}, {1412, 57049}, {1474, 57245}, {1819, 7649}, {2185, 55212}, {2187, 18155}, {2193, 59935}, {2194, 17896}, {3209, 15411}, {3733, 7080}, {4565, 5514}, {7011, 17926}, {7074, 7192}, {7254, 55116}, {7368, 17096}, {7952, 23189}, {8748, 57233}, {17925, 55111}, {43925, 55112}
X(61229) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 57213}, {10, 8058}, {125, 53557}, {244, 38357}, {1214, 17896}, {3341, 7253}, {5375, 27398}, {34591, 16596}, {38985, 55044}, {40586, 14298}, {40590, 14837}, {40591, 57101}, {40599, 57049}, {40611, 6129}, {47345, 59935}, {51574, 57245}, {55064, 5514}
X(61229) = X(i)-cross conjugate of X(j) for these {i, j}: {520, 1}, {656, 52389}, {8611, 226}, {14308, 9}, {53321, 4551}, {55242, 8808}
X(61229) = pole of line {3998, 56545} with respect to the Yff parabola
X(61229) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(107)}}, {{A, B, C, X(80), X(100)}}, {{A, B, C, X(108), X(57193)}}, {{A, B, C, X(109), X(296)}}, {{A, B, C, X(520), X(55044)}}, {{A, B, C, X(656), X(14304)}}, {{A, B, C, X(758), X(2829)}}, {{A, B, C, X(1021), X(2968)}}, {{A, B, C, X(2283), X(41342)}}, {{A, B, C, X(4242), X(37468)}}, {{A, B, C, X(8059), X(53642)}}, {{A, B, C, X(13138), X(40117)}}, {{A, B, C, X(52607), X(57117)}}, {{A, B, C, X(53321), X(57118)}}
X(61229) = barycentric product X(i)*X(j) for these (i, j): {10, 37141}, {37, 53642}, {100, 8808}, {108, 56944}, {181, 55211}, {189, 4551}, {190, 52384}, {271, 52607}, {282, 4566}, {285, 4605}, {307, 40117}, {309, 4559}, {321, 8059}, {1018, 1440}, {1020, 280}, {1413, 4033}, {1422, 3952}, {1441, 36049}, {1897, 52037}, {1903, 664}, {2357, 4554}, {2358, 4561}, {4552, 84}, {4998, 55242}, {13138, 226}, {13853, 643}, {18026, 41087}, {32652, 349}, {34404, 53321}, {39130, 651}, {41081, 61178}, {44327, 65}, {52078, 56235}, {52389, 653}, {52610, 7020}, {53013, 658}
X(61229) = barycentric quotient X(i)/X(j) for these (i, j): {3, 57213}, {37, 8058}, {42, 14298}, {65, 14837}, {71, 57101}, {72, 57245}, {84, 4560}, {100, 27398}, {108, 41083}, {109, 1817}, {181, 55212}, {189, 18155}, {210, 57049}, {225, 59935}, {226, 17896}, {228, 10397}, {268, 57081}, {271, 15411}, {282, 7253}, {647, 53557}, {651, 8822}, {656, 16596}, {661, 38357}, {822, 55044}, {906, 1819}, {1018, 7080}, {1020, 347}, {1400, 6129}, {1413, 1019}, {1415, 2360}, {1422, 7192}, {1436, 3737}, {1440, 7199}, {1880, 54239}, {1903, 522}, {2188, 23090}, {2192, 1021}, {2208, 7252}, {2357, 650}, {2358, 7649}, {4041, 5514}, {4551, 329}, {4552, 322}, {4557, 2324}, {4559, 40}, {4566, 40702}, {4605, 57810}, {4998, 55241}, {6612, 7203}, {7008, 17926}, {7118, 21789}, {7216, 38374}, {7367, 58329}, {8059, 81}, {8611, 7358}, {8808, 693}, {13138, 333}, {13853, 4077}, {21859, 21075}, {22341, 57233}, {32652, 284}, {32674, 3194}, {36049, 21}, {37141, 86}, {39130, 4391}, {40117, 29}, {40836, 57215}, {41086, 14331}, {41087, 521}, {44327, 314}, {52037, 4025}, {52384, 514}, {52389, 6332}, {52607, 342}, {52610, 7013}, {53010, 52355}, {53013, 3239}, {53321, 223}, {53642, 274}, {55208, 38362}, {55211, 18021}, {55212, 3318}, {55242, 11}, {56944, 35518}, {56972, 15419}
X(61229) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13138, 37141, 8059}

X(61230) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(7) AND CEVIAN-OF-X(100)

Barycentrics    a*(a-b-c)*(b-c)*((a-b)^2*(a+b)-2*(a^2-a*b+b^2)*c+(a+b)*c^2)*(a^3+(b-c)^2*c-a^2*(2*b+c)+a*(b^2+2*b*c-c^2)) : :

X(61230) lies on these lines: {1, 3676}, {33, 7649}, {55, 513}, {103, 15728}, {200, 522}, {220, 650}, {1024, 46393}, {1043, 18155}, {2192, 15313}, {2222, 2742}, {2254, 2342}, {2328, 3737}, {3887, 4845}, {4105, 21132}, {4724, 52429}, {6003, 51476}, {6366, 42064}, {9511, 52001}, {10482, 58322}, {14942, 36038}, {23838, 34894}, {52371, 53523}

X(61230) = trilinear pole of line {657, 2170}
X(61230) = perspector of circumconic {{A, B, C, X(34894), X(43762)}}
X(61230) = X(i)-isoconjugate-of-X(j) for these {i, j}: {59, 2826}, {100, 3660}, {101, 30379}, {109, 26015}, {651, 43065}, {692, 38468}, {901, 41556}, {934, 15733}, {1415, 37788}, {2283, 56850}, {10427, 14733}, {18801, 53887}, {23346, 56665}, {41555, 53243}
X(61230) = X(i)-Dao conjugate of X(j) for these {i, j}: {11, 26015}, {1015, 30379}, {1086, 38468}, {1146, 37788}, {6615, 2826}, {8054, 3660}, {14714, 15733}, {38979, 41556}, {38991, 43065}
X(61230) = X(i)-cross conjugate of X(j) for these {i, j}: {14392, 650}
X(61230) = pole of line {527, 18839} with respect to the incircle
X(61230) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(33)}}, {{A, B, C, X(11), X(35355)}}, {{A, B, C, X(100), X(885)}}, {{A, B, C, X(513), X(522)}}, {{A, B, C, X(1308), X(41162)}}, {{A, B, C, X(2254), X(35015)}}, {{A, B, C, X(3887), X(6366)}}, {{A, B, C, X(3900), X(28292)}}, {{A, B, C, X(7004), X(23696)}}, {{A, B, C, X(8058), X(15313)}}, {{A, B, C, X(42312), X(57081)}}, {{A, B, C, X(53523), X(53525)}}
X(61230) = barycentric product X(i)*X(j) for these (i, j): {1, 60483}, {2742, 4858}, {3900, 43762}, {15728, 3239}, {34894, 514}, {51567, 650}
X(61230) = barycentric quotient X(i)/X(j) for these (i, j): {513, 30379}, {514, 38468}, {522, 37788}, {649, 3660}, {650, 26015}, {657, 15733}, {663, 43065}, {1024, 56850}, {1635, 41556}, {2170, 2826}, {2742, 4564}, {10426, 37139}, {15728, 658}, {21127, 41555}, {23893, 56665}, {34894, 190}, {43762, 4569}, {51567, 4554}, {60483, 75}

X(61231) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(7) AND CEVIAN-OF-X(104)

Barycentrics    a*(a-b)*(a-c)*(a+b-c)*(a-b+c)*(a^3*(b+c)-a*(b-c)^2*(b+c)+(b^2-c^2)^2-a^2*(b^2+c^2)) : :
X(61231) = -1*X[10703]+2*X[39763]

X(61231) lies on these lines: {1, 4}, {40, 38507}, {42, 60718}, {59, 13589}, {100, 109}, {108, 36082}, {222, 11502}, {513, 23981}, {971, 34345}, {1214, 24433}, {1455, 52005}, {1458, 1647}, {1464, 14584}, {1465, 53525}, {1737, 14266}, {2222, 2720}, {3676, 41353}, {4242, 36106}, {4306, 6788}, {10703, 39763}, {21307, 54391}, {32651, 35320}, {34051, 60782}, {34465, 51236}, {34586, 51422}, {36059, 53279}, {36087, 36094}, {36090, 37136}, {42769, 56410}, {43043, 45885}, {51421, 56416}, {53160, 57105}

X(61231) = reflection of X(i) in X(j) for these {i,j}: {1, 34913}, {10703, 39763}
X(61231) = trilinear pole of line {2252, 8609}
X(61231) = perspector of circumconic {{A, B, C, X(653), X(4564)}}
X(61231) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 61214}, {11, 6099}, {21, 3657}, {80, 61043}, {513, 45393}, {521, 915}, {522, 36052}, {650, 2990}, {652, 37203}, {913, 6332}, {1946, 46133}, {2804, 15381}, {4391, 32655}, {7004, 36106}, {26932, 32698}, {39173, 43728}, {53549, 57753}
X(61231) = X(i)-Dao conjugate of X(j) for these {i, j}: {119, 522}, {32664, 61214}, {39002, 7004}, {39026, 45393}, {39053, 46133}, {39175, 37628}, {40611, 3657}, {42769, 21132}
X(61231) = X(i)-Ceva conjugate of X(j) for these {i, j}: {3658, 56410}, {36110, 109}
X(61231) = pole of line {23845, 39199} with respect to the circumcircle
X(61231) = pole of line {522, 35649} with respect to the Conway circle
X(61231) = pole of line {522, 5083} with respect to the incircle
X(61231) = pole of line {283, 3737} with respect to the Stammler hyperbola
X(61231) = pole of line {14837, 16578} with respect to the Steiner inellipse
X(61231) = pole of line {63, 20237} with respect to the Yff parabola
X(61231) = pole of line {332, 18155} with respect to the Wallace hyperbola
X(61231) = pole of line {522, 11570} with respect to the Suppa-Cucoanes circle
X(61231) = pole of line {17880, 52616} with respect to the dual conic of polar circle
X(61231) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1331)}}, {{A, B, C, X(4), X(100)}}, {{A, B, C, X(33), X(3939)}}, {{A, B, C, X(34), X(109)}}, {{A, B, C, X(108), X(1068)}}, {{A, B, C, X(225), X(4551)}}, {{A, B, C, X(278), X(651)}}, {{A, B, C, X(515), X(912)}}, {{A, B, C, X(1025), X(5236)}}, {{A, B, C, X(1457), X(51649)}}, {{A, B, C, X(1737), X(1785)}}, {{A, B, C, X(1848), X(3882)}}, {{A, B, C, X(1870), X(2720)}}, {{A, B, C, X(1877), X(18838)}}, {{A, B, C, X(2252), X(2635)}}, {{A, B, C, X(2356), X(54325)}}, {{A, B, C, X(2731), X(45766)}}, {{A, B, C, X(3738), X(55126)}}, {{A, B, C, X(4579), X(7009)}}, {{A, B, C, X(12608), X(34800)}}, {{A, B, C, X(15500), X(32641)}}, {{A, B, C, X(35015), X(42769)}}, {{A, B, C, X(36087), X(48380)}}, {{A, B, C, X(40950), X(53388)}}
X(61231) = barycentric product X(i)*X(j) for these (i, j): {108, 914}, {109, 48380}, {119, 37136}, {226, 3658}, {653, 912}, {664, 8609}, {1025, 52456}, {1737, 651}, {4564, 55126}, {11570, 655}, {12831, 37139}, {12832, 3257}, {14266, 24029}, {18026, 2252}, {18838, 190}, {39294, 42769}, {51649, 6335}, {56410, 92}, {56881, 57}, {61239, 7}
X(61231) = barycentric quotient X(i)/X(j) for these (i, j): {31, 61214}, {101, 45393}, {108, 37203}, {109, 2990}, {653, 46133}, {912, 6332}, {914, 35518}, {1400, 3657}, {1415, 36052}, {1737, 4391}, {2149, 6099}, {2252, 521}, {3658, 333}, {7113, 61043}, {7115, 36106}, {8609, 522}, {11570, 3904}, {12832, 3762}, {18838, 514}, {32669, 15381}, {32674, 915}, {37136, 57753}, {48380, 35519}, {51649, 905}, {51824, 61238}, {55126, 4858}, {56410, 63}, {56881, 312}, {61239, 8}
X(61231) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {515, 34913, 1}, {4551, 61227, 109}, {4551, 61228, 100}

X(61232) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(7) AND CEVIAN-OF-X(142)

Barycentrics    a*(a-b)*(a-c)*(2*a^2+(b-c)^2-3*a*(b+c)) : :

X(61232) lies on these lines: {3, 53397}, {9, 51300}, {55, 53391}, {100, 109}, {1018, 23704}, {2284, 35342}, {2310, 6594}, {3550, 16670}, {4069, 54440}, {4421, 55432}, {4436, 46973}, {5228, 6600}, {5528, 9355}, {8271, 51302}, {36086, 37212}, {37138, 37211}

X(61232) = trilinear pole of line {3748, 42438}
X(61232) = X(i)-isoconjugate-of-X(j) for these {i, j}: {11, 58104}, {649, 32015}
X(61232) = X(i)-Dao conjugate of X(j) for these {i, j}: {5375, 32015}
X(61232) = pole of line {63, 37111} with respect to the Yff parabola
X(61232) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1025), X(6666)}}, {{A, B, C, X(3748), X(23703)}}
X(61232) = barycentric product X(i)*X(j) for these (i, j): {100, 6666}, {190, 3748}, {1018, 17201}, {42438, 6606}, {58816, 644}, {61192, 9}
X(61232) = barycentric quotient X(i)/X(j) for these (i, j): {100, 32015}, {2149, 58104}, {3748, 514}, {6666, 693}, {17201, 7199}, {42438, 6362}, {58816, 24002}, {61192, 85}
X(61232) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 3939, 35338}

X(61233) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(8) AND CEVIAN-OF-X(21)

Barycentrics    a*(a-b)*(a-c)*(a-b-c)*(2*a*b*c+a^2*(b+c)-(b-c)^2*(b+c)) : :

X(61233) lies on these lines: {9, 11604}, {21, 55067}, {40, 20344}, {57, 26140}, {63, 150}, {100, 101}, {190, 653}, {643, 52914}, {1025, 4566}, {1281, 3501}, {1331, 1783}, {2222, 29163}, {2284, 21859}, {3239, 4115}, {3882, 14543}, {3939, 35349}, {4551, 57217}, {4712, 18413}, {5546, 53388}, {6332, 53332}, {9803, 58036}, {12736, 24036}, {16549, 25082}, {53761, 61172}, {61161, 61197}, {61180, 61236}

X(61233) = trilinear pole of line {14547, 40937}
X(61233) = X(i)-isoconjugate-of-X(j) for these {i, j}: {11, 32651}, {56, 56320}, {222, 14775}, {513, 2982}, {649, 60041}, {943, 3669}, {1015, 54952}, {1086, 15439}, {1175, 7178}, {1459, 40573}, {2170, 36048}, {2259, 3676}, {3733, 60188}, {7117, 58993}, {7180, 40412}, {7252, 52560}, {17094, 40570}, {40422, 57181}, {40435, 43924}
X(61233) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 56320}, {442, 514}, {942, 51664}, {5375, 60041}, {15607, 2170}, {16585, 24002}, {18591, 3676}, {39007, 3942}, {39026, 2982}, {40937, 4077}
X(61233) = pole of line {1019, 51664} with respect to the Stammler hyperbola
X(61233) = pole of line {9, 21} with respect to the Yff parabola
X(61233) = pole of line {1, 25885} with respect to the Hutson-Moses hyperbola
X(61233) = pole of line {3952, 4069} with respect to the dual conic of incircle
X(61233) = pole of line {312, 25082} with respect to the dual conic of Feuerbach hyperbola
X(61233) = pole of line {16586, 17755} with respect to the dual conic of Suppa-Cucoanes circle
X(61233) = intersection, other than A, B, C, of circumconics {{A, B, C, X(100), X(11604)}}, {{A, B, C, X(101), X(653)}}, {{A, B, C, X(190), X(4587)}}, {{A, B, C, X(644), X(6335)}}, {{A, B, C, X(1023), X(40937)}}, {{A, B, C, X(1026), X(6734)}}, {{A, B, C, X(3573), X(54356)}}
X(61233) = barycentric product X(i)*X(j) for these (i, j): {100, 6734}, {190, 40937}, {312, 61197}, {314, 61169}, {333, 61161}, {345, 61236}, {442, 643}, {1838, 4571}, {1859, 4561}, {2260, 646}, {2294, 645}, {3699, 942}, {3718, 53323}, {3952, 54356}, {4033, 46882}, {4076, 50354}, {4551, 51978}, {5249, 644}, {14547, 668}, {21675, 4612}, {31938, 6742}, {36797, 56839}, {40952, 7257}, {40967, 99}, {46884, 52609}, {52921, 59163}, {55010, 7259}, {61180, 78}, {61220, 8}
X(61233) = barycentric quotient X(i)/X(j) for these (i, j): {9, 56320}, {33, 14775}, {59, 36048}, {100, 60041}, {101, 2982}, {442, 4077}, {643, 40412}, {644, 40435}, {765, 54952}, {942, 3676}, {1018, 60188}, {1110, 15439}, {1783, 40573}, {1859, 7649}, {2149, 32651}, {2260, 3669}, {2294, 7178}, {3699, 40422}, {3939, 943}, {4551, 52560}, {5249, 24002}, {6734, 693}, {7012, 58993}, {8021, 3737}, {14547, 513}, {18591, 51664}, {23207, 1459}, {31938, 4467}, {33525, 2170}, {37993, 50354}, {39772, 31603}, {40937, 514}, {40952, 4017}, {40956, 43924}, {40967, 523}, {40978, 7180}, {46882, 1019}, {46884, 17925}, {50354, 1358}, {51978, 18155}, {52306, 3942}, {53323, 34}, {54356, 7192}, {56839, 17094}, {61161, 226}, {61169, 65}, {61180, 273}, {61197, 57}, {61220, 7}, {61236, 278}
X(61233) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 644, 4587}, {1018, 35341, 644}, {1018, 61237, 100}, {61161, 61197, 61220}

X(61234) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(8) AND CEVIAN-OF-X(42)

Barycentrics    a*(a-b)*(a-c)*(b*c*(b+c)+a*(b^2+c^2)) : :

X(61234) lies on these lines: {1, 3121}, {2, 17176}, {9, 53393}, {43, 7075}, {63, 20371}, {100, 101}, {116, 30016}, {190, 4598}, {312, 21369}, {514, 53355}, {645, 3570}, {649, 4427}, {650, 61172}, {661, 3909}, {750, 16549}, {789, 803}, {799, 4602}, {813, 8707}, {931, 28841}, {1025, 6649}, {1054, 24578}, {1150, 16552}, {1213, 25448}, {1755, 3985}, {2108, 25819}, {2170, 38484}, {2225, 4358}, {2229, 3231}, {2284, 61164}, {2319, 8616}, {3208, 18755}, {3294, 32917}, {3501, 5277}, {3952, 46148}, {3971, 53129}, {4011, 20665}, {4253, 37684}, {4434, 39258}, {4436, 24052}, {4553, 7239}, {4871, 20459}, {5235, 46196}, {5364, 29649}, {6377, 17475}, {17277, 29480}, {17754, 40750}, {18064, 29391}, {18169, 21838}, {20367, 24602}, {21366, 56524}, {22033, 57234}, {23354, 61175}, {30729, 61168}, {32919, 45751}, {33164, 56558}, {38346, 40614}, {40972, 59511}, {43077, 53625}, {53338, 61165}, {54325, 57165}

X(61234) = trilinear pole of line {1107, 2309}
X(61234) = X(i)-isoconjugate-of-X(j) for these {i, j}: {99, 40525}, {512, 40409}, {513, 1258}, {514, 57399}, {649, 40418}, {667, 1221}, {1086, 59102}, {3733, 60230}, {6377, 59094}, {53581, 59148}
X(61234) = X(i)-Dao conjugate of X(j) for these {i, j}: {1107, 4374}, {3122, 3125}, {3741, 661}, {5375, 40418}, {6631, 1221}, {21024, 20906}, {21838, 693}, {38986, 40525}, {39026, 1258}, {39054, 40409}, {51575, 514}, {59565, 1577}
X(61234) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4601, 1}
X(61234) = X(i)-cross conjugate of X(j) for these {i, j}: {50510, 18169}
X(61234) = pole of line {4557, 61164} with respect to the circumcircle
X(61234) = pole of line {1621, 34063} with respect to the Kiepert parabola
X(61234) = pole of line {1019, 1924} with respect to the Stammler hyperbola
X(61234) = pole of line {9, 43} with respect to the Yff parabola
X(61234) = pole of line {1, 22167} with respect to the Hutson-Moses hyperbola
X(61234) = pole of line {798, 4369} with respect to the Wallace hyperbola
X(61234) = intersection, other than A, B, C, of circumconics {{A, B, C, X(100), X(4594)}}, {{A, B, C, X(101), X(4598)}}, {{A, B, C, X(1018), X(4602)}}, {{A, B, C, X(1023), X(1107)}}, {{A, B, C, X(1026), X(3741)}}, {{A, B, C, X(3573), X(8707)}}, {{A, B, C, X(8632), X(50510)}}, {{A, B, C, X(20891), X(42723)}}, {{A, B, C, X(21838), X(27853)}}
X(61234) = barycentric product X(i)*X(j) for these (i, j): {1, 53338}, {100, 3741}, {101, 20891}, {1018, 16738}, {1107, 190}, {1197, 1978}, {2309, 668}, {3728, 99}, {3882, 56901}, {3903, 51575}, {4579, 59171}, {18091, 4553}, {18169, 3952}, {18830, 45216}, {21024, 662}, {21700, 4623}, {21713, 52935}, {21838, 799}, {22065, 6335}, {22206, 4610}, {23212, 57968}, {27880, 4594}, {30097, 644}, {36037, 51411}, {39780, 7257}, {40627, 4601}, {45208, 645}, {50510, 7035}, {53268, 75}, {59565, 932}, {61165, 81}
X(61234) = barycentric quotient X(i)/X(j) for these (i, j): {100, 40418}, {101, 1258}, {190, 1221}, {662, 40409}, {692, 57399}, {798, 40525}, {1018, 60230}, {1107, 514}, {1110, 59102}, {1197, 649}, {2309, 513}, {3728, 523}, {3741, 693}, {4579, 59158}, {4623, 59148}, {16738, 7199}, {18169, 7192}, {20891, 3261}, {21024, 1577}, {21700, 4705}, {21713, 4036}, {21838, 661}, {22065, 905}, {22206, 4024}, {22389, 1459}, {23212, 810}, {23473, 3777}, {27880, 2533}, {30097, 24002}, {39780, 4017}, {40627, 3125}, {45208, 7178}, {45216, 4083}, {50510, 244}, {51411, 36038}, {51575, 4374}, {53268, 1}, {53338, 75}, {59565, 20906}, {61165, 321}
X(61234) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 61163, 4427}, {1018, 61235, 100}, {2225, 4358, 20372}, {2229, 3231, 18792}

X(61235) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(8) AND CEVIAN-OF-X(43)

Barycentrics    a*(a-b)*(a-c)*(a*(b-c)^2+b*c*(b+c)) : :

X(61235) lies on these lines: {1, 6377}, {2, 38346}, {10, 20460}, {43, 3051}, {100, 101}, {116, 30039}, {190, 25577}, {649, 3952}, {650, 7239}, {668, 4598}, {799, 1019}, {812, 21580}, {813, 8706}, {2319, 16569}, {3570, 21362}, {3888, 23650}, {4576, 18197}, {4603, 17934}, {4781, 61163}, {5205, 20372}, {8709, 27805}, {16549, 56010}, {17277, 29384}, {17780, 46148}, {24003, 24491}, {32917, 46196}, {35326, 61164}

X(61235) = trilinear pole of line {17448, 22167}
X(61235) = X(i)-isoconjugate-of-X(j) for these {i, j}: {514, 57400}, {649, 32011}, {1019, 56256}, {3733, 56197}
X(61235) = X(i)-Dao conjugate of X(j) for these {i, j}: {3123, 21138}, {3840, 3835}, {5375, 32011}, {26772, 18081}, {59676, 514}
X(61235) = X(i)-Ceva conjugate of X(j) for these {i, j}: {5383, 1}
X(61235) = pole of line {9, 1575} with respect to the Yff parabola
X(61235) = pole of line {3768, 7199} with respect to the Wallace hyperbola
X(61235) = intersection, other than A, B, C, of circumconics {{A, B, C, X(101), X(32039)}}, {{A, B, C, X(668), X(25312)}}, {{A, B, C, X(799), X(22343)}}, {{A, B, C, X(1023), X(17448)}}, {{A, B, C, X(1026), X(3840)}}, {{A, B, C, X(3573), X(8706)}}, {{A, B, C, X(20892), X(42723)}}
X(61235) = barycentric product X(i)*X(j) for these (i, j): {1, 61183}, {100, 3840}, {101, 20892}, {1018, 17178}, {17448, 190}, {18102, 4553}, {18192, 3952}, {21025, 662}, {22066, 6335}, {22167, 99}, {22343, 668}, {25312, 87}
X(61235) = barycentric quotient X(i)/X(j) for these (i, j): {100, 32011}, {692, 57400}, {1018, 56197}, {3840, 693}, {4557, 56256}, {17178, 7199}, {17448, 514}, {18192, 7192}, {20892, 3261}, {21025, 1577}, {22066, 905}, {22167, 523}, {22343, 513}, {23213, 22090}, {25312, 6376}, {61183, 75}
X(61235) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 61234, 1018}

X(61236) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(8) AND CEVIAN-OF-X(72)

Barycentrics    a*(a-b)*(a-c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(2*a*b*c+a^2*(b+c)-(b-c)^2*(b+c)) : :

X(61236) lies on these lines: {4, 4253}, {19, 5620}, {36, 2202}, {40, 52011}, {53, 583}, {57, 18679}, {101, 108}, {109, 58965}, {112, 1983}, {162, 163}, {169, 208}, {232, 3002}, {297, 18206}, {318, 16549}, {393, 579}, {451, 7079}, {573, 1249}, {648, 3882}, {653, 1020}, {672, 1785}, {1018, 1897}, {1025, 18026}, {1030, 52166}, {1068, 41320}, {1475, 56814}, {1708, 55463}, {1741, 55462}, {1766, 18685}, {1845, 2170}, {1865, 15762}, {1875, 43065}, {1990, 2245}, {2332, 7414}, {3144, 7719}, {3430, 8885}, {3730, 7952}, {4242, 35342}, {4251, 7412}, {4262, 37441}, {4266, 40138}, {4559, 23706}, {5030, 37305}, {5081, 45751}, {5179, 51359}, {6591, 61205}, {7070, 51971}, {16552, 17555}, {16574, 17907}, {39690, 45929}, {44698, 48883}, {53323, 61161}, {61178, 61239}, {61180, 61233}

X(61236) = trilinear pole of line {1841, 1859}
X(61236) = perspector of circumconic {{A, B, C, X(7012), X(24000)}}
X(61236) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 56320}, {394, 14775}, {514, 1794}, {520, 40395}, {521, 2982}, {525, 1175}, {647, 40412}, {652, 60041}, {905, 943}, {1459, 40435}, {2259, 4025}, {2605, 57860}, {2968, 32651}, {3265, 40570}, {4467, 57691}, {7117, 54952}, {15439, 26932}, {22383, 40422}, {23090, 52560}, {23189, 60188}, {23224, 40447}, {34591, 36048}, {35072, 58993}, {40573, 57241}
X(61236) = X(i)-Dao conjugate of X(j) for these {i, j}: {442, 6332}, {942, 24018}, {15607, 34591}, {16585, 15413}, {18591, 4025}, {36103, 56320}, {39052, 40412}, {40937, 14208}, {52119, 20902}
X(61236) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1897, 61169}, {34922, 33}
X(61236) = pole of line {4858, 17761} with respect to the polar circle
X(61236) = pole of line {1490, 1766} with respect to the Yff parabola
X(61236) = intersection, other than A, B, C, of circumconics {{A, B, C, X(101), X(653)}}, {{A, B, C, X(108), X(52920)}}, {{A, B, C, X(162), X(4551)}}, {{A, B, C, X(163), X(1020)}}, {{A, B, C, X(823), X(1018)}}, {{A, B, C, X(1783), X(54240)}}, {{A, B, C, X(2294), X(56829)}}, {{A, B, C, X(4242), X(15762)}}, {{A, B, C, X(24035), X(40937)}}, {{A, B, C, X(32674), X(53323)}}
X(61236) = barycentric product X(i)*X(j) for these (i, j): {1, 61180}, {4, 61220}, {27, 61161}, {100, 1838}, {107, 56839}, {108, 6734}, {162, 442}, {278, 61233}, {286, 61169}, {1234, 32676}, {1252, 23595}, {1783, 5249}, {1841, 190}, {1844, 6742}, {1859, 664}, {1865, 662}, {1897, 942}, {2260, 6335}, {2294, 648}, {3952, 46883}, {4033, 46890}, {4242, 45926}, {4552, 46884}, {14547, 18026}, {15455, 44095}, {15742, 50354}, {18591, 823}, {23207, 52938}, {23752, 5379}, {40937, 653}, {40952, 811}, {40978, 6331}, {41393, 52921}, {53323, 75}, {54356, 61178}, {61197, 92}
X(61236) = barycentric quotient X(i)/X(j) for these (i, j): {19, 56320}, {108, 60041}, {162, 40412}, {442, 14208}, {445, 18160}, {692, 1794}, {942, 4025}, {1096, 14775}, {1783, 40435}, {1838, 693}, {1841, 514}, {1844, 4467}, {1859, 522}, {1865, 1577}, {1897, 40422}, {2260, 905}, {2294, 525}, {4303, 4131}, {5249, 15413}, {6734, 35518}, {7012, 54952}, {8021, 57081}, {8750, 943}, {14547, 521}, {14597, 4091}, {18591, 24018}, {18607, 30805}, {23207, 57241}, {23595, 23989}, {24019, 40395}, {24033, 58993}, {32674, 2982}, {32676, 1175}, {33525, 34591}, {40937, 6332}, {40952, 656}, {40956, 1459}, {40967, 52355}, {40978, 647}, {44095, 14838}, {46883, 7192}, {46884, 4560}, {46890, 1019}, {50354, 1565}, {53323, 1}, {56839, 3265}, {61161, 306}, {61169, 72}, {61180, 75}, {61197, 63}, {61220, 69}, {61233, 345}
X(61236) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {108, 1783, 101}, {1865, 44095, 46884}

X(61237) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(8) AND CEVIAN-OF-X(78)

Barycentrics    a*(a-b)*(a-c)*(-(a^2*(b-c)^2)+a^3*(b+c)-a*(b-c)^2*(b+c)+(b^2-c^2)^2) : :
X(61237) = -1*X[18239]+2*X[45119]

X(61237) lies on these lines: {1, 7117}, {9, 119}, {10, 15970}, {19, 117}, {40, 2883}, {46, 1729}, {57, 4904}, {71, 59644}, {100, 101}, {109, 1783}, {163, 1021}, {169, 16549}, {213, 1939}, {281, 1765}, {282, 60006}, {514, 4566}, {515, 2272}, {607, 1771}, {650, 4559}, {653, 1020}, {672, 8074}, {759, 55067}, {906, 23703}, {1025, 3732}, {1146, 58036}, {1158, 7079}, {1565, 53409}, {1625, 3737}, {1715, 41320}, {1726, 55478}, {1735, 5089}, {1764, 28921}, {1855, 12616}, {2077, 58325}, {2170, 12736}, {2252, 8756}, {2800, 34591}, {3509, 60369}, {3913, 22153}, {4551, 53761}, {4574, 61222}, {5882, 22088}, {8558, 60355}, {12672, 46830}, {13528, 51376}, {14543, 21362}, {17905, 34030}, {17911, 56861}, {18239, 45119}, {21859, 35326}, {21933, 40979}, {33810, 35072}, {35338, 61161}, {54156, 56857}, {61212, 61227}

X(61237) = midpoint of X(i) and X(j) for these {i,j}: {40, 58037}
X(61237) = reflection of X(i) in X(j) for these {i,j}: {18239, 45119}
X(61237) = trilinear pole of line {1108, 1864}
X(61237) = perspector of circumconic {{A, B, C, X(765), X(24032)}}
X(61237) = X(i)-isoconjugate-of-X(j) for these {i, j}: {108, 40527}, {513, 40399}, {514, 1167}, {521, 40397}, {649, 40424}, {1019, 56259}, {1459, 40444}, {14837, 57422}, {16596, 58984}
X(61237) = X(i)-Dao conjugate of X(j) for these {i, j}: {1108, 17896}, {1210, 6332}, {5375, 40424}, {6260, 514}, {7004, 26932}, {38983, 40527}, {39026, 40399}
X(61237) = X(i)-Ceva conjugate of X(j) for these {i, j}: {46102, 1}
X(61237) = X(i)-cross conjugate of X(j) for these {i, j}: {53288, 61227}
X(61237) = pole of line {4557, 14723} with respect to the circumcircle
X(61237) = pole of line {1621, 17221} with respect to the Kiepert parabola
X(61237) = pole of line {1019, 57212} with respect to the Stammler hyperbola
X(61237) = pole of line {24030, 24036} with respect to the Steiner inellipse
X(61237) = pole of line {3, 9} with respect to the Yff parabola
X(61237) = pole of line {1, 12059} with respect to the Hutson-Moses hyperbola
X(61237) = pole of line {16870, 24198} with respect to the dual conic of Yff parabola
X(61237) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(100), X(46435)}}, {{A, B, C, X(101), X(53288)}}, {{A, B, C, X(644), X(40117)}}, {{A, B, C, X(653), X(4587)}}, {{A, B, C, X(1021), X(40628)}}, {{A, B, C, X(1023), X(1108)}}, {{A, B, C, X(1026), X(1210)}}, {{A, B, C, X(17862), X(42723)}}
X(61237) = barycentric product X(i)*X(j) for these (i, j): {1, 61185}, {100, 1210}, {101, 17862}, {312, 61212}, {1071, 1897}, {1108, 190}, {1226, 692}, {1532, 36037}, {1864, 664}, {3611, 811}, {3699, 37566}, {13138, 6260}, {21933, 662}, {40628, 46102}, {40958, 668}, {40979, 4552}, {41543, 55185}, {41562, 6742}, {53288, 75}, {57285, 643}, {61227, 8}
X(61237) = barycentric quotient X(i)/X(j) for these (i, j): {100, 40424}, {101, 40399}, {652, 40527}, {692, 1167}, {1071, 4025}, {1108, 514}, {1210, 693}, {1226, 40495}, {1532, 36038}, {1783, 40444}, {1864, 522}, {3611, 656}, {4557, 56259}, {6260, 17896}, {17862, 3261}, {21933, 1577}, {23204, 1459}, {32652, 57422}, {32674, 40397}, {37566, 3676}, {40628, 26932}, {40958, 513}, {40979, 4560}, {41543, 55186}, {41562, 4467}, {53288, 1}, {57285, 4077}, {61185, 75}, {61212, 57}, {61227, 7}
X(61237) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {46, 7719, 1729}, {100, 61233, 1018}, {109, 35349, 1783}, {650, 4559, 61224}

X(61238) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(8) AND CEVIAN-OF-X(100)

Barycentrics    a*(a-b-c)*(b-c)*((a-b)^2*(a+b)+2*a*b*c-(a+b)*c^2)*(a^3-a*(b-c)^2-a^2*c-b^2*c+c^3) : :

X(61238) lies on these lines: {1, 53046}, {6, 650}, {9, 652}, {19, 649}, {55, 1946}, {57, 514}, {104, 2291}, {284, 1021}, {654, 900}, {657, 6544}, {665, 1945}, {673, 34234}, {909, 1635}, {1436, 4394}, {1936, 23696}, {1983, 23703}, {2195, 2342}, {2316, 3738}, {3570, 13136}, {9319, 36819}, {14307, 53285}, {14330, 39393}, {14331, 39943}, {18816, 60014}, {23615, 30223}, {24029, 53811}, {25954, 60025}, {34051, 43050}, {36795, 36799}, {37136, 37139}

X(61238) = isogonal conjugate of X(24029)
X(61238) = trilinear pole of line {663, 2310}
X(61238) = perspector of circumconic {{A, B, C, X(104), X(36123)}}
X(61238) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 24029}, {2, 23981}, {7, 2427}, {56, 2397}, {59, 10015}, {63, 23706}, {100, 1465}, {101, 22464}, {109, 908}, {190, 1457}, {222, 53151}, {517, 651}, {653, 22350}, {655, 34586}, {664, 2183}, {666, 53548}, {859, 4552}, {883, 51987}, {901, 52659}, {1025, 54364}, {1214, 4246}, {1262, 2804}, {1275, 53549}, {1332, 1875}, {1361, 13136}, {1402, 55258}, {1414, 21801}, {1415, 3262}, {1461, 6735}, {1769, 4564}, {1785, 1813}, {2149, 36038}, {2222, 16586}, {2720, 26611}, {3257, 53530}, {3310, 4998}, {4559, 17139}, {4565, 17757}, {4573, 51377}, {4617, 51380}, {4619, 35015}, {6516, 14571}, {7045, 46393}, {8677, 46102}, {15632, 34051}, {23703, 52031}, {23980, 54953}, {24028, 37136}, {31615, 42753}, {32714, 51379}, {32735, 51390}, {38828, 51433}, {39534, 44717}, {42752, 55194}, {42770, 59101}, {51407, 52928}, {52307, 55346}
X(61238) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 2397}, {3, 24029}, {11, 908}, {650, 36038}, {1015, 22464}, {1146, 3262}, {3119, 51416}, {3162, 23706}, {6615, 10015}, {8054, 1465}, {17115, 46393}, {32664, 23981}, {35508, 6735}, {36944, 42718}, {38979, 52659}, {38981, 26611}, {38984, 16586}, {38991, 517}, {39025, 2183}, {40605, 55258}, {40608, 21801}, {55053, 1457}, {55055, 53530}, {55064, 17757}, {55067, 17139}
X(61238) = X(i)-Ceva conjugate of X(j) for these {i, j}: {32641, 2250}, {36037, 2342}, {37136, 104}, {53811, 1}
X(61238) = X(i)-cross conjugate of X(j) for these {i, j}: {1635, 650}, {4530, 9}, {8648, 3737}
X(61238) = pole of line {1877, 6001} with respect to the orthic inconic
X(61238) = pole of line {8609, 44675} with respect to the Steiner inellipse
X(61238) = pole of line {24029, 55258} with respect to the Wallace hyperbola
X(61238) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(14204)}}, {{A, B, C, X(6), X(9)}}, {{A, B, C, X(11), X(35348)}}, {{A, B, C, X(100), X(885)}}, {{A, B, C, X(514), X(650)}}, {{A, B, C, X(521), X(7649)}}, {{A, B, C, X(522), X(9001)}}, {{A, B, C, X(649), X(652)}}, {{A, B, C, X(654), X(57174)}}, {{A, B, C, X(900), X(3738)}}, {{A, B, C, X(1019), X(36137)}}, {{A, B, C, X(1027), X(18191)}}, {{A, B, C, X(1635), X(4530)}}, {{A, B, C, X(1936), X(54407)}}, {{A, B, C, X(2342), X(34234)}}, {{A, B, C, X(3570), X(4435)}}, {{A, B, C, X(3737), X(43927)}}, {{A, B, C, X(4394), X(14298)}}, {{A, B, C, X(4895), X(6544)}}, {{A, B, C, X(8611), X(40628)}}, {{A, B, C, X(24029), X(53046)}}, {{A, B, C, X(35355), X(42552)}}, {{A, B, C, X(36037), X(57468)}}, {{A, B, C, X(40218), X(52663)}}, {{A, B, C, X(43728), X(43933)}}, {{A, B, C, X(45145), X(51565)}}, {{A, B, C, X(56757), X(56759)}}
X(61238) = barycentric product X(i)*X(j) for these (i, j): {1, 43728}, {11, 36037}, {104, 522}, {333, 55259}, {513, 51565}, {514, 52663}, {1024, 56753}, {1146, 37136}, {1309, 7004}, {1795, 44426}, {1809, 7649}, {2250, 4560}, {2310, 54953}, {2342, 693}, {2401, 9}, {2423, 312}, {2968, 36110}, {3239, 34051}, {3737, 38955}, {3738, 40437}, {4391, 909}, {10428, 4768}, {13136, 2170}, {14578, 46110}, {14776, 17880}, {14942, 57468}, {15635, 3699}, {16082, 652}, {18816, 663}, {23838, 36944}, {23978, 32669}, {24026, 2720}, {32641, 4858}, {34234, 650}, {34589, 53702}, {34858, 35519}, {36123, 521}, {36795, 649}, {36819, 885}, {37628, 4}, {43933, 78}, {46393, 59196}
X(61238) = barycentric quotient X(i)/X(j) for these (i, j): {6, 24029}, {9, 2397}, {11, 36038}, {25, 23706}, {31, 23981}, {33, 53151}, {41, 2427}, {104, 664}, {333, 55258}, {513, 22464}, {522, 3262}, {649, 1465}, {650, 908}, {654, 16586}, {663, 517}, {667, 1457}, {884, 54364}, {909, 651}, {1635, 52659}, {1795, 6516}, {1809, 4561}, {1946, 22350}, {1960, 53530}, {2170, 10015}, {2250, 4552}, {2299, 4246}, {2310, 2804}, {2342, 100}, {2401, 85}, {2423, 57}, {2720, 7045}, {3063, 2183}, {3271, 1769}, {3709, 21801}, {3737, 17139}, {3900, 6735}, {4041, 17757}, {4105, 51380}, {4162, 51433}, {4435, 51381}, {4814, 51362}, {4895, 1145}, {6608, 51416}, {8611, 51367}, {8648, 34586}, {14578, 1813}, {14776, 7012}, {14936, 46393}, {15635, 3676}, {16082, 46404}, {18191, 23788}, {18344, 1785}, {18816, 4572}, {32641, 4564}, {32669, 1262}, {32702, 7128}, {34051, 658}, {34234, 4554}, {34858, 109}, {36037, 4998}, {36110, 55346}, {36123, 18026}, {36795, 1978}, {36819, 883}, {37136, 1275}, {37628, 69}, {40437, 35174}, {41933, 37136}, {43728, 75}, {43933, 273}, {46384, 46398}, {46393, 26611}, {51565, 668}, {51824, 61231}, {52663, 190}, {53549, 24028}, {55259, 226}, {55943, 34085}, {57108, 51379}, {57468, 9436}, {58313, 1845}, {58369, 39776}

X(61239) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(8) AND CEVIAN-OF-X(104)

Barycentrics    a*(a-b)*(a-c)*(a^3*(b+c)-a*(b-c)^2*(b+c)+(b^2-c^2)^2-a^2*(b^2+c^2)) : :

X(61239) lies on these lines: {4, 9}, {46, 18343}, {100, 101}, {514, 1025}, {650, 2427}, {655, 24029}, {672, 4530}, {813, 929}, {1737, 52456}, {1983, 23703}, {2245, 56750}, {2250, 36910}, {2252, 14266}, {4041, 54325}, {5687, 56528}, {12247, 58036}, {16549, 26690}, {21859, 61197}, {26704, 29014}, {61178, 61236}

X(61239) = perspector of circumconic {{A, B, C, X(765), X(1897)}}
X(61239) = X(i)-isoconjugate-of-X(j) for these {i, j}: {7, 61214}, {81, 3657}, {513, 2990}, {514, 36052}, {693, 32655}, {905, 915}, {913, 4025}, {1086, 6099}, {1459, 37203}, {1565, 32698}, {2006, 61043}, {2401, 39173}, {3310, 57753}, {3669, 45393}, {3942, 36106}, {10015, 15381}, {22383, 46133}
X(61239) = X(i)-Dao conjugate of X(j) for these {i, j}: {119, 514}, {1737, 3904}, {8609, 36038}, {39002, 3942}, {39026, 2990}, {40586, 3657}, {42769, 6545}
X(61239) = pole of line {4557, 48387} with respect to the circumcircle
X(61239) = pole of line {1834, 56416} with respect to the Kiepert hyperbola
X(61239) = pole of line {1019, 1790} with respect to the Stammler hyperbola
X(61239) = pole of line {3239, 24036} with respect to the Steiner inellipse
X(61239) = pole of line {9, 48} with respect to the Yff parabola
X(61239) = pole of line {1, 18254} with respect to the Hutson-Moses hyperbola
X(61239) = pole of line {7199, 17206} with respect to the Wallace hyperbola
X(61239) = pole of line {4000, 24198} with respect to the dual conic of Yff parabola
X(61239) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(100)}}, {{A, B, C, X(9), X(4587)}}, {{A, B, C, X(19), X(101)}}, {{A, B, C, X(40), X(56410)}}, {{A, B, C, X(242), X(929)}}, {{A, B, C, X(281), X(644)}}, {{A, B, C, X(516), X(912)}}, {{A, B, C, X(573), X(29014)}}, {{A, B, C, X(655), X(32641)}}, {{A, B, C, X(914), X(5179)}}, {{A, B, C, X(1018), X(1826)}}, {{A, B, C, X(1023), X(8609)}}, {{A, B, C, X(1026), X(1737)}}, {{A, B, C, X(1839), X(35342)}}, {{A, B, C, X(1855), X(35341)}}, {{A, B, C, X(2183), X(2252)}}, {{A, B, C, X(3887), X(55126)}}, {{A, B, C, X(5011), X(35182)}}, {{A, B, C, X(6197), X(15439)}}, {{A, B, C, X(18838), X(54234)}}, {{A, B, C, X(21016), X(35309)}}, {{A, B, C, X(42723), X(48380)}}
X(61239) = barycentric product X(i)*X(j) for these (i, j): {1, 56881}, {10, 3658}, {100, 1737}, {101, 48380}, {119, 36037}, {190, 8609}, {318, 56410}, {1026, 52456}, {1783, 914}, {1897, 912}, {2252, 6335}, {11570, 51562}, {18838, 3699}, {34332, 36106}, {55126, 765}, {61231, 8}
X(61239) = barycentric quotient X(i)/X(j) for these (i, j): {41, 61214}, {42, 3657}, {101, 2990}, {119, 36038}, {692, 36052}, {912, 4025}, {914, 15413}, {1110, 6099}, {1737, 693}, {1783, 37203}, {1897, 46133}, {2252, 905}, {2361, 61043}, {3658, 86}, {3939, 45393}, {8609, 514}, {8750, 915}, {11570, 4453}, {18838, 3676}, {32739, 32655}, {36037, 57753}, {48380, 3261}, {55126, 1111}, {56410, 77}, {56881, 75}, {61231, 7}
X(61239) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 61171, 2427}, {1018, 35341, 4752}, {1018, 61237, 101}

X(61240) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(8) AND CEVIAN-OF-X(144)

Barycentrics    a*(a-b)*(a-c)*(a+b-c)*(a-b+c)*((a-b)^2+2*(a+b)*c-3*c^2)*(a^2+2*a*b-3*b^2-2*a*c+2*b*c+c^2) : :

X(61240) lies on these lines: {7, 13609}, {57, 3119}, {88, 43047}, {100, 53622}, {190, 53640}, {650, 4617}, {651, 46392}, {658, 57455}, {673, 2898}, {1025, 27834}, {1156, 1445}, {3160, 23587}, {3306, 36100}, {8732, 43762}, {9358, 36086}, {10405, 34234}, {37131, 37789}, {37206, 56543}

X(61240) = trilinear pole of line {1, 1419}
X(61240) = X(i)-isoconjugate-of-X(j) for these {i, j}: {55, 7658}, {56, 57064}, {57, 58835}, {109, 13609}, {144, 663}, {165, 650}, {284, 55285}, {522, 3207}, {657, 3160}, {1419, 3900}, {3063, 16284}, {3064, 22117}, {3737, 21872}, {4105, 9533}, {4130, 17106}, {6362, 33634}, {7252, 21060}, {8641, 31627}, {11051, 58877}, {50561, 57180}
X(61240) = X(i)-vertex conjugate of X(j) for these {i, j}: {55, 4617}
X(61240) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 57064}, {11, 13609}, {223, 7658}, {5452, 58835}, {10001, 16284}, {40590, 55285}
X(61240) = X(i)-cross conjugate of X(j) for these {i, j}: {650, 19605}, {934, 651}, {3900, 7}, {5022, 59}, {19541, 55346}, {53056, 7045}
X(61240) = pole of line {10860, 60966} with respect to the Yff parabola
X(61240) = pole of line {56355, 60966} with respect to the Hutson-Moses hyperbola
X(61240) = pole of line {346, 34060} with respect to the dual conic of Feuerbach hyperbola
X(61240) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(13138)}}, {{A, B, C, X(57), X(108)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(643), X(50392)}}, {{A, B, C, X(644), X(30610)}}, {{A, B, C, X(650), X(3119)}}, {{A, B, C, X(666), X(31343)}}, {{A, B, C, X(927), X(6613)}}, {{A, B, C, X(1025), X(5435)}}, {{A, B, C, X(1445), X(56543)}}, {{A, B, C, X(1638), X(42552)}}, {{A, B, C, X(2406), X(3306)}}, {{A, B, C, X(3900), X(13609)}}, {{A, B, C, X(3911), X(43047)}}, {{A, B, C, X(4619), X(8697)}}, {{A, B, C, X(6164), X(53544)}}, {{A, B, C, X(8056), X(36050)}}
X(61240) = barycentric product X(i)*X(j) for these (i, j): {1, 53640}, {100, 36620}, {109, 44186}, {3062, 664}, {10405, 651}, {11051, 4554}, {19605, 658}, {42872, 44327}, {53622, 75}, {55284, 65}, {56718, 927}, {60831, 644}
X(61240) = barycentric quotient X(i)/X(j) for these (i, j): {9, 57064}, {55, 58835}, {57, 7658}, {65, 55285}, {109, 165}, {165, 58877}, {650, 13609}, {651, 144}, {658, 31627}, {664, 16284}, {934, 3160}, {1415, 3207}, {1461, 1419}, {3062, 522}, {4551, 21060}, {4559, 21872}, {4569, 50560}, {4617, 9533}, {4626, 50561}, {6614, 17106}, {10405, 4391}, {11051, 650}, {19605, 3239}, {36059, 22117}, {36620, 693}, {42872, 14837}, {44186, 35519}, {53622, 1}, {53640, 75}, {55284, 314}, {56718, 50333}, {60831, 24002}, {61227, 41561}

X(61241) = AREAL CENTER OF THESE TRIANGLES: CEVIAN-OF-X(9) AND CEVIAN-OF-X(144)

Barycentrics    (a-b)*(a-c)*(a+b-c)^2*(a-b+c)^2*(-(b-c)^2+a*(b+c)) : :

X(61241) lies on these lines: {7, 2310}, {279, 34578}, {347, 17113}, {651, 658}, {934, 1292}, {1020, 58817}, {1418, 53241}, {1446, 54497}, {3939, 56543}, {4552, 4569}, {4565, 4616}, {4566, 41353}, {17092, 23062}, {24011, 56322}, {30682, 37800}, {35312, 35338}, {37787, 41351}, {41356, 61019}

X(61241) = trilinear pole of line {354, 10481}
X(61241) = X(i)-isoconjugate-of-X(j) for these {i, j}: {220, 58322}, {522, 59141}, {650, 10482}, {657, 2346}, {663, 6605}, {1170, 4105}, {1174, 3900}, {1253, 56322}, {3063, 56118}, {3119, 53243}, {8641, 32008}, {21453, 57180}, {21789, 56255}
X(61241) = X(i)-Dao conjugate of X(j) for these {i, j}: {142, 4130}, {1111, 24026}, {1212, 3239}, {3119, 24010}, {10001, 56118}, {17113, 56322}, {40606, 3900}
X(61241) = X(i)-Ceva conjugate of X(j) for these {i, j}: {7045, 279}, {24011, 7}
X(61241) = X(i)-cross conjugate of X(j) for these {i, j}: {10581, 354}, {21104, 10481}, {21127, 7}
X(61241) = pole of line {347, 4847} with respect to the dual conic of Feuerbach hyperbola
X(61241) = intersection, other than A, B, C, of circumconics {{A, B, C, X(142), X(38340)}}, {{A, B, C, X(651), X(1292)}}, {{A, B, C, X(658), X(35312)}}, {{A, B, C, X(1418), X(4565)}}, {{A, B, C, X(1638), X(21104)}}, {{A, B, C, X(2293), X(45244)}}, {{A, B, C, X(2310), X(21127)}}, {{A, B, C, X(4616), X(53242)}}
X(61241) = barycentric product X(i)*X(j) for these (i, j): {100, 53242}, {142, 658}, {354, 4569}, {1020, 16708}, {1088, 35338}, {1212, 36838}, {1229, 4617}, {1233, 1461}, {1275, 21104}, {1418, 4554}, {1475, 46406}, {2293, 52937}, {3925, 4616}, {4573, 52023}, {4626, 4847}, {10481, 664}, {10581, 57581}, {17169, 4566}, {20880, 934}, {21808, 4635}, {23062, 35341}, {23599, 4564}, {24011, 6608}, {35312, 7}, {35326, 57792}, {53236, 53321}, {53237, 6516}, {59181, 651}, {59457, 6362}
X(61241) = barycentric quotient X(i)/X(j) for these (i, j): {109, 10482}, {142, 3239}, {269, 58322}, {279, 56322}, {354, 3900}, {651, 6605}, {658, 32008}, {664, 56118}, {934, 2346}, {1020, 56255}, {1212, 4130}, {1233, 52622}, {1358, 56284}, {1415, 59141}, {1418, 650}, {1461, 1174}, {1475, 657}, {2293, 4105}, {2488, 3022}, {4566, 56157}, {4569, 57815}, {4617, 1170}, {4626, 21453}, {4847, 4163}, {6362, 4081}, {6608, 24010}, {7339, 53243}, {10481, 522}, {10581, 35508}, {17169, 7253}, {17194, 58329}, {18164, 1021}, {20229, 57180}, {20880, 4397}, {21104, 1146}, {21127, 3119}, {21808, 4171}, {22053, 57108}, {23599, 4858}, {35310, 4515}, {35312, 8}, {35326, 220}, {35338, 200}, {35341, 728}, {36838, 31618}, {48151, 2310}, {51463, 4528}, {52020, 4524}, {52023, 3700}, {53237, 44426}, {53238, 17926}, {53241, 28132}, {53242, 693}, {55282, 52335}, {59181, 4391}, {59457, 6606}
X(61241) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {658, 4626, 651}

X(61242) = X(2)X(3)∩X(195)X(15109)

Barycentrics    a^2 (a^14-7 a^12 (b^2+c^2)+3 a^10 (7 b^4+10 b^2 c^2+7 c^4)-5 a^8 (7 b^6+9 b^4 c^2+9 b^2 c^4+7 c^6)+a^6 (35 b^8+20 b^6 c^2+17 b^4 c^4+20 b^2 c^6+35 c^8)-3 a^4 (7 b^10-5 b^8 c^2-3 b^6 c^4-3 b^4 c^6-5 b^2 c^8+7 c^10)+a^2 (b^2-c^2)^2 (7 b^8-4 b^6 c^2-8 b^4 c^4-4 b^2 c^6+7 c^8)-(b^2-c^2)^6 (b^2+c^2)) : :
X(61242) = 6 R^4 X[2] - (R^4-16 r^2 s^2) X[3]

See Kadir Altintas and Angel Montesdeoca, euclid 6085.

X(61242) lies on these lines: {2, 3}, {195, 15109}, {13353, 44026}

X(61243) = X(2)X(3)∩X(511)X(13472)

Barycentrics    a^2 (4 a^8-11 a^4 b^2 c^2-8 a^6 (b^2+c^2)-(b^2-c^2)^2 (4 b^4+5 b^2 c^2+4 c^4)+8 a^2 (b^6+2 b^4 c^2+2 b^2 c^4+c^6)) : :

See Kadir Altintas and Angel Montesdeoca, euclid 6086.

X(61243) lies on these lines: {2, 3}, {511, 13472}, {3431, 13348}, {7712, 32142}, {7999, 50414}, {9707, 55646}, {11423, 22352}, {13452, 46850}, {15024, 55674}, {15080, 41597}, {23039, 23060}, {38942, 54044}

X(61244) = X(1)X(5)∩X(8)X(376)

Barycentrics    5*a^4 - 5*a^3*b - 2*a^2*b^2 + 5*a*b^3 - 3*b^4 - 5*a^3*c + 10*a^2*b*c - 5*a*b^2*c - 2*a^2*c^2 - 5*a*b*c^2 + 6*b^2*c^2 + 5*a*c^3 - 3*c^4 : :
X(61244) = 5 X[1] - 6 X[5], 2 X[1] - 3 X[355], 7 X[1] - 6 X[1483], 7 X[1] - 9 X[5587], X[1] - 3 X[5881], 8 X[1] - 9 X[5886], 11 X[1] - 12 X[5901], 23 X[1] - 27 X[7988], 17 X[1] - 21 X[7989], 13 X[1] - 15 X[8227], 19 X[1] - 21 X[9624], 17 X[1] - 18 X[10283], 3 X[1] - 4 X[18357], 5 X[1] - 9 X[37712], 11 X[1] - 15 X[37714], and many others

X(61244) = (Euler triangle,-8)-Miyamoto perspector. See the preamble just before X(61152).

X(61244) lies on these lines: {1, 5}, {3, 3626}, {4, 11278}, {8, 376}, {10, 3655}, {30, 3632}, {40, 4816}, {145, 3656}, {381, 3244}, {382, 28234}, {515, 1657}, {516, 49134}, {517, 3146}, {519, 3830}, {546, 16200}, {631, 38176}, {632, 30392}, {944, 3523}, {1000, 31795}, {1125, 15703}, {1385, 3525}, {1420, 11545}, {1482, 18483}, {1656, 13607}, {1698, 3653}, {2136, 16138}, {2771, 14923}, {2801, 25413}, {2802, 40266}, {3091, 33179}, {3241, 9955}, {3340, 11544}, {3534, 34641}, {3543, 20054}, {3545, 20057}, {3576, 12108}, {3616, 32900}, {3622, 38074}, {3623, 51709}, {3624, 47599}, {3627, 11531}, {3633, 14893}, {3634, 5790}, {3635, 18493}, {3636, 5055}, {3652, 5119}, {3679, 12100}, {3832, 58237}, {3845, 34747}, {3854, 5603}, {3860, 18492}, {3877, 56762}, {3880, 40263}, {3885, 20085}, {3913, 18519}, {4297, 59503}, {4299, 36920}, {4668, 45759}, {4677, 19710}, {4678, 15705}, {4691, 15718}, {4701, 31730}, {4745, 15722}, {4746, 51080}, {4915, 41854}, {5073, 28228}, {5221, 45287}, {5225, 37821}, {5229, 37820}, {5450, 12331}, {5550, 7967}, {5657, 21734}, {5690, 33923}, {5691, 5844}, {5704, 43734}, {5731, 61138}, {5795, 51572}, {5818, 15178}, {6361, 28208}, {7982, 12102}, {7987, 38112}, {7991, 28186}, {8168, 35448}, {8666, 18524}, {8715, 26321}, {10175, 37624}, {10222, 59387}, {10246, 19862}, {10247, 19925}, {10303, 31662}, {10573, 32636}, {10595, 38140}, {10915, 34717}, {10916, 34700}, {11224, 40273}, {11235, 18542}, {11236, 18544}, {11362, 51515}, {11500, 35252}, {11539, 58231}, {12017, 38191}, {12114, 35251}, {12127, 18529}, {12245, 28160}, {12513, 18518}, {12629, 18528}, {12701, 37006}, {12773, 25440}, {13743, 25439}, {14269, 51077}, {15688, 50827}, {15693, 38098}, {15863, 37828}, {16005, 31509}, {16139, 57279}, {18407, 20060}, {18419, 31794}, {19872, 38042}, {19924, 50789}, {20052, 50810}, {20053, 33697}, {20070, 28168}, {22938, 26726}, {25005, 50890}, {25405, 54361}, {25415, 39777}, {26285, 38665}, {28232, 49136}, {29010, 49503}, {29605, 36728}, {30286, 34753}, {31399, 58233}, {32141, 59325}, {32153, 59319}, {32612, 38669}, {33956, 47746}, {34628, 50823}, {34648, 50805}, {35404, 41869}, {36731, 49770}, {36867, 44229}, {37524, 41684}, {37567, 54134}, {38068, 58228}, {39899, 49536}, {45379, 49556}, {45380, 49555}, {48661, 58247}, {49491, 51040}, {50807, 50831}, {51529, 59332}, {51700, 54447}

X(61244) = reflection of X(i) in X(j) for these {i,j}: {1, 37705}, {3, 47745}, {145, 18480}, {355, 5881}, {3534, 34641}, {3633, 22791}, {3655, 50798}, {3656, 34627}, {8148, 31673}, {11531, 3627}, {12699, 18525}, {12702, 3625}, {18481, 8}, {18526, 10}, {20050, 11278}, {26726, 22938}, {31730, 4701}, {34628, 50823}, {34747, 3845}, {34748, 50796}, {37727, 355}, {39899, 49536}, {50805, 34648}
X(61244) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5881, 37705}, {1, 37705, 355}, {4, 20050, 11278}, {5, 37712, 355}, {8, 18481, 3654}, {10, 18526, 3655}, {80, 37738, 11373}, {145, 18480, 3656}, {145, 34627, 18480}, {355, 37727, 5886}, {944, 3617, 13624}, {3616, 50818, 32900}, {3617, 13624, 26446}, {3635, 50796, 18493}, {4701, 31730, 34718}, {5054, 51082, 3655}, {5252, 37706, 37739}, {8148, 18525, 31673}, {8148, 31673, 12699}, {9897, 37707, 1837}, {10944, 37711, 5722}, {12645, 12702, 3625}, {13607, 38155, 1656}, {18493, 34748, 3635}, {18526, 50798, 10}, {37710, 37740, 11374}

X(61245) = X(1)X(5)∩X(8)X(550)

Barycentrics    8*a^4 - 8*a^3*b - 3*a^2*b^2 + 8*a*b^3 - 5*b^4 - 8*a^3*c + 16*a^2*b*c - 8*a*b^2*c - 3*a^2*c^2 - 8*a*b*c^2 + 10*b^2*c^2 + 8*a*c^3 - 5*c^4 : :
X(61245) = 4 X[1] - 5 X[5], 3 X[1] - 5 X[355], 6 X[1] - 5 X[1483], 11 X[1] - 15 X[5587], X[1] - 5 X[5881], 13 X[1] - 15 X[5886], 9 X[1] - 10 X[5901], 37 X[1] - 45 X[7988], 27 X[1] - 35 X[7989], 21 X[1] - 25 X[8227], 31 X[1] - 35 X[9624], 14 X[1] - 15 X[10283], 7 X[1] - 10 X[18357], 2 X[1] - 5 X[37705], 7 X[1] - 15 X[37712], and many others

X(61245) lies on these lines: {1, 5}, {3, 4678}, {4, 20014}, {8, 550}, {10, 14869}, {20, 51515}, {30, 12245}, {40, 15686}, {140, 18526}, {145, 546}, {381, 50831}, {382, 3621}, {515, 4701}, {519, 15687}, {547, 37624}, {548, 59503}, {549, 944}, {632, 5790}, {946, 23046}, {962, 3627}, {1385, 3828}, {1482, 3845}, {3241, 38071}, {3243, 38137}, {3244, 38034}, {3529, 20052}, {3530, 3617}, {3622, 35018}, {3623, 3851}, {3625, 28160}, {3628, 7967}, {3632, 28174}, {3635, 38140}, {3655, 15713}, {3679, 17504}, {3850, 10247}, {3853, 8148}, {3857, 5603}, {3858, 59387}, {4297, 4669}, {4691, 6684}, {5066, 10595}, {5450, 51525}, {5657, 46853}, {5691, 33699}, {5731, 44682}, {5818, 15699}, {5882, 38042}, {7705, 50843}, {7987, 19711}, {7991, 28190}, {9053, 39884}, {9956, 19883}, {10175, 32900}, {10222, 12571}, {10246, 55856}, {10386, 12647}, {11737, 50797}, {12101, 34631}, {12103, 59417}, {12811, 54448}, {13607, 51108}, {14269, 20049}, {14893, 50805}, {15178, 38155}, {15711, 38066}, {15714, 50811}, {17564, 50890}, {19710, 34718}, {19875, 50832}, {19878, 38028}, {19925, 51091}, {22791, 58240}, {24467, 41348}, {25440, 51529}, {26321, 38665}, {28198, 50830}, {33179, 50796}, {34200, 50822}, {35404, 48661}, {35842, 42215}, {35843, 42216}, {38021, 41990}, {38022, 51106}, {38087, 50987}, {38098, 50825}, {38136, 51147}, {38175, 43175}, {44903, 50810}

X(61245) = midpoint of X(382) and X(3621)
X(61245) = reflection of X(i) in X(j) for these {i,j}: {5, 37705}, {145, 546}, {549, 50798}, {550, 8}, {1483, 355}, {3627, 18525}, {3845, 34627}, {5690, 47745}, {8148, 3853}, {10283, 37712}, {15686, 50823}, {18526, 140}, {19710, 34718}, {34631, 12101}, {34748, 5066}, {35404, 50864}, {37705, 5881}, {37727, 18357}, {44903, 50810}, {50805, 14893}, {50818, 547}, {50831, 381}
X(61245) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 38138, 5}, {355, 1483, 5}, {355, 8227, 18357}, {355, 37727, 8227}, {1483, 37705, 355}, {3655, 38081, 15713}, {4669, 31663, 5690}, {5818, 51700, 15699}, {8227, 37712, 355}, {10283, 18357, 5}, {10943, 11698, 5}, {18357, 37727, 10283}, {18526, 59388, 140}, {34773, 38112, 15712}, {37712, 37727, 18357}, {46933, 58230, 140}

X(61246) = X(1)X(5)∩X(8)X(1657)

Barycentrics    10*a^4 - 10*a^3*b - 3*a^2*b^2 + 10*a*b^3 - 7*b^4 - 10*a^3*c + 20*a^2*b*c - 10*a*b^2*c - 3*a^2*c^2 - 10*a*b*c^2 + 14*b^2*c^2 + 10*a*c^3 - 7*c^4 : :
X(61246) = 5 X[1] - 7 X[5], 3 X[1] - 7 X[355], 9 X[1] - 7 X[1483], 13 X[1] - 21 X[5587], X[1] + 7 X[5881], 17 X[1] - 21 X[5886], 6 X[1] - 7 X[5901], 47 X[1] - 63 X[7988], 33 X[1] - 49 X[7989], 27 X[1] - 35 X[8227], 41 X[1] - 49 X[9624], 19 X[1] - 21 X[10283], 4 X[1] - 7 X[18357], X[1] - 7 X[37705], 5 X[1] - 21 X[37712], 19 X[1] - 35 X[37714], and many others

X(61246) lies on these lines: {1, 5}, {4, 20054}, {8, 1657}, {10, 12108}, {30, 34641}, {40, 19710}, {140, 28236}, {376, 5690}, {515, 4746}, {519, 14893}, {547, 13607}, {548, 3626}, {549, 50871}, {551, 45757}, {944, 5054}, {946, 3860}, {962, 3830}, {1385, 10124}, {1482, 3839}, {3146, 12245}, {3244, 3850}, {3523, 34773}, {3525, 5790}, {3530, 38176}, {3543, 50830}, {3617, 61138}, {3625, 28212}, {3627, 3632}, {3628, 38155}, {3636, 12812}, {3679, 45759}, {3843, 20050}, {3853, 28234}, {3854, 38034}, {3858, 16200}, {3861, 11278}, {4297, 28224}, {4691, 58216}, {4701, 28146}, {4745, 6684}, {5066, 33179}, {5072, 20057}, {5691, 35404}, {5731, 58224}, {5818, 15703}, {5844, 12102}, {7967, 46936}, {8148, 10248}, {9956, 47599}, {11531, 15687}, {11737, 51087}, {12135, 44803}, {12702, 49138}, {14891, 38098}, {15691, 50827}, {15718, 53620}, {15862, 57288}, {18481, 59400}, {18526, 38042}, {23046, 34747}, {26321, 51525}, {28182, 49134}, {28208, 50814}, {30392, 55859}, {31145, 48661}, {31253, 55862}, {31423, 38081}, {34200, 51080}, {35641, 53517}, {35642, 53520}, {37624, 38074}, {38028, 55857}, {41106, 51092}, {41990, 51094}, {51109, 51700}, {58238, 59387}

X(61246) = midpoint of X(i) and X(j) for these {i,j}: {549, 50871}, {3543, 50830}, {3627, 3632}, {5881, 37705}, {15687, 50804}, {35404, 50817}
X(61246) = reflection of X(i) in X(j) for these {i,j}: {547, 50801}, {548, 3626}, {3244, 3850}, {5901, 355}, {11278, 3861}, {15691, 50827}, {51082, 10124}, {51087, 11737}
X(61246) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 37705, 37712}, {355, 5901, 18357}, {355, 7989, 38138}, {355, 37727, 7989}

X(61247) = X(1)X(5)∩X(8)X(3529)

Barycentrics    7*a^4 - 7*a^3*b - 2*a^2*b^2 + 7*a*b^3 - 5*b^4 - 7*a^3*c + 14*a^2*b*c - 7*a*b^2*c - 2*a^2*c^2 - 7*a*b*c^2 + 10*b^2*c^2 + 7*a*c^3 - 5*c^4 : :
X(61247) = 7 X[1] - 10 X[5], 2 X[1] - 5 X[355], 13 X[1] - 10 X[1483], 3 X[1] - 5 X[5587], X[1] + 5 X[5881], 4 X[1] - 5 X[5886], 17 X[1] - 20 X[5901], 11 X[1] - 15 X[7988], 23 X[1] - 35 X[7989], 19 X[1] - 25 X[8227], 29 X[1] - 35 X[9624], 9 X[1] - 10 X[10283], 11 X[1] - 20 X[18357], X[1] - 10 X[37705], X[1] - 5 X[37712], and many others

X(61247) lies on these lines: {1, 5}, {3, 4691}, {4, 20053}, {8, 3529}, {10, 15720}, {165, 59400}, {382, 3625}, {515, 3534}, {516, 4701}, {517, 3543}, {519, 14269}, {546, 3633}, {550, 4668}, {944, 10303}, {1385, 3533}, {3090, 32900}, {3241, 38140}, {3522, 4678}, {3524, 5731}, {3526, 22266}, {3576, 11812}, {3617, 58219}, {3621, 22793}, {3635, 3851}, {3653, 38042}, {3655, 3828}, {3656, 41099}, {3679, 28224}, {3845, 11224}, {4308, 43734}, {4677, 28174}, {5076, 12645}, {5122, 5770}, {5690, 44245}, {5691, 28212}, {5818, 46935}, {5844, 12101}, {5882, 19878}, {7991, 28182}, {9779, 10222}, {9956, 60781}, {10172, 10246}, {10175, 50801}, {10247, 50796}, {11230, 38074}, {12531, 16128}, {12702, 28172}, {15687, 58243}, {15711, 38112}, {15722, 51705}, {16138, 49163}, {17578, 58246}, {18480, 20014}, {18526, 51073}, {26066, 38214}, {28146, 50864}, {28150, 34641}, {28154, 50692}, {28164, 34718}, {28168, 50810}, {28186, 44903}, {28190, 50823}, {28208, 59417}, {30308, 50831}, {31673, 58247}, {37828, 38213}, {38034, 50799}, {50797, 51071}, {50806, 51096}, {50824, 54447}, {51709, 54448}

X(61247) = midpoint of X(i) and X(j) for these {i,j}: {3576, 50871}, {5881, 37712}, {18525, 51515}
X(61247) = reflection of X(i) in X(j) for these {i,j}: {1, 38138}, {165, 59400}, {355, 37712}, {944, 11231}, {3241, 38140}, {3655, 5790}, {3656, 59387}, {5731, 38176}, {5886, 355}, {10175, 50801}, {10246, 38155}, {10247, 50796}, {11224, 3845}, {18481, 5657}, {26446, 59388}, {37712, 37705}, {37727, 5886}, {50811, 38112}, {51093, 38034}, {51515, 47745}, {59420, 50827}
X(61247) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5731, 38176, 26446}, {5731, 59388, 38176}, {5790, 58230, 3828}, {5881, 37705, 355}, {17502, 53620, 26446}

X(61248) = X(1)X(5)∩X(8)X(28146)

Barycentrics    9*a^4 - 9*a^3*b - 2*a^2*b^2 + 9*a*b^3 - 7*b^4 - 9*a^3*c + 18*a^2*b*c - 9*a*b^2*c - 2*a^2*c^2 - 9*a*b*c^2 + 14*b^2*c^2 + 9*a*c^3 - 7*c^4 : :
X(61248) = 9 X[1] - 14 X[5], 2 X[1] - 7 X[355], 19 X[1] - 14 X[1483], 11 X[1] - 21 X[5587], 3 X[1] + 7 X[5881], 16 X[1] - 21 X[5886], 23 X[1] - 28 X[5901], 43 X[1] - 63 X[7988], 29 X[1] - 49 X[7989], 5 X[1] - 7 X[8227], 39 X[1] - 49 X[9624], 37 X[1] - 42 X[10283], 13 X[1] - 28 X[18357], X[1] + 14 X[37705], X[1] - 21 X[37712], and many others

X(61248) lies on these lines: {1, 5}, {2, 58232}, {3, 4745}, {8, 28146}, {20, 3654}, {381, 51096}, {382, 28194}, {515, 15696}, {517, 17578}, {519, 3843}, {548, 3679}, {631, 28204}, {944, 31662}, {946, 58238}, {1656, 51109}, {1657, 4669}, {1698, 45760}, {3091, 51092}, {3526, 3655}, {3528, 18481}, {3617, 31447}, {3627, 4677}, {3653, 16239}, {3656, 3832}, {3830, 58249}, {3839, 58240}, {3850, 51093}, {3851, 51095}, {3855, 10222}, {3858, 16189}, {3859, 11522}, {3861, 7982}, {4301, 12645}, {4668, 28186}, {4701, 48661}, {4746, 11362}, {4816, 28212}, {5055, 41150}, {5070, 5882}, {5072, 51071}, {5691, 28216}, {5790, 55863}, {7486, 15178}, {9588, 58190}, {12699, 47745}, {12812, 51105}, {14093, 51067}, {15687, 58245}, {15689, 51070}, {15712, 51066}, {15713, 58229}, {15717, 26446}, {17538, 51072}, {18480, 20054}, {18526, 38155}, {21734, 50821}, {21735, 51068}, {22793, 58244}, {28236, 31253}, {31425, 38112}, {31673, 51515}, {33179, 54448}, {34718, 49134}, {34747, 50807}, {44682, 50811}, {49138, 50864}, {50692, 50810}, {53620, 61138}

X(61248) = midpoint of X(5881) and X(37714)
X(61248) = reflection of X(i) in X(j) for these {i,j}: {14093, 51067}, {16189, 3858}
X(61248) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {355, 5881, 37727}, {944, 46932, 31662}, {37705, 37712, 355}

X(61249) = X(1)X(5)∩X(8)X(382)

Barycentrics    6*a^4 - 6*a^3*b - a^2*b^2 + 6*a*b^3 - 5*b^4 - 6*a^3*c + 12*a^2*b*c - 6*a*b^2*c - a^2*c^2 - 6*a*b*c^2 + 10*b^2*c^2 + 6*a*c^3 - 5*c^4 : :
X(61249) = 3 X[1] - 5 X[5], X[1] - 5 X[355], 7 X[1] - 5 X[1483], 7 X[1] - 15 X[5587], 3 X[1] + 5 X[5881], 11 X[1] - 15 X[5886], 4 X[1] - 5 X[5901], 29 X[1] - 45 X[7988], 19 X[1] - 35 X[7989], 17 X[1] - 25 X[8227], 27 X[1] - 35 X[9624], 13 X[1] - 15 X[10283], 2 X[1] - 5 X[18357], X[1] + 5 X[37705], X[1] + 15 X[37712], 9 X[1] - 25 X[37714], and many others

X(61249) lies on these lines: {1, 5}, {3, 34627}, {4, 31145}, {8, 382}, {10, 3530}, {20, 4678}, {30, 4669}, {40, 28190}, {140, 3828}, {145, 3855}, {381, 5734}, {404, 51529}, {515, 548}, {517, 3853}, {519, 546}, {547, 15178}, {550, 3679}, {551, 35018}, {631, 5790}, {632, 3655}, {944, 3526}, {946, 3856}, {962, 51515}, {1385, 16239}, {1482, 3832}, {1656, 38074}, {1657, 50864}, {2475, 50890}, {3146, 34718}, {3241, 3851}, {3244, 38140}, {3486, 31480}, {3522, 38066}, {3528, 3617}, {3600, 43734}, {3625, 22793}, {3626, 28160}, {3627, 9589}, {3628, 5882}, {3653, 55859}, {3654, 15704}, {3656, 3858}, {3843, 12645}, {3845, 7982}, {3850, 10222}, {3854, 50800}, {3857, 11522}, {3859, 19925}, {3861, 4301}, {3918, 26201}, {4297, 31447}, {4325, 40663}, {4330, 37006}, {4338, 41687}, {4677, 15687}, {4745, 34200}, {4746, 28150}, {5056, 38022}, {5066, 13464}, {5067, 10246}, {5070, 5818}, {5072, 34748}, {5073, 50810}, {5076, 58249}, {5079, 38314}, {5554, 56997}, {5657, 15696}, {5691, 28178}, {5816, 16674}, {6361, 49134}, {6684, 58219}, {6885, 37545}, {6906, 51525}, {6918, 15179}, {7486, 7967}, {7504, 51112}, {7991, 50823}, {8715, 38629}, {9041, 18553}, {9588, 18481}, {9656, 39542}, {9657, 10573}, {9670, 12647}, {9780, 55863}, {9956, 19878}, {10109, 51106}, {10165, 22266}, {10175, 51700}, {10299, 50825}, {11539, 30389}, {11545, 34753}, {11737, 51071}, {11812, 31666}, {12102, 34648}, {12103, 28208}, {12108, 51705}, {12245, 17578}, {12702, 28182}, {12811, 51709}, {13393, 50919}, {13729, 50907}, {13743, 38665}, {14869, 19875}, {15681, 51072}, {15688, 51068}, {15712, 38081}, {16189, 41991}, {17504, 51066}, {17800, 59503}, {18493, 54448}, {19876, 50832}, {20049, 50806}, {22799, 52367}, {25416, 38141}, {26321, 33814}, {26446, 44682}, {28172, 58206}, {28194, 50870}, {28212, 31673}, {28216, 33697}, {31420, 40587}, {31454, 35788}, {31786, 58632}, {33923, 50821}, {34631, 50689}, {34632, 49136}, {34747, 50799}, {38021, 50831}, {38071, 51093}, {38076, 51087}, {38083, 51082}, {38136, 49681}, {38175, 43161}, {38669, 45976}, {39884, 49688}, {47478, 51103}, {49138, 59417}, {50871, 55856}, {50885, 52090}, {50949, 52987}

X(61249) = midpoint of X(i) and X(j) for these {i,j}: {5, 5881}, {355, 37705}, {3625, 22793}, {4677, 15687}, {5690, 18525}, {12645, 22791}, {18480, 47745}, {39884, 49688}
X(61249) = reflection of X(i) in X(j) for these {i,j}: {4301, 3861}, {5882, 3628}, {5901, 18357}, {10222, 3850}, {12103, 43174}, {18357, 355}, {26201, 3918}, {31663, 4691}, {31786, 58632}, {34200, 4745}, {40273, 18480}, {51071, 11737}
X(61249) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 355, 38138}, {5, 37705, 5881}, {355, 5881, 5}, {355, 12738, 38157}, {355, 37712, 37705}, {355, 37727, 37714}, {944, 19877, 58230}, {1385, 31399, 16239}, {3861, 4301, 40273}, {4297, 31447, 58190}, {4301, 18480, 3861}, {5818, 18526, 38028}, {5881, 37714, 37727}, {9588, 18481, 46853}, {10222, 50796, 3850}, {11545, 45287, 34753}, {12645, 59387, 22791}, {18525, 59388, 5690}, {37714, 37727, 5}, {38112, 46853, 9588}

X(61250) = X(1)X(5)∩X(8)X(3543)

Barycentrics    7*a^4 - 7*a^3*b - a^2*b^2 + 7*a*b^3 - 6*b^4 - 7*a^3*c + 14*a^2*b*c - 7*a*b^2*c - a^2*c^2 - 7*a*b*c^2 + 12*b^2*c^2 + 7*a*c^3 - 6*c^4 : :
X(61250) = 7 X[1] - 12 X[5], X[1] - 6 X[355], 17 X[1] - 12 X[1483], 4 X[1] - 9 X[5587], 2 X[1] + 3 X[5881], 13 X[1] - 18 X[5886], 19 X[1] - 24 X[5901], 17 X[1] - 27 X[7988], 11 X[1] - 21 X[7989], 2 X[1] - 3 X[8227], 16 X[1] - 21 X[9624], 31 X[1] - 36 X[10283], 3 X[1] - 8 X[18357], X[1] + 4 X[37705], X[1] + 9 X[37712], and many others

X(61250) lies on these lines: {1, 5}, {4, 3625}, {8, 3543}, {10, 3524}, {30, 4668}, {40, 3529}, {145, 50796}, {165, 44245}, {376, 4691}, {381, 3633}, {515, 3522}, {517, 4816}, {519, 18492}, {546, 11224}, {944, 3533}, {946, 20050}, {1125, 38074}, {1385, 19872}, {1698, 15694}, {1699, 11278}, {3244, 38021}, {3361, 11545}, {3436, 36922}, {3525, 22266}, {3534, 3579}, {3545, 3635}, {3576, 9780}, {3621, 7982}, {3624, 18526}, {3632, 8148}, {3636, 50818}, {3653, 58231}, {3654, 44903}, {3655, 47598}, {3839, 20053}, {3858, 58239}, {3899, 56762}, {4297, 31425}, {4669, 6361}, {4677, 12101}, {4678, 31730}, {4701, 34648}, {4746, 50810}, {5055, 32900}, {5073, 5691}, {5175, 11525}, {5221, 9613}, {5258, 18518}, {5288, 18491}, {5550, 5882}, {5790, 13624}, {5818, 19862}, {7091, 43734}, {7319, 56038}, {7967, 15808}, {7987, 28224}, {7991, 28216}, {9579, 41684}, {9588, 38176}, {9623, 16132}, {9955, 51093}, {9956, 55860}, {10165, 46931}, {10175, 46934}, {11362, 50692}, {11499, 59319}, {11544, 18421}, {11812, 19875}, {13464, 54448}, {14872, 50193}, {15254, 38154}, {15711, 51066}, {16192, 38112}, {16200, 19925}, {18481, 34200}, {18493, 50797}, {18542, 31159}, {18544, 31160}, {18761, 48696}, {18990, 30286}, {19878, 51082}, {22758, 59325}, {22793, 51515}, {30315, 38028}, {30323, 51792}, {30389, 38042}, {33697, 34718}, {35252, 44425}, {38149, 43180}, {46932, 50828}, {46933, 51705}

X(61250) = midpoint of X(5881) and X(8227)
X(61250) = reflection of X(i) in X(j) for these {i,j}: {8227, 37714}, {35242, 3617}, {37714, 355}
X(61250) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 37705, 5881}, {1, 37712, 37705}, {355, 5881, 5587}, {355, 37705, 1}, {355, 37712, 5881}, {355, 37727, 38138}, {3621, 18483, 7982}, {3621, 59387, 18483}, {3624, 50871, 18526}, {3632, 18480, 31162}, {4678, 50864, 31730}, {8227, 37714, 5587}, {18480, 50798, 3632}, {18483, 47745, 3621}, {37727, 38138, 7989}, {47745, 59387, 7982}

X(61251) = X(1)X(5)∩X(8)X(3627)

Barycentrics    8*a^4 - 8*a^3*b - a^2*b^2 + 8*a*b^3 - 7*b^4 - 8*a^3*c + 16*a^2*b*c - 8*a*b^2*c - a^2*c^2 - 8*a*b*c^2 + 14*b^2*c^2 + 8*a*c^3 - 7*c^4 : :
X(61251) = 4 X[1] - 7 X[5], X[1] - 7 X[355], 10 X[1] - 7 X[1483], 3 X[1] - 7 X[5587], 5 X[1] + 7 X[5881], 5 X[1] - 7 X[5886], 11 X[1] - 14 X[5901], 13 X[1] - 21 X[7988], 25 X[1] - 49 X[7989], 23 X[1] - 35 X[8227], 37 X[1] - 49 X[9624], 6 X[1] - 7 X[10283], 5 X[1] - 14 X[18357], 2 X[1] + 7 X[37705], X[1] + 7 X[37712], and many others

X(61251) lies on these lines: {1, 5}, {4, 20052}, {8, 3627}, {10, 15712}, {30, 59388}, {140, 46932}, {145, 3850}, {381, 20049}, {515, 4745}, {516, 4746}, {517, 4525}, {519, 23046}, {546, 12645}, {547, 7967}, {548, 3617}, {549, 5731}, {550, 5657}, {632, 944}, {946, 41991}, {1385, 31253}, {1482, 3858}, {1657, 4678}, {3530, 58224}, {3534, 50822}, {3576, 15713}, {3621, 3843}, {3622, 12812}, {3623, 5072}, {3625, 58244}, {3626, 28172}, {3628, 18526}, {3632, 40273}, {3654, 28190}, {3679, 15686}, {3845, 5844}, {3853, 12245}, {3857, 9779}, {3860, 50805}, {3861, 8148}, {4669, 28146}, {5066, 10247}, {5603, 38071}, {5690, 15704}, {5691, 28182}, {5818, 55856}, {9778, 44903}, {9956, 55861}, {10109, 50818}, {10124, 58230}, {10164, 58216}, {10165, 11539}, {10172, 28236}, {10175, 50824}, {10246, 15699}, {10595, 12811}, {11224, 50804}, {11231, 14869}, {11362, 28154}, {11737, 34748}, {12102, 58249}, {12108, 46933}, {14891, 58218}, {14893, 31145}, {17504, 26446}, {17564, 59415}, {18480, 28234}, {19710, 50864}, {19711, 50811}, {22791, 47745}, {26321, 34474}, {28174, 33699}, {28208, 38127}, {28216, 34718}, {35018, 37624}, {38034, 50796}, {38144, 59399}, {41990, 51093}, {45759, 53620}, {45760, 46931}, {50826, 51066}, {50871, 54447}, {51095, 51709}

X(61251) = midpoint of X(i) and X(j) for these {i,j}: {4, 51515}, {355, 37712}, {5657, 18525}, {5790, 34627}, {5881, 5886}, {11224, 50804}, {37705, 38138}, {50798, 59387}
X(61251) = reflection of X(i) in X(j) for these {i,j}: {5, 38138}, {549, 5790}, {550, 5657}, {1483, 5886}, {3845, 59387}, {5886, 18357}, {7967, 547}, {8703, 38112}, {10247, 5066}, {10283, 5587}, {15699, 38074}, {17504, 38081}, {34773, 11231}, {37705, 37712}, {38034, 50796}, {38042, 38155}, {38138, 355}, {44903, 9778}, {45759, 53620}, {50824, 10175}, {50831, 10247}, {59399, 38144}, {59400, 59388}
X(61251) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {355, 5881, 18357}, {355, 37705, 5}, {1483, 18357, 5}, {1483, 37705, 5881}, {5587, 10283, 5}, {5881, 18357, 1483}, {10247, 50797, 54448}, {10247, 54448, 5066}, {10283, 38138, 5587}

X(61252) = X(1)X(5)∩X(8)X(9589)

Barycentrics    9*a^4 - 9*a^3*b - a^2*b^2 + 9*a*b^3 - 8*b^4 - 9*a^3*c + 18*a^2*b*c - 9*a*b^2*c - a^2*c^2 - 9*a*b*c^2 + 16*b^2*c^2 + 9*a*c^3 - 8*c^4 : :
X(61252) = 9 X[1] - 16 X[5], X[1] - 8 X[355], 23 X[1] - 16 X[1483], 5 X[1] - 12 X[5587], 3 X[1] + 4 X[5881], 17 X[1] - 24 X[5886], 25 X[1] - 32 X[5901], 11 X[1] - 18 X[7988], 13 X[1] - 20 X[8227], 3 X[1] - 4 X[9624], 41 X[1] - 48 X[10283], 11 X[1] - 32 X[18357], 5 X[1] + 16 X[37705], X[1] + 6 X[37712], and many others

X(61252) lies on these lines: {1, 5}, {3, 51066}, {4, 4677}, {8, 9589}, {10, 15717}, {20, 3679}, {40, 17800}, {140, 58229}, {165, 15696}, {381, 16189}, {382, 7991}, {515, 3528}, {519, 3832}, {548, 34628}, {631, 19875}, {944, 31399}, {946, 16191}, {962, 4816}, {1385, 55866}, {1698, 38155}, {1699, 47745}, {3090, 51110}, {3091, 51093}, {3146, 4669}, {3244, 54448}, {3339, 9657}, {3340, 9656}, {3522, 4745}, {3523, 58225}, {3526, 19876}, {3530, 50811}, {3545, 51097}, {3576, 55863}, {3624, 28236}, {3632, 4301}, {3633, 5734}, {3655, 16239}, {3656, 3856}, {3680, 34717}, {3843, 7982}, {3851, 51094}, {3853, 50865}, {3855, 11522}, {3861, 31162}, {4297, 58188}, {4309, 53052}, {4325, 53056}, {4338, 41684}, {4342, 7319}, {4668, 5691}, {4678, 28164}, {4701, 9812}, {4746, 20070}, {4882, 5176}, {4915, 5086}, {5056, 51105}, {5059, 51072}, {5067, 5882}, {5068, 51071}, {5070, 30315}, {5225, 8275}, {5493, 50692}, {5697, 9947}, {5790, 7987}, {5818, 34595}, {6684, 58217}, {7486, 25055}, {7962, 9671}, {9613, 30286}, {9670, 9819}, {9956, 30392}, {10222, 30308}, {10572, 31436}, {11224, 12645}, {11523, 34700}, {11531, 18480}, {11928, 16205}, {11929, 16204}, {12571, 20050}, {12767, 15863}, {15022, 51103}, {15683, 51070}, {18481, 31425}, {18526, 54447}, {20049, 50803}, {21734, 53620}, {22791, 58241}, {28194, 50874}, {28224, 31423}, {35242, 38176}, {38021, 50797}, {38042, 45760}, {50689, 58242}, {50693, 51068}, {54422, 59356}, {55860, 58232}

X(61252) = midpoint of X(5881) and X(9624)
X(61252) = reflection of X(1) in X(7989)
X(61252) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 4677, 58245}, {355, 5881, 37714}, {355, 37705, 5587}, {355, 37712, 1}, {5587, 5881, 37727}, {5691, 59388, 4668}, {5726, 10950, 1}, {5881, 37714, 1}, {12645, 18492, 11224}, {37705, 37727, 5881}, {37712, 37714, 5881}

X(61253) = X(1)X(5)∩X(8)X(3830)

Barycentrics    10*a^4 - 10*a^3*b - a^2*b^2 + 10*a*b^3 - 9*b^4 - 10*a^3*c + 20*a^2*b*c - 10*a*b^2*c - a^2*c^2 - 10*a*b*c^2 + 18*b^2*c^2 + 10*a*c^3 - 9*c^4 : :
5 X[1] - 9 X[5], X[1] - 9 X[355], 13 X[1] - 9 X[1483], 11 X[1] - 27 X[5587], 7 X[1] + 9 X[5881], 19 X[1] - 27 X[5886], 7 X[1] - 9 X[5901], 49 X[1] - 81 X[7988], 31 X[1] - 63 X[7989], 29 X[1] - 45 X[8227], 47 X[1] - 63 X[9624], 23 X[1] - 27 X[10283], X[1] - 3 X[18357], X[1] + 3 X[37705], 5 X[1] + 27 X[37712], and many others

X(61253) lies on these lines: {1, 5}, {8, 3830}, {10, 12100}, {30, 3626}, {140, 38155}, {145, 41106}, {376, 3617}, {381, 20050}, {515, 33923}, {517, 4536}, {519, 3860}, {546, 11278}, {547, 15808}, {548, 38176}, {944, 46219}, {1385, 55862}, {1657, 5690}, {3146, 12702}, {3244, 5066}, {3523, 5790}, {3525, 38042}, {3579, 12103}, {3621, 3839}, {3625, 14893}, {3628, 28236}, {3632, 3845}, {3634, 10124}, {3636, 10109}, {3655, 19872}, {3679, 19710}, {3850, 58237}, {3857, 16200}, {3861, 28234}, {4669, 33697}, {4691, 28208}, {4701, 58246}, {4746, 28198}, {4816, 12699}, {5054, 9780}, {5550, 15703}, {5691, 59400}, {5708, 43734}, {5818, 55857}, {5844, 18483}, {8148, 40273}, {9812, 58247}, {10246, 46936}, {11246, 43731}, {11362, 28182}, {11545, 32636}, {11849, 38629}, {12101, 34641}, {12108, 13624}, {12811, 33179}, {13607, 35018}, {14269, 50830}, {14892, 51087}, {15690, 38098}, {15699, 50871}, {18481, 45759}, {19709, 20057}, {19862, 47599}, {20054, 41099}, {23046, 50804}, {28174, 31673}, {30392, 55861}, {35242, 38112}, {37535, 38631}, {41869, 50823}, {41985, 51085}, {41992, 58231}, {46934, 50824}, {49134, 59503}, {51080, 58214}

X(61253) = midpoint of X(i) and X(j) for these {i,j}: {546, 47745}, {5881, 5901}, {12101, 34641}, {18357, 37705}
X(61253) = reflection of X(i) in X(j) for these {i,j}: {13607, 35018}, {33179, 12811}
X(61253) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {355, 5881, 38138}, {355, 37705, 18357}, {355, 37712, 5}, {5881, 38138, 5901}

X(61254) = X(1)X(5)∩X(8)X50689)

Barycentrics    7*a^4 - 7*a^3*b + a^2*b^2 + 7*a*b^3 - 8*b^4 - 7*a^3*c + 14*a^2*b*c - 7*a*b^2*c + a^2*c^2 - 7*a*b*c^2 + 16*b^2*c^2 + 7*a*c^3 - 8*c^4 : :
X(61254) = 7 X[1] - 16 X[5], X[1] + 8 X[355], 25 X[1] - 16 X[1483], X[1] - 4 X[5587], 5 X[1] + 4 X[5881], 5 X[1] - 8 X[5886], 23 X[1] - 32 X[5901], 5 X[1] - 14 X[7989], 11 X[1] - 20 X[8227], 19 X[1] - 28 X[9624], 13 X[1] - 16 X[10283], 5 X[1] - 32 X[18357], 11 X[1] + 16 X[37705], X[1] + 2 X[37712], X[1] - 10 X[37714], and many others

X(61254) lies on these lines: {1, 5}, {4, 4668}, {8, 50689}, {10, 3522}, {40, 5073}, {165, 3534}, {381, 11224}, {515, 3524}, {516, 3543}, {517, 14269}, {519, 9779}, {944, 10172}, {1385, 30315}, {1478, 30286}, {1698, 5731}, {1699, 4677}, {2093, 52665}, {3091, 3633}, {3146, 4691}, {3245, 5779}, {3419, 59389}, {3529, 5657}, {3533, 5818}, {3576, 15694}, {3586, 5817}, {3617, 50692}, {3621, 12571}, {3624, 46935}, {3625, 3832}, {3626, 9589}, {3632, 19925}, {3635, 5068}, {3654, 28182}, {3817, 50801}, {3839, 58243}, {3854, 20053}, {3855, 58239}, {3899, 15064}, {3968, 11220}, {4297, 58217}, {4301, 4816}, {4512, 59416}, {4669, 9812}, {4678, 51118}, {4745, 9778}, {4882, 5086}, {4915, 5176}, {5076, 7991}, {5079, 32900}, {5541, 54370}, {5603, 34747}, {5844, 58241}, {5903, 9947}, {7319, 12575}, {7967, 50871}, {7982, 51515}, {7987, 11231}, {9956, 30389}, {10164, 50864}, {10171, 51105}, {10175, 34627}, {11038, 51782}, {11522, 47745}, {11531, 18492}, {11812, 38042}, {12101, 28212}, {12245, 58248}, {12514, 38214}, {12645, 16189}, {15722, 17502}, {16200, 30308}, {16558, 48363}, {18391, 59372}, {25055, 28236}, {26446, 34200}, {28158, 38098}, {28164, 53620}, {28168, 38066}, {28190, 38081}, {28204, 30392}, {28224, 47598}, {30282, 37006}, {31397, 38158}, {34773, 58229}, {38083, 58230}, {38112, 44903}, {38213, 54286}, {38637, 59332}, {50862, 51068}, {51024, 51169}, {51094, 51709}

X(61254) = midpoint of X(7988) and X(37712)
X(61254) = reflection of X(i) in X(j) for these {i,j}: {1, 7988}, {7988, 5587}, {30392, 54447}, {58221, 19875}, {58230, 38083}
X(61254) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {165, 5790, 51066}, {355, 5587, 37712}, {355, 18357, 5881}, {355, 37714, 1}, {355, 38138, 5587}, {1699, 59388, 4677}, {5587, 5881, 5886}, {5587, 5886, 7989}, {5587, 37712, 1}, {5587, 38138, 37714}, {5726, 5727, 1}, {5881, 7989, 1}, {5881, 18357, 7989}, {5886, 18357, 5587}, {7989, 37714, 18357}, {10944, 50444, 1}, {16200, 38140, 30308}, {37712, 37714, 5587}, {38140, 50798, 16200}, {38155, 59387, 3679}, {50796, 59388, 1699}, {59387, 59417, 34648}

X(61255) = X(1)X(5)∩X(8)X(3843)

Barycentrics    6*a^4 - 6*a^3*b + a^2*b^2 + 6*a*b^3 - 7*b^4 - 6*a^3*c + 12*a^2*b*c - 6*a*b^2*c + a^2*c^2 - 6*a*b*c^2 + 14*b^2*c^2 + 6*a*c^3 - 7*c^4 : :
X(61255) = 3 X[1] - 7 X[5], X[1] + 7 X[355], 11 X[1] - 7 X[1483], 5 X[1] - 21 X[5587], 9 X[1] + 7 X[5881], 13 X[1] - 21 X[5886], 5 X[1] - 7 X[5901], 31 X[1] - 63 X[7988], 17 X[1] - 49 X[7989], 19 X[1] - 35 X[8227], 33 X[1] - 49 X[9624], 17 X[1] - 21 X[10283], X[1] - 7 X[18357], 5 X[1] + 7 X[37705], 11 X[1] + 21 X[37712], and many others

X(61255) lies on these lines: {1, 5}, {3, 38074}, {4, 34718}, {8, 3843}, {10, 548}, {20, 5790}, {30, 4745}, {140, 31399}, {382, 5690}, {515, 3530}, {517, 3861}, {519, 3850}, {546, 4301}, {547, 5882}, {550, 9588}, {551, 12812}, {631, 18525}, {944, 5070}, {946, 3859}, {1385, 48154}, {1482, 3855}, {1656, 34627}, {1657, 53620}, {3090, 50824}, {3091, 20049}, {3241, 5072}, {3526, 5818}, {3529, 38066}, {3545, 51092}, {3617, 33703}, {3626, 28212}, {3627, 3679}, {3628, 28204}, {3634, 45760}, {3653, 30315}, {3655, 55856}, {3656, 3857}, {3828, 12108}, {3832, 20052}, {3853, 11362}, {3856, 5844}, {3858, 7982}, {4317, 34753}, {4669, 14893}, {4677, 23046}, {4678, 48661}, {4691, 28146}, {5066, 10222}, {5067, 38028}, {5076, 50810}, {5079, 38022}, {5657, 17800}, {5691, 38112}, {5731, 55863}, {5734, 12645}, {5816, 16677}, {6147, 31410}, {6684, 58190}, {6912, 38629}, {6946, 38631}, {7486, 10246}, {7991, 15687}, {8703, 31425}, {9656, 10573}, {9671, 12647}, {9780, 58224}, {9947, 14988}, {9956, 16239}, {10109, 41150}, {10171, 32900}, {10386, 31436}, {11522, 38071}, {11545, 24470}, {11737, 51095}, {12102, 28194}, {12103, 50821}, {12135, 44958}, {12699, 59400}, {12702, 17578}, {12811, 13464}, {13743, 51525}, {14869, 50811}, {14891, 51069}, {14892, 51071}, {15022, 50818}, {15027, 50877}, {15178, 35018}, {15684, 51068}, {15686, 51066}, {15704, 38081}, {15712, 19875}, {16189, 50804}, {17583, 25005}, {18481, 44682}, {18483, 58244}, {19919, 48363}, {23323, 47490}, {26446, 46853}, {28182, 31673}, {28202, 50870}, {28208, 33923}, {28236, 51700}, {30389, 55859}, {31145, 50800}, {33697, 38127}, {38083, 55862}, {38140, 47745}, {38335, 51072}, {41991, 50799}, {41992, 50832}, {45757, 51108}, {45976, 51529}, {46031, 47491}, {46933, 61138}, {50802, 58240}, {50808, 58203}

X(61255) = midpoint of X(i) and X(j) for these {i,j}: {8, 40273}, {355, 18357}, {3853, 11362}, {4669, 14893}, {5901, 37705}
X(61255) = reflection of X(i) in X(j) for these {i,j}: {13464, 12811}, {14891, 51069}, {15178, 35018}
X(61255) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 1483, 9624}, {5, 37705, 37727}, {5, 37714, 18357}, {5, 37727, 5901}, {5, 38138, 37714}, {355, 5587, 37705}, {355, 37714, 5}, {355, 38138, 18357}, {3653, 30315, 55861}, {5587, 37705, 5901}, {5587, 37727, 5}, {5901, 18357, 5587}, {9956, 31662, 31253}, {11362, 18480, 3853}

X(61256) = X(1)X(5)∩X10)X(376)

Barycentrics    5*a^4 - 5*a^3*b + a^2*b^2 + 5*a*b^3 - 6*b^4 - 5*a^3*c + 10*a^2*b*c - 5*a*b^2*c + a^2*c^2 - 5*a*b*c^2 + 12*b^2*c^2 + 5*a*c^3 - 6*c^4 : :
X(61256) = 5 X[1] - 12 X[5], X[1] + 6 X[355], 19 X[1] - 12 X[1483], 2 X[1] - 9 X[5587], 4 X[1] + 3 X[5881], 11 X[1] - 18 X[5886], 17 X[1] - 24 X[5901], 13 X[1] - 27 X[7988], X[1] - 3 X[7989], 8 X[1] - 15 X[8227], 2 X[1] - 3 X[9624], 29 X[1] - 36 X[10283], X[1] - 8 X[18357], 3 X[1] + 4 X[37705], 5 X[1] + 9 X[37712], and many others

X(61256) lies on these lines: {1, 5}, {4, 3626}, {8, 3839}, {10, 376}, {40, 3146}, {145, 38021}, {165, 12103}, {381, 3632}, {382, 38176}, {515, 3523}, {519, 41106}, {546, 11531}, {944, 19862}, {946, 3621}, {1125, 34627}, {1385, 55857}, {1657, 3579}, {1698, 5054}, {1699, 4816}, {3090, 15808}, {3091, 16200}, {3244, 3545}, {3339, 11545}, {3421, 12777}, {3436, 18406}, {3524, 51080}, {3525, 3576}, {3624, 15703}, {3625, 7982}, {3628, 30392}, {3633, 9955}, {3635, 38076}, {3636, 5071}, {3654, 35404}, {3655, 34595}, {3679, 3830}, {3832, 28234}, {3845, 58248}, {3860, 4677}, {4007, 32431}, {4297, 61138}, {4663, 38144}, {4668, 12699}, {4678, 28194}, {4691, 6361}, {5055, 50871}, {5056, 13607}, {5066, 34747}, {5072, 33179}, {5220, 38154}, {5251, 18518}, {5258, 18491}, {5550, 10175}, {5657, 49138}, {5665, 5714}, {5693, 9947}, {5697, 51792}, {5731, 31399}, {5816, 16676}, {5882, 46934}, {6684, 21734}, {7160, 7319}, {7701, 54286}, {7987, 12108}, {7991, 12102}, {9588, 28160}, {9589, 59503}, {9613, 32636}, {9956, 19872}, {10124, 34773}, {10728, 38213}, {11237, 41870}, {11499, 59325}, {11522, 12645}, {12100, 18481}, {14872, 31794}, {15682, 38098}, {15705, 46933}, {15722, 58224}, {16132, 18528}, {16189, 38034}, {16192, 28186}, {16558, 19919}, {18398, 51789}, {18493, 51093}, {18526, 25055}, {18761, 35251}, {18908, 37625}, {19710, 51066}, {19877, 51705}, {20054, 51077}, {22758, 59319}, {26446, 33923}, {28224, 30389}, {28232, 50688}, {29601, 36662}, {30286, 57282}, {30424, 38149}, {31159, 45631}, {31160, 45630}, {31649, 51817}, {31662, 55858}, {31730, 53620}, {32900, 51105}, {34628, 45759}, {34631, 50803}, {34641, 41099}, {35409, 50862}, {37234, 48696}, {38071, 50804}, {38200, 43178}, {40273, 58245}, {41991, 58241}, {45757, 50824}, {48936, 59313}, {49232, 53520}, {49233, 53517}, {50687, 50827}, {52524, 59294}, {55856, 58231}

X(61256) = reflection of X(9624) in X(7989)
X(61256) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 18357, 5587}, {1, 37714, 18357}, {5, 355, 37712}, {8, 18492, 31162}, {8, 50796, 18492}, {355, 5587, 5881}, {355, 18357, 1}, {355, 37714, 5587}, {355, 38138, 37714}, {1698, 18525, 50811}, {1699, 4816, 8148}, {3091, 47745, 16200}, {3146, 38127, 40}, {3617, 31673, 40}, {3617, 59387, 31673}, {3679, 18480, 41869}, {3839, 50817, 31162}, {4691, 34648, 6361}, {5587, 5881, 8227}, {5587, 9624, 7989}, {9955, 50798, 3633}, {10826, 37709, 37704}, {12645, 38140, 11522}, {19925, 59388, 7982}

X(61257) = X(1)X(5)∩X(10)X(1657)

Barycentrics    5*a^4 - 5*a^3*b + 2*a^2*b^2 + 5*a*b^3 - 7*b^4 - 5*a^3*c + 10*a^2*b*c - 5*a*b^2*c + 2*a^2*c^2 - 5*a*b*c^2 + 14*b^2*c^2 + 5*a*c^3 - 7*c^4 : :
X(61257) = 5 X[1] - 14 X[5], 2 X[1] + 7 X[355], 23 X[1] - 14 X[1483], X[1] - 7 X[5587], 11 X[1] + 7 X[5881], 4 X[1] - 7 X[5886], 19 X[1] - 28 X[5901], 3 X[1] - 7 X[7988], 13 X[1] - 49 X[7989], 17 X[1] - 35 X[8227], 31 X[1] - 49 X[9624], 11 X[1] - 14 X[10283], X[1] - 28 X[18357], 13 X[1] + 14 X[37705], 5 X[1] + 7 X[37712], and many others

X(61257) lies on these lines: {1, 5}, {2, 31662}, {4, 38176}, {10, 1657}, {165, 19710}, {376, 26446}, {381, 28234}, {515, 5054}, {516, 3654}, {517, 3839}, {519, 58238}, {944, 46936}, {946, 51515}, {1698, 12108}, {1699, 3860}, {3091, 20054}, {3146, 5657}, {3244, 5072}, {3523, 5818}, {3525, 5731}, {3576, 10124}, {3579, 49138}, {3626, 3843}, {3632, 3850}, {3653, 28224}, {3655, 10175}, {3656, 9779}, {3679, 14893}, {3817, 50798}, {3828, 15718}, {3832, 58244}, {3851, 47745}, {3854, 20052}, {3855, 11278}, {3858, 11531}, {4668, 40273}, {4669, 50800}, {4677, 50807}, {4691, 48661}, {4746, 19925}, {5055, 28236}, {5066, 16200}, {5068, 33179}, {5079, 13607}, {5090, 44803}, {5603, 20049}, {5690, 12102}, {5691, 12103}, {7319, 31795}, {9780, 61138}, {10109, 50871}, {10165, 18525}, {10171, 41150}, {10172, 55857}, {10246, 50797}, {11230, 34627}, {11539, 58227}, {12100, 38042}, {12699, 59503}, {14269, 28228}, {15695, 50868}, {15699, 30392}, {15705, 28208}, {15722, 51080}, {17502, 50864}, {19709, 50801}, {19875, 28186}, {25055, 45757}, {26321, 38637}, {28146, 53620}, {28150, 38066}, {28178, 38081}, {28182, 35404}, {28232, 38098}, {31162, 59400}, {31399, 58224}, {31673, 49134}, {34773, 55862}, {35774, 53517}, {35775, 53520}, {38068, 58218}, {38083, 54445}, {51092, 51709}

X(61257) = midpoint of X(i) and X(j) for these {i,j}: {9779, 59388}, {38074, 54448}
X(61257) = reflection of X(i) in X(j) for these {i,j}: {3653, 54447}, {3656, 9779}, {9779, 38140}, {30392, 15699}, {54445, 38083}
X(61257) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {355, 5587, 5886}, {3830, 5790, 38127}, {5587, 37712, 5}, {5587, 37714, 38138}, {5587, 38138, 355}, {18357, 37714, 355}, {18357, 38138, 5587}, {38140, 59388, 3656}

X(61258) = X(1)X(5)∩X(10)X(382)

Barycentrics    3*a^4 - 3*a^3*b + 2*a^2*b^2 + 3*a*b^3 - 5*b^4 - 3*a^3*c + 6*a^2*b*c - 3*a*b^2*c + 2*a^2*c^2 - 3*a*b*c^2 + 10*b^2*c^2 + 3*a*c^3 - 5*c^4 : :
X(61258) = 3 X[1] - 10 X[5], 2 X[1] + 5 X[355], 17 X[1] - 10 X[1483], X[1] - 15 X[5587], 9 X[1] + 5 X[5881], 8 X[1] - 15 X[5886], 13 X[1] - 20 X[5901], 17 X[1] - 45 X[7988], X[1] - 5 X[7989], 11 X[1] - 25 X[8227], 3 X[1] - 5 X[9624], 23 X[1] - 30 X[10283], X[1] + 20 X[18357], 11 X[1] + 10 X[37705], 13 X[1] + 15 X[37712], and many others

X(61258) lies on these lines: {1, 5}, {3, 3828}, {4, 3654}, {8, 3855}, {10, 382}, {20, 5818}, {30, 9588}, {40, 3853}, {381, 4301}, {515, 3526}, {517, 3832}, {519, 3851}, {546, 3679}, {548, 5691}, {550, 19875}, {551, 5079}, {631, 9956}, {632, 30315}, {942, 31410}, {944, 7486}, {946, 4701}, {950, 31480}, {962, 38176}, {1385, 5067}, {1482, 38155}, {1656, 3655}, {1657, 34648}, {1698, 3530}, {1699, 3856}, {1737, 9657}, {3062, 38170}, {3090, 28204}, {3091, 3656}, {3146, 50821}, {3241, 3544}, {3359, 16138}, {3523, 28208}, {3525, 38083}, {3528, 9780}, {3533, 31666}, {3545, 10222}, {3576, 16239}, {3579, 33703}, {3617, 22793}, {3624, 28224}, {3626, 58247}, {3628, 3653}, {3632, 38034}, {3634, 55863}, {3817, 12645}, {3830, 43174}, {3843, 4691}, {3845, 7991}, {3850, 7982}, {3857, 50807}, {3858, 31162}, {3859, 22791}, {3861, 5690}, {4297, 22266}, {4323, 43734}, {4325, 24914}, {4338, 40663}, {4677, 38071}, {4745, 14269}, {5055, 5882}, {5056, 15178}, {5066, 11522}, {5068, 51709}, {5070, 10175}, {5072, 13464}, {5076, 5493}, {5122, 6885}, {5175, 51362}, {5603, 20014}, {5657, 17578}, {5734, 9955}, {5795, 31494}, {5816, 16814}, {6684, 15696}, {8148, 12571}, {9612, 11545}, {9656, 57282}, {9670, 10039}, {9779, 11278}, {10165, 55866}, {10171, 37624}, {11231, 15717}, {11531, 59400}, {11737, 51093}, {12368, 20379}, {12779, 52102}, {12811, 38021}, {12812, 50824}, {13624, 55864}, {14869, 19876}, {15025, 50877}, {15171, 31436}, {15681, 51069}, {15687, 51066}, {15712, 34628}, {16128, 59415}, {16192, 28190}, {17583, 34122}, {17800, 31673}, {18483, 59503}, {18493, 47745}, {18553, 47359}, {19709, 51091}, {24982, 56997}, {25055, 35018}, {28186, 31423}, {28194, 50800}, {28202, 50688}, {30389, 55856}, {31440, 42215}, {31730, 49134}, {33697, 49138}, {34638, 49133}, {34641, 50806}, {34773, 48154}, {34789, 38177}, {37545, 51755}, {38022, 50871}, {38058, 57003}, {38081, 50865}, {38089, 55701}, {38112, 41869}, {38127, 48661}, {41991, 50823}, {41992, 58229}, {46219, 51705}, {46932, 58216}, {47478, 51105}, {49136, 50808}, {49137, 50862}, {50689, 50810}, {50781, 55724}, {50803, 58249}, {50828, 55858}

X(61258) = reflection of X(i) in X(j) for these {i,j}: {9624, 5}, {30389, 55856}
X(61258) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 38138, 355}, {5, 355, 37727}, {5, 18357, 37714}, {5, 37714, 355}, {5, 37727, 5886}, {3843, 5790, 11362}, {3843, 11362, 12699}, {3861, 5690, 9589}, {5056, 34627, 15178}, {5072, 50798, 13464}, {5076, 38066, 5493}, {5587, 18357, 355}, {5587, 37714, 5}, {5790, 19925, 12699}, {5818, 18480, 26446}, {5818, 54448, 18480}, {7989, 9624, 5}, {9589, 18492, 3861}, {9956, 17502, 19877}, {9956, 59387, 18481}, {11362, 19925, 3843}, {13464, 38076, 5072}, {30315, 50811, 632}, {31663, 46933, 26446}

X(61259) = X(1)X(5)∩X(10)X(546)

Barycentrics    2*a^4 - 2*a^3*b + 3*a^2*b^2 + 2*a*b^3 - 5*b^4 - 2*a^3*c + 4*a^2*b*c - 2*a*b^2*c + 3*a^2*c^2 - 2*a*b*c^2 + 10*b^2*c^2 + 2*a*c^3 - 5*c^4 : :
X(61259) = X[1] - 5 X[5], 3 X[1] + 5 X[355], 9 X[1] - 5 X[1483], X[1] + 15 X[5587], 11 X[1] + 5 X[5881], 7 X[1] - 15 X[5886], 3 X[1] - 5 X[5901], 13 X[1] - 45 X[7988], 3 X[1] - 35 X[7989], 9 X[1] - 25 X[8227], 19 X[1] - 35 X[9624], 11 X[1] - 15 X[10283], X[1] + 5 X[18357], 7 X[1] + 5 X[37705], 17 X[1] + 15 X[37712], and many others

X(61259) lies on these lines: {1, 5}, {3, 9342}, {4, 28178}, {8, 3851}, {10, 546}, {30, 3828}, {40, 3845}, {140, 4297}, {145, 3544}, {376, 50800}, {381, 962}, {382, 9780}, {515, 3628}, {516, 3861}, {517, 3850}, {519, 11737}, {547, 1385}, {548, 11231}, {549, 5691}, {550, 1698}, {551, 47478}, {632, 18481}, {944, 5055}, {946, 4669}, {1125, 28224}, {1145, 38141}, {1478, 34753}, {1482, 3545}, {1537, 38177}, {1656, 34773}, {1699, 3857}, {1737, 24470}, {1902, 37984}, {2475, 22799}, {2550, 38139}, {2807, 45958}, {3090, 18525}, {3091, 4678}, {3416, 38136}, {3528, 46931}, {3529, 46932}, {3530, 3634}, {3576, 55856}, {3579, 3853}, {3616, 5079}, {3617, 3855}, {3627, 18492}, {3654, 23046}, {3679, 38071}, {3832, 12702}, {3833, 26201}, {3839, 48661}, {3843, 5657}, {3856, 18483}, {3858, 12699}, {3859, 11362}, {3860, 28194}, {3871, 38629}, {4301, 38176}, {4701, 5844}, {5046, 38058}, {5056, 10246}, {5068, 18493}, {5070, 5731}, {5071, 50824}, {5072, 5603}, {5076, 9778}, {5090, 44960}, {5122, 37281}, {5178, 17757}, {5223, 38137}, {5253, 51529}, {5428, 44425}, {5434, 15079}, {5663, 58487}, {5734, 51515}, {5762, 15481}, {5771, 44229}, {5789, 6826}, {5816, 16885}, {5842, 40260}, {5882, 44904}, {6147, 10590}, {6852, 38114}, {6884, 59382}, {6888, 38752}, {6901, 10742}, {6913, 32141}, {6918, 32153}, {6920, 18524}, {6946, 26321}, {7294, 36975}, {7686, 31835}, {7705, 11112}, {7967, 15022}, {7982, 59400}, {7987, 11539}, {7991, 41991}, {8148, 9779}, {8582, 50238}, {8703, 31423}, {9654, 54361}, {9782, 38755}, {9864, 38229}, {9945, 27529}, {10021, 31659}, {10109, 28204}, {10124, 28208}, {10164, 12103}, {10165, 48154}, {10171, 15178}, {10172, 13624}, {10222, 38155}, {10299, 46930}, {10386, 31434}, {10595, 50798}, {10627, 52796}, {11230, 12812}, {11372, 38170}, {11531, 50823}, {11545, 12047}, {11813, 15862}, {12100, 34648}, {12102, 28146}, {12135, 16868}, {12432, 14988}, {12645, 19709}, {13145, 31871}, {13257, 33668}, {13729, 22938}, {13743, 33814}, {14892, 47745}, {14893, 50821}, {15681, 50825}, {15686, 16192}, {15687, 19875}, {15690, 38068}, {15691, 50862}, {15703, 50864}, {15712, 30315}, {15713, 34628}, {15715, 50863}, {15723, 50833}, {15911, 52850}, {16125, 31750}, {16127, 33899}, {16616, 58630}, {16881, 58474}, {17504, 19876}, {17606, 18990}, {18538, 49602}, {18762, 49601}, {18874, 58469}, {20070, 38066}, {21677, 31160}, {26202, 46684}, {28164, 33923}, {28168, 44245}, {28198, 50803}, {28202, 51069}, {28216, 43174}, {30436, 36155}, {31162, 38081}, {31870, 56762}, {32431, 59680}, {33179, 51091}, {34200, 51079}, {34627, 37624}, {34718, 41106}, {35400, 50813}, {35788, 42270}, {35789, 42273}, {38047, 39884}, {38087, 50956}, {38098, 51074}, {38314, 50797}, {38602, 45976}, {39885, 59399}, {45310, 51714}, {47599, 51705}, {51111, 52795}, {54445, 55857}, {58216, 58441}, {58247, 59503}

X(61259) = midpoint of X(i) and X(j) for these {i,j}: {5, 18357}, {10, 546}, {140, 18480}, {355, 5901}, {547, 50796}, {548, 31673}, {3579, 3853}, {4701, 58240}, {5690, 40273}, {7686, 31835}, {9956, 19925}, {12100, 34648}, {12103, 33697}, {13145, 31871}, {14893, 50821}, {15691, 50862}, {16616, 58630}, {31870, 56762}
X(61259) = reflection of X(i) in X(j) for these {i,j}: {1125, 35018}, {3530, 3634}, {9955, 12811}, {13624, 16239}, {16881, 58474}, {18483, 3856}, {58469, 18874}
X(61259) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 355, 5901}, {5, 1483, 8227}, {5, 5587, 18357}, {5, 26470, 60759}, {5, 37705, 5886}, {5, 38138, 1}, {8, 3851, 38034}, {10, 38140, 546}, {12, 12019, 12433}, {80, 3614, 37737}, {355, 7989, 5}, {355, 8227, 1483}, {381, 5690, 40273}, {381, 5818, 5690}, {1483, 8227, 5901}, {1656, 59387, 34773}, {1837, 10592, 5719}, {3090, 18525, 38028}, {3090, 54448, 18525}, {3091, 5790, 22791}, {3858, 38112, 12699}, {5068, 59388, 18493}, {5587, 7989, 355}, {5886, 37714, 37705}, {5901, 18357, 355}, {7173, 37710, 1387}, {9956, 31663, 3828}, {10164, 33697, 12103}, {10172, 13624, 16239}, {10175, 18480, 140}, {11231, 31673, 548}, {17502, 51073, 140}, {18481, 54447, 632}, {18492, 26446, 3627}, {19875, 50799, 15687}, {34648, 38083, 12100}

X(61260) = X(1)X(5)∩X(10)X(3858)

Barycentrics    4*a^4 - 4*a^3*b + 7*a^2*b^2 + 4*a*b^3 - 11*b^4 - 4*a^3*c + 8*a^2*b*c - 4*a*b^2*c + 7*a^2*c^2 - 4*a*b*c^2 + 22*b^2*c^2 + 4*a*c^3 - 11*c^4 : :
X(61260) = 2 X[1] - 11 X[5], 7 X[1] + 11 X[355], 20 X[1] - 11 X[1483], X[1] + 11 X[5587], 25 X[1] + 11 X[5881], 5 X[1] - 11 X[5886], 13 X[1] - 22 X[5901], 3 X[1] - 11 X[7988], 5 X[1] - 77 X[7989], 19 X[1] - 55 X[8227], 41 X[1] - 77 X[9624], 8 X[1] - 11 X[10283], 5 X[1] + 22 X[18357], 16 X[1] + 11 X[37705], and many others

X(61260) lies on these lines: {1, 5}, {3, 46930}, {8, 12811}, {10, 3858}, {165, 33699}, {381, 28212}, {515, 15699}, {516, 3845}, {517, 38071}, {546, 5657}, {547, 59387}, {549, 10175}, {550, 11231}, {632, 10172}, {944, 12812}, {962, 3859}, {1698, 15704}, {2801, 38080}, {3091, 59503}, {3524, 58218}, {3544, 12645}, {3545, 5844}, {3616, 44904}, {3627, 9956}, {3628, 5731}, {3634, 44682}, {3817, 51077}, {3828, 35404}, {3839, 28216}, {3850, 5818}, {3853, 9780}, {3856, 12702}, {3857, 5690}, {3860, 9812}, {5055, 28224}, {5066, 5790}, {5070, 58228}, {5072, 51515}, {5073, 46932}, {5079, 51700}, {5603, 11737}, {5691, 14869}, {6929, 38149}, {7705, 50240}, {9778, 12101}, {10109, 10246}, {10164, 19710}, {10165, 55856}, {10171, 50824}, {11539, 28186}, {12100, 50800}, {12699, 41991}, {13743, 38636}, {14892, 38074}, {15022, 18526}, {15687, 26446}, {15696, 46931}, {15711, 58441}, {15714, 19876}, {17504, 28190}, {18481, 55859}, {18525, 35018}, {19709, 59388}, {19875, 28178}, {19877, 33923}, {22791, 38176}, {23046, 28174}, {28164, 38083}, {28204, 58234}, {28234, 38034}, {28236, 38022}, {31673, 46853}, {38028, 50796}, {38637, 45976}, {47599, 54445}, {51073, 58223}

X(61260) = midpoint of X(i) and X(j) for these {i,j}: {5055, 54448}, {5790, 9779}
X(61260) = reflection of X(i) in X(j) for these {i,j}: {9779, 5066}, {11539, 54447}, {54445, 47599}
X(61260) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 5587, 38138}, {5, 18357, 1483}, {5, 38138, 10283}, {1483, 5886, 10283}, {5587, 5886, 18357}, {5587, 7989, 5886}, {7989, 18357, 5}, {10283, 38138, 37705}, {38042, 38140, 3845}

X(61261) = X(1)X(5)∩X(10)X(381)

Barycentrics    a^4 - a^3*b + 2*a^2*b^2 + a*b^3 - 3*b^4 - a^3*c + 2*a^2*b*c - a*b^2*c + 2*a^2*c^2 - a*b*c^2 + 6*b^2*c^2 + a*c^3 - 3*c^4 : :
X(61261) = X[1] - 6 X[5], 2 X[1] + 3 X[355], 11 X[1] - 6 X[1483], X[1] + 9 X[5587], 7 X[1] + 3 X[5881], 4 X[1] - 9 X[5886], 7 X[1] - 12 X[5901], 7 X[1] - 27 X[7988], X[1] - 21 X[7989], X[1] - 3 X[8227], 11 X[1] - 21 X[9624], 13 X[1] - 18 X[10283], X[1] + 4 X[18357], 3 X[1] + 2 X[37705], 11 X[1] + 9 X[37712], and many others

X(61261) lies on these lines: {1, 5}, {2, 13624}, {3, 3634}, {4, 2355}, {8, 3545}, {9, 16139}, {10, 381}, {20, 11231}, {30, 1698}, {40, 546}, {43, 48903}, {44, 5816}, {46, 3652}, {104, 38182}, {140, 5691}, {145, 38074}, {165, 3627}, {376, 19877}, {377, 17619}, {382, 6684}, {392, 5187}, {403, 5090}, {405, 18491}, {442, 7700}, {474, 18761}, {515, 1656}, {516, 3843}, {517, 3091}, {519, 18493}, {547, 3624}, {550, 30315}, {551, 18526}, {568, 58474}, {631, 28160}, {632, 7987}, {942, 10590}, {944, 5056}, {946, 3626}, {950, 31479}, {958, 35252}, {962, 3855}, {993, 37251}, {1001, 18518}, {1071, 6993}, {1125, 3655}, {1155, 6917}, {1210, 9654}, {1329, 6841}, {1351, 38146}, {1352, 4663}, {1376, 35251}, {1385, 3090}, {1478, 17606}, {1482, 3625}, {1571, 53419}, {1657, 10164}, {1699, 3850}, {1737, 5221}, {1836, 18395}, {2475, 7705}, {2478, 18517}, {2551, 6849}, {2771, 15081}, {2948, 11801}, {3146, 31663}, {3244, 50798}, {3340, 11545}, {3416, 19130}, {3419, 4420}, {3436, 6896}, {3522, 28168}, {3523, 58219}, {3525, 17502}, {3526, 4297}, {3543, 46932}, {3544, 10222}, {3560, 5217}, {3576, 3628}, {3585, 24914}, {3616, 5071}, {3621, 5068}, {3622, 34627}, {3632, 11737}, {3633, 14892}, {3647, 26066}, {3679, 5066}, {3740, 16616}, {3751, 18358}, {3753, 6871}, {3754, 40266}, {3812, 40263}, {3814, 5794}, {3818, 38047}, {3826, 31672}, {3828, 3830}, {3832, 5657}, {3839, 6361}, {3844, 31670}, {3845, 19875}, {3854, 59417}, {3856, 9589}, {3857, 7991}, {3858, 28174}, {3859, 28212}, {3861, 9588}, {3868, 56762}, {3911, 9655}, {3925, 37406}, {3947, 15934}, {4301, 59503}, {4668, 30308}, {4691, 34718}, {4816, 5844}, {5010, 31649}, {5044, 6866}, {5045, 5261}, {5046, 18407}, {5054, 34648}, {5067, 5731}, {5070, 10165}, {5073, 12512}, {5076, 28150}, {5079, 10246}, {5080, 6900}, {5082, 51362}, {5086, 6873}, {5126, 6944}, {5204, 6911}, {5220, 5805}, {5225, 6893}, {5229, 6826}, {5248, 18524}, {5250, 38058}, {5270, 15079}, {5274, 31792}, {5302, 5791}, {5432, 16617}, {5435, 31776}, {5441, 5560}, {5445, 18513}, {5450, 45976}, {5499, 41859}, {5704, 6864}, {5708, 51755}, {5714, 5777}, {5759, 38179}, {5779, 30424}, {5787, 6881}, {5795, 31493}, {5880, 48668}, {5882, 10171}, {5885, 12528}, {5887, 6867}, {5927, 6984}, {6175, 10308}, {6199, 49618}, {6243, 31752}, {6246, 38752}, {6259, 12616}, {6395, 49619}, {6564, 13973}, {6565, 13911}, {6702, 10742}, {6705, 40267}, {6776, 38167}, {6796, 7489}, {6832, 26487}, {6835, 10526}, {6855, 7319}, {6862, 37600}, {6886, 10786}, {6912, 26285}, {6913, 11499}, {6914, 59325}, {6915, 26286}, {6918, 22758}, {6920, 32613}, {6924, 59319}, {6928, 15254}, {6929, 37568}, {6931, 17614}, {6946, 32612}, {6957, 10525}, {6959, 37605}, {6968, 12672}, {6982, 31788}, {6983, 26492}, {6996, 29608}, {7171, 50238}, {7373, 51782}, {7377, 16815}, {7384, 29591}, {7514, 8185}, {7530, 37557}, {7687, 12778}, {7968, 42274}, {7969, 42277}, {7982, 12811}, {8582, 17528}, {8703, 19876}, {9342, 37403}, {9582, 42225}, {9612, 11544}, {9613, 15325}, {9669, 31397}, {9779, 12245}, {9947, 10569}, {9957, 10591}, {10039, 10896}, {10109, 25055}, {10247, 47745}, {10265, 38755}, {10272, 12407}, {10304, 46930}, {10573, 17605}, {10588, 24929}, {10589, 24928}, {10625, 52796}, {10738, 38161}, {10915, 11235}, {10916, 11236}, {11362, 12571}, {11372, 38139}, {11491, 38183}, {11539, 34628}, {11684, 16159}, {12162, 58487}, {12368, 20304}, {12515, 34122}, {12611, 59415}, {12619, 16128}, {12645, 13464}, {12773, 59419}, {12779, 20299}, {12812, 28224}, {13665, 13936}, {13743, 25440}, {13785, 13883}, {13861, 15177}, {13893, 42215}, {13947, 42216}, {13996, 38077}, {14150, 26105}, {14217, 38141}, {14269, 50803}, {14647, 22792}, {14845, 58469}, {14869, 58221}, {14873, 41501}, {15022, 15178}, {15064, 31870}, {15068, 16473}, {15092, 38220}, {15171, 31434}, {15172, 51784}, {15681, 38068}, {15688, 50862}, {15689, 50829}, {15694, 31253}, {15696, 28172}, {15699, 34595}, {15703, 19878}, {15704, 16192}, {15707, 50815}, {15710, 51088}, {15712, 28190}, {15973, 48916}, {16138, 18540}, {16615, 27131}, {17057, 18406}, {17303, 32431}, {17308, 36728}, {17504, 58215}, {17530, 19860}, {17532, 24982}, {17533, 19861}, {17556, 24987}, {17563, 38761}, {17577, 25005}, {17578, 28154}, {18393, 41687}, {18435, 31728}, {18436, 31760}, {18482, 38057}, {18510, 49548}, {18512, 49547}, {18519, 25524}, {18529, 41854}, {18538, 18991}, {18583, 39885}, {18762, 18992}, {20330, 38154}, {23046, 50865}, {23259, 31439}, {24086, 41313}, {24387, 32049}, {24474, 58631}, {24603, 36731}, {25011, 44217}, {25561, 47359}, {25565, 38023}, {28198, 41099}, {28236, 37624}, {28452, 57288}, {29579, 36662}, {30332, 38149}, {31053, 33592}, {31162, 38071}, {31398, 44518}, {31666, 60781}, {31835, 37625}, {32537, 47746}, {32900, 38314}, {33858, 54318}, {34748, 50801}, {35018, 38028}, {35774, 42273}, {35775, 42270}, {36279, 37822}, {36996, 38172}, {37612, 38757}, {38052, 60901}, {38081, 58248}, {38107, 43180}, {38133, 38753}, {38151, 60922}, {38318, 43161}, {38335, 50808}, {38733, 51578}, {39899, 59408}, {41106, 53620}, {41984, 50833}, {42262, 49601}, {42265, 49602}, {42268, 49226}, {42269, 49227}, {43174, 48661}, {44904, 51700}, {44911, 47469}, {46028, 47033}, {46617, 46976}, {46704, 48939}, {47478, 50824}, {47743, 51788}, {48887, 48936}, {48926, 50417}, {48927, 48937}, {49137, 59420}, {49456, 51040}, {49573, 49590}, {49574, 49591}, {50816, 58202}

X(61261) = midpoint of X(i) and X(j) for these {i,j}: {1698, 18492}, {3091, 5818}, {8227, 37714}
X(61261) = reflection of X(i) in X(j) for these {i,j}: {355, 37714}, {7987, 632}, {8227, 5}
X(61261) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5587, 18357}, {1, 18357, 355}, {2, 18480, 18481}, {4, 9780, 3579}, {4, 9956, 26446}, {5, 355, 5886}, {5, 5587, 355}, {5, 5901, 7988}, {5, 18357, 1}, {5, 38138, 5901}, {8, 3545, 9955}, {8, 9955, 3656}, {10, 381, 12699}, {10, 12699, 3654}, {10, 18483, 12702}, {12, 10826, 5722}, {80, 11375, 37739}, {119, 12019, 12738}, {355, 5886, 37727}, {381, 12702, 18483}, {546, 38042, 40}, {547, 34773, 3624}, {944, 5056, 11230}, {946, 3626, 8148}, {1125, 18525, 3655}, {1125, 50796, 18525}, {1482, 5072, 3817}, {1737, 10895, 57282}, {1837, 7951, 11374}, {3090, 59387, 1385}, {3579, 9780, 26446}, {3579, 9956, 9780}, {3624, 34773, 3653}, {3634, 19925, 31673}, {3634, 31673, 3}, {3740, 16616, 37585}, {3832, 5657, 22793}, {3839, 46933, 6361}, {3850, 5690, 1699}, {3851, 5790, 946}, {3857, 38112, 40273}, {4297, 10172, 3526}, {5054, 50800, 34648}, {5055, 18525, 1125}, {5055, 50796, 3655}, {5056, 54448, 944}, {5252, 7741, 11373}, {5270, 15079, 17728}, {5587, 7988, 38138}, {5587, 7989, 5}, {5587, 8227, 37714}, {5691, 54447, 140}, {5790, 8148, 3626}, {5881, 7988, 5901}, {5881, 38138, 355}, {5901, 38138, 5881}, {6361, 46933, 50821}, {9624, 37712, 1483}, {9956, 38140, 4}, {10175, 19925, 3}, {10175, 31673, 3634}, {10590, 54361, 942}, {10592, 12019, 1}, {11375, 11376, 38063}, {12702, 18483, 12699}, {13464, 38155, 12645}, {31162, 38071, 50807}, {38112, 40273, 7991}

X(61262) = X(1)X(5)∩X(10)X(3850)

Barycentrics    2*a^4 - 2*a^3*b + 5*a^2*b^2 + 2*a*b^3 - 7*b^4 - 2*a^3*c + 4*a^2*b*c - 2*a*b^2*c + 5*a^2*c^2 - 2*a*b*c^2 + 14*b^2*c^2 + 2*a*c^3 - 7*c^4 : :
X(61262) = X[1] - 7 X[5], 5 X[1] + 7 X[355], 13 X[1] - 7 X[1483], X[1] + 7 X[5587], 17 X[1] + 7 X[5881], 3 X[1] - 7 X[5886], 4 X[1] - 7 X[5901], 5 X[1] - 21 X[7988], X[1] - 49 X[7989], 11 X[1] - 35 X[8227], 25 X[1] - 49 X[9624], 5 X[1] - 7 X[10283], 2 X[1] + 7 X[18357], 11 X[1] + 7 X[37705], 9 X[1] + 7 X[37712], and many others

X(61262) lies on these lines: {1, 5}, {2, 28186}, {4, 28182}, {8, 5072}, {10, 3850}, {30, 10164}, {40, 3858}, {140, 10172}, {165, 15687}, {381, 5657}, {515, 547}, {516, 546}, {517, 3956}, {519, 14892}, {548, 3634}, {549, 28190}, {550, 18492}, {632, 5691}, {944, 5079}, {946, 12811}, {1125, 12812}, {1385, 35018}, {1482, 5068}, {1656, 5731}, {1657, 19877}, {1698, 3627}, {1699, 38071}, {3090, 34773}, {3091, 5690}, {3526, 58224}, {3530, 31673}, {3544, 18493}, {3545, 5790}, {3576, 15699}, {3579, 3861}, {3628, 10165}, {3656, 59400}, {3754, 58683}, {3817, 5844}, {3828, 14893}, {3843, 9780}, {3845, 26446}, {3851, 5818}, {3853, 6684}, {3855, 12702}, {3856, 22793}, {3857, 12699}, {3859, 18483}, {3860, 28216}, {4297, 16239}, {4746, 9955}, {5055, 38028}, {5056, 18525}, {5071, 10246}, {5603, 19709}, {5843, 38158}, {6147, 54361}, {6893, 38149}, {6912, 33814}, {6946, 38602}, {7489, 59421}, {7967, 38022}, {7987, 55859}, {8703, 50799}, {9778, 14269}, {10109, 11230}, {10124, 17502}, {10157, 14988}, {10171, 28204}, {10222, 41989}, {10247, 38074}, {10895, 24470}, {11545, 17605}, {11813, 38214}, {12100, 28164}, {12101, 28150}, {12102, 31730}, {12108, 51073}, {12135, 35487}, {13391, 52796}, {13624, 48154}, {13743, 34474}, {14449, 31752}, {15682, 50825}, {15686, 19876}, {15693, 58218}, {15703, 54445}, {15704, 31423}, {15713, 58221}, {15759, 50862}, {17538, 46930}, {17577, 34122}, {17606, 34753}, {18481, 55856}, {19875, 23046}, {19883, 45757}, {20049, 59388}, {28168, 34200}, {28202, 41987}, {28208, 47599}, {28232, 51069}, {28236, 41150}, {30308, 50823}, {31732, 58531}, {31760, 31834}, {33697, 33923}, {33703, 46931}, {34380, 38146}, {37375, 38058}, {38155, 51096}, {38693, 45976}, {41106, 59417}, {41990, 50807}, {45959, 58487}, {46332, 51088}, {46933, 48661}, {50798, 51092}, {50864, 58230}

X(61262) = midpoint of X(i) and X(j) for these {i,j}: {5, 5587}, {165, 15687}, {355, 10283}, {381, 38042}, {946, 38176}, {1699, 38112}, {3656, 59400}, {3845, 26446}, {5790, 38034}, {5886, 38138}, {10165, 18480}, {10172, 19925}, {10175, 38140}, {11230, 50796}, {17502, 34648}, {19875, 23046}, {22791, 59503}, {38028, 59387}, {38155, 51709}
X(61262) = reflection of X(i) in X(j) for these {i,j}: {140, 10172}, {3817, 11737}, {10165, 3628}, {11230, 10109}, {17502, 10124}, {18357, 5587}, {19883, 45757}, {34200, 58441}
X(61262) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 10283, 7988}, {5, 18357, 5901}, {5, 37705, 8227}, {5, 38138, 5886}, {10, 3850, 40273}, {355, 7988, 10283}, {3545, 5790, 38034}, {3851, 5818, 22791}, {3851, 59503, 9779}, {5055, 59387, 38028}, {5071, 54448, 10246}, {5587, 5886, 38138}, {5587, 7988, 355}, {5818, 9779, 59503}, {7951, 12019, 5719}, {9779, 59503, 22791}, {10164, 10175, 38083}, {10175, 38076, 38140}, {10592, 10826, 12433}, {38071, 38112, 1699}

X(61263) = X(1)X(5)∩X(10)X(3851)

Barycentrics    a^4 - a^3*b + 4*a^2*b^2 + a*b^3 - 5*b^4 - a^3*c + 2*a^2*b*c - a*b^2*c + 4*a^2*c^2 - a*b*c^2 + 10*b^2*c^2 + a*c^3 - 5*c^4 : :
X(61263) = X[1] - 10 X[5], 4 X[1] + 5 X[355], 19 X[1] - 10 X[1483], X[1] + 5 X[5587], 13 X[1] + 5 X[5881], 2 X[1] - 5 X[5886], 11 X[1] - 20 X[5901], X[1] - 5 X[7988], X[1] + 35 X[7989], 7 X[1] - 25 X[8227], 17 X[1] - 35 X[9624], 7 X[1] - 10 X[10283], 7 X[1] + 20 X[18357], 17 X[1] + 10 X[37705], 7 X[1] + 5 X[37712], and many others

X(61263) lies on these lines: {1, 5}, {2, 17502}, {3, 10172}, {4, 11231}, {8, 3544}, {10, 3851}, {30, 54447}, {40, 3850}, {140, 18492}, {165, 3845}, {381, 516}, {382, 3634}, {515, 3653}, {517, 3545}, {546, 1698}, {547, 3576}, {631, 58219}, {944, 15022}, {946, 4691}, {1125, 5079}, {1385, 5056}, {1482, 4701}, {1656, 10165}, {1699, 3654}, {3090, 5731}, {3091, 5657}, {3523, 33697}, {3524, 28168}, {3526, 31673}, {3530, 19872}, {3534, 50803}, {3579, 3832}, {3624, 35018}, {3627, 31423}, {3628, 5691}, {3655, 5071}, {3656, 3817}, {3679, 11737}, {3820, 38200}, {3830, 10164}, {3839, 28146}, {3843, 6684}, {3853, 35242}, {3854, 6361}, {3855, 9780}, {3858, 30315}, {3859, 9588}, {4297, 5070}, {4301, 58247}, {4678, 5068}, {4679, 17057}, {4745, 50806}, {5054, 28164}, {5067, 13624}, {5076, 12512}, {5090, 16868}, {5122, 6826}, {5450, 38637}, {5603, 31145}, {5690, 12811}, {5805, 15481}, {5816, 16669}, {5817, 6843}, {5844, 14892}, {5880, 6702}, {6827, 38318}, {6854, 18516}, {6864, 37821}, {6871, 17619}, {6881, 38122}, {6886, 26487}, {6893, 18782}, {6896, 10526}, {6898, 18517}, {6907, 59389}, {6912, 34474}, {6920, 59421}, {6939, 37820}, {6946, 38693}, {6965, 18407}, {7987, 55856}, {8164, 8236}, {8728, 38399}, {9590, 49671}, {9778, 41099}, {9812, 41106}, {9864, 15092}, {9905, 20584}, {10109, 38028}, {10171, 10246}, {10222, 20014}, {10247, 38155}, {10404, 15079}, {11224, 59400}, {11539, 28190}, {12368, 15088}, {12515, 54370}, {12571, 12702}, {12779, 32767}, {12812, 34773}, {14269, 28150}, {15684, 59420}, {15687, 19876}, {15697, 51088}, {15699, 28186}, {15701, 50862}, {15703, 34648}, {15720, 31253}, {16138, 59333}, {17504, 58213}, {17606, 57282}, {18436, 58474}, {18493, 51515}, {19875, 28174}, {23046, 28178}, {24644, 38170}, {25055, 28224}, {25440, 38636}, {28158, 38068}, {28204, 54448}, {28208, 54445}, {28228, 38066}, {31162, 38112}, {31441, 53419}, {38052, 38139}, {38081, 58243}, {38107, 38158}, {38127, 50802}, {38151, 51516}, {38161, 38752}, {38179, 59385}, {38755, 59419}, {44580, 50820}, {46930, 50688}, {50797, 51103}, {50798, 51091}, {50800, 51705}, {50804, 51709}, {51069, 51074}, {55861, 58225}, {55863, 58220}

X(61263) = midpoint of X(5587) and X(7988)
X(61263) = reflection of X(i) in X(j) for these {i,j}: {5886, 7988}, {7988, 5}, {58221, 11539}, {58230, 19883}
X(61263) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5587, 38138}, {4, 19877, 31663}, {5, 5587, 5886}, {5, 10942, 7958}, {5, 18357, 8227}, {381, 10175, 26446}, {1656, 19925, 18481}, {1699, 38042, 3654}, {3091, 9956, 12699}, {3614, 10826, 11374}, {3654, 5066, 50807}, {3817, 5790, 3656}, {3855, 9780, 22793}, {5066, 38042, 1699}, {5068, 5818, 9955}, {5071, 59387, 11230}, {5587, 5886, 355}, {5587, 8227, 37712}, {5587, 37712, 18357}, {5790, 19709, 3817}, {5886, 37727, 10283}, {7173, 10827, 11373}, {7951, 37718, 17718}, {8227, 10283, 5886}, {8227, 18357, 37727}, {8227, 37712, 10283}, {10171, 50796, 10246}, {10283, 18357, 37712}, {10283, 37712, 37727}, {11230, 59387, 3655}, {12571, 31399, 12702}, {17718, 37718, 5722}, {18357, 37727, 355}

X(61264) = X(1)X(5)∩X(10)X(5068)

Barycentrics    a^4 - a^3*b + 7*a^2*b^2 + a*b^3 - 8*b^4 - a^3*c + 2*a^2*b*c - a*b^2*c + 7*a^2*c^2 - a*b*c^2 + 16*b^2*c^2 + a*c^3 - 8*c^4 : :
X(61264) = X[1] - 16 X[5], 7 X[1] + 8 X[355], 31 X[1] - 16 X[1483], X[1] + 4 X[5587], 11 X[1] + 4 X[5881], 3 X[1] - 8 X[5886], 17 X[1] - 32 X[5901], X[1] - 6 X[7988], X[1] + 14 X[7989], X[1] - 4 X[8227], 13 X[1] - 28 X[9624], 11 X[1] - 16 X[10283], 13 X[1] + 32 X[18357], 29 X[1] + 16 X[37705], 3 X[1] + 2 X[37712], and many others

X(61264) lies on these lines: {1, 5}, {2, 28164}, {4, 10172}, {10, 5068}, {20, 19872}, {40, 3851}, {165, 381}, {442, 59389}, {515, 5071}, {516, 1698}, {517, 19709}, {546, 31423}, {547, 34628}, {551, 54448}, {631, 28172}, {946, 3544}, {1125, 15022}, {1131, 49619}, {1132, 49618}, {1210, 15841}, {1329, 38200}, {1479, 38149}, {1656, 7987}, {1699, 3545}, {1750, 6829}, {2951, 6932}, {3090, 5691}, {3146, 51073}, {3339, 17606}, {3361, 10895}, {3522, 31253}, {3530, 58215}, {3543, 58441}, {3576, 5055}, {3583, 6939}, {3585, 6864}, {3624, 5056}, {3634, 3832}, {3656, 58241}, {3679, 3817}, {3814, 8580}, {3828, 9812}, {3839, 10164}, {3843, 28154}, {3850, 41869}, {3854, 19877}, {3855, 6684}, {3856, 31425}, {3858, 28182}, {3894, 15064}, {3947, 11038}, {4297, 7486}, {4301, 58248}, {4355, 5704}, {4512, 37375}, {4668, 5818}, {4677, 5603}, {4816, 5734}, {4882, 11681}, {4915, 11680}, {5010, 6913}, {5066, 26446}, {5067, 31673}, {5072, 7991}, {5079, 18480}, {5154, 8583}, {5432, 51792}, {5493, 46932}, {5790, 11224}, {5817, 9612}, {5902, 10157}, {6561, 9584}, {6702, 12767}, {6826, 18513}, {6843, 53056}, {6854, 41698}, {6881, 10857}, {6893, 18514}, {6918, 7280}, {6980, 30503}, {7603, 9592}, {7982, 38176}, {9582, 35787}, {9588, 18483}, {9589, 9780}, {9593, 39565}, {9620, 39601}, {9947, 50190}, {9955, 11531}, {10109, 50811}, {10171, 25055}, {10248, 46931}, {10591, 51784}, {10896, 53053}, {11001, 51078}, {11230, 30392}, {11519, 24387}, {11737, 31162}, {12100, 58213}, {12512, 50689}, {12699, 12811}, {12812, 58229}, {13893, 42270}, {13947, 42273}, {14892, 38034}, {15015, 38161}, {15056, 58474}, {15079, 38107}, {15088, 33535}, {15694, 28168}, {15703, 17502}, {15722, 58216}, {16189, 18493}, {16200, 51515}, {16853, 35202}, {17605, 18421}, {18424, 31441}, {18481, 35018}, {19003, 42262}, {19004, 42265}, {19708, 50866}, {19856, 36694}, {21153, 52269}, {25542, 38031}, {28150, 41099}, {28186, 50799}, {28232, 51074}, {28236, 51105}, {31434, 53052}, {33697, 46219}, {34648, 54445}, {34747, 59388}, {38028, 47478}, {38155, 51093}, {46936, 58225}, {50687, 59420}, {50796, 51110}, {50798, 51094}, {50800, 58230}, {50802, 59417}, {50828, 58227}, {51068, 51075}

X(61264) = midpoint of X(5587) and X(8227)
X(61264) = reflection of X(37714) in X(5587)
X(61264) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 5587, 7988}, {5, 7989, 1}, {11, 5726, 1}, {165, 54447, 19876}, {381, 54447, 165}, {1656, 18492, 7987}, {1699, 10175, 19875}, {3090, 5691, 34595}, {3545, 10175, 1699}, {3854, 19877, 51118}, {4677, 5603, 16191}, {5055, 38140, 3576}, {5056, 19925, 3624}, {5587, 5886, 37712}, {5587, 7988, 1}, {5790, 38021, 11224}, {5818, 11522, 4668}, {5886, 37712, 1}, {7173, 9578, 50444}, {7988, 7989, 5587}, {7988, 37712, 5886}, {8227, 37714, 1}, {9578, 50444, 1}, {9780, 12571, 9589}, {10171, 38076, 59387}, {10171, 59387, 25055}

X(61265) = X(1)X(5)∩X(2)X(28150)

Barycentrics    a^4 - a^3*b - 11*a^2*b^2 + a*b^3 + 10*b^4 - a^3*c + 2*a^2*b*c - a*b^2*c - 11*a^2*c^2 - a*b*c^2 - 20*b^2*c^2 + a*c^3 + 10*c^4 : :
X(61265) = X[1] + 20 X[5], 11 X[1] + 10 X[355], 41 X[1] - 20 X[1483], 2 X[1] + 5 X[5587], 16 X[1] + 5 X[5881], 3 X[1] - 10 X[5886], 19 X[1] - 40 X[5901], X[1] - 15 X[7988], X[1] + 5 X[7989], 4 X[1] - 25 X[8227], 2 X[1] - 5 X[9624], 13 X[1] - 20 X[10283], 23 X[1] + 40 X[18357], 43 X[1] + 20 X[37705], 9 X[1] + 5 X[37712], and many others

X(61265) lies on these lines: {1, 5}, {2, 28150}, {4, 19878}, {40, 5056}, {165, 547}, {381, 17502}, {382, 58219}, {516, 3090}, {546, 34595}, {946, 15022}, {1125, 3544}, {1656, 31663}, {1698, 5079}, {1699, 5055}, {3091, 10165}, {3526, 28154}, {3534, 58216}, {3545, 3576}, {3624, 3851}, {3817, 3828}, {3832, 28172}, {3845, 58221}, {3850, 7987}, {3855, 19862}, {3857, 58225}, {4669, 5603}, {4678, 28234}, {4691, 7982}, {4701, 5818}, {5067, 12571}, {5068, 5731}, {5072, 5691}, {5141, 25522}, {6990, 59389}, {7486, 18483}, {7967, 38076}, {8703, 58213}, {9622, 43614}, {10109, 26446}, {10175, 38021}, {11230, 19709}, {11522, 59503}, {12512, 60781}, {12699, 12812}, {13464, 20053}, {14892, 38028}, {15702, 28158}, {15703, 28146}, {15709, 59420}, {16191, 59400}, {16192, 28182}, {16200, 31145}, {18493, 38176}, {19708, 51076}, {19872, 22793}, {19875, 38034}, {19876, 28174}, {22791, 30315}, {25055, 38140}, {25639, 38200}, {28164, 41106}, {28178, 50807}, {28212, 44904}, {28224, 51110}, {28236, 51106}, {31424, 52795}, {31730, 46936}, {34773, 41989}, {38155, 51091}, {50823, 58241}, {51066, 58243}, {51515, 51709}

X(61265) = midpoint of X(5587) and X(9624)
X(61265) = reflection of X(5587) in X(7989)
X(61265) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 7988, 5587}, {3545, 10171, 3576}, {3817, 5071, 54447}, {3817, 54447, 31162}, {5056, 9779, 10172}, {5067, 12571, 35242}, {5587, 7988, 8227}, {5886, 38138, 1}, {9779, 10172, 40}, {19872, 22793, 31425}

X(61266) = X(1)X(5)∩X(2)X(28146)

Barycentrics    a^4 - a^3*b - 8*a^2*b^2 + a*b^3 + 7*b^4 - a^3*c + 2*a^2*b*c - a*b^2*c - 8*a^2*c^2 - a*b*c^2 - 14*b^2*c^2 + a*c^3 + 7*c^4 : :
X(61266) = X[1] + 14 X[5], 8 X[1] + 7 X[355], 29 X[1] - 14 X[1483], 3 X[1] + 7 X[5587], 23 X[1] + 7 X[5881], 2 X[1] - 7 X[5886], 13 X[1] - 28 X[5901], X[1] - 21 X[7988], 11 X[1] + 49 X[7989], X[1] - 7 X[8227], 19 X[1] - 49 X[9624], 9 X[1] - 14 X[10283], 17 X[1] + 28 X[18357], 31 X[1] + 14 X[37705], and many others

X(61266) lies on these lines: {1, 5}, {2, 28146}, {40, 35018}, {165, 15699}, {376, 58216}, {381, 10165}, {515, 19709}, {516, 1656}, {517, 5071}, {547, 1699}, {631, 28154}, {632, 28182}, {946, 5079}, {1125, 5072}, {1385, 5068}, {1482, 4746}, {1657, 19878}, {1698, 12812}, {3090, 9779}, {3091, 28160}, {3526, 12571}, {3528, 58214}, {3544, 18480}, {3545, 3653}, {3576, 5066}, {3579, 7486}, {3624, 3850}, {3627, 34595}, {3654, 10109}, {3655, 38140}, {3656, 4745}, {3817, 5055}, {3839, 17502}, {3843, 19862}, {3851, 18481}, {3854, 33697}, {3855, 13624}, {3858, 7987}, {5056, 5657}, {5067, 22793}, {5070, 18483}, {5603, 38176}, {5691, 12811}, {5790, 34641}, {5818, 20052}, {6841, 38122}, {9956, 15022}, {10164, 15703}, {10222, 20054}, {10247, 50804}, {11219, 38084}, {11737, 38028}, {12512, 55858}, {13464, 51515}, {14892, 25055}, {15681, 58218}, {15687, 58221}, {15693, 28158}, {15694, 28150}, {15701, 59420}, {15716, 50869}, {16192, 55859}, {18493, 28234}, {22791, 44904}, {28168, 41099}, {28174, 30308}, {28228, 50806}, {31730, 55857}, {34628, 58227}, {34648, 58230}, {35242, 48154}, {38021, 38042}, {38083, 59417}, {38107, 60945}, {41106, 54445}, {41150, 50796}, {41869, 55856}, {46219, 51118}, {48661, 51073}, {49138, 58219}, {50798, 51095}, {50800, 51108}

X(61266) = reflection of X(5886) in X(8227)
X(61266) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 7988, 5886}, {3090, 9779, 11231}, {3817, 5055, 26446}, {5790, 58238, 34641}, {9779, 11231, 12699}, {10109, 38034, 54447}, {38034, 54447, 3654}

X(61267) = X(1)X(5)∩X(2)X(28178)

Barycentrics    2*a^4 - 2*a^3*b - 13*a^2*b^2 + 2*a*b^3 + 11*b^4 - 2*a^3*c + 4*a^2*b*c - 2*a*b^2*c - 13*a^2*c^2 - 2*a*b*c^2 - 22*b^2*c^2 + 2*a*c^3 + 11*c^4 : :
X(61267) = X[1] + 11 X[5], 13 X[1] + 11 X[355], 23 X[1] - 11 X[1483], 5 X[1] + 11 X[5587], 37 X[1] + 11 X[5881], 3 X[1] - 11 X[5886], 5 X[1] - 11 X[5901], X[1] - 33 X[7988], 19 X[1] + 77 X[7989], 7 X[1] - 55 X[8227], 29 X[1] - 77 X[9624], 7 X[1] - 11 X[10283], 7 X[1] + 11 X[18357], 25 X[1] + 11 X[37705], and many others

X(61267) lies on these lines: {1, 5}, {2, 28178}, {10, 44904}, {30, 10171}, {140, 28182}, {381, 28190}, {515, 11737}, {516, 3628}, {517, 10109}, {546, 10165}, {547, 3817}, {946, 12812}, {1125, 12811}, {1656, 6361}, {1699, 15699}, {3090, 20070}, {3530, 12571}, {3534, 58218}, {3545, 38028}, {3576, 38071}, {3624, 3858}, {3845, 50866}, {3850, 28160}, {3851, 5731}, {3853, 19862}, {3856, 13624}, {3859, 4297}, {3860, 28164}, {3861, 28172}, {5055, 5657}, {5056, 22791}, {5066, 11230}, {5071, 34718}, {5072, 34773}, {5079, 5690}, {5550, 58228}, {5603, 51072}, {9812, 15703}, {9955, 10172}, {10124, 28146}, {10164, 47599}, {10175, 38098}, {10248, 55863}, {11224, 38081}, {11812, 28150}, {12046, 58487}, {12102, 58223}, {14891, 28158}, {14892, 38140}, {14893, 17502}, {15022, 18493}, {15690, 51074}, {15704, 34595}, {15713, 50807}, {16239, 18483}, {19709, 50864}, {19710, 50874}, {19878, 33923}, {22793, 48154}, {28194, 45757}, {28202, 41985}, {28216, 50802}, {28224, 58234}, {30392, 50799}, {31730, 55862}, {31751, 58531}, {33699, 58221}, {34556, 34559}, {34557, 34562}, {38021, 38112}, {38022, 59387}, {41869, 55859}, {41983, 59420}, {41989, 51700}, {46332, 50869}, {46936, 48661}, {50830, 58238}

X(61267) = midpoint of X(i) and X(j) for these {i,j}: {546, 10165}, {547, 3817}, {5066, 11230}, {5587, 5901}, {9955, 10172}, {10283, 18357}, {14893, 17502}
X(61267) = reflection of X(10172) in X(35018)
X(61267) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 8227, 18357}, {5886, 37712, 10283}, {5901, 18357, 37727}, {8227, 37712, 5886}

X(61268) = X(1)X(5)∩X(2)X(3579)

Barycentrics    a^4 - a^3*b - 4*a^2*b^2 + a*b^3 + 3*b^4 - a^3*c + 2*a^2*b*c - a*b^2*c - 4*a^2*c^2 - a*b*c^2 - 6*b^2*c^2 + a*c^3 + 3*c^4 : :
X(61268) = X[1] + 6 X[5], 4 X[1] + 3 X[355], 13 X[1] - 6 X[1483], 5 X[1] + 9 X[5587], 11 X[1] + 3 X[5881], 2 X[1] - 9 X[5886], 5 X[1] - 12 X[5901], X[1] + 27 X[7988], X[1] + 3 X[7989], X[1] - 15 X[8227], X[1] - 3 X[9624], 11 X[1] - 18 X[10283], 3 X[1] + 4 X[18357], 5 X[1] + 2 X[37705], 19 X[1] + 9 X[37712], and many others

X(61268) lies on these lines: {1, 5}, {2, 3579}, {3, 3817}, {4, 5550}, {8, 5071}, {10, 3656}, {30, 3624}, {40, 3628}, {57, 3652}, {79, 44257}, {140, 1699}, {145, 50804}, {165, 632}, {376, 58219}, {381, 1125}, {382, 10165}, {392, 6933}, {499, 17605}, {500, 26102}, {515, 3851}, {516, 3526}, {517, 3090}, {546, 3576}, {547, 1698}, {549, 30308}, {551, 18525}, {568, 31751}, {582, 17123}, {631, 9779}, {942, 10589}, {944, 5068}, {946, 1656}, {962, 5067}, {978, 48903}, {1155, 6862}, {1385, 3091}, {1482, 3626}, {1537, 38319}, {1538, 6847}, {1571, 3055}, {1836, 37524}, {3062, 38111}, {3085, 7743}, {3146, 17502}, {3452, 12864}, {3523, 28146}, {3525, 9812}, {3528, 10248}, {3533, 9778}, {3544, 15178}, {3545, 3616}, {3560, 5204}, {3582, 10404}, {3584, 45035}, {3617, 5056}, {3621, 5818}, {3622, 28204}, {3623, 38074}, {3625, 5790}, {3627, 7987}, {3632, 47478}, {3635, 50798}, {3636, 18526}, {3647, 16159}, {3679, 10109}, {3742, 40263}, {3753, 6931}, {3811, 3829}, {3816, 6841}, {3825, 28628}, {3830, 19883}, {3832, 28160}, {3838, 10200}, {3839, 33697}, {3843, 4297}, {3847, 54318}, {3850, 5691}, {3855, 5731}, {3857, 28186}, {3873, 56762}, {3947, 7373}, {4301, 10172}, {4420, 11680}, {4423, 6985}, {4663, 14561}, {4679, 41872}, {4701, 50805}, {4746, 51077}, {4816, 16200}, {4850, 8143}, {5045, 5226}, {5054, 19878}, {5066, 18492}, {5070, 6684}, {5072, 10246}, {5073, 58224}, {5087, 5302}, {5090, 7577}, {5126, 5229}, {5217, 6911}, {5220, 38108}, {5221, 12047}, {5225, 6826}, {5248, 37251}, {5253, 54441}, {5261, 51788}, {5265, 31776}, {5326, 59316}, {5433, 16617}, {5439, 10584}, {5444, 18514}, {5492, 24046}, {5493, 55860}, {5506, 24468}, {5657, 7486}, {5690, 11522}, {5703, 18527}, {5704, 5887}, {5708, 55108}, {5714, 6846}, {5748, 34790}, {5777, 50192}, {5779, 43180}, {5791, 21616}, {5805, 6861}, {5806, 6858}, {5812, 6832}, {5816, 16666}, {5817, 30340}, {5844, 44904}, {5883, 40266}, {5891, 58469}, {5927, 13373}, {6667, 12515}, {6824, 37582}, {6837, 17618}, {6849, 26105}, {6854, 10525}, {6856, 26129}, {6859, 50193}, {6860, 34339}, {6863, 12858}, {6864, 37820}, {6871, 17614}, {6879, 12672}, {6881, 7681}, {6891, 38037}, {6896, 18517}, {6898, 10526}, {6900, 18407}, {6912, 32612}, {6914, 59319}, {6915, 32613}, {6917, 37600}, {6920, 26286}, {6924, 59325}, {6929, 37605}, {6939, 37821}, {6946, 26285}, {6953, 26487}, {6956, 9856}, {6959, 37568}, {6978, 31788}, {6983, 12700}, {6993, 10598}, {7280, 31649}, {7294, 58887}, {7377, 29578}, {7713, 37942}, {7968, 42277}, {7969, 42274}, {7982, 12812}, {8164, 31792}, {8703, 58217}, {8728, 25522}, {8983, 13785}, {9575, 43291}, {9588, 28212}, {9589, 48154}, {9612, 15325}, {9654, 44675}, {9669, 13411}, {9904, 40685}, {9957, 10588}, {10129, 26202}, {10157, 50191}, {10164, 46219}, {10308, 27186}, {10394, 58569}, {10590, 24928}, {10591, 24929}, {10595, 20050}, {10698, 38182}, {10742, 32557}, {11235, 59719}, {11263, 48668}, {11372, 38171}, {11496, 35251}, {11531, 38112}, {11539, 50865}, {11684, 33592}, {11699, 15081}, {11737, 38022}, {11813, 26066}, {12053, 31479}, {12119, 38141}, {12512, 15720}, {12611, 31272}, {12773, 33709}, {12778, 12900}, {13178, 15092}, {13211, 15088}, {13665, 13971}, {13743, 17009}, {14269, 50828}, {14869, 16192}, {14892, 50824}, {15068, 16472}, {15699, 31162}, {15702, 28202}, {15703, 28194}, {15704, 58221}, {15707, 34638}, {16128, 57298}, {16160, 41858}, {16174, 38752}, {16475, 18358}, {16842, 35239}, {16862, 35238}, {17530, 19861}, {17533, 19860}, {17556, 24541}, {18393, 24914}, {18440, 38049}, {18538, 18992}, {18762, 18991}, {19877, 50821}, {20070, 46935}, {20084, 22936}, {22753, 35252}, {23039, 31757}, {23046, 34628}, {24206, 38035}, {24390, 30852}, {24789, 56843}, {25524, 37234}, {25561, 38023}, {25565, 47359}, {25639, 25681}, {26725, 46028}, {27131, 32635}, {28174, 31423}, {28182, 44682}, {28208, 41106}, {28216, 55862}, {29603, 36728}, {29821, 50558}, {30424, 38107}, {30827, 31419}, {30942, 48887}, {31253, 50806}, {31295, 35271}, {31399, 59503}, {31439, 32785}, {31666, 50689}, {31671, 38059}, {32900, 34627}, {33179, 59388}, {33858, 54392}, {34126, 34789}, {35774, 42583}, {35775, 42582}, {37612, 54370}, {38038, 58421}, {38040, 39885}, {38054, 60884}, {38071, 50811}, {38083, 46933}, {38084, 50908}, {38122, 42356}, {38150, 52265}, {38167, 39898}, {38335, 50870}, {39878, 51732}, {41983, 50812}, {41985, 50825}, {45384, 49548}, {45385, 49547}, {46617, 46975}, {46932, 50810}, {48667, 59419}, {48931, 48936}, {50194, 54361}, {55858, 58441}

X(61268) = midpoint of X(i) and X(j) for these {i,j}: {3528, 10248}, {7989, 9624}
X(61268) = reflection of X(i) in X(j) for these {i,j}: {7989, 5}, {16192, 14869}, {31423, 55856}
X(61268) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5587, 37705}, {1, 37705, 37727}, {2, 9955, 12699}, {4, 5550, 13624}, {5, 5886, 355}, {5, 5901, 5587}, {5, 8227, 5886}, {10, 18493, 3656}, {11, 37692, 11374}, {12, 23708, 11373}, {381, 1125, 18481}, {499, 17605, 57282}, {547, 22791, 1698}, {547, 38021, 3654}, {631, 9779, 22793}, {632, 40273, 165}, {944, 5068, 38140}, {946, 1656, 26446}, {946, 3634, 12702}, {946, 10171, 1656}, {962, 5067, 11231}, {1125, 18481, 3653}, {1482, 5079, 10175}, {1656, 12702, 3634}, {1698, 22791, 3654}, {1698, 38021, 22791}, {3525, 9812, 31663}, {3545, 3616, 18480}, {3545, 3655, 50799}, {3616, 18480, 3655}, {3617, 5603, 11278}, {3628, 38034, 40}, {3634, 12702, 26446}, {3636, 50796, 18526}, {3817, 19862, 18483}, {3850, 38028, 5691}, {5055, 18493, 10}, {5056, 5603, 9956}, {5066, 34773, 18492}, {5072, 10246, 19925}, {5226, 47743, 5045}, {5587, 5901, 37727}, {5587, 37727, 355}, {5690, 35018, 54447}, {5886, 37727, 5901}, {5901, 37705, 1}, {7741, 11375, 5722}, {7988, 8227, 5}, {9956, 11278, 3617}, {10165, 12571, 382}, {10826, 15950, 37739}, {11230, 13624, 5550}, {11522, 54447, 5690}, {18483, 19862, 3}, {18492, 25055, 34773}, {19878, 31730, 5054}, {19878, 50802, 31730}, {30308, 34595, 41869}, {34595, 41869, 549}, {46219, 48661, 10164}

X(61269) = X(1)X(5)∩X(2)X(28174)

Barycentrics    2*a^4 - 2*a^3*b - 7*a^2*b^2 + 2*a*b^3 + 5*b^4 - 2*a^3*c + 4*a^2*b*c - 2*a*b^2*c - 7*a^2*c^2 - 2*a*b*c^2 - 10*b^2*c^2 + 2*a*c^3 + 5*c^4 : :
X[1] + 5 X[5], 7 X[1] + 5 X[355], 11 X[1] - 5 X[1483], 3 X[1] + 5 X[5587], 19 X[1] + 5 X[5881], X[1] - 5 X[5886], 2 X[1] - 5 X[5901], X[1] + 15 X[7988], 13 X[1] + 35 X[7989], X[1] - 25 X[8227], 11 X[1] - 35 X[9624], 3 X[1] - 5 X[10283], 4 X[1] + 5 X[18357], 13 X[1] + 5 X[37705], 11 X[1] + 5 X[37712], and many others

X(61269) lies on these lines: {1, 5}, {2, 28174}, {3, 9779}, {8, 5079}, {10, 35018}, {30, 3817}, {40, 55856}, {140, 516}, {165, 11539}, {381, 5731}, {382, 5550}, {499, 24470}, {515, 5066}, {517, 547}, {519, 47478}, {546, 1125}, {548, 18483}, {549, 1699}, {550, 3624}, {551, 11737}, {632, 12699}, {944, 5072}, {946, 3628}, {962, 5070}, {1385, 3850}, {1482, 4678}, {1656, 5657}, {2807, 13363}, {3090, 5690}, {3091, 34773}, {3525, 48661}, {3530, 19862}, {3544, 3622}, {3545, 10246}, {3576, 3845}, {3579, 16239}, {3616, 3851}, {3653, 23046}, {3656, 38112}, {3830, 54445}, {3853, 12571}, {3855, 46934}, {3856, 31673}, {3857, 5691}, {3858, 18481}, {3860, 51705}, {3861, 4297}, {3878, 52795}, {3918, 26200}, {4301, 22266}, {4669, 5844}, {4691, 9956}, {4701, 13464}, {5054, 9812}, {5055, 5603}, {5067, 12702}, {5068, 18525}, {5071, 5790}, {5777, 58561}, {5817, 38041}, {5818, 20053}, {5883, 45310}, {6361, 46219}, {6684, 48154}, {6824, 8732}, {6912, 38602}, {6946, 33814}, {6985, 38031}, {8703, 30308}, {9778, 15694}, {9780, 58247}, {9911, 13154}, {10124, 10164}, {10248, 15696}, {10516, 38040}, {10595, 15022}, {11001, 50833}, {11038, 47743}, {11224, 50823}, {11278, 31399}, {11540, 50808}, {11591, 58469}, {11723, 15088}, {11724, 15092}, {12047, 34753}, {12100, 28146}, {12101, 28168}, {12108, 31730}, {12266, 20584}, {12811, 18480}, {13374, 31835}, {13743, 38693}, {14869, 34595}, {14892, 28204}, {14893, 28164}, {15325, 17605}, {15684, 58226}, {15686, 58221}, {15690, 28158}, {15699, 26446}, {15712, 41869}, {15713, 50865}, {15714, 58213}, {15759, 59420}, {16138, 35010}, {16200, 59400}, {17577, 34123}, {19709, 50824}, {20070, 60781}, {25055, 38071}, {25439, 38629}, {28150, 34200}, {28194, 47599}, {28198, 47598}, {30389, 41991}, {31423, 55861}, {31493, 38057}, {32558, 38755}, {33699, 50807}, {33923, 51118}, {34474, 45976}, {37251, 59421}, {37375, 38142}, {38037, 38171}, {38043, 38150}, {38053, 38139}, {38062, 49736}, {38068, 41985}, {38083, 38127}, {50796, 51106}, {50799, 51110}, {53809, 57305}, {58203, 58223}

X(61269) = midpoint of X(i) and X(j) for these {i,j}: {1, 38138}, {2, 38034}, {5, 5886}, {381, 38028}, {549, 1699}, {551, 38140}, {946, 11231}, {1483, 37712}, {1484, 5660}, {3545, 38022}, {3576, 3845}, {3653, 23046}, {3656, 38112}, {3817, 11230}, {5587, 10283}, {5603, 38042}, {5657, 22791}, {5817, 38041}, {10175, 51709}, {10516, 38040}, {11224, 50823}, {15699, 38021}, {16200, 59400}, {25055, 38071}, {34123, 38141}, {38037, 38171}, {38043, 38150}, {38053, 38139}, {50824, 59387}
X(61269) = reflection of X(i) in X(j) for these {i,j}: {547, 10171}, {5901, 5886}, {10164, 10124}, {10175, 10109}, {11231, 3628}, {38068, 41985}, {38083, 45757}, {38140, 11737}, {59420, 15759}
X(61269) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 5901, 18357}, {5, 10283, 5587}, {5, 37705, 7989}, {140, 9955, 40273}, {3090, 18493, 5690}, {3656, 54447, 38112}, {5055, 5603, 38042}, {5443, 7173, 37730}, {5587, 5886, 10283}, {5886, 7988, 5}, {7988, 8227, 5886}, {9956, 58240, 4691}, {10593, 11375, 12433}, {11230, 17502, 19883}, {12571, 13624, 3853}, {12811, 51700, 18480}, {19862, 22793, 3530}, {19878, 31663, 140}

X(61270) = X(1)X(5)∩X(2)X(28212)

Barycentrics    4*a^4 - 4*a^3*b - 11*a^2*b^2 + 4*a*b^3 + 7*b^4 - 4*a^3*c + 8*a^2*b*c - 4*a*b^2*c - 11*a^2*c^2 - 4*a*b*c^2 - 14*b^2*c^2 + 4*a*c^3 + 7*c^4 : :
X(61270) = 2 X[1] + 7 X[5], 11 X[1] + 7 X[355], 16 X[1] - 7 X[1483], 5 X[1] + 7 X[5587], 29 X[1] + 7 X[5881], X[1] - 7 X[5886], 5 X[1] - 14 X[5901], X[1] + 7 X[7988], 23 X[1] + 49 X[7989], X[1] + 35 X[8227], 13 X[1] - 49 X[9624], 4 X[1] - 7 X[10283], 13 X[1] + 14 X[18357], 20 X[1] + 7 X[37705], 17 X[1] + 7 X[37712], and many others

X(61270) lies on these lines: {1, 5}, {2, 28212}, {8, 12812}, {20, 58224}, {30, 9779}, {40, 55859}, {140, 6361}, {165, 15713}, {515, 38022}, {516, 549}, {517, 15699}, {546, 5731}, {547, 5603}, {548, 5550}, {550, 9955}, {632, 946}, {944, 12811}, {962, 16239}, {1125, 3627}, {1385, 3858}, {1482, 35018}, {1656, 46932}, {1699, 8703}, {3090, 59503}, {3091, 51700}, {3544, 18526}, {3545, 28224}, {3576, 15687}, {3616, 3850}, {3622, 5072}, {3624, 15712}, {3628, 5657}, {3653, 28190}, {3817, 3845}, {3839, 58230}, {3843, 46934}, {3857, 34773}, {4745, 10171}, {4746, 13464}, {5054, 28216}, {5055, 5844}, {5056, 20052}, {5066, 10246}, {5068, 37624}, {5071, 10247}, {5079, 10595}, {5690, 10172}, {5691, 41991}, {5790, 10109}, {5818, 44904}, {5843, 60967}, {7486, 8148}, {7967, 19709}, {9778, 11812}, {9812, 12100}, {10175, 34641}, {10304, 58218}, {11231, 22791}, {11362, 58244}, {11539, 28174}, {11737, 59387}, {12108, 48661}, {12528, 58605}, {12645, 15022}, {12699, 14869}, {12702, 48154}, {13743, 38637}, {14892, 38314}, {15703, 59417}, {17502, 19710}, {17504, 28178}, {19711, 50865}, {19883, 28146}, {20070, 55858}, {22793, 46853}, {23046, 25055}, {25557, 33709}, {26129, 50205}, {30308, 33699}, {31423, 41992}, {38037, 38111}, {38140, 41150}, {38636, 45976}, {41990, 51110}, {45757, 53620}, {46931, 58250}, {46936, 58249}, {50831, 51095}, {51092, 59388}

X(61270) = midpoint of X(i) and X(j) for these {i,j}: {3839, 58230}, {5886, 7988}
X(61270) = reflection of X(5) in X(7988)
X(61270) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 5886, 10283}, {5, 5901, 37705}, {5, 10283, 38138}, {547, 5603, 38112}, {3624, 40273, 15712}, {3817, 38028, 3845}, {5587, 5886, 5901}, {5587, 37705, 38138}, {10171, 51709, 38042}, {10283, 38138, 1483}, {11230, 38034, 549}, {31662, 51109, 38028}

X(61271) = X(1)X(5)∩X(2)X(28228)

Barycentrics    5*a^4 - 5*a^3*b - 13*a^2*b^2 + 5*a*b^3 + 8*b^4 - 5*a^3*c + 10*a^2*b*c - 5*a*b^2*c - 13*a^2*c^2 - 5*a*b*c^2 - 16*b^2*c^2 + 5*a*c^3 + 8*c^4 : :
X(61271) = 5 X[1] + 16 X[5], 13 X[1] + 8 X[355], 37 X[1] - 16 X[1483], 3 X[1] + 4 X[5587], 17 X[1] + 4 X[5881], X[1] - 8 X[5886], 11 X[1] - 32 X[5901], X[1] + 6 X[7988], X[1] + 2 X[7989], X[1] + 20 X[8227], X[1] - 4 X[9624], 9 X[1] - 16 X[10283], 31 X[1] + 32 X[18357], 47 X[1] + 16 X[37705], 5 X[1] + 2 X[37712], and many others

X(61271) lies on these lines: {1, 5}, {2, 28228}, {40, 46219}, {165, 5054}, {376, 1699}, {381, 30392}, {515, 41106}, {516, 3523}, {517, 15703}, {547, 58241}, {946, 3525}, {1125, 3146}, {1482, 30315}, {1656, 11531}, {1657, 7987}, {1698, 46936}, {3086, 59372}, {3090, 28234}, {3244, 15022}, {3543, 58227}, {3544, 13607}, {3576, 3830}, {3616, 3854}, {3632, 5056}, {3636, 5068}, {3679, 10171}, {3817, 3839}, {3828, 58243}, {3832, 15808}, {3860, 50811}, {4301, 19872}, {4668, 13464}, {4677, 10175}, {4915, 30852}, {5055, 16200}, {5067, 58248}, {5071, 34747}, {5550, 21734}, {5603, 10172}, {5657, 11522}, {6911, 51817}, {6913, 37587}, {7991, 11231}, {9589, 19862}, {9812, 15705}, {9956, 16189}, {10124, 31162}, {11224, 50817}, {12047, 60992}, {12100, 38034}, {12102, 58229}, {12108, 12699}, {12571, 46934}, {13462, 17605}, {13624, 49134}, {13865, 38122}, {13902, 42571}, {13959, 42570}, {14269, 31662}, {14893, 34628}, {15702, 28232}, {15722, 50806}, {15803, 38107}, {18393, 53056}, {18483, 49138}, {25681, 38200}, {26446, 47599}, {28160, 30389}, {28190, 50807}, {28212, 31423}, {30384, 53052}, {31399, 58239}, {33923, 41869}, {35774, 42557}, {35775, 42558}, {38042, 45757}, {50802, 54445}, {51080, 51109}, {51082, 51105}, {51103, 54448}

X(61271) = reflection of X(9624) in X(5886)
X(61271) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5886, 7988, 1}, {5886, 8227, 7988}, {5901, 37714, 1}, {7988, 37712, 5}, {7989, 9624, 1}, {11224, 54447, 51066}, {11230, 38021, 165}, {11375, 50444, 1}, {51709, 54447, 11224}

X(61272) = X(1)X(5)∩X(10)X(547)

Barycentrics    2*a^4 - 2*a^3*b - 5*a^2*b^2 + 2*a*b^3 + 3*b^4 - 2*a^3*c + 4*a^2*b*c - 2*a*b^2*c - 5*a^2*c^2 - 2*a*b*c^2 - 6*b^2*c^2 + 2*a*c^3 + 3*c^4 : :
X(61272) = X[1] + 3 X[5], 5 X[1] + 3 X[355], 7 X[1] - 3 X[1483], 7 X[1] + 9 X[5587], 13 X[1] + 3 X[5881], X[1] - 9 X[5886], X[1] - 3 X[5901], 5 X[1] + 27 X[7988], 11 X[1] + 21 X[7989], X[1] + 15 X[8227], 5 X[1] - 21 X[9624], 5 X[1] - 9 X[10283], 3 X[1] + X[37705], 23 X[1] + 9 X[37712], 17 X[1] + 15 X[37714], and many others

X(61272) lies on these lines: {1, 5}, {2, 12702}, {3, 5284}, {4, 28190}, {8, 5055}, {10, 547}, {30, 1125}, {36, 31649}, {40, 632}, {79, 5298}, {140, 946}, {145, 5071}, {165, 14869}, {244, 5492}, {381, 3616}, {382, 9779}, {405, 35252}, {442, 35459}, {474, 35251}, {484, 7294}, {499, 5221}, {515, 3850}, {516, 3530}, {517, 3628}, {519, 10109}, {546, 1385}, {548, 10165}, {549, 3624}, {550, 1699}, {551, 5066}, {912, 50192}, {944, 3851}, {962, 3526}, {1154, 58469}, {1159, 5704}, {1352, 38040}, {1386, 18358}, {1482, 3090}, {1537, 6952}, {1621, 37251}, {1656, 5603}, {1657, 54445}, {1698, 3656}, {1829, 37942}, {2475, 22938}, {2771, 12009}, {2772, 15229}, {2807, 12006}, {3058, 45035}, {3086, 6147}, {3091, 10246}, {3109, 60603}, {3218, 19919}, {3244, 47478}, {3337, 3652}, {3523, 48661}, {3524, 50806}, {3533, 20070}, {3534, 58224}, {3545, 3622}, {3576, 3627}, {3582, 3649}, {3621, 5056}, {3623, 50798}, {3625, 10175}, {3626, 5844}, {3636, 11737}, {3647, 4999}, {3653, 15687}, {3655, 18492}, {3720, 5453}, {3742, 31937}, {3754, 6667}, {3829, 22836}, {3833, 13145}, {3843, 5731}, {3845, 18481}, {3847, 30147}, {3848, 40296}, {3853, 4297}, {3858, 5691}, {3860, 28208}, {3861, 12571}, {3881, 56762}, {3884, 6668}, {3947, 51788}, {4301, 11231}, {4420, 24390}, {4663, 18583}, {4668, 38081}, {4691, 45757}, {4816, 59400}, {4870, 16137}, {4973, 22936}, {5054, 6361}, {5067, 46931}, {5068, 7967}, {5070, 5657}, {5072, 37624}, {5079, 5818}, {5177, 35272}, {5204, 6914}, {5217, 6924}, {5220, 20330}, {5225, 6917}, {5226, 7373}, {5229, 6929}, {5253, 13743}, {5259, 5428}, {5265, 18541}, {5302, 21616}, {5303, 28453}, {5326, 11010}, {5330, 38058}, {5433, 18393}, {5444, 15338}, {5708, 6824}, {5714, 6913}, {5734, 59503}, {5762, 15254}, {5771, 6861}, {5777, 50191}, {5779, 30340}, {5805, 38043}, {5806, 31838}, {5842, 40259}, {5843, 43180}, {5882, 38140}, {6097, 20470}, {6583, 20117}, {6675, 41012}, {6684, 16239}, {6839, 38033}, {6862, 36279}, {6888, 57298}, {6892, 38107}, {6901, 10738}, {6912, 37535}, {6915, 37621}, {6918, 32141}, {6920, 22765}, {6946, 11849}, {6949, 38114}, {6979, 59382}, {7292, 37360}, {7377, 29595}, {7486, 12245}, {7489, 38039}, {7514, 11365}, {7577, 12135}, {7743, 13411}, {7956, 37438}, {7968, 18538}, {7969, 18762}, {7982, 38112}, {7987, 15704}, {7991, 55861}, {8164, 18220}, {8167, 35239}, {8703, 41869}, {9041, 25565}, {9614, 10386}, {9778, 15720}, {9945, 52367}, {9957, 44685}, {10124, 19878}, {10248, 17800}, {10272, 12261}, {11011, 11545}, {11108, 26129}, {11263, 12611}, {11281, 46028}, {11372, 38111}, {11522, 19872}, {11539, 31162}, {11544, 12047}, {11684, 51409}, {11720, 11801}, {11723, 20304}, {11812, 28198}, {12005, 58605}, {12100, 19883}, {12101, 51109}, {12102, 28164}, {12103, 17502}, {12108, 28216}, {12773, 32558}, {12811, 15178}, {13665, 13959}, {13729, 22799}, {13785, 13902}, {13864, 34503}, {14131, 29349}, {14449, 31738}, {14844, 24161}, {14845, 16980}, {14891, 28202}, {14892, 50796}, {14893, 33697}, {14988, 31794}, {14993, 47272}, {15022, 59388}, {15688, 50833}, {15703, 19877}, {15714, 58215}, {15934, 47743}, {15973, 28352}, {16160, 26725}, {16862, 35448}, {17067, 29327}, {17397, 36728}, {17504, 50865}, {17531, 35000}, {17605, 18990}, {17923, 44225}, {18526, 19709}, {18644, 34830}, {18977, 35598}, {19843, 51572}, {19876, 58248}, {20057, 38074}, {23046, 50811}, {23323, 47469}, {24953, 41872}, {25485, 38182}, {25522, 51559}, {25561, 51006}, {25681, 31419}, {26201, 31871}, {28146, 33923}, {28150, 44245}, {28236, 41989}, {28628, 37356}, {30392, 41991}, {30950, 37365}, {31423, 55859}, {31650, 49177}, {31657, 38037}, {31732, 31834}, {31737, 44324}, {31760, 58531}, {32205, 58487}, {32789, 35610}, {32790, 35611}, {32900, 51103}, {33668, 48668}, {33814, 38038}, {34628, 50807}, {34632, 50825}, {34638, 51084}, {34718, 46933}, {35262, 50240}, {35641, 42583}, {35642, 42582}, {35762, 42273}, {35763, 42270}, {37290, 37605}, {37582, 55108}, {38029, 39884}, {38035, 48876}, {38053, 60901}, {38066, 46932}, {38220, 51872}, {39777, 41684}, {41984, 51075}, {41986, 50801}, {41987, 51074}, {42274, 44635}, {42277, 44636}, {46029, 51718}, {46930, 50872}, {47599, 50821}, {48903, 49997}, {48931, 48939}, {48933, 48936}, {49673, 51702}

X(61272) = midpoint of X(i) and X(j) for these {i,j}: {1, 18357}, {3, 40273}, {5, 5901}, {140, 946}, {546, 1385}, {547, 51709}, {548, 22793}, {551, 5066}, {1125, 9955}, {1386, 18358}, {3850, 51700}, {3853, 4297}, {3881, 56762}, {5806, 31838}, {6583, 20117}, {9956, 13464}, {10021, 33592}, {10272, 12261}, {11281, 46028}, {11720, 11801}, {11723, 20304}, {11729, 60759}, {12103, 51118}, {13624, 18483}, {14449, 31738}, {14893, 51705}, {15178, 19925}, {25561, 51006}, {26201, 31871}, {31732, 31834}, {46029, 51718}, {49673, 51702}
X(61272) = reflection of X(i) in X(j) for these {i,j}: {3861, 12571}, {6684, 16239}, {9956, 35018}, {12005, 58605}, {19925, 12811}, {31663, 12108}, {31760, 58531}, {58487, 32205}
X(61272) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5, 18357}, {1, 7173, 12019}, {2, 18493, 22791}, {3, 38034, 40273}, {5, 1483, 5587}, {5, 5886, 5901}, {5, 10283, 355}, {5, 38138, 7989}, {11, 5443, 37737}, {11, 37737, 12433}, {11, 38063, 1387}, {12, 37735, 1387}, {12, 38063, 37737}, {355, 5886, 9624}, {355, 7988, 5}, {355, 9624, 10283}, {381, 3616, 34773}, {496, 11375, 5719}, {499, 39542, 34753}, {946, 11230, 140}, {946, 19862, 3579}, {1125, 18483, 13624}, {1385, 3817, 546}, {1482, 3090, 38042}, {1656, 5603, 5690}, {1656, 8148, 9780}, {3545, 3622, 18525}, {3579, 11230, 19862}, {3579, 19862, 140}, {3622, 18525, 50824}, {3624, 12699, 549}, {3624, 38021, 12699}, {3653, 30308, 15687}, {3817, 15808, 31673}, {5056, 10595, 5790}, {5072, 37624, 59387}, {5079, 10247, 5818}, {5253, 13743, 38602}, {5443, 37735, 38063}, {5603, 9780, 8148}, {5886, 7988, 10283}, {5886, 8227, 5}, {5901, 18357, 1}, {7741, 15950, 37730}, {7743, 13411, 15172}, {7958, 26470, 5}, {7988, 9624, 355}, {7989, 37727, 38138}, {8148, 9780, 5690}, {8227, 9624, 7988}, {9624, 10283, 5901}, {9955, 13624, 18483}, {9956, 10171, 35018}, {10165, 22793, 548}, {10171, 13464, 9956}, {11375, 23708, 496}, {11376, 37692, 495}, {11544, 15325, 32636}, {11544, 32636, 24470}, {12047, 15325, 24470}, {12047, 32636, 11544}, {15808, 31673, 1385}, {17502, 51118, 12103}, {34638, 51084, 58187}, {34773, 38022, 3616}

X(61273) = X(1)X(5)∩X(2)X(50822)

Barycentrics    8*a^4 - 8*a^3*b - 13*a^2*b^2 + 8*a*b^3 + 5*b^4 - 8*a^3*c + 16*a^2*b*c - 8*a*b^2*c - 13*a^2*c^2 - 8*a*b*c^2 - 10*b^2*c^2 + 8*a*c^3 + 5*c^4 : :
4 X[1] + 5 X[5], 13 X[1] + 5 X[355], 14 X[1] - 5 X[1483], 7 X[1] + 5 X[5587], 31 X[1] + 5 X[5881], X[1] + 5 X[5886], X[1] - 10 X[5901], 3 X[1] + 5 X[7988], 37 X[1] + 35 X[7989], 11 X[1] + 25 X[8227], X[1] + 35 X[9624], 2 X[1] - 5 X[10283], 17 X[1] + 10 X[18357], 22 X[1] + 5 X[37705], 19 X[1] + 5 X[37712], and many others

X(61273) lies on these lines: {1, 5}, {2, 50822}, {30, 58230}, {145, 35018}, {165, 19711}, {404, 38636}, {515, 23046}, {516, 8703}, {517, 11539}, {546, 3622}, {547, 10247}, {549, 5603}, {550, 3616}, {551, 15687}, {632, 5657}, {944, 3857}, {946, 15704}, {962, 44682}, {1125, 14869}, {1385, 28172}, {1482, 19877}, {1656, 4678}, {1699, 33699}, {3090, 20014}, {3526, 58247}, {3530, 46934}, {3576, 15686}, {3623, 5079}, {3627, 5731}, {3628, 10595}, {3653, 28178}, {3656, 15713}, {3817, 50824}, {3828, 11230}, {3845, 9779}, {3850, 37624}, {4669, 38042}, {4691, 10172}, {4701, 38176}, {5066, 7967}, {5493, 10165}, {5690, 51073}, {5844, 15699}, {6906, 38637}, {6914, 7677}, {7982, 41992}, {8148, 16239}, {9778, 15711}, {9812, 19710}, {10109, 50831}, {10124, 59417}, {10171, 51091}, {11231, 13464}, {11540, 50872}, {12245, 48154}, {12645, 12812}, {12811, 18526}, {14892, 54448}, {15178, 41991}, {15688, 58226}, {15714, 31162}, {15808, 58219}, {16200, 50823}, {17504, 25055}, {20330, 27869}, {24558, 50238}, {28186, 38021}, {28190, 30392}, {28198, 58216}, {28216, 45759}, {28224, 38071}, {31948, 52293}, {38081, 54447}, {38137, 38316}, {38140, 51103}, {40266, 58605}, {50832, 51110}, {58190, 58220}

X(61273) = midpoint of X(9779) and X(10246)
X(61273) = reflection of X(i) in X(j) for these {i,j}: {3845, 9779}, {38081, 54447}, {45759, 54445}, {54448, 14892}
X(61273) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {547, 10247, 59400}, {5886, 5901, 10283}, {5886, 10283, 5}, {8227, 37705, 5}, {10283, 38138, 1}, {17502, 51108, 38028}, {18493, 51700, 3627}, {51073, 58240, 5690}

X(61274) = X(1)X(5)∩X(2)X(11224)

Barycentrics    7*a^4 - 7*a^3*b - 11*a^2*b^2 + 7*a*b^3 + 4*b^4 - 7*a^3*c + 14*a^2*b*c - 7*a*b^2*c - 11*a^2*c^2 - 7*a*b*c^2 - 8*b^2*c^2 + 7*a*c^3 + 4*c^4 : :
7 X[1] + 8 X[5], 11 X[1] + 4 X[355], 23 X[1] - 8 X[1483], 3 X[1] + 2 X[5587], 13 X[1] + 2 X[5881], X[1] + 4 X[5886], X[1] - 16 X[5901], 2 X[1] + 3 X[7988], 8 X[1] + 7 X[7989], X[1] + 2 X[8227], X[1] + 14 X[9624], 3 X[1] - 8 X[10283], 29 X[1] + 16 X[18357], 37 X[1] + 8 X[37705], 4 X[1] + X[37712], 2 X[1] + X[37714], and many others

X(61274) lies on these lines: {1, 5}, {2, 11224}, {10, 46935}, {40, 15720}, {165, 3524}, {226, 53058}, {515, 30308}, {516, 3522}, {517, 15694}, {551, 1699}, {946, 3529}, {962, 15808}, {1125, 7991}, {1385, 5073}, {1482, 55860}, {1656, 4668}, {1698, 10595}, {3090, 3633}, {3241, 10171}, {3485, 59372}, {3533, 3624}, {3534, 3576}, {3601, 38107}, {3622, 5691}, {3625, 7486}, {3632, 30315}, {3635, 5056}, {3649, 38041}, {3656, 11812}, {3679, 10172}, {3817, 38314}, {4297, 50692}, {4301, 46934}, {4677, 10247}, {4691, 46936}, {4816, 31399}, {5072, 32900}, {5076, 18493}, {5550, 9588}, {5734, 19862}, {5790, 34747}, {5844, 51066}, {6913, 37602}, {7982, 11231}, {8236, 18220}, {10124, 58243}, {10175, 51093}, {10246, 14269}, {10980, 44675}, {11038, 30330}, {11219, 38026}, {11230, 16200}, {11281, 16143}, {12101, 38034}, {12245, 19872}, {12699, 44245}, {13411, 30337}, {15711, 28174}, {16191, 19876}, {16192, 22791}, {17603, 30294}, {18492, 37624}, {19883, 59417}, {24644, 38053}, {26446, 38022}, {28168, 50806}, {28182, 58229}, {28216, 31162}, {28228, 51109}, {30384, 53054}, {31423, 58245}, {33179, 51515}, {38031, 59320}, {48154, 58239}, {50864, 51106}, {50871, 54448}, {51075, 59420}, {51103, 59387}, {51108, 54445}

X(61274) = reflection of X(i) in X(j) for these {i,j}: {8227, 5886}, {37712, 37714}
X(61274) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5886, 7988}, {1, 7988, 37712}, {1, 8227, 37714}, {1, 37735, 50444}, {551, 1699, 30392}, {1698, 10595, 16189}, {1699, 30392, 34628}, {3616, 11522, 7987}, {3624, 13464, 11531}, {5587, 10283, 1}, {5603, 25055, 165}, {5886, 10283, 5587}, {5901, 9624, 1}, {7988, 37712, 7989}, {10247, 54447, 4677}, {11230, 16200, 19875}, {31162, 38028, 58221}, {51110, 51709, 50865}

X(61275) = X(1)X(5)∩X(2)X(16200)

Barycentrics    5*a^4 - 5*a^3*b - 7*a^2*b^2 + 5*a*b^3 + 2*b^4 - 5*a^3*c + 10*a^2*b*c - 5*a*b^2*c - 7*a^2*c^2 - 5*a*b*c^2 - 4*b^2*c^2 + 5*a*c^3 + 2*c^4 : :
X(61275) = 5 X[1] + 4 X[5], 7 X[1] + 2 X[355], 13 X[1] - 4 X[1483], 2 X[1] + X[5587], 8 X[1] + X[5881], X[1] + 2 X[5886], X[1] + 8 X[5901], 11 X[1] + 7 X[7989], 4 X[1] + 5 X[8227], 2 X[1] + 7 X[9624], X[1] - 4 X[10283], 19 X[1] + 8 X[18357], 23 X[1] + 4 X[37705], 5 X[1] + X[37712], 13 X[1] + 5 X[37714], 11 X[1] - 2 X[37727], and many others

X(61275) lies on these lines: {1, 5}, {2, 16200}, {4, 3636}, {8, 10172}, {30, 30392}, {40, 3306}, {104, 32630}, {140, 11531}, {165, 3656}, {376, 516}, {515, 3839}, {517, 5054}, {519, 54447}, {547, 34747}, {631, 15808}, {946, 3146}, {962, 21734}, {997, 38200}, {999, 59372}, {1125, 3525}, {1385, 1657}, {1388, 9612}, {1482, 3624}, {1537, 25557}, {1656, 3632}, {1698, 10222}, {1699, 3830}, {3090, 3244}, {3091, 13607}, {3241, 10175}, {3304, 41870}, {3428, 38031}, {3524, 28228}, {3526, 11278}, {3534, 31662}, {3545, 28236}, {3621, 31399}, {3626, 5067}, {3633, 9956}, {3635, 5818}, {3653, 28174}, {3655, 14893}, {3679, 10247}, {3680, 59719}, {3817, 7967}, {3854, 5882}, {3860, 30308}, {3889, 20117}, {3890, 31870}, {3940, 38318}, {4297, 49138}, {4301, 35242}, {4312, 5126}, {4677, 38042}, {4860, 39782}, {5045, 5693}, {5048, 31434}, {5049, 41861}, {5056, 20057}, {5071, 38155}, {5231, 36922}, {5248, 45977}, {5258, 12001}, {5259, 10680}, {5437, 12703}, {5542, 41705}, {5550, 11362}, {5690, 16189}, {5691, 15178}, {5734, 6684}, {5770, 11518}, {5790, 51093}, {5844, 19875}, {5851, 50908}, {5852, 34647}, {5880, 14217}, {5887, 50190}, {6279, 11370}, {6280, 11371}, {6282, 38122}, {6745, 11525}, {6914, 37587}, {6946, 25439}, {7486, 20050}, {7987, 22791}, {7991, 12108}, {8148, 9588}, {8236, 61008}, {8545, 11038}, {9331, 34460}, {9579, 21842}, {9580, 37525}, {9589, 13624}, {9614, 34471}, {9626, 11365}, {9778, 50828}, {9812, 51705}, {9955, 37624}, {10124, 11224}, {10129, 16174}, {10164, 50814}, {10171, 51071}, {10304, 28232}, {11001, 51075}, {11014, 54392}, {11529, 44675}, {11539, 58241}, {11723, 33535}, {11849, 38636}, {12102, 34773}, {12103, 12699}, {12245, 19862}, {12702, 31425}, {13384, 30384}, {13462, 38041}, {14475, 28292}, {15016, 45776}, {15325, 18421}, {15682, 51085}, {15698, 51120}, {15705, 28194}, {15839, 24159}, {17146, 30196}, {18446, 59389}, {19709, 50871}, {19710, 28182}, {19876, 38112}, {22753, 34486}, {22758, 37602}, {22793, 49134}, {23598, 28537}, {24644, 38030}, {24929, 38107}, {25415, 31231}, {26726, 58421}, {28146, 58230}, {34628, 35404}, {35272, 38052}, {35810, 42557}, {35811, 42558}, {36975, 51790}, {37533, 41867}, {37535, 38637}, {37625, 58679}, {38066, 58238}, {38335, 58234}, {38941, 40719}, {41150, 51080}, {42568, 49226}, {42569, 49227}, {47096, 51713}, {47340, 51725}, {50802, 51106}, {50804, 51094}, {50810, 51109}, {50818, 51104}, {50967, 51156}, {50970, 51154}, {50973, 51003}, {50974, 51153}, {51005, 51178}, {51006, 51136}

X(61275) = midpoint of X(i) and X(j) for these {i,j}: {1, 7988}, {38066, 58238}
X(61275) = reflection of X(i) in X(j) for these {i,j}: {5587, 7988}, {7988, 5886}, {58221, 3653}
X(61275) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5443, 9578}, {1, 5886, 5587}, {1, 5901, 9624}, {1, 7989, 37727}, {1, 8227, 5881}, {1, 9624, 8227}, {1, 23708, 5727}, {1, 37692, 37709}, {1, 37714, 1483}, {1, 37735, 9581}, {1, 50444, 37730}, {5, 37712, 5587}, {165, 51110, 38028}, {551, 5603, 3576}, {1125, 7982, 31423}, {1125, 10595, 7982}, {1385, 11522, 41869}, {1656, 33179, 3632}, {1699, 10246, 50811}, {1699, 51105, 10246}, {3576, 5603, 31162}, {3616, 13464, 40}, {3656, 38028, 165}, {3817, 51103, 7967}, {5056, 20057, 47745}, {5587, 5886, 8227}, {5587, 9624, 5886}, {5734, 46934, 6684}, {5886, 10283, 1}, {5901, 10283, 5886}, {7989, 38138, 5587}, {10171, 51071, 59388}, {10246, 51709, 1699}, {10247, 11230, 3679}, {12699, 51700, 30389}, {15178, 18493, 5691}, {16189, 34595, 5690}, {51105, 51709, 50811}

X(61276) = X(1)X(5)∩X(2)X(10222)

Barycentrics    3*a^4 - 3*a^3*b - 4*a^2*b^2 + 3*a*b^3 + b^4 - 3*a^3*c + 6*a^2*b*c - 3*a*b^2*c - 4*a^2*c^2 - 3*a*b*c^2 - 2*b^2*c^2 + 3*a*c^3 + c^4 : :
3 X[1] + 2 X[5], 4 X[1] + X[355], 7 X[1] - 2 X[1483], 7 X[1] + 3 X[5587], 9 X[1] + X[5881], 2 X[1] + 3 X[5886], X[1] + 4 X[5901], 11 X[1] + 9 X[7988], 13 X[1] + 7 X[7989], 3 X[1] + 7 X[9624], X[1] - 6 X[10283], 11 X[1] + 4 X[18357], 13 X[1] + 2 X[37705], 17 X[1] + 3 X[37712], 3 X[1] + X[37714], 6 X[1] - X[37727], and many others

X(61276) lies on these lines: {1, 5}, {2, 10222}, {3, 551}, {4, 3655}, {8, 5067}, {10, 5070}, {20, 1385}, {30, 11522}, {40, 3530}, {140, 3654}, {145, 7486}, {165, 44682}, {381, 5882}, {382, 946}, {388, 25405}, {474, 37622}, {498, 5048}, {499, 11011}, {515, 3843}, {516, 15696}, {517, 631}, {519, 1656}, {546, 38021}, {547, 51093}, {548, 3576}, {549, 7991}, {550, 30389}, {575, 38023}, {576, 47358}, {632, 16189}, {912, 17609}, {942, 6892}, {944, 3832}, {958, 12001}, {960, 31458}, {962, 3528}, {997, 9710}, {1001, 10680}, {1056, 37821}, {1058, 37820}, {1125, 1482}, {1279, 5733}, {1319, 4317}, {1376, 12000}, {1388, 9657}, {1420, 39542}, {1621, 26286}, {1657, 51705}, {1698, 5844}, {1699, 3853}, {1836, 4325}, {2072, 47491}, {2646, 4309}, {3057, 31452}, {3086, 50194}, {3090, 3241}, {3091, 28204}, {3095, 22475}, {3244, 5790}, {3303, 6911}, {3304, 3560}, {3340, 15325}, {3445, 26728}, {3476, 31410}, {3485, 6930}, {3486, 7743}, {3487, 37822}, {3488, 18220}, {3522, 28198}, {3525, 50821}, {3529, 58232}, {3533, 34631}, {3534, 41150}, {3544, 50818}, {3564, 16491}, {3579, 15717}, {3621, 38176}, {3623, 5818}, {3624, 5690}, {3625, 10172}, {3627, 50811}, {3628, 3679}, {3632, 38042}, {3633, 54447}, {3634, 59503}, {3635, 10175}, {3652, 16137}, {3742, 37562}, {3746, 6924}, {3751, 38040}, {3812, 23340}, {3813, 6881}, {3817, 13607}, {3828, 50805}, {3830, 51106}, {3855, 7967}, {3858, 30308}, {3859, 18492}, {3861, 5691}, {3868, 59350}, {3869, 6583}, {3873, 5694}, {3892, 20117}, {3898, 31870}, {4295, 5126}, {4297, 17800}, {4312, 38041}, {4323, 31794}, {4330, 12701}, {4338, 37618}, {4666, 37374}, {4669, 15703}, {4677, 15699}, {4870, 6929}, {4930, 24391}, {5045, 5887}, {5054, 43174}, {5055, 51071}, {5068, 34627}, {5072, 50796}, {5076, 50806}, {5079, 50798}, {5090, 52295}, {5093, 49505}, {5223, 38043}, {5248, 22765}, {5253, 26285}, {5289, 5791}, {5432, 30323}, {5433, 25415}, {5434, 37290}, {5550, 11231}, {5563, 6914}, {5609, 50921}, {5657, 11278}, {5703, 31792}, {5707, 16483}, {5731, 22793}, {5735, 20330}, {5787, 40257}, {5805, 24299}, {5812, 6936}, {5883, 25413}, {5902, 58561}, {6361, 17502}, {6684, 8148}, {6700, 40587}, {6767, 11499}, {6832, 11240}, {6855, 15933}, {6861, 45700}, {6862, 10072}, {6885, 24929}, {6887, 34625}, {6937, 46920}, {6951, 35597}, {6955, 12700}, {6959, 10056}, {6966, 34339}, {6970, 9957}, {6983, 11239}, {7288, 50193}, {7373, 22758}, {7377, 29580}, {7387, 34643}, {7489, 8666}, {7491, 49736}, {7516, 37546}, {7553, 51719}, {7962, 31436}, {7978, 15057}, {7987, 28174}, {8550, 51006}, {8715, 34640}, {8981, 31440}, {8983, 31487}, {9606, 9620}, {9607, 9619}, {9656, 45287}, {9670, 30384}, {9671, 10572}, {9680, 49226}, {9714, 11365}, {9812, 49138}, {10021, 16126}, {10085, 16138}, {10165, 12702}, {10171, 47745}, {10179, 13374}, {10202, 45776}, {10299, 34632}, {10303, 50810}, {10386, 53054}, {10525, 10596}, {10526, 10597}, {10586, 26492}, {10587, 26487}, {10624, 37606}, {10679, 25524}, {10747, 47115}, {10805, 18516}, {10806, 18517}, {10883, 21740}, {10912, 59719}, {10915, 47746}, {10993, 17563}, {11009, 24914}, {11224, 31423}, {11281, 37401}, {11363, 37122}, {11496, 16203}, {11715, 16128}, {11720, 23236}, {11723, 15063}, {11724, 14981}, {11735, 16003}, {11799, 51713}, {12005, 40266}, {12268, 45398}, {12269, 45399}, {12515, 37612}, {12531, 38182}, {12647, 33176}, {12672, 13373}, {12704, 16139}, {12747, 33812}, {12758, 58604}, {13211, 20396}, {13384, 15171}, {13411, 31480}, {13462, 24470}, {13911, 35811}, {13973, 35810}, {14561, 49465}, {14869, 58245}, {14988, 18398}, {15022, 38074}, {15029, 50877}, {15069, 38315}, {15170, 37281}, {15694, 51109}, {15704, 50865}, {15774, 51712}, {15829, 31446}, {15952, 28619}, {16001, 50849}, {16002, 50852}, {16159, 35016}, {16202, 22753}, {16496, 18583}, {17529, 19861}, {17538, 28202}, {17575, 19860}, {17578, 28160}, {17583, 35262}, {18421, 34753}, {18526, 19925}, {19709, 51104}, {19862, 28234}, {19875, 55856}, {19876, 50823}, {19878, 38127}, {19883, 34718}, {19914, 32557}, {20057, 59388}, {21625, 51755}, {24206, 49681}, {24390, 56387}, {24467, 51816}, {24474, 58679}, {24475, 50190}, {24703, 51111}, {25416, 58421}, {25485, 57298}, {25555, 47359}, {28172, 58233}, {28212, 35242}, {28232, 58192}, {30315, 34747}, {30331, 38107}, {30392, 41869}, {31145, 38083}, {31454, 35775}, {31649, 41691}, {31663, 54445}, {32900, 38140}, {33337, 51517}, {33858, 37447}, {33862, 61155}, {33895, 45701}, {34507, 47356}, {35641, 35813}, {35642, 35812}, {36867, 49627}, {38030, 43177}, {38066, 51077}, {38108, 42871}, {38317, 49688}, {44911, 47490}, {48661, 58230}, {49134, 51118}, {49136, 51085}, {49137, 51075}, {49600, 56177}, {50817, 55862}, {50820, 58196}, {50832, 58229}, {50862, 58235}, {50878, 51522}, {50881, 51523}, {50886, 51524}, {50891, 51525}, {50898, 51526}, {50901, 51527}, {50905, 51528}, {50908, 51529}, {50913, 51530}, {50915, 51531}, {50918, 51534}, {50926, 51535}

X(61276) = midpoint of X(i) and X(j) for these {i,j}: {1, 8227}, {631, 5734}, {3616, 10595}, {3623, 5818}, {18493, 37624}
X(61276) = reflection of X(i) in X(j) for these {i,j}: {3522, 31666}, {15694, 51109}, {37714, 5}
X(61276) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5, 37727}, {1, 11, 37739}, {1, 5443, 5252}, {1, 5587, 1483}, {1, 5886, 355}, {1, 5901, 5886}, {1, 7741, 37740}, {1, 7951, 37738}, {1, 9581, 37728}, {1, 9624, 5}, {1, 10826, 37734}, {1, 10827, 1317}, {1, 11376, 5722}, {1, 15950, 11374}, {1, 23708, 10950}, {1, 37692, 10944}, {1, 37704, 12433}, {1, 37709, 12735}, {1, 37720, 37724}, {1, 37735, 1837}, {1, 50443, 37730}, {3, 13464, 3656}, {4, 15178, 3655}, {4, 38314, 15178}, {5, 5901, 9624}, {5, 9624, 5886}, {5, 37727, 355}, {140, 7982, 3654}, {548, 22791, 9589}, {551, 3656, 3653}, {551, 13464, 3}, {631, 10595, 5734}, {946, 3636, 10246}, {946, 10246, 18481}, {1125, 1482, 26446}, {1125, 11362, 3526}, {1385, 5603, 12699}, {1482, 3526, 11362}, {1621, 45977, 26286}, {3526, 11362, 26446}, {3576, 9589, 548}, {3616, 5734, 631}, {3622, 5603, 1385}, {3624, 16200, 5690}, {3635, 10175, 12645}, {3817, 13607, 18525}, {5493, 50828, 3}, {5550, 12245, 11231}, {5886, 37727, 5}, {5901, 10283, 1}, {7982, 25055, 140}, {8227, 37714, 5}, {10592, 12735, 37709}, {11230, 33179, 8}, {11374, 37739, 10954}, {11376, 37724, 37720}, {15178, 51709, 4}, {22791, 51700, 3576}, {30389, 31162, 550}, {37720, 37724, 5722}, {38314, 51709, 3655}

X(61277) = X(1)X(5)∩X(2)X(33179)

Barycentrics    5*a^4 - 5*a^3*b - 6*a^2*b^2 + 5*a*b^3 + b^4 - 5*a^3*c + 10*a^2*b*c - 5*a*b^2*c - 6*a^2*c^2 - 5*a*b*c^2 - 2*b^2*c^2 + 5*a*c^3 + c^4 : :
X(61277) = 5 X[1] + 2 X[5], 6 X[1] + X[355], 9 X[1] - 2 X[1483], 11 X[1] + 3 X[5587], 13 X[1] + X[5881], 4 X[1] + 3 X[5886], 3 X[1] + 4 X[5901], 19 X[1] + 9 X[7988], 3 X[1] + X[7989], 9 X[1] + 5 X[8227], X[1] + 6 X[10283], 17 X[1] + 4 X[18357], 19 X[1] + 2 X[37705], 25 X[1] + 3 X[37712], 23 X[1] + 5 X[37714], and many others

X(61277) lies on these lines: {1, 5}, {2, 33179}, {3, 3636}, {10, 55857}, {40, 3653}, {140, 16200}, {145, 11230}, {376, 962}, {381, 13607}, {498, 33176}, {517, 3523}, {519, 15703}, {547, 50804}, {549, 11531}, {550, 30392}, {551, 1482}, {631, 11278}, {944, 3839}, {946, 3655}, {1001, 12001}, {1125, 10247}, {1388, 57282}, {1656, 3244}, {1657, 4297}, {1699, 12102}, {3090, 20057}, {3146, 5603}, {3241, 9956}, {3485, 25405}, {3522, 31662}, {3525, 3616}, {3526, 15808}, {3576, 33923}, {3579, 5734}, {3624, 5844}, {3626, 5070}, {3628, 3632}, {3633, 38042}, {3635, 5790}, {3679, 47599}, {3742, 23340}, {3817, 18526}, {3851, 28236}, {3854, 18480}, {3860, 38021}, {3877, 6583}, {3889, 5694}, {5049, 5887}, {5055, 47745}, {5059, 58234}, {5067, 20050}, {5071, 51087}, {5079, 38155}, {5690, 10124}, {5691, 14893}, {5731, 49138}, {5882, 12571}, {5903, 58561}, {6861, 36867}, {7967, 9955}, {7982, 12108}, {7987, 45759}, {8148, 10165}, {9778, 31666}, {10179, 24474}, {10248, 28160}, {11231, 46934}, {11522, 34773}, {11737, 50871}, {12000, 25524}, {12103, 22791}, {12645, 51071}, {12701, 24926}, {13624, 21734}, {14093, 51120}, {14988, 50190}, {15570, 38108}, {15681, 51085}, {15684, 51075}, {15694, 51077}, {15699, 34747}, {15705, 31663}, {15718, 50814}, {15722, 41150}, {15723, 50827}, {16496, 38040}, {18220, 18527}, {19710, 31162}, {19862, 59503}, {19883, 50805}, {20054, 46935}, {25413, 58565}, {25439, 45976}, {28174, 30389}, {28194, 51106}, {28204, 41106}, {31399, 51515}, {31423, 51110}, {31730, 58230}, {32153, 37602}, {32613, 45977}, {32900, 59387}, {33812, 51517}, {34595, 38112}, {34718, 51108}, {34748, 51107}, {34923, 38512}, {35404, 40273}, {38022, 51093}, {38066, 51109}, {38107, 43179}, {42819, 60895}, {45701, 47746}, {47337, 47471}, {48661, 51705}, {55864, 58237}, {58238, 58441}, {58240, 59417}

X(61277) = midpoint of X(i) and X(j) for these {i,j}: {1, 9624}, {3090, 20057}
X(61277) = reflection of X(i) in X(j) for these {i,j}: {355, 7989}, {3526, 15808}
X(61277) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5443, 37738}, {1, 5886, 37727}, {1, 5901, 355}, {1, 8227, 1483}, {1, 9578, 12735}, {1, 11376, 37739}, {1, 16173, 37724}, {1, 23708, 37734}, {1, 32486, 37698}, {1, 37692, 1317}, {1, 37735, 37740}, {1, 50443, 37728}, {40, 51105, 51700}, {40, 51700, 3653}, {355, 5901, 5886}, {946, 37624, 3655}, {946, 51103, 37624}, {1125, 38127, 46219}, {1385, 10595, 3656}, {1483, 5901, 8227}, {1483, 8227, 355}, {3616, 10222, 26446}, {5067, 20050, 38176}, {5603, 15178, 18481}, {10246, 13464, 12699}, {10595, 38314, 1385}, {25055, 50817, 10124}

X(61278) = X(1)X(5)∩X(8)X(5070)

Barycentrics    6*a^4 - 6*a^3*b - 7*a^2*b^2 + 6*a*b^3 + b^4 - 6*a^3*c + 12*a^2*b*c - 6*a*b^2*c - 7*a^2*c^2 - 6*a*b*c^2 - 2*b^2*c^2 + 6*a*c^3 + c^4 : :
X(61278) = 3 X[1] + X[5], 7 X[1] + X[355], 5 X[1] - X[1483], 13 X[1] + 3 X[5587], 15 X[1] + X[5881], 5 X[1] + 3 X[5886], 23 X[1] + 9 X[7988], 25 X[1] + 7 X[7989], 11 X[1] + 5 X[8227], 9 X[1] + 7 X[9624], X[1] + 3 X[10283], 5 X[1] + X[18357], 11 X[1] + X[37705], 29 X[1] + 3 X[37712], 27 X[1] + 5 X[37714], and many others

X(61278) lies on these lines: {1, 5}, {3, 5734}, {4, 50806}, {8, 5070}, {10, 48154}, {20, 10246}, {30, 13464}, {40, 44682}, {140, 551}, {145, 5067}, {382, 5603}, {390, 38041}, {515, 3861}, {517, 3530}, {519, 3628}, {546, 5882}, {547, 51071}, {548, 1385}, {549, 7982}, {550, 3656}, {575, 51006}, {631, 1482}, {632, 25055}, {944, 3843}, {946, 3853}, {962, 15696}, {1125, 5844}, {1319, 24470}, {1353, 16491}, {1388, 4317}, {1537, 33668}, {1656, 3241}, {2098, 31452}, {2099, 34753}, {2475, 50843}, {3242, 38040}, {3243, 38043}, {3244, 11230}, {3303, 6924}, {3304, 6914}, {3525, 34718}, {3526, 3616}, {3533, 38066}, {3576, 46853}, {3623, 5790}, {3624, 38112}, {3627, 3655}, {3633, 59400}, {3635, 9956}, {3653, 7991}, {3654, 14869}, {3679, 55856}, {3832, 7967}, {3850, 28204}, {3855, 18525}, {3856, 9955}, {3858, 38021}, {3859, 18480}, {3884, 6583}, {3892, 5694}, {3897, 57003}, {4297, 28182}, {4309, 34471}, {4330, 24926}, {4669, 47599}, {5045, 14988}, {5046, 51112}, {5049, 10122}, {5056, 50798}, {5066, 51104}, {5068, 50818}, {5072, 34627}, {5079, 34748}, {5253, 33814}, {5289, 31458}, {5493, 31666}, {5550, 55866}, {5657, 55863}, {5707, 16486}, {5731, 17800}, {5762, 42819}, {5840, 33657}, {5883, 10284}, {5885, 58605}, {6361, 58230}, {6767, 32141}, {6861, 11240}, {6892, 15934}, {6912, 38631}, {6946, 38629}, {7373, 32153}, {8162, 11499}, {8261, 10179}, {8703, 30389}, {9041, 25555}, {9588, 16200}, {9710, 30144}, {9812, 49134}, {10109, 51107}, {10124, 51108}, {10165, 11278}, {10299, 50872}, {10303, 34631}, {10386, 13384}, {11011, 15325}, {11231, 15808}, {11482, 50999}, {11531, 31425}, {11539, 51110}, {11715, 12267}, {11735, 20379}, {11812, 41150}, {12100, 51106}, {12102, 28208}, {12103, 51705}, {12105, 47495}, {12108, 43174}, {12135, 52295}, {12245, 55864}, {12512, 31662}, {12645, 20057}, {12702, 15717}, {12877, 49113}, {13624, 28212}, {13743, 51529}, {13902, 31487}, {14131, 53790}, {14526, 15174}, {15606, 58535}, {15699, 51093}, {15704, 31162}, {15720, 50810}, {16137, 20323}, {16496, 59399}, {16619, 47593}, {17609, 24475}, {18583, 49465}, {19875, 55861}, {19883, 55862}, {19925, 32900}, {20049, 46935}, {28194, 33923}, {28198, 44245}, {28202, 51085}, {28234, 45760}, {29817, 37374}, {30308, 41991}, {30315, 51097}, {31454, 35642}, {31835, 34791}, {34747, 38081}, {35810, 35813}, {35811, 35812}, {37621, 45977}, {41985, 51069}, {44904, 51087}, {44961, 51713}, {45976, 51525}, {46219, 50805}, {47339, 47476}, {47341, 47472}, {47598, 51109}, {49137, 58235}, {50823, 55859}, {50830, 55860}, {52056, 52200}, {53620, 55857}, {58201, 58234}, {58469, 58533}

X(61278) = midpoint of X(i) and X(j) for these {i,j}: {1, 5901}, {140, 10222}, {546, 5882}, {547, 51071}, {548, 4301}, {1125, 33179}, {1483, 18357}, {3635, 9956}, {3884, 6583}, {9955, 13607}, {12735, 60759}, {13464, 15178}, {18583, 49465}, {19925, 32900}, {31835, 34791}, {34773, 40273}, {43174, 58240}
X(61278) = reflection of X(i) in X(j) for these {i,j}: {5885, 58605}, {10124, 51108}, {43174, 12108}, {51700, 3636}
X(61278) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 12, 12735}, {1, 1387, 12433}, {1, 5443, 1317}, {1, 5886, 1483}, {1, 9624, 37727}, {1, 10283, 5901}, {1, 11376, 37728}, {1, 37735, 37734}, {5, 1483, 5881}, {5, 5881, 18357}, {11, 38184, 60759}, {551, 10222, 140}, {1385, 4301, 548}, {1387, 12735, 5533}, {1482, 3622, 38028}, {1483, 5886, 18357}, {3616, 10247, 5690}, {3653, 7991, 15712}, {3655, 11522, 3627}, {5493, 31666, 34200}, {5603, 34773, 40273}, {5603, 37624, 34773}, {5881, 5886, 5}, {5882, 51709, 546}, {5901, 18357, 5886}, {9624, 37727, 5}, {10246, 10595, 22791}, {13464, 51103, 15178}, {37734, 37735, 12019}

X(61279) = X(1)X(5)∩X(8)X(60781)

Barycentrics    7*a^4 - 7*a^3*b - 8*a^2*b^2 + 7*a*b^3 + b^4 - 7*a^3*c + 14*a^2*b*c - 7*a*b^2*c - 8*a^2*c^2 - 7*a*b*c^2 - 2*b^2*c^2 + 7*a*c^3 + c^4 : :
X(61279) = 7 X[1] + 2 X[5], 8 X[1] + X[355], 11 X[1] - 2 X[1483], 5 X[1] + X[5587], 17 X[1] + X[5881], 2 X[1] + X[5886], 5 X[1] + 4 X[5901], 3 X[1] + X[7988], 29 X[1] + 7 X[7989], 13 X[1] + 5 X[8227], 11 X[1] + 7 X[9624], X[1] + 2 X[10283], 23 X[1] + 4 X[18357], 25 X[1] + 2 X[37705], 11 X[1] + X[37712], and many others

X(61279) lies on these lines: {1, 5}, {3, 61159}, {8, 60781}, {10, 55860}, {145, 38176}, {165, 15711}, {515, 14269}, {516, 3534}, {517, 3524}, {549, 11224}, {551, 10247}, {944, 50689}, {946, 5076}, {999, 17010}, {1125, 55858}, {1385, 3522}, {1482, 3636}, {1656, 3635}, {1699, 12101}, {3091, 32900}, {3241, 11230}, {3244, 10172}, {3529, 5731}, {3533, 3616}, {3543, 3655}, {3576, 28212}, {3622, 5657}, {3623, 9956}, {3625, 5070}, {3628, 3633}, {3654, 11812}, {3817, 50799}, {3890, 6583}, {4668, 55856}, {4691, 55857}, {5073, 13464}, {5697, 58561}, {5734, 13624}, {5790, 50804}, {5844, 25055}, {6911, 8162}, {6914, 37602}, {7967, 9779}, {7982, 51700}, {9778, 31662}, {9961, 26088}, {10164, 15722}, {10171, 50798}, {10186, 28913}, {10273, 58560}, {11038, 51788}, {13607, 18493}, {20070, 31666}, {28174, 30392}, {28182, 31162}, {28194, 58230}, {28202, 58234}, {28224, 38021}, {34747, 59400}, {34748, 38155}, {37533, 38122}, {38022, 54447}, {38042, 51093}, {38127, 50805}, {41150, 51077}, {45977, 59421}, {47746, 59719}

X(61279) = midpoint of X(7967) and X(9779)
X(61279) = reflection of X(i) in X(j) for these {i,j}: {9779, 51709}, {54447, 38022}
X(61279) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5219, 12735}, {1, 5901, 37727}, {1, 9624, 1483}, {1, 10283, 5886}, {551, 10247, 26446}, {3244, 10172, 51515}, {5587, 5901, 5886}, {5886, 37727, 5587}, {10595, 15178, 12699}, {13464, 37624, 18481}, {16200, 38028, 3654}, {16200, 51105, 38028}

X(61280) = X(1)X(5)∩X(8)X(55857)

Barycentrics    10*a^4 - 10*a^3*b - 11*a^2*b^2 + 10*a*b^3 + b^4 - 10*a^3*c + 20*a^2*b*c - 10*a*b^2*c - 11*a^2*c^2 - 10*a*b*c^2 - 2*b^2*c^2 + 10*a*c^3 + c^4 : :
X(61280) = 5 X[1] + X[5], 11 X[1] + X[355], 7 X[1] - X[1483], 7 X[1] + X[5587], 23 X[1] + X[5881], 3 X[1] + X[5886], 2 X[1] + X[5901], 13 X[1] + 3 X[7988], 41 X[1] + 7 X[7989], 19 X[1] + 5 X[8227], 17 X[1] + 7 X[9624], 8 X[1] + X[18357], 17 X[1] + X[37705], 15 X[1] + X[37712], 43 X[1] + 5 X[37714], and many others

X(61280) lies on these lines: {1, 5}, {2, 50830}, {8, 55857}, {140, 3636}, {376, 10246}, {515, 14893}, {516, 12103}, {517, 12100}, {519, 47599}, {546, 13607}, {549, 16200}, {551, 5844}, {946, 12102}, {1125, 55862}, {1385, 5493}, {1388, 24470}, {1482, 3523}, {1656, 20057}, {1657, 5731}, {3146, 10595}, {3241, 15703}, {3244, 3628}, {3525, 3622}, {3530, 11278}, {3576, 45759}, {3616, 46219}, {3623, 46936}, {3626, 48154}, {3632, 55856}, {3635, 10172}, {3653, 11224}, {3655, 28190}, {3656, 19710}, {3830, 5603}, {3839, 7967}, {3854, 18525}, {3860, 28224}, {5049, 14988}, {5054, 5657}, {5066, 28236}, {5070, 20050}, {5790, 38022}, {8236, 38041}, {8703, 30392}, {9957, 58561}, {10109, 38155}, {10165, 10222}, {10175, 45757}, {11011, 34753}, {11230, 51071}, {11531, 15712}, {11812, 51077}, {12266, 20585}, {12512, 58232}, {12702, 61138}, {13464, 28160}, {13747, 52074}, {15690, 28232}, {15718, 54445}, {15722, 50810}, {15808, 16239}, {19711, 58241}, {20054, 60781}, {25055, 38112}, {26446, 50817}, {28150, 51080}, {28216, 51705}, {28228, 31662}, {31835, 58609}, {35004, 58605}, {35018, 47745}, {38098, 41985}, {50821, 51106}, {50823, 51110}, {50832, 58221}, {51093, 59400}

X(61280) = midpoint of X(i) and X(j) for these {i,j}: {1, 10283}, {549, 16200}, {1483, 5587}, {3241, 38042}, {3244, 38176}, {3635, 10172}, {5603, 50824}, {5731, 22791}, {7967, 38034}, {8236, 38041}, {10165, 10222}, {10247, 38028}, {11230, 51071}, {38155, 51087}, {51093, 59400}
X(61280) = reflection of X(i) in X(j) for these {i,j}: {5901, 10283}, {10165, 51700}, {34200, 31662}, {38098, 41985}, {38127, 10124}, {38155, 10109}, {38176, 3628}
X(61280) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 15950, 12735}, {3636, 33179, 140}, {5886, 37712, 5}, {10247, 38314, 38028}, {51082, 51709, 3860}

X(61281) = X(1)X(5)∩X(8)X(46219)

Barycentrics    10*a^4 - 10*a^3*b - 9*a^2*b^2 + 10*a*b^3 - b^4 - 10*a^3*c + 20*a^2*b*c - 10*a*b^2*c - 9*a^2*c^2 - 10*a*b*c^2 + 2*b^2*c^2 + 10*a*c^3 - c^4 : :
X(61281) = 5 X[1] - X[5], 9 X[1] - X[355], 3 X[1] + X[1483], 19 X[1] - 3 X[5587], 17 X[1] - X[5881], 11 X[1] - 3 X[5886], 3 X[1] - X[5901], 41 X[1] - 9 X[7988], 39 X[1] - 7 X[7989], 21 X[1] - 5 X[8227], 23 X[1] - 7 X[9624], 7 X[1] - 3 X[10283], 7 X[1] - X[18357], 13 X[1] - X[37705], 35 X[1] - 3 X[37712], and many others

X(61281) lies on these lines: {1, 5}, {3, 20057}, {8, 46219}, {10, 55862}, {30, 13607}, {40, 45759}, {140, 3244}, {145, 3525}, {376, 1482}, {515, 12102}, {517, 33923}, {519, 10124}, {547, 47745}, {548, 11278}, {549, 50817}, {550, 16200}, {551, 47599}, {632, 3632}, {944, 3830}, {946, 14893}, {962, 1657}, {1159, 6049}, {1385, 12100}, {1388, 34753}, {3146, 7967}, {3241, 5054}, {3523, 3623}, {3526, 20050}, {3530, 28234}, {3533, 20054}, {3616, 55857}, {3622, 38042}, {3624, 59400}, {3626, 16239}, {3628, 3636}, {3633, 38112}, {3635, 5844}, {3653, 51097}, {3655, 19710}, {3656, 35404}, {3754, 58605}, {3839, 10595}, {3850, 28236}, {3854, 18493}, {3860, 12571}, {4297, 10222}, {4301, 28182}, {4999, 15862}, {5253, 51525}, {5330, 51112}, {5550, 51515}, {5734, 49134}, {5762, 15570}, {5790, 46936}, {5818, 34748}, {5840, 33658}, {5843, 43179}, {5882, 22793}, {5919, 24475}, {6767, 32153}, {7373, 32141}, {8703, 11531}, {9956, 51103}, {10179, 31835}, {11011, 24470}, {11263, 11274}, {11539, 34747}, {11812, 51095}, {12645, 15703}, {12702, 21734}, {12812, 38155}, {13464, 28224}, {14891, 51085}, {14988, 31792}, {15171, 33176}, {15694, 50830}, {15712, 30392}, {15713, 51094}, {15718, 50805}, {15808, 38176}, {18526, 38034}, {25055, 50831}, {26321, 38631}, {28198, 51080}, {28208, 50870}, {28228, 44245}, {31423, 50823}, {31663, 50814}, {34200, 51077}, {34641, 47598}, {35842, 42558}, {35843, 42557}, {38064, 51149}, {38066, 51092}, {38081, 51110}, {38083, 51106}, {41988, 50868}, {47340, 47476}

X(61281) = midpoint of X(i) and X(j) for these {i,j}: {140, 3244}, {547, 51087}, {548, 11278}, {944, 40273}, {1483, 5901}, {3635, 15178}, {13464, 32900}, {13607, 33179}, {14893, 51082}, {18357, 37727}, {34200, 51077}
X(61281) = reflection of X(i) in X(j) for these {i,j}: {3626, 16239}, {3628, 3636}, {3754, 58605}, {14891, 51085}, {50868, 41988}
X(61281) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1317, 37737}, {1, 1483, 5901}, {1, 37727, 10283}, {1, 37734, 1387}, {5, 37712, 18357}, {3241, 37624, 5690}, {5901, 18357, 8227}, {8227, 10283, 5901}, {10283, 37727, 18357}, {15808, 38176, 48154}

X(61282) = X(1)X(5)∩X(20)X(3655)

Barycentrics    9*a^4 - 9*a^3*b - 8*a^2*b^2 + 9*a*b^3 - b^4 - 9*a^3*c + 18*a^2*b*c - 9*a*b^2*c - 8*a^2*c^2 - 9*a*b*c^2 + 2*b^2*c^2 + 9*a*c^3 - c^4 : :
X(61282) = 9 X[1] - 2 X[5], 8 X[1] - X[355], 5 X[1] + 2 X[1483], 17 X[1] - 3 X[5587], 15 X[1] - X[5881], 10 X[1] - 3 X[5886], 11 X[1] - 4 X[5901], 37 X[1] - 9 X[7988], 5 X[1] - X[7989], 19 X[1] - 5 X[8227], 3 X[1] - X[9624], 13 X[1] - 6 X[10283], 25 X[1] - 4 X[18357], 23 X[1] - 2 X[37705], 31 X[1] - 3 X[37712], and many others

X(61282) lies on these lines: {1, 5}, {3, 51071}, {10, 55866}, {20, 3655}, {40, 58190}, {140, 51093}, {145, 55864}, {376, 58240}, {381, 51107}, {382, 3656}, {517, 3528}, {519, 3526}, {548, 7982}, {549, 51097}, {550, 16189}, {551, 5070}, {631, 3241}, {632, 4677}, {944, 17578}, {1385, 3623}, {1482, 15696}, {1656, 51103}, {3244, 26446}, {3524, 58232}, {3530, 3654}, {3579, 58188}, {3628, 51105}, {3632, 51700}, {3633, 38028}, {3635, 10246}, {3636, 12645}, {3679, 16239}, {3832, 28204}, {3843, 13464}, {3855, 51709}, {3859, 38021}, {3861, 11522}, {4301, 10247}, {4309, 5048}, {4317, 11011}, {4669, 46219}, {4745, 55858}, {5054, 51091}, {5055, 51104}, {5067, 38314}, {5603, 32900}, {5734, 7967}, {5844, 9588}, {6049, 31794}, {7486, 51087}, {7991, 46853}, {8703, 58245}, {9589, 34773}, {9961, 26089}, {10303, 51092}, {11231, 20050}, {11520, 59347}, {12245, 31447}, {12521, 22992}, {14869, 51094}, {15681, 58236}, {15694, 51096}, {15701, 58235}, {15703, 51106}, {15720, 51095}, {17504, 58229}, {17583, 50843}, {19862, 51515}, {25055, 48154}, {30389, 44682}, {30392, 31425}, {31666, 50810}, {32141, 37602}, {34595, 59400}, {34638, 58198}, {38176, 46934}, {40107, 49681}, {43174, 50805}, {47746, 56177}, {50808, 58192}, {51066, 55859}, {51108, 55857}, {51109, 55860}, {51110, 55856}, {51112, 57003}

X(61282) = reflection of X(15703) in X(51106)
X(61282) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1317, 11374}, {1, 1483, 5886}, {1, 37734, 11373}, {1483, 5881, 37727}, {3244, 37624, 26446}, {5881, 9624, 7989}, {5886, 37727, 5881}, {7967, 33179, 12699}, {10247, 13607, 18481}, {15888, 37722, 10523}

X(61283) = X(1)X(5)∩X(8)X(632)

Barycentrics    8*a^4 - 8*a^3*b - 7*a^2*b^2 + 8*a*b^3 - b^4 - 8*a^3*c + 16*a^2*b*c - 8*a*b^2*c - 7*a^2*c^2 - 8*a*b*c^2 + 2*b^2*c^2 + 8*a*c^3 - c^4 : :
X(61283) = 4 X[1] - X[5], 7 X[1] - X[355], 2 X[1] + X[1483], 5 X[1] - X[5587], 13 X[1] - X[5881], 3 X[1] - X[5886], 5 X[1] - 2 X[5901], 11 X[1] - 3 X[7988], 31 X[1] - 7 X[7989], 17 X[1] - 5 X[8227], 19 X[1] - 7 X[9624], 11 X[1] - 2 X[18357], 10 X[1] - X[37705], 9 X[1] - X[37712], 29 X[1] - 5 X[37714], 5 X[1] + X[37727], and many others

X(61283) lies on these lines: {1, 5}, {2, 50831}, {3, 3623}, {8, 632}, {10, 55859}, {30, 7967}, {140, 145}, {165, 15714}, {515, 15687}, {516, 10222}, {517, 3892}, {519, 11231}, {546, 10595}, {547, 34748}, {548, 8148}, {549, 3241}, {550, 1482}, {551, 38042}, {944, 3627}, {946, 32900}, {1125, 38176}, {1353, 3242}, {1385, 3635}, {1698, 41992}, {2098, 10386}, {3244, 5690}, {3303, 32153}, {3304, 32141}, {3525, 20014}, {3526, 3621}, {3530, 12245}, {3533, 20052}, {3534, 58238}, {3576, 17504}, {3616, 55856}, {3617, 16239}, {3622, 3628}, {3636, 10172}, {3654, 19711}, {3655, 15686}, {3656, 28186}, {3845, 5603}, {3857, 18493}, {3858, 9779}, {3877, 51112}, {3957, 37364}, {4301, 28154}, {4678, 46219}, {5066, 50818}, {5330, 50241}, {5428, 16202}, {5708, 6049}, {5771, 36867}, {5790, 15699}, {5843, 8236}, {5853, 38111}, {5882, 22791}, {5919, 14988}, {6767, 6914}, {6924, 7373}, {7508, 54391}, {7715, 11396}, {7979, 36966}, {8162, 22758}, {8192, 37440}, {9053, 38110}, {9812, 35404}, {9957, 24475}, {10124, 31145}, {10175, 38022}, {10263, 58535}, {10284, 12005}, {11230, 51087}, {11694, 50923}, {11737, 54448}, {11812, 50822}, {11849, 38693}, {12100, 50805}, {12702, 46853}, {12710, 31792}, {15690, 50872}, {15694, 20049}, {15711, 50810}, {15713, 26446}, {18480, 41991}, {18481, 28182}, {19116, 44636}, {19117, 44635}, {19512, 29585}, {19710, 28216}, {20070, 44245}, {22765, 59421}, {23046, 28204}, {23410, 34667}, {24467, 37556}, {25055, 38081}, {25439, 33814}, {28178, 50811}, {28190, 31162}, {28236, 50803}, {31730, 58240}, {33591, 34729}, {33658, 33668}, {34200, 34631}, {34474, 37535}, {35810, 42216}, {35811, 42215}, {38053, 38170}, {38071, 59387}, {38155, 51104}, {38315, 59399}, {46332, 50809}, {46933, 55862}, {46934, 48154}, {48876, 51147}, {49478, 51046}, {50778, 51048}, {50804, 51110}, {50821, 51091}, {50825, 58234}, {50826, 51094}, {50828, 51095}, {50830, 51096}, {50977, 51145}, {50978, 51000}, {50979, 50998}, {50985, 51148}, {50986, 50999}, {50987, 51149}, {51001, 51183}, {51047, 51055}, {51146, 51184}, {51180, 51193}, {58203, 58236}

X(61283) = midpoint of X(i) and X(j) for these {i,j}: {145, 59503}, {1482, 5731}, {1483, 10283}, {3241, 10246}, {3244, 10165}, {3655, 16200}, {5587, 37727}, {7967, 10247}, {11230, 51087}, {26446, 51093}, {34748, 59388}, {50805, 59417}, {50831, 59400}
X(61283) = reflection of X(i) in X(j) for these {i,j}: {5, 10283}, {549, 10246}, {550, 5731}, {3845, 5603}, {5587, 5901}, {5690, 10165}, {10165, 15178}, {10172, 3636}, {10283, 1}, {11230, 51103}, {15699, 38314}, {35404, 9812}, {37705, 5587}, {38042, 551}, {38081, 25055}, {38112, 38028}, {38138, 5886}, {38170, 38053}, {38176, 1125}, {50823, 26446}, {59388, 547}, {59399, 38315}, {59400, 2}, {59417, 12100}, {59503, 140}
X(61283) = complement of X(51515)
X(61283) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1317, 495}, {1, 1483, 5}, {1, 7972, 15950}, {1, 37727, 5901}, {1, 37734, 496}, {1, 37738, 37737}, {1, 37740, 1387}, {8, 51700, 632}, {145, 37624, 140}, {495, 496, 8068}, {495, 1484, 5}, {1483, 37705, 37727}, {3244, 15178, 5690}, {3622, 12645, 3628}, {3654, 50832, 19711}, {5882, 33179, 22791}, {5886, 38138, 5}, {5901, 37705, 5}, {5901, 37727, 37705}, {10222, 13607, 34773}, {10246, 34718, 54445}, {10283, 38138, 5886}, {10595, 18526, 546}, {38028, 38112, 11539}, {50805, 58230, 59417}, {58230, 59417, 12100}

X(61284) = X(1)X(5)∩X(8)X(3533)

Barycentrics    7*a^4 - 7*a^3*b - 6*a^2*b^2 + 7*a*b^3 - b^4 - 7*a^3*c + 14*a^2*b*c - 7*a*b^2*c - 6*a^2*c^2 - 7*a*b*c^2 + 2*b^2*c^2 + 7*a*c^3 - c^4 : :
X(61284) = 7 X[1] - 2 X[5], 6 X[1] - X[355], 3 X[1] + 2 X[1483], 13 X[1] - 3 X[5587], 11 X[1] - X[5881], 8 X[1] - 3 X[5886], 9 X[1] - 4 X[5901], 29 X[1] - 9 X[7988], 27 X[1] - 7 X[7989], 3 X[1] - X[8227], 17 X[1] - 7 X[9624], 11 X[1] - 6 X[10283], 19 X[1] - 4 X[18357], 17 X[1] - 2 X[37705], 23 X[1] - 3 X[37712], 5 X[1] - X[37714], and many others

X(61284) lies on these lines: {1, 5}, {3, 3635}, {4, 32900}, {8, 3533}, {10, 55858}, {40, 34200}, {140, 3633}, {145, 10303}, {515, 5076}, {517, 3522}, {519, 15694}, {550, 11224}, {551, 12645}, {632, 4668}, {944, 3543}, {946, 14269}, {962, 3529}, {1125, 55860}, {1385, 3241}, {1482, 3534}, {3244, 6684}, {3525, 20053}, {3526, 3625}, {3560, 8162}, {3616, 60781}, {3621, 11231}, {3622, 46935}, {3632, 38028}, {3634, 51515}, {3636, 5790}, {3653, 5690}, {3679, 47598}, {3885, 5885}, {3957, 46920}, {4345, 31795}, {4691, 46219}, {5073, 5882}, {5250, 51112}, {5550, 38176}, {5603, 50689}, {5691, 12101}, {5731, 11278}, {5734, 28160}, {6361, 58240}, {6924, 37602}, {7982, 44245}, {7987, 15711}, {9956, 38314}, {10044, 39781}, {10595, 28204}, {11220, 26089}, {11239, 26492}, {11240, 26487}, {11522, 28224}, {12512, 51077}, {12571, 18525}, {13464, 18526}, {15570, 60895}, {15722, 34718}, {15862, 26066}, {16189, 28174}, {16200, 28216}, {18493, 28236}, {19875, 50831}, {19925, 51107}, {24299, 36867}, {25055, 50804}, {25439, 37535}, {28158, 58236}, {31423, 34747}, {34748, 47745}, {38066, 51096}, {43174, 58230}, {44903, 50811}, {47746, 56176}

X(61284) = reflection of X(i) in X(j) for these {i,j}: {355, 8227}, {4668, 632}
X(61284) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1483, 355}, {1, 5881, 10283}, {1, 7972, 11375}, {1, 37727, 5886}, {1, 37734, 5722}, {1, 37738, 11374}, {1, 37740, 11373}, {145, 15178, 26446}, {355, 1483, 37727}, {944, 33179, 3656}, {1482, 13607, 3655}, {5882, 10247, 12699}, {7967, 10222, 18481}, {7967, 20057, 10222}, {13607, 51071, 1482}

X(61285) = X(1)X(5)∩X(40)X(3635)

Barycentrics    13*a^4 - 13*a^3*b - 11*a^2*b^2 + 13*a*b^3 - 2*b^4 - 13*a^3*c + 26*a^2*b*c - 13*a*b^2*c - 11*a^2*c^2 - 13*a*b*c^2 + 4*b^2*c^2 + 13*a*c^3 - 2*c^4 : :
X(61285) = 13 X[1] - 4 X[5], 11 X[1] - 2 X[355], 5 X[1] + 4 X[1483], 4 X[1] - X[5587], 10 X[1] - X[5881], 5 X[1] - 2 X[5886], 17 X[1] - 8 X[5901], 3 X[1] - X[7988], 25 X[1] - 7 X[7989], 14 X[1] - 5 X[8227], 16 X[1] - 7 X[9624], 7 X[1] - 4 X[10283], 35 X[1] - 8 X[18357], 31 X[1] - 4 X[37705], 7 X[1] - X[37712], 23 X[1] - 5 X[37714], and many others

X(61285) lies on these lines: {1, 5}, {40, 3635}, {145, 10165}, {165, 15759}, {515, 50687}, {516, 7967}, {517, 15688}, {519, 15709}, {1698, 51515}, {3241, 3576}, {3244, 5657}, {3526, 4816}, {3533, 4746}, {3622, 10172}, {3623, 5731}, {3624, 38176}, {3632, 11231}, {3633, 15178}, {3654, 51094}, {3655, 11224}, {3679, 15723}, {3817, 50818}, {4512, 51112}, {4677, 38028}, {5126, 16236}, {5603, 34648}, {5691, 32900}, {5790, 51087}, {5844, 30392}, {5882, 20057}, {6173, 11274}, {8236, 60946}, {8275, 37606}, {9778, 51077}, {9779, 51074}, {10164, 50817}, {10171, 51104}, {10222, 28154}, {10246, 15701}, {10247, 15684}, {11230, 34748}, {11531, 41981}, {11849, 38637}, {12245, 31425}, {16189, 34773}, {16191, 28174}, {17502, 50805}, {19875, 41984}, {19876, 59400}, {25439, 34474}, {26446, 34747}, {28164, 35409}, {28182, 34628}, {28198, 58238}, {28236, 38021}, {33179, 33697}, {37535, 38636}, {38042, 51110}, {38140, 50871}, {38314, 54447}, {50194, 59372}, {50810, 51095}, {50828, 51092}, {50831, 51066}, {51096, 58441}, {51103, 59388}

X(61285) = reflection of X(54447) in X(38314)
X(61285) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1483, 5881}, {1, 7972, 5219}, {1, 37712, 10283}, {1, 37727, 8227}, {1, 37740, 37704}, {1483, 18357, 37727}, {3623, 13607, 7982}, {3633, 15178, 31423}, {5881, 5886, 5587}, {5881, 8227, 18357}, {7967, 16200, 50811}, {7967, 51071, 16200}, {8227, 37712, 5587}, {10283, 18357, 5886}, {10283, 37712, 8227}, {10283, 37727, 37712}

X(61286) = X(1)X(5)∩X(3)X(3241)

Barycentrics    6*a^4 - 6*a^3*b - 5*a^2*b^2 + 6*a*b^3 - b^4 - 6*a^3*c + 12*a^2*b*c - 6*a*b^2*c - 5*a^2*c^2 - 6*a*b*c^2 + 2*b^2*c^2 + 6*a*c^3 - c^4 : :
X(61286) = 3 X[1] - X[5], 5 X[1] - X[355], 11 X[1] - 3 X[5587], 9 X[1] - X[5881], 7 X[1] - 3 X[5886], 25 X[1] - 9 X[7988], 23 X[1] - 7 X[7989], 13 X[1] - 5 X[8227], 15 X[1] - 7 X[9624], 5 X[1] - 3 X[10283], 4 X[1] - X[18357], 7 X[1] - X[37705], 19 X[1] - 3 X[37712], 21 X[1] - 5 X[37714], 3 X[1] + X[37727], 13 X[1] - 3 X[38138], and many others

X(61286) lies on these lines: {1, 5}, {3, 3241}, {8, 3526}, {10, 16239}, {20, 1482}, {21, 51112}, {30, 4301}, {40, 46853}, {140, 519}, {145, 631}, {354, 13375}, {382, 944}, {404, 50843}, {515, 3853}, {517, 548}, {546, 13464}, {547, 51103}, {549, 9588}, {550, 3655}, {551, 3628}, {575, 9041}, {632, 3679}, {912, 31792}, {946, 3861}, {962, 17800}, {999, 32141}, {1125, 48154}, {1159, 4308}, {1319, 34753}, {1353, 16496}, {1385, 3244}, {1392, 34611}, {1656, 34748}, {1698, 59400}, {2098, 4309}, {2099, 4317}, {2475, 10031}, {2802, 5885}, {3057, 24475}, {3090, 38022}, {3091, 50800}, {3095, 22713}, {3109, 14480}, {3158, 47746}, {3295, 32153}, {3303, 6914}, {3304, 6924}, {3476, 6147}, {3522, 34631}, {3523, 34718}, {3524, 51092}, {3525, 31145}, {3528, 12702}, {3564, 49465}, {3576, 44682}, {3579, 58190}, {3616, 5070}, {3621, 55864}, {3622, 5067}, {3625, 11231}, {3627, 3656}, {3632, 38112}, {3633, 26446}, {3636, 9956}, {3653, 14869}, {3654, 15712}, {3754, 33812}, {3828, 55862}, {3832, 10595}, {3843, 5603}, {3845, 11522}, {3850, 51709}, {3851, 34627}, {3855, 18493}, {3856, 18480}, {3857, 38021}, {3859, 9955}, {3868, 59347}, {3871, 25416}, {3877, 57003}, {3880, 13373}, {3895, 37612}, {3898, 5694}, {3957, 37374}, {4297, 11278}, {4325, 11009}, {4669, 10124}, {4677, 11539}, {4745, 47598}, {4995, 5559}, {5048, 15171}, {5049, 58561}, {5066, 51107}, {5079, 38074}, {5253, 12331}, {5428, 34486}, {5493, 44245}, {5731, 8148}, {5762, 42871}, {5771, 24299}, {5843, 30331}, {5846, 40107}, {5883, 58605}, {5884, 10284}, {5919, 15174}, {6049, 11041}, {6863, 11240}, {6885, 15934}, {6906, 51529}, {6918, 15933}, {6958, 11239}, {7330, 51779}, {7486, 59388}, {7508, 8666}, {7962, 10386}, {7980, 45476}, {7981, 45477}, {7984, 23236}, {7991, 8703}, {8192, 9714}, {8550, 50998}, {9589, 16200}, {9657, 39542}, {9711, 30144}, {9780, 51515}, {9945, 14923}, {9957, 10391}, {10074, 14882}, {10109, 51104}, {10244, 34730}, {10257, 47536}, {10303, 20049}, {10572, 33176}, {10698, 13100}, {11011, 18990}, {11230, 47745}, {11280, 15326}, {11366, 32147}, {11367, 32146}, {11396, 37122}, {11735, 20396}, {11812, 51096}, {11849, 38602}, {12100, 43174}, {12102, 51082}, {12103, 28194}, {12108, 50821}, {12135, 15559}, {12245, 15717}, {12630, 38121}, {12699, 28190}, {12811, 50796}, {13369, 13600}, {13384, 31436}, {13624, 28234}, {13743, 38669}, {13869, 53809}, {15034, 50923}, {15122, 47489}, {15170, 37290}, {15699, 51105}, {15704, 16189}, {15723, 51068}, {16195, 34729}, {16491, 59399}, {16619, 47472}, {17388, 59680}, {17438, 59671}, {17504, 51094}, {17538, 50872}, {18524, 45977}, {19066, 31487}, {19512, 29574}, {19543, 48858}, {19862, 38176}, {19875, 55859}, {19876, 41992}, {20050, 55863}, {22249, 51701}, {22935, 51714}, {24467, 31393}, {25055, 55856}, {25439, 32612}, {25555, 51006}, {27529, 34126}, {28154, 58206}, {28202, 58203}, {31452, 34471}, {31454, 35763}, {31835, 58679}, {33923, 51705}, {33925, 52272}, {33956, 59719}, {34200, 51095}, {34380, 49684}, {35738, 36440}, {35812, 49232}, {35813, 49233}, {36846, 37615}, {37621, 54391}, {38076, 41989}, {38081, 50804}, {38110, 49688}, {38665, 45976}, {44452, 47490}, {46219, 53620}, {47341, 47593}, {47599, 51108}, {48661, 49138}, {48876, 49681}, {49136, 58236}, {49490, 51046}, {49529, 51732}, {50317, 50637}, {50689, 50806}, {50790, 53093}, {50828, 58232}, {51577, 59572}, {59417, 61138}

X(61286) = midpoint of X(i) and X(j) for these {i,j}: {1, 1483}, {5, 37727}, {145, 5690}, {549, 51093}, {550, 7982}, {551, 51087}, {944, 22791}, {1353, 16496}, {1385, 3244}, {1482, 34773}, {1484, 7972}, {3057, 24475}, {3241, 50824}, {3635, 13607}, {3679, 50831}, {4297, 11278}, {5882, 10222}, {5884, 10284}, {13369, 13600}, {15122, 47489}, {20049, 50830}, {25416, 33814}, {32213, 37740}, {32214, 37738}, {32900, 33179}, {34747, 50823}, {48876, 49681}, {49490, 51046}
X(61286) = reflection of X(i) in X(j) for these {i,j}: {10, 51700}, {140, 15178}, {546, 13464}, {547, 51103}, {4669, 10124}, {5493, 44245}, {5901, 1}, {9956, 3636}, {11362, 3530}, {18357, 5901}, {31835, 58679}, {49529, 51732}
X(61286) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 355, 10283}, {1, 7972, 12}, {1, 10944, 37737}, {1, 10950, 1387}, {1, 12737, 61148}, {1, 37707, 15950}, {1, 37727, 5}, {1, 37728, 12433}, {1, 37733, 19907}, {1, 37734, 37730}, {1, 37738, 495}, {1, 37740, 496}, {5, 1483, 37727}, {5, 10283, 9624}, {5, 37705, 37714}, {8, 37624, 38028}, {145, 10246, 5690}, {355, 9624, 5}, {382, 5734, 22791}, {382, 10247, 5734}, {944, 5734, 382}, {944, 10247, 22791}, {944, 20057, 10247}, {1317, 10957, 37738}, {1385, 11362, 3530}, {1482, 7967, 34773}, {3616, 12645, 38042}, {3623, 7967, 1482}, {3653, 34747, 50823}, {3654, 30389, 15712}, {3655, 7982, 550}, {3871, 37535, 33814}, {5882, 51071, 10222}, {5886, 37714, 5}, {10595, 18525, 38034}, {10958, 37734, 37740}, {15888, 37726, 5}, {20049, 38066, 50830}

X(61287) = X(1)X(5)∩X(3)X(3244)

Barycentrics    5*a^4 - 5*a^3*b - 4*a^2*b^2 + 5*a*b^3 - b^4 - 5*a^3*c + 10*a^2*b*c - 5*a*b^2*c - 4*a^2*c^2 - 5*a*b*c^2 + 2*b^2*c^2 + 5*a*c^3 - c^4 : :
X(61287) = 5 X[1] - 2 X[5], 4 X[1] - X[355], X[1] + 2 X[1483], 3 X[1] - X[5587], 7 X[1] - X[5881], 7 X[1] - 4 X[5901], 7 X[1] - 3 X[7988], 19 X[1] - 7 X[7989], 11 X[1] - 5 X[8227], 13 X[1] - 7 X[9624], 3 X[1] - 2 X[10283], 13 X[1] - 4 X[18357], 11 X[1] - 2 X[37705], 5 X[1] - X[37712], 17 X[1] - 5 X[37714], and many others

X(61287) lies on these lines: {1, 5}, {2, 38176}, {3, 3244}, {4, 20057}, {8, 3525}, {10, 37624}, {20, 11278}, {30, 16200}, {40, 33923}, {140, 3632}, {145, 1385}, {165, 45759}, {376, 517}, {381, 28236}, {515, 3656}, {516, 1482}, {519, 3653}, {549, 30392}, {550, 11531}, {551, 5790}, {631, 20050}, {912, 5919}, {944, 3146}, {946, 18526}, {962, 28154}, {1056, 37820}, {1058, 37821}, {1125, 12645}, {1159, 4315}, {1479, 33176}, {1656, 3636}, {1698, 51700}, {1699, 14893}, {2783, 50130}, {3109, 30221}, {3476, 50194}, {3488, 37822}, {3524, 31662}, {3526, 3626}, {3534, 28228}, {3576, 3654}, {3579, 21734}, {3622, 9956}, {3633, 5690}, {3652, 15174}, {3679, 10124}, {3746, 32153}, {3839, 5603}, {3854, 9955}, {3860, 38034}, {3871, 32612}, {3880, 10202}, {3885, 35004}, {3890, 5694}, {3895, 25416}, {3913, 16203}, {4297, 8148}, {4301, 28172}, {4308, 31794}, {4677, 38112}, {5045, 39779}, {5055, 38155}, {5066, 50871}, {5070, 15808}, {5563, 32141}, {5604, 6280}, {5605, 6279}, {5691, 12102}, {5697, 24475}, {5734, 22793}, {5770, 24929}, {5779, 43179}, {5787, 32905}, {5805, 15570}, {5816, 46845}, {5853, 38030}, {5883, 11274}, {5885, 14923}, {5887, 8236}, {6767, 22758}, {7373, 11499}, {7982, 12103}, {8666, 37621}, {8703, 51094}, {8715, 22560}, {9053, 38029}, {9779, 10595}, {9812, 28208}, {9905, 20585}, {9957, 12711}, {10164, 15718}, {10175, 50798}, {10199, 38752}, {10303, 20054}, {10525, 10805}, {10526, 10806}, {10528, 26492}, {10529, 26487}, {10596, 18516}, {10597, 18517}, {10893, 18545}, {10894, 18543}, {10914, 13373}, {11011, 57282}, {11224, 19710}, {11230, 38314}, {11260, 24299}, {11500, 12001}, {11812, 50830}, {12000, 12114}, {12005, 25413}, {12245, 13624}, {12331, 33812}, {12513, 16202}, {12675, 23340}, {13464, 18525}, {15185, 31786}, {15681, 28232}, {15685, 51120}, {15686, 58241}, {15693, 51085}, {15694, 34641}, {15701, 50827}, {15702, 58234}, {15705, 17502}, {15722, 50828}, {16128, 25485}, {16189, 28182}, {16191, 28178}, {18391, 25405}, {19512, 29602}, {19875, 59400}, {20323, 39781}, {21842, 41687}, {24474, 58609}, {24927, 56176}, {25055, 38042}, {26285, 38693}, {26286, 59421}, {26726, 33814}, {28150, 58238}, {28186, 31162}, {28190, 50865}, {32613, 54391}, {33703, 58237}, {33956, 45701}, {34627, 38140}, {35262, 50843}, {35788, 42558}, {35789, 42557}, {37615, 38122}, {38022, 45757}, {41106, 50799}, {43273, 51149}, {49498, 51046}, {49536, 53091}, {50796, 51107}, {50805, 50814}, {50810, 51092}, {50821, 54445}, {50967, 51146}, {50970, 51145}, {50973, 51000}, {50974, 51193}, {50998, 51136}, {50999, 51178}, {51105, 54447}

X(61287) = midpoint of X(i) and X(j) for these {i,j}: {145, 5657}, {3241, 7967}, {3576, 51093}, {5790, 34748}, {5886, 37727}, {9778, 34631}, {11224, 50811}, {38112, 50831}, {50818, 59387}
X(61287) = reflection of X(i) in X(j) for these {i,j}: {8, 11231}, {355, 5886}, {3576, 50824}, {3654, 3576}, {3655, 7967}, {3656, 10247}, {3679, 38028}, {4677, 38112}, {5587, 10283}, {5657, 1385}, {5660, 19907}, {5790, 551}, {5881, 38138}, {5886, 1}, {10175, 51103}, {10247, 51071}, {11231, 15178}, {26446, 10246}, {34627, 38140}, {34718, 10164}, {37712, 5}, {38138, 5901}, {50798, 10175}, {51515, 10}, {59387, 51709}, {59388, 11230}, {59417, 17502}, {59503, 10165}
X(61287) = anticomplement of X(38176)
X(61287) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1483, 37727}, {1, 5587, 10283}, {1, 5727, 1387}, {1, 5881, 5901}, {1, 7972, 5252}, {1, 10944, 11374}, {1, 10950, 11373}, {1, 37706, 11376}, {1, 37707, 11375}, {1, 37708, 15950}, {1, 37709, 37737}, {1, 37727, 355}, {1, 37734, 37739}, {1, 37740, 5722}, {4, 20057, 33179}, {944, 3623, 10222}, {944, 10222, 12699}, {1482, 5882, 18481}, {3244, 13607, 3}, {3623, 32900, 12699}, {3635, 5882, 1482}, {3636, 47745, 1656}, {5054, 38127, 26446}, {5587, 10283, 5886}, {5881, 7988, 38138}, {5901, 7988, 5886}, {5901, 38138, 7988}, {10165, 59503, 26446}, {10222, 32900, 944}, {10246, 26446, 3653}, {10246, 59503, 10165}, {12100, 50817, 3654}, {12735, 37728, 1}, {34718, 58230, 10164}, {37733, 37739, 355}, {38066, 58441, 26446}, {38314, 59388, 11230}, {50824, 51093, 3654}, {51091, 51705, 50805}

X(61288) = X(1)X(5)∩X(3)X(51093)

Barycentrics    9*a^4 - 9*a^3*b - 7*a^2*b^2 + 9*a*b^3 - 2*b^4 - 9*a^3*c + 18*a^2*b*c - 9*a*b^2*c - 7*a^2*c^2 - 9*a*b*c^2 + 4*b^2*c^2 + 9*a*c^3 - 2*c^4 : :
X(61288) = 9 X[1] - 4 X[5], 7 X[1] - 2 X[355], X[1] + 4 X[1483], 8 X[1] - 3 X[5587], 6 X[1] - X[5881], 11 X[1] - 6 X[5886], 13 X[1] - 8 X[5901], 19 X[1] - 9 X[7988], 17 X[1] - 7 X[7989], 12 X[1] - 7 X[9624], 17 X[1] - 12 X[10283], 23 X[1] - 8 X[18357], 19 X[1] - 4 X[37705], 13 X[1] - 3 X[37712], 3 X[1] - X[37714], and many others

X(61288) lies on these lines: {1, 5}, {3, 51093}, {4, 51071}, {8, 55864}, {20, 3241}, {30, 16189}, {40, 3244}, {140, 4677}, {145, 3576}, {165, 58190}, {376, 51091}, {382, 10222}, {515, 3623}, {517, 15696}, {519, 631}, {548, 3655}, {550, 51094}, {551, 5067}, {632, 51066}, {944, 3635}, {946, 20057}, {1385, 3633}, {1482, 9589}, {1656, 51105}, {1657, 58240}, {1698, 37624}, {1699, 18526}, {2646, 31436}, {3090, 51103}, {3340, 4317}, {3522, 51092}, {3524, 51096}, {3525, 4669}, {3526, 3679}, {3529, 51095}, {3530, 30389}, {3533, 4745}, {3545, 51107}, {3616, 31399}, {3621, 10165}, {3622, 47745}, {3624, 12645}, {3628, 51110}, {3632, 10246}, {3636, 59388}, {3653, 50831}, {3654, 44682}, {3656, 3853}, {3680, 6955}, {3832, 13464}, {3843, 11522}, {3855, 38021}, {3859, 30308}, {3871, 59332}, {3880, 15016}, {3885, 12005}, {4309, 7962}, {4325, 25415}, {4330, 30323}, {4338, 11009}, {4668, 45760}, {5048, 9670}, {5070, 25055}, {5071, 51104}, {5288, 16202}, {5493, 34631}, {5541, 37612}, {5690, 30392}, {5691, 10247}, {5693, 5919}, {5707, 16490}, {5735, 42871}, {5844, 7987}, {6684, 20050}, {6885, 11518}, {6936, 11523}, {6937, 12625}, {7486, 38314}, {7491, 34690}, {7966, 12704}, {8192, 9625}, {8726, 12127}, {9614, 33176}, {9657, 11011}, {10543, 41691}, {10595, 18492}, {10597, 18406}, {11224, 18481}, {11274, 38665}, {11499, 37602}, {11531, 34773}, {12001, 44425}, {12513, 34486}, {13384, 31452}, {15069, 49465}, {15570, 38036}, {15712, 58229}, {15720, 58232}, {16132, 54176}, {16203, 48696}, {16236, 37582}, {16239, 19875}, {18543, 52850}, {19872, 38176}, {19876, 50804}, {20014, 54445}, {20049, 50828}, {20053, 38127}, {21734, 51705}, {28182, 58239}, {28234, 35242}, {31775, 34699}, {31789, 34749}, {32141, 37587}, {43174, 50817}, {45391, 55016}, {50870, 51082}, {51109, 60781}, {54391, 59331}, {54422, 59347}

X(61288) = reflection of X(i) in X(j) for these {i,j}: {1698, 37624}, {5071, 51104}, {5881, 37714}, {8227, 1}, {18492, 10595}
X(61288) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5881, 9624}, {1, 7972, 37709}, {1, 7989, 10283}, {1, 10950, 37704}, {1, 37706, 50443}, {1, 37707, 5219}, {1, 37712, 5901}, {1, 37727, 5881}, {145, 13607, 3576}, {944, 3635, 16200}, {944, 16200, 41869}, {3241, 5882, 7982}, {3244, 7967, 40}, {3576, 11362, 31425}, {3622, 47745, 54447}, {3632, 10246, 31423}, {5881, 8227, 37714}, {5881, 9624, 5587}, {5882, 7982, 50811}, {12735, 37739, 1}, {15888, 26481, 37719}, {18526, 33179, 1699}, {26476, 37722, 37720}, {37719, 37720, 8068}

X(61289) = X(1)X(5)∩X(145)X(165)

Barycentrics    15*a^4 - 15*a^3*b - 11*a^2*b^2 + 15*a*b^3 - 4*b^4 - 15*a^3*c + 30*a^2*b*c - 15*a*b^2*c - 11*a^2*c^2 - 15*a*b*c^2 + 8*b^2*c^2 + 15*a*c^3 - 4*c^4 : :
X(61289) = 15 X[1] - 8 X[5], 11 X[1] - 4 X[355], X[1] - 8 X[1483], 13 X[1] - 6 X[5587], 9 X[1] - 2 X[5881], 19 X[1] - 12 X[5886], 23 X[1] - 16 X[5901], 16 X[1] - 9 X[7988], 17 X[1] - 10 X[8227], 3 X[1] - 2 X[9624], 31 X[1] - 24 X[10283], 37 X[1] - 16 X[18357], 29 X[1] - 8 X[37705], 10 X[1] - 3 X[37712], and many others

X(61289) lies on these lines: {1, 5}, {3, 34747}, {20, 3244}, {30, 51094}, {40, 32900}, {145, 165}, {376, 5882}, {382, 16200}, {519, 3523}, {551, 30315}, {631, 3632}, {632, 50804}, {944, 9589}, {1388, 30286}, {1482, 28168}, {1490, 32905}, {1657, 7982}, {1699, 3623}, {3091, 50871}, {3146, 3241}, {3525, 3679}, {3528, 28234}, {3529, 51077}, {3543, 51095}, {3576, 31447}, {3626, 55864}, {3633, 7967}, {3635, 5691}, {3636, 7486}, {3655, 33923}, {3656, 12102}, {3830, 10222}, {3832, 20057}, {3839, 11522}, {3843, 33179}, {3854, 30308}, {4317, 18421}, {4668, 10246}, {4677, 5054}, {4816, 10165}, {5067, 47745}, {5493, 51080}, {5844, 16192}, {9671, 33176}, {10124, 51066}, {10164, 20014}, {10303, 34641}, {11278, 17800}, {11407, 12437}, {12100, 31425}, {12103, 50811}, {12108, 50824}, {13464, 50818}, {15022, 50801}, {15178, 19875}, {15703, 51110}, {15705, 43174}, {15717, 20050}, {16191, 41869}, {19876, 55862}, {20052, 58441}, {25055, 31399}, {31436, 53054}, {34595, 37624}, {38066, 58232}, {38176, 55866}, {47096, 47491}, {47337, 47489}, {49140, 51120}, {50831, 58229}

X(61289) = reflection of X(7989) in X(1)
X(61289) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 37707, 5726}, {5, 37712, 37714}, {3632, 13607, 30392}, {3633, 7967, 7987}, {5882, 51093, 7991}

X(61290) = X(1)X(5)∩X(145)X(3241)

Barycentrics    18*a^4 - 18*a^3*b - 13*a^2*b^2 + 18*a*b^3 - 5*b^4 - 18*a^3*c + 36*a^2*b*c - 18*a*b^2*c - 13*a^2*c^2 - 18*a*b*c^2 + 10*b^2*c^2 + 18*a*c^3 - 5*c^4 : :
X(61290) = 9 X[1] - 5 X[5], 13 X[1] - 5 X[355], X[1] - 5 X[1483], 31 X[1] - 15 X[5587], 21 X[1] - 5 X[5881], 23 X[1] - 15 X[5886], 7 X[1] - 5 X[5901], 77 X[1] - 45 X[7988], 67 X[1] - 35 X[7989], 41 X[1] - 25 X[8227], 51 X[1] - 35 X[9624], 19 X[1] - 15 X[10283], 11 X[1] - 5 X[18357], 17 X[1] - 5 X[37705], and many others

X(61290) lies on these lines: {1, 5}, {8, 55863}, {20, 34631}, {30, 51091}, {140, 4669}, {145, 3528}, {382, 3241}, {404, 38629}, {519, 3530}, {546, 51071}, {547, 51106}, {548, 5882}, {550, 51093}, {631, 31145}, {944, 17800}, {1482, 28190}, {3244, 28174}, {3526, 34748}, {3529, 51092}, {3534, 58249}, {3628, 51108}, {3635, 28224}, {3655, 46853}, {3828, 15178}, {3832, 50818}, {3853, 10222}, {3856, 13464}, {3859, 51078}, {3861, 28204}, {4301, 28186}, {4677, 14869}, {4678, 10246}, {4691, 45760}, {4701, 13607}, {5690, 20053}, {5734, 18526}, {5844, 31663}, {6906, 38631}, {7486, 50798}, {7967, 15717}, {9041, 33749}, {9778, 15696}, {11278, 28182}, {11362, 17502}, {11737, 51107}, {11812, 58232}, {12245, 58188}, {12645, 19877}, {14891, 58223}, {15686, 58245}, {15687, 51097}, {15723, 58235}, {17504, 58225}, {17578, 22791}, {19711, 58229}, {19878, 51700}, {19883, 48154}, {20057, 38034}, {22266, 38176}, {30389, 50823}, {34200, 51096}, {34718, 61138}, {35018, 51103}, {38028, 46933}, {38335, 58236}, {44682, 50831}, {47478, 51104}

X(61290) = midpoint of X(i) and X(j) for these {i,j}: {18526, 40273}, {34200, 51096}
X(61290) = reflection of X(11737) in X(51107)
X(61290) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 38138, 5901}, {5901, 18357, 7988}, {20053, 58230, 5690}

X(61291) = X(1)X(5)∩X(40)X(145)

Barycentrics    7*a^4 - 7*a^3*b - 5*a^2*b^2 + 7*a*b^3 - 2*b^4 - 7*a^3*c + 14*a^2*b*c - 7*a*b^2*c - 5*a^2*c^2 - 7*a*b*c^2 + 4*b^2*c^2 + 7*a*c^3 - 2*c^4 : :
X(61291) = 7 X[1] - 4 X[5], 5 X[1] - 2 X[355], X[1] - 4 X[1483], 4 X[1] - X[5881], 3 X[1] - 2 X[5886], 11 X[1] - 8 X[5901], 5 X[1] - 3 X[7988], 13 X[1] - 7 X[7989], 8 X[1] - 5 X[8227], 10 X[1] - 7 X[9624], 5 X[1] - 4 X[10283], 17 X[1] - 8 X[18357], 13 X[1] - 4 X[37705], 3 X[1] - X[37712], 11 X[1] - 5 X[37714], and many others

X(61291) lies on these lines: {1, 5}, {3, 3633}, {4, 3635}, {8, 10165}, {10, 3533}, {30, 11224}, {40, 145}, {104, 25439}, {140, 4668}, {165, 3655}, {390, 41705}, {480, 38031}, {515, 3241}, {516, 944}, {517, 3534}, {519, 3158}, {551, 54447}, {631, 3625}, {730, 22713}, {758, 34716}, {946, 3623}, {956, 34486}, {962, 28172}, {1125, 60781}, {1385, 3632}, {1392, 40264}, {1482, 5073}, {1698, 12645}, {1699, 10247}, {2136, 59333}, {2802, 34701}, {3174, 12629}, {3476, 11529}, {3523, 20053}, {3525, 4691}, {3586, 5048}, {3601, 5770}, {3616, 10172}, {3621, 6684}, {3624, 37624}, {3636, 5818}, {3653, 38112}, {3654, 15711}, {3656, 12101}, {3679, 10246}, {3817, 34627}, {3871, 38693}, {3885, 5884}, {3893, 9940}, {3913, 37561}, {4315, 11041}, {4677, 11812}, {5076, 5691}, {5258, 16202}, {5288, 10267}, {5603, 28236}, {5690, 30389}, {5693, 9957}, {5734, 31673}, {5790, 25055}, {5840, 34719}, {5841, 34690}, {6261, 32905}, {6911, 37602}, {6913, 8162}, {7991, 34773}, {8192, 9626}, {8236, 29007}, {8666, 59331}, {8715, 34474}, {8726, 11519}, {9579, 11009}, {9589, 11278}, {9613, 11011}, {9779, 13464}, {10171, 38074}, {10175, 38314}, {10179, 18908}, {10269, 48696}, {10700, 36939}, {10902, 12513}, {10914, 15016}, {11014, 36846}, {11230, 50798}, {11362, 20050}, {11522, 18525}, {11531, 18481}, {12005, 14923}, {12034, 36911}, {12119, 25416}, {12245, 35242}, {12437, 37526}, {12625, 22837}, {12647, 13384}, {12678, 16205}, {12680, 13600}, {12699, 16189}, {12700, 49178}, {13624, 31425}, {13893, 35842}, {13947, 35843}, {14872, 31792}, {15071, 23340}, {15325, 30286}, {15722, 50821}, {16191, 28186}, {16236, 36279}, {17502, 34718}, {19710, 58243}, {19875, 38028}, {20013, 61122}, {24467, 37563}, {25716, 38941}, {28150, 51077}, {28164, 51082}, {28174, 34628}, {28178, 58241}, {28228, 34631}, {28232, 50872}, {31145, 38127}, {31190, 33812}, {31231, 41684}, {31399, 46934}, {33337, 54286}, {33956, 56177}, {34595, 51700}, {34641, 58441}, {34791, 37625}, {36977, 41863}, {37006, 51792}, {38021, 59387}, {38155, 51103}, {39885, 49465}, {47538, 54995}, {48661, 58240}, {50800, 50871}, {50801, 51104}, {50804, 51066}, {50810, 51096}, {50817, 51705}, {54391, 59421}

X(61291) = midpoint of X(i) and X(j) for these {i,j}: {145, 5731}, {165, 34747}, {5603, 50818}, {10246, 34748}
X(61291) = reflection of X(i) in X(j) for these {i,j}: {8, 10165}, {40, 5731}, {165, 3655}, {355, 10283}, {1699, 10247}, {3576, 7967}, {3632, 59503}, {3679, 10246}, {4677, 26446}, {5587, 1}, {5603, 51071}, {5731, 5882}, {5881, 5587}, {10165, 13607}, {12645, 38176}, {16200, 3241}, {18908, 10179}, {26446, 50824}, {31145, 38127}, {31162, 16200}, {34627, 3817}, {34641, 58441}, {34718, 17502}, {37712, 5886}, {38155, 51103}, {38176, 15178}, {47745, 10172}, {50798, 11230}, {50804, 59400}, {50817, 59417}, {51515, 11231}, {59388, 551}, {59417, 51705}, {59503, 1385}
X(61291) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 355, 9624}, {1, 5727, 37704}, {1, 5881, 8227}, {1, 7988, 10283}, {1, 9897, 23708}, {1, 37706, 9581}, {1, 37707, 9578}, {1, 37708, 5219}, {1, 37711, 50443}, {1, 37712, 5886}, {1, 37714, 5901}, {145, 5882, 40}, {355, 7988, 5587}, {355, 10283, 7988}, {551, 59388, 54447}, {944, 3244, 7982}, {1317, 37740, 1}, {1483, 37727, 1}, {4677, 30392, 26446}, {5587, 9624, 7988}, {5722, 12735, 1}, {5886, 37712, 5587}, {7988, 10283, 9624}, {10222, 18526, 5691}, {10246, 51515, 11231}, {11231, 51515, 3679}, {12645, 15178, 1698}, {18525, 33179, 11522}, {26446, 50824, 30392}, {31145, 54445, 38127}, {32213, 37726, 7951}, {37734, 37738, 1}

X(61292) = X(1)X(5)∩X(8)X(5040)

Barycentrics    10*a^4 - 10*a^3*b - 7*a^2*b^2 + 10*a*b^3 - 3*b^4 - 10*a^3*c + 20*a^2*b*c - 10*a*b^2*c - 7*a^2*c^2 - 10*a*b*c^2 + 6*b^2*c^2 + 10*a*c^3 - 3*c^4 : :
X(61292) = 5 X[1] - 3 X[5], 7 X[1] - 3 X[355], X[1] - 3 X[1483], 17 X[1] - 9 X[5587], 11 X[1] - 3 X[5881], 13 X[1] - 9 X[5886], 4 X[1] - 3 X[5901], 43 X[1] - 27 X[7988], 37 X[1] - 21 X[7989], 23 X[1] - 15 X[8227], 29 X[1] - 21 X[9624], 11 X[1] - 9 X[10283], 3 X[1] - X[37705], 25 X[1] - 9 X[37712], 31 X[1] - 15 X[37714], and many others

X(61292) lies on these lines: {1, 5}, {3, 20050}, {8, 5054}, {10, 10124}, {30, 3244}, {140, 3626}, {145, 376}, {381, 20057}, {517, 12103}, {519, 12100}, {546, 28236}, {547, 3636}, {548, 28234}, {549, 3632}, {944, 1657}, {962, 49134}, {1125, 47599}, {1385, 3625}, {1482, 3146}, {3241, 3830}, {3523, 3621}, {3524, 20054}, {3525, 3617}, {3579, 5844}, {3616, 15703}, {3622, 50798}, {3623, 3839}, {3627, 16200}, {3628, 15808}, {3633, 3655}, {3634, 15178}, {3635, 14893}, {3653, 4668}, {3754, 12009}, {3853, 58237}, {3854, 10595}, {3860, 18480}, {3871, 38602}, {4816, 26446}, {5288, 5428}, {5550, 37624}, {5790, 46934}, {6361, 50805}, {6691, 33812}, {7982, 28178}, {8703, 34747}, {9780, 12645}, {9955, 50803}, {9957, 41562}, {10222, 12102}, {11531, 15704}, {11539, 50804}, {11540, 38098}, {11544, 45287}, {11812, 34641}, {11849, 51529}, {12101, 51095}, {12245, 21734}, {12699, 35404}, {14869, 30392}, {15686, 58248}, {15705, 20014}, {15718, 20053}, {16239, 38176}, {18481, 19710}, {18493, 41106}, {19512, 29601}, {19862, 51700}, {20052, 38066}, {28164, 58240}, {28182, 49138}, {28208, 51091}, {28228, 58244}, {28232, 58203}, {33699, 51094}, {35018, 38155}, {35418, 50809}, {37535, 51525}, {38071, 50871}, {41983, 50827}, {43174, 58219}, {46936, 59388}, {47478, 50801}, {49503, 51046}, {50865, 58239}, {51515, 58233}, {58232, 58441}

X(61292) = midpoint of X(i) and X(j) for these {i,j}: {145, 34773}, {1483, 37727}, {3655, 50831}, {8703, 34747}, {11531, 15704}, {18526, 22791}, {34748, 50824}
X(61292) = reflection of X(i) in X(j) for these {i,j}: {140, 13607}, {546, 33179}, {18357, 1}, {34641, 11812}, {40273, 10222}, {47745, 3628}
X(61292) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 18357, 5901}, {1385, 38127, 12108}, {3241, 18526, 22791}, {3623, 50818, 18525}, {3655, 50817, 45759}

X(61293) = X(1)X(5)∩X(8)X(14869)

Barycentrics    16*a^4 - 16*a^3*b - 11*a^2*b^2 + 16*a*b^3 - 5*b^4 - 16*a^3*c + 32*a^2*b*c - 16*a*b^2*c - 11*a^2*c^2 - 16*a*b*c^2 + 10*b^2*c^2 + 16*a*c^3 - 5*c^4 : :
X(61293) = 8 X[1] - 5 X[5], 11 X[1] - 5 X[355], 2 X[1] - 5 X[1483], 9 X[1] - 5 X[5587], 17 X[1] - 5 X[5881], 7 X[1] - 5 X[5886], 13 X[1] - 10 X[5901], 23 X[1] - 15 X[7988], 59 X[1] - 35 X[7989], 37 X[1] - 25 X[8227], 47 X[1] - 35 X[9624], 6 X[1] - 5 X[10283], 19 X[1] - 10 X[18357], 14 X[1] - 5 X[37705], and many others

X(61293) lies on these lines: {1, 5}, {3, 20014}, {8, 14869}, {20, 58247}, {140, 4678}, {145, 550}, {515, 33699}, {517, 15686}, {519, 17502}, {546, 3623}, {549, 7967}, {632, 12645}, {944, 15704}, {1385, 4701}, {3241, 15687}, {3244, 28160}, {3530, 3621}, {3543, 58238}, {3576, 19711}, {3627, 18526}, {3655, 15714}, {3828, 38028}, {3845, 10247}, {3857, 10595}, {4669, 10165}, {4677, 50832}, {4691, 11231}, {5603, 23046}, {5657, 15712}, {5690, 32900}, {5731, 5844}, {5882, 31663}, {7982, 28182}, {9779, 41991}, {10172, 51108}, {10175, 51106}, {10246, 11539}, {11224, 28190}, {11278, 28172}, {11362, 58219}, {12245, 46853}, {12512, 28234}, {15178, 41992}, {15692, 58226}, {15699, 59388}, {15720, 20052}, {19710, 50805}, {19877, 55859}, {19883, 38042}, {20049, 34200}, {20070, 58249}, {25439, 51529}, {28146, 51082}, {28168, 51077}, {28174, 51093}, {34628, 58243}, {34631, 44903}, {34667, 38322}, {37624, 55856}, {38022, 38155}, {38034, 51071}, {41990, 51709}, {45759, 59417}, {51079, 51096}, {51700, 55861}, {55864, 58233}

X(61293) = midpoint of X(i) and X(j) for these {i,j}: {7967, 34748}, {10247, 50818}
X(61293) = reflection of X(i) in X(j) for these {i,j}: {549, 7967}, {3845, 10247}, {11231, 13607}, {37705, 5886}, {37712, 5901}, {38034, 51071}, {38112, 50824}, {38138, 1}, {50823, 3576}, {51515, 140}, {59400, 10246}
X(61293) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7967, 31145, 58230}, {10246, 59400, 11539}

X(61294) = X(1)X(5)∩X(8)X(30389)

Barycentrics    11*a^4 - 11*a^3*b - 7*a^2*b^2 + 11*a*b^3 - 4*b^4 - 11*a^3*c + 22*a^2*b*c - 11*a*b^2*c - 7*a^2*c^2 - 11*a*b*c^2 + 8*b^2*c^2 + 11*a*c^3 - 4*c^4 : :
X(61294) = 11 X[1] - 8 X[5], 7 X[1] - 4 X[355], 5 X[1] - 8 X[1483], 3 X[1] - 2 X[5587], 5 X[1] - 2 X[5881], 5 X[1] - 4 X[5886], 19 X[1] - 16 X[5901], 4 X[1] - 3 X[7988], 10 X[1] - 7 X[7989], 13 X[1] - 10 X[8227], 17 X[1] - 14 X[9624], 9 X[1] - 8 X[10283], 25 X[1] - 16 X[18357], 17 X[1] - 8 X[37705], 8 X[1] - 5 X[37714], and many others

X(61294) lies on these lines: {1, 5}, {8, 30389}, {145, 516}, {165, 519}, {515, 11224}, {517, 15681}, {944, 3633}, {962, 41690}, {1319, 30286}, {1385, 4668}, {1482, 33697}, {1698, 13607}, {1699, 3241}, {1768, 3895}, {2829, 34719}, {3158, 33956}, {3244, 5691}, {3476, 10980}, {3486, 30337}, {3488, 30326}, {3523, 4701}, {3576, 4677}, {3579, 58192}, {3616, 30315}, {3623, 9779}, {3624, 47745}, {3625, 9588}, {3632, 5657}, {3635, 11522}, {3653, 59400}, {3655, 14891}, {3656, 51094}, {3679, 7967}, {4293, 16236}, {4297, 20050}, {4304, 8275}, {4669, 54445}, {4816, 6684}, {5537, 30283}, {5770, 30282}, {5842, 34690}, {5844, 15690}, {5854, 34701}, {5855, 34716}, {7982, 18526}, {8148, 28154}, {8666, 59421}, {8715, 38693}, {9589, 28172}, {9778, 20049}, {9819, 18452}, {10031, 35262}, {10106, 59372}, {10164, 31145}, {10172, 25055}, {10175, 51105}, {10246, 19875}, {10247, 50806}, {11231, 12645}, {11540, 50824}, {12546, 17772}, {12647, 53054}, {15178, 34595}, {16191, 28224}, {16200, 28204}, {17632, 20789}, {18391, 53058}, {18492, 33179}, {19876, 38028}, {19925, 20057}, {20053, 43174}, {25439, 38669}, {28146, 50805}, {28150, 34631}, {28158, 50872}, {28174, 50831}, {28186, 58241}, {28212, 58203}, {28216, 58243}, {28228, 51096}, {30308, 50803}, {31662, 38066}, {38042, 41985}, {38112, 50804}, {38155, 38314}, {50798, 51110}, {50864, 51091}, {51072, 51085}, {58201, 58248}

X(61294) = midpoint of X(9778) and X(20049)
X(61294) = reflection of X(i) in X(j) for these {i,j}: {1699, 3241}, {3632, 5657}, {3679, 7967}, {4677, 3576}, {5657, 5882}, {5660, 1317}, {5881, 5886}, {5886, 1483}, {10247, 51087}, {11224, 51093}, {11231, 32900}, {12645, 11231}, {31145, 10164}, {37712, 1}, {50804, 38112}, {50865, 11224}, {50871, 59387}, {51515, 1385}, {59387, 51071}
X(61294) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5881, 7989}, {1, 37708, 5726}, {1, 37712, 7988}, {944, 3633, 7991}, {1317, 5727, 1}, {1483, 5881, 1}, {3244, 5691, 16189}, {3632, 5882, 7987}, {3679, 7967, 30392}, {5886, 7989, 7988}, {7988, 37712, 37714}, {12735, 37704, 1}, {37709, 37734, 1}, {50871, 51071, 30308}

X(61295) = X(1)X(5)∩X(30)X(145)

Barycentrics    8*a^4 - 8*a^3*b - 5*a^2*b^2 + 8*a*b^3 - 3*b^4 - 8*a^3*c + 16*a^2*b*c - 8*a*b^2*c - 5*a^2*c^2 - 8*a*b*c^2 + 6*b^2*c^2 + 8*a*c^3 - 3*c^4 : :
X(61295) = 4 X[1] - 3 X[5], 5 X[1] - 3 X[355], 2 X[1] - 3 X[1483], 13 X[1] - 9 X[5587], 7 X[1] - 3 X[5881], 11 X[1] - 9 X[5886], 7 X[1] - 6 X[5901], 35 X[1] - 27 X[7988], 29 X[1] - 21 X[7989], 19 X[1] - 15 X[8227], 25 X[1] - 21 X[9624], 10 X[1] - 9 X[10283], 3 X[1] - 2 X[18357], 17 X[1] - 9 X[37712], 23 X[1] - 15 X[37714], and many others

X(61295) lies on these lines: {1, 5}, {3, 3621}, {8, 549}, {10, 11539}, {30, 145}, {140, 3617}, {376, 20014}, {381, 3623}, {515, 11278}, {517, 15704}, {519, 3579}, {546, 10247}, {547, 3622}, {548, 12245}, {550, 944}, {631, 51515}, {632, 9780}, {956, 5428}, {1125, 38083}, {1385, 3626}, {1388, 11545}, {1482, 3627}, {1657, 58247}, {1698, 38081}, {2099, 11544}, {2801, 10284}, {3241, 3845}, {3244, 15687}, {3295, 31649}, {3524, 20052}, {3526, 58233}, {3530, 59503}, {3534, 20049}, {3576, 4816}, {3616, 15699}, {3625, 5690}, {3628, 37624}, {3632, 3655}, {3633, 15686}, {3634, 13607}, {3635, 18480}, {3654, 15714}, {3679, 15713}, {3850, 10595}, {3857, 59387}, {3858, 5603}, {3871, 12773}, {3898, 56762}, {3935, 37364}, {4668, 50804}, {4677, 19711}, {4678, 5054}, {4701, 50821}, {4746, 50828}, {5076, 58238}, {5204, 32141}, {5217, 32153}, {5550, 5790}, {5657, 44682}, {5731, 46853}, {5843, 30332}, {5903, 39777}, {6361, 19710}, {7502, 8192}, {7966, 26921}, {7982, 28186}, {8256, 33337}, {8715, 38602}, {8981, 35842}, {9053, 48906}, {9798, 37936}, {9802, 16116}, {9955, 51071}, {9956, 15808}, {10031, 17564}, {10124, 46933}, {10222, 18483}, {10680, 54177}, {11531, 28178}, {11849, 38669}, {12100, 31145}, {12101, 51092}, {12108, 58230}, {12699, 33699}, {13966, 35843}, {14892, 50797}, {15178, 19862}, {15693, 58228}, {16200, 40273}, {16239, 46931}, {18242, 32905}, {18493, 20057}, {19512, 29583}, {19872, 41992}, {20053, 34718}, {20054, 34200}, {21850, 51147}, {24475, 50193}, {25005, 50843}, {26285, 51529}, {28190, 41706}, {28198, 51096}, {28458, 56091}, {29588, 36728}, {31730, 51082}, {32612, 51525}, {33179, 38034}, {33697, 50870}, {33923, 59417}, {34719, 50846}, {37535, 38665}, {46932, 47598}, {49447, 51047}, {49468, 51048}, {49515, 51046}, {51118, 58240}, {51705, 58219}

X(61295) = midpoint of X(i) and X(j) for these {i,j}: {145, 18526}, {3534, 20049}, {3633, 18481}, {10680, 54177}, {12702, 20050}, {34748, 50818}
X(61295) = reflection of X(i) in X(j) for these {i,j}: {5, 1483}, {10, 32900}, {550, 944}, {1483, 37727}, {3625, 13624}, {3627, 1482}, {3845, 3241}, {5690, 5882}, {5881, 5901}, {11698, 1317}, {12245, 548}, {12645, 140}, {18242, 32905}, {18480, 3635}, {21850, 51147}, {22791, 3244}, {31145, 12100}, {37705, 1}, {47745, 15178}, {50823, 3655}, {50831, 34748}, {51118, 58240}, {59400, 7967}
X(61295) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 37705, 5}, {10, 32900, 50824}, {140, 12645, 59400}, {145, 50818, 18526}, {355, 10283, 5}, {496, 11698, 5}, {944, 20050, 12702}, {1317, 37706, 496}, {1385, 38112, 14869}, {1483, 37705, 1}, {1484, 10942, 5}, {1484, 11698, 39692}, {3625, 5882, 13624}, {3625, 13624, 5690}, {3655, 50823, 17504}, {5790, 51700, 55856}, {5881, 5901, 38138}, {5881, 7988, 355}, {5901, 38138, 5}, {7967, 12645, 140}, {10283, 38138, 7988}, {15178, 47745, 38042}, {18480, 51087, 3635}, {18526, 34748, 145}, {20057, 34627, 18493}, {37624, 59388, 3628}, {37707, 37734, 495}

X(61296) = X(1)X(5)∩X(2)X(13607)

Barycentrics    5*a^4 - 5*a^3*b - 3*a^2*b^2 + 5*a*b^3 - 2*b^4 - 5*a^3*c + 10*a^2*b*c - 5*a*b^2*c - 3*a^2*c^2 - 5*a*b*c^2 + 4*b^2*c^2 + 5*a*c^3 - 2*c^4 : :
X(61296) = 5 X[1] - 4 X[5], 3 X[1] - 2 X[355], 3 X[1] - 4 X[1483], 4 X[1] - 3 X[5587], 7 X[1] - 6 X[5886], 9 X[1] - 8 X[5901], 11 X[1] - 9 X[7988], 9 X[1] - 7 X[7989], 6 X[1] - 5 X[8227], 8 X[1] - 7 X[9624], 13 X[1] - 12 X[10283], 11 X[1] - 8 X[18357], 7 X[1] - 4 X[37705], 5 X[1] - 3 X[37712], 7 X[1] - 5 X[37714], and many others

X(61296) lies on these lines: {1, 5}, {2, 13607}, {3, 3632}, {4, 3244}, {8, 3523}, {10, 3525}, {20, 20050}, {30, 11531}, {40, 376}, {84, 12703}, {98, 28548}, {100, 59332}, {104, 8715}, {140, 30392}, {145, 515}, {150, 25716}, {165, 33923}, {381, 33179}, {382, 11278}, {516, 49138}, {517, 1657}, {549, 50804}, {551, 5818}, {572, 4007}, {631, 3626}, {912, 5697}, {946, 3241}, {950, 5811}, {956, 10902}, {958, 34486}, {993, 15862}, {1000, 4314}, {1064, 50637}, {1071, 3880}, {1125, 59388}, {1158, 3895}, {1159, 4355}, {1385, 3679}, {1420, 10573}, {1482, 3830}, {1512, 49627}, {1698, 10246}, {1699, 10222}, {2077, 3913}, {2098, 3586}, {2099, 9613}, {2800, 3885}, {2948, 12898}, {2975, 59331}, {3057, 5693}, {3090, 3636}, {3091, 20057}, {3158, 49169}, {3208, 58036}, {3242, 39885}, {3243, 60895}, {3333, 3476}, {3340, 45287}, {3486, 31393}, {3522, 20054}, {3524, 34641}, {3526, 38176}, {3529, 28228}, {3543, 51077}, {3555, 37625}, {3601, 12647}, {3616, 46936}, {3617, 10165}, {3621, 5731}, {3622, 10175}, {3623, 3854}, {3624, 5790}, {3625, 5657}, {3635, 5603}, {3640, 6280}, {3641, 6279}, {3653, 51066}, {3654, 16192}, {3655, 4677}, {3656, 14893}, {3680, 5553}, {3689, 36972}, {3746, 22758}, {3845, 51094}, {3860, 51097}, {3871, 5450}, {3872, 5178}, {3889, 31870}, {3890, 20117}, {3893, 31788}, {4298, 11041}, {4668, 12108}, {4678, 54445}, {4701, 10164}, {4816, 9588}, {4857, 37821}, {4915, 8726}, {5010, 32153}, {5048, 9614}, {5059, 28232}, {5067, 15808}, {5071, 50801}, {5128, 21578}, {5176, 56387}, {5204, 36920}, {5251, 16202}, {5258, 10267}, {5270, 37820}, {5290, 50194}, {5550, 31399}, {5563, 11499}, {5687, 37561}, {5734, 18483}, {5768, 12437}, {5777, 5919}, {5789, 24929}, {5817, 43179}, {5836, 15016}, {5840, 26726}, {5844, 7991}, {5854, 12119}, {5855, 54422}, {5884, 14923}, {5887, 41864}, {6253, 34749}, {6261, 36846}, {6765, 38455}, {6788, 13625}, {6796, 54391}, {6906, 25439}, {6924, 37587}, {6996, 29605}, {7280, 32141}, {7397, 49765}, {7705, 50890}, {7962, 10572}, {7966, 36922}, {7984, 12407}, {8148, 9589}, {8192, 15177}, {8666, 11491}, {9041, 51136}, {9336, 34460}, {9549, 44039}, {9579, 25415}, {9580, 30323}, {9583, 49232}, {9612, 11011}, {9625, 9798}, {9837, 12644}, {9848, 9957}, {9956, 15703}, {10039, 13384}, {10085, 49163}, {10106, 11529}, {10124, 19875}, {10172, 46934}, {10247, 11522}, {10248, 31673}, {10284, 40266}, {10310, 30283}, {10444, 17377}, {10532, 18406}, {10595, 19925}, {10680, 44425}, {10785, 45701}, {10786, 45700}, {10896, 33176}, {10914, 12675}, {11010, 24467}, {11012, 12513}, {11014, 12625}, {11037, 14563}, {11180, 51089}, {11224, 12699}, {11260, 33597}, {11274, 50907}, {11715, 12531}, {11826, 47746}, {11843, 49556}, {11844, 49555}, {12000, 18761}, {12001, 18491}, {12102, 16189}, {12263, 22713}, {12331, 32612}, {12629, 16132}, {12649, 52026}, {12650, 37569}, {12678, 12700}, {12688, 13600}, {12704, 36977}, {12773, 26285}, {13253, 52860}, {13893, 35763}, {13947, 35762}, {14217, 25416}, {14912, 49536}, {15570, 38150}, {15600, 53599}, {15692, 50827}, {15702, 38098}, {15705, 31145}, {15718, 50821}, {15720, 31662}, {15722, 38066}, {15803, 41687}, {16125, 34195}, {16236, 50193}, {18421, 18990}, {18519, 37622}, {18544, 52850}, {18908, 58679}, {19647, 50001}, {19710, 34628}, {20008, 54051}, {20014, 31730}, {20049, 20070}, {20053, 59417}, {20420, 36867}, {21740, 22837}, {21842, 31231}, {24928, 54134}, {25440, 38665}, {28174, 58245}, {28208, 48661}, {28538, 50973}, {29010, 49498}, {31434, 34471}, {31663, 34718}, {32537, 56177}, {33697, 58240}, {34200, 50830}, {34595, 38042}, {34631, 51096}, {34648, 51091}, {35404, 50831}, {35514, 43181}, {36698, 49770}, {37618, 41684}, {38028, 55862}, {38036, 42871}, {38064, 50953}, {38068, 51072}, {38074, 51103}, {38076, 51107}, {38154, 42819}, {38460, 40257}, {39605, 48856}, {41099, 51095}, {47599, 51700}, {50789, 54169}, {52769, 59414}

X(61296) = midpoint of X(i) and X(j) for these {i,j}: {20, 20050}, {36977, 54177}
X(61296) = reflection of X(i) in X(j) for these {i,j}: {1, 37727}, {4, 3244}, {8, 5882}, {40, 944}, {355, 1483}, {376, 51082}, {381, 51087}, {382, 11278}, {2948, 12898}, {3543, 51077}, {3621, 11362}, {3632, 3}, {3893, 31788}, {4677, 3655}, {5691, 1482}, {5693, 3057}, {5881, 1}, {6326, 7972}, {6788, 13625}, {7982, 145}, {7991, 18481}, {9589, 8148}, {9897, 12737}, {10914, 12675}, {11180, 51089}, {12245, 4297}, {12407, 7984}, {12531, 11715}, {12645, 1385}, {12688, 13600}, {12704, 36977}, {12751, 1317}, {14217, 25416}, {14872, 9957}, {14923, 5884}, {17857, 37738}, {18525, 10222}, {31145, 51705}, {31162, 51093}, {33697, 58240}, {34627, 51071}, {34631, 51096}, {34648, 51091}, {36922, 7966}, {37625, 3555}, {39885, 3242}, {40266, 10284}, {41869, 7982}, {47745, 13607}, {50789, 54169}, {50804, 549}, {50817, 376}, {50830, 34200}, {50871, 381}, {50907, 11274}, {51093, 34748}, {54134, 24928}
X(61296) = anticomplement of X(47745)
X(61296) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 80, 50443}, {1, 355, 8227}, {1, 1837, 37704}, {1, 5531, 45770}, {1, 5534, 6326}, {1, 5587, 9624}, {1, 5726, 37737}, {1, 5881, 5587}, {1, 7989, 5901}, {1, 9897, 10826}, {1, 37706, 5727}, {1, 37707, 37709}, {1, 37708, 9578}, {1, 37710, 5219}, {1, 37711, 9581}, {1, 37712, 5}, {1, 37714, 5886}, {4, 3244, 16200}, {8, 3523, 38127}, {8, 5882, 3576}, {40, 944, 50811}, {119, 32214, 37720}, {355, 1483, 1}, {355, 5901, 7989}, {355, 8227, 5587}, {355, 37727, 1483}, {944, 12245, 4297}, {1317, 1837, 1}, {1385, 3679, 31423}, {1385, 12645, 3679}, {1482, 5691, 31162}, {3621, 5731, 11362}, {3623, 59387, 13464}, {3636, 38155, 3090}, {3655, 5690, 7987}, {3871, 38669, 5450}, {4297, 12245, 40}, {4668, 30389, 26446}, {4677, 7987, 5690}, {4816, 9588, 59503}, {5252, 37734, 1}, {5534, 37706, 5881}, {5691, 51093, 1482}, {5727, 6326, 5587}, {5731, 11362, 35242}, {5790, 15178, 3624}, {5881, 8227, 355}, {5886, 37705, 37714}, {5901, 7989, 8227}, {7972, 37706, 1}, {9956, 37624, 25055}, {10222, 18525, 1699}, {10247, 18480, 11522}, {10595, 19925, 38021}, {10595, 34627, 19925}, {10942, 37726, 7741}, {10944, 37740, 1}, {10950, 37738, 1}, {11373, 12735, 1}, {12512, 50810, 40}, {12751, 37704, 5587}, {13607, 47745, 2}, {13624, 59503, 9588}, {19925, 51071, 10595}, {26470, 32213, 37719}, {34627, 51071, 38021}, {37624, 50798, 9956}, {38098, 51085, 15702}, {50817, 51082, 50811}

X(61297) = X(1)X(5)∩X(8)X(3530)

Barycentrics    12*a^4 - 12*a^3*b - 7*a^2*b^2 + 12*a*b^3 - 5*b^4 - 12*a^3*c + 24*a^2*b*c - 12*a*b^2*c - 7*a^2*c^2 - 12*a*b*c^2 + 10*b^2*c^2 + 12*a*c^3 - 5*c^4 : :
X(61297) = 6 X[1] - 5 X[5], 7 X[1] - 5 X[355], and many others

X(61297) lies on these lines: {1, 5}, {3, 31145}, {4, 34748}, {8, 3530}, {20, 5844}, {30, 47536}, {140, 53620}, {145, 382}, {519, 550}, {546, 3241}, {548, 944}, {549, 4669}, {631, 4678}, {632, 3828}, {1385, 4691}, {1482, 3853}, {3146, 50805}, {3526, 7967}, {3528, 3621}, {3529, 20049}, {3544, 50797}, {3617, 55863}, {3623, 3855}, {3625, 58219}, {3627, 4301}, {3628, 50798}, {3633, 28174}, {3635, 38034}, {3655, 9588}, {3679, 14869}, {3832, 10247}, {3845, 10222}, {3850, 34627}, {3856, 5603}, {3857, 13464}, {3859, 59387}, {3861, 5734}, {4677, 17504}, {4701, 5690}, {5067, 37624}, {5070, 51700}, {5073, 34631}, {5731, 58190}, {5790, 48154}, {7991, 15686}, {8148, 33703}, {8715, 51529}, {9589, 28186}, {10031, 13747}, {10246, 16239}, {11362, 31663}, {11522, 23046}, {11531, 28190}, {11563, 47491}, {12102, 50864}, {12245, 15696}, {12605, 34667}, {12812, 38074}, {13607, 19878}, {14269, 51092}, {15178, 19883}, {15646, 47490}, {15687, 51093}, {15699, 51108}, {15717, 59503}, {17800, 28212}, {18553, 50998}, {22791, 28236}, {28216, 49138}, {31454, 35842}, {32900, 38028}, {33923, 34718}, {34641, 50822}, {35018, 38314}, {38071, 51071}, {38137, 42871}, {41991, 50871}, {43174, 45759}, {44245, 50810}, {44267, 47489}, {49136, 50872}, {50804, 50826}

X(61297) = reflection of X(i) in X(j) for these {i,j}: {5, 37727}, {15687, 51093}, {37705, 1483}, {44267, 47489}, {47745, 32900}
X(61297) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 37727, 1483}, {1483, 37705, 10283}, {1483, 38138, 1}, {4701, 17502, 5690}, {5734, 18525, 3861}, {5901, 37714, 5}, {9624, 18357, 5}, {11362, 34773, 46853}, {12645, 58230, 4678}, {32900, 47745, 38028}

X(61298) = X(5)X(39494)∩X(1116)X(10224)

Barycentrics    (b-c)*(b+c)*(a^2*b^2*(a^2-b^2)^4*(a^2+b^2)+(a^2-b^2)^2*(a^8-3*a^2*b^6-b^8)*c^2+(-3*a^10+a^8*b^2+6*a^6*b^4-4*a^4*b^6+3*b^10)*c^4+(2*a^8-3*a^6*b^2-4*a^4*b^4-2*b^8)*c^6+(2*a^6+5*a^4*b^2-2*b^6)*c^8-(3*a^4+a^2*b^2-3*b^4)*c^10+(a-b)*(a+b)*c^12) : :

See Antreas Hatzipolakis and Ivan Pavlov, euclid 6029.

X(61298) lies on these lines: {5, 39494}, {1116, 10224}, {1594, 39512}, {10280, 39503}, {11615, 39509}, {18308, 50136}, {32478, 33332}

X(61299) = X(26)X(1853)∩X(30)X(511)

Barycentrics    2*a^10+a^6*(b^2-c^2)^2-4*a^8*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)+a^2*(b^2-c^2)^2*(b^4+3*b^2*c^2+c^4)+a^4*(b^6+2*b^4*c^2+2*b^2*c^4+c^6) : :

See Antreas Hatzipolakis and Ivan Pavlov, euclid 6029.

X(61299) lies on these lines: {4, 13353}, {5, 22352}, {22, 34514}, {23, 15027}, {26, 1853}, {30, 511}, {52, 45732}, {125, 37936}, {140, 13419}, {143, 7553}, {146, 46445}, {154, 31181}, {156, 11206}, {186, 38728}, {265, 37925}, {382, 7592}, {428, 13364}, {546, 44829}, {548, 45286}, {1495, 37938}, {1533, 44283}, {1658, 23329}, {2937, 34826}, {3530, 17712}, {3627, 11750}, {3853, 15807}, {5073, 12174}, {5189, 22115}, {5498, 46265}, {5876, 16659}, {5899, 13171}, {5946, 7540}, {6723, 44900}, {6756, 12006}, {7502, 11550}, {7514, 36990}, {7555, 21243}, {7574, 14157}, {7575, 38729}, {7728, 46440}, {7748, 39524}, {10096, 32237}, {10113, 47096}, {10116, 14449}, {10192, 13371}, {10193, 15331}, {10263, 11264}, {10540, 20125}, {10610, 15559}, {10627, 12134}, {11455, 18564}, {11565, 12241}, {11695, 13163}, {11818, 46264}, {11819, 13630}, {12046, 23411}, {12107, 20299}, {12121, 37944}, {12140, 37931}, {12168, 35452}, {12278, 17800}, {12362, 45958}, {12605, 32137}, {13292, 16982}, {13363, 13490}, {13421, 32358}, {13451, 43573}, {13565, 34002}, {13598, 45970}, {13851, 43893}, {14791, 31383}, {14927, 18420}, {15061, 37940}, {15088, 37942}, {15761, 23324}, {16621, 52073}, {16655, 45959}, {16881, 18128}, {17714, 18381}, {18282, 32767}, {18403, 51548}, {18572, 51403}, {19154, 23327}, {20379, 47342}, {20396, 37897}, {21849, 45969}, {21969, 45730}, {22251, 51393}, {23325, 44278}, {23328, 48368}, {23332, 44213}, {23335, 32171}, {31305, 32140}, {33533, 46448}, {35018, 44862}, {37924, 50435}, {40111, 51360}, {45186, 45731}, {45971, 46850}, {47341, 51425}, {52397, 54042}

X(61299) = pole of line {125, 15026} with respect to the Jerabek hyperbola
X(61299) = pole of line {110, 7525} with respect to the Stammler hyperbola
X(61299) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {30, 1503, 1154}, {10263, 34224, 11264}, {10540, 46450, 51391}, {11264, 34224, 45734}, {29012, 44407, 30}

X(61300) = X(51)X(476)∩X(511)X(930)

Barycentrics    a^2*(a^2*b^2*(a^2-b^2)^4-2*a^2*b^2*(a^2-b^2)^2*(a^2+b^2)*c^2+(a^8+2*a^6*b^2+2*a^2*b^6+b^8)*c^4-(a^2+b^2)*(3*a^4+a^2*b^2+3*b^4)*c^6+(3*a^4+4*a^2*b^2+3*b^4)*c^8-(a^2+b^2)*c^10)*(a^10*c^2-b^4*c^2*(b^2-c^2)^3+a^8*(b^4-2*b^2*c^2-4*c^4)+a^6*(-3*b^6+2*b^4*c^2+2*b^2*c^4+6*c^6)+a^4*(3*b^8-4*b^6*c^2+2*b^2*c^6-4*c^8)-a^2*(b-c)*(b+c)*(b^8-3*b^6*c^2+b^4*c^4-b^2*c^6+c^8)) : :

See Antreas Hatzipolakis and Ivan Pavlov, euclid 6029.

X(61300) lies on the circumcircle and these lines: {51, 476}, {98, 1510}, {99, 1154}, {511, 930}, {512, 1141}, {567, 691}, {933, 34397}, {1291, 5012}, {2715, 2965}, {22456, 32002}, {46966, 54034}

X(61300) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(51), X(512)}}, {{A, B, C, X(74), X(98)}}, {{A, B, C, X(187), X(567)}}, {{A, B, C, X(249), X(288)}}, {{A, B, C, X(511), X(1510)}}, {{A, B, C, X(1157), X(5012)}}, {{A, B, C, X(2065), X(57639)}}, {{A, B, C, X(14587), X(50946)}} and {{A, B, C, X(51480), X(52179)}}



leftri

Vertex Square Sum and Product: X(61301)-X(61418)

rightri

This preamble and centers X(61301)-X(61418) were contributed by Ivan Pavlov on Jan 31, 2024.

Given a reference triangle ABC, for any central triangle XYZ the barycentric sum X^2+Y^2+Z^2 is a triangle center. We call this expression the vertex square sum of XYZ. A curious example is that the vertex square sum of the anticevian triangle of a point P is P^2. Some other examples:

We call the barycentric product X*Y*Z the vertex product of XYZ. Note that the vertex product of the anticevian triangle of a point P is P^3.

X(61301) = VERTEX SQUARE SUM OF ABC-X3 REFLECTIONS TRIANGLE

Barycentrics    9*a^8+(b^2-c^2)^4-16*a^6*(b^2+c^2)+2*a^4*(3*b^2+c^2)*(b^2+3*c^2) : :

X(61301) lies on these lines: {2, 340}, {3, 40138}, {4, 54660}, {5, 3087}, {6, 631}, {20, 393}, {53, 33703}, {95, 51171}, {216, 15717}, {376, 1990}, {548, 59657}, {590, 19039}, {615, 19040}, {1249, 3528}, {3090, 6749}, {3108, 52188}, {3163, 10304}, {3523, 5158}, {3524, 5702}, {3526, 38292}, {3543, 61315}, {3839, 61327}, {3855, 6748}, {5056, 61340}, {5063, 5286}, {5065, 5319}, {5067, 40065}, {5070, 33636}, {5304, 33871}, {7493, 52418}, {7735, 30739}, {11063, 61128}, {15526, 52711}, {15640, 36430}, {15696, 42459}, {16310, 43448}, {19053, 55889}, {19054, 55884}, {21734, 22052}, {21843, 40135}, {32787, 55895}, {32788, 55899}, {34828, 56013}, {36751, 61138}, {36841, 53021}, {37067, 59373}, {40884, 52710}, {45245, 58188}, {46853, 59649}, {49140, 61314}

X(61301) = pole of line {3090, 11425} with respect to the Kiepert hyperbola
X(61301) = pole of line {5158, 6509} with respect to the Stammler hyperbola
X(61301) = pole of line {32828, 37638} with respect to the Wallace hyperbola
X(61301) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1105), X(54660)}}, {{A, B, C, X(41890), X(56266)}}, {{A, B, C, X(43530), X(46952)}}
X(61301) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3524, 5702, 52703}

X(61302) = VERTEX SQUARE SUM OF ANTI-AQUILA TRIANGLE

Barycentrics    6*a^2+4*a*(b+c)+(b+c)^2 : :

X(61302) lies on these lines: {1, 3943}, {2, 4969}, {6, 3616}, {8, 61313}, {10, 1100}, {37, 3636}, {44, 551}, {45, 3622}, {69, 25503}, {86, 17366}, {141, 29614}, {145, 594}, {329, 19748}, {524, 17250}, {572, 22791}, {597, 16826}, {604, 3649}, {1086, 26626}, {1125, 4700}, {1213, 1449}, {1266, 4670}, {1404, 15950}, {1698, 50131}, {2325, 39260}, {2345, 20057}, {3241, 61321}, {3285, 8025}, {3589, 17244}, {3623, 26039}, {3629, 17322}, {3630, 17326}, {3631, 17400}, {3632, 17303}, {3634, 4982}, {3635, 5750}, {3686, 19878}, {3707, 15808}, {3723, 4029}, {3758, 49742}, {3759, 6707}, {3834, 17023}, {3898, 21864}, {3945, 26104}, {3986, 16671}, {4080, 19741}, {4273, 28619}, {4285, 49997}, {4364, 20072}, {4370, 16672}, {4389, 17045}, {4393, 4472}, {4395, 41847}, {4409, 35578}, {4415, 19722}, {4422, 29570}, {4470, 50120}, {4665, 29584}, {4667, 41311}, {4687, 6329}, {4688, 4758}, {4727, 51071}, {4747, 49747}, {4748, 15534}, {4798, 16834}, {4856, 31253}, {4909, 17231}, {5253, 54409}, {5257, 16668}, {5308, 47352}, {5839, 19877}, {7113, 16503}, {7227, 17393}, {7228, 17396}, {7238, 17399}, {7277, 17321}, {8584, 17256}, {9300, 29634}, {10022, 17160}, {16522, 16823}, {16590, 51108}, {16676, 51105}, {16777, 54389}, {17027, 50180}, {17230, 17381}, {17241, 51127}, {17248, 32455}, {17266, 48310}, {17289, 29619}, {17312, 51128}, {17317, 51126}, {17332, 37677}, {17337, 28639}, {17346, 25358}, {17355, 46845}, {17367, 49738}, {17387, 20582}, {17391, 34573}, {24512, 29822}, {24603, 50124}, {28337, 29593}, {29585, 61344}, {29588, 50097}, {29595, 31285}, {29604, 50125}, {29608, 50132}, {29612, 49731}, {29833, 30588}, {37654, 46934}, {40688, 42025}, {48830, 53534}

X(61302) = pole of line {28179, 47661} with respect to the Steiner circumellipse
X(61302) = pole of line {28179, 47767} with respect to the Steiner inellipse
X(61302) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 17369, 50113}, {1125, 16666, 17330}, {1125, 4700, 52706}, {2325, 51103, 39260}, {4670, 17395, 49727}, {16666, 52706, 4700}, {17045, 17379, 17365}, {29586, 46922, 4364}

X(61303) = VERTEX SQUARE SUM OF ANTI-ARA TRIANGLE

Barycentrics    (a^4-(b^2-c^2)^2)^2*(2*a^4+(b^2+c^2)^2) : :

X(61303) lies on these lines: {4, 36417}, {25, 3456}, {107, 111}, {231, 59229}, {232, 7495}, {1194, 41366}, {1506, 2207}, {1968, 16063}, {1995, 61314}, {2052, 43528}, {10301, 27376}, {14581, 54381}, {26257, 37765}, {26283, 52945}, {27371, 52905}

X(61303) = intersection, other than A, B, C, of circumconics {{A, B, C, X(111), X(3456)}}, {{A, B, C, X(7755), X(9076)}}, {{A, B, C, X(17983), X(60125)}}
X(61303) = barycentric product X(i)*X(j) for these (i, j): {393, 7820}
X(61303) = barycentric quotient X(i)/X(j) for these (i, j): {7820, 3926}

X(61304) = VERTEX SQUARE SUM OF ANTI-ARTZT TRIANGLE

Barycentrics    19*a^4+7*b^4-10*b^2*c^2+7*c^4+2*a^2*(b^2+c^2) : :

X(61304) lies on these lines: {2, 6}, {98, 3839}, {1285, 8352}, {3543, 9753}, {3767, 47617}, {3972, 7620}, {5007, 32988}, {5286, 35287}, {5305, 32985}, {5309, 35927}, {5319, 32989}, {5346, 34511}, {5355, 7618}, {5368, 32829}, {5395, 11172}, {5485, 35954}, {6055, 14853}, {6392, 8369}, {7754, 33197}, {7755, 32971}, {7812, 32972}, {7817, 32974}, {7856, 32990}, {8587, 14484}, {8596, 33187}, {8787, 44534}, {9734, 15692}, {9752, 11179}, {9939, 33180}, {10304, 47113}, {11148, 11156}, {11167, 54639}, {11842, 57634}, {14001, 59780}, {14036, 60200}, {15721, 22712}, {18842, 44543}, {21309, 37350}, {30435, 32984}, {33272, 51224}, {33748, 38227}, {35955, 46453}, {37071, 50974}, {41895, 52942}, {43537, 54487}, {50979, 58883}, {54539, 54866}, {60212, 60648}

X(61304) = intersection, other than A, B, C, of circumconics {{A, B, C, X(325), X(53101)}}, {{A, B, C, X(3620), X(11172)}}, {{A, B, C, X(5395), X(9770)}}, {{A, B, C, X(7736), X(60648)}}, {{A, B, C, X(8587), X(15589)}}, {{A, B, C, X(11163), X(54639)}}
X(61304) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 51170, 9770}, {2, 5304, 5032}, {2, 9740, 3620}, {230, 42849, 23053}, {230, 59373, 2}, {23053, 59373, 42849}

X(61305) = VERTEX SQUARE SUM OF 2ND ANTI-CONWAY TRIANGLE

Barycentrics    -2*a^6*(b^2-c^2)^2*(b^2+c^2)+a^4*(b^2-c^2)^2*(b^4-b^2*c^2+c^4)+a^8*(b^4+b^2*c^2+c^4) : :

X(61305) lies on these lines: {6, 52967}, {25, 61334}, {32, 682}, {39, 14853}, {115, 34096}, {216, 14561}, {232, 9753}, {263, 3117}, {393, 800}, {1084, 40825}, {1351, 11672}, {2548, 45210}, {5480, 54991}, {5661, 48901}, {7737, 33874}, {14651, 33885}, {15004, 40588}, {34815, 35071}, {36425, 41278}

X(61305) = pole of line {44173, 52613} with respect to the polar circle
X(61305) = intersection, other than A, B, C, of circumconics {{A, B, C, X(32), X(1093)}}, {{A, B, C, X(263), X(9792)}}, {{A, B, C, X(393), X(14575)}}, {{A, B, C, X(27369), X(52247)}}, {{A, B, C, X(33581), X(43975)}}, {{A, B, C, X(36434), X(44162)}}
X(61305) = barycentric product X(i)*X(j) for these (i, j): {25, 30258}, {32, 52247}, {51, 9792}, {14569, 43975}
X(61305) = barycentric quotient X(i)/X(j) for these (i, j): {9792, 34384}, {30258, 305}, {52247, 1502}
X(61305) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2211, 40981, 32}

X(61306) = VERTEX SQUARE SUM OF ANTI-EHRMANN-MID TRIANGLE

Barycentrics    11*a^8+8*(b^2-c^2)^4-14*a^6*(b^2+c^2)-8*a^2*(b^2-c^2)^2*(b^2+c^2)+a^4*(3*b^4+38*b^2*c^2+3*c^4) : :

X(61306) lies on these lines: {6, 50957}, {30, 53}, {376, 61314}, {393, 15708}, {1989, 33871}, {1990, 15699}, {3163, 3545}, {3284, 14269}, {5054, 18487}, {5055, 5158}, {10304, 52945}, {10979, 15707}, {15860, 19709}, {50687, 61315}

X(61306) = pole of line {15686, 18390} with respect to the Kiepert hyperbola

X(61307) = VERTEX SQUARE SUM OF ANTI-EULER TRIANGLE

Barycentrics    11*a^8+3*(b^2-c^2)^4-24*a^6*(b^2+c^2)-8*a^2*(b^2-c^2)^2*(b^2+c^2)+2*a^4*(9*b^4+14*b^2*c^2+9*c^4) : :

X(61307) lies on circumconic {{A, B, C, X(1217), X(57822)}} and on these lines: {2, 340}, {3, 393}, {6, 3525}, {20, 61315}, {53, 17538}, {577, 3091}, {631, 40138}, {1990, 3524}, {3087, 3090}, {3163, 15708}, {3529, 36748}, {3543, 61327}, {3544, 6748}, {3628, 15905}, {5067, 6749}, {5158, 10303}, {5286, 7550}, {5306, 52188}, {5702, 15702}, {7772, 46952}, {10304, 52945}, {12108, 59657}, {15692, 61312}, {15697, 36430}, {15705, 18487}, {15860, 36413}, {22052, 50693}, {33871, 37689}, {36412, 50688}, {38292, 55858}, {40065, 60781}

X(61307) = pole of line {32838, 37638} with respect to the Wallace hyperbola

X(61308) = VERTEX SQUARE SUM OF ANTI-INNER-GREBE TRIANGLE

Barycentrics    11*a^4-(b^2-c^2)^2+2*a^2*(b^2+c^2-4*S) : :

X(61308) lies on these lines: {6, 376}, {32, 7586}, {1132, 7755}, {1270, 7820}, {1271, 61311}, {3053, 43510}, {3068, 6424}, {3593, 61310}, {5008, 61322}, {5286, 6561}, {5306, 23273}, {5418, 31407}, {6419, 49038}, {6564, 44596}, {7585, 61328}, {7735, 13785}, {7736, 35255}, {7737, 61323}, {7747, 43507}, {7753, 8972}, {7772, 43512}, {8253, 31404}, {8376, 26457}, {9300, 43509}, {9542, 9675}, {12963, 31400}, {13941, 61329}, {18512, 18907}, {19054, 58803}, {41411, 44597}, {43448, 52666}, {44595, 61389}

X(61309) = VERTEX SQUARE SUM OF ANTI-OUTER-GREBE TRIANGLE

Barycentrics    11*a^4-(b^2-c^2)^2+2*a^2*(b^2+c^2+4*S) : :

X(61309) lies on these lines: {6, 376}, {32, 7585}, {1131, 7755}, {1270, 61310}, {1271, 7820}, {3053, 43509}, {3069, 6423}, {3595, 61311}, {5008, 61323}, {5286, 6560}, {5306, 23267}, {5420, 31407}, {6420, 49039}, {6565, 44595}, {7586, 61329}, {7735, 13665}, {7736, 35256}, {7737, 61322}, {7747, 43508}, {7753, 13941}, {7772, 43511}, {8252, 31404}, {8375, 26462}, {8972, 61328}, {9300, 43510}, {12968, 31400}, {18510, 18907}, {19053, 58804}, {31403, 41411}, {41410, 44594}, {43448, 52667}, {44596, 61388}

X(61310) = VERTEX SQUARE SUM OF 1ST ANTI-KENMOTU CENTERS TRIANGLE

Barycentrics    (a^2+2*b^2)*(a^2+2*c^2)+4*(b^2+c^2)*S : :

X(61310) lies on these lines: {32, 492}, {69, 61328}, {141, 5475}, {371, 7874}, {639, 7867}, {1270, 61309}, {3593, 61308}, {3763, 13785}, {5490, 7755}, {5590, 7820}, {9675, 45472}, {26361, 31274}, {32805, 61329}, {32812, 32977}

X(61311) = VERTEX SQUARE SUM OF 2ND ANTI-KENMOTU CENTERS TRIANGLE

Barycentrics    (a^2+2*b^2)*(a^2+2*c^2)-4*(b^2+c^2)*S : :

X(61311) lies on these lines: {32, 491}, {69, 61329}, {141, 5475}, {372, 7874}, {640, 7867}, {1271, 61308}, {3595, 61309}, {3763, 13665}, {5491, 7755}, {5591, 7820}, {26362, 31274}, {32806, 61328}, {32813, 32977}

X(61312) = VERTEX SQUARE SUM OF ANTI-X3-ABC REFLECTIONS TRIANGLE

Barycentrics    6*a^8+(b^2-c^2)^4-16*a^6*(b^2+c^2)-6*a^2*(b^2-c^2)^2*(b^2+c^2)+a^4*(15*b^4+14*b^2*c^2+15*c^4) : :

X(61312) lies on these lines: {2, 57895}, {3, 52945}, {4, 61340}, {5, 22052}, {6, 31457}, {20, 36412}, {53, 46853}, {140, 52704}, {216, 3530}, {233, 3526}, {376, 61327}, {549, 3284}, {571, 9698}, {577, 631}, {1990, 12100}, {3163, 3524}, {3523, 5158}, {6748, 16239}, {6749, 14869}, {7755, 50660}, {8589, 16310}, {10304, 61315}, {10979, 15717}, {15515, 46262}, {15606, 50671}, {15692, 61307}, {15693, 52703}, {17504, 18487}, {19708, 36430}, {21843, 33871}, {36751, 59655}

X(61312) = pole of line {12812, 37505} with respect to the Kiepert hyperbola

X(61313) = VERTEX SQUARE SUM OF AQUILA TRIANGLE

Barycentrics    3*a^2+4*a*(b+c)+4*(b+c)^2 : :

X(61313) lies on these lines: {2, 3943}, {6, 10}, {8, 61302}, {44, 19875}, {45, 1698}, {75, 25503}, {145, 17398}, {474, 59235}, {594, 3616}, {599, 4472}, {1100, 4668}, {1125, 50087}, {1213, 46932}, {1266, 17325}, {1268, 17259}, {2321, 19878}, {2345, 16675}, {3624, 16777}, {3632, 16884}, {3634, 17281}, {3636, 17299}, {3739, 49533}, {3763, 34824}, {3828, 24693}, {3834, 17308}, {4029, 31253}, {4361, 29614}, {4363, 17250}, {4389, 17118}, {4413, 19297}, {4670, 15533}, {4675, 50993}, {4708, 49721}, {4727, 25055}, {4758, 50076}, {4873, 19872}, {4969, 53620}, {5224, 31300}, {5550, 50113}, {5936, 17366}, {7227, 20073}, {9709, 54409}, {9780, 17369}, {15668, 17230}, {16676, 19876}, {17244, 17293}, {17251, 20072}, {17289, 20181}, {17290, 29608}, {17313, 29591}, {17330, 26039}, {17349, 32089}, {17354, 60710}, {17381, 43985}, {25358, 50107}, {26077, 27164}, {29576, 61344}, {29585, 61343}, {29596, 31244}, {29603, 50120}, {29619, 48630}, {32101, 37677}, {48809, 49701}, {48851, 49699}, {52716, 59519}

X(61313) = perspector of circumconic {{A, B, C, X(835), X(58128)}}
X(61313) = pole of line {145, 4205} with respect to the Kiepert hyperbola
X(61313) = pole of line {28209, 47659} with respect to the Steiner circumellipse
X(61313) = pole of line {6590, 28209} with respect to the Steiner inellipse
X(61313) = pole of line {3828, 4657} with respect to the dual conic of Yff parabola
X(61313) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2214), X(40434)}}, {{A, B, C, X(43531), X(55955)}}
X(61313) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 61321, 16672}, {17327, 28604, 17118}, {26039, 46933, 17330}, {46932, 54389, 1213}

X(61314) = VERTEX SQUARE SUM OF EHRMANN-MID TRIANGLE

Barycentrics    2*a^8+3*(b^2-c^2)^4-2*a^2*(b^2-c^2)^2*(b^2+c^2)+a^4*(-3*b^4+10*b^2*c^2-3*c^4) : :

X(61314) lies on circumconic {{A, B, C, X(14860), X(17505)}} and on these lines: {3, 52945}, {4, 3163}, {5, 18487}, {6, 17505}, {53, 3284}, {216, 3628}, {233, 5079}, {376, 61306}, {393, 3091}, {546, 1990}, {577, 3529}, {1989, 7545}, {1995, 61303}, {3018, 7747}, {3090, 61327}, {6103, 14002}, {7749, 47322}, {7772, 46257}, {12812, 52704}, {13621, 52166}, {14869, 42459}, {15816, 46686}, {16303, 39565}, {16310, 35007}, {36427, 50691}, {40138, 50689}, {49140, 61301}, {60781, 61340}

X(61314) = pole of line {3853, 13568} with respect to the Kiepert hyperbola
X(61314) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {393, 61315, 5158}, {546, 1990, 15860}, {5158, 61315, 36412}

X(61315) = VERTEX SQUARE SUM OF EULER TRIANGLE

Barycentrics    a^8+8*a^4*b^2*c^2+3*(b^2-c^2)^4-4*a^2*(b^2-c^2)^2*(b^2+c^2) : :

X(61315) lies on these lines: {2, 36430}, {3, 53}, {4, 3284}, {5, 52703}, {6, 546}, {20, 61307}, {50, 43618}, {216, 3090}, {233, 15022}, {381, 1990}, {393, 3091}, {577, 3146}, {632, 36751}, {1249, 15860}, {1989, 11818}, {2165, 13861}, {2549, 31861}, {3003, 43620}, {3087, 50689}, {3163, 3839}, {3543, 61301}, {3545, 18487}, {3628, 42459}, {3832, 40138}, {3843, 6749}, {5071, 52704}, {5076, 15905}, {5702, 41099}, {6389, 56022}, {7737, 16310}, {8797, 58454}, {10303, 10979}, {10304, 61312}, {11063, 12106}, {12811, 59649}, {13351, 18367}, {15704, 36748}, {17538, 22052}, {18323, 47144}, {18424, 40135}, {18571, 47275}, {33871, 43448}, {34288, 46030}, {50687, 61306}

X(61315) = pole of line {382, 13568} with respect to the Kiepert hyperbola
X(61315) = intersection, other than A, B, C, of circumconics {{A, B, C, X(14860), X(32533)}}, {{A, B, C, X(41891), X(55982)}}
X(61315) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5158, 36412, 3091}, {5158, 61314, 393}, {36412, 61314, 5158}, {36430, 61327, 52945}, {52945, 61327, 2}

X(61316) = VERTEX SQUARE SUM OF EXTOUCH TRIANGLE

Barycentrics    a^2*(-a+b+c)^2*(b^2+c^2) : :

X(61316) lies on these lines: {1, 25061}, {9, 21795}, {37, 40940}, {38, 39}, {63, 6184}, {200, 14936}, {210, 16588}, {220, 1260}, {346, 59761}, {480, 30706}, {518, 23653}, {800, 3949}, {968, 1500}, {1196, 21830}, {1334, 20967}, {1575, 24177}, {2340, 20229}, {3681, 23988}, {3683, 40599}, {3688, 40972}, {3693, 56078}, {3730, 20760}, {3917, 46148}, {5364, 20683}, {5741, 42723}, {20247, 25888}, {20684, 23638}, {25100, 26102}, {28070, 35508}

X(61316) = X(i)-isoconjugate-of-X(j) for these {i, j}: {82, 279}, {83, 269}, {251, 1088}, {308, 1106}, {479, 56245}, {658, 18108}, {934, 10566}, {1014, 18097}, {1119, 34055}, {1176, 1847}, {1407, 3112}, {1427, 52394}, {1435, 1799}, {3668, 52376}, {4566, 39179}, {4577, 7216}, {4593, 7250}, {4616, 55240}, {4628, 59941}, {4635, 18105}, {4637, 58784}, {7045, 61404}, {7099, 46104}, {7177, 32085}, {18087, 61373}, {18833, 52410}, {46289, 57792}
X(61316) = X(i)-Dao conjugate of X(j) for these {i, j}: {39, 57792}, {141, 279}, {6552, 308}, {6600, 83}, {14714, 10566}, {17115, 61404}, {24771, 3112}, {34452, 1407}, {40585, 1088}, {55050, 7250}
X(61316) = X(i)-Ceva conjugate of X(j) for these {i, j}: {7256, 4524}, {33299, 3688}
X(61316) = pole of line {279, 52376} with respect to the Stammler hyperbola
X(61316) = pole of line {1407, 57792} with respect to the Wallace hyperbola
X(61316) = intersection, other than A, B, C, of circumconics {{A, B, C, X(38), X(2328)}}, {{A, B, C, X(39), X(40972)}}, {{A, B, C, X(220), X(3954)}}, {{A, B, C, X(346), X(14827)}}
X(61316) = barycentric product X(i)*X(j) for these (i, j): {100, 58335}, {141, 220}, {200, 38}, {312, 40972}, {346, 39}, {1021, 35309}, {1043, 21035}, {1253, 1930}, {1260, 427}, {1265, 1843}, {1401, 5423}, {1802, 20883}, {1964, 341}, {2084, 7258}, {2287, 3954}, {2530, 4578}, {3005, 7256}, {3051, 59761}, {3239, 46148}, {3665, 480}, {3688, 8}, {3703, 55}, {3900, 4553}, {3917, 7046}, {3933, 7071}, {3939, 48278}, {4020, 7101}, {4163, 46153}, {4524, 4576}, {4528, 46162}, {4568, 657}, {7259, 8061}, {14827, 8024}, {14936, 61406}, {15523, 2328}, {16696, 4515}, {17187, 4082}, {17442, 3692}, {21016, 2327}, {21123, 6558}, {33299, 9}
X(61316) = barycentric quotient X(i)/X(j) for these (i, j): {38, 1088}, {39, 279}, {141, 57792}, {200, 3112}, {220, 83}, {341, 18833}, {346, 308}, {657, 10566}, {688, 7250}, {1253, 82}, {1260, 1799}, {1334, 18097}, {1401, 479}, {1634, 4616}, {1802, 34055}, {1843, 1119}, {1923, 1106}, {1964, 269}, {2084, 7216}, {2328, 52394}, {2530, 59941}, {3022, 18101}, {3051, 1407}, {3665, 57880}, {3688, 7}, {3703, 6063}, {3917, 7056}, {3954, 1446}, {4020, 7177}, {4082, 56251}, {4171, 18070}, {4515, 56186}, {4524, 58784}, {4553, 4569}, {4568, 46406}, {6602, 56245}, {7046, 46104}, {7071, 32085}, {7256, 689}, {7258, 37204}, {7259, 4593}, {8012, 18087}, {8641, 18108}, {14827, 251}, {14936, 61404}, {17442, 1847}, {20775, 7053}, {21035, 3668}, {21123, 58817}, {21814, 1427}, {27369, 1398}, {33299, 85}, {40972, 57}, {41267, 1042}, {41331, 52410}, {46148, 658}, {46153, 4626}, {48278, 52621}, {50521, 43932}, {52562, 18088}, {58335, 693}, {59761, 40016}
X(61316) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {220, 1260, 14827}

X(61317) = VERTEX SQUARE SUM OF INNER-FERMAT TRIANGLE

Barycentrics    4*a^4+(b^2-c^2)^2+a^2*(b^2+c^2-2*sqrt(3)*S) : :

X(61317) lies on these lines: {2, 6}, {4, 54485}, {14, 3767}, {15, 7739}, {32, 10653}, {61, 5319}, {62, 21157}, {376, 19781}, {393, 34534}, {617, 41753}, {2548, 37832}, {2549, 36967}, {3053, 42943}, {3458, 34288}, {5007, 37825}, {5254, 42154}, {5309, 10654}, {5334, 53430}, {5613, 7755}, {6294, 13357}, {6298, 41620}, {7737, 36969}, {7746, 42910}, {7753, 18582}, {7765, 42150}, {7772, 42152}, {9606, 43238}, {9607, 36836}, {11080, 35906}, {11648, 42085}, {14537, 41117}, {16925, 30472}, {18907, 43416}, {22331, 42148}, {22332, 42945}, {30435, 37333}, {31417, 42581}, {35007, 42151}, {36296, 61370}, {36760, 43454}, {36968, 41409}, {37171, 53441}, {39593, 42511}, {41100, 41408}, {42501, 44535}, {42940, 44518}, {42998, 52688}

X(61317) = X(i)-complementary conjugate of X(j) for these {i, j}: {54940, 2887}
X(61317) = pole of line {2, 54940} with respect to the Kiepert hyperbola
X(61317) = intersection, other than A, B, C, of circumconics {{A, B, C, X(69), X(54485)}}, {{A, B, C, X(299), X(34288)}}, {{A, B, C, X(325), X(11080)}}, {{A, B, C, X(393), X(34541)}}, {{A, B, C, X(394), X(34534)}}, {{A, B, C, X(3458), X(15066)}}
X(61317) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 16644, 9300}, {6, 230, 61331}, {6, 5306, 61318}, {3068, 3069, 34541}, {32787, 32788, 5859}, {36760, 43454, 44465}, {37640, 37641, 3180}

X(61318) = VERTEX SQUARE SUM OF OUTER-FERMAT TRIANGLE

Barycentrics    4*a^4+(b^2-c^2)^2+a^2*(b^2+c^2+2*sqrt(3)*S) : :

X(61318) lies on these lines: {2, 6}, {4, 54484}, {13, 3767}, {16, 7739}, {32, 10654}, {61, 21156}, {62, 5319}, {376, 19780}, {393, 34533}, {616, 41751}, {2548, 37835}, {2549, 36968}, {3053, 42942}, {3457, 34288}, {5007, 37824}, {5254, 42155}, {5309, 10653}, {5335, 53442}, {5617, 7755}, {6299, 41621}, {6581, 13357}, {7737, 36970}, {7746, 42911}, {7753, 18581}, {7765, 42151}, {7772, 42149}, {9606, 43239}, {9607, 36843}, {11085, 35906}, {11648, 42086}, {14537, 41118}, {16925, 30471}, {18907, 43417}, {22331, 42147}, {22332, 42944}, {30435, 37332}, {31417, 42580}, {35007, 42150}, {36297, 61371}, {36759, 43455}, {36967, 41408}, {37170, 53429}, {39593, 42510}, {41101, 41409}, {42500, 44535}, {42941, 44518}, {42999, 52689}

X(61318) = X(i)-complementary conjugate of X(j) for these {i, j}: {54939, 2887}
X(61318) = pole of line {2, 54939} with respect to the Kiepert hyperbola
X(61318) = intersection, other than A, B, C, of circumconics {{A, B, C, X(69), X(54484)}}, {{A, B, C, X(298), X(34288)}}, {{A, B, C, X(325), X(11085)}}, {{A, B, C, X(393), X(34540)}}, {{A, B, C, X(394), X(34533)}}, {{A, B, C, X(3457), X(15066)}}
X(61318) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 16645, 9300}, {6, 230, 61332}, {6, 5306, 61317}, {3068, 3069, 34540}, {32787, 32788, 5858}, {37640, 37641, 3181}

X(61319) = VERTEX SQUARE SUM OF 7TH FERMAT-DAO TRIANGLE

Barycentrics    3*a^4-(b^2-c^2)^2+3*a^2*(b^2+c^2+2*sqrt(3)*S) : :

X(61319) lies on these lines: {6, 13}, {32, 40922}, {395, 48311}, {396, 48313}, {397, 47863}, {398, 47861}, {574, 42510}, {620, 37786}, {2549, 49826}, {5008, 36769}, {5334, 31683}, {5611, 38736}, {6772, 35749}, {7603, 42599}, {7747, 41973}, {9115, 37640}, {9763, 31274}, {10611, 18581}, {11543, 47855}, {15513, 42794}, {20583, 40671}, {22513, 42998}, {36766, 43014}, {42089, 61332}, {43229, 47857}, {49947, 49953}

X(61319) = pole of line {30, 48311} with respect to the Kiepert hyperbola
X(61319) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 9112, 115}, {115, 9112, 5472}

X(61320) = VERTEX SQUARE SUM OF 8TH FERMAT-DAO TRIANGLE

Barycentrics    3*a^4-(b^2-c^2)^2+3*a^2*(b^2+c^2-2*sqrt(3)*S) : :

X(61320) lies on these lines: {6, 13}, {32, 40921}, {395, 48314}, {396, 48312}, {397, 47862}, {398, 47864}, {574, 42511}, {620, 37785}, {2549, 49827}, {5008, 41621}, {5335, 31684}, {5615, 38736}, {6775, 36327}, {7603, 42598}, {7747, 41974}, {9117, 37641}, {9761, 31274}, {10612, 18582}, {11542, 47856}, {15513, 42793}, {20583, 40672}, {22512, 42999}, {42092, 61331}, {43015, 60069}, {43228, 47858}, {49948, 49952}

X(61320) = pole of line {30, 48312} with respect to the Kiepert hyperbola
X(61320) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 9113, 115}, {115, 9113, 5471}

X(61321) = VERTEX SQUARE SUM OF OUTER-GARCIA TRIANGLE

Barycentrics    a^2+2*(b+c)^2 : :

X(61321) lies on these lines: {1, 4727}, {2, 3943}, {3, 29061}, {6, 8}, {7, 48635}, {9, 5560}, {10, 45}, {37, 1698}, {44, 3679}, {69, 7227}, {75, 3763}, {86, 17309}, {141, 17118}, {145, 26039}, {190, 17251}, {192, 17327}, {193, 4478}, {220, 7359}, {239, 47352}, {319, 6144}, {320, 599}, {344, 31285}, {346, 1213}, {524, 61343}, {536, 17308}, {572, 18526}, {894, 4445}, {966, 17340}, {1086, 21358}, {1100, 3633}, {1125, 2321}, {1268, 27268}, {1278, 17307}, {1376, 19297}, {1460, 6058}, {1575, 29827}, {1766, 18480}, {1900, 3983}, {1990, 7046}, {2228, 4492}, {2276, 30970}, {2968, 52703}, {3241, 61302}, {3244, 4058}, {3247, 34595}, {3589, 4405}, {3616, 50113}, {3617, 17330}, {3618, 4399}, {3619, 7263}, {3620, 7228}, {3622, 17314}, {3623, 17388}, {3625, 50131}, {3626, 50115}, {3632, 16666}, {3634, 4029}, {3644, 17326}, {3707, 4691}, {3712, 31477}, {3715, 8013}, {3729, 17239}, {3739, 17267}, {3741, 39966}, {3758, 15534}, {3761, 59519}, {3834, 31139}, {3875, 17385}, {3950, 16674}, {3969, 19701}, {4022, 7241}, {4034, 16669}, {4060, 4982}, {4102, 58820}, {4277, 52959}, {4286, 10479}, {4289, 16788}, {4361, 17289}, {4364, 50107}, {4370, 31722}, {4384, 6687}, {4389, 29591}, {4390, 7113}, {4431, 4657}, {4439, 48809}, {4461, 17246}, {4470, 17392}, {4472, 17316}, {4480, 4643}, {4644, 15533}, {4659, 17237}, {4664, 29610}, {4667, 50076}, {4668, 16670}, {4669, 4700}, {4670, 17294}, {4675, 29594}, {4678, 37654}, {4686, 17306}, {4688, 17284}, {4690, 50127}, {4699, 17265}, {4702, 48851}, {4726, 17304}, {4739, 17282}, {4740, 17305}, {4748, 49742}, {4751, 17268}, {4764, 17324}, {4772, 17283}, {4798, 29574}, {4898, 46845}, {4908, 16676}, {4967, 17279}, {4971, 26626}, {5043, 16549}, {5101, 8756}, {5222, 50098}, {5224, 17262}, {5227, 5356}, {5231, 8609}, {5232, 17334}, {5257, 16677}, {5275, 60459}, {5278, 6539}, {5306, 7172}, {5564, 17368}, {5687, 54409}, {5692, 21864}, {5790, 21943}, {5880, 50995}, {7229, 17365}, {7232, 17116}, {7238, 21356}, {7277, 32099}, {7321, 48634}, {9766, 30179}, {10436, 17229}, {10713, 61073}, {11679, 50052}, {13846, 56386}, {13847, 56385}, {15593, 41325}, {15668, 17233}, {16522, 49495}, {16590, 51066}, {16815, 17342}, {16832, 41310}, {17023, 50120}, {17117, 17371}, {17143, 60861}, {17151, 17384}, {17227, 51186}, {17230, 17313}, {17231, 25590}, {17238, 17255}, {17242, 28653}, {17250, 24441}, {17259, 17280}, {17264, 29576}, {17270, 17351}, {17288, 48640}, {17301, 29604}, {17310, 41847}, {17320, 25503}, {17346, 51353}, {17350, 32025}, {17353, 28634}, {17366, 32087}, {17776, 19744}, {18230, 28635}, {19722, 20017}, {19822, 37674}, {20055, 46922}, {21018, 38406}, {24603, 41313}, {25055, 39260}, {25384, 27474}, {29579, 34824}, {29583, 49738}, {29586, 50121}, {29603, 50089}, {29605, 50084}, {29613, 37756}, {29617, 51185}, {30811, 31025}, {31187, 32779}, {31995, 48632}, {34773, 59680}, {36409, 49459}, {36478, 50086}, {36534, 50790}, {37660, 51583}, {38023, 50020}, {38047, 50022}, {38087, 49772}, {38315, 50017}, {40713, 49947}, {40714, 49948}, {40940, 60267}, {48805, 49700}, {48849, 53534}, {48852, 52963}, {49483, 49509}, {49710, 50308}, {49726, 54280}, {49727, 50993}

X(61321) = reflection of X(i) in X(j) for these {i,j}: {17325, 17308}
X(61321) = perspector of circumconic {{A, B, C, X(8707), X(58128)}}
X(61321) = pole of line {29058, 57157} with respect to the circumcircle
X(61321) = pole of line {3617, 5051} with respect to the Kiepert hyperbola
X(61321) = pole of line {28209, 47660} with respect to the Steiner circumellipse
X(61321) = pole of line {28209, 47765} with respect to the Steiner inellipse
X(61321) = pole of line {16705, 26860} with respect to the Wallace hyperbola
X(61321) = pole of line {28187, 57158} with respect to the dual conic of incircle
X(61321) = pole of line {3828, 17327} with respect to the dual conic of Yff parabola
X(61321) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1220), X(5560)}}, {{A, B, C, X(2298), X(39983)}}, {{A, B, C, X(14624), X(27797)}}, {{A, B, C, X(17369), X(34258)}}
X(61321) = barycentric product X(i)*X(j) for these (i, j): {190, 47873}, {11237, 8}
X(61321) = barycentric quotient X(i)/X(j) for these (i, j): {11237, 7}, {47873, 514}
X(61321) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3943, 16672}, {2, 4665, 17119}, {8, 2345, 17369}, {10, 17281, 45}, {75, 17292, 17290}, {190, 29593, 17251}, {239, 61344, 47352}, {346, 1213, 16675}, {536, 17308, 17325}, {594, 17369, 8}, {894, 4445, 40341}, {894, 48630, 4445}, {1086, 29611, 21358}, {1278, 17307, 17323}, {1698, 4873, 37}, {2321, 17303, 16777}, {3617, 54389, 17330}, {3661, 4363, 599}, {3729, 17239, 17253}, {3739, 17286, 17267}, {4058, 5750, 17299}, {4361, 17289, 47355}, {4470, 29616, 17392}, {4472, 50097, 17316}, {4659, 17237, 49747}, {4699, 17285, 17265}, {4873, 59772, 1698}, {4908, 52706, 16676}, {5749, 17362, 6}, {5750, 17299, 16884}, {10436, 17229, 17311}, {16672, 61313, 2}, {16676, 19875, 52706}, {17233, 28604, 15668}, {17275, 17355, 16885}, {17290, 17292, 3763}, {17290, 17293, 17292}, {17320, 29608, 25503}

X(61322) = VERTEX SQUARE SUM OF 1ST HALF-SQUARES TRIANGLE

Barycentrics    5*a^4+(b^2-c^2)^2+2*a^2*(b^2+c^2+4*S) : :

X(61322) lies on these lines: {2, 6}, {20, 6423}, {1132, 7745}, {1249, 5200}, {1285, 42215}, {1587, 45515}, {1588, 19102}, {3053, 43512}, {3091, 49221}, {3127, 40065}, {3522, 12968}, {3523, 6422}, {5008, 61308}, {5024, 43510}, {5062, 5286}, {5281, 31459}, {5305, 7581}, {6199, 60655}, {6221, 46453}, {6421, 42523}, {6462, 16925}, {6463, 7839}, {7000, 39876}, {7582, 30435}, {7737, 61309}, {7738, 43511}, {8416, 36701}, {8577, 52223}, {9541, 41411}, {9600, 15692}, {13935, 45512}, {18907, 23273}, {19116, 37342}, {23249, 61388}, {43124, 49039}, {43507, 53419}, {43620, 61328}, {49016, 50721}

X(61322) = intersection, other than A, B, C, of circumconics {{A, B, C, X(492), X(52223)}}, {{A, B, C, X(8577), X(17811)}}
X(61322) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 3069, 37665}, {6, 32787, 26462}, {6, 44595, 2}, {6, 5304, 61323}, {6, 7735, 7585}, {3068, 3069, 45472}, {37640, 37641, 591}

X(61323) = VERTEX SQUARE SUM OF 2ND HALF-SQUARES TRIANGLE

Barycentrics    5*a^4+(b^2-c^2)^2+2*a^2*(b^2+c^2-4*S) : :

X(61323) lies on these lines: {2, 6}, {20, 6424}, {1131, 7745}, {1249, 5410}, {1285, 42216}, {1587, 19105}, {1588, 45514}, {3053, 43511}, {3091, 49220}, {3128, 40065}, {3311, 21737}, {3522, 12963}, {3523, 6421}, {5008, 61309}, {5024, 43509}, {5058, 5286}, {5305, 7582}, {6395, 60656}, {6398, 46453}, {6422, 42522}, {6462, 7839}, {6463, 16925}, {7374, 39875}, {7581, 21736}, {7737, 61308}, {7738, 43512}, {8396, 36703}, {8576, 52223}, {9540, 45513}, {9542, 9600}, {9674, 9692}, {18907, 23267}, {19117, 37343}, {23259, 61389}, {43125, 49038}, {43508, 53419}, {43620, 61329}, {49017, 50722}

X(61323) = intersection, other than A, B, C, of circumconics {{A, B, C, X(491), X(52223)}}, {{A, B, C, X(8576), X(17811)}}
X(61323) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 3068, 37665}, {6, 31403, 14930}, {6, 32788, 26457}, {6, 44596, 2}, {6, 5304, 61322}, {6, 7735, 7586}, {3068, 3069, 45473}, {37640, 37641, 1991}

X(61324) = VERTEX SQUARE SUM OF INCENTRAL TRIANGLE

Barycentrics    a^2*(b+c)^2*(2*a^2+b^2+c^2+2*a*(b+c)) : :

X(61324) lies on these lines: {2, 61341}, {6, 593}, {42, 2054}, {386, 20859}, {672, 2092}, {1084, 21814}, {1185, 4277}, {2238, 27065}, {2251, 20456}, {2271, 42295}, {2308, 20666}, {3051, 4263}, {3240, 52651}, {3995, 35068}, {6155, 6536}, {10026, 17184}, {17163, 61342}, {20675, 33774}, {21341, 29821}, {47417, 47430}

X(61324) = X(i)-Dao conjugate of X(j) for these {i, j}: {17045, 76}
X(61324) = X(i)-Ceva conjugate of X(j) for these {i, j}: {8701, 8663}
X(61324) = pole of line {4079, 8663} with respect to the Brocard inellipse
X(61324) = intersection, other than A, B, C, of circumconics {{A, B, C, X(593), X(1500)}}, {{A, B, C, X(1171), X(6537)}}, {{A, B, C, X(2054), X(6536)}}
X(61324) = barycentric product X(i)*X(j) for these (i, j): {6, 6537}, {37, 6155}, {42, 6536}, {181, 41002}, {1500, 17045}, {21705, 58}
X(61324) = barycentric quotient X(i)/X(j) for these (i, j): {6155, 274}, {6536, 310}, {6537, 76}, {21705, 313}, {41002, 18021}
X(61324) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 35216, 593}

X(61325) = VERTEX SQUARE SUM OF INVERSE-IN-EXCIRCLES TRIANGLE

Barycentrics    a^2*(b^4-b^3*c+4*b^2*c^2-b*c^3+c^4+a^2*(b^2+b*c+c^2)+2*a*(b^3+c^3)) : :

X(61325) lies on these lines: {2, 37}, {6, 61412}, {55, 1201}, {57, 893}, {978, 18235}, {980, 30038}, {995, 37619}, {1193, 1403}, {1423, 2999}, {1914, 37504}, {2176, 28272}, {3052, 55673}, {4689, 28370}, {5256, 28369}, {5437, 17053}, {8610, 37682}, {10459, 17599}, {17050, 24175}, {17187, 46513}, {17448, 37655}, {17594, 21214}, {21796, 23511}, {24177, 30097}, {24528, 37676}, {26626, 27455}, {28386, 54418}, {28629, 52541}, {30646, 56518}

X(61325) = pole of line {10, 31785} with respect to the dual conic of Yff parabola
X(61325) = intersection, other than A, B, C, of circumconics {{A, B, C, X(57), X(17787)}}, {{A, B, C, X(312), X(1432)}}, {{A, B, C, X(346), X(893)}}
X(61325) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3210, 17787}, {3752, 28358, 2}

X(61326) = VERTEX SQUARE SUM OF INVERSE-IN-INCIRCLE TRIANGLE

Barycentrics    a^2*(-2*a*(b-c)^2*(b+c)+(b-c)^2*(b^2-b*c+c^2)+a^2*(b^2+b*c+c^2)) : :

X(61326) lies on these lines: {6, 41}, {37, 11038}, {57, 14936}, {241, 59405}, {269, 34497}, {279, 1418}, {1002, 2276}, {1015, 7290}, {1107, 4648}, {1202, 20995}, {1212, 38053}, {2191, 16968}, {2293, 17474}, {3243, 6184}, {4860, 43046}, {5222, 42290}, {9336, 16487}, {10580, 21856}, {10980, 16588}, {16604, 37650}, {16781, 21002}, {21059, 33863}, {21795, 44841}, {24274, 57022}, {24727, 54338}, {37587, 52969}

X(61326) = pole of line {6589, 17427} with respect to the Steiner inellipse
X(61326) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(23062)}}, {{A, B, C, X(41), X(279)}}, {{A, B, C, X(48), X(30682)}}, {{A, B, C, X(1002), X(1471)}}
X(61326) = barycentric product X(i)*X(j) for these (i, j): {11033, 8083}
X(61326) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1458, 1475, 6}

X(61327) = VERTEX SQUARE SUM OF JOHNSON TRIANGLE

Barycentrics    a^8+2*(b^2-c^2)^4-2*a^6*(b^2+c^2)-4*a^2*(b^2-c^2)^2*(b^2+c^2)+3*a^4*(b^2+c^2)^2 : :

X(61327) lies on circumconic {{A, B, C, X(40448), X(55958)}} and on these lines: {2, 36430}, {4, 577}, {5, 1990}, {6, 3851}, {32, 231}, {53, 140}, {115, 33871}, {216, 1656}, {233, 393}, {340, 52247}, {376, 61312}, {381, 3284}, {574, 53416}, {1657, 22052}, {1879, 5065}, {2165, 7755}, {3078, 15004}, {3087, 3854}, {3090, 61314}, {3163, 3545}, {3543, 61307}, {3839, 61301}, {3850, 6749}, {3858, 6748}, {5055, 18487}, {5063, 9220}, {5068, 40138}, {5072, 15860}, {5073, 36748}, {5475, 16310}, {6103, 10314}, {7533, 10311}, {7570, 22240}, {7747, 46262}, {7772, 50137}, {10299, 36422}, {11331, 14767}, {14581, 56965}, {14593, 52975}, {14864, 17849}, {15262, 50718}, {15526, 52710}, {36751, 46219}, {39601, 40135}, {40885, 52712}, {42459, 55856}, {43620, 58265}, {44904, 59649}

X(61327) = pole of line {550, 11438} with respect to the Kiepert hyperbola
X(61327) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 61315, 52945}, {5055, 52703, 52704}, {18487, 52704, 52703}, {52945, 61315, 36430}

X(61328) = VERTEX SQUARE SUM OF 1ST KENMOTU-CENTERS TRIANGLE

Barycentrics    2*a^4-(b^2-c^2)^2+2*a^2*(b^2+c^2+2*S) : :

X(61328) lies on these lines: {6, 13}, {32, 638}, {39, 42216}, {69, 61310}, {187, 35255}, {372, 9698}, {485, 7755}, {491, 7820}, {574, 31403}, {615, 1506}, {1151, 31483}, {1504, 6561}, {1587, 7772}, {2548, 7586}, {3070, 7765}, {5007, 7583}, {5058, 44647}, {5368, 49220}, {6408, 31492}, {6417, 35831}, {6422, 7756}, {6423, 7749}, {6450, 31457}, {6460, 53096}, {7585, 61308}, {7739, 23267}, {8972, 61309}, {8980, 35767}, {8981, 35007}, {9341, 18965}, {11648, 23249}, {12815, 42582}, {13903, 22331}, {13939, 31417}, {14537, 42215}, {31401, 43510}, {31407, 42523}, {31450, 43511}, {31463, 61388}, {31465, 42261}, {32806, 61311}, {43620, 61322}

X(61328) = pole of line {323, 8962} with respect to the Stammler hyperbola
X(61328) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 13665, 5309}, {6, 7753, 61329}, {6423, 31481, 7749}

X(61329) = VERTEX SQUARE SUM OF 2ND KENMOTU-CENTERS TRIANGLE

Barycentrics    2*a^4-(b^2-c^2)^2+2*a^2*(b^2+c^2-2*S) : :

X(61329) lies on these lines: {6, 13}, {32, 637}, {39, 42215}, {69, 61311}, {187, 35256}, {371, 9698}, {486, 7755}, {492, 7820}, {574, 9541}, {590, 1506}, {1505, 6560}, {1588, 7772}, {2548, 7585}, {3071, 7765}, {5007, 7584}, {5062, 44648}, {5368, 49221}, {6407, 31492}, {6418, 35830}, {6421, 7756}, {6424, 7749}, {6431, 31483}, {6449, 31457}, {6459, 53096}, {7586, 61309}, {7739, 23273}, {9341, 18966}, {9675, 61389}, {11648, 23259}, {12815, 42583}, {13886, 31417}, {13941, 61308}, {13961, 22331}, {13966, 35007}, {13967, 35766}, {14537, 42216}, {31401, 43509}, {31407, 42522}, {31450, 43512}, {32805, 61310}, {43620, 61323}

X(61329) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 13785, 5309}, {6, 7753, 61328}

X(61330) = VERTEX SQUARE SUM OF 5TH MIXTILINEAR TRIANGLE

Barycentrics    9*a^2-2*a*(b+c)+(b+c)^2 : :

X(61330) lies on these lines: {2, 44}, {6, 145}, {8, 4700}, {9, 1475}, {10, 391}, {45, 3622}, {144, 3618}, {190, 17014}, {193, 17230}, {279, 60856}, {597, 4419}, {894, 37681}, {966, 46932}, {1219, 16466}, {1266, 4454}, {1449, 3161}, {1897, 5702}, {1992, 17354}, {2276, 24507}, {2321, 20053}, {2325, 3241}, {2345, 4678}, {3008, 35578}, {3589, 26104}, {3600, 54377}, {3617, 17369}, {3621, 17281}, {3623, 16666}, {3624, 3973}, {3632, 17355}, {3636, 3731}, {3672, 17350}, {3707, 9780}, {3759, 4461}, {3945, 17120}, {3946, 4488}, {4273, 17539}, {4274, 59299}, {4290, 30652}, {4344, 10005}, {4346, 17367}, {4363, 24599}, {4373, 17366}, {4422, 29621}, {4452, 17351}, {4473, 29585}, {4667, 29627}, {4676, 4779}, {4704, 36409}, {4727, 20049}, {4759, 48830}, {4869, 17353}, {4873, 20050}, {4969, 31145}, {5032, 6542}, {5232, 17368}, {5269, 6555}, {5304, 37764}, {5750, 19877}, {5839, 16671}, {6172, 17023}, {6173, 31189}, {7277, 32093}, {8584, 17269}, {11008, 17285}, {11019, 55993}, {11160, 29587}, {12848, 41804}, {15828, 16673}, {16676, 31722}, {16706, 20059}, {16831, 61023}, {17245, 30712}, {17257, 29614}, {17280, 51170}, {17304, 60957}, {17321, 61006}, {17330, 26039}, {17332, 25503}, {17339, 29619}, {17358, 20080}, {17395, 51185}, {20014, 50131}, {20054, 50087}, {20214, 32774}, {21796, 39956}, {26668, 61009}, {26818, 28778}, {27064, 37666}, {27191, 59375}, {27797, 60082}, {29624, 46922}, {31227, 51406}, {34824, 37650}, {36534, 50835}, {41140, 52709}, {47359, 49699}, {49701, 50300}, {49703, 50130}, {49709, 59406}

X(61330) = perspector of circumconic {{A, B, C, X(4597), X(8706)}}
X(61330) = pole of line {4777, 47890} with respect to the Steiner circumellipse
X(61330) = pole of line {2490, 4777} with respect to the Steiner inellipse
X(61330) = pole of line {5235, 18600} with respect to the Wallace hyperbola
X(61330) = intersection, other than A, B, C, of circumconics {{A, B, C, X(89), X(23617)}}, {{A, B, C, X(1222), X(5558)}}, {{A, B, C, X(30588), X(56258)}}, {{A, B, C, X(30608), X(52549)}}, {{A, B, C, X(44794), X(54389)}}
X(61330) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3758, 4747}, {6, 54389, 145}, {145, 54389, 346}, {190, 59373, 17014}, {1449, 4029, 20057}, {3161, 20057, 4029}, {5222, 50127, 4454}, {7277, 53665, 32093}, {17120, 26685, 3945}, {17330, 26039, 46933}, {17350, 51171, 3672}, {17369, 37654, 3617}, {31722, 38314, 16676}

X(61331) = VERTEX SQUARE SUM OF INNER-NAPOLEON TRIANGLE

Barycentrics    (b^2-c^2)^2-3*a^2*(b^2+c^2)+2*sqrt(3)*a^2*S : :

X(61331) lies on circumconic {{A, B, C, X(5422), X(21462)}} and on these lines: {2, 6}, {4, 53443}, {13, 31415}, {14, 2549}, {15, 9113}, {16, 7737}, {18, 3767}, {32, 42149}, {39, 40694}, {61, 31401}, {62, 2548}, {115, 5617}, {202, 31409}, {398, 5013}, {574, 5471}, {1080, 53505}, {1285, 19780}, {1352, 6114}, {1506, 40693}, {1570, 59403}, {2395, 57122}, {3053, 16773}, {3094, 16940}, {3390, 31411}, {5023, 42944}, {5024, 42975}, {5052, 22715}, {5111, 59397}, {5254, 42153}, {5321, 44459}, {5334, 53442}, {5475, 10653}, {5615, 37348}, {6115, 14561}, {6771, 41672}, {6775, 22491}, {6776, 53466}, {7127, 9599}, {7603, 18582}, {7618, 12154}, {7739, 16268}, {7745, 22238}, {7747, 42151}, {7748, 42159}, {7756, 42160}, {9112, 46054}, {9605, 42989}, {11486, 15484}, {11543, 15048}, {11648, 41120}, {13083, 41621}, {13881, 42599}, {14482, 42987}, {14537, 42510}, {14853, 53431}, {15815, 42147}, {16242, 21843}, {16963, 41406}, {18907, 42913}, {22513, 41071}, {31400, 42999}, {31404, 42998}, {31417, 42990}, {31450, 42991}, {31455, 42152}, {31460, 54402}, {33388, 47863}, {36185, 47322}, {36968, 43618}, {36970, 43619}, {37177, 53464}, {37512, 42150}, {37835, 43620}, {39590, 42161}, {39593, 49859}, {39601, 42111}, {42087, 44541}, {42092, 61320}, {42155, 53418}, {42163, 44518}, {42164, 44519}, {42942, 53095}, {43404, 43448}, {43454, 46053}

X(61331) = X(i)-complementary conjugate of X(j) for these {i, j}: {43953, 2887}
X(61331) = pole of line {2, 43953} with respect to the Kiepert hyperbola
X(61331) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 16645, 230}, {6, 230, 61317}, {6, 31489, 396}, {6, 3815, 61332}, {574, 5471, 10654}, {3619, 11489, 23303}, {7736, 37641, 6}, {16242, 41407, 21843}

X(61332) = VERTEX SQUARE SUM OF OUTER-NAPOLEON TRIANGLE

Barycentrics    (b^2-c^2)^2-3*a^2*(b^2+c^2)-2*sqrt(3)*a^2*S : :

X(61332) lies on circumconic {{A, B, C, X(5422), X(21461)}} and on these lines: {2, 6}, {4, 53431}, {13, 2549}, {14, 31415}, {15, 7737}, {16, 9112}, {17, 3767}, {32, 42152}, {39, 40693}, {61, 2548}, {62, 31401}, {115, 5613}, {203, 31409}, {383, 53505}, {397, 5013}, {574, 5472}, {1285, 19781}, {1352, 6115}, {1506, 40694}, {1570, 59404}, {2307, 9596}, {2395, 57123}, {3053, 16772}, {3094, 16941}, {3365, 31411}, {5023, 42945}, {5024, 42974}, {5052, 22714}, {5111, 59398}, {5254, 42156}, {5318, 44463}, {5335, 53430}, {5475, 10654}, {5611, 37348}, {6114, 14561}, {6772, 22492}, {6774, 41672}, {6776, 53455}, {7127, 31497}, {7603, 18581}, {7618, 12155}, {7739, 16267}, {7745, 22236}, {7747, 42150}, {7748, 42162}, {7756, 42161}, {9113, 46053}, {9605, 42988}, {11485, 15484}, {11542, 15048}, {11648, 41119}, {13084, 41620}, {13881, 42598}, {14482, 42986}, {14537, 42511}, {14853, 53443}, {15815, 42148}, {16241, 21843}, {16962, 41407}, {18907, 42912}, {22512, 41070}, {31400, 42998}, {31404, 42999}, {31417, 42991}, {31450, 42990}, {31455, 42149}, {31460, 54403}, {33389, 47864}, {36186, 47322}, {36967, 43618}, {36969, 43619}, {37178, 53453}, {37512, 42151}, {37832, 43620}, {39590, 42160}, {39593, 49860}, {39601, 42114}, {42088, 44541}, {42089, 61319}, {42154, 53418}, {42165, 44519}, {42166, 44518}, {42943, 53095}, {43403, 43448}, {43455, 46054}

X(61332) = X(i)-complementary conjugate of X(j) for these {i, j}: {43954, 2887}
X(61332) = pole of line {2, 43954} with respect to the Kiepert hyperbola
X(61332) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 16644, 230}, {6, 230, 61318}, {6, 31489, 395}, {6, 3815, 61331}, {574, 5472, 10653}, {3619, 11488, 23302}, {7736, 37640, 6}, {16241, 41406, 21843}

X(61333) = VERTEX SQUARE SUM OF 2ND NEUBERG TRIANGLE

Barycentrics    a^8+2*a^6*(b^2+c^2)-2*a^2*(b^2-c^2)^2*(b^2+c^2)+(b^2-c^2)^2*(b^4+c^4)+2*a^4*(3*b^4+5*b^2*c^2+3*c^4) : :

X(61333) lies on circumconic {{A, B, C, X(6531), X(16989)}} and on these lines: {2, 6}, {4, 46311}, {32, 9744}, {114, 5039}, {232, 3117}, {262, 3767}, {315, 13356}, {393, 56920}, {3095, 5286}, {3972, 52674}, {5017, 37182}, {5052, 9753}, {7710, 39656}, {7737, 43460}, {7763, 13357}, {8573, 20885}, {10796, 43450}, {14031, 44539}, {14853, 38383}, {16925, 51580}, {20065, 34870}, {30435, 37466}, {31400, 40108}, {33181, 35701}, {33187, 44532}, {33269, 44530}, {54731, 54826}

X(61333) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 230, 16989}, {6, 325, 7736}, {7735, 7736, 39095}, {7774, 16989, 39101}

X(61334) = VERTEX SQUARE SUM OF ORTHIC TRIANGLE

Barycentrics    -2*a^6*(b^2-c^2)^2*(b^2+c^2)+a^8*(b^4+c^4)+a^4*(b^2-c^2)^2*(b^4+c^4) : :

X(61334) lies on these lines: {25, 61305}, {32, 44077}, {184, 52967}, {216, 37649}, {232, 56297}, {393, 8794}, {800, 16318}, {1084, 42295}, {1974, 61360}, {1993, 11672}, {3051, 8265}, {3060, 23584}, {4232, 51336}, {9699, 39013}, {13366, 40588}, {61346, 61374}

X(61334) = pole of line {28706, 33769} with respect to the Stammler hyperbola
X(61334) = intersection, other than A, B, C, of circumconics {{A, B, C, X(393), X(61361)}}, {{A, B, C, X(6747), X(58306)}}, {{A, B, C, X(6752), X(13409)}}
X(61334) = barycentric product X(i)*X(j) for these (i, j): {4, 6752}, {184, 6747}, {13409, 25}, {21638, 51}
X(61334) = barycentric quotient X(i)/X(j) for these (i, j): {6747, 18022}, {6752, 69}, {13409, 305}, {21638, 34384}
X(61334) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {32, 44077, 61361}

X(61335) = VERTEX SQUARE SUM OF 3RD TRI-SQUARES-CENTRAL TRIANGLE

Barycentrics    3*a^4-3*(b^2-c^2)^2+2*a^2*(3*b^2+3*c^2+8*S) : :

X(61335) lies on these lines: {5, 6}, {1504, 23249}, {2549, 23267}, {3054, 43881}, {5062, 32785}, {6199, 7737}, {6395, 31401}, {6460, 31483}, {7585, 61308}, {7739, 18512}, {9602, 42643}, {12962, 42275}, {23259, 44594}, {31481, 32786}, {39593, 43386}, {42264, 49260}, {44595, 61337}

X(61335) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 2548, 61336}, {19103, 42277, 6}

X(61336) = VERTEX SQUARE SUM OF 4TH TRI-SQUARES-CENTRAL TRIANGLE

Barycentrics    3*a^4-3*(b^2-c^2)^2+2*a^2*(3*b^2+3*c^2-8*S) : :

X(61336) lies on these lines: {5, 6}, { }, {2549, 23273}, {3054, 43882}, {5058, 32786}, {6199, 31401}, {6395, 7737}, {6435, 31463}, {7586, 61309}, {7739, 18510}, {12969, 42276}, {23249, 44597}, {39593, 43387}, {42263, 49263}, {44596, 61338}

X(61336) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 2548, 61335}, {19104, 42274, 6}

X(61337) = VERTEX SQUARE SUM OF 3RD TRI-SQUARES TRIANGLE

Barycentrics    3*a^4-(b^2-c^2)^2+a^2*(3*b^2+3*c^2+10*S) : :

X(61337) lies on these lines: {6, 13}, {20, 1504}, {32, 19103}, {140, 5062}, {3090, 31411}, {5041, 36714}, {5070, 31481}, {7737, 26462}, {9674, 21735}, {9675, 44594}, {11648, 22541}, {13920, 32788}, {44595, 61335}

X(61338) = VERTEX SQUARE SUM OF 4TH TRI-SQUARES TRIANGLE

Barycentrics    3*a^4-(b^2-c^2)^2+a^2*(3*b^2+3*c^2-10*S) : :

X(61338) lies on these lines: {6, 13}, {20, 1505}, {32, 19104}, {140, 5058}, {3524, 9675}, {5041, 36709}, {7737, 26457}, {11648, 19101}, {13849, 32787}, {44596, 61336}

X(61339) = VERTEX SQUARE SUM OF X-PARABOLA-TANGENTIAL TRIANGLE

Barycentrics    (b^2-c^2)^4 : :
X(61339) = -3*X[2]+X[33799], 3*X[671]+X[31998], -3*X[892]+X[31372], -3*X[2482]+4*X[36953], X[17948]+2*X[36523], -X[35511]+9*X[41135]

X(61339) lies on cubic K1152 and on these lines: {2, 33799}, {115, 523}, {148, 4590}, {230, 37897}, {338, 15449}, {524, 39563}, {543, 14588}, {671, 31998}, {688, 6071}, {892, 31372}, {1084, 2489}, {1989, 23967}, {2482, 36953}, {3124, 30452}, {6368, 41181}, {7748, 40879}, {9233, 41762}, {15527, 34294}, {16316, 47298}, {17948, 36523}, {18122, 39565}, {23897, 24348}, {23903, 24345}, {23942, 36223}, {28175, 41180}, {33919, 42344}, {35511, 41135}, {36207, 44518}, {37512, 44386}, {39691, 51429}

X(61339) = midpoint of X(i) and X(j) for these {i,j}: {148, 4590}, {41135, 57539}, {892, 54104}
X(61339) = reflection of X(i) in X(j) for these {i,j}: {115, 31644}, {23991, 115}, {23992, 23991}, {4590, 40553}, {44398, 57515}
X(61339) = complement of X(33799)
X(61339) = perspector of circumconic {{A, B, C, X(5466), X(8029)}}
X(61339) = X(i)-isoconjugate-of-X(j) for these {i, j}: {163, 31614}, {249, 24041}, {662, 59152}, {922, 42370}, {1101, 4590}, {4575, 55270}, {4592, 47443}, {23357, 24037}, {23889, 45773}, {23995, 34537}, {46254, 47390}
X(61339) = X(i)-Dao conjugate of X(j) for these {i, j}: {115, 31614}, {136, 55270}, {512, 23357}, {523, 4590}, {647, 47389}, {1084, 59152}, {3005, 249}, {5139, 47443}, {18314, 34537}, {33919, 23992}, {39061, 42370}
X(61339) = X(i)-Ceva conjugate of X(j) for these {i, j}: {115, 8029}, {8754, 22260}, {23588, 15475}, {23962, 23105}, {57552, 5466}
X(61339) = X(i)-complementary conjugate of X(j) for these {i, j}: {14052, 21259}, {36953, 42327}, {36955, 2887}
X(61339) = pole of line {2396, 4235} with respect to the polar circle
X(61339) = pole of line {690, 13187} with respect to the Kiepert hyperbola
X(61339) = pole of line {33906, 45291} with respect to the Steiner circumellipse
X(61339) = pole of line {1648, 33906} with respect to the Steiner inellipse
X(61339) = pole of line {385, 3266} with respect to the dual conic of Stammler hyperbola
X(61339) = pole of line {249, 524} with respect to the dual conic of Wallace hyperbola
X(61339) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(23991)}}, {{A, B, C, X(115), X(40429)}}, {{A, B, C, X(523), X(8029)}}, {{A, B, C, X(1648), X(36953)}}, {{A, B, C, X(2489), X(8430)}}, {{A, B, C, X(4590), X(45212)}}, {{A, B, C, X(19598), X(33799)}}, {{A, B, C, X(23992), X(35511)}}, {{A, B, C, X(51258), X(51441)}}
X(61339) = barycentric product X(i)*X(j) for these (i, j): {115, 115}, {125, 8754}, {523, 8029}, {1084, 23962}, {1109, 2643}, {1365, 4092}, {2971, 339}, {3124, 338}, {5489, 58757}, {5532, 7314}, {6058, 7336}, {12078, 40524}, {16732, 21833}, {20975, 2970}, {21043, 3120}, {21131, 4024}, {22260, 850}, {23099, 44173}, {23105, 512}, {30452, 30465}, {30453, 30468}, {33919, 5466}, {34294, 39691}, {41221, 8901}, {42344, 671}, {42345, 42553}, {45775, 46277}, {51441, 868}, {55195, 55197}, {58908, 6328}
X(61339) = barycentric quotient X(i)/X(j) for these (i, j): {115, 4590}, {125, 47389}, {338, 34537}, {512, 59152}, {523, 31614}, {671, 42370}, {1084, 23357}, {1109, 24037}, {1365, 7340}, {2489, 47443}, {2501, 55270}, {2643, 24041}, {2971, 250}, {3124, 249}, {4092, 6064}, {4117, 23995}, {8029, 99}, {8754, 18020}, {9178, 45773}, {9427, 23963}, {15630, 57742}, {21043, 4600}, {21131, 4610}, {21833, 4567}, {22260, 110}, {23099, 1576}, {23105, 670}, {23610, 14574}, {23962, 44168}, {33919, 5468}, {42068, 57655}, {42344, 524}, {42553, 14588}, {45775, 896}, {51441, 57991}, {55195, 55196}, {55197, 55194}, {55278, 55227}
X(61339) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {115, 523, 23991}, {523, 23991, 23992}, {523, 31644, 115}, {523, 57515, 44398}, {30452, 30453, 51428}, {33799, 40429, 2}

X(61340) = VERTEX SQUARE SUM OF X3-ABC REFLECTIONS TRIANGLE

Barycentrics    3*a^8+4*(b^2-c^2)^4-10*a^6*(b^2+c^2)-12*a^2*(b^2-c^2)^2*(b^2+c^2)+a^4*(15*b^4+14*b^2*c^2+15*c^4) : :

X(61340) lies on circumconic {{A, B, C, X(55958), X(60007)}} and on these lines: {2, 36430}, {4, 61312}, {5, 577}, {53, 16239}, {216, 5070}, {233, 7486}, {631, 36412}, {1656, 5158}, {1990, 15699}, {2165, 9698}, {2963, 13342}, {3284, 5055}, {3526, 10979}, {3528, 36422}, {3843, 22052}, {5056, 61301}, {5067, 33630}, {6749, 12812}, {9220, 15515}, {15703, 52703}, {36751, 55866}, {52975, 56892}, {60781, 61314}

X(61340) = pole of line {578, 14869} with respect to the Kiepert hyperbola

X(61341) = VERTEX SQUARE SUM OF GEMINI 15 TRIANGLE

Barycentrics    (b+c)^2*(3*a^4+b^2*c^2+2*a*(b+c)*(a*(2*a+b)+(a+b)*c)) : :

X(61341) lies on these lines: {2, 61324}, {6, 261}, {37, 1084}, {740, 61342}, {1213, 3912}, {1575, 2092}, {2238, 17260}, {3124, 29822}, {3755, 23897}, {4357, 10026}, {6537, 25354}, {16589, 20363}, {17045, 35119}, {20666, 33682}, {27268, 60676}, {52651, 59297}

X(61341) = pole of line {3846, 24603} with respect to the Kiepert hyperbola
X(61341) = pole of line {4824, 46390} with respect to the Steiner inellipse

X(61342) = VERTEX SQUARE SUM OF GEMINI 16 TRIANGLE

Barycentrics    (b+c)^2*(a^4+3*b^2*c^2+2*a*(b+c)*(a^2+2*b*c+a*(b+c))) : :

X(61342) lies on these lines: {10, 115}, {740, 61341}, {1213, 1738}, {1500, 24044}, {1575, 3634}, {2023, 30761}, {3124, 31025}, {3912, 17056}, {3948, 29610}, {9780, 60676}, {17163, 61324}, {20970, 50018}, {29633, 52538}

X(61342) = pole of line {740, 3775} with respect to the Kiepert hyperbola

X(61343) = VERTEX SQUARE SUM OF GEMINI 20 TRIANGLE

Barycentrics    5*b^2+8*b*c+5*c^2 : :

X(61343) lies on these lines: {2, 4405}, {8, 597}, {10, 4755}, {75, 141}, {239, 48310}, {524, 61321}, {1125, 50084}, {2321, 4708}, {2345, 3629}, {3617, 17269}, {3626, 17359}, {3630, 4445}, {3631, 7231}, {3679, 4422}, {3943, 29593}, {4007, 17045}, {4058, 17239}, {4060, 17385}, {4361, 51128}, {4363, 22165}, {4395, 29611}, {4399, 5222}, {4472, 17294}, {4473, 17330}, {4690, 49726}, {4701, 50124}, {4798, 17390}, {4873, 49737}, {4971, 17308}, {5564, 29630}, {6707, 17309}, {8584, 17369}, {10022, 17374}, {17119, 20582}, {17229, 29571}, {17243, 24603}, {17292, 50098}, {17299, 29603}, {17303, 29605}, {17325, 28309}, {17340, 32025}, {17388, 29586}, {17395, 29591}, {17398, 29588}, {28634, 31183}, {28653, 29625}, {29585, 61313}, {29594, 34824}, {29604, 50112}, {29610, 50113}, {29616, 49738}, {34573, 42696}, {42697, 50991}, {49727, 51142}, {49769, 50312}

X(61343) = pole of line {3837, 47910} with respect to the Steiner inellipse
X(61343) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {594, 3661, 4665}, {594, 48630, 48636}, {594, 48635, 48628}, {2345, 4478, 3629}, {3617, 17269, 49731}, {3661, 17227, 48635}, {3661, 48628, 17227}, {4399, 17293, 51126}, {4445, 7227, 3630}, {4665, 48636, 3661}, {17228, 48631, 141}, {48628, 48635, 7263}

X(61344) = VERTEX SQUARE SUM OF GEMINI 28 TRIANGLE

Barycentrics    3*a^2+2*(b^2+b*c+c^2) : :

X(61344) lies on these lines: {1, 17269}, {2, 45}, {6, 319}, {7, 34573}, {8, 597}, {9, 4708}, {10, 50300}, {37, 29603}, {44, 17251}, {75, 29630}, {86, 17267}, {141, 4644}, {145, 50097}, {193, 48635}, {239, 47352}, {320, 21358}, {344, 17398}, {346, 17045}, {524, 29611}, {536, 29598}, {594, 3618}, {599, 3758}, {894, 3763}, {1001, 24295}, {1010, 30906}, {1100, 17286}, {1125, 41313}, {1213, 26685}, {1376, 4471}, {1449, 17229}, {1743, 17239}, {2325, 41312}, {2345, 3589}, {2999, 50052}, {3246, 48851}, {3619, 17365}, {3620, 7277}, {3624, 4755}, {3632, 50124}, {3633, 50084}, {3634, 5880}, {3729, 17323}, {3731, 25498}, {3739, 31183}, {3943, 26626}, {4000, 7227}, {4360, 53664}, {4387, 29647}, {4393, 50087}, {4395, 48310}, {4407, 5220}, {4643, 29604}, {4648, 30833}, {4657, 17262}, {4659, 17382}, {4664, 29614}, {4670, 17284}, {4675, 29596}, {4690, 16670}, {4758, 29600}, {4798, 5750}, {4969, 59373}, {4971, 17014}, {5224, 16885}, {5263, 26083}, {5294, 5737}, {5695, 29633}, {5772, 9053}, {5839, 6329}, {6144, 17287}, {6687, 16832}, {7222, 48631}, {7228, 51128}, {7229, 7263}, {7238, 35578}, {9780, 49731}, {10436, 17265}, {15534, 17360}, {16394, 19867}, {16666, 17294}, {16667, 17372}, {16669, 17270}, {16672, 17264}, {16675, 17322}, {16706, 17118}, {16777, 17280}, {16826, 17342}, {16831, 41310}, {16884, 17233}, {17023, 17281}, {17116, 17370}, {17119, 17367}, {17120, 17228}, {17121, 48630}, {17230, 46922}, {17237, 50127}, {17243, 29624}, {17253, 17307}, {17255, 17306}, {17256, 29608}, {17259, 17303}, {17261, 17400}, {17266, 41847}, {17268, 17394}, {17277, 32089}, {17285, 17311}, {17295, 37677}, {17321, 17340}, {17326, 17336}, {17335, 29610}, {17338, 28653}, {17346, 29591}, {17348, 59772}, {17352, 28604}, {17356, 25590}, {17362, 51171}, {17378, 29587}, {17392, 29579}, {17395, 50107}, {19701, 33157}, {19722, 32858}, {19808, 37679}, {26251, 37540}, {26738, 30811}, {27474, 36409}, {29576, 61313}, {29585, 61302}, {29609, 51488}, {29615, 51185}, {29627, 49738}, {29646, 49453}, {29659, 48805}, {29676, 32780}, {30116, 48860}, {30832, 31056}, {32099, 32455}, {33159, 36554}, {36478, 48829}, {36479, 48810}, {38023, 50017}, {38047, 49772}, {38049, 50020}, {38089, 50022}, {38315, 50015}, {49769, 50302}

X(61344) = pole of line {3936, 26626} with respect to the Kiepert hyperbola
X(61344) = pole of line {900, 47693} with respect to the Steiner circumellipse
X(61344) = pole of line {900, 48069} with respect to the Steiner inellipse
X(61344) = pole of line {519, 21358} with respect to the dual conic of Yff parabola
X(61344) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(996), X(17305)}}, {{A, B, C, X(1016), X(17325)}}
X(61344) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17354, 45}, {2, 17369, 4363}, {2, 190, 17325}, {2, 26039, 4472}, {2, 4363, 17290}, {2, 4364, 25503}, {2, 4454, 26104}, {2, 4470, 34824}, {2, 54389, 4364}, {6, 17289, 17293}, {6, 17293, 4445}, {9, 17385, 17327}, {44, 17308, 17251}, {190, 17325, 24441}, {320, 29613, 21358}, {894, 17371, 3763}, {1100, 17286, 17309}, {2345, 5222, 4665}, {3589, 4665, 5222}, {3729, 17384, 17323}, {4454, 26104, 49741}, {4657, 17355, 17262}, {4670, 17284, 17313}, {4798, 17279, 29571}, {4798, 29571, 15668}, {5750, 29571, 4798}, {6329, 48636, 5839}, {7227, 51126, 4000}, {10436, 17357, 17265}, {17023, 17281, 17318}, {17120, 17228, 40341}, {17264, 17397, 16672}, {17280, 17381, 16777}, {17285, 17379, 17311}, {17289, 17368, 6}, {17303, 17353, 17259}, {17307, 17350, 17253}, {17322, 17339, 16675}, {47352, 61321, 239}

X(61345) = VERTEX PRODUCT OF ANTI-ARTZT TRIANGLE

Barycentrics    (5*a^2-b^2-c^2)*(2*(a^2+b^2)-c^2)*(2*a^2-b^2+2*c^2) : :

X(61345) lies on these lines: {2, 187}, {25, 17983}, {1384, 52141}, {1992, 50729}, {2408, 8644}, {9084, 11636}, {10511, 17503}, {11059, 27088}, {11168, 42365}, {13366, 43697}, {14614, 35138}, {15534, 20380}, {23054, 23055}, {26255, 55029}, {37904, 52692}, {40022, 40826}

X(61345) = X(i)-isoconjugate-of-X(j) for these {i, j}: {574, 55923}, {17414, 37216}, {21448, 36263}
X(61345) = X(i)-Dao conjugate of X(j) for these {i, j}: {11147, 599}, {35133, 3906}
X(61345) = X(i)-cross conjugate of X(j) for these {i, j}: {1992, 598}
X(61345) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(1992)}}, {{A, B, C, X(4), X(23334)}}, {{A, B, C, X(25), X(187)}}, {{A, B, C, X(98), X(8182)}}, {{A, B, C, X(262), X(8176)}}, {{A, B, C, X(316), X(17503)}}, {{A, B, C, X(1153), X(7607)}}, {{A, B, C, X(1494), X(55848)}}, {{A, B, C, X(1499), X(3849)}}, {{A, B, C, X(5569), X(60175)}}, {{A, B, C, X(6325), X(47075)}}, {{A, B, C, X(7937), X(60286)}}, {{A, B, C, X(11165), X(11167)}}, {{A, B, C, X(14614), X(37745)}}, {{A, B, C, X(15471), X(60124)}}, {{A, B, C, X(25409), X(31173)}}, {{A, B, C, X(31614), X(34245)}}, {{A, B, C, X(35266), X(51372)}}, {{A, B, C, X(44678), X(54477)}}, {{A, B, C, X(47101), X(54851)}}, {{A, B, C, X(47102), X(54608)}}, {{A, B, C, X(52454), X(54642)}}
X(61345) = barycentric product X(i)*X(j) for these (i, j): {1384, 40826}, {1499, 35138}, {1992, 598}, {11059, 1383}, {18818, 27088}, {43697, 58782}, {51541, 52141}
X(61345) = barycentric quotient X(i)/X(j) for these (i, j): {598, 5485}, {1383, 21448}, {1384, 574}, {1499, 3906}, {1992, 599}, {2408, 23288}, {4232, 5094}, {6791, 8288}, {8644, 17414}, {11059, 9464}, {11636, 1296}, {27088, 39785}, {35138, 35179}, {35266, 13857}, {36277, 36263}, {43697, 55977}, {51438, 51397}, {52141, 42008}, {55927, 55923}
X(61345) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 47075, 55164}, {1383, 51541, 598}

X(61346) = VERTEX PRODUCT OF 2ND ANTI-CONWAY TRIANGLE

Barycentrics    a^4*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(-(b^2-c^2)^2+a^2*(b^2+c^2)) : :

X(61346) lies on these lines: {4, 20965}, {6, 6995}, {25, 263}, {51, 217}, {53, 17500}, {232, 20859}, {418, 52967}, {1395, 1977}, {1501, 1974}, {1613, 4232}, {1625, 41588}, {1899, 3331}, {2207, 6524}, {2212, 7109}, {3080, 42068}, {3124, 44079}, {3231, 6353}, {3289, 33586}, {8041, 12294}, {9407, 61361}, {11433, 32445}, {14567, 44077}, {18950, 41367}, {21753, 44086}, {32064, 38297}, {33522, 40805}, {40938, 46906}, {61334, 61374}

X(61346) = X(i)-isoconjugate-of-X(j) for these {i, j}: {54, 40364}, {63, 34384}, {75, 34386}, {95, 304}, {97, 561}, {255, 57790}, {276, 326}, {305, 2167}, {656, 55218}, {811, 15414}, {1102, 8795}, {1502, 2169}, {1928, 14533}, {2148, 40050}, {2616, 52608}, {3926, 40440}, {4602, 23286}, {6507, 57844}, {15412, 55202}, {17206, 56189}, {24037, 53576}, {44687, 57918}
X(61346) = X(i)-Dao conjugate of X(j) for these {i, j}: {130, 4143}, {206, 34386}, {216, 40050}, {512, 53576}, {3162, 34384}, {6523, 57790}, {14363, 1502}, {15259, 276}, {15450, 52617}, {17423, 15414}, {40368, 97}, {40369, 14533}, {40588, 305}, {40596, 55218}, {52878, 6393}
X(61346) = X(i)-Ceva conjugate of X(j) for these {i, j}: {3199, 40981}
X(61346) = intersection, other than A, B, C, of circumconics {{A, B, C, X(51), X(263)}}, {{A, B, C, X(217), X(1501)}}, {{A, B, C, X(418), X(6620)}}, {{A, B, C, X(3051), X(6531)}}, {{A, B, C, X(3199), X(36417)}}, {{A, B, C, X(27369), X(27370)}}
X(61346) = barycentric product X(i)*X(j) for these (i, j): {4, 40981}, {19, 2179}, {25, 51}, {32, 53}, {112, 55219}, {216, 2207}, {217, 393}, {311, 44162}, {343, 36417}, {418, 6524}, {512, 52604}, {1093, 44088}, {1393, 2212}, {1395, 7069}, {1501, 324}, {1576, 51513}, {1625, 2489}, {1953, 1973}, {1974, 5}, {2181, 31}, {2211, 60517}, {2501, 61194}, {3049, 61193}, {3199, 6}, {11060, 11062}, {12077, 61206}, {13450, 14575}, {14569, 184}, {14570, 57204}, {14573, 60828}, {14574, 23290}, {14576, 60501}, {14601, 39569}, {15451, 32713}, {15897, 2980}, {17500, 27369}, {21807, 2203}, {27371, 46288}, {27374, 32085}, {30493, 6059}, {33578, 61110}, {35360, 669}, {39530, 46319}, {40354, 52945}, {41221, 57655}, {42293, 6529}, {44707, 7337}, {52439, 5562}, {52967, 6531}, {61362, 61378}
X(61346) = barycentric quotient X(i)/X(j) for these (i, j): {5, 40050}, {25, 34384}, {32, 34386}, {51, 305}, {53, 1502}, {112, 55218}, {217, 3926}, {311, 40360}, {324, 40362}, {393, 57790}, {418, 4176}, {1084, 53576}, {1501, 97}, {1625, 52608}, {1917, 2169}, {1953, 40364}, {1974, 95}, {2179, 304}, {2181, 561}, {2207, 276}, {3049, 15414}, {3199, 76}, {6524, 57844}, {9233, 14533}, {9426, 23286}, {13450, 44161}, {14569, 18022}, {15451, 52617}, {15897, 7796}, {27371, 52568}, {27374, 3933}, {35360, 4609}, {36417, 275}, {40373, 19210}, {40981, 69}, {42068, 8901}, {42293, 4143}, {44088, 3964}, {44162, 54}, {51513, 44173}, {52439, 8795}, {52604, 670}, {52967, 6393}, {55219, 3267}, {57204, 15412}, {61194, 4563}, {61383, 39287}
X(61346) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {25, 2211, 3051}, {1974, 36417, 1501}

X(61347) = VERTEX PRODUCT OF ANTI-EHRMANN-MID TRIANGLE

Barycentrics    (a^2-b^2-c^2)*(a^5-2*a*(b^2-c^2)^2+a^3*(b^2+c^2))^2 : :

X(61347) lies on these lines: {3, 5640}, {51, 3284}, {381, 46808}, {1495, 15860}, {1995, 2967}, {2972, 3066}, {3129, 56515}, {3130, 56514}, {5158, 34416}, {5476, 44891}, {10545, 14919}, {11002, 56266}, {14575, 52153}, {17810, 26898}, {18485, 36430}, {20192, 44892}, {44084, 44162}

X(61347) = X(i)-Dao conjugate of X(j) for these {i, j}: {4550, 57822}
X(61347) = pole of line {549, 57822} with respect to the Stammler hyperbola
X(61347) = intersection, other than A, B, C, of circumconics {{A, B, C, X(381), X(18485)}}, {{A, B, C, X(5158), X(18479)}}, {{A, B, C, X(14483), X(34417)}}
X(61347) = barycentric product X(i)*X(j) for these (i, j): {3, 36430}, {381, 5158}, {1531, 51544}, {14919, 18485}, {18484, 18877}, {34417, 37638}
X(61347) = barycentric quotient X(i)/X(j) for these (i, j): {5158, 57822}, {18485, 46106}, {34417, 43530}, {36430, 264}

X(61348) = VERTEX PRODUCT OF ANTI-EULER TRIANGLE

Barycentrics    (a^4-(b^2-c^2)^2)^2*(3*a^4+(b^2-c^2)^2-4*a^2*(b^2+c^2)) : :

X(61348) lies on these lines: {2, 26870}, {4, 54}, {25, 393}, {51, 1249}, {53, 154}, {107, 43662}, {110, 37192}, {182, 6819}, {264, 7494}, {297, 14826}, {324, 7493}, {427, 7710}, {428, 10002}, {436, 35260}, {631, 26907}, {1096, 40982}, {1217, 11414}, {1495, 6618}, {1585, 12257}, {1586, 12256}, {1853, 53506}, {1990, 17810}, {2052, 6353}, {2207, 3051}, {3079, 44082}, {3087, 6755}, {3089, 41365}, {3147, 44732}, {4186, 56864}, {5085, 37873}, {5200, 12148}, {5702, 34565}, {6530, 6995}, {6619, 11550}, {6620, 27376}, {6748, 17809}, {6776, 52280}, {6820, 9306}, {7378, 16264}, {7392, 17907}, {7394, 37766}, {7714, 52448}, {8889, 14165}, {9777, 40138}, {10565, 43981}, {11245, 15258}, {11433, 41204}, {12147, 52291}, {13366, 40065}, {13394, 41244}, {14853, 56297}, {14978, 47525}, {15466, 40132}, {18533, 60776}, {18679, 37367}, {18950, 43462}, {19189, 26874}, {22080, 37410}, {32000, 43653}, {32064, 52249}, {33630, 34417}, {45105, 60120}

X(61348) = perspector of circumconic {{A, B, C, X(6529), X(16813)}}
X(61348) = X(i)-isoconjugate-of-X(j) for these {i, j}: {255, 8797}, {326, 3527}, {394, 56033}, {1102, 34818}, {6507, 8796}
X(61348) = X(i)-Dao conjugate of X(j) for these {i, j}: {5522, 3265}, {6523, 8797}, {15259, 3527}
X(61348) = pole of line {6587, 15422} with respect to the circumcircle
X(61348) = pole of line {3265, 6368} with respect to the polar circle
X(61348) = pole of line {389, 3183} with respect to the Jerabek hyperbola
X(61348) = pole of line {1853, 6748} with respect to the Kiepert hyperbola
X(61348) = pole of line {12077, 44705} with respect to the orthic inconic
X(61348) = pole of line {3964, 5562} with respect to the Stammler hyperbola
X(61348) = pole of line {4176, 52347} with respect to the Wallace hyperbola
X(61348) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(6755)}}, {{A, B, C, X(25), X(54)}}, {{A, B, C, X(51), X(11424)}}, {{A, B, C, X(184), X(26907)}}, {{A, B, C, X(275), X(393)}}, {{A, B, C, X(2165), X(11427)}}, {{A, B, C, X(2980), X(11206)}}, {{A, B, C, X(3199), X(6759)}}, {{A, B, C, X(4994), X(45105)}}, {{A, B, C, X(6524), X(8884)}}, {{A, B, C, X(6525), X(38808)}}, {{A, B, C, X(8573), X(34818)}}, {{A, B, C, X(16318), X(47122)}}, {{A, B, C, X(18925), X(34449)}}
X(61348) = barycentric product X(i)*X(j) for these (i, j): {107, 47122}, {275, 6755}, {393, 631}, {1093, 36748}, {2207, 44149}, {3087, 4}, {11402, 2052}, {26907, 8794}, {52188, 58879}, {58878, 60120}
X(61348) = barycentric quotient X(i)/X(j) for these (i, j): {393, 8797}, {631, 3926}, {1096, 56033}, {2207, 3527}, {3087, 69}, {6524, 8796}, {6755, 343}, {11402, 394}, {36748, 3964}, {47122, 3265}, {52439, 34818}, {58879, 46951}
X(61348) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {25, 14569, 6525}, {25, 393, 6524}, {393, 6525, 14569}, {1629, 11547, 4}, {6755, 11402, 3087}

X(61349) = VERTEX PRODUCT OF ANTI-EXCENTERS-REFLECTIONS TRIANGLE

Barycentrics    a^2*((a^2-b^2)^2+2*(a^2+b^2)*c^2-3*c^4)*(a^4-3*b^4+2*b^2*c^2+c^4+2*a^2*(b-c)*(b+c))*(a^4-(b^2-c^2)^2)^2 : :

X(61349) lies on these lines: {4, 64}, {25, 800}, {51, 14642}, {107, 33586}, {122, 45188}, {253, 7398}, {427, 40124}, {460, 15591}, {683, 41530}, {1073, 5020}, {1096, 1426}, {1194, 15661}, {1301, 3563}, {2207, 44079}, {3066, 52448}, {3079, 9924}, {6059, 57652}, {7396, 14572}, {9792, 45099}, {11589, 21312}, {14248, 34854}, {14249, 37874}, {15394, 34405}, {17928, 57414}, {18288, 34815}, {36876, 37475}, {36878, 60428}, {39109, 44084}, {41085, 52566}

X(61349) = X(i)-isoconjugate-of-X(j) for these {i, j}: {20, 326}, {63, 37669}, {75, 35602}, {122, 24041}, {204, 4176}, {255, 14615}, {304, 15905}, {394, 18750}, {610, 3926}, {662, 20580}, {799, 58796}, {822, 55224}, {1097, 15394}, {1102, 1249}, {1259, 33673}, {1264, 1394}, {1790, 42699}, {1804, 52346}, {1895, 3964}, {3719, 18623}, {4592, 8057}, {6507, 15466}, {7055, 7070}, {7183, 27382}, {19611, 53050}, {24018, 36841}, {42658, 55202}, {46254, 47409}
X(61349) = X(i)-Dao conjugate of X(j) for these {i, j}: {206, 35602}, {1084, 20580}, {3005, 122}, {3162, 37669}, {3343, 4176}, {5139, 8057}, {6523, 14615}, {14092, 3926}, {15259, 20}, {38996, 58796}, {40839, 305}
X(61349) = X(i)-Ceva conjugate of X(j) for these {i, j}: {6526, 41489}, {41489, 2207}
X(61349) = X(i)-cross conjugate of X(j) for these {i, j}: {20975, 58757}, {52439, 2207}
X(61349) = pole of line {11381, 14642} with respect to the Jerabek hyperbola
X(61349) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(18913)}}, {{A, B, C, X(4), X(25)}}, {{A, B, C, X(6), X(800)}}, {{A, B, C, X(32), X(9786)}}, {{A, B, C, X(51), X(45099)}}, {{A, B, C, X(64), X(33581)}}, {{A, B, C, X(111), X(43670)}}, {{A, B, C, X(154), X(5895)}}, {{A, B, C, X(184), X(10605)}}, {{A, B, C, X(393), X(55415)}}, {{A, B, C, X(459), X(41489)}}, {{A, B, C, X(512), X(15311)}}, {{A, B, C, X(801), X(6531)}}, {{A, B, C, X(1096), X(6059)}}, {{A, B, C, X(1974), X(17810)}}, {{A, B, C, X(1976), X(6391)}}, {{A, B, C, X(2353), X(6247)}}, {{A, B, C, X(2501), X(40144)}}, {{A, B, C, X(3172), X(15005)}}, {{A, B, C, X(3343), X(47437)}}, {{A, B, C, X(5020), X(6620)}}, {{A, B, C, X(6523), X(36434)}}, {{A, B, C, X(6525), X(52439)}}, {{A, B, C, X(12250), X(32319)}}, {{A, B, C, X(15427), X(42658)}}, {{A, B, C, X(15873), X(27375)}}, {{A, B, C, X(17510), X(39268)}}, {{A, B, C, X(34427), X(58784)}}, {{A, B, C, X(36616), X(54496)}}, {{A, B, C, X(51385), X(58757)}}
X(61349) = barycentric product X(i)*X(j) for these (i, j): {4, 41489}, {6, 6526}, {25, 459}, {115, 15384}, {158, 2155}, {393, 64}, {1073, 6524}, {1093, 14642}, {1096, 2184}, {1118, 30457}, {1249, 31942}, {1301, 2501}, {1974, 52581}, {2052, 33581}, {2207, 253}, {2489, 53639}, {3124, 44181}, {13157, 61362}, {15394, 36434}, {19614, 6520}, {22260, 55268}, {32713, 58759}, {33584, 52583}, {34403, 52439}, {36417, 41530}, {46639, 58757}
X(61349) = barycentric quotient X(i)/X(j) for these (i, j): {25, 37669}, {32, 35602}, {64, 3926}, {107, 55224}, {393, 14615}, {459, 305}, {512, 20580}, {669, 58796}, {1073, 4176}, {1096, 18750}, {1301, 4563}, {1824, 42699}, {1974, 15905}, {2155, 326}, {2207, 20}, {2489, 8057}, {2971, 1562}, {3124, 122}, {3172, 53050}, {6059, 27382}, {6524, 15466}, {6526, 76}, {7337, 18623}, {14642, 3964}, {15384, 4590}, {17510, 2063}, {19614, 1102}, {22260, 55269}, {30457, 1264}, {31942, 34403}, {32713, 36841}, {33581, 394}, {33584, 28419}, {36417, 154}, {36434, 14249}, {41489, 69}, {44079, 45200}, {44181, 34537}, {52439, 1249}, {52581, 40050}, {53639, 52608}, {57204, 42658}, {58759, 52617}
X(61349) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {25, 41489, 33581}

X(61350) = VERTEX PRODUCT OF ANTI-INNER-GREBE TRIANGLE

Barycentrics    a^4*(a^2-S) : :

X(61350) lies on these lines: {32, 184}, {251, 18993}, {1180, 19011}, {1692, 8576}, {3053, 5409}, {5012, 18994}, {5408, 12963}, {5412, 19034}, {6424, 10133}, {6636, 9995}, {9994, 34945}, {10329, 44605}, {14153, 45403}, {26454, 46288}

X(61350) = X(i)-isoconjugate-of-X(j) for these {i, j}: {75, 5491}, {304, 24243}, {305, 19217}, {494, 561}, {1307, 20948}, {1577, 54984}, {1928, 26461}, {8946, 40364}, {18833, 45594}
X(61350) = X(i)-Dao conjugate of X(j) for these {i, j}: {206, 5491}, {33365, 1502}, {40368, 494}, {40369, 26461}
X(61350) = X(i)-Ceva conjugate of X(j) for these {i, j}: {36417, 61351}
X(61350) = pole of line {76, 5491} with respect to the Stammler hyperbola
X(61350) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(61368)}}, {{A, B, C, X(32), X(6424)}}, {{A, B, C, X(184), X(10133)}}, {{A, B, C, X(3051), X(3069)}}, {{A, B, C, X(26461), X(61353)}}, {{A, B, C, X(45596), X(61369)}}, {{A, B, C, X(46288), X(61351)}}
X(61350) = barycentric product X(i)*X(j) for these (i, j): {6, 6424}, {184, 52291}, {1974, 487}, {2207, 51905}, {3069, 32}, {10133, 25}, {17432, 61206}, {19216, 1973}, {26494, 61351}, {36417, 8223}, {44162, 46743}, {45596, 6423}, {53061, 5412}
X(61350) = barycentric quotient X(i)/X(j) for these (i, j): {32, 5491}, {487, 40050}, {1501, 494}, {1576, 54984}, {1974, 24243}, {3069, 1502}, {6424, 76}, {9233, 26461}, {10133, 305}, {14574, 1307}, {19216, 40364}, {41331, 45594}, {44162, 8946}, {46743, 40360}, {52291, 18022}, {61351, 26503}
X(61350) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {32, 1501, 61351}, {32, 184, 61368}

X(61351) = VERTEX PRODUCT OF ANTI-OUTER-GREBE TRIANGLE

Barycentrics    a^4*(a^2+S) : :

X(61351) lies on these lines: {32, 184}, {251, 18994}, {1180, 19012}, {1692, 8577}, {3053, 5408}, {5012, 18993}, {5409, 12968}, {5413, 19031}, {6423, 10132}, {6636, 9994}, {8962, 12963}, {9995, 34945}, {10329, 44604}, {14153, 45402}, {26461, 46288}

X(61351) = X(i)-isoconjugate-of-X(j) for these {i, j}: {75, 5490}, {304, 24244}, {305, 19218}, {493, 561}, {1306, 20948}, {1577, 54983}, {1928, 26454}, {8948, 40364}, {18833, 26347}
X(61351) = X(i)-Dao conjugate of X(j) for these {i, j}: {206, 5490}, {33364, 1502}, {40368, 493}, {40369, 26454}
X(61351) = X(i)-Ceva conjugate of X(j) for these {i, j}: {36417, 61350}
X(61351) = pole of line {76, 5490} with respect to the Stammler hyperbola
X(61351) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(61369)}}, {{A, B, C, X(32), X(6423)}}, {{A, B, C, X(184), X(10132)}}, {{A, B, C, X(3051), X(3068)}}, {{A, B, C, X(26454), X(61352)}}, {{A, B, C, X(45595), X(61368)}}, {{A, B, C, X(46288), X(61350)}}
X(61351) = barycentric product X(i)*X(j) for these (i, j): {6, 6423}, {184, 5200}, {1974, 488}, {2207, 51946}, {3068, 32}, {10132, 25}, {17431, 61206}, {19215, 1973}, {26503, 61350}, {36417, 8222}, {44162, 46742}, {45595, 6424}, {53060, 5413}
X(61351) = barycentric quotient X(i)/X(j) for these (i, j): {32, 5490}, {488, 40050}, {1501, 493}, {1576, 54983}, {1974, 24244}, {3068, 1502}, {5200, 18022}, {6423, 76}, {9233, 26454}, {10132, 305}, {14574, 1306}, {19215, 40364}, {41331, 26347}, {44162, 8948}, {46742, 40360}, {61350, 26494}
X(61351) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {32, 1501, 61350}, {32, 184, 61369}

X(61352) = VERTEX PRODUCT OF 1ST ANTI-KENMOTU CENTERS TRIANGLE

Barycentrics    a^4*(b^2+c^2+2*S) : :

X(61352) lies on these lines: {2, 44587}, {6, 588}, {22, 12968}, {32, 184}, {251, 45402}, {372, 20859}, {577, 26454}, {1180, 45434}, {1504, 32568}, {2979, 45435}, {3124, 8577}, {3155, 6423}, {8627, 41411}, {18993, 20965}, {34482, 44605}, {34945, 44604}, {44595, 55888}

X(61352) = X(i)-isoconjugate-of-X(j) for these {i, j}: {75, 60274}
X(61352) = X(i)-Dao conjugate of X(j) for these {i, j}: {206, 60274}, {13882, 1502}
X(61352) = pole of line {3049, 58825} with respect to the Brocard inellipse
X(61352) = pole of line {15234, 34845} with respect to the Kiepert hyperbola
X(61352) = pole of line {76, 590} with respect to the Stammler hyperbola
X(61352) = intersection, other than A, B, C, of circumconics {{A, B, C, X(32), X(588)}}, {{A, B, C, X(26454), X(61351)}}
X(61352) = barycentric product X(i)*X(j) for these (i, j): {32, 45472}, {184, 32588}, {1504, 6}, {13882, 26454}, {26338, 6424}, {32568, 8577}
X(61352) = barycentric quotient X(i)/X(j) for these (i, j): {32, 60274}, {1504, 76}, {32568, 45805}, {32588, 18022}, {45472, 1502}
X(61352) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {32, 3051, 61353}, {32, 61369, 3051}

X(61353) = VERTEX PRODUCT OF 2ND ANTI-KENMOTU CENTERS TRIANGLE

Barycentrics    a^4*(b^2+c^2-2*S) : :

X(61353) lies on these lines: {2, 44586}, {6, 589}, {22, 12963}, {32, 184}, {251, 45403}, {371, 20859}, {577, 26461}, {1180, 45435}, {1505, 32575}, {2979, 45434}, {3124, 8576}, {3156, 6424}, {8627, 41410}, {18994, 20965}, {34482, 44604}, {34945, 44605}, {44596, 55883}

X(61353) = X(i)-isoconjugate-of-X(j) for these {i, j}: {75, 60275}
X(61353) = X(i)-Dao conjugate of X(j) for these {i, j}: {206, 60275}, {13934, 1502}
X(61353) = pole of line {3049, 58827} with respect to the Brocard inellipse
X(61353) = pole of line {15233, 34845} with respect to the Kiepert hyperbola
X(61353) = pole of line {76, 615} with respect to the Stammler hyperbola
X(61353) = intersection, other than A, B, C, of circumconics {{A, B, C, X(32), X(589)}}, {{A, B, C, X(26461), X(61350)}}
X(61353) = barycentric product X(i)*X(j) for these (i, j): {32, 45473}, {184, 32587}, {1505, 6}, {13934, 26461}, {26337, 6423}, {32575, 8576}
X(61353) = barycentric quotient X(i)/X(j) for these (i, j): {32, 60275}, {1505, 76}, {32575, 45806}, {32587, 18022}, {45473, 1502}
X(61353) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {32, 3051, 61352}, {32, 61368, 3051}

X(61354) = VERTEX PRODUCT OF ANTI-ORTHOCENTROIDAL TRIANGLE

Barycentrics    a^6*(a^2-b^2-b*c-c^2)*(a^2-b^2+b*c-c^2)*((a^2-b^2)^2+(a^2+b^2)*c^2-2*c^4)*(a^4-2*b^4+b^2*c^2+c^4+a^2*(b^2-2*c^2)) : :

X(61354) lies on these lines: {6, 40355}, {25, 32715}, {74, 5012}, {184, 1576}, {3167, 9717}, {11245, 12079}, {11402, 60499}, {14264, 18445}, {14355, 56792}, {14385, 22115}, {16030, 46090}, {40353, 58941}, {54034, 58308}

X(61354) = perspector of circumconic {{A, B, C, X(32640), X(32712)}}
X(61354) = X(i)-isoconjugate-of-X(j) for these {i, j}: {75, 14254}, {92, 57482}, {94, 14206}, {328, 1784}, {561, 14583}, {823, 18557}, {1969, 56399}, {1989, 46234}, {2166, 3260}, {2173, 20573}, {14592, 24001}, {18558, 57973}, {20948, 41392}, {32680, 41079}, {35139, 36035}, {51254, 57806}
X(61354) = X(i)-Dao conjugate of X(j) for these {i, j}: {206, 14254}, {11597, 3260}, {22391, 57482}, {34544, 46234}, {36896, 20573}, {40368, 14583}
X(61354) = X(i)-Ceva conjugate of X(j) for these {i, j}: {15395, 32640}, {32715, 14270}
X(61354) = pole of line {3260, 14254} with respect to the Stammler hyperbola
X(61354) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(25), X(14270)}}, {{A, B, C, X(50), X(5063)}}, {{A, B, C, X(184), X(14355)}}, {{A, B, C, X(1511), X(52438)}}, {{A, B, C, X(1576), X(52603)}}, {{A, B, C, X(14385), X(40352)}}, {{A, B, C, X(23606), X(34980)}}, {{A, B, C, X(40355), X(51821)}}, {{A, B, C, X(57136), X(58941)}}
X(61354) = barycentric product X(i)*X(j) for these (i, j): {50, 74}, {184, 57487}, {186, 18877}, {323, 40352}, {1494, 19627}, {1511, 40353}, {2159, 6149}, {2433, 52603}, {2436, 53233}, {2624, 36034}, {11062, 46090}, {11079, 3043}, {14264, 52557}, {14270, 44769}, {14380, 14591}, {14385, 6}, {14919, 34397}, {15395, 18334}, {22115, 8749}, {23357, 56792}, {32640, 526}, {32715, 8552}, {36423, 50464}, {39290, 57136}, {40354, 52437}, {48451, 52179}, {52668, 9717}
X(61354) = barycentric quotient X(i)/X(j) for these (i, j): {32, 14254}, {50, 3260}, {74, 20573}, {184, 57482}, {1501, 14583}, {6149, 46234}, {8749, 18817}, {14270, 41079}, {14385, 76}, {14574, 41392}, {14575, 56399}, {14585, 51254}, {15395, 57546}, {18877, 328}, {19627, 30}, {32640, 35139}, {32715, 46456}, {34397, 46106}, {39201, 18557}, {40351, 18384}, {40352, 94}, {40354, 6344}, {51821, 57486}, {52557, 52552}, {56792, 23962}, {57136, 5664}, {57487, 18022}, {58310, 18558}
X(61354) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {184, 51821, 40352}

X(61355) = VERTEX PRODUCT OF ANTI-X3-ABC REFLECTIONS TRIANGLE

Barycentrics    a^4*(-a^2+b^2+c^2)^2*(2*a^4+(b^2-c^2)^2-3*a^2*(b^2+c^2)) : :

X(61355) lies on these lines: {2, 43998}, {3, 1199}, {140, 22269}, {184, 418}, {216, 44111}, {2055, 15033}, {3078, 6748}, {3284, 34565}, {5012, 34003}, {6641, 9777}, {13366, 22052}, {14152, 14157}, {19210, 22115}, {58267, 58550}

X(61355) = perspector of circumconic {{A, B, C, X(32661), X(35324)}}
X(61355) = X(i)-isoconjugate-of-X(j) for these {i, j}: {92, 39284}, {158, 40410}, {823, 39183}, {1173, 57806}, {1969, 33631}, {6521, 31626}, {24006, 33513}
X(61355) = X(i)-Dao conjugate of X(j) for these {i, j}: {233, 18027}, {1147, 40410}, {1493, 264}, {22391, 39284}
X(61355) = X(i)-Ceva conjugate of X(j) for these {i, j}: {15958, 32320}
X(61355) = pole of line {264, 1656} with respect to the Stammler hyperbola
X(61355) = intersection, other than A, B, C, of circumconics {{A, B, C, X(140), X(418)}}, {{A, B, C, X(184), X(13366)}}, {{A, B, C, X(577), X(22052)}}, {{A, B, C, X(6748), X(18877)}}, {{A, B, C, X(26880), X(59176)}}
X(61355) = barycentric product X(i)*X(j) for these (i, j): {140, 577}, {418, 59183}, {1092, 6748}, {1232, 14585}, {13366, 394}, {15958, 35441}, {17168, 4055}, {17438, 255}, {19210, 233}, {20879, 52430}, {22052, 3}, {23606, 40684}, {32078, 97}, {32320, 35311}, {35324, 520}
X(61355) = barycentric quotient X(i)/X(j) for these (i, j): {140, 18027}, {184, 39284}, {418, 31610}, {577, 40410}, {13366, 2052}, {14533, 39286}, {14575, 33631}, {14585, 1173}, {17438, 57806}, {19210, 31617}, {22052, 264}, {23606, 31626}, {32078, 324}, {32661, 33513}, {35324, 6528}, {39201, 39183}, {44088, 59142}, {59183, 57844}
X(61355) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {184, 577, 61394}, {184, 61394, 418}, {13366, 22052, 32078}, {23606, 61394, 184}

X(61356) = VERTEX PRODUCT OF ANTI-INNER-YFF TRIANGLE

Barycentrics    a^2*(a^4-2*a*b*c*(b+c)+(b^2-c^2)^2-2*a^2*(b^2+c^2)) : :

X(61356) lies on these lines: {1, 1993}, {6, 31}, {25, 20961}, {38, 45728}, {43, 5422}, {81, 11269}, {149, 37685}, {184, 20959}, {323, 29814}, {386, 16472}, {394, 3720}, {601, 40245}, {611, 3938}, {613, 11031}, {899, 10601}, {940, 29662}, {968, 2323}, {1064, 1468}, {1193, 22766}, {1197, 42295}, {1203, 37571}, {1351, 54312}, {1397, 40952}, {1457, 18967}, {1482, 36750}, {1994, 17018}, {2003, 34036}, {2206, 46882}, {2271, 52426}, {3120, 37543}, {3240, 34545}, {3271, 5320}, {3751, 54444}, {4332, 19349}, {4336, 19354}, {4414, 55399}, {5012, 37576}, {7592, 37529}, {9777, 20962}, {11402, 37580}, {15004, 23638}, {15066, 26102}, {15988, 33171}, {17811, 30950}, {20963, 39643}, {25960, 28920}, {26625, 29845}, {26657, 29851}, {32912, 55400}, {34611, 50303}, {34986, 39543}, {36749, 37698}, {37538, 52434}, {37625, 54421}, {44104, 52020}, {44105, 57652}

X(61356) = X(i)-Ceva conjugate of X(j) for these {i, j}: {58992, 649}
X(61356) = pole of line {649, 17412} with respect to the Brocard inellipse
X(61356) = pole of line {86, 10198} with respect to the Stammler hyperbola
X(61356) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(6), X(56041)}}, {{A, B, C, X(31), X(57709)}}, {{A, B, C, X(42), X(26363)}}, {{A, B, C, X(1126), X(61357)}}
X(61356) = barycentric product X(i)*X(j) for these (i, j): {26363, 6}
X(61356) = barycentric quotient X(i)/X(j) for these (i, j): {26363, 76}
X(61356) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 42, 61357}, {6, 55, 61395}, {6, 61398, 31}, {20959, 21746, 184}

X(61357) = VERTEX PRODUCT OF ANTI-OUTER-YFF TRIANGLE

Barycentrics    a^2*(a^4+2*a*b*c*(b+c)+(b^2-c^2)^2-2*a^2*(b^2+c^2)) : :

X(61357) lies on these lines: {1, 5422}, {6, 31}, {25, 20962}, {38, 45729}, {43, 1993}, {181, 44104}, {184, 20958}, {197, 52434}, {386, 14793}, {394, 899}, {611, 17017}, {613, 3938}, {1193, 22767}, {1397, 51377}, {1468, 10269}, {1994, 3240}, {3060, 37576}, {3120, 34048}, {3157, 24443}, {3720, 10601}, {3924, 7078}, {4383, 29662}, {4414, 55400}, {5050, 54312}, {5329, 56878}, {5783, 8013}, {7592, 37699}, {9777, 20961}, {10246, 37509}, {11124, 22383}, {11269, 32911}, {15004, 21746}, {15018, 29814}, {15066, 16569}, {17018, 34545}, {17594, 54444}, {17825, 30950}, {21760, 42295}, {25961, 28965}, {27639, 36942}, {32912, 55399}, {36753, 37698}, {37557, 50593}, {40982, 44086}, {54301, 54418}

X(61357) = pole of line {649, 52307} with respect to the Brocard inellipse
X(61357) = pole of line {86, 10200} with respect to the Stammler hyperbola
X(61357) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(6), X(56352)}}, {{A, B, C, X(31), X(52186)}}, {{A, B, C, X(42), X(26364)}}, {{A, B, C, X(1126), X(61356)}}
X(61357) = barycentric product X(i)*X(j) for these (i, j): {26364, 6}
X(61357) = barycentric quotient X(i)/X(j) for these (i, j): {26364, 76}
X(61357) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 42, 61356}, {6, 55, 61396}, {6, 61397, 31}, {9777, 37580, 20961}, {20958, 23638, 184}

X(61358) = VERTEX PRODUCT OF AQUILA TRIANGLE

Barycentrics    a^2*(a+2*(b+c)) : :

X(61358) lies on these lines: {1, 748}, {2, 3775}, {6, 31}, {8, 32772}, {9, 1962}, {10, 19684}, {36, 386}, {38, 3751}, {41, 6186}, {43, 81}, {44, 37593}, {51, 2187}, {58, 5010}, {63, 4722}, {69, 32781}, {86, 26037}, {100, 28523}, {101, 28326}, {141, 29663}, {145, 32943}, {165, 9340}, {171, 3240}, {181, 604}, {192, 32938}, {193, 26034}, {197, 2317}, {200, 16667}, {210, 1100}, {213, 21820}, {226, 33128}, {238, 17018}, {239, 32771}, {244, 1282}, {255, 16473}, {306, 26061}, {320, 33125}, {321, 49488}, {387, 10590}, {404, 55103}, {495, 48861}, {518, 17017}, {519, 24552}, {524, 33080}, {576, 37619}, {581, 7688}, {584, 28625}, {601, 35000}, {602, 37509}, {612, 1449}, {614, 44841}, {740, 26223}, {749, 757}, {869, 20963}, {894, 32860}, {896, 17594}, {899, 940}, {964, 59302}, {968, 1743}, {982, 17012}, {984, 17011}, {995, 16474}, {999, 1066}, {1064, 44414}, {1079, 24443}, {1150, 6685}, {1171, 59243}, {1185, 21760}, {1191, 2334}, {1203, 3915}, {1211, 29647}, {1215, 3187}, {1386, 3938}, {1402, 1405}, {1403, 19369}, {1404, 1460}, {1451, 2594}, {1458, 52424}, {1471, 52423}, {1478, 48857}, {1497, 16472}, {1621, 16468}, {1698, 4658}, {1724, 59301}, {1757, 28606}, {1864, 4336}, {1999, 32931}, {2003, 9316}, {2093, 4642}, {2181, 2331}, {2206, 4273}, {2212, 44097}, {2223, 7772}, {2258, 2316}, {2356, 44086}, {2650, 11529}, {2887, 31034}, {2895, 32784}, {3017, 7951}, {3122, 3196}, {3210, 32940}, {3214, 5711}, {3219, 17592}, {3242, 29819}, {3244, 4082}, {3434, 50282}, {3589, 24943}, {3618, 33171}, {3666, 4663}, {3683, 16669}, {3715, 16777}, {3720, 3789}, {3740, 37595}, {3741, 49685}, {3745, 4849}, {3750, 16477}, {3755, 33094}, {3757, 17121}, {3758, 4418}, {3759, 32914}, {3764, 4285}, {3773, 20017}, {3778, 4270}, {3791, 26227}, {3821, 32859}, {3826, 37631}, {3846, 29829}, {3870, 16475}, {3873, 29821}, {3891, 49477}, {3896, 3923}, {3914, 24725}, {3917, 53005}, {3924, 44840}, {3930, 16972}, {3935, 17716}, {3936, 25453}, {3966, 29685}, {3989, 5220}, {3995, 50281}, {4011, 41241}, {4023, 6703}, {4028, 5294}, {4035, 30768}, {4042, 30970}, {4046, 17369}, {4062, 32777}, {4085, 6327}, {4272, 20966}, {4281, 10457}, {4290, 4735}, {4302, 48870}, {4360, 32925}, {4362, 46897}, {4365, 49486}, {4393, 32928}, {4414, 4641}, {4417, 29631}, {4429, 32949}, {4430, 17025}, {4646, 5183}, {4651, 19717}, {4672, 32929}, {4685, 19738}, {4716, 28605}, {4734, 32845}, {4850, 32913}, {4851, 29687}, {4868, 49500}, {4966, 29677}, {4970, 32933}, {4972, 31134}, {4981, 29644}, {5007, 37586}, {5147, 39024}, {5158, 23207}, {5192, 35633}, {5223, 42039}, {5230, 8164}, {5233, 29845}, {5247, 10448}, {5264, 50587}, {5272, 17450}, {5278, 43223}, {5299, 41265}, {5313, 37587}, {5326, 37646}, {5396, 39523}, {5710, 8168}, {5718, 24892}, {5741, 29635}, {5847, 33074}, {5905, 33145}, {6057, 17388}, {6187, 20958}, {6535, 17299}, {6767, 16466}, {7191, 49490}, {7226, 17013}, {7277, 11246}, {7296, 17798}, {8013, 17303}, {9332, 61156}, {9342, 36634}, {10327, 50284}, {10434, 46822}, {10453, 32944}, {10589, 11269}, {10601, 25941}, {11679, 31264}, {12943, 48842}, {14996, 17122}, {14997, 17123}, {15523, 38047}, {16569, 37633}, {16668, 21870}, {16670, 37553}, {16690, 40433}, {16704, 32916}, {16706, 33069}, {16834, 31161}, {16948, 37574}, {17020, 17063}, {17024, 49675}, {17032, 20142}, {17070, 17775}, {17120, 32932}, {17126, 60714}, {17135, 25496}, {17147, 32935}, {17150, 32920}, {17165, 32921}, {17300, 25961}, {17350, 32936}, {17352, 29851}, {17364, 33067}, {17367, 33123}, {17379, 59296}, {17455, 23644}, {17483, 33149}, {17484, 33154}, {17717, 33142}, {17723, 29690}, {17770, 32950}, {17778, 25957}, {18064, 24524}, {18134, 29850}, {18995, 61386}, {18996, 61387}, {19701, 59306}, {19714, 59309}, {19734, 28248}, {19742, 29822}, {19743, 19998}, {19785, 32856}, {19786, 33065}, {20011, 32941}, {20012, 32945}, {20018, 54331}, {20075, 50303}, {20086, 33086}, {20983, 57096}, {21748, 44094}, {21753, 40728}, {21814, 23543}, {21936, 61365}, {23579, 50598}, {24349, 32924}, {25502, 37687}, {25960, 29837}, {26098, 33136}, {26102, 37680}, {26222, 32927}, {27064, 32915}, {27538, 58820}, {29633, 32782}, {29636, 33126}, {29643, 33118}, {29650, 46909}, {29654, 33122}, {29659, 33075}, {29662, 37662}, {29667, 32861}, {29671, 33114}, {29673, 33070}, {29678, 35466}, {29679, 32846}, {29818, 42871}, {29849, 33121}, {29852, 33124}, {29856, 30831}, {29867, 30811}, {30950, 37679}, {31019, 33132}, {31053, 33135}, {32455, 44419}, {32773, 32843}, {32774, 33064}, {32776, 33066}, {32780, 33077}, {32842, 33169}, {32848, 33163}, {32854, 49524}, {32855, 33170}, {32858, 33159}, {32863, 33174}, {32865, 33112}, {32917, 37652}, {32918, 37683}, {32930, 49470}, {33071, 33120}, {33073, 33117}, {33088, 33162}, {33092, 33166}, {33093, 33165}, {33096, 33134}, {33097, 33131}, {33101, 33155}, {33103, 33150}, {33105, 33137}, {33107, 33141}, {33111, 33139}, {33127, 40940}, {33771, 51817}, {33779, 51356}, {34048, 42289}, {34379, 54311}, {35238, 36742}, {37677, 59295}, {37684, 59298}, {38315, 41711}, {39247, 39248}, {40976, 44105}, {44104, 52434}, {49487, 50194}, {50487, 54279}, {50491, 57129}, {50558, 56762}, {50581, 57280}

X(61358) = isogonal conjugate of X(30598)
X(61358) = trilinear pole of line {4826, 4834}
X(61358) = perspector of circumconic {{A, B, C, X(101), X(36074)}}
X(61358) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 30598}, {2, 25417}, {7, 56203}, {57, 42030}, {75, 56343}, {76, 34819}, {81, 60203}, {86, 56221}, {89, 30590}, {92, 56070}, {190, 48074}, {274, 28625}, {513, 32042}, {514, 37211}, {693, 8652}, {1698, 30597}, {18160, 58954}
X(61358) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 30598}, {206, 56343}, {5452, 42030}, {22391, 56070}, {32664, 25417}, {39026, 32042}, {40586, 60203}, {40600, 56221}, {51572, 75}, {53167, 3261}, {55053, 48074}
X(61358) = X(i)-Ceva conjugate of X(j) for these {i, j}: {584, 2304}, {4658, 16777}, {8694, 649}
X(61358) = pole of line {46107, 50450} with respect to the polar circle
X(61358) = pole of line {649, 3709} with respect to the Brocard inellipse
X(61358) = pole of line {3136, 44412} with respect to the Kiepert hyperbola
X(61358) = pole of line {86, 3624} with respect to the Stammler hyperbola
X(61358) = pole of line {6586, 48003} with respect to the Steiner inellipse
X(61358) = pole of line {1018, 52923} with respect to the Hutson-Moses hyperbola
X(61358) = pole of line {310, 16709} with respect to the Wallace hyperbola
X(61358) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2308)}}, {{A, B, C, X(6), X(1255)}}, {{A, B, C, X(31), X(1126)}}, {{A, B, C, X(42), X(1698)}}, {{A, B, C, X(55), X(3715)}}, {{A, B, C, X(81), X(21793)}}, {{A, B, C, X(672), X(4654)}}, {{A, B, C, X(674), X(4802)}}, {{A, B, C, X(748), X(757)}}, {{A, B, C, X(749), X(756)}}, {{A, B, C, X(893), X(10987)}}, {{A, B, C, X(902), X(2258)}}, {{A, B, C, X(1011), X(31902)}}, {{A, B, C, X(1096), X(61399)}}, {{A, B, C, X(1174), X(41423)}}, {{A, B, C, X(1918), X(40735)}}, {{A, B, C, X(2268), X(2316)}}, {{A, B, C, X(2269), X(2364)}}, {{A, B, C, X(2276), X(28605)}}, {{A, B, C, X(3678), X(20970)}}, {{A, B, C, X(3927), X(7085)}}, {{A, B, C, X(4826), X(4938)}}, {{A, B, C, X(21035), X(30596)}}, {{A, B, C, X(21747), X(40148)}}, {{A, B, C, X(28625), X(56926)}}
X(61358) = barycentric product X(i)*X(j) for these (i, j): {1, 16777}, {19, 3927}, {37, 4658}, {42, 5333}, {100, 4813}, {101, 4802}, {106, 4727}, {109, 4820}, {110, 4838}, {111, 4938}, {190, 4834}, {292, 4716}, {1018, 4840}, {1293, 4949}, {1333, 4066}, {1698, 6}, {2161, 4880}, {2177, 30589}, {2259, 3824}, {2308, 43260}, {3445, 4898}, {3715, 57}, {4007, 56}, {4557, 4960}, {4654, 55}, {4756, 649}, {4810, 813}, {4823, 692}, {4826, 99}, {4877, 65}, {4942, 9315}, {4958, 901}, {5221, 9}, {28605, 31}, {28841, 4963}, {30596, 32}, {31902, 71}, {34820, 5586}, {36074, 522}, {47902, 59120}, {48005, 662}, {53585, 8652}, {58290, 799}
X(61358) = barycentric quotient X(i)/X(j) for these (i, j): {6, 30598}, {31, 25417}, {32, 56343}, {41, 56203}, {42, 60203}, {55, 42030}, {101, 32042}, {184, 56070}, {213, 56221}, {560, 34819}, {667, 48074}, {692, 37211}, {1698, 76}, {1918, 28625}, {2177, 30590}, {3715, 312}, {3927, 304}, {4007, 3596}, {4066, 27801}, {4654, 6063}, {4658, 274}, {4716, 1921}, {4727, 3264}, {4756, 1978}, {4802, 3261}, {4813, 693}, {4820, 35519}, {4823, 40495}, {4826, 523}, {4834, 514}, {4838, 850}, {4840, 7199}, {4877, 314}, {4880, 20924}, {4938, 3266}, {4960, 52619}, {5221, 85}, {5333, 310}, {16777, 75}, {28605, 561}, {30596, 1502}, {31902, 44129}, {32739, 8652}, {34819, 30597}, {36074, 664}, {48005, 1577}, {58290, 661}
X(61358) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 32911, 748}, {6, 55, 2308}, {31, 17782, 902}, {31, 42, 2177}, {42, 2308, 55}, {43, 81, 750}, {210, 1100, 5311}, {899, 940, 17124}, {1215, 49489, 3187}, {3052, 21747, 31}, {3666, 4663, 32912}, {3750, 16477, 17127}, {3870, 16475, 17469}, {3936, 25453, 31237}, {4028, 5294, 33156}, {4028, 59408, 5294}, {4393, 32937, 32928}, {4430, 17025, 17598}, {4651, 19717, 50302}, {4849, 16666, 3745}, {5220, 20182, 3989}, {5247, 19767, 10448}, {7226, 17013, 17600}, {14547, 61397, 1253}, {17165, 45222, 32921}, {17600, 49712, 7226}, {32946, 50287, 4972}, {33088, 59406, 33162}, {37509, 37698, 602}, {37652, 59297, 32917}

X(61359) = VERTEX PRODUCT OF ARTZT TRIANGLE

Barycentrics    (2*a^2*b^2+(a^2+b^2)*c^2-c^4)*(3*a^4+(b^2-c^2)^2)*(-b^4+b^2*c^2+a^2*(b^2+2*c^2)) : :

X(61359) lies on these lines: {2, 51}, {25, 6531}, {327, 40022}, {1194, 43718}, {1513, 40814}, {1799, 42299}, {2351, 42288}, {3291, 51997}, {3981, 51543}, {9465, 14252}, {20885, 23210}

X(61359) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3403, 40799}, {40802, 52134}
X(61359) = X(i)-Dao conjugate of X(j) for these {i, j}: {7710, 183}
X(61359) = X(i)-Ceva conjugate of X(j) for these {i, j}: {42299, 6776}
X(61359) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6524)}}, {{A, B, C, X(25), X(511)}}, {{A, B, C, X(1501), X(23611)}}, {{A, B, C, X(1799), X(6776)}}, {{A, B, C, X(2351), X(3917)}}, {{A, B, C, X(9755), X(15819)}}, {{A, B, C, X(13857), X(14583)}}, {{A, B, C, X(14853), X(45094)}}, {{A, B, C, X(46316), X(52658)}}
X(61359) = barycentric product X(i)*X(j) for these (i, j): {262, 7735}, {263, 40814}, {327, 40825}, {2186, 4008}, {26714, 30735}, {40822, 46319}, {42313, 6620}, {43718, 43976}
X(61359) = barycentric quotient X(i)/X(j) for these (i, j): {262, 40824}, {263, 40802}, {1513, 51373}, {4008, 3403}, {6620, 458}, {7735, 183}, {26714, 35575}, {40814, 20023}, {40825, 182}, {43976, 44144}, {46319, 40799}

X(61360) = VERTEX PRODUCT OF 7TH BROCARD TRIANGLE

Barycentrics    a^4*(-a^2+b^2+c^2)^2*(a^4+(b^2-c^2)^2) : :

X(61360) lies on these lines: {2, 248}, {25, 32}, {110, 51336}, {184, 14600}, {394, 577}, {418, 14585}, {426, 39643}, {571, 1613}, {647, 59190}, {1501, 61374}, {1974, 61334}, {3051, 14575}, {5063, 40156}, {6638, 10316}, {10311, 52280}, {14713, 40947}

X(61360) = X(i)-isoconjugate-of-X(j) for these {i, j}: {63, 57851}, {92, 34405}, {158, 42407}, {304, 57684}, {561, 56364}, {1969, 56307}, {56004, 57806}
X(61360) = X(i)-Dao conjugate of X(j) for these {i, j}: {1147, 42407}, {3162, 57851}, {3767, 1502}, {6389, 18027}, {14713, 2052}, {22391, 34405}, {40368, 56364}, {53848, 305}
X(61360) = X(i)-Ceva conjugate of X(j) for these {i, j}: {110, 58310}, {51336, 184}
X(61360) = pole of line {2485, 58310} with respect to the circumcircle
X(61360) = pole of line {52584, 58310} with respect to the MacBeath circumconic
X(61360) = pole of line {393, 3926} with respect to the Stammler hyperbola
X(61360) = intersection, other than A, B, C, of circumconics {{A, B, C, X(25), X(426)}}, {{A, B, C, X(184), X(1899)}}, {{A, B, C, X(394), X(2207)}}, {{A, B, C, X(418), X(6751)}}, {{A, B, C, X(577), X(36417)}}, {{A, B, C, X(647), X(22391)}}, {{A, B, C, X(2351), X(31635)}}, {{A, B, C, X(3051), X(27373)}}, {{A, B, C, X(3199), X(3767)}}, {{A, B, C, X(14575), X(17409)}}, {{A, B, C, X(31636), X(60495)}}, {{A, B, C, X(34859), X(59190)}}
X(61360) = barycentric product X(i)*X(j) for these (i, j): {3, 40947}, {25, 426}, {32, 6389}, {54, 6751}, {184, 1899}, {394, 42295}, {1092, 41762}, {1632, 39201}, {1974, 44141}, {2083, 48}, {3767, 577}, {14575, 41009}, {14585, 41760}, {17871, 52430}, {39643, 6}
X(61360) = barycentric quotient X(i)/X(j) for these (i, j): {25, 57851}, {184, 34405}, {426, 305}, {577, 42407}, {1501, 56364}, {1899, 18022}, {1974, 57684}, {2083, 1969}, {3767, 18027}, {6389, 1502}, {6751, 311}, {14575, 56307}, {14585, 56004}, {39643, 76}, {40947, 264}, {41009, 44161}, {42295, 2052}, {44141, 40050}

X(61361) = VERTEX PRODUCT OF 8TH BROCARD TRIANGLE

Barycentrics    a^8*(-a^2+b^2+c^2)^2 : :

X(61361) lies on these lines: {6, 35225}, {32, 44077}, {184, 14600}, {248, 5012}, {1501, 9233}, {9407, 61346}, {9544, 23357}, {14567, 61374}, {14585, 23606}, {22075, 52435}, {23158, 56389}, {35088, 44175}, {36425, 40372}, {44078, 52967}

X(61361) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 44161}, {75, 18027}, {76, 57806}, {92, 18022}, {158, 1502}, {264, 1969}, {305, 6521}, {317, 57898}, {393, 1928}, {561, 2052}, {823, 44173}, {850, 57973}, {1093, 40364}, {1096, 40362}, {6520, 40050}, {6528, 20948}, {7017, 57787}, {14213, 57844}, {14618, 57968}, {17879, 57556}, {23962, 23999}, {37778, 57999}, {40703, 60199}, {44130, 52575}
X(61361) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 44161}, {130, 15415}, {206, 18027}, {1147, 1502}, {6338, 40359}, {6503, 40362}, {22391, 18022}, {37867, 40050}, {39469, 35088}, {40368, 2052}, {40369, 393}
X(61361) = X(i)-Ceva conjugate of X(j) for these {i, j}: {14575, 40373}, {41937, 14574}
X(61361) = pole of line {1502, 18027} with respect to the Stammler hyperbola
X(61361) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(33728)}}, {{A, B, C, X(184), X(9418)}}, {{A, B, C, X(394), X(18899)}}, {{A, B, C, X(577), X(41331)}}, {{A, B, C, X(1501), X(14585)}}, {{A, B, C, X(9247), X(57405)}}, {{A, B, C, X(14575), X(23606)}}, {{A, B, C, X(22391), X(59190)}}, {{A, B, C, X(39469), X(44175)}}, {{A, B, C, X(44077), X(44088)}}
X(61361) = barycentric product X(i)*X(j) for these (i, j): {31, 52430}, {32, 577}, {48, 9247}, {110, 58310}, {184, 184}, {255, 560}, {418, 54034}, {1092, 1974}, {1259, 41280}, {1264, 41281}, {1397, 6056}, {1501, 394}, {1576, 39201}, {1804, 9448}, {1917, 326}, {1973, 4100}, {2175, 7335}, {2206, 4055}, {2351, 52435}, {3049, 32661}, {3926, 9233}, {3964, 44162}, {7125, 9447}, {10547, 20775}, {14533, 217}, {14573, 5562}, {14574, 520}, {14575, 3}, {14585, 6}, {14586, 42293}, {14600, 3289}, {14908, 23200}, {17974, 9418}, {18604, 2205}, {19210, 40981}, {19627, 50433}, {22075, 60495}, {22391, 59190}, {23606, 25}, {23963, 3269}, {23979, 39687}, {28724, 41331}, {32320, 61206}, {34980, 57655}, {35071, 41937}, {36433, 393}, {40373, 69}, {44077, 59176}, {44088, 54}, {46088, 61194}, {52411, 52425}, {52436, 55549}, {58354, 8789}
X(61361) = barycentric quotient X(i)/X(j) for these (i, j): {3, 44161}, {32, 18027}, {184, 18022}, {255, 1928}, {394, 40362}, {560, 57806}, {577, 1502}, {1092, 40050}, {1259, 44159}, {1501, 2052}, {1804, 41287}, {1917, 158}, {3926, 40359}, {3964, 40360}, {4100, 40364}, {6056, 40363}, {7055, 41289}, {7335, 41283}, {9233, 393}, {9247, 1969}, {14533, 57790}, {14573, 8795}, {14574, 6528}, {14575, 264}, {14585, 76}, {14600, 60199}, {23216, 2970}, {23606, 305}, {36425, 36426}, {36433, 3926}, {39201, 44173}, {40372, 52448}, {40373, 4}, {41281, 1118}, {41286, 7337}, {41937, 57556}, {42293, 15415}, {44088, 311}, {44162, 1093}, {52430, 561}, {54034, 57844}, {58310, 850}, {58354, 18901}
X(61361) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {32, 44077, 61334}

X(61362) = VERTEX PRODUCT OF CIRCUMORTHIC TRIANGLE

Barycentrics    a^2*((a^2-b^2)^2-(a^2+b^2)*c^2)*(a^4-(b^2-c^2)^2)^2*(a^4-b^2*c^2+c^4-a^2*(b^2+2*c^2)) : :

X(61362) lies on these lines: {4, 54}, {22, 97}, {24, 8883}, {25, 8745}, {95, 7494}, {96, 3542}, {110, 467}, {154, 14533}, {393, 14593}, {683, 34384}, {933, 3563}, {1176, 8795}, {1495, 33629}, {1501, 2207}, {1974, 6524}, {1976, 8794}, {2052, 19128}, {3547, 19179}, {4993, 5133}, {5012, 33971}, {6620, 40146}, {7387, 19173}, {7500, 43768}, {7503, 19172}, {7512, 19185}, {11062, 56308}, {14569, 18384}, {14576, 57703}, {15139, 53506}, {15422, 53149}, {15760, 19176}, {19149, 19180}, {19192, 26907}, {19209, 41715}, {30506, 40393}, {34405, 44128}, {44080, 59172}, {47328, 52418}

X(61362) = isogonal conjugate of X(52347)
X(61362) = trilinear pole of line {2489, 58756}
X(61362) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 52347}, {3, 18695}, {5, 326}, {48, 28706}, {53, 1102}, {63, 343}, {69, 44706}, {75, 5562}, {216, 304}, {217, 40364}, {255, 311}, {306, 16697}, {324, 6507}, {336, 44716}, {345, 44708}, {394, 14213}, {418, 561}, {662, 60597}, {799, 17434}, {1264, 1393}, {1790, 42698}, {1928, 44088}, {1953, 3926}, {2181, 4176}, {2617, 3265}, {3718, 30493}, {3998, 17167}, {4592, 6368}, {4602, 42293}, {7055, 7069}, {7182, 44707}, {14208, 23181}, {14570, 24018}, {15451, 55202}, {17880, 44710}, {18180, 52396}, {20336, 44709}, {24041, 35442}, {57968, 58305}
X(61362) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 52347}, {206, 5562}, {1084, 60597}, {1249, 28706}, {3005, 35442}, {3162, 343}, {5139, 6368}, {6523, 311}, {15259, 5}, {36103, 18695}, {38996, 17434}, {40368, 418}, {40369, 44088}, {46604, 60824}
X(61362) = X(i)-Ceva conjugate of X(j) for these {i, j}: {8884, 8882}
X(61362) = X(i)-cross conjugate of X(j) for these {i, j}: {58757, 32713}
X(61362) = pole of line {16040, 23286} with respect to the circumcircle
X(61362) = pole of line {5562, 6751} with respect to the Stammler hyperbola
X(61362) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(18925)}}, {{A, B, C, X(4), X(25)}}, {{A, B, C, X(6), X(11427)}}, {{A, B, C, X(22), X(6620)}}, {{A, B, C, X(32), X(578)}}, {{A, B, C, X(51), X(3574)}}, {{A, B, C, X(54), X(39287)}}, {{A, B, C, X(111), X(5392)}}, {{A, B, C, X(184), X(1176)}}, {{A, B, C, X(251), X(6531)}}, {{A, B, C, X(275), X(8882)}}, {{A, B, C, X(393), X(8745)}}, {{A, B, C, X(512), X(18400)}}, {{A, B, C, X(669), X(61346)}}, {{A, B, C, X(1495), X(44079)}}, {{A, B, C, X(1614), X(40352)}}, {{A, B, C, X(2351), X(9292)}}, {{A, B, C, X(2353), X(9833)}}, {{A, B, C, X(2857), X(16277)}}, {{A, B, C, X(3199), X(6750)}}, {{A, B, C, X(3456), X(13419)}}, {{A, B, C, X(3519), X(18946)}}, {{A, B, C, X(6145), X(32346)}}, {{A, B, C, X(6759), X(33581)}}, {{A, B, C, X(8794), X(15422)}}, {{A, B, C, X(8795), X(19174)}}, {{A, B, C, X(8884), X(14518)}}, {{A, B, C, X(10619), X(51477)}}, {{A, B, C, X(11060), X(18388)}}, {{A, B, C, X(11206), X(34207)}}, {{A, B, C, X(12254), X(34448)}}, {{A, B, C, X(13854), X(43717)}}, {{A, B, C, X(14569), X(58757)}}, {{A, B, C, X(15033), X(40354)}}, {{A, B, C, X(21659), X(52153)}}, {{A, B, C, X(32713), X(53176)}}, {{A, B, C, X(34397), X(52417)}}, {{A, B, C, X(36616), X(54930)}}, {{A, B, C, X(40144), X(56363)}}, {{A, B, C, X(41762), X(44128)}}, {{A, B, C, X(44057), X(51513)}}, {{A, B, C, X(44077), X(52432)}}, {{A, B, C, X(60114), X(60775)}}
X(61362) = barycentric product X(i)*X(j) for these (i, j): {4, 8882}, {6, 8884}, {19, 2190}, {25, 275}, {32, 8795}, {107, 2623}, {110, 15422}, {158, 2148}, {184, 8794}, {393, 54}, {1093, 14533}, {1096, 2167}, {1141, 52418}, {1501, 57844}, {1973, 40440}, {1974, 276}, {2052, 54034}, {2169, 6520}, {2207, 95}, {2501, 933}, {3049, 52779}, {5317, 56254}, {6524, 97}, {8745, 96}, {11547, 41271}, {14573, 18027}, {14859, 36423}, {15352, 58308}, {15412, 32713}, {16081, 58306}, {16813, 512}, {18315, 58757}, {18831, 2489}, {19174, 251}, {19189, 6531}, {23286, 6529}, {23964, 8901}, {24019, 2616}, {33629, 6526}, {34384, 36417}, {34386, 52439}, {38808, 41489}, {40354, 43752}, {40402, 51887}, {42401, 58310}, {42405, 669}, {44162, 57790}, {52917, 55253}, {58756, 648}
X(61362) = barycentric quotient X(i)/X(j) for these (i, j): {4, 28706}, {6, 52347}, {19, 18695}, {25, 343}, {32, 5562}, {54, 3926}, {97, 4176}, {275, 305}, {276, 40050}, {393, 311}, {512, 60597}, {669, 17434}, {933, 4563}, {1096, 14213}, {1395, 44708}, {1501, 418}, {1824, 42698}, {1973, 44706}, {1974, 216}, {2148, 326}, {2169, 1102}, {2190, 304}, {2203, 16697}, {2207, 5}, {2211, 44716}, {2489, 6368}, {2623, 3265}, {3124, 35442}, {6524, 324}, {8745, 39113}, {8794, 18022}, {8795, 1502}, {8882, 69}, {8884, 76}, {8901, 36793}, {9233, 44088}, {9426, 42293}, {14533, 3964}, {14569, 45793}, {14573, 577}, {14581, 1568}, {15412, 52617}, {15422, 850}, {16813, 670}, {18831, 52608}, {19174, 8024}, {19189, 6393}, {23286, 4143}, {32713, 14570}, {34854, 60524}, {36417, 51}, {36434, 13450}, {40354, 44715}, {40440, 40364}, {40825, 42353}, {41270, 51386}, {41271, 52350}, {42405, 4609}, {44077, 52032}, {44162, 217}, {52418, 1273}, {52439, 53}, {52917, 55252}, {54034, 394}, {57204, 15451}, {57260, 53174}, {57790, 40360}, {57844, 40362}, {58306, 36212}, {58308, 52613}, {58756, 525}, {58757, 18314}, {60779, 8800}, {61206, 23181}, {61346, 61378}, {61349, 13157}
X(61362) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {25, 54034, 8882}, {275, 8884, 19174}

X(61363) = VERTEX PRODUCT OF 2ND EULER TRIANGLE

Barycentrics    a^2*(-a^2+b^2+c^2)^2*(a^4+b^4-2*(a^2+b^2)*c^2+c^4)*(a^4-2*a^2*b^2+(b^2-c^2)^2)*(-(b^2-c^2)^2+a^2*(b^2+c^2)) : :

X(61363) lies on these lines: {4, 52}, {51, 36412}, {161, 17849}, {184, 216}, {217, 61378}, {418, 6751}, {925, 1298}, {2165, 58550}, {2393, 32319}, {3155, 10665}, {3156, 10666}, {3564, 56304}, {5562, 10600}, {18475, 20574}, {21243, 34965}, {34853, 45118}, {41271, 41891}, {52350, 54032}

X(61363) = trilinear pole of line {34983, 42293}
X(61363) = X(i)-isoconjugate-of-X(j) for these {i, j}: {24, 40440}, {47, 8795}, {275, 1748}, {317, 2190}, {2167, 11547}, {2169, 59139}, {8884, 44179}, {15422, 55249}, {42405, 55216}
X(61363) = X(i)-Dao conjugate of X(j) for these {i, j}: {5, 317}, {130, 924}, {2972, 6563}, {14363, 59139}, {15450, 57065}, {34853, 8795}, {37864, 8884}, {40588, 11547}
X(61363) = X(i)-Ceva conjugate of X(j) for these {i, j}: {2351, 418}, {56272, 216}
X(61363) = pole of line {317, 1147} with respect to the Stammler hyperbola
X(61363) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(51)}}, {{A, B, C, X(5), X(6641)}}, {{A, B, C, X(68), X(59176)}}, {{A, B, C, X(216), X(324)}}, {{A, B, C, X(520), X(41724)}}, {{A, B, C, X(847), X(2351)}}, {{A, B, C, X(3199), X(10600)}}, {{A, B, C, X(5392), X(55549)}}, {{A, B, C, X(5593), X(27352)}}, {{A, B, C, X(5889), X(23606)}}, {{A, B, C, X(6751), X(14569)}}, {{A, B, C, X(13754), X(58305)}}, {{A, B, C, X(17434), X(51481)}}, {{A, B, C, X(32078), X(61111)}}, {{A, B, C, X(42487), X(44176)}}, {{A, B, C, X(44088), X(47328)}}
X(61363) = barycentric product X(i)*X(j) for these (i, j): {5, 55549}, {51, 52350}, {216, 68}, {324, 59176}, {418, 5392}, {1820, 44706}, {2165, 5562}, {2351, 343}, {16391, 53}, {17434, 925}, {20563, 217}, {30450, 58305}, {32734, 60597}, {34385, 46394}, {42293, 46134}, {44088, 57904}, {52347, 60501}, {56272, 577}, {57875, 61378}
X(61363) = barycentric quotient X(i)/X(j) for these (i, j): {51, 11547}, {53, 59139}, {68, 276}, {216, 317}, {217, 24}, {418, 1993}, {925, 42405}, {1820, 40440}, {2165, 8795}, {2351, 275}, {5392, 57844}, {5562, 7763}, {6751, 41770}, {14593, 8794}, {15451, 57065}, {16391, 34386}, {17434, 6563}, {20563, 57790}, {23181, 55227}, {30450, 54950}, {32734, 16813}, {40981, 8745}, {42293, 924}, {44088, 571}, {46394, 52}, {52350, 34384}, {55549, 95}, {56272, 18027}, {58305, 52584}, {59176, 97}, {60501, 8884}, {61194, 52917}, {61378, 467}
X(61363) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2351, 55549, 59176}

X(61364) = VERTEX PRODUCT OF EXTANGENTS TRIANGLE

Barycentrics    a^4*(a+b-c)*(a-b+c)*(b+c)^2 : :

X(61364) lies on these lines: {6, 16872}, {7, 1403}, {8, 34247}, {11, 55035}, {12, 1284}, {32, 41280}, {37, 22298}, {42, 181}, {55, 941}, {56, 5132}, {109, 39441}, {237, 7122}, {256, 5143}, {560, 40981}, {604, 1911}, {1259, 54383}, {1376, 55094}, {1423, 4551}, {1469, 2594}, {1918, 40935}, {1974, 9448}, {2171, 23928}, {2212, 61050}, {2223, 2269}, {2245, 22301}, {7109, 21815}

X(61364) = isogonal conjugate of X(18021)
X(61364) = perspector of circumconic {{A, B, C, X(4559), X(58969)}}
X(61364) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 18021}, {2, 52379}, {8, 873}, {11, 24037}, {21, 310}, {55, 57992}, {58, 40072}, {60, 561}, {69, 57779}, {75, 261}, {76, 2185}, {81, 28660}, {85, 7058}, {86, 314}, {99, 18155}, {270, 305}, {274, 333}, {283, 57796}, {284, 6385}, {286, 332}, {304, 46103}, {312, 1509}, {341, 552}, {514, 4631}, {521, 55229}, {522, 4623}, {593, 28659}, {643, 52619}, {645, 7199}, {670, 3737}, {757, 3596}, {763, 30713}, {799, 4560}, {812, 36806}, {849, 40363}, {905, 55233}, {1043, 57785}, {1098, 6063}, {1111, 6064}, {1444, 44130}, {1502, 2150}, {1577, 55196}, {1812, 44129}, {2170, 34537}, {2189, 40364}, {2321, 57949}, {2326, 57918}, {3061, 7307}, {3261, 4612}, {3701, 6628}, {4357, 52550}, {4391, 4610}, {4563, 57215}, {4590, 4858}, {4601, 17197}, {4602, 7252}, {4625, 7253}, {4636, 40495}, {6332, 55231}, {7054, 20567}, {7182, 59482}, {7192, 7257}, {7258, 17096}, {7304, 27424}, {7340, 24026}, {8822, 57795}, {12836, 14124}, {14024, 57987}, {17185, 40827}, {17206, 31623}, {17880, 18020}, {17925, 55207}, {17926, 55205}, {20568, 30606}, {20882, 31620}, {21789, 55213}, {23189, 57968}, {24041, 34387}, {26932, 46254}, {30940, 36800}, {35519, 52935}, {40075, 52380}, {40213, 55194}
X(61364) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 18021}, {10, 40072}, {206, 261}, {223, 57992}, {512, 11}, {3005, 34387}, {4075, 40363}, {15267, 6063}, {32664, 52379}, {38986, 18155}, {38996, 4560}, {40368, 60}, {40586, 28660}, {40590, 6385}, {40600, 314}, {40607, 3596}, {40611, 310}, {55060, 52619}, {56325, 1502}
X(61364) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4998, 4559}
X(61364) = X(i)-cross conjugate of X(j) for these {i, j}: {7063, 53581}
X(61364) = pole of line {2295, 44411} with respect to the Kiepert hyperbola
X(61364) = pole of line {261, 18021} with respect to the Stammler hyperbola
X(61364) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(39780)}}, {{A, B, C, X(32), X(941)}}, {{A, B, C, X(42), X(872)}}, {{A, B, C, X(213), X(2298)}}, {{A, B, C, X(228), X(2205)}}, {{A, B, C, X(512), X(55035)}}, {{A, B, C, X(560), X(669)}}, {{A, B, C, X(904), X(9403)}}, {{A, B, C, X(1084), X(61052)}}, {{A, B, C, X(1400), X(18097)}}, {{A, B, C, X(1974), X(40952)}}, {{A, B, C, X(2054), X(2206)}}, {{A, B, C, X(3051), X(27042)}}, {{A, B, C, X(3778), X(7148)}}, {{A, B, C, X(5051), X(27369)}}, {{A, B, C, X(6378), X(14624)}}, {{A, B, C, X(7143), X(52020)}}, {{A, B, C, X(18099), X(20964)}}, {{A, B, C, X(18112), X(20984)}}, {{A, B, C, X(26115), X(41267)}}, {{A, B, C, X(50487), X(51377)}}
X(61364) = barycentric product X(i)*X(j) for these (i, j): {7, 7109}, {12, 32}, {57, 872}, {109, 4079}, {181, 6}, {184, 8736}, {213, 65}, {220, 7143}, {560, 6358}, {604, 756}, {1016, 1356}, {1018, 51641}, {1037, 21813}, {1042, 1334}, {1084, 4998}, {1252, 61052}, {1253, 7147}, {1254, 41}, {1275, 7063}, {1365, 23990}, {1395, 3949}, {1397, 594}, {1400, 42}, {1402, 37}, {1403, 6378}, {1407, 7064}, {1408, 762}, {1409, 1824}, {1415, 4705}, {1425, 607}, {1426, 52370}, {1441, 2205}, {1500, 56}, {1501, 34388}, {1576, 55197}, {1880, 228}, {1918, 226}, {1922, 7235}, {1973, 201}, {1974, 26942}, {2149, 2643}, {2171, 31}, {2175, 6354}, {2197, 25}, {2200, 225}, {2207, 7066}, {2212, 37755}, {2298, 59174}, {2333, 73}, {2971, 44717}, {3027, 51856}, {3049, 61178}, {3124, 59}, {3690, 608}, {3709, 53321}, {4551, 798}, {4552, 669}, {4557, 7180}, {4559, 512}, {4565, 58289}, {7104, 7211}, {14827, 6046}, {16947, 6535}, {18097, 41267}, {20975, 7115}, {21794, 6186}, {21815, 56358}, {21859, 667}, {23067, 2489}, {23099, 55194}, {23979, 4092}, {28654, 41280}, {32674, 55230}, {32675, 42666}, {40147, 52024}, {40521, 57181}, {41526, 7148}, {42661, 8687}, {50487, 651}, {52205, 61059}, {52386, 7337}, {52410, 6057}, {52411, 7140}, {53581, 664}, {55234, 8750}, {56285, 9247}, {57185, 692}, {57652, 71}, {58301, 61170}, {60542, 60542}, {61048, 61402}
X(61364) = barycentric quotient X(i)/X(j) for these (i, j): {6, 18021}, {12, 1502}, {31, 52379}, {32, 261}, {37, 40072}, {42, 28660}, {57, 57992}, {59, 34537}, {65, 6385}, {109, 52612}, {181, 76}, {201, 40364}, {213, 314}, {560, 2185}, {594, 40363}, {604, 873}, {669, 4560}, {692, 4631}, {756, 28659}, {798, 18155}, {872, 312}, {1020, 55213}, {1084, 11}, {1254, 20567}, {1356, 1086}, {1397, 1509}, {1400, 310}, {1402, 274}, {1408, 57949}, {1415, 4623}, {1425, 57918}, {1500, 3596}, {1501, 60}, {1576, 55196}, {1880, 57796}, {1917, 2150}, {1918, 333}, {1924, 3737}, {1973, 57779}, {1974, 46103}, {2149, 24037}, {2171, 561}, {2175, 7058}, {2197, 305}, {2200, 332}, {2205, 21}, {2333, 44130}, {3124, 34387}, {3690, 57919}, {4079, 35519}, {4117, 2170}, {4551, 4602}, {4552, 4609}, {4559, 670}, {4998, 44168}, {6354, 41283}, {6358, 1928}, {7063, 1146}, {7064, 59761}, {7109, 8}, {7143, 57792}, {7180, 52619}, {7235, 44169}, {8736, 18022}, {8750, 55233}, {9426, 7252}, {9427, 3271}, {9447, 1098}, {9448, 7054}, {9459, 30606}, {16947, 6628}, {20616, 40088}, {21751, 3794}, {21815, 3705}, {21859, 6386}, {23067, 52608}, {23099, 55195}, {23216, 7117}, {23979, 7340}, {23990, 6064}, {26942, 40050}, {28654, 44159}, {32674, 55229}, {34067, 36806}, {34388, 40362}, {41280, 593}, {42068, 8735}, {44162, 2189}, {50487, 4391}, {51641, 7199}, {52065, 4516}, {52410, 552}, {53581, 522}, {55197, 44173}, {57185, 40495}, {57652, 44129}, {59174, 20911}, {61048, 61403}, {61052, 23989}, {61059, 56660}
X(61364) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1400, 52024, 39780}

X(61365) = VERTEX PRODUCT OF FUHRMANN TRIANGLE

Barycentrics    a^2*(b*(a+b)-c^2)*(-b^2+c*(a+c)) : :

X(61365) lies on these lines: {1, 20966}, {31, 3122}, {42, 2277}, {51, 1015}, {209, 8610}, {244, 3772}, {291, 32925}, {560, 6186}, {982, 29845}, {3056, 40148}, {3121, 61366}, {3124, 23543}, {3778, 5311}, {4446, 32928}, {7032, 20961}, {15004, 34543}, {17053, 40952}, {17065, 32914}, {21330, 24943}, {21936, 61358}, {24046, 33150}, {24575, 26037}, {28288, 29677}

X(61366) = VERTEX PRODUCT OF 2ND FUHRMANN TRIANGLE

Barycentrics    a^2*(b^2+(a-c)*c)*((a-b)*b+c^2) : :

X(61366) lies on circumconic {{A, B, C, X(25), X(14008)}} and on these lines: {2, 5826}, {25, 41}, {43, 3034}, {51, 14936}, {57, 20974}, {649, 26892}, {661, 1836}, {1146, 37354}, {2170, 29662}, {3121, 61365}, {6187, 9447}, {7109, 59800}, {8049, 47775}, {9352, 24484}, {16588, 51377}, {17451, 29678}, {20665, 20962}, {20989, 32664}

X(61366) = barycentric product X(i)*X(j) for these (i, j): {14008, 42}
X(61366) = barycentric quotient X(i)/X(j) for these (i, j): {14008, 310}

X(61367) = VERTEX PRODUCT OF INNER-GARCIA TRIANGLE

Barycentrics    a^2*(a^2-b*(b+c))*(a^2-c*(b+c)) : :

X(61367) lies on circumconic {{A, B, C, X(2053), X(7299)}} and on these lines: {31, 172}, {110, 7262}, {394, 53542}, {579, 6186}, {748, 7193}, {756, 2175}, {896, 9306}, {1962, 5320}, {2112, 36808}, {2310, 6056}, {2979, 24436}, {3573, 32860}, {5310, 52405}, {17125, 26889}, {17796, 20988}, {32852, 56529}

X(61367) = pole of line {932, 29041} with respect to the Hutson-Moses hyperbola
X(61367) = barycentric product X(i)*X(j) for these (i, j): {7299, 9}
X(61367) = barycentric quotient X(i)/X(j) for these (i, j): {7299, 85}

X(61368) = VERTEX PRODUCT OF INNER-GREBE TRIANGLE

Barycentrics    a^4*(b^2+c^2-S) : :

X(61368) lies on these lines: {2, 13885}, {6, 494}, {32, 184}, {251, 10792}, {371, 1194}, {1180, 9994}, {1184, 6424}, {1196, 8576}, {1613, 44586}, {1915, 45403}, {2979, 9995}, {5052, 8577}, {5058, 42295}, {6421, 32562}, {13345, 26454}, {19011, 34945}, {19012, 34482}

X(61368) = perspector of circumconic {{A, B, C, X(1307), X(1576)}}
X(61368) = X(i)-isoconjugate-of-X(j) for these {i, j}: {75, 60205}
X(61368) = X(i)-Dao conjugate of X(j) for these {i, j}: {206, 60205}
X(61368) = pole of line {1592, 34845} with respect to the Kiepert hyperbola
X(61368) = pole of line {76, 3069} with respect to the Stammler hyperbola
X(61368) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(61350)}}, {{A, B, C, X(32), X(494)}}, {{A, B, C, X(184), X(45401)}}, {{A, B, C, X(1501), X(26461)}}, {{A, B, C, X(45595), X(61351)}}
X(61368) = barycentric product X(i)*X(j) for these (i, j): {3, 45401}, {6, 6421}, {32, 5591}, {184, 3128}, {10133, 26374}, {19447, 8946}, {45414, 6424}, {45727, 6423}
X(61368) = barycentric quotient X(i)/X(j) for these (i, j): {32, 60205}, {3128, 18022}, {5591, 1502}, {6421, 76}, {19447, 46743}, {45401, 264}
X(61368) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {32, 184, 61350}, {32, 3051, 61369}, {3051, 61353, 32}

X(61369) = VERTEX PRODUCT OF OUTER-GREBE TRIANGLE

Barycentrics    a^4*(b^2+c^2+S) : :

X(61369) lies on these lines: {2, 13938}, {6, 493}, {32, 184}, {251, 10793}, {372, 1194}, {1180, 9995}, {1184, 6423}, {1196, 8577}, {1613, 44587}, {1915, 45402}, {2979, 9994}, {5052, 8576}, {5062, 42295}, {6422, 32569}, {13345, 26461}, {19011, 34482}, {19012, 34945}

X(61369) = perspector of circumconic {{A, B, C, X(1306), X(1576)}}
X(61369) = X(i)-isoconjugate-of-X(j) for these {i, j}: {75, 60204}
X(61369) = X(i)-Dao conjugate of X(j) for these {i, j}: {206, 60204}
X(61369) = pole of line {1591, 34845} with respect to the Kiepert hyperbola
X(61369) = pole of line {76, 3068} with respect to the Stammler hyperbola
X(61369) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(61351)}}, {{A, B, C, X(32), X(493)}}, {{A, B, C, X(184), X(45400)}}, {{A, B, C, X(1501), X(26454)}}, {{A, B, C, X(45596), X(61350)}}
X(61369) = barycentric product X(i)*X(j) for these (i, j): {3, 45400}, {6, 6422}, {32, 5590}, {184, 3127}, {10132, 26373}, {19446, 8948}, {45415, 6423}, {45726, 6424}
X(61369) = barycentric quotient X(i)/X(j) for these (i, j): {32, 60204}, {3127, 18022}, {5590, 1502}, {6422, 76}, {19446, 46742}, {45400, 264}
X(61369) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {32, 184, 61351}, {32, 3051, 61368}, {3051, 61352, 32}

X(61370) = VERTEX PRODUCT OF 1ST HALF-DIAMONDS TRIANGLE

Barycentrics    3*a^2*(-2*a^4+(b^2-c^2)^2+a^2*(b^2+c^2))-2*sqrt(3)*(2*a^4+2*(b^2-c^2)^2-a^2*(b^2+c^2))*S : :

X(61370) lies on these lines: {2, 13}, {14, 14177}, {23, 22510}, {110, 22511}, {476, 2381}, {619, 41001}, {1495, 61371}, {1637, 6137}, {1989, 3458}, {3003, 36298}, {3129, 11063}, {5995, 34376}, {6104, 34009}, {9143, 16268}, {10616, 15769}, {11537, 30452}, {14170, 46855}, {15360, 16267}, {30460, 41995}, {30465, 53430}, {32460, 53454}, {36296, 61317}, {36316, 54490}, {38432, 46854}, {39555, 44462}

X(61370) = perspector of circumconic {{A, B, C, X(11080), X(23895)}}
X(61370) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1094, 11118}, {2151, 40706}, {6149, 11120}, {38404, 51806}, {47482, 52414}
X(61370) = X(i)-vertex conjugate of X(j) for these {i, j}: {11142, 20578}
X(61370) = X(i)-Dao conjugate of X(j) for these {i, j}: {395, 7799}, {619, 298}, {14993, 11120}, {15295, 16460}, {30468, 3268}, {40578, 40706}
X(61370) = X(i)-Ceva conjugate of X(j) for these {i, j}: {476, 20578}, {36211, 36299}
X(61370) = pole of line {11142, 20578} with respect to the circumcircle
X(61370) = pole of line {23870, 46708} with respect to the Steiner circumellipse
X(61370) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(395)}}, {{A, B, C, X(14), X(624)}}, {{A, B, C, X(16), X(619)}}, {{A, B, C, X(530), X(54490)}}, {{A, B, C, X(533), X(618)}}, {{A, B, C, X(616), X(1138)}}, {{A, B, C, X(622), X(1141)}}, {{A, B, C, X(1989), X(11078)}}, {{A, B, C, X(6137), X(11131)}}, {{A, B, C, X(11080), X(16770)}}, {{A, B, C, X(11142), X(34534)}}
X(61370) = barycentric product X(i)*X(j) for these (i, j): {13, 395}, {1989, 619}, {3457, 41001}, {3480, 51270}, {10217, 23715}, {11078, 8015}, {11080, 533}, {11081, 43086}, {11082, 6672}, {14447, 36839}, {16255, 18777}, {16770, 36305}, {20578, 35315}, {34295, 41889}, {35444, 476}, {36307, 9117}, {40709, 462}, {52193, 8737}
X(61370) = barycentric quotient X(i)/X(j) for these (i, j): {13, 40706}, {395, 298}, {462, 470}, {533, 11129}, {619, 7799}, {1989, 11120}, {3457, 6151}, {5995, 10410}, {6672, 11133}, {8015, 11092}, {8737, 38427}, {11060, 16460}, {11080, 11118}, {11081, 38404}, {35330, 17402}, {35444, 3268}, {36305, 19778}, {52153, 47482}
X(61370) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 3457, 8014}, {1989, 11081, 36299}

X(61371) = VERTEX PRODUCT OF 2ND HALF-DIAMONDS TRIANGLE

Barycentrics    3*a^2*(-2*a^4+(b^2-c^2)^2+a^2*(b^2+c^2))+2*sqrt(3)*(2*a^4+2*(b^2-c^2)^2-a^2*(b^2+c^2))*S : :

X(61371) lies on these lines: {2, 14}, {13, 14181}, {23, 22511}, {110, 22510}, {476, 2380}, {618, 41000}, {1495, 61370}, {1637, 6138}, {1989, 3457}, {3003, 36299}, {3130, 11063}, {5994, 34374}, {6105, 34008}, {9143, 16267}, {10617, 15768}, {11549, 30453}, {14169, 46854}, {15360, 16268}, {30463, 41996}, {30468, 53442}, {32461, 53465}, {36297, 61318}, {36317, 54489}, {38431, 46855}, {39554, 44466}

X(61371) = perspector of circumconic {{A, B, C, X(11085), X(23896)}}
X(61371) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1095, 11117}, {2152, 40707}, {6149, 11119}, {38403, 51805}, {47481, 52414}
X(61371) = X(i)-vertex conjugate of X(j) for these {i, j}: {11141, 20579}
X(61371) = X(i)-Dao conjugate of X(j) for these {i, j}: {396, 7799}, {618, 299}, {14993, 11119}, {15295, 16459}, {30465, 3268}, {40579, 40707}
X(61371) = X(i)-Ceva conjugate of X(j) for these {i, j}: {476, 20579}, {36210, 36298}
X(61371) = pole of line {11141, 20579} with respect to the circumcircle
X(61371) = pole of line {23871, 46709} with respect to the Steiner circumellipse
X(61371) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(396)}}, {{A, B, C, X(13), X(623)}}, {{A, B, C, X(15), X(618)}}, {{A, B, C, X(531), X(54489)}}, {{A, B, C, X(532), X(619)}}, {{A, B, C, X(617), X(1138)}}, {{A, B, C, X(621), X(1141)}}, {{A, B, C, X(1989), X(11092)}}, {{A, B, C, X(6138), X(11130)}}, {{A, B, C, X(11085), X(16771)}}, {{A, B, C, X(11141), X(34533)}}
X(61371) = barycentric product X(i)*X(j) for these (i, j): {14, 396}, {1989, 618}, {3458, 41000}, {3479, 51277}, {10218, 23714}, {11085, 532}, {11086, 43085}, {11087, 6671}, {11092, 8014}, {14446, 36840}, {16256, 18776}, {16771, 36304}, {20579, 35314}, {35443, 476}, {36310, 9115}, {40710, 463}, {52194, 8738}
X(61371) = barycentric quotient X(i)/X(j) for these (i, j): {14, 40707}, {396, 299}, {463, 471}, {532, 11128}, {618, 7799}, {1989, 11119}, {3458, 2981}, {5994, 10409}, {6671, 11132}, {8014, 11078}, {8738, 38428}, {11060, 16459}, {11085, 11117}, {11086, 38403}, {35329, 17403}, {35443, 3268}, {36304, 19779}, {52153, 47481}
X(61371) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14, 3458, 8015}, {1989, 11086, 36298}

X(61372) = VERTEX PRODUCT OF HATZIPOLAKIS-MOSES TRIANGLE

Barycentrics    a^4*((a^2-b^2)^2-(a^2+b^2)*c^2)*(a^4-b^2*c^2+c^4-a^2*(b^2+2*c^2))*(a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)-2*a^2*(b^4-b^2*c^2+c^4)) : :

X(61372) lies on these lines: {20, 54}, {96, 10539}, {160, 184}, {393, 14593}, {512, 2623}, {933, 59025}, {1147, 8883}, {1181, 16035}, {1503, 8901}, {3796, 16030}, {8882, 44080}, {10420, 45135}, {14560, 14595}

X(61372) = perspector of circumconic {{A, B, C, X(8882), X(14586)}}
X(61372) = X(i)-isoconjugate-of-X(j) for these {i, j}: {75, 60035}, {311, 36053}, {799, 35361}, {1300, 18695}, {1953, 40832}, {2618, 18878}, {2986, 14213}
X(61372) = X(i)-vertex conjugate of X(j) for these {i, j}: {571, 2623}
X(61372) = X(i)-Dao conjugate of X(j) for these {i, j}: {113, 311}, {206, 60035}, {38996, 35361}, {39021, 15415}
X(61372) = X(i)-Ceva conjugate of X(j) for these {i, j}: {45135, 571}
X(61372) = pole of line {571, 2623} with respect to the circumcircle
X(61372) = pole of line {311, 5891} with respect to the Stammler hyperbola
X(61372) = intersection, other than A, B, C, of circumconics {{A, B, C, X(184), X(512)}}, {{A, B, C, X(393), X(571)}}, {{A, B, C, X(403), X(3135)}}, {{A, B, C, X(1300), X(40352)}}, {{A, B, C, X(2623), X(14533)}}, {{A, B, C, X(2715), X(58312)}}, {{A, B, C, X(13352), X(44080)}}, {{A, B, C, X(14560), X(34397)}}, {{A, B, C, X(41271), X(58308)}}
X(61372) = barycentric product X(i)*X(j) for these (i, j): {686, 933}, {1725, 2148}, {2190, 2315}, {3003, 54}, {3580, 54034}, {11077, 1986}, {13754, 8882}, {14533, 403}, {14586, 55121}, {15329, 2623}, {15958, 47236}, {16237, 58308}, {18315, 21731}, {23286, 61209}, {41270, 52451}, {43768, 51821}, {44084, 97}, {52000, 57703}
X(61372) = barycentric quotient X(i)/X(j) for these (i, j): {32, 60035}, {54, 40832}, {669, 35361}, {933, 57932}, {2315, 18695}, {3003, 311}, {13754, 28706}, {14533, 57829}, {14573, 14910}, {14586, 18878}, {21731, 18314}, {44084, 324}, {54034, 2986}, {55121, 15415}, {58308, 15421}
X(61372) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {184, 54034, 59172}

X(61373) = VERTEX PRODUCT OF HONSBERGER TRIANGLE

Barycentrics    a*(a+b-c)^2*(a-b+c)^2*((a-b)^2-(a+b)*c)*(a^2+c*(-b+c)-a*(b+2*c)) : :

X(61373) lies on these lines: {1, 2942}, {7, 55}, {21, 42311}, {25, 1119}, {31, 269}, {41, 57}, {56, 479}, {63, 6605}, {165, 10482}, {279, 1617}, {527, 46678}, {884, 43930}, {1014, 2194}, {1088, 7677}, {1202, 38818}, {1261, 57815}, {1396, 2204}, {1407, 42290}, {1418, 59141}, {1427, 1462}, {1621, 42309}, {4617, 61376}, {5173, 38459}, {5273, 32008}, {7053, 61375}, {7154, 37102}, {8814, 37262}, {10481, 15931}, {14021, 60076}, {15728, 53243}, {17092, 56359}, {31618, 31643}

X(61373) = isogonal conjugate of X(3059)
X(61373) = trilinear pole of line {3063, 3669}
X(61373) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 3059}, {2, 8012}, {6, 51972}, {8, 2293}, {9, 1212}, {21, 21039}, {41, 1229}, {55, 4847}, {57, 45791}, {78, 1827}, {85, 8551}, {100, 6608}, {142, 220}, {190, 10581}, {200, 354}, {210, 17194}, {219, 1855}, {312, 20229}, {318, 22079}, {333, 21795}, {346, 1475}, {480, 10481}, {644, 21127}, {650, 35341}, {664, 6607}, {728, 1418}, {1021, 35310}, {1043, 52020}, {1233, 14827}, {1253, 20880}, {1265, 40983}, {1334, 16713}, {2287, 21808}, {2328, 3925}, {2342, 51416}, {2488, 3699}, {3239, 35326}, {3900, 35338}, {3939, 6362}, {4105, 35312}, {4515, 18164}, {4578, 48151}, {4845, 61035}, {5423, 61376}, {6067, 10482}, {6602, 59181}, {7046, 22053}, {7368, 13156}, {18087, 61316}, {42064, 61030}, {59217, 59269}
X(61373) = X(i)-vertex conjugate of X(j) for these {i, j}: {21, 52013}
X(61373) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 3059}, {9, 51972}, {223, 4847}, {478, 1212}, {3160, 1229}, {5452, 45791}, {6609, 354}, {8054, 6608}, {17113, 20880}, {32664, 8012}, {36908, 3925}, {39025, 6607}, {40611, 21039}, {40617, 6362}, {52879, 61035}, {55053, 10581}
X(61373) = X(i)-Ceva conjugate of X(j) for these {i, j}: {10509, 1170}
X(61373) = X(i)-cross conjugate of X(j) for these {i, j}: {649, 4617}, {7290, 59193}, {51652, 651}, {58817, 934}
X(61373) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10578)}}, {{A, B, C, X(7), X(57)}}, {{A, B, C, X(21), X(25)}}, {{A, B, C, X(27), X(11349)}}, {{A, B, C, X(28), X(103)}}, {{A, B, C, X(34), X(1002)}}, {{A, B, C, X(63), X(3598)}}, {{A, B, C, X(81), X(14828)}}, {{A, B, C, X(84), X(972)}}, {{A, B, C, X(278), X(43736)}}, {{A, B, C, X(279), X(4350)}}, {{A, B, C, X(513), X(38454)}}, {{A, B, C, X(675), X(55987)}}, {{A, B, C, X(934), X(4619)}}, {{A, B, C, X(961), X(52013)}}, {{A, B, C, X(1156), X(36976)}}, {{A, B, C, X(1170), X(21453)}}, {{A, B, C, X(1174), X(2346)}}, {{A, B, C, X(1407), X(59242)}}, {{A, B, C, X(1411), X(37703)}}, {{A, B, C, X(1412), X(7339)}}, {{A, B, C, X(1427), X(34855)}}, {{A, B, C, X(1476), X(1477)}}, {{A, B, C, X(1803), X(40443)}}, {{A, B, C, X(1817), X(37102)}}, {{A, B, C, X(2291), X(7676)}}, {{A, B, C, X(2717), X(10428)}}, {{A, B, C, X(4617), X(53632)}}, {{A, B, C, X(11051), X(11495)}}, {{A, B, C, X(30295), X(53181)}}, {{A, B, C, X(33765), X(38859)}}, {{A, B, C, X(36100), X(39732)}}, {{A, B, C, X(39743), X(56045)}}
X(61373) = barycentric product X(i)*X(j) for these (i, j): {1, 10509}, {269, 32008}, {278, 40443}, {479, 6605}, {1014, 60229}, {1088, 1174}, {1170, 7}, {1407, 57815}, {1418, 59475}, {1803, 273}, {1847, 47487}, {2346, 279}, {3669, 6606}, {10482, 23062}, {21453, 57}, {24002, 53243}, {31618, 56}, {38835, 60811}, {42309, 59193}, {42310, 59242}, {42311, 6}, {55281, 7216}, {56118, 738}, {56322, 934}, {57880, 59141}, {58322, 658}
X(61373) = barycentric quotient X(i)/X(j) for these (i, j): {1, 51972}, {6, 3059}, {7, 1229}, {31, 8012}, {34, 1855}, {55, 45791}, {56, 1212}, {57, 4847}, {109, 35341}, {269, 142}, {279, 20880}, {479, 59181}, {604, 2293}, {608, 1827}, {649, 6608}, {667, 10581}, {738, 10481}, {1014, 16713}, {1042, 21808}, {1088, 1233}, {1106, 1475}, {1170, 8}, {1174, 200}, {1397, 20229}, {1400, 21039}, {1402, 21795}, {1407, 354}, {1412, 17194}, {1418, 6067}, {1427, 3925}, {1461, 35338}, {1465, 51416}, {1803, 78}, {2175, 8551}, {2346, 346}, {3063, 6607}, {3669, 6362}, {4617, 35312}, {6605, 5423}, {6606, 646}, {6610, 61035}, {7023, 1418}, {7099, 22053}, {7216, 55282}, {7366, 61376}, {10482, 728}, {10509, 75}, {21453, 312}, {31618, 3596}, {32008, 341}, {34855, 51384}, {40443, 345}, {42309, 59202}, {42310, 59260}, {42311, 76}, {43924, 21127}, {43932, 21104}, {47487, 3692}, {52411, 22079}, {53243, 644}, {53321, 35310}, {55281, 7258}, {56118, 30693}, {56255, 4082}, {56322, 4397}, {57181, 2488}, {57815, 59761}, {58322, 3239}, {59141, 480}, {60229, 3701}
X(61373) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {57, 1174, 1170}, {21453, 40443, 2346}

X(61374) = VERTEX PRODUCT OF 2ND HYACINTH TRIANGLE

Barycentrics    a^4*(a^2-b^2-c^2)*(-2*a^2*(b^2-c^2)^2+a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)) : :

X(61374) lies on these lines: {3, 11821}, {25, 393}, {32, 33581}, {51, 20975}, {154, 237}, {156, 3133}, {184, 418}, {185, 417}, {228, 22368}, {235, 16035}, {248, 1915}, {571, 1660}, {800, 44079}, {852, 1899}, {1204, 53852}, {1501, 61360}, {1624, 13567}, {3003, 45979}, {3051, 36425}, {3135, 26864}, {5191, 17423}, {6638, 6776}, {7494, 22062}, {9407, 44077}, {12256, 23256}, {12257, 23246}, {13409, 47195}, {14567, 61361}, {15143, 36998}, {15329, 45968}, {15653, 26897}, {22363, 23196}, {23221, 52144}, {23291, 38283}, {23292, 54003}, {23332, 53246}, {23635, 58550}, {27369, 42671}, {34093, 34978}, {40352, 54034}, {51950, 52162}, {61334, 61346}

X(61374) = isogonal conjugate of X(57775)
X(61374) = perspector of circumconic {{A, B, C, X(6529), X(32661)}}
X(61374) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 57775}, {3, 57972}, {4, 57955}, {19, 40830}, {69, 821}, {75, 1105}, {92, 801}, {158, 57800}, {255, 57843}, {264, 775}, {326, 57677}, {1969, 41890}, {57648, 57806}
X(61374) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 57775}, {6, 40830}, {206, 1105}, {1147, 57800}, {2883, 264}, {3269, 3267}, {6509, 18022}, {6523, 57843}, {13567, 305}, {14091, 18027}, {15259, 57677}, {22391, 801}, {36033, 57955}, {36103, 57972}, {59527, 1502}
X(61374) = X(i)-Ceva conjugate of X(j) for these {i, j}: {25, 44079}, {112, 3049}, {16035, 800}
X(61374) = pole of line {3049, 6587} with respect to the circumcircle
X(61374) = pole of line {1637, 30442} with respect to the Brocard inellipse
X(61374) = pole of line {264, 1105} with respect to the Stammler hyperbola
X(61374) = pole of line {4176, 18022} with respect to the Wallace hyperbola
X(61374) = intersection, other than A, B, C, of circumconics {{A, B, C, X(25), X(417)}}, {{A, B, C, X(32), X(6525)}}, {{A, B, C, X(184), X(185)}}, {{A, B, C, X(235), X(418)}}, {{A, B, C, X(393), X(577)}}, {{A, B, C, X(3289), X(13567)}}, {{A, B, C, X(14575), X(52439)}}, {{A, B, C, X(14642), X(37669)}}, {{A, B, C, X(20775), X(41005)}}, {{A, B, C, X(26880), X(52566)}}
X(61374) = barycentric product X(i)*X(j) for these (i, j): {3, 800}, {19, 820}, {25, 6509}, {31, 6508}, {32, 41005}, {48, 774}, {185, 6}, {235, 577}, {393, 417}, {394, 44079}, {520, 61204}, {1624, 647}, {3053, 45199}, {13567, 184}, {14585, 44131}, {14642, 2883}, {15905, 52566}, {16035, 216}, {17858, 9247}, {18603, 228}, {18877, 51403}, {19166, 217}, {19180, 51}, {33581, 45200}, {39201, 41678}, {41580, 60495}
X(61374) = barycentric quotient X(i)/X(j) for these (i, j): {3, 40830}, {6, 57775}, {19, 57972}, {32, 1105}, {48, 57955}, {184, 801}, {185, 76}, {235, 18027}, {393, 57843}, {417, 3926}, {577, 57800}, {774, 1969}, {800, 264}, {820, 304}, {1624, 6331}, {1973, 821}, {2207, 57677}, {6508, 561}, {6509, 305}, {9247, 775}, {13567, 18022}, {14575, 41890}, {14585, 57648}, {16035, 276}, {18603, 57796}, {19166, 57790}, {19180, 34384}, {41005, 1502}, {44079, 2052}, {52566, 52581}, {61204, 6528}
X(61374) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {184, 418, 20775}, {1661, 8573, 25}

X(61375) = VERTEX PRODUCT OF INCIRCLE-CIRCLES TRIANGLE

Barycentrics    a^2*(a^2+4*a*b+b^2-c^2)*(a^2-b^2+4*a*c+c^2) : :

X(61375) lies on these lines: {21, 999}, {31, 26864}, {36, 1036}, {41, 2308}, {55, 1100}, {956, 51591}, {1402, 34446}, {1460, 6187}, {2194, 37519}, {3295, 25417}, {6186, 7083}, {7053, 61373}, {14974, 40148}, {16352, 52133}, {21010, 26867}

X(61375) = isogonal conjugate of X(42696)
X(61375) = trilinear pole of line {3063, 50512}
X(61375) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 42696}, {2, 3305}, {8, 7190}, {9, 52422}, {57, 42032}, {75, 3295}, {86, 3697}, {92, 55466}, {100, 48268}, {190, 47965}, {312, 52424}, {319, 56843}, {332, 53861}, {668, 48340}, {799, 58299}, {4373, 4917}, {30598, 51572}
X(61375) = X(i)-vertex conjugate of X(j) for these {i, j}: {25417, 25417}
X(61375) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 42696}, {206, 3295}, {478, 52422}, {5452, 42032}, {8054, 48268}, {22391, 55466}, {32664, 3305}, {38996, 58299}, {40600, 3697}, {55053, 47965}
X(61375) = pole of line {3295, 42696} with respect to the Stammler hyperbola
X(61375) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(6), X(593)}}, {{A, B, C, X(21), X(25)}}, {{A, B, C, X(36), X(1460)}}, {{A, B, C, X(42), X(3445)}}, {{A, B, C, X(106), X(2258)}}, {{A, B, C, X(184), X(7053)}}, {{A, B, C, X(221), X(32319)}}, {{A, B, C, X(292), X(2221)}}, {{A, B, C, X(595), X(14974)}}, {{A, B, C, X(604), X(6612)}}, {{A, B, C, X(608), X(2215)}}, {{A, B, C, X(649), X(57663)}}, {{A, B, C, X(893), X(21448)}}, {{A, B, C, X(902), X(58148)}}, {{A, B, C, X(957), X(1824)}}, {{A, B, C, X(967), X(2162)}}, {{A, B, C, X(999), X(1402)}}, {{A, B, C, X(1042), X(11036)}}, {{A, B, C, X(1333), X(36743)}}, {{A, B, C, X(1397), X(1398)}}, {{A, B, C, X(1400), X(9965)}}, {{A, B, C, X(1407), X(2350)}}, {{A, B, C, X(1412), X(2279)}}, {{A, B, C, X(2160), X(55985)}}, {{A, B, C, X(2203), X(44094)}}, {{A, B, C, X(2206), X(3941)}}, {{A, B, C, X(2214), X(56045)}}, {{A, B, C, X(2248), X(36614)}}, {{A, B, C, X(2299), X(26864)}}, {{A, B, C, X(7083), X(14975)}}, {{A, B, C, X(7123), X(40746)}}, {{A, B, C, X(8770), X(30650)}}, {{A, B, C, X(16352), X(46503)}}, {{A, B, C, X(19302), X(34819)}}, {{A, B, C, X(34445), X(60671)}}
X(61375) = barycentric product X(i)*X(j) for these (i, j): {25, 30679}, {3296, 6}, {52188, 999}
X(61375) = barycentric quotient X(i)/X(j) for these (i, j): {6, 42696}, {31, 3305}, {32, 3295}, {55, 42032}, {56, 52422}, {184, 55466}, {213, 3697}, {604, 7190}, {649, 48268}, {667, 47965}, {669, 58299}, {999, 46951}, {1397, 52424}, {1919, 48340}, {3296, 76}, {30679, 305}, {52188, 58029}

X(61376) = VERTEX PRODUCT OF INVERSE-IN-INCIRCLE TRIANGLE

Barycentrics    a^2*(a+b-c)*(a-b+c)*(-(b-c)^2+a*(b+c)) : :

X(61376) lies on these lines: {1, 3522}, {2, 4334}, {6, 34821}, {7, 3720}, {31, 56}, {38, 241}, {42, 57}, {55, 42314}, {65, 4322}, {73, 32636}, {77, 17017}, {222, 1471}, {226, 30950}, {244, 1427}, {269, 479}, {354, 1418}, {497, 3000}, {553, 42289}, {604, 57656}, {612, 4321}, {664, 32924}, {674, 22435}, {748, 6180}, {756, 8581}, {899, 5435}, {902, 1617}, {991, 10980}, {1014, 17187}, {1044, 14986}, {1055, 14827}, {1066, 37582}, {1149, 13462}, {1193, 3361}, {1200, 23653}, {1202, 20995}, {1214, 46901}, {1254, 37566}, {1357, 1402}, {1400, 1401}, {1412, 1416}, {1423, 28361}, {1434, 10458}, {1445, 32912}, {1448, 28082}, {1450, 1464}, {1463, 28387}, {1467, 3924}, {1475, 20229}, {1742, 10580}, {2187, 26866}, {2340, 51302}, {2635, 17728}, {3218, 25941}, {3219, 25889}, {3333, 4300}, {3338, 4303}, {3600, 10459}, {3914, 60992}, {3938, 60786}, {4298, 59305}, {4318, 29818}, {4327, 5311}, {4343, 60955}, {4617, 61373}, {4860, 14547}, {5018, 7191}, {5265, 28352}, {7175, 22343}, {7176, 21352}, {7271, 10582}, {10391, 21346}, {10481, 17169}, {17061, 43036}, {17077, 59306}, {17092, 17449}, {17093, 41355}, {21747, 55086}, {22060, 35270}, {23154, 28270}, {24550, 26840}, {24943, 56367}, {27339, 30970}, {28739, 29677}, {28774, 29865}, {29662, 54366}, {29663, 56460}, {31241, 52358}, {32915, 39126}, {32930, 40862}, {33143, 57477}, {33147, 37798}, {40961, 53538}, {41539, 53531}, {49676, 56559}

X(61376) = isogonal conjugate of X(56118)
X(61376) = perspector of circumconic {{A, B, C, X(1461), X(58103)}}
X(61376) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 56118}, {2, 6605}, {8, 2346}, {9, 32008}, {21, 56157}, {55, 57815}, {75, 10482}, {76, 59141}, {200, 21453}, {220, 31618}, {284, 56127}, {312, 1174}, {318, 47487}, {333, 56255}, {346, 1170}, {480, 42311}, {644, 56322}, {728, 10509}, {1803, 7101}, {2287, 60229}, {3059, 59475}, {3699, 58322}, {3886, 59193}, {3900, 6606}, {4041, 55281}, {4397, 53243}, {5423, 61373}, {7046, 40443}, {37658, 42310}, {56284, 57731}
X(61376) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 56118}, {142, 341}, {206, 10482}, {223, 57815}, {478, 32008}, {1212, 3596}, {6609, 21453}, {32664, 6605}, {40590, 56127}, {40606, 312}, {40611, 56157}
X(61376) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1415, 43924}, {1418, 1475}, {4617, 649}
X(61376) = pole of line {1043, 3717} with respect to the Stammler hyperbola
X(61376) = intersection, other than A, B, C, of circumconics {{A, B, C, X(25), X(3598)}}, {{A, B, C, X(31), X(269)}}, {{A, B, C, X(42), X(56783)}}, {{A, B, C, X(56), X(354)}}, {{A, B, C, X(142), X(61412)}}, {{A, B, C, X(603), X(22053)}}, {{A, B, C, X(1042), X(1416)}}, {{A, B, C, X(1191), X(1212)}}, {{A, B, C, X(1201), X(4847)}}, {{A, B, C, X(1400), X(43915)}}, {{A, B, C, X(1407), X(1418)}}, {{A, B, C, X(1457), X(48151)}}, {{A, B, C, X(1827), X(20991)}}, {{A, B, C, X(2390), X(6362)}}, {{A, B, C, X(2488), X(6186)}}, {{A, B, C, X(20070), X(22334)}}
X(61376) = barycentric product X(i)*X(j) for these (i, j): {1, 1418}, {31, 59181}, {41, 53242}, {48, 53237}, {109, 21104}, {142, 56}, {348, 40983}, {354, 57}, {479, 8012}, {1014, 21808}, {1042, 16713}, {1088, 20229}, {1106, 1229}, {1212, 269}, {1233, 1397}, {1400, 17169}, {1401, 18087}, {1402, 16708}, {1404, 53240}, {1407, 4847}, {1412, 3925}, {1416, 51384}, {1427, 17194}, {1428, 53239}, {1434, 52020}, {1458, 53241}, {1461, 6362}, {1475, 7}, {1827, 7177}, {1847, 22079}, {1855, 7053}, {2293, 279}, {2488, 658}, {3059, 738}, {4565, 55282}, {4617, 6608}, {10481, 6}, {10581, 4626}, {13156, 221}, {15185, 17107}, {18164, 65}, {20880, 604}, {21127, 934}, {22053, 278}, {23599, 692}, {35310, 7203}, {35312, 649}, {35326, 3676}, {35338, 3669}, {35341, 43932}, {39950, 43915}, {42290, 59217}, {48151, 651}, {51972, 7023}, {52023, 58}, {53238, 73}, {61034, 7153}, {61241, 663}
X(61376) = barycentric quotient X(i)/X(j) for these (i, j): {6, 56118}, {31, 6605}, {32, 10482}, {56, 32008}, {57, 57815}, {65, 56127}, {142, 3596}, {269, 31618}, {354, 312}, {560, 59141}, {604, 2346}, {738, 42311}, {1042, 60229}, {1106, 1170}, {1212, 341}, {1233, 40363}, {1397, 1174}, {1400, 56157}, {1402, 56255}, {1407, 21453}, {1418, 75}, {1461, 6606}, {1475, 8}, {1827, 7101}, {2293, 346}, {2488, 3239}, {3059, 30693}, {3925, 30713}, {4565, 55281}, {4847, 59761}, {6362, 52622}, {7023, 10509}, {7099, 40443}, {7366, 61373}, {8012, 5423}, {10481, 76}, {10581, 4163}, {13156, 57793}, {16708, 40072}, {17169, 28660}, {18164, 314}, {20229, 200}, {20880, 28659}, {21104, 35519}, {21127, 4397}, {21143, 56284}, {21795, 4082}, {21808, 3701}, {22053, 345}, {22079, 3692}, {23599, 40495}, {35312, 1978}, {35326, 3699}, {35338, 646}, {40983, 281}, {43915, 4043}, {43924, 56322}, {48151, 4391}, {52020, 2321}, {52023, 313}, {52411, 47487}, {53237, 1969}, {53238, 44130}, {53242, 20567}, {57181, 58322}, {59181, 561}, {59217, 28809}, {61034, 4110}, {61241, 4572}
X(61376) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {56, 1042, 1201}, {56, 1407, 31}, {56, 7248, 61412}, {57, 1458, 42}, {222, 1471, 2308}, {354, 22053, 2293}, {1357, 1402, 59173}, {3361, 4306, 1193}, {20995, 61326, 1202}

X(61377) = VERTEX PRODUCT OF 2ND JENKINS TRIANGLE

Barycentrics    (a-b-c)*(b+c)^2*(b^2+c^2+a*(b+c)) : :

X(61377) lies on these lines: {8, 9}, {37, 27714}, {594, 756}, {2171, 3695}, {3701, 21030}, {3703, 17452}, {3704, 21033}, {4046, 42446}, {4136, 42712}, {17314, 33163}, {20653, 21810}, {21081, 24048}, {21712, 34528}

X(61377) = perspector of circumconic {{A, B, C, X(3699), X(4103)}}
X(61377) = X(i)-isoconjugate-of-X(j) for these {i, j}: {593, 961}, {1014, 1169}, {1396, 1798}, {1408, 14534}, {1412, 2363}, {2298, 7341}, {3669, 58982}, {7342, 30710}, {52410, 52550}
X(61377) = X(i)-Dao conjugate of X(j) for these {i, j}: {960, 1412}, {2092, 757}, {3125, 7203}, {3666, 1434}, {40599, 2363}, {52087, 7341}, {59509, 552}, {59577, 14534}
X(61377) = X(i)-Ceva conjugate of X(j) for these {i, j}: {2321, 21033}
X(61377) = pole of line {1434, 6628} with respect to the Wallace hyperbola
X(61377) = pole of line {17205, 53545} with respect to the dual conic of Wallace hyperbola
X(61377) = intersection, other than A, B, C, of circumconics {{A, B, C, X(8), X(594)}}, {{A, B, C, X(9), X(756)}}, {{A, B, C, X(346), X(6057)}}, {{A, B, C, X(391), X(1211)}}, {{A, B, C, X(429), X(452)}}, {{A, B, C, X(1228), X(27523)}}, {{A, B, C, X(1697), X(52567)}}, {{A, B, C, X(2092), X(4266)}}, {{A, B, C, X(2171), X(54359)}}, {{A, B, C, X(2292), X(5250)}}, {{A, B, C, X(2321), X(6535)}}, {{A, B, C, X(3685), X(4037)}}, {{A, B, C, X(3686), X(3687)}}, {{A, B, C, X(3691), X(21699)}}, {{A, B, C, X(3701), X(56311)}}, {{A, B, C, X(3886), X(18697)}}, {{A, B, C, X(41003), X(52653)}}
X(61377) = barycentric product X(i)*X(j) for these (i, j): {10, 3704}, {313, 40966}, {341, 52567}, {1089, 960}, {1211, 2321}, {1228, 1334}, {2092, 30713}, {2269, 28654}, {2292, 3701}, {3687, 594}, {3695, 46878}, {3710, 429}, {3910, 4103}, {3965, 6358}, {4036, 61223}, {4082, 41003}, {4086, 61172}, {4357, 6057}, {4515, 45196}, {18697, 210}, {20653, 8}, {21033, 321}, {21124, 30730}, {21810, 312}
X(61377) = barycentric quotient X(i)/X(j) for these (i, j): {210, 2363}, {341, 52550}, {756, 961}, {960, 757}, {1089, 31643}, {1193, 7341}, {1211, 1434}, {1334, 1169}, {2092, 1412}, {2269, 593}, {2292, 1014}, {2318, 1798}, {2321, 14534}, {3687, 1509}, {3704, 86}, {3710, 57853}, {3725, 1408}, {3939, 58982}, {3965, 2185}, {4103, 6648}, {4357, 552}, {6042, 24471}, {6057, 1220}, {6535, 60086}, {17185, 763}, {18697, 57785}, {20653, 7}, {20967, 849}, {21033, 81}, {21124, 17096}, {21810, 57}, {30713, 40827}, {40521, 36098}, {40966, 58}, {42661, 43924}, {50330, 7203}, {52567, 269}, {59174, 1106}, {61168, 4565}, {61172, 1414}, {61223, 52935}

X(61378) = VERTEX PRODUCT OF JOHNSON TRIANGLE

Barycentrics    (a^2-b^2-c^2)*(a*(b^2-c^2)^2-a^3*(b^2+c^2))^2 : :

X(61378) lies on these lines: {2, 1972}, {3, 143}, {4, 51888}, {5, 324}, {6, 6641}, {25, 22240}, {51, 216}, {52, 31388}, {97, 53863}, {160, 34751}, {184, 5158}, {217, 61363}, {237, 47328}, {275, 41202}, {343, 44716}, {373, 6509}, {382, 58878}, {389, 26897}, {426, 10601}, {476, 24977}, {577, 15004}, {852, 5943}, {1093, 13599}, {1199, 14152}, {1576, 56308}, {1994, 54375}, {2052, 57528}, {2351, 14575}, {2971, 14593}, {3003, 58550}, {3078, 23607}, {3131, 56515}, {3132, 56514}, {3148, 44162}, {3284, 34565}, {5067, 14059}, {5480, 26905}, {5640, 6638}, {6530, 34965}, {6688, 44436}, {6755, 42459}, {7394, 18437}, {7494, 16989}, {8041, 23611}, {8613, 60693}, {10095, 46025}, {10254, 34333}, {11002, 26874}, {11402, 15851}, {11451, 38283}, {14627, 19210}, {15860, 44111}, {17810, 26898}, {18114, 44891}, {20819, 43653}, {21849, 34003}, {22052, 44107}, {22112, 53852}, {26880, 34417}, {30506, 32428}, {34836, 39569}, {34985, 41212}, {35012, 52212}, {37439, 41005}, {37649, 44888}, {41169, 41588}, {42400, 44924}, {45198, 57529}, {46106, 59531}, {52945, 53386}, {58468, 58533}

X(61378) = midpoint of X(i) and X(j) for these {i,j}: {30506, 56302}
X(61378) = perspector of circumconic {{A, B, C, X(1625), X(32662)}}
X(61378) = X(i)-isoconjugate-of-X(j) for these {i, j}: {54, 40440}, {95, 2190}, {275, 2167}, {276, 2148}, {661, 52939}, {2169, 8795}, {2616, 18831}, {3708, 57573}, {46089, 57806}
X(61378) = X(i)-Dao conjugate of X(j) for these {i, j}: {5, 95}, {130, 23286}, {216, 276}, {6368, 339}, {6663, 264}, {14363, 8795}, {15450, 15412}, {36830, 52939}, {39171, 57765}, {40588, 275}, {46394, 36794}, {52032, 34384}, {52869, 43752}, {52878, 19189}
X(61378) = X(i)-Ceva conjugate of X(j) for these {i, j}: {5, 36412}, {216, 46394}, {250, 1625}, {35360, 17434}
X(61378) = X(i)-cross conjugate of X(j) for these {i, j}: {24862, 15451}, {41212, 34983}
X(61378) = pole of line {6130, 23286} with respect to the polar circle
X(61378) = pole of line {686, 12077} with respect to the Brocard inellipse
X(61378) = pole of line {684, 2525} with respect to the MacBeath inconic
X(61378) = pole of line {95, 140} with respect to the Stammler hyperbola
X(61378) = pole of line {1232, 34384} with respect to the Wallace hyperbola
X(61378) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(17434)}}, {{A, B, C, X(3), X(3078)}}, {{A, B, C, X(5), X(418)}}, {{A, B, C, X(51), X(1173)}}, {{A, B, C, X(97), X(57273)}}, {{A, B, C, X(184), X(15451)}}, {{A, B, C, X(216), X(324)}}, {{A, B, C, X(264), X(11197)}}, {{A, B, C, X(343), X(59208)}}, {{A, B, C, X(5562), X(26907)}}, {{A, B, C, X(13599), X(23606)}}, {{A, B, C, X(14569), X(40981)}}, {{A, B, C, X(14593), X(55219)}}, {{A, B, C, X(15033), X(53386)}}, {{A, B, C, X(20975), X(24862)}}, {{A, B, C, X(23607), X(60828)}}, {{A, B, C, X(45793), X(57195)}}
X(61378) = barycentric product X(i)*X(j) for these (i, j): {3, 36412}, {53, 5562}, {110, 57195}, {184, 45793}, {216, 5}, {217, 311}, {219, 41279}, {250, 39019}, {264, 46394}, {324, 418}, {343, 51}, {467, 61363}, {577, 60828}, {1087, 48}, {1625, 6368}, {1953, 44706}, {3078, 31626}, {3199, 52347}, {12077, 23181}, {14391, 36831}, {14570, 15451}, {14577, 60824}, {15780, 21354}, {16697, 21807}, {17434, 35360}, {18695, 2179}, {21011, 44709}, {23582, 41212}, {23607, 97}, {24862, 249}, {28706, 40981}, {31610, 32078}, {32662, 55132}, {34983, 648}, {40449, 42445}, {42459, 8798}, {44708, 7069}, {44715, 52945}, {44716, 60517}, {52604, 60597}
X(61378) = barycentric quotient X(i)/X(j) for these (i, j): {5, 276}, {51, 275}, {53, 8795}, {110, 52939}, {216, 95}, {217, 54}, {250, 57573}, {311, 57790}, {324, 57844}, {343, 34384}, {418, 97}, {1087, 1969}, {1625, 18831}, {1953, 40440}, {2179, 2190}, {3078, 40684}, {3199, 8884}, {5562, 34386}, {14569, 8794}, {14585, 46089}, {15451, 15412}, {23607, 324}, {24862, 338}, {32078, 59183}, {34983, 525}, {35360, 42405}, {36412, 264}, {39019, 339}, {40981, 8882}, {41212, 15526}, {41279, 331}, {42293, 23286}, {44088, 14533}, {45793, 18022}, {46394, 3}, {52604, 16813}, {52945, 43752}, {52967, 19189}, {57195, 850}, {59142, 39286}, {60828, 18027}, {61193, 52779}, {61194, 933}, {61346, 61362}, {61363, 57875}
X(61378) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 13409, 2972}, {2, 30258, 13409}, {5, 15912, 14978}, {5, 324, 11197}, {5, 42453, 324}, {5, 6663, 60828}, {51, 216, 418}, {216, 418, 32078}, {3078, 23607, 36412}, {5943, 46832, 852}, {17810, 52703, 26898}, {31626, 39243, 3}

X(61379) = VERTEX PRODUCT OF MCCAY TRIANGLE

Barycentrics    a^2*(2*(a^4-a^2*b^2+b^4)-3*(a^2+b^2)*c^2+c^4)*(2*a^4+b^4-3*b^2*c^2+2*c^4-a^2*(3*b^2+2*c^2)) : :

X(61379) lies on these lines: {2, 575}, {6, 23200}, {25, 14567}, {51, 1383}, {111, 184}, {182, 2987}, {251, 15004}, {263, 1692}, {308, 57908}, {393, 44102}, {588, 44656}, {589, 44657}, {1974, 33631}, {1976, 39764}, {1993, 44504}, {3049, 9178}, {3228, 35178}, {5050, 40802}, {5967, 16081}, {7485, 44507}, {8541, 8882}, {8566, 10485}, {8770, 17809}, {8791, 59175}, {11166, 53845}, {11179, 39120}, {11402, 21448}, {18818, 43697}, {21637, 51316}, {30535, 39561}, {32621, 60775}, {40103, 44109}, {40815, 46124}, {44509, 55567}, {44510, 55566}

X(61379) = perspector of circumconic {{A, B, C, X(35178), X(59007)}}
X(61379) = X(i)-isoconjugate-of-X(j) for these {i, j}: {63, 52282}, {75, 576}
X(61379) = X(i)-vertex conjugate of X(j) for these {i, j}: {588, 589}
X(61379) = X(i)-Dao conjugate of X(j) for these {i, j}: {206, 576}, {3162, 52282}
X(61379) = pole of line {15073, 44496} with respect to the Jerabek hyperbola
X(61379) = pole of line {576, 15850} with respect to the Stammler hyperbola
X(61379) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}}, {{A, B, C, X(4), X(3455)}}, {{A, B, C, X(32), X(575)}}, {{A, B, C, X(51), X(8541)}}, {{A, B, C, X(54), X(8753)}}, {{A, B, C, X(64), X(54894)}}, {{A, B, C, X(69), X(51477)}}, {{A, B, C, X(182), X(1692)}}, {{A, B, C, X(184), X(3049)}}, {{A, B, C, X(511), X(39764)}}, {{A, B, C, X(512), X(3431)}}, {{A, B, C, X(576), X(15850)}}, {{A, B, C, X(598), X(57729)}}, {{A, B, C, X(895), X(2351)}}, {{A, B, C, X(1173), X(2353)}}, {{A, B, C, X(1177), X(32319)}}, {{A, B, C, X(1843), X(15004)}}, {{A, B, C, X(1974), X(13366)}}, {{A, B, C, X(2065), X(34214)}}, {{A, B, C, X(2207), X(43908)}}, {{A, B, C, X(3224), X(55999)}}, {{A, B, C, X(5050), X(40825)}}, {{A, B, C, X(5052), X(39561)}}, {{A, B, C, X(5466), X(38397)}}, {{A, B, C, X(5486), X(14593)}}, {{A, B, C, X(6323), X(17503)}}, {{A, B, C, X(7708), X(8584)}}, {{A, B, C, X(8601), X(56362)}}, {{A, B, C, X(9468), X(34396)}}, {{A, B, C, X(9515), X(18842)}}, {{A, B, C, X(9716), X(58941)}}, {{A, B, C, X(11405), X(17810)}}, {{A, B, C, X(11422), X(32740)}}, {{A, B, C, X(14248), X(14528)}}, {{A, B, C, X(14483), X(14906)}}, {{A, B, C, X(14484), X(41533)}}, {{A, B, C, X(14494), X(39644)}}, {{A, B, C, X(14498), X(30541)}}, {{A, B, C, X(14908), X(55980)}}, {{A, B, C, X(17809), X(19118)}}, {{A, B, C, X(19151), X(22259)}}, {{A, B, C, X(20251), X(44557)}}, {{A, B, C, X(27375), X(60126)}}, {{A, B, C, X(34986), X(53059)}}, {{A, B, C, X(35473), X(57598)}}, {{A, B, C, X(35926), X(46522)}}, {{A, B, C, X(40810), X(51335)}}, {{A, B, C, X(52174), X(53777)}}, {{A, B, C, X(52239), X(54637)}}
X(61379) = barycentric product X(i)*X(j) for these (i, j): {6, 7607}, {32, 57908}, {523, 59007}, {35178, 512}
X(61379) = barycentric quotient X(i)/X(j) for these (i, j): {25, 52282}, {32, 576}, {7607, 76}, {35178, 670}, {57908, 1502}, {59007, 99}

X(61380) = VERTEX PRODUCT OF 7TH MIXTILINEAR TRIANGLE

Barycentrics    a^2*(a+b-c)^2*(a-b+c)^2*((a-b)^2+2*(a+b)*c-3*c^2)*(a^2+2*a*b-3*b^2-2*a*c+2*b*c+c^2) : :

X(61380) lies on these lines: {56, 20978}, {57, 7955}, {738, 5575}, {934, 5022}, {1434, 26818}, {1477, 41426}, {3062, 7091}, {3304, 52013}, {6611, 57663}, {9533, 56043}, {10405, 40420}, {13609, 55030}

X(61380) = X(i)-isoconjugate-of-X(j) for these {i, j}: {100, 57064}, {144, 200}, {165, 346}, {190, 58835}, {220, 16284}, {341, 3207}, {480, 31627}, {728, 3160}, {765, 13609}, {1043, 21872}, {1419, 5423}, {2287, 21060}, {4578, 7658}, {6602, 50560}, {7101, 22117}, {7259, 55285}
X(61380) = X(i)-Dao conjugate of X(j) for these {i, j}: {513, 13609}, {6609, 144}, {8054, 57064}, {55053, 58835}
X(61380) = X(i)-cross conjugate of X(j) for these {i, j}: {3271, 43932}, {7023, 1407}
X(61380) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(20978)}}, {{A, B, C, X(25), X(26827)}}, {{A, B, C, X(56), X(57)}}, {{A, B, C, X(64), X(1019)}}, {{A, B, C, X(513), X(55030)}}, {{A, B, C, X(608), X(53088)}}, {{A, B, C, X(1015), X(2207)}}, {{A, B, C, X(1413), X(3669)}}, {{A, B, C, X(1438), X(5575)}}, {{A, B, C, X(1462), X(3445)}}, {{A, B, C, X(3500), X(53089)}}, {{A, B, C, X(7023), X(17106)}}
X(61380) = barycentric product X(i)*X(j) for these (i, j): {6, 60831}, {269, 3062}, {1106, 44186}, {1422, 42872}, {3669, 61240}, {3676, 53622}, {10405, 1407}, {11051, 279}, {19605, 738}, {36620, 56}, {43924, 53640}, {55284, 7250}
X(61380) = barycentric quotient X(i)/X(j) for these (i, j): {269, 16284}, {479, 50560}, {649, 57064}, {667, 58835}, {738, 31627}, {1015, 13609}, {1042, 21060}, {1106, 165}, {1407, 144}, {3062, 341}, {7023, 3160}, {7250, 55285}, {7366, 1419}, {10405, 59761}, {11051, 346}, {19605, 30693}, {36620, 3596}, {52410, 3207}, {53622, 3699}, {60831, 76}, {61240, 646}

X(61381) = VERTEX PRODUCT OF MOSES-STEINER OSCULATORY TRIANGLE

Barycentrics    b^2*c^2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(3*a^4+(b^2-c^2)^2-2*a^2*(b^2+c^2)) : :

X(61381) lies on circumconic {{A, B, C, X(1799), X(7607)}} and on these lines: {2, 44145}, {4, 1216}, {25, 183}, {76, 460}, {110, 5392}, {154, 338}, {184, 41760}, {311, 14826}, {324, 6353}, {419, 2001}, {421, 9306}, {427, 43976}, {428, 33706}, {468, 2052}, {847, 7505}, {1235, 6620}, {1316, 23606}, {1629, 21213}, {1632, 2351}, {2970, 15466}, {3186, 47328}, {3517, 14978}, {6403, 30506}, {6524, 37778}, {6755, 41584}, {11402, 40814}, {14569, 21447}, {14593, 53371}, {34397, 59156}, {35259, 45793}, {38282, 46106}, {52147, 52297}

X(61381) = pole of line {3005, 46953} with respect to the polar circle
X(61381) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2970, 37453, 15466}

X(61382) = VERTEX PRODUCT OF MOSES-STEINER REFLECTION TRIANGLE

Barycentrics    (a^2-b^2-c^2)*(a^2+2*b^2-c^2)*(a^2-b^2+2*c^2) : :

X(61382) lies on circumconic {{A, B, C, X(15031), X(60101)}} and on these lines: {2, 5034}, {125, 1799}, {305, 37638}, {343, 4563}, {1078, 26913}, {3917, 30786}, {11056, 13567}, {16275, 23332}, {23293, 33651}, {26958, 40022}, {37636, 37803}

X(61382) = pole of line {3815, 52297} with respect to the Wallace hyperbola
X(61382) = barycentric product X(i)*X(j) for these (i, j): {15031, 69}
X(61382) = barycentric quotient X(i)/X(j) for these (i, j): {15031, 4}

X(61383) = VERTEX PRODUCT OF 1ST ORTHOSYMMEDIAL TRIANGLE

Barycentrics    a^4*(a^2+b^2)*(a^2+c^2)*(a^4-(b^2-c^2)^2) : :

X(61383) lies on these lines: {4, 59180}, {25, 251}, {83, 427}, {112, 39449}, {428, 32085}, {468, 1799}, {827, 2374}, {1176, 19118}, {1974, 17409}, {5064, 32581}, {5094, 39668}, {6353, 52898}, {7484, 26224}, {10130, 37453}, {10551, 44084}, {15369, 33632}, {16277, 60133}, {17997, 47230}, {20960, 36414}, {21213, 51862}, {41293, 41295}, {42288, 54034}, {44102, 58761}

X(61383) = X(i)-isoconjugate-of-X(j) for these {i, j}: {38, 305}, {39, 40364}, {48, 52568}, {63, 8024}, {69, 1930}, {75, 3933}, {141, 304}, {306, 16703}, {326, 1235}, {336, 51371}, {525, 55239}, {561, 3917}, {799, 2525}, {826, 55202}, {1502, 4020}, {1923, 40360}, {1928, 20775}, {1964, 40050}, {3112, 4175}, {3665, 3718}, {3703, 7182}, {3926, 20883}, {4561, 48084}, {4568, 15413}, {4576, 14208}, {4592, 23285}, {8061, 52608}, {16696, 40071}, {16747, 52396}, {16887, 20336}, {20898, 57852}, {33299, 57918}, {34055, 59995}, {45220, 59154}, {52369, 61407}
X(61383) = X(i)-Dao conjugate of X(j) for these {i, j}: {206, 3933}, {1249, 52568}, {3162, 8024}, {5139, 23285}, {15259, 1235}, {34452, 4175}, {38996, 2525}, {40368, 3917}, {40369, 20775}, {41884, 40050}
X(61383) = pole of line {2528, 23285} with respect to the polar circle
X(61383) = pole of line {3933, 22424} with respect to the Stammler hyperbola
X(61383) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(9465)}}, {{A, B, C, X(6), X(5359)}}, {{A, B, C, X(25), X(1974)}}, {{A, B, C, X(32), X(30435)}}, {{A, B, C, X(83), X(52580)}}, {{A, B, C, X(251), X(39449)}}, {{A, B, C, X(428), X(27369)}}, {{A, B, C, X(468), X(3080)}}, {{A, B, C, X(1501), X(14601)}}, {{A, B, C, X(2207), X(8743)}}, {{A, B, C, X(2489), X(37765)}}, {{A, B, C, X(10312), X(57260)}}, {{A, B, C, X(14569), X(61346)}}, {{A, B, C, X(16277), X(18105)}}, {{A, B, C, X(39951), X(53059)}}, {{A, B, C, X(40146), X(40352)}}, {{A, B, C, X(41272), X(60181)}}, {{A, B, C, X(47443), X(61206)}}
X(61383) = barycentric product X(i)*X(j) for these (i, j): {4, 46288}, {19, 46289}, {25, 251}, {32, 32085}, {112, 18105}, {250, 51906}, {308, 44162}, {1176, 2207}, {1395, 56245}, {1501, 46104}, {1799, 36417}, {1843, 59996}, {1973, 82}, {1974, 83}, {2489, 827}, {2501, 4630}, {4577, 57204}, {10311, 42288}, {10547, 393}, {14248, 33632}, {16277, 17409}, {17980, 56975}, {18098, 2203}, {27369, 52395}, {28724, 52439}, {32676, 55240}, {34294, 57655}, {39287, 61346}, {40144, 8793}, {41489, 51508}, {42396, 669}, {44089, 733}, {44091, 57421}, {51862, 57260}, {58784, 61206}, {59188, 60125}
X(61383) = barycentric quotient X(i)/X(j) for these (i, j): {4, 52568}, {25, 8024}, {32, 3933}, {82, 40364}, {83, 40050}, {251, 305}, {308, 40360}, {669, 2525}, {827, 52608}, {1501, 3917}, {1843, 59995}, {1917, 4020}, {1973, 1930}, {1974, 141}, {2203, 16703}, {2207, 1235}, {2211, 51371}, {2489, 23285}, {3051, 4175}, {4630, 4563}, {9233, 20775}, {10547, 3926}, {18105, 3267}, {27369, 7794}, {32085, 1502}, {32676, 55239}, {34072, 55202}, {36417, 427}, {40351, 46147}, {42068, 39691}, {42396, 4609}, {44089, 35540}, {44091, 42554}, {44162, 39}, {46104, 40362}, {46288, 69}, {46289, 304}, {51906, 339}, {57204, 826}, {59188, 45201}, {61206, 4576}

X(61384) = VERTEX PRODUCT OF 1ST PARRY TRIANGLE

Barycentrics    a^4*(a^2+b^2-2*c^2)*(a^2-2*b^2+c^2)*(3*a^4+b^4-b^2*c^2+c^4-2*a^2*(b^2+c^2)) : :

X(61384) lies on circumconic {{A, B, C, X(1974), X(10552)}} and on these lines: {32, 10558}, {111, 42295}, {251, 21460}, {1501, 32740}, {1627, 10559}, {3051, 52668}, {19626, 41278}, {32729, 51819}, {40825, 57485}, {41272, 44167}

X(61384) = X(i)-isoconjugate-of-X(j) for these {i, j}: {14210, 56057}
X(61384) = X(i)-Dao conjugate of X(j) for these {i, j}: {15477, 56057}
X(61384) = barycentric product X(i)*X(j) for these (i, j): {10552, 41936}, {32729, 9131}
X(61384) = barycentric quotient X(i)/X(j) for these (i, j): {32729, 9133}, {32740, 56057}
X(61384) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1501, 32740, 52142}

X(61385) = VERTEX PRODUCT OF 1ST SHARYGIN TRIANGLE

Barycentrics    a^3*(b^2+a*c)*(a^2-b*c)*(a*b+c^2) : :

X(61385) lies on these lines: {31, 893}, {41, 904}, {60, 1178}, {238, 17493}, {604, 7121}, {748, 7018}, {1432, 1471}, {1927, 18266}, {1966, 25863}, {2112, 51979}, {8300, 18786}, {9468, 19554}, {19580, 27982}, {25848, 30660}, {30658, 51328}, {51947, 51948}, {57074, 57157}, {58981, 59052}

X(61385) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 30669}, {75, 18787}, {171, 334}, {172, 18895}, {238, 30642}, {291, 1909}, {292, 1920}, {335, 894}, {337, 7009}, {385, 40098}, {660, 4374}, {741, 1237}, {1215, 18827}, {1916, 6645}, {1921, 30657}, {1966, 30663}, {2295, 40017}, {2533, 4589}, {3805, 41072}, {3963, 37128}, {3978, 52205}, {4032, 36800}, {4367, 4583}, {4369, 4562}, {4444, 18047}, {4518, 7176}, {4639, 57234}, {4876, 7196}, {6649, 60577}, {7061, 52085}, {7077, 7205}, {7081, 7233}, {7122, 44172}, {14603, 51856}, {17103, 43534}, {18905, 40834}, {41534, 51859}, {51868, 51920}
X(61385) = X(i)-Dao conjugate of X(j) for these {i, j}: {206, 18787}, {1966, 14603}, {8299, 1237}, {9467, 30663}, {9470, 30642}, {19557, 1920}, {32664, 30669}, {39029, 1909}, {39031, 6645}
X(61385) = X(i)-Ceva conjugate of X(j) for these {i, j}: {9468, 31}
X(61385) = X(i)-cross conjugate of X(j) for these {i, j}: {51328, 31}
X(61385) = pole of line {1215, 8033} with respect to the Stammler hyperbola
X(61385) = intersection, other than A, B, C, of circumconics {{A, B, C, X(31), X(238)}}, {{A, B, C, X(41), X(60)}}, {{A, B, C, X(604), X(1914)}}, {{A, B, C, X(893), X(17493)}}, {{A, B, C, X(1178), X(18786)}}, {{A, B, C, X(1429), X(38252)}}, {{A, B, C, X(1691), X(51328)}}, {{A, B, C, X(3747), X(57157)}}, {{A, B, C, X(5009), X(8300)}}, {{A, B, C, X(18756), X(18757)}}
X(61385) = barycentric product X(i)*X(j) for these (i, j): {171, 30658}, {238, 893}, {239, 904}, {242, 7116}, {350, 7104}, {694, 8300}, {1178, 2238}, {1431, 3684}, {1580, 59480}, {1581, 51328}, {1914, 256}, {1927, 56660}, {1933, 40099}, {1967, 4366}, {2201, 7015}, {2210, 257}, {3747, 40432}, {3903, 8632}, {4455, 4603}, {5009, 52651}, {14599, 7018}, {16514, 40763}, {17493, 31}, {18786, 6}, {18892, 44187}, {29055, 4435}, {32010, 41333}, {33295, 40729}, {39044, 9468}
X(61385) = barycentric quotient X(i)/X(j) for these (i, j): {31, 30669}, {32, 18787}, {238, 1920}, {256, 18895}, {257, 44172}, {292, 30642}, {893, 334}, {904, 335}, {1178, 40017}, {1428, 7196}, {1429, 7205}, {1914, 1909}, {1927, 52205}, {1933, 6645}, {1967, 40098}, {2210, 894}, {2238, 1237}, {3747, 3963}, {4366, 1926}, {5009, 8033}, {7018, 44170}, {7104, 291}, {7116, 337}, {8300, 3978}, {8632, 4374}, {9468, 30663}, {14598, 30657}, {14599, 171}, {14604, 18267}, {17493, 561}, {18786, 76}, {18892, 172}, {18894, 7122}, {30658, 7018}, {39044, 14603}, {40729, 43534}, {41333, 1215}, {41532, 51859}, {41882, 52085}, {51328, 1966}, {51979, 51868}, {59480, 1934}

X(61386) = VERTEX PRODUCT OF 2ND INNER-SODDY TRIANGLE

Barycentrics    a^2*(a+b-c)*(a-b+c)*(a^2-a*(b+c)-2*S) : :

X(61386) lies on circumconic {{A, B, C, X(56), X(8576)}} and on these lines: {31, 56}, {42, 6502}, {55, 6410}, {604, 60850}, {605, 2178}, {1055, 53065}, {1400, 8576}, {1475, 53066}, {2067, 2308}, {3720, 30385}, {4414, 13389}, {13388, 17017}, {18995, 61358}

X(61386) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 15890}, {8, 34216}
X(61386) = X(i)-Dao conjugate of X(j) for these {i, j}: {31535, 3596}, {32664, 15890}
X(61386) = X(i)-Ceva conjugate of X(j) for these {i, j}: {6186, 61387}
X(61386) = barycentric product X(i)*X(j) for these (i, j): {482, 6}, {16213, 51842}, {31535, 60850}
X(61386) = barycentric quotient X(i)/X(j) for these (i, j): {31, 15890}, {482, 76}, {604, 34216}
X(61386) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {31, 56, 61387}

X(61387) = VERTEX PRODUCT OF 2ND OUTER-SODDY TRIANGLE

Barycentrics    a^2*(a+b-c)*(a-b+c)*(a^2-a*(b+c)+2*S) : :

X(61387) lies on circumconic {{A, B, C, X(56), X(8577)}} and on these lines: {31, 56}, {42, 2067}, {55, 6409}, {604, 60849}, {606, 2178}, {1055, 53066}, {1400, 8577}, {1475, 53065}, {2308, 6502}, {3720, 30386}, {4414, 13388}, {13389, 17017}, {18996, 61358}

X(61387) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 15889}, {8, 34215}
X(61387) = X(i)-Dao conjugate of X(j) for these {i, j}: {31534, 3596}, {32664, 15889}
X(61387) = X(i)-Ceva conjugate of X(j) for these {i, j}: {6186, 61386}
X(61387) = barycentric product X(i)*X(j) for these (i, j): {481, 6}, {16214, 51841}, {31534, 60849}
X(61387) = barycentric quotient X(i)/X(j) for these (i, j): {31, 15889}, {481, 76}, {604, 34215}
X(61387) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {31, 56, 61386}

X(61388) = VERTEX PRODUCT OF 1ST TRI-SQUARES TRIANGLE

Barycentrics    4*a^4-(b^2-c^2)^2+a^2*(b^2+c^2+6*S) : :

X(61388) lies on these lines: {2, 38423}, {4, 19102}, {6, 30}, {99, 12159}, {115, 1327}, {230, 485}, {371, 12124}, {372, 7736}, {486, 5062}, {491, 7835}, {492, 7926}, {524, 13644}, {574, 53131}, {590, 40286}, {597, 13763}, {1285, 19054}, {1328, 53418}, {1384, 13712}, {1504, 6781}, {1587, 5304}, {1992, 13669}, {3053, 44647}, {3055, 43255}, {3068, 13651}, {3815, 8376}, {3830, 19099}, {5023, 9680}, {5024, 41946}, {5418, 12968}, {5420, 31489}, {6396, 31403}, {6418, 12601}, {6420, 44597}, {6422, 42261}, {6426, 31406}, {6454, 31400}, {6460, 45512}, {6564, 13834}, {7581, 8982}, {7585, 41410}, {7735, 35822}, {7749, 10195}, {9112, 36468}, {9113, 36450}, {9681, 12962}, {11292, 45574}, {12222, 45576}, {13637, 26613}, {13639, 13833}, {13662, 13663}, {13665, 13711}, {14930, 45513}, {15484, 32788}, {15513, 31483}, {15655, 52045}, {19101, 33457}, {19105, 30435}, {23249, 61322}, {31404, 35813}, {31415, 42603}, {31463, 61328}, {31465, 37512}, {31467, 41964}, {37637, 42602}, {39383, 61390}, {39876, 45544}, {42269, 49221}, {43460, 45407}, {43503, 49261}, {44596, 61309}

X(61388) = pole of line {381, 49114} with respect to the Kiepert hyperbola
X(61388) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4846), X(54874)}}, {{A, B, C, X(34288), X(54627)}}
X(61388) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 45515, 19102}, {6, 18907, 61389}, {6564, 44595, 13834}, {12968, 31411, 5418}, {42216, 46264, 6560}

X(61389) = VERTEX PRODUCT OF 2ND TRI-SQUARES TRIANGLE

Barycentrics    4*a^4-(b^2-c^2)^2+a^2*(b^2+c^2-6*S) : :

X(61389) lies on these lines: {2, 38424}, {4, 19105}, {6, 30}, {99, 12158}, {115, 1328}, {230, 486}, {371, 7736}, {372, 12123}, {485, 5058}, {491, 7926}, {492, 7835}, {524, 13763}, {574, 53130}, {597, 13644}, {615, 40287}, {1285, 19053}, {1327, 53418}, {1384, 13835}, {1505, 6781}, {1588, 5304}, {1992, 13789}, {3053, 44648}, {3055, 43254}, {3069, 13770}, {3815, 8375}, {3830, 19100}, {5013, 9681}, {5024, 41945}, {5418, 31489}, {5420, 12963}, {6417, 12602}, {6419, 44594}, {6421, 42260}, {6425, 31406}, {6453, 31400}, {6459, 45513}, {6565, 13711}, {7582, 26441}, {7586, 41411}, {7735, 35823}, {7749, 10194}, {9112, 36449}, {9113, 36467}, {9675, 61329}, {9680, 31401}, {11291, 45575}, {12221, 45577}, {13757, 26613}, {13759, 13769}, {13782, 13783}, {13785, 13834}, {14930, 45512}, {15484, 32787}, {15655, 52046}, {19102, 30435}, {22541, 33456}, {23259, 61323}, {31404, 35812}, {31415, 42602}, {31467, 41963}, {37637, 42603}, {39384, 61391}, {39875, 45545}, {42268, 49220}, {43460, 45406}, {43504, 49262}, {44595, 61308}

X(61389) = pole of line {381, 49115} with respect to the Kiepert hyperbola
X(61389) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4846), X(54876)}}, {{A, B, C, X(34288), X(54628)}}
X(61389) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 45514, 19105}, {6, 18907, 61388}, {6565, 44596, 13711}, {42215, 46264, 6561}

X(61390) = VERTEX PRODUCT OF 3RD TRI-SQUARES TRIANGLE

Barycentrics    a^6+3*a^2*(b^2-c^2)^2-4*a^4*(b^2+c^2)-2*(2*a^4-(b^2-c^2)^2+a^2*(b^2+c^2))*S : :

X(61390) lies on cubic K233 and on these lines: {2, 372}, {6, 6219}, {371, 55501}, {492, 18819}, {925, 8940}, {1321, 1899}, {1993, 49018}, {2165, 58826}, {3068, 24246}, {3156, 31411}, {5200, 53060}, {6564, 22554}, {7581, 13440}, {7745, 9777}, {8563, 32497}, {10132, 44647}, {10665, 52077}, {12124, 32568}, {16232, 41011}, {19006, 19446}, {39383, 61388}, {41516, 47731}, {43653, 53487}, {45420, 54031}, {49019, 53863}

X(61390) = X(i)-isoconjugate-of-X(j) for these {i, j}: {75, 8950}, {493, 55398}, {5408, 19218}
X(61390) = X(i)-Dao conjugate of X(j) for these {i, j}: {206, 8950}, {485, 69}, {24246, 5490}, {33364, 492}, {45472, 42009}
X(61390) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4, 41515}, {18819, 485}
X(61390) = X(i)-cross conjugate of X(j) for these {i, j}: {44647, 3068}, {53060, 24246}
X(61390) = pole of line {6291, 41515} with respect to the Jerabek hyperbola
X(61390) = pole of line {590, 8563} with respect to the Kiepert hyperbola
X(61390) = pole of line {6562, 14325} with respect to the orthic inconic
X(61390) = pole of line {371, 8950} with respect to the Stammler hyperbola
X(61390) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(3068)}}, {{A, B, C, X(4), X(488)}}, {{A, B, C, X(6), X(5408)}}, {{A, B, C, X(372), X(6423)}}, {{A, B, C, X(1327), X(32421)}}, {{A, B, C, X(1328), X(55041)}}
X(61390) = barycentric product X(i)*X(j) for these (i, j): {264, 53060}, {3068, 485}, {11090, 5200}, {13882, 18819}, {24246, 4}, {34391, 6423}, {41515, 488}
X(61390) = barycentric quotient X(i)/X(j) for these (i, j): {32, 8950}, {485, 5490}, {3068, 492}, {5200, 1585}, {6423, 371}, {8577, 493}, {10132, 5408}, {13882, 42009}, {24246, 69}, {39383, 1306}, {41515, 24244}, {44647, 641}, {53060, 3}, {54031, 54983}
X(61390) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 21463, 8944}, {485, 8944, 2}, {8035, 8577, 485}

X(61391) = VERTEX PRODUCT OF 4TH TRI-SQUARES TRIANGLE

Barycentrics    a^6+3*a^2*(b^2-c^2)^2-4*a^4*(b^2+c^2)+2*(2*a^4-(b^2-c^2)^2+a^2*(b^2+c^2))*S : :

X(61391) lies on cubic K233 and on these lines: {2, 371}, {6, 6220}, {372, 55502}, {491, 18820}, {925, 8944}, {1322, 1899}, {1993, 49019}, {2165, 58824}, {2362, 41011}, {3069, 24245}, {6565, 22553}, {7582, 13429}, {7584, 8964}, {7745, 9777}, {8564, 32494}, {10133, 44648}, {10666, 52077}, {12123, 32575}, {19005, 19447}, {39384, 61389}, {41515, 47731}, {43653, 53488}, {45421, 54030}, {49018, 53863}, {52291, 53061}

X(61391) = X(i)-isoconjugate-of-X(j) for these {i, j}: {75, 53062}, {494, 55397}, {5409, 19217}
X(61391) = X(i)-Dao conjugate of X(j) for these {i, j}: {206, 53062}, {486, 69}, {24245, 5491}, {33365, 491}, {45473, 42060}
X(61391) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4, 41516}, {18820, 486}
X(61391) = X(i)-cross conjugate of X(j) for these {i, j}: {44648, 3069}, {53061, 24245}
X(61391) = pole of line {6406, 41516} with respect to the Jerabek hyperbola
X(61391) = pole of line {615, 8564} with respect to the Kiepert hyperbola
X(61391) = pole of line {6562, 14326} with respect to the orthic inconic
X(61391) = pole of line {372, 53062} with respect to the Stammler hyperbola
X(61391) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(3069)}}, {{A, B, C, X(4), X(487)}}, {{A, B, C, X(6), X(5409)}}, {{A, B, C, X(371), X(6424)}}, {{A, B, C, X(1327), X(55040)}}, {{A, B, C, X(1328), X(32419)}}, {{A, B, C, X(2165), X(55477)}}
X(61391) = barycentric product X(i)*X(j) for these (i, j): {264, 53061}, {3069, 486}, {11091, 52291}, {13934, 18820}, {24245, 4}, {34392, 6424}, {41516, 487}, {55471, 8038}
X(61391) = barycentric quotient X(i)/X(j) for these (i, j): {32, 53062}, {486, 5491}, {3069, 491}, {6424, 372}, {8576, 494}, {10133, 5409}, {13934, 42060}, {24245, 69}, {39384, 1307}, {41516, 24243}, {44648, 642}, {52291, 1586}, {53061, 3}, {54030, 54984}
X(61391) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 21464, 8940}, {486, 8940, 2}, {8036, 8576, 486}, {14593, 56891, 61390}

X(61392) = VERTEX PRODUCT OF 5TH VIJAY TRIANGLE

Barycentrics    (a^2+b^2-c^2)^2*(a^2-b^2+c^2)^2*((a+b-c)*(a-b+c)*(a^3-2*b*c*(b+c)-a*(b+c)^2)+(4*a*b*c+2*(a^2-(b-c)^2)*(b+c))*S) : :

X(61392) lies on these lines: {4, 1123}, {19, 208}, {27, 1659}, {92, 1586}, {278, 2362}, {917, 54018}, {1096, 5200}, {1785, 6212}, {1838, 6213}, {7952, 42013}, {8747, 60850}, {13435, 55569}, {14121, 17555}, {30557, 55963}, {34121, 54394}, {40573, 60851}, {55110, 61401}, {58840, 60584}

X(61392) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 30556}, {48, 56385}, {63, 2066}, {69, 53065}, {72, 1806}, {78, 6502}, {219, 13389}, {255, 14121}, {326, 60852}, {345, 53064}, {394, 42013}, {577, 60853}, {605, 56386}, {906, 54019}, {1124, 30557}, {1259, 16232}, {1267, 53066}, {2289, 13390}, {3083, 5414}, {3719, 60849}, {13388, 60848}, {13425, 53063}, {55388, 60851}
X(61392) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 56385}, {3162, 2066}, {5190, 54019}, {6523, 14121}, {13388, 55388}, {13389, 326}, {15259, 60852}, {36103, 30556}
X(61392) = X(i)-Ceva conjugate of X(j) for these {i, j}: {158, 61393}
X(61392) = X(i)-cross conjugate of X(j) for these {i, j}: {34, 61393}, {60850, 1659}
X(61392) = pole of line {6332, 54019} with respect to the polar circle
X(61392) = pole of line {54239, 58838} with respect to the orthic inconic
X(61392) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(27)}}, {{A, B, C, X(19), X(2362)}}, {{A, B, C, X(28), X(1586)}}, {{A, B, C, X(34), X(13390)}}, {{A, B, C, X(57), X(486)}}, {{A, B, C, X(158), X(1123)}}, {{A, B, C, X(225), X(1659)}}, {{A, B, C, X(279), X(1132)}}, {{A, B, C, X(485), X(2006)}}, {{A, B, C, X(1328), X(52374)}}, {{A, B, C, X(1336), X(36123)}}, {{A, B, C, X(1400), X(2067)}}, {{A, B, C, X(1422), X(46433)}}, {{A, B, C, X(2385), X(54017)}}, {{A, B, C, X(3591), X(44794)}}, {{A, B, C, X(5230), X(56386)}}, {{A, B, C, X(7129), X(42013)}}, {{A, B, C, X(8557), X(30557)}}, {{A, B, C, X(13388), X(37550)}}, {{A, B, C, X(52082), X(60854)}}
X(61392) = barycentric product X(i)*X(j) for these (i, j): {34, 60854}, {264, 60850}, {273, 7133}, {278, 7090}, {318, 61401}, {331, 60851}, {1118, 56386}, {1123, 13390}, {1659, 4}, {2052, 2067}, {2362, 92}, {13387, 61393}, {13388, 158}, {13437, 14121}, {13438, 60853}, {36127, 54017}, {46107, 54018}, {53063, 57806}, {58840, 653}
X(61392) = barycentric quotient X(i)/X(j) for these (i, j): {4, 56385}, {19, 30556}, {25, 2066}, {34, 13389}, {158, 60853}, {393, 14121}, {608, 6502}, {1096, 42013}, {1118, 13390}, {1123, 56386}, {1395, 53064}, {1474, 1806}, {1659, 69}, {1805, 6514}, {1973, 53065}, {2067, 394}, {2207, 60852}, {2362, 63}, {5414, 1259}, {7090, 345}, {7133, 78}, {7337, 60849}, {7649, 54019}, {13388, 326}, {13389, 55388}, {13390, 1267}, {13438, 13388}, {14121, 13425}, {16232, 3083}, {30557, 3719}, {53063, 255}, {53066, 2289}, {54017, 52616}, {54018, 1331}, {56386, 1264}, {58840, 6332}, {60849, 1124}, {60850, 3}, {60851, 219}, {60852, 60848}, {60854, 3718}, {61393, 13386}, {61400, 52419}, {61401, 77}
X(61392) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {19, 225, 61393}

X(61393) = VERTEX PRODUCT OF 6TH VIJAY TRIANGLE

Barycentrics    (a^2+b^2-c^2)^2*(a^2-b^2+c^2)^2*((a+b-c)*(a-b+c)*(a^3-2*b*c*(b+c)-a*(b+c)^2)-(4*a*b*c+2*(a^2-(b-c)^2)*(b+c))*S) : :

X(61393) lies on these lines: {4, 1336}, {19, 208}, {27, 6502}, {92, 1585}, {278, 13459}, {917, 54016}, {1096, 52291}, {1785, 6213}, {1838, 6212}, {7090, 17555}, {7133, 7952}, {8747, 60849}, {13386, 31408}, {13424, 55573}, {30556, 55963}, {34125, 54394}, {40573, 60852}, {55110, 61400}, {58838, 60584}

X(61393) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 30557}, {48, 56386}, {63, 5414}, {69, 53066}, {72, 1805}, {78, 2067}, {219, 13388}, {255, 7090}, {326, 60851}, {345, 53063}, {394, 7133}, {577, 60854}, {606, 56385}, {906, 54017}, {1259, 2362}, {1335, 30556}, {1659, 2289}, {2066, 3084}, {3719, 60850}, {5391, 53065}, {13389, 60847}, {13458, 53064}, {55387, 60852}
X(61393) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 56386}, {3162, 5414}, {5190, 54017}, {6523, 7090}, {13388, 326}, {13389, 55387}, {15259, 60851}, {36103, 30557}
X(61393) = X(i)-Ceva conjugate of X(j) for these {i, j}: {158, 61392}
X(61393) = X(i)-cross conjugate of X(j) for these {i, j}: {34, 61392}, {60849, 13390}
X(61393) = pole of line {6332, 54017} with respect to the polar circle
X(61393) = pole of line {54239, 58840} with respect to the orthic inconic
X(61393) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(27)}}, {{A, B, C, X(19), X(14121)}}, {{A, B, C, X(28), X(1585)}}, {{A, B, C, X(34), X(1659)}}, {{A, B, C, X(57), X(485)}}, {{A, B, C, X(158), X(1336)}}, {{A, B, C, X(225), X(13390)}}, {{A, B, C, X(279), X(1131)}}, {{A, B, C, X(486), X(2006)}}, {{A, B, C, X(1123), X(36123)}}, {{A, B, C, X(1327), X(52374)}}, {{A, B, C, X(1400), X(6502)}}, {{A, B, C, X(1422), X(46434)}}, {{A, B, C, X(2385), X(54019)}}, {{A, B, C, X(3590), X(44794)}}, {{A, B, C, X(5230), X(56385)}}, {{A, B, C, X(7129), X(7133)}}, {{A, B, C, X(8557), X(30556)}}, {{A, B, C, X(13389), X(37550)}}, {{A, B, C, X(52082), X(60853)}}
X(61393) = barycentric product X(i)*X(j) for these (i, j): {34, 60853}, {264, 60849}, {273, 42013}, {318, 61400}, {331, 60852}, {1118, 56385}, {1336, 1659}, {2052, 6502}, {13386, 61392}, {13389, 158}, {13390, 4}, {13459, 7090}, {13460, 60854}, {14121, 278}, {16232, 92}, {36127, 54019}, {46107, 54016}, {53064, 57806}, {58838, 653}
X(61393) = barycentric quotient X(i)/X(j) for these (i, j): {4, 56386}, {19, 30557}, {25, 5414}, {34, 13388}, {158, 60854}, {393, 7090}, {608, 2067}, {1096, 7133}, {1118, 1659}, {1336, 56385}, {1395, 53063}, {1474, 1805}, {1659, 5391}, {1806, 6514}, {1973, 53066}, {2066, 1259}, {2207, 60851}, {2362, 3084}, {6502, 394}, {7090, 13458}, {7337, 60850}, {7649, 54017}, {13388, 55387}, {13389, 326}, {13390, 69}, {13460, 13389}, {14121, 345}, {16232, 63}, {30556, 3719}, {42013, 78}, {53064, 255}, {53065, 2289}, {54016, 1331}, {54019, 52616}, {56385, 1264}, {58838, 6332}, {60849, 3}, {60850, 1335}, {60851, 60847}, {60852, 219}, {60853, 3718}, {61392, 13387}, {61400, 77}, {61401, 52420}
X(61393) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {19, 225, 61392}

X(61394) = VERTEX PRODUCT OF X3-ABC REFLECTIONS TRIANGLE

Barycentrics    a^4*(-a^2+b^2+c^2)^2*(a^4+2*(b^2-c^2)^2-3*a^2*(b^2+c^2)) : :

X(61394) lies on these lines: {3, 143}, {6, 32078}, {51, 22052}, {97, 6638}, {182, 34003}, {184, 418}, {216, 34565}, {550, 14569}, {1656, 4994}, {2055, 26876}, {2972, 52170}, {3131, 10633}, {3132, 10632}, {3284, 26907}, {6641, 17810}, {9703, 19210}, {10979, 15004}, {15905, 26865}, {37457, 47328}, {46760, 57528}

X(61394) = X(i)-isoconjugate-of-X(j) for these {i, j}: {92, 60120}, {6521, 56338}, {13472, 57806}
X(61394) = X(i)-Dao conjugate of X(j) for these {i, j}: {22391, 60120}
X(61394) = pole of line {140, 264} with respect to the Stammler hyperbola
X(61394) = pole of line {1232, 18022} with respect to the Wallace hyperbola
X(61394) = intersection, other than A, B, C, of circumconics {{A, B, C, X(184), X(1173)}}, {{A, B, C, X(418), X(1656)}}, {{A, B, C, X(577), X(10979)}}
X(61394) = barycentric product X(i)*X(j) for these (i, j): {1656, 577}, {10979, 3}, {15004, 394}
X(61394) = barycentric quotient X(i)/X(j) for these (i, j): {184, 60120}, {1656, 18027}, {10979, 264}, {14585, 13472}, {15004, 2052}, {23606, 56338}
X(61394) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {184, 577, 61355}, {184, 61355, 23606}, {418, 61355, 184}

X(61395) = VERTEX PRODUCT OF INNER-YFF TRIANGLE

Barycentrics    a^2*(a^4+(b^2-c^2)^2-2*a^2*(b^2+b*c+c^2)) : :

X(61395) lies on these lines: {6, 31}, {38, 611}, {51, 2175}, {58, 16473}, {171, 1993}, {181, 184}, {213, 21807}, {218, 28125}, {219, 756}, {238, 5422}, {244, 52424}, {394, 750}, {595, 16472}, {601, 36747}, {602, 36752}, {607, 2181}, {612, 2323}, {613, 17469}, {614, 52423}, {748, 10601}, {896, 55400}, {940, 29678}, {1193, 11249}, {1201, 18967}, {1203, 5697}, {1254, 19349}, {1397, 13366}, {1405, 2187}, {1460, 11402}, {1468, 22350}, {1469, 26889}, {1482, 16466}, {1486, 20961}, {1707, 54444}, {1994, 17126}, {2162, 45843}, {2650, 7078}, {2911, 40967}, {2999, 5536}, {3060, 7295}, {3072, 7592}, {3195, 44097}, {3271, 15004}, {3715, 17796}, {3792, 7485}, {3938, 45728}, {4383, 24892}, {5012, 5329}, {5320, 23638}, {5706, 10894}, {7083, 9777}, {8772, 54416}, {11680, 32911}, {15066, 17122}, {15988, 26034}, {17124, 17811}, {17125, 17825}, {17127, 34545}, {19369, 26892}, {20958, 44104}, {24725, 34048}, {25961, 26657}, {32912, 45729}, {33127, 37543}, {34611, 50282}, {34857, 52431}, {36263, 55405}, {37557, 41329}, {37625, 54418}, {40728, 42295}, {54301, 54421}

X(61395) = isogonal conjugate of X(57883)
X(61395) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 57883}, {2, 56041}, {75, 57709}, {85, 2337}
X(61395) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 57883}, {206, 57709}, {32664, 56041}
X(61395) = pole of line {86, 499} with respect to the Stammler hyperbola
X(61395) = pole of line {310, 57883} with respect to the Wallace hyperbola
X(61395) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(61356)}}, {{A, B, C, X(31), X(60501)}}, {{A, B, C, X(42), X(498)}}, {{A, B, C, X(55), X(1454)}}, {{A, B, C, X(1011), X(14016)}}, {{A, B, C, X(7085), X(26921)}}
X(61395) = barycentric product X(i)*X(j) for these (i, j): {19, 26921}, {498, 6}, {1454, 9}, {14016, 71}
X(61395) = barycentric quotient X(i)/X(j) for these (i, j): {6, 57883}, {31, 56041}, {32, 57709}, {498, 76}, {1454, 85}, {2175, 2337}, {14016, 44129}, {26921, 304}
X(61395) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 31, 61396}, {6, 55, 61356}, {6, 61397, 42}, {611, 55399, 38}, {1460, 11402, 52434}, {16466, 44414, 49487}, {40958, 61399, 31}

X(61396) = VERTEX PRODUCT OF OUTER-YFF TRIANGLE

Barycentrics    a^2*(a^4+(b^2-c^2)^2-2*a^2*(b^2-b*c+c^2)) : :

X(61396) lies on these lines: {1, 54444}, {6, 31}, {25, 52434}, {38, 613}, {51, 1397}, {58, 14793}, {81, 37373}, {171, 5422}, {181, 15004}, {184, 3271}, {197, 20962}, {222, 244}, {238, 1993}, {394, 748}, {595, 16473}, {601, 36752}, {602, 36747}, {608, 2181}, {611, 17469}, {614, 2003}, {750, 10601}, {756, 55432}, {896, 55399}, {1096, 52413}, {1193, 10269}, {1203, 37525}, {1428, 26892}, {1460, 9777}, {1468, 22767}, {1473, 53542}, {1994, 17127}, {2175, 13366}, {2176, 45843}, {2310, 19354}, {3060, 5329}, {3073, 7592}, {3157, 28082}, {3938, 45729}, {5012, 7295}, {5272, 22128}, {5320, 20959}, {7083, 11402}, {7186, 7485}, {8614, 17054}, {8772, 16502}, {10246, 16466}, {15066, 17123}, {17124, 17825}, {17125, 17811}, {17126, 34545}, {20961, 37538}, {20991, 38296}, {21746, 44104}, {24725, 37543}, {25960, 26625}, {27518, 37652}, {28965, 29851}, {32577, 34046}, {32912, 45728}, {33127, 34048}, {36263, 55406}

X(61396) = isogonal conjugate of X(57884)
X(61396) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 57884}, {2, 56352}, {75, 52186}, {312, 7130}
X(61396) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 57884}, {206, 52186}, {32664, 56352}
X(61396) = X(i)-Ceva conjugate of X(j) for these {i, j}: {36082, 649}
X(61396) = pole of line {86, 498} with respect to the Stammler hyperbola
X(61396) = pole of line {310, 57884} with respect to the Wallace hyperbola
X(61396) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(61357)}}, {{A, B, C, X(42), X(499)}}, {{A, B, C, X(55), X(7082)}}, {{A, B, C, X(7085), X(24467)}}
X(61396) = barycentric product X(i)*X(j) for these (i, j): {19, 24467}, {57, 7082}, {499, 6}, {10052, 2164}
X(61396) = barycentric quotient X(i)/X(j) for these (i, j): {6, 57884}, {31, 56352}, {32, 52186}, {499, 76}, {1397, 7130}, {7082, 312}, {24467, 304}
X(61396) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 31, 61395}, {6, 55, 61357}, {6, 61398, 42}, {613, 55400, 38}, {2308, 40958, 31}

X(61397) = VERTEX PRODUCT OF INNER-YFF TANGENTS TRIANGLE

Barycentrics    a^2*(a-b-c)*(a^3+a^2*(b+c)-(b-c)^2*(b+c)-a*(b^2+c^2)) : :

X(61397) lies on these lines: {1, 6883}, {3, 2594}, {6, 31}, {11, 4383}, {12, 5706}, {22, 56878}, {25, 692}, {33, 2911}, {35, 16473}, {38, 12594}, {40, 54301}, {43, 1936}, {44, 7082}, {46, 1079}, {47, 11248}, {51, 1486}, {56, 1066}, {63, 45729}, {65, 7078}, {81, 5218}, {100, 1993}, {154, 20989}, {155, 11499}, {165, 2003}, {181, 6056}, {184, 197}, {200, 2323}, {210, 219}, {218, 1864}, {220, 3715}, {221, 37567}, {222, 1155}, {227, 19349}, {239, 28934}, {255, 11509}, {354, 52424}, {386, 26357}, {394, 1376}, {430, 45886}, {497, 32911}, {498, 5707}, {511, 37577}, {517, 57277}, {518, 55399}, {580, 37579}, {581, 37601}, {582, 5399}, {595, 26358}, {602, 11510}, {607, 1859}, {611, 3666}, {613, 3744}, {614, 18839}, {651, 3474}, {940, 5432}, {1001, 10601}, {1040, 3751}, {1103, 37550}, {1181, 11500}, {1191, 2098}, {1193, 10966}, {1203, 1697}, {1364, 23122}, {1397, 20958}, {1399, 10310}, {1460, 44085}, {1468, 22072}, {1473, 8679}, {1621, 5422}, {1708, 8758}, {1737, 60691}, {1743, 30223}, {1754, 3173}, {1757, 24430}, {1770, 8757}, {1771, 56293}, {1783, 1857}, {1788, 3562}, {1824, 39109}, {1834, 10953}, {1836, 34048}, {1837, 16471}, {1858, 54295}, {2175, 10833}, {2183, 2187}, {2192, 52371}, {2999, 54408}, {3057, 16466}, {3058, 50282}, {3072, 11501}, {3074, 37529}, {3190, 3939}, {3193, 5552}, {3198, 19350}, {3295, 37509}, {3683, 55432}, {3713, 4046}, {3746, 16472}, {3870, 45728}, {3915, 10965}, {3938, 12595}, {3990, 43214}, {4185, 22300}, {4255, 37564}, {4336, 7069}, {4413, 17811}, {4423, 17825}, {4513, 6057}, {4640, 55400}, {4641, 9371}, {4663, 10391}, {4849, 19354}, {5048, 16483}, {5128, 34043}, {5135, 54312}, {5204, 34046}, {5217, 36746}, {5220, 24431}, {5247, 22760}, {5274, 14997}, {5281, 37685}, {5315, 7962}, {5396, 40292}, {5398, 8069}, {5730, 33177}, {5752, 8193}, {5904, 33178}, {6180, 11246}, {7004, 32912}, {7071, 44097}, {7299, 10982}, {7354, 9370}, {7592, 11491}, {9629, 56534}, {9709, 22136}, {10267, 36752}, {10388, 16469}, {10589, 37680}, {10822, 40944}, {10832, 36741}, {10964, 51773}, {10975, 19035}, {10976, 19036}, {11249, 54427}, {11376, 50759}, {11402, 20986}, {11507, 52408}, {11849, 36749}, {12161, 32141}, {13329, 37578}, {13384, 16474}, {15837, 54358}, {16059, 36942}, {16434, 50362}, {16577, 60912}, {16980, 22654}, {17718, 37543}, {17810, 20988}, {17824, 32347}, {18445, 18524}, {18451, 18491}, {19541, 45885}, {20683, 22131}, {20872, 33586}, {21853, 52033}, {22117, 37541}, {22769, 26889}, {23071, 36279}, {23853, 37510}, {24892, 37679}, {24914, 41344}, {24929, 39523}, {26040, 37659}, {26935, 58690}, {27521, 31034}, {29678, 37674}, {31479, 45923}, {33925, 55086}, {34545, 61155}, {35197, 37572}, {35238, 37483}, {35258, 54444}, {36753, 37621}, {37366, 38472}, {41338, 56418}, {44105, 52427}, {44631, 45468}, {44632, 45469}, {45269, 49500}, {45424, 55398}, {45425, 55397}, {53525, 55437}, {54401, 58630}, {54430, 59301}, {56549, 57118}

X(61397) = isogonal conjugate of X(7318)
X(61397) = perspector of circumconic {{A, B, C, X(101), X(32698)}}
X(61397) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 7318}, {7, 90}, {56, 20570}, {57, 2994}, {77, 7040}, {81, 60249}, {85, 2164}, {269, 36626}, {273, 1069}, {278, 6513}, {693, 36082}, {1088, 7072}, {2185, 7363}, {4573, 55248}
X(61397) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 20570}, {3, 7318}, {63, 7182}, {5452, 2994}, {6506, 15413}, {6600, 36626}, {40586, 60249}, {59973, 34387}
X(61397) = X(i)-Ceva conjugate of X(j) for these {i, j}: {33, 55}, {46, 2178}, {52186, 6}
X(61397) = pole of line {37, 169} with respect to the Feuerbach hyperbola
X(61397) = pole of line {86, 7318} with respect to the Stammler hyperbola
X(61397) = pole of line {310, 7318} with respect to the Wallace hyperbola
X(61397) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(61398)}}, {{A, B, C, X(6), X(913)}}, {{A, B, C, X(9), X(54285)}}, {{A, B, C, X(31), X(1406)}}, {{A, B, C, X(33), X(1079)}}, {{A, B, C, X(42), X(5552)}}, {{A, B, C, X(46), X(55)}}, {{A, B, C, X(59), X(1857)}}, {{A, B, C, X(71), X(21853)}}, {{A, B, C, X(209), X(21077)}}, {{A, B, C, X(212), X(3157)}}, {{A, B, C, X(220), X(56535)}}, {{A, B, C, X(672), X(5905)}}, {{A, B, C, X(1011), X(3559)}}, {{A, B, C, X(1068), X(14547)}}, {{A, B, C, X(2053), X(26890)}}, {{A, B, C, X(2192), X(2361)}}, {{A, B, C, X(3779), X(20930)}}, {{A, B, C, X(7074), X(52371)}}, {{A, B, C, X(7077), X(12329)}}, {{A, B, C, X(21188), X(43046)}}, {{A, B, C, X(37538), X(46366)}}
X(61397) = barycentric product X(i)*X(j) for these (i, j): {21, 21853}, {33, 6505}, {46, 9}, {55, 5905}, {59, 6506}, {100, 46389}, {200, 56848}, {281, 3157}, {1068, 219}, {1406, 346}, {1783, 59973}, {1800, 1826}, {1857, 6511}, {2178, 8}, {2323, 56417}, {3193, 37}, {3559, 71}, {5552, 6}, {20930, 41}, {21077, 284}, {21188, 3939}, {31631, 42}, {51648, 644}, {52033, 78}, {55214, 643}, {56535, 7110}
X(61397) = barycentric quotient X(i)/X(j) for these (i, j): {6, 7318}, {9, 20570}, {41, 90}, {42, 60249}, {46, 85}, {55, 2994}, {181, 7363}, {212, 6513}, {220, 36626}, {607, 7040}, {1068, 331}, {1406, 279}, {1800, 17206}, {2175, 2164}, {2178, 7}, {3157, 348}, {3193, 274}, {3559, 44129}, {5552, 76}, {5905, 6063}, {6056, 6512}, {6505, 7182}, {6506, 34387}, {6511, 7055}, {14827, 7072}, {20930, 20567}, {21077, 349}, {21188, 52621}, {21853, 1441}, {31631, 310}, {32739, 36082}, {46389, 693}, {51648, 24002}, {52033, 273}, {52425, 1069}, {55214, 4077}, {55247, 55213}, {56535, 17095}, {56848, 1088}, {57124, 57215}, {59973, 15413}
X(61397) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 55, 61398}, {31, 61357, 6}, {35, 16473, 36742}, {43, 1936, 11502}, {46, 3157, 1406}, {46, 56535, 3157}, {184, 51377, 197}, {582, 5399, 7742}, {1253, 14547, 55}, {1253, 61358, 14547}, {1468, 22072, 22768}, {2066, 5414, 54285}, {2183, 2187, 15494}, {9370, 37537, 7354}

X(61398) = VERTEX PRODUCT OF OUTER-YFF TANGENTS TRIANGLE

Barycentrics    a^2*(a-b-c)*(a^3+a^2*(b+c)-(b-c)^2*(b+c)-a*(b^2-4*b*c+c^2)) : :

X(61398) lies on these lines: {1, 90}, {6, 31}, {11, 940}, {25, 20986}, {33, 44105}, {35, 16472}, {37, 7082}, {38, 12595}, {48, 15494}, {51, 197}, {56, 1064}, {58, 26357}, {63, 45728}, {81, 497}, {100, 5422}, {154, 20988}, {165, 52423}, {171, 11502}, {182, 37577}, {184, 1486}, {210, 55432}, {215, 16686}, {219, 3683}, {222, 354}, {333, 27518}, {390, 37685}, {394, 1001}, {500, 7742}, {518, 55400}, {580, 37601}, {581, 37579}, {601, 11509}, {608, 1859}, {611, 3744}, {613, 3666}, {651, 3475}, {692, 11402}, {942, 1406}, {991, 37578}, {999, 1464}, {1036, 54417}, {1040, 16475}, {1100, 19354}, {1124, 31588}, {1155, 52424}, {1181, 11496}, {1191, 34471}, {1193, 22768}, {1203, 3601}, {1335, 31589}, {1376, 10601}, {1386, 10391}, {1397, 10833}, {1407, 4860}, {1437, 11365}, {1451, 4300}, {1457, 3304}, {1468, 10966}, {1470, 37469}, {1471, 22053}, {1479, 5707}, {1480, 25415}, {1497, 11510}, {1621, 1993}, {1776, 28606}, {1836, 37543}, {1837, 5711}, {1864, 3745}, {1994, 61155}, {2175, 20959}, {2187, 2317}, {2192, 7073}, {2194, 7083}, {2286, 51657}, {2323, 4512}, {2646, 16466}, {3058, 50303}, {3295, 36750}, {3486, 57280}, {3746, 16473}, {3796, 20872}, {3870, 45729}, {3938, 12594}, {4252, 37564}, {4258, 52426}, {4383, 5432}, {4413, 17825}, {4423, 17811}, {4640, 55399}, {4666, 22128}, {5119, 44414}, {5204, 37501}, {5217, 36745}, {5218, 32911}, {5220, 55438}, {5228, 11246}, {5274, 14996}, {5284, 15066}, {5311, 7069}, {5315, 13384}, {5396, 8069}, {5398, 40292}, {5452, 20229}, {5706, 6284}, {5710, 10950}, {6056, 22131}, {7004, 17017}, {7050, 52371}, {7078, 37080}, {7962, 16474}, {8757, 13407}, {8758, 45126}, {9370, 15888}, {9581, 37559}, {9668, 45923}, {9669, 45931}, {10267, 36747}, {10310, 37514}, {10383, 16469}, {10589, 37633}, {10832, 36740}, {10982, 11500}, {11031, 17599}, {11193, 57174}, {11248, 36752}, {11501, 37699}, {11508, 37698}, {11518, 34043}, {11849, 36753}, {11934, 22383}, {12410, 55098}, {14100, 54358}, {14621, 28934}, {15004, 51377}, {15338, 37537}, {16541, 37492}, {16678, 37474}, {17718, 34048}, {17810, 20989}, {22132, 44707}, {22769, 26892}, {26927, 58617}, {29815, 40269}, {31757, 39582}, {33105, 37674}, {36749, 37621}, {37034, 58469}, {37516, 54312}, {37542, 37734}, {37580, 44085}, {44086, 52427}, {45422, 55398}, {45423, 55397}, {50195, 57277}, {55323, 57652}

X(61398) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 56231}, {7, 7162}
X(61398) = X(i)-Dao conjugate of X(j) for these {i, j}: {32664, 56231}
X(61398) = X(i)-Ceva conjugate of X(j) for these {i, j}: {57709, 6}
X(61398) = pole of line {649, 34948} with respect to the circumcircle
X(61398) = pole of line {3, 37} with respect to the Feuerbach hyperbola
X(61398) = pole of line {650, 44410} with respect to the MacBeath circumconic
X(61398) = pole of line {8676, 58888} with respect to the orthic inconic
X(61398) = pole of line {86, 3193} with respect to the Stammler hyperbola
X(61398) = pole of line {2140, 43054} with respect to the dual conic of Yff parabola
X(61398) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(42), X(10527)}}, {{A, B, C, X(55), X(90)}}, {{A, B, C, X(71), X(56269)}}, {{A, B, C, X(209), X(12609)}}, {{A, B, C, X(212), X(1069)}}, {{A, B, C, X(284), X(54285)}}, {{A, B, C, X(672), X(13401)}}, {{A, B, C, X(1253), X(7072)}}, {{A, B, C, X(2361), X(7050)}}, {{A, B, C, X(7073), X(7074)}}
X(61398) = barycentric product X(i)*X(j) for these (i, j): {100, 13401}, {3338, 9}, {10044, 2337}, {10527, 6}, {12609, 284}, {17412, 664}, {32561, 7}, {42012, 57}
X(61398) = barycentric quotient X(i)/X(j) for these (i, j): {31, 56231}, {41, 7162}, {3338, 85}, {10527, 76}, {12609, 349}, {13401, 693}, {17412, 522}, {32561, 8}, {42012, 312}
X(61398) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 55, 61397}, {31, 61356, 6}, {35, 16472, 36754}, {212, 2293, 55}, {991, 55086, 37578}, {1397, 21746, 37538}, {2293, 2308, 212}

X(61399) = VERTEX PRODUCT OF MOSES-MIYAMOTO TRIANGLE

Barycentrics    2*a^5-3*a^4*(b+c)+a^2*(b-c)^2*(b+c) : :

X(61399) lies on these lines: {1, 60970}, {6, 31}, {44, 21039}, {171, 37659}, {213, 3010}, {692, 2260}, {750, 25878}, {1193, 13329}, {1201, 1471}, {1254, 1456}, {1400, 2175}, {1405, 7083}, {1458, 3449}, {1723, 28125}, {1743, 28043}, {2223, 21748}, {2317, 3941}, {2347, 60722}, {2643, 40977}, {3195, 44100}, {3332, 5230}, {3340, 3924}, {4336, 8557}, {4648, 29661}, {6610, 9340}, {7991, 16469}, {8647, 21746}, {20990, 22356}, {22117, 41422}, {33104, 37681}

X(61399) = X(i)-isoconjugate-of-X(j) for these {i, j}: {75, 13404}, {693, 43344}
X(61399) = X(i)-Dao conjugate of X(j) for these {i, j}: {206, 13404}, {52818, 76}
X(61399) = X(i)-Ceva conjugate of X(j) for these {i, j}: {53243, 649}
X(61399) = pole of line {649, 51652} with respect to the Brocard inellipse
X(61399) = pole of line {86, 11019} with respect to the Stammler hyperbola
X(61399) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(42), X(13405)}}, {{A, B, C, X(55), X(3449)}}, {{A, B, C, X(58), X(20978)}}, {{A, B, C, X(672), X(52819)}}, {{A, B, C, X(2276), X(25001)}}, {{A, B, C, X(41423), X(41441)}}
X(61399) = barycentric product X(i)*X(j) for these (i, j): {13405, 6}, {15837, 57}, {25001, 31}, {52819, 55}
X(61399) = barycentric quotient X(i)/X(j) for these (i, j): {32, 13404}, {13405, 76}, {15837, 312}, {25001, 561}, {32739, 43344}, {52819, 6063}
X(61399) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 1253, 42}, {6, 21059, 2293}, {6, 31, 20978}, {31, 61395, 40958}, {2293, 21059, 902}

X(61400) = VERTEX PRODUCT OF 1ST MOSES-MIYAMOTO-APOLLONIUS TRIANGLE TRIANGLE

Barycentrics    a*(a+b-c)*(a-b+c)*((a^2-(b-c)^2)*(b+c)-2*a*S) : :

X(61400) lies on these lines: {7, 13389}, {25, 34}, {57, 6502}, {223, 2067}, {269, 60849}, {278, 2362}, {1407, 13460}, {1418, 34125}, {3752, 19013}, {7133, 55424}, {8817, 56385}, {13388, 16440}, {15728, 54016}, {55110, 61393}

X(61400) = X(i)-isoconjugate-of-X(j) for these {i, j}: {8, 5414}, {9, 30557}, {55, 56386}, {78, 7133}, {200, 13388}, {212, 60854}, {219, 7090}, {312, 53066}, {341, 53063}, {345, 60851}, {346, 2067}, {1260, 1659}, {1265, 60850}, {1805, 2321}, {2362, 3692}, {3939, 54017}, {4587, 58840}, {13458, 60852}, {14121, 60847}
X(61400) = X(i)-Dao conjugate of X(j) for these {i, j}: {223, 56386}, {478, 30557}, {6609, 13388}, {13388, 345}, {13389, 13458}, {40617, 54017}, {40837, 60854}
X(61400) = X(i)-Ceva conjugate of X(j) for these {i, j}: {278, 61401}
X(61400) = X(i)-cross conjugate of X(j) for these {i, j}: {1407, 61401}, {60849, 16232}
X(61400) = pole of line {1854, 30376} with respect to the Feuerbach hyperbola
X(61400) = pole of line {481, 21621} with respect to the dual conic of Yff parabola
X(61400) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(57)}}, {{A, B, C, X(25), X(42013)}}, {{A, B, C, X(28), X(6212)}}, {{A, B, C, X(34), X(13390)}}, {{A, B, C, X(56), X(2362)}}, {{A, B, C, X(105), X(7348)}}, {{A, B, C, X(614), X(56385)}}, {{A, B, C, X(1104), X(30556)}}, {{A, B, C, X(1413), X(2067)}}, {{A, B, C, X(1828), X(60853)}}, {{A, B, C, X(7347), X(9309)}}, {{A, B, C, X(40956), X(53064)}}, {{A, B, C, X(45818), X(46434)}}, {{A, B, C, X(57656), X(60850)}}
X(61400) = barycentric product X(i)*X(j) for these (i, j): {273, 6502}, {279, 42013}, {331, 53064}, {1088, 60852}, {1119, 30556}, {1407, 60853}, {1435, 56385}, {1847, 2066}, {13386, 61401}, {13388, 13459}, {13389, 278}, {13390, 57}, {14121, 269}, {16232, 7}, {24002, 54016}, {32714, 54019}, {52419, 61392}, {58838, 934}, {60849, 85}, {61393, 77}
X(61400) = barycentric quotient X(i)/X(j) for these (i, j): {34, 7090}, {56, 30557}, {57, 56386}, {278, 60854}, {604, 5414}, {608, 7133}, {1106, 2067}, {1395, 60851}, {1397, 53066}, {1398, 2362}, {1407, 13388}, {1408, 1805}, {1435, 1659}, {1806, 1792}, {2066, 3692}, {3669, 54017}, {6502, 78}, {13388, 13458}, {13389, 345}, {13390, 312}, {13459, 60853}, {13460, 14121}, {14121, 341}, {16232, 8}, {30556, 1265}, {42013, 346}, {43923, 58840}, {52410, 53063}, {53063, 60847}, {53064, 219}, {53065, 1260}, {54016, 644}, {54019, 15416}, {56385, 52406}, {58838, 4397}, {60849, 9}, {60852, 200}, {60853, 59761}, {61393, 318}, {61401, 13387}
X(61400) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {34, 1435, 61401}, {13389, 13390, 42013}

X(61401) = VERTEX PRODUCT OF 2ND MOSES-MIYAMOTO-APOLLONIUS TRIANGLE TRIANGLE

Barycentrics    a*(a+b-c)*(a-b+c)*((a^2-(b-c)^2)*(b+c)+2*a*S) : :

X(61401) lies on these lines: {7, 1659}, {25, 34}, {57, 2067}, {223, 6502}, {269, 60850}, {278, 13459}, {1407, 13438}, {1418, 34121}, {3752, 19014}, {8817, 56386}, {13389, 16441}, {15728, 54018}, {42013, 55455}, {55110, 61392}

X(61401) = X(i)-isoconjugate-of-X(j) for these {i, j}: {8, 2066}, {9, 30556}, {55, 56385}, {78, 42013}, {200, 13389}, {212, 60853}, {219, 14121}, {312, 53065}, {341, 53064}, {345, 60852}, {346, 6502}, {1260, 13390}, {1265, 60849}, {1806, 2321}, {3692, 16232}, {3939, 54019}, {4587, 58838}, {7090, 60848}, {13425, 60851}
X(61401) = X(i)-Dao conjugate of X(j) for these {i, j}: {223, 56385}, {478, 30556}, {6609, 13389}, {13388, 13425}, {13389, 345}, {40617, 54019}, {40837, 60853}
X(61401) = X(i)-Ceva conjugate of X(j) for these {i, j}: {278, 61400}
X(61401) = X(i)-cross conjugate of X(j) for these {i, j}: {1407, 61400}, {60850, 2362}
X(61401) = pole of line {1854, 30375} with respect to the Feuerbach hyperbola
X(61401) = pole of line {482, 21621} with respect to the dual conic of Yff parabola
X(61401) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(57)}}, {{A, B, C, X(25), X(7133)}}, {{A, B, C, X(28), X(6213)}}, {{A, B, C, X(34), X(1659)}}, {{A, B, C, X(56), X(2067)}}, {{A, B, C, X(105), X(7347)}}, {{A, B, C, X(614), X(56386)}}, {{A, B, C, X(1104), X(30557)}}, {{A, B, C, X(1413), X(6502)}}, {{A, B, C, X(1828), X(60854)}}, {{A, B, C, X(7348), X(9309)}}, {{A, B, C, X(40956), X(53063)}}, {{A, B, C, X(45818), X(46433)}}, {{A, B, C, X(57656), X(60849)}}
X(61401) = barycentric product X(i)*X(j) for these (i, j): {269, 7090}, {279, 7133}, {331, 53063}, {1088, 60851}, {1119, 30557}, {1407, 60854}, {1435, 56386}, {1659, 57}, {1847, 5414}, {2067, 273}, {2362, 7}, {13387, 61400}, {13388, 278}, {13389, 13437}, {24002, 54018}, {32714, 54017}, {52420, 61393}, {58840, 934}, {60850, 85}, {61392, 77}
X(61401) = barycentric quotient X(i)/X(j) for these (i, j): {34, 14121}, {56, 30556}, {57, 56385}, {278, 60853}, {604, 2066}, {608, 42013}, {1106, 6502}, {1395, 60852}, {1397, 53065}, {1398, 16232}, {1407, 13389}, {1408, 1806}, {1435, 13390}, {1659, 312}, {1805, 1792}, {2067, 78}, {2362, 8}, {3669, 54019}, {5414, 3692}, {7090, 341}, {7133, 346}, {13388, 345}, {13389, 13425}, {13437, 60854}, {13438, 7090}, {30557, 1265}, {43923, 58838}, {52410, 53064}, {53063, 219}, {53064, 60848}, {53066, 1260}, {54017, 15416}, {54018, 644}, {56386, 52406}, {58840, 4397}, {60850, 9}, {60851, 200}, {60854, 59761}, {61392, 318}, {61400, 13386}
X(61401) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {34, 1435, 61400}, {1659, 13388, 7133}, {55455, 55460, 42013}

X(61402) = VERTEX PRODUCT OF GEMINI 49 TRIANGLE

Barycentrics    (a-b)^2*(a-c)^2*(b+c)^2 : :

X(61402) lies on these lines: {2, 7035}, {190, 26853}, {661, 3952}, {668, 26824}, {1016, 20016}, {1018, 58288}, {1252, 4076}, {2238, 3943}, {3948, 52959}, {4024, 4103}, {4033, 58361}, {4115, 58294}, {4562, 31290}, {4568, 49273}, {26795, 36863}, {27807, 29416}, {40521, 50487}

X(61402) = isotomic conjugate of X(61403)
X(61402) = trilinear pole of line {4103, 40501}
X(61402) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 61403}, {58, 16726}, {60, 53538}, {110, 8042}, {244, 593}, {757, 1015}, {763, 3122}, {764, 4556}, {849, 1086}, {873, 1977}, {1019, 3733}, {1106, 26856}, {1333, 17205}, {1357, 2185}, {1358, 2150}, {1408, 17197}, {1412, 18191}, {1509, 3248}, {2170, 7341}, {2206, 16727}, {3121, 6628}, {3249, 4623}, {4610, 8027}, {4858, 7342}, {7192, 57129}, {7203, 7252}, {7254, 57200}, {21143, 52935}, {30576, 43922}, {52379, 61048}
X(61402) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 61403}, {10, 16726}, {37, 17205}, {244, 8042}, {594, 21208}, {740, 35119}, {4075, 1086}, {6552, 26856}, {40599, 18191}, {40603, 16727}, {40607, 1015}, {55065, 6545}, {56325, 1358}, {59577, 17197}
X(61402) = X(i)-cross conjugate of X(j) for these {i, j}: {594, 4103}, {756, 3952}, {1500, 40521}, {4099, 4552}
X(61402) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(661)}}, {{A, B, C, X(6), X(58288)}}, {{A, B, C, X(10), X(19998)}}, {{A, B, C, X(37), X(58294)}}, {{A, B, C, X(279), X(4099)}}, {{A, B, C, X(594), X(3943)}}, {{A, B, C, X(740), X(58784)}}, {{A, B, C, X(1500), X(50487)}}, {{A, B, C, X(1509), X(26853)}}, {{A, B, C, X(3952), X(7035)}}, {{A, B, C, X(3995), X(18098)}}, {{A, B, C, X(4651), X(56251)}}, {{A, B, C, X(6057), X(28654)}}, {{A, B, C, X(6539), X(40098)}}, {{A, B, C, X(8013), X(20016)}}, {{A, B, C, X(31290), X(57554)}}
X(61402) = barycentric product X(i)*X(j) for these (i, j): {12, 4076}, {190, 4103}, {1016, 594}, {1018, 4033}, {1089, 765}, {1252, 28654}, {1500, 31625}, {3952, 3952}, {4024, 6632}, {4036, 57731}, {4600, 6535}, {4601, 762}, {4605, 6558}, {4705, 57950}, {4998, 6057}, {6058, 6064}, {7035, 756}, {15742, 3695}, {21859, 646}, {27808, 4557}, {30730, 4552}, {34388, 6065}, {35068, 57566}, {40521, 668}, {52623, 59149}, {61405, 61406}
X(61402) = barycentric quotient X(i)/X(j) for these (i, j): {2, 61403}, {10, 17205}, {12, 1358}, {37, 16726}, {59, 7341}, {181, 1357}, {210, 18191}, {321, 16727}, {346, 26856}, {594, 1086}, {661, 8042}, {756, 244}, {762, 3125}, {765, 757}, {872, 3248}, {1016, 1509}, {1018, 1019}, {1089, 1111}, {1110, 849}, {1252, 593}, {1500, 1015}, {2171, 53538}, {2321, 17197}, {3214, 17214}, {3690, 3937}, {3695, 1565}, {3710, 17219}, {3949, 3942}, {3952, 7192}, {3971, 23824}, {4006, 18184}, {4013, 6549}, {4024, 6545}, {4033, 7199}, {4037, 27918}, {4053, 53546}, {4069, 3737}, {4075, 21208}, {4076, 261}, {4079, 21143}, {4092, 7336}, {4103, 514}, {4158, 7215}, {4551, 7203}, {4552, 17096}, {4557, 3733}, {4567, 763}, {4574, 7254}, {4600, 6628}, {4601, 57949}, {4605, 58817}, {4705, 764}, {4849, 18211}, {4998, 552}, {6046, 41292}, {6057, 11}, {6058, 1365}, {6065, 60}, {6535, 3120}, {6632, 4610}, {7035, 873}, {7064, 3271}, {7109, 1977}, {7140, 2969}, {7141, 2973}, {20691, 16742}, {21021, 7200}, {21803, 53541}, {21859, 3669}, {24044, 59746}, {27808, 52619}, {28654, 23989}, {30730, 4560}, {35068, 35119}, {40521, 513}, {50487, 8027}, {52609, 15419}, {52623, 23100}, {53581, 3249}, {57566, 57554}, {57731, 52935}, {57950, 4623}, {58289, 8034}, {59149, 4556}, {61059, 61061}, {61164, 18200}, {61364, 61048}, {61405, 61404}, {61406, 61407}
X(61402) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4562, 54099, 31290}, {7035, 61406, 2}

X(61403) = VERTEX PRODUCT OF GEMINI 50 TRIANGLE

Barycentrics    (a+b)^2*(b-c)^2*(a+c)^2 : :

X(61403) lies on these lines: {2, 799}, {244, 7192}, {279, 4637}, {552, 593}, {1015, 26845}, {1019, 38346}, {1509, 4610}, {2669, 19998}, {3124, 31290}, {4089, 17205}, {4366, 8025}, {4560, 7208}, {4576, 17154}, {10330, 17103}, {16703, 39747}, {16705, 26844}, {16714, 30593}, {16726, 16727}, {16741, 17495}, {16748, 26819}, {17187, 39734}, {17493, 26858}, {23989, 53543}

X(61403) = isotomic conjugate of X(61402)
X(61403) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 61402}, {101, 40521}, {594, 1110}, {692, 4103}, {756, 1252}, {762, 4570}, {765, 1500}, {872, 1016}, {1018, 4557}, {1089, 23990}, {2149, 6057}, {2171, 6065}, {3939, 21859}, {4069, 4559}, {4079, 57731}, {4564, 7064}, {4705, 59149}, {6066, 6358}, {6632, 50487}, {7035, 7109}, {53581, 57950}
X(61403) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 61402}, {513, 1500}, {514, 594}, {650, 6057}, {661, 756}, {812, 35068}, {1015, 40521}, {1086, 4103}, {4988, 6535}, {16726, 4115}, {40617, 21859}, {40620, 3952}, {40625, 30730}, {50330, 762}, {55067, 4069}
X(61403) = X(i)-Ceva conjugate of X(j) for these {i, j}: {873, 7192}
X(61403) = X(i)-cross conjugate of X(j) for these {i, j}: {8042, 7192}
X(61403) = pole of line {41333, 52963} with respect to the Stammler hyperbola
X(61403) = pole of line {2238, 3943} with respect to the Wallace hyperbola
X(61403) = pole of line {20295, 23789} with respect to the dual conic of Yff parabola
X(61403) = pole of line {762, 6535} with respect to the dual conic of Wallace hyperbola
X(61403) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(244)}}, {{A, B, C, X(6), X(38346)}}, {{A, B, C, X(279), X(4089)}}, {{A, B, C, X(799), X(7192)}}, {{A, B, C, X(1358), X(23989)}}, {{A, B, C, X(4637), X(17096)}}, {{A, B, C, X(16726), X(37128)}}, {{A, B, C, X(16727), X(17205)}}, {{A, B, C, X(17154), X(57566)}}, {{A, B, C, X(33779), X(40620)}}, {{A, B, C, X(54118), X(58373)}}
X(61403) = barycentric product X(i)*X(j) for these (i, j): {11, 552}, {244, 873}, {799, 8042}, {1019, 7199}, {1086, 1509}, {1111, 757}, {1357, 18021}, {1358, 261}, {1434, 17197}, {3120, 6628}, {3125, 57949}, {3248, 57992}, {3733, 52619}, {4610, 6545}, {4616, 56283}, {4623, 764}, {7192, 7192}, {7336, 7340}, {15419, 17925}, {16726, 274}, {16727, 81}, {16732, 763}, {17096, 4560}, {17205, 86}, {18155, 7203}, {18191, 57785}, {21143, 52612}, {23100, 4556}, {23989, 593}, {26856, 279}, {34387, 7341}, {35119, 57554}, {40213, 4637}, {52379, 53538}, {61404, 61407}
X(61403) = barycentric quotient X(i)/X(j) for these (i, j): {2, 61402}, {11, 6057}, {60, 6065}, {244, 756}, {261, 4076}, {513, 40521}, {514, 4103}, {552, 4998}, {593, 1252}, {757, 765}, {763, 4567}, {764, 4705}, {849, 1110}, {873, 7035}, {1015, 1500}, {1019, 1018}, {1086, 594}, {1111, 1089}, {1357, 181}, {1358, 12}, {1365, 6058}, {1509, 1016}, {1565, 3695}, {1977, 7109}, {2969, 7140}, {2973, 7141}, {3120, 6535}, {3125, 762}, {3248, 872}, {3249, 53581}, {3271, 7064}, {3669, 21859}, {3733, 4557}, {3737, 4069}, {3937, 3690}, {3942, 3949}, {4556, 59149}, {4560, 30730}, {4610, 6632}, {4623, 57950}, {6545, 4024}, {6549, 4013}, {6628, 4600}, {7192, 3952}, {7199, 4033}, {7200, 21021}, {7203, 4551}, {7215, 4158}, {7254, 4574}, {7336, 4092}, {7341, 59}, {8027, 50487}, {8034, 58289}, {8042, 661}, {15419, 52609}, {16726, 37}, {16727, 321}, {16742, 20691}, {17096, 4552}, {17197, 2321}, {17205, 10}, {17214, 3214}, {17219, 3710}, {18184, 4006}, {18191, 210}, {18200, 61164}, {18211, 4849}, {21143, 4079}, {21208, 4075}, {23100, 52623}, {23824, 3971}, {23989, 28654}, {26856, 346}, {27918, 4037}, {35119, 35068}, {41292, 6046}, {52619, 27808}, {52935, 57731}, {53538, 2171}, {53541, 21803}, {53546, 4053}, {57554, 57566}, {57949, 4601}, {58817, 4605}, {59746, 24044}, {61048, 61364}, {61061, 61059}, {61404, 61405}, {61407, 61406}
X(61403) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {873, 61407, 2}, {4576, 18827, 17154}, {7192, 40620, 244}

X(61404) = VERTEX PRODUCT OF GEMINI 51 TRIANGLE

Barycentrics    (a^2+b^2)*(b-c)^2*(a^2+c^2) : :

X(61404) lies on these lines: {2, 3112}, {6, 25049}, {39, 54118}, {75, 27004}, {82, 4000}, {83, 4080}, {141, 8050}, {244, 4369}, {321, 39979}, {689, 59045}, {756, 27800}, {1015, 23989}, {1086, 1977}, {1365, 61061}, {3120, 4107}, {3121, 14296}, {3124, 35119}, {3218, 3405}, {4576, 40857}, {4599, 24145}, {5723, 18097}, {6377, 27009}, {6650, 33150}, {7336, 61053}, {8033, 26838}, {16706, 27066}, {17045, 17724}, {17165, 24256}, {17302, 17961}, {18087, 18098}, {18088, 33112}, {18089, 18103}, {20859, 55026}, {21907, 52376}, {26815, 39925}, {26846, 39786}, {27005, 27070}

X(61404) = isotomic conjugate of X(61406)
X(61404) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 61406}, {38, 1252}, {39, 765}, {59, 33299}, {100, 46148}, {101, 4553}, {110, 35309}, {141, 1110}, {644, 46153}, {692, 4568}, {1016, 1964}, {1018, 1634}, {1023, 46162}, {1026, 46163}, {1923, 31625}, {1930, 23990}, {2149, 3703}, {2284, 35333}, {2530, 59149}, {3051, 7035}, {3688, 4564}, {3954, 4570}, {4020, 15742}, {4567, 21035}, {4587, 46152}, {4600, 21814}, {4601, 41267}, {4619, 58335}, {4998, 40972}, {6632, 50521}, {7045, 61316}, {21123, 57731}, {35334, 53280}
X(61404) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 61406}, {244, 35309}, {513, 39}, {514, 141}, {650, 3703}, {661, 38}, {1015, 4553}, {1086, 4568}, {4369, 16587}, {4521, 4884}, {4988, 15523}, {6615, 33299}, {8054, 46148}, {17115, 61316}, {40620, 4576}, {40627, 21035}, {41884, 1016}, {50330, 3954}, {50497, 21814}
X(61404) = X(i)-Ceva conjugate of X(j) for these {i, j}: {83, 10566}, {3112, 58784}
X(61404) = X(i)-cross conjugate of X(j) for these {i, j}: {8034, 7192}, {16592, 244}
X(61404) = pole of line {10566, 20295} with respect to the Kiepert hyperbola
X(61404) = pole of line {649, 23791} with respect to the dual conic of Yff parabola
X(61404) = pole of line {47712, 48152} with respect to the dual conic of Hutson-Moses hyperbola
X(61404) = pole of line {3954, 15523} with respect to the dual conic of Wallace hyperbola
X(61404) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(244)}}, {{A, B, C, X(42), X(38346)}}, {{A, B, C, X(513), X(54118)}}, {{A, B, C, X(514), X(8050)}}, {{A, B, C, X(661), X(40471)}}, {{A, B, C, X(764), X(39724)}}, {{A, B, C, X(812), X(3952)}}, {{A, B, C, X(1015), X(1977)}}, {{A, B, C, X(1019), X(4551)}}, {{A, B, C, X(1086), X(2969)}}, {{A, B, C, X(3124), X(39786)}}, {{A, B, C, X(4107), X(4369)}}, {{A, B, C, X(4554), X(58373)}}, {{A, B, C, X(7208), X(17126)}}, {{A, B, C, X(8034), X(16587)}}, {{A, B, C, X(8054), X(16726)}}, {{A, B, C, X(16704), X(41252)}}, {{A, B, C, X(17205), X(17761)}}, {{A, B, C, X(21143), X(39746)}}, {{A, B, C, X(29822), X(44572)}}
X(61404) = barycentric product X(i)*X(j) for these (i, j): {244, 3112}, {689, 8034}, {1015, 308}, {1019, 18070}, {1086, 83}, {1111, 82}, {1176, 2973}, {1509, 34294}, {1565, 32085}, {1577, 39179}, {1799, 2969}, {1977, 40016}, {3120, 52394}, {3733, 52618}, {3937, 46104}, {10566, 514}, {16726, 56186}, {16727, 18098}, {16732, 52376}, {17197, 18097}, {17205, 18082}, {17925, 4580}, {18101, 7}, {18105, 52619}, {18108, 693}, {18113, 4373}, {18833, 3248}, {20022, 43920}, {23100, 4628}, {23989, 251}, {55240, 7199}, {58784, 7192}, {61403, 61405}
X(61404) = barycentric quotient X(i)/X(j) for these (i, j): {2, 61406}, {11, 3703}, {82, 765}, {83, 1016}, {244, 38}, {251, 1252}, {308, 31625}, {513, 4553}, {514, 4568}, {649, 46148}, {661, 35309}, {764, 2530}, {876, 52922}, {1015, 39}, {1027, 35333}, {1086, 141}, {1111, 1930}, {1357, 1401}, {1358, 3665}, {1565, 3933}, {1977, 3051}, {2170, 33299}, {2969, 427}, {2973, 1235}, {3112, 7035}, {3120, 15523}, {3121, 21814}, {3122, 21035}, {3125, 3954}, {3248, 1964}, {3271, 3688}, {3733, 1634}, {3756, 4884}, {3937, 3917}, {4128, 40936}, {4580, 52609}, {4628, 59149}, {6545, 16892}, {7192, 4576}, {7199, 55239}, {7200, 16720}, {8027, 50521}, {8034, 3005}, {10566, 190}, {14936, 61316}, {16592, 16587}, {16726, 16696}, {16727, 16703}, {17205, 16887}, {17925, 41676}, {18070, 4033}, {18101, 8}, {18105, 4557}, {18107, 4595}, {18108, 100}, {18111, 18047}, {18113, 145}, {21132, 48278}, {21143, 21123}, {21755, 21752}, {21823, 21818}, {22096, 20775}, {22373, 22367}, {23345, 46162}, {23989, 8024}, {32085, 15742}, {34294, 594}, {39179, 662}, {42067, 1843}, {43920, 20021}, {43921, 46149}, {43922, 46150}, {43923, 46152}, {43924, 46153}, {43925, 35325}, {43926, 36827}, {43929, 46163}, {46288, 23990}, {46289, 1110}, {48151, 35335}, {51906, 1500}, {52376, 4567}, {52394, 4600}, {52618, 27808}, {55240, 1018}, {58784, 3952}, {61403, 61407}, {61405, 61402}
X(61404) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3112, 61405}

X(61405) = VERTEX PRODUCT OF GEMINI 52 TRIANGLE

Barycentrics    (a^2+b^2)*(b+c)^2*(a^2+c^2) : :

X(61405) lies on these lines: {2, 3112}, {10, 22026}, {75, 27066}, {82, 2345}, {83, 6539}, {251, 14624}, {594, 2238}, {661, 1215}, {862, 7140}, {1018, 18101}, {1500, 3948}, {2295, 18091}, {3219, 3405}, {3952, 52651}, {3963, 39998}, {4599, 24146}, {6058, 61059}, {17165, 20859}, {17289, 27004}, {24256, 55026}, {27061, 39044}, {35309, 59511}, {40016, 60230}

X(61405) = isotomic conjugate of X(61407)
X(61405) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 61407}, {38, 593}, {39, 757}, {58, 16696}, {81, 17187}, {141, 849}, {552, 40972}, {763, 21035}, {873, 3051}, {1019, 1634}, {1333, 16887}, {1401, 2185}, {1437, 17171}, {1509, 1964}, {2150, 3665}, {2206, 16703}, {2530, 4556}, {4576, 57129}, {4610, 50521}, {6628, 21814}, {7341, 33299}, {21123, 52935}, {30576, 46150}, {36066, 46387}, {41267, 57949}, {41331, 57992}
X(61405) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 61407}, {10, 16696}, {37, 16887}, {1500, 56537}, {4075, 141}, {38978, 46387}, {40586, 17187}, {40603, 16703}, {40607, 39}, {41884, 1509}, {55065, 16892}, {56325, 3665}
X(61405) = X(i)-cross conjugate of X(j) for these {i, j}: {58289, 3952}
X(61405) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(661)}}, {{A, B, C, X(6), X(27041)}}, {{A, B, C, X(10), X(4651)}}, {{A, B, C, X(37), X(3995)}}, {{A, B, C, X(251), X(27067)}}, {{A, B, C, X(594), X(6535)}}, {{A, B, C, X(740), X(27807)}}, {{A, B, C, X(1215), X(3952)}}, {{A, B, C, X(1500), X(7109)}}, {{A, B, C, X(2171), X(56258)}}, {{A, B, C, X(3112), X(58784)}}, {{A, B, C, X(4099), X(17127)}}, {{A, B, C, X(5750), X(24067)}}, {{A, B, C, X(7148), X(56197)}}, {{A, B, C, X(9278), X(39747)}}, {{A, B, C, X(18082), X(56251)}}, {{A, B, C, X(18098), X(56186)}}, {{A, B, C, X(20965), X(26772)}}, {{A, B, C, X(27040), X(39998)}}, {{A, B, C, X(39698), X(52208)}}
X(61405) = barycentric product X(i)*X(j) for these (i, j): {10, 18082}, {37, 56186}, {42, 56251}, {251, 28654}, {594, 83}, {1016, 34294}, {1018, 18070}, {1089, 82}, {1176, 7141}, {1500, 308}, {1799, 7140}, {3112, 756}, {3690, 46104}, {3952, 58784}, {4033, 55240}, {4557, 52618}, {4628, 52623}, {10566, 4103}, {14624, 27067}, {16889, 56196}, {18097, 2321}, {18098, 321}, {18105, 27808}, {18833, 872}, {31625, 51906}, {32085, 3695}, {40016, 7109}, {52394, 6535}, {56245, 6358}, {58289, 689}, {61402, 61404}
X(61405) = barycentric quotient X(i)/X(j) for these (i, j): {2, 61407}, {10, 16887}, {12, 3665}, {37, 16696}, {42, 17187}, {82, 757}, {83, 1509}, {181, 1401}, {251, 593}, {321, 16703}, {594, 141}, {756, 38}, {762, 3954}, {872, 1964}, {1089, 1930}, {1500, 39}, {1826, 17171}, {3112, 873}, {3690, 3917}, {3695, 3933}, {3952, 4576}, {4024, 16892}, {4033, 55239}, {4036, 48084}, {4079, 21123}, {4103, 4568}, {4557, 1634}, {4580, 15419}, {4628, 4556}, {4705, 2530}, {6057, 3703}, {6535, 15523}, {7064, 3688}, {7109, 3051}, {7140, 427}, {7141, 1235}, {16889, 33947}, {18070, 7199}, {18082, 86}, {18097, 1434}, {18098, 81}, {18099, 17103}, {18105, 3733}, {18833, 57992}, {21021, 16720}, {21867, 41582}, {27067, 16705}, {28654, 8024}, {34294, 1086}, {34857, 46160}, {36081, 36066}, {40521, 4553}, {40607, 56537}, {41013, 16747}, {46289, 849}, {46390, 46387}, {50487, 50521}, {51906, 1015}, {52376, 763}, {52394, 6628}, {52618, 52619}, {55240, 1019}, {56186, 274}, {56245, 2185}, {56251, 310}, {58289, 3005}, {58784, 7192}, {61402, 61406}, {61404, 61403}
X(61405) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3112, 61404}

X(61406) = VERTEX PRODUCT OF GEMINI 53 TRIANGLE

Barycentrics    (a-b)^2*(a-c)^2*(b^2+c^2) : :

X(61406) lies on these lines: {2, 7035}, {100, 21005}, {190, 20295}, {661, 54099}, {668, 17494}, {765, 32842}, {1016, 1252}, {1018, 18197}, {1978, 57056}, {3005, 52922}, {3807, 47894}, {3952, 27805}, {4033, 18155}, {4076, 5211}, {4103, 21196}, {4115, 24083}, {4467, 57030}, {4553, 50521}, {4562, 7192}, {4568, 16892}, {4576, 35309}, {5378, 33170}, {6632, 33168}, {9362, 27013}, {16587, 61407}, {17280, 57950}, {17495, 27044}, {17759, 31625}, {27134, 36863}, {29824, 37686}, {30635, 50107}, {33946, 49302}

X(61406) = isotomic conjugate of X(61404)
X(61406) = trilinear pole of line {4553, 4568}
X(61406) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 61404}, {82, 1015}, {83, 3248}, {244, 251}, {512, 39179}, {604, 18101}, {649, 18108}, {667, 10566}, {757, 51906}, {764, 4628}, {849, 34294}, {1019, 18105}, {1086, 46289}, {1111, 46288}, {1357, 56245}, {1977, 3112}, {3121, 52394}, {3122, 52376}, {3733, 55240}, {4599, 8034}, {18113, 38266}, {34055, 42067}, {57129, 58784}
X(61406) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 61404}, {39, 1086}, {141, 1015}, {1215, 16592}, {3124, 8034}, {3161, 18101}, {4075, 34294}, {5375, 18108}, {6631, 10566}, {34452, 1977}, {39054, 39179}, {40585, 244}, {40607, 51906}, {40938, 2969}
X(61406) = X(i)-cross conjugate of X(j) for these {i, j}: {38, 4576}, {39, 4553}, {141, 4568}, {16587, 35309}, {56537, 668}
X(61406) = pole of line {20045, 33889} with respect to the Yff parabola
X(61406) = pole of line {1086, 1977} with respect to the Wallace hyperbola
X(61406) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(38)}}, {{A, B, C, X(39), X(50521)}}, {{A, B, C, X(83), X(20295)}}, {{A, B, C, X(141), X(16704)}}, {{A, B, C, X(251), X(21005)}}, {{A, B, C, X(308), X(17494)}}, {{A, B, C, X(310), X(37686)}}, {{A, B, C, X(1252), X(31625)}}, {{A, B, C, X(1930), X(30635)}}, {{A, B, C, X(1964), X(30650)}}, {{A, B, C, X(3665), X(23297)}}, {{A, B, C, X(3703), X(8024)}}, {{A, B, C, X(3954), X(5291)}}, {{A, B, C, X(4080), X(41252)}}, {{A, B, C, X(4576), X(7035)}}, {{A, B, C, X(6542), X(15523)}}, {{A, B, C, X(17165), X(38830)}}, {{A, B, C, X(17442), X(54123)}}, {{A, B, C, X(17759), X(21814)}}, {{A, B, C, X(20352), X(40016)}}, {{A, B, C, X(21035), X(39745)}}, {{A, B, C, X(34537), X(57566)}}, {{A, B, C, X(39698), X(46160)}}
X(61406) = barycentric product X(i)*X(j) for these (i, j): {38, 7035}, {190, 4568}, {1016, 141}, {1018, 55239}, {1252, 8024}, {1634, 27808}, {1930, 765}, {1978, 46148}, {2530, 57950}, {3665, 4076}, {3703, 4998}, {3952, 4576}, {3954, 4601}, {4553, 668}, {15523, 4600}, {15742, 3933}, {16892, 6632}, {23990, 52568}, {31625, 39}, {35309, 799}, {41676, 52609}, {48084, 57731}, {52922, 874}, {61402, 61407}
X(61406) = barycentric quotient X(i)/X(j) for these (i, j): {2, 61404}, {8, 18101}, {38, 244}, {39, 1015}, {100, 18108}, {141, 1086}, {145, 18113}, {190, 10566}, {427, 2969}, {594, 34294}, {662, 39179}, {765, 82}, {1016, 83}, {1018, 55240}, {1110, 46289}, {1235, 2973}, {1252, 251}, {1401, 1357}, {1500, 51906}, {1634, 3733}, {1843, 42067}, {1930, 1111}, {1964, 3248}, {2530, 764}, {3005, 8034}, {3051, 1977}, {3665, 1358}, {3688, 3271}, {3703, 11}, {3917, 3937}, {3933, 1565}, {3952, 58784}, {3954, 3125}, {4033, 18070}, {4553, 513}, {4557, 18105}, {4567, 52376}, {4568, 514}, {4576, 7192}, {4595, 18107}, {4600, 52394}, {4884, 3756}, {7035, 3112}, {8024, 23989}, {15523, 3120}, {15742, 32085}, {16587, 16592}, {16696, 16726}, {16703, 16727}, {16720, 7200}, {16887, 17205}, {16892, 6545}, {18047, 18111}, {20021, 43920}, {20775, 22096}, {21035, 3122}, {21123, 21143}, {21752, 21755}, {21814, 3121}, {21818, 21823}, {22367, 22373}, {23990, 46288}, {27808, 52618}, {31625, 308}, {33299, 2170}, {35309, 661}, {35325, 43925}, {35333, 1027}, {35335, 48151}, {36827, 43926}, {40936, 4128}, {41676, 17925}, {46148, 649}, {46149, 43921}, {46150, 43922}, {46152, 43923}, {46153, 43924}, {46162, 23345}, {46163, 43929}, {48278, 21132}, {50521, 8027}, {52609, 4580}, {52922, 876}, {55239, 7199}, {59149, 4628}, {61316, 14936}, {61402, 61405}, {61407, 61403}
X(61406) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 61402, 7035}

X(61407) = VERTEX PRODUCT OF GEMINI 54 TRIANGLE

Barycentrics    (a+b)^2*(a+c)^2*(b^2+c^2) : :

X(61407) lies on these lines: {2, 799}, {38, 4576}, {86, 5284}, {244, 59622}, {274, 39747}, {310, 27163}, {593, 763}, {756, 54099}, {2308, 6629}, {2668, 29822}, {2669, 4651}, {3666, 16741}, {3995, 52137}, {7192, 8034}, {7304, 16704}, {16587, 61406}, {16696, 16703}, {16738, 16748}, {16739, 18601}, {16887, 17187}, {17140, 18827}, {17165, 56696}, {17184, 51370}, {17206, 61409}, {17208, 18169}, {18600, 52379}, {19742, 27162}, {26769, 36860}, {26819, 30940}, {27017, 34021}, {27145, 34022}, {29824, 39915}

X(61407) = isotomic conjugate of X(61405)
X(61407) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 61405}, {42, 18098}, {82, 1500}, {83, 872}, {181, 56245}, {213, 18082}, {251, 756}, {594, 46289}, {765, 51906}, {1018, 18105}, {1089, 46288}, {1110, 34294}, {1918, 56186}, {2205, 56251}, {3112, 7109}, {4557, 55240}, {4599, 58289}, {4628, 4705}, {18099, 40729}, {36081, 46390}, {52369, 61383}
X(61407) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 61405}, {39, 594}, {141, 1500}, {513, 51906}, {514, 34294}, {3124, 58289}, {6626, 18082}, {34021, 56186}, {34452, 7109}, {40585, 756}, {40592, 18098}, {40620, 58784}, {40938, 7140}
X(61407) = pole of line {1500, 41333} with respect to the Stammler hyperbola
X(61407) = pole of line {594, 2238} with respect to the Wallace hyperbola
X(61407) = pole of line {17176, 23812} with respect to the dual conic of Yff parabola
X(61407) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(38)}}, {{A, B, C, X(39), X(16748)}}, {{A, B, C, X(141), X(8025)}}, {{A, B, C, X(593), X(16696)}}, {{A, B, C, X(799), X(4576)}}, {{A, B, C, X(1509), X(16703)}}, {{A, B, C, X(1930), X(30636)}}, {{A, B, C, X(1964), X(30651)}}, {{A, B, C, X(3051), X(16738)}}, {{A, B, C, X(3108), X(40432)}}, {{A, B, C, X(3404), X(40738)}}, {{A, B, C, X(3665), X(8024)}}, {{A, B, C, X(3703), X(23297)}}, {{A, B, C, X(5284), X(32009)}}, {{A, B, C, X(7192), X(8033)}}, {{A, B, C, X(8034), X(16587)}}, {{A, B, C, X(15523), X(29586)}}, {{A, B, C, X(30940), X(38830)}}, {{A, B, C, X(46149), X(60680)}}
X(61407) = barycentric product X(i)*X(j) for these (i, j): {38, 873}, {141, 1509}, {261, 3665}, {593, 8024}, {1019, 55239}, {1401, 18021}, {1444, 16747}, {1634, 52619}, {1930, 757}, {1964, 57992}, {2530, 4623}, {3703, 552}, {3954, 57949}, {4576, 7192}, {15419, 41676}, {15523, 6628}, {16696, 274}, {16703, 81}, {16887, 86}, {16892, 4610}, {17171, 17206}, {17187, 310}, {21123, 52612}, {48084, 52935}, {61403, 61406}
X(61407) = barycentric quotient X(i)/X(j) for these (i, j): {2, 61405}, {38, 756}, {39, 1500}, {81, 18098}, {86, 18082}, {141, 594}, {274, 56186}, {310, 56251}, {427, 7140}, {593, 251}, {757, 82}, {763, 52376}, {849, 46289}, {873, 3112}, {1015, 51906}, {1019, 55240}, {1086, 34294}, {1235, 7141}, {1401, 181}, {1434, 18097}, {1509, 83}, {1634, 4557}, {1930, 1089}, {1964, 872}, {2185, 56245}, {2530, 4705}, {3005, 58289}, {3051, 7109}, {3665, 12}, {3688, 7064}, {3703, 6057}, {3733, 18105}, {3917, 3690}, {3933, 3695}, {3954, 762}, {4553, 40521}, {4556, 4628}, {4568, 4103}, {4576, 3952}, {6628, 52394}, {7192, 58784}, {7199, 18070}, {8024, 28654}, {15419, 4580}, {15523, 6535}, {16696, 37}, {16703, 321}, {16705, 27067}, {16720, 21021}, {16747, 41013}, {16887, 10}, {16892, 4024}, {17103, 18099}, {17171, 1826}, {17187, 42}, {21123, 4079}, {33947, 16889}, {36066, 36081}, {41582, 21867}, {46160, 34857}, {46387, 46390}, {48084, 4036}, {50521, 50487}, {52619, 52618}, {55239, 4033}, {56537, 40607}, {57992, 18833}, {61403, 61404}, {61406, 61402}
X(61407) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 61403, 873}

X(61408) = VERTEX PRODUCT OF GEMINI 66 TRIANGLE

Barycentrics    b*c*(b+c)^2*((a+b)^2+(2*a+b)*c+c^2) : :

X(61408) lies on these lines: {2, 37}, {306, 24066}, {1089, 6535}, {1230, 18697}, {1724, 27368}, {1930, 59203}, {2895, 17762}, {3178, 4066}, {3969, 4053}, {4024, 27575}, {4647, 6536}, {5249, 24058}, {7283, 37032}, {20896, 53478}, {21073, 24044}, {21810, 56810}, {24077, 27184}, {27570, 52579}

X(61408) = X(i)-Dao conjugate of X(j) for these {i, j}: {3743, 1100}, {41809, 30581}, {41820, 81}
X(61408) = pole of line {16732, 17205} with respect to the dual conic of Stammler hyperbola
X(61408) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(1089)}}, {{A, B, C, X(37), X(6535)}}, {{A, B, C, X(75), X(28654)}}, {{A, B, C, X(313), X(28653)}}, {{A, B, C, X(594), X(17303)}}, {{A, B, C, X(3666), X(17011)}}, {{A, B, C, X(3743), X(28606)}}, {{A, B, C, X(4261), X(4272)}}, {{A, B, C, X(4359), X(52576)}}, {{A, B, C, X(4886), X(32851)}}, {{A, B, C, X(6358), X(28605)}}, {{A, B, C, X(6539), X(28604)}}, {{A, B, C, X(17495), X(47679)}}
X(61408) = barycentric product X(i)*X(j) for these (i, j): {313, 3743}, {321, 41809}, {1089, 17322}, {4033, 47679}, {4886, 6358}, {17011, 28654}, {27801, 4272}
X(61408) = barycentric quotient X(i)/X(j) for these (i, j): {1089, 1224}, {1203, 849}, {3743, 58}, {4103, 59085}, {4272, 1333}, {4886, 2185}, {17011, 593}, {17322, 757}, {41809, 81}, {41820, 30581}, {47679, 1019}
X(61408) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {321, 27569, 2}, {321, 42710, 75}

X(61409) = VERTEX PRODUCT OF GEMINI 68 TRIANGLE

Barycentrics    a^2*(a+b)*(a+c)*(b*(a+b)+(a+b)*c+c^2) : :

X(61409) lies on these lines: {1, 27660}, {2, 6}, {21, 16466}, {27, 20028}, {31, 3736}, {36, 58}, {42, 4476}, {63, 54308}, {110, 28476}, {171, 35983}, {213, 3219}, {222, 1014}, {238, 10458}, {239, 10471}, {284, 21764}, {310, 7304}, {314, 3187}, {386, 34281}, {387, 37191}, {444, 44097}, {608, 14014}, {894, 30599}, {959, 5323}, {1010, 57280}, {1011, 50598}, {1029, 13584}, {1043, 20040}, {1171, 1400}, {1258, 39747}, {1333, 40214}, {1437, 27652}, {1453, 54356}, {1922, 37128}, {2194, 3415}, {2221, 27174}, {2300, 17011}, {2316, 4627}, {3240, 56181}, {3286, 39673}, {3786, 3920}, {4001, 16887}, {4210, 5156}, {4260, 54341}, {4273, 5332}, {4276, 5313}, {4641, 16696}, {4653, 5315}, {4658, 59305}, {5208, 7191}, {5256, 17185}, {5271, 10455}, {5299, 60721}, {5711, 14005}, {6327, 33730}, {7192, 23092}, {7357, 31909}, {7419, 10457}, {7449, 40952}, {9965, 18600}, {11115, 20036}, {13588, 17126}, {13731, 36750}, {14009, 33107}, {14011, 54355}, {14636, 51340}, {16468, 18169}, {16469, 17194}, {16470, 28287}, {16736, 37520}, {17012, 25059}, {17017, 35623}, {17139, 19785}, {17147, 33296}, {17167, 40940}, {17191, 27664}, {17206, 61407}, {17751, 56018}, {18171, 27632}, {18191, 27668}, {18200, 27673}, {19513, 37509}, {21814, 28643}, {22086, 42744}, {22383, 27648}, {25417, 56066}, {25526, 31339}, {27624, 46882}, {28660, 40394}, {30984, 32946}, {32933, 56023}, {36742, 61109}, {39734, 55968}, {40611, 55101}, {41723, 54418}, {54321, 54411}

X(61409) = trilinear pole of line {8637, 834}
X(61409) = perspector of circumconic {{A, B, C, X(99), X(4556)}}
X(61409) = X(i)-isoconjugate-of-X(j) for these {i, j}: {10, 2214}, {37, 43531}, {213, 57824}, {661, 835}, {756, 56047}, {798, 57977}, {1018, 43927}, {1824, 57876}, {4036, 58951}, {15232, 53081}, {41013, 57704}
X(61409) = X(i)-Dao conjugate of X(j) for these {i, j}: {6626, 57824}, {31998, 57977}, {36830, 835}, {39016, 523}, {39054, 37218}, {40589, 43531}, {41849, 313}
X(61409) = X(i)-Ceva conjugate of X(j) for these {i, j}: {40409, 41849}
X(61409) = pole of line {99, 835} with respect to the Kiepert parabola
X(61409) = pole of line {525, 7192} with respect to the MacBeath circumconic
X(61409) = pole of line {6, 10} with respect to the Stammler hyperbola
X(61409) = pole of line {523, 16695} with respect to the Steiner circumellipse
X(61409) = pole of line {523, 52597} with respect to the Steiner inellipse
X(61409) = pole of line {2, 313} with respect to the Wallace hyperbola
X(61409) = pole of line {525, 7192} with respect to the dual conic of nine-point circle
X(61409) = pole of line {1125, 4225} with respect to the dual conic of Yff parabola
X(61409) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(19684)}}, {{A, B, C, X(2), X(58)}}, {{A, B, C, X(6), X(2206)}}, {{A, B, C, X(27), X(14829)}}, {{A, B, C, X(36), X(3936)}}, {{A, B, C, X(56), X(19701)}}, {{A, B, C, X(57), X(1150)}}, {{A, B, C, X(60), X(333)}}, {{A, B, C, X(69), X(1790)}}, {{A, B, C, X(81), X(849)}}, {{A, B, C, X(86), X(593)}}, {{A, B, C, X(89), X(37683)}}, {{A, B, C, X(106), X(19740)}}, {{A, B, C, X(141), X(17187)}}, {{A, B, C, X(325), X(17209)}}, {{A, B, C, X(343), X(44709)}}, {{A, B, C, X(391), X(2316)}}, {{A, B, C, X(469), X(4225)}}, {{A, B, C, X(501), X(2895)}}, {{A, B, C, X(524), X(834)}}, {{A, B, C, X(649), X(50252)}}, {{A, B, C, X(940), X(2221)}}, {{A, B, C, X(959), X(5739)}}, {{A, B, C, X(966), X(44103)}}, {{A, B, C, X(967), X(5737)}}, {{A, B, C, X(1126), X(19717)}}, {{A, B, C, X(1185), X(1922)}}, {{A, B, C, X(1193), X(1211)}}, {{A, B, C, X(1203), X(41809)}}, {{A, B, C, X(1213), X(1400)}}, {{A, B, C, X(1258), X(32911)}}, {{A, B, C, X(1412), X(8025)}}, {{A, B, C, X(1413), X(19727)}}, {{A, B, C, X(1434), X(29766)}}, {{A, B, C, X(2003), X(3578)}}, {{A, B, C, X(2210), X(2238)}}, {{A, B, C, X(2303), X(56045)}}, {{A, B, C, X(2334), X(19722)}}, {{A, B, C, X(2392), X(23879)}}, {{A, B, C, X(2987), X(25898)}}, {{A, B, C, X(3231), X(8637)}}, {{A, B, C, X(3876), X(14555)}}, {{A, B, C, X(5276), X(57397)}}, {{A, B, C, X(5278), X(56343)}}, {{A, B, C, X(5323), X(27174)}}, {{A, B, C, X(5331), X(56224)}}, {{A, B, C, X(5333), X(56066)}}, {{A, B, C, X(5741), X(43071)}}, {{A, B, C, X(10026), X(42664)}}, {{A, B, C, X(14552), X(56005)}}, {{A, B, C, X(16704), X(52615)}}, {{A, B, C, X(16738), X(39747)}}, {{A, B, C, X(17277), X(55968)}}, {{A, B, C, X(17379), X(25417)}}, {{A, B, C, X(18134), X(33949)}}, {{A, B, C, X(19741), X(41434)}}, {{A, B, C, X(19746), X(41436)}}, {{A, B, C, X(27164), X(37128)}}, {{A, B, C, X(29767), X(42302)}}, {{A, B, C, X(30962), X(39734)}}, {{A, B, C, X(32782), X(33935)}}, {{A, B, C, X(39700), X(57743)}}, {{A, B, C, X(44396), X(47842)}}
X(61409) = barycentric product X(i)*X(j) for these (i, j): {110, 45746}, {190, 52615}, {284, 33949}, {386, 86}, {670, 8637}, {834, 99}, {1014, 3876}, {1333, 33935}, {1509, 56926}, {1790, 469}, {4623, 50488}, {5224, 58}, {14349, 662}, {17206, 44103}, {23879, 4556}, {28606, 81}, {33948, 3733}, {42664, 4610}, {42714, 849}, {47842, 52935}, {56810, 593}
X(61409) = barycentric quotient X(i)/X(j) for these (i, j): {58, 43531}, {86, 57824}, {99, 57977}, {110, 835}, {386, 10}, {593, 56047}, {662, 37218}, {834, 523}, {1333, 2214}, {1790, 57876}, {3733, 43927}, {3876, 3701}, {5224, 313}, {5331, 34265}, {8637, 512}, {14349, 1577}, {23879, 52623}, {28606, 321}, {33935, 27801}, {33948, 27808}, {33949, 349}, {34281, 59305}, {42664, 4024}, {44103, 1826}, {45746, 850}, {47842, 4036}, {50488, 4705}, {52615, 514}, {56810, 28654}, {56926, 594}
X(61409) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 27644, 27643}, {6, 40153, 81}, {58, 1193, 4225}, {58, 1790, 593}, {81, 32911, 333}, {81, 42025, 18166}, {81, 5333, 940}, {86, 41629, 29766}, {940, 52897, 5333}, {2308, 17187, 58}, {5256, 17185, 25060}, {19734, 27623, 2}

X(61410) = VERTEX PRODUCT OF GEMINI 69 TRIANGLE

Barycentrics    b*c*(b+c)^2*(a^2-b^2+b*c-c^2) : :

X(61410) lies on these lines: {2, 37}, {756, 27700}, {850, 1577}, {1089, 21674}, {1211, 20896}, {1264, 5905}, {2064, 3219}, {2273, 26223}, {2895, 20929}, {2901, 3924}, {3262, 59712}, {3264, 20887}, {3266, 46238}, {3695, 27687}, {3701, 27690}, {3932, 27692}, {3936, 4053}, {3948, 27709}, {3971, 27701}, {3977, 22003}, {4600, 57802}, {4647, 27714}, {6358, 28654}, {7283, 11101}, {17484, 17789}, {17788, 37656}, {20234, 21810}, {20444, 21873}, {27706, 52579}, {27708, 52353}, {37247, 56538}, {42005, 52576}

X(61410) = perspector of circumconic {{A, B, C, X(313), X(668)}}
X(61410) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 34079}, {513, 32671}, {593, 6187}, {604, 52380}, {649, 36069}, {667, 37140}, {759, 1333}, {849, 2161}, {1408, 2341}, {1411, 2150}, {1474, 57736}, {2206, 24624}, {3122, 9273}, {3125, 9274}, {6740, 16947}, {7342, 36910}
X(61410) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 34079}, {37, 759}, {758, 7113}, {3161, 52380}, {3936, 30576}, {4075, 2161}, {5375, 36069}, {5664, 7202}, {6631, 37140}, {7359, 51420}, {34586, 1333}, {35069, 58}, {35204, 2150}, {38982, 649}, {39026, 32671}, {40584, 849}, {40603, 24624}, {40612, 593}, {40624, 60571}, {51574, 57736}, {51583, 81}, {53982, 1474}, {56325, 1411}, {59577, 2341}
X(61410) = pole of line {1474, 6591} with respect to the polar circle
X(61410) = pole of line {513, 1330} with respect to the Steiner circumellipse
X(61410) = pole of line {513, 3454} with respect to the Steiner inellipse
X(61410) = pole of line {3952, 4064} with respect to the Yff parabola
X(61410) = pole of line {81, 4556} with respect to the Wallace hyperbola
X(61410) = pole of line {1230, 4391} with respect to the dual conic of circumcircle
X(61410) = pole of line {905, 1790} with respect to the dual conic of polar circle
X(61410) = pole of line {514, 7202} with respect to the dual conic of Stammler hyperbola
X(61410) = pole of line {10, 24186} with respect to the dual conic of Yff parabola
X(61410) = pole of line {649, 3125} with respect to the dual conic of Wallace hyperbola
X(61410) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(860)}}, {{A, B, C, X(10), X(32779)}}, {{A, B, C, X(12), X(17720)}}, {{A, B, C, X(37), X(4024)}}, {{A, B, C, X(75), X(850)}}, {{A, B, C, X(226), X(33133)}}, {{A, B, C, X(312), X(28654)}}, {{A, B, C, X(320), X(17322)}}, {{A, B, C, X(321), X(52623)}}, {{A, B, C, X(345), X(52369)}}, {{A, B, C, X(350), X(40075)}}, {{A, B, C, X(536), X(6370)}}, {{A, B, C, X(594), X(17281)}}, {{A, B, C, X(758), X(23879)}}, {{A, B, C, X(1089), X(4671)}}, {{A, B, C, X(1575), X(2610)}}, {{A, B, C, X(2245), X(4261)}}, {{A, B, C, X(3218), X(3666)}}, {{A, B, C, X(3772), X(6354)}}, {{A, B, C, X(4080), X(37759)}}, {{A, B, C, X(4242), X(46534)}}, {{A, B, C, X(4359), X(20924)}}, {{A, B, C, X(4707), X(17495)}}, {{A, B, C, X(4850), X(18593)}}, {{A, B, C, X(5620), X(31845)}}, {{A, B, C, X(8620), X(42666)}}, {{A, B, C, X(16706), X(27712)}}, {{A, B, C, X(17321), X(41804)}}, {{A, B, C, X(17923), X(19786)}}, {{A, B, C, X(21056), X(21877)}}, {{A, B, C, X(21674), X(27757)}}, {{A, B, C, X(24530), X(27710)}}, {{A, B, C, X(30713), X(42033)}}, {{A, B, C, X(33157), X(36954)}}, {{A, B, C, X(51663), X(57037)}}, {{A, B, C, X(53527), X(57039)}}
X(61410) = barycentric product X(i)*X(j) for these (i, j): {10, 35550}, {313, 758}, {321, 3936}, {1089, 320}, {1227, 4013}, {1978, 2610}, {2245, 27801}, {3701, 41804}, {4033, 4707}, {4053, 76}, {4585, 52623}, {5081, 57807}, {6370, 668}, {17923, 52369}, {18593, 30713}, {20336, 860}, {20566, 4736}, {20924, 594}, {27808, 53527}, {28654, 3218}, {32851, 6358}, {34388, 4511}, {40075, 756}, {42666, 6386}
X(61410) = barycentric quotient X(i)/X(j) for these (i, j): {8, 52380}, {10, 759}, {12, 1411}, {36, 849}, {37, 34079}, {72, 57736}, {100, 36069}, {101, 32671}, {190, 37140}, {313, 14616}, {320, 757}, {321, 24624}, {594, 2161}, {756, 6187}, {758, 58}, {860, 28}, {1089, 80}, {1443, 7341}, {1464, 1408}, {2245, 1333}, {2321, 2341}, {2323, 2150}, {2610, 649}, {3028, 52440}, {3218, 593}, {3695, 1807}, {3701, 6740}, {3710, 1793}, {3724, 2206}, {3936, 81}, {3949, 52431}, {3992, 56950}, {4013, 1168}, {4033, 47318}, {4053, 6}, {4391, 60571}, {4511, 60}, {4567, 9273}, {4570, 9274}, {4585, 4556}, {4707, 1019}, {4736, 36}, {5081, 270}, {6057, 52371}, {6358, 2006}, {6370, 513}, {6535, 34857}, {6739, 51420}, {7206, 56422}, {15523, 46160}, {18593, 1412}, {20336, 57985}, {20924, 1509}, {21081, 56405}, {21828, 57129}, {21859, 32675}, {28654, 18359}, {31845, 30117}, {32851, 2185}, {34388, 18815}, {35069, 7113}, {35550, 86}, {40075, 873}, {40988, 3285}, {41804, 1014}, {42666, 667}, {42701, 40214}, {44113, 2203}, {51465, 16700}, {51583, 30576}, {51663, 43924}, {52369, 52351}, {52440, 7342}, {52623, 60074}, {53527, 3733}, {56189, 39277}, {56193, 14560}, {57807, 52392}
X(61410) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {321, 27569, 4671}, {321, 42710, 312}, {6358, 52369, 28654}

X(61411) = VERTEX PRODUCT OF GEMINI 78 TRIANGLE

Barycentrics    (a^2+(b-c)^2)*(a+b-c)*(a-b+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2) : :

X(61411) lies on these lines: {2, 92}, {4, 4310}, {34, 1458}, {225, 8801}, {242, 16020}, {608, 1119}, {614, 1851}, {1435, 36570}, {1838, 36574}, {1848, 36503}, {1863, 21450}, {2201, 7225}, {4000, 28110}, {28080, 28102}, {41786, 53510}

X(61411) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 56243}, {78, 7123}, {212, 30701}, {219, 56179}, {283, 56260}, {345, 7084}, {652, 52778}, {1037, 3692}, {1260, 7131}, {1802, 8817}, {2318, 40403}, {52425, 57925}
X(61411) = X(i)-Dao conjugate of X(j) for these {i, j}: {1565, 52616}, {4000, 30681}, {6554, 345}, {15487, 78}, {18589, 3694}, {36103, 56243}, {39060, 54967}, {40837, 30701}, {59619, 52406}
X(61411) = pole of line {650, 44448} with respect to the polar circle
X(61411) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(614)}}, {{A, B, C, X(92), X(1851)}}, {{A, B, C, X(279), X(28110)}}, {{A, B, C, X(281), X(8751)}}, {{A, B, C, X(608), X(5089)}}, {{A, B, C, X(1441), X(7195)}}, {{A, B, C, X(3673), X(58018)}}, {{A, B, C, X(6350), X(7289)}}, {{A, B, C, X(16502), X(40937)}}, {{A, B, C, X(27509), X(36570)}}, {{A, B, C, X(28079), X(51400)}}, {{A, B, C, X(28082), X(41785)}}
X(61411) = barycentric product X(i)*X(j) for these (i, j): {4, 7195}, {34, 3673}, {273, 614}, {278, 4000}, {286, 40961}, {1088, 40987}, {1118, 17170}, {1119, 497}, {1396, 53510}, {1434, 52577}, {1441, 4211}, {1847, 2082}, {1851, 7}, {1863, 479}, {16502, 331}, {16750, 1880}, {28017, 92}, {48398, 653}
X(61411) = barycentric quotient X(i)/X(j) for these (i, j): {19, 56243}, {34, 56179}, {108, 52778}, {273, 57925}, {278, 30701}, {497, 1265}, {608, 7123}, {614, 78}, {1119, 8817}, {1395, 7084}, {1396, 40403}, {1398, 1037}, {1435, 7131}, {1473, 1259}, {1633, 4571}, {1851, 8}, {1863, 5423}, {1880, 56260}, {2082, 3692}, {3673, 3718}, {3914, 3710}, {4000, 345}, {4211, 21}, {5324, 1792}, {6554, 30681}, {7083, 1260}, {7195, 69}, {7289, 3719}, {8020, 1334}, {16502, 219}, {16583, 3694}, {17170, 1264}, {18026, 54967}, {21750, 52370}, {28017, 63}, {40934, 2318}, {40961, 72}, {40987, 200}, {42067, 14935}, {48398, 6332}, {48403, 52355}, {52577, 2321}, {54240, 42384}

X(61412) = VERTEX PRODUCT OF GEMINI 81 TRIANGLE

Barycentrics    a^2*(a+b-c)*(a-b+c)*(b^2+c^2+a*(b+c)) : :

X(61412) lies on these lines: {2, 7}, {6, 61325}, {12, 32781}, {31, 56}, {38, 65}, {42, 1403}, {55, 31884}, {73, 57743}, {81, 1429}, {109, 28479}, {208, 7103}, {218, 23089}, {222, 604}, {241, 28390}, {310, 10030}, {388, 26034}, {593, 1412}, {873, 1434}, {896, 28352}, {902, 16064}, {942, 9840}, {950, 50419}, {1122, 1427}, {1193, 20967}, {1284, 3720}, {1319, 17469}, {1357, 28360}, {1376, 54338}, {1401, 1402}, {1404, 2003}, {1405, 52424}, {1418, 28350}, {1428, 2308}, {1460, 9316}, {1463, 2239}, {1466, 7085}, {1467, 28376}, {1475, 20665}, {1707, 3361}, {1730, 24177}, {1755, 2260}, {1756, 24239}, {1764, 3663}, {1788, 33163}, {2183, 3752}, {2227, 59308}, {2269, 3666}, {2347, 2999}, {2352, 22053}, {3210, 3212}, {3339, 59311}, {3503, 17752}, {3669, 8042}, {3670, 35650}, {3674, 16705}, {3937, 40956}, {3946, 18163}, {4001, 15983}, {4215, 17187}, {4292, 15971}, {4352, 37555}, {4359, 16609}, {5221, 36263}, {5252, 33074}, {5255, 37328}, {5709, 50425}, {6763, 19879}, {7004, 40959}, {7053, 7366}, {7146, 28606}, {7225, 37543}, {7293, 37583}, {9310, 17811}, {10473, 42289}, {10521, 20367}, {10980, 44843}, {12588, 33080}, {13724, 37566}, {15973, 24470}, {16579, 18726}, {17787, 32939}, {18206, 30038}, {18838, 28377}, {19514, 37582}, {19591, 37683}, {21370, 40968}, {24914, 26061}, {26892, 40958}, {28356, 40961}, {28367, 28391}, {28368, 53538}, {28370, 36277}, {28371, 60715}, {30545, 30964}, {33162, 40663}, {37653, 56928}, {40151, 57663}, {40886, 43040}

X(61412) = perspector of circumconic {{A, B, C, X(664), X(1461)}}
X(61412) = X(i)-isoconjugate-of-X(j) for these {i, j}: {8, 2298}, {9, 1220}, {21, 14624}, {41, 1240}, {55, 30710}, {210, 14534}, {220, 31643}, {281, 1791}, {318, 2359}, {346, 961}, {522, 36147}, {644, 4581}, {645, 57162}, {650, 8707}, {1018, 57161}, {1169, 3701}, {1500, 52550}, {2194, 60264}, {2287, 60086}, {2321, 2363}, {3239, 36098}, {3900, 6648}, {4391, 32736}, {4397, 8687}, {15420, 56183}
X(61412) = X(i)-Dao conjugate of X(j) for these {i, j}: {223, 30710}, {478, 1220}, {960, 2321}, {1211, 312}, {1214, 60264}, {2092, 341}, {3125, 4086}, {3160, 1240}, {3666, 30713}, {17419, 4397}, {38992, 3239}, {39015, 522}, {40611, 14624}, {52087, 8}, {59509, 3596}
X(61412) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1020, 3669}, {1414, 43924}, {1434, 54308}, {24471, 1193}
X(61412) = X(i)-cross conjugate of X(j) for these {i, j}: {2300, 1193}
X(61412) = pole of line {1459, 23865} with respect to the circumcircle
X(61412) = pole of line {284, 1043} with respect to the Stammler hyperbola
X(61412) = pole of line {522, 52595} with respect to the Steiner inellipse
X(61412) = pole of line {333, 17787} with respect to the Wallace hyperbola
X(61412) = pole of line {1, 15971} with respect to the dual conic of Yff parabola
X(61412) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(56)}}, {{A, B, C, X(6), X(5749)}}, {{A, B, C, X(7), X(1407)}}, {{A, B, C, X(9), X(31)}}, {{A, B, C, X(42), X(45218)}}, {{A, B, C, X(57), X(1106)}}, {{A, B, C, X(63), X(603)}}, {{A, B, C, X(81), X(894)}}, {{A, B, C, X(154), X(27382)}}, {{A, B, C, X(189), X(20348)}}, {{A, B, C, X(221), X(329)}}, {{A, B, C, X(222), X(56367)}}, {{A, B, C, X(226), X(1042)}}, {{A, B, C, X(269), X(873)}}, {{A, B, C, X(307), X(52373)}}, {{A, B, C, X(527), X(6371)}}, {{A, B, C, X(604), X(2285)}}, {{A, B, C, X(649), X(3509)}}, {{A, B, C, X(908), X(1457)}}, {{A, B, C, X(960), X(1191)}}, {{A, B, C, X(1201), X(3452)}}, {{A, B, C, X(1211), X(26580)}}, {{A, B, C, X(1333), X(5279)}}, {{A, B, C, X(1399), X(3219)}}, {{A, B, C, X(1400), X(16947)}}, {{A, B, C, X(1406), X(5905)}}, {{A, B, C, X(1427), X(52358)}}, {{A, B, C, X(1462), X(41246)}}, {{A, B, C, X(1472), X(42467)}}, {{A, B, C, X(1473), X(27509)}}, {{A, B, C, X(1944), X(26884)}}, {{A, B, C, X(2092), X(5257)}}, {{A, B, C, X(2350), X(17754)}}, {{A, B, C, X(2390), X(3910)}}, {{A, B, C, X(3004), X(33864)}}, {{A, B, C, X(3218), X(52440)}}, {{A, B, C, X(3423), X(4252)}}, {{A, B, C, X(3556), X(27540)}}, {{A, B, C, X(3662), X(7248)}}, {{A, B, C, X(3725), X(59207)}}, {{A, B, C, X(5435), X(57663)}}, {{A, B, C, X(14529), X(28950)}}, {{A, B, C, X(17420), X(40880)}}, {{A, B, C, X(20911), X(27184)}}, {{A, B, C, X(20991), X(27508)}}, {{A, B, C, X(21454), X(40151)}}, {{A, B, C, X(27064), X(43070)}}, {{A, B, C, X(27539), X(56841)}}, {{A, B, C, X(28997), X(47380)}}, {{A, B, C, X(29967), X(60679)}}, {{A, B, C, X(30827), X(32577)}}, {{A, B, C, X(40869), X(40976)}}, {{A, B, C, X(51871), X(56555)}}, {{A, B, C, X(53280), X(53337)}}
X(61412) = barycentric product X(i)*X(j) for these (i, j): {1, 24471}, {109, 3004}, {226, 40153}, {269, 960}, {1014, 2292}, {1088, 20967}, {1193, 7}, {1211, 1412}, {1228, 16947}, {1333, 45196}, {1400, 16705}, {1402, 16739}, {1407, 3687}, {1408, 18697}, {1414, 50330}, {1415, 4509}, {1423, 27455}, {1427, 17185}, {1431, 59509}, {1432, 28369}, {1434, 2092}, {1461, 3910}, {1829, 77}, {1847, 22074}, {1848, 222}, {2269, 279}, {2300, 85}, {2354, 348}, {3666, 57}, {3668, 4267}, {3669, 3882}, {3674, 6}, {3676, 53280}, {3725, 57785}, {3965, 738}, {4357, 56}, {4572, 57157}, {6371, 664}, {17096, 61168}, {17420, 934}, {20653, 7341}, {20911, 604}, {21124, 4565}, {22097, 278}, {22345, 273}, {40976, 7056}, {41003, 58}, {43924, 53332}, {43932, 61223}, {46878, 7053}, {48131, 651}, {52326, 658}, {52567, 757}, {54308, 65}, {54314, 603}, {57158, 6614}, {59174, 873}, {61172, 7203}
X(61412) = barycentric quotient X(i)/X(j) for these (i, j): {7, 1240}, {56, 1220}, {57, 30710}, {109, 8707}, {226, 60264}, {269, 31643}, {603, 1791}, {604, 2298}, {757, 52550}, {960, 341}, {1042, 60086}, {1106, 961}, {1193, 8}, {1211, 30713}, {1400, 14624}, {1408, 2363}, {1412, 14534}, {1415, 36147}, {1434, 40827}, {1461, 6648}, {1829, 318}, {1848, 7017}, {2092, 2321}, {2269, 346}, {2292, 3701}, {2300, 9}, {2354, 281}, {3004, 35519}, {3666, 312}, {3674, 76}, {3687, 59761}, {3725, 210}, {3733, 57161}, {3882, 646}, {3910, 52622}, {3965, 30693}, {4267, 1043}, {4357, 3596}, {4503, 4494}, {4719, 4673}, {6371, 522}, {16705, 28660}, {16739, 40072}, {16947, 1169}, {17420, 4397}, {20911, 28659}, {20967, 200}, {22074, 3692}, {22076, 3710}, {22097, 345}, {22345, 78}, {24471, 75}, {27455, 27424}, {28369, 17787}, {40153, 333}, {40966, 4082}, {40976, 7046}, {41003, 313}, {43924, 4581}, {44092, 53008}, {45196, 27801}, {48131, 4391}, {50330, 4086}, {51641, 57162}, {52326, 3239}, {52411, 2359}, {52567, 1089}, {53280, 3699}, {54308, 314}, {57157, 663}, {59174, 756}, {61168, 30730}
X(61412) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1423, 28387}, {2, 9965, 20348}, {56, 7248, 61376}, {57, 1423, 2}, {65, 28386, 10459}, {1400, 56556, 672}, {1400, 59173, 57}, {1401, 1402, 1458}, {1403, 1469, 42}, {3666, 22097, 2269}, {28389, 32636, 28385}

X(61413) = VERTEX PRODUCT OF GEMINI 85 TRIANGLE

Barycentrics    b*(a+b-c)*c*(a-b+c)*(a^2+2*b*c-a*(b+c)) : :

X(61413) lies on these lines: {2, 4554}, {7, 350}, {8, 2898}, {75, 31627}, {76, 279}, {85, 5226}, {192, 7205}, {226, 40030}, {304, 1446}, {305, 61414}, {312, 1088}, {321, 7182}, {345, 1996}, {346, 57792}, {347, 30737}, {348, 349}, {658, 32939}, {668, 6555}, {693, 3434}, {883, 23612}, {948, 28809}, {1233, 17093}, {1323, 3761}, {1441, 6340}, {1909, 3160}, {1920, 20567}, {2481, 5274}, {2550, 59508}, {3685, 9446}, {3729, 6168}, {3760, 10481}, {3911, 7243}, {4331, 30660}, {4358, 21609}, {4441, 9436}, {4454, 4569}, {4461, 50560}, {4566, 24282}, {4572, 6382}, {4625, 8033}, {4659, 52980}, {5273, 30988}, {5435, 10030}, {5905, 7055}, {6376, 31994}, {7017, 13149}, {7081, 14189}, {9312, 56714}, {10584, 40619}, {14727, 45252}, {16090, 45962}, {17076, 37798}, {17082, 56554}, {17144, 32003}, {17165, 35312}, {20911, 40702}, {21580, 56084}, {24349, 31526}, {24524, 25718}, {25278, 25719}, {26125, 31008}, {27394, 31637}, {28605, 52421}, {30567, 42309}, {31995, 40593}, {42034, 59200}, {43946, 59572}, {49483, 59601}

X(61413) = trilinear pole of line {20907, 42341}
X(61413) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 9439}, {41, 9309}, {55, 9315}, {2175, 9311}, {2223, 6169}, {9447, 32023}, {20287, 57264}
X(61413) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 9439}, {223, 9315}, {1376, 30706}, {2275, 3056}, {3160, 9309}, {3663, 3057}, {4885, 14936}, {39066, 672}, {40593, 9311}, {41006, 14100}, {48315, 926}
X(61413) = X(i)-Ceva conjugate of X(j) for these {i, j}: {2481, 40704}, {4554, 4885}, {56264, 60720}
X(61413) = pole of line {926, 40704} with respect to the Steiner circumellipse
X(61413) = pole of line {4885, 52621} with respect to the dual conic of incircle
X(61413) = pole of line {668, 883} with respect to the dual conic of Feuerbach hyperbola
X(61413) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(1376)}}, {{A, B, C, X(279), X(45205)}}, {{A, B, C, X(3434), X(28999)}}, {{A, B, C, X(3729), X(6557)}}, {{A, B, C, X(4554), X(8817)}}, {{A, B, C, X(6180), X(40160)}}, {{A, B, C, X(6384), X(18031)}}, {{A, B, C, X(9312), X(27818)}}, {{A, B, C, X(16283), X(16588)}}, {{A, B, C, X(32023), X(40704)}}
X(61413) = barycentric product X(i)*X(j) for these (i, j): {75, 9312}, {561, 9316}, {1231, 56014}, {1376, 6063}, {3729, 85}, {3967, 57785}, {4449, 4572}, {4513, 57792}, {4554, 4885}, {6180, 76}, {18031, 6168}, {18743, 27829}, {20567, 9310}, {20907, 664}, {21052, 4625}, {23989, 61415}, {34018, 40883}, {42341, 46135}
X(61413) = barycentric quotient X(i)/X(j) for these (i, j): {1, 9439}, {7, 9309}, {57, 9315}, {85, 9311}, {673, 6169}, {1376, 55}, {3212, 20287}, {3729, 9}, {3967, 210}, {4014, 3271}, {4449, 663}, {4513, 220}, {4554, 30610}, {4885, 650}, {4942, 3715}, {6063, 32023}, {6168, 672}, {6180, 6}, {6384, 60812}, {7209, 27498}, {9310, 41}, {9312, 1}, {9316, 31}, {16283, 14827}, {17218, 3737}, {18199, 7252}, {20907, 522}, {20980, 3063}, {21052, 4041}, {21139, 2170}, {22091, 1946}, {27829, 8056}, {36620, 60813}, {40883, 3693}, {41355, 1458}, {42341, 926}, {46135, 14727}, {56014, 1172}, {56714, 2340}, {56783, 51845}, {59507, 3057}, {59573, 14100}, {61415, 1252}
X(61413) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6063, 60720}, {312, 1088, 40704}, {321, 37780, 7182}, {348, 349, 34284}, {348, 57477, 17087}, {2481, 32023, 5274}, {4358, 59181, 21609}, {4554, 6063, 2}, {7196, 30545, 7}

X(61414) = VERTEX PRODUCT OF GEMINI 86 TRIANGLE

Barycentrics    b*c*(-a+b+c)^2*(a^2+2*b*c+a*(b+c)) : :

X(61414) lies on these lines: {2, 1240}, {8, 210}, {305, 61413}, {321, 3718}, {345, 19608}, {346, 59761}, {561, 60720}, {941, 41839}, {2064, 56555}, {2269, 30568}, {3436, 42485}, {3617, 34258}, {3717, 31330}, {4494, 5745}, {4671, 56745}, {5273, 17787}, {5328, 45242}, {5744, 19811}, {17790, 37642}, {19767, 34064}, {20336, 20928}, {26132, 52043}, {31993, 34284}, {34255, 41828}, {44140, 55095}

X(61414) = X(i)-isoconjugate-of-X(j) for these {i, j}: {604, 959}, {941, 1106}, {1397, 44733}, {1407, 2258}, {16947, 60321}, {31359, 52410}, {32693, 43924}, {52931, 57129}
X(61414) = X(i)-Dao conjugate of X(j) for these {i, j}: {3161, 959}, {6552, 941}, {17417, 43924}, {23880, 53543}, {24771, 2258}, {34261, 56}
X(61414) = pole of line {1408, 52410} with respect to the Stammler hyperbola
X(61414) = pole of line {4462, 6371} with respect to the Steiner circumellipse
X(61414) = pole of line {6371, 20317} with respect to the Steiner inellipse
X(61414) = pole of line {1014, 1407} with respect to the Wallace hyperbola
X(61414) = pole of line {650, 52622} with respect to the dual conic of incircle
X(61414) = pole of line {3831, 24175} with respect to the dual conic of Yff parabola
X(61414) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(958)}}, {{A, B, C, X(8), X(11679)}}, {{A, B, C, X(210), X(346)}}, {{A, B, C, X(497), X(5307)}}, {{A, B, C, X(940), X(3057)}}, {{A, B, C, X(941), X(2268)}}, {{A, B, C, X(2478), X(44734)}}, {{A, B, C, X(2551), X(54396)}}, {{A, B, C, X(3701), X(59761)}}, {{A, B, C, X(3714), X(56086)}}, {{A, B, C, X(3877), X(46880)}}, {{A, B, C, X(3880), X(23880)}}, {{A, B, C, X(5019), X(17053)}}, {{A, B, C, X(6557), X(19582)}}, {{A, B, C, X(10436), X(18228)}}, {{A, B, C, X(14555), X(31623)}}
X(61414) = barycentric product X(i)*X(j) for these (i, j): {314, 3714}, {2268, 28659}, {3596, 958}, {3713, 76}, {3718, 54396}, {10436, 341}, {11679, 312}, {23880, 646}, {31625, 53561}, {34284, 346}, {50457, 7258}, {52406, 5307}, {58332, 6386}, {59761, 940}
X(61414) = barycentric quotient X(i)/X(j) for these (i, j): {8, 959}, {200, 2258}, {312, 44733}, {341, 31359}, {346, 941}, {644, 32693}, {646, 32038}, {940, 1407}, {958, 56}, {1043, 5331}, {1265, 34259}, {1468, 1106}, {1867, 1426}, {2268, 604}, {3596, 58008}, {3701, 60321}, {3713, 6}, {3714, 65}, {3952, 52931}, {4185, 1398}, {5019, 52410}, {5307, 1435}, {7256, 931}, {8672, 7250}, {10436, 269}, {11679, 57}, {17418, 43924}, {20007, 45784}, {23880, 3669}, {31993, 1427}, {34284, 279}, {43067, 43932}, {44734, 1396}, {50457, 7216}, {53526, 53538}, {53561, 1015}, {54396, 34}, {54417, 1408}, {58332, 667}, {59305, 1042}, {59761, 34258}
X(61414) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {312, 3975, 18228}

X(61415) = VERTEX PRODUCT OF GEMINI 88 TRIANGLE

Barycentrics    a*(a-b)^2*(a-c)^2*(a+b-c)*(a-b+c)*(a^2+2*b*c-a*(b+c)) : :

X(61415) lies on these lines: {2, 1252}, {100, 30626}, {644, 9358}, {765, 56718}, {1016, 1262}, {4564, 5382}, {4885, 28999}, {6516, 29006}, {6940, 61106}, {14589, 28984}, {28965, 59149}, {29005, 40865}, {44717, 57757}

X(61415) = X(i)-isoconjugate-of-X(j) for these {i, j}: {11, 9315}, {1086, 9439}, {2170, 9309}, {3271, 9311}, {3675, 6169}, {6377, 60812}, {17435, 51845}
X(61415) = X(i)-Dao conjugate of X(j) for these {i, j}: {48315, 52305}
X(61415) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(1376)}}, {{A, B, C, X(100), X(28999)}}, {{A, B, C, X(39293), X(57757)}}
X(61415) = barycentric product X(i)*X(j) for these (i, j): {765, 9312}, {1016, 6180}, {1252, 61413}, {1275, 4513}, {1376, 4998}, {3729, 4564}, {7035, 9316}, {31615, 4885}, {39293, 56714}
X(61415) = barycentric quotient X(i)/X(j) for these (i, j): {59, 9309}, {1110, 9439}, {1376, 11}, {2149, 9315}, {3729, 4858}, {4014, 7336}, {4449, 21132}, {4513, 1146}, {4564, 9311}, {4885, 40166}, {4998, 32023}, {6180, 1086}, {9310, 2170}, {9312, 1111}, {9316, 244}, {16283, 14936}, {31615, 30610}, {42341, 52305}, {61413, 23989}
X(61415) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4998, 31615, 1252}

X(61416) = VERTEX PRODUCT OF GEMINI 92 TRIANGLE

Barycentrics    b*(a^2+b^2)*c*(a^2+c^2)*(a^2*b+(a+b)^2*c+b*c^2) : :

X(61416) lies on cubic K286 and on these lines: {1, 18040}, {2, 3112}, {6, 76}, {75, 16549}, {82, 5156}, {1423, 18097}, {3405, 16574}, {4645, 18088}, {8033, 39276}, {16889, 32784}, {17026, 18087}, {17027, 18089}, {17028, 18109}, {17030, 18094}, {18091, 50302}, {26035, 27005}, {26100, 27067}, {29509, 29534}, {32085, 37101}

X(61416) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1923, 40024}, {1964, 39971}, {3051, 39717}
X(61416) = X(i)-Dao conjugate of X(j) for these {i, j}: {41884, 39971}
X(61416) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(17031)}}, {{A, B, C, X(6), X(24512)}}, {{A, B, C, X(75), X(40094)}}, {{A, B, C, X(76), X(20913)}}, {{A, B, C, X(732), X(8033)}}
X(61416) = barycentric product X(i)*X(j) for these (i, j): {18833, 20985}, {20913, 83}, {24325, 3112}, {24512, 308}
X(61416) = barycentric quotient X(i)/X(j) for these (i, j): {83, 39971}, {308, 40024}, {3112, 39717}, {18082, 56131}, {20913, 141}, {20985, 1964}, {21146, 2530}, {22099, 4020}, {24325, 38}, {24512, 39}, {56186, 56122}

X(61417) = VERTEX PRODUCT OF GEMINI 100 TRIANGLE

Barycentrics    -(b*c*(a*(b-c)+b*c)*(-(a*b)+(a+b)*c)*(b*c*(b+c)+a*(b^2+c^2))) : :

X(61417) lies on these lines: {2, 330}, {38, 42027}, {81, 39914}, {87, 32772}, {310, 27447}, {321, 51837}, {561, 6383}, {693, 27466}, {1150, 2319}, {3741, 23473}, {7155, 10453}, {20945, 30090}, {27436, 27458}, {27446, 27454}, {30054, 52573}, {31330, 45782}

X(61417) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1258, 2209}, {2176, 57399}, {20979, 59102}
X(61417) = X(i)-Dao conjugate of X(j) for these {i, j}: {1107, 51902}, {21024, 53676}, {21838, 43}, {51575, 2176}, {59565, 20691}
X(61417) = pole of line {27644, 51319} with respect to the Wallace hyperbola
X(61417) = pole of line {3840, 22189} with respect to the dual conic of Yff parabola
X(61417) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(3741)}}, {{A, B, C, X(81), X(37596)}}, {{A, B, C, X(310), X(1909)}}, {{A, B, C, X(561), X(6376)}}, {{A, B, C, X(693), X(19567)}}, {{A, B, C, X(873), X(31997)}}, {{A, B, C, X(2275), X(2350)}}, {{A, B, C, X(16606), X(27447)}}, {{A, B, C, X(20917), X(40013)}}
X(61417) = barycentric product X(i)*X(j) for these (i, j): {1107, 6383}, {3741, 6384}, {16738, 60244}, {20891, 330}, {27424, 30097}, {53679, 59565}
X(61417) = barycentric quotient X(i)/X(j) for these (i, j): {87, 57399}, {330, 1258}, {932, 59102}, {1107, 2176}, {2309, 2209}, {3741, 43}, {6383, 1221}, {6384, 40418}, {16738, 27644}, {18169, 38832}, {20891, 192}, {21024, 20691}, {23473, 56806}, {30097, 1423}, {45209, 1918}, {45217, 2205}, {50510, 8640}, {51575, 51902}, {53338, 52923}, {59565, 53676}, {60244, 60230}
X(61417) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 27424, 27438}, {6384, 27424, 2}

X(61418) = VERTEX PRODUCT OF GEMINI 106 TRIANGLE

Barycentrics    (b^2+c^2)*(a^2+2*b^2+c^2)*(a^2+b^2+2*c^2) : :

X(61418) lies on these lines: {2, 3108}, {66, 3410}, {141, 52554}, {427, 31078}, {599, 16949}, {1031, 1369}, {1634, 15246}, {2896, 41513}, {3314, 3613}, {4576, 17949}, {7409, 8801}, {7779, 40425}, {7837, 41917}, {7953, 9076}, {8024, 14125}, {8891, 23297}, {9464, 59758}, {15523, 17192}, {16990, 45838}, {17280, 39728}, {17302, 33090}, {21248, 31125}, {33091, 39724}, {35137, 43098}, {37636, 60527}, {39722, 39723}, {46226, 57421}

X(61418) = isotomic conjugate of X(59180)
X(61418) = trilinear pole of line {31067, 826}
X(61418) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 59180}, {82, 5007}, {251, 17469}, {560, 52570}, {3589, 46289}, {4599, 8664}, {7927, 34072}, {17457, 59996}, {34055, 44091}, {55240, 61211}
X(61418) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 59180}, {39, 3589}, {141, 5007}, {3124, 8664}, {6374, 52570}, {6665, 6292}, {15449, 7927}, {40585, 17469}, {40938, 428}
X(61418) = X(i)-Ceva conjugate of X(j) for these {i, j}: {10159, 52554}
X(61418) = X(i)-cross conjugate of X(j) for these {i, j}: {141, 10159}, {2528, 4576}, {57063, 4568}, {57222, 41676}
X(61418) = pole of line {34573, 52554} with respect to the Kiepert hyperbola
X(61418) = pole of line {3589, 59180} with respect to the Wallace hyperbola
X(61418) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(66)}}, {{A, B, C, X(39), X(7772)}}, {{A, B, C, X(76), X(7760)}}, {{A, B, C, X(251), X(31124)}}, {{A, B, C, X(305), X(31078)}}, {{A, B, C, X(523), X(39998)}}, {{A, B, C, X(1235), X(60285)}}, {{A, B, C, X(1843), X(39955)}}, {{A, B, C, X(1916), X(55085)}}, {{A, B, C, X(1930), X(17192)}}, {{A, B, C, X(2528), X(7779)}}, {{A, B, C, X(3108), X(52554)}}, {{A, B, C, X(3917), X(56266)}}, {{A, B, C, X(4576), X(31614)}}, {{A, B, C, X(5189), X(57222)}}, {{A, B, C, X(6353), X(31107)}}, {{A, B, C, X(7409), X(8362)}}, {{A, B, C, X(7794), X(14125)}}, {{A, B, C, X(7829), X(11606)}}, {{A, B, C, X(7856), X(54122)}}, {{A, B, C, X(8041), X(31613)}}, {{A, B, C, X(8891), X(9464)}}, {{A, B, C, X(9698), X(35005)}}, {{A, B, C, X(16703), X(39747)}}, {{A, B, C, X(17280), X(33091)}}, {{A, B, C, X(17302), X(39723)}}, {{A, B, C, X(18840), X(52568)}}, {{A, B, C, X(21248), X(52898)}}, {{A, B, C, X(27376), X(43681)}}, {{A, B, C, X(31067), X(31068)}}, {{A, B, C, X(33090), X(39722)}}, {{A, B, C, X(37125), X(37353)}}, {{A, B, C, X(40002), X(40042)}}, {{A, B, C, X(42554), X(59180)}}, {{A, B, C, X(46225), X(51860)}}, {{A, B, C, X(55767), X(60129)}}
X(61418) = barycentric product X(i)*X(j) for these (i, j): {427, 57852}, {1235, 41435}, {3108, 8024}, {10159, 141}, {23285, 7953}, {31065, 4576}, {31067, 99}, {31068, 31125}, {35137, 826}, {40425, 7794}, {52554, 76}, {57421, 59995}
X(61418) = barycentric quotient X(i)/X(j) for these (i, j): {2, 59180}, {38, 17469}, {39, 5007}, {76, 52570}, {141, 3589}, {427, 428}, {826, 7927}, {1235, 44142}, {1634, 61211}, {1843, 44091}, {3005, 8664}, {3108, 251}, {3665, 7198}, {3703, 4030}, {3917, 22352}, {3933, 7767}, {3954, 21802}, {4576, 10330}, {7794, 6292}, {7953, 827}, {8024, 39998}, {8041, 11205}, {10159, 83}, {16703, 16707}, {16887, 17200}, {16892, 48101}, {31065, 58784}, {31067, 523}, {31068, 52898}, {35137, 4577}, {40425, 52395}, {41435, 1176}, {41651, 41650}, {46748, 40003}, {48084, 48152}, {52554, 6}, {55239, 18062}, {57421, 59996}, {57852, 1799}, {59995, 42554}
X(61418) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3108, 10159, 2}, {3108, 57852, 31068}, {10159, 57852, 3108}

X(61419) = ISOGONAL CONJUGATE OF X(16256)

Barycentrics    a^2*(Sqrt[3]*b^2 + 2*S)*(Sqrt[3]*c^2 + 2*S)*(2*(-2*a^2 + b^2 + c^2)*S + Sqrt[3]*(3*a^2*(-a^2 + b^2 + c^2) - 4*S^2)) : :

X(61419) lies on these lines: {15, 1337}, {16, 512}, {62, 34317}, {691, 2380}, {2379, 10409}, {5237, 39262}, {6582, 40707}, {10646, 38403}, {11084, 32662}, {11119, 36969}

X(61419) = isogonal conjugate of X(16256)
X(61419) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 16256}, {61068, 41000}
X(61419) = crossdifference of every pair of points on line {396, 35443}
X(61419) = barycentric product X(i)*X(j) for these {i,j}: {530, 2981}, {9200, 10409}, {11537, 38403}
X(61419) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 16256}, {530, 41000}, {2981, 43091}, {11537, 43085}, {16459, 36316}

X(61420) = ISOGONAL CONJUGATE OF X(16255)

Barycentrics    a^2*(Sqrt[3]*b^2 - 2*S)*(Sqrt[3]*c^2 - 2*S)*(-2*(-2*a^2 + b^2 + c^2)*S + Sqrt[3]*(3*a^2*(-a^2 + b^2 + c^2) - 4*S^2)) : :

X(61420) lies on these lines: {15, 512}, {16, 1338}, {61, 34318}, {691, 2381}, {2378, 10410}, {5238, 39261}, {6295, 40706}, {10645, 38404}, {11089, 32662}, {11120, 36970}

X(61420) = isogonal conjugate of X(16255)
X(61420) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 16255}, {61069, 41001}
X(61420) = crossdifference of every pair of points on line {395, 35444}
X(61420) = barycentric product X(i)*X(j) for these {i,j}: {531, 6151}, {9201, 10410}, {11549, 38404}
X(61420) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 16255}, {531, 41001}, {6151, 43092}, {11549, 43086}, {16460, 36317}

X(61421) = MIDPOINT OF X(1916) AND X(3903)

Barycentrics    a^2*(b^2 + a*c)*(a*b + c^2)*(a^3*b^2 - a^2*b^3 - a^2*b^2*c + a*b^3*c + b^4*c + a^3*c^2 - a^2*b*c^2 - b^3*c^2 - a^2*c^3 + a*b*c^3 - b^2*c^3 + b*c^4) : :

X(61421) lies on the cubic K359 and these lines: {1, 256}, {39, 512}, {805, 3110}, {1015, 1967}, {1916, 3903}, {2023, 40608}, {20683, 40873}, {41517, 59480}

X(61421) = midpoint of X(1916) and X(3903)
X(61421) = reflection of X(40608) in X(2023)
X(61421) = Gallatly-circle-inverse of X(45902)
X(61421) = crossdifference of every pair of points on line {385, 3287}
X(61421) = {X(805),X(40432)}-harmonic conjugate of X(3110)

X(61422) = X(1)X(513)∩X(2)X(59486)

Barycentrics    a*(a + b - 2*c)*(a - 2*b + c)*(a^4*b - 3*a^3*b^2 + 2*a^2*b^3 + a^4*c + a^2*b^2*c - b^4*c - 3*a^3*c^2 + a^2*b*c^2 - 2*a*b^2*c^2 + b^3*c^2 + 2*a^2*c^3 + b^2*c^3 - b*c^4) : :

X(61422) lies on the cubic K359 and these lines: {1, 513}, {2, 59486}, {6, 39154}, {517, 2087}, {901, 5091}, {1083, 5376}, {1168, 30116}, {1318, 4618}, {1320, 14839}, {3257, 60698}, {4792, 20331}, {24482, 46779}, {34583, 52206}

X(61422) = {X(1),X(1022)}-harmonic conjugate of X(34230)

X(61423) = ISOGONAL CONJUGATE OF X(14887)

Barycentrics    (b - c)^2*(-a^4 + a^3*b - a*b^3 + b^4 + a^3*c - a^2*b*c + a*b^2*c - b^3*c - a*b*c^2 + a*c^3 + b*c^3 - c^4)*(a^4 - a^3*b - a*b^3 + b^4 - a^3*c + a^2*b*c + a*b^2*c - b^3*c - a*b*c^2 + a*c^3 + b*c^3 - c^4) : :

X(61423) lies on the cubic K165 and these lines: {2, 14888}, {3, 34179}, {523, 34896}, {867, 42753}, {1086, 8578}, {5190, 35967}, {5730, 6790}, {14825, 53578}, {40150, 54231}

X(61423) = isogonal conjugate of X(14887)
X(61423) = complement of X(14888)
X(61423) = circumcircle-inverse of X(34179)
X(61423) = X(i)-isoconjugate of X(j) for these (i,j): {1, 14887}, {9, 57240}, {100, 39026}, {150, 1110}, {765, 20999}, {1252, 16560}, {4570, 22321}, {8578, 57731}, {15624, 31634}, {20940, 23990}
X(61423) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 14887}, {478, 57240}, {513, 20999}, {514, 150}, {661, 16560}, {4988, 21091}, {8054, 39026}, {50330, 22321}
X(61423) = trilinear pole of line {24136, 46384}
X(61423) = barycentric product X(i)*X(j) for these {i,j}: {1086, 44184}, {23100, 40150}, {23989, 34179}
X(61423) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 14887}, {56, 57240}, {244, 16560}, {649, 39026}, {1015, 20999}, {1086, 150}, {1111, 20940}, {3120, 21091}, {3125, 22321}, {3937, 22145}, {6545, 21202}, {14377, 31634}, {21143, 8578}, {27846, 27943}, {34179, 1252}, {40150, 59149}, {44184, 1016}

X(61424) = ISOGONAL CONJUGATE OF X(6790)

Barycentrics    a^2*(a^4 + a^3*b + a*b^3 + b^4 - 3*a^3*c - a^2*b*c - a*b^2*c - 3*b^3*c + 2*a^2*c^2 - 3*a*b*c^2 + 2*b^2*c^2 + 3*a*c^3 + 3*b*c^3 - 3*c^4)*(a^4 - 3*a^3*b + 2*a^2*b^2 + 3*a*b^3 - 3*b^4 + a^3*c - a^2*b*c - 3*a*b^2*c + 3*b^3*c - a*b*c^2 + 2*b^2*c^2 + a*c^3 - 3*b*c^3 + c^4) : :

X(61424) lies on the the conic {{A,B,C,X(1),X(6)}}, cubic K165, and these lines: {1, 42753}, {86, 3109}, {106, 20999}, {952, 1120}, {996, 25385}, {1222, 24390}, {2810, 60049}, {2841, 36052}, {2969, 36123}, {5687, 40436}, {8578, 23345}, {9268, 14260}, {37129, 46119}, {42752, 43692}, {56783, 59490}

X(61424) = reflection of X(20999) in X(106)
X(61424) = isogonal conjugate of X(6790)
X(61424) = isogonal conjugate of the anticomplement of X(6788)
X(61424) = X(1)-isoconjugate of X(6790)
X(61424) = X(3)-Dao conjugate of X(6790)
X(61424) = barycentric product X(513)*X(46119)
X(61424) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 6790}, {46119, 668}

X(61425) = ISOGONAL CONJUGATE OF X(38941)

Barycentrics    a^2*(a^4 - 3*a^3*b + 4*a^2*b^2 - 3*a*b^3 + b^4 + a^3*c - a^2*b*c - a*b^2*c + b^3*c - 2*a^2*c^2 + 5*a*b*c^2 - 2*b^2*c^2 - a*c^3 - b*c^3 + c^4)*(a^4 + a^3*b - 2*a^2*b^2 - a*b^3 + b^4 - 3*a^3*c - a^2*b*c + 5*a*b^2*c - b^3*c + 4*a^2*c^2 - a*b*c^2 - 2*b^2*c^2 - 3*a*c^3 + b*c^3 + c^4) : :

X(61425) lies on the cubic K165 and these lines: {55, 61210}, {101, 23858}, {200, 1023}, {220, 23344}, {952, 14942}, {953, 42771}, {1043, 3109}, {2342, 3022}, {4604, 36942}, {4638, 14260}, {5091, 61230}, {42752, 43692}

X(61425) = reflection of X(23858) in X(101)
X(61425) = isogonal conjugate of X(38941)
X(61425) = X(1)-isoconjugate of X(38941)
X(61425) = X(3)-Dao conjugate of X(38941)
X(61425) = trilinear pole of line {657, 902}
X(61425) = barycentric quotient X(6)/X(38941)

X(61426) = X(1)X(514)&cap:X(2)X(34906)

Barycentrics    (a^2 + b^2 - a*c - b*c)*(a^2 - a*b - b*c + c^2)*(2*a^6 - 3*a^5*b + a^3*b^3 - a^2*b^4 + 2*a*b^5 - b^6 - 3*a^5*c + 6*a^4*b*c - 2*a^3*b^2*c + a^2*b^3*c - 3*a*b^4*c + b^5*c - 2*a^3*b*c^2 + a*b^3*c^2 + b^4*c^2 + a^3*c^3 + a^2*b*c^3 + a*b^2*c^3 - 2*b^3*c^3 - a^2*c^4 - 3*a*b*c^4 + b^2*c^4 + 2*a*c^5 + b*c^5 - c^6) : :

X(61426) lies on the cubic K165 and these lines: {1, 514}, {2, 34906}, {3, 34179}, {4, 5377}, {8, 35313}, {516, 24980}, {927, 953}, {952, 14942}, {3675, 60060}, {5138, 51832}, {52227, 56900}

X(61427) = ISOGONAL CONJUGATE OF X(5088)

Barycentrics    a^2*(a^2*b^2 - b^4 + a^3*c - a*b^2*c - 2*a^2*c^2 + b^2*c^2 + a*c^3)*(a^3*b - 2*a^2*b^2 + a*b^3 + a^2*c^2 - a*b*c^2 + b^2*c^2 - c^4) : :

X(61427) lies on these lines: {1, 185}, {33, 181}, {55, 1945}, {72, 190}, {101, 228}, {200, 1018}, {213, 2332}, {220, 4557}, {292, 42662}, {295, 4584}, {517, 1952}, {674, 42064}, {926, 2250}, {1949, 2192}, {2223, 2342}, {2713, 15168}, {2808, 18446}, {2821, 61230}, {3465, 7281}, {3887, 60135}, {5088, 53211}, {5119, 7220}, {7038, 16389}, {18785, 53549}, {52222, 53249}, {52825, 56359}

X(61427) = isogonal conjugate of X(5088)
X(61427) = isogonal conjugate of the anticomplement of X(5179)
X(61427) = X(1937)-Ceva conjugate of X(1945)
X(61427) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5088}, {7, 1936}, {57, 1944}, {58, 44150}, {69, 1430}, {75, 26884}, {77, 243}, {81, 8680}, {85, 1951}, {86, 851}, {222, 1948}, {269, 7360}, {274, 42669}, {278, 6518}, {279, 58325}, {310, 44112}, {333, 51645}, {348, 2202}, {603, 57812}, {649, 15418}, {905, 1981}, {1439, 15146}, {4025, 23353}, {7182, 51726}
X(61427) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 5088}, {10, 44150}, {206, 26884}, {5375, 15418}, {5452, 1944}, {6600, 7360}, {7952, 57812}, {40586, 8680}, {40600, 851}
X(61427) = trilinear pole of line {42, 657}
X(61427) = barycentric product X(i)*X(j) for these {i,j}: {8, 1945}, {9, 1937}, {10, 2249}, {33, 40843}, {37, 37142}, {42, 35145}, {55, 1952}, {213, 57980}, {281, 296}, {318, 1949}, {607, 57801}, {657, 53211}, {1897, 52222}, {4041, 41206}, {55232, 59041}
X(61427) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 5088}, {32, 26884}, {33, 1948}, {37, 44150}, {41, 1936}, {42, 8680}, {55, 1944}, {100, 15418}, {212, 6518}, {213, 851}, {220, 7360}, {281, 57812}, {296, 348}, {607, 243}, {1253, 58325}, {1402, 51645}, {1918, 42669}, {1937, 85}, {1945, 7}, {1949, 77}, {1952, 6063}, {1973, 1430}, {2175, 1951}, {2205, 44112}, {2212, 2202}, {2249, 86}, {2332, 15146}, {8750, 1981}, {26885, 40888}, {35145, 310}, {37142, 274}, {40843, 7182}, {41206, 4625}, {52222, 4025}, {53211, 46406}, {57801, 57918}, {57980, 6385}, {59041, 55231}
X(61427) = {X(3022),X(34457)}-harmonic conjugate of X(5185)

X(61428) = X(1)X(3309)∩X(104)X(6078)

Barycentrics    a*(a^2 - a*b + 2*b^2 - 2*a*c - b*c + c^2)*(a^2 - 2*a*b + b^2 - a*c - b*c + 2*c^2)*(2*a^5 - 2*a^4*b + a^3*b^2 + a^2*b^3 - 3*a*b^4 + b^5 - 2*a^4*c - a^2*b^2*c + 4*a*b^3*c - b^4*c + a^3*c^2 - a^2*b*c^2 - 2*a*b^2*c^2 + a^2*c^3 + 4*a*b*c^3 - 3*a*c^4 - b*c^4 + c^5) : :

X(61428) lies on these lines: {1, 3309}, {104, 6078}, {517, 1280}, {518, 53298}, {1477, 2730}, {5088, 35160}, {18450, 43760}, {47043, 60576}

X(61429) = X(1)X(522)∩X(104)X(1309)

Barycentrics    (a^3 - a^2*b - a*b^2 + b^3 + 2*a*b*c - a*c^2 - b*c^2)*(a^3 - a*b^2 - a^2*c + 2*a*b*c - b^2*c - a*c^2 + c^3)*(a^6*b - 2*a^4*b^3 + a^2*b^5 + a^6*c - 4*a^5*b*c + 3*a^4*b^2*c + 2*a^3*b^3*c - 3*a^2*b^4*c + 2*a*b^5*c - b^6*c + 3*a^4*b*c^2 - 4*a^3*b^2*c^2 + 2*a^2*b^3*c^2 - b^5*c^2 - 2*a^4*c^3 + 2*a^3*b*c^3 + 2*a^2*b^2*c^3 - 4*a*b^3*c^3 + 2*b^4*c^3 - 3*a^2*b*c^4 + 2*b^3*c^4 + a^2*c^5 + 2*a*b*c^5 - b^2*c^5 - b*c^6) : :

X(61429) lies on these lines: {1, 522}, {104, 1309}, {515, 38955}, {517, 10538}, {5088, 18816}, {14266, 37002}, {36037, 52407}

X(61430) = ISOGONAL CONJUGATE OF X(52481)

Barycentrics    a*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^8 - a^7*b - 3*a^6*b^2 + 3*a^5*b^3 + 3*a^4*b^4 - 3*a^3*b^5 - a^2*b^6 + a*b^7 - a^7*c + 4*a^6*b*c + a^5*b^2*c - 7*a^4*b^3*c + a^3*b^4*c + 2*a^2*b^5*c - a*b^6*c + b^7*c - 3*a^6*c^2 + a^5*b*c^2 + 5*a^4*b^2*c^2 - a^3*b^3*c^2 - 2*a^2*b^4*c^2 + 3*a^5*c^3 - 7*a^4*b*c^3 - a^3*b^2*c^3 + 6*a^2*b^3*c^3 - b^5*c^3 + 3*a^4*c^4 + a^3*b*c^4 - 2*a^2*b^2*c^4 - 3*a^3*c^5 + 2*a^2*b*c^5 - b^3*c^5 - a^2*c^6 - a*b*c^6 + a*c^7 + b*c^7 - a*b*c*(a^5 - 2*a^4*b - 2*a^3*b^2 + 4*a^2*b^3 + a*b^4 - 2*b^5 - 2*a^4*c + 5*a^3*b*c - a^2*b^2*c - 5*a*b^3*c + 3*b^4*c - 2*a^3*c^2 - a^2*b*c^2 + 4*a*b^2*c^2 - b^3*c^2 + 4*a^2*c^3 - 5*a*b*c^3 - b^2*c^3 + a*c^4 + 3*b*c^4 - 2*c^5)*J) : :

X(61430) lies on these lines: {4, 10782}, {104, 18210}, {517, 1113}, {1114, 1870}, {1312, 17757}, {2575, 43692}, {3262, 15164}

X(61430) = reflection of X(1114) in X(34592)
X(61430) = isogonal conjugate of X(52481)
X(61430) = symgonal image of X(34592)
X(61430) = X(1)-isoconjugate of X(52481)
X(61430) = X(3)-Dao conjugate of X(52481)
X(61430) = barycentric quotient X(6)/X(52481)

X(61431) = ISOGONAL CONJUGATE OF X(52482)

Barycentrics    a*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^8 - a^7*b - 3*a^6*b^2 + 3*a^5*b^3 + 3*a^4*b^4 - 3*a^3*b^5 - a^2*b^6 + a*b^7 - a^7*c + 4*a^6*b*c + a^5*b^2*c - 7*a^4*b^3*c + a^3*b^4*c + 2*a^2*b^5*c - a*b^6*c + b^7*c - 3*a^6*c^2 + a^5*b*c^2 + 5*a^4*b^2*c^2 - a^3*b^3*c^2 - 2*a^2*b^4*c^2 + 3*a^5*c^3 - 7*a^4*b*c^3 - a^3*b^2*c^3 + 6*a^2*b^3*c^3 - b^5*c^3 + 3*a^4*c^4 + a^3*b*c^4 - 2*a^2*b^2*c^4 - 3*a^3*c^5 + 2*a^2*b*c^5 - b^3*c^5 - a^2*c^6 - a*b*c^6 + a*c^7 + b*c^7 + a*b*c*(a^5 - 2*a^4*b - 2*a^3*b^2 + 4*a^2*b^3 + a*b^4 - 2*b^5 - 2*a^4*c + 5*a^3*b*c - a^2*b^2*c - 5*a*b^3*c + 3*b^4*c - 2*a^3*c^2 - a^2*b*c^2 + 4*a*b^2*c^2 - b^3*c^2 + 4*a^2*c^3 - 5*a*b*c^3 - b^2*c^3 + a*c^4 + 3*b*c^4 - 2*c^5)*J) : :

X(61431) lies on these lines: {4, 10781}, {104, 18210}, {517, 1114}, {1113, 1870}, {1313, 17757}, {2574, 43692}, {3262, 15165}

X(61431) = reflection of X(1113) in X(34593)
X(61431) = isogonal conjugate of X(52482)
X(61431) = symgonal image of X(34593)
X(61431) = X(1)-isoconjugate of X(52482)
X(61431) = X(3)-Dao conjugate of X(52482)
X(61431) = barycentric quotient X(6)/X(52482)

X(61432) = X(1)X(523)∩X(23)X(5143)

Barycentrics    a*(a^2 - a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^4 - b^4 - 2*a^2*b*c + b^3*c + b^2*c^2 + b*c^3 - c^4) : :

X(61432) lies on these lines: {1, 523}, {23, 5143}, {30, 8481}, {88, 1290}, {476, 741}, {691, 759}, {740, 6740}, {1411, 5018}, {2222, 53933}, {3938, 50145}, {3943, 7359}, {5160, 5524}, {5520, 37691}, {11072, 11537}, {11073, 11549}, {34209, 56843}, {34311, 35466}

X(61432) = X(758)-isoconjugate of X(59827)
X(61432) = barycentric product X(i)*X(j) for these {i,j}: {2503, 14616}, {18359, 24436}
X(61432) = barycentric quotient X(i)/X(j) for these {i,j}: {2503, 758}, {24436, 3218}, {34079, 59827}

X(61433) = X(1)X(513)∩X(106)X(2703)

Barycentrics    a^2*(a + b - 2*c)*(a - 2*b + c)*(a^3*b^2 - a*b^4 - a^2*b^2*c + a^3*c^2 - a^2*b*c^2 + b^3*c^2 + b^2*c^3 - a*c^4) : :

X(61433) lies on these lines: {1, 513}, {106, 2703}, {740, 1320}, {741, 901}, {1168, 4555}, {2234, 4792}, {4674, 18792}

X(61434) = X(1)X(514)∩X(105)X(1929)

Barycentrics    a*(a^2 + b^2 - a*c - b*c)*(a^2 - a*b - b*c + c^2)*(a^3*b - b^4 + a^3*c - 2*a^2*b*c - a*b^2*c + b^3*c - a*b*c^2 + 2*b^2*c^2 + b*c^3 - c^4) : :

X(61434) lies on these lines: {1, 514}, {105, 1929}, {740, 7281}, {741, 927}, {3120, 46784}, {3944, 57494}, {5143, 56853}, {6654, 29821}, {34906, 60353}

X(61435) = X(1)X(513)∩X(36)X(909)

Barycentrics    a^2*(a + b - 2*c)*(a - 2*b + c)*(a^4*b - 2*a^3*b^2 + 2*a*b^4 - b^5 + a^4*c + a^2*b^2*c - 2*a*b^3*c - 2*a^3*c^2 + a^2*b*c^2 + b^3*c^2 - 2*a*b*c^3 + b^2*c^3 + 2*a*c^4 - c^5) : :
X(61435) = 3 X[36] - 2 X[2183]

X(61435) lies on these lines: {1, 513}, {36, 909}, {103, 677}, {106, 1458}, {516, 1320}, {1168, 6549}, {2222, 34051}, {3000, 4792}, {3220, 32719}, {3257, 60885}, {8679, 33844}, {15635, 60787}, {36125, 54234}, {38541, 59326}, {55432, 59234}

X(61435) = X(i)-isoconjugate of X(j) for these (i,j): {519, 2717}, {902, 35164}
X(61435) = X(i)-Dao conjugate of X(j) for these (i,j): {35116, 4358}, {40594, 35164}
X(61435) = crossdifference of every pair of points on line {44, 23757}
X(61435) = barycentric product X(i)*X(j) for these {i,j}: {88, 2801}, {1320, 43047}, {9268, 57442}
X(61435) = barycentric quotient X(i)/X(j) for these {i,j}: {88, 35164}, {2801, 4358}, {9456, 2717}

X(61436) = X(1)X(514)∩X(103)X(516)

Barycentrics    (a^2 + b^2 - a*c - b*c)*(a^2 - a*b - b*c + c^2)*(2*a^5 - 2*a^4*b - a^3*b^2 - a^2*b^3 + 3*a*b^4 - b^5 - 2*a^4*c + 4*a^3*b*c + a^2*b^2*c - 2*a*b^3*c - b^4*c - a^3*c^2 + a^2*b*c^2 - 2*a*b^2*c^2 + 2*b^3*c^2 - a^2*c^3 - 2*a*b*c^3 + 2*b^2*c^3 + 3*a*c^4 - b*c^4 - c^5) : :

X(61436) lies on these lines: {1, 514}, {103, 516}, {519, 34906}, {1282, 3234}, {2809, 34805}, {5537, 28071}, {6654, 11019}, {40554, 50441}

X(61436) = midpoint of X(927) and X(14942)
X(61436) = reflection of X(i) in X(j) for these {i,j}: {1282, 3234}, {50441, 40554}

X(61437) = X(1)X(676)∩X(100)X(516)

Barycentrics    (2*a - b - c)*(a^5 - a^3*b^2 - a^2*b^3 + b^5 - 2*a^4*c + 2*a^3*b*c + 2*a*b^3*c - 2*b^4*c - a^2*b*c^2 - a*b^2*c^2 + 2*a^2*c^3 + 2*b^2*c^3 - a*c^4 - b*c^4)*(a^5 - 2*a^4*b + 2*a^2*b^3 - a*b^4 + 2*a^3*b*c - a^2*b^2*c - b^4*c - a^3*c^2 - a*b^2*c^2 + 2*b^3*c^2 - a^2*c^3 + 2*a*b*c^3 - 2*b*c^4 + c^5) : :

X(61437) lies on these lines: {1, 676}, {100, 516}, {1023, 1145}, {3762, 36944}, {4597, 35164}, {6174, 23703}, {11219, 34234}, {14554, 60782}

X(61437) = X(i)-isoconjugate of X(j) for these (i,j): {106, 2801}, {2316, 43047}
X(61437) = X(i)-Dao conjugate of X(j) for these (i,j): {214, 2801}, {6544, 57442}
X(61437) = trilinear pole of line {44, 23757}
X(61437) = barycentric product X(i)*X(j) for these {i,j}: {44, 35164}, {2717, 4358}
X(61437) = barycentric quotient X(i)/X(j) for these {i,j}: {44, 2801}, {1319, 43047}, {1647, 57442}, {2717, 88}, {35164, 20568}

X(61438) = ISOGONAL CONJUGATE OF X(14201)

Barycentrics    a*(2*a^2 - a*b + b^2 - a*c - 2*b*c + c^2)*(a^4 - 2*a^3*b + a^2*b^2 - 2*a*b^3 + 2*b^4 - 2*a^3*c + 2*a^2*b*c - 2*b^3*c + 2*a^2*c^2 + 2*a*b*c^2 + b^2*c^2 - 2*a*c^3 - 2*b*c^3 + c^4)*(a^4 - 2*a^3*b + 2*a^2*b^2 - 2*a*b^3 + b^4 - 2*a^3*c + 2*a^2*b*c + 2*a*b^2*c - 2*b^3*c + a^2*c^2 + b^2*c^2 - 2*a*c^3 - 2*b*c^3 + 2*c^4) : :

X(61438) lies on the cubic K040 and these lines: {1, 2820}, {518, 644}, {3675, 28071}, {23704, 53552}

X(61438) = isogonal conjugate of X(14201)
X(61438) = X(1)-isoconjugate of X(14201)
X(61438) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 14201}, {16593, 57036}, {39048, 26007}
X(61438) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 14201}, {1279, 26007}, {3008, 57036}

X(61439) = SYMGONAL IMAGE OF X(7426)

Barycentrics    (2*a^2 + 2*b^2 - c^2)*(2*a^2 - b^2 + 2*c^2)*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6 + 2*a^4*c^2 - 3*a^2*b^2*c^2 + 2*b^4*c^2 - a^2*c^4 + 2*b^2*c^4 - 2*c^6) : :

X(61439) lies on the cubic K025 and these lines: {2, 34213}, {4, 575}, {30, 11636}, {316, 34319}, {671, 32217}, {1383, 5309}, {3906, 8599}, {7426, 53950}, {11632, 44266}, {14568, 37909}, {14666, 26613}, {14876, 22336}, {34175, 52173}

X(61439) = reflection of X(53950) in X(7426)
X(61439) = anticomplement of X(52105)
X(61439) = antigonal image of X(10989)
X(61439) = symgonal image of X(7426)
X(61439) = barycentric product X(i)*X(j) for these {i,j}: {598, 10989}, {12367, 40826}
X(61439) = barycentric quotient X(i)/X(j) for these {i,j}: {10989, 599}, {12367, 574}

X(61440) = SYMGONAL IMAGE OF X(186))

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^4 - 2*a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2)*(a^4 - a^2*b^2 - 2*a^2*c^2 - b^2*c^2 + c^4)*(a^10 - a^8*b^2 - 2*a^6*b^4 + 2*a^4*b^6 + a^2*b^8 - b^10 - a^8*c^2 + a^6*b^2*c^2 - 3*a^2*b^6*c^2 + 3*b^8*c^2 - 2*a^6*c^4 + 4*a^2*b^4*c^4 - 2*b^6*c^4 + 2*a^4*c^6 - 3*a^2*b^2*c^6 - 2*b^4*c^6 + a^2*c^8 + 3*b^2*c^8 - c^10) : :
X(61440) = 2 X[37938] - 3 X[57381], 4 X[44234] - 3 X[57377]

X(61440) lies on the cubics K025 and K466 and these lines: {3, 52677}, {4, 54}, {20, 57474}, {30, 933}, {96, 5963}, {186, 1141}, {252, 17506}, {316, 18831}, {1157, 13619}, {1263, 27953}, {1300, 46966}, {3153, 46664}, {5449, 52122}, {5899, 38577}, {5962, 14106}, {6143, 25042}, {10295, 40631}, {13558, 37932}, {18533, 57489}, {19189, 37954}, {21844, 59287}, {25044, 34797}, {30522, 50463}, {32423, 59494}, {37938, 57381}, {38946, 47110}, {44138, 46138}, {44234, 57377}, {47105, 52445}

X(61440) = reflection of X(i) in X(j) for these {i,j}: {4, 44057}, {3153, 46664}, {52998, 186}
X(61440) = circumcircle-inverse of X(52677)
X(61440) = polar-circle-inverse of X(3574)
X(61440) = circumcircle-of-anticomplementary-triangle-inverse of X(32346)
X(61440) = antigonal image of X(3153)
X(61440) = symgonal image of X(186)
X(61440) = X(46138)-Ceva conjugate of X(275)
X(61440) = X(i)-Dao conjugate of X(j) for these (i,j): {186, 1154}, {38542, 34900}, {46664, 6368}
X(61440) = barycentric product X(i)*X(j) for these {i,j}: {275, 3153}, {276, 56924}
X(61440) = barycentric quotient X(i)/X(j) for these {i,j}: {3153, 343}, {56924, 216}
X(61440) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 59275, 52677}, {54, 19177, 275}

X(61441) = SYMGONAL IMAGE OF X(1594)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 + a^4*b^2*c^2 + b^6*c^2 + 2*a^2*c^6 + b^2*c^6 - c^8)*(a^8 - 2*a^6*b^2 + 2*a^4*b^4 - 2*a^2*b^6 + b^8 - 2*a^6*c^2 + a^4*b^2*c^2 + a^2*b^4*c^2 - 2*b^6*c^2 - a^2*b^2*c^4 + 2*a^2*c^6 + 2*b^2*c^6 - c^8)*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 + a^4*b^2*c^2 - a^2*b^4*c^2 + 2*b^6*c^2 + 2*a^4*c^4 + a^2*b^2*c^4 - 2*a^2*c^6 - 2*b^2*c^6 + c^8) : :

X(61441) lies on the cubic K024 and these lines: {4, 7730}, {30, 18401}, {933, 1166}, {3520, 15620}, {7488, 20625}, {7577, 8157}, {13506, 18381}, {23319, 52677}, {31724, 53808}, {38946, 47105}, {47110, 52445}

X(61441) = reflection of X(i) in X(j) for these {i,j}: {933, 1594}, {7488, 20625}
X(61441) = antigonal image of X(7488)
X(61441) = symgonal image of X(1594)
X(61441) = barycentric product X(7488)*X(9381)
X(61441) = barycentric quotient X(52998)/X(16039)

X(61442) = SYMGONAL IMAGE OF X(11585)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + c^4)*(a^10 - 2*a^8*b^2 + a^6*b^4 + a^4*b^6 - 2*a^2*b^8 + b^10 - 3*a^8*c^2 + 5*a^6*b^2*c^2 + 5*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 - 7*a^4*b^2*c^4 - 7*a^2*b^4*c^4 + 2*b^6*c^4 + 2*a^4*c^6 + 7*a^2*b^2*c^6 + 2*b^4*c^6 - 3*a^2*c^8 - 3*b^2*c^8 + c^10)*(a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - 2*a^8*c^2 + 5*a^6*b^2*c^2 - 7*a^4*b^4*c^2 + 7*a^2*b^6*c^2 - 3*b^8*c^2 + a^6*c^4 - 7*a^2*b^4*c^4 + 2*b^6*c^4 + a^4*c^6 + 5*a^2*b^2*c^6 + 2*b^4*c^6 - 2*a^2*c^8 - 3*b^2*c^8 + c^10) : :
X(61442) = 5 X[31282] - 4 X[34843]

X(61442) lies on the cubic K025 and these lines: {4, 12825}, {24, 135}, {30, 1299}, {136, 34756}, {403, 15478}, {5523, 47108}, {8882, 45179}, {11585, 13398}, {31282, 34843}, {34150, 47109}

X(61442) = reflection of X(i) in X(j) for these {i,j}: {24, 135}, {13398, 11585}
X(61442) = isogonal conjugate of X(54061)
X(61442) = antigonal image of X(24)
X(61442) = symgonal image of X(11585)
X(61442) = X(1)-isoconjugate of X(54061)
X(61442) = X(3)-Dao conjugate of X(54061)
X(61442) = cevapoint of X(403) and X(46443)
X(61442) = trilinear pole of line {6753, 40939}
X(61442) = barycentric product X(53953)*X(57065)
X(61442) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 54061}, {8745, 37951}, {52952, 20771}

X(61443) = CIRCUMCIRCLE-INVERSE OF X(5486)

Barycentrics    a^2*(a^4 - 4*a^2*b^2 + b^4 - c^4)*(a^4 - b^4 - 4*a^2*c^2 + c^4)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - a^4*c^2 + 9*a^2*b^2*c^2 - 4*b^4*c^2 - a^2*c^4 - 4*b^2*c^4 + c^6) : :

X(61443) lies on the cubic K039 and these lines: {3, 524}, {23, 39157}, {74, 352}, {186, 2770}, {187, 52234}, {378, 5913}, {511, 6096}, {1499, 34519}, {1995, 32133}, {2781, 40115}, {5621, 57466}, {5866, 56443}, {7464, 34320}, {13754, 40078}

X(61443) = circumcircle-inverse of X(5486)
X(61443) = barycentric product X(i)*X(j) for these {i,j}: {5486, 41617}, {13608, 52496}
X(61443) = barycentric quotient X(i)/X(j) for these {i,j}: {5486, 55973}, {41617, 11185}, {41618, 37855}

X(61444) = ISOGONAL CONJUGATE OF X(34171)

Barycentrics    a^2*(a^4 - 4*a^2*b^2 + b^4 + a^2*c^2 + b^2*c^2)*(a^4 + a^2*b^2 - 4*a^2*c^2 + b^2*c^2 + c^4)*(a^4*b^2 - b^6 + a^4*c^2 - 4*a^2*b^2*c^2 + 2*b^4*c^2 + 2*b^2*c^4 - c^6) : :

X(61444) lies on the cubic K039 and these lines: {3, 669}, {23, 44182}, {186, 2374}, {187, 5166}, {3455, 5866}, {7482, 31655}, {11634, 34169}

X(61444) = isogonal conjugate of X(34171)
X(61444) = isogonal conjugate of the anticomplement of X(47078)
X(61444) = X(i)-isoconjugate of X(j) for these (i,j): {1, 34171}, {36150, 47286}
X(61444) = X(3)-Dao conjugate of X(34171)
X(61444) = crossdifference of every pair of points on line {3291, 55271}
X(61444) = barycentric product X(i)*X(j) for these {i,j}: {2854, 41909}, {9177, 44182}, {34161, 46783}
X(61444) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 34171}, {2854, 47286}, {9177, 126}, {34161, 52501}, {52197, 14263}

X(61445) = CIRCUMCIRCLE-INVERSE OF X(1176)

Barycentrics    a^2*(a^2 + b^2)*(a^2 - b^2 - c^2)*(a^2 + c^2)*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 + a^4*b^2*c^2 - a^2*b^4*c^2 - a^2*b^2*c^4 + 2*b^4*c^4 + 2*a^2*c^6 - c^8) : :

X(61445) lies on the cubic K039 and these lines: {3, 1176}, {186, 827}, {251, 6032}, {858, 9076}, {1157, 40083}, {3005, 56917}, {3455, 60463}, {7386, 57480}, {9862, 46450}, {32581, 52295}, {39504, 58852}

X(61445) = circumcircle-inverse of X(1176)
X(61445) = symgonal image of X(22473)
X(61445) = X(9076)-Ceva conjugate of X(1176)

X(61446) = CIRCUMCIRCLE-INVERSE OF X(35364)

Barycentrics    a^2*(a^4 - a^2*b^2 + 2*b^4 - 2*a^2*c^2 - b^2*c^2 + c^4)*(a^4 - 2*a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + 2*c^4)*(2*a^6 - 2*a^4*b^2 + a^2*b^4 - b^6 - 2*a^4*c^2 + b^4*c^2 + a^2*c^4 + b^2*c^4 - c^6) : :
X(61446) = 3 X[2065] - X[2987]

X(61446) lies on the cubic K039 and these lines: {3, 512}, {74, 5866}, {186, 691}, {187, 5961}, {376, 36891}, {511, 1976}, {842, 52515}, {3098, 52091}, {3455, 13754}, {4226, 34175}, {7473, 16188}, {7809, 8781}, {15478, 54060}, {18876, 54061}, {35142, 35474}, {40428, 54086}, {46264, 56572}, {51456, 55142}

X(61446) = isogonal conjugate of X(34174)
X(61446) = circumcircle-inverse of X(35364)
X(61446) = isogonal conjugate of the anticomplement of X(47082)
X(61446) = X(i)-isoconjugate of X(j) for these (i,j): {1, 34174}, {842, 1733}, {5641, 8772}
X(61446) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 34174}, {23967, 51481}, {42426, 44145}
X(61446) = crossdifference of every pair of points on line {230, 55267}
X(61446) = barycentric product X(i)*X(j) for these {i,j}: {542, 2987}, {1640, 10425}, {2247, 8773}, {5191, 8781}, {6103, 43705}, {14999, 35364}, {34157, 46786}, {34369, 52091}, {36891, 48451}, {42065, 60502}, {51474, 52515}
X(61446) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 34174}, {542, 51481}, {2247, 1733}, {2987, 5641}, {5191, 230}, {6041, 55122}, {6103, 44145}, {10425, 6035}, {32654, 842}, {34157, 46787}, {34369, 14265}, {35364, 14223}, {48451, 36875}

X(61447) = ISOGONAL CONJUGATE OF X(47104)

Barycentrics    a^2*(a^3 - a^2*b - a*b^2 + b^3 - 2*a*b*c + a*c^2 + b*c^2)*(a^3 + a*b^2 - a^2*c - 2*a*b*c + b^2*c - a*c^2 + c^3)*(a^4*b - b^5 + a^4*c - 2*a^3*b*c - a^2*b^2*c + a*b^3*c + b^4*c - a^2*b*c^2 + a*b*c^3 + b*c^4 - c^5) : :

X(61447) lies on the cubic K039 and these lines: {3, 667}, {186, 2691}, {3286, 15382}, {3455, 51632}, {4236, 34173}, {5172, 6091}, {5866, 34442}

X(61447) = isogonal conjugate of X(47104)
X(61447) = isogonal conjugate of the anticomplement of X(47083)
X(61447) = X(i)-isoconjugate of X(j) for these (i,j): {1, 47104}, {1738, 2752}
X(61447) = X(3)-Dao conjugate of X(47104)
X(61447) = barycentric product X(i)*X(j) for these {i,j}: {2836, 2991}, {34159, 46784}
X(61447) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 47104}, {34159, 52502}

X(61448) = ISOGONAL CONJUGATE OF X(52447)

Barycentrics    a^2*(a^4 - 2*a^2*b^2 + b^4 + 4*a^2*c^2 + 4*b^2*c^2 - 5*c^4)*(a^4 + 4*a^2*b^2 - 5*b^4 - 2*a^2*c^2 + 4*b^2*c^2 + c^4)*(4*a^6 - 7*a^4*b^2 + 2*a^2*b^4 + b^6 - 7*a^4*c^2 + 6*a^2*b^2*c^2 - b^4*c^2 + 2*a^2*c^4 - b^2*c^4 + c^6) : :
X(61448) = 3 X[186] + X[841], 3 X[376] + X[47103], X[9060] - 5 X[37952]

X(61448) lies on the cubic K039 and these lines: {3, 1495}, {186, 841}, {187, 32663}, {376, 47103}, {574, 51990}, {3515, 58082}, {5866, 15469}, {6091, 39986}, {9060, 37952}, {10295, 46436}, {37460, 52452}

X(61448) = midpoint of X(10295) and X(46436)
X(61448) = isogonal conjugate of X(52447)
X(61448) = circumcircle-inverse of X(3426)
X(61448) = X(1)-isoconjugate of X(52447)
X(61448) = X(3)-Dao conjugate of X(52447)
X(61448) = barycentric product X(i)*X(j) for these {i,j}: {3426, 40112}, {36889, 58267}
X(61448) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 52447}, {3426, 58268}, {10295, 52147}, {40112, 44133}, {51990, 34802}, {58267, 376}

X(61449) = CIRCUMCIRCLE-INVERSE OF X(55977)

Barycentrics    a^2*(a^2 + b^2 - 5*c^2)*(a^2 - b^2 - c^2)*(a^2 - 5*b^2 + c^2)*(6*a^8 - 7*a^6*b^2 - 5*a^4*b^4 + 7*a^2*b^6 - b^8 - 7*a^6*c^2 + 26*a^4*b^2*c^2 - 11*a^2*b^4*c^2 - 5*a^4*c^4 - 11*a^2*b^2*c^4 + 2*b^4*c^4 + 7*a^2*c^6 - c^8) : :

X(61449) lies on the cubic K039 and these lines: {3, 8681}, {186, 1296}, {8644, 20186}, {19708, 47074}, {32127, 47412}, {38951, 54995}, {52496, 53961}

X(61449) = circumcircle-inverse of X(55977)

X(61450) = CIRCUMCIRCLE-INVERSE OF X(10097)

Barycentrics    a^2*(a^2 + b^2 - 2*c^2)*(a^2 - b^2 - c^2)*(a^2 - 2*b^2 + c^2)*(2*a^8 - 2*a^6*b^2 - a^4*b^4 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 + 4*a^4*b^2*c^2 - 2*a^2*b^4*c^2 - a^4*c^4 - 2*a^2*b^2*c^4 + 2*b^4*c^4 + 2*a^2*c^6 - c^8) : :

X(61450) lies on the cubic K039 and these lines: {3, 647}, {74, 352}, {111, 186}, {187, 2393}, {230, 36180}, {2489, 50381}, {5866, 10766}, {6091, 14909}, {10316, 51253}, {14580, 19330}, {15013, 30786}, {34169, 36166}, {46783, 53929}

X(61450) = circumcircle-inverse of X(10097)
X(61450) = crossdifference of every pair of points on line {468, 18311}
X(61450) = barycentric quotient X(14908)/X(53929)

X(61451) = CIRCUMCIRCLE-INVERSE OF X(34437)

Barycentrics    a^2*(b^2 + c^2)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 + a^4*c^2 + a^2*b^2*c^2 + b^4*c^2 - a^2*c^4 - b^2*c^4 - c^6)*(a^6 + a^4*b^2 - a^2*b^4 - b^6 - a^4*c^2 + a^2*b^2*c^2 - b^4*c^2 - a^2*c^4 + b^2*c^4 + c^6) : :

X(61451) lies on the cubics K039 and K939 and these lines: {3, 34437}, {186, 29011}, {305, 1369}, {427, 46654}, {827, 15246}, {1157, 40079}, {3933, 61219}, {5189, 52445}, {12011, 40083}, {34418, 40080}

X(61451) = isogonal conjugate of X(38946)
X(61451) = circumcircle-inverse of X(34437)
X(61451) = X(i)-isoconjugate of X(j) for these (i,j): {1, 38946}, {82, 5189}, {83, 16546}, {251, 20916}, {3112, 19596}, {18627, 56245}, {21064, 52376}, {37221, 40583}
X(61451) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 38946}, {141, 5189}, {34452, 19596}, {40585, 20916}
X(61451) = barycentric product X(i)*X(j) for these {i,j}: {39, 54459}, {141, 34437}
X(61451) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 38946}, {38, 20916}, {39, 5189}, {1401, 18627}, {1964, 16546}, {3051, 19596}, {20775, 22121}, {21035, 21064}, {21123, 21176}, {34437, 83}, {41272, 8877}, {54459, 308}

X(61452) = CIRCUMCIRCLE-INVERSE OF X(5505)

Barycentrics    a^2*(5*a^2 - b^2 - c^2)*(a^6 - 4*a^4*b^2 - a^2*b^4 + 4*b^6 - a^4*c^2 + 6*a^2*b^2*c^2 - b^4*c^2 - a^2*c^4 - 4*b^2*c^4 + c^6)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - 4*a^4*c^2 + 6*a^2*b^2*c^2 - 4*b^4*c^2 - a^2*c^4 - b^2*c^4 + 4*c^6) : :

X(61452) lies on the cubic K039 and these lines: {3, 2854}, {111, 186}, {1296, 7492}, {4232, 5512}, {5961, 40078}, {10304, 14360}, {23699, 35485}

X(61452) = isogonal conjugate of X(38951)
X(61452) = circumcircle-inverse of X(5505)
X(61452) = X(i)-isoconjugate of X(j) for these (i,j): {1, 38951}, {7426, 55923}
X(61452) = X(3)-Dao conjugate of X(38951)
X(61452) = barycentric product X(1992)*X(5505)
X(61452) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 38951}, {1384, 7426}, {5505, 5485}

X(61453) = ISOGONAL CONJUGATE OF X(47106)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^3 + a^2*b + a*b^2 + b^3 - a^2*c - a*b*c - b^2*c - a*c^2 - b*c^2 + c^3)*(a^3 - a^2*b - a*b^2 + b^3 + a^2*c - a*b*c - b^2*c + a*c^2 - b*c^2 + c^3)*(a^3 - a^2*b - a*b^2 + b^3 - a^2*c - 2*a*b*c + b^2*c - a*c^2 + b*c^2 + c^3) : :

X(61453) lies on the cubic K039 and these lines: {3, 18210}, {186, 915}, {906, 18591}, {2164, 16553}, {2218, 2915}, {3455, 40084}, {3651, 5840}, {5172, 18593}, {5521, 30733}, {13397, 21907}, {34430, 36152}

X(61453) = isogonal conjugate of X(47106)
X(61453) = X(i)-isoconjugate of X(j) for these (i,j): {1, 47106}, {2074, 23604}, {32849, 46886}, {37799, 39943}
X(61453) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 47106}, {219, 32849}
X(61453) = barycentric product X(i)*X(j) for these {i,j}: {3173, 11604}, {11517, 21907}
X(61453) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 47106}, {2911, 56877}, {11517, 32849}, {37579, 37799}, {41332, 2074}, {41608, 37783}

X(61454) = X(3)X(14417)∩X(186)X(2770)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^6 - 2*a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 - a^2*c^4 - b^2*c^4)*(a^4*b^2 - b^6 + a^4*c^2 - 2*a^2*b^2*c^2 + b^4*c^2 + b^2*c^4 - c^6)*(a^6 - a^2*b^4 - 2*a^4*c^2 + 4*a^2*b^2*c^2 - b^4*c^2 - 2*a^2*c^4 + c^6) : :

X(61454) lies on the cubic K039 and these lines: {3, 14417}, {186, 2770}, {187, 1576}, {1560, 46592}, {2373, 52501}, {5866, 54060}, {6091, 18876}, {7418, 23699}, {34158, 42665}

X(61454) = X(37220)-isoconjugate of X(44467)
X(61454) = barycentric product X(i)*X(j) for these {i,j}: {2770, 14961}, {34158, 52501}
X(61454) = barycentric quotient X(i)/X(j) for these {i,j}: {32741, 60133}, {34158, 46783}, {51962, 52490}

X(61455) = X(186)X(2752)∩X(187)X(1415)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^5 - a^4*b - a*b^4 + b^5 - a^3*b*c - a*b^3*c + a^2*b*c^2 + a*b^2*c^2 + 2*a*b*c^3 - a*c^4 - b*c^4)*(a^4*b - b^5 + a^4*c - 2*a^3*b*c + b^4*c + b*c^4 - c^5)*(a^5 - a*b^4 - a^4*c - a^3*b*c + a^2*b^2*c + 2*a*b^3*c - b^4*c + a*b^2*c^2 - a*b*c^3 - a*c^4 + c^5) : :

X(61455) lies on the cubic K039 and these lines: {186, 2752}, {187, 1415}, {3455, 34442}, {4244, 20621}, {7425, 47104}, {26703, 52502}, {51632, 54060}

X(61455) = barycentric product X(34160)*X(52502)
X(61455) = barycentric quotient X(34160)/X(46784)

X(61456) = CIRCUMCIRCLE-INVERSE OF X(34207)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 + a^4*c^2 + 2*a^2*b^2*c^2 + b^4*c^2 - a^2*c^4 - b^2*c^4 - c^6)*(a^4*b^2 - b^6 + a^4*c^2 - 2*a^2*b^2*c^2 + b^4*c^2 + b^2*c^4 - c^6)*(a^6 + a^4*b^2 - a^2*b^4 - b^6 - a^4*c^2 + 2*a^2*b^2*c^2 - b^4*c^2 - a^2*c^4 + b^2*c^4 + c^6) : :

X(61456) lies on the cubic K039 and these lines: {3, 206}, {69, 34237}, {186, 39417}, {3053, 46769}, {3265, 8673}, {3546, 52583}, {6720, 10257}, {7386, 13575}, {7485, 40358}, {10316, 60840}, {11574, 39129}, {15478, 40079}, {40080, 54061}

X(61456) = circumcircle-inverse of X(34207)
X(61456) = X(i)-isoconjugate of X(j) for these (i,j): {3162, 37220}, {18596, 60133}, {36095, 47125}
X(61456) = X(i)-Dao conjugate of X(j) for these (i,j): {5181, 1370}, {61067, 41361}
X(61456) = crossdifference of every pair of points on line {3162, 47125}
X(61456) = barycentric product X(i)*X(j) for these {i,j}: {858, 52041}, {13575, 14961}, {39172, 52512}
X(61456) = barycentric quotient X(i)/X(j) for these {i,j}: {2393, 41361}, {14580, 41766}, {14961, 1370}, {34207, 60133}, {39172, 52513}, {42665, 47125}, {52041, 2373}
X(61456) = {X(3),X(52041)}-harmonic conjugate of X(39172)

X(61457) = X(3)X(32285)∩X(186)X(40120)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - a^4*c^2 + 8*a^2*b^2*c^2 - 3*b^4*c^2 - a^2*c^4 - 3*b^2*c^4 + c^6)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - 2*a^4*c^2 + 5*a^2*b^2*c^2 - b^4*c^2 - 2*a^2*c^4 - b^2*c^4 + c^6)*(a^6 - 2*a^4*b^2 - 2*a^2*b^4 + b^6 - a^4*c^2 + 5*a^2*b^2*c^2 - b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6) : :

X(61457) lies on the cubic K039 and these lines: {3, 32285}, {186, 40120}, {9909, 40324}, {18876, 40078}, {21312, 41521}, {34866, 40347}, {40082, 40083}

X(61457) = barycentric quotient X(i)/X(j) for these {i,j}: {40320, 37777}, {41619, 37784}

X(61458) = CIRCUMCIRCLE-INVERSE OF X(34802)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(3*a^6 - 5*a^4*b^2 + a^2*b^4 + b^6 - 5*a^4*c^2 + 2*a^2*b^2*c^2 - b^4*c^2 + a^2*c^4 - b^2*c^4 + c^6)*(a^6 + 2*a^4*b^2 - 7*a^2*b^4 + 4*b^6 - a^4*c^2 + 6*a^2*b^2*c^2 - 7*b^4*c^2 - a^2*c^4 + 2*b^2*c^4 + c^6)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 + 2*a^4*c^2 + 6*a^2*b^2*c^2 + 2*b^4*c^2 - 7*a^2*c^4 - 7*b^2*c^4 + 4*c^6) : :

X(61458) lies on the cubic K039 and these lines: {2, 52447}, {3, 15738}, {186, 9060}, {187, 14910}, {3455, 15469}, {6091, 40047}, {10298, 53958}, {18533, 53993}

X(61458) = circumcircle-inverse of X(34802)
X(61458) = barycentric product X(i)*X(j) for these {i,j}: {34802, 37645}, {47391, 58268}
X(61458) = barycentric quotient X(i)/X(j) for these {i,j}: {34802, 60256}, {47391, 40112}

X(61459) = CIRCUMCIRCLE-INVERSE OF X(10293)

Barycentrics    a^2*(a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + 4*b^2*c^2 + c^4)*(a^8 + 3*a^6*b^2 - 8*a^4*b^4 + 3*a^2*b^6 + b^8 - 2*a^6*c^2 + 6*a^4*b^2*c^2 + 6*a^2*b^4*c^2 - 2*b^6*c^2 - 11*a^2*b^2*c^4 + 2*a^2*c^6 + 2*b^2*c^6 - c^8)*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 + 3*a^6*c^2 + 6*a^4*b^2*c^2 - 11*a^2*b^4*c^2 + 2*b^6*c^2 - 8*a^4*c^4 + 6*a^2*b^2*c^4 + 3*a^2*c^6 - 2*b^2*c^6 + c^8) : :

X(61459) lies on the cubic K039 and these lines: {3, 541}, {186, 43660}, {187, 18877}, {378, 53832}, {5866, 39986}, {6091, 15469}, {7464, 52447}

X(61459) = isogonal conjugate of X(47103)
X(61459) = circumcircle-inverse of X(10293)
X(61459) = X(1)-isoconjugate of X(47103)
X(61459) = X(3)-Dao conjugate of X(47103)
X(61459) = barycentric product X(10293)*X(15066)
X(61459) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 47103}, {5063, 7464}, {10293, 34289}, {52438, 40114}

X(61460) = CIRCUMCIRCLE-INVERSE OF X(10099)

Barycentrics    a^2*(a^2 + b^2 - a*c - b*c)*(a^2 - b^2 - c^2)*(a^2 - a*b - b*c + c^2)*(a^7*b - a^6*b^2 - a^5*b^3 + a^4*b^4 - a^3*b^5 + a^2*b^6 + a*b^7 - b^8 + a^7*c - a^3*b^4*c - a^6*c^2 + 2*a^3*b^3*c^2 - a^2*b^4*c^2 - a^5*c^3 + 2*a^3*b^2*c^3 - a*b^4*c^3 + a^4*c^4 - a^3*b*c^4 - a^2*b^2*c^4 - a*b^3*c^4 + 2*b^4*c^4 - a^3*c^5 + a^2*c^6 + a*c^7 - c^8) : :

X(61460) lies on the cubic K039 and these lines: {3, 905}, {74, 35185}, {105, 186}, {187, 32658}, {2223, 3827}, {3455, 5172}, {18876, 51632}, {34173, 50402}, {46784, 53964}

X(61460) = circumcircle-inverse of X(10099)
X(61460) = X(1861)-isoconjugate of X(53964)
X(61460) = barycentric quotient X(32658)/X(53964)

X(61461) = CIRCUMCIRCLE-INVERSE OF X(4846)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^4 + 4*a^2*b^2 + b^4 - 2*a^2*c^2 - 2*b^2*c^2 + c^4)*(a^4 - 2*a^2*b^2 + b^4 + 4*a^2*c^2 - 2*b^2*c^2 + c^4)*(a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - 3*a^8*c^2 + 7*a^6*b^2*c^2 - 3*a^4*b^4*c^2 - 3*a^2*b^6*c^2 + 2*b^8*c^2 + 2*a^6*c^4 - 3*a^4*b^2*c^4 + 8*a^2*b^4*c^4 - 3*b^6*c^4 + 2*a^4*c^6 - 3*a^2*b^2*c^6 - 3*b^4*c^6 - 3*a^2*c^8 + 2*b^2*c^8 + c^10) : :

X(61461) lies on the cubic K039 and these lines: {3, 4549}, {23, 47103}, {26, 59429}, {186, 1302}, {187, 15469}, {1609, 52165}, {3455, 39986}, {5866, 40047}, {7488, 39263}, {32110, 32738}, {37940, 56709}

X(61461) = circumcircle-inverse of X(4846)
X(61461) = barycentric product X(15136)*X(34289)
X(61461) = barycentric quotient X(15136)/X(15066)

X(61462) = CIRCUMCIRCLE-INVERSE OF X(14380)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^4 - 2*a^2*b^2 + b^4 + a^2*c^2 + b^2*c^2 - 2*c^4)*(a^4 + a^2*b^2 - 2*b^4 - 2*a^2*c^2 + b^2*c^2 + c^4)*(2*a^10 - 2*a^8*b^2 - 5*a^6*b^4 + 7*a^4*b^6 - a^2*b^8 - b^10 - 2*a^8*c^2 + 12*a^6*b^2*c^2 - 7*a^4*b^4*c^2 - 6*a^2*b^6*c^2 + 3*b^8*c^2 - 5*a^6*c^4 - 7*a^4*b^2*c^4 + 14*a^2*b^4*c^4 - 2*b^6*c^4 + 7*a^4*c^6 - 6*a^2*b^2*c^6 - 2*b^4*c^6 - a^2*c^8 + 3*b^2*c^8 - c^10) : :
X(61462) = X[110] - 3 X[38719], X[2693] - 3 X[15055], X[7728] - 3 X[57336], 3 X[14644] - X[44992], 3 X[15041] + X[38595], 5 X[38728] - 3 X[57344]

X(61462) lies on the cubic K039 and these lines: {3, 520}, {74, 186}, {110, 38719}, {113, 40557}, {125, 34150}, {185, 14385}, {187, 18877}, {523, 53716}, {1157, 46090}, {1204, 14264}, {1552, 2777}, {2071, 36831}, {2693, 15055}, {3269, 48451}, {3357, 52646}, {5663, 38625}, {5961, 11589}, {6699, 16177}, {6760, 44715}, {7728, 57336}, {8779, 32640}, {9717, 10605}, {11204, 57488}, {11438, 35908}, {12096, 13754}, {13851, 14989}, {14644, 44992}, {15041, 38595}, {15404, 51394}, {17986, 20417}, {18808, 59291}, {18931, 36875}, {26937, 56686}, {32112, 53719}, {38728, 57344}, {46632, 55141}

X(61462) = midpoint of X(i) and X(j) for these {i,j}: {74, 1304}, {13289, 13997}
X(61462) = reflection of X(i) in X(j) for these {i,j}: {113, 40557}, {16177, 6699}
X(61462) = isogonal conjugate of X(47111)
X(61462) = circumcircle-inverse of X(14380)
X(61462) = isogonal conjugate of the anticomplement of X(47087)
X(61462) = X(i)-isoconjugate of X(j) for these (i,j): {1, 47111}, {162, 53159}, {1784, 2693}
X(61462) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 47111}, {125, 53159}
X(61462) = crossdifference of every pair of points on line {1990, 14401}
X(61462) = barycentric product X(i)*X(j) for these {i,j}: {394, 1552}, {2777, 14919}, {12113, 40384}, {46788, 51475}
X(61462) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 47111}, {647, 53159}, {1552, 2052}, {2777, 46106}, {7740, 14920}, {12113, 36789}, {18877, 2693}, {51475, 46789}

X(61463) = CIRCUMCIRCLE-INVERSE OF X(3657)

Barycentrics    a^2*(a^4 - 2*a^2*b^2 + b^4 - a^3*c + a^2*b*c + a*b^2*c - b^3*c - a^2*c^2 - b^2*c^2 + a*c^3 + b*c^3)*(a^4 - a^3*b - a^2*b^2 + a*b^3 + a^2*b*c + b^3*c - 2*a^2*c^2 + a*b*c^2 - b^2*c^2 - b*c^3 + c^4)*(a^5*b - a^4*b^2 - 2*a^3*b^3 + 2*a^2*b^4 + a*b^5 - b^6 + a^5*c + a^3*b^2*c - 2*a*b^4*c - a^4*c^2 + a^3*b*c^2 - 2*a^2*b^2*c^2 + a*b^3*c^2 + b^4*c^2 - 2*a^3*c^3 + a*b^2*c^3 + 2*a^2*c^4 - 2*a*b*c^4 + b^2*c^4 + a*c^5 - c^6) : :

X(61463) lies on the cubic K039 and these lines: {3, 513}, {74, 6099}, {186, 915}, {187, 32655}, {3658, 38952}, {5172, 5961}, {13754, 34442}, {37966, 42422}, {45393, 48698}

X(61463) = isogonal conjugate of X(39991)
X(61463) = circumcircle-inverse of X(3657)
X(61463) = isogonal conjugate of the anticomplement of X(47086)
X(61463) = X(i)-isoconjugate of X(j) for these (i,j): {1, 39991}, {1737, 2687}, {14224, 61231}
X(61463) = X(3)-Dao conjugate of X(39991)
X(61463) = barycentric product X(i)*X(j) for these {i,j}: {2771, 2990}, {39173, 52499}
X(61463) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 39991}, {2771, 48380}, {2990, 46141}, {32655, 2687}, {61214, 14224}

X(61464) = CIRCUMCIRCLE-INVERSE OF X(2435)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 + a^2*c^4 + b^2*c^4 - 2*c^6)*(a^6 + a^2*b^4 - 2*b^6 - a^4*c^2 + b^4*c^2 - a^2*c^4 + c^6)*(2*a^12 - 2*a^10*b^2 - 3*a^8*b^4 + 2*a^6*b^6 + 2*a^4*b^8 - b^12 - 2*a^10*c^2 + 8*a^8*b^2*c^2 - 2*a^6*b^4*c^2 - 2*a^4*b^6*c^2 - 4*a^2*b^8*c^2 + 2*b^10*c^2 - 3*a^8*c^4 - 2*a^6*b^2*c^4 + 4*a^2*b^6*c^4 + b^8*c^4 + 2*a^6*c^6 - 2*a^4*b^2*c^6 + 4*a^2*b^4*c^6 - 4*b^6*c^6 + 2*a^4*c^8 - 4*a^2*b^2*c^8 + b^4*c^8 + 2*b^2*c^10 - c^12) : :

X(61464) lies on the cubic K039 and these lines: {3, 2435}, {74, 46967}, {186, 1297}, {187, 40082}, {3455, 11589}, {34146, 42671}, {54086, 57761}

X(61464) = circumcircle-inverse of X(2435)
X(61464) = barycentric quotient X(36201)/X(60516)

X(61465) = CIRCUMCIRCLE-INVERSE OF X(43709)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(2*a^8 - 2*a^6*b^2 - a^4*b^4 + b^8 - 2*a^6*c^2 + 4*a^4*b^2*c^2 - 4*b^6*c^2 - a^4*c^4 + 6*b^4*c^4 - 4*b^2*c^6 + c^8)*(a^8 - a^6*b^2 + a^4*b^4 - 3*a^2*b^6 + 2*b^8 - 4*a^6*c^2 + a^4*b^2*c^2 + 2*a^2*b^4*c^2 - 3*b^6*c^2 + 6*a^4*c^4 + a^2*b^2*c^4 + b^4*c^4 - 4*a^2*c^6 - b^2*c^6 + c^8)*(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8 - a^6*c^2 + a^4*b^2*c^2 + a^2*b^4*c^2 - b^6*c^2 + a^4*c^4 + 2*a^2*b^2*c^4 + b^4*c^4 - 3*a^2*c^6 - 3*b^2*c^6 + 2*c^8) : :

X(61465) lies on the cubic K039 and these lines: {3, 924}, {74, 46969}, {186, 1299}, {3581, 13557}, {5961, 13754}, {7471, 42424}, {14222, 53788}
on K039

X(61465) = circumcircle-inverse of X(43709)
X(61465) = barycentric product X(17702)*X(43756)

X(61466) = X(3)X(3566)∩X(186)X(40120)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8 - a^6*c^2 + 3*a^4*b^2*c^2 + 3*a^2*b^4*c^2 - b^6*c^2 - a^4*c^4 - 4*a^2*b^2*c^4 - b^4*c^4 + a^2*c^6 + b^2*c^6)*(a^6*b^2 - a^4*b^4 - a^2*b^6 + b^8 + a^6*c^2 - 2*a^4*b^2*c^2 + 2*a^2*b^4*c^2 - 3*b^6*c^2 - a^4*c^4 + 2*a^2*b^2*c^4 + 4*b^4*c^4 - a^2*c^6 - 3*b^2*c^6 + c^8)*(a^8 - a^6*b^2 - a^4*b^4 + a^2*b^6 - 4*a^6*c^2 + 3*a^4*b^2*c^2 - 4*a^2*b^4*c^2 + b^6*c^2 + 6*a^4*c^4 + 3*a^2*b^2*c^4 - b^4*c^4 - 4*a^2*c^6 - b^2*c^6 + c^8) : :

X(61466) lies on the cubic K039 and these lines: {3, 3566}, {186, 40120}, {187, 15478}, {3455, 54061}, {5866, 5961}, {6091, 13754}, {19128, 35296}

X(61466) = barycentric product X(14984)*X(56006)

X(61467) = CIRCUMCIRCLE-INVERSE OF X(14220)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^8 + a^6*b^2 - 4*a^4*b^4 + a^2*b^6 + b^8 - 3*a^6*c^2 + 2*a^4*b^2*c^2 + 2*a^2*b^4*c^2 - 3*b^6*c^2 + 3*a^4*c^4 - 2*a^2*b^2*c^4 + 3*b^4*c^4 - a^2*c^6 - b^2*c^6)*(a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8 + a^6*c^2 + 4*a^4*b^2*c^2 - 3*a^2*b^4*c^2 - 2*b^6*c^2 - 3*a^4*c^4 - 3*a^2*b^2*c^4 + 6*b^4*c^4 + 3*a^2*c^6 - 2*b^2*c^6 - c^8)*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6 + a^6*c^2 + 2*a^4*b^2*c^2 - 2*a^2*b^4*c^2 - b^6*c^2 - 4*a^4*c^4 + 2*a^2*b^2*c^4 + 3*b^4*c^4 + a^2*c^6 - 3*b^2*c^6 + c^8) : :

X(61467) lies on the cubic K039 and these lines: {3, 9033}, {74, 16186}, {107, 186}, {133, 46587}, {187, 32663}, {1294, 46789}, {2777, 39985}, {5961, 40082}, {6086, 53178}, {7480, 47111}, {11589, 13754}, {51895, 55127}

X(61467) = circumcircle-inverse of X(14220)
X(61467) = X(1294)-isoconjugate of X(36063)
X(61467) = barycentric product X(i)*X(j) for these {i,j}: {477, 44436}, {39174, 46789}
X(61467) = barycentric quotient X(i)/X(j) for these {i,j}: {32663, 1294}, {39174, 46788}, {44436, 35520}, {47433, 11251}, {51964, 52493}

X(61468) = X(3)X(521)∩X(104)X(186)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^3 - a^2*b - a*b^2 + b^3 + 2*a*b*c - a*c^2 - b*c^2)*(a^3 - a*b^2 - a^2*c + 2*a*b*c - b^2*c - a*c^2 + c^3)*(a^8*b - 2*a^6*b^3 + 2*a^2*b^7 - b^9 + a^8*c - 2*a^7*b*c + a^6*b^2*c + a^5*b^3*c - 4*a^4*b^4*c + 4*a^3*b^5*c + a^2*b^6*c - 3*a*b^7*c + b^8*c + a^6*b*c^2 + 4*a^4*b^3*c^2 - 7*a^2*b^5*c^2 + 2*b^7*c^2 - 2*a^6*c^3 + a^5*b*c^3 + 4*a^4*b^2*c^3 - 8*a^3*b^3*c^3 + 4*a^2*b^4*c^3 + 3*a*b^5*c^3 - 2*b^6*c^3 - 4*a^4*b*c^4 + 4*a^2*b^3*c^4 + 4*a^3*b*c^5 - 7*a^2*b^2*c^5 + 3*a*b^3*c^5 + a^2*b*c^6 - 2*b^3*c^6 + 2*a^2*c^7 - 3*a*b*c^7 + 2*b^2*c^7 + b*c^8 - c^9) : :

X(61468) lies on the cubic K039 and these lines: {3, 521}, {74, 2720}, {104, 186}, {187, 14578}, {2694, 52499}, {6001, 53252}, {40082, 51632}

X(61468) = X(1785)-isoconjugate of X(2694)
X(61468) = barycentric quotient X(14578)/X(2694)

X(61469) = CIRCUMCIRCLE-INVERSE OF X(34801)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^6 + a^4*b^2 - 5*a^2*b^4 + 3*b^6 - a^4*c^2 + 2*a^2*b^2*c^2 - 5*b^4*c^2 - a^2*c^4 + b^2*c^4 + c^6)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 + a^4*c^2 + 2*a^2*b^2*c^2 + b^4*c^2 - 5*a^2*c^4 - 5*b^2*c^4 + 3*c^6)*(2*a^12 - 5*a^10*b^2 + a^8*b^4 + 6*a^6*b^6 - 4*a^4*b^8 - a^2*b^10 + b^12 - 5*a^10*c^2 + 14*a^8*b^2*c^2 - 14*a^6*b^4*c^2 + 4*a^4*b^6*c^2 + 3*a^2*b^8*c^2 - 2*b^10*c^2 + a^8*c^4 - 14*a^6*b^2*c^4 + 8*a^4*b^4*c^4 - 2*a^2*b^6*c^4 - b^8*c^4 + 6*a^6*c^6 + 4*a^4*b^2*c^6 - 2*a^2*b^4*c^6 + 4*b^6*c^6 - 4*a^4*c^8 + 3*a^2*b^2*c^8 - b^4*c^8 - a^2*c^10 - 2*b^2*c^10 + c^12) : :

X(61469) lies on the cubic K039 and these lines: {3, 10938}, {186, 53958}, {187, 40047}, {3546, 59430}, {10257, 53832}, {15469, 54060}, {17928, 58081}, {18876, 39986}

X(61469) = circumcircle-inverse of X(34801)

X(61470) = ISOGONAL CONJUGATE OF X(47108)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(2*a^4 - a^2*b^2 + b^4 - a^2*c^2 - 2*b^2*c^2 + c^4)*(a^10 - 3*a^8*b^2 + 3*a^6*b^4 + a^4*b^6 - 4*a^2*b^8 + 2*b^10 - 3*a^8*c^2 + 8*a^6*b^2*c^2 - 5*a^4*b^4*c^2 + 8*a^2*b^6*c^2 - 4*b^8*c^2 + 2*a^6*c^4 - 10*a^4*b^2*c^4 - 5*a^2*b^4*c^4 + b^6*c^4 + 2*a^4*c^6 + 8*a^2*b^2*c^6 + 3*b^4*c^6 - 3*a^2*c^8 - 3*b^2*c^8 + c^10)*(a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - 3*a^8*c^2 + 8*a^6*b^2*c^2 - 10*a^4*b^4*c^2 + 8*a^2*b^6*c^2 - 3*b^8*c^2 + 3*a^6*c^4 - 5*a^4*b^2*c^4 - 5*a^2*b^4*c^4 + 3*b^6*c^4 + a^4*c^6 + 8*a^2*b^2*c^6 + b^4*c^6 - 4*a^2*c^8 - 4*b^2*c^8 + 2*c^10) : :

X(61470) lies on the cubic K039 and these lines: {3, 6132}, {186, 3565}, {187, 54061}, {3455, 15478}, {4226, 31842}, {5866, 13754}, {5961, 6091}

X(61470) = isogonal conjugate of X(47108)
X(61470) = X(1)-isoconjugate of X(47108)
X(61470) = X(3)-Dao conjugate of X(47108)
X(61470) = barycentric quotient X(6)/X(47108)

X(61471) = X(3)X(44809)∩X(74)X(12011)

Barycentrics    a^2*(a^2 - b^2 - b*c - c^2)*(a^2 - b^2 + b*c - c^2)*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)*(a^12 - 4*a^10*b^2 + 7*a^8*b^4 - 8*a^6*b^6 + 7*a^4*b^8 - 4*a^2*b^10 + b^12 - 3*a^10*c^2 + 8*a^8*b^2*c^2 - 5*a^6*b^4*c^2 - 5*a^4*b^6*c^2 + 8*a^2*b^8*c^2 - 3*b^10*c^2 + 2*a^8*c^4 - 6*a^6*b^2*c^4 + 2*a^4*b^4*c^4 - 6*a^2*b^6*c^4 + 2*b^8*c^4 + 2*a^6*c^6 + 5*a^4*b^2*c^6 + 5*a^2*b^4*c^6 + 2*b^6*c^6 - 3*a^4*c^8 - 4*a^2*b^2*c^8 - 3*b^4*c^8 + a^2*c^10 + b^2*c^10)*(a^12 - 3*a^10*b^2 + 2*a^8*b^4 + 2*a^6*b^6 - 3*a^4*b^8 + a^2*b^10 - 4*a^10*c^2 + 8*a^8*b^2*c^2 - 6*a^6*b^4*c^2 + 5*a^4*b^6*c^2 - 4*a^2*b^8*c^2 + b^10*c^2 + 7*a^8*c^4 - 5*a^6*b^2*c^4 + 2*a^4*b^4*c^4 + 5*a^2*b^6*c^4 - 3*b^8*c^4 - 8*a^6*c^6 - 5*a^4*b^2*c^6 - 6*a^2*b^4*c^6 + 2*b^6*c^6 + 7*a^4*c^8 + 8*a^2*b^2*c^8 + 2*b^4*c^8 - 4*a^2*c^10 - 3*b^2*c^10 + c^12) : :

X(61471) lies on the cubic K039 and these lines: {3, 44809}, {74, 12011}, {186, 930}, {1157, 13754}, {2914, 52603}, {5961, 34418}, {14072, 23181}

X(61472) = X(13)X(5466)∩X(14)X(530)

Barycentrics    (a^2 - 2*b^2 + c^2)*(-a^2 - b^2 + 2*c^2)*((2*a^2 - b^2 - c^2)*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4) - 2*Sqrt[3]*(b^2 - c^2)^2*S) : :

X(61472) lies on the cubic K061a and these lines: {13, 5466}, {14, 530}, {15, 52748}, {30, 17964}, {111, 6108}, {531, 17948}, {533, 892}, {691, 11586}, {3642, 52756}, {5979, 31125}, {6109, 16092}, {6110, 17983}, {6772, 14995}, {9214, 10654}, {10653, 52450}, {11626, 53807}, {16241, 52750}, {31709, 34169}, {37834, 52747}, {37835, 52751}, {41022, 48983}

X(61473) = X(13)X(2394)∩X(14)X(471)

Barycentrics    (a^4 - 2*a^2*b^2 + b^4 + a^2*c^2 + b^2*c^2 - 2*c^4)*(a^4 + a^2*b^2 - 2*b^4 - 2*a^2*c^2 + b^2*c^2 + c^4)*((2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)^2 + 2*Sqrt[3]*(a^2 - b^2 - c^2)*(b^2 - c^2)^2*S) : :

X(61473) lies on the cubic K061a and these lines: {13, 2394}, {14, 471}, {30, 34329}, {74, 41022}, {530, 1494}, {531, 51227}, {533, 44769}, {3642, 35910}, {7687, 43962}, {11092, 46788}, {11586, 36308}, {14919, 41887}, {17986, 41023}, {43961, 55319}

X(61474) = X(13)X(531)∩X(14)X(5466)

Barycentrics    (a^2 - 2*b^2 + c^2)*(-a^2 - b^2 + 2*c^2)*((2*a^2 - b^2 - c^2)*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4) + 2*Sqrt[3]*(b^2 - c^2)^2*S) : :

X(61474) lies on the cubic K061b and these lines: {13, 531}, {14, 5466}, {16, 52749}, {30, 17964}, {111, 6109}, {530, 17948}, {532, 892}, {691, 15743}, {3643, 52756}, {5978, 31125}, {6108, 16092}, {6111, 17983}, {6775, 14995}, {9214, 10653}, {10654, 52450}, {11624, 53806}, {16242, 52751}, {31710, 34169}, {37831, 52747}, {37832, 52750}, {41023, 48983}

X(61475) = X(13)X(470)∩X(14)X(2394)

Barycentrics    (a^4 - 2*a^2*b^2 + b^4 + a^2*c^2 + b^2*c^2 - 2*c^4)*(a^4 + a^2*b^2 - 2*b^4 - 2*a^2*c^2 + b^2*c^2 + c^4)*((2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)^2 - 2*Sqrt[3]*(a^2 - b^2 - c^2)*(b^2 - c^2)^2*S) : :

X(61475) lies on the cubic K061b and these lines: {13, 470}, {14, 2394}, {30, 34329}, {74, 41023}, {530, 51227}, {531, 1494}, {532, 44769}, {3643, 35910}, {7687, 43961}, {11078, 46788}, {14919, 41888}, {15743, 36311}, {17986, 41022}, {43962, 55319}

X(61476) = X(1)X(513)∩X(36)X(106)

Barycentrics    a^2*(a + b - 2*c)*(a - 2*b + c)*(a^2*b - b^3 + a^2*c - 4*a*b*c + 2*b^2*c + 2*b*c^2 - c^3) : :

X(61476) lies on the cubic K086 and these lines: {1, 513}, {36, 106}, {80, 519}, {88, 3245}, {238, 39154}, {350, 4555}, {517, 1739}, {899, 4792}, {1323, 56049}, {1387, 34590}, {1417, 5193}, {1785, 36125}, {1795, 10428}, {2316, 5526}, {3259, 24222}, {3583, 38950}, {5080, 20039}, {5100, 49998}, {5563, 16944}, {9259, 17969}, {9456, 16784}, {13752, 46190}, {17109, 39264}, {17320, 52553}, {24201, 53530}, {37602, 40215}, {38512, 56804}

X(61476) = midpoint of X(5080) and X(20039)
X(61476) = reflection of X(i) in X(j) for these {i,j}: {36, 1149}, {34590, 1387}
X(61476) = X(i)-isoconjugate of X(j) for these (i,j): {44, 37222}, {101, 46781}, {519, 2718}, {902, 35175}, {52479, 56644}
X(61476) = X(i)-Dao conjugate of X(j) for these (i,j): {1015, 46781}, {35129, 4358}, {40594, 35175}, {40595, 37222}
X(61476) = crossdifference of every pair of points on line {44, 6544}
X(61476) = barycentric product X(i)*X(j) for these {i,j}: {88, 2802}, {106, 30566}, {513, 46779}, {1320, 43048}, {3257, 24457}
X(61476) = barycentric quotient X(i)/X(j) for these {i,j}: {88, 35175}, {106, 37222}, {513, 46781}, {2802, 4358}, {9456, 2718}, {24457, 3762}, {30566, 3264}, {46779, 668}
X(61476) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {106, 901, 36}, {106, 39148, 901}, {901, 1318, 106}, {1149, 43922, 106}, {1318, 39148, 36}, {14260, 45247, 1}

X(61477) = X(1)X(514)∩X(36)X(105)

Barycentrics    (a^2 + b^2 - a*c - b*c)*(a^2 - a*b - b*c + c^2)*(2*a^3 - 2*a^2*b + a*b^2 - b^3 - 2*a^2*c + b^2*c + a*c^2 + b*c^2 - c^3) : :

X(61477) lies on the cubic K086 and these lines: {1, 514}, {36, 105}, {80, 294}, {106, 927}, {238, 516}, {239, 53382}, {241, 60060}, {519, 666}, {528, 35113}, {752, 56855}, {1125, 40724}, {1785, 36124}, {1795, 36041}, {2481, 50023}, {3234, 52084}, {3322, 5723}, {3583, 13576}, {4432, 46798}, {5011, 18785}, {5199, 6559}, {6381, 51560}, {6654, 50114}, {9321, 43065}, {9453, 24231}, {17729, 53241}, {28071, 60885}, {28580, 56851}, {29571, 56895}, {31637, 49768}, {33682, 56852}, {40540, 50441}, {50300, 60857}, {50303, 56850}

X(61477) = midpoint of X(666) and X(14942)
X(61477) = reflection of X(50441) in X(40540)
X(61477) = X(i)-isoconjugate of X(j) for these (i,j): {101, 52228}, {518, 840}, {672, 37131}, {2223, 18821}, {3126, 59021}, {14191, 34230}
X(61477) = X(i)-Dao conjugate of X(j) for these (i,j): {1015, 52228}, {35113, 3912}, {52884, 1026}
X(61477) = crossdifference of every pair of points on line {672, 53555}
X(61477) = barycentric product X(i)*X(j) for these {i,j}: {75, 51922}, {528, 673}, {693, 52227}, {1027, 42722}, {1643, 51560}, {2246, 2481}, {5723, 14942}, {36816, 52761}, {39293, 52946}
X(61477) = barycentric quotient X(i)/X(j) for these {i,j}: {105, 37131}, {513, 52228}, {528, 3912}, {673, 18821}, {1438, 840}, {1642, 4712}, {1643, 2254}, {2246, 518}, {5723, 9436}, {51922, 1}, {52227, 100}, {52969, 2340}, {52985, 1026}
X(61477) = {X(927),X(56783)}-harmonic conjugate of X(1323)

X(61478) = X(1)X(900)∩X(36)X(100)

Barycentrics    (2*a - b - c)*(a^3 - 2*a^2*b - 2*a*b^2 + b^3 + 4*a*b*c - a*c^2 - b*c^2)*(a^3 - a*b^2 - 2*a^2*c + 4*a*b*c - b^2*c - 2*a*c^2 + c^3) : :
X(61478) = 4 X[14028] - 3 X[16173]

X(61478) lies on the cubic K086 and these lines: {1, 900}, {36, 100}, {80, 106}, {214, 4738}, {903, 4089}, {952, 41343}, {1023, 4370}, {1120, 26726}, {1317, 23703}, {1320, 39697}, {4597, 35175}, {6174, 36924}, {6224, 20042}, {11274, 52924}, {12773, 23404}, {14028, 16173}, {23888, 60692}, {41191, 46781}

X(61478) = midpoint of X(6224) and X(20042)
X(61478) = reflection of X(i) in X(j) for these {i,j}: {80, 1647}, {17780, 214}
X(61478) = X(i)-isoconjugate of X(j) for these (i,j): {106, 2802}, {649, 46779}, {901, 24457}, {2316, 43048}, {9456, 30566}
X(61478) = X(i)-Dao conjugate of X(j) for these (i,j): {214, 2802}, {4370, 30566}, {5375, 46779}, {38979, 24457}
X(61478) = trilinear pole of line {44, 6544}
X(61478) = barycentric product X(i)*X(j) for these {i,j}: {44, 35175}, {100, 46781}, {519, 37222}, {2718, 4358}
X(61478) = barycentric quotient X(i)/X(j) for these {i,j}: {44, 2802}, {100, 46779}, {519, 30566}, {1319, 43048}, {1635, 24457}, {2718, 88}, {4530, 51442}, {35175, 20568}, {37222, 903}, {46781, 693}

X(61479) = X(1)X(523)∩X(36)X(759)

Barycentrics    (a + b)*(a + c)*(a^2 - a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(2*a^4 - a^3*b - a^2*b^2 + a*b^3 - b^4 - a^3*c - a^2*c^2 + 2*b^2*c^2 + a*c^3 - c^4) : :

X(61479) lies on the cubic K086 and these lines: {1, 523}, {30, 35466}, {36, 759}, {80, 5127}, {106, 476}, {519, 6740}, {1785, 2074}, {2341, 5526}, {3011, 7469}, {13746, 18120}, {24880, 36154}, {24883, 36171}, {24902, 36155}, {31059, 46800}, {34172, 36175}, {34209, 56402}, {37168, 47185}, {46441, 56425}

X(61479) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 56645, 52639}, {52639, 56950, 1}

X(61480) = X(1)X(2254)∩X(36)X(101)

Barycentrics    a^2*(a*b - b^2 + a*c - c^2)*(a^3 - a^2*b - a*b^2 + b^3 - a^2*c - b^2*c + 2*a*c^2 + 2*b*c^2 - 2*c^3)*(a^3 - a^2*b + 2*a*b^2 - 2*b^3 - a^2*c + 2*b^2*c - a*c^2 - b*c^2 + c^3) : :

X(61480) lies on the cubic K086 and these lines: {1, 2254}, {36, 101}, {80, 10708}, {103, 59021}, {106, 4845}, {214, 1025}, {519, 664}, {926, 34230}, {1026, 4712}, {1362, 2283}, {2284, 6184}, {9319, 34905}, {37131, 37138}, {41353, 53531}

X(61480) = X(i)-isoconjugate of X(j) for these (i,j): {2, 51922}, {105, 528}, {294, 5723}, {514, 52227}, {666, 1643}, {673, 2246}, {1642, 6185}, {34018, 52969}, {42722, 43929}, {52761, 52902}
X(61480) = X(i)-Dao conjugate of X(j) for these (i,j): {32664, 51922}, {39046, 528}
X(61480) = trilinear pole of line {672, 53555}
X(61480) = barycentric product X(i)*X(j) for these {i,j}: {100, 52228}, {518, 37131}, {672, 18821}, {840, 3912}, {34230, 46791}, {53583, 59021}
X(61480) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 51922}, {672, 528}, {692, 52227}, {840, 673}, {1026, 42722}, {1458, 5723}, {2223, 2246}, {18821, 18031}, {34230, 46790}, {37131, 2481}, {42079, 1642}, {52228, 693}, {54325, 52985}

X(61481) = X(1)X(522)∩X(36)X(80)

Barycentrics    (a^3 - a^2*b - a*b^2 + b^3 + 2*a*b*c - a*c^2 - b*c^2)*(a^3 - a*b^2 - a^2*c + 2*a*b*c - b^2*c - a*c^2 + c^3)*(2*a^4 - 2*a^3*b - a^2*b^2 + 2*a*b^3 - b^4 - 2*a^3*c + 4*a^2*b*c - 2*a*b^2*c - a^2*c^2 - 2*a*b*c^2 + 2*b^2*c^2 + 2*a*c^3 - c^4) : :
X(61481) = 3 X[3582] - X[56825]

X(61481) lies on the cubic K086 and these lines: {1, 522}, {10, 56757}, {11, 55314}, {36, 80}, {106, 1309}, {499, 18340}, {519, 1795}, {952, 3319}, {1387, 3326}, {1809, 6735}, {2716, 10058}, {2720, 53877}, {2829, 57441}, {3582, 56825}, {5126, 60062}, {5526, 52663}, {8069, 56752}, {9436, 54953}, {10538, 38460}, {10572, 58743}, {10573, 14266}, {21842, 31866}, {31680, 56814}, {35013, 39758}, {38955, 41684}

X(61481) = midpoint of X(i) and X(j) for these {i,j}: {104, 56690}, {10538, 38460}, {36037, 51565}
X(61481) = reflection of X(i) in X(j) for these {i,j}: {1785, 44675}, {3326, 1387}, {60062, 5126}
X(61481) = X(i)-isoconjugate of X(j) for these (i,j): {109, 37629}, {517, 953}, {14260, 52479}, {23981, 46041}, {35011, 42757}
X(61481) = X(i)-Dao conjugate of X(j) for these (i,j): {11, 37629}, {35587, 23757}, {39535, 1785}, {61066, 908}
X(61481) = crossdifference of every pair of points on line {2183, 53046}
X(61481) = barycentric product X(i)*X(j) for these {i,j}: {952, 34234}, {2265, 18816}, {43043, 51565}
X(61481) = barycentric quotient X(i)/X(j) for these {i,j}: {650, 37629}, {909, 953}, {952, 908}, {2265, 517}, {6075, 42754}, {34234, 46136}, {43043, 22464}, {52478, 52031}, {61238, 46041}
X(61481) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 56638, 52640}, {1309, 36123, 1785}, {36944, 56638, 1}

X(61482) = X(1)X(1769)∩X(36)X(109)

Barycentrics    a^2*(a^2*b - b^3 + a^2*c - 2*a*b*c + b^2*c + b*c^2 - c^3)*(a^4 - 2*a^2*b^2 + b^4 - 2*a^3*c + 2*a^2*b*c + 2*a*b^2*c - 2*b^3*c + a^2*c^2 - 4*a*b*c^2 + b^2*c^2 + 2*a*c^3 + 2*b*c^3 - 2*c^4)*(a^4 - 2*a^3*b + a^2*b^2 + 2*a*b^3 - 2*b^4 + 2*a^2*b*c - 4*a*b^2*c + 2*b^3*c - 2*a^2*c^2 + 2*a*b*c^2 + b^2*c^2 - 2*b*c^3 + c^4) : :

X(61482) lies on the cubic K086 and these lines: {1, 1769}, {36, 109}, {80, 10703}, {102, 59018}, {106, 1795}, {519, 1785}, {1361, 23981}, {1519, 50899}, {1772, 2800}, {1845, 23706}, {2316, 52431}, {2427, 23980}, {8677, 14260}

X(61482) = X(i)-isoconjugate of X(j) for these (i,j): {104, 952}, {2265, 34234}, {36944, 52478}, {43043, 52663}
X(61482) = X(40613)-Dao conjugate of X(952)
X(61482) = trilinear pole of line {2183, 53046}
X(61482) = barycentric product X(i)*X(j) for these {i,j}: {651, 37629}, {908, 953}, {2183, 46136}, {24029, 46041}, {52031, 52479}, {53045, 59018}
X(61482) = barycentric quotient X(i)/X(j) for these {i,j}: {953, 34234}, {1457, 43043}, {2183, 952}, {37629, 4391}, {59018, 53811}

X(61483) = X(1)X(3667)∩X(106)X(519)

Barycentrics    (a^2 - 4*a*b + b^2 + a*c + b*c)*(a^2 + a*b - 4*a*c + b*c + c^2)*(2*a^3 - 2*a^2*b - 3*a*b^2 + b^3 - 2*a^2*c + 8*a*b*c - b^2*c - 3*a*c^2 - b*c^2 + c^3) : :

X(61483) lies on the cubic K086 and these lines: {1, 3667}, {36, 2743}, {80, 53618}, {106, 519}, {1811, 25438}, {5526, 40400}, {38604, 53799}

X(61483) = midpoint of X(1120) and X(6079)
X(61483) = reflection of X(26727) in X(15637)
X(61483) = X(3880)-isoconjugate of X(43081)
X(61483) = barycentric product X(1120)*X(43055)
X(61483) = barycentric quotient X(43055)/X(1266)

X(61484) = X(1)X(2827)∩X(36)X(1293)

Barycentrics    a^2*(a*b + b^2 + a*c - 4*b*c + c^2)*(a^3 - 3*a^2*b - 2*a*b^2 + 2*b^3 - a^2*c + 8*a*b*c - 2*b^2*c - a*c^2 - 3*b*c^2 + c^3)*(a^3 - a^2*b - a*b^2 + b^3 - 3*a^2*c + 8*a*b*c - 3*b^2*c - 2*a*c^2 - 2*b*c^2 + 2*c^3) : :

X(61484) lies on the cubic K086 and these lines: {1, 2827}, {36, 1293}, {519, 3699}, {6018, 23832}, {6085, 45247}, {17460, 23705}
on K086

X(61484) = X(i)-isoconjugate of X(j) for these (i,j): {5854, 8686}, {40400, 43055}
X(61484) = barycentric quotient X(1149)/X(43055)

X(61485) = X(3)X(512)∩X(230)X(511)

Barycentrics    a^2*(a^12*b^4 - 5*a^10*b^6 + 10*a^8*b^8 - 10*a^6*b^10 + 5*a^4*b^12 - a^2*b^14 + 6*a^12*b^2*c^2 - 19*a^10*b^4*c^2 + 33*a^8*b^6*c^2 - 30*a^6*b^8*c^2 + 16*a^4*b^10*c^2 - 7*a^2*b^12*c^2 + b^14*c^2 + a^12*c^4 - 19*a^10*b^2*c^4 + 26*a^8*b^4*c^4 - 24*a^6*b^6*c^4 + 3*a^4*b^8*c^4 + 11*a^2*b^10*c^4 - 6*b^12*c^4 - 5*a^10*c^6 + 33*a^8*b^2*c^6 - 24*a^6*b^4*c^6 + 24*a^4*b^6*c^6 - 11*a^2*b^8*c^6 + 15*b^10*c^6 + 10*a^8*c^8 - 30*a^6*b^2*c^8 + 3*a^4*b^4*c^8 - 11*a^2*b^6*c^8 - 20*b^8*c^8 - 10*a^6*c^10 + 16*a^4*b^2*c^10 + 11*a^2*b^4*c^10 + 15*b^6*c^10 + 5*a^4*c^12 - 7*a^2*b^2*c^12 - 6*b^4*c^12 - a^2*c^14 + b^2*c^14) : :
X(61485) = 5 X[631] - X[46046], X[12833] + 3 X[34473], X[14113] - 3 X[38737]

X(61485 lies on the cubic K418 and these lines: {3, 512}, {98, 15631}, {230, 511}, {631, 46046}, {12833, 34473}, {14113, 38737}, {32484, 35438}, {35387, 46627}, {48445, 56437}

X(61485) = midpoint of X(98) and X(15631)
X(61485) = X(511)-line conjugate of X(230)

X(61486) = X(2)X(1499)∩X(110)X(37745)

Barycentrics    2*a^12 - 12*a^10*b^2 + 51*a^8*b^4 + 31*a^6*b^6 - 39*a^4*b^8 - 3*a^2*b^10 + 2*b^12 - 12*a^10*c^2 + 6*a^8*b^2*c^2 - 147*a^6*b^4*c^2 - 111*a^4*b^6*c^2 + 141*a^2*b^8*c^2 - 21*b^10*c^2 + 51*a^8*c^4 - 147*a^6*b^2*c^4 + 558*a^4*b^4*c^4 - 210*a^2*b^6*c^4 + 6*b^8*c^4 + 31*a^6*c^6 - 111*a^4*b^2*c^6 - 210*a^2*b^4*c^6 + 58*b^6*c^6 - 39*a^4*c^8 + 141*a^2*b^2*c^8 + 6*b^4*c^8 - 3*a^2*c^10 - 21*b^2*c^10 + 2*c^12 : :

X(61486) lies on the cubic K794 and these lines: {2, 1499}, {110, 37745}, {524, 9146}, {543, 50566}, {858, 37746}, {3589, 57508}, {5913, 9877}, {8593, 37860}, {9169, 34806}

X(61486) = reflection of X(i) in X(j) for these {i,j}: {34806, 9169}, {57508, 3589}

X(61487) = X(3)X(526)∩X(30)X(110)

Barycentrics    a^2*(a^18*b^2 - 7*a^16*b^4 + 21*a^14*b^6 - 35*a^12*b^8 + 35*a^10*b^10 - 21*a^8*b^12 + 7*a^6*b^14 - a^4*b^16 + a^18*c^2 - a^14*b^4*c^2 - 22*a^12*b^6*c^2 + 57*a^10*b^8*c^2 - 46*a^8*b^10*c^2 + 5*a^6*b^12*c^2 + 6*a^4*b^14*c^2 + 2*a^2*b^16*c^2 - 2*b^18*c^2 - 7*a^16*c^4 - a^14*b^2*c^4 + 54*a^12*b^4*c^4 - 67*a^10*b^6*c^4 - 16*a^8*b^8*c^4 + 63*a^6*b^10*c^4 - 16*a^4*b^12*c^4 - 19*a^2*b^14*c^4 + 9*b^16*c^4 + 21*a^14*c^6 - 22*a^12*b^2*c^6 - 67*a^10*b^4*c^6 + 144*a^8*b^6*c^6 - 73*a^6*b^8*c^6 - 34*a^4*b^10*c^6 + 45*a^2*b^12*c^6 - 14*b^14*c^6 - 35*a^12*c^8 + 57*a^10*b^2*c^8 - 16*a^8*b^4*c^8 - 73*a^6*b^6*c^8 + 90*a^4*b^8*c^8 - 28*a^2*b^10*c^8 + 7*b^12*c^8 + 35*a^10*c^10 - 46*a^8*b^2*c^10 + 63*a^6*b^4*c^10 - 34*a^4*b^6*c^10 - 28*a^2*b^8*c^10 - 21*a^8*c^12 + 5*a^6*b^2*c^12 - 16*a^4*b^4*c^12 + 45*a^2*b^6*c^12 + 7*b^8*c^12 + 7*a^6*c^14 + 6*a^4*b^2*c^14 - 19*a^2*b^4*c^14 - 14*b^6*c^14 - a^4*c^16 + 2*a^2*b^2*c^16 + 9*b^4*c^16 - 2*b^2*c^18) : :
X(61487) = 3 X[3] - 2 X[39987], 3 X[14933] - 4 X[39987], 5 X[15051] - 2 X[51231], 3 X[32609] - 2 X[42742]

X(61487) lies on the cubic K905 and these lines: {3, 526}, {30, 110}, {74, 16170}, {265, 3134}, {1511, 15329}, {5663, 46585}, {15051, 51231}, {32609, 42742}

X(61487) = reflection of X(i) in X(j) for these {i,j}: {265, 3134}, {14933, 3}, {15329, 1511}

X(61488) = X(2)X(1499)∩X(141)X(57508)

Barycentrics    4*a^12 - 24*a^10*b^2 - 33*a^8*b^4 + 89*a^6*b^6 + 57*a^4*b^8 - 33*a^2*b^10 + 4*b^12 - 24*a^10*c^2 + 282*a^8*b^2*c^2 - 321*a^6*b^4*c^2 - 357*a^4*b^6*c^2 + 147*a^2*b^8*c^2 - 15*b^10*c^2 - 33*a^8*c^4 - 321*a^6*b^2*c^4 + 1116*a^4*b^4*c^4 - 258*a^2*b^6*c^4 + 12*b^8*c^4 + 89*a^6*c^6 - 357*a^4*b^2*c^6 - 258*a^2*b^4*c^6 + 62*b^6*c^6 + 57*a^4*c^8 + 147*a^2*b^2*c^8 + 12*b^4*c^8 - 33*a^2*c^10 - 15*b^2*c^10 + 4*c^12 : :

X(61488) lies on the cubic K1274 and these lines: {2, 1499}, {141, 57508}, {524, 5914}, {6076, 15304}, {14916, 34806}, {32269, 37745}, {39075, 52231}, {52141, 56429}

X(61488) = midpoint of X(i) and X(j) for these {i,j}: {141, 57508}, {14916, 34806}
X(61488) = reflection of X(50565) in X(9172)
X(61488) = orthoptic-circle-of-the-Steiner-inellipse-inverse of X(43674)

X(61489) = SYMGONAL IMAGE OF X(25)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 + 2*a^2*b^2*c^2 - a^2*c^4 - b^2*c^4)*(a^6 + a^4*b^2 - a^2*b^4 - b^6 + a^4*c^2 - 2*a^2*b^2*c^2 + b^4*c^2 - a^2*c^4 + b^2*c^4 - c^6)*(a^6 - a^2*b^4 - a^4*c^2 + 2*a^2*b^2*c^2 - b^4*c^2 - a^2*c^4 + c^6) : :

X(61489) lies on the cubic K025 and these lines:" {4, 1177}, {25, 339}, {30, 10423}, {1300, 47110}, {1370, 53822}, {5962, 47105}, {7500, 52513}, {16172, 34175}, {18533, 18876}, {40009, 46140}, {55129, 60040}

X(61489) = reflection of X(i) in X(j) for these {i,j}: {1289, 25}, {1370, 53822}
X(61489) = antigonal image of X(1370)
X(61489) = symgonal image of X(25)
X(61489) = X(46140)-Ceva conjugate of X(60133)
X(61489) = X(18669)-isoconjugate of X(52041)
X(61489) = X(i)-Dao conjugate of X(j) for these (i,j): {25, 2393}, {55069, 42665}
X(61489) = trilinear pole of line {3162, 47125}
X(61489) = barycentric product X(i)*X(j) for these {i,j}: {1370, 60133}, {2373, 41361}, {3162, 46140}, {52513, 58075}
X(61489) = barycentric quotient X(i)/X(j) for these {i,j}: {159, 14961}, {1177, 52041}, {3162, 2393}, {10423, 56008}, {41361, 858}, {41766, 5523}, {52588, 42665}, {57086, 61198}, {58075, 52512}, {60133, 13575}

X(61490) = SYMGONAL IMAGE OF X(50)

Barycentrics    a^2*(a^8 - 2*a^6*b^2 + 2*a^4*b^4 - 2*a^2*b^6 + b^8 - 3*a^6*c^2 + 2*a^4*b^2*c^2 + 2*a^2*b^4*c^2 - 3*b^6*c^2 + 3*a^4*c^4 - 2*a^2*b^2*c^4 + 3*b^4*c^4 - a^2*c^6 - b^2*c^6)*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 + a^4*b^2*c^2 - a^2*b^4*c^2 + 2*b^6*c^2 - a^2*b^2*c^4 - 2*b^4*c^4 + 2*a^2*c^6 + 2*b^2*c^6 - c^8)*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6 - 2*a^6*c^2 + 2*a^4*b^2*c^2 - 2*a^2*b^4*c^2 - b^6*c^2 + 2*a^4*c^4 + 2*a^2*b^2*c^4 + 3*b^4*c^4 - 2*a^2*c^6 - 3*b^2*c^6 + c^8) : :

X(61490) lies on the cubic K289 and these lines: {4, 10414}, {50, 1291}, {511, 14979}, {1154, 35372}, {1157, 14859}, {3432, 34148}, {3447, 15107}

X(61490) = reflection of X(1291) in X(50)
X(61490) = symgonal image of X(50)
X(61490) = barycentric product X(24978)*X(39448)
X(61490) = barycentric quotient X(2070)/X(18122)

X(61491) = SYMGONAL IMAGE OF X(55)

Barycentrics    a*(a^3 - a^2*b - a*b^2 + b^3 - 2*a^2*c + 2*a*b*c - 2*b^2*c + a*c^2 + b*c^2)*(a^3 - a^2*b + a*b^2 - b^3 - a^2*c + b^2*c + a*c^2 + b*c^2 - c^3)*(a^3 - 2*a^2*b + a*b^2 - a^2*c + 2*a*b*c + b^2*c - a*c^2 - 2*b*c^2 + c^3) : :
X(61491) = 2 X[3428] - 3 X[38694], 4 X[32613] - 3 X[38712]

X(61491) lies on the cubic K and these lines: {4, 528}, {55, 1292}, {105, 517}, {2809, 37569}, {2814, 61230}, {3428, 38694}, {3434, 5511}, {5537, 34578}, {5597, 48542}, {5598, 48541}, {5842, 44983}, {10679, 28915}, {10699, 37533}, {20075, 34547}, {32613, 38712}, {34036, 57250}, {36976, 43762}, {38575, 44455}, {39732, 51567}

X(61491) = midpoint of X(i) and X(j) for these {i,j}: {20075, 34547}, {38575, 44455}
X(61491) = reflection of X(i) in X(j) for these {i,j}: {1292, 55}, {3434, 5511}, {10699, 37533}
X(61491) = antigonal image of X(3434)
X(61491) = symgonal image of X(55)
X(61491) = X(i)-isoconjugate of X(j) for these (i,j): {3433, 26015}, {30379, 40141}, {43065, 44178}
X(61491) = X(i)-Dao conjugate of X(j) for these (i,j): {55, 15733}, {5511, 2826}
X(61491) = barycentric product X(i)*X(j) for these {i,j}: {169, 51567}, {2742, 26546}, {34894, 37800}, {40576, 60483}
X(61491) = barycentric quotient X(i)/X(j) for these {i,j}: {169, 26015}, {1486, 43065}, {3434, 37788}, {5452, 15733}, {34036, 30379}, {37800, 38468}, {51567, 57773}, {56913, 3660}

X(61492) = SYMGONAL IMAGE OF X(56)

Barycentrics    a*(a + b - c)*(a - b + c)*(a^3 - a^2*b - a*b^2 + b^3 + 2*a*b*c - a*c^2 - b*c^2)*(a^3 - a*b^2 - a^2*c + 2*a*b*c - b^2*c - a*c^2 + c^3)*(a^4 - b^4 + 2*a^2*b*c - 2*a*b^2*c - 2*a*b*c^2 + 2*b^2*c^2 - c^4) : :
X(61492) = 2 X[10310] - 3 X[38715], 4 X[32612] - 3 X[38696]

X(61492) lies on these lines: {1, 42464}, {4, 11}, {36, 49207}, {46, 1795}, {57, 998}, {123, 3436}, {517, 1295}, {529, 10715}, {961, 34051}, {1470, 54064}, {1766, 57061}, {2098, 38564}, {2804, 23087}, {3304, 10271}, {5011, 32669}, {7219, 36977}, {8679, 10763}, {10310, 38715}, {12513, 52112}, {20076, 34188}, {32612, 38696}, {35448, 38622}

X(61492) = midpoint of X(20076) and X(34188)
X(61492) = reflection of X(i) in X(j) for these {i,j}: {108, 56}, {3436, 123}, {35448, 38622}
X(61492) = antigonal image of X(3436)
X(61492) = symgonal image of X(56)
X(61492) = X(18816)-Ceva conjugate of X(34051)
X(61492) = X(i)-isoconjugate of X(j) for these (i,j): {1785, 39167}, {2183, 34277}, {3435, 6735}, {22350, 43742}, {46393, 46640}
X(61492) = X(i)-Dao conjugate of X(j) for these (i,j): {56, 517}, {123, 2804}
X(61492) = trilinear pole of line {478, 6588}
X(61492) = barycentric product X(i)*X(j) for these {i,j}: {104, 57477}, {478, 18816}, {3436, 34051}, {6588, 54953}, {16082, 56414}, {21147, 34234}, {21186, 37136}
X(61492) = barycentric quotient X(i)/X(j) for these {i,j}: {104, 34277}, {478, 517}, {1766, 6735}, {2720, 46640}, {6588, 2804}, {14578, 39167}, {17408, 14571}, {18816, 57879}, {21147, 908}, {22132, 51379}, {32702, 40097}, {34051, 8048}, {41600, 51407}, {57477, 3262}

X(61493) = SYMGONAL IMAGE OF X(57)

Barycentrics    a*(a + b - c)*(a - b + c)*(a^2 - 2*a*b + b^2 + a*c + b*c - 2*c^2)*(a^2 + a*b - 2*b^2 - 2*a*c + b*c + c^2)*(a^3 + a^2*b - a*b^2 - b^3 + a^2*c - 2*a*b*c + b^2*c - a*c^2 + b*c^2 - c^3) : :
X(61493) = 3 X[57] - 2 X[52879], 3 X[934] - 4 X[52879]

X(61493) lies on the curve Q001 and these lines: {4, 653}, {57, 934}, {65, 34068}, {189, 1121}, {329, 5514}, {517, 972}, {937, 3339}, {2093, 4845}, {2095, 53804}, {2184, 41798}, {3345, 60047}, {5011, 36141}, {9965, 34546}, {36100, 37139}, {44978, 48359}

X(61493) = reflection of X(i) in X(j) for these {i,j}: {329, 5514}, {934, 57}
X(61493) = isogonal conjugate of X(56763)
X(61493) = antigonal image of X(329)
X(61493) = symgonal image of X(57)
X(61493) = X(1121)-Ceva conjugate of X(34056)
X(61493) = X(i)-isoconjugate of X(j) for these (i,j): {1, 56763}, {84, 6603}, {268, 23710}, {280, 1055}, {282, 1155}, {527, 2192}, {1323, 7367}, {1433, 60431}, {1436, 6745}, {2188, 37805}, {6139, 44327}, {6366, 36049}, {6510, 7008}, {7118, 30806}, {14392, 37141}, {14414, 40117}, {41087, 52891}
X(61493) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 56763}, {57, 527}, {5514, 6366}
X(61493) = trilinear pole of line {223, 6129}
X(61493) = barycentric product X(i)*X(j) for these {i,j}: {223, 1121}, {329, 34056}, {342, 60047}, {347, 1156}, {2291, 40702}, {6129, 35157}, {14256, 41798}, {14298, 60487}, {14733, 17896}, {14837, 37139}
X(61493) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 56763}, {40, 6745}, {196, 37805}, {198, 6603}, {208, 23710}, {221, 1155}, {223, 527}, {347, 30806}, {1121, 34404}, {1156, 280}, {2199, 1055}, {2291, 282}, {2331, 60431}, {3194, 52891}, {6129, 6366}, {6611, 6610}, {7011, 6510}, {14256, 37780}, {14733, 13138}, {18889, 7367}, {32728, 32652}, {34056, 189}, {34068, 2192}, {36141, 36049}, {37139, 44327}, {60047, 271}

X(61494) = SYMGONAL IMAGE OF X(67)

Barycentrics    (a^2 + b^2 - 2*c^2)*(a^2 - 2*b^2 + c^2)*(a^4 - a^2*b^2 + b^4 - c^4)*(a^4 - b^4 - a^2*c^2 + c^4)*(3*a^8 - 2*a^6*b^2 - 2*a^4*b^4 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 + 3*a^4*b^2*c^2 - a^2*b^4*c^2 - 2*a^4*c^4 - a^2*b^2*c^4 + 2*b^4*c^4 + 2*a^2*c^6 - c^8) : :

X(61494) lies on the cubic K273 and these lines: {2, 41511}, {4, 10630}, {6, 10415}, {67, 111}, {524, 55839}, {542, 39413}, {8877, 40057}
on K273

X(61494) = antigonal image of X(11061)
X(61494) = symgonal image of X(67)
X(61494) = isogonal conjugate of the complement of X(55839)
X(61494) = X(671)-Ceva conjugate of X(10415)
X(61494) = X(10417)-isoconjugate of X(16568)
X(61494) = X(67)-Dao conjugate of X(524)
X(61494) = barycentric product X(i)*X(j) for these {i,j}: {67, 10416}, {671, 15900}, {10415, 11061}
X(61494) = barycentric quotient X(i)/X(j) for these {i,j}: {3455, 10417}, {10415, 14364}, {10416, 316}, {11061, 7664}, {15900, 524}, {51240, 6593}

X(61495) = SYMGONAL IMAGE OF X(74)

Barycentrics    a^2*(a^4 - 2*a^2*b^2 + b^4 + a^2*c^2 + b^2*c^2 - 2*c^4)^2*(a^4 + a^2*b^2 - 2*b^4 - 2*a^2*c^2 + b^2*c^2 + c^4)^2*(a^10 + a^8*b^2 - 8*a^6*b^4 + 8*a^4*b^6 - a^2*b^8 - b^10 + a^8*c^2 + 9*a^6*b^2*c^2 - 6*a^4*b^4*c^2 - 7*a^2*b^6*c^2 + 3*b^8*c^2 - 8*a^6*c^4 - 6*a^4*b^2*c^4 + 16*a^2*b^4*c^4 - 2*b^6*c^4 + 8*a^4*c^6 - 7*a^2*b^2*c^6 - 2*b^4*c^6 - a^2*c^8 + 3*b^2*c^8 - c^10) : :

X(61495) lies on the cubic K447 and these lines: {3, 15404}, {4, 5627}, {74, 52546}, {185, 3470}, {2132, 6000}, {5663, 50467}, {10264, 10745}, {14264, 14685}, {34568, 38937}, {51346, 56576}
on K447

X(61495) = antigonal image of X(146)
X(61495) = symgonal image of X(74)
X(61495) = X(1494)-Ceva conjugate of X(40384)
X(61495) = X(i)-isoconjugate of X(j) for these (i,j): {1099, 34178}, {42074, 57766}
X(61495) = X(74)-Dao conjugate of X(30)
X(61495) = barycentric product X(i)*X(j) for these {i,j}: {146, 40384}, {1494, 36896}
X(61495) = barycentric quotient X(i)/X(j) for these {i,j}: {146, 36789}, {36896, 30}, {40353, 34178}, {40384, 57766}

X(61496) = SYMGONAL IMAGE OF X(98)

Barycentrics    b^2*c^2*(a^4 + b^4 - a^2*c^2 - b^2*c^2)^2*(-a^4 + a^2*b^2 + b^2*c^2 - c^4)^2*(-a^8 - a^6*b^2 + 2*a^4*b^4 - a^2*b^6 + b^8 - a^6*c^2 + 3*a^4*b^2*c^2 - a^2*b^4*c^2 - b^6*c^2 + 2*a^4*c^4 - a^2*b^2*c^4 - a^2*c^6 - b^2*c^6 + c^8) : :

X(61496) lies on the cubic K1134 and these lines: {4, 6071}, {76, 15407}, {98, 9469}, {879, 14510}, {1316, 14265}, {2782, 18858}, {12203, 47385}, {14096, 58728}, {14382, 34156}, {37455, 47382}, {47388, 51244}

X(61496) = antigonal image of X(147)
X(61496) = symgonal image of X(98)
X(61496) = X(290)-Ceva conjugate of X(34536)
X(61496) = X(i)-isoconjugate of X(j) for these (i,j): {9473, 42075}, {23996, 34130}
X(61496) = X(98)-Dao conjugate of X(511)
X(61496) = cevapoint of X(36899) and X(52162)
X(61496) = barycentric product X(i)*X(j) for these {i,j}: {147, 34536}, {290, 36899}, {52162, 57541}
X(61496) = barycentric quotient X(i)/X(j) for these {i,j}: {147, 36790}, {16559, 23996}, {34536, 9473}, {36899, 511}, {41932, 34130}, {52162, 11672}

X(61497) = SYMGONAL IMAGE OF X(99)

Barycentrics    b^2*(a^2 - b^2)^2*c^2*(a^2 - c^2)^2*(a^4 - a^2*b^2 - b^4 - a^2*c^2 + 3*b^2*c^2 - c^4) : :

X(61497) lies on these lines: {4, 6072}, {76, 5108}, {194, 39292}, {384, 4590}, {880, 14509}, {1316, 31614}, {23105, 53080}, {43714, 57739}, {44168, 52568}

X(61497) = isotomic conjugate of X(19610)
X(61497) = antigonal image of X(148)
X(61497) = symgonal image of X(99)
X(61497) = isotomic conjugate of the isogonal conjugate of X(31632)
X(61497) = X(670)-Ceva conjugate of X(34537)
X(61497) = X(i)-isoconjugate of X(j) for these (i,j): {31, 19610}, {669, 9396}, {1084, 9395}, {1924, 9293}, {4117, 35511}
X(61497) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 19610}, {99, 512}, {9428, 9293}
X(61497) = cevapoint of X(20998) and X(31998)
X(61497) = barycentric product X(i)*X(j) for these {i,j}: {76, 31632}, {148, 34537}, {670, 31998}, {2644, 4602}, {4609, 9218}, {20939, 24037}, {20998, 44168}
X(61497) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 19610}, {148, 3124}, {670, 9293}, {799, 9396}, {2644, 798}, {4590, 9217}, {9218, 669}, {10278, 22260}, {11053, 21906}, {17085, 61052}, {20939, 2643}, {20998, 1084}, {24037, 9395}, {31632, 6}, {31998, 512}, {34537, 35511}, {46291, 5027}

X(61498) = SYMGONAL IMAGE OF X(109)

Barycentrics    a^2*(a - b)^2*(a - c)^2*(a + b - c)^2*(a - b + c)^2*(a^6 - a^5*b - a^4*b^2 + a^2*b^4 + a*b^5 - b^6 - a^5*c + 3*a^4*b*c - 3*a*b^4*c + b^5*c - a^4*c^2 - 2*a^2*b^2*c^2 + 2*a*b^3*c^2 + b^4*c^2 + 2*a*b^2*c^3 - 2*b^3*c^3 + a^2*c^4 - 3*a*b*c^4 + b^2*c^4 + a*c^5 + b*c^5 - c^6) : :

X(61498) lies on these lines: {4, 52109}, {40, 59}, {65, 7128}, {1262, 10571}, {2818, 59103}, {7177, 7339}, {24027, 34043}, {34913, 57105}

X(61498) = antigonal image of X(33650)
X(61498) = symgonal image of X(109)
X(61498) = X(664)-Ceva conjugate of X(1262)
X(61498) = X(24026)-isoconjugate of X(34189)
X(61498) = X(109)-Dao conjugate of X(522)
X(61498) = barycentric product X(1262)*X(33650)
X(61498) = barycentric quotient X(i)/X(j) for these {i,j}: {23979, 34189}, {33650, 23978}

X(61499) = SYMGONAL IMAGE OF X(111)

Barycentrics    a^2*(a^2 + b^2 - 2*c^2)^2*(a^2 - 2*b^2 + c^2)^2*(a^6 + a^4*b^2 - a^2*b^4 - b^6 + a^4*c^2 - 5*a^2*b^2*c^2 + 3*b^4*c^2 - a^2*c^4 + 3*b^2*c^4 - c^6) : :

X(61499) lies on the cubics K072 and K273 and these lines: {2, 10415}, {4, 6076}, {6, 10630}, {524, 55838}, {671, 25328}, {895, 10417}, {5466, 14515}, {5968, 11637}, {7827, 57539}, {14262, 41511}

X(61499) = antigonal image of X(14360)
X(61499) = symgonal image of X(111)
X(61499) = isogonal conjugate of the complement of X(55838)
X(61499) = X(671)-Ceva conjugate of X(10630)
X(61499) = X(i)-isoconjugate of X(j) for these (i,j): {896, 41498}, {13574, 42081}, {22259, 24038}
X(61499) = X(i)-Dao conjugate of X(j) for these (i,j): {111, 524}, {15899, 41498}
X(61499) = cevapoint of X(2930) and X(15899)
X(61499) = barycentric product X(i)*X(j) for these {i,j}: {671, 15899}, {2930, 57539}, {10630, 14360}, {18310, 34574}
X(61499) = barycentric quotient X(i)/X(j) for these {i,j}: {111, 41498}, {2930, 2482}, {10630, 13574}, {14360, 36792}, {15899, 524}, {16563, 24038}, {18310, 52629}, {41936, 22259}

X(61500) = SYMGONAL IMAGE OF X(112)

Barycentrics    a^2*(a^2 - b^2)^2*(a^2 - c^2)^2*(a^2 + b^2 - c^2)^2*(a^2 - b^2 + c^2)^2*(a^10 - a^8*b^2 - 2*a^6*b^4 + 2*a^4*b^6 + a^2*b^8 - b^10 - a^8*c^2 + 5*a^6*b^2*c^2 - 2*a^4*b^4*c^2 - 3*a^2*b^6*c^2 + b^8*c^2 - 2*a^6*c^4 - 2*a^4*b^2*c^4 + 4*a^2*b^4*c^4 + 2*a^4*c^6 - 3*a^2*b^2*c^6 + a^2*c^8 + b^2*c^8 - c^10) : :

X(61500) lies on these lines: {20, 250}, {64, 15384}, {249, 35602}, {8743, 23964}, {10282, 57655}, {18121, 32230}, {39297, 51884}, {52448, 58273}, {52917, 60352}

X(61500) = antigonal image of X(13219)
X(61500) = symgonal image of X(112)
X(61500) = X(648)-Ceva conjugate of X(23964)
X(61500) = X(i)-isoconjugate of X(j) for these (i,j): {2632, 13573}, {17879, 34190}
X(61500) = X(112)-Dao conjugate of X(525)
X(61500) = cevapoint of X(10117) and X(40596)
X(61500) = barycentric product X(i)*X(j) for these {i,j}: {648, 40596}, {10117, 23582}, {13219, 23964}
X(61500) = barycentric quotient X(i)/X(j) for these {i,j}: {10117, 15526}, {13219, 36793}, {23964, 13573}, {40596, 525}, {41937, 34190}

X(61501) = MIDPOINT OF X(107) AND X(14249)

Barycentrics    (a^2 + b^2 - c^2)^2*(a^2 - b^2 + c^2)^2*(a^6 - 2*a^4*b^2 + a^2*b^4 + 3*a^4*b*c - 2*a^2*b^3*c - b^5*c - 2*a^4*c^2 + 2*a^2*b^2*c^2 - 2*a^2*b*c^3 + 2*b^3*c^3 + a^2*c^4 - b*c^5)*(a^6 - 2*a^4*b^2 + a^2*b^4 - 3*a^4*b*c + 2*a^2*b^3*c + b^5*c - 2*a^4*c^2 + 2*a^2*b^2*c^2 + 2*a^2*b*c^3 - 2*b^3*c^3 + a^2*c^4 + b*c^5)*(a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8 + a^6*c^2 + 4*a^4*b^2*c^2 - 3*a^2*b^4*c^2 - 2*b^6*c^2 - 3*a^4*c^4 - 3*a^2*b^2*c^4 + 6*b^4*c^4 + 3*a^2*c^6 - 2*b^2*c^6 - c^8) : :
X(61501) = X[14059] - 3 X[57301]

X(61501) lies on the curve Q011 and these lines: {3, 107}, {133, 1515}, {1075, 5656}, {1249, 47433}, {5667, 6525}, {6716, 53844}, {10745, 52448}, {14059, 57301}, {14363, 14862}, {22337, 59424}, {34549, 36876}

X(61501) = midpoint of X(107) and X(14249)
X(61501) = reflection of X(53844) in X(6716)
X(61501) = X(i)-Ceva conjugate of X(j) for these (i,j): {107, 6086}, {34538, 2442}
X(61501) = barycentric product X(i)*X(j) for these {i,j}: {2404, 6086}, {34538, 35579}
X(61501) = barycentric quotient X(i)/X(j) for these {i,j}: {2442, 6080}, {6086, 2416}
X(61501) = {X(51385),X(58341)}-harmonic conjugate of X(1515)

X(61502) = MIDPOINT OF X(476) AND X(14254)

Barycentrics    (a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^2 - b^2 + a*c + c^2)*(a^6 - 2*a^4*b^2 + a^2*b^4 + 2*a^4*b*c - a^2*b^3*c - b^5*c - 2*a^4*c^2 + a^2*b^2*c^2 - a^2*b*c^3 + 2*b^3*c^3 + a^2*c^4 - b*c^5)*(a^6 - 2*a^4*b^2 + a^2*b^4 - 2*a^4*b*c + a^2*b^3*c + b^5*c - 2*a^4*c^2 + a^2*b^2*c^2 + a^2*b*c^3 - 2*b^3*c^3 + a^2*c^4 + b*c^5)*(a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8 + a^6*c^2 + 2*a^4*b^2*c^2 - 2*a^2*b^4*c^2 - b^6*c^2 - 3*a^4*c^4 - 2*a^2*b^2*c^4 + 4*b^4*c^4 + 3*a^2*c^6 - b^2*c^6 - c^8) : :
X(61502) = 3 X[14993] + X[41512], X[14670] - 3 X[57305]

X(61502) lies on the curve Q011 and these lines: {3, 476}, {265, 36172}, {523, 10272}, {1522, 1523}, {5655, 14993}, {14670, 57305}, {18319, 52010}, {20957, 52449}, {22104, 47055}, {34193, 51835}

X(61502) = midpoint of X(i) and X(j) for these {i,j}: {476, 14254}, {18319, 52010}
X(61502) = reflection of X(47055) in X(22104)
X(61502) = X(36034)-complementary conjugate of X(16171)
X(61502) = X(476)-Ceva conjugate of X(16171)
X(61502) = barycentric product X(2410)*X(16171)
X(61502) = barycentric quotient X(i)/X(j) for these {i,j}: {2437, 16170}, {16171, 2411}

X(61503) = MIDPOINT OF X(691) AND X(14246)

Barycentrics    a^2*(a^2 + b^2 - 2*c^2)*(a^2 - 2*b^2 + c^2)*(a^4 - b^4 + 2*a^2*b*c - b^3*c + b^2*c^2 - b*c^3 - c^4)*(a^4 - b^4 - 2*a^2*b*c + b^3*c + b^2*c^2 + b*c^3 - c^4)*(2*a^6 - 2*a^4*b^2 + a^2*b^4 - b^6 - 2*a^4*c^2 + b^4*c^2 + a^2*c^4 + b^2*c^4 - c^6) : :

X(61503) lies on the curve Q011 and these lines: {3, 691}, {110, 15899}, {111, 36830}, {542, 1550}, {620, 47291}, {3005, 7711}, {5108, 34320}, {34810, 51926}, {38552, 53155}, {38953, 59422}

X(61503) = midpoint of X(691) and X(14246)
X(61503) = X(691)-Ceva conjugate of X(20403)
X(61503) = barycentric product X(i)*X(j) for these {i,j}: {20403, 50941}, {34539, 35582}
X(61503) = barycentric quotient X(20403)/X(50942)

X(61504) = MIDPOINT OF X(930) AND X(25043)

Barycentrics    (a^2 - b^2 - b*c - c^2)*(a^2 - b^2 + b*c - c^2)*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)*(a^4 - a^2*b^2 + b^4 - 2*a^2*c^2 - 2*b^2*c^2 + c^4)*(a^4 - 2*a^2*b^2 + b^4 - a^2*c^2 - 2*b^2*c^2 + c^4)*(a^6 - 2*a^4*b^2 + a^2*b^4 + a^2*b^3*c - b^5*c - 2*a^4*c^2 - a^2*b^2*c^2 + a^2*b*c^3 + 2*b^3*c^3 + a^2*c^4 - b*c^5)*(a^6 - 2*a^4*b^2 + a^2*b^4 - a^2*b^3*c + b^5*c - 2*a^4*c^2 - a^2*b^2*c^2 - a^2*b*c^3 - 2*b^3*c^3 + a^2*c^4 + b*c^5) : :
X(61504) = 3 X[23516] - 4 X[46954]

X(61504) lies on the curve Q011 and these lines: {2, 38899}, {3, 252}, {128, 1154}, {137, 32551}, {6592, 18807}, {8562, 11701}, {13372, 15345}, {13856, 21975}, {14071, 24147}, {23516, 46954}

X(61504) = midpoint of X(930) and X(25043)
X(61504) = reflection of X(i) in X(j) for these {i,j}: {137, 32551}, {15345, 13372}, {18807, 6592}
X(61504) = complement of X(38899)
X(61504) = X(36134)-complementary conjugate of X(25149)
X(61504) = X(930)-Ceva conjugate of X(25149)
X(61504) = barycentric quotient X(i)/X(j) for these {i,j}: {2439, 54049}, {25149, 2413}

X(61505) = MIDPOINT OF X(1297) AND X(39265)

Barycentrics    a^2*(b - c)^2*(b + c)^2*(a^2 - b^2 - c^2)*(a^4 - b^4 + a^2*b*c - b^3*c - b*c^3 - c^4)*(a^4 - b^4 - a^2*b*c + b^3*c + b*c^3 - c^4)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 + a^2*c^4 + b^2*c^4 - 2*c^6)*(a^6 + a^2*b^4 - 2*b^6 - a^4*c^2 + b^4*c^2 - a^2*c^4 + c^6) : :

X(61505) lies on the curve Q011 and these lines: {3, 112}, {127, 525}, {339, 43673}, {2435, 3269}, {2508, 41172}, {10749, 56687}, {12918, 52485}, {13219, 56601}, {19163, 47105}, {35071, 52590}

X(61505) = midpoint of X(1297) and X(39265)
X(61505) = X(293)-complementary conjugate of X(2881)
X(61505) = X(1297)-Ceva conjugate of X(2881)
X(61505) = X(2312)-isoconjugate of X(39297)
X(61505) = X(2881)-Dao conjugate of X(56794)
X(61505) = barycentric product X(i)*X(j) for these {i,j}: {1297, 57606}, {2419, 2881}
X(61505) = barycentric quotient X(i)/X(j) for these {i,j}: {1297, 39297}, {2435, 2867}, {2881, 2409}, {57606, 30737}

X(61506) = X(2)X(51)∩X(4)X(74)

Barycentrics    a^6 + a^4*b^2 - 3*a^2*b^4 + b^6 + a^4*c^2 + 6*a^2*b^2*c^2 - b^4*c^2 - 3*a^2*c^4 - b^2*c^4 + c^6 : :
X(61506) = X[4] + 2 X[11438], 2 X[5] + X[37489], 2 X[25] + X[1899], X[25] + 2 X[13567], 4 X[25] - X[31383], X[1899] - 4 X[13567], 2 X[1899] + X[31383], 8 X[13567] + X[31383], 4 X[26869] + X[31383], 4 X[140] - X[37483], X[394] - 4 X[6677], X[394] + 2 X[41588], 2 X[6677] + X[41588], X[6090] - 3 X[47597], 5 X[631] - 2 X[37480], X[686] + 2 X[47206], 2 X[1368] + X[33586], 2 X[1596] + X[10605], 5 X[3618] - 2 X[11511], X[6515] + 2 X[9306], X[10602] + 2 X[41585], 2 X[18390] + X[18533], X[18396] + 2 X[37458], X[18451] - 4 X[44233], X[18917] + 2 X[46261]

X(61506) lies on these lines: {2, 51}, {3, 16657}, {4, 74}, {5, 3066}, {6, 468}, {23, 18911}, {24, 12022}, {25, 1503}, {32, 6388}, {64, 1906}, {68, 7506}, {69, 5651}, {110, 37644}, {140, 10982}, {141, 11284}, {154, 11245}, {160, 44890}, {182, 7493}, {184, 6353}, {185, 3089}, {193, 3292}, {235, 9786}, {317, 450}, {343, 5020}, {381, 20192}, {389, 3542}, {394, 6677}, {427, 17810}, {428, 1853}, {460, 53017}, {462, 41039}, {463, 41038}, {523, 2433}, {524, 6090}, {542, 26255}, {568, 5654}, {576, 5972}, {578, 3147}, {631, 11424}, {686, 47206}, {800, 47195}, {852, 6389}, {858, 31670}, {879, 47004}, {973, 6639}, {1112, 15131}, {1181, 21841}, {1192, 1885}, {1316, 1648}, {1350, 30739}, {1351, 11064}, {1352, 1995}, {1368, 33586}, {1370, 29317}, {1495, 4232}, {1593, 15873}, {1596, 10605}, {1598, 16654}, {1656, 45089}, {1843, 60774}, {1907, 40686}, {1974, 41719}, {1992, 5642}, {1993, 59543}, {2355, 5928}, {2452, 16319}, {2453, 47146}, {2549, 5112}, {2715, 2770}, {3090, 3574}, {3098, 46336}, {3124, 3767}, {3168, 11547}, {3448, 14002}, {3515, 12241}, {3517, 6146}, {3518, 9833}, {3526, 3527}, {3541, 10110}, {3546, 45186}, {3548, 5446}, {3549, 5462}, {3564, 35259}, {3567, 7505}, {3575, 18405}, {3581, 4549}, {3618, 11511}, {3796, 10154}, {4194, 58889}, {4846, 11799}, {5050, 13394}, {5064, 23332}, {5067, 44300}, {5085, 44210}, {5094, 5480}, {5159, 21850}, {5189, 43621}, {5198, 6247}, {5449, 7528}, {5596, 44091}, {5663, 44275}, {5946, 10201}, {5965, 6515}, {6524, 6747}, {6560, 47631}, {6561, 47632}, {6593, 32227}, {6622, 43831}, {6642, 41587}, {6676, 10601}, {6696, 11403}, {6759, 18916}, {6791, 6793}, {6794, 36191}, {6800, 7426}, {6816, 46730}, {6995, 11550}, {6997, 21243}, {7383, 11695}, {7391, 26913}, {7394, 23293}, {7484, 21167}, {7494, 18928}, {7499, 17825}, {7500, 29323}, {7507, 11745}, {7529, 12359}, {7558, 15024}, {7694, 50707}, {7714, 32064}, {7739, 46906}, {7795, 37338}, {8546, 32218}, {8550, 15448}, {8721, 20897}, {9155, 34511}, {9169, 37809}, {9716, 32226}, {9729, 59349}, {9777, 23292}, {9781, 37119}, {9815, 13160}, {9820, 37493}, {9936, 18350}, {9971, 12099}, {10192, 11402}, {10257, 44413}, {10297, 40909}, {10300, 48874}, {10301, 31860}, {10539, 18951}, {10546, 41724}, {10565, 22352}, {10594, 14216}, {10602, 41585}, {10653, 32460}, {10654, 32461}, {11003, 37760}, {11061, 32235}, {11173, 24855}, {11176, 14397}, {11206, 18950}, {11354, 47563}, {11381, 18913}, {11427, 15004}, {11430, 35486}, {11442, 13595}, {11457, 34484}, {11477, 59767}, {12024, 34782}, {12106, 32423}, {12118, 12310}, {12160, 59659}, {12161, 44232}, {12167, 23326}, {12828, 19136}, {13142, 35602}, {13198, 44080}, {13352, 38793}, {13364, 60763}, {13383, 36752}, {13568, 37197}, {13621, 25738}, {14165, 41371}, {14361, 61348}, {14461, 20477}, {14763, 51171}, {14790, 43817}, {15018, 52300}, {15053, 44440}, {15107, 16063}, {15139, 56918}, {15805, 34002}, {16048, 26579}, {16051, 51212}, {16187, 40107}, {16238, 36747}, {16655, 26944}, {17907, 41203}, {17928, 54040}, {18281, 34128}, {18381, 37122}, {18390, 18533}, {18396, 37458}, {18451, 44233}, {18909, 26883}, {18917, 46261}, {18952, 37440}, {19161, 44084}, {20021, 34098}, {20266, 26892}, {23049, 54381}, {25406, 35268}, {26540, 33849}, {27362, 57529}, {29181, 31152}, {31099, 48901}, {31802, 58465}, {31815, 49673}, {31884, 43957}, {32110, 49669}, {33971, 51358}, {34351, 37506}, {34397, 51730}, {34507, 54013}, {34815, 37072}, {35228, 37920}, {35264, 45968}, {36889, 39453}, {36989, 56924}, {37897, 48906}, {37899, 48905}, {37904, 43273}, {37974, 42085}, {37975, 42086}, {38064, 47596}, {39522, 44452}, {39656, 40884}, {44107, 53857}, {44211, 47391}, {46517, 48910}, {47097, 54131}, {47147, 57586}, {47251, 52743}, {47255, 58900}, {47311, 51024}, {52249, 52448}, {56391, 58265}

X(61506) = midpoint of X(25) and X(26869)
X(61506) = reflection of X(i) in X(j) for these {i,j}: {1899, 26869}, {26869, 13567}, {35259, 44212}
X(61506) = crossdifference of every pair of points on line {1636, 3288}
X(61506) = perspector of the cevian triangle of X(524) and the 11th Brocard triangle
X(61506) = barycentric product X(16080)*X(44892)
X(61506) = barycentric quotient X(44892)/X(11064)
X(61506) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5640, 14561}, {2, 10519, 5650}, {2, 15360, 54173}, {2, 54132, 13857}, {3, 21970, 32269}, {3, 37648, 54012}, {4, 37643, 125}, {6, 32113, 5486}, {23, 18911, 46264}, {24, 39571, 19467}, {25, 1899, 31383}, {25, 13567, 1899}, {69, 40132, 5651}, {107, 43462, 4}, {125, 34417, 4}, {182, 32223, 7493}, {576, 5972, 37645}, {1995, 3580, 1352}, {3066, 37638, 5}, {3518, 18912, 9833}, {4232, 6776, 1495}, {5480, 47296, 5094}, {5651, 41586, 69}, {6353, 11433, 184}, {6353, 14912, 35260}, {6677, 41588, 394}, {6995, 23291, 11550}, {7494, 18928, 43650}, {8550, 15448, 26864}, {9777, 37453, 23292}, {10154, 45298, 3796}, {10594, 26879, 14216}, {11433, 35260, 14912}, {11550, 44106, 6995}, {14912, 35260, 184}, {15107, 16063, 48873}, {16051, 51212, 51360}, {17810, 26958, 427}, {20192, 44569, 381}, {26917, 38848, 4}, {30739, 47582, 1350}, {31860, 36990, 10301}, {32269, 37648, 3}

X(61507) = X(2)X(154)∩X(3)X(15448)

Barycentrics    4*a^6 - 3*a^4*b^2 - 2*a^2*b^4 + b^6 - 3*a^4*c^2 + 12*a^2*b^2*c^2 - b^4*c^2 - 2*a^2*c^4 - b^2*c^4 + c^6 : :
X[5] + 2 X[43586], X[25] + 2 X[53415], 2 X[140] + X[46261], X[6090] + 3 X[47597], 7 X[3090] - X[18396], 2 X[6677] + X[9306], 4 X[6677] - X[13567], 2 X[9306] + X[13567], 5 X[15692] - X[46349], 5 X[31255] + X[31383]

X(61507) lies on these lines: {2, 154}, {3, 15448}, {4, 59767}, {5, 1511}, {6, 40132}, {20, 41424}, {23, 48881}, {25, 29181}, {53, 450}, {110, 8550}, {140, 16187}, {141, 468}, {184, 59699}, {373, 597}, {436, 37873}, {511, 44212}, {524, 6090}, {549, 14915}, {550, 32237}, {682, 37338}, {858, 10546}, {1092, 15873}, {1112, 40929}, {1316, 11053}, {1350, 4232}, {1352, 47296}, {1368, 29012}, {1495, 30739}, {1915, 40326}, {1995, 5480}, {2777, 44273}, {2883, 17928}, {3066, 37645}, {3090, 18396}, {3091, 53050}, {3098, 37897}, {3292, 3629}, {3523, 5646}, {3546, 16621}, {3564, 6677}, {3589, 8546}, {3630, 41586}, {3818, 5159}, {3819, 10154}, {5020, 14561}, {5055, 59648}, {5254, 20998}, {5650, 21167}, {5654, 6642}, {5891, 44211}, {5894, 10117}, {5913, 20194}, {5943, 34382}, {5967, 32525}, {6353, 10519}, {6723, 18553}, {6804, 17821}, {7386, 59411}, {7426, 7998}, {7575, 35254}, {7605, 14389}, {7667, 44082}, {8369, 35282}, {8542, 47457}, {8703, 32267}, {10168, 12045}, {10170, 34351}, {10300, 48898}, {10301, 51163}, {10314, 59558}, {11002, 20192}, {11059, 59552}, {11188, 23326}, {11328, 59656}, {11427, 59551}, {14826, 26958}, {15030, 23328}, {15036, 35492}, {15066, 32269}, {15069, 37643}, {15131, 35904}, {15139, 34774}, {15435, 47355}, {15692, 46349}, {16051, 36990}, {16058, 59623}, {17809, 18928}, {17810, 37669}, {18358, 37911}, {20112, 57618}, {22165, 32225}, {22483, 23308}, {26864, 54012}, {30769, 51537}, {31255, 31383}, {31860, 51212}, {32223, 48876}, {33979, 37689}, {34147, 41005}, {35268, 43957}, {36176, 47166}, {37638, 54013}, {37904, 50965}, {37910, 48880}, {38793, 44218}, {40330, 52290}, {40911, 55626}, {41167, 47249}, {43598, 43895}, {47311, 51022}, {47315, 48884}, {48910, 52301}

X(61507) = midpoint of X(2) and X(35259)
X(61507) = perspector of the anticevian triangle of X(524) and the 11th Brocard triangle
X(61507) = crossdifference of every pair of points on line {12379, 20186}
X(61507) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 35260, 5085}, {2, 35266, 51737}, {110, 37648, 8550}, {468, 5651, 141}, {1495, 30739, 44882}, {1995, 11064, 5480}, {5020, 59543, 23292}, {5650, 44210, 21167}, {6642, 59659, 12233}, {6677, 9306, 13567}, {10301, 51360, 51163}

X(61508) = BROCARD-CIRCLE-INVERSE OF X(74)

Barycentrics    a^2*(4*a^12 - 8*a^10*b^2 + 2*a^8*b^4 + 4*a^6*b^6 - 4*a^4*b^8 + 4*a^2*b^10 - 2*b^12 - 8*a^10*c^2 + 11*a^8*b^2*c^2 - 3*a^6*b^4*c^2 + 6*a^4*b^6*c^2 - a^2*b^8*c^2 - 5*b^10*c^2 + 2*a^8*c^4 - 3*a^6*b^2*c^4 - 9*a^4*b^4*c^4 - 3*a^2*b^6*c^4 + 11*b^8*c^4 + 4*a^6*c^6 + 6*a^4*b^2*c^6 - 3*a^2*b^4*c^6 - 8*b^6*c^6 - 4*a^4*c^8 - a^2*b^2*c^8 + 11*b^4*c^8 + 4*a^2*c^10 - 5*b^2*c^10 - 2*c^12) : :

X(61508) lies on these lines: {2, 5191}, {74, 182}, {112, 574}, {186, 15922}, {187, 34235}, {353, 3569}, {3094, 9408}, {3098, 52630}, {3269, 10485}, {3431, 15920}, {5116, 9412}, {5667, 35485}, {6091, 61128}, {7422, 10788}, {7790, 50934}, {8744, 46942}, {11179, 18331}, {12017, 35936}, {12176, 48982}, {15921, 38698}, {26864, 48871}, {35493, 38553}, {35925, 52772}, {37991, 44821}, {40856, 61102}, {43461, 46657}

X(61508) = reflection of X(9999) in X(51800)
X(61508) = Brocard-circle-inverse of X(74)
X(61508) = Schoutte-circle- inverse of X(34235)
X(61508) = psi-transform of X(1495)

X(61509) = MIDPOINT OF X(5) AND X(7)

Barycentrics    2*a^6-3*(b-c)^4*(b+c)^2+2*a*(b-c)^2*(b+c)^3+a^4*(-5*b^2+4*b*c-5*c^2)-2*a^3*(b+c)*(b^2+c^2)+2*a^2*(b-c)^2*(3*b^2+b*c+3*c^2) : :
X(61509) = -X[1]+3*X[38041], -X[2]+3*X[38080], -X[3]+3*X[38111], -X[4]+3*X[38137], -X[6]+3*X[38164], -X[8]+3*X[38170], -X[10]+3*X[38172], -X[11]+3*X[38173], -X[12]+3*X[38174], -X[144]+5*X[1656], X[355]+3*X[59372], 3*X[381]+X[36996] and many others

X(61509) lies on these lines: {1, 38041}, {2, 38080}, {3, 38111}, {4, 38137}, {5, 7}, {6, 38164}, {8, 38170}, {9, 3628}, {10, 38172}, {11, 38173}, {12, 38174}, {30, 5732}, {140, 142}, {143, 58472}, {144, 1656}, {355, 59372}, {381, 36996}, {390, 10283}, {495, 60924}, {496, 60923}, {516, 548}, {517, 33558}, {518, 61510}, {527, 547}, {542, 51195}, {546, 971}, {549, 5759}, {550, 21151}, {590, 60916}, {615, 60915}, {632, 59381}, {952, 5542}, {954, 6924}, {1001, 7508}, {1353, 59405}, {1385, 38054}, {1482, 59412}, {1483, 11038}, {2550, 5844}, {2801, 61553}, {3090, 20059}, {3091, 60884}, {3526, 21168}, {3530, 5735}, {3564, 51150}, {3579, 38123}, {3627, 59385}, {3845, 36991}, {3850, 38150}, {3853, 18482}, {3856, 59389}, {3861, 31672}, {3982, 10157}, {4312, 5886}, {5055, 60984}, {5067, 61006}, {5223, 38042}, {5572, 58561}, {5690, 38052}, {5698, 38043}, {5720, 6147}, {5845, 18583}, {5850, 9956}, {5851, 60759}, {5852, 61512}, {5853, 61597}, {5856, 61562}, {5880, 20330}, {6172, 15699}, {6666, 48154}, {6859, 60975}, {6862, 8732}, {6911, 30275}, {6959, 8232}, {7238, 48888}, {7583, 60914}, {7584, 60913}, {7988, 41705}, {8226, 13243}, {8227, 11544}, {8703, 38065}, {9776, 37364}, {9955, 61556}, {10021, 17768}, {10109, 60963}, {10124, 38093}, {10592, 60909}, {10593, 60910}, {11230, 51090}, {11372, 38034}, {11540, 38067}, {11662, 61016}, {12108, 21153}, {12619, 38207}, {12811, 38139}, {12812, 60962}, {13861, 60897}, {15251, 50307}, {15325, 60883}, {15712, 59418}, {16239, 20195}, {18230, 55856}, {18357, 43180}, {18444, 20420}, {18480, 38151}, {19116, 60887}, {21841, 60879}, {21850, 38143}, {22791, 38036}, {22793, 43182}, {22938, 38152}, {23513, 41694}, {24467, 60955}, {24470, 55108}, {24474, 50238}, {26921, 50394}, {27475, 51046}, {28160, 43176}, {28204, 51098}, {30331, 61278}, {30340, 37705}, {30424, 61272}, {34380, 47595}, {34753, 52819}, {34773, 38030}, {35018, 38108}, {38022, 50836}, {38024, 50824}, {38053, 51700}, {38079, 50997}, {38081, 50835}, {38083, 50834}, {38086, 50979}, {38092, 50823}, {38094, 50821}, {38109, 41700}, {38112, 40333}, {38115, 48906}, {38124, 38602}, {38186, 51732}, {38317, 51144}, {38318, 60942}, {38454, 61533}, {43179, 61280}, {47598, 60999}, {47599, 60986}, {51190, 59399}, {51559, 60959}, {55862, 58433}, {58604, 61601}, {59850, 59883}

X(61509) = midpoint of X(i) and X(j) for these {i,j}: {5, 7}, {550, 31671}, {5805, 31657}, {5880, 20330}, {18482, 43177}, {22793, 43182}, {38111, 59386}, {38137, 59380}
X(61509) = reflection of X(i) in X(j) for these {i,j}: {140, 142}, {143, 58472}, {30331, 61278}, {3853, 18482}, {31672, 3861}, {5572, 58561}, {60901, 3850}, {61511, 61595}, {61596, 61511}, {9, 3628}
X(61509) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 7, 5843}, {7, 38107, 5}, {9, 38171, 3628}, {142, 5762, 140}, {527, 61511, 61596}, {527, 61595, 61511}, {3090, 20059, 51516}, {5805, 31657, 30}, {20195, 38113, 16239}, {21151, 31671, 550}, {38150, 60901, 3850}, {59381, 60996, 632}, {61511, 61595, 547}, {61545, 61549, 61510}

X(61510) = MIDPOINT OF X(5) AND X(8)

Barycentrics    2*a^4-4*a^3*(b+c)+4*a*(b-c)^2*(b+c)-3*(b^2-c^2)^2+a^2*(b^2+8*b*c+c^2) : :
X(61510) = -3*X[2]+X[1483], -X[3]+5*X[3617], X[4]+7*X[4678], -X[6]+3*X[38165], -X[7]+3*X[38170], -X[9]+3*X[38175], -X[11]+3*X[38177], -X[12]+3*X[38178], -X[145]+5*X[1656], -3*X[165]+2*X[44245], 3*X[381]+X[12245], X[382]+3*X[59417] and many others

X(61510) lies on these lines: {1, 3628}, {2, 1483}, {3, 3617}, {4, 4678}, {5, 8}, {6, 38165}, {7, 38170}, {9, 38175}, {10, 140}, {11, 38177}, {12, 38178}, {21, 12331}, {30, 40}, {35, 51525}, {80, 7161}, {143, 23841}, {145, 1656}, {153, 47032}, {165, 44245}, {381, 12245}, {382, 59417}, {442, 59416}, {495, 10573}, {496, 12647}, {498, 37728}, {515, 548}, {516, 61596}, {517, 546}, {518, 61509}, {519, 547}, {528, 61621}, {542, 50951}, {549, 944}, {550, 5657}, {551, 47599}, {590, 35843}, {615, 35842}, {631, 18526}, {632, 9780}, {730, 61625}, {740, 61623}, {758, 61552}, {946, 4669}, {956, 6924}, {958, 7508}, {960, 58632}, {962, 3845}, {1071, 9952}, {1125, 48154}, {1145, 5086}, {1159, 5261}, {1352, 59407}, {1353, 59406}, {1376, 32153}, {1387, 17606}, {1484, 4187}, {1698, 16239}, {1699, 3856}, {1706, 24467}, {1737, 20323}, {1829, 16198}, {1837, 15172}, {2098, 10593}, {2099, 10592}, {2550, 5843}, {2800, 56762}, {2801, 13145}, {2802, 58674}, {2809, 61602}, {2817, 61603}, {3057, 12019}, {3090, 3621}, {3091, 8148}, {3241, 15699}, {3243, 38171}, {3244, 11230}, {3336, 18990}, {3338, 5252}, {3416, 34380}, {3421, 6917}, {3526, 7967}, {3530, 5881}, {3543, 50797}, {3564, 49524}, {3576, 12108}, {3579, 12103}, {3614, 11009}, {3616, 55856}, {3622, 5070}, {3623, 5067}, {3624, 61287}, {3625, 10175}, {3627, 12702}, {3632, 5886}, {3633, 54447}, {3634, 15178}, {3635, 10172}, {3653, 11540}, {3655, 11812}, {3656, 7989}, {3661, 19512}, {3697, 58675}, {3753, 24475}, {3817, 11278}, {3820, 10943}, {3828, 13607}, {3830, 20070}, {3843, 54448}, {3850, 4668}, {3851, 61260}, {3853, 11362}, {3859, 4301}, {3860, 31162}, {3861, 12699}, {3871, 7489}, {3918, 5885}, {3968, 12005}, {4002, 10202}, {4297, 34200}, {4478, 24220}, {4511, 61148}, {4651, 37365}, {4677, 8227}, {4701, 13464}, {4711, 7686}, {4745, 6684}, {4746, 9955}, {4816, 16200}, {4848, 24470}, {4861, 19907}, {4867, 38109}, {5055, 10595}, {5056, 20052}, {5071, 50805}, {5082, 6929}, {5260, 37621}, {5326, 24926}, {5330, 17533}, {5424, 15174}, {5428, 11491}, {5432, 37706}, {5433, 37707}, {5439, 58605}, {5493, 28182}, {5499, 12247}, {5506, 34352}, {5531, 33858}, {5554, 8728}, {5559, 37718}, {5599, 32147}, {5600, 32146}, {5687, 6914}, {5722, 37556}, {5731, 15712}, {5762, 24393}, {5779, 59413}, {5805, 59414}, {5836, 14988}, {5841, 54288}, {5846, 18583}, {5847, 61624}, {5853, 61511}, {5854, 24387}, {5855, 61512}, {6101, 16980}, {6147, 9578}, {6735, 33596}, {6737, 51362}, {6842, 11698}, {6861, 10528}, {6862, 7080}, {6940, 12773}, {6996, 51353}, {7294, 38763}, {7516, 8192}, {7525, 9798}, {7583, 35788}, {7584, 35789}, {7609, 33076}, {7680, 46028}, {7968, 13993}, {7969, 13925}, {7982, 12811}, {7983, 38229}, {7991, 12102}, {8168, 37622}, {8193, 17714}, {8703, 34627}, {9053, 24206}, {9588, 58190}, {9623, 37700}, {9933, 59553}, {10021, 44669}, {10039, 37080}, {10096, 51693}, {10106, 34753}, {10124, 19875}, {10303, 58230}, {10827, 39542}, {10916, 32537}, {10942, 31419}, {10944, 15325}, {10950, 37571}, {11014, 61032}, {11224, 41989}, {11522, 61263}, {11849, 31649}, {12047, 36920}, {12079, 36155}, {12101, 28194}, {12104, 32613}, {12107, 15177}, {12135, 21841}, {12410, 13861}, {12433, 31397}, {12512, 15691}, {12531, 38752}, {12785, 50708}, {13624, 28236}, {14647, 52683}, {14839, 61550}, {14891, 50811}, {14893, 22793}, {15170, 37702}, {15338, 37006}, {15686, 50822}, {15687, 48661}, {15690, 51067}, {15692, 50826}, {15694, 50818}, {15702, 50832}, {16137, 37719}, {16192, 18481}, {16210, 32162}, {17527, 32214}, {18492, 61257}, {18538, 35641}, {18762, 35642}, {18908, 37562}, {19065, 19117}, {19066, 19116}, {19709, 34631}, {19876, 41984}, {19883, 51087}, {20053, 61273}, {20400, 26087}, {21031, 26470}, {21850, 38144}, {22851, 50853}, {22896, 50856}, {22938, 38156}, {24028, 35194}, {24914, 37708}, {24987, 50205}, {25005, 52264}, {25055, 50804}, {25416, 38044}, {26878, 31789}, {28160, 43174}, {28164, 58203}, {28178, 31673}, {28190, 31730}, {28198, 50827}, {28217, 59851}, {28581, 61522}, {29207, 50312}, {30315, 61275}, {30331, 38179}, {31434, 37739}, {31657, 38200}, {31794, 51782}, {31948, 35487}, {32157, 61622}, {32515, 50772}, {33091, 37360}, {33699, 34632}, {34595, 61288}, {34641, 47478}, {34791, 58561}, {35400, 50863}, {35404, 50867}, {35810, 42582}, {35811, 42583}, {37281, 37532}, {37298, 50890}, {37561, 51529}, {37698, 59311}, {38022, 51093}, {38040, 49681}, {38047, 51732}, {38079, 51000}, {38083, 51071}, {38087, 50979}, {38111, 40333}, {38116, 48906}, {38128, 38602}, {38139, 43166}, {38154, 60901}, {38167, 49684}, {38314, 50831}, {38317, 51147}, {38455, 61534}, {41869, 61254}, {41983, 51705}, {43827, 50476}, {45976, 54391}, {46219, 46932}, {46930, 55866}, {46931, 55858}, {46934, 55857}, {49163, 51781}, {50825, 50871}, {51073, 61290}, {51192, 59399}, {54324, 59588}

X(61510) = midpoint of X(i) and X(j) for these {i,j}: {3, 37705}, {5, 8}, {355, 5690}, {381, 50823}, {549, 50798}, {550, 18525}, {944, 61245}, {1385, 47745}, {1483, 12645}, {3625, 10222}, {3627, 12702}, {3845, 34718}, {4701, 13464}, {5493, 33697}, {5657, 61251}, {5790, 59400}, {5881, 34773}, {6101, 16980}, {8703, 34627}, {10283, 51515}, {10916, 32537}, {11362, 18480}, {11698, 19914}, {15686, 50864}, {15687, 50810}, {33699, 34632}, {34641, 51709}, {38112, 59388}, {38138, 59503}, {61249, 61524}
X(61510) = reflection of X(i) in X(j) for these {i,j}: {1, 3628}, {140, 10}, {143, 23841}, {10222, 61272}, {1483, 51700}, {12103, 3579}, {12699, 3861}, {14893, 50796}, {15178, 3634}, {18480, 61255}, {18481, 33923}, {22791, 3850}, {3244, 61278}, {3655, 11812}, {3656, 11737}, {3853, 18480}, {31162, 3860}, {34200, 50821}, {34773, 3530}, {34791, 58561}, {40273, 19925}, {546, 18357}, {548, 61524}, {50811, 14891}, {50824, 10124}, {5885, 3918}, {5901, 9956}, {61280, 10172}, {61286, 1125}, {61292, 15178}, {61597, 5901}, {61601, 61553}, {946, 61259}, {960, 58632}
X(61510) = complement of X(1483)
X(61510) = anticomplement of X(51700)
X(61510) = X(i)-Dao conjugate of X(j) for these {i, j}: {51700, 51700}
X(61510) = pole of line {28221, 48391} with respect to the circumcircle
X(61510) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 38042, 3628}, {2, 12645, 1483}, {2, 1483, 51700}, {3, 3617, 38112}, {3, 37705, 28224}, {3, 59388, 37705}, {4, 4678, 59503}, {5, 59400, 8}, {5, 8, 5844}, {8, 5818, 1482}, {10, 47745, 1385}, {10, 5882, 11231}, {10, 952, 140}, {145, 1656, 10283}, {355, 3654, 5691}, {355, 3679, 5690}, {355, 5690, 30}, {515, 61524, 548}, {517, 19925, 40273}, {519, 5901, 61597}, {519, 9956, 5901}, {549, 61245, 944}, {550, 61251, 18525}, {632, 61295, 10246}, {944, 50798, 61245}, {946, 61259, 5066}, {958, 32141, 7508}, {1385, 47745, 952}, {1482, 5790, 5818}, {1482, 5818, 5}, {1656, 51515, 145}, {1698, 37727, 38028}, {2802, 61553, 61601}, {3090, 3621, 10247}, {3244, 11230, 61278}, {3244, 31399, 11230}, {3579, 28186, 12103}, {3617, 59388, 3}, {3625, 10175, 10222}, {3627, 12702, 28216}, {3633, 54447, 61276}, {5260, 38665, 37621}, {5493, 33697, 28182}, {5587, 22791, 3850}, {5657, 18525, 550}, {5881, 26446, 34773}, {5901, 61628, 61551}, {5901, 9956, 547}, {7967, 46933, 3526}, {7982, 61261, 38034}, {10175, 10222, 61272}, {10175, 61272, 12812}, {10827, 41687, 39542}, {10944, 18395, 15325}, {11362, 18480, 28174}, {11362, 38155, 18480}, {11362, 61255, 3853}, {12702, 59387, 3627}, {18357, 40273, 19925}, {18480, 38155, 61255}, {19925, 40273, 546}, {26446, 34773, 3530}, {34627, 38066, 8703}, {34627, 51068, 38066}, {34718, 38074, 3845}, {35788, 49233, 7583}, {35789, 49232, 7584}, {37702, 45081, 15170}, {37710, 40663, 18990}, {38034, 61261, 12811}, {38074, 51072, 34718}, {38138, 59503, 28212}, {50798, 53620, 549}, {55856, 61283, 3616}, {61249, 61524, 515}, {61545, 61549, 61509}

X(61511) = MIDPOINT OF X(5) AND X(9)

Barycentrics    2*a^6-2*a^5*(b+c)+(b-c)^4*(b+c)^2-4*a*(b-c)^2*(b+c)^3-5*a^4*(b^2+c^2)+6*a^3*(b+c)*(b^2+c^2)+2*a^2*(b-c)^2*(b^2+3*b*c+c^2) : :
X(61511) = -X[1]+3*X[38043], 3*X[2]+X[5779], X[3]+3*X[5817], -X[4]+3*X[38139], -X[6]+3*X[38166], -X[7]+5*X[1656], -X[8]+3*X[38175], -X[10]+3*X[38179], -X[11]+3*X[38180], -X[12]+3*X[38181], X[144]+7*X[3090], 3*X[381]+X[5759] and many others

X(61511) lies on these lines: {1, 38043}, {2, 5779}, {3, 5817}, {4, 38139}, {5, 9}, {6, 38166}, {7, 1656}, {8, 38175}, {10, 38179}, {11, 38180}, {12, 38181}, {30, 31658}, {140, 971}, {142, 3628}, {143, 58473}, {144, 3090}, {381, 5759}, {382, 59418}, {390, 5790}, {442, 61012}, {495, 15299}, {496, 15298}, {498, 60910}, {499, 60909}, {516, 546}, {518, 5901}, {527, 547}, {528, 61553}, {549, 5732}, {550, 21153}, {632, 38122}, {944, 16860}, {952, 1001}, {954, 12433}, {984, 15251}, {1156, 38752}, {1385, 38059}, {1445, 24470}, {1482, 5686}, {1483, 38316}, {1536, 60709}, {1594, 60879}, {1698, 12679}, {2476, 61026}, {2550, 6929}, {2801, 61531}, {3062, 31423}, {3091, 21168}, {3243, 10283}, {3305, 8727}, {3526, 21151}, {3579, 38130}, {3624, 38030}, {3627, 59389}, {3826, 60911}, {3845, 38075}, {3850, 18482}, {3851, 59385}, {3925, 34789}, {4187, 60969}, {4193, 61025}, {4312, 54447}, {4422, 48888}, {5055, 6172}, {5056, 59386}, {5070, 59380}, {5079, 60983}, {5220, 20330}, {5223, 5886}, {5542, 11230}, {5690, 38057}, {5694, 30329}, {5714, 60941}, {5719, 5728}, {5729, 6861}, {5763, 6846}, {5768, 11108}, {5777, 50205}, {5789, 17559}, {5811, 50726}, {5818, 52653}, {5844, 24393}, {5845, 24206}, {5851, 58421}, {5853, 61510}, {5856, 60759}, {5857, 61512}, {6007, 61527}, {6068, 23513}, {6147, 6887}, {6173, 15699}, {6253, 41872}, {6690, 58683}, {6856, 61009}, {6858, 12848}, {6881, 37787}, {6882, 60981}, {6922, 60958}, {6982, 40333}, {7308, 37364}, {7393, 60897}, {7486, 20059}, {7741, 60919}, {7951, 60883}, {8226, 27065}, {8236, 12645}, {8581, 15325}, {8703, 38067}, {8976, 60887}, {9780, 38121}, {10021, 61525}, {10157, 51489}, {10175, 51090}, {10392, 24929}, {10398, 11374}, {10576, 60913}, {10577, 60914}, {10861, 13747}, {11372, 26446}, {11793, 58534}, {12528, 17590}, {12619, 38216}, {12630, 51515}, {12812, 61000}, {13374, 58678}, {13405, 15008}, {14561, 50995}, {14848, 50996}, {15171, 15837}, {15254, 18357}, {15481, 61269}, {15570, 61280}, {15587, 47742}, {15703, 59374}, {15726, 61614}, {15733, 61533}, {16239, 43177}, {16814, 53599}, {17768, 61530}, {18412, 37737}, {18446, 50202}, {18480, 38158}, {20195, 38111}, {21850, 38145}, {22791, 38037}, {28224, 43175}, {30424, 38172}, {34595, 52665}, {34773, 38031}, {35018, 60942}, {35595, 37374}, {37406, 54370}, {37532, 60949}, {37705, 38154}, {38022, 51099}, {38025, 50824}, {38036, 61268}, {38079, 51002}, {38080, 60963}, {38081, 51102}, {38083, 51100}, {38088, 50979}, {38097, 50823}, {38101, 50821}, {38115, 47355}, {38117, 48906}, {38123, 51073}, {38126, 43166}, {38131, 38602}, {38317, 51150}, {39542, 41712}, {40273, 42356}, {40659, 58632}, {42819, 61286}, {42871, 61278}, {47599, 60999}, {48154, 58433}, {51194, 59399}, {51514, 60957}, {58608, 58631}, {61520, 61559}, {61549, 61621}

X(61511) = midpoint of X(i) and X(j) for these {i,j}: {3, 60901}, {5, 9}, {550, 31672}, {3826, 60911}, {5220, 20330}, {5694, 30329}, {5779, 31657}, {5817, 38113}, {11793, 58534}, {13374, 58678}, {38139, 59381}, {38171, 51516}, {42356, 60912}, {58608, 58631}, {61509, 61596}
X(61511) = reflection of X(i) in X(j) for these {i,j}: {140, 6666}, {142, 3628}, {143, 58473}, {18482, 3850}, {20330, 61272}, {40273, 42356}, {40659, 58632}, {42871, 61278}, {61286, 42819}, {61509, 61595}
X(61511) = complement of X(31657)
X(61511) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5779, 31657}, {3, 5817, 60901}, {5, 9, 5762}, {7, 1656, 38171}, {9, 38108, 5}, {142, 38318, 3628}, {144, 3090, 38107}, {527, 61595, 61509}, {547, 61509, 61595}, {547, 61539, 61535}, {971, 6666, 140}, {1656, 51516, 7}, {3091, 21168, 31671}, {3526, 60884, 21151}, {3628, 5843, 142}, {5056, 61006, 59386}, {5070, 59380, 60996}, {18583, 61522, 5901}, {18583, 61529, 61522}, {21153, 31672, 550}, {38111, 55856, 20195}, {38113, 60901, 3}, {61509, 61596, 527}, {61517, 61546, 61524}, {61522, 61528, 18583}

X(61512) = MIDPOINT OF X(5) AND X(12)

Barycentrics    -2*(b-c)^4*(b+c)^3+2*a^5*(b^2+b*c+c^2)-2*a^4*(b+c)*(b^2+b*c+c^2)+a*(b^2-c^2)^2*(2*b^2-3*b*c+2*c^2)+2*a^2*(b-c)^2*(b+c)*(2*b^2+3*b*c+2*c^2)+a^3*(-4*b^4+b^3*c+4*b^2*c^2+b*c^3-4*c^4) : :
X(61512) = -X[2]+3*X[38085], -X[3]+3*X[38114], -X[4]+3*X[38142], -X[6]+3*X[38169], -X[7]+3*X[38174], -X[8]+3*X[38178], -X[9]+3*X[38181], -X[10]+3*X[38183], 3*X[381]+X[11491], X[382]+3*X[59421], -3*X[549]+X[30264], -X[550]+3*X[21155] and many others

X(61512) lies on these lines: {1, 5}, {2, 38085}, {3, 38114}, {4, 38142}, {6, 38169}, {7, 38174}, {8, 38178}, {9, 38181}, {10, 38183}, {30, 31659}, {140, 3822}, {143, 58476}, {381, 11491}, {382, 59421}, {442, 26878}, {529, 547}, {546, 5842}, {549, 30264}, {550, 21155}, {758, 9956}, {1329, 61530}, {1385, 38062}, {1482, 5141}, {1656, 2975}, {2475, 33814}, {2476, 5690}, {3090, 20060}, {3579, 38134}, {3628, 3814}, {3845, 38078}, {4996, 45976}, {5253, 34126}, {5499, 16113}, {5790, 6874}, {5844, 25639}, {5849, 18583}, {5852, 61509}, {5855, 61510}, {5857, 61511}, {5949, 59680}, {6763, 54447}, {6830, 34773}, {6831, 28186}, {6842, 28174}, {6862, 10590}, {6863, 10599}, {6888, 10742}, {6901, 38752}, {6914, 10895}, {6917, 10588}, {6928, 10585}, {6941, 38034}, {6952, 38135}, {6971, 38028}, {6980, 22791}, {7504, 22765}, {7548, 18524}, {7680, 40273}, {8703, 38070}, {9654, 32153}, {10021, 33961}, {10129, 25413}, {11230, 51111}, {11263, 12619}, {11681, 38042}, {11849, 17577}, {12623, 61622}, {12877, 37230}, {13565, 58631}, {13743, 22799}, {15699, 31157}, {18480, 38162}, {19925, 46028}, {21850, 38148}, {22938, 38163}, {24387, 61597}, {31260, 55856}, {31479, 32141}, {31657, 38206}, {37438, 61614}, {38022, 51112}, {38027, 50824}, {38083, 51113}, {38091, 50979}, {38100, 50823}, {38105, 50821}, {38120, 48906}, {38160, 60901}, {39504, 61519}, {39505, 61547}, {41858, 41991}, {44235, 61518}, {47400, 53809}, {61557, 61581}

X(61512) = midpoint of X(i) and X(j) for these {i,j}: {5, 12}, {37710, 61148}, {38114, 59392}, {38142, 59382}
X(61512) = reflection of X(i) in X(j) for these {i,j}: {140, 6668}, {143, 58476}, {4999, 3628}
X(61512) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 10283, 7741}, {5, 119, 61259}, {5, 5901, 60759}, {12, 38109, 5}, {12, 38184, 61278}, {12, 8068, 37737}, {1484, 15888, 61281}, {5886, 37710, 61148}, {37710, 61148, 952}

X(61513) = MIDPOINT OF X(5) AND X(15)

Barycentrics    2*a^6-5*a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)+2*a^2*(b^4-4*b^2*c^2+c^4)+2*sqrt(3)*(2*a^4+(b^2-c^2)^2-3*a^2*(b^2+c^2))*S : :

X(61513) lies on these lines: {2, 5611}, {3, 59397}, {5, 15}, {13, 30560}, {16, 38230}, {17, 20429}, {30, 5459}, {61, 53465}, {62, 10617}, {114, 6109}, {140, 143}, {187, 11542}, {230, 22691}, {303, 47517}, {381, 36993}, {396, 11136}, {397, 39554}, {485, 10671}, {486, 10667}, {531, 547}, {546, 21401}, {549, 14538}, {550, 21158}, {597, 44488}, {621, 1656}, {623, 630}, {952, 11707}, {1080, 47610}, {1352, 42152}, {1353, 36757}, {2080, 37340}, {3055, 11543}, {3530, 36755}, {3627, 41036}, {3845, 36992}, {5055, 51484}, {5613, 41943}, {5617, 16962}, {5886, 51688}, {5901, 44659}, {6669, 61576}, {6780, 59402}, {8838, 37975}, {10124, 48313}, {10283, 51689}, {10723, 60273}, {12042, 41070}, {14561, 42092}, {15122, 47575}, {15699, 50855}, {16181, 58912}, {16241, 44223}, {16529, 22507}, {16967, 53469}, {18358, 43197}, {18582, 43618}, {19780, 40693}, {20415, 44667}, {23004, 38229}, {31709, 34602}, {32225, 46862}, {32460, 47324}, {33417, 59404}, {33518, 42143}, {35229, 42598}, {36760, 53455}, {36958, 42992}, {36967, 59401}, {37851, 50213}, {38022, 50854}, {38042, 50853}, {38079, 51017}, {38317, 51161}, {40334, 55856}, {41586, 46833}, {42121, 51206}, {49106, 51753}, {51162, 52994}

X(61513) = midpoint of X(i) and X(j) for these {i,j}: {5, 15}, {396, 52650}, {1080, 47610}, {7684, 13350}, {12042, 41070}, {15122, 47575}, {16181, 58912}, {42912, 52266}, {51162, 52994}
X(61513) = reflection of X(i) in X(j) for these {i,j}: {140, 6671}, {143, 58477}, {36755, 3530}, {623, 3628}, {61514, 14693}
X(61513) = pole of line {62, 1506} with respect to the Kiepert hyperbola
X(61513) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {15, 59403, 5}, {17, 39555, 53429}, {140, 61537, 61538}, {511, 58477, 143}, {511, 6671, 140}, {6109, 14138, 10613}, {7684, 13350, 30}, {7684, 45879, 13350}, {10613, 14138, 42912}, {11272, 58445, 61514}, {61514, 61537, 18583}

X(61514) = MIDPOINT OF X(5) AND X(16)

Barycentrics    2*a^6-5*a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)+2*a^2*(b^4-4*b^2*c^2+c^4)-2*sqrt(3)*(2*a^4+(b^2-c^2)^2-3*a^2*(b^2+c^2))*S : :

X(61514) lies on these lines: {2, 5615}, {3, 59398}, {5, 16}, {14, 30559}, {15, 38230}, {18, 20428}, {30, 5460}, {61, 10616}, {62, 53454}, {114, 6108}, {140, 143}, {187, 11543}, {230, 22692}, {302, 47519}, {381, 36995}, {383, 47611}, {395, 11135}, {398, 39555}, {485, 10672}, {486, 10668}, {530, 547}, {546, 21402}, {549, 14539}, {550, 21159}, {597, 44487}, {622, 1656}, {624, 629}, {952, 11708}, {1352, 42149}, {1353, 36758}, {2080, 37341}, {3055, 11542}, {3530, 36756}, {3627, 41037}, {3845, 36994}, {5055, 51485}, {5613, 16963}, {5617, 41944}, {5886, 51690}, {5901, 44660}, {6670, 61576}, {6779, 59401}, {8836, 37974}, {10124, 48314}, {10283, 51691}, {10723, 60272}, {12042, 41071}, {14561, 42089}, {15122, 47576}, {15699, 50858}, {16182, 58913}, {16242, 52650}, {16530, 22509}, {16966, 53458}, {18358, 43198}, {18581, 43618}, {19781, 40694}, {20416, 44666}, {23005, 38229}, {32225, 46863}, {32461, 47324}, {33416, 59403}, {33517, 42146}, {35230, 42599}, {36759, 53466}, {36765, 43200}, {36959, 42993}, {36968, 59402}, {37852, 50214}, {38022, 50857}, {38042, 50856}, {38079, 51019}, {38317, 51162}, {40335, 55856}, {41586, 46834}, {42124, 51207}, {49105, 51754}, {51161, 52994}

X(61514) = midpoint of X(i) and X(j) for these {i,j}: {5, 16}, {383, 47611}, {395, 44223}, {7685, 13349}, {12042, 41071}, {15122, 47576}, {16182, 58913}, {42913, 52263}, {51161, 52994}
X(61514) = reflection of X(i) in X(j) for these {i,j}: {140, 6672}, {143, 58478}, {36756, 3530}, {624, 3628}, {61513, 14693}
X(61514) = pole of line {61, 1506} with respect to the Kiepert hyperbola
X(61514) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16, 59404, 5}, {18, 39554, 53441}, {140, 61538, 61537}, {511, 58478, 143}, {6108, 14139, 10614}, {7685, 13349, 30}, {7685, 45880, 13349}, {10614, 14139, 42913}, {11272, 58445, 61513}, {61513, 61538, 18583}

X(61515) = MIDPOINT OF X(5) AND X(17)

Barycentrics    3*(2*a^6-5*a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)+2*a^2*(b^4-4*b^2*c^2+c^4))+2*sqrt(3)*(2*a^4+9*(b^2-c^2)^2-11*a^2*(b^2+c^2))*S : :

X(61515) lies on these lines: {2, 16629}, {3, 33413}, {5, 14}, {18, 38231}, {30, 22832}, {140, 6669}, {187, 31705}, {381, 22532}, {495, 22930}, {496, 22929}, {532, 547}, {546, 21401}, {549, 22890}, {590, 35847}, {615, 35848}, {624, 629}, {627, 1656}, {952, 11739}, {3090, 22113}, {3091, 48666}, {3845, 52838}, {3850, 22795}, {5055, 51486}, {5886, 22652}, {5965, 12812}, {7583, 49239}, {7584, 49238}, {10283, 22912}, {10592, 22904}, {10593, 22905}, {10611, 12815}, {11132, 59635}, {11230, 51116}, {11602, 38229}, {13861, 22657}, {15325, 18973}, {15699, 50859}, {19070, 19116}, {19071, 19117}, {20415, 61560}, {21841, 22482}, {22892, 31710}, {22894, 42915}, {22896, 38042}, {22900, 23303}, {22901, 42914}, {22906, 42124}, {22907, 42098}, {23302, 31704}, {33465, 35018}, {35230, 42166}, {36782, 42488}, {37463, 41055}, {37825, 49907}, {51208, 59399}

X(61515) = midpoint of X(i) and X(j) for these {i,j}: {5, 17}, {22832, 49106}
X(61515) = reflection of X(i) in X(j) for these {i,j}: {140, 6673}, {22795, 3850}, {629, 3628}
X(61515) = pole of line {16, 49106} with respect to the Kiepert hyperbola
X(61515) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 61537, 20253}, {17, 22891, 8259}, {12812, 18583, 61516}, {22832, 49106, 30}

X(61516) = MIDPOINT OF X(5) AND X(18)

Barycentrics    3*(2*a^6-5*a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)+2*a^2*(b^4-4*b^2*c^2+c^4))-2*sqrt(3)*(2*a^4+9*(b^2-c^2)^2-11*a^2*(b^2+c^2))*S : :

X(61516) lies on these lines: {2, 16628}, {3, 33412}, {5, 13}, {17, 38231}, {30, 22831}, {140, 6670}, {187, 31706}, {381, 22531}, {495, 22885}, {496, 22884}, {533, 547}, {546, 21402}, {549, 22843}, {590, 35849}, {615, 35846}, {623, 630}, {628, 1656}, {952, 11740}, {3090, 22114}, {3091, 48665}, {3845, 52839}, {3850, 22794}, {5055, 51487}, {5886, 22651}, {5965, 12812}, {7583, 49237}, {7584, 49236}, {10283, 22867}, {10592, 22859}, {10593, 22860}, {10612, 12815}, {11133, 59635}, {11230, 51117}, {11603, 38229}, {13861, 22656}, {15325, 18972}, {15699, 50860}, {19069, 19117}, {19072, 19116}, {20416, 61560}, {21841, 22481}, {22848, 31709}, {22850, 42914}, {22851, 38042}, {22855, 42915}, {22856, 23302}, {22861, 42095}, {22862, 42121}, {23303, 31703}, {33464, 35018}, {35229, 42163}, {37464, 41054}, {37824, 49908}, {42489, 59402}, {51209, 59399}

X(61516) = midpoint of X(i) and X(j) for these {i,j}: {5, 18}, {22831, 49105}
X(61516) = reflection of X(i) in X(j) for these {i,j}: {140, 6674}, {22794, 3850}, {630, 3628}
X(61516) = pole of line {15, 49105} with respect to the Kiepert hyperbola
X(61516) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 61538, 20252}, {18, 22846, 8260}, {12812, 18583, 61515}, {22831, 49105, 30}

X(61517) = MIDPOINT OF X(5) AND X(19)

Barycentrics    2*a^9+a^5*(b^2-c^2)^2-3*a*(b^2-c^2)^4-5*a^7*(b^2+c^2)+a^6*(b+c)*(b^2+c^2)+(b-c)^4*(b+c)^3*(b^2+c^2)+5*a^3*(b^2-c^2)^2*(b^2+c^2)-a^2*(b-c)^2*(b+c)*(b^4-2*b^3*c-2*b^2*c^2-2*b*c^3+c^4)-a^4*(b^5+3*b^4*c+3*b*c^4+c^5) : :
X(61517) = -3*X[549]+X[30265], -X[550]+3*X[21160], -5*X[1656]+X[4329], 7*X[3090]+X[20061], -3*X[3845]+X[52840], -3*X[15699]+X[31158], -5*X[31261]+7*X[55856], -3*X[38042]+X[50861], -X[51210]+3*X[59399]

X(61517) lies on these lines: {5, 19}, {140, 40530}, {516, 546}, {534, 547}, {549, 30265}, {550, 21160}, {952, 51687}, {1486, 13861}, {1656, 4329}, {1871, 52259}, {3090, 20061}, {3628, 18589}, {3668, 34753}, {3827, 18583}, {3845, 52840}, {5901, 44661}, {8680, 61539}, {12106, 39475}, {15699, 31158}, {31261, 55856}, {38042, 50861}, {44233, 44670}, {46181, 61550}, {51210, 59399}

X(61517) = midpoint of X(i) and X(j) for these {i,j}: {5, 19}
X(61517) = reflection of X(i) in X(j) for these {i,j}: {140, 40530}, {18589, 3628}
X(61517) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {61511, 61524, 61546}

X(61518) = MIDPOINT OF X(5) AND X(33)

Barycentrics    2*a^10-2*a^9*(b+c)-5*a^8*(b^2+c^2)+4*a^7*(b+c)*(b^2+c^2)+2*a^5*b*c*(b+c)*(b^2+c^2)+(b^2-c^2)^4*(b^2+c^2)+2*a^6*(b-c)^2*(b^2+b*c+c^2)+2*a*(b-c)^4*(b+c)^3*(b^2+3*b*c+c^2)-4*a^3*(b-c)^2*(b+c)*(b^4+3*b^3*c+3*b^2*c^2+3*b*c^3+c^4)-2*a^2*(b^2-c^2)^2*(2*b^4+b^3*c-4*b^2*c^2+b*c^3+2*c^4)+4*a^4*(b^6+b^5*c-2*b^4*c^2-2*b^2*c^4+b*c^5+c^6) : :
X(61518) = -3*X[549]+X[36984], -5*X[1656]+X[52365], -3*X[3845]+X[52848], 3*X[5886]+X[36985]

X(61518) lies on these lines: {5, 33}, {140, 58402}, {197, 13861}, {515, 546}, {549, 36984}, {1656, 52365}, {2823, 61535}, {3628, 34822}, {3845, 52848}, {5886, 36985}, {39504, 60745}, {44232, 61520}, {44233, 44670}, {44235, 61512}, {44236, 61521}, {61540, 61541}

X(61518) = midpoint of X(i) and X(j) for these {i,j}: {5, 33}
X(61518) = reflection of X(i) in X(j) for these {i,j}: {140, 58402}, {34822, 3628}
X(61518) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {546, 5901, 61519}

X(61519) = MIDPOINT OF X(5) AND X(34)

Barycentrics    2*a^10-2*a^9*(b+c)+4*a^7*(b-c)^2*(b+c)+a^8*(-5*b^2+8*b*c-5*c^2)+(b^2-c^2)^4*(b^2+c^2)+2*a*(b-c)^4*(b+c)^3*(b^2-3*b*c+c^2)+2*a^5*b*c*(b+c)*(3*b^2-8*b*c+3*c^2)+2*a^6*(b^4-3*b^3*c+8*b^2*c^2-3*b*c^3+c^4)-2*a^2*(b^2-c^2)^2*(2*b^4-5*b^3*c+8*b^2*c^2-5*b*c^3+2*c^4)-4*a^3*(b-c)^2*(b^5-4*b^3*c^2-4*b^2*c^3+c^5)+4*a^4*(b^6-3*b^5*c+4*b^3*c^3-3*b*c^5+c^6) : :
X(61519) = -3*X[549]+X[36986], -5*X[1656]+X[52366], -3*X[3845]+X[52849]

X(61519) lies on these lines: {5, 34}, {140, 58403}, {515, 546}, {549, 36986}, {1656, 52366}, {2840, 61568}, {3628, 34823}, {3827, 18583}, {3845, 52849}, {13861, 22654}, {39504, 61512}, {44232, 61521}, {44233, 61534}, {44235, 60759}, {44236, 61520}, {61530, 61571}, {61535, 61536}, {61557, 61558}

X(61519) = midpoint of X(i) and X(j) for these {i,j}: {5, 34}
X(61519) = reflection of X(i) in X(j) for these {i,j}: {140, 58403}, {34823, 3628}
X(61519) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {546, 5901, 61518}

X(61520) = MIDPOINT OF X(5) AND X(35)

Barycentrics    2*a^7-2*a^6*(b+c)+(b-c)^4*(b+c)^3+a^5*(-5*b^2+2*b*c-5*c^2)-a*(b^2-c^2)^2*(b^2-b*c+c^2)-4*a^2*(b-c)^2*(b+c)*(b^2+b*c+c^2)+a^4*(b+c)*(5*b^2-2*b*c+5*c^2)+a^3*(4*b^4-3*b^3*c-3*b*c^3+4*c^4) : :
X(61520) = 3*X[2]+X[11849], -3*X[549]+X[11012], -5*X[1656]+X[52367], 7*X[3090]+X[20066], -X[3627]+3*X[52850], 3*X[4995]+X[26470], -X[5086]+3*X[38042], 3*X[5886]+X[11010], -X[6842]+3*X[38114], X[6906]+3*X[59382], -X[11280]+5*X[61276], X[15338]+3*X[38109] and many others

X(61520) lies on these lines: {2, 11849}, {5, 35}, {30, 31659}, {119, 31649}, {140, 517}, {442, 33814}, {498, 6914}, {549, 11012}, {952, 2646}, {1484, 3746}, {1656, 52367}, {1900, 21841}, {2077, 5499}, {2779, 61547}, {3035, 3628}, {3085, 32153}, {3090, 20066}, {3627, 52850}, {3822, 26086}, {3911, 58561}, {4995, 26470}, {4999, 5844}, {5086, 38042}, {5218, 6862}, {5433, 10283}, {5690, 7483}, {5719, 13750}, {5745, 58640}, {5840, 6668}, {5843, 59476}, {5886, 11010}, {6675, 24982}, {6713, 33281}, {6745, 58632}, {6842, 38114}, {6853, 35000}, {6888, 18524}, {6906, 59382}, {6920, 38752}, {6952, 37621}, {7489, 27529}, {7504, 10738}, {9047, 18583}, {9956, 10021}, {10095, 38472}, {10197, 32612}, {10225, 11263}, {11011, 15325}, {11277, 31663}, {11280, 61276}, {11929, 19535}, {12619, 35016}, {13405, 58569}, {13411, 14988}, {14217, 38410}, {14526, 45065}, {14794, 52793}, {15178, 61566}, {15338, 38109}, {15699, 31159}, {16160, 44425}, {16617, 61259}, {17531, 38762}, {19914, 51683}, {22765, 37291}, {24953, 38112}, {28174, 52265}, {31262, 55856}, {31835, 59719}, {37568, 61272}, {44232, 61518}, {44236, 61519}, {46684, 49107}, {61511, 61559}, {61526, 61536}

X(61520) = midpoint of X(i) and X(j) for these {i,j}: {5, 35}
X(61520) = reflection of X(i) in X(j) for these {i,j}: {140, 58404}, {11011, 61278}, {25639, 3628}, {33281, 51700}
X(61520) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {140, 5901, 61521}, {140, 61533, 5901}, {517, 58404, 140}, {5218, 6862, 32141}, {5901, 61614, 61530}, {10021, 61562, 9956}

X(61521) = MIDPOINT OF X(5) AND X(36)

Barycentrics    2*a^7-2*a^6*(b+c)+(b-c)^4*(b+c)^3+a^5*(-5*b^2+6*b*c-5*c^2)-4*a^2*(b-c)^2*(b+c)*(b^2+c^2)-a*(b^2-c^2)^2*(b^2-3*b*c+c^2)+a^3*(b^2+c^2)*(4*b^2-9*b*c+4*c^2)+a^4*(b+c)*(5*b^2-6*b*c+5*c^2) : :
X(61521) = 3*X[2]+X[22765], X[119]+3*X[5298], X[484]+3*X[5886], -3*X[549]+X[2077], -5*X[631]+X[35000], X[1155]+2*X[61272], X[1325]+3*X[57325], -X[1484]+3*X[3582], -5*X[1656]+X[5080], 7*X[3090]+X[20067], 7*X[3624]+X[5535], -3*X[3845]+X[52851] and many others

X(61521) lies on these lines: {2, 22765}, {5, 36}, {30, 6713}, {119, 5298}, {140, 517}, {484, 5886}, {496, 32760}, {499, 5172}, {515, 61553}, {519, 61562}, {529, 58421}, {535, 547}, {549, 2077}, {631, 35000}, {946, 10225}, {952, 1319}, {1155, 61272}, {1325, 57325}, {1482, 17566}, {1484, 3582}, {1532, 38602}, {1656, 5080}, {1878, 21841}, {2078, 10943}, {2392, 61536}, {3035, 5844}, {3086, 32141}, {3090, 20067}, {3624, 5535}, {3628, 3814}, {3816, 7508}, {3845, 52851}, {3911, 14988}, {4640, 11230}, {5048, 61278}, {5122, 61269}, {5126, 18357}, {5131, 8227}, {5176, 38042}, {5193, 10942}, {5432, 10283}, {5442, 27247}, {5537, 14869}, {5570, 5719}, {5690, 13747}, {5841, 6667}, {6700, 58641}, {6797, 44675}, {6882, 34126}, {6905, 57298}, {6911, 41345}, {6945, 18515}, {6949, 37535}, {6959, 7288}, {6979, 26321}, {8254, 61547}, {9037, 18583}, {10021, 61552}, {10199, 32613}, {10738, 13587}, {11928, 19537}, {13411, 58561}, {15326, 23513}, {15699, 31160}, {18838, 34753}, {19907, 40663}, {20418, 28224}, {22835, 40273}, {24953, 31263}, {24987, 52264}, {25405, 61286}, {31224, 61146}, {31659, 51700}, {37737, 53615}, {38752, 54391}, {44232, 61519}, {44236, 61518}, {44898, 53809}, {58453, 58604}, {61556, 61559}

X(61521) = midpoint of X(i) and X(j) for these {i,j}: {5, 36}, {946, 10225}, {1532, 38602}, {11813, 41347}, {19907, 40663}
X(61521) = reflection of X(i) in X(j) for these {i,j}: {140, 6681}, {3814, 3628}, {40273, 22835}, {5048, 61278}, {61286, 25405}
X(61521) = pole of line {12758, 37734} with respect to the Feuerbach hyperbola
X(61521) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {140, 5901, 61520}, {517, 6681, 140}, {1125, 61541, 5901}, {6959, 7288, 32153}, {11230, 41347, 11813}

X(61522) = MIDPOINT OF X(5) AND X(37)

Barycentrics    a^5*(b+c)+2*a*(b-c)^2*(b+c)^3+b*c*(b^2-c^2)^2-a^2*b*c*(b^2+c^2)-3*a^3*(b+c)*(b^2+c^2) : :
X(61522) = 3*X[2]+X[20430], -X[3]+5*X[4687], X[4]+7*X[27268], -X[75]+5*X[1656], X[192]+7*X[3090], 3*X[381]+X[30273], -3*X[549]+X[30271], X[984]+3*X[5886], -X[1278]+17*X[7486], -X[3696]+3*X[38042], -3*X[3845]+X[52852], X[3993]+3*X[10175] and many others

X(61522) lies on these lines: {2, 20430}, {3, 4687}, {4, 27268}, {5, 37}, {30, 4755}, {75, 1656}, {140, 4698}, {143, 58485}, {192, 3090}, {381, 30273}, {517, 3842}, {518, 5901}, {536, 547}, {549, 30271}, {726, 11272}, {740, 9956}, {742, 24206}, {952, 15569}, {984, 5886}, {1278, 7486}, {2805, 61562}, {3628, 3739}, {3696, 38042}, {3845, 52852}, {3993, 10175}, {4664, 5055}, {4681, 35018}, {4688, 15699}, {4699, 5067}, {4704, 5056}, {4709, 31399}, {4751, 5070}, {4772, 46936}, {5071, 51040}, {5779, 27475}, {5790, 49470}, {7697, 32453}, {9624, 49448}, {9955, 29054}, {10124, 51049}, {10222, 49457}, {10247, 49450}, {10283, 49478}, {11178, 50779}, {11230, 24325}, {11737, 51041}, {11793, 58554}, {13374, 58693}, {13476, 58561}, {14561, 49509}, {15687, 51042}, {15694, 51044}, {15702, 51064}, {15703, 51039}, {17260, 37510}, {20718, 61541}, {22271, 58632}, {23513, 51062}, {24220, 29369}, {28581, 61510}, {29331, 48888}, {31238, 55856}, {37365, 44307}, {38083, 50096}, {38107, 51052}, {38108, 51058}, {38317, 49481}, {44233, 44670}, {44671, 61526}, {49474, 54447}, {49490, 61276}, {49498, 61275}, {50094, 51709}, {58620, 58631}, {61558, 61621}

X(61522) = midpoint of X(i) and X(j) for these {i,j}: {5, 37}, {381, 51045}, {549, 51038}, {10222, 49457}, {11178, 50779}, {11793, 58554}, {13374, 58693}, {15687, 51042}, {50094, 51709}, {58620, 58631}, {61549, 61623}
X(61522) = reflection of X(i) in X(j) for these {i,j}: {140, 4698}, {143, 58485}, {13476, 58561}, {22271, 58632}, {3739, 3628}, {51041, 11737}, {51049, 10124}
X(61522) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 37, 29010}, {381, 51488, 51045}, {547, 61623, 61549}, {5901, 61511, 18583}, {18583, 61511, 61528}, {18583, 61529, 61511}

X(61523) = MIDPOINT OF X(5) AND X(38)

Barycentrics    b*(b-c)^2*c*(b+c)^3+2*a^5*(b^2+c^2)-a^4*(b+c)*(b^2+c^2)+3*a*(b^2-c^2)^2*(b^2+c^2)-5*a^3*(b^2+c^2)^2+a^2*(b^5-3*b^3*c^2-3*b^2*c^3+c^5) : :
X(61523) = -3*X[549]+X[30272], -5*X[1656]+X[17165], 7*X[3090]+X[20068], -3*X[3845]+X[52853], -X[4692]+3*X[38042], -3*X[15699]+X[31161], -5*X[31264]+7*X[55856]

X(61523) lies on these lines: {5, 38}, {140, 6682}, {518, 61526}, {537, 547}, {549, 30272}, {714, 61549}, {758, 5901}, {1215, 3628}, {1484, 12770}, {1656, 17165}, {3090, 20068}, {3845, 52853}, {4692, 38042}, {5769, 17599}, {9020, 18583}, {9956, 59717}, {15699, 31161}, {31264, 55856}, {46183, 61550}

X(61523) = midpoint of X(i) and X(j) for these {i,j}: {5, 38}
X(61523) = reflection of X(i) in X(j) for these {i,j}: {140, 6682}, {1215, 3628}
X(61523) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5901, 61539, 20575}

X(61524) = MIDPOINT OF X(5) AND X(40)

Barycentrics    2*a^4+2*a^3*(b+c)-2*a*(b-c)^2*(b+c)+(b^2-c^2)^2-a^2*(3*b^2+4*b*c+3*c^2) : :
X(61524) = -X[1]+3*X[549], 3*X[2]+X[12702], 3*X[3]+X[8], X[20]+3*X[5790], -X[145]+9*X[3524], 3*X[165]+X[355], 3*X[376]+5*X[3617], 3*X[381]+X[6361], -X[382]+5*X[5818], -3*X[547]+4*X[3634], -3*X[551]+X[11278], -5*X[631]+X[1482] and many others

X(61524) lies on these lines: {1, 549}, {2, 12702}, {3, 8}, {4, 28178}, {5, 40}, {10, 30}, {11, 5445}, {12, 79}, {20, 5790}, {21, 35000}, {35, 5428}, {42, 5453}, {46, 495}, {55, 12433}, {65, 5719}, {71, 7359}, {80, 15338}, {98, 29137}, {140, 517}, {143, 58487}, {145, 3524}, {165, 355}, {186, 12135}, {191, 11698}, {376, 3617}, {381, 6361}, {382, 5818}, {392, 52264}, {405, 35448}, {496, 5119}, {498, 37567}, {500, 3293}, {515, 548}, {516, 546}, {518, 40296}, {519, 12100}, {547, 3634}, {551, 11278}, {572, 4969}, {573, 17369}, {582, 5264}, {590, 35611}, {594, 37508}, {615, 35610}, {631, 1482}, {632, 5886}, {730, 32516}, {756, 5492}, {758, 11277}, {912, 31787}, {946, 3628}, {958, 35238}, {960, 47742}, {962, 1656}, {993, 8256}, {1000, 5265}, {1006, 11849}, {1056, 37545}, {1146, 24047}, {1155, 10039}, {1159, 5703}, {1210, 15172}, {1329, 61580}, {1350, 38116}, {1376, 35239}, {1385, 3244}, {1387, 5433}, {1483, 3576}, {1537, 6949}, {1571, 15048}, {1572, 31406}, {1657, 59387}, {1702, 19116}, {1703, 19117}, {1706, 3587}, {1737, 15171}, {1788, 3295}, {1836, 10592}, {1837, 59316}, {1902, 21841}, {2093, 11374}, {2095, 37407}, {2325, 29327}, {2475, 38058}, {2771, 3678}, {2800, 61551}, {2802, 61566}, {2807, 11591}, {2808, 61615}, {2809, 61565}, {2816, 61603}, {2817, 61571}, {3035, 3878}, {3057, 15325}, {3085, 6147}, {3090, 20070}, {3091, 48661}, {3098, 49524}, {3214, 48927}, {3219, 19919}, {3241, 15693}, {3296, 5708}, {3336, 15888}, {3339, 41870}, {3359, 10942}, {3416, 48906}, {3428, 6924}, {3474, 9654}, {3475, 31480}, {3522, 59388}, {3523, 3623}, {3526, 5603}, {3534, 53620}, {3545, 46932}, {3560, 6244}, {3584, 3649}, {3612, 37728}, {3616, 5054}, {3621, 15692}, {3624, 3656}, {3625, 14891}, {3626, 28204}, {3627, 5587}, {3632, 3655}, {3636, 50829}, {3650, 17757}, {3651, 18524}, {3679, 8703}, {3697, 40263}, {3698, 16617}, {3712, 37619}, {3740, 31937}, {3753, 6675}, {3817, 35018}, {3820, 12514}, {3822, 61552}, {3828, 5066}, {3839, 50809}, {3844, 18358}, {3845, 19875}, {3847, 60759}, {3850, 5493}, {3851, 9812}, {3853, 19925}, {3857, 61263}, {3858, 7989}, {3861, 31399}, {3876, 40266}, {3877, 13747}, {3911, 9957}, {3916, 6735}, {3918, 10021}, {3919, 11281}, {3927, 7080}, {3940, 59591}, {3968, 58449}, {3987, 35466}, {4002, 54357}, {4015, 56762}, {4187, 35460}, {4220, 60459}, {4295, 31479}, {4301, 11230}, {4421, 49168}, {4668, 45759}, {4669, 15759}, {4677, 15711}, {4678, 10304}, {4701, 50827}, {4745, 15690}, {4746, 58187}, {4848, 24929}, {5010, 10950}, {5046, 22938}, {5055, 19877}, {5057, 6842}, {5071, 46931}, {5079, 9779}, {5080, 47032}, {5090, 37458}, {5092, 5846}, {5122, 10106}, {5128, 31434}, {5183, 12047}, {5204, 12647}, {5217, 10573}, {5221, 10056}, {5231, 10943}, {5250, 17527}, {5251, 31649}, {5252, 58887}, {5260, 13743}, {5261, 18541}, {5285, 44220}, {5326, 5443}, {5330, 34123}, {5432, 5903}, {5434, 37524}, {5435, 7373}, {5444, 11280}, {5482, 45955}, {5550, 15694}, {5554, 16370}, {5563, 45081}, {5584, 11499}, {5599, 35245}, {5600, 35244}, {5691, 15704}, {5722, 10386}, {5732, 38126}, {5734, 55863}, {5759, 38121}, {5762, 5880}, {5777, 58632}, {5837, 59675}, {5840, 61553}, {5881, 16192}, {5882, 17502}, {6001, 31835}, {6097, 52139}, {6200, 49233}, {6211, 24697}, {6221, 19065}, {6284, 12019}, {6396, 49232}, {6398, 19066}, {6583, 58607}, {6644, 8193}, {6745, 14988}, {6831, 48363}, {6851, 18231}, {6853, 38114}, {6883, 10306}, {6893, 35514}, {6902, 10738}, {6903, 33110}, {6907, 55104}, {6908, 27525}, {6914, 10310}, {6940, 22765}, {6960, 38752}, {6985, 9709}, {6986, 37621}, {7280, 10944}, {7294, 37735}, {7354, 37572}, {7502, 37557}, {7508, 26285}, {7583, 49227}, {7584, 49226}, {7688, 21677}, {7718, 55572}, {7967, 15717}, {7968, 35256}, {7969, 35255}, {7970, 38750}, {7978, 38794}, {7982, 10283}, {7983, 38739}, {7984, 38728}, {7987, 31425}, {8227, 55856}, {8728, 37584}, {8981, 35774}, {9591, 37936}, {9612, 41348}, {9668, 54361}, {9911, 13861}, {9941, 42787}, {10124, 19862}, {10165, 10222}, {10172, 12812}, {10247, 15720}, {10264, 12778}, {10299, 20054}, {10303, 10595}, {10572, 11545}, {10593, 12701}, {10697, 38774}, {10698, 38762}, {10703, 38786}, {10914, 59491}, {11014, 19907}, {11024, 50726}, {11113, 25005}, {11194, 49169}, {11224, 61277}, {11246, 37719}, {11363, 37935}, {11373, 31231}, {11500, 33899}, {11522, 55859}, {11531, 61276}, {11540, 19883}, {11699, 13392}, {11737, 38083}, {12017, 51192}, {12101, 51069}, {12103, 12512}, {12106, 49553}, {12197, 50250}, {12261, 40685}, {12368, 14677}, {12446, 18227}, {12527, 51362}, {12571, 28232}, {12572, 16004}, {12690, 20066}, {12735, 21842}, {12737, 13144}, {12738, 16132}, {12780, 47611}, {12781, 47610}, {12782, 32521}, {12898, 15051}, {13211, 34153}, {13363, 58469}, {13369, 34790}, {13405, 31794}, {13411, 50193}, {13451, 58474}, {13465, 41543}, {13528, 31777}, {13911, 42216}, {13936, 31439}, {13966, 35775}, {13973, 42215}, {14128, 52796}, {14449, 31760}, {14636, 17751}, {14646, 48664}, {14814, 34560}, {14893, 28202}, {15016, 15104}, {15064, 31828}, {15177, 37814}, {15178, 28234}, {15326, 37710}, {15680, 59415}, {15681, 38074}, {15686, 38081}, {15687, 18492}, {15688, 34627}, {15689, 50864}, {15695, 51068}, {15698, 31145}, {15699, 31162}, {15700, 20050}, {15701, 38314}, {15702, 46934}, {15705, 20052}, {15706, 20053}, {15707, 20057}, {15708, 34631}, {15709, 50872}, {15713, 25055}, {15716, 58224}, {15973, 48924}, {16189, 61279}, {16210, 35241}, {16371, 35252}, {16408, 26062}, {17564, 19861}, {18242, 40256}, {18391, 28466}, {18406, 44258}, {18453, 21530}, {18518, 37426}, {18519, 55868}, {19710, 51066}, {19711, 51093}, {19872, 38021}, {19878, 47598}, {20653, 38430}, {21077, 28645}, {21850, 38047}, {22249, 51693}, {22799, 37437}, {22935, 51717}, {24466, 38128}, {24467, 37560}, {26066, 31419}, {26115, 48917}, {26321, 37403}, {26470, 50031}, {27385, 37562}, {27529, 51409}, {28172, 58203}, {28228, 48154}, {28905, 48900}, {29054, 61549}, {29309, 31285}, {29331, 50022}, {29576, 36728}, {30264, 38129}, {30282, 37739}, {30340, 38065}, {30389, 61287}, {30392, 61284}, {30478, 40587}, {30503, 37700}, {30970, 37365}, {31253, 47599}, {31397, 37582}, {31435, 51559}, {31657, 41548}, {31659, 31806}, {31671, 40333}, {31752, 31834}, {31776, 51782}, {31803, 58675}, {31855, 48897}, {32213, 59333}, {32635, 48668}, {33703, 54448}, {33878, 59406}, {34466, 61527}, {34628, 61250}, {35258, 50241}, {35457, 37291}, {35459, 37298}, {35788, 42259}, {35789, 42258}, {37256, 59416}, {37289, 56877}, {37499, 61321}, {37563, 37722}, {37616, 37734}, {37624, 54445}, {37729, 54295}, {37950, 47321}, {38043, 43166}, {38057, 60901}, {38071, 50865}, {38118, 51732}, {38144, 48873}, {38165, 48874}, {38176, 44245}, {41684, 59325}, {41985, 51120}, {44225, 52412}, {44452, 47471}, {44580, 51071}, {44663, 59719}, {47478, 50802}, {47745, 58190}, {48903, 56191}, {49163, 61122}, {49452, 51046}, {49462, 51045}, {49493, 51048}, {50797, 50813}, {50804, 58217}, {50817, 50832}, {51077, 51088}, {51775, 59615}, {55646, 59407}, {55861, 61270}, {56387, 61146}, {58221, 61296}, {58245, 61275}

X(61524) = midpoint of X(i) and X(j) for these {i,j}: {3, 5690}, {5, 40}, {8, 34773}, {10, 3579}, {165, 38112}, {355, 550}, {548, 61510}, {549, 3654}, {1145, 38602}, {1385, 11362}, {3098, 49524}, {3416, 48906}, {3632, 61295}, {3655, 50823}, {3679, 8703}, {5493, 22793}, {5499, 16139}, {5691, 15704}, {6684, 43174}, {10264, 12778}, {11500, 33899}, {11698, 12515}, {12368, 14677}, {12572, 16004}, {12702, 22791}, {12780, 47611}, {12781, 47610}, {12782, 32521}, {13211, 34153}, {13369, 34790}, {15973, 48924}, {18242, 40256}, {18480, 31730}, {18481, 37705}, {26921, 37424}, {31777, 37290}, {31787, 58643}, {31788, 31837}, {31806, 35004}, {34718, 50824}, {34748, 50830}, {37950, 47321}, {38028, 59417}, {48887, 48919}, {48917, 48933}
X(61524) = reflection of X(i) in X(j) for these {i,j}: {140, 6684}, {143, 58487}, {10222, 51700}, {1385, 3530}, {1482, 61278}, {11699, 13392}, {12103, 12512}, {12261, 40685}, {14449, 31760}, {18357, 10}, {18358, 3844}, {18525, 61253}, {22791, 61272}, {22793, 3850}, {3853, 19925}, {31834, 31752}, {31835, 58630}, {4, 61259}, {40273, 5}, {4297, 33923}, {546, 9956}, {548, 31663}, {551, 11812}, {5066, 3828}, {5777, 58632}, {5901, 140}, {51118, 3861}, {51693, 22249}, {51700, 12108}, {51705, 14891}, {51709, 10124}, {56762, 4015}, {61249, 61510}, {61269, 11231}, {61280, 10165}, {61286, 1385}, {61597, 15178}, {946, 3628}, {9955, 3634}
X(61524) = complement of X(22791)
X(61524) = anticomplement of X(61272)
X(61524) = X(i)-Dao conjugate of X(j) for these {i, j}: {61272, 61272}
X(61524) = pole of line {48182, 48250} with respect to the orthoptic circle of the Steiner inellipse
X(61524) = pole of line {28175, 39534} with respect to the polar circle
X(61524) = pole of line {31792, 37734} with respect to the Feuerbach hyperbola
X(61524) = pole of line {17496, 57066} with respect to the Steiner inellipse
X(61524) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1138), X(36944)}}, {{A, B, C, X(11684), X(26202)}}, {{A, B, C, X(13606), X(51565)}}, {{A, B, C, X(34234), X(60172)}}
X(61524) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5442, 5298}, {2, 12702, 22791}, {2, 22791, 61272}, {3, 12645, 5731}, {3, 2975, 38602}, {3, 5657, 5690}, {3, 59503, 944}, {3, 8, 34773}, {4, 38042, 61259}, {5, 28174, 40273}, {5, 40, 28174}, {10, 30, 18357}, {10, 31730, 18480}, {10, 3579, 30}, {10, 50808, 31673}, {35, 40663, 37730}, {40, 1698, 12699}, {40, 54447, 9589}, {40, 9588, 26446}, {46, 495, 24470}, {140, 517, 5901}, {140, 6684, 61614}, {165, 355, 550}, {165, 38112, 28186}, {376, 3617, 18525}, {498, 37567, 39542}, {515, 31663, 548}, {515, 61510, 61249}, {516, 9956, 546}, {517, 6684, 140}, {546, 9956, 61262}, {548, 61510, 515}, {548, 61539, 61556}, {550, 38112, 355}, {631, 1482, 38028}, {631, 59417, 1482}, {946, 11231, 3628}, {962, 1656, 38034}, {1145, 38602, 952}, {1155, 10039, 18990}, {1385, 11362, 5844}, {1385, 31447, 10164}, {1385, 5844, 61286}, {1482, 38028, 61278}, {1483, 15712, 3576}, {1698, 12699, 5}, {1737, 37568, 15171}, {3085, 36279, 6147}, {3523, 12245, 10246}, {3524, 34718, 50824}, {3579, 18480, 31730}, {3579, 50821, 10}, {3612, 41687, 37728}, {3616, 50810, 8148}, {3632, 3655, 61295}, {3634, 28194, 9955}, {3634, 9955, 547}, {3679, 18481, 37705}, {3679, 35242, 18481}, {3828, 28198, 5066}, {3850, 28216, 22793}, {4668, 50811, 61244}, {5054, 8148, 3616}, {5119, 24914, 496}, {5128, 31434, 57282}, {5432, 5903, 37737}, {5433, 5697, 1387}, {5445, 11010, 11}, {5493, 22793, 28216}, {5690, 34773, 8}, {5818, 9778, 382}, {5886, 31423, 632}, {5901, 61530, 61535}, {6001, 58630, 31835}, {6284, 18395, 12019}, {6361, 9780, 381}, {6684, 13464, 58441}, {6684, 43174, 517}, {7991, 31423, 5886}, {10165, 10222, 51700}, {10175, 22793, 3850}, {10222, 51700, 61280}, {11231, 28212, 61269}, {11362, 31447, 3530}, {12108, 51700, 10165}, {12512, 28160, 12103}, {12514, 37828, 3820}, {12699, 26446, 1698}, {15178, 28234, 61597}, {15704, 38138, 5691}, {17504, 50823, 3655}, {18481, 35242, 8703}, {18525, 38066, 3617}, {19875, 41869, 61261}, {19925, 28146, 3853}, {26066, 54286, 31419}, {28178, 61259, 4}, {28224, 33923, 4297}, {31399, 51118, 38140}, {31425, 37727, 44682}, {31787, 58643, 912}, {31788, 31837, 14988}, {33814, 38602, 17100}, {33923, 38127, 61246}, {38068, 51709, 10124}, {38140, 51118, 3861}, {41869, 61261, 3845}, {61517, 61546, 61511}

X(61525) = MIDPOINT OF X(5) AND X(41)

Barycentrics    2*a^8-2*a^7*(b+c)+3*a^4*(b^2-c^2)^2-5*a^6*(b^2+c^2)+5*a^5*(b+c)*(b^2+c^2)-a*(b-c)^2*(b+c)^3*(b^2-b*c+c^2)+(b-c)^4*(b+c)^2*(b^2+b*c+c^2)-a^2*(b-c)^2*(b^2+c^2)*(b^2+b*c+c^2)-a^3*(b+c)*(2*b^4+b^3*c-8*b^2*c^2+b*c^3+2*c^4) : :
X(61525) = -5*X[1656]+X[21285], 7*X[3090]+X[20071], -3*X[3845]+X[52855], -3*X[15699]+X[31135], -5*X[31240]+7*X[55856]

X(61525) lies on these lines: {5, 41}, {140, 31284}, {766, 20575}, {1656, 21285}, {2389, 61533}, {2809, 5901}, {3090, 20071}, {3628, 17046}, {3845, 52855}, {8679, 18583}, {10021, 61511}, {15699, 31135}, {31240, 55856}, {44233, 61526}

X(61525) = midpoint of X(i) and X(j) for these {i,j}: {5, 41}
X(61525) = reflection of X(i) in X(j) for these {i,j}: {140, 31284}, {17046, 3628}

X(61526) = MIDPOINT OF X(5) AND X(42)

Barycentrics    2*a^6*(b+c)+b*(b-c)^2*c*(b+c)^3-5*a^4*(b+c)*(b^2+c^2)+a*(b^2-c^2)^2*(b^2+c^2)-a^3*(b^2+c^2)^2+a^2*(b+c)*(3*b^4-b^3*c-6*b^2*c^2-b*c^3+3*c^4) : :
X(61526) = -5*X[1656]+X[17135], 7*X[3090]+X[20011], -3*X[3845]+X[52856], -3*X[15699]+X[31136], -5*X[31241]+7*X[55856]

X(61526) lies on these lines: {5, 42}, {140, 6685}, {518, 61523}, {519, 547}, {674, 18583}, {1656, 17135}, {2813, 61563}, {3090, 20011}, {3628, 3741}, {3845, 52856}, {5754, 26115}, {14973, 58632}, {15699, 31136}, {31241, 55856}, {39505, 60759}, {44233, 61525}, {44671, 61522}, {61520, 61536}, {61531, 61626}, {61541, 61547}, {61554, 61562}

X(61526) = midpoint of X(i) and X(j) for these {i,j}: {5, 42}
X(61526) = reflection of X(i) in X(j) for these {i,j}: {140, 6685}, {14973, 58632}, {3741, 3628}
X(61526) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5901, 61527, 547}, {18583, 61533, 20575}, {61554, 61562, 61616}

X(61527) = MIDPOINT OF X(5) AND X(43)

Barycentrics    -2*a^5*b*c+2*a^6*(b+c)+b*(b-c)^2*c*(b+c)^3-5*a^4*(b+c)*(b^2+c^2)-a^3*(b^2+c^2)*(b^2-7*b*c+c^2)+a*(b^2-c^2)^2*(b^2-5*b*c+c^2)+a^2*(b+c)*(3*b^4-b^3*c-6*b^2*c^2-b*c^3+3*c^4) : :
X(61527) = -5*X[1656]+X[10453], 7*X[3090]+X[20012], -3*X[3845]+X[52857], 3*X[5790]+X[20037], -3*X[15699]+X[31137], -5*X[31242]+7*X[55856]

X(61527) lies on these lines: {5, 43}, {140, 6686}, {519, 547}, {952, 995}, {1401, 34753}, {1656, 10453}, {2810, 61535}, {3090, 20012}, {3628, 3840}, {3845, 52857}, {5790, 20037}, {6007, 61511}, {9025, 18583}, {15699, 31137}, {20575, 61562}, {29353, 61614}, {31242, 55856}, {34466, 61524}

X(61527) = midpoint of X(i) and X(j) for these {i,j}: {5, 43}
X(61527) = reflection of X(i) in X(j) for these {i,j}: {140, 6686}, {3840, 3628}
X(61527) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {547, 61526, 5901}

X(61528) = MIDPOINT OF X(5) AND X(44)

Barycentrics    2*a^6-a^5*(b+c)-2*a*(b-c)^2*(b+c)^3-5*a^4*(b^2+c^2)+3*a^3*(b+c)*(b^2+c^2)+(b^2-c^2)^2*(b^2-b*c+c^2)+a^2*(2*b^4+b^3*c-8*b^2*c^2+b*c^3+2*c^4) : :
X(61528) = 3*X[238]+X[355], -X[320]+5*X[1656], -3*X[1279]+X[1483], 3*X[1757]+5*X[8227], 7*X[3090]+X[20072], -3*X[3845]+X[52858], 3*X[5790]+X[49709], 3*X[5886]+X[49712], 3*X[10175]+X[49710], 3*X[10247]+X[49714], -3*X[15699]+X[31138], X[24844]+3*X[37756] and many others

X(61528) lies on these lines: {5, 44}, {140, 6687}, {238, 355}, {320, 1656}, {518, 5901}, {536, 61621}, {547, 4715}, {752, 9956}, {952, 3246}, {1279, 1483}, {1757, 8227}, {3090, 20072}, {3628, 3834}, {3845, 52858}, {4422, 29331}, {5790, 49709}, {5886, 49712}, {6684, 15310}, {10175, 49710}, {10222, 49701}, {10247, 49714}, {15699, 31138}, {17335, 36530}, {17338, 48908}, {24844, 37756}, {25891, 51559}, {31243, 55856}, {49675, 61277}

X(61528) = midpoint of X(i) and X(j) for these {i,j}: {5, 44}, {10222, 49701}
X(61528) = reflection of X(i) in X(j) for these {i,j}: {140, 6687}, {3834, 3628}
X(61528) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5901, 61511, 61529}, {18583, 61511, 61522}, {18583, 61529, 5901}

X(61529) = MIDPOINT OF X(5) AND X(45)

Barycentrics    2*a^6-4*a^5*(b+c)-8*a*(b-c)^2*(b+c)^3-5*a^4*(b^2+c^2)+12*a^3*(b+c)*(b^2+c^2)+(b^2-c^2)^2*(b^2-4*b*c+c^2)+2*a^2*(b^4+2*b^3*c-4*b^2*c^2+2*b*c^3+c^4) : :
X(61529) = -5*X[1656]+X[42697], 7*X[3090]+X[20073], -3*X[3845]+X[52859], -3*X[15699]+X[31139], -5*X[31244]+7*X[55856]

X(61529) lies on these lines: {5, 45}, {140, 31285}, {518, 5901}, {545, 547}, {1656, 42697}, {3090, 20073}, {3564, 36404}, {3628, 34824}, {3845, 52859}, {9956, 28580}, {15699, 31139}, {31244, 55856}

X(61529) = midpoint of X(i) and X(j) for these {i,j}: {5, 45}
X(61529) = reflection of X(i) in X(j) for these {i,j}: {140, 31285}, {34824, 3628}
X(61529) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5901, 61511, 61528}, {5901, 61528, 18583}, {61522, 61528, 5901}

X(61530) = MIDPOINT OF X(5) AND X(46)

Barycentrics    2*a^7+(b-c)^4*(b+c)^3-7*a^5*(b^2+c^2)-2*a^2*(b-c)^2*(b+c)*(b^2+3*b*c+c^2)+a^4*(b+c)*(b^2+4*b*c+c^2)-a*(b^2-c^2)^2*(3*b^2-8*b*c+3*c^2)+a^3*(8*b^4-8*b^3*c-4*b^2*c^2-8*b*c^3+8*c^4) : :
X(61530) = -5*X[1656]+X[11415], -X[3436]+3*X[38042], -3*X[3845]+X[52860], 3*X[5790]+X[20076], -3*X[10283]+X[30323], X[12704]+3*X[26446], -3*X[17728]+X[32214], X[37567]+2*X[61272]

X(61530) lies on these lines: {5, 46}, {56, 952}, {57, 10942}, {119, 3336}, {140, 517}, {474, 5690}, {495, 17437}, {546, 61559}, {758, 61551}, {1155, 37290}, {1329, 61512}, {1482, 6921}, {1656, 11415}, {1788, 6911}, {2098, 31452}, {2829, 61553}, {3338, 32213}, {3339, 37713}, {3436, 38042}, {3628, 21616}, {3845, 52860}, {5446, 35059}, {5771, 8728}, {5790, 20076}, {5844, 59691}, {5883, 31659}, {5886, 7294}, {5903, 11729}, {6922, 28174}, {6958, 22791}, {6959, 36279}, {6967, 12702}, {7681, 40273}, {8069, 12433}, {9956, 61539}, {10283, 30323}, {12704, 26446}, {13226, 37002}, {17728, 32214}, {17768, 61511}, {18357, 37281}, {24928, 61286}, {32157, 33179}, {37567, 61272}, {37821, 61259}, {41347, 57288}, {61519, 61571}

X(61530) = midpoint of X(i) and X(j) for these {i,j}: {5, 46}, {5690, 10680}
X(61530) = reflection of X(i) in X(j) for these {i,j}: {140, 58405}, {2098, 61278}, {21616, 3628}, {37821, 61259}, {40273, 7681}, {5901, 61534}, {61286, 24928}
X(61530) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {140, 61541, 5901}, {517, 58405, 140}, {5901, 61614, 61520}

X(61531) = MIDPOINT OF X(5) AND X(48)

Barycentrics    2*a^9-7*a^7*(b^2+c^2)-3*a^3*(b^2-c^2)^2*(b^2+c^2)+(b-c)^4*(b+c)^3*(b^2+b*c+c^2)+4*a^5*(2*b^4+b^2*c^2+2*c^4)+a^4*(b^5+b^3*c^2+b^2*c^3+c^5)-2*a^2*(b^7-b^5*c^2-b^2*c^5+c^7) : :
X(61531) = -5*X[1656]+X[21270], 7*X[3090]+X[20074], -3*X[3845]+X[52862], -3*X[15699]+X[31163], -5*X[31265]+7*X[55856]

X(61531) lies on these lines: {5, 48}, {140, 916}, {1656, 21270}, {2801, 61511}, {3090, 20074}, {3628, 20305}, {3845, 52862}, {5901, 44661}, {8679, 18583}, {9956, 29219}, {15699, 31163}, {31265, 55856}, {61526, 61626}, {61533, 61606}

X(61531) = midpoint of X(i) and X(j) for these {i,j}: {5, 48}
X(61531) = reflection of X(i) in X(j) for these {i,j}: {140, 58406}, {20305, 3628}
X(61531) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {916, 58406, 140}

X(61532) = MIDPOINT OF X(5) AND X(53)

Barycentrics    (-(b^2-c^2)^2+a^2*(b^2+c^2))*(-2*a^2*(b^2-c^2)^2*(b^2+c^2)+(b^2-c^2)^2*(b^4-b^2*c^2+c^4)+a^4*(b^4+b^2*c^2+c^4)) : :
X(61532) = 3*X[381]+X[33971], X[382]+3*X[20792], -3*X[549]+X[36988], -5*X[1656]+X[20477], -5*X[3091]+X[18437]

X(61532) lies on these lines: {5, 53}, {51, 129}, {140, 58408}, {157, 13861}, {324, 23607}, {381, 33971}, {382, 20792}, {418, 14129}, {546, 575}, {549, 36988}, {1352, 61315}, {1656, 20477}, {2790, 46030}, {3091, 18437}, {3549, 43131}, {3628, 34828}, {5480, 34981}, {5562, 10216}, {6751, 15226}, {7528, 43132}, {10796, 11818}, {11272, 21474}, {12026, 61573}, {12106, 14693}, {30258, 52247}, {30259, 39504}, {34836, 42453}, {37466, 56892}, {39081, 42350}, {44232, 58436}, {44233, 61609}, {52280, 59532}

X(61532) = midpoint of X(i) and X(j) for these {i,j}: {5, 53}
X(61532) = reflection of X(i) in X(j) for these {i,j}: {140, 58408}, {34828, 3628}
X(61532) = pole of line {389, 7747} with respect to the Kiepert hyperbola
X(61532) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(27358)}}, {{A, B, C, X(5), X(52247)}}, {{A, B, C, X(216), X(30258)}}, {{A, B, C, X(324), X(32428)}}, {{A, B, C, X(9792), X(11062)}}, {{A, B, C, X(13450), X(27359)}}, {{A, B, C, X(46394), X(60828)}}
X(61532) = barycentric product X(i)*X(j) for these (i, j): {5, 52247}, {30258, 324}, {45793, 9792}
X(61532) = barycentric quotient X(i)/X(j) for these (i, j): {30258, 97}, {52247, 95}, {61305, 54034}
X(61532) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {36412, 39569, 5}

X(61533) = MIDPOINT OF X(5) AND X(55)

Barycentrics    2*a^7-2*a^6*(b+c)+(b-c)^4*(b+c)^3-5*a^5*(b^2+c^2)+5*a^4*(b+c)*(b^2+c^2)-a*(b^2-c^2)^2*(b^2+c^2)-2*a^2*(b-c)^2*(b+c)*(2*b^2+3*b*c+2*c^2)+4*a^3*(b^4-b^2*c^2+c^4) : :
X(61533) = 3*X[381]+X[37000], -3*X[549]+X[3428], -5*X[1656]+X[3434], -X[2099]+3*X[10283], 7*X[3090]+X[20075], -5*X[3091]+X[18499], -X[3419]+3*X[38042], 7*X[3526]+X[44455], 7*X[3624]+X[12703], -3*X[3845]+X[36999], -5*X[6974]+X[18519], 3*X[10056]+X[22758] and many others

X(61533) lies on these lines: {2, 10596}, {3, 10532}, {5, 55}, {12, 32760}, {30, 7680}, {40, 26725}, {100, 6881}, {119, 3584}, {140, 517}, {143, 58490}, {153, 28461}, {355, 10543}, {381, 37000}, {390, 6859}, {442, 11849}, {495, 6914}, {518, 61539}, {528, 547}, {546, 5842}, {549, 3428}, {551, 6713}, {674, 18583}, {912, 13405}, {946, 31659}, {952, 24929}, {1482, 7483}, {1484, 15170}, {1532, 59382}, {1621, 6882}, {1656, 3434}, {1824, 21841}, {2099, 10283}, {2389, 61525}, {2807, 61565}, {2875, 61619}, {2886, 3628}, {3035, 11230}, {3085, 3560}, {3090, 20075}, {3091, 18499}, {3295, 6862}, {3303, 32214}, {3419, 38042}, {3526, 44455}, {3564, 47373}, {3583, 38109}, {3624, 12703}, {3652, 13995}, {3746, 26470}, {3822, 5840}, {3845, 36999}, {3850, 18407}, {3871, 6852}, {4999, 10222}, {5119, 5432}, {5172, 18990}, {5173, 34753}, {5218, 6911}, {5281, 6826}, {5428, 31799}, {5433, 25415}, {5499, 31777}, {5535, 11218}, {5687, 6861}, {5690, 6675}, {5719, 14988}, {5770, 10578}, {5843, 8255}, {5855, 61597}, {6175, 13199}, {6830, 61155}, {6831, 37621}, {6833, 16202}, {6837, 18518}, {6841, 11491}, {6858, 17784}, {6860, 18544}, {6872, 11929}, {6887, 59591}, {6889, 35448}, {6897, 35251}, {6910, 10680}, {6924, 40292}, {6929, 31479}, {6930, 8164}, {6933, 11928}, {6974, 18519}, {6977, 10587}, {7489, 17757}, {8186, 48519}, {8187, 48520}, {8226, 18524}, {8582, 50205}, {10021, 44669}, {10056, 22758}, {10198, 11248}, {10267, 37356}, {10310, 44222}, {10527, 12000}, {10738, 17530}, {10786, 37234}, {11281, 35004}, {11496, 26487}, {11729, 12758}, {12115, 28444}, {13383, 40635}, {15699, 31140}, {15733, 61511}, {16140, 17699}, {19919, 41571}, {22765, 37298}, {22791, 52265}, {23340, 24541}, {24987, 33596}, {25466, 26285}, {26326, 26422}, {26327, 26398}, {26363, 37622}, {26446, 37569}, {31245, 55856}, {35258, 37826}, {36976, 38107}, {37291, 45977}, {38028, 61146}, {38113, 54203}, {38454, 61509}, {44233, 44670}, {50194, 61278}, {51787, 61269}, {54158, 59381}, {57327, 61491}, {58631, 61559}, {59719, 61551}, {61531, 61606}, {61540, 61547}

X(61533) = midpoint of X(i) and X(j) for these {i,j}: {5, 55}, {495, 6914}, {5690, 37533}, {7680, 32613}, {19919, 41571}, {22758, 32213}
X(61533) = reflection of X(i) in X(j) for these {i,j}: {140, 6690}, {143, 58490}, {18407, 3850}, {2886, 3628}, {5173, 58561}, {50194, 61278}
X(61533) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {140, 5901, 61534}, {517, 6690, 140}, {3085, 3560, 10942}, {3295, 6862, 10943}, {5901, 61524, 61541}, {5901, 61614, 61535}, {7680, 32613, 30}, {11496, 26487, 37406}, {20575, 61526, 18583}

X(61534) = MIDPOINT OF X(5) AND X(56)

Barycentrics    2*a^7-2*a^6*(b+c)+(b-c)^4*(b+c)^3+a^5*(-5*b^2+8*b*c-5*c^2)-a*(b^2-c^2)^2*(b^2-4*b*c+c^2)-2*a^2*(b-c)^2*(b+c)*(2*b^2-b*c+2*c^2)+a^4*(b+c)*(5*b^2-8*b*c+5*c^2)+4*a^3*(b^4-3*b^3*c+3*b^2*c^2-3*b*c^3+c^4) : :
X(61534) = 3*X[381]+X[37002], -3*X[549]+X[10310], -5*X[631]+X[35448], -5*X[1656]+X[3436], -X[2098]+3*X[10283], 7*X[3090]+X[20076], 7*X[3624]+X[12704], -3*X[3845]+X[37001], 3*X[5790]+X[36977], 3*X[10072]+X[11499], -3*X[15699]+X[31141], 3*X[17728]+X[45770] and many others

X(61534) lies on these lines: {2, 10597}, {3, 10531}, {5, 56}, {30, 7681}, {36, 37290}, {46, 5433}, {65, 11729}, {79, 8227}, {119, 5563}, {140, 517}, {381, 37002}, {496, 6924}, {518, 61551}, {529, 547}, {546, 2829}, {549, 10310}, {551, 31659}, {631, 35448}, {912, 58573}, {946, 6713}, {952, 1210}, {999, 6959}, {1329, 3628}, {1389, 3616}, {1476, 6944}, {1482, 13747}, {1512, 24927}, {1532, 37535}, {1656, 3436}, {1828, 21841}, {2098, 10283}, {2390, 20575}, {2841, 61568}, {3035, 10222}, {3086, 6911}, {3090, 20076}, {3304, 32213}, {3333, 37713}, {3560, 7288}, {3582, 26470}, {3585, 23513}, {3600, 6981}, {3624, 12704}, {3816, 26286}, {3825, 5841}, {3845, 37001}, {4187, 22765}, {4190, 11928}, {4999, 11230}, {5253, 6842}, {5265, 6893}, {5432, 30323}, {5552, 12001}, {5690, 19861}, {5719, 50196}, {5790, 36977}, {5844, 8256}, {5854, 61562}, {6583, 58604}, {6675, 37532}, {6700, 58645}, {6738, 61286}, {6831, 57298}, {6834, 16203}, {6880, 10586}, {6885, 47743}, {6914, 40293}, {6921, 10679}, {6931, 11929}, {6947, 35252}, {6953, 18519}, {6970, 14986}, {8679, 18583}, {10021, 17768}, {10072, 11499}, {10200, 11249}, {10269, 37406}, {10595, 17566}, {11375, 17437}, {14988, 34753}, {15699, 31141}, {17728, 45770}, {18480, 20418}, {22753, 26492}, {24390, 45976}, {25524, 37438}, {30143, 51700}, {31246, 55856}, {32554, 34126}, {33709, 40259}, {33862, 49736}, {36972, 59400}, {37582, 55108}, {38028, 52265}, {38455, 61510}, {44233, 61519}, {44898, 52200}, {54134, 61295}, {57302, 61492}

X(61534) = midpoint of X(i) and X(j) for these {i,j}: {5, 56}, {496, 6924}, {5901, 61530}, {7681, 32612}, {11499, 32214}, {54134, 61295}
X(61534) = reflection of X(i) in X(j) for these {i,j}: {140, 6691}, {1329, 3628}, {50196, 58561}
X(61534) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {140, 5901, 61533}, {517, 6691, 140}, {999, 6959, 10942}, {3086, 6911, 10943}, {5901, 61530, 517}, {5901, 61535, 61541}, {7681, 32612, 30}, {10072, 11499, 32214}, {22753, 26492, 37356}

X(61535) = MIDPOINT OF X(5) AND X(57)

Barycentrics    2*a^7-a*(b-3*c)*(b-c)^2*(3*b-c)*(b+c)^2+(b-c)^4*(b+c)^3+a^5*(-7*b^2+4*b*c-7*c^2)+a^4*(b+c)*(b^2+c^2)-2*a^2*(b-c)^2*(b+c)*(b^2+b*c+c^2)+2*a^3*(4*b^4-7*b^3*c+2*b^2*c^2-7*b*c^3+4*c^4) : :
X(61535) = 3*X[2]+X[2095], -X[329]+5*X[1656], 3*X[381]+X[2096], -3*X[549]+X[6282], -X[550]+3*X[21164], X[2093]+3*X[5886], X[2094]+3*X[5055], X[2097]+3*X[14561], 7*X[3090]+X[9965], -X[3421]+3*X[38042], -17*X[7486]+X[20214], -X[7962]+3*X[10283] and many others

X(61535) lies on these lines: {2, 2095}, {3, 5804}, {5, 57}, {30, 7682}, {140, 517}, {329, 1656}, {381, 2096}, {518, 61628}, {527, 547}, {546, 61556}, {549, 6282}, {550, 21164}, {952, 999}, {1210, 37281}, {1482, 17567}, {1532, 27003}, {2093, 5886}, {2094, 5055}, {2097, 14561}, {2810, 61527}, {2823, 61518}, {2835, 20575}, {3090, 9965}, {3306, 6907}, {3359, 28174}, {3421, 38042}, {3452, 3628}, {5435, 6913}, {5439, 52265}, {5690, 16408}, {5708, 6944}, {5762, 8257}, {5843, 61022}, {6147, 6959}, {6859, 12848}, {6862, 36279}, {6891, 22791}, {6893, 37545}, {6924, 12433}, {6954, 38028}, {6970, 15934}, {6973, 18541}, {7486, 20214}, {7956, 37356}, {7962, 10283}, {9843, 37623}, {9954, 58632}, {12915, 58561}, {13364, 46174}, {15699, 31142}, {17527, 37532}, {17564, 37533}, {18583, 34371}, {20196, 55856}, {24474, 52264}, {26921, 51559}, {31272, 38039}, {35102, 61557}, {38122, 54159}, {38171, 52457}, {42356, 60759}, {46028, 61552}, {51788, 61286}, {57318, 61493}, {58604, 61562}, {61519, 61536}, {61613, 61617}

X(61535) = midpoint of X(i) and X(j) for these {i,j}: {5, 57}
X(61535) = reflection of X(i) in X(j) for these {i,j}: {140, 6692}, {12915, 58561}, {3452, 3628}, {40273, 7956}, {61286, 51788}, {9954, 58632}
X(61535) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {517, 6692, 140}, {547, 61539, 61511}, {5901, 61530, 61524}, {5901, 61614, 61533}, {61534, 61541, 5901}

X(61536) = MIDPOINT OF X(5) AND X(58)

Barycentrics    2*a^7-2*a^4*b*c*(b+c)+a^5*(-5*b^2+2*b*c-5*c^2)+a*b*c*(b^2-c^2)^2+(b-c)^2*(b+c)^3*(b^2-b*c+c^2)-a^2*(b+c)*(b^4-3*b^3*c+6*b^2*c^2-3*b*c^3+c^4)+a^3*(3*b^4-3*b^3*c-2*b^2*c^2-3*b*c^3+3*c^4) : :
X(61536) = X[355]+3*X[5429], -3*X[549]+X[3430], X[1046]+3*X[5886], -X[1330]+5*X[1656], 7*X[3090]+X[20077], 3*X[10165]+X[54160], -3*X[11230]+X[56949], -X[36974]+3*X[38042]

X(61536) lies on these lines: {5, 58}, {30, 7683}, {140, 143}, {355, 5429}, {517, 8258}, {540, 547}, {549, 3430}, {758, 5901}, {1046, 5886}, {1330, 1656}, {2392, 61521}, {2792, 9955}, {2825, 61565}, {2842, 10272}, {3090, 20077}, {3454, 3628}, {3794, 7483}, {6703, 50418}, {9956, 38456}, {10165, 54160}, {11230, 56949}, {15973, 35466}, {17770, 61558}, {29097, 40273}, {34753, 35650}, {34773, 54136}, {36974, 38042}, {48909, 56778}, {61519, 61535}, {61520, 61526}, {61541, 61571}

X(61536) = midpoint of X(i) and X(j) for these {i,j}: {5, 58}, {34773, 54136}
X(61536) = reflection of X(i) in X(j) for these {i,j}: {140, 6693}, {3454, 3628}
X(61536) = pole of line {572, 1506} with respect to the Kiepert hyperbola
X(61536) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {511, 6693, 140}, {10021, 61554, 5901}

X(61537) = MIDPOINT OF X(5) AND X(61)

Barycentrics    3*(2*a^6-5*a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)+2*a^2*(b^4-4*b^2*c^2+c^4))+2*sqrt(3)*(2*a^4+(b^2-c^2)^2-3*a^2*(b^2+c^2))*S : :

X(61537) lies on circumconic {{A, B, C, X(11087), X(45108)}} and on these lines: {5, 14}, {15, 36959}, {18, 59403}, {30, 51753}, {62, 52650}, {140, 143}, {303, 633}, {397, 32134}, {533, 547}, {546, 20252}, {549, 14540}, {634, 47517}, {635, 3628}, {1506, 11543}, {3329, 37463}, {3398, 41035}, {5007, 14136}, {5459, 22831}, {5611, 11289}, {5873, 37640}, {6115, 12830}, {6771, 51754}, {7745, 11542}, {9300, 52266}, {9698, 14137}, {10613, 42925}, {14561, 42152}, {15092, 47862}, {16267, 16627}, {16772, 44223}, {20429, 42992}, {22532, 59244}, {33413, 59396}, {42814, 59401}, {42936, 59404}, {44107, 46833}, {47611, 52688}, {53431, 54297}

X(61537) = midpoint of X(i) and X(j) for these {i,j}: {5, 61}
X(61537) = reflection of X(i) in X(j) for these {i,j}: {140, 6694}, {20415, 20394}, {635, 3628}
X(61537) = pole of line {16, 1506} with respect to the Kiepert hyperbola
X(61537) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {140, 61538, 61514}, {511, 6694, 140}, {11272, 25555, 61538}, {20253, 61515, 5}, {20394, 41022, 20415}

X(61538) = MIDPOINT OF X(5) AND X(62)

Barycentrics    3*(2*a^6-5*a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)+2*a^2*(b^4-4*b^2*c^2+c^4))-2*sqrt(3)*(2*a^4+(b^2-c^2)^2-3*a^2*(b^2+c^2))*S : :

X(61538) lies on circumconic {{A, B, C, X(11082), X(45108)}} and on these lines: {5, 13}, {16, 36958}, {17, 59404}, {30, 51754}, {61, 44223}, {140, 143}, {302, 634}, {398, 32134}, {532, 547}, {546, 20253}, {549, 14541}, {633, 47519}, {636, 3628}, {1506, 11542}, {3329, 37464}, {3398, 41034}, {5007, 14137}, {5460, 22832}, {5615, 11290}, {5872, 37641}, {6114, 12830}, {6774, 51753}, {7745, 11543}, {9300, 52263}, {9698, 14136}, {10614, 42924}, {14561, 42149}, {15092, 47861}, {16268, 16626}, {16773, 52650}, {20428, 42993}, {22531, 59245}, {33412, 59394}, {42813, 59402}, {42937, 59403}, {44107, 46834}, {47610, 52689}, {53443, 54298}

X(61538) = midpoint of X(i) and X(j) for these {i,j}: {5, 62}
X(61538) = reflection of X(i) in X(j) for these {i,j}: {140, 6695}, {20416, 20395}, {636, 3628}
X(61538) = pole of line {15, 1506} with respect to the Kiepert hyperbola
X(61538) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {140, 61537, 61513}, {511, 6695, 140}, {11272, 25555, 61537}, {20252, 61516, 5}, {20395, 41023, 20416}

X(61539) = MIDPOINT OF X(5) AND X(63)

Barycentrics    2*a^7+(b-c)^4*(b+c)^3-7*a^5*(b^2+c^2)+a^4*(b+c)*(b^2+c^2)-3*a*(b^2-c^2)^2*(b^2+c^2)-2*a^2*(b-c)^2*(b+c)*(b^2+b*c+c^2)+4*a^3*(2*b^4+b^2*c^2+2*c^4) : :
X(61539) = -X[3]+5*X[55868], -X[550]+3*X[21165], -5*X[632]+7*X[55867], -X[1478]+3*X[38042], -5*X[1656]+X[5905], 7*X[3090]+X[20078], 3*X[5657]+X[18519], -3*X[15699]+X[31164], -5*X[31266]+7*X[55856], -3*X[38171]+X[61011], -5*X[48154]+4*X[58463]

X(61539) lies on these lines: {3, 55868}, {5, 63}, {30, 5771}, {140, 912}, {143, 58491}, {144, 6859}, {191, 26470}, {226, 3628}, {355, 30264}, {515, 548}, {518, 61533}, {527, 547}, {549, 13226}, {550, 21165}, {632, 55867}, {758, 5901}, {952, 993}, {1385, 18253}, {1478, 38042}, {1656, 5905}, {2792, 61599}, {2801, 58674}, {3090, 20078}, {3218, 6881}, {3219, 6882}, {3652, 15908}, {3679, 12119}, {3927, 6862}, {3956, 6684}, {4999, 5694}, {5250, 32214}, {5273, 5770}, {5657, 18519}, {5690, 10310}, {5719, 18389}, {5744, 6911}, {5768, 28466}, {5791, 24467}, {5841, 18357}, {6265, 31157}, {6675, 24475}, {6713, 10176}, {6734, 37290}, {6858, 9965}, {6892, 54398}, {7330, 37406}, {8680, 61517}, {9028, 61545}, {9956, 61530}, {10202, 54357}, {10225, 49732}, {10942, 26066}, {10943, 12514}, {12005, 58449}, {12738, 21155}, {12751, 38129}, {15699, 31164}, {16617, 24474}, {18249, 31838}, {18444, 28465}, {18583, 34377}, {26446, 37725}, {26921, 37356}, {31266, 55856}, {31446, 37534}, {38171, 61011}, {46179, 61550}, {46180, 61625}, {47742, 58632}, {48154, 58463}

X(61539) = midpoint of X(i) and X(j) for these {i,j}: {5, 63}, {5690, 22758}
X(61539) = reflection of X(i) in X(j) for these {i,j}: {140, 5745}, {143, 58491}, {226, 3628}
X(61539) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {140, 31835, 61551}, {912, 5745, 140}, {5273, 5770, 6883}, {5791, 24467, 37438}, {20575, 61523, 5901}, {61511, 61535, 547}, {61524, 61556, 548}, {61614, 61628, 61562}

X(61540) = MIDPOINT OF X(5) AND X(64)

Barycentrics    2*a^10-a^8*(b^2+c^2)+16*a^4*(b^2-c^2)^2*(b^2+c^2)+(b^2-c^2)^4*(b^2+c^2)-4*a^2*(b-c)^2*(b+c)^2*(2*b^2+c^2)*(b^2+2*c^2)-2*a^6*(5*b^4-12*b^2*c^2+5*c^4) : :
X(61540) = 3*X[2]+X[13093], -7*X[3]+3*X[11206], -3*X[154]+5*X[15712], 3*X[376]+X[34780], 3*X[381]+X[12250], X[382]+3*X[54050], -3*X[549]+X[1498], -X[550]+3*X[10606], -5*X[631]+X[12315], -X[1353]+3*X[52028], -5*X[1656]+X[6225], X[1657]+3*X[32064] and many others

X(61540) lies on these lines: {2, 13093}, {3, 11206}, {4, 34469}, {5, 64}, {20, 44683}, {24, 43903}, {30, 3357}, {74, 3575}, {125, 44226}, {140, 6000}, {143, 58492}, {154, 15712}, {376, 34780}, {378, 18914}, {381, 12250}, {382, 54050}, {468, 12290}, {495, 10076}, {496, 10060}, {546, 15311}, {548, 1503}, {549, 1498}, {550, 10606}, {590, 35865}, {615, 35864}, {631, 12315}, {952, 12262}, {1192, 7715}, {1204, 6756}, {1353, 52028}, {1593, 18916}, {1595, 10605}, {1596, 26937}, {1597, 18913}, {1598, 18920}, {1656, 6225}, {1657, 32064}, {1853, 3627}, {2777, 3853}, {2883, 3628}, {2935, 32358}, {3089, 3426}, {3091, 48672}, {3516, 31804}, {3523, 32063}, {3524, 14530}, {3526, 5656}, {3530, 6759}, {3545, 54211}, {3564, 12084}, {3845, 5895}, {3850, 15105}, {3861, 23325}, {5066, 5893}, {5663, 15115}, {5886, 9899}, {6001, 31835}, {6146, 13399}, {6285, 15325}, {6288, 41738}, {6293, 45956}, {6676, 10575}, {6776, 55575}, {7464, 12325}, {7583, 49251}, {7584, 49250}, {7729, 45957}, {7973, 10283}, {8254, 44236}, {8546, 15579}, {8567, 8703}, {9730, 44544}, {9914, 13861}, {9919, 34484}, {9920, 16661}, {9924, 33543}, {10151, 23294}, {10192, 12108}, {10257, 18439}, {10282, 12100}, {10539, 16976}, {10592, 12940}, {10593, 12950}, {10990, 11572}, {11202, 44762}, {11204, 33923}, {11245, 14865}, {11381, 21841}, {11411, 54992}, {11412, 47091}, {11468, 16659}, {11598, 32423}, {12085, 18934}, {12102, 23324}, {12103, 18400}, {12111, 47090}, {12134, 44247}, {12162, 16196}, {12779, 38042}, {12964, 35255}, {12970, 35256}, {13474, 20417}, {13491, 52262}, {13568, 16198}, {13630, 18583}, {14641, 44201}, {14869, 58795}, {14915, 44158}, {15060, 36982}, {15062, 34664}, {16194, 30443}, {16197, 32348}, {16655, 21663}, {17821, 44682}, {17822, 44413}, {18909, 55571}, {19087, 19117}, {19088, 19116}, {20584, 49108}, {26883, 37935}, {31830, 61542}, {31861, 46373}, {32111, 43608}, {32137, 44233}, {32345, 36966}, {32743, 61598}, {33703, 47582}, {34779, 51732}, {34785, 44245}, {35497, 46818}, {36201, 61543}, {36851, 48874}, {37477, 43813}, {39884, 61088}, {41588, 47527}, {44232, 61548}, {50434, 58922}, {61518, 61541}, {61533, 61547}, {61546, 61627}

X(61540) = midpoint of X(i) and X(j) for these {i,j}: {5, 64}, {550, 14216}, {3357, 6247}, {3627, 20427}, {5894, 18381}, {15105, 22802}, {36851, 48874}, {39884, 61088}
X(61540) = reflection of X(i) in X(j) for these {i,j}: {140, 6696}, {143, 58492}, {16252, 25563}, {2883, 3628}, {22802, 3850}, {34779, 51732}, {34782, 33923}, {34785, 44245}, {546, 20299}, {5893, 32767}, {51491, 3861}, {6759, 3530}, {61598, 32743}
X(61540) = pole of line {11414, 11449} with respect to the Stammler hyperbola
X(61540) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {64, 40686, 5878}, {1853, 20427, 3627}, {2883, 23329, 3628}, {3357, 18381, 5894}, {3357, 6247, 30}, {5878, 40686, 5}, {5893, 32767, 5066}, {5894, 6247, 18381}, {6000, 25563, 16252}, {6696, 16252, 25563}, {8567, 9833, 8703}, {10606, 14216, 550}, {11204, 34782, 33923}, {12290, 43607, 468}, {15105, 23332, 22802}, {15311, 20299, 546}, {16252, 25563, 140}, {22802, 23332, 3850}, {23325, 51491, 3861}

X(61541) = MIDPOINT OF X(5) AND X(65)

Barycentrics    a*(a^5*(b+c)-2*a^3*(b-c)^2*(b+c)+a*(b-c)^4*(b+c)-a^4*(b+c)^2-(b^2-c^2)^2*(b^2-3*b*c+c^2)+a^2*(2*b^4-b^3*c-4*b^2*c^2-b*c^3+2*c^4)) : :
X(61541) = -X[72]+3*X[38042], -3*X[354]+X[1483], -3*X[549]+X[14110], X[946]+3*X[3919], -X[1385]+3*X[5883], -5*X[1656]+X[3869], -X[3057]+3*X[10283], -X[3059]+3*X[38170], -5*X[3091]+X[40266], -5*X[3698]+3*X[38112], -3*X[3742]+2*X[51700], -3*X[3753]+X[5690] and many others

X(61541) lies on these lines: {1, 6924}, {3, 9352}, {5, 65}, {12, 53615}, {30, 7686}, {46, 6914}, {57, 32153}, {72, 38042}, {119, 3649}, {140, 517}, {143, 58493}, {354, 1483}, {355, 5270}, {474, 1482}, {515, 5885}, {516, 13145}, {518, 61509}, {519, 6583}, {546, 6001}, {547, 44663}, {548, 40296}, {549, 14110}, {758, 9956}, {912, 9947}, {942, 952}, {946, 3919}, {960, 3628}, {1159, 6918}, {1319, 61148}, {1385, 5883}, {1389, 5253}, {1656, 3869}, {1788, 6862}, {1858, 12019}, {2095, 19520}, {2390, 13364}, {2771, 11801}, {2778, 61548}, {2800, 9955}, {2802, 33179}, {2818, 5462}, {3057, 10283}, {3059, 38170}, {3091, 40266}, {3339, 24467}, {3485, 6959}, {3556, 13861}, {3560, 7098}, {3577, 37534}, {3698, 38112}, {3742, 51700}, {3753, 5690}, {3827, 18583}, {3830, 9961}, {3845, 12688}, {3850, 31937}, {3853, 16616}, {3868, 5790}, {3873, 12645}, {3878, 11230}, {3880, 61597}, {4004, 6922}, {4067, 31399}, {4084, 5694}, {4295, 6929}, {4511, 45976}, {4757, 20117}, {4848, 55108}, {5045, 61286}, {5049, 61281}, {5221, 22758}, {5267, 41347}, {5425, 37733}, {5439, 38028}, {5603, 6958}, {5693, 61261}, {5697, 61276}, {5777, 61259}, {5806, 40273}, {5836, 5844}, {5884, 18480}, {5886, 5903}, {6147, 10942}, {6917, 18391}, {6921, 10595}, {6940, 35459}, {7489, 56288}, {7672, 38107}, {7951, 45288}, {9957, 61278}, {10095, 42450}, {10178, 44245}, {10202, 34773}, {10222, 59691}, {10247, 14923}, {10273, 12672}, {10679, 37282}, {11011, 19907}, {11231, 31806}, {11281, 31659}, {11507, 52272}, {11529, 37700}, {11551, 11698}, {12005, 28204}, {12245, 37462}, {12433, 50195}, {12619, 33592}, {12675, 28224}, {12758, 38044}, {13369, 28186}, {13375, 20323}, {13750, 37730}, {14529, 32046}, {14872, 38138}, {15016, 18481}, {15178, 58565}, {15699, 31165}, {17016, 45931}, {17564, 23340}, {17609, 61283}, {18398, 37727}, {18838, 18990}, {19524, 22765}, {19860, 37532}, {20718, 61522}, {21740, 37251}, {25917, 55856}, {26286, 30147}, {26321, 26877}, {26446, 37625}, {27003, 37535}, {28174, 31788}, {30143, 32613}, {30274, 37739}, {31649, 41542}, {31792, 61280}, {31803, 38140}, {33596, 33814}, {33858, 44425}, {33862, 35016}, {34242, 57303}, {34718, 57005}, {37621, 48363}, {38177, 46685}, {50190, 61287}, {50192, 61292}, {50193, 61272}, {54318, 59318}, {55174, 61617}, {59719, 61562}, {61518, 61540}, {61526, 61547}, {61536, 61571}

X(61541) = midpoint of X(i) and X(j) for these {i,j}: {5, 65}, {355, 24475}, {946, 35004}, {1389, 34353}, {3754, 31870}, {4084, 5694}, {4757, 20117}, {5690, 24474}, {5884, 18480}, {7686, 34339}, {10107, 13374}, {10273, 38034}, {22791, 37562}
X(61541) = reflection of X(i) in X(j) for these {i,j}: {1, 58561}, {140, 3812}, {143, 58493}, {15178, 58565}, {3853, 16616}, {31835, 9956}, {31937, 3850}, {40273, 5806}, {42450, 10095}, {548, 40296}, {5777, 61259}, {5885, 33815}, {61286, 5045}, {72, 58632}, {960, 3628}, {9957, 61278}
X(61541) = pole of line {39200, 48281} with respect to the DeLongchamps ellipse
X(61541) = pole of line {10222, 10572} with respect to the Feuerbach hyperbola
X(61541) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 65, 14988}, {72, 38042, 58632}, {515, 33815, 5885}, {517, 3812, 140}, {758, 9956, 31835}, {3753, 24474, 5690}, {5901, 61521, 1125}, {5901, 61524, 61533}, {5901, 61535, 61534}, {7686, 34339, 30}, {10107, 13374, 517}

X(61542) = MIDPOINT OF X(5) AND X(66)

Barycentrics    2*a^12+a^8*(b^2-c^2)^2-4*a^4*b^2*c^2*(b^2-c^2)^2-3*a^10*(b^2+c^2)-3*(b^2-c^2)^4*(b^2+c^2)^2+5*a^2*(b^2-c^2)^2*(b^2+c^2)^3-2*a^6*(b^2+c^2)*(b^4+c^4) : :
X(61542) = -X[182]+3*X[23332], -3*X[549]+X[36989], -5*X[632]+3*X[23041], -X[1353]+3*X[23327], -5*X[1656]+X[5596], X[2892]+3*X[38724], 7*X[3090]+X[20079], -5*X[3763]+X[9833], -X[5480]+3*X[23325]

X(61542) lies on these lines: {5, 66}, {30, 34177}, {140, 1503}, {141, 18381}, {143, 58494}, {159, 7516}, {182, 23332}, {206, 3628}, {511, 61544}, {546, 34146}, {549, 36989}, {550, 34775}, {632, 23041}, {1352, 1368}, {1353, 23327}, {1594, 26926}, {1656, 5596}, {1658, 44883}, {2393, 44324}, {2781, 11801}, {2892, 38724}, {3090, 20079}, {3098, 41362}, {3548, 18440}, {3564, 13371}, {3589, 32767}, {3627, 34778}, {3630, 34788}, {3763, 9833}, {3818, 6247}, {3827, 31835}, {5094, 6776}, {5480, 23325}, {5894, 48884}, {6000, 40670}, {6644, 39884}, {6696, 29012}, {7484, 32064}, {7734, 11178}, {9756, 30794}, {9968, 12811}, {9969, 16198}, {10516, 14216}, {11585, 13562}, {13861, 34207}, {14791, 48876}, {15116, 32423}, {15311, 48889}, {15583, 34507}, {15699, 31166}, {18376, 51163}, {18383, 29181}, {18405, 48873}, {18583, 20300}, {19150, 32351}, {21167, 34785}, {23042, 51126}, {23324, 48901}, {23328, 48898}, {23329, 44882}, {31267, 55856}, {31830, 61540}, {34774, 38317}, {34786, 48881}, {36201, 61548}, {36990, 37458}, {40686, 46264}, {41729, 51732}, {48154, 58450}

X(61542) = midpoint of X(i) and X(j) for these {i,j}: {5, 66}, {141, 18381}, {550, 34775}, {3098, 41362}, {3627, 34778}, {3630, 34788}, {3818, 6247}, {5894, 48884}, {15583, 34507}, {23300, 34118}, {34786, 48881}
X(61542) = reflection of X(i) in X(j) for these {i,j}: {140, 6697}, {143, 58494}, {10282, 34573}, {18583, 20300}, {206, 3628}, {3589, 32767}, {41729, 51732}, {61610, 24206}
X(61542) = pole of line {3517, 7755} with respect to the Kiepert hyperbola
X(61542) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1503, 24206, 61610}, {1503, 34573, 10282}, {1503, 6697, 140}, {23300, 34118, 3564}, {32064, 40330, 39879}

X(61543) = MIDPOINT OF X(5) AND X(67)

Barycentrics    (a^2-b^2-c^2)*(2*a^10-3*a^8*(b^2+c^2)-a^4*b^2*c^2*(b^2+c^2)+3*(b^2-c^2)^4*(b^2+c^2)+2*a^6*(b^4+b^2*c^2+c^4)-a^2*(b^2-c^2)^2*(4*b^4+11*b^2*c^2+4*c^4)) : :
X(61543) = 3*X[2]+X[32306], X[69]+3*X[38724], -3*X[141]+X[12584], 3*X[381]+X[32247], -X[399]+5*X[40330], -3*X[549]+X[32233], -3*X[597]+X[41731], -5*X[632]+3*X[15462], -X[1351]+5*X[15081], -5*X[1656]+X[11061], -7*X[3090]+3*X[45016], -5*X[3091]+X[48679] and many others

X(61543) lies on these lines: {2, 32306}, {3, 18125}, {5, 67}, {30, 8262}, {49, 5622}, {68, 23296}, {69, 38724}, {74, 39884}, {125, 3292}, {140, 542}, {141, 12584}, {143, 58495}, {182, 40685}, {265, 48876}, {381, 32247}, {399, 40330}, {495, 32308}, {496, 32307}, {511, 11801}, {524, 20301}, {546, 2781}, {549, 32233}, {575, 8254}, {576, 10224}, {590, 35877}, {597, 41731}, {615, 35876}, {632, 15462}, {895, 3519}, {952, 32238}, {1216, 14984}, {1351, 15081}, {1352, 10264}, {1503, 18571}, {1656, 11061}, {2836, 31835}, {2854, 61545}, {3090, 45016}, {3091, 48679}, {3448, 32254}, {3619, 32609}, {3628, 6593}, {3850, 32271}, {5621, 37814}, {5663, 18358}, {5886, 32261}, {7399, 14094}, {7583, 49265}, {7584, 49264}, {8550, 34331}, {9140, 30739}, {10272, 24206}, {10283, 32298}, {10510, 37938}, {10519, 12902}, {10592, 32289}, {10593, 32290}, {10733, 48874}, {10752, 38136}, {11898, 25320}, {12106, 34118}, {13861, 32262}, {14644, 21850}, {14677, 36990}, {15059, 38110}, {15061, 48906}, {15074, 32260}, {15118, 20396}, {15325, 32243}, {15699, 34319}, {18583, 20304}, {19116, 32253}, {19117, 32252}, {20126, 41737}, {21841, 32239}, {25328, 34507}, {25329, 38317}, {25555, 41595}, {31833, 51522}, {32234, 50979}, {32250, 37934}, {32278, 38042}, {36201, 61540}, {38079, 41720}, {38790, 51537}, {41584, 44795}, {47341, 47558}, {52296, 53092}

X(61543) = midpoint of X(i) and X(j) for these {i,j}: {5, 67}, {68, 23296}, {74, 39884}, {265, 48876}, {1352, 10264}, {10733, 48874}, {14677, 36990}, {15074, 32260}, {25328, 34507}, {32257, 36253}, {32274, 49116}, {47341, 47558}
X(61543) = reflection of X(i) in X(j) for these {i,j}: {140, 6698}, {143, 58495}, {182, 40685}, {10272, 24206}, {11694, 20582}, {15118, 20396}, {18583, 20304}, {32271, 3850}, {41595, 25555}, {6593, 3628}
X(61543) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {542, 20582, 11694}, {542, 6698, 140}, {32257, 36253, 14984}, {32274, 49116, 30}

X(61544) = MIDPOINT OF X(5) AND X(68)

Barycentrics    (a^2-b^2-c^2)*(2*a^8+3*(b^2-c^2)^4-3*a^6*(b^2+c^2)-5*a^2*(b^2-c^2)^2*(b^2+c^2)+a^4*(3*b^4+2*b^2*c^2+3*c^4)) : :
X(61544) = 3*X[2]+X[12429], -2*X[156]+3*X[61606], 3*X[381]+X[11411], -3*X[549]+X[12118], -5*X[632]+3*X[47391], -5*X[1656]+X[6193], -7*X[3090]+3*X[3167], -3*X[5066]+2*X[5448], 3*X[5886]+X[9896], 3*X[5891]+X[21651], -X[9833]+3*X[10154], -X[9928]+3*X[38042] and many others

X(61544) lies on these lines: {2, 12429}, {3, 15077}, {4, 11469}, {5, 6}, {20, 41467}, {30, 3357}, {69, 18920}, {113, 16624}, {125, 16196}, {140, 5449}, {143, 546}, {156, 61606}, {235, 11442}, {265, 12605}, {343, 12362}, {381, 11411}, {427, 13142}, {468, 14516}, {495, 10071}, {496, 10055}, {511, 61542}, {520, 59741}, {539, 547}, {542, 16252}, {548, 13470}, {549, 12118}, {550, 12293}, {590, 35837}, {615, 35836}, {632, 47391}, {912, 9947}, {952, 12259}, {1069, 10593}, {1092, 5159}, {1093, 44228}, {1147, 3628}, {1154, 12235}, {1216, 14984}, {1598, 39884}, {1656, 6193}, {1885, 15062}, {1899, 6823}, {3089, 18440}, {3090, 3167}, {3091, 9777}, {3157, 10592}, {3527, 38136}, {3547, 48906}, {3549, 31804}, {3575, 3580}, {3627, 12163}, {3818, 15873}, {3850, 22660}, {3853, 52101}, {5066, 5448}, {5446, 16198}, {5663, 32392}, {5886, 9896}, {5889, 23047}, {5891, 21651}, {5907, 44920}, {5921, 6622}, {6146, 6676}, {6515, 7507}, {6643, 48876}, {6756, 18474}, {6759, 19154}, {6815, 26869}, {7393, 12309}, {7399, 18912}, {7512, 12310}, {7514, 9937}, {7525, 32048}, {7542, 44076}, {9306, 58465}, {9825, 13567}, {9833, 10154}, {9908, 13861}, {9928, 38042}, {9933, 10283}, {10020, 32391}, {10112, 23292}, {10151, 12111}, {10297, 18436}, {10539, 37942}, {10600, 35067}, {11245, 13160}, {11264, 61619}, {11424, 45303}, {11572, 41586}, {11793, 34382}, {11801, 31834}, {12100, 20191}, {12106, 19908}, {12134, 21841}, {12162, 44226}, {12241, 21243}, {12278, 37931}, {12282, 15056}, {12370, 34826}, {12811, 15083}, {12812, 41597}, {13346, 23332}, {13364, 58545}, {13383, 61612}, {13434, 37454}, {14914, 20080}, {15047, 37347}, {15115, 20396}, {15151, 46850}, {15325, 18970}, {15760, 18914}, {15761, 18356}, {16659, 47093}, {18394, 47339}, {18451, 44960}, {18488, 18555}, {18855, 47735}, {19467, 37638}, {19588, 40330}, {20302, 49673}, {23294, 47090}, {23325, 34380}, {26879, 43597}, {26937, 44241}, {32064, 39568}, {32111, 43895}, {32269, 61139}, {32539, 44235}, {34381, 58631}, {34782, 44277}, {34801, 38443}, {37452, 38724}, {41615, 43598}, {43588, 46029}, {43839, 48154}, {45184, 47478}, {52250, 56267}

X(61544) = midpoint of X(i) and X(j) for these {i,j}: {5, 68}, {550, 12293}, {3627, 12163}, {9927, 12359}, {15761, 18356}, {41362, 46730}
X(61544) = reflection of X(i) in X(j) for these {i,j}: {140, 5449}, {143, 58496}, {1147, 3628}, {15115, 20396}, {22660, 3850}, {34782, 44277}, {548, 44158}, {61607, 5}
X(61544) = pole of line {1993, 3515} with respect to the Stammler hyperbola
X(61544) = pole of line {7763, 32001} with respect to the Wallace hyperbola
X(61544) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2165), X(15077)}}, {{A, B, C, X(18855), X(56892)}}
X(61544) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 3564, 61607}, {5, 68, 3564}, {68, 14852, 5}, {1656, 6193, 59553}, {5449, 44665, 140}, {6515, 7507, 31802}, {7399, 18912, 45298}, {12370, 34826, 52262}, {13754, 58496, 143}, {15760, 25738, 18914}, {17702, 44158, 548}, {18474, 41587, 6756}, {41362, 46730, 30}

X(61545) = MIDPOINT OF X(5) AND X(69)

Barycentrics    2*a^6-5*a^4*(b^2+c^2)-3*(b^2-c^2)^2*(b^2+c^2)+a^2*(6*b^4+8*b^2*c^2+6*c^4) : :
X(61545) = -3*X[2]+X[1353], -X[3]+5*X[3620], 3*X[4]+X[55584], -3*X[20]+7*X[55616], -X[193]+5*X[1656], 3*X[376]+X[48662], -3*X[549]+X[6776], -X[550]+3*X[10519], -2*X[597]+3*X[47599], -5*X[631]+X[39899], -5*X[632]+7*X[3619]

X(61545) lies on these lines: {2, 1353}, {3, 3620}, {4, 55584}, {5, 69}, {6, 3628}, {20, 55616}, {30, 599}, {110, 6676}, {140, 141}, {143, 9822}, {156, 19126}, {159, 7525}, {183, 9754}, {193, 1656}, {298, 52263}, {299, 52266}, {323, 37454}, {343, 5651}, {376, 48662}, {381, 50978}, {511, 546}, {518, 61509}, {524, 547}, {542, 12100}, {548, 1503}, {549, 6776}, {550, 10519}, {575, 34573}, {576, 3630}, {597, 47599}, {631, 39899}, {632, 3619}, {732, 61625}, {742, 61623}, {952, 49511}, {1216, 14913}, {1511, 32275}, {1843, 6101}, {1899, 7734}, {1992, 15699}, {1993, 11548}, {2080, 7767}, {2393, 44324}, {2781, 61598}, {2810, 61602}, {2854, 61543}, {3054, 39764}, {3066, 10128}, {3090, 5093}, {3091, 44456}, {3098, 12103}, {3146, 55593}, {3314, 56370}, {3410, 7667}, {3416, 5844}, {3448, 43957}, {3525, 55705}, {3526, 14912}, {3529, 55604}, {3530, 15069}, {3533, 33748}, {3543, 50954}, {3589, 5965}, {3618, 55856}, {3627, 33878}, {3629, 38317}, {3751, 38042}, {3763, 16239}, {3818, 3853}, {3830, 61044}, {3845, 50990}, {3850, 10516}, {3856, 53023}, {3857, 55724}, {3860, 51189}, {3861, 31670}, {5028, 43291}, {5032, 15703}, {5055, 11160}, {5066, 5480}, {5067, 51170}, {5070, 51171}, {5071, 50962}, {5085, 12108}, {5133, 15108}, {5159, 15066}, {5181, 32423}, {5476, 47478}, {5544, 11433}, {5663, 32257}, {5843, 47595}, {5845, 61596}, {5846, 61597}, {5847, 5901}, {5848, 61562}, {5876, 37511}, {5891, 44920}, {5969, 61600}, {6403, 23039}, {6723, 53415}, {6756, 37494}, {7380, 17375}, {7393, 19588}, {7499, 11003}, {7505, 46444}, {7516, 19459}, {7789, 47113}, {7794, 18860}, {7800, 52771}, {7819, 11842}, {7854, 8722}, {7998, 10300}, {7999, 12272}, {8354, 13188}, {8357, 13108}, {8703, 11180}, {9024, 61601}, {9028, 61539}, {9306, 19154}, {9825, 37489}, {9956, 34379}, {9967, 15067}, {9969, 14449}, {10020, 59778}, {10096, 32217}, {10109, 15533}, {10124, 21358}, {10154, 14826}, {10168, 51143}, {10283, 51192}, {10303, 55697}, {10691, 11442}, {10754, 38229}, {11008, 11482}, {11179, 11812}, {11230, 51196}, {11261, 32449}, {11444, 18438}, {11454, 44247}, {11477, 12811}, {11540, 38064}, {11574, 32142}, {11645, 15691}, {11737, 20423}, {11793, 34382}, {11801, 14984}, {12007, 20582}, {12017, 14869}, {12101, 41152}, {12102, 53097}, {12105, 47449}, {12106, 37488}, {12212, 15993}, {12294, 15060}, {12589, 15172}, {13383, 13562}, {13567, 16187}, {13861, 37491}, {14269, 54174}, {14561, 35018}, {14643, 32244}, {14645, 61576}, {14677, 41737}, {14891, 43273}, {14893, 47354}, {14929, 35930}, {14994, 32515}, {15035, 32272}, {15325, 39897}, {15520, 42786}, {15534, 38079}, {15589, 37071}, {15686, 51023}, {15687, 50967}, {15690, 48898}, {15692, 50981}, {15694, 50974}, {15702, 50987}, {15704, 55610}, {15712, 25406}, {15812, 32140}, {15850, 53845}, {16196, 43608}, {16197, 31831}, {16238, 21230}, {16990, 37451}, {17538, 55624}, {17714, 37485}, {17811, 34966}, {18350, 19121}, {18538, 35840}, {18553, 29181}, {18762, 35841}, {19130, 55719}, {19924, 50982}, {21167, 55669}, {21357, 22151}, {22112, 45298}, {25337, 61610}, {25555, 32455}, {26543, 50205}, {28194, 50788}, {28204, 50787}, {29012, 55612}, {29317, 55592}, {30258, 40996}, {31835, 34381}, {31884, 44245}, {32110, 44683}, {32220, 44282}, {32234, 38794}, {32863, 37360}, {33699, 54170}, {33751, 41982}, {33884, 46517}, {33923, 46264}, {34002, 46442}, {34200, 44882}, {34371, 61620}, {34577, 58437}, {34773, 39885}, {35255, 49228}, {35256, 49229}, {35259, 47316}, {35283, 41586}, {35400, 51216}, {35401, 51213}, {35404, 51217}, {37340, 59244}, {37341, 59245}, {37439, 45794}, {37477, 39871}, {37638, 37911}, {37931, 41398}, {38071, 54132}, {38072, 50989}, {38171, 51194}, {38176, 49536}, {38228, 59635}, {39561, 51126}, {39882, 42787}, {40670, 58549}, {41614, 44911}, {41981, 59411}, {41983, 51737}, {42143, 51207}, {42146, 51206}, {43621, 55591}, {44212, 54013}, {44264, 47450}, {47279, 47341}, {47342, 47447}, {47352, 50961}, {48310, 51140}, {48880, 55605}, {48881, 55608}, {48885, 55619}, {48896, 50965}, {48905, 55622}, {49684, 61278}, {50693, 55632}, {50980, 51027}, {50986, 59373}, {51016, 51021}, {51018, 51020}, {51538, 55580}, {53092, 55861}, {55606, 58203}, {55626, 58196}, {61547, 61551}

X(61545) = midpoint of X(i) and X(j) for these {i,j}: {5, 69}, {141, 34507}, {381, 50978}, {549, 50955}, {550, 18440}, {576, 3630}, {1216, 14913}, {1350, 39884}, {1352, 48876}, {1353, 11898}, {1511, 32275}, {1843, 6101}, {3627, 33878}, {5876, 37511}, {8703, 11180}, {11178, 22165}, {14677, 41737}, {14929, 35930}, {15069, 48906}, {15686, 51023}, {15687, 50967}, {33699, 54170}, {34773, 39885}, {36990, 48874}, {40107, 43150}, {47279, 47341}, {51163, 55587}
X(61545) = reflection of X(i) in X(j) for these {i,j}: {140, 141}, {143, 9822}, {10168, 51143}, {1353, 51732}, {11179, 11812}, {11574, 32142}, {12007, 58445}, {12103, 3098}, {12105, 47449}, {14449, 9969}, {14893, 47354}, {15690, 54169}, {18583, 24206}, {20423, 11737}, {21850, 3850}, {3853, 3818}, {31670, 3861}, {32455, 25555}, {34200, 50977}, {43273, 14891}, {46264, 33923}, {48906, 3530}, {49684, 61278}, {546, 18358}, {5066, 11178}, {575, 34573}, {50979, 10124}, {54131, 3860}, {6, 3628}, {61624, 18583}
X(61545) = complement of X(1353)
X(61545) = anticomplement of X(51732)
X(61545) = X(i)-Dao conjugate of X(j) for these {i, j}: {51732, 51732}
X(61545) = pole of line {3566, 23042} with respect to the 1st Brocard circle
X(61545) = pole of line {3526, 5013} with respect to the Kiepert hyperbola
X(61545) = pole of line {3060, 5093} with respect to the Stammler hyperbola
X(61545) = pole of line {6563, 31072} with respect to the Steiner inellipse
X(61545) = pole of line {631, 7752} with respect to the Wallace hyperbola
X(61545) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3527), X(14906)}}, {{A, B, C, X(8797), X(16774)}}
X(61545) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11898, 1353}, {2, 1353, 51732}, {5, 69, 34380}, {69, 40330, 1351}, {141, 34507, 3564}, {141, 3564, 140}, {193, 1656, 59399}, {511, 18358, 546}, {524, 18583, 61624}, {524, 24206, 18583}, {599, 1352, 48876}, {1350, 1352, 39884}, {1350, 39884, 30}, {1351, 40330, 5}, {1352, 48873, 47353}, {1352, 54173, 36990}, {3090, 20080, 5093}, {3619, 5050, 632}, {3763, 38110, 16239}, {3818, 55587, 51163}, {10516, 21850, 3850}, {10519, 14927, 55629}, {10519, 18440, 550}, {12007, 20582, 58445}, {15703, 51175, 5032}, {18440, 55629, 14927}, {18583, 24206, 547}, {21356, 50955, 549}, {21358, 50979, 10124}, {36990, 54173, 48874}, {39884, 48876, 1350}, {40107, 43150, 1503}, {48874, 48876, 54173}, {61509, 61510, 61549}

X(61546) = MIDPOINT OF X(5) AND X(71)

Barycentrics    2*a^8*(b+c)+b*(b-c)^4*c*(b+c)^3+a*(b^2-c^2)^4-7*a^6*(b+c)*(b^2+c^2)-2*a^3*(b^2-c^2)^2*(b^2+c^2)+a^5*(b^2+c^2)^2-a^2*(b-c)^2*(b+c)*(3*b^4+8*b^3*c+8*b^2*c^2+8*b*c^3+3*c^4)+a^4*(b+c)*(8*b^4+b^3*c+4*b^2*c^2+b*c^3+8*c^4) : :
X(61546) = -5*X[1656]+X[17220], -4*X[16239]+X[43165], 3*X[26446]+X[33536]

X(61546) lies on these lines: {5, 71}, {30, 51758}, {140, 916}, {516, 546}, {674, 18583}, {1656, 17220}, {2772, 61548}, {3628, 34830}, {8053, 32141}, {9028, 61539}, {16239, 43165}, {20718, 61522}, {26446, 33536}, {61540, 61627}

X(61546) = midpoint of X(i) and X(j) for these {i,j}: {5, 71}
X(61546) = reflection of X(i) in X(j) for these {i,j}: {140, 58410}, {34830, 3628}
X(61546) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {916, 58410, 140}, {61511, 61524, 61517}

X(61547) = MIDPOINT OF X(5) AND X(73)

Barycentrics    2*a^9*(b+c)-2*a^8*(b+c)^2+b*c*(b^2-c^2)^4+a*(b-c)^4*(b+c)^3*(b^2-b*c+c^2)-a^7*(b+c)*(7*b^2-8*b*c+7*c^2)+2*a^2*(b^2-c^2)^2*(b^4-2*b^3*c+b^2*c^2-2*b*c^3+c^4)+a^6*(6*b^4+6*b^3*c-4*b^2*c^2+6*b*c^3+6*c^4)-a^4*(b-c)^2*(6*b^4+11*b^3*c+8*b^2*c^2+11*b*c^3+6*c^4)+a^5*(b+c)*(9*b^4-19*b^3*c+22*b^2*c^2-19*b*c^3+9*c^4)-a^3*(b-c)^2*(5*b^5+b^4*c+b*c^4+5*c^5) : :
X(61547) =

X(61547) lies on these lines: {5, 73}, {30, 51759}, {140, 58411}, {515, 546}, {2779, 61520}, {3628, 34831}, {8254, 61521}, {8679, 18583}, {14988, 20617}, {39505, 61512}, {61526, 61541}, {61533, 61540}, {61545, 61551}

X(61547) = midpoint of X(i) and X(j) for these {i,j}: {5, 73}
X(61547) = reflection of X(i) in X(j) for these {i,j}: {140, 58411}, {34831, 3628}

X(61548) = MIDPOINT OF X(5) AND X(74)

Barycentrics    2*a^10-3*a^8*(b^2+c^2)+(b^2-c^2)^4*(b^2+c^2)-2*a^6*(2*b^4-7*b^2*c^2+2*c^4)-3*a^2*(b^2-c^2)^2*(2*b^4+3*b^2*c^2+2*c^4)+a^4*(b^2+c^2)*(10*b^4-21*b^2*c^2+10*c^4) : :
X(61548) = 3*X[2]+X[10620], X[20]+3*X[38724], -X[110]+3*X[549], -X[146]+5*X[1656], -3*X[182]+X[25329], 3*X[376]+X[12902], 3*X[381]+X[12244], -X[382]+5*X[15081], -X[399]+5*X[631], 3*X[568]+X[13201], -5*X[632]+3*X[14643], X[1352]+3*X[5621] and many others

X(61548) lies on these lines: {2, 10620}, {3, 2888}, {4, 14677}, {5, 74}, {20, 38724}, {30, 125}, {67, 48906}, {110, 549}, {113, 3628}, {140, 5663}, {141, 32305}, {143, 58498}, {146, 1656}, {182, 25329}, {185, 5498}, {265, 550}, {376, 12902}, {381, 12244}, {382, 15081}, {399, 631}, {468, 12292}, {495, 10081}, {496, 10065}, {511, 13358}, {541, 547}, {542, 12100}, {546, 2777}, {548, 13470}, {568, 13201}, {590, 35827}, {615, 35826}, {632, 14643}, {690, 61560}, {952, 11709}, {974, 23336}, {1154, 11806}, {1204, 10224}, {1352, 5621}, {1353, 5622}, {1495, 22249}, {1503, 18571}, {1511, 3530}, {1539, 3850}, {1595, 11566}, {1657, 38633}, {2574, 31682}, {2575, 31681}, {2771, 6684}, {2772, 61546}, {2773, 61564}, {2774, 61565}, {2775, 61567}, {2776, 61568}, {2778, 61541}, {2779, 61520}, {2780, 61572}, {2781, 18583}, {2914, 43845}, {2931, 7525}, {3024, 15325}, {3047, 40111}, {3090, 38789}, {3091, 38790}, {3098, 25328}, {3357, 44235}, {3520, 43575}, {3523, 12317}, {3524, 14683}, {3564, 49116}, {3579, 13605}, {3580, 37950}, {3618, 48679}, {3627, 14644}, {3845, 10721}, {3853, 7687}, {3861, 13202}, {5050, 32247}, {5054, 12308}, {5066, 15088}, {5067, 15046}, {5085, 25336}, {5432, 19470}, {5433, 7727}, {5609, 12108}, {5642, 11812}, {5655, 11539}, {5719, 59817}, {5886, 9904}, {5944, 17701}, {5946, 13417}, {6000, 44234}, {6070, 38610}, {6101, 21649}, {6102, 11803}, {6143, 43807}, {6247, 13289}, {6644, 13171}, {6676, 44573}, {6698, 18358}, {7471, 47852}, {7516, 12168}, {7583, 49217}, {7584, 49216}, {7689, 23306}, {7706, 23315}, {7722, 37118}, {7723, 10257}, {7731, 37481}, {7978, 10283}, {8254, 10628}, {8674, 61566}, {8703, 9140}, {8901, 14933}, {9143, 15693}, {9729, 11561}, {9730, 38898}, {9919, 13861}, {9970, 38110}, {10020, 15738}, {10095, 11807}, {10096, 44673}, {10117, 12106}, {10125, 13491}, {10165, 11699}, {10212, 13367}, {10226, 32607}, {10303, 20125}, {10575, 18282}, {10592, 12373}, {10593, 12374}, {10706, 15699}, {10733, 15027}, {10752, 59399}, {11061, 12017}, {11250, 19353}, {11270, 18562}, {11557, 12006}, {11559, 58805}, {11562, 15101}, {11579, 48876}, {11597, 61134}, {11645, 32218}, {11746, 13451}, {11749, 14851}, {11800, 13391}, {11818, 13203}, {12026, 45147}, {12042, 15357}, {12103, 36253}, {12133, 21841}, {12236, 14449}, {12261, 28174}, {12284, 23039}, {12358, 16196}, {12359, 12901}, {12368, 38042}, {12584, 21167}, {12812, 38791}, {12893, 44882}, {12900, 48154}, {13163, 18488}, {13210, 42787}, {13211, 34773}, {13293, 23328}, {13339, 27866}, {13363, 41671}, {13393, 30714}, {13416, 44324}, {13434, 43391}, {13445, 43893}, {13561, 43604}, {13754, 46114}, {14094, 14869}, {14106, 24043}, {14157, 16532}, {14508, 57305}, {14708, 52262}, {14915, 25338}, {14934, 40630}, {15035, 15712}, {15036, 17504}, {15042, 61138}, {15051, 23236}, {15063, 16239}, {15089, 43574}, {15102, 20791}, {15106, 18580}, {15311, 46031}, {15342, 38739}, {15473, 16198}, {15535, 53710}, {15545, 34473}, {15647, 16531}, {16163, 33923}, {16168, 55319}, {16219, 19506}, {16340, 46632}, {16772, 36208}, {16773, 36209}, {16881, 46430}, {17853, 51425}, {17854, 44452}, {17856, 46817}, {18281, 18931}, {18364, 59493}, {18430, 23294}, {18556, 42739}, {18570, 18911}, {18933, 58378}, {19059, 19117}, {19060, 19116}, {20191, 34577}, {20299, 45971}, {20301, 29181}, {21451, 33541}, {22250, 48378}, {22584, 45957}, {23181, 56373}, {25320, 33878}, {25321, 55705}, {25330, 55646}, {25331, 55699}, {25335, 55676}, {25406, 32306}, {25487, 43588}, {26446, 33535}, {30507, 36966}, {32111, 44282}, {32138, 49673}, {32273, 48881}, {32608, 44450}, {34200, 38726}, {34209, 36164}, {34468, 51394}, {34753, 59818}, {35018, 36518}, {35255, 49268}, {35256, 49269}, {35498, 43808}, {36177, 54085}, {36201, 61542}, {37459, 38641}, {38022, 50878}, {38081, 50877}, {38083, 50876}, {38626, 55862}, {38723, 46853}, {40915, 46066}, {41595, 50664}, {41673, 44683}, {44232, 61540}, {44267, 50434}, {44961, 47296}, {45113, 51872}, {49671, 54012}

X(61548) = midpoint of X(i) and X(j) for these {i,j}: {3, 10264}, {4, 14677}, {5, 74}, {67, 48906}, {113, 51522}, {125, 12041}, {141, 32305}, {265, 550}, {549, 20126}, {1511, 16003}, {1539, 10990}, {3098, 25328}, {3448, 34153}, {3579, 13605}, {3580, 37950}, {3627, 20127}, {6070, 38610}, {6101, 21649}, {6247, 13289}, {6699, 20417}, {7689, 23306}, {8703, 9140}, {10113, 16111}, {10733, 15704}, {11562, 15101}, {11579, 48876}, {12042, 15357}, {12359, 12901}, {13211, 34773}, {13445, 43893}, {13491, 21650}, {14708, 54376}, {15535, 53710}, {16219, 23332}, {16340, 46632}, {22584, 45957}, {32273, 48881}, {34209, 36164}, {36253, 37853}, {44267, 50434}
X(61548) = reflection of X(i) in X(j) for these {i,j}: {113, 3628}, {140, 6699}, {143, 58498}, {10096, 44673}, {10272, 140}, {1495, 22249}, {1511, 3530}, {1539, 3850}, {11557, 12006}, {11561, 9729}, {11694, 549}, {11801, 125}, {11807, 10095}, {12103, 37853}, {13202, 3861}, {13392, 12108}, {14449, 12236}, {16163, 33923}, {18358, 6698}, {20304, 20397}, {3853, 7687}, {31834, 12358}, {41595, 50664}, {44961, 47296}, {46686, 15088}, {5, 40685}, {546, 20304}, {5066, 45311}, {5609, 13392}, {5642, 11812}, {61574, 6723}, {61598, 61574}, {7687, 20396}
X(61548) = pole of line {2070, 15035} with respect to the Stammler hyperbola
X(61548) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 10264, 32423}, {3, 3448, 34153}, {4, 15041, 14677}, {5, 15061, 40685}, {30, 125, 11801}, {74, 15057, 15061}, {74, 15059, 7728}, {74, 15061, 5}, {110, 38728, 549}, {113, 34128, 3628}, {125, 16111, 10113}, {140, 5663, 10272}, {185, 5498, 15806}, {265, 15055, 550}, {541, 61574, 61598}, {541, 6723, 61574}, {1511, 38727, 3530}, {1539, 23515, 3850}, {2777, 20304, 546}, {2777, 20397, 20304}, {3523, 12317, 32609}, {5609, 38793, 13392}, {5663, 6699, 140}, {6699, 20417, 5663}, {6723, 61574, 547}, {7687, 34584, 3853}, {7687, 38725, 20396}, {7728, 15061, 15059}, {10113, 12041, 16111}, {10113, 16111, 30}, {10264, 34153, 3448}, {10733, 38788, 15704}, {10990, 23515, 1539}, {14644, 15021, 20127}, {14644, 20127, 3627}, {15027, 38788, 10733}, {15088, 46686, 5066}, {20126, 38728, 110}, {20396, 34584, 7687}, {34128, 51522, 113}, {45311, 46686, 15088}

X(61549) = MIDPOINT OF X(5) AND X(75)

Barycentrics    2*a^4*b*c+a*(b-c)^2*(b+c)^3+3*b*c*(b^2-c^2)^2-5*a^2*b*c*(b^2+c^2)-a^3*(b+c)*(b^2+c^2) : :
X(61549) = -3*X[2]+X[51046], -X[3]+5*X[4699], X[4]+7*X[4772], -X[192]+5*X[1656], X[546]+4*X[4739], -3*X[549]+X[30273], -5*X[632]+7*X[4751], -X[984]+3*X[38042], X[1278]+7*X[3090], -3*X[3845]+X[51063], -X[3993]+3*X[11230], -X[4664]+3*X[15699] and many others

X(61549) lies on these lines: {2, 51046}, {3, 4699}, {4, 4772}, {5, 75}, {30, 4688}, {37, 3628}, {140, 3739}, {143, 58499}, {192, 1656}, {381, 51048}, {518, 61509}, {536, 547}, {546, 4739}, {549, 30273}, {632, 4751}, {714, 61523}, {726, 9956}, {740, 5901}, {742, 18583}, {744, 20575}, {746, 20576}, {952, 24325}, {984, 38042}, {1278, 3090}, {2805, 61601}, {3564, 49481}, {3696, 5844}, {3845, 51063}, {3993, 11230}, {4032, 34753}, {4359, 37365}, {4664, 15699}, {4686, 35018}, {4687, 55856}, {4698, 48154}, {4704, 5067}, {4709, 10222}, {4726, 12812}, {4740, 5055}, {4755, 47599}, {4788, 7486}, {4821, 5056}, {5070, 27268}, {5071, 51039}, {5790, 24349}, {5886, 49474}, {6924, 54410}, {8680, 61517}, {9055, 24206}, {10124, 51045}, {10175, 50117}, {10283, 49470}, {11737, 51038}, {14213, 59520}, {14891, 51042}, {14893, 51041}, {15686, 51065}, {15687, 51044}, {15694, 51043}, {15973, 20892}, {16239, 31238}, {19546, 31025}, {21443, 32515}, {27484, 60922}, {28581, 61597}, {29054, 61524}, {31399, 49520}, {34200, 51049}, {38028, 40328}, {38081, 50075}, {38083, 50777}, {38171, 51058}, {38176, 49510}, {49445, 54447}, {49450, 59400}, {49469, 61276}, {49471, 61278}, {49496, 59399}, {51047, 51488}, {61511, 61621}

X(61549) = midpoint of X(i) and X(j) for these {i,j}: {5, 75}, {381, 51048}, {549, 51040}, {4709, 10222}, {15686, 51065}, {15687, 51044}
X(61549) = reflection of X(i) in X(j) for these {i,j}: {140, 3739}, {143, 58499}, {14893, 51041}, {37, 3628}, {34200, 51049}, {49471, 61278}, {51038, 11737}, {51042, 14891}, {51045, 10124}, {61623, 61522}
X(61549) = complement of X(51046)
X(61549) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {536, 61522, 61623}, {547, 61623, 61522}, {3739, 29010, 140}, {61509, 61510, 61545}

X(61550) = MIDPOINT OF X(5) AND X(76)

Barycentrics    -3*b^2*c^2*(b^2-c^2)^2+a^4*(b^4+c^4)-a^2*(b^6-6*b^4*c^2-6*b^2*c^4+c^6) : :
X(61550) = 3*X[2]+X[13108], X[20]+3*X[48663], -3*X[141]+X[52996], -X[194]+5*X[1656], 3*X[381]+X[12251], X[382]+3*X[6194], -3*X[549]+X[11257], -X[550]+3*X[22712], -5*X[632]+3*X[11171], -X[1916]+3*X[38229], 7*X[3090]+X[20081], -5*X[3091]+X[48673] and many others

X(61550) lies on circumconic {{A, B, C, X(327), X(43458)}} and on these lines: {2, 13108}, {3, 17128}, {4, 7929}, {5, 76}, {20, 48663}, {30, 5188}, {39, 3055}, {98, 44224}, {140, 620}, {141, 52996}, {143, 58500}, {194, 1656}, {311, 59566}, {381, 12251}, {382, 6194}, {385, 32134}, {495, 10079}, {496, 10063}, {511, 546}, {538, 547}, {549, 11257}, {550, 22712}, {590, 35867}, {615, 35866}, {632, 11171}, {698, 24206}, {726, 9956}, {730, 5901}, {732, 18583}, {734, 20575}, {736, 20576}, {952, 12263}, {1352, 40279}, {1916, 38229}, {3090, 20081}, {3091, 48673}, {3102, 18762}, {3103, 18538}, {3104, 42163}, {3105, 42166}, {3106, 42599}, {3107, 42598}, {3525, 32523}, {3526, 7709}, {3530, 15819}, {3564, 24256}, {3627, 9821}, {3734, 10104}, {3832, 22728}, {3850, 14881}, {3855, 44434}, {3856, 22682}, {3861, 22681}, {3906, 59741}, {5054, 32522}, {5055, 32520}, {5070, 32519}, {5886, 9902}, {6683, 48154}, {7486, 20105}, {7583, 49253}, {7584, 49252}, {7751, 10796}, {7757, 15699}, {7767, 39266}, {7786, 55856}, {7824, 13188}, {7832, 38224}, {7874, 34127}, {7976, 10283}, {8252, 32471}, {8253, 32470}, {8782, 38732}, {9752, 32886}, {9917, 13861}, {10109, 14711}, {10358, 17131}, {10592, 12837}, {10593, 12836}, {11539, 61132}, {11737, 44422}, {12054, 38664}, {12108, 21163}, {12143, 21841}, {12782, 38042}, {13085, 16509}, {14449, 27375}, {14651, 46226}, {14839, 61510}, {14853, 32868}, {14994, 34380}, {15069, 31958}, {15325, 18982}, {15687, 33706}, {16239, 31239}, {19089, 19117}, {19090, 19116}, {19522, 31026}, {20190, 38627}, {20582, 59739}, {22650, 61258}, {22713, 61297}, {32449, 38317}, {32451, 59399}, {32465, 42488}, {32466, 42489}, {32828, 37466}, {32970, 53103}, {37512, 51524}, {38110, 40332}, {42788, 51373}, {44562, 47599}, {46179, 61539}, {46180, 61557}, {46181, 61517}, {46183, 61523}, {46283, 53419}, {52261, 59197}

X(61550) = midpoint of X(i) and X(j) for these {i,j}: {4, 32521}, {5, 76}, {3627, 9821}, {6248, 49111}, {13108, 32448}, {15687, 33706}
X(61550) = reflection of X(i) in X(j) for these {i,j}: {140, 3934}, {143, 58500}, {14449, 27375}, {14881, 3850}, {39, 3628}, {32516, 140}, {44422, 11737}, {61625, 11272}
X(61550) = complement of X(32448)
X(61550) = pole of line {3094, 7765} with respect to the Kiepert hyperbola
X(61550) = pole of line {31072, 53331} with respect to the Steiner inellipse
X(61550) = pole of line {182, 43459} with respect to the Wallace hyperbola
X(61550) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 13108, 32448}, {5, 76, 32515}, {76, 7697, 5}, {140, 2782, 32516}, {538, 11272, 61625}, {547, 61625, 11272}, {2782, 3934, 140}, {3090, 20081, 32447}, {6248, 49111, 30}, {6248, 9466, 49111}, {31239, 40108, 16239}

X(61551) = MIDPOINT OF X(5) AND X(78)

Barycentrics    2*a^7-4*a^6*(b+c)+(b-c)^4*(b+c)^3+4*a^3*b*c*(-3*b^2+b*c-3*c^2)+a^5*(-3*b^2+8*b*c-3*c^2)+a*(b^2-c^2)^2*(b^2+4*b*c+c^2)-2*a^2*(b-c)^2*(b+c)*(3*b^2+b*c+3*c^2)+a^4*(b+c)*(9*b^2-8*b*c+9*c^2) : :
X(61551) = -5*X[1656]+X[12649], 7*X[3090]+X[20013], -3*X[10283]+X[36846], -3*X[11230]+X[49627]

X(61551) lies on these lines: {3, 13257}, {5, 78}, {8, 11729}, {140, 912}, {518, 61534}, {519, 547}, {548, 40262}, {758, 61530}, {936, 37438}, {952, 1329}, {997, 10942}, {1210, 3628}, {1387, 38177}, {1656, 12649}, {2800, 61524}, {3035, 5694}, {3090, 20013}, {3560, 27383}, {3940, 6959}, {5260, 38033}, {5440, 37290}, {5445, 38763}, {5720, 37356}, {5780, 6862}, {5844, 6736}, {6265, 21031}, {6981, 20007}, {7491, 27131}, {10021, 61511}, {10176, 31659}, {10283, 36846}, {10573, 37737}, {10943, 25681}, {11230, 49627}, {13465, 38762}, {14988, 47742}, {19861, 32213}, {22935, 57288}, {24475, 52264}, {59719, 61533}, {61545, 61547}

X(61551) = midpoint of X(i) and X(j) for these {i,j}: {5, 78}
X(61551) = reflection of X(i) in X(j) for these {i,j}: {140, 6700}, {1210, 3628}
X(61551) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {140, 31835, 61539}, {912, 6700, 140}, {936, 37713, 37438}, {5901, 61628, 61510}

X(61552) = MIDPOINT OF X(5) AND X(79)

Barycentrics    2*a^7-3*(b-c)^4*(b+c)^3+a^5*(-3*b^2+2*b*c-3*c^2)-3*a^3*b*c*(b^2+c^2)+a*(b^2-c^2)^2*(b^2+b*c+c^2)-a^4*(b+c)*(3*b^2-2*b*c+3*c^2)+2*a^2*(b-c)^2*(b+c)*(3*b^2+2*b*c+3*c^2) : :
X(61552) = 3*X[2]+X[16150], -X[40]+3*X[5499], 3*X[381]+X[16116], -3*X[549]+X[16113], X[1482]+3*X[2475], -5*X[1656]+X[3648], 7*X[3090]+X[20084], -5*X[3091]+X[48668], -3*X[3817]+X[26202], -X[5441]+3*X[10283], -X[5690]+3*X[6175], 5*X[5818]+3*X[14450] and many others

X(61552) lies on these lines: {2, 16150}, {5, 79}, {30, 551}, {36, 31649}, {40, 5499}, {65, 11544}, {140, 6701}, {381, 16116}, {442, 26878}, {495, 16153}, {496, 16152}, {546, 5885}, {549, 16113}, {590, 35855}, {615, 35854}, {758, 61510}, {952, 3649}, {1482, 2475}, {1656, 3648}, {2771, 11801}, {3090, 20084}, {3091, 48668}, {3628, 3647}, {3817, 26202}, {3822, 61524}, {3850, 10265}, {5441, 10283}, {5690, 6175}, {5818, 14450}, {5843, 13159}, {5886, 16118}, {6841, 13226}, {7583, 49243}, {7584, 49242}, {9955, 33709}, {10021, 61521}, {10543, 61278}, {10592, 16140}, {10593, 16141}, {10902, 28178}, {11277, 31663}, {11684, 38042}, {11849, 35982}, {12026, 61571}, {12679, 16160}, {13861, 16119}, {14526, 37080}, {15174, 61280}, {15325, 18977}, {15678, 38022}, {15911, 28190}, {16114, 21841}, {16137, 61286}, {16617, 61269}, {17768, 61511}, {19079, 19117}, {19080, 19116}, {20323, 33593}, {21669, 37535}, {22791, 47032}, {28174, 37401}, {33668, 37230}, {45976, 48698}, {46028, 61535}, {50194, 61292}

X(61552) = midpoint of X(i) and X(j) for these {i,j}: {5, 79}, {5499, 16159}, {16125, 49107}, {22791, 47032}, {33668, 37230}
X(61552) = reflection of X(i) in X(j) for these {i,j}: {140, 6701}, {10543, 61278}, {22798, 3850}, {3647, 3628}, {31649, 61272}, {61286, 16137}
X(61552) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16125, 49107, 30}

X(61553) = MIDPOINT OF X(5) AND X(80)

Barycentrics    2*a^7-4*a^6*(b+c)-3*(b-c)^4*(b+c)^3+2*a^2*(b-c)^2*(b+c)*(b^2+6*b*c+c^2)+a^5*(b^2+10*b*c+c^2)+a^4*(b+c)*(5*b^2-14*b*c+5*c^2)+a*(b^2-c^2)^2*(5*b^2-11*b*c+5*c^2)+a^3*(-8*b^4+b^3*c+16*b^2*c^2+b*c^3-8*c^4) : :
X(61553) = 3*X[2]+X[12747], X[8]+3*X[51517], X[149]+3*X[5790], 3*X[381]+X[12247], -3*X[549]+X[12119], -X[1145]+3*X[38177], -X[1385]+3*X[59419], -X[1537]+3*X[38141], -5*X[1656]+X[6224], 7*X[3090]+X[20085], -5*X[3091]+X[48667], -2*X[3530]+3*X[38133] and many others

X(61553) lies on these lines: {1, 5}, {2, 12747}, {8, 51517}, {21, 33814}, {30, 6246}, {100, 7489}, {104, 37251}, {140, 6702}, {143, 58501}, {149, 5790}, {153, 6900}, {214, 3628}, {381, 12247}, {515, 61521}, {517, 58683}, {528, 61511}, {546, 2800}, {549, 12119}, {590, 35853}, {615, 35852}, {1145, 38177}, {1385, 59419}, {1389, 38038}, {1537, 38141}, {1656, 6224}, {2771, 11801}, {2801, 61509}, {2802, 58674}, {2829, 61530}, {3036, 3878}, {3090, 20085}, {3091, 48667}, {3530, 38133}, {3627, 12515}, {3845, 34789}, {3850, 12611}, {5046, 5690}, {5657, 48680}, {5779, 45043}, {5818, 12331}, {5840, 61524}, {5844, 11813}, {6797, 14988}, {6839, 10742}, {6852, 38752}, {6905, 28186}, {6915, 51529}, {6920, 12690}, {6949, 34773}, {6979, 18525}, {7504, 34123}, {7508, 61614}, {7583, 49241}, {7584, 49240}, {9803, 38755}, {9912, 13861}, {9956, 10021}, {9963, 59350}, {10031, 38022}, {10124, 38104}, {10175, 22935}, {10265, 18480}, {10698, 38034}, {11230, 33337}, {11715, 28224}, {12137, 21841}, {12761, 33899}, {12773, 59387}, {12832, 24470}, {13226, 28452}, {15178, 33709}, {15325, 18976}, {16128, 18492}, {18990, 20118}, {19077, 19117}, {19078, 19116}, {19914, 22791}, {21635, 38140}, {22799, 22805}, {22938, 28174}, {28190, 38761}, {31272, 38028}, {32153, 54361}, {32557, 51700}, {32558, 37624}, {35016, 38219}, {38071, 50908}, {38084, 50843}, {38197, 51732}, {38390, 53800}, {48154, 58453}, {50824, 59377}

X(61553) = midpoint of X(i) and X(j) for these {i,j}: {5, 80}, {355, 1484}, {3627, 12515}, {5690, 10738}, {6246, 12619}, {10265, 18480}, {12690, 51525}, {12737, 37705}, {12761, 33899}, {19914, 22791}, {61510, 61601}
X(61553) = reflection of X(i) in X(j) for these {i,j}: {119, 61259}, {140, 6702}, {143, 58501}, {1317, 61278}, {12611, 3850}, {15178, 33709}, {19907, 61272}, {214, 3628}, {5901, 60759}, {61286, 1387}, {61562, 9956}
X(61553) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {214, 38182, 3628}, {355, 37718, 1484}, {952, 1387, 61286}, {952, 60759, 5901}, {952, 61259, 119}, {952, 61272, 19907}, {952, 61278, 1317}, {1317, 38044, 61278}, {6246, 12619, 30}, {10738, 59415, 5690}, {12611, 38161, 3850}, {12737, 37705, 952}, {19907, 23513, 61272}, {19914, 59391, 22791}, {61510, 61601, 2802}

X(61554) = MIDPOINT OF X(5) AND X(81)

Barycentrics    2*a^7+2*a^6*(b+c)+a^5*(-5*b^2+2*b*c-5*c^2)-5*a^4*(b+c)*(b^2+c^2)+(b-c)^2*(b+c)^3*(b^2+c^2)+a*(b^2-c^2)^2*(b^2+5*b*c+c^2)+2*a^2*(b+c)*(b^4-4*b^2*c^2+c^4)+a^3*(2*b^4-7*b^3*c-8*b^2*c^2-7*b*c^3+2*c^4) : :
X(61554) = -5*X[1656]+X[2895], 7*X[3090]+X[20086], -3*X[15699]+X[31143], -5*X[31247]+7*X[55856]

X(61554) lies on these lines: {5, 81}, {30, 37527}, {140, 970}, {524, 547}, {758, 5901}, {1211, 3628}, {1656, 2895}, {2836, 10272}, {3090, 20086}, {15699, 31143}, {31247, 55856}, {35103, 61561}, {61526, 61562}

X(61554) = midpoint of X(i) and X(j) for these {i,j}: {5, 81}
X(61554) = reflection of X(i) in X(j) for these {i,j}: {140, 6703}, {1211, 3628}
X(61554) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5901, 61536, 10021}

X(61555) = MIDPOINT OF X(5) AND X(83)

Barycentrics    2*a^8-3*a^6*(b^2+c^2)+(b^2-c^2)^2*(b^4+5*b^2*c^2+c^4)-2*a^4*(2*b^4+9*b^2*c^2+2*c^4)+a^2*(4*b^6-13*b^4*c^2-13*b^2*c^4+4*c^6) : :
X(61555) = 3*X[2]+X[13111], 3*X[381]+X[12252], -3*X[549]+X[12122], -X[550]+3*X[9751], -5*X[1656]+X[2896], 7*X[3090]+X[20088], -5*X[3091]+X[48674], 3*X[5886]+X[9903], -X[7977]+3*X[10283], -X[11606]+3*X[38229], -X[12783]+3*X[38042], 3*X[14561]+X[24273] and many others

X(61555) lies on these lines: {2, 13111}, {5, 83}, {30, 6249}, {140, 6704}, {230, 12815}, {381, 12252}, {495, 10080}, {496, 10064}, {546, 3589}, {547, 754}, {549, 12122}, {550, 9751}, {590, 35869}, {615, 35868}, {732, 18583}, {952, 12264}, {1656, 2896}, {2782, 51827}, {3090, 20088}, {3091, 48674}, {3627, 8725}, {3628, 6292}, {3850, 22803}, {3851, 7875}, {5079, 7806}, {5886, 9903}, {7583, 49255}, {7584, 49254}, {7935, 10358}, {7977, 10283}, {8150, 10796}, {9918, 13861}, {9956, 17766}, {10592, 12944}, {10593, 12954}, {11272, 44237}, {11606, 38229}, {12144, 21841}, {12783, 38042}, {14561, 24273}, {15325, 18983}, {15699, 31168}, {15819, 54167}, {19091, 19117}, {19092, 19116}, {22728, 42787}, {31268, 55856}, {32521, 54155}

X(61555) = midpoint of X(i) and X(j) for these {i,j}: {5, 83}, {3627, 8725}, {6249, 49112}, {32521, 54155}
X(61555) = reflection of X(i) in X(j) for these {i,j}: {140, 6704}, {22803, 3850}, {6292, 3628}
X(61555) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6249, 49112, 30}

X(61556) = MIDPOINT OF X(5) AND X(84)

Barycentrics    2*a^7+(b-c)^4*(b+c)^3+a^5*(-7*b^2+12*b*c-7*c^2)+a^4*(b+c)*(b^2+c^2)-2*a^2*(b-c)^2*(b+c)*(b^2+b*c+c^2)-a*(b^2-c^2)^2*(3*b^2+2*b*c+3*c^2)+2*a^3*(b-c)^2*(4*b^2+3*b*c+4*c^2) : :
X(61556) = 3*X[2]+X[12684], 3*X[381]+X[12246], X[382]+3*X[54052], -3*X[549]+X[1490], -5*X[1656]+X[6223], -5*X[3091]+X[48664], -7*X[3526]+3*X[5658], -X[5690]+3*X[14647], 3*X[5886]+X[7992], -X[7971]+3*X[10283], X[10864]+3*X[26446], -3*X[11230]+X[54227] and many others

X(61556) lies on these lines: {2, 12684}, {3, 5273}, {4, 13226}, {5, 84}, {30, 6245}, {140, 971}, {355, 10270}, {381, 12246}, {382, 54052}, {495, 10085}, {496, 1709}, {515, 548}, {546, 61535}, {549, 1490}, {550, 5771}, {590, 35845}, {615, 35844}, {952, 3913}, {1012, 12433}, {1071, 5719}, {1158, 28174}, {1385, 9948}, {1656, 6223}, {2808, 5482}, {2829, 61530}, {3091, 48664}, {3337, 7965}, {3358, 5762}, {3526, 5658}, {3628, 6260}, {3850, 22792}, {5450, 7508}, {5690, 14647}, {5708, 37434}, {5745, 31805}, {5779, 6926}, {5789, 6916}, {5791, 9841}, {5817, 16863}, {5886, 7992}, {5901, 6001}, {5927, 52264}, {6147, 6847}, {6256, 61259}, {6675, 10167}, {6691, 31871}, {6713, 31828}, {6824, 31657}, {6918, 60901}, {6952, 41543}, {6972, 13257}, {7171, 37424}, {7330, 37364}, {7483, 11220}, {7583, 49235}, {7584, 49234}, {7958, 35010}, {7971, 10283}, {7995, 11373}, {8727, 24470}, {9910, 13861}, {9955, 61509}, {10200, 16112}, {10592, 12678}, {10593, 12679}, {10864, 26446}, {11227, 50205}, {11230, 54227}, {11246, 15911}, {11374, 30304}, {12100, 40262}, {12136, 21841}, {12608, 61269}, {12616, 18357}, {12667, 38042}, {12688, 15325}, {14646, 48661}, {15071, 37737}, {15712, 52026}, {16116, 38039}, {18525, 38754}, {19067, 19117}, {19068, 19116}, {24645, 41870}, {26877, 37447}, {28178, 48482}, {32137, 46174}, {37692, 41706}, {61521, 61559}

X(61556) = midpoint of X(i) and X(j) for these {i,j}: {5, 84}, {550, 5787}, {1385, 9948}, {6245, 34862}, {12114, 33899}
X(61556) = reflection of X(i) in X(j) for these {i,j}: {140, 6705}, {18357, 12616}, {22792, 3850}, {6256, 61259}, {6260, 3628}
X(61556) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 13226, 34753}, {548, 61539, 61524}, {971, 6705, 140}, {5787, 52027, 550}, {6245, 34862, 30}, {12114, 33899, 952}

X(61557) = MIDPOINT OF X(5) AND X(85)

Barycentrics    2*a^6*b*c-2*a^3*b*(b-c)^2*c*(b+c)-3*b*(b-c)^4*c*(b+c)^2-a*(b-c)^4*(b+c)^3+a^5*(b+c)*(b^2+c^2)+2*a^2*(b-c)^2*(b^4+6*b^3*c+5*b^2*c^2+6*b*c^3+c^4)-a^4*(2*b^4+7*b^3*c+7*b*c^3+2*c^4) : :
X(61557) = -5*X[1656]+X[3177], 7*X[3090]+X[20089], -3*X[15699]+X[31169], -5*X[31269]+7*X[55856], -2*X[44570]+3*X[47599]

X(61557) lies on these lines: {5, 85}, {140, 6706}, {518, 61509}, {547, 44664}, {1212, 3628}, {1656, 3177}, {3090, 20089}, {5901, 28850}, {15699, 31169}, {18357, 61602}, {31269, 55856}, {35102, 61535}, {44570, 47599}, {46180, 61550}, {61512, 61581}, {61519, 61558}

X(61557) = midpoint of X(i) and X(j) for these {i,j}: {5, 85}
X(61557) = reflection of X(i) in X(j) for these {i,j}: {140, 6706}, {1212, 3628}

X(61558) = MIDPOINT OF X(5) AND X(86)

Barycentrics    2*a^6+2*a^5*(b+c)+5*a*(b-c)^2*(b+c)^3+a^4*(-5*b^2+2*b*c-5*c^2)-7*a^3*(b+c)*(b^2+c^2)+(b^2-c^2)^2*(b^2+5*b*c+c^2)+a^2*(2*b^4-7*b^3*c-8*b^2*c^2-7*b*c^3+2*c^4) : :
X(61558) = -X[1654]+5*X[1656], 7*X[3090]+X[20090], 3*X[5886]+X[24342], -3*X[11230]+X[25354], -3*X[15699]+X[31144], -5*X[31248]+7*X[55856], -3*X[38042]+X[42334]

X(61558) lies on these lines: {5, 86}, {140, 6707}, {524, 547}, {740, 5901}, {952, 5625}, {1213, 3628}, {1654, 1656}, {2796, 61561}, {3090, 20090}, {4733, 5844}, {5886, 24342}, {10021, 17768}, {11230, 25354}, {15699, 31144}, {17770, 61536}, {31248, 55856}, {38042, 42334}, {61519, 61557}, {61522, 61621}

X(61558) = midpoint of X(i) and X(j) for these {i,j}: {5, 86}
X(61558) = reflection of X(i) in X(j) for these {i,j}: {140, 6707}, {1213, 3628}

X(61559) = MIDPOINT OF X(5) AND X(90)

Barycentrics    2*a^10-2*a^9*(b+c)+(b-c)^6*(b+c)^4+a^8*(-9*b^2+8*b*c-9*c^2)+2*a^2*b*c*(b^2-c^2)^2*(b^2-4*b*c+c^2)-4*a*(b-c)^4*(b+c)^3*(b^2+b*c+c^2)+2*a^7*(b+c)*(5*b^2-4*b*c+5*c^2)+2*a^6*(7*b^4-9*b^3*c+8*b^2*c^2-9*b*c^3+7*c^4)+2*a^3*(b-c)^2*(b+c)*(7*b^4+6*b^3*c+6*b^2*c^2+6*b*c^3+7*c^4)+2*a^5*(-9*b^5+b^4*c+b*c^4-9*c^5)+2*a^4*(-4*b^6+5*b^5*c+2*b^4*c^2-2*b^3*c^3+2*b^2*c^4+5*b*c^5-4*c^6) : :
X(61559) =

X(61559) lies on these lines: {5, 90}, {140, 58415}, {546, 61530}, {912, 5045}, {3628, 41540}, {5553, 13226}, {5840, 61524}, {7702, 34753}, {46028, 61535}, {58631, 61533}, {61511, 61520}, {61521, 61556}

X(61559) = midpoint of X(i) and X(j) for these {i,j}: {5, 90}
X(61559) = reflection of X(i) in X(j) for these {i,j}: {140, 58415}, {41540, 3628}

X(61560) = MIDPOINT OF X(5) AND X(98)

Barycentrics    2*a^8-3*a^6*(b^2+c^2)+(b^2-c^2)^2*(b^4-3*b^2*c^2+c^4)+a^4*(4*b^4-2*b^2*c^2+4*c^4)+a^2*(-4*b^6+3*b^4*c^2+3*b^2*c^4-4*c^6) : :
X(61560) = 3*X[3]+X[148], -X[4]+3*X[38229], X[20]+3*X[38732], -X[99]+3*X[549], X[110]+3*X[14849], -3*X[140]+2*X[620], -X[147]+5*X[1656], 3*X[376]+X[38733], 3*X[568]+X[39836], -5*X[631]+X[13188], -5*X[632]+3*X[15561], -X[1657]+9*X[38634] and many others

X(61560) lies on these lines: {2, 7711}, {3, 148}, {4, 38229}, {5, 83}, {13, 22893}, {14, 22847}, {20, 38732}, {30, 115}, {39, 42788}, {99, 549}, {110, 14849}, {114, 3628}, {140, 620}, {143, 58502}, {147, 1656}, {376, 38733}, {381, 7806}, {495, 10069}, {496, 10053}, {517, 58610}, {542, 547}, {543, 12100}, {546, 2794}, {548, 23698}, {550, 6321}, {568, 39836}, {590, 35825}, {615, 35824}, {623, 6771}, {624, 6774}, {631, 13188}, {632, 15561}, {671, 8703}, {690, 61548}, {952, 11710}, {1506, 12830}, {1657, 38634}, {1916, 32521}, {2023, 5305}, {2482, 11812}, {2783, 61562}, {2784, 9956}, {2785, 61564}, {2786, 61565}, {2787, 61566}, {2788, 61567}, {2789, 61568}, {2790, 44233}, {2791, 61570}, {2792, 61571}, {2793, 61572}, {2795, 11277}, {3023, 15325}, {3044, 40111}, {3090, 5984}, {3091, 38744}, {3524, 20094}, {3530, 33813}, {3534, 41135}, {3564, 5031}, {3579, 11599}, {3627, 14639}, {3767, 44531}, {3845, 9166}, {3850, 10991}, {3853, 38735}, {3861, 39838}, {4027, 32992}, {4187, 5985}, {5025, 32151}, {5054, 12243}, {5055, 7875}, {5066, 5461}, {5152, 44224}, {5663, 33511}, {5719, 59815}, {5886, 9860}, {5946, 39846}, {5986, 37439}, {5989, 32832}, {6034, 21850}, {6054, 15699}, {6101, 39817}, {6214, 6230}, {6215, 6231}, {6644, 39832}, {6680, 44237}, {6721, 48154}, {6770, 59384}, {6773, 59383}, {6777, 37835}, {6778, 37832}, {6795, 59251}, {7516, 39803}, {7525, 39828}, {7583, 49213}, {7584, 49212}, {7668, 24975}, {7746, 14880}, {7755, 14881}, {7761, 10104}, {7762, 36864}, {7824, 35464}, {7844, 9996}, {7970, 10283}, {8157, 34845}, {8587, 54715}, {8591, 15693}, {8596, 15698}, {8724, 11539}, {8782, 42787}, {9167, 11540}, {9756, 40250}, {9861, 13861}, {9864, 38042}, {10109, 14971}, {10124, 31274}, {10264, 18332}, {10304, 12355}, {10592, 12184}, {10593, 12185}, {10723, 15704}, {10753, 59399}, {11057, 60175}, {11230, 21636}, {11646, 48906}, {11676, 38230}, {11801, 15359}, {11818, 39842}, {12011, 60749}, {12041, 16278}, {12054, 52034}, {12101, 41151}, {12103, 38734}, {12106, 39857}, {12108, 38748}, {12117, 45759}, {12131, 21841}, {12176, 15980}, {12177, 38110}, {12812, 38745}, {13178, 34773}, {13363, 58503}, {13451, 58518}, {13881, 40279}, {14449, 39806}, {14510, 57310}, {14568, 35002}, {14692, 55859}, {14869, 23235}, {14981, 16239}, {15061, 22265}, {15300, 44580}, {15535, 32423}, {15690, 36523}, {15692, 35369}, {15701, 52695}, {15712, 21166}, {15713, 41134}, {18122, 49006}, {18538, 50720}, {18762, 50719}, {19055, 19117}, {19056, 19116}, {19905, 50979}, {20252, 41023}, {20253, 41022}, {20399, 38627}, {20415, 61515}, {20416, 61516}, {21843, 44532}, {22249, 47326}, {22507, 33415}, {22509, 33414}, {22791, 38220}, {23039, 39808}, {24472, 34753}, {32046, 57011}, {32515, 56370}, {33923, 38738}, {34200, 38736}, {35018, 36519}, {35255, 49266}, {35256, 49267}, {37459, 38642}, {37481, 39837}, {38022, 50881}, {38081, 50880}, {38083, 50879}, {38731, 46853}, {46053, 53430}, {46054, 53442}, {47200, 57588}, {49214, 52048}, {49215, 52047}, {52090, 55856}, {53797, 55313}, {54718, 60103}

X(61560) = midpoint of X(i) and X(j) for these {i,j}: {5, 98}, {13, 47611}, {14, 47610}, {114, 51523}, {115, 12042}, {548, 61600}, {549, 11632}, {550, 6321}, {671, 8703}, {1916, 32521}, {3579, 11599}, {3627, 38741}, {3845, 14830}, {6036, 11623}, {6055, 49102}, {6101, 39817}, {9302, 54964}, {10264, 18332}, {10723, 15704}, {10991, 22505}, {11646, 48906}, {12041, 16278}, {12188, 51872}, {13178, 34773}, {15535, 53725}, {18122, 49006}, {19905, 50979}, {20398, 35021}, {22515, 38749}, {38734, 38747}
X(61560) = reflection of X(i) in X(j) for these {i,j}: {114, 3628}, {140, 6036}, {143, 58502}, {11801, 15359}, {12103, 38747}, {14449, 39806}, {2482, 11812}, {22505, 3850}, {22566, 10109}, {33813, 3530}, {38738, 33923}, {39838, 3861}, {47326, 22249}, {546, 61576}, {5066, 5461}, {61561, 140}, {61575, 6722}, {61576, 20398}, {61599, 61575}
X(61560) = complement of X(51872)
X(61560) = pole of line {9479, 24978} with respect to the nine-point circle
X(61560) = pole of line {5466, 11606} with respect to the orthoptic circle of the Steiner inellipse
X(61560) = pole of line {542, 1691} with respect to the Kiepert hyperbola
X(61560) = pole of line {9301, 54439} with respect to the Stammler hyperbola
X(61560) = pole of line {1640, 14316} with respect to the Steiner inellipse
X(61560) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12188, 51872}, {98, 14061, 6033}, {99, 38739, 549}, {114, 34127, 3628}, {114, 38740, 34127}, {115, 12042, 30}, {115, 38749, 22515}, {115, 6055, 12042}, {140, 2782, 61561}, {542, 61575, 61599}, {542, 6722, 61575}, {2482, 26614, 11812}, {2782, 6036, 140}, {2794, 20398, 61576}, {2794, 61576, 546}, {3090, 5984, 38743}, {6033, 14061, 5}, {6033, 38224, 14061}, {6036, 11623, 2782}, {6321, 34473, 550}, {6722, 61575, 547}, {9166, 14830, 3845}, {10723, 38742, 15704}, {10991, 23514, 22505}, {11632, 38739, 99}, {12042, 22515, 38749}, {12042, 49102, 115}, {14639, 38741, 3627}, {14971, 22566, 10109}, {15535, 53725, 32423}, {20398, 35021, 2794}, {22505, 23514, 3850}, {33813, 38737, 3530}, {34127, 51523, 114}

X(61561) = MIDPOINT OF X(5) AND X(99)

Barycentrics    2*a^8+b^8-b^6*c^2-b^2*c^6+c^8-7*a^6*(b^2+c^2)+a^4*(8*b^4+6*b^2*c^2+8*c^4)-a^2*(4*b^6+b^4*c^2+b^2*c^4+4*c^6) : :
X(61561) = 3*X[2]+X[13188], 3*X[3]+X[147], X[20]+3*X[38743], -X[98]+3*X[549], X[110]+3*X[14850], -X[148]+5*X[1656], 3*X[262]+X[19910], 3*X[376]+X[38744], 3*X[381]+X[13172], -X[385]+3*X[38230], -X[546]+4*X[20399], 3*X[568]+X[39807] and many others

X(61561) lies on circumconic {{A, B, C, X(5966), X(41533)}} and on these lines: {2, 13188}, {3, 147}, {5, 99}, {20, 38743}, {30, 114}, {98, 549}, {110, 14850}, {115, 3628}, {140, 620}, {143, 58503}, {148, 1656}, {187, 12830}, {230, 1569}, {262, 19910}, {376, 38744}, {381, 13172}, {385, 38230}, {495, 10089}, {496, 10086}, {517, 51578}, {524, 32135}, {538, 14693}, {542, 12100}, {543, 547}, {546, 20399}, {548, 2794}, {550, 6033}, {568, 39807}, {590, 35879}, {615, 35878}, {618, 13350}, {619, 13349}, {631, 12188}, {632, 23235}, {671, 15699}, {690, 10272}, {952, 11711}, {1353, 5182}, {1657, 38635}, {2080, 7799}, {2548, 44532}, {2783, 61566}, {2784, 13624}, {2785, 61571}, {2786, 61563}, {2787, 61562}, {2792, 61564}, {2795, 10021}, {2796, 61558}, {2797, 61569}, {2798, 61570}, {2799, 61573}, {3027, 15325}, {3090, 20094}, {3091, 38733}, {3524, 5984}, {3526, 14651}, {3530, 12042}, {3564, 5026}, {3579, 21636}, {3627, 38730}, {3845, 10723}, {3850, 10992}, {3853, 38746}, {3861, 39809}, {4027, 35297}, {5013, 44536}, {5055, 8591}, {5066, 36521}, {5071, 12355}, {5149, 59545}, {5186, 21841}, {5351, 6778}, {5352, 6777}, {5461, 47599}, {5463, 22509}, {5464, 22507}, {5611, 30471}, {5615, 30472}, {5663, 33512}, {5719, 24472}, {5886, 13174}, {5946, 39817}, {5969, 18583}, {5976, 6390}, {5985, 37298}, {5988, 37599}, {6054, 8703}, {6055, 11812}, {6101, 39846}, {6337, 37466}, {6644, 39803}, {6722, 48154}, {7486, 35369}, {7516, 39832}, {7525, 39857}, {7583, 49267}, {7584, 49266}, {7806, 32519}, {7807, 32448}, {7820, 40108}, {7835, 11171}, {7863, 49111}, {7907, 13108}, {7983, 10283}, {8151, 13187}, {8369, 10352}, {8781, 54868}, {8782, 32447}, {9167, 10124}, {9479, 11620}, {9734, 9996}, {9772, 37450}, {9864, 34773}, {9880, 11737}, {10109, 15300}, {10353, 11842}, {10592, 13182}, {10593, 13183}, {10722, 15704}, {10754, 59399}, {11005, 34153}, {11007, 30789}, {11177, 15693}, {11230, 11599}, {11272, 44237}, {11539, 11632}, {11818, 39813}, {12040, 19911}, {12093, 16316}, {12103, 38736}, {12106, 39828}, {12108, 38737}, {12117, 15687}, {12177, 48876}, {12243, 15694}, {12812, 15092}, {13175, 13861}, {13178, 38042}, {13363, 58502}, {13451, 58517}, {14061, 55856}, {14449, 39835}, {14509, 57310}, {14645, 61624}, {14830, 17504}, {14869, 38664}, {14929, 54103}, {15048, 44534}, {15171, 15452}, {15535, 40685}, {15703, 41135}, {15712, 34473}, {15815, 43449}, {15850, 39601}, {16239, 31274}, {18331, 32609}, {19108, 19117}, {19109, 19116}, {20398, 38628}, {20576, 59546}, {21445, 36811}, {22247, 47598}, {22265, 38794}, {23039, 39837}, {23514, 35018}, {31128, 57607}, {32134, 39652}, {32423, 53735}, {33923, 38749}, {34200, 38747}, {34380, 50567}, {34383, 46172}, {34753, 59815}, {35103, 61554}, {35255, 49212}, {35256, 49213}, {35930, 46236}, {36776, 47611}, {37481, 39808}, {38022, 50886}, {38081, 50885}, {38083, 50884}, {38742, 46853}, {39091, 47618}, {39504, 39816}, {40111, 58058}, {44347, 59707}, {47288, 57307}, {53797, 55312}

X(61561) = midpoint of X(i) and X(j) for these {i,j}: {3, 51872}, {5, 99}, {114, 33813}, {115, 51524}, {548, 61599}, {549, 8724}, {550, 6033}, {3579, 21636}, {3627, 38730}, {6054, 8703}, {6101, 39846}, {6390, 37459}, {8151, 13187}, {9864, 34773}, {10722, 15704}, {10992, 22515}, {11005, 34153}, {12040, 19911}, {12042, 14981}, {12117, 15687}, {12177, 48876}, {20399, 35022}, {22505, 38738}, {36776, 47611}, {38736, 38745}
X(61561) = reflection of X(i) in X(j) for these {i,j}: {115, 3628}, {140, 620}, {143, 58503}, {12042, 3530}, {12103, 38736}, {14449, 39835}, {15535, 40685}, {22515, 3850}, {38734, 15092}, {38749, 33923}, {39809, 3861}, {49102, 10124}, {546, 61575}, {6055, 11812}, {61560, 140}, {61575, 20399}, {61576, 6721}, {61600, 61576}, {9880, 11737}
X(61561) = pole of line {5207, 5965} with respect to the Wallace hyperbola
X(61561) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {99, 15561, 5}, {114, 2482, 33813}, {114, 33813, 30}, {114, 38738, 22505}, {114, 39838, 22566}, {140, 2782, 61560}, {148, 1656, 38229}, {543, 61576, 61600}, {543, 6721, 61576}, {548, 61599, 2794}, {620, 2782, 140}, {3090, 20094, 38732}, {6033, 21166, 550}, {6390, 37459, 32515}, {6721, 61576, 547}, {8724, 38750, 98}, {8724, 41134, 549}, {10722, 38731, 15704}, {10992, 36519, 22515}, {11272, 44237, 61555}, {12042, 38748, 3530}, {14981, 38748, 12042}, {20399, 23698, 61575}, {20399, 35022, 23698}, {20576, 59546, 61625}, {22505, 33813, 38738}, {22515, 36519, 3850}, {23698, 61575, 546}, {38751, 51524, 3628}

X(61562) = MIDPOINT OF X(5) AND X(100)

Barycentrics    2*a^7-2*a^6*(b+c)+(b-c)^4*(b+c)^3+a^5*(-5*b^2+2*b*c-5*c^2)+5*a^4*(b+c)*(b^2+c^2)-a*(b^2-c^2)^2*(b^2-5*b*c+c^2)-2*a^2*(b-c)^2*(b+c)*(2*b^2+3*b*c+2*c^2)+a^3*(4*b^4-7*b^3*c-4*b^2*c^2-7*b*c^3+4*c^4) : :
X(61562) = -3*X[2]+X[1484], 3*X[3]+X[153], X[20]+3*X[38755], -X[104]+3*X[549], -X[149]+5*X[1656], 3*X[165]+X[16128], X[355]+3*X[15015], 3*X[376]+X[38756], 3*X[381]+X[13199], -5*X[631]+X[12773], 5*X[632]+X[38665], -X[1320]+3*X[10283] and many others

X(61562) lies on these lines: {2, 1484}, {3, 153}, {5, 100}, {10, 140}, {11, 3628}, {20, 38755}, {30, 119}, {80, 5432}, {104, 549}, {143, 58504}, {149, 1656}, {165, 16128}, {355, 15015}, {376, 38756}, {381, 13199}, {495, 10090}, {496, 10087}, {517, 58613}, {519, 61521}, {528, 547}, {542, 51199}, {546, 5840}, {548, 2829}, {550, 10742}, {590, 35883}, {615, 35882}, {631, 12773}, {632, 38665}, {900, 61621}, {912, 58641}, {1145, 4511}, {1317, 15325}, {1320, 10283}, {1387, 5919}, {1483, 13747}, {1537, 28212}, {1657, 38636}, {1737, 41541}, {1862, 21841}, {2771, 6684}, {2783, 61560}, {2787, 61561}, {2800, 61524}, {2801, 58674}, {2802, 5901}, {2803, 61569}, {2804, 61570}, {2805, 61522}, {2806, 61573}, {2810, 46174}, {2932, 6914}, {3090, 20095}, {3091, 48680}, {3254, 38171}, {3530, 37725}, {3564, 51157}, {3579, 21635}, {3654, 13253}, {3738, 61571}, {3820, 7508}, {3845, 10724}, {3850, 10993}, {3853, 38758}, {3856, 59390}, {3887, 61563}, {3925, 38114}, {4996, 17757}, {5083, 34753}, {5433, 7972}, {5445, 41689}, {5528, 38108}, {5531, 31423}, {5541, 5886}, {5552, 6924}, {5657, 48667}, {5660, 12515}, {5690, 6265}, {5719, 12736}, {5745, 58659}, {5762, 6594}, {5771, 9946}, {5790, 6224}, {5818, 12747}, {5843, 10427}, {5848, 61545}, {5851, 61596}, {5854, 61534}, {5856, 61509}, {6073, 38617}, {6154, 23513}, {6246, 61259}, {6326, 26446}, {6667, 20104}, {6675, 34122}, {6681, 33812}, {6690, 6702}, {6691, 61286}, {6797, 13411}, {6940, 35451}, {6959, 59591}, {7483, 59415}, {7525, 54065}, {7583, 48715}, {7584, 48714}, {8674, 10272}, {8703, 10711}, {9024, 18583}, {9956, 10021}, {10225, 51569}, {10592, 13273}, {10593, 13274}, {10707, 15699}, {10728, 15704}, {10755, 59399}, {10769, 38229}, {11230, 21630}, {11540, 38069}, {11729, 23340}, {12019, 12743}, {12103, 38757}, {12108, 21154}, {12499, 42787}, {12531, 59400}, {12611, 28174}, {12645, 17566}, {12653, 61276}, {12699, 15017}, {12737, 38028}, {12751, 34773}, {12811, 38141}, {13222, 13861}, {13257, 26878}, {13363, 58508}, {13405, 58587}, {13451, 58522}, {14217, 38034}, {14513, 57313}, {14869, 38669}, {15171, 39692}, {15712, 38693}, {16174, 61269}, {16239, 31235}, {17564, 32213}, {19112, 19117}, {19113, 19116}, {19914, 38112}, {20119, 38170}, {20575, 61527}, {22560, 45701}, {22937, 46684}, {25337, 61626}, {25485, 50841}, {26364, 32141}, {28194, 50845}, {28204, 50844}, {31073, 57605}, {31272, 55856}, {32423, 53743}, {33923, 38761}, {34123, 51700}, {34200, 38759}, {34380, 51007}, {35255, 48700}, {35256, 48701}, {37459, 38643}, {38022, 50891}, {38081, 50890}, {38083, 50889}, {38629, 55862}, {38754, 46853}, {40111, 58056}, {44254, 50038}, {45310, 47599}, {53800, 55317}, {58405, 58591}, {58604, 61535}, {59719, 61541}, {61526, 61554}

X(61562) = midpoint of X(i) and X(j) for these {i,j}: {3, 11698}, {5, 100}, {10, 22935}, {11, 51525}, {119, 33814}, {548, 61605}, {550, 10742}, {1145, 19907}, {1484, 12331}, {3579, 21635}, {5690, 6265}, {6073, 38617}, {8703, 10711}, {10728, 15704}, {10993, 22938}, {12751, 34773}, {20400, 35023}, {22799, 24466}, {37725, 38602}
X(61562) = reflection of X(i) in X(j) for these {i,j}: {11, 3628}, {140, 3035}, {143, 58504}, {22938, 3850}, {38602, 3530}, {38761, 33923}, {546, 61580}, {6246, 61259}, {60759, 58421}, {61553, 9956}, {61566, 140}, {61580, 20400}, {61601, 60759}
X(61562) = complement of X(1484)
X(61562) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12331, 1484}, {10, 22935, 952}, {100, 38752, 5}, {104, 38762, 549}, {119, 24466, 22799}, {119, 33814, 30}, {119, 6174, 33814}, {140, 952, 61566}, {528, 58421, 60759}, {528, 60759, 61601}, {548, 61605, 2829}, {952, 3035, 140}, {1145, 19907, 5844}, {3090, 20095, 51517}, {5840, 20400, 61580}, {5840, 61580, 546}, {9956, 61520, 10021}, {10742, 34474, 550}, {20400, 35023, 5840}, {22799, 33814, 24466}, {31235, 34126, 16239}, {31235, 37726, 34126}, {37725, 38760, 38602}, {38602, 38760, 3530}, {38722, 51506, 7508}, {38763, 51525, 3628}, {58421, 60759, 547}, {61526, 61616, 61554}, {61614, 61628, 61539}

X(61563) = MIDPOINT OF X(5) AND X(101)

Barycentrics    2*a^8-2*a^7*(b+c)-a*(b-c)^4*(b+c)^3+a^6*(-5*b^2+2*b*c-5*c^2)+5*a^5*(b+c)*(b^2+c^2)+(b-c)^4*(b+c)^2*(b^2+b*c+c^2)-2*a^3*(b-c)^2*(b+c)*(b^2+3*b*c+c^2)+a^4*(b^2-3*b*c+c^2)*(3*b^2+4*b*c+3*c^2)-a^2*(b-c)^2*(b^4-2*b^3*c-4*b^2*c^2-2*b*c^3+c^4) : :
X(61563) = 3*X[2]+X[38572], 3*X[3]+X[152], X[20]+3*X[38767], -X[103]+3*X[549], -X[150]+5*X[1656], 3*X[376]+X[38768], -X[546]+4*X[20401], -5*X[631]+X[38574], 5*X[632]+X[38666], X[1282]+3*X[5886], 7*X[3090]+X[20096], -3*X[3845]+X[10725] and many others

X(61563) lies on these lines: {2, 38572}, {3, 152}, {5, 101}, {20, 38767}, {30, 118}, {103, 549}, {116, 3628}, {140, 2808}, {143, 58505}, {150, 1656}, {376, 38768}, {517, 28346}, {544, 547}, {546, 20401}, {548, 61604}, {550, 10741}, {631, 38574}, {632, 38666}, {928, 61571}, {952, 11712}, {1282, 5886}, {1362, 15325}, {2772, 61546}, {2774, 10272}, {2784, 9956}, {2786, 61561}, {2801, 61511}, {2807, 61564}, {2809, 5901}, {2810, 18583}, {2811, 61569}, {2812, 61570}, {2813, 61526}, {3090, 20096}, {3530, 38601}, {3845, 10725}, {3850, 33520}, {3853, 38770}, {3887, 61562}, {5185, 21841}, {5719, 11028}, {5762, 28345}, {8703, 10710}, {9518, 61573}, {10283, 10695}, {10708, 15699}, {10727, 15704}, {10756, 59399}, {12103, 38769}, {12108, 51528}, {13363, 58507}, {13451, 58521}, {14869, 38668}, {15712, 38692}, {15735, 38112}, {18413, 37737}, {31273, 55856}, {32423, 53747}, {33923, 38773}, {34200, 38771}, {34753, 59813}, {34773, 50903}, {37459, 38644}, {38022, 50898}, {38042, 50896}, {38081, 50897}, {38083, 50895}, {38630, 55862}, {38766, 46853}, {40111, 58057}, {48154, 58418}, {57315, 60065}

X(61563) = midpoint of X(i) and X(j) for these {i,j}: {5, 101}, {116, 51526}, {118, 38599}, {548, 61604}, {550, 10741}, {8703, 10710}, {10727, 15704}, {15735, 38112}, {20401, 35024}, {34773, 50903}
X(61563) = reflection of X(i) in X(j) for these {i,j}: {116, 3628}, {140, 6710}, {143, 58505}, {38601, 3530}, {38773, 33923}, {546, 61579}, {61565, 140}, {61577, 58420}, {61579, 20401}, {61602, 61577}
X(61563) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {101, 38764, 5}, {103, 38774, 549}, {118, 38599, 30}, {140, 2808, 61565}, {544, 58420, 61577}, {544, 61577, 61602}, {2808, 6710, 140}, {10741, 38690, 550}, {38601, 38772, 3530}, {38775, 51526, 3628}, {58420, 61577, 547}

X(61564) = MIDPOINT OF X(5) AND X(102)

Barycentrics    2*a^10-3*a^8*(b-c)^2-2*a^9*(b+c)-a*(b-c)^6*(b+c)^3+5*a^3*(b-c)^4*(b+c)*(b^2+c^2)+(b^2-c^2)^4*(b^2-b*c+c^2)-a^2*(b-c)^2*(b+c)^2*(2*b^2+b*c+2*c^2)*(3*b^2-4*b*c+3*c^2)+a^7*(b+c)*(7*b^2-12*b*c+7*c^2)-a^5*(b-c)^2*(b+c)*(9*b^2-10*b*c+9*c^2)-a^6*(4*b^4+9*b^3*c-24*b^2*c^2+9*b*c^3+4*c^4)+a^4*(b-c)^2*(10*b^4+19*b^3*c+6*b^2*c^2+19*b*c^3+10*c^4) : :
X(61564) = 3*X[2]+X[38573], 3*X[3]+X[33650], X[20]+3*X[38779], -X[109]+3*X[549], -X[151]+5*X[1656], 3*X[376]+X[38780], -3*X[547]+4*X[58426], -5*X[631]+X[38579], 5*X[632]+X[38667], -3*X[3845]+X[10726], -X[3853]+6*X[38782], -3*X[10283]+X[10696] and many others

X(61564) lies on these lines: {2, 38573}, {3, 33650}, {5, 102}, {20, 38779}, {30, 124}, {109, 549}, {117, 3628}, {140, 2818}, {143, 58506}, {151, 1656}, {376, 38780}, {546, 61585}, {547, 58426}, {550, 10747}, {631, 38579}, {632, 38667}, {928, 61565}, {952, 11713}, {1364, 15325}, {1845, 37737}, {2773, 61548}, {2779, 10272}, {2785, 61560}, {2792, 61561}, {2800, 61524}, {2807, 61563}, {2814, 61567}, {2815, 61568}, {2816, 9955}, {2817, 5901}, {2819, 61572}, {3040, 47742}, {3530, 38607}, {3738, 61566}, {3845, 10726}, {3853, 38782}, {5432, 52129}, {5719, 59816}, {8703, 10716}, {9532, 61573}, {10283, 10696}, {10709, 15699}, {10732, 15704}, {10757, 59399}, {12016, 34753}, {12103, 38781}, {12108, 51534}, {13363, 58513}, {13451, 58526}, {13532, 34773}, {14869, 38674}, {15712, 38697}, {32423, 53749}, {33923, 38785}, {34200, 38783}, {38022, 50901}, {38042, 50899}, {38081, 50900}, {38778, 46853}, {40111, 58051}, {48154, 58419}

X(61564) = midpoint of X(i) and X(j) for these {i,j}: {5, 102}, {117, 51527}, {124, 38600}, {550, 10747}, {8703, 10716}, {10732, 15704}, {13532, 34773}
X(61564) = reflection of X(i) in X(j) for these {i,j}: {117, 3628}, {140, 6711}, {143, 58506}, {38607, 3530}, {38785, 33923}, {546, 61585}, {61571, 140}, {61578, 58426}, {61603, 61578}
X(61564) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {102, 38776, 5}, {109, 38786, 549}, {124, 38600, 30}, {140, 2818, 61571}, {547, 61603, 61578}, {10747, 38691, 550}, {38607, 38784, 3530}, {38787, 51527, 3628}, {58426, 61578, 547}

X(61565) = MIDPOINT OF X(5) AND X(103)

Barycentrics    2*a^8-a^6*(b-c)^2-2*a^7*(b+c)-a*(b-c)^4*(b+c)^3+(b-c)^4*(b+c)^2*(b^2+b*c+c^2)-a^5*(b+c)*(3*b^2-8*b*c+3*c^2)+2*a^3*(b-c)^2*(b+c)*(3*b^2+b*c+3*c^2)+a^4*(3*b^4-5*b^3*c+2*b^2*c^2-5*b*c^3+3*c^4)-a^2*(b-c)^2*(5*b^4+6*b^3*c+12*b^2*c^2+6*b*c^3+5*c^4) : :
X(61565) = 3*X[2]+X[38574], 3*X[3]+X[150], -X[101]+3*X[549], -X[152]+5*X[1656], -3*X[547]+4*X[58418], -5*X[631]+X[38572], 5*X[632]+X[38668], -7*X[3090]+3*X[38767], -5*X[3091]+X[38768], -9*X[3524]+X[20096], -3*X[3845]+X[10727], 2*X[3850]+X[33521]

X(61565) lies on these lines: {2, 38574}, {3, 150}, {5, 103}, {30, 116}, {101, 549}, {118, 3628}, {140, 2808}, {143, 58507}, {152, 1656}, {517, 58612}, {544, 12100}, {546, 61577}, {547, 58418}, {548, 61602}, {550, 10739}, {631, 38572}, {632, 38668}, {928, 61564}, {952, 11714}, {2772, 10272}, {2774, 61548}, {2784, 13624}, {2786, 61560}, {2801, 58674}, {2807, 61533}, {2809, 61524}, {2820, 61567}, {2821, 61568}, {2822, 61569}, {2823, 61518}, {2824, 61572}, {2825, 61536}, {3022, 15325}, {3041, 47742}, {3046, 40111}, {3090, 38767}, {3091, 38768}, {3524, 20096}, {3530, 38599}, {3627, 38765}, {3845, 10727}, {3850, 33521}, {3887, 61566}, {5719, 59813}, {5886, 39156}, {8703, 10708}, {10283, 10697}, {10710, 15699}, {10725, 15704}, {10758, 59399}, {11028, 34753}, {12103, 38771}, {12108, 38772}, {12812, 38769}, {13363, 58505}, {13451, 58519}, {14512, 57315}, {14869, 38666}, {15712, 38690}, {20401, 55862}, {32423, 53751}, {34773, 50896}, {37459, 38645}, {38022, 50905}, {38042, 50903}, {38081, 50904}, {38083, 50902}, {48154, 58420}

X(61565) = midpoint of X(i) and X(j) for these {i,j}: {5, 103}, {116, 38601}, {118, 51528}, {548, 61602}, {550, 10739}, {3627, 38765}, {8703, 10708}, {10725, 15704}, {34773, 50896}
X(61565) = reflection of X(i) in X(j) for these {i,j}: {118, 3628}, {140, 6712}, {143, 58507}, {12103, 38771}, {38599, 3530}, {546, 61577}, {61563, 140}, {61579, 58418}, {61604, 61579}
X(61565) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {103, 31273, 10741}, {103, 57297, 5}, {116, 38601, 30}, {140, 2808, 61563}, {547, 61604, 61579}, {2808, 6712, 140}, {10725, 38766, 15704}, {10739, 38692, 550}, {10741, 57297, 31273}, {58418, 61579, 547}

X(61566) = MIDPOINT OF X(5) AND X(104)

Barycentrics    2*a^7-5*a^5*(b-c)^2-2*a^6*(b+c)+(b-c)^4*(b+c)^3-a*(b^2-c^2)^2*(b^2-b*c+c^2)-2*a^2*(b-c)^2*(b+c)*(2*b^2-b*c+2*c^2)+a^4*(b+c)*(5*b^2-8*b*c+5*c^2)+a^3*(4*b^4-11*b^3*c+12*b^2*c^2-11*b*c^3+4*c^4) : :
X(61566) = -3*X[2]+X[11698], 3*X[3]+X[149], X[20]+3*X[51517], -X[100]+3*X[549], -X[153]+5*X[1656], 3*X[376]+X[48680], 3*X[381]+X[12248], -5*X[631]+X[12331], 5*X[632]+X[38669], -X[1537]+3*X[38044], -X[1657]+9*X[38637], X[1768]+3*X[5886] and many others

X(61566) lies on these lines: {2, 11698}, {3, 149}, {5, 104}, {10, 140}, {11, 30}, {20, 51517}, {21, 35451}, {65, 1387}, {80, 5433}, {100, 549}, {119, 3628}, {143, 58508}, {153, 1656}, {376, 48680}, {381, 12248}, {495, 10074}, {496, 10058}, {515, 61521}, {517, 58611}, {528, 12100}, {546, 2829}, {547, 3822}, {548, 5840}, {550, 10738}, {590, 35857}, {615, 35856}, {631, 12331}, {632, 38669}, {1125, 2771}, {1317, 24926}, {1483, 19914}, {1537, 38044}, {1657, 38637}, {1768, 5886}, {2783, 61561}, {2787, 61560}, {2800, 5885}, {2801, 61511}, {2802, 61524}, {2818, 46174}, {2826, 61567}, {2827, 61568}, {2828, 61569}, {2830, 61572}, {2831, 61573}, {2932, 10527}, {3045, 40111}, {3090, 38755}, {3091, 38756}, {3336, 12515}, {3524, 20095}, {3530, 6154}, {3579, 21630}, {3616, 48667}, {3627, 38753}, {3649, 38063}, {3654, 12653}, {3655, 9897}, {3738, 61564}, {3845, 10728}, {3850, 22799}, {3861, 38141}, {3887, 61565}, {3911, 6797}, {4996, 5428}, {5066, 45310}, {5083, 5719}, {5432, 7972}, {5443, 33668}, {5444, 41689}, {5533, 14792}, {5690, 12737}, {5731, 12747}, {5844, 25416}, {6075, 38617}, {6174, 11812}, {6246, 28186}, {6264, 26446}, {6265, 11219}, {6675, 34123}, {6681, 28204}, {6691, 6702}, {6700, 58659}, {6924, 10785}, {7583, 48701}, {7584, 48700}, {7993, 31423}, {8068, 18990}, {8227, 16128}, {8674, 61548}, {8703, 10707}, {9624, 12767}, {9913, 13861}, {9955, 33709}, {10109, 59376}, {10124, 31235}, {10202, 11729}, {10246, 12247}, {10283, 10698}, {10592, 12763}, {10593, 12764}, {10711, 15699}, {10724, 15704}, {10759, 59399}, {10767, 14677}, {10778, 34153}, {10943, 38722}, {11230, 21635}, {11263, 12611}, {11277, 13624}, {11567, 61597}, {11570, 37737}, {11571, 15950}, {11737, 38084}, {11813, 33856}, {12019, 37605}, {12102, 59390}, {12103, 38759}, {12106, 54065}, {12108, 38760}, {12138, 21841}, {12531, 61295}, {12736, 34753}, {12738, 24953}, {12751, 38042}, {12812, 38319}, {13151, 33598}, {13205, 45700}, {13235, 42787}, {13253, 61276}, {13363, 58504}, {13451, 58475}, {13747, 37705}, {14511, 57313}, {14869, 38665}, {15178, 61520}, {15712, 34474}, {16174, 40273}, {16239, 37725}, {17100, 24390}, {17566, 18526}, {18480, 59419}, {18481, 37718}, {18493, 32558}, {18543, 19537}, {19081, 19117}, {19082, 19116}, {19907, 38032}, {20118, 37730}, {20400, 38631}, {22837, 32198}, {24466, 33923}, {25485, 61278}, {26492, 32153}, {28174, 41347}, {32423, 53753}, {32454, 32521}, {32636, 33593}, {33657, 61286}, {33812, 58404}, {33858, 45764}, {34122, 52264}, {34789, 38034}, {35255, 48714}, {35256, 48715}, {37459, 38646}, {37582, 41166}, {38022, 50908}, {38081, 50907}, {38083, 50906}, {38119, 51732}, {38182, 61259}, {48154, 58421}, {53800, 55314}

X(61566) = midpoint of X(i) and X(j) for these {i,j}: {3, 1484}, {5, 104}, {11, 38602}, {80, 34773}, {119, 51529}, {548, 61601}, {550, 10738}, {1385, 10265}, {1483, 19914}, {3579, 21630}, {3627, 38753}, {5690, 12737}, {6075, 38617}, {6713, 20418}, {8703, 10707}, {10724, 15704}, {10767, 14677}, {10778, 34153}, {10943, 38722}, {11219, 38028}, {11698, 12773}, {11715, 12619}, {11729, 13226}, {12515, 22791}, {12531, 61295}, {22837, 32198}, {22938, 38761}, {32454, 32521}, {33814, 37726}
X(61566) = reflection of X(i) in X(j) for these {i,j}: {119, 3628}, {140, 6713}, {143, 58508}, {12103, 38759}, {12611, 61272}, {18357, 6702}, {19907, 51700}, {22799, 3850}, {24466, 33923}, {25485, 61278}, {33814, 3530}, {40273, 16174}, {546, 60759}, {5066, 45310}, {52836, 3861}, {6174, 11812}, {61562, 140}, {61580, 6667}, {61605, 61580}, {9955, 33709}
X(61566) = complement of X(11698)
X(61566) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12773, 11698}, {11, 38602, 30}, {11, 38761, 22938}, {104, 31272, 10742}, {104, 57298, 5}, {119, 34126, 3628}, {140, 952, 61562}, {547, 61605, 61580}, {548, 61601, 5840}, {952, 6713, 140}, {2829, 60759, 546}, {3582, 46816, 11}, {6667, 61580, 547}, {10724, 38754, 15704}, {10738, 38693, 550}, {10742, 57298, 31272}, {11715, 12619, 952}, {12515, 16173, 22791}, {12611, 32557, 61272}, {19907, 38032, 51700}, {21154, 33814, 3530}, {22799, 23513, 3850}, {22938, 38602, 38761}, {34126, 51529, 119}, {38141, 52836, 3861}, {38753, 59391, 3627}

X(61567) = MIDPOINT OF X(5) AND X(105)

Barycentrics    2*a^8-4*a^7*(b+c)+(b-c)^4*(b+c)^2*(b^2+c^2)+a^6*(b^2+6*b*c+c^2)+2*a^5*(b^3+c^3)+a^4*(-3*b^4+3*b^3*c-10*b^2*c^2+3*b*c^3-3*c^4)-a^2*(b-c)^2*(b^4-7*b^3*c-4*b^2*c^2-7*b*c^3+c^4)-a*(b-c)^2*(b+c)*(2*b^4+3*b^3*c-6*b^2*c^2+3*b*c^3+2*c^4)+a^3*(b+c)*(4*b^4-15*b^3*c+24*b^2*c^2-15*b*c^3+4*c^4) : :
X(61567) = 3*X[2]+X[38575], 3*X[3]+X[34547], -3*X[549]+X[1292], -5*X[631]+X[38589], 5*X[632]+X[38670], -5*X[1656]+X[20344], 7*X[3090]+X[20097], -3*X[3845]+X[10729], X[5540]+3*X[5886], -3*X[10283]+X[10699], -X[10712]+3*X[15699], -X[10760]+3*X[59399] and many others

X(61567) lies on these lines: {2, 38575}, {3, 34547}, {5, 105}, {30, 5511}, {120, 3628}, {140, 6714}, {143, 58509}, {528, 547}, {549, 1292}, {550, 15521}, {631, 38589}, {632, 38670}, {952, 11716}, {1358, 15325}, {1656, 20344}, {2775, 61548}, {2788, 61560}, {2795, 10021}, {2809, 5901}, {2814, 61564}, {2820, 61565}, {2826, 61566}, {2832, 61568}, {2833, 61569}, {2834, 44233}, {2835, 20575}, {2836, 10272}, {2837, 61572}, {2838, 61573}, {3090, 20097}, {3530, 38619}, {3845, 10729}, {5540, 5886}, {5719, 59814}, {9519, 61614}, {10283, 10699}, {10712, 15699}, {10760, 59399}, {14869, 38684}, {15704, 44983}, {15712, 38712}, {32423, 53756}, {34124, 52264}, {37459, 38647}, {38022, 50913}, {38042, 50911}, {38081, 50912}, {40111, 58055}, {48154, 58422}

X(61567) = midpoint of X(i) and X(j) for these {i,j}: {5, 105}, {120, 51530}, {550, 15521}, {5511, 38603}, {15704, 44983}
X(61567) = reflection of X(i) in X(j) for these {i,j}: {120, 3628}, {140, 6714}, {143, 58509}, {38619, 3530}
X(61567) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {105, 57299, 5}, {5511, 38603, 30}, {6714, 28915, 140}, {15521, 38694, 550}

X(61568) = MIDPOINT OF X(5) AND X(106)

Barycentrics    2*a^7-4*a^6*(b+c)+a^5*(-5*b^2+18*b*c-5*c^2)+(b-c)^2*(b+c)^3*(b^2-3*b*c+c^2)-a*(b^2-c^2)^2*(2*b^2-9*b*c+2*c^2)+2*a^4*(b+c)*(5*b^2-9*b*c+5*c^2)+a^3*(5*b^4-27*b^3*c+34*b^2*c^2-27*b*c^3+5*c^4)-a^2*(b+c)*(7*b^4-21*b^3*c+26*b^2*c^2-21*b*c^3+7*c^4) : :
X(61568) = 3*X[2]+X[38576], 3*X[3]+X[34548], -3*X[547]+2*X[61582], -3*X[549]+X[1293], -5*X[631]+X[38590], 5*X[632]+X[38671], X[1054]+3*X[5886], -5*X[1656]+X[21290], 7*X[3090]+X[20098], -3*X[3845]+X[10730], -3*X[10283]+X[10700], -X[10713]+3*X[15699] and many others

X(61568) lies on these lines: {2, 38576}, {3, 34548}, {5, 106}, {30, 5510}, {121, 3628}, {140, 6715}, {143, 58510}, {547, 61582}, {549, 1293}, {550, 15522}, {631, 38590}, {632, 38671}, {952, 11717}, {1054, 5886}, {1357, 15325}, {1656, 21290}, {2776, 61548}, {2789, 61560}, {2796, 61558}, {2802, 5901}, {2810, 18583}, {2815, 61564}, {2821, 61565}, {2827, 61566}, {2832, 61567}, {2839, 61569}, {2840, 61519}, {2841, 61534}, {2842, 10272}, {2843, 61572}, {2844, 61573}, {3090, 20098}, {3530, 38620}, {3845, 10730}, {5719, 59812}, {10283, 10700}, {10713, 15699}, {10761, 59399}, {11230, 11814}, {13541, 61276}, {14664, 28174}, {14869, 38685}, {15704, 44984}, {15712, 38713}, {36939, 61272}, {37459, 38648}, {38022, 50915}, {38042, 50914}, {40111, 58054}, {48154, 58423}

X(61568) = midpoint of X(i) and X(j) for these {i,j}: {5, 106}, {121, 51531}, {550, 15522}, {5510, 38604}, {15704, 44984}
X(61568) = reflection of X(i) in X(j) for these {i,j}: {121, 3628}, {140, 6715}, {143, 58510}, {38620, 3530}
X(61568) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {106, 57300, 5}, {5510, 38604, 30}, {6715, 53790, 140}, {15522, 38695, 550}

X(61569) = MIDPOINT OF X(5) AND X(107)

Barycentrics    (2*a^4-(b^2-c^2)^2-a^2*(b^2+c^2))*(a^12-3*a^10*(b^2+c^2)+6*a^6*(b^2-c^2)^2*(b^2+c^2)+a^8*(b^4+3*b^2*c^2+c^4)-(b^2-c^2)^4*(b^4+5*b^2*c^2+c^4)-a^4*(b^2-c^2)^2*(9*b^4+4*b^2*c^2+9*c^4)+a^2*(b^2-c^2)^2*(5*b^6+3*b^4*c^2+3*b^2*c^4+5*c^6)) : :
X(61569) = 3*X[2]+X[38577], 3*X[3]+X[34549], X[113]+3*X[14847], 3*X[381]+X[5667], -3*X[549]+X[1294], -5*X[631]+X[38591], 5*X[632]+X[38672], -5*X[1656]+X[34186], -3*X[3845]+X[10152], -3*X[10283]+X[10701], -X[10714]+3*X[15699], -X[10762]+3*X[59399]

X(61569) lies on circumconic {{A, B, C, X(11589), X(18401)}} and on these lines: {2, 38577}, {3, 34549}, {5, 107}, {30, 133}, {113, 14847}, {122, 3628}, {140, 6716}, {143, 58511}, {381, 5667}, {402, 34334}, {546, 2777}, {547, 9530}, {549, 1294}, {550, 22337}, {631, 38591}, {632, 38672}, {952, 11718}, {1656, 34186}, {2790, 44233}, {2797, 61561}, {2803, 61562}, {2811, 61563}, {2816, 9955}, {2822, 61565}, {2828, 61566}, {2833, 61567}, {2839, 61568}, {2845, 61570}, {2846, 61571}, {2847, 61572}, {2848, 61573}, {3324, 15325}, {3530, 38621}, {3627, 23240}, {3845, 10152}, {3850, 49117}, {5663, 24930}, {5719, 59824}, {9033, 10272}, {9528, 10021}, {10283, 10701}, {10714, 15699}, {10762, 59399}, {12106, 14703}, {13451, 58530}, {13861, 14673}, {14869, 38686}, {15704, 44985}, {15712, 38714}, {32423, 53757}, {34297, 34582}, {35018, 36520}, {37459, 38649}, {38042, 50916}, {40111, 58067}, {48154, 58424}

X(61569) = midpoint of X(i) and X(j) for these {i,j}: {5, 107}, {122, 51532}, {133, 38605}, {550, 22337}, {3627, 23240}, {15704, 44985}, {49117, 52057}
X(61569) = reflection of X(i) in X(j) for these {i,j}: {122, 3628}, {140, 6716}, {143, 58511}, {38621, 3530}, {49117, 3850}, {546, 61592}, {61583, 58431}
X(61569) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {107, 57301, 5}, {133, 38605, 30}, {2777, 61592, 546}, {9530, 58431, 61583}, {22337, 23239, 550}, {58431, 61583, 547}

X(61570) = MIDPOINT OF X(5) AND X(108)

Barycentrics    2*a^13-2*a^12*(b+c)+a^11*(-7*b^2+6*b*c-7*c^2)+(b-c)^6*(b+c)^5*(b^2+c^2)-a*(b-c)^4*(b+c)^4*(b^2-6*b*c+c^2)*(b^2-b*c+c^2)+a^9*(b^2+c^2)*(7*b^2-19*b*c+7*c^2)+a^10*(b+c)*(7*b^2-4*b*c+7*c^2)-a^8*(b-c)^2*(b+c)*(7*b^2+2*b*c+7*c^2)-2*a^6*(b-c)^2*(b+c)*(b^4+7*b^3*c+6*b^2*c^2+7*b*c^3+c^4)+2*a^7*(b-c)^2*(b^4+9*b^3*c+7*b^2*c^2+9*b*c^3+c^4)-a^2*(b-c)^4*(b+c)^3*(5*b^4+4*b^3*c-6*b^2*c^2+4*b*c^3+5*c^4)-2*a^5*(b-c)^2*(4*b^6+2*b^5*c-11*b^4*c^2-14*b^3*c^3-11*b^2*c^4+2*b*c^5+4*c^6)+2*a^4*(b-c)^2*(b+c)*(4*b^6+7*b^5*c-4*b^4*c^2-6*b^3*c^3-4*b^2*c^4+7*b*c^5+4*c^6)+a^3*(b^2-c^2)^2*(5*b^6-20*b^5*c+5*b^4*c^2+12*b^3*c^3+5*b^2*c^4-20*b*c^5+5*c^6) : :
X(61570) = 3*X[2]+X[38578], 3*X[3]+X[34550], -3*X[547]+2*X[61584], -3*X[549]+X[1295], -5*X[631]+X[38592], 5*X[632]+X[38673], -5*X[1656]+X[34188], -3*X[3845]+X[10731], -3*X[10283]+X[10702], -X[10715]+3*X[15699], -X[10763]+3*X[59399], -7*X[14869]+X[38687] and many others

X(61570) lies on these lines: {2, 38578}, {3, 34550}, {5, 108}, {30, 25640}, {123, 3628}, {140, 6717}, {143, 58512}, {546, 2829}, {547, 61584}, {549, 1295}, {550, 33566}, {631, 38592}, {632, 38673}, {952, 11719}, {1359, 15325}, {1656, 34188}, {2778, 61541}, {2791, 61560}, {2798, 61561}, {2804, 61562}, {2812, 61563}, {2817, 5901}, {2823, 61518}, {2834, 44233}, {2840, 61519}, {2845, 61569}, {2849, 61571}, {2850, 10272}, {2851, 61572}, {3530, 38622}, {3845, 10731}, {5719, 59820}, {9528, 11277}, {10283, 10702}, {10715, 15699}, {10763, 59399}, {12106, 54064}, {14869, 38687}, {15704, 44986}, {15712, 38715}, {23711, 60758}, {38042, 50917}, {40111, 58063}, {48154, 58425}

X(61570) = midpoint of X(i) and X(j) for these {i,j}: {5, 108}, {123, 51533}, {550, 33566}, {15704, 44986}, {25640, 38606}
X(61570) = reflection of X(i) in X(j) for these {i,j}: {123, 3628}, {140, 6717}, {143, 58512}, {38622, 3530}
X(61570) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {108, 57302, 5}, {25640, 38606, 30}, {33566, 38696, 550}

X(61571) = MIDPOINT OF X(5) AND X(109)

Barycentrics    2*a^10-2*a^9*(b+c)-a*(b-c)^6*(b+c)^3+a^8*(-7*b^2+6*b*c-7*c^2)+(b^2-c^2)^4*(b^2-b*c+c^2)-3*a^5*(b-c)^2*(b+c)*(3*b^2+2*b*c+3*c^2)+a^3*(b-c)^4*(b+c)*(5*b^2+8*b*c+5*c^2)+a^7*(b+c)*(7*b^2-4*b*c+7*c^2)-a^4*(b-c)^2*(2*b^4-11*b^3*c-14*b^2*c^2-11*b*c^3+2*c^4)-a^2*(b^2-c^2)^2*(2*b^4+3*b^3*c-8*b^2*c^2+3*b*c^3+2*c^4)+a^6*(8*b^4-17*b^3*c+8*b^2*c^2-17*b*c^3+8*c^4) : :
X(61571) = 3*X[2]+X[38579], 3*X[3]+X[151], -X[102]+3*X[549], -3*X[547]+4*X[58419], -5*X[631]+X[38573], 5*X[632]+X[38674], -5*X[1656]+X[33650], -7*X[3090]+3*X[38779], -5*X[3091]+X[38780], -3*X[3845]+X[10732], -3*X[10283]+X[10703]

X(61571) lies on these lines: {2, 38579}, {3, 151}, {5, 109}, {30, 117}, {102, 549}, {124, 3628}, {140, 2818}, {143, 58513}, {495, 1795}, {546, 61578}, {547, 58419}, {548, 61603}, {550, 10740}, {631, 38573}, {632, 38674}, {928, 61563}, {952, 11700}, {1361, 15325}, {1656, 33650}, {2773, 10272}, {2779, 61520}, {2785, 61561}, {2792, 61560}, {2800, 5885}, {2807, 61533}, {2816, 31663}, {2817, 61524}, {2835, 20575}, {2841, 61534}, {2846, 61569}, {2849, 61570}, {2852, 61572}, {2853, 61573}, {3042, 47742}, {3090, 38779}, {3091, 38780}, {3530, 38600}, {3627, 38777}, {3738, 61562}, {3845, 10732}, {5433, 52129}, {5719, 12016}, {8703, 10709}, {10283, 10703}, {10716, 15699}, {10726, 15704}, {10764, 59399}, {12026, 61552}, {12103, 38783}, {12108, 38784}, {12812, 38781}, {13363, 58506}, {13451, 58520}, {13532, 38042}, {14690, 28174}, {14869, 38667}, {15712, 38691}, {32423, 53758}, {34753, 59816}, {34773, 50899}, {38022, 50918}, {40111, 58060}, {47115, 61286}, {48154, 58426}, {61519, 61530}, {61536, 61541}

X(61571) = midpoint of X(i) and X(j) for these {i,j}: {5, 109}, {117, 38607}, {124, 51534}, {548, 61603}, {550, 10740}, {3627, 38777}, {8703, 10709}, {10726, 15704}, {34773, 50899}
X(61571) = reflection of X(i) in X(j) for these {i,j}: {124, 3628}, {140, 6718}, {143, 58513}, {12103, 38783}, {38600, 3530}, {546, 61578}, {61286, 47115}, {61564, 140}, {61585, 58419}
X(61571) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {109, 57303, 5}, {117, 38607, 30}, {140, 2818, 61564}, {2818, 6718, 140}, {10726, 38778, 15704}, {10740, 38697, 550}, {58419, 61585, 547}

X(61572) = MIDPOINT OF X(5) AND X(111)

Barycentrics    2*a^10-7*a^8*(b^2+c^2)+(b-c)^2*(b+c)^2*(b^2+c^2)*(b^4-4*b^2*c^2+c^4)+6*a^6*(b^4+3*b^2*c^2+c^4)+a^4*(b^2+c^2)*(6*b^4-25*b^2*c^2+6*c^4)+a^2*(-8*b^8+41*b^6*c^2-58*b^4*c^4+41*b^2*c^6-8*c^8) : :
X(61572) = 3*X[2]+X[11258], X[4]+3*X[52698], X[20]+3*X[38799], 3*X[376]+X[38800], 3*X[381]+X[14654], -3*X[549]+X[1296], -5*X[631]+X[38593], 5*X[632]+X[38675], -X[1353]+3*X[36696], -5*X[1656]+X[14360], 7*X[3090]+X[20099], -3*X[3845]+X[10734] and many others

X(61572) lies on these lines: {2, 11258}, {4, 52698}, {5, 111}, {20, 38799}, {30, 5512}, {126, 3628}, {140, 6719}, {143, 58514}, {376, 38800}, {381, 14654}, {543, 547}, {546, 23699}, {549, 1296}, {550, 22338}, {631, 38593}, {632, 38675}, {952, 11721}, {1353, 36696}, {1656, 14360}, {2780, 61548}, {2793, 61560}, {2805, 61522}, {2813, 61526}, {2819, 61564}, {2824, 61565}, {2830, 61566}, {2837, 61567}, {2843, 61568}, {2847, 61569}, {2851, 61570}, {2852, 61571}, {2854, 10272}, {3090, 20099}, {3325, 15325}, {3530, 38623}, {3564, 28662}, {3845, 10734}, {3853, 38802}, {5066, 32424}, {5719, 59819}, {8703, 38797}, {9129, 32423}, {10283, 10704}, {10717, 15699}, {10765, 59399}, {11619, 11620}, {11644, 13595}, {12103, 38801}, {12106, 14657}, {14515, 57361}, {14693, 25338}, {14869, 38688}, {15563, 39504}, {15693, 37749}, {15704, 44987}, {15712, 38716}, {33923, 38805}, {34200, 38803}, {37459, 38651}, {38022, 50926}, {38042, 50924}, {38081, 50925}, {38798, 46853}, {40111, 58059}, {44233, 61573}, {44282, 47325}, {48154, 58427}, {52141, 57619}

X(61572) = midpoint of X(i) and X(j) for these {i,j}: {5, 111}, {126, 51535}, {550, 22338}, {3845, 14666}, {5512, 14650}, {15704, 44987}
X(61572) = reflection of X(i) in X(j) for these {i,j}: {126, 3628}, {140, 6719}, {143, 58514}, {38623, 3530}, {38805, 33923}
X(61572) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {111, 38796, 5}, {1296, 38806, 549}, {5512, 14650, 30}, {5512, 9172, 14650}, {6719, 33962, 140}, {38623, 38804, 3530}, {38807, 51535, 3628}

X(61573) = MIDPOINT OF X(5) AND X(112)

Barycentrics    2*a^14-7*a^12*(b^2+c^2)+(b-c)^4*(b+c)^4*(b^2+c^2)*(b^4+c^4)-3*a^6*(b^2-c^2)^2*(2*b^4+b^2*c^2+2*c^4)+a^8*(b^2+c^2)*(3*b^4-11*b^2*c^2+3*c^4)+a^4*(b-c)^2*(b+c)^2*(b^2+c^2)*(3*b^4+b^2*c^2+3*c^4)+2*a^10*(3*b^4+5*b^2*c^2+3*c^4)-a^2*(b^2-c^2)^2*(2*b^8+3*b^6*c^2-2*b^4*c^4+3*b^2*c^6+2*c^8) : :
X(61573) = 3*X[2]+X[13310], -5*X[3]+X[12253], 3*X[376]+X[48658], 3*X[381]+X[13200], -3*X[547]+4*X[58430], -3*X[549]+X[1297], -5*X[631]+X[13115], 5*X[632]+X[38676], -5*X[1656]+X[13219], -X[1657]+9*X[38639], -5*X[3091]+X[48681], -3*X[3845]+X[10735] and many others

X(61573) lies on these lines: {2, 13310}, {3, 12253}, {5, 112}, {30, 132}, {114, 52951}, {127, 3628}, {140, 6720}, {143, 58515}, {376, 48658}, {381, 13200}, {495, 13312}, {496, 13311}, {546, 2794}, {547, 58430}, {549, 1297}, {550, 12918}, {590, 35881}, {615, 35880}, {631, 13115}, {632, 38676}, {952, 11722}, {1656, 13219}, {1657, 38639}, {2781, 18583}, {2799, 61561}, {2806, 61562}, {2825, 61536}, {2831, 61566}, {2838, 61567}, {2844, 61568}, {2848, 61569}, {2853, 61571}, {3091, 48681}, {3320, 15325}, {3530, 38624}, {3564, 28343}, {3845, 10735}, {3850, 14900}, {5719, 59821}, {5886, 13221}, {6102, 16225}, {7583, 49271}, {7584, 49270}, {9517, 10272}, {9518, 61563}, {9530, 12100}, {9532, 61564}, {10283, 10705}, {10592, 13296}, {10593, 13297}, {10718, 15699}, {10766, 59399}, {10796, 14676}, {11641, 13861}, {11818, 51240}, {12026, 61532}, {12106, 19165}, {12503, 42787}, {12784, 34773}, {13166, 21841}, {13280, 38042}, {13451, 58529}, {14693, 44234}, {14869, 38689}, {15704, 44988}, {15712, 38717}, {16224, 16881}, {18121, 39854}, {19114, 19117}, {19115, 19116}, {32423, 53760}, {35255, 49218}, {35256, 49219}, {37459, 38652}, {40111, 58064}, {44233, 61572}, {48154, 58428}

X(61573) = midpoint of X(i) and X(j) for these {i,j}: {5, 112}, {127, 51536}, {132, 38608}, {550, 12918}, {12784, 34773}, {14689, 19160}, {14900, 19163}, {15704, 44988}
X(61573) = reflection of X(i) in X(j) for these {i,j}: {127, 3628}, {140, 6720}, {143, 58515}, {19163, 3850}, {38624, 3530}, {546, 61591}, {61586, 58430}
X(61573) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {112, 57304, 5}, {132, 14689, 19160}, {132, 38608, 30}, {2794, 61591, 546}, {12918, 38699, 550}, {19160, 38608, 14689}, {58430, 61586, 547}

X(61574) = MIDPOINT OF X(5) AND X(113)

Barycentrics    3*a^8*(b^2+c^2)-2*(b^2-c^2)^4*(b^2+c^2)+a^6*(-7*b^4+2*b^2*c^2-7*c^4)+a^2*(b^2-c^2)^2*(3*b^4-5*b^2*c^2+3*c^4)+3*a^4*(b^6+c^6) : :
X(61574) = 3*X[2]+X[7728], -X[20]+5*X[38794], -X[74]+5*X[1656], X[110]+3*X[381], X[146]+7*X[3090], -X[265]+5*X[3091], X[382]+3*X[15035], X[399]+7*X[3851], -X[477]+3*X[45694], -3*X[549]+X[16111], -5*X[631]+X[20127], -5*X[632]+X[14677]

X(61574) lies on circumconic {{A, B, C, X(13530), X(43917)}} and on these lines: {2, 7728}, {3, 1539}, {4, 1511}, {5, 113}, {20, 38794}, {30, 5972}, {49, 43865}, {74, 1656}, {110, 381}, {128, 43966}, {140, 2777}, {141, 32271}, {143, 5448}, {146, 3090}, {156, 12228}, {265, 3091}, {382, 15035}, {399, 3851}, {403, 1112}, {468, 58885}, {477, 45694}, {498, 12374}, {499, 12373}, {511, 44961}, {517, 58671}, {526, 39509}, {541, 547}, {542, 5066}, {546, 9820}, {548, 48378}, {549, 16111}, {550, 13202}, {567, 3047}, {631, 20127}, {632, 14677}, {690, 61575}, {858, 51548}, {952, 11723}, {1209, 11805}, {1216, 11807}, {1495, 18572}, {1514, 15122}, {1531, 7575}, {1553, 16340}, {1568, 11563}, {1594, 12133}, {1614, 11565}, {1657, 15051}, {1699, 12778}, {1986, 5876}, {2072, 32111}, {2771, 46028}, {2772, 61577}, {2773, 61578}, {2774, 61579}, {2775, 61581}, {2776, 61582}, {2778, 61584}, {2779, 61585}, {2780, 40340}, {2781, 24206}, {2854, 19130}, {2931, 13861}, {3024, 7951}, {3028, 7741}, {3043, 18350}, {3146, 38723}, {3448, 3545}, {3523, 38788}, {3526, 15055}, {3530, 37853}, {3534, 15036}, {3544, 12317}, {3627, 16163}, {3628, 6699}, {3817, 12261}, {3818, 6593}, {3830, 15040}, {3832, 12383}, {3843, 10733}, {3845, 5642}, {3850, 7687}, {3855, 20125}, {3858, 30714}, {3861, 13392}, {4549, 10201}, {5050, 41737}, {5055, 10620}, {5068, 15081}, {5070, 15041}, {5071, 20126}, {5072, 14094}, {5076, 15020}, {5079, 15054}, {5181, 21850}, {5465, 22566}, {5480, 14984}, {5640, 12284}, {5790, 7978}, {5886, 12368}, {5891, 13417}, {5892, 17855}, {5907, 11557}, {5943, 11806}, {6053, 12811}, {6070, 21315}, {6102, 12825}, {6288, 11702}, {6564, 49269}, {6565, 49268}, {6776, 19155}, {6841, 52831}, {6881, 52820}, {7393, 9919}, {7514, 10117}, {7529, 12168}, {7577, 12292}, {7579, 16261}, {7722, 18435}, {7723, 10254}, {7731, 15056}, {7984, 18493}, {7988, 33535}, {8674, 61580}, {8976, 19060}, {8998, 42215}, {9033, 61592}, {9140, 12308}, {9143, 41106}, {9517, 61591}, {9706, 43835}, {9781, 12273}, {9904, 54447}, {9970, 10516}, {10024, 12358}, {10088, 10896}, {10091, 10895}, {10095, 12236}, {10109, 45311}, {10224, 32137}, {10263, 44958}, {10297, 46817}, {10539, 18379}, {10564, 44267}, {10576, 49216}, {10577, 49217}, {10627, 15761}, {10628, 13565}, {10657, 42918}, {10658, 42919}, {10767, 38752}, {10819, 23261}, {10820, 23251}, {10990, 55856}, {11064, 47336}, {11230, 11709}, {11479, 12412}, {11558, 46114}, {11591, 13406}, {11597, 22804}, {11598, 22802}, {11694, 14893}, {11699, 38140}, {11720, 18480}, {11735, 61272}, {11746, 13358}, {11793, 58536}, {11799, 51391}, {12039, 25561}, {12106, 12893}, {12140, 23047}, {12302, 31861}, {12812, 20397}, {12898, 59387}, {13148, 34826}, {13211, 61261}, {13374, 58680}, {13416, 15760}, {13421, 44960}, {13470, 16252}, {13665, 19110}, {13754, 41671}, {13785, 19111}, {13915, 42265}, {13951, 19059}, {13979, 42262}, {13990, 42216}, {14157, 27866}, {14561, 14982}, {15021, 55857}, {15026, 46430}, {15058, 22584}, {15068, 19504}, {15085, 17810}, {15090, 15123}, {15092, 15359}, {15113, 15125}, {15131, 50008}, {15350, 44673}, {15462, 36990}, {15463, 35488}, {15472, 37197}, {15473, 21841}, {15535, 23514}, {15647, 19506}, {15687, 22251}, {15806, 43393}, {16105, 32142}, {16165, 44288}, {16168, 36169}, {16278, 51872}, {18279, 59654}, {18377, 20773}, {18440, 52699}, {18538, 46688}, {18553, 25556}, {18762, 46689}, {19051, 42561}, {19052, 31412}, {19140, 32274}, {19163, 53760}, {19481, 58807}, {19924, 32218}, {20417, 35018}, {20771, 32171}, {21316, 33505}, {22051, 40240}, {22109, 37440}, {22265, 38743}, {22505, 53725}, {22515, 53735}, {22660, 46085}, {22799, 53753}, {22938, 53743}, {23323, 30522}, {24981, 38071}, {25321, 32272}, {25329, 47354}, {25487, 44279}, {25564, 43615}, {32110, 44282}, {32210, 60780}, {32269, 47334}, {32438, 61589}, {32743, 49673}, {33547, 39504}, {33851, 48901}, {33923, 48375}, {34126, 53715}, {34127, 53709}, {35265, 58789}, {36172, 57306}, {37347, 54376}, {37938, 51403}, {38609, 46045}, {38633, 55866}, {39565, 46301}, {42270, 49223}, {42273, 49222}, {43598, 54073}, {43614, 58881}, {43807, 43866}, {43893, 51392}, {44271, 59495}, {44283, 51394}, {44920, 61619}, {45147, 61587}, {47055, 59370}, {49117, 53757}, {52070, 58435}, {55121, 61590}, {57584, 59648}

X(61574) = midpoint of X(i) and X(j) for these {i,j}: {3, 1539}, {4, 1511}, {5, 113}, {110, 10113}, {128, 43966}, {141, 32271}, {146, 51522}, {265, 5609}, {468, 58885}, {546, 10272}, {550, 13202}, {858, 51548}, {1209, 11805}, {1216, 11807}, {1495, 18572}, {1514, 15122}, {1531, 7575}, {1553, 16340}, {1568, 11563}, {1986, 5876}, {3627, 16163}, {3818, 6593}, {3845, 5642}, {3861, 13392}, {5181, 21850}, {5465, 22566}, {5907, 11557}, {5972, 46686}, {6053, 36253}, {6102, 12825}, {6288, 11702}, {6699, 38791}, {7687, 16534}, {7723, 38898}, {7728, 12041}, {10264, 15063}, {10297, 46817}, {10564, 44267}, {11064, 47336}, {11558, 46114}, {11561, 45959}, {11597, 22804}, {11598, 22802}, {11694, 14893}, {11720, 18480}, {11793, 58536}, {11799, 51391}, {12295, 34153}, {12824, 15060}, {13374, 58680}, {15647, 19506}, {16165, 44288}, {16278, 51872}, {18377, 20773}, {18553, 25556}, {19140, 32274}, {19163, 53760}, {21316, 33505}, {22505, 53725}, {22515, 53735}, {22660, 46085}, {22799, 53753}, {22938, 53743}, {23323, 51425}, {25487, 44279}, {25561, 25566}, {33851, 48901}, {34128, 38789}, {37938, 51403}, {38609, 46045}, {43893, 51392}, {44271, 59495}, {44283, 51394}, {49117, 53757}, {61548, 61598}
X(61574) = reflection of X(i) in X(j) for these {i,j}: {125, 15088}, {140, 12900}, {143, 58516}, {10264, 20396}, {11735, 61272}, {12236, 10095}, {12358, 14128}, {13358, 11746}, {13630, 9826}, {15123, 15090}, {15359, 15092}, {19481, 58807}, {20304, 5}, {20379, 20304}, {20417, 40685}, {37853, 3530}, {38632, 6053}, {40685, 35018}, {44673, 15350}, {45311, 10109}, {548, 48378}, {6699, 3628}, {61548, 6723}, {7687, 3850}, {974, 12006}
X(61574) = complement of X(12041)
X(61574) = pole of line {3003, 6781} with respect to the Kiepert hyperbola
X(61574) = pole of line {15055, 34152} with respect to the Stammler hyperbola
X(61574) = pole of line {14391, 46425} with respect to the dual conic of DeLongchamps circle
X(61574) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12244, 38728}, {3, 1539, 34584}, {4, 14643, 1511}, {5, 10264, 23515}, {5, 125, 15088}, {5, 43831, 12006}, {110, 381, 10113}, {113, 23515, 15063}, {113, 36518, 5}, {125, 15088, 20304}, {146, 15061, 51522}, {146, 3090, 15061}, {399, 3851, 14644}, {541, 6723, 61548}, {546, 10272, 17702}, {632, 14677, 38727}, {1568, 11563, 13391}, {1656, 38789, 74}, {2777, 12900, 140}, {3526, 38790, 15055}, {3843, 32609, 10733}, {3845, 34153, 12295}, {3850, 32423, 7687}, {5448, 44235, 143}, {5642, 12295, 34153}, {5663, 12006, 974}, {5663, 15088, 125}, {5663, 9826, 13630}, {5972, 46686, 30}, {7687, 16534, 32423}, {7687, 38792, 16534}, {7723, 12824, 38898}, {7728, 38728, 12244}, {10264, 15063, 5663}, {10264, 23515, 20396}, {10706, 15059, 10620}, {12244, 38728, 12041}, {12825, 16222, 6102}, {13202, 38793, 550}, {13358, 13364, 11746}, {13630, 15114, 20379}, {15060, 38898, 7723}, {15063, 23515, 10264}, {61548, 61598, 541}

X(61575) = MIDPOINT OF X(5) AND X(114)

Barycentrics    3*a^6*(b^2+c^2)-(b^2-c^2)^2*(2*b^4-b^2*c^2+2*c^4)+a^2*(b^2+c^2)*(4*b^4-5*b^2*c^2+4*c^4)-a^4*(5*b^4+2*b^2*c^2+5*c^4) : :
X(61575) = X[4]+3*X[15561], -X[20]+5*X[38750], -X[98]+5*X[1656], X[99]+3*X[381], X[147]+7*X[3090], -X[148]+9*X[3545], X[382]+3*X[21166], X[546]+2*X[20399], -X[550]+3*X[38748], -5*X[631]+X[38741], -5*X[632]+3*X[38737], -X[671]+5*X[19709] and many others

X(61575) lies on these lines: {2, 5191}, {3, 7899}, {4, 15561}, {5, 39}, {20, 38750}, {30, 620}, {98, 1656}, {99, 381}, {140, 2794}, {143, 58517}, {147, 3090}, {148, 3545}, {156, 39805}, {230, 41675}, {262, 10290}, {382, 21166}, {403, 5186}, {498, 12185}, {499, 12184}, {517, 58662}, {542, 547}, {543, 5066}, {546, 20399}, {549, 7853}, {550, 38748}, {567, 3044}, {590, 13670}, {597, 25562}, {615, 13790}, {618, 22797}, {619, 22796}, {631, 38741}, {632, 38737}, {671, 19709}, {690, 61574}, {804, 6140}, {952, 11724}, {1154, 39835}, {1539, 53710}, {1594, 12131}, {2482, 3845}, {2548, 44534}, {2783, 60759}, {2784, 61577}, {2785, 61578}, {2786, 61579}, {2787, 61580}, {2788, 61581}, {2789, 61582}, {2790, 23333}, {2791, 61584}, {2792, 61585}, {2793, 40340}, {2795, 46028}, {2797, 61592}, {2799, 61591}, {3023, 7951}, {3027, 7741}, {3091, 6321}, {3146, 38731}, {3314, 37446}, {3398, 16984}, {3523, 38742}, {3526, 34473}, {3530, 38747}, {3564, 41672}, {3583, 15452}, {3627, 38738}, {3628, 6036}, {3788, 40279}, {3818, 5026}, {3830, 41134}, {3832, 13172}, {3843, 10723}, {3850, 38746}, {3851, 13188}, {3858, 10992}, {3860, 36521}, {4027, 32967}, {5050, 50641}, {5054, 7937}, {5055, 6054}, {5056, 14651}, {5071, 11632}, {5072, 23235}, {5077, 11151}, {5079, 38664}, {5149, 7862}, {5182, 18440}, {5461, 10109}, {5613, 6777}, {5617, 6778}, {5640, 39808}, {5790, 7970}, {5886, 9864}, {5891, 39846}, {5969, 19130}, {5976, 7752}, {5984, 7486}, {5985, 7504}, {5986, 7571}, {5987, 7570}, {6055, 15699}, {6564, 49267}, {6565, 49266}, {6841, 52822}, {6881, 52821}, {7393, 9861}, {7514, 39857}, {7529, 39803}, {7687, 33512}, {7737, 37466}, {7746, 12829}, {7749, 32151}, {7769, 37243}, {7771, 34510}, {7809, 9301}, {7814, 48673}, {7821, 32521}, {7861, 32516}, {7874, 44224}, {7887, 10352}, {7901, 12054}, {7912, 9821}, {7925, 35002}, {7983, 18493}, {8290, 22803}, {8591, 41106}, {8703, 9167}, {8976, 19056}, {8997, 42215}, {9166, 48657}, {9781, 39807}, {9830, 25561}, {9860, 54447}, {9880, 38071}, {10011, 14693}, {10086, 10896}, {10089, 10895}, {10095, 39806}, {10104, 37637}, {10113, 53735}, {10175, 21636}, {10516, 12177}, {10576, 49212}, {10577, 49213}, {10768, 38752}, {10796, 15484}, {10991, 55856}, {11005, 14643}, {11230, 11710}, {11623, 35018}, {11711, 18480}, {11725, 61272}, {11793, 58537}, {11801, 50711}, {12100, 22247}, {12106, 39825}, {12117, 14269}, {12811, 38628}, {12812, 20398}, {13178, 61261}, {13364, 58518}, {13374, 58681}, {13665, 19108}, {13754, 58503}, {13785, 19109}, {13861, 39828}, {13951, 19055}, {13989, 42216}, {14692, 15022}, {15056, 39837}, {15068, 39839}, {15088, 15359}, {15535, 23515}, {16509, 25486}, {16626, 47860}, {16627, 47859}, {18350, 58058}, {18483, 51578}, {18502, 39652}, {18553, 32135}, {18572, 47326}, {19163, 53737}, {21850, 50567}, {22799, 53733}, {22938, 53729}, {24206, 32149}, {31275, 58849}, {31861, 39812}, {34126, 53722}, {34128, 53709}, {34990, 38393}, {35930, 44532}, {36170, 53793}, {36173, 57311}, {36776, 59402}, {37345, 37647}, {38220, 61268}, {38634, 55866}, {38642, 40108}, {39504, 42862}, {41099, 52695}

X(61575) = midpoint of X(i) and X(j) for these {i,j}: {2, 22566}, {3, 22505}, {4, 33813}, {5, 114}, {99, 22515}, {115, 51872}, {147, 51523}, {546, 61561}, {550, 39838}, {597, 25562}, {618, 22797}, {619, 22796}, {1539, 53710}, {2482, 3845}, {3627, 38738}, {3818, 5026}, {5976, 14881}, {6033, 12042}, {6036, 38745}, {6054, 49102}, {6321, 51524}, {7687, 33512}, {8290, 22803}, {10113, 53735}, {11711, 18480}, {11793, 58537}, {13374, 58681}, {16509, 25486}, {18483, 51578}, {18553, 32135}, {18572, 47326}, {19163, 53737}, {21850, 50567}, {22799, 53733}, {22938, 53729}, {34127, 38743}, {38383, 49111}, {61560, 61599}
X(61575) = reflection of X(i) in X(j) for these {i,j}: {115, 15092}, {140, 6721}, {143, 58517}, {11725, 61272}, {12100, 22247}, {14693, 10011}, {15359, 15088}, {38747, 3530}, {39806, 10095}, {5461, 10109}, {6036, 3628}, {61560, 6722}, {61561, 20399}, {61576, 5}
X(61575) = inverse of X(51872) in nine-point circle
X(61575) = inverse of X(9999) in orthoptic circle of the Steiner inellipse
X(61575) = complement of X(12042)
X(61575) = pole of line {804, 8552} with respect to the nine-point circle
X(61575) = pole of line {8782, 9147} with respect to the orthoptic circle of the Steiner inellipse
X(61575) = pole of line {511, 38737} with respect to the Kiepert hyperbola
X(61575) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14830, 26614}, {2, 6033, 12042}, {2, 9862, 38739}, {5, 115, 15092}, {99, 381, 22515}, {114, 115, 51872}, {114, 23514, 14981}, {114, 36519, 5}, {115, 15092, 61576}, {115, 51872, 2782}, {147, 3090, 38224}, {147, 38224, 51523}, {542, 6722, 61560}, {546, 61561, 23698}, {547, 61560, 6722}, {1656, 38743, 98}, {2782, 15092, 115}, {2794, 6721, 140}, {3526, 38744, 34473}, {3851, 13188, 14639}, {5055, 12188, 14061}, {6033, 38739, 9862}, {6054, 14061, 12188}, {6114, 6115, 2023}, {12042, 22566, 6033}, {12188, 14061, 49102}, {20399, 23698, 61561}, {31274, 38749, 549}, {38748, 39838, 550}, {61560, 61599, 542}

X(61576) = MIDPOINT OF X(5) AND X(115)

Barycentrics    a^6*(b^2+c^2)+a^4*(-3*b^4+2*b^2*c^2-3*c^4)-(b^2-c^2)^2*(2*b^4-3*b^2*c^2+2*c^4)+a^2*(b^2+c^2)*(4*b^4-7*b^2*c^2+4*c^4) : :
X(61576) = 3*X[2]+X[6321], 3*X[3]+X[10723], -X[20]+5*X[38739], X[98]+3*X[381], -X[99]+5*X[1656], -X[147]+9*X[3545], X[148]+7*X[3090], X[355]+3*X[38220], -X[376]+3*X[26614], X[382]+3*X[34473], -X[550]+3*X[38737], -5*X[631]+X[38730] and many others

X(61576) lies on these lines: {2, 6321}, {3, 10723}, {4, 12042}, {5, 39}, {13, 22507}, {14, 22509}, {20, 38739}, {30, 5461}, {83, 38228}, {98, 381}, {99, 1656}, {113, 15535}, {140, 6722}, {143, 58518}, {147, 3545}, {148, 3090}, {156, 39834}, {355, 38220}, {376, 26614}, {382, 34473}, {403, 12131}, {498, 13183}, {499, 13182}, {512, 46172}, {517, 58661}, {542, 5066}, {543, 547}, {546, 2794}, {549, 9880}, {550, 38737}, {567, 58058}, {620, 3628}, {625, 32515}, {631, 38730}, {632, 38748}, {671, 5055}, {690, 20304}, {804, 11620}, {952, 11725}, {1154, 39806}, {1352, 6034}, {1539, 53709}, {1594, 5186}, {1916, 7697}, {2031, 43291}, {2080, 14041}, {2482, 15699}, {2783, 61580}, {2784, 61579}, {2785, 61585}, {2786, 61577}, {2787, 60759}, {2790, 46030}, {2792, 61578}, {2795, 61581}, {2796, 61582}, {2797, 61583}, {2798, 61584}, {2799, 61586}, {3023, 7741}, {3027, 7951}, {3044, 18350}, {3091, 5984}, {3095, 32966}, {3146, 38742}, {3523, 38731}, {3526, 7918}, {3530, 38736}, {3627, 38740}, {3832, 9862}, {3839, 14830}, {3843, 10722}, {3845, 6055}, {3850, 11623}, {3851, 12188}, {3858, 10991}, {4027, 33013}, {4045, 51520}, {5025, 49111}, {5026, 38317}, {5068, 52090}, {5071, 8724}, {5072, 38664}, {5079, 23235}, {5152, 15031}, {5459, 25559}, {5460, 25560}, {5462, 61588}, {5469, 5613}, {5470, 5617}, {5475, 12829}, {5477, 59399}, {5478, 6774}, {5479, 6771}, {5640, 39837}, {5663, 15359}, {5790, 7983}, {5886, 13178}, {5891, 39817}, {5969, 24206}, {5985, 37375}, {6054, 19709}, {6230, 32787}, {6231, 32788}, {6564, 49213}, {6565, 49212}, {6669, 61513}, {6670, 61514}, {6781, 38230}, {6841, 52821}, {6881, 52822}, {7393, 13175}, {7486, 20094}, {7514, 39828}, {7529, 39832}, {7687, 33511}, {7745, 41675}, {7790, 40108}, {7814, 32520}, {7970, 18493}, {8976, 19109}, {8980, 42215}, {9183, 39492}, {9478, 15980}, {9781, 39836}, {9830, 32135}, {9864, 61261}, {10003, 46029}, {10053, 10896}, {10069, 10895}, {10095, 39835}, {10104, 13881}, {10109, 36523}, {10113, 53725}, {10172, 51578}, {10175, 11599}, {10242, 14712}, {10272, 50711}, {10352, 44543}, {10576, 49266}, {10577, 49267}, {10769, 38752}, {10992, 31274}, {11152, 32994}, {11161, 14848}, {11177, 41106}, {11230, 11711}, {11646, 14561}, {11710, 18480}, {11724, 61272}, {11793, 58538}, {12101, 41148}, {12106, 39854}, {12117, 15694}, {12132, 37943}, {12243, 14692}, {12355, 15703}, {12811, 38627}, {12812, 20399}, {13174, 54447}, {13364, 58517}, {13374, 58682}, {13665, 19055}, {13754, 58502}, {13785, 19056}, {13861, 39857}, {13862, 22681}, {13951, 19108}, {13967, 42216}, {14120, 53793}, {14644, 18332}, {14645, 61545}, {15056, 39808}, {15068, 39810}, {15081, 15545}, {15342, 38724}, {16001, 32553}, {16002, 32552}, {16278, 23515}, {18800, 38079}, {19905, 38072}, {20428, 22510}, {20429, 22511}, {22247, 47599}, {22489, 25164}, {22490, 25154}, {22799, 53722}, {22938, 53720}, {23004, 59403}, {23005, 59404}, {31513, 57310}, {31709, 52650}, {31710, 44223}, {31861, 39841}, {32134, 39590}, {34126, 53733}, {34128, 53710}, {34981, 34989}, {34990, 38394}, {35930, 44531}, {36174, 57307}, {37242, 43620}, {37459, 53419}, {38635, 55866}, {39503, 46482}, {41060, 47610}, {41061, 47611}, {42270, 50719}, {42273, 50720}, {44282, 47326}, {49117, 53723}, {58610, 58631}

X(61576) = midpoint of X(i) and X(j) for these {i,j}: {3, 22515}, {4, 12042}, {5, 115}, {98, 22505}, {113, 15535}, {148, 51524}, {381, 49102}, {546, 61560}, {549, 9880}, {550, 39809}, {620, 38734}, {1539, 53709}, {3627, 38749}, {3845, 6055}, {5478, 6774}, {5479, 6771}, {6033, 51523}, {6321, 33813}, {7687, 33511}, {9183, 39492}, {10113, 53725}, {11632, 22566}, {11710, 18480}, {11793, 58538}, {13374, 58682}, {14639, 34127}, {16001, 32553}, {16002, 32552}, {20252, 20253}, {22799, 53722}, {22938, 53720}, {23514, 38229}, {31709, 52650}, {31710, 44223}, {37459, 53419}, {41060, 47610}, {41061, 47611}, {49117, 53723}, {58610, 58631}, {61561, 61600}
X(61576) = reflection of X(i) in X(j) for these {i,j}: {140, 6722}, {143, 58518}, {11724, 61272}, {38736, 3530}, {39835, 10095}, {5, 15092}, {620, 3628}, {61560, 20398}, {61561, 6721}, {61575, 5}
X(61576) = inverse of X(1569) in Kiepert hyperbola
X(61576) = complement of X(33813)
X(61576) = pole of line {511, 1569} with respect to the Kiepert hyperbola
X(61576) = pole of line {3569, 53374} with respect to the Steiner inellipse
X(61576) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 13172, 38750}, {3, 14061, 34127}, {3, 14639, 22515}, {4, 38224, 12042}, {5, 23514, 15092}, {5, 38229, 115}, {5, 51872, 36519}, {98, 381, 22505}, {115, 15092, 61575}, {115, 23514, 5}, {148, 15561, 51524}, {148, 3090, 15561}, {381, 9166, 49102}, {543, 6721, 61561}, {546, 61560, 2794}, {547, 61561, 6721}, {2009, 2010, 1569}, {2794, 20398, 61560}, {3091, 14651, 6033}, {3526, 38733, 21166}, {3545, 11632, 22566}, {5071, 41135, 8724}, {6033, 14651, 51523}, {6321, 38750, 13172}, {6722, 23698, 140}, {9880, 14971, 549}, {12355, 15703, 41134}, {14061, 14639, 3}, {20252, 20253, 542}, {22505, 49102, 98}, {23514, 38229, 2782}, {38737, 39809, 550}, {61561, 61600, 543}

X(61577) = MIDPOINT OF X(5) AND X(116)

Barycentrics    -2*a^5*b*c*(b+c)+2*a*(b-c)^4*(b+c)^3+a^6*(b^2+c^2)-2*(b-c)^4*(b+c)^2*(b^2+b*c+c^2)-2*a^3*(b-c)^2*(b^3+c^3)+2*a^4*(-b^4+b^3*c+b^2*c^2+b*c^3-c^4)+a^2*(b-c)^2*(3*b^4+2*b^3*c+4*b^2*c^2+2*b*c^3+3*c^4) : :
X(61577) = 3*X[2]+X[10739], 3*X[3]+X[10725], -X[101]+5*X[1656], X[103]+3*X[381], X[150]+7*X[3090], -X[152]+9*X[3545], X[382]+3*X[38692], -5*X[632]+3*X[38772], -X[1282]+9*X[54447], -5*X[3091]+X[10741], X[3146]+3*X[38766], -7*X[3526]+3*X[38690]

X(61577) lies on these lines: {2, 10739}, {3, 10725}, {4, 38601}, {5, 116}, {30, 6712}, {101, 1656}, {103, 381}, {140, 58418}, {143, 58519}, {150, 3090}, {152, 3545}, {382, 38692}, {517, 58665}, {544, 547}, {546, 61565}, {567, 58057}, {632, 38772}, {928, 61585}, {952, 11726}, {1282, 54447}, {1362, 7951}, {1539, 53714}, {1594, 5185}, {2772, 61574}, {2774, 20304}, {2784, 61575}, {2786, 61576}, {2801, 61580}, {2807, 61578}, {2809, 9956}, {2810, 24206}, {2811, 61583}, {2812, 61584}, {2813, 40340}, {2822, 61592}, {2825, 61591}, {3022, 7741}, {3041, 3814}, {3046, 18350}, {3091, 10741}, {3146, 38766}, {3526, 38690}, {3627, 38773}, {3628, 6710}, {3843, 10727}, {3851, 38574}, {3858, 33521}, {3887, 60759}, {5055, 10708}, {5072, 38668}, {5079, 38666}, {5790, 10695}, {5886, 50896}, {6841, 52825}, {6881, 52823}, {7486, 20096}, {9518, 61586}, {10113, 53751}, {10172, 28346}, {10697, 18493}, {10710, 19709}, {10770, 38752}, {11230, 11712}, {11714, 18480}, {11728, 61272}, {11793, 58540}, {12811, 38769}, {12812, 20401}, {13364, 58521}, {13374, 58684}, {13754, 58507}, {17606, 18413}, {22515, 53732}, {22799, 53750}, {22938, 53741}, {28345, 38318}, {31841, 35967}, {33520, 55856}, {34126, 53746}, {34127, 53721}, {34128, 53712}, {50903, 61261}, {58612, 58631}

X(61577) = midpoint of X(i) and X(j) for these {i,j}: {4, 38601}, {5, 116}, {150, 51526}, {546, 61565}, {1539, 53714}, {3627, 38773}, {10113, 53751}, {10739, 38599}, {10741, 51528}, {11714, 18480}, {11793, 58540}, {13374, 58684}, {22515, 53732}, {22799, 53750}, {22938, 53741}, {58612, 58631}, {61563, 61602}
X(61577) = reflection of X(i) in X(j) for these {i,j}: {140, 58418}, {143, 58519}, {11728, 61272}, {6710, 3628}, {61563, 58420}, {61579, 5}
X(61577) = complement of X(38599)
X(61577) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 57297, 38601}, {5, 116, 2808}, {5, 2808, 61579}, {150, 3090, 38764}, {150, 38764, 51526}, {544, 58420, 61563}, {547, 61563, 58420}, {61563, 61602, 544}

X(61578) = MIDPOINT OF X(5) AND X(117)

Barycentrics    2*a*(b-c)^6*(b+c)^3+3*a^8*(b^2+c^2)-2*(b^2-c^2)^4*(b^2-b*c+c^2)-2*a^7*(b+c)*(b^2+b*c+c^2)+2*a^5*(b-c)^2*(b+c)*(3*b^2+4*b*c+3*c^2)-2*a^3*(b-c)^4*(b+c)*(3*b^2+5*b*c+3*c^2)+a^6*(-7*b^4+8*b^3*c+4*b^2*c^2+8*b*c^3-7*c^4)+a^4*(b-c)^2*(3*b^4-8*b^3*c-14*b^2*c^2-8*b*c^3+3*c^4)+a^2*(b^2-c^2)^2*(3*b^4+4*b^3*c-12*b^2*c^2+4*b*c^3+3*c^4) : :
X(61578) = 3*X[2]+X[10740], 3*X[3]+X[10726], -X[102]+5*X[1656], X[109]+3*X[381], X[151]+7*X[3090], X[382]+3*X[38697], -3*X[547]+2*X[58426], -5*X[632]+3*X[38784], -5*X[3091]+X[10747], X[3146]+3*X[38778], -7*X[3526]+3*X[38691], -9*X[3545]+X[33650]

X(61578) lies on these lines: {2, 10740}, {3, 10726}, {4, 38607}, {5, 117}, {30, 6718}, {102, 1656}, {109, 381}, {140, 58419}, {143, 58520}, {151, 3090}, {382, 38697}, {517, 58670}, {546, 61571}, {547, 58426}, {567, 58051}, {632, 38784}, {928, 61579}, {952, 11727}, {1361, 7741}, {1364, 7951}, {1539, 53717}, {1795, 10895}, {1845, 17606}, {2773, 61574}, {2779, 20304}, {2785, 61575}, {2792, 61576}, {2800, 9955}, {2807, 61577}, {2814, 61581}, {2815, 61582}, {2816, 3634}, {2817, 9956}, {2819, 40340}, {2846, 61592}, {2853, 61591}, {3040, 25639}, {3042, 3814}, {3091, 10747}, {3146, 38778}, {3526, 38691}, {3545, 33650}, {3627, 38785}, {3628, 6711}, {3738, 61580}, {3843, 10732}, {3851, 38579}, {5055, 10709}, {5072, 38674}, {5079, 38667}, {5790, 10696}, {5886, 50899}, {6841, 52830}, {6881, 52824}, {9532, 61586}, {10113, 53758}, {10703, 18493}, {10716, 19709}, {10771, 38752}, {11230, 11713}, {11700, 18480}, {11734, 61272}, {11793, 58541}, {12811, 38781}, {13364, 58526}, {13374, 58685}, {13532, 61261}, {13754, 58513}, {14690, 22793}, {18350, 58060}, {22505, 53724}, {22515, 53734}, {22799, 53752}, {22938, 53742}, {28204, 47115}, {34126, 53748}, {34128, 53713}

X(61578) = midpoint of X(i) and X(j) for these {i,j}: {4, 38607}, {5, 117}, {151, 51527}, {546, 61571}, {1539, 53717}, {3627, 38785}, {10113, 53758}, {10740, 38600}, {10747, 51534}, {11700, 18480}, {11793, 58541}, {13374, 58685}, {14690, 22793}, {22505, 53724}, {22515, 53734}, {22799, 53752}, {22938, 53742}, {61564, 61603}
X(61578) = reflection of X(i) in X(j) for these {i,j}: {140, 58419}, {143, 58520}, {11734, 61272}, {6711, 3628}, {61564, 58426}, {61585, 5}
X(61578) = complement of X(38600)
X(61578) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10740, 38600}, {5, 117, 2818}, {5, 2818, 61585}, {151, 3090, 38776}, {151, 38776, 51527}, {547, 61564, 58426}, {547, 61603, 61564}

X(61579) = MIDPOINT OF X(5) AND X(118)

Barycentrics    2*a*(b-c)^4*(b+c)^3+3*a^6*(b^2+c^2)-2*(b-c)^4*(b+c)^2*(b^2+b*c+c^2)+2*a^3*(b-c)^2*(b+c)*(b^2+3*b*c+c^2)-2*a^5*(b+c)*(2*b^2-b*c+2*c^2)+a^2*(b-c)^2*(b^4-2*b^3*c-4*b^2*c^2-2*b*c^3+c^4)-2*a^4*(b^4-b^3*c-3*b^2*c^2-b*c^3+c^4) : :
X(61579) = 3*X[2]+X[10741], 3*X[3]+X[10727], -3*X[5]+X[116], -X[20]+5*X[38774], X[101]+3*X[381], -X[103]+5*X[1656], -X[150]+9*X[3545], X[152]+7*X[3090], X[382]+3*X[38690], X[546]+2*X[20401], -3*X[547]+2*X[58418], -3*X[549]+X[38773] and many others

X(61579) lies on these lines: {2, 10741}, {3, 10727}, {4, 38599}, {5, 116}, {20, 38774}, {30, 6710}, {101, 381}, {103, 1656}, {140, 58420}, {143, 58521}, {150, 3545}, {152, 3090}, {382, 38690}, {403, 5185}, {517, 58664}, {544, 5066}, {546, 20401}, {547, 58418}, {549, 38773}, {550, 38772}, {567, 3046}, {631, 38765}, {928, 61578}, {952, 11728}, {1362, 7741}, {1539, 53712}, {2772, 20304}, {2774, 61574}, {2784, 61576}, {2786, 61575}, {2801, 58604}, {2807, 61585}, {2809, 9955}, {2810, 19130}, {2811, 61592}, {2820, 61581}, {2821, 61582}, {2822, 61583}, {2823, 61584}, {2824, 40340}, {2825, 61586}, {3022, 7951}, {3041, 25639}, {3091, 10739}, {3523, 38766}, {3526, 38692}, {3530, 38771}, {3627, 38775}, {3628, 6712}, {3843, 10725}, {3850, 38770}, {3851, 38572}, {3858, 33520}, {3887, 61580}, {5055, 10710}, {5072, 38666}, {5079, 38668}, {5790, 10697}, {5886, 50903}, {6841, 52823}, {6881, 52825}, {9518, 61591}, {10113, 53747}, {10695, 18493}, {10708, 19709}, {10772, 38752}, {11230, 11714}, {11712, 18480}, {11726, 61272}, {11793, 58542}, {12811, 38630}, {13364, 58519}, {13374, 58686}, {13754, 58505}, {17605, 18413}, {18350, 58057}, {18482, 28345}, {18483, 28346}, {22505, 53721}, {22515, 53730}, {22799, 53746}, {22938, 53739}, {24045, 56785}, {33521, 55856}, {34126, 53750}, {34128, 53714}, {39156, 54447}, {50896, 61261}

X(61579) = midpoint of X(i) and X(j) for these {i,j}: {4, 38599}, {5, 118}, {152, 51528}, {546, 61563}, {1539, 53712}, {6712, 38769}, {10113, 53747}, {10739, 51526}, {10741, 38601}, {11712, 18480}, {11793, 58542}, {13374, 58686}, {18482, 28345}, {18483, 28346}, {22505, 53721}, {22515, 53730}, {22799, 53746}, {22938, 53739}, {61565, 61604}
X(61579) = reflection of X(i) in X(j) for these {i,j}: {140, 58420}, {143, 58521}, {11726, 61272}, {38771, 3530}, {6712, 3628}, {61563, 20401}, {61565, 58418}, {61577, 5}
X(61579) = complement of X(38601)
X(61579) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10741, 38601}, {5, 118, 2808}, {5, 2808, 61577}, {152, 3090, 57297}, {152, 57297, 51528}, {547, 61604, 61565}, {1656, 38767, 103}, {3526, 38768, 38692}, {10710, 31273, 38574}

X(61580) = MIDPOINT OF X(5) AND X(119)

Barycentrics    -2*(b-c)^4*(b+c)^3+2*a^5*(b^2+b*c+c^2)-2*a^4*(b+c)*(b^2+b*c+c^2)+a*(b^2-c^2)^2*(2*b^2-7*b*c+2*c^2)+2*a^2*(b-c)^2*(b+c)*(2*b^2+3*b*c+2*c^2)+a^3*(-4*b^4+5*b^3*c+4*b^2*c^2+5*b*c^3-4*c^4) : :
X(61580) = 3*X[2]+X[10742], 3*X[3]+X[10728], -X[20]+5*X[38762], X[100]+3*X[381], -X[104]+5*X[1656], -X[149]+9*X[3545], X[153]+7*X[3090], X[382]+3*X[34474], -3*X[549]+5*X[31235], -X[550]+3*X[38760], -5*X[631]+X[38753], -5*X[632]+3*X[21154] and many others

X(61580) lies on these lines: {1, 5}, {2, 10742}, {3, 10728}, {4, 33814}, {10, 12611}, {20, 38762}, {30, 3035}, {100, 381}, {104, 1656}, {140, 2829}, {143, 58522}, {149, 3545}, {153, 3090}, {214, 18480}, {382, 34474}, {390, 6973}, {403, 1862}, {498, 12764}, {499, 12763}, {517, 58663}, {528, 5066}, {546, 5840}, {547, 3822}, {549, 31235}, {550, 38760}, {567, 3045}, {631, 38753}, {632, 21154}, {908, 33594}, {1145, 11681}, {1320, 18493}, {1329, 61524}, {1532, 28174}, {1537, 5690}, {1539, 53711}, {1594, 12138}, {1698, 12515}, {1768, 54447}, {2476, 34122}, {2771, 3812}, {2783, 61576}, {2787, 61575}, {2800, 3918}, {2801, 61577}, {2802, 9955}, {2803, 61592}, {2806, 61591}, {2826, 61581}, {2827, 61582}, {2828, 61583}, {2830, 40340}, {2831, 61586}, {2932, 37234}, {3036, 25639}, {3091, 10738}, {3523, 38754}, {3526, 38693}, {3530, 38759}, {3560, 38722}, {3627, 24466}, {3628, 6713}, {3738, 61578}, {3818, 51157}, {3826, 60911}, {3832, 13199}, {3843, 10724}, {3845, 6174}, {3850, 38758}, {3851, 12331}, {3858, 10993}, {3859, 12558}, {3887, 61579}, {4193, 34123}, {4293, 6959}, {4996, 37251}, {5055, 10711}, {5071, 38084}, {5072, 38665}, {5079, 38669}, {5141, 48667}, {5154, 18525}, {5218, 6929}, {5499, 38411}, {5790, 10698}, {5818, 19914}, {5848, 18358}, {6154, 38071}, {6246, 22935}, {6564, 48715}, {6565, 48714}, {6594, 18482}, {6668, 10021}, {6829, 13257}, {6839, 38142}, {6841, 9945}, {6852, 38135}, {6881, 13226}, {6882, 28186}, {6907, 32554}, {6924, 12943}, {6945, 38034}, {6965, 59382}, {6975, 38032}, {6980, 33108}, {6990, 12690}, {7393, 9913}, {7489, 38114}, {7514, 54065}, {7705, 40266}, {8674, 61574}, {8976, 19082}, {9024, 19130}, {9668, 32141}, {10087, 10896}, {10090, 10895}, {10109, 45310}, {10113, 53743}, {10175, 12619}, {10202, 17661}, {10265, 38182}, {10427, 60901}, {10576, 48700}, {10577, 48701}, {10707, 19709}, {11230, 11715}, {11231, 46684}, {11570, 17606}, {11793, 58543}, {12653, 38021}, {12665, 24475}, {12767, 30315}, {12811, 38629}, {12812, 38631}, {13271, 45701}, {13364, 58475}, {13374, 58687}, {13624, 58453}, {13665, 19112}, {13743, 17100}, {13754, 58504}, {13785, 19113}, {13922, 42215}, {13951, 19081}, {13991, 42216}, {14873, 30449}, {15015, 18492}, {18350, 58056}, {18524, 37375}, {18861, 45976}, {19163, 53745}, {20418, 35018}, {21850, 51007}, {22505, 53720}, {22515, 53729}, {22798, 51569}, {26364, 35249}, {26446, 34789}, {31775, 55297}, {33337, 50796}, {34127, 53722}, {34128, 53715}, {38637, 55866}, {44257, 46816}, {51706, 59419}, {58613, 58631}

X(61580) = midpoint of X(i) and X(j) for these {i,j}: {3, 22799}, {4, 33814}, {5, 119}, {10, 12611}, {11, 11698}, {100, 22938}, {153, 51529}, {214, 18480}, {355, 19907}, {546, 61562}, {550, 52836}, {1145, 22791}, {1317, 37705}, {1484, 37725}, {1537, 5690}, {1539, 53711}, {3627, 24466}, {3818, 51157}, {3845, 6174}, {6246, 22935}, {6594, 18482}, {6713, 38757}, {10113, 53743}, {10427, 60901}, {10738, 51525}, {10742, 38602}, {11793, 58543}, {12619, 21635}, {12665, 24475}, {13374, 58687}, {19163, 53745}, {21850, 51007}, {22505, 53720}, {22515, 53729}, {22798, 51569}, {34126, 38755}, {58613, 58631}, {61566, 61605}
X(61580) = reflection of X(i) in X(j) for these {i,j}: {140, 58421}, {143, 58522}, {1387, 61272}, {13624, 58453}, {38759, 3530}, {45310, 10109}, {6713, 3628}, {60759, 5}, {61562, 20400}, {61566, 6667}
X(61580) = inverse of X(11698) in nine-point circle
X(61580) = complement of X(38602)
X(61580) = pole of line {900, 11698} with respect to the nine-point circle
X(61580) = pole of line {2245, 35459} with respect to the Kiepert hyperbola
X(61580) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10742, 38602}, {5, 11698, 11}, {5, 12, 61272}, {5, 1484, 23513}, {5, 37705, 7741}, {11, 11698, 952}, {11, 119, 11698}, {12, 39692, 1387}, {100, 381, 22938}, {119, 23513, 37725}, {153, 3090, 57298}, {153, 57298, 51529}, {546, 61562, 5840}, {547, 61566, 6667}, {547, 61605, 61566}, {1656, 38755, 104}, {2829, 58421, 140}, {3091, 10738, 38141}, {3526, 38756, 38693}, {3851, 12331, 59391}, {5587, 15017, 6265}, {5818, 19914, 38177}, {5840, 20400, 61562}, {8227, 12737, 38044}, {10175, 21635, 12619}, {10711, 31272, 12773}, {22935, 38140, 6246}, {23477, 23517, 37705}, {23513, 37725, 1484}, {31235, 38761, 549}, {38141, 51525, 10738}, {38760, 52836, 550}, {39692, 61272, 60759}

X(61581) = MIDPOINT OF X(5) AND X(120)

Barycentrics    -2*(b-c)^4*(b+c)^2*(b^2+c^2)+3*a^3*b*c*(b+c)*(b^2-4*b*c+c^2)+2*a^6*(b^2+b*c+c^2)-4*a^5*(b+c)*(b^2+b*c+c^2)+a^4*(2*b^4+7*b^3*c+12*b^2*c^2+7*b*c^3+2*c^4)-a^2*(b-c)^2*(2*b^4+9*b^3*c+6*b^2*c^2+9*b*c^3+2*c^4)+a*(b-c)^2*(b+c)*(4*b^4+b^3*c-2*b^2*c^2+b*c^3+4*c^4) : :
X(61581) = 3*X[2]+X[10743], 3*X[3]+X[10729], -X[105]+5*X[1656], 3*X[381]+X[1292], X[382]+3*X[38712], 7*X[3090]+X[20344], -5*X[3091]+X[15521], -7*X[3526]+3*X[38694], -9*X[3545]+X[34547], -5*X[3843]+X[44983], 7*X[3851]+X[38589], 3*X[5055]+X[10712] and many others

X(61581) lies on these lines: {2, 10743}, {3, 10729}, {4, 38619}, {5, 120}, {105, 1656}, {140, 58422}, {381, 1292}, {382, 38712}, {528, 547}, {567, 58055}, {952, 11730}, {1358, 7951}, {2476, 34124}, {2775, 61574}, {2788, 61575}, {2795, 61576}, {2809, 9956}, {2814, 61578}, {2820, 61579}, {2826, 61580}, {2832, 61582}, {2833, 61583}, {2834, 60769}, {2835, 61585}, {2836, 20304}, {2837, 40340}, {2838, 61586}, {3021, 7741}, {3039, 3814}, {3090, 20344}, {3091, 15521}, {3526, 38694}, {3545, 34547}, {3628, 6714}, {3843, 44983}, {3851, 38589}, {5055, 10712}, {5072, 38684}, {5079, 38670}, {5540, 54447}, {5790, 10699}, {5886, 50911}, {6881, 52826}, {7486, 20097}, {9520, 61592}, {9523, 61591}, {10773, 38752}, {11230, 11716}, {18350, 58053}, {33970, 38319}, {61512, 61557}

X(61581) = midpoint of X(i) and X(j) for these {i,j}: {4, 38619}, {5, 120}, {10743, 38603}, {20344, 51530}
X(61581) = reflection of X(i) in X(j) for these {i,j}: {140, 58422}, {6714, 3628}
X(61581) = complement of X(38603)
X(61581) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10743, 38603}, {4, 57327, 38619}, {3090, 20344, 57299}, {20344, 57299, 51530}

X(61582) = MIDPOINT OF X(5) AND X(121)

Barycentrics    -3*a^4*(b+c)^3+3*a^5*(b^2+c^2)-2*(b-c)^2*(b+c)^3*(b^2-3*b*c+c^2)+2*a*(b^2-c^2)^2*(2*b^2-9*b*c+2*c^2)+a^3*(-7*b^4+18*b^3*c+8*b^2*c^2+18*b*c^3-7*c^4)+a^2*(b+c)*(5*b^4-16*b^2*c^2+5*c^4) : :
X(61582) = 3*X[2]+X[10744], 3*X[3]+X[10730], -X[106]+5*X[1656], 3*X[381]+X[1293], X[382]+3*X[38713], -3*X[547]+X[61568], -X[1054]+9*X[54447], 7*X[3090]+X[21290], -5*X[3091]+X[15522], -7*X[3526]+3*X[38695], -9*X[3545]+X[34548], -5*X[3843]+X[44984] and many others

X(61582) lies on these lines: {2, 10744}, {3, 10730}, {4, 38620}, {5, 121}, {106, 1656}, {140, 58423}, {143, 58523}, {381, 1293}, {382, 38713}, {547, 61568}, {567, 58054}, {952, 11731}, {1054, 54447}, {1357, 7951}, {2776, 61574}, {2789, 61575}, {2796, 61576}, {2802, 9956}, {2810, 24206}, {2815, 61578}, {2821, 61579}, {2827, 61580}, {2832, 61581}, {2839, 61583}, {2840, 61584}, {2841, 61585}, {2842, 20304}, {2843, 40340}, {2844, 61586}, {3038, 3814}, {3090, 21290}, {3091, 15522}, {3526, 38695}, {3545, 34548}, {3628, 6715}, {3843, 44984}, {3851, 38590}, {5055, 10713}, {5072, 38685}, {5079, 38671}, {5790, 10700}, {5886, 50914}, {6018, 7741}, {6881, 52827}, {7486, 20098}, {9524, 61592}, {9527, 61591}, {10175, 11814}, {10774, 38752}, {11230, 11717}, {11231, 14664}, {18350, 58052}, {36939, 38083}

X(61582) = midpoint of X(i) and X(j) for these {i,j}: {4, 38620}, {5, 121}, {10744, 38604}, {21290, 51531}
X(61582) = reflection of X(i) in X(j) for these {i,j}: {140, 58423}, {143, 58523}, {6715, 3628}
X(61582) = complement of X(38604)
X(61582) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10744, 38604}, {4, 57328, 38620}, {5, 121, 53790}, {3090, 21290, 57300}, {21290, 57300, 51531}

X(61583) = MIDPOINT OF X(5) AND X(122)

Barycentrics    a^14*(b^2+c^2)-(b-c)^6*(b+c)^6*(2*b^2+c^2)*(b^2+2*c^2)+a^12*(b^4-6*b^2*c^2+c^4)+a^2*(b-c)^4*(b+c)^4*(b^2+c^2)*(4*b^4-11*b^2*c^2+4*c^4)-a^10*(b^2+c^2)*(18*b^4-37*b^2*c^2+18*c^4)-a^6*(b-c)^2*(b+c)^2*(b^2+c^2)*(35*b^4+24*b^2*c^2+35*c^4)+a^8*(b^2-c^2)^2*(40*b^4+51*b^2*c^2+40*c^4)+a^4*(b^2-c^2)^2*(9*b^8+38*b^6*c^2+2*b^4*c^4+38*b^2*c^6+9*c^8) : :
X(61583) = -9*X[2]+X[5667], 3*X[3]+X[10152], -X[107]+5*X[1656], 3*X[381]+X[1294], X[382]+3*X[38714], -3*X[549]+X[3184], -5*X[631]+X[23240], 7*X[3090]+X[34186], -5*X[3091]+X[22337], -7*X[3526]+3*X[23239], -9*X[3545]+X[34549], -5*X[3843]+X[44985] and many others

X(61583) lies on these lines: {2, 5667}, {3, 10152}, {4, 38621}, {5, 122}, {30, 34842}, {107, 1656}, {140, 2777}, {143, 58524}, {381, 1294}, {382, 38714}, {547, 9530}, {549, 3184}, {567, 58067}, {631, 23240}, {952, 11732}, {2790, 23333}, {2797, 61576}, {2803, 60759}, {2811, 61577}, {2816, 3634}, {2822, 61579}, {2828, 61580}, {2833, 61581}, {2839, 61582}, {2845, 61584}, {2846, 61585}, {2847, 40340}, {2848, 61586}, {3090, 34186}, {3091, 22337}, {3324, 7951}, {3526, 23239}, {3545, 34549}, {3628, 6716}, {3843, 44985}, {3845, 38956}, {3851, 38591}, {5055, 10714}, {5066, 20203}, {5072, 38686}, {5079, 38672}, {5790, 10701}, {5886, 50916}, {6699, 15184}, {6881, 52828}, {7158, 7741}, {7393, 14673}, {7514, 14703}, {9033, 20304}, {10775, 38752}, {11230, 11718}, {13364, 58530}, {15051, 57472}, {18350, 58048}, {18570, 40082}, {34127, 53723}, {34128, 53716}, {47055, 49673}, {52057, 55856}

X(61583) = midpoint of X(i) and X(j) for these {i,j}: {3, 49117}, {4, 38621}, {5, 122}, {10745, 38605}, {34186, 51532}
X(61583) = reflection of X(i) in X(j) for these {i,j}: {140, 58424}, {143, 58524}, {6716, 3628}, {61569, 58431}, {61592, 5}
X(61583) = complement of X(38605)
X(61583) = pole of line {6086, 8552} with respect to the nine-point circle
X(61583) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 57329, 38621}, {5, 122, 53803}, {5, 53803, 61592}, {122, 36520, 5}, {547, 61569, 58431}, {3090, 34186, 57301}, {9530, 58431, 61569}, {34186, 57301, 51532}

X(61584) = MIDPOINT OF X(5) AND X(123)

Barycentrics    -(a^9*(2*b-3*c)*(3*b-2*c)*(b^2+c^2))-2*(b-c)^6*(b+c)^5*(b^2+c^2)+2*a^11*(b^2-b*c+c^2)+2*a^7*(b-c)^2*(b^2-3*b*c+c^2)*(2*b^2+b*c+2*c^2)+2*a^8*(b-c)^2*(b+c)*(3*b^2-b*c+3*c^2)-2*a^10*(b^3+c^3)-2*a^6*(b-c)^2*(b+c)*(2*b^4-9*b^3*c-9*b*c^3+2*c^4)+a*(b^2-c^2)^4*(2*b^4-9*b^3*c+6*b^2*c^2-9*b*c^3+2*c^4)+2*a^2*(b-c)^4*(b+c)^3*(3*b^4+4*b^3*c+4*b*c^3+3*c^4)+2*a^5*(b-c)^2*(2*b^6+2*b^5*c-11*b^4*c^2-10*b^3*c^3-11*b^2*c^4+2*b*c^5+2*c^6)-2*a^3*(b^2-c^2)^2*(3*b^6-10*b^5*c+2*b^3*c^3-10*b*c^5+3*c^6)-2*a^4*(b-c)^2*(2*b^7+13*b^6*c+9*b^5*c^2+9*b^2*c^5+13*b*c^6+2*c^7) : :
X(61584) = 3*X[2]+X[10746], 3*X[3]+X[10731], -X[108]+5*X[1656], 3*X[381]+X[1295], X[382]+3*X[38715], -3*X[547]+X[61570], 7*X[3090]+X[34188], -5*X[3091]+X[33566], -7*X[3526]+3*X[38696], -9*X[3545]+X[34550], -5*X[3843]+X[44986], 7*X[3851]+X[38592] and many others

X(61584) lies on these lines: {2, 10746}, {3, 10731}, {4, 38622}, {5, 123}, {108, 1656}, {140, 2829}, {143, 58525}, {381, 1295}, {382, 38715}, {547, 61570}, {567, 58063}, {952, 11733}, {1359, 7951}, {2778, 61574}, {2791, 61575}, {2798, 61576}, {2804, 60759}, {2812, 61577}, {2817, 9956}, {2823, 61579}, {2834, 60769}, {2840, 61582}, {2845, 61583}, {2849, 61585}, {2850, 20304}, {2851, 40340}, {3090, 34188}, {3091, 33566}, {3318, 7741}, {3526, 38696}, {3545, 34550}, {3628, 6717}, {3843, 44986}, {3851, 38592}, {5055, 10715}, {5072, 38687}, {5079, 38673}, {5790, 10702}, {5886, 50917}, {6881, 52829}, {7514, 54064}, {9528, 46028}, {10776, 38752}, {11230, 11719}, {18350, 58050}, {38319, 56890}

X(61584) = midpoint of X(i) and X(j) for these {i,j}: {4, 38622}, {5, 123}, {10746, 38606}, {34188, 51533}
X(61584) = reflection of X(i) in X(j) for these {i,j}: {140, 58425}, {143, 58525}, {6717, 3628}
X(61584) = complement of X(38606)
X(61584) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10746, 38606}, {4, 57330, 38622}, {2829, 58425, 140}, {3090, 34188, 57302}, {34188, 57302, 51533}

X(61585) = MIDPOINT OF X(5) AND X(124)

Barycentrics    2*a*(b-c)^6*(b+c)^3+a^8*(b^2+c^2)+6*a^5*(b-c)^2*(b+c)*(b^2+c^2)-2*(b^2-c^2)^4*(b^2-b*c+c^2)-6*a^3*(b-c)^4*(b+c)*(b^2+b*c+c^2)-2*a^7*(b^3+c^3)-a^6*(b^4-4*b^3*c+4*b^2*c^2-4*b*c^3+c^4)-a^4*(b-c)^2*(3*b^4+12*b^3*c+10*b^2*c^2+12*b*c^3+3*c^4)+a^2*(b^2-c^2)^2*(5*b^4-4*b^2*c^2+5*c^4) : :
X(61585) = 3*X[2]+X[10747], 3*X[3]+X[10732], -3*X[5]+X[117], -X[20]+5*X[38786], X[102]+3*X[381], -X[109]+5*X[1656], -X[151]+9*X[3545], X[382]+3*X[38691], -3*X[547]+2*X[58419], -3*X[549]+X[38785], -X[550]+3*X[38784], -5*X[631]+X[38777] and many others

X(61585) lies on these lines: {2, 10747}, {3, 10732}, {4, 38600}, {5, 117}, {20, 38786}, {30, 6711}, {102, 381}, {109, 1656}, {140, 58426}, {143, 58526}, {151, 3545}, {382, 38691}, {546, 61564}, {547, 58419}, {549, 38785}, {550, 38784}, {567, 58060}, {631, 38777}, {928, 61577}, {952, 11734}, {1361, 7951}, {1364, 7741}, {1539, 53713}, {1845, 17605}, {2773, 20304}, {2779, 61574}, {2785, 61576}, {2792, 61575}, {2800, 3918}, {2807, 61579}, {2816, 12571}, {2817, 9955}, {2835, 61581}, {2841, 61582}, {2846, 61583}, {2849, 61584}, {2852, 40340}, {2853, 61586}, {3040, 3814}, {3042, 25639}, {3090, 33650}, {3091, 10740}, {3523, 38778}, {3526, 38697}, {3530, 38783}, {3627, 38787}, {3628, 6718}, {3738, 60759}, {3843, 10726}, {3850, 38782}, {3851, 38573}, {5055, 10716}, {5072, 38667}, {5079, 38674}, {5790, 10703}, {5886, 13532}, {6841, 52824}, {6881, 52830}, {9532, 61591}, {10113, 53749}, {10696, 18493}, {10709, 19709}, {10777, 38752}, {11230, 11700}, {11231, 14690}, {11713, 18480}, {11727, 61272}, {13364, 58520}, {13754, 58506}, {18350, 58051}, {22515, 53731}, {22799, 53748}, {22938, 53740}, {34126, 53752}, {34127, 53724}, {34128, 53717}, {50899, 61261}

X(61585) = midpoint of X(i) and X(j) for these {i,j}: {4, 38600}, {5, 124}, {546, 61564}, {1539, 53713}, {6718, 38781}, {10113, 53749}, {10740, 51527}, {10747, 38607}, {11713, 18480}, {22515, 53731}, {22799, 53748}, {22938, 53740}, {33650, 51534}
X(61585) = reflection of X(i) in X(j) for these {i,j}: {140, 58426}, {143, 58526}, {11727, 61272}, {38783, 3530}, {6718, 3628}, {61571, 58419}, {61578, 5}
X(61585) = complement of X(38607)
X(61585) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 38776, 38600}, {5, 124, 2818}, {5, 2818, 61578}, {547, 61571, 58419}, {1656, 38779, 109}, {3090, 33650, 57303}, {3526, 38780, 38697}, {33650, 57303, 51534}

X(61586) = MIDPOINT OF X(5) AND X(127)

Barycentrics    a^12*(b^2+c^2)+a^10*(-3*b^4+2*b^2*c^2-3*c^4)-2*(b-c)^4*(b+c)^4*(b^2+c^2)*(b^4+c^4)-a^6*(b^2-c^2)^2*(2*b^4+3*b^2*c^2+2*c^4)+a^8*(b^2+c^2)*(4*b^4-7*b^2*c^2+4*c^4)+a^2*(b^2-c^2)^2*(5*b^8+3*b^6*c^2+8*b^4*c^4+3*b^2*c^6+5*c^8)-3*a^4*(b^10-b^6*c^4-b^4*c^6+c^10) : :
X(61586) = 3*X[2]+X[10749], 3*X[3]+X[10735], -X[112]+5*X[1656], 3*X[381]+X[1297], X[382]+3*X[38717], -3*X[547]+2*X[58430], -3*X[549]+X[14689], 7*X[3090]+X[13219], -5*X[3091]+X[12918], -7*X[3526]+3*X[38699], -9*X[3545]+X[12384], 7*X[3832]+X[12253] and many others

X(61586) lies on these lines: {2, 10749}, {3, 10735}, {4, 38624}, {5, 127}, {30, 34841}, {112, 1656}, {140, 2794}, {143, 58528}, {381, 1297}, {382, 38717}, {403, 12145}, {498, 13297}, {499, 13296}, {547, 58430}, {549, 14689}, {567, 58064}, {1594, 13166}, {2781, 24206}, {2799, 61576}, {2806, 60759}, {2825, 61579}, {2831, 61580}, {2838, 61581}, {2844, 61582}, {2848, 61583}, {2853, 61585}, {3090, 13219}, {3091, 12918}, {3320, 7951}, {3526, 38699}, {3545, 12384}, {3628, 6720}, {3832, 12253}, {3843, 44988}, {3851, 13115}, {5055, 10718}, {5066, 9530}, {5072, 38689}, {5079, 38676}, {5790, 10705}, {5886, 13280}, {6020, 7741}, {6564, 49219}, {6565, 49218}, {6881, 52833}, {7393, 11641}, {7514, 19165}, {8976, 19115}, {9517, 20304}, {9518, 61577}, {9532, 61578}, {10576, 49270}, {10577, 49271}, {10780, 38752}, {10895, 13117}, {10896, 13116}, {11230, 11722}, {12265, 18480}, {12784, 61261}, {13099, 18493}, {13221, 54447}, {13364, 58529}, {13565, 61588}, {13665, 19093}, {13785, 19094}, {13918, 42215}, {13951, 19114}, {13985, 42216}, {14900, 55856}, {15026, 16224}, {18350, 58049}, {28343, 38317}, {34126, 53755}, {34128, 53719}, {37242, 51454}, {38639, 55866}, {44912, 46186}

X(61586) = midpoint of X(i) and X(j) for these {i,j}: {3, 19163}, {4, 38624}, {5, 127}, {1297, 19160}, {10749, 38608}, {12265, 18480}, {13219, 51536}
X(61586) = reflection of X(i) in X(j) for these {i,j}: {140, 58428}, {143, 58528}, {6720, 3628}, {61573, 58430}, {61591, 5}
X(61586) = complement of X(38608)
X(61586) = pole of line {2881, 44813} with respect to the nine-point circle
X(61586) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10749, 38608}, {4, 57332, 38624}, {5, 127, 53795}, {5, 53795, 61591}, {381, 1297, 19160}, {547, 61573, 58430}, {2794, 58428, 140}, {3090, 13219, 57304}, {3526, 48681, 38699}, {13219, 57304, 51536}

X(61587) = MIDPOINT OF X(5) AND X(128)

Barycentrics    ((a^2-b^2)^4*(3*a^4+2*b^4)-(a^2-b^2)^2*(12*a^6-2*a^4*b^2+7*b^6)*c^2+(20*a^8-16*a^6*b^2+7*a^4*b^4-6*a^2*b^6+10*b^8)*c^4-(20*a^6+5*a^4*b^2+6*a^2*b^4+10*b^6)*c^6+(15*a^4+14*a^2*b^2+10*b^4)*c^8-(8*a^2+7*b^2)*c^10+2*c^12)*(-(b^2-c^2)^2+a^2*(b^2+c^2)) : :
X(61587) = 3*X[2]+X[31656], 3*X[3]+X[44981], 3*X[381]+X[930], X[382]+3*X[38706], -3*X[547]+X[12026], -X[1141]+5*X[1656], -7*X[3090]+3*X[57324], -7*X[3526]+3*X[38710], -9*X[3545]+X[11671], -5*X[3843]+X[44976], 7*X[3851]+X[13512], -9*X[5055]+X[38587] and many others

X(61587) lies on these lines: {2, 31656}, {3, 44981}, {4, 38615}, {5, 128}, {30, 13372}, {140, 58429}, {381, 930}, {382, 38706}, {546, 6592}, {547, 12026}, {567, 58062}, {1141, 1656}, {2072, 14769}, {3090, 57324}, {3327, 7951}, {3526, 38710}, {3545, 11671}, {3628, 5972}, {3843, 44976}, {3851, 13512}, {5055, 38587}, {5056, 47065}, {5072, 38681}, {5079, 38683}, {6288, 14071}, {7159, 7741}, {7393, 15960}, {7514, 15959}, {7550, 14652}, {10109, 25339}, {10276, 14788}, {13160, 31607}, {13505, 15056}, {14674, 54000}, {15088, 45258}, {18350, 58068}, {36518, 43966}, {44674, 50708}, {45147, 61574}

X(61587) = midpoint of X(i) and X(j) for these {i,j}: {4, 38615}, {5, 128}, {137, 14072}, {546, 6592}, {6288, 14071}, {31656, 38618}
X(61587) = reflection of X(i) in X(j) for these {i,j}: {140, 58429}, {12026, 58432}, {34837, 3628}, {45258, 15088}, {61594, 5}
X(61587) = inverse of X(14072) in nine-point circle
X(61587) = complement of X(38618)
X(61587) = pole of line {14072, 25149} with respect to the nine-point circle
X(61587) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 31656, 38618}, {4, 57316, 38615}, {5, 1263, 23516}, {5, 14072, 137}, {5, 14073, 25147}, {5, 23237, 128}, {5, 25150, 61594}, {5, 31376, 34768}, {128, 137, 14072}, {137, 14072, 25150}, {547, 12026, 58432}, {3628, 32423, 34837}

X(61588) = MIDPOINT OF X(5) AND X(129)

Barycentrics    a^2*(a^4*b^4*(a^2-b^2)^6+b^2*(a^2-b^2)^4*(a^8-2*a^6*b^2-2*a^4*b^4+2*b^8)*c^2+(a^2-b^2)^3*(a^10-3*a^8*b^2+2*a^4*b^6+8*b^10)*c^4-(a^2-b^2)^2*(6*a^10+2*a^6*b^4-a^4*b^6+2*a^2*b^8-11*b^10)*c^6+(a-b)*(a+b)*(15*a^10+7*a^8*b^2+4*a^6*b^4-2*a^4*b^6-4*a^2*b^8+4*b^10)*c^8+(-20*a^10-a^8*b^2+14*a^6*b^4+16*a^4*b^6+8*a^2*b^8-2*b^10)*c^10+(15*a^8-2*a^6*b^2-26*a^4*b^4-24*a^2*b^6-4*b^8)*c^12+(-6*a^6+10*a^4*b^2+24*a^2*b^4+11*b^6)*c^14+(a^4-8*a^2*b^2-8*b^4)*c^16+2*b^2*c^18)*(-(b^2-c^2)^2+a^2*(b^2+c^2)) : :
X(61588) = 3*X[3]+X[44989], X[4]+3*X[57335], 3*X[381]+X[1303], -X[1298]+5*X[1656], -7*X[3090]+3*X[57333], -5*X[3843]+X[44991], -9*X[5055]+X[38594], 3*X[5891]+X[21661]

X(61588) lies on these lines: {3, 44989}, {4, 57335}, {5, 129}, {30, 34839}, {381, 1303}, {567, 58065}, {1298, 1656}, {3090, 57333}, {3628, 34838}, {3843, 44991}, {5055, 38594}, {5462, 61576}, {5891, 21661}, {7393, 22551}, {13364, 61594}, {13565, 61586}, {18350, 58069}, {20304, 32438}

X(61588) = midpoint of X(i) and X(j) for these {i,j}: {5, 129}
X(61588) = reflection of X(i) in X(j) for these {i,j}: {34838, 3628}, {61589, 5}

X(61589) = MIDPOINT OF X(5) AND X(130)

Barycentrics    a^2*(a^4*b^4*(a^2-b^2)^6-b^2*(a^2-b^2)^4*(3*a^8+2*a^6*b^2-2*a^4*b^4+2*b^8)*c^2+(a^2-b^2)^3*(a^10+13*a^8*b^2+2*a^4*b^6-8*b^10)*c^4-(a^2-b^2)^2*(6*a^10+20*a^8*b^2-6*a^6*b^4-a^4*b^6-6*a^2*b^8+9*b^10)*c^6+(a-b)*(a+b)*(15*a^10+7*a^8*b^2-12*a^6*b^4-2*a^4*b^6+12*a^2*b^8+4*b^10)*c^8-(20*a^10-15*a^8*b^2+2*a^6*b^4+20*a^4*b^6+8*a^2*b^8-14*b^10)*c^10+(15*a^8-2*a^6*b^2+22*a^4*b^4+24*a^2*b^6-4*b^8)*c^12-(6*a^6+10*a^4*b^2+24*a^2*b^4+9*b^6)*c^14+(a^4+8*a^2*b^2+8*b^4)*c^16-2*b^2*c^18)*(-(b^2-c^2)^2+a^2*(b^2+c^2)) : :
X(61589) = 3*X[3]+X[44991], X[4]+3*X[57333], -3*X[5]+X[129], 3*X[381]+X[1298], -X[1303]+5*X[1656], -7*X[3090]+3*X[57335], -5*X[3843]+X[44989], 7*X[3851]+X[38594]

X(61589) lies on these lines: {3, 44991}, {4, 57333}, {5, 129}, {30, 34838}, {381, 1298}, {567, 58069}, {1303, 1656}, {3090, 57335}, {3628, 34839}, {3843, 44989}, {3851, 38594}, {18350, 58065}, {32438, 61574}

X(61589) = midpoint of X(i) and X(j) for these {i,j}: {5, 130}
X(61589) = reflection of X(i) in X(j) for these {i,j}: {34839, 3628}, {61588, 5}

X(61590) = MIDPOINT OF X(5) AND X(131)

Barycentrics    3*a^14*(b^2+c^2)-(b^2-c^2)^6*(2*b^4+3*b^2*c^2+2*c^4)-a^12*(13*b^4+10*b^2*c^2+13*c^4)+a^10*(b^2+c^2)*(22*b^4-5*b^2*c^2+22*c^4)+a^2*(b^2-c^2)^4*(8*b^6+3*b^4*c^2+3*b^2*c^4+8*c^6)-a^4*(b^2-c^2)^2*(13*b^8-2*b^6*c^2+14*b^4*c^4-2*b^2*c^6+13*c^8)-a^8*(20*b^8+19*b^6*c^2-6*b^4*c^4+19*b^2*c^6+20*c^8)+a^6*(15*b^10+b^8*c^2-4*b^6*c^4-4*b^4*c^6+b^2*c^8+15*c^10) : :
X(61590) = 3*X[3]+X[44990], X[4]+3*X[57314], 3*X[381]+X[925], -X[1300]+5*X[1656], -7*X[3090]+3*X[57334], -5*X[3091]+X[13556], -7*X[3526]+3*X[38718], -5*X[3843]+X[44974]

X(61590) lies on these lines: {3, 44990}, {4, 57314}, {5, 131}, {30, 34844}, {140, 6723}, {381, 925}, {567, 58061}, {1300, 1656}, {3090, 57334}, {3091, 13556}, {3526, 38718}, {3628, 34840}, {3843, 44974}, {7514, 13558}, {7741, 59811}, {7951, 59810}, {10003, 46029}, {18350, 58066}, {47055, 49673}, {55121, 61574}

X(61590) = midpoint of X(i) and X(j) for these {i,j}: {5, 131}
X(61590) = reflection of X(i) in X(j) for these {i,j}: {34840, 3628}, {61593, 5}
X(61590) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 131, 53802}, {5, 53802, 61593}

X(61591) = MIDPOINT OF X(5) AND X(132)

Barycentrics    3*a^12*(b^2+c^2)+3*a^8*b^2*c^2*(b^2+c^2)-2*(b-c)^4*(b+c)^4*(b^2+c^2)*(b^4+c^4)+a^6*(b^2-c^2)^2*(2*b^4-b^2*c^2+2*c^4)-a^10*(5*b^4+2*b^2*c^2+5*c^4)+a^2*(b^2-c^2)^2*(3*b^8+b^6*c^2+b^2*c^6+3*c^8)-a^4*(b^10-b^6*c^4-b^4*c^6+c^10) : :
X(61591) = -9*X[2]+X[12253], -3*X[5]+X[127], X[112]+3*X[381], X[382]+3*X[38699], -X[1297]+5*X[1656], 7*X[3090]+X[12384], -5*X[3091]+X[10749], -7*X[3526]+3*X[38717], -9*X[3545]+X[13219], 7*X[3832]+X[13200], -5*X[3843]+X[10735], 7*X[3851]+X[13310]

X(61591) lies on these lines: {2, 12253}, {3, 19160}, {4, 38608}, {5, 127}, {30, 6720}, {112, 381}, {140, 58430}, {143, 58529}, {382, 38699}, {403, 13166}, {498, 12955}, {499, 12945}, {517, 58673}, {546, 2794}, {547, 9530}, {567, 58049}, {1297, 1656}, {1503, 46173}, {1539, 53719}, {1594, 12145}, {2781, 6697}, {2799, 61575}, {2806, 61580}, {2825, 61577}, {2831, 60759}, {2848, 61592}, {2853, 61578}, {3090, 12384}, {3091, 10749}, {3320, 7741}, {3526, 38717}, {3545, 13219}, {3627, 14689}, {3628, 34841}, {3818, 28343}, {3832, 13200}, {3843, 10735}, {3851, 13310}, {3858, 14900}, {5055, 13115}, {5072, 38676}, {5079, 38689}, {5790, 13099}, {5886, 12784}, {6020, 7951}, {6033, 52951}, {6102, 16224}, {6564, 49271}, {6565, 49270}, {6841, 52833}, {7393, 12413}, {7564, 53767}, {8976, 19094}, {9517, 61574}, {9518, 61579}, {9523, 61581}, {9527, 61582}, {9532, 61585}, {10113, 53760}, {10254, 20410}, {10576, 49218}, {10577, 49219}, {10705, 18493}, {10718, 19709}, {10895, 13312}, {10896, 13311}, {11230, 12265}, {11722, 18480}, {11818, 40121}, {12106, 34217}, {12162, 16225}, {12408, 54447}, {13280, 61261}, {13665, 19114}, {13754, 58515}, {13785, 19115}, {13861, 19165}, {13923, 42215}, {13951, 19093}, {13992, 42216}, {18350, 58064}, {22515, 53737}, {22799, 53755}, {22938, 53745}, {44233, 61593}

X(61591) = midpoint of X(i) and X(j) for these {i,j}: {3, 19160}, {4, 38608}, {5, 132}, {112, 19163}, {546, 61573}, {1539, 53719}, {3627, 14689}, {3818, 28343}, {10113, 53760}, {10749, 51536}, {11722, 18480}, {12918, 38624}, {22515, 53737}, {22799, 53755}, {22938, 53745}
X(61591) = reflection of X(i) in X(j) for these {i,j}: {140, 58430}, {143, 58529}, {34841, 3628}, {61586, 5}
X(61591) = complement of X(38624)
X(61591) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12918, 38624}, {5, 132, 53795}, {5, 53795, 61586}, {112, 381, 19163}, {546, 61573, 2794}, {3526, 48658, 38717}

X(61592) = MIDPOINT OF X(5) AND X(133)

Barycentrics    3*a^14*(b^2+c^2)+a^12*(-9*b^4+6*b^2*c^2-9*c^4)-(b^2-c^2)^6*(2*b^4+7*b^2*c^2+2*c^4)+5*a^8*(b^2-c^2)^2*(4*b^4-3*b^2*c^2+4*c^4)+a^10*(2*b^6+b^4*c^2+b^2*c^4+2*c^6)+a^2*(b^2-c^2)^4*(4*b^6-13*b^4*c^2-13*b^2*c^4+4*c^6)-a^6*(b^2-c^2)^2*(25*b^6+b^4*c^2+b^2*c^4+25*c^6)+a^4*(b^2-c^2)^2*(7*b^8+34*b^6*c^2-50*b^4*c^4+34*b^2*c^6+7*c^8) : :
X(61592) = 3*X[2]+X[22337], 3*X[3]+X[44985], 3*X[4]+X[23240], -3*X[5]+X[122], X[107]+3*X[381], X[382]+3*X[23239], -3*X[547]+2*X[58424], -X[1294]+5*X[1656], 7*X[3090]+X[34549], -5*X[3091]+X[10745], -7*X[3526]+3*X[38714], -9*X[3545]+X[34186] and many others

X(61592) lies on these lines: {2, 22337}, {3, 44985}, {4, 23240}, {5, 122}, {30, 6716}, {107, 381}, {140, 58431}, {143, 58530}, {382, 23239}, {517, 58668}, {546, 2777}, {547, 58424}, {550, 38956}, {567, 58048}, {1294, 1656}, {1539, 53716}, {2790, 46030}, {2797, 61575}, {2803, 61580}, {2811, 61579}, {2816, 12571}, {2822, 61577}, {2828, 60759}, {2846, 61578}, {2848, 61591}, {3090, 34549}, {3091, 10745}, {3184, 3627}, {3324, 7741}, {3526, 38714}, {3545, 34186}, {3628, 34842}, {3832, 5667}, {3843, 10152}, {3851, 38577}, {3858, 52057}, {5055, 38591}, {5066, 9530}, {5072, 38672}, {5079, 38686}, {6841, 52828}, {7158, 7951}, {9033, 61574}, {9520, 61581}, {9524, 61582}, {9528, 46028}, {9529, 40340}, {10113, 53757}, {10701, 18493}, {10714, 19709}, {11718, 18480}, {11732, 61272}, {11897, 34601}, {11911, 47111}, {13364, 58524}, {13754, 58511}, {13861, 14703}, {18350, 58067}, {22505, 53723}, {24930, 46686}, {44235, 61593}, {50916, 61261}

X(61592) = midpoint of X(i) and X(j) for these {i,j}: {4, 38605}, {5, 133}, {107, 49117}, {546, 61569}, {550, 38956}, {1539, 53716}, {3184, 3627}, {10113, 53757}, {10745, 51532}, {11718, 18480}, {22337, 38621}, {22505, 53723}, {24930, 46686}
X(61592) = reflection of X(i) in X(j) for these {i,j}: {140, 58431}, {143, 58530}, {11732, 61272}, {34842, 3628}, {61583, 5}
X(61592) = complement of X(38621)
X(61592) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 22337, 38621}, {5, 133, 53803}, {5, 53803, 61583}, {107, 381, 49117}, {546, 61569, 2777}

X(61593) = MIDPOINT OF X(5) AND X(136)

Barycentrics    a^14*(b^2+c^2)-3*a^12*(b^2+c^2)^2-(b^2-c^2)^6*(2*b^4+b^2*c^2+2*c^4)+a^10*(b^2+c^2)*(2*b^4+9*b^2*c^2+2*c^4)+a^2*(b^2-c^2)^4*(8*b^6+b^4*c^2+b^2*c^4+8*c^6)-3*a^8*(3*b^6*c^2+2*b^4*c^4+3*b^2*c^6)-a^4*(b^2-c^2)^2*(11*b^8-6*b^6*c^2+2*b^4*c^4-6*b^2*c^6+11*c^8)+a^6*(5*b^10-5*b^8*c^2+4*b^6*c^4+4*b^4*c^6-5*b^2*c^8+5*c^10) : :
X(61593) = 3*X[2]+X[13556], 3*X[3]+X[44974], X[4]+3*X[57334], -3*X[5]+X[131], 3*X[381]+X[1300], X[382]+3*X[38718], -X[925]+5*X[1656], -7*X[3090]+3*X[57314], -5*X[3843]+X[44990]

X(61593) lies on these lines: {2, 13556}, {3, 44974}, {4, 57334}, {5, 131}, {30, 34840}, {381, 1300}, {382, 38718}, {546, 9820}, {567, 58066}, {925, 1656}, {3090, 57314}, {3628, 34844}, {3843, 44990}, {5961, 12106}, {7741, 59810}, {7951, 59811}, {11818, 39118}, {13558, 13861}, {18350, 58061}, {20304, 55121}, {23306, 34981}, {39504, 42862}, {44233, 61591}, {44235, 61592}

X(61593) = midpoint of X(i) and X(j) for these {i,j}: {5, 136}
X(61593) = reflection of X(i) in X(j) for these {i,j}: {34844, 3628}, {61590, 5}
X(61593) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 136, 53802}, {5, 53802, 61590}

X(61594) = MIDPOINT OF X(5) AND X(137)

Barycentrics    (-(b^2-c^2)^2+a^2*(b^2+c^2))*(a^12-4*a^10*(b^2+c^2)+(b^2-c^2)^4*(2*b^4-b^2*c^2+2*c^4)-2*a^2*(b-c)^2*(b+c)^2*(b^2+c^2)*(4*b^4-5*b^2*c^2+4*c^4)+a^8*(8*b^4+6*b^2*c^2+8*c^4)-12*a^6*(b^6+c^6)+a^4*(13*b^8-11*b^6*c^2+5*b^4*c^4-11*b^2*c^6+13*c^8)) : :
X(61594) = -3*X[2]+X[38615], 3*X[3]+X[44976], -3*X[5]+X[128], 3*X[381]+X[1141], X[382]+3*X[38710], X[399]+3*X[34308], -3*X[547]+X[6592], -X[930]+5*X[1656], 7*X[3090]+X[11671], -5*X[3091]+X[31656], -7*X[3526]+3*X[38706], -5*X[3843]+X[44981] and many others

X(61594) lies on these lines: {2, 38615}, {3, 44976}, {4, 38618}, {5, 128}, {30, 10615}, {125, 43966}, {140, 58432}, {252, 16764}, {381, 1141}, {382, 38710}, {399, 34308}, {403, 15367}, {546, 12026}, {547, 6592}, {567, 58068}, {930, 1656}, {3090, 11671}, {3091, 31656}, {3327, 7741}, {3526, 38706}, {3628, 13372}, {3843, 44981}, {3850, 7687}, {3851, 38587}, {5055, 13512}, {5072, 38683}, {5079, 38681}, {5191, 50471}, {5640, 13505}, {5663, 45258}, {6140, 25149}, {7159, 7951}, {7173, 14101}, {7604, 24144}, {8254, 34598}, {9781, 13504}, {12106, 23320}, {13364, 61588}, {13595, 34418}, {13861, 15959}, {14652, 34484}, {14674, 54001}, {14769, 50137}, {18350, 58062}, {19552, 24147}, {20304, 45147}, {20413, 23280}, {22804, 27196}, {32744, 44674}, {38640, 55866}

X(61594) = midpoint of X(i) and X(j) for these {i,j}: {4, 38618}, {5, 137}, {125, 43966}, {128, 1263}, {546, 12026}, {19552, 24147}, {22804, 27196}, {23516, 25147}
X(61594) = reflection of X(i) in X(j) for these {i,j}: {140, 58432}, {13372, 3628}, {3628, 25339}, {6592, 58429}, {61587, 5}
X(61594) = inverse of X(1263) in nine-point circle
X(61594) = complement of X(38615)
X(61594) = pole of line {1263, 25149} with respect to the nine-point circle
X(61594) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 1263, 128}, {5, 13856, 23281}, {5, 25147, 137}, {5, 25150, 61587}, {128, 1263, 25150}, {128, 137, 1263}, {137, 23516, 5}, {547, 6592, 58429}, {3091, 47065, 31656}

X(61595) = MIDPOINT OF X(5) AND X(142)

Barycentrics    2*a^4*b*c+a^5*(b+c)-2*(b-c)^4*(b+c)^2+3*a*(b-c)^2*(b+c)^3-4*a^3*(b+c)*(b^2+c^2)+2*a^2*(b-c)^2*(b^2-b*c+c^2) : :
X(61595) = -9*X[2]+X[5759], X[4]+3*X[38122], X[7]+7*X[3090], -X[9]+5*X[1656], X[119]+3*X[38205], -X[144]+17*X[7486], X[355]+3*X[38053], 3*X[381]+X[5732], 5*X[631]+3*X[59385], 5*X[632]+3*X[38137], X[946]+3*X[38204], X[1352]+3*X[38186] and many others

X(61595) lies on these lines: {2, 5759}, {3, 18482}, {4, 38122}, {5, 142}, {7, 3090}, {9, 1656}, {10, 20330}, {30, 60999}, {119, 38205}, {140, 516}, {144, 7486}, {355, 38053}, {381, 5732}, {390, 7743}, {485, 60921}, {486, 60920}, {517, 3826}, {518, 6583}, {527, 547}, {631, 59385}, {632, 38137}, {942, 21617}, {946, 38204}, {1001, 6911}, {1125, 40262}, {1352, 38186}, {1482, 38200}, {1538, 7988}, {1698, 38036}, {2550, 5886}, {2801, 61577}, {3091, 21151}, {3243, 5790}, {3254, 38752}, {3358, 5437}, {3525, 59418}, {3526, 21153}, {3545, 36991}, {3616, 38149}, {3624, 38031}, {3628, 5762}, {3763, 38143}, {3817, 37364}, {3825, 58608}, {3834, 48888}, {3838, 6667}, {3851, 59389}, {4312, 17605}, {4321, 9654}, {4326, 9669}, {5044, 55108}, {5055, 5779}, {5056, 5817}, {5067, 18230}, {5070, 5735}, {5071, 36996}, {5079, 59380}, {5087, 51090}, {5141, 10861}, {5220, 38179}, {5223, 54447}, {5249, 10157}, {5439, 6991}, {5528, 51517}, {5542, 10175}, {5603, 40333}, {5715, 16853}, {5728, 6829}, {5777, 60991}, {5806, 8728}, {5818, 11038}, {5833, 30827}, {5843, 35018}, {5853, 5901}, {5856, 58421}, {5880, 6862}, {5918, 41858}, {5927, 27186}, {6067, 34790}, {6684, 50394}, {6832, 37582}, {6846, 34862}, {6854, 24929}, {6858, 52457}, {6859, 60987}, {6874, 10394}, {6882, 51489}, {6887, 31445}, {6891, 38037}, {6975, 60988}, {6983, 60943}, {7504, 60969}, {7741, 14100}, {7951, 8581}, {7958, 9856}, {8226, 11227}, {8227, 10310}, {8255, 15008}, {8727, 10156}, {8732, 57282}, {9780, 38126}, {9947, 51706}, {10427, 23513}, {10595, 59413}, {11484, 60897}, {11495, 22793}, {11662, 60954}, {11793, 58472}, {12573, 15325}, {12618, 34824}, {13374, 58634}, {14561, 47595}, {14848, 51152}, {15587, 25639}, {15699, 60986}, {15733, 27869}, {16668, 45942}, {17245, 53599}, {17529, 31793}, {17567, 59412}, {17606, 18412}, {17612, 52255}, {18483, 43151}, {18493, 38121}, {19541, 41867}, {19709, 38065}, {19862, 38151}, {22835, 51100}, {24393, 38042}, {26470, 38206}, {27147, 36652}, {31235, 38152}, {31245, 54203}, {31260, 38153}, {31822, 44222}, {34753, 60945}, {37356, 42356}, {38028, 43175}, {38030, 61261}, {38113, 55856}, {38117, 47355}, {38130, 51073}, {40330, 59405}, {42582, 60914}, {42583, 60913}, {51514, 60977}, {51516, 60933}, {58561, 61033}, {58563, 58631}

X(61595) = midpoint of X(i) and X(j) for these {i,j}: {3, 18482}, {5, 142}, {10, 20330}, {5805, 31658}, {11495, 22793}, {11793, 58472}, {13374, 58634}, {18483, 43151}, {38107, 38318}, {43177, 60901}, {58563, 58631}, {61509, 61511}
X(61595) = reflection of X(i) in X(j) for these {i,j}: {140, 58433}, {6666, 3628}, {61033, 58561}
X(61595) = complement of X(31658)
X(61595) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5805, 31658}, {3, 38150, 18482}, {5, 38111, 60901}, {5, 38171, 142}, {7, 3090, 38108}, {9, 1656, 38318}, {142, 43177, 38111}, {516, 58433, 140}, {547, 61509, 61511}, {3091, 21151, 31672}, {3526, 31671, 21153}, {3628, 5762, 6666}, {18493, 38121, 43166}, {20195, 38150, 3}, {38111, 60901, 43177}, {38113, 55856, 61001}, {43177, 60901, 971}, {61509, 61511, 527}

X(61596) = MIDPOINT OF X(5) AND X(144)

Barycentrics    6*a^6-4*a^5*(b+c)-(b-c)^4*(b+c)^2-6*a*(b-c)^2*(b+c)^3+a^4*(-15*b^2+4*b*c-15*c^2)+10*a^3*(b+c)*(b^2+c^2)+2*a^2*(b-c)^2*(5*b^2+7*b*c+5*c^2) : :
X(61596) = -X[3]+5*X[61006], -4*X[142]+5*X[48154], -3*X[549]+X[36996], -X[550]+3*X[21168], -5*X[632]+3*X[59380], -X[1483]+3*X[52653], -5*X[1656]+X[20059], -7*X[3090]+3*X[51514], -2*X[3530]+3*X[59381], -2*X[3850]+3*X[5817], -3*X[3853]+2*X[52835], -4*X[3856]+3*X[59385] and many others

X(61596) lies on these lines: {3, 61006}, {5, 144}, {7, 3628}, {9, 140}, {30, 5759}, {142, 48154}, {143, 58534}, {516, 61510}, {518, 61597}, {527, 547}, {546, 5762}, {548, 971}, {549, 36996}, {550, 21168}, {632, 59380}, {952, 51090}, {1483, 52653}, {1656, 20059}, {3090, 51514}, {3219, 13257}, {3530, 59381}, {3564, 51144}, {3850, 5817}, {3853, 52835}, {3856, 59385}, {3859, 5735}, {3861, 31671}, {3927, 5804}, {4312, 38042}, {5066, 5805}, {5223, 5844}, {5732, 34200}, {5845, 61545}, {5850, 5901}, {5851, 61562}, {5856, 61601}, {6173, 47599}, {6666, 55862}, {6675, 61025}, {7525, 60897}, {10124, 61023}, {11372, 28212}, {11540, 38065}, {12100, 31658}, {12108, 21151}, {12811, 38137}, {12812, 38108}, {13925, 60913}, {13993, 60914}, {15172, 60910}, {15481, 61605}, {15587, 58632}, {15699, 60984}, {16198, 60879}, {16239, 18230}, {18481, 52665}, {18538, 60915}, {18762, 60916}, {24470, 61014}, {26446, 41705}, {28204, 50837}, {30424, 38179}, {34380, 50995}, {34753, 60961}, {35018, 38107}, {38080, 60971}, {38082, 60963}, {38171, 60933}, {38318, 60962}, {44245, 59418}, {47598, 60986}, {50205, 60969}, {50394, 60959}, {52264, 61026}

X(61596) = midpoint of X(i) and X(j) for these {i,j}: {5, 144}, {550, 60884}
X(61596) = reflection of X(i) in X(j) for these {i,j}: {140, 9}, {143, 58534}, {15587, 58632}, {3853, 60901}, {31671, 3861}, {61509, 61511}, {7, 3628}
X(61596) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 5843, 140}, {144, 51516, 5}, {527, 61511, 61509}, {18230, 38111, 16239}, {21168, 60884, 550}, {61509, 61511, 547}, {61623, 61624, 61597}

X(61597) = MIDPOINT OF X(5) AND X(145)

Barycentrics    6*a^4-8*a^3*(b+c)+8*a*(b-c)^2*(b+c)+a^2*(-5*b^2+16*b*c-5*c^2)-(b^2-c^2)^2 : :
X(61597) = -X[3]+5*X[3623], -4*X[10]+5*X[48154], -2*X[40]+3*X[34200], -2*X[355]+3*X[5066], -X[382]+9*X[58238], -3*X[546]+4*X[946], -3*X[549]+X[12245], -X[550]+3*X[7967], -4*X[551]+3*X[47598], -5*X[632]+7*X[3622], -8*X[1125]+7*X[55862], -4*X[1385]+3*X[12100] and many others

X(61597) lies on these lines: {1, 140}, {3, 3623}, {4, 61295}, {5, 145}, {8, 3628}, {10, 48154}, {30, 944}, {40, 34200}, {65, 12735}, {143, 58535}, {355, 5066}, {381, 50831}, {382, 58238}, {515, 61292}, {516, 32900}, {517, 548}, {518, 61596}, {519, 547}, {542, 51145}, {546, 946}, {549, 12245}, {550, 7967}, {551, 47598}, {632, 3622}, {1125, 55862}, {1317, 11009}, {1320, 61105}, {1385, 12100}, {1387, 33176}, {1656, 3621}, {1698, 61279}, {1885, 31948}, {2098, 15172}, {2801, 26200}, {2802, 6583}, {3090, 20014}, {3091, 61251}, {3242, 34380}, {3243, 5843}, {3295, 7508}, {3303, 12104}, {3530, 10246}, {3564, 51147}, {3576, 61282}, {3616, 16239}, {3617, 55856}, {3625, 11230}, {3627, 18526}, {3632, 38042}, {3633, 5886}, {3654, 41983}, {3655, 11531}, {3656, 14893}, {3679, 47599}, {3817, 61255}, {3845, 34748}, {3850, 5603}, {3853, 5691}, {3856, 59387}, {3857, 58236}, {3859, 5881}, {3860, 34627}, {3861, 5734}, {3874, 10284}, {3877, 50243}, {3880, 61541}, {3889, 25413}, {3892, 35004}, {4297, 15691}, {4301, 28186}, {4393, 19512}, {4677, 38022}, {4678, 5070}, {5048, 37730}, {5055, 20049}, {5067, 20052}, {5563, 33814}, {5657, 12108}, {5731, 44245}, {5790, 20050}, {5818, 10109}, {5836, 58561}, {5842, 32905}, {5846, 61545}, {5853, 61509}, {5854, 61534}, {5855, 61533}, {5882, 11278}, {6049, 37545}, {6914, 12000}, {6924, 12001}, {7373, 18221}, {7525, 12410}, {7583, 35810}, {7584, 35811}, {7979, 50708}, {7982, 12103}, {8192, 17714}, {8227, 34747}, {8703, 34631}, {9041, 61621}, {9053, 18583}, {9778, 41981}, {10021, 22837}, {10096, 47321}, {10124, 38314}, {11011, 13407}, {11224, 18481}, {11522, 61244}, {11540, 38066}, {11545, 15079}, {11567, 61566}, {11737, 50798}, {11812, 34718}, {12101, 28204}, {12135, 16198}, {12331, 45977}, {12630, 38107}, {12699, 16189}, {12702, 33923}, {12811, 18493}, {13464, 18357}, {13925, 49232}, {13993, 49233}, {14839, 61625}, {14891, 50810}, {14892, 47745}, {14988, 34791}, {15171, 37734}, {15178, 28234}, {15686, 50872}, {15687, 50818}, {15699, 31145}, {15702, 50822}, {15712, 59417}, {15973, 20041}, {16191, 41869}, {16211, 32162}, {17609, 58605}, {18483, 58237}, {18538, 35842}, {18762, 35843}, {19875, 50830}, {19907, 25416}, {19925, 61246}, {22793, 50862}, {22867, 51689}, {22912, 51691}, {23340, 24475}, {24387, 61512}, {25405, 34753}, {25917, 58675}, {26088, 31871}, {26921, 37556}, {28150, 58206}, {28194, 51095}, {28581, 61549}, {31162, 51094}, {31663, 58187}, {32153, 37622}, {33591, 51696}, {37738, 39542}, {38040, 49688}, {38165, 49690}, {38315, 51732}, {38460, 61148}, {41982, 51705}, {41989, 61260}, {42871, 60896}, {43824, 50476}, {44234, 51725}, {44682, 58230}, {44904, 61272}, {46933, 55861}, {46934, 55859}

X(61597) = midpoint of X(i) and X(j) for these {i,j}: {4, 61295}, {5, 145}, {381, 50831}, {549, 50805}, {550, 8148}, {1482, 1483}, {3244, 10222}, {3627, 18526}, {3845, 34748}, {3874, 10284}, {5882, 11278}, {7982, 34773}, {8703, 34631}, {15686, 50872}, {15687, 50818}, {18525, 61297}, {19907, 25416}, {22791, 37727}, {23340, 24475}, {32900, 58240}
X(61597) = reflection of X(i) in X(j) for these {i,j}: {10, 61278}, {140, 1}, {143, 58535}, {1385, 61281}, {12103, 34773}, {12702, 33923}, {14893, 3656}, {15690, 3655}, {18357, 13464}, {18525, 3861}, {3853, 22791}, {31871, 26088}, {34200, 50824}, {34627, 3860}, {34718, 11812}, {37705, 3850}, {47745, 61259}, {5690, 51700}, {50798, 11737}, {50810, 14891}, {50823, 10124}, {5836, 58561}, {5901, 33179}, {61246, 19925}, {61249, 9955}, {61286, 3635}, {61510, 5901}, {61524, 15178}, {8, 3628}
X(61597) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5690, 51700}, {1, 5844, 140}, {3, 3623, 61283}, {8, 10283, 3628}, {40, 61284, 50824}, {145, 10595, 12645}, {519, 33179, 5901}, {519, 5901, 61510}, {1317, 11009, 18990}, {1385, 51071, 61281}, {1482, 1483, 30}, {1482, 3241, 1483}, {1656, 3621, 59400}, {2098, 37728, 15172}, {3090, 20014, 51515}, {3244, 10222, 952}, {3616, 38112, 16239}, {3622, 59503, 632}, {3627, 61293, 18526}, {3632, 61276, 38042}, {5603, 37705, 3850}, {5690, 38028, 31423}, {5734, 61297, 3861}, {5844, 51700, 5690}, {5882, 11278, 28174}, {5901, 61510, 547}, {7967, 8148, 550}, {7982, 34773, 28212}, {7982, 61287, 34773}, {10247, 12645, 10595}, {10595, 12645, 5}, {11224, 61288, 18481}, {12245, 37624, 549}, {15178, 28234, 61524}, {16189, 61291, 12699}, {16191, 61289, 41869}, {16200, 37727, 22791}, {18493, 38138, 12811}, {22791, 28224, 3853}, {22791, 37727, 28224}, {28212, 34773, 12103}, {32900, 58240, 516}, {37624, 50805, 12245}, {38314, 50823, 10124}, {47745, 51709, 61259}, {61623, 61624, 61596}

X(61598) = MIDPOINT OF X(5) AND X(146)

Barycentrics    2*a^10-19*a^2*b^2*c^2*(b^2-c^2)^2+3*a^8*(b^2+c^2)-3*(b^2-c^2)^4*(b^2+c^2)-18*a^6*(b^4-b^2*c^2+c^4)+a^4*(b^2+c^2)*(16*b^4-27*b^2*c^2+16*c^4) : :
X(61598) = -2*X[125]+3*X[5066], -3*X[376]+5*X[22251], -3*X[549]+X[12244], -5*X[632]+3*X[15041], -X[1657]+5*X[20125], -X[3448]+3*X[3845], -2*X[3530]+3*X[14643], 3*X[3830]+X[14683], -5*X[3843]+X[12317], -4*X[3856]+3*X[14644]

X(61598) lies on these lines: {4, 11703}, {5, 146}, {30, 110}, {74, 3628}, {113, 140}, {125, 5066}, {143, 58536}, {265, 3861}, {376, 22251}, {389, 546}, {399, 3627}, {541, 547}, {542, 12101}, {548, 2777}, {549, 12244}, {550, 13392}, {632, 15041}, {690, 61599}, {1511, 12103}, {1514, 13417}, {1539, 3853}, {1657, 20125}, {1986, 44226}, {2771, 40273}, {2772, 61602}, {2773, 61603}, {2774, 61604}, {2781, 61545}, {3448, 3845}, {3530, 14643}, {3830, 14683}, {3843, 12317}, {3850, 10264}, {3856, 14644}, {3857, 15081}, {3858, 13393}, {3859, 16003}, {3860, 9140}, {5609, 13202}, {5642, 15690}, {5844, 12368}, {5893, 10628}, {5972, 12100}, {6000, 13402}, {6699, 48154}, {7525, 9919}, {7722, 10151}, {8674, 61605}, {8717, 60749}, {9143, 33699}, {9904, 38042}, {10096, 32110}, {10109, 15059}, {10113, 14893}, {10124, 38728}, {10125, 11454}, {10303, 38633}, {10657, 42136}, {10658, 42137}, {11440, 12010}, {11472, 39504}, {11558, 13754}, {11591, 44756}, {11670, 12019}, {11694, 15691}, {11699, 28186}, {11737, 20126}, {11805, 15089}, {11807, 14449}, {12102, 14094}, {12108, 15055}, {12112, 46440}, {12133, 16198}, {12168, 17714}, {12374, 15172}, {12412, 43841}, {12778, 28216}, {12811, 15054}, {12812, 36518}, {12900, 55862}, {12902, 15687}, {13171, 49671}, {13358, 13451}, {13471, 38610}, {13925, 49216}, {13993, 49217}, {14708, 44920}, {14892, 15088}, {14982, 34380}, {15020, 58196}, {15030, 15101}, {15035, 44245}, {15036, 20127}, {15046, 55856}, {15061, 35018}, {15704, 32609}, {16010, 38136}, {16111, 34200}, {16534, 34584}, {17538, 38638}, {18323, 51882}, {18507, 35311}, {18538, 35826}, {18762, 35827}, {20417, 44904}, {31726, 50708}, {32227, 47630}, {32254, 51538}, {32743, 61540}, {33535, 38034}, {38788, 58190}, {39884, 51941}, {45971, 46261}

X(61598) = midpoint of X(i) and X(j) for these {i,j}: {5, 146}, {399, 3627}, {550, 38790}, {1539, 15063}, {5609, 13202}, {9143, 33699}, {10721, 34153}, {39884, 51941}
X(61598) = reflection of X(i) in X(j) for these {i,j}: {140, 113}, {143, 58536}, {10264, 3850}, {11801, 46686}, {12103, 1511}, {13471, 38610}, {14449, 11807}, {14677, 3530}, {15690, 5642}, {15691, 11694}, {265, 3861}, {20126, 11737}, {20127, 33923}, {22051, 11805}, {3853, 1539}, {548, 10272}, {550, 13392}, {51522, 40685}, {61540, 32743}, {61548, 61574}, {74, 3628}, {9140, 3860}
X(61598) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {146, 38789, 5}, {541, 61574, 61548}, {1539, 32423, 3853}, {2777, 10272, 548}, {5655, 10721, 34153}, {5655, 7728, 10721}, {5663, 46686, 11801}, {10721, 34153, 30}, {11801, 46686, 546}, {36518, 40685, 12812}, {61548, 61574, 547}

X(61599) = MIDPOINT OF X(5) AND X(147)

Barycentrics    2*a^8+3*a^6*(b^2+c^2)-6*a^4*(b^4+b^2*c^2+c^4)-(b^2-c^2)^2*(3*b^4+b^2*c^2+3*c^4)+a^2*(4*b^6+b^4*c^2+b^2*c^4+4*c^6) : :
X(61599) = -9*X[4]+X[35369], -2*X[115]+3*X[5066], -X[148]+3*X[3845], -4*X[620]+3*X[12100], -5*X[1656]+X[5984], -2*X[3530]+3*X[15561], 3*X[3830]+X[20094], 2*X[3850]+X[52090], X[3853]+2*X[14981], -4*X[3856]+3*X[14639], -5*X[3858]+3*X[38732]

X(61599) lies on circumconic {{A, B, C, X(52094), X(54734)}} and on these lines: {4, 35369}, {5, 147}, {30, 99}, {98, 3628}, {114, 140}, {115, 5066}, {143, 58537}, {148, 3845}, {302, 48656}, {303, 48655}, {395, 6778}, {396, 6777}, {542, 547}, {543, 12101}, {546, 2782}, {548, 2794}, {549, 7931}, {550, 38744}, {620, 12100}, {671, 3860}, {690, 61598}, {952, 21636}, {1656, 5984}, {2482, 15690}, {2783, 61601}, {2784, 5901}, {2785, 61603}, {2786, 61604}, {2787, 61605}, {2792, 61539}, {3530, 15561}, {3564, 35377}, {3627, 13188}, {3830, 20094}, {3850, 52090}, {3853, 14981}, {3856, 14639}, {3858, 38732}, {3861, 6321}, {4027, 8361}, {5182, 33213}, {5305, 12830}, {5613, 40335}, {5617, 40334}, {5844, 9864}, {5986, 11548}, {5987, 37454}, {6036, 48154}, {6055, 47599}, {6721, 55862}, {7525, 9861}, {7771, 32151}, {7804, 44237}, {7922, 42787}, {8363, 10353}, {8364, 10352}, {8591, 33699}, {9860, 38042}, {9880, 41987}, {9996, 15482}, {10109, 14061}, {10124, 23234}, {10303, 38634}, {11177, 15699}, {11623, 44904}, {11632, 11737}, {11703, 45108}, {11812, 14830}, {12102, 23235}, {12103, 33813}, {12108, 34473}, {12131, 16198}, {12185, 15172}, {12243, 38071}, {12811, 38229}, {12812, 36519}, {13925, 49212}, {13993, 49213}, {14677, 14850}, {14892, 15092}, {14893, 22515}, {15687, 38733}, {15691, 38736}, {15759, 41134}, {15928, 39504}, {17538, 38635}, {17714, 39803}, {18538, 35824}, {18762, 35825}, {19710, 52695}, {21166, 44245}, {28204, 50882}, {31406, 43449}, {32552, 44382}, {32553, 44383}, {33505, 39845}, {33923, 38741}, {34200, 38749}, {35018, 38224}, {38742, 58190}, {39832, 49671}, {39838, 51524}, {47478, 49102}

X(61599) = midpoint of X(i) and X(j) for these {i,j}: {5, 147}, {550, 38744}, {3627, 13188}, {3845, 48657}, {6033, 51872}, {8591, 33699}, {14981, 22505}, {39838, 51524}
X(61599) = reflection of X(i) in X(j) for these {i,j}: {140, 114}, {143, 58537}, {11632, 11737}, {12103, 33813}, {14830, 11812}, {15690, 2482}, {3853, 22505}, {38741, 33923}, {548, 61561}, {5066, 22566}, {671, 3860}, {6321, 3861}, {61560, 61575}, {61600, 546}, {98, 3628}
X(61599) = pole of line {1649, 39091} with respect to the orthoptic circle of the Steiner inellipse
X(61599) = pole of line {2076, 6034} with respect to the Kiepert hyperbola
X(61599) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {147, 38743, 5}, {542, 61575, 61560}, {546, 2782, 61600}, {2794, 61561, 548}, {6033, 51872, 30}, {6033, 6054, 51872}, {6033, 8724, 10722}, {61560, 61575, 547}

X(61600) = MIDPOINT OF X(5) AND X(148)

Barycentrics    2*a^8-5*a^6*(b^2+c^2)+2*a^4*(b^4+5*b^2*c^2+c^4)-(b^2-c^2)^2*(3*b^4-7*b^2*c^2+3*c^4)+a^2*(b^2+c^2)*(4*b^4-11*b^2*c^2+4*c^4) : :
X(61600) = -2*X[114]+3*X[5066], -X[147]+3*X[3845], -X[550]+3*X[14651], -4*X[620]+5*X[48154], -5*X[1656]+X[20094], -2*X[2482]+3*X[47599], 7*X[3090]+X[35369], -2*X[3530]+3*X[38224], 3*X[3830]+X[5984], -2*X[3850]+3*X[14639], -5*X[3858]+3*X[38743], -5*X[3859]+2*X[14981]

X(61600) lies on these lines: {5, 148}, {30, 98}, {99, 3628}, {114, 5066}, {115, 140}, {143, 58538}, {147, 3845}, {428, 5987}, {542, 12101}, {543, 547}, {546, 2782}, {548, 23698}, {549, 12355}, {550, 14651}, {620, 48154}, {952, 11599}, {1656, 20094}, {1916, 60176}, {2482, 47599}, {2783, 61605}, {2784, 61604}, {2786, 61602}, {2787, 61601}, {2792, 61603}, {3090, 35369}, {3530, 38224}, {3627, 12188}, {3830, 5984}, {3850, 14639}, {3853, 22515}, {3858, 38743}, {3859, 14981}, {3860, 6054}, {3861, 6033}, {5055, 8596}, {5186, 16198}, {5349, 6777}, {5350, 6778}, {5461, 47598}, {5844, 13178}, {5969, 61545}, {5992, 24808}, {6034, 51732}, {6036, 12100}, {6055, 15690}, {6722, 55862}, {7525, 13175}, {8370, 10353}, {8591, 15699}, {8724, 11737}, {9166, 10124}, {9880, 14893}, {10096, 47326}, {10303, 38635}, {11177, 33699}, {11602, 23005}, {11603, 23004}, {11646, 34380}, {12042, 12103}, {12102, 38664}, {12108, 21166}, {12117, 14891}, {12243, 15687}, {12811, 23235}, {12812, 23514}, {13174, 38042}, {13183, 15172}, {13925, 49266}, {13993, 49267}, {14061, 16239}, {14062, 32520}, {14136, 25608}, {14137, 25609}, {14677, 14849}, {15092, 44904}, {15561, 35018}, {15691, 38747}, {16278, 32423}, {17538, 38634}, {17714, 39832}, {18538, 35878}, {18583, 32135}, {18762, 35879}, {23046, 48657}, {28204, 50887}, {32134, 52034}, {32515, 53419}, {33923, 38730}, {34200, 38738}, {34473, 44245}, {38220, 51700}, {38731, 58190}, {39803, 49671}, {39809, 51523}, {46169, 46172}, {54395, 57588}

X(61600) = midpoint of X(i) and X(j) for these {i,j}: {5, 148}, {549, 12355}, {550, 38733}, {3627, 12188}, {11177, 33699}, {12243, 15687}, {39809, 51523}
X(61600) = reflection of X(i) in X(j) for these {i,j}: {140, 115}, {143, 58538}, {12103, 12042}, {12117, 14891}, {14893, 9880}, {15690, 6055}, {3853, 22515}, {34200, 49102}, {38730, 33923}, {548, 61560}, {51872, 3850}, {6033, 3861}, {6054, 3860}, {61561, 61576}, {61599, 546}, {8724, 11737}, {99, 3628}
X(61600) = pole of line {5965, 11602} with respect to the Kiepert hyperbola
X(61600) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {99, 38229, 3628}, {115, 10992, 34127}, {148, 38732, 5}, {543, 61576, 61561}, {546, 2782, 61599}, {6321, 11632, 10723}, {12355, 41135, 549}, {14639, 51872, 3850}, {14651, 38733, 550}, {23698, 61560, 548}, {61561, 61576, 547}

X(61601) = MIDPOINT OF X(5) AND X(149)

Barycentrics    2*a^7-2*a^6*(b+c)-a^5*(b+c)^2-3*(b-c)^4*(b+c)^3+a^4*(b+c)*(b^2+4*b*c+c^2)+2*a^2*(b-c)^2*(b+c)*(2*b^2-b*c+2*c^2)+a*(b^2-c^2)^2*(3*b^2-5*b*c+3*c^2)+a^3*(-4*b^4+7*b^3*c-12*b^2*c^2+7*b*c^3-4*c^4) : :
X(61601) = -2*X[119]+3*X[5066], -X[153]+3*X[3845], -3*X[549]+X[13199], -5*X[1656]+X[20095], -4*X[3035]+5*X[48154], -2*X[3530]+3*X[57298], -5*X[3858]+3*X[38755], -5*X[3859]+2*X[37725], -X[5528]+3*X[38171], -X[5541]+3*X[38042]

X(61601) lies on these lines: {5, 149}, {11, 35}, {30, 104}, {80, 5844}, {100, 3628}, {119, 5066}, {143, 58539}, {153, 3845}, {528, 547}, {546, 946}, {548, 5840}, {549, 13199}, {550, 48680}, {1387, 12743}, {1483, 12747}, {1656, 20095}, {1862, 16198}, {2771, 40273}, {2783, 61599}, {2787, 61600}, {2800, 61603}, {2801, 61604}, {2802, 58674}, {2805, 61549}, {3035, 48154}, {3254, 5843}, {3530, 57298}, {3627, 12773}, {3850, 11698}, {3853, 22938}, {3858, 38755}, {3859, 37725}, {3860, 10711}, {3861, 10742}, {3887, 61602}, {5528, 38171}, {5541, 38042}, {5690, 37718}, {5790, 9802}, {5848, 61624}, {5856, 61596}, {5901, 20288}, {6174, 47599}, {6224, 10283}, {6326, 38034}, {6667, 55862}, {6713, 12100}, {7525, 13222}, {9024, 61545}, {10124, 38762}, {10247, 20085}, {10265, 28174}, {10303, 38636}, {10543, 16173}, {10609, 38044}, {12019, 12758}, {12102, 38669}, {12103, 38602}, {12108, 34474}, {12515, 28216}, {12690, 19907}, {12699, 12767}, {12737, 28224}, {12811, 38665}, {12812, 23513}, {13253, 22791}, {13274, 15172}, {13925, 48714}, {13993, 48715}, {13996, 38177}, {14217, 28212}, {14893, 22799}, {15687, 38756}, {15691, 38759}, {16239, 31272}, {17538, 38637}, {18538, 35882}, {18762, 35883}, {22935, 61272}, {24466, 34200}, {28204, 50892}, {29349, 46171}, {33337, 61278}, {33812, 61280}, {34123, 50238}, {35018, 38752}, {37722, 56790}, {38693, 44245}, {45310, 47598}, {58604, 61509}

X(61601) = midpoint of X(i) and X(j) for these {i,j}: {5, 149}, {550, 48680}, {1483, 12747}, {1484, 10738}, {3627, 12773}, {12690, 19907}, {22938, 37726}
X(61601) = reflection of X(i) in X(j) for these {i,j}: {100, 3628}, {140, 11}, {143, 58539}, {10711, 3860}, {10742, 3861}, {11698, 3850}, {12103, 38602}, {22935, 61272}, {3853, 22938}, {33337, 61278}, {548, 61566}, {61510, 61553}, {61562, 60759}, {61605, 546}
X(61601) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11, 10993, 34126}, {149, 51517, 5}, {528, 60759, 61562}, {546, 952, 61605}, {1484, 10738, 30}, {10707, 10738, 1484}, {11698, 59391, 3850}, {60759, 61562, 547}

X(61602) = MIDPOINT OF X(5) AND X(150)

Barycentrics    2*a^8-2*a^7*(b+c)+3*a*(b-c)^4*(b+c)^3+a^6*(-3*b^2+2*b*c-3*c^2)-3*(b-c)^4*(b+c)^2*(b^2+b*c+c^2)-a^4*(b^2+c^2)*(b^2+b*c+c^2)-2*a^3*(b-c)^2*(b+c)*(3*b^2+b*c+3*c^2)+a^5*(b+c)*(5*b^2-4*b*c+5*c^2)+a^2*(b-c)^2*(5*b^4+6*b^3*c+12*b^2*c^2+6*b*c^3+5*c^4) : :
X(61602) = -2*X[118]+3*X[5066], -X[152]+3*X[3845], -X[1282]+3*X[38042], -5*X[1656]+X[20096], -2*X[3530]+3*X[57297], -5*X[3858]+3*X[38767], -4*X[6710]+5*X[48154], -4*X[6712]+3*X[12100], -6*X[10124]+5*X[38774], 2*X[12102]+X[38668], -4*X[12108]+3*X[38690]

X(61602) lies on these lines: {5, 150}, {30, 103}, {101, 3628}, {116, 140}, {118, 5066}, {143, 58540}, {152, 3845}, {544, 547}, {546, 2808}, {548, 61565}, {1282, 38042}, {1656, 20096}, {2772, 61598}, {2784, 5901}, {2786, 61600}, {2801, 61509}, {2807, 61603}, {2809, 61510}, {2810, 61545}, {3530, 57297}, {3627, 38574}, {3858, 38767}, {3860, 10710}, {3861, 10741}, {3887, 61601}, {5185, 16198}, {5844, 50896}, {6710, 48154}, {6712, 12100}, {10124, 38774}, {12102, 38668}, {12103, 38601}, {12108, 38690}, {12811, 38666}, {12812, 51526}, {15687, 38768}, {15691, 38771}, {16239, 31273}, {18357, 61557}, {35018, 38764}, {38692, 44245}, {55862, 58418}

X(61602) = midpoint of X(i) and X(j) for these {i,j}: {5, 150}, {3627, 38574}
X(61602) = reflection of X(i) in X(j) for these {i,j}: {101, 3628}, {140, 116}, {143, 58540}, {10710, 3860}, {10741, 3861}, {12103, 38601}, {548, 61565}, {61563, 61577}, {61604, 546}
X(61602) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {544, 61577, 61563}, {546, 2808, 61604}, {61563, 61577, 547}

X(61603) = MIDPOINT OF X(5) AND X(151)

Barycentrics    2*a^10-2*a^9*(b+c)+3*a^8*(b+c)^2+3*a*(b-c)^6*(b+c)^3-3*(b^2-c^2)^4*(b^2-b*c+c^2)+a^7*(b+c)*(3*b^2-16*b*c+3*c^2)+a^5*(b-c)^2*(b+c)*(3*b^2+26*b*c+3*c^2)-a^3*(b-c)^4*(b+c)*(7*b^2+20*b*c+7*c^2)+a^2*b*c*(b^2-c^2)^2*(13*b^2-32*b*c+13*c^2)+a^6*(-18*b^4+7*b^3*c+32*b^2*c^2+7*b*c^3-18*c^4)+a^4*(b-c)^2*(16*b^4+3*b^3*c-22*b^2*c^2+3*b*c^3+16*c^4) : :
X(61603) = -2*X[124]+3*X[5066], -9*X[547]+8*X[58426], -2*X[3530]+3*X[57303], -3*X[3845]+X[33650], -5*X[3858]+3*X[38779], -4*X[6711]+5*X[48154], -4*X[6718]+3*X[12100], -6*X[10124]+5*X[38786], 2*X[12102]+X[38674], -4*X[12108]+3*X[38691], -4*X[12811]+X[38667]

X(61603) lies on these lines: {5, 151}, {30, 109}, {102, 3628}, {117, 140}, {124, 5066}, {143, 58541}, {546, 2818}, {547, 58426}, {548, 61571}, {928, 61604}, {2773, 61598}, {2785, 61599}, {2792, 61600}, {2800, 61601}, {2807, 61602}, {2816, 61524}, {2817, 61510}, {3530, 57303}, {3627, 38579}, {3738, 61605}, {3845, 33650}, {3858, 38779}, {3860, 10716}, {3861, 10747}, {5844, 50899}, {6711, 48154}, {6718, 12100}, {10124, 38786}, {12102, 38674}, {12103, 38607}, {12108, 38691}, {12811, 38667}, {12812, 51527}, {15687, 38780}, {15691, 38783}, {35018, 38776}, {38697, 44245}, {55862, 58419}

X(61603) = midpoint of X(i) and X(j) for these {i,j}: {5, 151}, {3627, 38579}
X(61603) = reflection of X(i) in X(j) for these {i,j}: {102, 3628}, {140, 117}, {143, 58541}, {10716, 3860}, {10747, 3861}, {12103, 38607}, {548, 61571}, {61564, 61578}
X(61603) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {61564, 61578, 547}

X(61604) = MIDPOINT OF X(5) AND X(152)

Barycentrics    2*a^8-2*a^7*(b+c)+3*a*(b-c)^4*(b+c)^3-3*(b-c)^4*(b+c)^2*(b^2+b*c+c^2)+a^6*(5*b^2+2*b*c+5*c^2)+2*a^3*(b-c)^2*(b+c)*(5*b^2+7*b*c+5*c^2)-a^5*(b+c)*(11*b^2-12*b*c+11*c^2)-a^4*(b^4+b^3*c-14*b^2*c^2+b*c^3+c^4)-a^2*(b-c)^2*(3*b^4+10*b^3*c+20*b^2*c^2+10*b*c^3+3*c^4) : :
X(61604) = -2*X[116]+3*X[5066], -X[150]+3*X[3845], -9*X[547]+8*X[58418], -2*X[3530]+3*X[38764], 3*X[3830]+X[20096], -4*X[6710]+3*X[12100], -4*X[6712]+5*X[48154], -6*X[10109]+5*X[31273], 2*X[12102]+X[38666], -4*X[12108]+3*X[38692]

X(61604) lies on these lines: {5, 152}, {30, 101}, {103, 3628}, {116, 5066}, {118, 140}, {143, 58542}, {150, 3845}, {544, 12101}, {546, 2808}, {547, 58418}, {548, 61563}, {550, 38768}, {928, 61603}, {2774, 61598}, {2784, 61600}, {2786, 61599}, {2801, 61601}, {3530, 38764}, {3627, 38572}, {3830, 20096}, {3860, 10708}, {3861, 10739}, {3887, 61605}, {5844, 50903}, {6710, 12100}, {6712, 48154}, {10109, 31273}, {12102, 38666}, {12103, 38599}, {12108, 38692}, {12811, 38668}, {12812, 51528}, {33923, 38765}, {34200, 38773}, {35018, 57297}, {38042, 39156}, {38690, 44245}, {38766, 58190}, {55862, 58420}

X(61604) = midpoint of X(i) and X(j) for these {i,j}: {5, 152}, {550, 38768}, {3627, 38572}
X(61604) = reflection of X(i) in X(j) for these {i,j}: {103, 3628}, {140, 118}, {143, 58542}, {10708, 3860}, {10739, 3861}, {12103, 38599}, {38765, 33923}, {548, 61563}, {61565, 61579}, {61602, 546}
X(61604) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {152, 38767, 5}, {61565, 61579, 547}

X(61605) = MIDPOINT OF X(5) AND X(153)

Barycentrics    2*a^7-2*a^6*(b+c)-3*(b-c)^4*(b+c)^3-a^5*(b^2-14*b*c+c^2)+a^4*(b+c)*(b^2-12*b*c+c^2)+2*a^2*(b-c)^2*(b+c)*(2*b^2+7*b*c+2*c^2)+a*(b^2-c^2)^2*(3*b^2-13*b*c+3*c^2)-a^3*(4*b^4+b^3*c-20*b^2*c^2+b*c^3+4*c^4) : :
X(61605) = -2*X[11]+3*X[5066], -X[149]+3*X[3845], -3*X[549]+X[12248], -X[1768]+3*X[38042], -4*X[3035]+3*X[12100], -2*X[3530]+3*X[38752], 3*X[3830]+X[20095], -4*X[3856]+3*X[59391], -5*X[3858]+3*X[51517], -5*X[3859]+2*X[37726]

X(61605) lies on these lines: {5, 153}, {11, 5066}, {12, 46816}, {30, 100}, {72, 39776}, {80, 3649}, {104, 3628}, {119, 140}, {143, 58543}, {149, 3845}, {528, 12101}, {546, 946}, {547, 3822}, {548, 2829}, {549, 12248}, {550, 38756}, {956, 18542}, {1484, 3850}, {1768, 38042}, {2771, 3754}, {2783, 61600}, {2787, 61599}, {2800, 56762}, {2801, 61509}, {2827, 21714}, {3035, 12100}, {3530, 38752}, {3627, 12331}, {3738, 61603}, {3830, 20095}, {3853, 22799}, {3856, 59391}, {3858, 51517}, {3859, 37726}, {3860, 10707}, {3861, 10738}, {3887, 61604}, {5690, 16128}, {5790, 9809}, {5844, 12751}, {6174, 15690}, {6264, 38034}, {6265, 28224}, {6713, 48154}, {7525, 9913}, {8674, 61598}, {10109, 31272}, {10265, 61259}, {10303, 38637}, {11545, 11571}, {12019, 17660}, {12102, 38665}, {12103, 33814}, {12108, 38693}, {12138, 16198}, {12247, 38138}, {12515, 19919}, {12653, 22791}, {12764, 15172}, {12811, 38669}, {12812, 51529}, {13925, 48700}, {13993, 48701}, {14893, 22938}, {15017, 38028}, {15481, 61596}, {15687, 48680}, {17538, 38636}, {18538, 35856}, {18762, 35857}, {19925, 58613}, {20418, 44904}, {22935, 28186}, {28204, 50909}, {28212, 34789}, {33923, 38753}, {34122, 50238}, {34200, 38761}, {34474, 44245}, {35018, 57298}, {37705, 48667}, {38754, 58190}, {51525, 52836}, {55862, 58421}, {56416, 61225}

X(61605) = midpoint of X(i) and X(j) for these {i,j}: {5, 153}, {550, 38756}, {3627, 12331}, {5690, 16128}, {10742, 11698}, {22799, 37725}, {37705, 48667}, {51525, 52836}
X(61605) = reflection of X(i) in X(j) for these {i,j}: {104, 3628}, {140, 119}, {143, 58543}, {10265, 61259}, {1484, 3850}, {10707, 3860}, {10738, 3861}, {12103, 33814}, {15690, 6174}, {3853, 22799}, {38753, 33923}, {548, 61562}, {61566, 61580}, {61601, 546}
X(61605) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {153, 38755, 5}, {546, 952, 61601}, {2829, 61562, 548}, {10711, 10742, 11698}, {10742, 11698, 30}, {61566, 61580, 547}

X(61606) = MIDPOINT OF X(5) AND X(154)

Barycentrics    6*a^10-19*a^8*(b^2+c^2)+3*(b^2-c^2)^4*(b^2+c^2)-4*a^2*(b^2-c^2)^2*(2*b^4-b^2*c^2+2*c^4)+2*a^6*(9*b^4+4*b^2*c^2+9*c^4) : :
X(61606) = 3*X[2]+X[32063], -X[64]+7*X[14869], 2*X[156]+X[61544], 2*X[206]+X[18358], X[381]+3*X[35260], X[546]+2*X[10282], -3*X[549]+X[10606], -5*X[631]+X[35450], 5*X[632]+X[1498], -5*X[1656]+X[32064], -X[1853]+3*X[15699], X[2883]+2*X[3530] and many others

X(61606) lies on these lines: {2, 32063}, {5, 154}, {30, 10192}, {51, 21841}, {64, 14869}, {140, 6000}, {143, 58544}, {156, 61544}, {184, 37942}, {206, 18358}, {381, 35260}, {468, 5890}, {546, 10282}, {547, 1503}, {549, 10606}, {631, 35450}, {632, 1498}, {1154, 13383}, {1656, 32064}, {1853, 15699}, {2390, 20575}, {2393, 13364}, {2777, 34200}, {2781, 10272}, {2883, 3530}, {3090, 14530}, {3357, 12108}, {3525, 12315}, {3542, 11402}, {3564, 10201}, {3627, 17821}, {3628, 6759}, {3819, 16197}, {3850, 18376}, {3856, 34786}, {3858, 17845}, {3861, 34785}, {5054, 5656}, {5055, 11206}, {5066, 18400}, {5067, 34780}, {5070, 34781}, {5654, 10154}, {5878, 15712}, {5891, 6676}, {5892, 6677}, {5893, 12103}, {5895, 46853}, {6146, 44108}, {6225, 15720}, {6247, 16239}, {6756, 44082}, {7505, 18914}, {7542, 18435}, {7583, 11242}, {7584, 11241}, {9919, 44832}, {10096, 58439}, {10109, 23325}, {10124, 23329}, {10151, 11464}, {10182, 12100}, {10249, 31267}, {10250, 51732}, {10300, 38795}, {10303, 13093}, {10533, 18762}, {10534, 18538}, {10675, 43102}, {10676, 43103}, {11064, 36987}, {11243, 11543}, {11244, 11542}, {11245, 37943}, {11456, 52297}, {11737, 23324}, {11812, 23328}, {12324, 46219}, {12811, 41362}, {12812, 50414}, {13367, 44226}, {13451, 44668}, {14216, 55856}, {14845, 34750}, {14855, 16196}, {15067, 41580}, {15325, 32065}, {15448, 18388}, {15693, 54050}, {15717, 48672}, {16534, 44201}, {16618, 54042}, {17813, 59399}, {18381, 35018}, {18405, 38071}, {18475, 44920}, {18950, 19347}, {19357, 44960}, {20299, 48154}, {20300, 60764}, {20427, 44682}, {22660, 44277}, {22802, 33923}, {23047, 26882}, {30402, 42143}, {30403, 42146}, {31834, 41589}, {34002, 41715}, {40660, 61272}, {40686, 55859}, {41983, 46265}, {44245, 51491}, {44904, 45185}, {46817, 52262}, {61531, 61533}

X(61606) = midpoint of X(i) and X(j) for these {i,j}: {5, 154}, {2883, 11204}, {5654, 10154}, {6759, 23332}, {15067, 41580}, {16252, 58434}, {18376, 34782}
X(61606) = reflection of X(i) in X(j) for these {i,j}: {140, 58434}, {143, 58544}, {10250, 51732}, {11204, 3530}, {12100, 10182}, {18376, 3850}, {23324, 11737}, {23325, 10109}, {23328, 11812}, {23329, 10124}, {23332, 3628}
X(61606) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6000, 58434, 140}, {6696, 16252, 14862}, {10182, 15311, 12100}, {13383, 61608, 61607}, {16252, 58434, 6000}, {44233, 61610, 61612}, {44233, 61619, 18583}

X(61607) = MIDPOINT OF X(5) AND X(155)

Barycentrics    (a^2-b^2-c^2)*(2*a^8-(b^2-c^2)^4-7*a^6*(b^2+c^2)-a^2*(b^2-c^2)^2*(b^2+c^2)+a^4*(7*b^4-6*b^2*c^2+7*c^4)) : :
X(61607) = 3*X[2]+X[12164], X[4]+3*X[3167], 3*X[381]+X[6193], -3*X[547]+2*X[5449], -3*X[549]+X[12163], -X[550]+3*X[47391], -5*X[1656]+X[11411], -5*X[3091]+X[12429], -3*X[3845]+X[12293], -9*X[5640]+X[12282], X[5878]+3*X[37497], X[6225]+3*X[54992]

X(61607) lies on these lines: {2, 12164}, {3, 11821}, {4, 3167}, {5, 6}, {20, 26864}, {25, 31802}, {30, 156}, {49, 12605}, {52, 21841}, {54, 34664}, {110, 3575}, {113, 22970}, {140, 9729}, {143, 44233}, {184, 12362}, {185, 11064}, {193, 6622}, {235, 1993}, {381, 6193}, {389, 6677}, {394, 6823}, {403, 56292}, {427, 11441}, {468, 5889}, {495, 1069}, {496, 3157}, {511, 15585}, {539, 5066}, {546, 5448}, {547, 5449}, {548, 12038}, {549, 12163}, {550, 47391}, {576, 15873}, {578, 41619}, {858, 43605}, {912, 5045}, {1092, 31829}, {1093, 59661}, {1154, 13383}, {1181, 1368}, {1192, 59551}, {1204, 16976}, {1216, 16197}, {1351, 3089}, {1568, 6146}, {1593, 37645}, {1595, 18451}, {1596, 34966}, {1598, 21850}, {1656, 11411}, {1885, 34148}, {3091, 12429}, {3193, 37368}, {3292, 43831}, {3521, 22115}, {3527, 56268}, {3530, 7689}, {3542, 12160}, {3547, 48876}, {3549, 58891}, {3627, 12118}, {3628, 12359}, {3629, 51734}, {3845, 12293}, {3850, 9927}, {3853, 17702}, {5050, 6804}, {5446, 14984}, {5480, 52016}, {5562, 6676}, {5640, 12282}, {5663, 15115}, {5876, 52262}, {5878, 37497}, {5907, 23292}, {6053, 13474}, {6090, 6815}, {6101, 16618}, {6102, 16238}, {6225, 54992}, {6241, 47090}, {6243, 37971}, {6643, 19347}, {6696, 22967}, {6756, 10539}, {6816, 11402}, {7352, 15325}, {7487, 8780}, {7499, 11444}, {7514, 9908}, {7529, 12166}, {7542, 18436}, {7553, 10540}, {7592, 45298}, {7667, 52525}, {7734, 37515}, {7789, 59556}, {8909, 42215}, {9306, 9825}, {9544, 12225}, {9545, 52069}, {9703, 18563}, {9707, 44239}, {9781, 12271}, {9786, 59543}, {9896, 61261}, {9925, 12309}, {9928, 22791}, {9932, 12106}, {9933, 37705}, {9937, 13861}, {9970, 23296}, {10011, 40326}, {10019, 50435}, {10024, 50461}, {10055, 10592}, {10071, 10593}, {10095, 12235}, {10110, 34382}, {10154, 17834}, {10192, 44277}, {10257, 34783}, {10263, 46817}, {10272, 44232}, {10297, 44076}, {10691, 10984}, {10982, 52077}, {11245, 43816}, {11426, 18537}, {11427, 11479}, {11449, 37931}, {11572, 24981}, {11585, 18445}, {11803, 13451}, {12084, 46373}, {12241, 34986}, {12259, 61272}, {12279, 47091}, {12289, 47339}, {12301, 31861}, {12310, 20125}, {12370, 43865}, {12893, 13392}, {13160, 15135}, {13352, 13488}, {13364, 58496}, {13367, 35240}, {13374, 34381}, {13490, 20424}, {13567, 58465}, {14389, 15056}, {14449, 45780}, {14516, 23047}, {14530, 31305}, {14531, 32269}, {14790, 41735}, {14853, 19588}, {15087, 50143}, {15122, 45957}, {15316, 39522}, {15887, 16625}, {16195, 35260}, {18531, 31804}, {18909, 30771}, {20302, 39504}, {20420, 41608}, {22550, 37777}, {23039, 34002}, {23335, 32139}, {26329, 42022}, {26879, 43866}, {26958, 43594}, {31803, 51720}, {32063, 34938}, {32166, 45969}, {32369, 32423}, {34609, 34781}, {34796, 38942}, {35602, 44241}, {35836, 42273}, {35837, 42270}, {37490, 44211}, {37942, 41587}, {43588, 49673}, {44201, 44516}, {44247, 51394}, {44271, 54217}, {46030, 58726}, {48154, 52104}

X(61607) = midpoint of X(i) and X(j) for these {i,j}: {5, 155}, {1147, 22660}, {1596, 34966}, {2883, 13346}, {3627, 12118}, {5448, 41597}, {5480, 52016}, {9928, 22791}, {9933, 37705}, {9970, 23296}, {12359, 15083}, {23335, 32139}, {44271, 54217}
X(61607) = reflection of X(i) in X(j) for these {i,j}: {140, 9820}, {143, 58545}, {12235, 10095}, {12259, 61272}, {12359, 3628}, {12893, 13392}, {13383, 61608}, {44158, 43839}, {46730, 44277}, {546, 5448}, {548, 12038}, {61544, 5}, {7689, 3530}, {9927, 3850}
X(61607) = X(i)-Ceva conjugate of X(j) for these {i, j}: {45300, 3}
X(61607) = pole of line {1593, 1993} with respect to the Stammler hyperbola
X(61607) = pole of line {7763, 32000} with respect to the Wallace hyperbola
X(61607) = intersection, other than A, B, C, of circumconics {{A, B, C, X(68), X(43670)}}, {{A, B, C, X(2165), X(15740)}}
X(61607) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 1353, 39571}, {5, 155, 3564}, {5, 3564, 61544}, {52, 51425, 21841}, {155, 14852, 9936}, {155, 5654, 5}, {185, 11064, 16196}, {235, 1993, 13142}, {389, 59659, 6677}, {1147, 22660, 30}, {1154, 61608, 13383}, {3542, 12160, 41588}, {5448, 41597, 44665}, {5448, 44665, 546}, {6643, 19347, 48906}, {7542, 18436, 44683}, {9820, 44158, 43839}, {10192, 46730, 44277}, {11585, 18445, 18914}, {11591, 61619, 140}, {13383, 61608, 61606}, {13754, 43839, 44158}

X(61608) = MIDPOINT OF X(5) AND X(156)

Barycentrics    2*a^10-7*a^8*(b^2+c^2)+(b^2-c^2)^4*(b^2+c^2)-2*a^2*(b^2-c^2)^2*(b^4-b^2*c^2+c^4)+4*a^6*(2*b^4+b^2*c^2+2*c^4)-2*a^4*(b^6+c^6) : :
X(61608) = 3*X[2]+X[32139], X[26]+3*X[5654], 3*X[154]+X[18569], X[155]+3*X[10201], -3*X[549]+X[32138], X[1498]+3*X[18281], -X[1658]+3*X[10192], -X[7689]+3*X[34477], -3*X[11202]+X[44242], -X[14216]+5*X[31283], X[17845]+3*X[18568]

X(61608) lies on these lines: {2, 32139}, {4, 35265}, {5, 156}, {26, 5654}, {30, 5448}, {49, 403}, {110, 10024}, {113, 13367}, {140, 5663}, {143, 21841}, {154, 18569}, {155, 10201}, {185, 44452}, {265, 35487}, {389, 44232}, {468, 6102}, {546, 13403}, {549, 32138}, {550, 11064}, {578, 46030}, {1147, 15761}, {1154, 13383}, {1199, 21451}, {1216, 25337}, {1495, 11819}, {1498, 18281}, {1503, 10224}, {1594, 10540}, {1614, 2072}, {1656, 18911}, {1658, 10192}, {1885, 43394}, {2883, 11250}, {3089, 39522}, {3530, 32210}, {3542, 12161}, {3549, 15068}, {3564, 19155}, {3574, 13490}, {3589, 18553}, {3628, 13561}, {3850, 18379}, {3851, 14389}, {5012, 50143}, {5066, 8254}, {5498, 6696}, {5609, 12827}, {5876, 7542}, {5891, 7568}, {5944, 12605}, {6000, 23336}, {6639, 11441}, {6640, 11456}, {6676, 11591}, {6677, 12006}, {6759, 13371}, {7505, 18445}, {7583, 32170}, {7584, 32169}, {7689, 34477}, {7728, 35491}, {9544, 16868}, {9545, 44958}, {9704, 12022}, {9705, 50435}, {9707, 18404}, {9714, 31815}, {10018, 34783}, {10019, 10113}, {10020, 13754}, {10095, 44233}, {10125, 44158}, {10226, 15311}, {10254, 14516}, {10255, 34224}, {10257, 13491}, {10263, 37971}, {10575, 15122}, {10610, 34664}, {10619, 36518}, {10627, 16618}, {10982, 44275}, {11202, 44242}, {11423, 45967}, {11464, 18563}, {11542, 32208}, {11543, 32207}, {11750, 44110}, {11799, 34148}, {11808, 13451}, {12103, 46114}, {12106, 12233}, {12241, 44235}, {12412, 34864}, {12900, 18128}, {13160, 18350}, {13292, 37942}, {13406, 44665}, {13630, 16238}, {14156, 46850}, {14216, 31283}, {14449, 25338}, {14862, 14915}, {14940, 43605}, {15067, 34002}, {15120, 37984}, {15325, 32143}, {16197, 32142}, {16619, 45186}, {17845, 18568}, {18377, 34782}, {18388, 31830}, {18439, 37118}, {18475, 52073}, {18583, 18874}, {18914, 44911}, {18952, 19347}, {20304, 45732}, {20773, 32364}, {21659, 23323}, {22467, 59648}, {31834, 34577}, {32358, 43844}, {34798, 37931}, {35266, 38322}, {37347, 43598}, {37452, 52525}, {37495, 47096}, {43595, 44960}, {43651, 50139}, {43831, 51393}, {44213, 46730}, {44407, 50414}, {45959, 52262}, {45970, 46031}

X(61608) = midpoint of X(i) and X(j) for these {i,j}: {5, 156}, {1147, 15761}, {1658, 22660}, {2883, 11250}, {5448, 10282}, {6759, 13371}, {9820, 16252}, {13383, 61607}, {18377, 34782}
X(61608) = reflection of X(i) in X(j) for these {i,j}: {140, 58435}, {143, 58546}, {13561, 3628}, {18379, 3850}, {23336, 43839}, {32210, 3530}, {44158, 10125}, {6696, 5498}
X(61608) = pole of line {11412, 11440} with respect to the Stammler hyperbola
X(61608) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {49, 403, 12370}, {113, 13367, 52070}, {140, 10272, 59659}, {5448, 10282, 30}, {5663, 58435, 140}, {6000, 43839, 23336}, {16534, 44516, 5907}, {44158, 58434, 10125}, {45959, 58407, 52262}, {61606, 61607, 13383}

X(61609) = MIDPOINT OF X(5) AND X(157)

Barycentrics    2*a^12-7*a^10*(b^2+c^2)+(b^2-c^2)^4*(b^4+c^4)-a^2*(b-c)^2*(b+c)^2*(b^2+c^2)*(5*b^4-8*b^2*c^2+5*c^4)+2*a^4*(b^2-c^2)^2*(5*b^4+7*b^2*c^2+5*c^4)+a^8*(11*b^4+6*b^2*c^2+11*c^4)-2*a^6*(6*b^6+b^4*c^2+b^2*c^4+6*c^6) : :
X(61609) = -5*X[1656]+X[41761]

X(61609) lies on these lines: {5, 157}, {30, 37813}, {53, 7746}, {140, 1503}, {468, 33971}, {1656, 41761}, {2790, 6036}, {2871, 18583}, {3564, 19156}, {3628, 23333}, {3850, 18380}, {3934, 16197}, {6676, 26880}, {7542, 18437}, {7886, 58408}, {13383, 32428}, {18953, 19347}, {20477, 32832}, {25337, 61618}, {44233, 61532}

X(61609) = midpoint of X(i) and X(j) for these {i,j}: {5, 157}
X(61609) = reflection of X(i) in X(j) for these {i,j}: {140, 58436}, {18380, 3850}, {23333, 3628}
X(61609) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {140, 61610, 61611}, {1503, 58436, 140}

X(61610) = MIDPOINT OF X(5) AND X(159)

Barycentrics    2*a^12+4*a^4*b^2*c^2*(b^2-c^2)^2-3*a^10*(b^2+c^2)+(b^2-c^2)^4*(b^2+c^2)^2-3*a^8*(b^4+6*b^2*c^2+c^4)+2*a^6*(b^2+c^2)*(3*b^4+4*b^2*c^2+3*c^4)-a^2*(b^2-c^2)^2*(3*b^6+b^4*c^2+b^2*c^4+3*c^6) : :
X(61610) = 3*X[2]+X[39879], 3*X[154]+X[1352], X[546]+2*X[15582], 3*X[547]+2*X[15580], -X[1353]+3*X[19153], -5*X[1656]+X[36851], -X[3357]+3*X[21167], 7*X[3619]+X[34781], 2*X[3628]+X[15581], -5*X[3763]+X[14216], -X[5596]+5*X[14530], X[5878]+3*X[31884]

X(61610) lies on these lines: {2, 39879}, {3, 35219}, {5, 159}, {6, 21841}, {30, 15577}, {140, 1503}, {141, 6759}, {143, 58547}, {154, 1352}, {156, 206}, {182, 1660}, {468, 6776}, {511, 15585}, {542, 58439}, {546, 15582}, {547, 15580}, {548, 35228}, {1351, 37971}, {1353, 19153}, {1614, 26926}, {1656, 36851}, {2393, 13364}, {2883, 3098}, {3357, 21167}, {3530, 44883}, {3542, 19459}, {3619, 34781}, {3628, 15581}, {3763, 14216}, {3818, 34782}, {3827, 5901}, {3850, 18382}, {5596, 14530}, {5878, 31884}, {5893, 29317}, {5894, 55649}, {6756, 20987}, {7499, 11206}, {7542, 18440}, {7667, 13203}, {8549, 31267}, {8550, 23042}, {9833, 10516}, {9924, 14561}, {9967, 51425}, {10018, 39874}, {10154, 37488}, {10300, 32125}, {10539, 13562}, {10691, 41602}, {11202, 44882}, {11414, 28419}, {11574, 59659}, {11591, 34146}, {11898, 41719}, {12100, 15578}, {14643, 38885}, {14810, 15311}, {14927, 47090}, {15068, 16618}, {15583, 38317}, {16196, 17821}, {16238, 23041}, {20427, 55646}, {21850, 34787}, {22051, 44668}, {22802, 48881}, {25337, 61545}, {25338, 61624}, {26156, 52525}, {34117, 34380}, {34507, 34774}, {34750, 37649}, {34777, 59399}, {36989, 39884}, {47093, 51212}, {48672, 55639}, {48880, 51491}, {58434, 58445}, {61626, 61628}

X(61610) = midpoint of X(i) and X(j) for these {i,j}: {5, 159}, {141, 6759}, {2883, 3098}, {3818, 34782}, {15580, 20300}, {15581, 23300}, {15585, 16252}, {19149, 48876}, {21850, 34787}, {22802, 48881}, {34507, 34774}, {36989, 39884}, {48880, 51491}
X(61610) = reflection of X(i) in X(j) for these {i,j}: {140, 58437}, {143, 58547}, {18382, 3850}, {20299, 34573}, {23300, 3628}, {44883, 3530}, {548, 35228}, {61542, 24206}
X(61610) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1503, 24206, 61542}, {1503, 34573, 20299}, {1503, 58437, 140}, {15585, 16252, 511}, {61606, 61612, 44233}

X(61611) = MIDPOINT OF X(5) AND X(160)

Barycentrics    b^2*c^2*(b^2-c^2)^4+2*a^10*(b^2+c^2)-a^8*(7*b^4+12*b^2*c^2+7*c^4)+a^2*(b^2-c^2)^2*(b^6-2*b^4*c^2-2*b^2*c^4+c^6)+a^6*(9*b^6+8*b^4*c^2+8*b^2*c^4+9*c^6)-5*a^4*(b^8-b^6*c^2-b^2*c^6+c^8) : :
X(61611) =

X(61611) lies on these lines: {5, 160}, {114, 6676}, {140, 1503}, {182, 52261}, {468, 43461}, {546, 39506}, {626, 16197}, {1506, 6748}, {2393, 10003}, {3628, 34845}, {59531, 59654}

X(61611) = midpoint of X(i) and X(j) for these {i,j}: {5, 160}
X(61611) = reflection of X(i) in X(j) for these {i,j}: {140, 58438}, {34845, 3628}
X(61611) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {140, 61610, 61609}, {1503, 58438, 140}

X(61612) = MIDPOINT OF X(5) AND X(161)

Barycentrics    2*a^16-7*a^14*(b^2+c^2)+(b^2-c^2)^6*(b^2+c^2)^2+a^6*(b-c)^2*(b+c)^2*(b^2+c^2)*(3*b^4+2*b^2*c^2+3*c^4)+3*a^10*(b^2+c^2)*(3*b^4+4*b^2*c^2+3*c^4)+a^12*(5*b^4+2*b^2*c^2+5*c^4)-a^2*(b^2-c^2)^4*(5*b^6+b^4*c^2+b^2*c^4+5*c^6)-3*a^8*(5*b^8+4*b^6*c^2+6*b^4*c^4+4*b^2*c^6+5*c^8)+a^4*(b^2-c^2)^2*(7*b^8-4*b^6*c^2+2*b^4*c^4-4*b^2*c^6+7*c^8) : :
X(61612) =

X(61612) lies on these lines: {5, 161}, {140, 13470}, {143, 16252}, {159, 10201}, {184, 21841}, {547, 58437}, {1503, 25337}, {1594, 9920}, {2393, 13364}, {6676, 18474}, {6677, 18475}, {10020, 34782}, {10282, 44232}, {13383, 61544}, {13490, 56924}, {16197, 21243}, {18445, 37971}, {23336, 34785}, {32358, 32379}

X(61612) = midpoint of X(i) and X(j) for these {i,j}: {5, 161}
X(61612) = reflection of X(i) in X(j) for these {i,j}: {140, 58439}
X(61612) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {18400, 58439, 140}, {44233, 61610, 61606}

X(61613) = MIDPOINT OF X(5) AND X(164)

Barycentrics    sqrt(b*(b^2-(-a+c)^2))*(2*a^5-(b-c)^3*(b+c)^2+3*a*(b^2-c^2)^2-5*a^3*(b^2+c^2)+a^2*(b^3-b^2*c+b*c^2-c^3))+sqrt(c*(-(a-b)^2+c^2))*(2*a^5+(b-c)^3*(b+c)^2+3*a*(b^2-c^2)^2-5*a^3*(b^2+c^2)+a^2*(-b^3+b^2*c-b*c^2+c^3))+sqrt(a*(a^2-(b-c)^2))*(-2*a^5+(b-c)^2*(b+c)^3-3*a*(b^2-c^2)^2+5*a^3*(b^2+c^2)-a^2*(b^3+b^2*c+b*c^2+c^3)) : :

X(61613) lies on these lines: {3, 58708}, {5, 164}, {30, 58709}, {140, 53810}, {177, 34753}, {355, 55168}, {547, 58707}, {549, 12844}, {632, 58713}, {952, 12523}, {1483, 55175}, {1656, 9807}, {3090, 58706}, {3628, 21633}, {5067, 58716}, {5070, 58717}, {5886, 55169}, {5901, 55174}, {10283, 12656}, {12614, 40273}, {15699, 58711}, {16239, 58719}, {18357, 55171}, {35018, 58705}, {48154, 58718}, {55170, 61272}, {55172, 61286}, {55173, 61278}, {55176, 61281}, {55856, 58712}, {61535, 61617}

X(61613) = midpoint of X(i) and X(j) for these {i,j}: {5, 164}
X(61613) = reflection of X(i) in X(j) for these {i,j}: {140, 58440}, {21633, 3628}, {40273, 12614}, {55173, 61278}, {61286, 55172}
X(61613) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {53810, 58440, 140}

X(61614) = MIDPOINT OF X(5) AND X(165)

Barycentrics    6*a^4+2*a^3*(b+c)-2*a*(b-c)^2*(b+c)+3*(b^2-c^2)^2-a^2*(9*b^2+4*b*c+9*c^2) : :
X(61614) = -X[1]+7*X[14869], -5*X[4]+29*X[46930], X[8]+11*X[15720], X[10]+2*X[3530], X[40]+5*X[632], -X[145]+25*X[631], X[355]+5*X[15712], -X[382]+13*X[19877], -X[546]+4*X[3634], X[548]+2*X[9956], X[550]+5*X[1698], -X[946]+4*X[16239] and many others

X(61614) lies on these lines: {1, 14869}, {2, 28174}, {3, 5260}, {4, 46930}, {5, 165}, {8, 15720}, {10, 3530}, {12, 5131}, {30, 10164}, {40, 632}, {140, 517}, {143, 58548}, {145, 631}, {354, 34753}, {355, 15712}, {381, 28182}, {382, 19877}, {484, 5326}, {498, 24470}, {515, 12100}, {516, 547}, {546, 3634}, {548, 9956}, {549, 952}, {550, 1698}, {946, 16239}, {962, 46219}, {1006, 12690}, {1385, 3625}, {1482, 10303}, {1483, 30392}, {1656, 9812}, {1699, 15699}, {2801, 58674}, {3035, 10176}, {3336, 34502}, {3523, 34773}, {3524, 5790}, {3525, 12702}, {3526, 22791}, {3528, 46932}, {3529, 46931}, {3533, 18493}, {3579, 3628}, {3616, 55863}, {3627, 35242}, {3632, 61290}, {3653, 61283}, {3654, 10283}, {3740, 47742}, {3828, 28160}, {3845, 54447}, {3850, 31730}, {3853, 12512}, {3911, 5049}, {4015, 26201}, {4301, 45760}, {4669, 51084}, {4677, 50832}, {4746, 31662}, {5010, 12019}, {5054, 5657}, {5055, 9778}, {5066, 10172}, {5067, 48661}, {5070, 6361}, {5432, 5719}, {5442, 15888}, {5445, 37730}, {5587, 8703}, {5603, 15694}, {5663, 52796}, {5691, 46853}, {5731, 15693}, {5771, 10202}, {5843, 38130}, {5844, 10165}, {5886, 11539}, {5919, 15325}, {6175, 38142}, {6907, 32554}, {7294, 11010}, {7508, 61553}, {7967, 15708}, {7987, 37705}, {8227, 55859}, {9519, 61567}, {9588, 16200}, {9779, 15703}, {9940, 58688}, {9955, 28232}, {10109, 50808}, {10124, 11230}, {10299, 46933}, {10592, 58887}, {10593, 59316}, {10627, 58487}, {10942, 21164}, {11277, 61622}, {11362, 51700}, {11540, 51709}, {11545, 37600}, {12101, 28158}, {12104, 26086}, {12433, 24914}, {12571, 44904}, {12699, 55856}, {12811, 51118}, {12812, 18483}, {13369, 58632}, {13587, 38058}, {13624, 28236}, {13993, 31439}, {14893, 28154}, {15686, 61260}, {15687, 19876}, {15690, 28168}, {15691, 28172}, {15697, 50800}, {15701, 50824}, {15702, 59417}, {15704, 16192}, {15706, 38074}, {15707, 53620}, {15709, 38022}, {15716, 50864}, {15717, 18525}, {15718, 34627}, {15719, 50798}, {15721, 34718}, {15723, 34632}, {15726, 61511}, {15735, 38774}, {15759, 50796}, {16191, 61277}, {16881, 31737}, {17340, 59680}, {17504, 19875}, {17549, 34122}, {18480, 33923}, {18481, 44682}, {18907, 31441}, {19708, 54448}, {19711, 50811}, {22793, 35018}, {23046, 61264}, {28194, 47598}, {28202, 47478}, {28204, 41983}, {28443, 34474}, {29353, 61527}, {30389, 61295}, {31162, 61270}, {31399, 58190}, {31443, 43291}, {31649, 59326}, {31666, 47745}, {31673, 44245}, {31835, 40296}, {34380, 38118}, {34628, 61257}, {37438, 61512}, {37712, 38081}, {38176, 44580}, {47359, 50980}, {50823, 61287}, {50865, 61266}, {50949, 51137}, {50950, 50987}, {50952, 51184}, {50977, 51124}, {51066, 61247}, {53809, 57306}, {55861, 61268}, {58615, 58643}, {59675, 61031}

X(61614) = midpoint of X(i) and X(j) for these {i,j}: {3, 38042}, {5, 165}, {10, 17502}, {549, 26446}, {1385, 38127}, {3576, 38112}, {3579, 3817}, {3654, 10283}, {3655, 59400}, {4677, 61293}, {5587, 8703}, {5657, 38028}, {5690, 10246}, {6684, 58441}, {9940, 58688}, {10164, 11231}, {10165, 50821}, {17504, 19875}, {34773, 59388}, {38176, 51705}, {50811, 61251}, {50823, 61287}, {50824, 59503}, {58615, 58643}
X(61614) = reflection of X(i) in X(j) for these {i,j}: {140, 58441}, {143, 58548}, {10165, 11812}, {1699, 61267}, {11230, 10124}, {16200, 61278}, {17502, 3530}, {18357, 38042}, {3817, 3628}, {40273, 3817}, {5066, 10172}, {61246, 59388}, {61269, 2}, {61280, 38028}, {61286, 10246}
X(61614) = complement of X(38034)
X(61614) = pole of line {4977, 31131} with respect to the orthoptic circle of the Steiner inellipse
X(61614) = pole of line {17496, 45341} with respect to the Steiner inellipse
X(61614) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 28174, 61269}, {3, 38042, 28186}, {5, 165, 28178}, {10, 17502, 28224}, {40, 632, 61272}, {140, 61524, 5901}, {140, 6684, 61524}, {517, 58441, 140}, {549, 38112, 3576}, {550, 1698, 61259}, {1699, 15699, 61267}, {3530, 28224, 17502}, {3576, 26446, 38112}, {3576, 38112, 952}, {3579, 3628, 40273}, {3579, 3817, 28216}, {3628, 28216, 3817}, {3634, 31663, 546}, {5054, 5657, 38028}, {5445, 52793, 37730}, {5587, 8703, 28190}, {5844, 11812, 10165}, {6684, 58441, 517}, {10124, 28212, 11230}, {10164, 11231, 30}, {10165, 50821, 5844}, {10172, 28146, 5066}, {15701, 59503, 54445}, {15713, 50826, 3654}, {16192, 61261, 15704}, {22793, 51073, 35018}, {28186, 38042, 18357}, {51088, 51705, 44580}, {54445, 59503, 50824}, {61539, 61562, 61628}

X(61615) = MIDPOINT OF X(5) AND X(170)

Barycentrics    10*a^2*b^2*(b-c)^2*c^2+2*a^7*(b+c)+b*(b-c)^4*c*(b+c)^2+a^6*(-6*b^2+2*b*c-6*c^2)+a*(b-c)^4*(b+c)*(b^2+c^2)+3*a^5*(b+c)*(b^2-6*b*c+c^2)-6*a^3*(b-c)^2*(b+c)*(b^2+b*c+c^2)+a^4*(2*b^2-b*c+2*c^2)*(3*b^2+8*b*c+3*c^2) : :
X(61615) = -X[550]+3*X[47641], -5*X[15712]+3*X[52155]

X(61615) lies on these lines: {5, 170}, {140, 43158}, {516, 548}, {550, 47641}, {2140, 40273}, {2808, 61524}, {3579, 43168}, {3628, 34848}, {15712, 52155}, {34753, 39789}

X(61615) = midpoint of X(i) and X(j) for these {i,j}: {5, 170}, {3579, 43168}
X(61615) = reflection of X(i) in X(j) for these {i,j}: {140, 43158}, {34848, 3628}, {40273, 2140}

X(61616) = MIDPOINT OF X(5) AND X(171)

Barycentrics    2*a^7+a^5*(-5*b^2+2*b*c-5*c^2)+5*a*b*c*(b^2-c^2)^2+(b-c)^2*(b+c)^3*(b^2-b*c+c^2)+a^3*(3*b^4-7*b^3*c-6*b^2*c^2-7*b*c^3+3*c^4)-a^2*(b^5+b^3*c^2+b^2*c^3+c^5) : :
X(61616) = -5*X[1656]+X[4388], 7*X[3090]+X[20101]

X(61616) lies on these lines: {5, 171}, {140, 517}, {547, 752}, {750, 30448}, {1656, 4388}, {2792, 61560}, {3090, 20101}, {3628, 3846}, {9025, 18583}, {9956, 38456}, {61526, 61554}

X(61616) = midpoint of X(i) and X(j) for these {i,j}: {5, 171}
X(61616) = reflection of X(i) in X(j) for these {i,j}: {140, 58443}, {3846, 3628}
X(61616) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {517, 58443, 140}, {61554, 61562, 61526}

X(61617) = MIDPOINT OF X(5) AND X(177)

Barycentrics    ((b^2-c^2)^2-a^2*(b^2+c^2))*cos(A/2)+(a^4+2*(b^2-c^2)^2-3*a^2*(b^2+c^2))*cos(B/2)+(a^4+2*(b^2-c^2)^2-3*a^2*(b^2+c^2))*cos(C/2)+(a^4+(b^2-c^2)^2-2*a^2*(b^2+c^2))*(sin((A-B)/2)+sin((A-C)/2)) : :

X(61617) lies on these lines: {5, 177}, {140, 58444}, {912, 12813}, {952, 12908}, {1483, 11191}, {1656, 11691}, {3628, 18258}, {5571, 58561}, {7670, 38107}, {8422, 10283}, {14988, 31768}, {28174, 31790}, {32183, 61278}, {55174, 61541}, {61535, 61613}

X(61617) = midpoint of X(i) and X(j) for these {i,j}: {5, 177}
X(61617) = reflection of X(i) in X(j) for these {i,j}: {140, 58444}, {18258, 3628}, {32183, 61278}, {5571, 58561}

X(61618) = MIDPOINT OF X(5) AND X(183)

Barycentrics    2*a^8-7*a^6*(b^2+c^2)+(b^2-c^2)^2*(b^4-8*b^2*c^2+c^4)-a^2*(b^2+c^2)*(7*b^4-24*b^2*c^2+7*c^4)+a^4*(11*b^4+6*b^2*c^2+11*c^4) : :
X(61618) = -5*X[1656]+X[7774], -X[11163]+3*X[15699]

X(61618) lies on these lines: {5, 183}, {30, 8722}, {140, 620}, {524, 547}, {1656, 7774}, {3090, 7941}, {3628, 3815}, {6321, 59635}, {6390, 49793}, {7697, 37459}, {7822, 16239}, {7886, 48154}, {7915, 55862}, {10356, 12811}, {10796, 13468}, {11163, 15699}, {11594, 25338}, {25337, 61609}, {32189, 61625}, {34229, 35930}

X(61618) = midpoint of X(i) and X(j) for these {i,j}: {5, 183}
X(61618) = reflection of X(i) in X(j) for these {i,j}: {140, 58446}, {3815, 3628}
X(61618) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2782, 58446, 140}, {7697, 37688, 37459}

X(61619) = MIDPOINT OF X(5) AND X(184)

Barycentrics    2*a^10-7*a^8*(b^2+c^2)+(b^2-c^2)^4*(b^2+c^2)+4*a^6*(2*b^4+b^2*c^2+2*c^4)-2*a^4*(b^6-2*b^4*c^2-2*b^2*c^4+c^6)-2*a^2*(b^8-b^6*c^2-b^2*c^6+c^8) : :
X(61619) = -5*X[1656]+X[11442], 3*X[6800]+X[31723], -X[7502]+3*X[13394], -X[8541]+3*X[59399], -3*X[34513]+X[44239]

X(61619) lies on circumconic {{A, B, C, X(34449), X(54498)}} and on these lines: {2, 15032}, {5, 156}, {6, 10201}, {30, 11430}, {49, 13160}, {54, 10024}, {110, 37347}, {140, 9729}, {143, 13383}, {154, 11818}, {161, 13861}, {376, 59771}, {381, 14389}, {389, 10020}, {399, 48411}, {403, 567}, {468, 5946}, {511, 25337}, {542, 547}, {546, 8254}, {549, 11064}, {578, 15761}, {1154, 6676}, {1199, 58805}, {1209, 43844}, {1495, 13490}, {1503, 39504}, {1568, 37513}, {1614, 5576}, {1656, 11442}, {1658, 12233}, {1660, 46030}, {1994, 7552}, {2072, 5012}, {2387, 20576}, {2393, 13364}, {2875, 61533}, {3448, 54000}, {3521, 35491}, {3547, 16266}, {3549, 6515}, {3574, 11819}, {3575, 5944}, {3580, 15087}, {3628, 21243}, {3796, 14791}, {5133, 10540}, {5446, 12242}, {5448, 52073}, {5449, 43588}, {5462, 44232}, {5562, 7568}, {5609, 37454}, {5654, 7514}, {5663, 52262}, {5892, 5972}, {5907, 6689}, {6000, 44236}, {6101, 34002}, {6102, 7542}, {6639, 7592}, {6677, 13363}, {6800, 31723}, {7495, 23039}, {7499, 15067}, {7502, 13394}, {7505, 36753}, {7540, 26881}, {7564, 9833}, {7577, 11003}, {7706, 11202}, {7745, 19627}, {8541, 59399}, {8780, 56965}, {9704, 14516}, {9715, 31815}, {9730, 44452}, {10018, 37481}, {10019, 43865}, {10095, 21841}, {10096, 58551}, {10182, 16531}, {10192, 12106}, {10254, 12022}, {10282, 31830}, {10605, 18580}, {10610, 12605}, {10627, 16197}, {11264, 61544}, {11272, 14917}, {11427, 39522}, {11438, 34477}, {11464, 38321}, {11563, 16657}, {11649, 13451}, {11799, 15033}, {12006, 16238}, {12007, 45969}, {12100, 46114}, {12241, 13406}, {13292, 32136}, {13391, 16618}, {13561, 18914}, {13568, 15331}, {14156, 16836}, {14449, 22051}, {14788, 18350}, {14790, 43841}, {14805, 52069}, {14852, 17809}, {14862, 46849}, {15053, 44214}, {15367, 58068}, {15807, 44226}, {16655, 33332}, {16881, 18282}, {18128, 32767}, {18451, 60763}, {19347, 32140}, {22352, 51392}, {23336, 40647}, {26879, 43845}, {31181, 46264}, {31833, 32171}, {34330, 47296}, {34513, 44239}, {34545, 37943}, {35487, 43821}, {37440, 45089}, {37452, 61134}, {37636, 50461}, {43651, 50143}, {43831, 52070}, {44234, 58434}, {44665, 46029}, {44911, 45298}, {44920, 61574}, {45780, 58480}, {47391, 50008}

X(61619) = midpoint of X(i) and X(j) for these {i,j}: {5, 184}, {18388, 18475}
X(61619) = reflection of X(i) in X(j) for these {i,j}: {140, 58447}, {143, 58550}, {21243, 3628}, {47328, 10095}
X(61619) = pole of line {52, 44242} with respect to the Jerabek hyperbola
X(61619) = pole of line {7526, 11412} with respect to the Stammler hyperbola
X(61619) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {54, 10024, 12370}, {140, 15806, 9820}, {140, 61607, 11591}, {389, 44516, 10020}, {12006, 58435, 16238}, {13630, 58407, 140}, {18388, 18475, 30}, {18583, 44233, 13364}, {18583, 61606, 44233}, {37649, 51425, 5}

X(61620) = MIDPOINT OF X(5) AND X(189)

Barycentrics    2*a^10-2*a*(b-c)^6*(b+c)^3-3*(b-c)^4*(b+c)^6+2*a^7*(b+c)*(b^2+c^2)-3*a^8*(3*b^2-4*b*c+3*c^2)+2*a^2*(b-c)^2*(b+c)^2*(2*b^2+b*c+2*c^2)*(3*b^2-2*b*c+3*c^2)-2*a^5*(b-c)^2*(b+c)*(3*b^2+2*b*c+3*c^2)+2*a^3*(b-c)^4*(b+c)*(3*b^2+4*b*c+3*c^2)+2*a^6*(9*b^4-19*b^3*c+12*b^2*c^2-19*b*c^3+9*c^4)-2*a^4*(b-c)^2*(10*b^4+3*b^3*c+6*b^2*c^2+3*b*c^3+10*c^4) : :
X(61620) = -5*X[1656]+X[20211], 7*X[3090]+X[20215], -3*X[15699]+X[60876], -4*X[16239]+5*X[20197], -4*X[20201]+5*X[48154]

X(61620) lies on these lines: {5, 189}, {140, 20205}, {223, 3628}, {515, 548}, {1656, 20211}, {3090, 20215}, {15699, 60876}, {16239, 20197}, {20201, 48154}, {34371, 61545}

X(61620) = midpoint of X(i) and X(j) for these {i,j}: {5, 189}
X(61620) = reflection of X(i) in X(j) for these {i,j}: {140, 20205}, {223, 3628}

X(61621) = MIDPOINT OF X(5) AND X(190)

Barycentrics    2*a^6-2*a^5*(b+c)-3*a*(b-c)^2*(b+c)^3+a^4*(-5*b^2+2*b*c-5*c^2)+5*a^3*(b+c)*(b^2+c^2)+(b^2-c^2)^2*(b^2+b*c+c^2)+a^2*(2*b^4-3*b^3*c-8*b^2*c^2-3*b*c^3+2*c^4) : :
X(61621) = 3*X[2]+X[24844], -X[3]+5*X[4473], 3*X[381]+X[24817], -3*X[549]+X[24813], -X[903]+3*X[15699], -5*X[1656]+X[4440], X[3627]+13*X[52885], 3*X[5055]+X[17487], X[5066]+2*X[36522], 3*X[5886]+X[24821], -3*X[10283]+X[24841], -3*X[11230]+X[53601] and many others

X(61621) lies on these lines: {2, 24844}, {3, 4473}, {5, 190}, {30, 4370}, {140, 4422}, {143, 58553}, {381, 24817}, {495, 24846}, {496, 24845}, {528, 61510}, {536, 61528}, {537, 5901}, {545, 547}, {546, 29243}, {549, 24813}, {900, 61562}, {903, 15699}, {952, 4432}, {1086, 3628}, {1656, 4440}, {2325, 29331}, {2786, 61561}, {2796, 9956}, {3627, 52885}, {3850, 24827}, {4437, 34380}, {5055, 17487}, {5066, 36522}, {5690, 7609}, {5843, 16593}, {5845, 61545}, {5886, 24821}, {9041, 61597}, {9055, 18583}, {10283, 24841}, {10592, 24836}, {10593, 24837}, {11230, 53601}, {13861, 24822}, {15325, 24816}, {19116, 24819}, {19117, 24818}, {20533, 51516}, {21841, 24814}, {24715, 38042}, {27191, 55856}, {32029, 59399}, {36237, 38752}, {36477, 54389}, {40480, 48154}, {61511, 61549}, {61522, 61558}

X(61621) = midpoint of X(i) and X(j) for these {i,j}: {5, 190}
X(61621) = reflection of X(i) in X(j) for these {i,j}: {140, 4422}, {143, 58553}, {1086, 3628}, {24827, 3850}

X(61622) = MIDPOINT OF X(5) AND X(191)

Barycentrics    2*a^7+a^4*(b+c)^3-2*a^2*(b-c)^2*(b+c)^3+(b-c)^4*(b+c)^3-a*(b^2-c^2)^2*(3*b^2+b*c+3*c^2)-a^5*(7*b^2+2*b*c+7*c^2)+a^3*(8*b^4+3*b^3*c+3*b*c^3+8*c^4) : :
X(61622) = 3*X[2]+X[13465], X[8]+3*X[28453], -3*X[549]+X[16132], -X[1483]+3*X[5426], -5*X[1656]+X[14450], -X[2475]+3*X[38042], 7*X[3090]+X[31888], 3*X[5790]+X[15680], X[7701]+3*X[26446], -3*X[10246]+7*X[15676], -3*X[10283]+X[16126], -2*X[11277]+3*X[61614] and many others

X(61622) lies on these lines: {2, 13465}, {5, 191}, {8, 28453}, {10, 30}, {12, 1749}, {21, 952}, {79, 3614}, {119, 3652}, {140, 2771}, {442, 19919}, {549, 16132}, {758, 5901}, {1125, 12009}, {1385, 44254}, {1483, 5426}, {1656, 14450}, {1737, 45065}, {2475, 38042}, {3090, 31888}, {3584, 13995}, {3628, 11263}, {3649, 34753}, {5428, 15931}, {5659, 16139}, {5690, 13743}, {5771, 6841}, {5790, 15680}, {6675, 10202}, {7701, 26446}, {10246, 15676}, {10283, 16126}, {10955, 16141}, {10993, 47033}, {11277, 61614}, {11684, 51409}, {12623, 61512}, {13852, 56288}, {15672, 50824}, {15674, 38028}, {17757, 52126}, {17768, 61511}, {18990, 41542}, {21677, 31649}, {24470, 41697}, {28443, 34773}, {31650, 33858}, {31835, 59719}, {32141, 37292}, {32157, 61510}, {33592, 61269}, {34195, 61278}, {35016, 61286}, {37230, 61259}

X(61622) = midpoint of X(i) and X(j) for these {i,j}: {5, 191}, {10, 22936}, {442, 19919}, {3652, 5499}, {5690, 13743}, {13465, 33668}, {16139, 16160}, {21677, 31649}
X(61622) = reflection of X(i) in X(j) for these {i,j}: {140, 58449}, {1385, 44254}, {11263, 3628}, {34195, 61278}, {37230, 61259}, {40273, 6841}, {5901, 10021}, {61286, 35016}
X(61622) = complement of X(33668)
X(61622) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 13465, 33668}, {10, 22936, 30}, {758, 10021, 5901}, {2771, 58449, 140}, {16139, 16160, 28174}

X(61623) = MIDPOINT OF X(5) AND X(192)

Barycentrics    -2*a^4*b*c+2*a^5*(b+c)+3*a*(b-c)^2*(b+c)^3-b*c*(b^2-c^2)^2+3*a^2*b*c*(b^2+c^2)-5*a^3*(b+c)*(b^2+c^2) : :
X(61623) = -X[3]+5*X[4704], X[546]+4*X[4681], -5*X[632]+7*X[27268], -X[1278]+5*X[1656], 7*X[3090]+X[4788], X[3644]+4*X[35018], -4*X[3739]+5*X[48154], -3*X[3853]+2*X[52852], -5*X[4687]+4*X[16239], -2*X[4688]+3*X[47599], -8*X[4698]+7*X[55862], -5*X[4699]+7*X[55856] and many others

X(61623) lies on these lines: {3, 4704}, {5, 192}, {30, 4664}, {37, 140}, {75, 3628}, {143, 58554}, {381, 51047}, {518, 61596}, {536, 547}, {546, 4681}, {549, 51039}, {632, 27268}, {726, 5901}, {740, 61510}, {742, 61545}, {952, 3993}, {984, 5844}, {1278, 1656}, {3090, 4788}, {3644, 35018}, {3739, 48154}, {3853, 52852}, {3995, 37365}, {4687, 16239}, {4688, 47599}, {4698, 55862}, {4699, 55856}, {4718, 12812}, {4740, 15699}, {4755, 47598}, {4772, 5070}, {4821, 5067}, {5843, 51058}, {5886, 49445}, {9055, 18583}, {9956, 28522}, {10124, 51048}, {10222, 49520}, {10247, 31302}, {10283, 24349}, {11230, 50117}, {11737, 51040}, {14891, 51044}, {14893, 51038}, {15686, 51064}, {15687, 51043}, {30271, 34200}, {34380, 49509}, {38042, 49474}, {49479, 61278}, {49532, 61276}

X(61623) = midpoint of X(i) and X(j) for these {i,j}: {5, 192}, {381, 51047}, {549, 51039}, {10222, 49520}, {15686, 51064}, {15687, 51043}, {20430, 51046}
X(61623) = reflection of X(i) in X(j) for these {i,j}: {140, 37}, {143, 58554}, {14893, 51038}, {34200, 51045}, {49479, 61278}, {51040, 11737}, {51044, 14891}, {51048, 10124}, {61549, 61522}, {75, 3628}
X(61623) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {536, 61522, 61549}, {4664, 20430, 51046}, {20430, 51046, 30}, {51048, 51488, 10124}, {61522, 61549, 547}, {61596, 61597, 61624}

X(61624) = MIDPOINT OF X(5) AND X(193)

Barycentrics    6*a^6-15*a^4*(b^2+c^2)-(b^2-c^2)^2*(b^2+c^2)+2*a^2*(5*b^4-4*b^2*c^2+5*c^4) : :
X(61624) = -5*X[3]+9*X[33748], -X[141]+3*X[15520], -X[182]+3*X[8584], -X[546]+4*X[576], -X[549]+3*X[5032], -X[550]+3*X[14912], -4*X[597]+3*X[47598], -2*X[599]+3*X[47599], -5*X[632]+7*X[51171], -2*X[1350]+3*X[34200], -2*X[1352]+3*X[5066], -5*X[1656]+X[20080] and many others

X(61624) lies on these lines: {3, 33748}, {5, 193}, {6, 140}, {30, 1351}, {69, 3628}, {141, 15520}, {143, 34382}, {182, 8584}, {195, 21841}, {381, 50986}, {428, 14683}, {468, 11004}, {511, 548}, {518, 61596}, {524, 547}, {542, 12101}, {546, 576}, {549, 5032}, {550, 14912}, {597, 47598}, {599, 47599}, {632, 51171}, {952, 51196}, {1350, 34200}, {1352, 5066}, {1493, 21637}, {1503, 48942}, {1570, 5305}, {1656, 20080}, {1993, 6677}, {1994, 6676}, {3180, 52263}, {3181, 52266}, {3530, 5050}, {3543, 51172}, {3589, 22330}, {3618, 16239}, {3620, 55856}, {3627, 39899}, {3630, 38317}, {3631, 25555}, {3751, 5844}, {3793, 32447}, {3845, 5921}, {3850, 14853}, {3853, 5102}, {3859, 15069}, {3860, 11180}, {3861, 18440}, {5052, 32515}, {5071, 51175}, {5095, 32423}, {5159, 37644}, {5476, 14892}, {5843, 51194}, {5847, 61510}, {5848, 61601}, {5901, 34379}, {5965, 11803}, {6144, 12812}, {6193, 14914}, {6329, 40107}, {6467, 10263}, {6756, 46444}, {7508, 37492}, {7525, 37491}, {7766, 56370}, {7774, 10011}, {8537, 16198}, {8550, 37517}, {8681, 13451}, {8703, 55584}, {9777, 10128}, {9825, 37493}, {10095, 14913}, {10096, 32113}, {10109, 14848}, {10124, 50978}, {10519, 12108}, {11008, 35018}, {11160, 15699}, {11179, 15690}, {11255, 43588}, {11422, 47582}, {11432, 45073}, {11477, 12103}, {11548, 45794}, {11594, 39912}, {11737, 50955}, {13392, 52699}, {13861, 19588}, {14449, 32284}, {14645, 61561}, {14810, 58187}, {14891, 50967}, {14893, 20423}, {15122, 47463}, {15448, 19155}, {15516, 20583}, {15533, 38079}, {15686, 51028}, {15687, 48662}, {15691, 44882}, {15692, 51181}, {15694, 51179}, {15702, 51184}, {15712, 55705}, {15759, 55629}, {15988, 50205}, {16475, 51700}, {16619, 47281}, {16981, 37899}, {17504, 55692}, {17714, 19459}, {18396, 31802}, {18919, 23335}, {19139, 44233}, {19154, 33591}, {21167, 55710}, {21356, 51174}, {21358, 50985}, {22862, 51206}, {22906, 51207}, {25338, 61610}, {25406, 44245}, {26864, 47630}, {26869, 47629}, {26926, 32165}, {27377, 59661}, {29181, 55718}, {33239, 33684}, {33750, 55595}, {33878, 33923}, {34507, 44904}, {34774, 34788}, {35283, 44107}, {35400, 51211}, {35404, 51213}, {36749, 40318}, {37454, 37779}, {37645, 37911}, {37784, 52262}, {41624, 43461}, {41982, 51737}, {41983, 54173}, {41987, 47353}, {44234, 47457}, {44264, 52238}, {44452, 47461}, {44682, 55697}, {45759, 54174}, {46267, 50982}, {46817, 53778}, {46853, 55593}, {48881, 55721}, {48901, 51022}, {48904, 55717}, {48920, 55719}, {49505, 61278}, {50965, 55581}, {50970, 55625}, {50983, 55709}, {50987, 51214}, {51138, 55690}, {55610, 58190}, {56021, 60693}

X(61624) = midpoint of X(i) and X(j) for these {i,j}: {5, 193}, {381, 50986}, {549, 50962}, {550, 44456}, {576, 3629}, {1351, 1353}, {3627, 39899}, {6467, 10263}, {8550, 37517}, {11477, 48906}, {15686, 51028}, {15687, 50974}, {16619, 47281}, {34774, 34788}, {44882, 55720}, {46817, 53778}, {48874, 55722}, {48881, 55721}
X(61624) = reflection of X(i) in X(j) for these {i,j}: {140, 6}, {143, 58555}, {11180, 3860}, {12103, 48906}, {14893, 20423}, {14913, 10095}, {15690, 11179}, {18440, 3861}, {18583, 5097}, {26926, 32165}, {3589, 22330}, {3631, 25555}, {3853, 21850}, {33878, 33923}, {34200, 50979}, {40107, 6329}, {48876, 51732}, {49505, 61278}, {50955, 11737}, {50967, 14891}, {50978, 10124}, {50982, 46267}, {69, 3628}, {61545, 18583}
X(61624) = pole of line {1656, 7748} with respect to the Kiepert hyperbola
X(61624) = pole of line {5422, 6090} with respect to the Stammler hyperbola
X(61624) = pole of line {3533, 32817} with respect to the Wallace hyperbola
X(61624) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 48876, 51732}, {69, 11482, 59399}, {69, 59399, 3628}, {193, 5093, 5}, {524, 18583, 61545}, {524, 5097, 18583}, {576, 3629, 3564}, {1351, 1353, 30}, {1351, 1992, 1353}, {6144, 53858, 14561}, {8981, 13966, 44535}, {11179, 55722, 48874}, {14912, 44456, 550}, {18583, 61545, 547}, {34380, 51732, 48876}, {34382, 58555, 143}, {44882, 51132, 55720}, {48876, 51732, 140}, {50978, 59373, 10124}, {61596, 61597, 61623}

X(61625) = MIDPOINT OF X(5) AND X(194)

Barycentrics    -(b^2*c^2*(b^2-c^2)^2)+2*a^6*(b^2+c^2)-a^4*(5*b^4+12*b^2*c^2+5*c^4)+3*a^2*(b^6+c^6) : :
X(61625) = 3*X[2]+X[32520], X[4]+3*X[32519], -3*X[262]+2*X[3850], -3*X[549]+X[12251], -X[550]+3*X[7709], -5*X[1656]+X[20081], X[1657]+3*X[44434], 7*X[3090]+X[20105], -3*X[3097]+X[5690], -2*X[3530]+3*X[11171], -5*X[3858]+3*X[48663], -4*X[3934]+5*X[48154] and many others

X(61625) lies on these lines: {2, 32520}, {3, 7766}, {4, 32519}, {5, 194}, {30, 3095}, {39, 140}, {76, 3628}, {99, 32134}, {143, 58556}, {262, 3850}, {397, 32466}, {398, 32465}, {511, 548}, {538, 547}, {546, 2782}, {549, 12251}, {550, 7709}, {698, 18583}, {726, 5901}, {730, 61510}, {732, 61545}, {1569, 7745}, {1656, 20081}, {1657, 44434}, {3090, 20105}, {3094, 34380}, {3097, 5690}, {3104, 42925}, {3105, 42924}, {3530, 11171}, {3564, 32449}, {3853, 14881}, {3858, 48663}, {3934, 48154}, {5007, 33813}, {5066, 6248}, {5188, 34200}, {5368, 38748}, {5844, 12782}, {6194, 15712}, {6321, 7858}, {6683, 55862}, {7525, 9917}, {7697, 35018}, {7781, 10796}, {7786, 16239}, {7798, 10104}, {8703, 32522}, {9466, 47599}, {9821, 33923}, {9902, 38042}, {10109, 11055}, {11812, 61132}, {12100, 13334}, {12108, 22712}, {12143, 16198}, {12836, 15172}, {13331, 51732}, {13925, 49252}, {13993, 49253}, {14839, 61597}, {14891, 33706}, {14893, 44422}, {18502, 23235}, {18538, 35866}, {18762, 35867}, {18906, 59399}, {20576, 59546}, {22676, 41981}, {31276, 55856}, {32189, 61618}, {32467, 35002}, {32470, 42215}, {32471, 42216}, {32523, 44245}, {44562, 47598}, {46180, 61539}, {54187, 55167}

X(61625) = midpoint of X(i) and X(j) for these {i,j}: {5, 194}, {550, 48673}, {3095, 32448}, {32449, 52997}
X(61625) = reflection of X(i) in X(j) for these {i,j}: {140, 39}, {143, 58556}, {14893, 44422}, {18583, 44423}, {3853, 14881}, {32521, 3530}, {33706, 14891}, {548, 32516}, {61550, 11272}, {76, 3628}, {9821, 33923}
X(61625) = pole of line {24206, 44453} with respect to the Kiepert hyperbola
X(61625) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {39, 32515, 140}, {194, 32447, 5}, {511, 32516, 548}, {538, 11272, 61550}, {698, 44423, 18583}, {3095, 32448, 30}, {3095, 7757, 32448}, {7709, 48673, 550}, {11171, 32521, 3530}, {11272, 61550, 547}, {20576, 59546, 61561}

X(61626) = MIDPOINT OF X(5) AND X(197)

Barycentrics    2*a^10-4*a^7*b*c*(b+c)+2*a*b*(b-c)^4*c*(b+c)^3+a^8*(-5*b^2+4*b*c-5*c^2)+10*a^5*b*c*(b+c)*(b^2+c^2)+(b^2-c^2)^4*(b^2+c^2)+4*a^4*(b-c)^2*(b^2+b*c+c^2)*(b^2+3*b*c+c^2)-4*a^3*b*(b-c)^2*c*(b+c)*(2*b^2+3*b*c+2*c^2)+2*a^6*(b^4-5*b^3*c-5*b*c^3+c^4)-2*a^2*(b^2-c^2)^2*(2*b^4+b^3*c-4*b^2*c^2+b*c^3+2*c^4) : :
X(61626) = -5*X[1656]+X[36844]

X(61626) lies on these lines: {5, 197}, {33, 21841}, {140, 515}, {1656, 36844}, {3628, 23304}, {5432, 36985}, {16197, 34822}, {25337, 61562}, {26487, 52259}, {44233, 44670}, {61526, 61531}, {61610, 61628}

X(61626) = midpoint of X(i) and X(j) for these {i,j}: {5, 197}
X(61626) = reflection of X(i) in X(j) for these {i,j}: {23304, 3628}

X(61627) = MIDPOINT OF X(5) AND X(198)

Barycentrics    2*a^9+2*a^8*(b+c)+(b-c)^4*(b+c)^5+a*(b-c)^4*(b+c)^2*(b^2+c^2)+3*a^4*(b-c)^2*(b+c)*(3*b^2+2*b*c+3*c^2)-a^2*(b-c)^2*(b+c)^3*(5*b^2-8*b*c+5*c^2)-a^6*(b+c)*(7*b^2-4*b*c+7*c^2)-a^7*(7*b^2+4*b*c+7*c^2)-a^3*(b-c)^2*(5*b^4+14*b^3*c+22*b^2*c^2+14*b*c^3+5*c^4)+a^5*(9*b^4+10*b^3*c+6*b^2*c^2+10*b*c^3+9*c^4) : :
X(61627) = -5*X[1656]+X[21279]

X(61627) lies on these lines: {5, 198}, {140, 971}, {1656, 21279}, {1827, 21841}, {2807, 61563}, {3628, 21239}, {5432, 15430}, {8679, 18583}, {44233, 44670}, {61540, 61546}

X(61627) = midpoint of X(i) and X(j) for these {i,j}: {5, 198}
X(61627) = reflection of X(i) in X(j) for these {i,j}: {21239, 3628}

X(61628) = MIDPOINT OF X(5) AND X(200)

Barycentrics    2*a^7-4*a^6*(b+c)+(b-c)^4*(b+c)^3+a^5*(-3*b^2+4*b*c-3*c^2)+9*a^4*(b+c)*(b^2+c^2)+a*(b^2-c^2)^2*(b^2+10*b*c+c^2)-2*a^2*(b-c)^2*(b+c)*(3*b^2+5*b*c+3*c^2)-2*a^3*b*c*(7*b^2+6*b*c+7*c^2) : :
X(61628) = -5*X[1656]+X[36845], 7*X[3090]+X[20015], -3*X[15699]+X[31146], -5*X[31249]+7*X[55856], X[37822]+3*X[46917]

X(61628) lies on these lines: {5, 200}, {140, 20103}, {210, 5771}, {518, 61535}, {519, 547}, {912, 58650}, {952, 997}, {1656, 36845}, {2801, 58674}, {3090, 20015}, {3579, 59687}, {3628, 11019}, {3697, 52265}, {5719, 18391}, {5780, 7080}, {5790, 6859}, {6001, 31835}, {6684, 58629}, {11729, 59400}, {15699, 31146}, {15733, 61511}, {17625, 34753}, {18491, 28174}, {21075, 37281}, {31249, 55856}, {37822, 46917}, {44847, 49176}, {52796, 61166}, {60759, 60761}, {61610, 61626}

X(61628) = midpoint of X(i) and X(j) for these {i,j}: {5, 200}, {3579, 59687}
X(61628) = reflection of X(i) in X(j) for these {i,j}: {140, 20103}, {11019, 3628}
X(61628) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {61510, 61551, 5901}, {61539, 61562, 61614}

X(61629) = X(3)X(6) ∩ X(155)X(157)

Barycentrics    a^2*(a^10-3*(b^2+c^2)*a^8+2*(3*b^4+4*b^2*c^2+3*c^4)*a^6-10*(b^2+c^2)*(b^4+c^4)*a^4+(9*b^8-2*b^4*c^4+9*c^8)*a^2-(b^4-c^4)*(b^2-c^2)*(3*b^4-2*b^2*c^2+3*c^4)) : :

See Kadir Altintas and César Lozada, Romantics of Geometry 14151 - Feb 10, 2024.

X(61629) lies on these lines: {3, 6}, {4, 8905}, {25, 52032}, {155, 157}, {317, 59228}, {427, 14593}, {1352, 52347}, {1993, 60776}, {3135, 33586}, {3148, 44716}, {5446, 15827}, {5480, 59702}, {6403, 9723}, {6503, 47328}, {9744, 59226}, {12160, 44200}, {18420, 44388}, {18494, 23698}, {39641, 39642}

X(61629) = pole of the line {2, 60776} with respect to the Stammler hyperbola
X(61629) = pole of the line {76, 6193} with respect to the Steiner-Wallace hyperbola
X(61629) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (3, 1351, 571), (3, 41169, 6)

X(61630) = X(1)X(3) ∩ X(144)X(4308)

Barycentrics    a*(a+b-c)*(a-b+c)*(a^4-4*(b+c)*a^3+2*(b^2+16*b*c+c^2)*a^2+4*(b+c)*(b^2-4*b*c+c^2)*a-3*(b^2-c^2)^2) : :

See Tran Viet Hung and César Lozada, Romantics of Geometry - Feb 10, 2024.

X(61630) lies on these lines: {1, 3}, {144, 4308}, {269, 45219}, {279, 19604}, {1149, 7273}, {1201, 36636}, {1476, 3928}, {3243, 6049}, {3600, 60961}, {3680, 5435}, {3877, 7091}, {4311, 12246}, {4853, 8170}, {5316, 8165}, {5665, 38314}, {8166, 50443}, {8169, 8583}, {10106, 18228}, {11523, 61014}, {12447, 37709}, {50810, 56038}, {58679, 60937}

X(61630) = (X(56), X(7991))-harmonic conjugate of X(57)

X(61631) = X(2)X(11623) ∩ X(3)X(64)

Barycentrics    a^2*(a^6 + 4*a^4*b^2 - 7*a^2*b^4 + 2*b^6 + 4*a^4*c^2 - 2*a^2*b^2*c^2 + 6*b^4*c^2 - 7*a^2*c^4 + 6*b^2*c^4 + 2*c^6) : :

X(61631) lies on these lines: {2, 11623}, {3, 64}, {23, 30270}, {32, 3292}, {39, 11284}, {187, 6090}, {468, 7801}, {574, 2502}, {576, 11328}, {1316, 45330}, {1995, 36212}, {3117, 7772}, {5028, 5106}, {5112, 7818}, {5158, 8542}, {6390, 61507}, {7813, 61506}, {8722, 15066}, {9027, 58265}, {9177, 14685}, {11171, 16187}, {18860, 35259}, {21512, 55637}, {23061, 37465}, {34511, 40132}, {37479, 40916}, {37914, 52987}, {39785, 47597}, {41266, 53097}

X(61631) = crossdifference of every pair of points on line {6587, 9185}
X(61631) = {X(5651),X(9155)}-harmonic conjugate of X(574)

X(61632) = X(15)X(9155) ∩ X(16)X(5651)

Barycentrics    a^2*(2*a^8 - 2*a^6*b^2 + 3*a^4*b^4 - 4*a^2*b^6 + b^8 - 2*a^6*c^2 + 3*a^4*b^2*c^2 + 6*a^2*b^4*c^2 + b^6*c^2 + 3*a^4*c^4 + 6*a^2*b^2*c^4 + 12*b^4*c^4 - 4*a^2*c^6 + b^2*c^6 + c^8 + 2*Sqrt[3]*(2*a^4*b^2 - 3*a^2*b^4 + b^6 + 2*a^4*c^2 + a^2*b^2*c^2 + 4*b^4*c^2 - 3*a^2*c^4 + 4*b^2*c^4 + c^6)*S) : :

X(61632) lies on the Parry circel and these lines: {15, 9155}, {16, 5651}, {23, 11131}, {62, 37338}, {352, 41406}, {3106, 14704}, {3170, 3292}, {5463, 32461}, {5617, 11007}, {9158, 36185}, {9999, 14169}, {11673, 44718}, {40580, 41167}

X(61632) = psi-transform of X(14539)

X(61633) = X(15)X(5651) ∩ X(16)X(9155)

Barycentrics    a^2*(2*a^8 - 2*a^6*b^2 + 3*a^4*b^4 - 4*a^2*b^6 + b^8 - 2*a^6*c^2 + 3*a^4*b^2*c^2 + 6*a^2*b^4*c^2 + b^6*c^2 + 3*a^4*c^4 + 6*a^2*b^2*c^4 + 12*b^4*c^4 - 4*a^2*c^6 + b^2*c^6 + c^8 - 2*Sqrt[3]*(2*a^4*b^2 - 3*a^2*b^4 + b^6 + 2*a^4*c^2 + a^2*b^2*c^2 + 4*b^4*c^2 - 3*a^2*c^4 + 4*b^2*c^4 + c^6)*S) : :

X(61633) lies on the Parry circel and these lines: {2, 36776}, {15, 5651}, {16, 9155}, {23, 11130}, {61, 37338}, {352, 41407}, {3107, 14705}, {3171, 3292}, {5464, 32460}, {5613, 11007}, {9158, 36186}, {9999, 14170}, {11673, 44719}, {40581, 41167}

X(61633) = circumcircle-of-outer-Napoleon-triangle-inverse of X(36776)
X(61633) = psi-transform of X(14538)

X(61634) = X(3)X(67) ∩ X(13)X(114)

Barycentrics    Sqrt[3]*(4*a^6*b^2 - 5*a^4*b^4 + 2*a^2*b^6 - b^8 + 4*a^6*c^2 - 6*a^4*b^2*c^2 + 2*a^2*b^4*c^2 - 5*a^4*c^4 + 2*a^2*b^2*c^4 + 2*b^4*c^4 + 2*a^2*c^6 - c^8) - (4*a^6 - 4*a^4*b^2 + 2*a^2*b^4 - 2*b^6 - 4*a^4*c^2 + 2*b^4*c^2 + 2*a^2*c^4 + 2*b^2*c^4 - 2*c^6)*S : :
X(61634) = X[41021] + 2 X[52090], 4 X[5] - 3 X[5470], X[6778] - 4 X[51872], 2 X[98] - 3 X[21157], 4 X[618] - 3 X[21157], 2 X[115] - 3 X[36765], 3 X[41042] - 2 X[41060], 4 X[620] - 3 X[21156], 2 X[5459] - 3 X[23234], 4 X[6036] - 5 X[36770], 2 X[6321] - 3 X[59395], 4 X[22796] - 3 X[59395], 4 X[6670] - 3 X[14651], 2 X[6771] - 3 X[15561], 2 X[11632] - 3 X[22490], X[13103] - 3 X[38743], 2 X[22797] - 3 X[38743], X[14692] + 2 X[25560], 3 X[22510] - 4 X[52266], X[36329] + 2 X[36363], X[36344] + 2 X[47867]

X(61634) lies on these lines: {3, 67}, {4, 35688}, {5, 5470}, {13, 114}, {14, 2782}, {16, 5613}, {30, 9116}, {98, 618}, {99, 5474}, {115, 36765}, {147, 616}, {148, 5479}, {383, 530}, {543, 41042}, {617, 14145}, {619, 6770}, {620, 21156}, {1080, 6298}, {2784, 51114}, {2794, 5473}, {3023, 12942}, {3027, 12952}, {3564, 22997}, {5459, 23234}, {5460, 12243}, {5979, 9750}, {6033, 36962}, {6036, 36770}, {6321, 22796}, {6670, 14651}, {6771, 15561}, {6773, 22689}, {6774, 12188}, {6777, 23013}, {6780, 22507}, {6782, 9113}, {6783, 41406}, {8292, 45109}, {9749, 54570}, {9762, 42036}, {9880, 22577}, {9916, 39803}, {11290, 38664}, {11299, 12154}, {11304, 41063}, {11312, 11623}, {11632, 22490}, {12177, 22998}, {12184, 18974}, {12185, 13076}, {13103, 22797}, {13188, 48655}, {14539, 51013}, {14692, 25560}, {16529, 36759}, {20429, 25156}, {22510, 52266}, {22566, 25154}, {22568, 41035}, {22578, 25164}, {23698, 36961}, {33460, 41041}, {36329, 36363}, {36344, 47867}, {38745, 41061}, {41070, 54140}, {43452, 47860}

X(61634) = midpoint of X(i) and X(j) for these {i,j}: {147, 616}, {13188, 48655}
X(61634) = reflection of X(i) in X(j) for these {i,j}: {13, 114}, {14, 5617}, {98, 618}, {148, 5479}, {5464, 8724}, {5474, 99}, {5613, 51872}, {6321, 22796}, {6770, 619}, {6773, 32553}, {6778, 5613}, {12188, 6774}, {12243, 5460}, {13103, 22797}, {22577, 9880}, {22578, 25164}, {25154, 22566}, {25156, 20429}, {36776, 14981}, {36962, 6033}, {41043, 6054}, {41061, 38745}, {42036, 9762}, {51203, 12177}, {54140, 41070}, {54570, 9749}
X(61634) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {98, 618, 21157}, {6321, 22796, 59395}, {13103, 38743, 22797}

X(61635) = X(1)X(168) ∩ X(56)X(266)

Barycentrics    a*(2*a*(a+b-3*c)*(a-3*b+c)+(a+b+c)*((-a+b+c)*(a+b+c)*sin(A/2)+2*a*(a+b-3*c)*sin(B/2)+2*a*(a-3*b+c)*sin(C/2))) : :

See Tran Viet Hung and César Lozada, Romantics of Geometry - Feb 11, 2024.

X(61635) lies on these lines: {1, 168}, {56, 266}, {1420, 7370}, {11923, 12523}

X(61635) = isogonal conjugate of X(12644)
X(61635) = X(i)-beth conjugate of-X(j) for these (i, j): (21, 12518), (12646, 12646)
X(61635) = X(i)-isoconjugate of-X(j) for these {i, j}: {188, 24242}, {258, 24158}
X(61635) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (8078, 556), (12646, 312), (42622, 24158)
X(61635) = barycentric product X(i)*X(j) for these {i,j}: {57, 12646}, {174, 8078}, {5430, 7370}
X(61635) = trilinear product X(i)*X(j) for these {i,j}: {56, 12646}, {266, 8078}
X(61635) = trilinear quotient X(i)/X(j) for these (i,j): (173, 24158), (266, 24242), (5430, 7027), (8078, 188), (12646, 8)
X(61635) = (X(16011), X(42622))-harmonic conjugate of X(266)

X(61636) = X(3)X(6) ∩ X(264)X(9792)

Barycentrics    a^2*((b^4+b^2*c^2+c^4)*a^12-(b^2+c^2)*(5*b^4-b^2*c^2+5*c^4)*a^10+(2*b^4+3*b^2*c^2+2*c^4)*(5*b^4-6*b^2*c^2+5*c^4)*a^8-2*(b^2+c^2)*(5*b^8+5*c^8-(8*b^4-7*b^2*c^2+8*c^4)*b^2*c^2)*a^6+(5*b^8+5*c^8-(b^2+c^2)^2*b^2*c^2)*(b^2-c^2)^2*a^4-(b^2-c^2)^4*(b^4+c^4)*b^2*c^2-(b^6+c^6)*(b^2-c^2)^2*(b^4-4*b^2*c^2+c^4)*a^2) : :
Barycentrics    (SB+SC)*(S^4+(4*R^2-SW)*(S^2*SA-(2*R^2-SW)*(SA^2-SB*SC))) : :

See Kadir Altintas and César Lozada, euclid 6103 - Feb 14, 2024.

X(61636) lies on these lines: {3, 6}, {51, 52253}, {95, 11412}, {264, 9792}, {1993, 21638}, {3567, 36794}, {21243, 34836}, {39641, 39642}

X(61636) = pole of the line {184, 39530} with respect to the Jerabek circumhyperbola
X(61636) = (X(19161), X(50647))-harmonic conjugate of X(389)

X(61637) = X(30)X(511) ∩ X(74)X(953)

Barycentrics    a^2*(b - c)*(a^4*b - 2*a^2*b^3 + b^5 + a^4*c - 2*a^3*b*c + 2*a*b^3*c - b^4*c + 2*a*b^2*c^2 - b^3*c^2 - 2*a^2*c^3 + 2*a*b*c^3 - b^2*c^3 - b*c^4 + c^5) : :

X(61637) lies on these lines: {1, 13868}, {30, 511}, {36, 2605}, {40, 46611}, {74, 953}, {110, 901}, {113, 31841}, {125, 3259}, {265, 40100}, {399, 38584}, {484, 3737}, {649, 22356}, {902, 1459}, {1112, 1830}, {1511, 38614}, {2077, 48389}, {3024, 3025}, {3028, 4017}, {3245, 50349}, {3746, 57130}, {5570, 39540}, {5583, 18839}, {5972, 22102}, {7728, 38954}, {9904, 33811}, {10016, 10117}, {10412, 56845}, {10620, 38586}, {10721, 44979}, {10733, 44973}, {10778, 31512}, {11670, 23152}, {12041, 38617}, {13289, 39479}, {14115, 34949}, {14315, 53549}, {14643, 57313}, {15035, 38705}, {15054, 38682}, {15055, 38707}, {15061, 57320}, {19470, 23153}, {20293, 21282}, {20316, 21241}, {22765, 48382}, {24201, 59817}, {25405, 34954}, {31523, 52478}, {33645, 59818}, {35000, 48391}, {38474, 39547}, {38497, 38513}, {38508, 38512}, {38555, 38569}, {38566, 38568}, {44409, 53615}, {47379, 53314}, {53248, 53295}, {53256, 53306}

X(61637) = isogonal conjugate of X(53611)
X(61637) = Thomson-isogonal conjugate of X(43655)
X(61637) = crossdifference of every pair of points on line {6, 6788}
X(61637) = {X(40),X(53406)}-harmonic conjugate of X(46611)

X(61638) = X(30)X(511) ∩ X(74)X(901)

Barycentrics    a^2*(a^2 - b^2 + b*c - c^2)*(a^4*b^2 - 2*a^2*b^4 + b^6 - 2*a^3*b^2*c + a^2*b^3*c + 2*a*b^4*c - b^5*c + a^4*c^2 - 2*a^3*b*c^2 + 4*a^2*b^2*c^2 - 2*a*b^3*c^2 - b^4*c^2 + a^2*b*c^3 - 2*a*b^2*c^3 + 2*b^3*c^3 - 2*a^2*c^4 + 2*a*b*c^4 - b^2*c^4 - b*c^5 + c^6) : :

X(61638) lies on the cubic K274 and these lines: {3, 13868}, {5, 31847}, {30, 511}, {36, 1464}, {59, 23071}, {74, 901}, {110, 859}, {113, 3259}, {125, 31841}, {143, 31825}, {265, 5080}, {381, 30438}, {399, 38586}, {484, 4551}, {549, 34583}, {1112, 1884}, {1482, 13744}, {1532, 46044}, {2077, 12041}, {2931, 10016}, {2948, 5535}, {3024, 13756}, {3814, 20304}, {3937, 38602}, {5057, 18330}, {5172, 10088}, {5537, 51522}, {5538, 33535}, {5570, 15904}, {5692, 15067}, {5693, 5876}, {5694, 11591}, {5883, 13363}, {5884, 13630}, {5885, 12006}, {5902, 5946}, {5972, 61521}, {6583, 13753}, {6699, 22102}, {6713, 46174}, {7727, 23153}, {7728, 40100}, {9826, 18838}, {10095, 31870}, {10263, 37625}, {10620, 38584}, {10627, 31806}, {10721, 44973}, {10733, 44979}, {10767, 31512}, {11813, 12261}, {11849, 38566}, {12100, 46171}, {12236, 53615}, {12383, 20067}, {12702, 38497}, {12893, 39479}, {13145, 13752}, {13364, 15049}, {13491, 15071}, {14094, 38682}, {14115, 15325}, {14128, 20117}, {14513, 18524}, {14643, 57320}, {15035, 38707}, {15055, 38705}, {15061, 57313}, {15095, 15101}, {17757, 34151}, {18357, 29958}, {22148, 38573}, {22791, 42448}, {22938, 38389}, {23154, 34773}, {24201, 59818}, {31803, 45959}, {31828, 32137}, {33645, 59817}, {38555, 38568}, {38761, 58893}, {43394, 43610}, {43803, 43809}, {53525, 53812}

X(61638) = isogonal conjugate of X(43655)
X(61638) = Thomson-isogonal conjugate of X(53611)
X(61638) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {36, 6126, 47379}, {36, 47379, 51881}, {31847, 31849, 5}

X(61639) = (name pending)

Barycentrics    a*(a^6-3*(b+c)*a^5-(2*b^2+11*b*c+2*c^2)*a^4+6*(b+c)*(b^2+b*c+c^2)*a^3+(b^4+c^4+2*(7*b^2+17*b*c+7*c^2)*b*c)*a^2-3*(b^2-c^2)^2*b*c-3*(b^2-c^2)*(b-c)*(b^2+4*b*c+c^2)*a) : :
X(61639) = (S^2+4*(52*R^2+32*R*r+5*r^2)*r^2)*X(1)+(S^2-4*(4*R^2-2*R*r-r^2)*r^2)*X(201)

See Tran Viet Hung and César Lozada, Romantics of Geometry - Feb 20, 2024.

X(61639) lies on these lines: {1, 201}

X(61640) = CENTROID OF THE PEDAL TRIANGLE OF X(8)

Barycentrics    a^2*(-b^4+2*b^3*c+2*b^2*c^2+2*b*c^3-c^4-2*a*b*c*(b+c)+a^2*(b^2+c^2)) : :
X(61640) = X[8]+2*X[29958], -4*X[10]+X[23154], 2*X[72]+X[16980], X[185]+2*X[14872], -2*X[354]+3*X[373], -X[962]+4*X[44865], -X[3555]+4*X[58497], -5*X[3697]+2*X[11573], -4*X[3740]+3*X[5650], -X[3868]+4*X[23841], -4*X[4015]+X[23156], -X[4430]+3*X[5640] and many others

X(61640) lies on these lines: {2, 2810}, {8, 29958}, {10, 23154}, {22, 43146}, {38, 23638}, {51, 518}, {63, 51377}, {72, 16980}, {181, 32912}, {184, 45729}, {185, 14872}, {200, 26892}, {210, 3917}, {354, 373}, {511, 3578}, {513, 34612}, {517, 17781}, {611, 5320}, {674, 21969}, {899, 1401}, {962, 44865}, {1376, 3937}, {1425, 9370}, {2292, 50580}, {2818, 59388}, {3060, 4661}, {3271, 3938}, {3434, 38389}, {3555, 58497}, {3690, 5220}, {3697, 11573}, {3701, 50628}, {3740, 5650}, {3751, 40952}, {3819, 23155}, {3868, 23841}, {3873, 5943}, {3939, 16064}, {4015, 23156}, {4126, 4553}, {4430, 5640}, {5101, 30620}, {5223, 26893}, {5422, 43149}, {5432, 61166}, {6075, 15842}, {9004, 61663}, {11246, 22278}, {12680, 58690}, {13374, 27355}, {15004, 45728}, {16588, 46148}, {17718, 61643}, {22076, 41229}, {22769, 43650}, {23630, 33299}, {24390, 56885}, {26910, 61156}, {29349, 49719}, {30493, 56198}, {30628, 58534}, {31018, 35645}, {31785, 56879}, {32925, 35104}, {34048, 53548}, {45990, 60731}, {58646, 61686}

X(61640) = midpoint of X(i) and X(j) for these {i,j}: {8, 30438}, {3060, 4661}
X(61640) = reflection of X(i) in X(j) for these {i,j}: {11246, 22278}, {23155, 3819}, {354, 375}, {30438, 29958}, {3873, 5943}, {3917, 210}, {42448, 30438}, {61678, 354}
X(61640) = pole of line {2821, 47837} with respect to the orthoptic circle of the Steiner inellipse
X(61640) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 29958, 42448}, {210, 8679, 3917}, {354, 375, 373}, {354, 9026, 61678}, {373, 61678, 354}, {3060, 4661, 9052}

X(61641) = CENTROID OF THE PEDAL TRIANGLE OF X(17)

Barycentrics    a^2*(a^6*(b^2+c^2)+a^4*(-3*b^4+b^2*c^2-3*c^4)-(b^2-c^2)^2*(b^4-5*b^2*c^2+c^4)+3*a^2*(b^6-3*b^4*c^2-3*b^2*c^4+c^6)-6*sqrt(3)*a^2*b^2*c^2*S) : :

X(61641) lies on these lines: {2, 11624}, {6, 11451}, {17, 1154}, {51, 396}, {61, 13364}, {373, 43229}, {395, 6688}, {397, 5892}, {398, 14845}, {2979, 16644}, {3060, 49905}, {3132, 41476}, {3412, 10095}, {3819, 23302}, {5318, 14855}, {5340, 20791}, {5640, 49947}, {5663, 41121}, {5890, 42156}, {5891, 42598}, {5943, 11626}, {5946, 16267}, {6000, 42166}, {11002, 49862}, {12006, 42992}, {13363, 61719}, {13391, 41943}, {15026, 61698}, {15060, 30439}, {16241, 54044}, {18435, 18582}, {18874, 42991}, {19294, 21461}, {30440, 42506}, {32142, 42979}, {34327, 51890}, {36987, 42945}, {40280, 41112}, {43238, 54041}, {49874, 61136}

X(61641) = midpoint of X(i) and X(j) for these {i,j}: {17, 61697}
X(61641) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 11451, 61642}, {5943, 43228, 11626}, {30439, 49907, 15060}

X(61642) = CENTROID OF THE PEDAL TRIANGLE OF X(18)

Barycentrics    a^2*(a^6*(b^2+c^2)+a^4*(-3*b^4+b^2*c^2-3*c^4)-(b^2-c^2)^2*(b^4-5*b^2*c^2+c^4)+3*a^2*(b^6-3*b^4*c^2-3*b^2*c^4+c^6)+6*sqrt(3)*a^2*b^2*c^2*S) : :

X(61642) lies on these lines: {2, 11626}, {6, 11451}, {18, 1154}, {51, 395}, {62, 13364}, {373, 43228}, {396, 6688}, {397, 14845}, {398, 5892}, {2979, 16645}, {3060, 49906}, {3411, 10095}, {3819, 23303}, {5321, 14855}, {5339, 20791}, {5640, 49948}, {5663, 41122}, {5890, 42153}, {5891, 42599}, {5943, 11624}, {5946, 16268}, {6000, 42163}, {11002, 49861}, {12006, 42993}, {13391, 41944}, {15026, 61697}, {15060, 30440}, {16242, 54044}, {18435, 18581}, {18874, 42990}, {19295, 21462}, {30439, 42507}, {32142, 42978}, {34328, 51891}, {36987, 42944}, {40280, 41113}, {43239, 54041}, {49873, 61136}

X(61642) = midpoint of X(i) and X(j) for these {i,j}: {18, 61698}
X(61642) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 11451, 61641}, {5943, 43229, 11624}, {30440, 49908, 15060}

X(61643) = CENTROID OF THE PEDAL TRIANGLE OF X(21)

Barycentrics    a*(a^3*(b-c)^2+2*a^2*b*c*(b+c)-2*b*(b-c)^2*c*(b+c)-a*(b^4-2*b^3*c-2*b^2*c^2-2*b*c^3+c^4)) : :
X(61643) = 2*X[6675]+X[18180], 5*X[15674]+X[41723]

X(61643) lies on circumconic {{A, B, C, X(13480), X(32021)}} and on these lines: {2, 51}, {21, 46623}, {81, 3292}, {125, 37360}, {184, 25514}, {185, 6824}, {354, 61647}, {374, 61651}, {375, 61648}, {389, 6852}, {468, 6703}, {517, 15670}, {851, 17194}, {852, 18592}, {896, 39793}, {940, 5320}, {1211, 41586}, {1495, 4228}, {1699, 46521}, {1730, 30944}, {1764, 37319}, {2836, 3742}, {3271, 33105}, {3475, 61678}, {3690, 54357}, {3720, 20967}, {3838, 38389}, {3937, 5249}, {4224, 22352}, {4995, 22278}, {5482, 17529}, {5562, 6861}, {5663, 44257}, {5907, 6884}, {6176, 19245}, {6675, 18180}, {6690, 51377}, {6834, 27355}, {6837, 11381}, {6853, 10110}, {6888, 9729}, {6952, 11695}, {7419, 48894}, {7683, 27687}, {8731, 22080}, {10198, 16980}, {10544, 21674}, {11284, 37674}, {15488, 16865}, {15674, 41723}, {16434, 22112}, {17049, 33119}, {17056, 18191}, {17167, 37370}, {17718, 61640}, {18165, 35466}, {19544, 34417}, {21746, 24892}, {23638, 29678}, {24597, 35612}, {25444, 48887}, {25525, 26892}, {25648, 48931}, {26724, 40649}, {28258, 54356}, {28628, 42448}, {33142, 39543}, {35996, 44106}, {61650, 61688}

X(61643) = midpoint of X(i) and X(j) for these {i,j}: {21, 61699}
X(61643) = reflection of X(i) in X(j) for these {i,j}: {58889, 61699}
X(61643) = inverse of X(3742) in Thomson-Gibert-Moses hyperbola
X(61643) = pole of line {6776, 6869} with respect to the Jerabek hyperbola
X(61643) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 37521, 5650}, {354, 61661, 61670}, {4228, 37527, 1495}, {6675, 18180, 22076}, {18165, 35466, 40952}

X(61644) = CENTROID OF THE PEDAL TRIANGLE OF X(22)

Barycentrics    a^6+(b^2-c^2)^2*(b^2+c^2)-2*a^2*(b^4+c^4) : :
X(61644) = 2*X[22]+X[11550], X[184]+2*X[343], -5*X[631]+2*X[11430], -X[1993]+4*X[58447], 2*X[7502]+X[18474], 2*X[7555]+X[34514], X[8541]+2*X[16789], X[15760]+2*X[44201], 2*X[34986]+X[45794]

X(61644) lies on these lines: {2, 51}, {3, 125}, {5, 32269}, {6, 16511}, {20, 11572}, {22, 11550}, {23, 3818}, {25, 10516}, {26, 1209}, {30, 45303}, {67, 32227}, {68, 47525}, {69, 3292}, {76, 46247}, {110, 34507}, {140, 13142}, {141, 468}, {154, 61739}, {156, 21230}, {182, 3580}, {183, 47200}, {184, 343}, {185, 3547}, {206, 59778}, {264, 41203}, {376, 23329}, {381, 32620}, {382, 35240}, {389, 7558}, {427, 29181}, {524, 61690}, {542, 6800}, {547, 20192}, {549, 39242}, {569, 7568}, {575, 37644}, {576, 14389}, {577, 44888}, {597, 61657}, {599, 5642}, {631, 11430}, {852, 22062}, {858, 3098}, {1092, 7542}, {1204, 6823}, {1216, 6639}, {1316, 7761}, {1350, 5094}, {1352, 1495}, {1503, 35268}, {1531, 4549}, {1533, 11472}, {1594, 46728}, {1648, 32761}, {1656, 3066}, {1853, 59411}, {1899, 7494}, {1993, 58447}, {1995, 24206}, {2393, 61685}, {3054, 22111}, {3124, 7746}, {3410, 26881}, {3448, 15080}, {3519, 9704}, {3528, 43608}, {3549, 5562}, {3574, 17834}, {3581, 7706}, {3619, 40132}, {3642, 32461}, {3643, 32460}, {3690, 56456}, {3734, 5112}, {3763, 11284}, {3788, 54332}, {3937, 56457}, {4232, 40330}, {4550, 11799}, {5050, 61712}, {5056, 11821}, {5070, 44300}, {5085, 26869}, {5092, 18911}, {5169, 15107}, {5188, 14003}, {5189, 7703}, {5309, 46906}, {5447, 6640}, {5480, 37454}, {5486, 32127}, {5544, 46219}, {5663, 44262}, {5891, 10201}, {5972, 15066}, {6070, 6795}, {6368, 14582}, {6388, 7749}, {6515, 13366}, {6636, 23293}, {6689, 36749}, {6723, 21766}, {6791, 37637}, {6997, 44106}, {7400, 26937}, {7426, 11178}, {7484, 26958}, {7492, 48898}, {7499, 13567}, {7502, 18474}, {7503, 32348}, {7505, 11793}, {7512, 18381}, {7516, 43817}, {7519, 48889}, {7525, 34826}, {7539, 17810}, {7552, 10628}, {7555, 34514}, {7556, 41171}, {7667, 23332}, {7748, 39691}, {7801, 9155}, {7810, 35282}, {7822, 37338}, {7854, 20968}, {7999, 14940}, {8266, 44886}, {8541, 16789}, {8542, 32113}, {8548, 32263}, {8722, 47526}, {8889, 33522}, {9306, 37636}, {9715, 61139}, {9832, 47220}, {9996, 37906}, {10104, 47201}, {10154, 44082}, {10297, 35254}, {10323, 20299}, {10545, 42786}, {10546, 37760}, {10564, 18580}, {10565, 31383}, {10619, 12429}, {10984, 12359}, {11003, 41724}, {11007, 11657}, {11056, 18906}, {11064, 48876}, {11204, 44458}, {11331, 39604}, {11381, 59349}, {11422, 37779}, {11444, 58805}, {11574, 60774}, {13160, 46730}, {14810, 16063}, {15004, 37649}, {15059, 41462}, {15060, 44278}, {15067, 41670}, {15069, 24981}, {15246, 26913}, {15431, 49135}, {15644, 37119}, {15760, 44201}, {17811, 37453}, {18358, 37897}, {18390, 35921}, {18400, 44837}, {18553, 32237}, {19129, 58357}, {20113, 37827}, {20126, 44751}, {21167, 43957}, {21358, 47597}, {22336, 34817}, {22416, 38356}, {23061, 59771}, {23291, 33750}, {26879, 37515}, {29317, 31133}, {30739, 47296}, {31099, 48873}, {31152, 31884}, {32110, 50008}, {32142, 60780}, {32222, 36832}, {32423, 34513}, {32767, 47528}, {34330, 44324}, {34986, 45794}, {35283, 44212}, {36987, 44441}, {37118, 37480}, {37124, 43462}, {37198, 40686}, {37893, 51458}, {37900, 48884}, {37904, 47354}, {40879, 51429}, {41167, 47004}, {41244, 53386}, {41603, 44883}, {46517, 48881}, {47097, 54169}, {47208, 49111}, {47311, 50965}, {47563, 48815}, {51756, 56924}, {52292, 59767}, {52297, 53415}, {54042, 61736}, {54048, 61711}, {54994, 61744}, {61667, 61683}, {61682, 61689}

X(61644) = midpoint of X(i) and X(j) for these {i,j}: {22, 61700}, {154, 61739}, {343, 13394}
X(61644) = reflection of X(i) in X(j) for these {i,j}: {184, 13394}, {11550, 61700}, {13394, 6676}, {32607, 38727}, {35268, 44210}, {39242, 549}, {61700, 21243}, {61743, 2}
X(61644) = perspector of circumconic {{A, B, C, X(44061), X(54899)}}
X(61644) = pole of line {4549, 6776} with respect to the Jerabek hyperbola
X(61644) = pole of line {3815, 16310} with respect to the Kiepert hyperbola
X(61644) = pole of line {182, 186} with respect to the Stammler hyperbola
X(61644) = pole of line {6334, 23878} with respect to the Steiner inellipse
X(61644) = pole of line {183, 340} with respect to the Wallace hyperbola
X(61644) = pole of line {3268, 3906} with respect to the dual conic of polar circle
X(61644) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(57268)}}, {{A, B, C, X(262), X(265)}}, {{A, B, C, X(263), X(43697)}}, {{A, B, C, X(9516), X(42313)}}
X(61644) = barycentric product X(i)*X(j) for these (i, j): {5475, 69}
X(61644) = barycentric quotient X(i)/X(j) for these (i, j): {5475, 4}
X(61644) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15360, 5476}, {2, 43653, 3917}, {2, 511, 61743}, {2, 54173, 13857}, {2, 5640, 38317}, {2, 61506, 373}, {2, 61646, 61645}, {3, 37638, 125}, {5, 32269, 34417}, {22, 21243, 11550}, {22, 61700, 29012}, {67, 32227, 32235}, {140, 37648, 22112}, {141, 468, 5651}, {343, 13394, 3564}, {343, 6676, 184}, {373, 32225, 61506}, {599, 61680, 6090}, {631, 37643, 54012}, {1350, 5094, 51360}, {1352, 7493, 1495}, {1503, 44210, 35268}, {1656, 21970, 3066}, {1899, 7494, 22352}, {3564, 6676, 13394}, {3580, 7495, 182}, {5169, 15107, 48901}, {5650, 61691, 2}, {5972, 40107, 15066}, {6090, 61680, 5642}, {12359, 34002, 10984}, {15069, 26864, 24981}, {15080, 38397, 3448}, {17702, 38727, 32607}, {21243, 29012, 61700}, {24206, 32223, 1995}, {31884, 61735, 31152}, {37454, 47582, 5480}, {37649, 41588, 15004}

X(61645) = CENTROID OF THE PEDAL TRIANGLE OF X(24)

Barycentrics    a^6-2*a^2*(b^2-c^2)^2+(b^2-c^2)^2*(b^2+c^2) : :
X(61645) = 2*X[235]+X[1204], -X[1092]+4*X[16238], -X[10539]+4*X[44232], -4*X[21841]+X[26883], X[31725]+2*X[43604]

X(61645) lies on these lines: {2, 51}, {3, 12897}, {4, 11270}, {6, 13622}, {22, 32223}, {23, 26913}, {24, 18400}, {25, 125}, {26, 43817}, {32, 44887}, {66, 44091}, {107, 52249}, {140, 11424}, {143, 60780}, {154, 26869}, {184, 468}, {185, 3542}, {186, 18390}, {235, 1204}, {343, 5651}, {378, 10193}, {389, 7505}, {394, 41586}, {403, 11438}, {406, 58889}, {420, 40814}, {427, 34417}, {428, 23332}, {436, 43462}, {459, 61348}, {542, 35264}, {549, 16657}, {569, 10020}, {578, 10018}, {973, 15026}, {1092, 16238}, {1147, 59648}, {1192, 37197}, {1350, 31255}, {1368, 32269}, {1495, 1899}, {1501, 1648}, {1503, 44082}, {1514, 44957}, {1568, 37489}, {1629, 16080}, {1656, 3574}, {1754, 46555}, {1843, 23327}, {1906, 6696}, {1993, 5972}, {1995, 21243}, {3089, 11381}, {3147, 13367}, {3167, 5642}, {3168, 14165}, {3292, 6515}, {3410, 10546}, {3515, 21659}, {3517, 61139}, {3518, 18381}, {3526, 10982}, {3527, 26861}, {3548, 45186}, {3567, 14940}, {3575, 23324}, {3580, 9306}, {3589, 16789}, {3628, 45089}, {3818, 13595}, {3830, 15061}, {3937, 20266}, {4232, 23291}, {5020, 37638}, {5064, 61735}, {5094, 17810}, {5198, 40686}, {5422, 58447}, {5446, 6640}, {5448, 37490}, {5449, 7506}, {5462, 6639}, {5654, 14831}, {5663, 44270}, {5890, 37943}, {5893, 45004}, {6143, 9781}, {6388, 42295}, {6403, 23048}, {6524, 42452}, {6676, 37648}, {6723, 30744}, {6747, 47204}, {6759, 26879}, {6776, 44110}, {7391, 48943}, {7404, 27355}, {7487, 11572}, {7493, 22352}, {7494, 54012}, {7499, 22112}, {7552, 15045}, {7558, 11695}, {7576, 23325}, {7687, 35480}, {7703, 37349}, {7706, 10254}, {8538, 37649}, {8541, 10169}, {8584, 47459}, {8780, 24981}, {9730, 10201}, {9777, 52292}, {9786, 43831}, {9927, 45735}, {10110, 37119}, {10154, 35268}, {10282, 18912}, {10539, 44232}, {10545, 37353}, {10594, 20299}, {10605, 51403}, {10619, 17821}, {10984, 13383}, {11064, 41588}, {11123, 55265}, {11202, 12022}, {11225, 61681}, {11402, 61680}, {11427, 34565}, {11430, 46265}, {11433, 13366}, {11444, 43581}, {11657, 57592}, {12106, 18474}, {12111, 21451}, {13321, 61711}, {13352, 44452}, {13394, 45298}, {13403, 32534}, {13451, 34331}, {13851, 18533}, {14569, 53506}, {14583, 14847}, {14644, 18376}, {14845, 60763}, {15004, 23292}, {15043, 58805}, {15059, 31074}, {15072, 46451}, {15107, 31101}, {15466, 41203}, {16194, 44275}, {16227, 44282}, {16311, 42453}, {18396, 55572}, {18555, 43898}, {18950, 35260}, {18951, 43844}, {19130, 31236}, {20304, 44288}, {21841, 26883}, {21970, 30771}, {22802, 43599}, {23294, 34484}, {24913, 37507}, {25563, 35502}, {25739, 47485}, {26276, 33796}, {26881, 37760}, {26882, 43808}, {31133, 45311}, {31725, 43604}, {32263, 34966}, {34477, 39242}, {34507, 43811}, {34785, 44879}, {34986, 37644}, {35225, 52153}, {36749, 43839}, {36753, 44516}, {37440, 61299}, {37487, 44438}, {37913, 48898}, {38228, 52247}, {38848, 52295}, {40673, 61683}, {43607, 44803}, {44084, 54384}, {44111, 53857}, {44211, 44665}, {44212, 44569}, {44407, 51519}, {51363, 59229}, {53863, 59771}, {58434, 61690}, {59553, 61658}

X(61645) = midpoint of X(i) and X(j) for these {i,j}: {24, 61701}
X(61645) = pole of line {6241, 6776} with respect to the Jerabek hyperbola
X(61645) = pole of line {3815, 16318} with respect to the Kiepert hyperbola
X(61645) = pole of line {183, 31255} with respect to the Wallace hyperbola
X(61645) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(11270), X(54032)}}, {{A, B, C, X(13622), X(42313)}}
X(61645) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11451, 38317}, {2, 43653, 5650}, {2, 51, 61743}, {2, 61506, 51}, {2, 61646, 61644}, {24, 61701, 18400}, {25, 125, 11550}, {25, 26958, 125}, {51, 61691, 2}, {343, 6677, 5651}, {468, 11245, 10192}, {1899, 6353, 1495}, {3089, 26937, 11381}, {3518, 26917, 18381}, {4232, 23291, 31383}, {6353, 37643, 1899}, {6515, 59543, 3292}, {10192, 11245, 184}, {10192, 13567, 11245}, {13595, 23293, 3818}, {14644, 18559, 18376}, {21970, 30771, 33586}, {30771, 33586, 51360}

X(61646) = CENTROID OF THE PEDAL TRIANGLE OF X(26)

Barycentrics    a^6+(b^2-c^2)^2*(b^2+c^2)-2*a^2*(b^4-b^2*c^2+c^4) : :
X(61646) = X[26]+2*X[5449], X[68]+2*X[10282], -4*X[140]+X[13346], -X[156]+4*X[18282], -X[1147]+4*X[10020], 5*X[1656]+X[17834], 2*X[1658]+X[9927], -X[3357]+4*X[44158], -7*X[3526]+X[37498], 5*X[3763]+X[37491], -3*X[5054]+X[37497], X[6759]+2*X[12359] and many others

X(61646) lies on circumconic {{A, B, C, X(262), X(22466)}} and on these lines: {2, 51}, {3, 2929}, {5, 11745}, {6, 58447}, {20, 13851}, {22, 125}, {23, 11550}, {25, 3818}, {26, 5449}, {30, 11204}, {52, 6639}, {68, 10282}, {69, 38282}, {76, 420}, {140, 13346}, {141, 6677}, {154, 542}, {156, 18282}, {182, 6676}, {184, 3580}, {206, 58439}, {343, 468}, {389, 3549}, {394, 5972}, {403, 18418}, {406, 15488}, {419, 54393}, {427, 32269}, {428, 45303}, {441, 5171}, {451, 10441}, {465, 9735}, {466, 9736}, {524, 58434}, {569, 45967}, {575, 11433}, {576, 23292}, {578, 7542}, {1092, 10018}, {1147, 10020}, {1209, 7506}, {1350, 6723}, {1352, 6353}, {1368, 3098}, {1370, 48880}, {1495, 11442}, {1503, 10154}, {1589, 43144}, {1590, 43141}, {1656, 17834}, {1658, 9927}, {1853, 9909}, {1899, 7493}, {1993, 41586}, {2052, 41203}, {2070, 18474}, {2072, 37478}, {2351, 34218}, {3066, 7539}, {3089, 44870}, {3131, 40709}, {3132, 40710}, {3167, 5965}, {3292, 45794}, {3357, 44158}, {3410, 37760}, {3448, 26881}, {3526, 37498}, {3529, 43608}, {3534, 15061}, {3541, 13598}, {3542, 5907}, {3546, 13348}, {3547, 9729}, {3548, 15644}, {3564, 10192}, {3581, 10254}, {3763, 37491}, {3788, 52261}, {3796, 26869}, {3926, 59559}, {3933, 59651}, {4207, 48940}, {4212, 48938}, {4213, 48902}, {4232, 18553}, {4550, 46030}, {5012, 43810}, {5020, 24206}, {5050, 32068}, {5054, 37497}, {5066, 51993}, {5092, 7494}, {5094, 33586}, {5097, 11427}, {5133, 34417}, {5159, 52987}, {5475, 54082}, {5562, 7505}, {5644, 47352}, {5651, 37636}, {5663, 44278}, {5889, 58805}, {5890, 7552}, {6101, 60780}, {6310, 59534}, {6515, 34986}, {6636, 26913}, {6640, 10625}, {6759, 12359}, {6995, 48889}, {7378, 48895}, {7386, 14810}, {7387, 20299}, {7394, 44106}, {7395, 32348}, {7396, 48873}, {7400, 17704}, {7426, 44082}, {7495, 43650}, {7499, 37648}, {7512, 26917}, {7556, 25739}, {7561, 13323}, {7689, 15761}, {7706, 46029}, {7734, 21167}, {7767, 59656}, {7822, 9917}, {8681, 61683}, {8780, 15069}, {8889, 31670}, {8964, 12975}, {9544, 41724}, {9714, 13419}, {9715, 44829}, {9738, 55885}, {9739, 55890}, {10104, 44347}, {10112, 19357}, {10182, 47391}, {10201, 13754}, {10257, 37480}, {10298, 50435}, {10300, 55637}, {10565, 23291}, {10601, 44469}, {10691, 55649}, {10984, 26879}, {11064, 52297}, {11178, 44212}, {11179, 18950}, {11202, 34351}, {11225, 11402}, {11245, 13394}, {11265, 13970}, {11266, 13909}, {11412, 14940}, {11438, 15760}, {11454, 52403}, {11459, 37943}, {11511, 16789}, {11572, 31304}, {11585, 46728}, {11645, 32064}, {11649, 34751}, {11657, 36190}, {12084, 20191}, {12085, 25563}, {12088, 23294}, {12161, 44516}, {12242, 37493}, {12429, 17821}, {13289, 46085}, {13347, 16197}, {13366, 37644}, {13391, 61736}, {13561, 17714}, {14070, 14852}, {14389, 15004}, {14787, 14845}, {14790, 32767}, {14826, 43150}, {15056, 21451}, {15059, 31101}, {15060, 44270}, {15083, 61608}, {15107, 31074}, {15303, 15533}, {15305, 46451}, {16051, 33522}, {16066, 37823}, {16163, 35472}, {16266, 43839}, {16276, 61382}, {17702, 18324}, {17810, 19130}, {17811, 40107}, {17825, 58445}, {17907, 59529}, {18388, 37489}, {18911, 22352}, {19161, 58480}, {20397, 33532}, {20850, 36990}, {21659, 38444}, {21663, 44440}, {22104, 36192}, {22165, 47544}, {22819, 52287}, {22820, 52286}, {23606, 44891}, {25738, 45730}, {26540, 37527}, {26937, 46850}, {29317, 34609}, {29323, 34608}, {30744, 51360}, {31152, 45311}, {31383, 32237}, {32046, 34577}, {32139, 52104}, {32152, 56372}, {32401, 38450}, {33533, 50140}, {34002, 37515}, {34481, 53475}, {34514, 37936}, {34782, 44277}, {34826, 37440}, {37119, 45186}, {37439, 42786}, {37494, 51392}, {37669, 52290}, {37911, 51742}, {37942, 44683}, {39568, 40686}, {40341, 59551}, {41171, 47485}, {41628, 61655}, {41671, 41716}, {42459, 53496}, {44210, 44569}, {44837, 61701}, {48876, 53415}, {48891, 59343}, {50676, 61378}, {51212, 52299}, {52016, 58437}, {52404, 58378}, {61658, 61690}, {61666, 61685}

X(61646) = midpoint of X(i) and X(j) for these {i,j}: {26, 61702}, {1853, 9909}, {14070, 14852}
X(61646) = reflection of X(i) in X(j) for these {i,j}: {11202, 34351}, {18381, 61702}, {3167, 61681}, {47391, 10182}, {59553, 58434}, {61702, 5449}
X(61646) = pole of line {182, 11443} with respect to the Stammler hyperbola
X(61646) = pole of line {183, 22468} with respect to the Wallace hyperbola
X(61646) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3060, 61743}, {2, 43653, 3819}, {2, 5943, 38317}, {2, 61506, 5943}, {23, 23293, 11550}, {25, 21243, 3818}, {25, 37638, 21243}, {26, 5449, 18381}, {26, 61702, 44407}, {69, 38282, 59543}, {343, 468, 9306}, {343, 9306, 34507}, {394, 37453, 5972}, {524, 58434, 59553}, {1658, 9927, 34785}, {1853, 9909, 29012}, {3167, 61680, 61681}, {3819, 43653, 50977}, {3917, 61691, 2}, {5449, 44407, 61702}, {5965, 61681, 3167}, {5972, 12828, 34155}, {6676, 13567, 182}, {7542, 41587, 578}, {7689, 15761, 22802}, {10565, 23291, 46264}, {12359, 13383, 6759}, {14070, 14852, 18400}, {21243, 32223, 25}, {23292, 41588, 576}, {26937, 59349, 46850}, {34351, 44665, 11202}, {44277, 61544, 34782}

X(61647) = CENTROID OF THE PEDAL TRIANGLE OF X(31)

Barycentrics    4*a^3+a^2*(b+c)+(b-c)^2*(b+c) : :
X(61647) = X[306]+2*X[3791], X[1072]+2*X[5398], X[3187]+2*X[59692], -4*X[20106]+X[32852]

X(61647) lies on these lines: {1, 24597}, {2, 5847}, {6, 2438}, {31, 516}, {44, 17602}, {58, 23536}, {69, 29855}, {171, 26723}, {226, 2308}, {306, 3791}, {354, 61643}, {373, 61687}, {519, 33114}, {527, 33143}, {551, 46909}, {612, 38057}, {614, 37642}, {740, 35263}, {748, 39595}, {750, 3008}, {896, 3663}, {902, 3755}, {908, 16468}, {1072, 5398}, {1125, 1150}, {1155, 17366}, {1193, 10165}, {1203, 37701}, {1386, 17726}, {1453, 5230}, {1468, 23675}, {1471, 34050}, {1707, 19785}, {1738, 17126}, {1788, 4348}, {2321, 50756}, {2887, 28498}, {2895, 29874}, {3006, 49684}, {3120, 21747}, {3187, 59692}, {3416, 30768}, {3452, 29683}, {3618, 29828}, {3712, 4852}, {3751, 26228}, {3772, 41011}, {3879, 29632}, {3883, 29631}, {3911, 4989}, {3936, 51196}, {3946, 4414}, {3977, 32921}, {3989, 5325}, {3994, 59579}, {4001, 26128}, {4035, 29865}, {4054, 4672}, {4104, 19742}, {4353, 36263}, {4357, 29636}, {4362, 5294}, {4416, 32775}, {4641, 5852}, {4663, 17724}, {4684, 29638}, {4831, 17345}, {4847, 17469}, {4856, 50753}, {4933, 49543}, {5222, 11200}, {5269, 38200}, {5306, 61651}, {5315, 16173}, {5322, 5324}, {5361, 29648}, {5372, 29666}, {5657, 54418}, {5707, 5886}, {5745, 17017}, {6734, 16478}, {7290, 11269}, {7988, 16469}, {8229, 39870}, {11038, 37666}, {13405, 61358}, {14206, 23689}, {16477, 17719}, {16704, 26230}, {17023, 32917}, {17127, 24210}, {17147, 59544}, {17150, 56520}, {17279, 49990}, {17352, 60423}, {17353, 17763}, {17355, 50754}, {17716, 25006}, {17723, 31187}, {17728, 61680}, {17768, 50103}, {17781, 33152}, {18653, 59243}, {20045, 49529}, {20106, 32852}, {23677, 40977}, {24248, 36277}, {27628, 37609}, {28234, 49487}, {28472, 44416}, {28526, 50102}, {29634, 37652}, {29654, 54311}, {29681, 37685}, {29821, 59491}, {29833, 50290}, {29857, 51192}, {29859, 33082}, {29871, 32863}, {30652, 33131}, {30653, 33134}, {31229, 33070}, {32928, 56078}, {32941, 50758}, {33071, 41806}, {33088, 56519}, {33089, 50017}, {33115, 49476}, {33122, 34379}, {33124, 41629}, {33129, 50307}, {33158, 50292}, {33160, 50306}, {35290, 46908}, {37646, 61649}, {40128, 51406}, {42051, 59574}, {46897, 59408}, {46904, 50114}, {48857, 59337}, {49482, 50755}, {49497, 50744}, {49681, 50743}, {49685, 50748}, {51408, 61660}

X(61647) = midpoint of X(i) and X(j) for these {i,j}: {31, 33128}
X(61647) = reflection of X(i) in X(j) for these {i,j}: {3914, 33128}, {33128, 40940}
X(61647) = perspector of circumconic {{A, B, C, X(44876), X(54564)}}
X(61647) = pole of line {379, 29603} with respect to the dual conic of Yff parabola
X(61647) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 17718, 61652}, {31, 33128, 516}, {31, 40940, 3914}, {516, 40940, 33128}, {1386, 35466, 29639}, {3011, 61652, 17718}, {16704, 26230, 49511}

X(61648) = CENTROID OF THE PEDAL TRIANGLE OF X(35)

Barycentrics    2*a^3-a*(b-c)^2-3*a^2*(b+c)+2*(b-c)^2*(b+c) : :
X(61648) = -X[3916]+4*X[58404], -4*X[6668]+X[6734], 2*X[8068]+X[41541], 2*X[14526]+X[45065], X[15837]+2*X[21617]

X(61648) lies on circumconic {{A, B, C, X(43731), X(60668)}} and on these lines: {1, 1656}, {2, 210}, {5, 37080}, {11, 3748}, {12, 515}, {35, 28146}, {37, 29678}, {55, 1538}, {65, 498}, {79, 31663}, {100, 3838}, {125, 17056}, {140, 13407}, {165, 61716}, {200, 31245}, {226, 1155}, {230, 61688}, {375, 61643}, {381, 59337}, {388, 37605}, {392, 10197}, {442, 59719}, {495, 1319}, {499, 17609}, {516, 4995}, {517, 3584}, {519, 38027}, {553, 58441}, {631, 10404}, {908, 3683}, {942, 37731}, {950, 3614}, {954, 11502}, {1001, 30852}, {1100, 29683}, {1125, 15888}, {1212, 61706}, {1260, 4413}, {1376, 31266}, {1385, 37719}, {1386, 29665}, {1478, 37600}, {1621, 5087}, {1698, 3940}, {1737, 5719}, {1836, 5218}, {1837, 5703}, {1859, 37799}, {2098, 51784}, {2099, 31434}, {2348, 61651}, {2476, 56176}, {2886, 3689}, {2887, 30823}, {3011, 37662}, {3035, 5249}, {3057, 3085}, {3058, 3817}, {3158, 31140}, {3295, 37692}, {3303, 8227}, {3304, 3624}, {3338, 3526}, {3485, 59417}, {3486, 54448}, {3487, 24914}, {3576, 11237}, {3582, 5049}, {3585, 28168}, {3601, 10895}, {3612, 9654}, {3649, 6684}, {3666, 17719}, {3698, 5552}, {3744, 17717}, {3745, 5718}, {3746, 9955}, {3752, 33127}, {3771, 30818}, {3812, 27529}, {3822, 5440}, {3844, 30831}, {3874, 20104}, {3893, 10528}, {3911, 5326}, {3916, 58404}, {3922, 37828}, {3925, 6745}, {3944, 4689}, {3947, 7354}, {3962, 26066}, {3967, 33113}, {3983, 19854}, {4003, 33144}, {4005, 5791}, {4009, 33116}, {4193, 51715}, {4292, 52793}, {4423, 30827}, {4640, 31053}, {4679, 5748}, {4727, 21943}, {4849, 24892}, {4860, 31231}, {4892, 59679}, {4914, 26227}, {5048, 15950}, {5126, 5444}, {5173, 5659}, {5183, 39542}, {5204, 5290}, {5205, 41878}, {5217, 9612}, {5220, 55867}, {5221, 31423}, {5231, 41711}, {5252, 6879}, {5266, 37693}, {5270, 13624}, {5393, 32083}, {5405, 32082}, {5426, 31160}, {5433, 21620}, {5434, 10165}, {5443, 9957}, {5445, 31794}, {5572, 61017}, {5658, 33993}, {5660, 10157}, {5726, 13384}, {5777, 17637}, {5794, 10585}, {5818, 37724}, {5844, 10039}, {5886, 5919}, {5902, 11231}, {5965, 37631}, {6668, 6734}, {6692, 31235}, {6767, 23708}, {6825, 7957}, {6833, 12680}, {6852, 58631}, {6862, 14872}, {6935, 12678}, {6949, 13374}, {6952, 12675}, {6972, 58567}, {7140, 23710}, {7483, 21077}, {7951, 24929}, {7987, 9657}, {7988, 10389}, {8068, 41541}, {8162, 37704}, {8232, 31391}, {8255, 61015}, {8758, 29640}, {9578, 34471}, {9671, 41864}, {9779, 10385}, {10198, 25917}, {10543, 19925}, {10572, 10592}, {10578, 10589}, {10950, 38155}, {11019, 37703}, {11219, 17660}, {11281, 24982}, {12047, 28174}, {12607, 24541}, {12699, 31452}, {12943, 30282}, {13464, 45081}, {13747, 51706}, {14100, 60943}, {14110, 26487}, {14526, 45065}, {14547, 45885}, {15170, 61269}, {15174, 61259}, {15254, 27131}, {15338, 28158}, {15837, 21617}, {15904, 58671}, {16610, 33130}, {17357, 29865}, {17615, 58578}, {17619, 30143}, {17720, 37593}, {17724, 24239}, {17758, 24784}, {17775, 50307}, {18221, 46931}, {18480, 37571}, {18493, 31480}, {21075, 24953}, {21870, 33137}, {24210, 37691}, {24655, 27267}, {25415, 39782}, {25466, 27385}, {26878, 41697}, {27777, 50104}, {29662, 49478}, {29680, 49465}, {29681, 37651}, {29817, 31272}, {29846, 44417}, {30615, 30741}, {31776, 59319}, {31792, 37735}, {32557, 51103}, {32938, 59769}, {33073, 37764}, {33115, 59596}, {33593, 61562}, {34612, 59584}, {36920, 50194}, {38318, 41861}, {41546, 46684}, {44785, 61004}, {45931, 56535}, {61652, 61661}

X(61648) = midpoint of X(i) and X(j) for these {i,j}: {35, 61703}, {3584, 37701}
X(61648) = reflection of X(i) in X(j) for these {i,j}: {4870, 37701}
X(61648) = pole of line {390, 5697} with respect to the Feuerbach hyperbola
X(61648) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 54447, 61717}, {2, 17718, 354}, {2, 3475, 17728}, {2, 354, 61649}, {11, 13405, 3748}, {12, 13411, 2646}, {35, 61703, 28146}, {55, 5219, 17605}, {140, 13407, 32636}, {226, 10164, 11246}, {354, 61686, 61653}, {498, 11374, 65}, {517, 37701, 4870}, {908, 6690, 3683}, {1125, 15888, 20323}, {1737, 5719, 44840}, {3584, 37701, 517}, {5218, 5226, 1836}, {5432, 11246, 10164}, {5552, 28628, 3698}, {5886, 10056, 5919}, {6745, 58463, 3925}, {10039, 37737, 11011}, {10164, 11246, 1155}, {17605, 52638, 55}, {17718, 17728, 3475}, {21617, 59476, 15837}, {54447, 61717, 17606}, {61643, 61672, 375}

X(61649) = CENTROID OF THE PEDAL TRIANGLE OF X(36)

Barycentrics    2*a^3-3*a*(b-c)^2-a^2*(b+c)+2*(b-c)^2*(b+c) : :
X(61649) = X[80]+2*X[5126], -4*X[142]+X[44785], X[484]+2*X[7743], X[1512]+2*X[20418], 2*X[1538]+X[1768], -4*X[3035]+X[3689], X[3218]+2*X[5087], X[3583]+2*X[5122], -7*X[3624]+X[4867], 2*X[5123]+X[54391], -X[5440]+4*X[6681], -4*X[6713]+X[50371] and many others

X(61649) lies on these lines: {1, 3526}, {2, 210}, {5, 32636}, {10, 20323}, {11, 516}, {12, 10172}, {36, 28160}, {55, 31231}, {56, 5587}, {57, 7082}, {65, 499}, {80, 5126}, {140, 37080}, {142, 44785}, {165, 11238}, {392, 10199}, {484, 7743}, {496, 37568}, {498, 17609}, {515, 5298}, {517, 3582}, {519, 34123}, {527, 38095}, {535, 59419}, {553, 10171}, {908, 5852}, {942, 37701}, {952, 1319}, {971, 11219}, {1104, 28096}, {1125, 31260}, {1159, 39782}, {1210, 2646}, {1279, 1647}, {1376, 31224}, {1388, 61291}, {1420, 37712}, {1456, 43043}, {1458, 45885}, {1478, 61263}, {1512, 20418}, {1538, 1768}, {1638, 52305}, {1656, 3338}, {1698, 3304}, {1736, 53525}, {1738, 43055}, {1770, 10593}, {1776, 37789}, {1788, 11376}, {1836, 5435}, {1837, 5704}, {1861, 23711}, {2099, 61275}, {2348, 51406}, {3008, 31192}, {3011, 3756}, {3035, 3689}, {3057, 3086}, {3058, 10164}, {3090, 10404}, {3218, 5087}, {3296, 60781}, {3303, 31423}, {3336, 9955}, {3339, 61271}, {3340, 61274}, {3361, 10895}, {3576, 61717}, {3579, 37720}, {3583, 5122}, {3584, 5049}, {3614, 4298}, {3624, 4867}, {3628, 13407}, {3634, 15888}, {3660, 5660}, {3679, 35272}, {3683, 3816}, {3698, 10527}, {3715, 20196}, {3745, 17726}, {3748, 5432}, {3752, 29662}, {3817, 11246}, {3824, 31262}, {3825, 3916}, {3838, 27003}, {3874, 20107}, {3893, 10529}, {3925, 6692}, {3962, 25681}, {3999, 17719}, {4003, 17720}, {4009, 37758}, {4292, 7173}, {4317, 61261}, {4413, 5231}, {4423, 31249}, {4519, 17740}, {4663, 37651}, {4679, 5744}, {4682, 29680}, {4689, 24217}, {4777, 47828}, {4857, 5442}, {4860, 5219}, {4863, 59572}, {4870, 5902}, {4906, 29665}, {4995, 58441}, {5010, 18527}, {5048, 28234}, {5054, 59337}, {5121, 5972}, {5123, 54391}, {5128, 50444}, {5131, 28146}, {5183, 28212}, {5204, 9581}, {5218, 8236}, {5221, 8227}, {5265, 54361}, {5326, 13405}, {5434, 10175}, {5437, 31245}, {5440, 6681}, {5443, 31794}, {5445, 9957}, {5563, 9956}, {5708, 37692}, {5722, 37600}, {5770, 37566}, {5817, 54366}, {5851, 30379}, {5853, 6174}, {5919, 10072}, {6684, 37722}, {6691, 6734}, {6713, 50371}, {6745, 31235}, {6834, 12680}, {6891, 7957}, {6949, 12675}, {6952, 13374}, {6959, 14872}, {6960, 58567}, {6969, 12678}, {7294, 13411}, {7677, 60782}, {7741, 37582}, {7964, 37364}, {7989, 9657}, {8167, 55867}, {8666, 17619}, {8679, 61674}, {8732, 31391}, {8758, 16610}, {9001, 47803}, {9026, 61672}, {9047, 33852}, {9300, 61688}, {9612, 61265}, {9669, 58887}, {9670, 35242}, {9843, 24953}, {9940, 17637}, {10200, 25917}, {10202, 61722}, {10283, 11011}, {10573, 61287}, {10584, 24703}, {10896, 15803}, {10916, 13747}, {11237, 54447}, {11260, 25005}, {11518, 34595}, {12019, 21578}, {12047, 34753}, {12701, 47743}, {13462, 61254}, {13624, 37702}, {13898, 51842}, {13955, 51841}, {14100, 61019}, {14110, 26492}, {15079, 18480}, {15170, 61614}, {15310, 34583}, {15326, 28172}, {15837, 61016}, {15866, 25414}, {16602, 24892}, {17566, 56176}, {17603, 38122}, {17717, 37520}, {17724, 24216}, {17768, 45310}, {17780, 49694}, {18395, 24928}, {18990, 61262}, {22793, 37524}, {23708, 36279}, {24231, 37691}, {24386, 34612}, {24390, 58405}, {24470, 61267}, {24618, 28901}, {25377, 31289}, {25405, 41684}, {27529, 34791}, {28534, 59377}, {29607, 36236}, {30823, 49676}, {31246, 57279}, {31479, 51816}, {31795, 59325}, {33176, 41687}, {37567, 50443}, {37646, 61647}, {37662, 61652}, {37731, 50192}, {37735, 50193}, {38063, 53615}, {38138, 45287}, {38214, 51714}, {38460, 44784}, {38941, 43037}, {39542, 61270}, {41341, 44425}, {43065, 61730}, {50302, 58414}, {51415, 60414}, {57282, 61266}, {58563, 61017}

X(61649) = midpoint of X(i) and X(j) for these {i,j}: {36, 37718}, {41700, 59372}
X(61649) = pole of line {390, 2801} with respect to the Feuerbach hyperbola
X(61649) = pole of line {5723, 29571} with respect to the dual conic of Yff parabola
X(61649) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17728, 354}, {2, 354, 61648}, {11, 3911, 1155}, {36, 37718, 28160}, {57, 7988, 61716}, {1210, 5433, 2646}, {1737, 15325, 1319}, {1837, 7288, 37605}, {3086, 24914, 3057}, {3218, 31272, 5087}, {3816, 59491, 3683}, {4857, 5442, 31663}, {5231, 31190, 4413}, {5432, 11019, 3748}, {5435, 10589, 1836}, {5704, 7288, 1837}, {5902, 11230, 4870}, {7988, 61716, 17605}, {10072, 26446, 5919}, {24239, 37634, 3745}

X(61650) = CENTROID OF THE PEDAL TRIANGLE OF X(37)

Barycentrics    a*(a^3*(b+c)-(b^2-c^2)^2+a^2*(b^2+c^2)-a*(b+c)*(b^2-6*b*c+c^2)) : :
X(61650) = 2*X[17332]+X[54344]

X(61650) lies on these lines: {1, 37503}, {2, 34377}, {6, 354}, {9, 5902}, {37, 517}, {44, 942}, {45, 65}, {101, 1100}, {165, 54285}, {391, 4430}, {518, 17330}, {966, 3681}, {1213, 3740}, {2097, 37674}, {2161, 50195}, {2178, 3576}, {2183, 21808}, {2245, 16601}, {2262, 5919}, {2270, 10389}, {2325, 3754}, {2646, 19297}, {3057, 16672}, {3196, 44840}, {3554, 47299}, {3698, 61321}, {3707, 3874}, {3731, 21853}, {3753, 17281}, {3812, 17369}, {3833, 5750}, {3848, 17398}, {3873, 37654}, {3880, 50113}, {3881, 4700}, {3943, 5836}, {4969, 34791}, {5044, 52706}, {5045, 16666}, {5257, 10176}, {5572, 18413}, {5819, 7671}, {5883, 50115}, {5903, 16676}, {5943, 9017}, {6791, 61672}, {8609, 17451}, {10175, 24005}, {10202, 54405}, {10207, 44547}, {15668, 43216}, {16521, 20358}, {16670, 18398}, {16675, 21871}, {17049, 49756}, {17245, 24471}, {17332, 54344}, {17392, 34371}, {17718, 61506}, {21864, 50193}, {22278, 56926}, {24476, 36404}, {31792, 39260}, {36744, 59337}, {37080, 54409}, {41581, 46907}, {61643, 61688}, {61663, 61668}

X(61650) = midpoint of X(i) and X(j) for these {i,j}: {37, 61704}
X(61650) = pole of line {4394, 48344} with respect to the DeLongchamps ellipse
X(61650) = intersection, other than A, B, C, of circumconics {{A, B, C, X(994), X(2191)}}, {{A, B, C, X(46018), X(57656)}}
X(61650) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37, 61704, 517}, {354, 374, 6}

X(61651) = CENTROID OF THE PEDAL TRIANGLE OF X(41)

Barycentrics    4*a^4+a^2*(b-c)^2-5*a^3*(b+c)-a*(b-c)^2*(b+c)+(b^2-c^2)^2 : :

X(61651) lies on these lines: {2, 51152}, {6, 17728}, {41, 515}, {44, 5432}, {218, 26446}, {226, 2246}, {354, 51406}, {374, 61643}, {672, 10164}, {910, 11246}, {1023, 49626}, {1125, 21373}, {2082, 5603}, {2280, 40869}, {2348, 61648}, {3475, 40131}, {3707, 5741}, {4675, 31203}, {5306, 61647}, {14439, 59584}, {16670, 31231}, {26258, 51194}, {30742, 51190}, {38028, 43065}, {46835, 61717}, {61506, 61652}

X(61651) = midpoint of X(i) and X(j) for these {i,j}: {41, 61706}
X(61651) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {41, 61706, 515}

X(61652) = CENTROID OF THE PEDAL TRIANGLE OF X(42)

Barycentrics    2*a^3+5*a^2*(b+c)-(b-c)^2*(b+c) : :
X(61652) = -X[4001]+4*X[6685]

X(61652) lies on these lines: {1, 31018}, {2, 34379}, {6, 2438}, {10, 31034}, {42, 516}, {75, 49986}, {193, 29828}, {226, 33128}, {354, 373}, {518, 17726}, {527, 46904}, {614, 11038}, {750, 4667}, {899, 3664}, {908, 4649}, {1051, 33152}, {1126, 12047}, {1155, 7277}, {1203, 28027}, {1215, 17772}, {1468, 10165}, {2308, 13405}, {2999, 59372}, {3240, 50307}, {3634, 31017}, {3666, 5852}, {3740, 37631}, {3751, 29639}, {3755, 24725}, {3879, 32931}, {3914, 61716}, {3936, 30768}, {3946, 32856}, {4001, 6685}, {4009, 17390}, {4023, 4670}, {4028, 26223}, {4035, 26061}, {4054, 49488}, {4062, 17355}, {4104, 19684}, {4431, 14459}, {4663, 5718}, {4684, 32944}, {4706, 7228}, {4722, 5745}, {4856, 50756}, {5205, 20090}, {5311, 21060}, {5316, 9345}, {5587, 5713}, {5657, 54421}, {5712, 38057}, {5847, 46897}, {5850, 46901}, {6791, 51406}, {7988, 11269}, {16173, 16474}, {16666, 17602}, {17012, 24231}, {17023, 33065}, {17150, 59730}, {17300, 60423}, {17392, 61686}, {17592, 17781}, {25385, 49685}, {26227, 51196}, {29832, 49536}, {29855, 51171}, {31179, 33114}, {32852, 53663}, {33070, 49529}, {33112, 49772}, {33122, 38049}, {33143, 50114}, {33156, 50115}, {37651, 60414}, {37662, 61649}, {48870, 59337}, {49479, 49987}, {49482, 50744}, {49490, 49989}, {61506, 61651}, {61648, 61661}, {61670, 61672}, {61688, 61694}

X(61652) = midpoint of X(i) and X(j) for these {i,j}: {42, 61707}
X(61652) = reflection of X(i) in X(j) for these {i,j}: {41011, 61707}
X(61652) = pole of line {31016, 55161} with respect to the dual conic of Yff parabola
X(61652) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 17718, 61647}, {42, 61707, 516}, {516, 61707, 41011}, {3879, 32931, 49990}, {17718, 61647, 3011}, {25385, 49685, 50758}, {61670, 61672, 61687}

X(61653) = CENTROID OF THE PEDAL TRIANGLE OF X(46)

Barycentrics    a*(a^4*(b+c)+2*a^2*b*c*(b+c)-2*a^3*(b+c)^2-(b-c)^2*(b+c)^3+2*a*(b-c)^2*(b^2+3*b*c+c^2)) : :
X(61653) = 2*X[46]+X[1898], 2*X[942]+X[41686], 2*X[1210]+X[41538]

X(61653) lies on these lines: {1, 58630}, {2, 210}, {5, 65}, {11, 41539}, {43, 8758}, {46, 1898}, {55, 15299}, {56, 17857}, {165, 61718}, {200, 33925}, {375, 61662}, {497, 7673}, {517, 11238}, {553, 15064}, {612, 12595}, {613, 3745}, {942, 41686}, {997, 20323}, {1058, 3057}, {1155, 1708}, {1210, 41538}, {1376, 55871}, {1427, 45885}, {1728, 11509}, {1788, 1858}, {1837, 6836}, {3035, 16465}, {3059, 8257}, {3303, 58643}, {3304, 34790}, {3305, 58651}, {3336, 40263}, {3683, 15297}, {3697, 15888}, {3711, 58650}, {3748, 42884}, {3870, 42886}, {4423, 58648}, {4511, 46677}, {5220, 55870}, {5221, 5777}, {5432, 5728}, {5434, 18908}, {5730, 16842}, {5844, 5919}, {5902, 54447}, {5927, 11246}, {6827, 7957}, {6854, 10404}, {6870, 54361}, {6879, 13374}, {6880, 12675}, {6883, 37080}, {6889, 24914}, {6905, 12680}, {6911, 14872}, {6992, 58637}, {7082, 37541}, {7672, 10589}, {7676, 14100}, {9657, 9947}, {9844, 15338}, {10157, 61716}, {10399, 31423}, {10895, 37544}, {12848, 31391}, {13243, 60782}, {14054, 26364}, {15059, 15904}, {15842, 26015}, {17441, 38472}, {17658, 51463}, {18397, 18838}, {18412, 31231}, {21077, 50208}, {23622, 39246}, {26723, 45946}, {37585, 37702}, {41711, 51380}, {49980, 56187}

X(61653) = midpoint of X(i) and X(j) for these {i,j}: {46, 61709}
X(61653) = reflection of X(i) in X(j) for these {i,j}: {1898, 61709}, {354, 17728}
X(61653) = pole of line {390, 10043} with respect to the Feuerbach hyperbola
X(61653) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 61663, 354}, {354, 61686, 61648}, {1708, 11502, 1155}

X(61654) = CENTROID OF THE PEDAL TRIANGLE OF X(48)

Barycentrics    4*a^5-a^4*(b+c)+(b-c)^2*(b+c)^3-4*a^3*(b^2+c^2) : :
X(61654) = -X[307]+4*X[58406]

X(61654) lies on these lines: {1, 8756}, {2, 9028}, {6, 17728}, {9, 6878}, {10, 22356}, {19, 5603}, {37, 7117}, {44, 5433}, {48, 515}, {71, 10164}, {219, 26446}, {281, 7967}, {306, 30882}, {307, 58406}, {355, 23073}, {374, 51406}, {604, 61706}, {610, 1699}, {946, 2173}, {1125, 54324}, {1385, 7359}, {1732, 7288}, {1855, 2302}, {1953, 59644}, {2267, 40869}, {2317, 20262}, {3475, 54385}, {3817, 61725}, {4297, 22357}, {5227, 27395}, {5790, 20818}, {5844, 59671}, {7289, 24553}, {8680, 35290}, {8804, 22054}, {11230, 59681}, {17718, 61680}, {21011, 38155}, {21748, 24005}, {24315, 26006}, {24541, 50198}, {26063, 54447}, {27382, 54445}, {29639, 47209}, {30902, 40940}, {35263, 46898}, {38028, 40937}

X(61654) = midpoint of X(i) and X(j) for these {i,j}: {48, 61710}
X(61654) = reflection of X(i) in X(j) for these {i,j}: {1826, 61710}, {61710, 40942}
X(61654) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {48, 40942, 1826}, {48, 61710, 515}, {515, 40942, 61710}

X(61655) = CENTROID OF THE PEDAL TRIANGLE OF X(49)

Barycentrics    4*a^6+2*a^2*b^2*c^2-5*a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2) : :
X(61655) = 2*X[49]+X[1594], 2*X[7542]+X[56292], -X[10024]+4*X[15806], -X[35491]+4*X[43394]

X(61655) lies on these lines: {2, 3167}, {5, 9545}, {6, 40317}, {22, 37645}, {49, 1594}, {51, 61681}, {54, 9820}, {110, 5133}, {140, 43845}, {154, 34603}, {156, 15559}, {184, 858}, {195, 10020}, {323, 6676}, {394, 7495}, {399, 44236}, {427, 9544}, {428, 35265}, {468, 1994}, {597, 15531}, {631, 58891}, {1147, 13160}, {1199, 16238}, {1353, 52297}, {1368, 11003}, {1493, 58435}, {1995, 11427}, {2979, 13394}, {3060, 7426}, {3292, 37636}, {3431, 44249}, {3580, 34986}, {3917, 40112}, {5012, 11064}, {5066, 15046}, {5422, 59543}, {5642, 5943}, {5654, 52069}, {5946, 59648}, {5972, 13366}, {6146, 9706}, {6677, 34545}, {6776, 30744}, {6800, 52397}, {7391, 26864}, {7394, 8780}, {7485, 37669}, {7542, 56292}, {7571, 54013}, {8550, 26913}, {8584, 47455}, {8703, 34796}, {9306, 14389}, {9704, 13371}, {9705, 12134}, {10018, 12161}, {10024, 15806}, {10182, 14831}, {10254, 11935}, {10257, 15032}, {10546, 59699}, {10601, 59551}, {11004, 41588}, {11206, 31133}, {11225, 61691}, {11422, 13567}, {11449, 12233}, {11451, 61507}, {12225, 19357}, {12370, 35487}, {13292, 14940}, {13352, 47096}, {13434, 59659}, {14118, 61607}, {14627, 44232}, {15033, 51425}, {15087, 44452}, {16868, 43595}, {17809, 18911}, {18445, 37118}, {22115, 61619}, {22660, 34005}, {25740, 43588}, {26879, 43839}, {26881, 37900}, {29012, 44108}, {31101, 48906}, {35266, 51130}, {35491, 43394}, {37347, 40111}, {37453, 37644}, {37472, 61608}, {38323, 47391}, {39899, 52298}, {41628, 61646}, {46451, 61606}, {55038, 58434}

X(61655) = midpoint of X(i) and X(j) for these {i,j}: {49, 61711}
X(61655) = reflection of X(i) in X(j) for these {i,j}: {1594, 61711}
X(61655) = inverse of X(41578) in Thomson-Gibert-Moses hyperbola
X(61655) = pole of line {10313, 30744} with respect to the Kiepert hyperbola
X(61655) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 23292, 5133}, {427, 9544, 46818}, {3060, 10192, 7426}, {5642, 61659, 5943}, {9306, 14389, 37990}, {9544, 59771, 427}, {59553, 61690, 2}

X(61656) = CENTROID OF THE PEDAL TRIANGLE OF X(50)

Barycentrics    4*a^8+(b^2-c^2)^4-7*a^6*(b^2+c^2)-a^2*(b^2-c^2)^2*(b^2+c^2)+a^4*(3*b^4+4*b^2*c^2+3*c^4) : :

X(61656) lies on these lines: {2, 6}, {30, 50}, {53, 18559}, {112, 47144}, {115, 58267}, {140, 41335}, {186, 1138}, {187, 3018}, {231, 2072}, {328, 53474}, {338, 40884}, {403, 39176}, {519, 41666}, {530, 41635}, {531, 41645}, {538, 41653}, {539, 41664}, {549, 566}, {571, 38321}, {577, 11648}, {754, 41659}, {1576, 50707}, {1637, 55130}, {2493, 7426}, {3003, 3163}, {3845, 9220}, {5063, 5309}, {5421, 40136}, {5915, 53505}, {6644, 34288}, {6749, 7577}, {7514, 7739}, {7753, 37347}, {8553, 18324}, {10510, 56370}, {11077, 40631}, {11079, 40630}, {16303, 18579}, {18316, 51545}, {18405, 54943}, {23200, 57598}, {32113, 47200}, {35921, 50660}, {36851, 60150}, {37943, 52418}, {37980, 44533}, {39484, 43620}, {41719, 60657}, {42459, 48368}, {44529, 47097}

X(61656) = midpoint of X(i) and X(j) for these {i,j}: {2, 41626}, {50, 1989}
X(61656) = reflection of X(i) in X(j) for these {i,j}: {1989, 16310}, {53416, 1989}
X(61656) = complement of X(52149)
X(61656) = perspector of circumconic {{A, B, C, X(99), X(54738)}}
X(61656) = X(i)-Ceva conjugate of X(j) for these {i, j}: {54959, 523}
X(61656) = X(i)-complementary conjugate of X(j) for these {i, j}: {18316, 2887}, {54959, 42327}, {58983, 4369}
X(61656) = pole of line {669, 58346} with respect to the circumcircle
X(61656) = pole of line {15543, 23301} with respect to the nine-point circle
X(61656) = pole of line {2501, 14566} with respect to the polar circle
X(61656) = pole of line {2, 265} with respect to the Kiepert hyperbola
X(61656) = pole of line {6, 34834} with respect to the Stammler hyperbola
X(61656) = pole of line {523, 14582} with respect to the Steiner inellipse
X(61656) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(1138)}}, {{A, B, C, X(323), X(14910)}}, {{A, B, C, X(1989), X(3580)}}, {{A, B, C, X(11064), X(11070)}}, {{A, B, C, X(14389), X(30537)}}, {{A, B, C, X(18316), X(52149)}}, {{A, B, C, X(34288), X(37644)}}, {{A, B, C, X(37638), X(52154)}}
X(61656) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 41626, 524}, {30, 16310, 1989}, {30, 1989, 53416}, {50, 1989, 30}, {187, 3018, 47322}, {230, 24855, 37637}, {395, 396, 3580}, {549, 14836, 566}, {7735, 11580, 230}

X(61657) = CENTROID OF THE PEDAL TRIANGLE OF X(51)

Barycentrics    2*a^6+6*a^2*(b^2-c^2)^2-7*a^4*(b^2+c^2)-(b^2-c^2)^2*(b^2+c^2) : :
X(61657) = -4*X[51]+X[428], 2*X[568]+X[34664], 2*X[3060]+X[7667], -10*X[3567]+X[3575], -7*X[9781]+X[16658], -4*X[10110]+X[16654], X[11225]+2*X[58470], 2*X[11232]+X[12134], 5*X[11451]+X[41628], 2*X[11745]+X[12024], X[12605]+8*X[16881], 2*X[13142]+7*X[15043] and many others

X(61657) lies on these lines: {2, 5093}, {4, 3531}, {5, 37644}, {6, 468}, {25, 14912}, {30, 11002}, {51, 428}, {125, 44107}, {140, 15018}, {182, 47582}, {193, 11284}, {235, 11432}, {323, 61624}, {343, 38317}, {373, 524}, {389, 974}, {427, 9777}, {511, 43957}, {523, 58900}, {546, 3448}, {547, 7605}, {568, 34664}, {575, 32269}, {576, 37648}, {597, 61644}, {1173, 26879}, {1199, 21841}, {1351, 30739}, {1353, 1995}, {1495, 12007}, {1594, 18947}, {1899, 52285}, {1906, 5656}, {1907, 3527}, {1992, 6090}, {1994, 6677}, {3060, 7667}, {3292, 32455}, {3564, 5640}, {3567, 3575}, {3580, 15019}, {3589, 41586}, {3629, 5651}, {5007, 35282}, {5032, 47597}, {5050, 44210}, {5064, 18950}, {5097, 11064}, {5305, 39024}, {5422, 7499}, {5476, 45303}, {5642, 20583}, {5645, 16239}, {5943, 5965}, {5972, 22330}, {6515, 37439}, {6676, 34545}, {6755, 56296}, {6776, 10301}, {6794, 57586}, {6800, 37904}, {7493, 53091}, {7495, 51732}, {7712, 47630}, {8550, 34417}, {8584, 61507}, {9781, 16658}, {9820, 32263}, {10019, 12233}, {10110, 16654}, {10182, 37505}, {11003, 37897}, {11179, 47312}, {11225, 58470}, {11232, 12134}, {11402, 35260}, {11424, 23328}, {11427, 52297}, {11451, 41628}, {11477, 54012}, {11482, 37645}, {11745, 12024}, {12605, 16881}, {12834, 37636}, {13142, 15043}, {13394, 39561}, {13490, 45969}, {13567, 15004}, {14627, 16238}, {15037, 16618}, {15038, 52262}, {15087, 44233}, {15448, 44109}, {15516, 32223}, {16198, 43808}, {16222, 32423}, {18358, 41724}, {18911, 21850}, {20423, 47311}, {21167, 43650}, {21849, 29317}, {21970, 53092}, {22521, 40884}, {23047, 39571}, {23292, 34565}, {23325, 45089}, {26926, 58471}, {31670, 47095}, {32235, 41595}, {32237, 33749}, {32358, 58531}, {33872, 51611}, {37643, 52293}, {37779, 61545}, {37899, 48906}, {37910, 48912}, {37911, 59771}, {38136, 61700}, {39522, 47090}, {39871, 44084}, {40132, 51170}, {42873, 43462}, {44080, 44489}, {44413, 47091}, {44456, 46336}, {51358, 60693}, {53858, 59767}, {58434, 61659}

X(61657) = midpoint of X(i) and X(j) for these {i,j}: {51, 61712}, {13321, 45967}, {35283, 61658}
X(61657) = reflection of X(i) in X(j) for these {i,j}: {11245, 61712}, {35283, 5943}
X(61657) = pole of line {5480, 40673} with respect to the Jerabek hyperbola
X(61657) = pole of line {5094, 59229} with respect to the Kiepert hyperbola
X(61657) = pole of line {352, 1499} with respect to the orthic inconic
X(61657) = pole of line {41614, 53091} with respect to the Stammler hyperbola
X(61657) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 61506, 61690}, {51, 11245, 428}, {51, 61712, 1503}, {3060, 45298, 7667}, {3527, 18916, 1907}, {3580, 15019, 18583}, {3580, 18583, 37454}, {5422, 41588, 7499}, {5943, 5965, 35283}, {5943, 61677, 61658}, {9777, 26869, 14853}, {11433, 14853, 26869}, {13321, 45967, 30}, {14853, 26869, 427}, {18911, 21850, 46517}, {61506, 61690, 468}

X(61658) = CENTROID OF THE PEDAL TRIANGLE OF X(52)

Barycentrics    2*a^6-5*a^4*(b^2+c^2)-(b^2-c^2)^2*(b^2+c^2)+4*a^2*(b^4-b^2*c^2+c^4) : :
X(61658) = -4*X[143]+X[12134], -9*X[373]+8*X[13361], -3*X[568]+X[38321], X[3575]+2*X[10112], -3*X[3917]+4*X[7734], -4*X[5446]+X[16655], X[5889]+2*X[12241], -3*X[5890]+X[44458], X[7553]+2*X[10116], 2*X[11264]+X[11819], -4*X[11745]+X[14516], 2*X[12362]+X[14531] and many others

X(61658) lies on these lines: {2, 6}, {4, 54930}, {5, 15004}, {22, 8550}, {30, 52}, {51, 3564}, {68, 381}, {76, 54798}, {94, 54769}, {125, 61624}, {143, 12134}, {161, 15580}, {184, 1353}, {195, 9820}, {297, 7760}, {317, 56296}, {324, 6748}, {373, 13361}, {376, 17834}, {427, 576}, {428, 542}, {467, 1990}, {468, 34986}, {511, 7667}, {519, 41668}, {530, 41637}, {531, 41647}, {538, 41655}, {539, 973}, {547, 1209}, {549, 569}, {567, 44201}, {568, 38321}, {575, 7499}, {598, 54636}, {648, 52280}, {671, 33513}, {754, 41661}, {800, 52032}, {1147, 44211}, {1351, 1899}, {1352, 9777}, {1368, 8538}, {1370, 11477}, {1493, 10020}, {1503, 3060}, {1539, 12101}, {1853, 5102}, {1999, 26611}, {2052, 27377}, {2917, 37940}, {3066, 14826}, {3070, 13428}, {3071, 13439}, {3087, 41244}, {3167, 61506}, {3292, 6677}, {3311, 11090}, {3312, 11091}, {3524, 37476}, {3543, 6225}, {3574, 61544}, {3575, 10112}, {3592, 56498}, {3594, 56497}, {3796, 14912}, {3819, 32068}, {3845, 18474}, {3917, 7734}, {5012, 12007}, {5050, 43653}, {5064, 20423}, {5093, 45303}, {5097, 21243}, {5133, 41724}, {5305, 60524}, {5446, 16655}, {5480, 11442}, {5485, 54797}, {5642, 32226}, {5889, 12241}, {5890, 44458}, {5943, 5965}, {6419, 56506}, {6420, 56504}, {6425, 56500}, {6426, 56499}, {6503, 8573}, {6676, 13366}, {6696, 43813}, {6747, 59661}, {6749, 52253}, {6776, 33586}, {6803, 11431}, {6997, 15069}, {7493, 17809}, {7529, 9936}, {7553, 10116}, {7576, 46443}, {7714, 50974}, {7745, 45793}, {7757, 35937}, {7758, 37344}, {7762, 40814}, {7812, 52281}, {8541, 15809}, {8703, 37478}, {9140, 23315}, {9544, 15448}, {9967, 10691}, {10192, 61685}, {10201, 12161}, {10982, 11411}, {11179, 37488}, {11232, 44407}, {11264, 11819}, {11402, 13394}, {11438, 44268}, {11441, 15873}, {11550, 21850}, {11745, 14516}, {12100, 37513}, {12160, 16072}, {12162, 44804}, {12359, 36749}, {12362, 14531}, {12585, 60774}, {12605, 58806}, {13157, 14642}, {13754, 16657}, {14627, 48411}, {15019, 37990}, {16252, 46451}, {16982, 45732}, {17364, 54284}, {18358, 44107}, {18583, 34565}, {18912, 31180}, {18916, 37498}, {18917, 44413}, {18951, 36747}, {19131, 50979}, {21841, 43844}, {22330, 37454}, {23039, 45967}, {23332, 61739}, {24981, 44106}, {26871, 55437}, {26872, 55438}, {26942, 54444}, {27376, 52282}, {31383, 39899}, {34507, 37439}, {34511, 35302}, {35266, 44077}, {35296, 59546}, {37340, 40712}, {37341, 40711}, {37452, 51885}, {37472, 44158}, {37897, 44110}, {43650, 48876}, {43957, 44479}, {44210, 44470}, {44270, 51425}, {44442, 54132}, {46517, 55718}, {52433, 59702}, {54629, 54922}, {54710, 54784}, {54761, 54778}, {54764, 54776}, {54765, 54782}, {54785, 54867}, {54801, 54927}, {54911, 54926}, {55038, 58434}, {56292, 59659}, {59553, 61645}, {61646, 61690}

X(61658) = midpoint of X(i) and X(j) for these {i,j}: {2, 41628}, {52, 61713}, {3060, 45968}, {5889, 52069}, {13490, 32358}
X(61658) = reflection of X(i) in X(j) for these {i,j}: {11245, 11225}, {12134, 13490}, {12162, 44804}, {13490, 143}, {3819, 32068}, {3917, 45298}, {35283, 61657}, {428, 21849}, {5943, 61677}, {52069, 12241}, {6146, 61713}, {61713, 13292}
X(61658) = isotomic conjugate of X(54922)
X(61658) = X(i)-Ceva conjugate of X(j) for these {i, j}: {54629, 2}
X(61658) = X(i)-complementary conjugate of X(j) for these {i, j}: {54666, 2887}
X(61658) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {54629, 6327}
X(61658) = pole of line {23301, 34963} with respect to the nine-point circle
X(61658) = pole of line {5, 6467} with respect to the Jerabek hyperbola
X(61658) = pole of line {2, 1879} with respect to the Kiepert hyperbola
X(61658) = pole of line {3566, 30451} with respect to the orthic inconic
X(61658) = pole of line {6, 15024} with respect to the Stammler hyperbola
X(61658) = pole of line {523, 46451} with respect to the Steiner circumellipse
X(61658) = pole of line {2, 54922} with respect to the Wallace hyperbola
X(61658) = pole of line {525, 15340} with respect to the dual conic of 1st DrozFarny circle
X(61658) = pole of line {525, 55190} with respect to the dual conic of orthoptic circle of the Steiner inellipse
X(61658) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(21841)}}, {{A, B, C, X(6), X(54798)}}, {{A, B, C, X(69), X(54930)}}, {{A, B, C, X(323), X(54769)}}, {{A, B, C, X(394), X(43844)}}, {{A, B, C, X(524), X(39284)}}, {{A, B, C, X(599), X(54636)}}, {{A, B, C, X(1989), X(53414)}}, {{A, B, C, X(1992), X(54797)}}, {{A, B, C, X(1993), X(3527)}}, {{A, B, C, X(5468), X(33513)}}, {{A, B, C, X(37672), X(60120)}}, {{A, B, C, X(41628), X(54864)}}
X(61658) = barycentric product X(i)*X(j) for these (i, j): {264, 43844}, {21841, 69}
X(61658) = barycentric quotient X(i)/X(j) for these (i, j): {2, 54922}, {21841, 4}, {43844, 3}
X(61658) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 41628, 524}, {6, 343, 37649}, {6, 6515, 343}, {30, 13292, 61713}, {30, 61713, 6146}, {52, 61713, 30}, {68, 37493, 45089}, {143, 32358, 12134}, {184, 41588, 32269}, {193, 11433, 394}, {394, 11433, 37648}, {395, 396, 53414}, {511, 11225, 11245}, {542, 21849, 428}, {1353, 41588, 184}, {1993, 13567, 11064}, {1993, 37644, 13567}, {1994, 3580, 23292}, {3060, 45968, 1503}, {3629, 13567, 1993}, {3917, 61712, 45298}, {5422, 45794, 141}, {5943, 61677, 61657}, {5965, 61657, 35283}, {5965, 61677, 5943}, {13366, 41586, 6676}, {23292, 32455, 1994}, {34380, 45298, 3917}, {34545, 37636, 3589}, {34545, 37779, 37636}, {41724, 53863, 5133}

X(61659) = CENTROID OF THE PEDAL TRIANGLE OF X(54)

Barycentrics    4*a^6+a^2*(b^2-c^2)^2-6*a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2) : :
X(61659) = X[4]+5*X[54], 5*X[6]+X[13622], X[185]+2*X[15739], X[546]+2*X[20585], -2*X[548]+5*X[10610], 2*X[973]+X[21660], X[1209]+2*X[1493], -5*X[2888]+17*X[7486], -5*X[3519]+23*X[55860], -8*X[3856]+5*X[22804], 7*X[3857]+5*X[36966], -11*X[5072]+5*X[6288] and many others

X(61659) lies on these lines: {2, 5965}, {4, 54}, {6, 13622}, {51, 10192}, {125, 11245}, {161, 32367}, {185, 15739}, {195, 394}, {373, 59553}, {389, 46265}, {427, 44109}, {428, 44108}, {468, 34565}, {539, 3167}, {546, 20585}, {548, 10610}, {549, 1154}, {567, 1568}, {597, 61667}, {826, 1640}, {973, 21660}, {1209, 1493}, {1853, 11402}, {1993, 19150}, {1994, 41586}, {2888, 7486}, {2917, 55578}, {3519, 55860}, {3534, 3796}, {3742, 61669}, {3856, 22804}, {3857, 36966}, {5012, 51360}, {5041, 44887}, {5066, 23516}, {5072, 6288}, {5133, 24981}, {5422, 9977}, {5462, 59648}, {5476, 35264}, {5480, 44110}, {5640, 41713}, {5642, 5943}, {5890, 10193}, {5972, 34545}, {6030, 19924}, {6152, 40632}, {6467, 51994}, {7592, 23329}, {7691, 15717}, {8995, 12971}, {9544, 19130}, {9972, 59543}, {10115, 12606}, {10169, 40673}, {10303, 15801}, {11271, 15605}, {11422, 21243}, {11423, 20299}, {11550, 17809}, {11804, 47117}, {12266, 13607}, {12965, 13986}, {13394, 21969}, {13399, 15032}, {13431, 21230}, {13472, 26917}, {13567, 44111}, {13857, 51138}, {14156, 15037}, {14389, 34986}, {14627, 44516}, {14826, 15022}, {14853, 44082}, {15704, 20424}, {15750, 32333}, {15800, 17800}, {22112, 37669}, {22330, 41596}, {23358, 35479}, {26879, 34564}, {31255, 55711}, {32223, 53863}, {32345, 46373}, {33565, 57714}, {33992, 35885}, {34566, 61691}, {37645, 43650}, {42059, 43834}, {43573, 61711}, {58434, 61657}

X(61659) = midpoint of X(i) and X(j) for these {i,j}: {2, 55038}, {54, 61715}
X(61659) = reflection of X(i) in X(j) for these {i,j}: {3574, 61715}, {41578, 5943}, {61715, 12242}
X(61659) = inverse of X(12007) in Jerabek hyperbola
X(61659) = inverse of X(5943) in Thomson-Gibert-Moses hyperbola
X(61659) = perspector of circumconic {{A, B, C, X(16813), X(34580)}}
X(61659) = pole of line {389, 12007} with respect to the Jerabek hyperbola
X(61659) = pole of line {12077, 13412} with respect to the orthic inconic
X(61659) = pole of line {5097, 5562} with respect to the Stammler hyperbola
X(61659) = pole of line {37647, 52347} with respect to the Wallace hyperbola
X(61659) = intersection, other than A, B, C, of circumconics {{A, B, C, X(275), X(13622)}}, {{A, B, C, X(8884), X(22268)}}
X(61659) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55038, 5965}, {54, 3574, 10619}, {54, 61715, 18400}, {1994, 58447, 41586}, {3574, 10619, 32340}, {5943, 61655, 5642}, {12242, 18400, 61715}, {13366, 23292, 125}, {18400, 61715, 3574}, {40632, 58489, 6152}

X(61660) = CENTROID OF THE PEDAL TRIANGLE OF X(57)

Barycentrics    a*(a^4*(b+c)-2*a^3*(b+c)^2-(b-c)^2*(b+c)^3+2*a*(b-c)^2*(b^2+4*b*c+c^2)) : :
X(61660) = -4*X[11019]+X[17642]

X(61660) lies on these lines: {1, 58643}, {2, 210}, {6, 46344}, {11, 65}, {51, 61671}, {55, 21153}, {56, 33995}, {57, 971}, {72, 5316}, {78, 20323}, {373, 374}, {553, 5927}, {899, 21346}, {936, 3304}, {938, 3057}, {942, 1656}, {1155, 1445}, {1170, 10939}, {1418, 2635}, {1466, 10396}, {1471, 51361}, {1475, 3119}, {1836, 17604}, {1887, 40836}, {1998, 3689}, {3059, 4413}, {3149, 12680}, {3243, 51380}, {3303, 61122}, {3306, 5784}, {3338, 6918}, {3339, 17634}, {3555, 6700}, {3601, 33575}, {3660, 18412}, {3698, 6734}, {3868, 5328}, {3893, 12649}, {3911, 5728}, {3983, 15888}, {4009, 20946}, {4654, 10157}, {4860, 8581}, {5044, 11518}, {5218, 5572}, {5221, 12688}, {5228, 9817}, {5289, 54392}, {5435, 10391}, {5531, 5563}, {5851, 60932}, {5902, 7988}, {5919, 28234}, {6745, 15185}, {6834, 37566}, {6864, 10404}, {6865, 7957}, {6927, 12675}, {6956, 13374}, {8167, 58651}, {9581, 37544}, {9848, 37567}, {9940, 10399}, {10389, 38031}, {10582, 58648}, {11018, 31231}, {11019, 17642}, {11510, 12333}, {12516, 12863}, {13411, 17609}, {15299, 37541}, {15844, 17606}, {17366, 23710}, {17559, 45120}, {24928, 37736}, {27383, 34791}, {31391, 60939}, {31793, 37723}, {36002, 60948}, {37240, 60985}, {38150, 61716}, {38375, 40133}, {41712, 54408}, {41863, 58649}, {45744, 49980}, {51408, 61647}, {52638, 61016}

X(61660) = midpoint of X(i) and X(j) for these {i,j}: {57, 61718}
X(61660) = reflection of X(i) in X(j) for these {i,j}: {1864, 61718}
X(61660) = perspector of circumconic {{A, B, C, X(32041), X(55002)}}
X(61660) = pole of line {390, 515} with respect to the Feuerbach hyperbola
X(61660) = pole of line {1465, 29571} with respect to the dual conic of Yff parabola
X(61660) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {57, 61718, 971}, {354, 61653, 210}, {354, 61686, 17718}, {373, 61662, 374}, {971, 61718, 1864}, {17728, 61663, 354}

X(61661) = CENTROID OF THE PEDAL TRIANGLE OF X(58)

Barycentrics    4*a^3-a*(b-c)^2+2*a^2*(b+c)+(b-c)^2*(b+c) : :
X(61661) = -4*X[6693]+X[41014]

X(61661) lies on these lines: {1, 15670}, {2, 6}, {3, 48857}, {4, 54587}, {11, 2308}, {21, 49739}, {27, 1990}, {30, 58}, {31, 3058}, {32, 48848}, {37, 5325}, {42, 4995}, {44, 39595}, {57, 2160}, {63, 17246}, {171, 49732}, {226, 7277}, {345, 17388}, {354, 61643}, {375, 61687}, {376, 387}, {381, 5292}, {386, 549}, {440, 3284}, {442, 49744}, {469, 6749}, {519, 3704}, {530, 41639}, {531, 41649}, {538, 41657}, {539, 41669}, {540, 16052}, {547, 45939}, {551, 58386}, {553, 1086}, {583, 1764}, {594, 50052}, {595, 15170}, {740, 59574}, {754, 41663}, {896, 4854}, {967, 34288}, {1100, 5745}, {1108, 25080}, {1171, 1989}, {1193, 5298}, {1203, 3582}, {1468, 5434}, {1714, 44217}, {1761, 2257}, {1999, 3943}, {2221, 55906}, {2245, 18163}, {2482, 40621}, {2796, 25607}, {2999, 47057}, {3052, 10385}, {3241, 56313}, {3452, 16669}, {3524, 4255}, {3534, 48837}, {3666, 16585}, {3687, 4969}, {3752, 18593}, {3755, 50808}, {3756, 5642}, {3769, 49524}, {3772, 4654}, {3816, 16468}, {3826, 37604}, {3929, 8557}, {4000, 18625}, {4052, 54553}, {4205, 49729}, {4256, 12100}, {4257, 8703}, {4267, 14636}, {4360, 59583}, {4364, 29841}, {4370, 35652}, {4415, 4641}, {4421, 50282}, {4649, 6690}, {4653, 15673}, {4658, 6675}, {4683, 4831}, {4697, 50755}, {4722, 29683}, {4733, 59628}, {4753, 59726}, {4851, 56519}, {4966, 6679}, {5021, 7739}, {5051, 50215}, {5158, 7536}, {5222, 43066}, {5230, 11237}, {5273, 16777}, {5295, 50053}, {5309, 36728}, {5398, 28459}, {5429, 44669}, {5432, 61358}, {5846, 33121}, {5852, 33152}, {6173, 37887}, {6175, 24883}, {6661, 17034}, {6693, 41014}, {6793, 61673}, {6841, 56402}, {7227, 55095}, {7490, 40138}, {7741, 56343}, {8731, 18185}, {9607, 37416}, {10032, 33100}, {10072, 16466}, {10168, 50595}, {10449, 48859}, {10479, 50323}, {11235, 50303}, {11238, 11269}, {11246, 33128}, {11679, 17369}, {13478, 54586}, {15677, 16948}, {15762, 52954}, {16418, 48846}, {16579, 56531}, {17020, 40612}, {17045, 38000}, {17061, 32913}, {17070, 33097}, {17126, 49719}, {17340, 26065}, {17374, 20106}, {17390, 33116}, {17469, 51463}, {17525, 52680}, {17602, 32912}, {17747, 60697}, {17768, 33135}, {18191, 40952}, {18201, 59477}, {18206, 50178}, {19875, 51667}, {20182, 55868}, {20359, 22277}, {21024, 50162}, {21104, 31148}, {21487, 36741}, {23967, 35080}, {24477, 38315}, {24880, 49743}, {24931, 49718}, {25441, 49716}, {25466, 48825}, {26723, 37520}, {28610, 49747}, {29845, 41002}, {33296, 59538}, {37595, 54357}, {37597, 40133}, {41638, 49572}, {41648, 49571}, {42034, 49726}, {42047, 49721}, {42049, 50120}, {43043, 52423}, {44210, 54426}, {45222, 51583}, {49462, 59544}, {49470, 59580}, {49554, 51005}, {50104, 50292}, {50113, 56523}, {50222, 53423}, {50223, 53426}, {50591, 54169}, {51406, 61688}, {51408, 61663}, {52187, 57663}, {54497, 54697}, {54676, 54768}, {54699, 54700}, {61648, 61652}

X(61661) = midpoint of X(i) and X(j) for these {i,j}: {2, 41629}, {58, 3017}
X(61661) = reflection of X(i) in X(j) for these {i,j}: {1834, 3017}
X(61661) = perspector of circumconic {{A, B, C, X(99), X(55003)}}
X(61661) = X(i)-complementary conjugate of X(j) for these {i, j}: {26734, 626}, {60172, 2887}
X(61661) = pole of line {14321, 59914} with respect to the Spieker circle
X(61661) = pole of line {2, 17190} with respect to the Kiepert hyperbola
X(61661) = pole of line {523, 11125} with respect to the Steiner inellipse
X(61661) = pole of line {57066, 59589} with respect to the dual conic of incircle
X(61661) = pole of line {30, 1125} with respect to the dual conic of Yff parabola
X(61661) = intersection, other than A, B, C, of circumconics {{A, B, C, X(57), X(56440)}}, {{A, B, C, X(69), X(54587)}}, {{A, B, C, X(323), X(1171)}}, {{A, B, C, X(333), X(10543)}}, {{A, B, C, X(391), X(52187)}}, {{A, B, C, X(966), X(34288)}}, {{A, B, C, X(967), X(15066)}}, {{A, B, C, X(1213), X(1989)}}, {{A, B, C, X(2160), X(2287)}}, {{A, B, C, X(3578), X(24624)}}, {{A, B, C, X(3936), X(60139)}}, {{A, B, C, X(4417), X(54586)}}, {{A, B, C, X(9164), X(37792)}}, {{A, B, C, X(14534), X(37631)}}, {{A, B, C, X(17398), X(30537)}}, {{A, B, C, X(39980), X(56439)}}, {{A, B, C, X(41629), X(54553)}}
X(61661) = barycentric product X(i)*X(j) for these (i, j): {10543, 7}, {53588, 53589}
X(61661) = barycentric quotient X(i)/X(j) for these (i, j): {10543, 8}
X(61661) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 16704, 3578}, {2, 333, 49730}, {2, 3578, 1211}, {2, 37631, 17056}, {2, 41629, 524}, {2, 4921, 49724}, {2, 49730, 1213}, {2, 50256, 3936}, {2, 81, 37631}, {6, 37642, 37646}, {6, 37646, 37662}, {30, 3017, 1834}, {58, 3017, 30}, {81, 31204, 37635}, {81, 32911, 323}, {323, 35466, 51415}, {376, 387, 48842}, {549, 48861, 386}, {1999, 44416, 3943}, {5292, 48870, 381}, {32787, 32788, 17330}, {35466, 37631, 2}, {37640, 37641, 391}, {37642, 37666, 6}, {39107, 39108, 37792}, {61643, 61670, 354}

X(61662) = CENTROID OF THE PEDAL TRIANGLE OF X(63)

Barycentrics    a*(-4*a^3*b*c+a^4*(b+c)-(b-c)^2*(b+c)^3+4*a*b*c*(b^2+c^2)) : :
X(61662) = 2*X[63]+X[1824], -4*X[5745]+X[17441]

X(61662) lies on these lines: {2, 34381}, {10, 26933}, {38, 40962}, {63, 1824}, {72, 1150}, {210, 3917}, {354, 61643}, {373, 374}, {375, 61653}, {392, 46909}, {896, 12723}, {942, 24597}, {1155, 21867}, {1827, 1936}, {1828, 6734}, {2000, 24320}, {2355, 37581}, {3198, 22060}, {3753, 33114}, {3937, 5784}, {4414, 40965}, {5745, 17441}, {5791, 18732}, {7085, 21370}, {9004, 17718}, {12721, 36263}, {12722, 36277}, {16064, 56178}, {18210, 25939}, {21015, 21621}, {24476, 35466}, {24892, 40961}, {26884, 59681}, {28052, 61160}, {29855, 58581}, {40985, 54289}, {61667, 61668}, {61672, 61673}

X(61662) = midpoint of X(i) and X(j) for these {i,j}: {63, 61720}
X(61662) = reflection of X(i) in X(j) for these {i,j}: {1824, 61720}
X(61662) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {210, 61671, 3917}, {374, 61660, 373}

X(61663) = CENTROID OF THE PEDAL TRIANGLE OF X(65)

Barycentrics    a*(a^4*(b+c)+2*a*(b^2-c^2)^2-(b-c)^2*(b+c)*(b^2+c^2)-2*a^3*(b^2+b*c+c^2)) : :
X(61663) = 2*X[10]+X[14054], X[950]+2*X[12432], -X[1829]+4*X[58493], -3*X[5640]+X[41717], 2*X[6738]+X[15556], -X[7354]+4*X[37544]

X(61663) lies on these lines: {1, 6883}, {2, 210}, {4, 65}, {6, 5089}, {10, 14054}, {11, 5173}, {12, 942}, {40, 10399}, {42, 8758}, {51, 3827}, {55, 1708}, {56, 33597}, {57, 11502}, {72, 3715}, {125, 15904}, {181, 40959}, {226, 15064}, {375, 61669}, {480, 8257}, {497, 7672}, {517, 3058}, {553, 2801}, {912, 4654}, {950, 12432}, {960, 5047}, {971, 11246}, {997, 3304}, {1006, 37080}, {1071, 5221}, {1155, 7411}, {1202, 38375}, {1376, 16465}, {1445, 37578}, {1699, 61718}, {1788, 37112}, {1829, 58493}, {2194, 4233}, {2346, 3748}, {2551, 3868}, {2646, 6986}, {2771, 33519}, {2836, 45237}, {2982, 36122}, {3057, 6992}, {3059, 60987}, {3336, 13369}, {3338, 6911}, {3474, 10394}, {3485, 6886}, {3649, 5777}, {3811, 37249}, {3812, 4197}, {3870, 33925}, {3874, 21075}, {4511, 20323}, {4640, 55873}, {4860, 17625}, {4878, 21346}, {5178, 5836}, {5218, 11020}, {5432, 11018}, {5433, 16193}, {5640, 41717}, {5693, 30326}, {5729, 7082}, {5884, 41561}, {5903, 9580}, {5904, 11518}, {5927, 61716}, {5943, 41581}, {6684, 10122}, {6738, 15556}, {6826, 10404}, {6829, 58631}, {6830, 13374}, {6887, 11375}, {6905, 12675}, {6987, 7957}, {6989, 24914}, {6991, 17606}, {7069, 42289}, {7354, 37544}, {7474, 18165}, {7671, 10385}, {8270, 61398}, {9004, 61640}, {9844, 12953}, {9943, 17637}, {10388, 30330}, {10389, 15104}, {10398, 30223}, {10543, 31793}, {11019, 18839}, {11237, 18908}, {11501, 41537}, {11509, 37287}, {11529, 18397}, {12680, 50701}, {12710, 37568}, {12711, 37567}, {12848, 14100}, {13750, 37438}, {14110, 37724}, {15726, 60951}, {15733, 34612}, {15888, 34790}, {16137, 31835}, {17552, 25917}, {17660, 60782}, {18389, 18838}, {20229, 53413}, {20277, 61358}, {20292, 41871}, {21454, 40269}, {22321, 40635}, {24473, 31141}, {24982, 39772}, {26040, 41228}, {28466, 59337}, {31391, 60975}, {34339, 37401}, {34381, 61666}, {36016, 60713}, {37106, 58637}, {37300, 56176}, {40659, 60978}, {40663, 50195}, {40940, 45946}, {51408, 61661}, {54357, 58651}, {58563, 61008}, {58565, 58636}, {58578, 59491}, {61650, 61668}

X(61663) = midpoint of X(i) and X(j) for these {i,j}: {65, 61722}
X(61663) = reflection of X(i) in X(j) for these {i,j}: {1858, 61722}, {41581, 5943}, {61669, 375}, {61722, 44547}
X(61663) = perspector of circumconic {{A, B, C, X(26706), X(32041)}}
X(61663) = pole of line {521, 26546} with respect to the polar circle
X(61663) = pole of line {4, 390} with respect to the Feuerbach hyperbola
X(61663) = pole of line {3827, 58889} with respect to the Jerabek hyperbola
X(61663) = pole of line {1865, 5089} with respect to the Kiepert hyperbola
X(61663) = pole of line {650, 1734} with respect to the orthic inconic
X(61663) = pole of line {16577, 29571} with respect to the dual conic of Yff parabola
X(61663) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(40141)}}, {{A, B, C, X(158), X(7162)}}, {{A, B, C, X(1002), X(1118)}}, {{A, B, C, X(1857), X(59269)}}, {{A, B, C, X(27475), X(56231)}}
X(61663) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {65, 1864, 1836}, {65, 1898, 4295}, {65, 61722, 6001}, {210, 354, 17718}, {354, 61649, 3742}, {354, 61653, 2}, {354, 61660, 17728}, {1737, 13407, 6881}, {3681, 38057, 210}, {6001, 44547, 61722}, {6001, 61722, 1858}, {15104, 41861, 10389}, {15185, 17658, 41711}

X(61664) = CENTROID OF THE PEDAL TRIANGLE OF X(66)

Barycentrics    a^2*(a^10*(b^2+c^2)-a^8*(b^2+c^2)^2-(b^4-c^4)^2*(b^4-4*b^2*c^2+c^4)-2*a^6*(b^6+c^6)+2*a^4*(b^8-b^6*c^2-b^2*c^6+c^8)+a^2*(b^10-b^8*c^2-b^2*c^8+c^10)) : :
X(61664) = X[52]+2*X[34118], -X[1177]+4*X[58495], -X[5596]+4*X[58547], -3*X[5640]+X[41719], X[15583]+2*X[41579], 2*X[18382]+X[37511], -X[34774]+4*X[58532], -X[44492]+4*X[58496], -X[54334]+3*X[61735]

X(61664) lies on these lines: {2, 2393}, {4, 66}, {6, 14580}, {24, 35370}, {51, 51745}, {52, 34118}, {125, 1205}, {141, 1209}, {159, 182}, {206, 1995}, {511, 14852}, {524, 61666}, {575, 10274}, {599, 34751}, {858, 3313}, {895, 39125}, {924, 1640}, {1177, 58495}, {1503, 9730}, {1594, 50649}, {1853, 9971}, {2781, 23324}, {2854, 23326}, {5596, 58547}, {5640, 41719}, {5943, 19153}, {6000, 52989}, {7393, 34787}, {7487, 58492}, {7576, 36201}, {7716, 52028}, {7729, 36990}, {8681, 11216}, {9019, 23332}, {10169, 40673}, {10192, 40670}, {10249, 14070}, {11511, 14913}, {12272, 28708}, {13567, 51994}, {15577, 37513}, {15583, 41579}, {18382, 37511}, {18911, 36851}, {18919, 32366}, {19506, 48895}, {31166, 45979}, {31267, 40132}, {32110, 44883}, {34774, 58532}, {44492, 58496}, {54334, 61735}

X(61664) = midpoint of X(i) and X(j) for these {i,j}: {66, 61723}, {599, 34751}, {1853, 9971}, {7729, 36990}
X(61664) = reflection of X(i) in X(j) for these {i,j}: {10192, 40670}, {19153, 5943}, {31166, 45979}, {40673, 10169}, {61683, 61676}, {61723, 9969}
X(61664) = pole of line {8541, 11550} with respect to the Jerabek hyperbola
X(61664) = pole of line {14580, 27376} with respect to the Kiepert hyperbola
X(61664) = pole of line {2485, 30209} with respect to the orthic inconic
X(61664) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {66, 61723, 34146}, {2393, 61676, 61683}, {9969, 34146, 61723}

X(61665) = CENTROID OF THE PEDAL TRIANGLE OF X(67)

Barycentrics    a^2*(a^10*(b^2+c^2)+a^2*(b-c)^2*(b+c)^2*(b^2+c^2)*(b^4-5*b^2*c^2+c^4)-(b^4-c^4)^2*(b^4-5*b^2*c^2+c^4)-a^8*(b^4+4*b^2*c^2+c^4)+a^6*(-2*b^6+5*b^4*c^2+5*b^2*c^4-2*c^6)+a^4*(2*b^8-b^6*c^2-4*b^4*c^4-b^2*c^6+2*c^8)) : :
X(61665) = -X[5095]+4*X[58495], -3*X[5640]+X[41720], 2*X[6698]+X[32299], -4*X[9822]+X[56565], -5*X[11451]+3*X[52699], -X[15074]+4*X[20396], 2*X[15118]+X[32260], X[16003]+2*X[43130], -X[47280]+4*X[60774]

X(61665) lies on circumconic {{A, B, C, X(5505), X(46105)}} and on these lines: {2, 2854}, {4, 67}, {6, 5505}, {125, 2393}, {186, 12367}, {524, 45237}, {526, 1640}, {542, 9730}, {599, 14852}, {1209, 5181}, {2930, 15462}, {3060, 13169}, {5095, 58495}, {5621, 37487}, {5622, 11464}, {5640, 41720}, {5642, 61676}, {5663, 47353}, {5943, 15303}, {6593, 16042}, {6644, 11579}, {6698, 32299}, {7669, 14649}, {9019, 10989}, {9027, 47465}, {9140, 11188}, {9822, 56565}, {11451, 52699}, {11574, 44321}, {12039, 32235}, {12824, 16776}, {14982, 18420}, {15074, 20396}, {15118, 32260}, {16003, 43130}, {17853, 32250}, {18374, 37962}, {19151, 32154}, {19153, 32251}, {25489, 52171}, {32242, 41255}, {33851, 35921}, {34319, 41670}, {47280, 60774}, {47341, 47558}

X(61665) = midpoint of X(i) and X(j) for these {i,j}: {67, 9971}, {3060, 13169}, {9140, 11188}, {17853, 32250}, {32260, 40673}
X(61665) = reflection of X(i) in X(j) for these {i,j}: {11574, 44321}, {12824, 16776}, {15303, 5943}, {34319, 41670}, {40673, 15118}, {40949, 9971}, {5642, 61676}, {6, 12099}, {6593, 40670}, {9971, 32246}
X(61665) = pole of line {5523, 5913} with respect to the Kiepert hyperbola
X(61665) = pole of line {2492, 2780} with respect to the orthic inconic
X(61665) = pole of line {47549, 58357} with respect to the Stammler hyperbola
X(61665) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {67, 9971, 2781}, {2781, 32246, 9971}, {2781, 9971, 40949}

X(61666) = CENTROID OF THE PEDAL TRIANGLE OF X(68)

Barycentrics    a^2*(a^2-b^2-c^2)*(a^6*(b^2+c^2)-a^4*(b^2+c^2)^2+(b^2-c^2)^2*(b^4-4*b^2*c^2+c^4)-a^2*(b^2+c^2)*(b^4-4*b^2*c^2+c^4)) : :
X(61666) = 2*X[5]+X[21651], -3*X[373]+2*X[59553], 2*X[389]+X[12429], -7*X[3090]+X[12271], 5*X[3091]+X[12282], -4*X[5462]+X[6193], -X[5562]+4*X[61544], -2*X[5654]+3*X[14845], -X[9936]+4*X[58545], -4*X[10110]+X[12164], X[10575]+2*X[12293], -X[10625]+4*X[12359]

X(61666) lies on these lines: {2, 34382}, {4, 52}, {5, 21651}, {6, 1196}, {51, 3564}, {125, 343}, {155, 9777}, {161, 44470}, {184, 8548}, {216, 23158}, {373, 59553}, {389, 12429}, {394, 8538}, {511, 1853}, {524, 61664}, {539, 41578}, {542, 41580}, {569, 9937}, {1147, 5422}, {1209, 20302}, {1640, 8673}, {1843, 41588}, {1899, 37511}, {1995, 41619}, {2782, 42453}, {2854, 10192}, {3090, 12271}, {3091, 12282}, {3357, 17834}, {3580, 27365}, {3796, 19131}, {5449, 37636}, {5462, 6193}, {5562, 61544}, {5651, 34966}, {5654, 14845}, {5891, 14852}, {5946, 9825}, {6146, 31829}, {6353, 12272}, {6467, 6676}, {7529, 17836}, {9019, 15583}, {9730, 11245}, {9936, 58545}, {10110, 12164}, {10154, 34750}, {10539, 19458}, {10565, 12283}, {10575, 12293}, {10625, 12359}, {11090, 12603}, {11091, 12604}, {11427, 32284}, {12239, 35837}, {12240, 35836}, {12309, 36752}, {14855, 17702}, {15004, 19139}, {15019, 41597}, {15060, 44920}, {17810, 43130}, {21243, 50649}, {21312, 37478}, {21849, 47353}, {23307, 43817}, {31180, 45780}, {34381, 61663}, {35264, 44077}, {51140, 58470}, {61646, 61685}

X(61666) = midpoint of X(i) and X(j) for these {i,j}: {68, 61724}
X(61666) = reflection of X(i) in X(j) for these {i,j}: {3167, 5943}, {34750, 10154}, {52, 61724}, {5891, 14852}, {61724, 12235}
X(61666) = perspector of circumconic {{A, B, C, X(3565), X(30450)}}
X(61666) = pole of line {3564, 8538} with respect to the Jerabek hyperbola
X(61666) = pole of line {193, 1147} with respect to the Stammler hyperbola
X(61666) = pole of line {9723, 57518} with respect to the Wallace hyperbola
X(61666) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(847), X(8770)}}, {{A, B, C, X(5392), X(6391)}}, {{A, B, C, X(14593), X(53059)}}
X(61666) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {68, 61724, 13754}, {5020, 6391, 52077}, {5943, 8681, 3167}, {6391, 14913, 40337}, {12235, 13754, 61724}, {13754, 61724, 52}

X(61667) = CENTROID OF THE PEDAL TRIANGLE OF X(69)

Barycentrics    a^2*(-b^6-4*a^2*b^2*c^2+5*b^4*c^2+5*b^2*c^4-c^6+a^4*(b^2+c^2)) : :
X(61667) = -2*X[6]+3*X[373], X[185]+2*X[15069], -X[193]+3*X[5640], -X[1205]+4*X[32257], -5*X[1656]+2*X[32284], -7*X[3090]+4*X[44495], -X[3313]+4*X[3631], -7*X[3619]+6*X[15082], -5*X[3620]+3*X[7998], X[3630]+2*X[41579], -5*X[3763]+2*X[32366], -2*X[3819]+3*X[21356] and many others

X(61667) lies on these lines: {2, 8681}, {4, 69}, {6, 373}, {51, 524}, {125, 126}, {159, 35268}, {185, 15069}, {193, 5640}, {216, 9155}, {343, 8263}, {394, 8541}, {512, 55271}, {520, 1640}, {568, 11898}, {569, 9925}, {577, 33926}, {597, 61659}, {599, 1853}, {1147, 5050}, {1205, 32257}, {1353, 13363}, {1656, 32284}, {1974, 35259}, {1992, 5943}, {1993, 9813}, {3060, 11160}, {3090, 44495}, {3313, 3631}, {3410, 12058}, {3564, 9730}, {3619, 15082}, {3620, 7998}, {3630, 41579}, {3763, 32366}, {3819, 21356}, {5032, 11451}, {5085, 13367}, {5092, 11579}, {5093, 11484}, {5095, 41670}, {5663, 32275}, {5891, 14984}, {5921, 15072}, {6000, 11180}, {6144, 58471}, {6688, 59373}, {6776, 16836}, {6800, 19126}, {7789, 51611}, {7848, 47282}, {8549, 43652}, {8567, 9924}, {8584, 40670}, {9004, 61640}, {9019, 22165}, {9306, 41614}, {9723, 9734}, {9967, 15067}, {9969, 40341}, {9971, 15533}, {9977, 55713}, {10170, 14852}, {10601, 53019}, {10602, 17811}, {11002, 20080}, {11008, 58555}, {11171, 20794}, {11470, 17814}, {11472, 33878}, {11511, 15066}, {11793, 15073}, {12093, 37688}, {12220, 33884}, {13321, 51175}, {13391, 50978}, {13754, 50955}, {14826, 44079}, {14915, 18440}, {15045, 50974}, {15589, 51412}, {19121, 35265}, {19124, 37497}, {19127, 44110}, {19129, 32609}, {19137, 40318}, {20775, 21163}, {21849, 50992}, {22152, 32447}, {22829, 47355}, {30714, 48906}, {32062, 47353}, {32621, 43650}, {34229, 51426}, {34750, 43653}, {36987, 54173}, {37473, 45187}, {39899, 40280}, {41593, 52697}, {43844, 44480}, {44323, 51143}, {51128, 61045}, {61644, 61683}, {61662, 61668}

X(61667) = midpoint of X(i) and X(j) for these {i,j}: {69, 11188}, {568, 11898}, {3060, 11160}, {5921, 15072}, {9971, 15533}
X(61667) = reflection of X(i) in X(j) for these {i,j}: {1353, 13363}, {1843, 11188}, {1992, 5943}, {11188, 14913}, {12294, 15030}, {15030, 1352}, {15067, 61545}, {15072, 52520}, {21969, 9971}, {3917, 599}, {32062, 47353}, {36987, 54173}, {40673, 2}, {44323, 51143}, {51, 29959}, {5095, 41670}, {6, 61676}, {6776, 16836}, {61692, 6}, {8584, 40670}, {9967, 15067}
X(61667) = complement of X(15531)
X(61667) = perspector of circumconic {{A, B, C, X(1296), X(6331)}}
X(61667) = pole of line {524, 1899} with respect to the Jerabek hyperbola
X(61667) = pole of line {3291, 5254} with respect to the Kiepert hyperbola
X(61667) = pole of line {14272, 14570} with respect to the Kiepert parabola
X(61667) = pole of line {2489, 20186} with respect to the orthic inconic
X(61667) = pole of line {184, 1992} with respect to the Stammler hyperbola
X(61667) = pole of line {30476, 35522} with respect to the Steiner inellipse
X(61667) = pole of line {3, 11059} with respect to the Wallace hyperbola
X(61667) = pole of line {30209, 59933} with respect to the dual conic of DeLongchamps circle
X(61667) = pole of line {3143, 20975} with respect to the dual conic of Wallace hyperbola
X(61667) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(39238)}}, {{A, B, C, X(76), X(55977)}}, {{A, B, C, X(264), X(21448)}}, {{A, B, C, X(44144), X(50406)}}, {{A, B, C, X(44146), X(57467)}}
X(61667) = barycentric product X(i)*X(j) for these (i, j): {3917, 50406}
X(61667) = barycentric quotient X(i)/X(j) for these (i, j): {50406, 46104}
X(61667) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 8681, 40673}, {6, 61676, 373}, {6, 9027, 61692}, {69, 11188, 511}, {373, 61692, 6}, {511, 11188, 1843}, {511, 1352, 15030}, {511, 14913, 11188}, {511, 15030, 12294}, {524, 29959, 51}, {599, 2393, 3917}, {3620, 12272, 11574}, {9306, 41614, 44102}

X(61668) = CENTROID OF THE PEDAL TRIANGLE OF X(71)

Barycentrics    2*a^5-3*a^4*(b+c)-(b-c)^2*(b+c)^3-2*a*(b^2-c^2)^2+4*a^2*(b+c)*(b^2+c^2) : :

X(61668) lies on these lines: {2, 9028}, {4, 9}, {6, 2438}, {12, 44}, {45, 1837}, {48, 10165}, {51, 210}, {125, 1213}, {219, 5886}, {388, 1732}, {391, 26227}, {692, 28060}, {908, 17277}, {916, 9730}, {952, 40937}, {1125, 22356}, {1731, 10039}, {1848, 40435}, {1853, 61693}, {1953, 28234}, {2173, 6684}, {3553, 3924}, {3686, 3949}, {3707, 21075}, {5219, 37650}, {5224, 18650}, {5257, 16788}, {7359, 9956}, {10172, 40942}, {10175, 61710}, {11231, 59681}, {15805, 37713}, {16305, 47098}, {17220, 31018}, {24317, 26006}, {24390, 52978}, {24982, 50198}, {25568, 37654}, {31144, 31153}, {31163, 60986}, {40530, 40999}, {61650, 61663}, {61662, 61667}

X(61668) = midpoint of X(i) and X(j) for these {i,j}: {71, 61725}
X(61668) = reflection of X(i) in X(j) for these {i,j}: {1839, 61725}
X(61668) = perspector of circumconic {{A, B, C, X(1897), X(44876)}}
X(61668) = pole of line {1864, 3690} with respect to the Feuerbach hyperbola
X(61668) = pole of line {1834, 3011} with respect to the Kiepert hyperbola
X(61668) = pole of line {4000, 4256} with respect to the dual conic of Yff parabola
X(61668) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 26063, 1826}, {10, 54324, 8756}, {71, 61725, 516}, {516, 61725, 1839}

X(61669) = CENTROID OF THE PEDAL TRIANGLE OF X(72)

Barycentrics    a*(-2*a^3*b*c+a^4*(b+c)-2*a^2*b*c*(b+c)+2*a*b*c*(b+c)^2-(b-c)^2*(b+c)*(b^2+c^2)) : :
X(61669) = -5*X[3876]+2*X[37613], X[3962]+2*X[44545], -4*X[5044]+X[18732], -X[14054]+4*X[58497]

X(61669) lies on these lines: {2, 34381}, {4, 8}, {6, 354}, {9, 17441}, {38, 2347}, {44, 40959}, {51, 518}, {120, 125}, {165, 1763}, {209, 22278}, {210, 1853}, {375, 61663}, {912, 9730}, {942, 32911}, {1405, 32912}, {1722, 5902}, {1762, 23693}, {1836, 21867}, {1876, 34048}, {2809, 40998}, {3576, 54305}, {3742, 61659}, {3876, 37613}, {3917, 34371}, {3962, 44545}, {4383, 24476}, {4523, 4703}, {4683, 18252}, {5044, 18732}, {5692, 44662}, {7078, 44086}, {7289, 7484}, {9028, 11245}, {10202, 15805}, {10319, 26867}, {11227, 26890}, {14054, 58497}, {17592, 56219}, {18210, 25091}, {21319, 40937}, {21692, 61162}, {22076, 45120}, {31143, 31154}

X(61669) = midpoint of X(i) and X(j) for these {i,j}: {72, 61726}, {3681, 41717}
X(61669) = reflection of X(i) in X(j) for these {i,j}: {1829, 61726}, {61663, 375}
X(61669) = perspector of circumconic {{A, B, C, X(1292), X(6335)}}
X(61669) = pole of line {8642, 48383} with respect to the circumcircle
X(61669) = pole of line {1837, 4319} with respect to the Feuerbach hyperbola
X(61669) = pole of line {3290, 53417} with respect to the Kiepert hyperbola
X(61669) = pole of line {1437, 41610} with respect to the Stammler hyperbola
X(61669) = pole of line {24177, 34847} with respect to the dual conic of Yff parabola
X(61669) = pole of line {3140, 18210} with respect to the dual conic of Wallace hyperbola
X(61669) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(57656)}}, {{A, B, C, X(92), X(2191)}}, {{A, B, C, X(46108), X(57469)}}
X(61669) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {72, 14557, 26893}, {517, 61726, 1829}, {3681, 41717, 517}

X(61670) = CENTROID OF THE PEDAL TRIANGLE OF X(81)

Barycentrics    a^2*(-b^4+6*b^2*c^2-c^4+6*a*b*c*(b+c)+a^2*(b^2+6*b*c+c^2)) : :

X(61670) lies on these lines: {6, 373}, {81, 511}, {354, 61643}, {851, 18164}, {896, 4890}, {940, 5650}, {3690, 37595}, {3745, 9049}, {4260, 7998}, {4649, 51377}, {4658, 22076}, {5049, 15670}, {5050, 44104}, {5085, 44094}, {5138, 6800}, {5320, 35259}, {5640, 37685}, {5707, 15030}, {9155, 17474}, {10170, 45931}, {12045, 37680}, {14915, 45923}, {15082, 37633}, {18185, 22080}, {23841, 55103}, {35268, 37538}, {61652, 61672}

X(61670) = midpoint of X(i) and X(j) for these {i,j}: {81, 61728}
X(61670) = reflection of X(i) in X(j) for these {i,j}: {40952, 61728}
X(61670) = pole of line {1992, 17561} with respect to the Stammler hyperbola
X(61670) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {81, 61728, 511}, {354, 61661, 61643}, {511, 61728, 40952}

X(61671) = CENTROID OF THE PEDAL TRIANGLE OF X(84)

Barycentrics    a*(2*a^3*(b-c)^2+a^4*(b+c)-(b-c)^2*(b+c)^3-2*a*(b-c)^2*(b^2+c^2)) : :
X(61671) = X[84]+2*X[5908], 2*X[6245]+X[51490], -4*X[6705]+X[52097]

X(61671) lies on these lines: {2, 374}, {19, 1407}, {51, 61660}, {57, 1422}, {63, 21871}, {65, 603}, {77, 15509}, {84, 5908}, {154, 354}, {189, 54008}, {210, 3917}, {222, 2182}, {513, 23615}, {517, 3928}, {940, 7289}, {1108, 61412}, {1122, 3772}, {1401, 40962}, {1427, 3942}, {1824, 3937}, {1829, 37566}, {1864, 26892}, {2170, 59173}, {2299, 18191}, {2385, 11246}, {3198, 22053}, {3666, 18161}, {3745, 22769}, {3784, 5784}, {3880, 42049}, {3911, 14557}, {4641, 16560}, {5287, 24328}, {5902, 39980}, {5918, 44670}, {5928, 26871}, {6245, 51490}, {6705, 52097}, {7291, 17074}, {8581, 40635}, {8808, 11212}, {9850, 41682}, {10167, 44661}, {12555, 60990}, {14829, 43216}, {15309, 60172}, {17441, 17603}, {17616, 61720}, {18162, 37595}, {18163, 18176}, {18184, 53083}, {18623, 46330}, {18735, 37520}, {21621, 26932}, {24471, 37642}, {31231, 51413}, {34381, 37521}, {41772, 56084}

X(61671) = X(i)-Dao conjugate of X(j) for these {i, j}: {20205, 329}
X(61671) = X(i)-Ceva conjugate of X(j) for these {i, j}: {6614, 513}
X(61671) = pole of line {6129, 6608} with respect to the DeLongchamps ellipse
X(61671) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(189), X(6611)}}, {{A, B, C, X(1422), X(2217)}}, {{A, B, C, X(6612), X(59263)}}
X(61671) = barycentric product X(i)*X(j) for these (i, j): {269, 56942}, {20205, 57}, {20231, 44190}
X(61671) = barycentric quotient X(i)/X(j) for these (i, j): {20205, 312}, {20231, 198}, {56942, 341}
X(61671) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {57, 1422, 6611}, {84, 5908, 40953}, {222, 21370, 2182}, {3917, 61662, 210}

X(61672) = CENTROID OF THE PEDAL TRIANGLE OF X(100)

Barycentrics    a*(-2*b*c+a*(b+c))*(-2*a*b*c+a^2*(b+c)-(b-c)^2*(b+c)) : :
X(61672) = X[11]+2*X[61166], X[3032]+2*X[4013], -4*X[3035]+X[3937], X[6154]+2*X[38390], -4*X[20400]+X[31849], -X[22321]+4*X[46694], X[34151]+2*X[55317]

X(61672) lies on these lines: {2, 2810}, {11, 61166}, {51, 34372}, {100, 29349}, {119, 517}, {120, 125}, {165, 21361}, {354, 3756}, {373, 17718}, {374, 43960}, {375, 61643}, {513, 6174}, {661, 6184}, {891, 4728}, {899, 52896}, {1769, 3310}, {2807, 5660}, {3030, 3120}, {3032, 4013}, {3035, 3937}, {3681, 3705}, {3939, 52242}, {3989, 61051}, {4557, 45885}, {5552, 42448}, {6154, 38390}, {6745, 29353}, {6791, 61650}, {9026, 61649}, {10440, 22020}, {17441, 18236}, {17728, 61678}, {20400, 31849}, {22321, 46694}, {23154, 26364}, {26611, 42759}, {27529, 29958}, {30566, 61177}, {34151, 55317}, {35281, 36280}, {44396, 51429}, {52659, 53548}, {61652, 61670}, {61662, 61673}

X(61672) = midpoint of X(i) and X(j) for these {i,j}: {100, 61729}
X(61672) = reflection of X(i) in X(j) for these {i,j}: {3937, 34583}, {34583, 3035}, {38389, 61729}, {61674, 2}
X(61672) = perspector of circumconic {{A, B, C, X(517), X(536)}}
X(61672) = X(i)-isoconjugate-of-X(j) for these {i, j}: {104, 37129}, {739, 34234}, {909, 3227}, {2401, 34075}, {2423, 4607}, {10428, 36872}, {13136, 23892}, {31002, 34858}, {36037, 43928}
X(61672) = X(i)-Dao conjugate of X(j) for these {i, j}: {1145, 36798}, {3259, 43928}, {13466, 18816}, {14434, 15635}, {16586, 31002}, {23980, 3227}, {39011, 2401}, {40613, 37129}, {40614, 34234}, {52875, 38955}
X(61672) = pole of line {16082, 43928} with respect to the polar circle
X(61672) = pole of line {13466, 23980} with respect to the Steiner inellipse
X(61672) = pole of line {3140, 35353} with respect to the dual conic of Wallace hyperbola
X(61672) = intersection, other than A, B, C, of circumconics {{A, B, C, X(517), X(891)}}, {{A, B, C, X(536), X(46805)}}, {{A, B, C, X(899), X(6735)}}, {{A, B, C, X(908), X(1769)}}, {{A, B, C, X(1145), X(30583)}}, {{A, B, C, X(1532), X(52890)}}, {{A, B, C, X(2397), X(36847)}}, {{A, B, C, X(3230), X(41389)}}, {{A, B, C, X(4009), X(51379)}}, {{A, B, C, X(14404), X(51377)}}, {{A, B, C, X(14431), X(17757)}}, {{A, B, C, X(14433), X(51381)}}, {{A, B, C, X(15632), X(23980)}}, {{A, B, C, X(28603), X(51362)}}, {{A, B, C, X(30592), X(51409)}}, {{A, B, C, X(42758), X(42764)}}
X(61672) = barycentric product X(i)*X(j) for these (i, j): {100, 42764}, {517, 536}, {899, 908}, {1145, 52900}, {1465, 4009}, {1769, 23891}, {2183, 6381}, {2397, 891}, {3230, 3262}, {3310, 41314}, {10015, 23343}, {14404, 55258}, {14430, 24029}, {17139, 52959}, {17757, 52897}, {26611, 45145}, {51362, 52901}, {51367, 52890}, {51390, 52902}, {52896, 6735}
X(61672) = barycentric quotient X(i)/X(j) for these (i, j): {517, 3227}, {536, 18816}, {890, 2423}, {891, 2401}, {899, 34234}, {908, 31002}, {1646, 15635}, {2183, 37129}, {2397, 889}, {2427, 898}, {3230, 104}, {3310, 43928}, {4009, 36795}, {4526, 43728}, {14404, 55259}, {17757, 60288}, {21801, 41683}, {23343, 13136}, {42764, 693}, {45145, 59196}, {52902, 55943}, {52959, 38955}, {59797, 45145}
X(61672) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 2810, 61674}, {100, 61729, 29349}, {375, 61648, 61643}, {61652, 61687, 61670}

X(61673) = CENTROID OF THE PEDAL TRIANGLE OF X(103)

Barycentrics    (b-c)^2*(a^2-3*b^2-2*b*c-3*c^2+2*a*(b+c)) : :
X(61673) = X[150]+2*X[17044], -X[3732]+4*X[40483], 2*X[9436]+X[17747], -4*X[40480]+X[57018]

X(61673) lies on these lines: {2, 5845}, {11, 244}, {69, 30790}, {80, 43057}, {116, 514}, {150, 17044}, {325, 27487}, {551, 28877}, {599, 12035}, {952, 10708}, {1358, 21044}, {2246, 31192}, {3119, 3942}, {3665, 21049}, {3732, 40483}, {3807, 4437}, {4415, 36482}, {4675, 5219}, {5316, 17237}, {5848, 17392}, {5851, 6173}, {6006, 57439}, {6793, 61661}, {7179, 27475}, {7202, 38375}, {8287, 40615}, {9436, 17747}, {13609, 26932}, {16593, 24318}, {17181, 21258}, {21239, 27471}, {23816, 44317}, {24237, 45678}, {24712, 26007}, {33864, 51384}, {34122, 46894}, {34578, 37718}, {40480, 57018}, {40629, 52593}, {50011, 51415}, {61662, 61672}

X(61673) = reflection of X(i) in X(j) for these {i,j}: {51406, 2}
X(61673) = perspector of circumconic {{A, B, C, X(514), X(2400)}}
X(61673) = center of circumconic {{A, B, C, X(5222), X(29616)}}
X(61673) = X(i)-isoconjugate-of-X(j) for these {i, j}: {59, 42317}, {100, 26716}, {692, 32040}, {1110, 55937}, {2398, 36136}, {23990, 55983}, {32721, 42719}
X(61673) = X(i)-Dao conjugate of X(j) for these {i, j}: {514, 55937}, {1086, 32040}, {4988, 54668}, {6615, 42317}, {8054, 26716}
X(61673) = X(i)-Ceva conjugate of X(j) for these {i, j}: {5222, 30520}, {55937, 514}
X(61673) = X(i)-complementary conjugate of X(j) for these {i, j}: {21446, 17072}, {37223, 27076}, {39749, 21260}, {39959, 3835}, {52013, 4885}
X(61673) = pole of line {11, 24012} with respect to the nine-point circle
X(61673) = pole of line {1897, 41321} with respect to the polar circle
X(61673) = pole of line {661, 3676} with respect to the Kiepert hyperbola
X(61673) = pole of line {1086, 4081} with respect to the Steiner inellipse
X(61673) = pole of line {313, 42712} with respect to the dual conic of Stammler hyperbola
X(61673) = pole of line {514, 676} with respect to the dual conic of Yff parabola
X(61673) = pole of line {523, 24002} with respect to the dual conic of Hutson-Moses hyperbola
X(61673) = pole of line {10, 17747} with respect to the dual conic of Wallace hyperbola
X(61673) = intersection, other than A, B, C, of circumconics {{A, B, C, X(514), X(676)}}, {{A, B, C, X(1086), X(15634)}}, {{A, B, C, X(1647), X(29616)}}, {{A, B, C, X(35158), X(51406)}}, {{A, B, C, X(42316), X(56787)}}, {{A, B, C, X(53525), X(59215)}}
X(61673) = barycentric product X(i)*X(j) for these (i, j): {1086, 29616}, {1111, 5223}, {2170, 59200}, {4858, 59215}, {10004, 1146}, {23989, 42316}
X(61673) = barycentric quotient X(i)/X(j) for these (i, j): {514, 32040}, {649, 26716}, {1086, 55937}, {1111, 55983}, {2170, 42317}, {3120, 54668}, {5223, 765}, {10004, 1275}, {23989, 59259}, {29616, 1016}, {42316, 1252}, {59215, 4564}
X(61673) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5845, 51406}, {116, 1565, 1146}, {116, 58898, 1565}

X(61674) = CENTROID OF THE PEDAL TRIANGLE OF X(104)

Barycentrics    a*(b-c)^2*(a^3-a*(b-c)^2-2*b*c*(b+c)) : :
X(61674) = X[1484]+2*X[46174], -4*X[3911]+X[51377], 2*X[5083]+X[22321], -X[15906]+4*X[58587], 2*X[20418]+X[31849], -5*X[31235]+2*X[61166], -3*X[59377]+X[61729]

X(61674) lies on these lines: {2, 2810}, {11, 513}, {51, 17728}, {104, 61731}, {125, 53837}, {210, 12035}, {244, 665}, {354, 33883}, {374, 51406}, {499, 23154}, {528, 34583}, {867, 17059}, {999, 33848}, {1086, 42759}, {1357, 3120}, {1401, 29662}, {1484, 46174}, {1647, 3271}, {1797, 36280}, {2611, 4139}, {2807, 11219}, {2836, 3742}, {2841, 16173}, {2842, 32557}, {3086, 42448}, {3756, 18191}, {3911, 51377}, {3917, 34372}, {3942, 42753}, {4893, 20974}, {5083, 22321}, {5514, 46660}, {5577, 42754}, {8679, 61649}, {9052, 33852}, {10707, 29349}, {14027, 47014}, {15906, 58587}, {17463, 53525}, {17606, 41682}, {20418, 31849}, {23711, 42072}, {23989, 47780}, {24512, 36404}, {28161, 44311}, {28393, 53393}, {31148, 61076}, {31235, 61166}, {32636, 58889}, {33142, 40649}, {43043, 53548}, {44312, 47779}, {52242, 53298}, {59377, 61729}

X(61674) = midpoint of X(i) and X(j) for these {i,j}: {104, 61731}
X(61674) = reflection of X(i) in X(j) for these {i,j}: {61672, 2}
X(61674) = perspector of circumconic {{A, B, C, X(513), X(2401)}}
X(61674) = X(i)-isoconjugate-of-X(j) for these {i, j}: {190, 32722}, {765, 957}, {1110, 58007}, {2397, 36137}, {4570, 54933}
X(61674) = X(i)-Dao conjugate of X(j) for these {i, j}: {513, 957}, {514, 58007}, {50330, 54933}, {55053, 32722}
X(61674) = X(i)-Ceva conjugate of X(j) for these {i, j}: {957, 513}
X(61674) = pole of line {4014, 53525} with respect to the incircle
X(61674) = pole of line {6335, 53151} with respect to the polar circle
X(61674) = pole of line {900, 4162} with respect to the Feuerbach hyperbola
X(61674) = pole of line {21894, 31946} with respect to the Kiepert hyperbola
X(61674) = pole of line {3835, 3960} with respect to the dual conic of Yff parabola
X(61674) = pole of line {2530, 55126} with respect to the dual conic of Hutson-Moses hyperbola
X(61674) = pole of line {321, 17757} with respect to the dual conic of Wallace hyperbola
X(61674) = intersection, other than A, B, C, of circumconics {{A, B, C, X(513), X(3310)}}, {{A, B, C, X(665), X(57468)}}, {{A, B, C, X(956), X(2087)}}, {{A, B, C, X(1015), X(15635)}}
X(61674) = barycentric product X(i)*X(j) for these (i, j): {1086, 956}, {1111, 2267}
X(61674) = barycentric quotient X(i)/X(j) for these (i, j): {667, 32722}, {956, 1016}, {1015, 957}, {1086, 58007}, {2267, 765}, {3125, 54933}
X(61674) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 2810, 61672}, {11, 3937, 38389}, {11, 58893, 38390}, {15635, 33646, 3259}

X(61675) = CENTROID OF THE PEDAL TRIANGLE OF X(115)

Barycentrics    a^8*(b^2+c^2)+a^6*(-3*b^4+2*b^2*c^2-3*c^4)-a^2*(b^2-c^2)^2*(b^4-3*b^2*c^2+c^4)+a^4*(b^2+c^2)*(3*b^4-5*b^2*c^2+3*c^4) : :
X(61675) = -3*X[2]+X[51383], 2*X[11554]+X[38734], -4*X[44381]+X[51439]

X(61675) lies on these lines: {2, 51383}, {6, 110}, {39, 13363}, {51, 2871}, {115, 5663}, {143, 7755}, {230, 511}, {338, 53348}, {373, 3815}, {395, 34373}, {396, 34375}, {526, 1637}, {568, 3767}, {1112, 6103}, {1614, 44537}, {1989, 12824}, {1990, 44084}, {2079, 15035}, {2088, 44468}, {2549, 40280}, {2781, 6034}, {3003, 53494}, {3054, 5650}, {3580, 34827}, {5007, 10095}, {5085, 9609}, {5093, 34809}, {5254, 9730}, {5309, 5946}, {5943, 9300}, {6794, 46430}, {6800, 44524}, {7735, 11002}, {7736, 12093}, {7746, 15067}, {7753, 13364}, {7765, 12006}, {7772, 15026}, {7998, 37637}, {9698, 32205}, {10413, 20304}, {11060, 52951}, {11063, 15107}, {11459, 13881}, {11554, 38734}, {11610, 14495}, {13137, 34369}, {13207, 39095}, {13345, 61194}, {14113, 48721}, {14644, 15538}, {14915, 50387}, {14984, 61733}, {15028, 22332}, {15055, 34866}, {15060, 18362}, {15072, 44518}, {15080, 44522}, {16981, 37689}, {25153, 25163}, {25173, 54472}, {25178, 54473}, {25231, 25232}, {26869, 61714}, {34990, 57257}, {43448, 61136}, {43662, 59115}, {44381, 51439}, {46906, 59208}, {51335, 53264}

X(61675) = midpoint of X(i) and X(j) for these {i,j}: {51, 6784}, {115, 15544}, {11624, 11626}, {25153, 25163}, {25173, 54472}, {25178, 54473}, {25231, 25232}
X(61675) = complement of X(51383)
X(61675) = perspector of circumconic {{A, B, C, X(691), X(1138)}}
X(61675) = X(i)-complementary conjugate of X(j) for these {i, j}: {11060, 16591}
X(61675) = pole of line {9148, 26869} with respect to the orthocentroidal circle
X(61675) = pole of line {114, 858} with respect to the Kiepert hyperbola
X(61675) = pole of line {74, 3563} with respect to the orthic inconic
X(61675) = pole of line {1989, 2395} with respect to the Steiner inellipse
X(61675) = pole of line {1511, 9517} with respect to the dual conic of DeLongchamps circle
X(61675) = pole of line {14566, 52628} with respect to the dual conic of Wallace hyperbola
X(61675) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2493), X(57728)}}, {{A, B, C, X(5968), X(14495)}}
X(61675) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 3124, 2493}, {6, 44533, 110}, {51, 6784, 2871}, {115, 15544, 5663}, {5640, 61742, 16776}, {11624, 11626, 2854}

X(61676) = CENTROID OF THE PEDAL TRIANGLE OF X(141)

Barycentrics    a^2*(-b^6+2*a^2*b^2*c^2+5*b^4*c^2+5*b^2*c^4-c^6+a^4*(b^2+c^2)) : :
X(61676) = -X[6]+3*X[373], X[69]+3*X[5640], 2*X[140]+X[43130], X[1843]+5*X[3763], -X[1992]+5*X[11451], X[3060]+3*X[21356], -7*X[3090]+X[50649], -X[3313]+7*X[3619], -5*X[3618]+X[15531], 5*X[3620]+3*X[11002], -4*X[3628]+X[44479], X[3630]+2*X[58555] and many others

X(61676) lies on these lines: {2, 2393}, {5, 141}, {6, 373}, {49, 5050}, {51, 599}, {66, 6815}, {67, 61679}, {69, 5640}, {140, 43130}, {159, 5085}, {160, 21163}, {182, 43586}, {206, 35259}, {375, 9004}, {512, 18310}, {524, 5943}, {542, 5892}, {547, 14984}, {570, 9155}, {597, 6688}, {1176, 35265}, {1177, 35904}, {1352, 9730}, {1503, 16836}, {1593, 7716}, {1843, 3763}, {1992, 11451}, {2056, 37083}, {2854, 3589}, {3003, 37338}, {3055, 17430}, {3060, 21356}, {3090, 50649}, {3098, 31861}, {3313, 3619}, {3564, 13363}, {3618, 15531}, {3620, 11002}, {3628, 44479}, {3630, 58555}, {3631, 58532}, {3818, 14915}, {3819, 9019}, {3917, 9971}, {5020, 19136}, {5067, 15073}, {5092, 34513}, {5157, 6800}, {5159, 8705}, {5181, 45237}, {5462, 34507}, {5642, 61665}, {5663, 18358}, {5944, 20190}, {6000, 47354}, {6467, 47355}, {6697, 15126}, {6803, 58492}, {7392, 58483}, {8548, 39561}, {8550, 11695}, {9924, 31521}, {10219, 48310}, {10516, 15030}, {11178, 13754}, {11180, 15045}, {11459, 19161}, {11511, 16187}, {11649, 47556}, {12045, 51126}, {12084, 55649}, {12220, 33879}, {14845, 20423}, {15074, 55856}, {15116, 26156}, {15122, 43129}, {15491, 51426}, {15581, 37515}, {16042, 53777}, {16511, 60774}, {17710, 51128}, {17825, 32621}, {18440, 40280}, {18553, 40647}, {19596, 22352}, {20791, 51023}, {20987, 35268}, {21637, 32251}, {21849, 50991}, {21969, 50993}, {22165, 58470}, {25555, 32284}, {26206, 39125}, {32237, 37283}, {32246, 37454}, {34382, 38317}, {34817, 55591}, {35283, 41670}, {37439, 54347}, {37950, 55653}, {40673, 47352}, {41597, 44494}, {46305, 52961}, {46847, 52520}, {51127, 61045}, {51744, 53415}, {51962, 52152}

X(61676) = midpoint of X(i) and X(j) for these {i,j}: {2, 29959}, {6, 61667}, {51, 599}, {67, 61679}, {141, 16776}, {1352, 9730}, {1843, 54334}, {3917, 9971}, {5181, 45237}, {5642, 61665}, {11459, 19161}, {46847, 52520}, {61664, 61683}
X(61676) = reflection of X(i) in X(j) for these {i,j}: {10170, 24206}, {15531, 22829}, {16776, 9822}, {3819, 20582}, {45237, 58495}, {597, 6688}, {5943, 40670}, {9969, 16776}
X(61676) = perspector of circumconic {{A, B, C, X(1296), X(11794)}}
X(61676) = pole of line {10602, 15534} with respect to the Jerabek hyperbola
X(61676) = pole of line {39, 30739} with respect to the Kiepert hyperbola
X(61676) = pole of line {1992, 5012} with respect to the Stammler hyperbola
X(61676) = pole of line {1078, 11059} with respect to the Wallace hyperbola
X(61676) = pole of line {2485, 30209} with respect to the dual conic of DeLongchamps circle
X(61676) = pole of line {7668, 14279} with respect to the dual conic of Wallace hyperbola
X(61676) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3613), X(21448)}}, {{A, B, C, X(27375), X(38005)}}, {{A, B, C, X(36952), X(55977)}}
X(61676) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 29959, 2393}, {6, 61667, 9027}, {141, 16776, 511}, {141, 9822, 9969}, {373, 61667, 6}, {511, 24206, 10170}, {511, 9822, 16776}, {524, 40670, 5943}, {1843, 5650, 54334}, {3589, 14913, 32366}, {6688, 8681, 597}, {9019, 20582, 3819}, {9971, 21358, 3917}, {34573, 41579, 11574}

X(61677) = CENTROID OF THE PEDAL TRIANGLE OF X(143)

Barycentrics    2*a^6-6*a^4*(b^2+c^2)-(b^2-c^2)^2*(b^2+c^2)+a^2*(5*b^4-8*b^2*c^2+5*c^4) : :
X(61677) = X[52]+3*X[45967], 3*X[373]+X[41628], 7*X[568]+X[18564], 5*X[3567]+X[10112], X[6102]+2*X[40240], X[13142]+2*X[15012], 3*X[13321]+X[61713], 2*X[16982]+X[17712], X[32165]+2*X[58533], X[34796]+3*X[61744]

X(61677) lies on these lines: {2, 15520}, {6, 58447}, {51, 542}, {52, 45967}, {125, 53863}, {143, 44407}, {343, 25555}, {373, 41628}, {389, 22530}, {511, 10691}, {524, 6688}, {568, 18564}, {575, 41588}, {576, 11433}, {599, 5644}, {1368, 55716}, {1915, 41672}, {1994, 5972}, {3060, 29317}, {3564, 58470}, {3567, 10112}, {3580, 34565}, {5097, 6723}, {5133, 44107}, {5422, 58445}, {5642, 55038}, {5643, 15108}, {5943, 5965}, {6102, 40240}, {6388, 45843}, {6515, 24206}, {6676, 15516}, {6677, 32455}, {7386, 55720}, {7494, 55710}, {8584, 59553}, {9777, 19130}, {10168, 43653}, {10601, 40107}, {11232, 13490}, {11245, 21849}, {11427, 55714}, {11482, 26958}, {12834, 37779}, {13142, 15012}, {13321, 61713}, {13366, 32223}, {13419, 45730}, {13482, 38727}, {15004, 21243}, {16881, 30522}, {16982, 17712}, {18950, 20423}, {19150, 32263}, {20583, 58434}, {21230, 46084}, {22330, 23292}, {27377, 59529}, {32165, 58533}, {32225, 34566}, {32267, 44108}, {33522, 55687}, {34545, 41586}, {34564, 52525}, {34796, 61744}, {43143, 55885}, {43145, 55890}, {44935, 46850}, {51170, 59543}, {53415, 61624}, {61506, 61681}

X(61677) = midpoint of X(i) and X(j) for these {i,j}: {51, 11225}, {143, 45969}, {5943, 61658}, {11232, 13490}, {11245, 21849}, {13419, 45730}, {44935, 46850}
X(61677) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {51, 11225, 542}, {143, 45969, 44407}, {11245, 21849, 29012}, {16982, 50476, 17712}, {61657, 61658, 5943}

X(61678) = CENTROID OF THE PEDAL TRIANGLE OF X(145)

Barycentrics    a^2*(-4*a*b*c*(b+c)+a^2*(b^2+c^2)-(b^2+c^2)*(b^2-4*b*c+c^2)) : :
X(61678) = -4*X[354]+3*X[373], 2*X[3555]+X[23154], -2*X[3681]+3*X[5650], -4*X[3874]+X[16980], -5*X[3889]+2*X[29958], -4*X[34791]+X[42448]

X(61678) lies on these lines: {51, 2810}, {181, 54352}, {210, 9039}, {354, 373}, {511, 4430}, {518, 3917}, {2841, 51093}, {3243, 26892}, {3475, 61643}, {3555, 23154}, {3681, 5650}, {3819, 4661}, {3868, 45955}, {3870, 3937}, {3874, 16980}, {3881, 15049}, {3889, 29958}, {8679, 21969}, {9004, 61692}, {9052, 23155}, {13366, 43149}, {17449, 23638}, {17728, 61672}, {22068, 54327}, {22352, 22769}, {23653, 46148}, {34791, 42448}

X(61678) = reflection of X(i) in X(j) for these {i,j}: {15049, 3881}, {4661, 3819}, {51, 3873}, {61640, 354}
X(61678) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {354, 61640, 373}, {354, 9026, 61640}, {2810, 3873, 51}

X(61679) = CENTROID OF THE PEDAL TRIANGLE OF X(146)

Barycentrics    a^2*(-b^10+b^8*c^2+b^2*c^8-c^10-2*a^6*(b^2-c^2)^2+a^8*(b^2+c^2)-3*a^4*b^2*c^2*(b^2+c^2)+a^2*(2*b^4-b^2*c^2+c^4)*(b^4-b^2*c^2+2*c^4)) : :
X(61679) = -5*X[2]+4*X[44321], X[52]+2*X[5609], 2*X[389]+X[14094], -X[1205]+4*X[6593], X[1986]+2*X[6053], 2*X[5446]+X[23236], -X[5562]+4*X[16534], -3*X[5650]+4*X[5972], X[7731]+5*X[20125], -4*X[9729]+X[15054], -2*X[10170]+3*X[14643], -X[10733]+4*X[58536] and many others

X(61679) lies on circumconic {{A, B, C, X(842), X(43917)}} and on these lines: {2, 44321}, {5, 113}, {23, 110}, {25, 56568}, {51, 542}, {52, 5609}, {67, 61676}, {74, 7550}, {146, 15072}, {155, 5898}, {156, 21660}, {184, 45016}, {206, 2916}, {389, 14094}, {399, 568}, {512, 13291}, {576, 52124}, {1092, 2937}, {1112, 1843}, {1205, 6593}, {1511, 7555}, {1531, 7574}, {1986, 6053}, {1995, 52098}, {2393, 34319}, {2781, 3917}, {3016, 3124}, {3060, 9143}, {3066, 11806}, {3111, 54085}, {3448, 3818}, {4550, 10620}, {5085, 13171}, {5446, 23236}, {5562, 16534}, {5621, 43650}, {5650, 5972}, {5651, 15106}, {5655, 13754}, {5878, 13203}, {5892, 20126}, {5943, 9140}, {6000, 10706}, {6090, 17847}, {6102, 20193}, {7512, 13289}, {7540, 17702}, {7552, 10628}, {7565, 46847}, {7570, 15059}, {7731, 20125}, {8681, 41720}, {9155, 23217}, {9729, 15054}, {9976, 44107}, {10170, 14643}, {10272, 15067}, {10733, 58536}, {11002, 11800}, {11061, 11188}, {11381, 38791}, {11470, 19504}, {11694, 54042}, {11807, 12383}, {12317, 58498}, {12412, 37506}, {12828, 44079}, {13198, 21637}, {13201, 33884}, {13348, 15020}, {13366, 34155}, {14448, 45187}, {14831, 56567}, {14982, 44084}, {14984, 21969}, {15004, 39562}, {15021, 17704}, {15034, 15644}, {15039, 37484}, {15055, 37126}, {15102, 16261}, {15131, 34146}, {15133, 58545}, {15303, 40673}, {15462, 22352}, {15531, 25321}, {17855, 54012}, {18553, 52191}, {19161, 32235}, {20772, 54384}, {21639, 41743}, {25335, 58495}, {25338, 32269}, {25556, 44109}, {30714, 45186}, {32226, 40914}, {32620, 45619}, {41512, 43087}, {41724, 58481}, {41737, 60774}, {44082, 45082}, {58885, 61598}

X(61679) = midpoint of X(i) and X(j) for these {i,j}: {146, 15072}, {399, 568}, {3060, 9143}, {11061, 11188}, {52098, 52989}
X(61679) = reflection of X(i) in X(j) for these {i,j}: {125, 41670}, {10264, 13363}, {15030, 113}, {15067, 10272}, {20126, 5892}, {21649, 568}, {21650, 15030}, {3917, 5642}, {32260, 11188}, {40673, 15303}, {45956, 11561}, {51, 12824}, {568, 11557}, {54042, 11694}, {67, 61676}, {61692, 5095}, {74, 16836}, {9140, 5943}
X(61679) = pole of line {30, 5622} with respect to the Jerabek hyperbola
X(61679) = pole of line {542, 43574} with respect to the Stammler hyperbola
X(61679) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {113, 5663, 15030}, {125, 41670, 373}, {399, 11557, 21649}, {542, 12824, 51}, {2781, 5642, 3917}, {2854, 5095, 61692}, {5663, 11561, 45956}, {5663, 13363, 10264}, {5663, 15030, 21650}, {5663, 41670, 125}, {15063, 25711, 185}

X(61680) = CENTROID OF THE PEDAL TRIANGLE OF X(154)

Barycentrics    5*a^6-3*a^2*(b^2-c^2)^2-4*a^4*(b^2+c^2)+2*(b^2-c^2)^2*(b^2+c^2) : :
X(61680) = 2*X[2]+X[154], 4*X[5]+5*X[17821], X[26]+8*X[58435], -X[64]+10*X[631], 8*X[140]+X[1498], 4*X[141]+5*X[19132], X[155]+8*X[10020], 4*X[206]+5*X[3763], 2*X[376]+X[61721], X[381]+2*X[11202], -4*X[549]+X[10606], -4*X[597]+X[17813] and many others

X(61680) lies on these lines: {2, 154}, {3, 113}, {4, 15448}, {5, 17821}, {6, 468}, {23, 35228}, {25, 53023}, {26, 58435}, {64, 631}, {107, 15274}, {110, 15069}, {125, 26864}, {140, 1498}, {141, 19132}, {155, 10020}, {159, 11284}, {160, 852}, {161, 5020}, {184, 26869}, {206, 3763}, {221, 5433}, {297, 53017}, {373, 2393}, {376, 61721}, {381, 11202}, {382, 32237}, {394, 59551}, {470, 41038}, {471, 41039}, {523, 14401}, {549, 10606}, {576, 21970}, {590, 17820}, {597, 17813}, {599, 5642}, {615, 17819}, {632, 14216}, {858, 48905}, {879, 47249}, {1181, 10018}, {1316, 44526}, {1350, 7493}, {1351, 32223}, {1495, 5094}, {1514, 35485}, {1619, 16419}, {1656, 10282}, {1660, 43650}, {1899, 52297}, {1971, 31489}, {1995, 15577}, {2192, 5432}, {2433, 47251}, {2453, 16319}, {2781, 7998}, {2883, 3523}, {2917, 7506}, {2930, 32227}, {3066, 14389}, {3090, 34782}, {3147, 9786}, {3167, 5965}, {3292, 40341}, {3357, 15720}, {3522, 5893}, {3524, 15311}, {3525, 6247}, {3526, 6759}, {3528, 51491}, {3530, 5878}, {3533, 34781}, {3541, 16654}, {3542, 11425}, {3566, 50571}, {3574, 55578}, {3589, 8547}, {3618, 15585}, {3619, 34774}, {3624, 40660}, {3628, 9833}, {3819, 41580}, {3830, 32267}, {3851, 34785}, {3917, 45979}, {4232, 5480}, {4413, 18621}, {4550, 15138}, {5054, 6000}, {5055, 18400}, {5056, 41362}, {5064, 44082}, {5070, 18381}, {5071, 23324}, {5072, 34786}, {5079, 18383}, {5159, 46264}, {5596, 34573}, {5640, 44668}, {5650, 34146}, {5654, 34351}, {5894, 15717}, {5943, 34751}, {6144, 41586}, {6293, 11793}, {6353, 14853}, {6642, 44516}, {6676, 17811}, {6677, 17825}, {6684, 7973}, {6696, 10303}, {6776, 47296}, {6793, 45141}, {6794, 47166}, {6795, 12068}, {7387, 43839}, {7395, 32345}, {7426, 54131}, {7494, 21167}, {7495, 19149}, {7496, 15578}, {7505, 12022}, {7542, 17814}, {7575, 40909}, {7694, 44216}, {7712, 30745}, {7729, 16836}, {8252, 10533}, {8253, 10534}, {8254, 17846}, {8550, 37643}, {8719, 40884}, {8780, 21243}, {9125, 55121}, {9306, 19131}, {9707, 14940}, {9820, 17834}, {9909, 29317}, {10096, 39522}, {10125, 32139}, {10193, 15701}, {10201, 47391}, {10272, 17835}, {10541, 54012}, {10546, 34775}, {10601, 58439}, {11002, 37907}, {11204, 15693}, {11216, 51185}, {11241, 13847}, {11242, 13846}, {11243, 16645}, {11244, 16644}, {11402, 61645}, {11410, 51403}, {11444, 41589}, {11464, 14644}, {11472, 18580}, {11477, 32269}, {11550, 52298}, {11745, 43841}, {11746, 15073}, {12017, 41603}, {12024, 18925}, {12163, 61608}, {12241, 14528}, {12293, 32171}, {12315, 25563}, {12324, 55864}, {12902, 40291}, {13093, 14862}, {13383, 37498}, {13567, 14912}, {13861, 58407}, {13881, 20998}, {14156, 35243}, {14165, 37070}, {14530, 20299}, {14561, 44212}, {14826, 59699}, {14852, 32423}, {14927, 30769}, {15066, 17847}, {15080, 15647}, {15122, 35237}, {15270, 37338}, {15271, 59706}, {15534, 32225}, {15576, 51358}, {15582, 16042}, {15694, 23329}, {15712, 20427}, {15750, 43831}, {16051, 44882}, {16238, 37514}, {16266, 18282}, {16658, 37119}, {17704, 36982}, {17718, 61654}, {17728, 61647}, {17826, 23303}, {17827, 23302}, {17849, 58436}, {18376, 19709}, {18388, 55572}, {20208, 34147}, {21850, 47316}, {21969, 58544}, {22352, 31255}, {25335, 32235}, {26255, 38072}, {26881, 30744}, {26882, 52296}, {29323, 34609}, {30402, 43028}, {30403, 43029}, {30739, 32125}, {31152, 35268}, {31423, 40658}, {31670, 37897}, {31884, 44210}, {32216, 36201}, {32445, 44535}, {32460, 42154}, {32461, 42155}, {32767, 55857}, {32903, 49136}, {33504, 35901}, {34330, 61702}, {34380, 37672}, {34780, 50414}, {35486, 37487}, {35602, 54040}, {36851, 51126}, {36989, 37454}, {37201, 41427}, {37637, 47200}, {37648, 53093}, {37760, 59771}, {37813, 54375}, {37904, 51024}, {37910, 43621}, {37911, 48906}, {37974, 42097}, {37975, 42096}, {39879, 58445}, {40916, 44883}, {41373, 58438}, {42263, 47631}, {42264, 47632}, {43957, 55673}, {44084, 44439}, {44538, 54096}, {45185, 55860}, {46034, 52288}, {46336, 55676}, {46349, 58762}, {47148, 47284}, {47255, 52743}, {47582, 55722}, {48872, 51360}, {51519, 61711}, {59777, 61610}

X(61680) = midpoint of X(i) and X(j) for these {i,j}: {2, 35260}, {154, 61735}
X(61680) = reflection of X(i) in X(j) for these {i,j}: {154, 35260}, {1853, 61735}, {35260, 10192}, {61735, 2}
X(61680) = inverse of X(599) in Thomson-Gibert-Moses hyperbola
X(61680) = perspector of circumconic {{A, B, C, X(30247), X(48373)}}
X(61680) = pole of line {31174, 52720} with respect to the orthocentroidal circle
X(61680) = pole of line {40673, 44439} with respect to the Jerabek hyperbola
X(61680) = pole of line {5094, 7735} with respect to the Kiepert hyperbola
X(61680) = pole of line {5502, 35278} with respect to the Kiepert parabola
X(61680) = pole of line {1499, 54259} with respect to the orthic inconic
X(61680) = pole of line {1350, 2071} with respect to the Stammler hyperbola
X(61680) = pole of line {30769, 37668} with respect to the Wallace hyperbola
X(61680) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1350), X(10249)}}, {{A, B, C, X(3424), X(11744)}}, {{A, B, C, X(5486), X(42287)}}, {{A, B, C, X(23332), X(34412)}}
X(61680) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11206, 23332}, {2, 13394, 5085}, {2, 1503, 61735}, {2, 35259, 10516}, {2, 35265, 61700}, {2, 35266, 47353}, {2, 38918, 53015}, {3, 5972, 59767}, {4, 15448, 41424}, {25, 61743, 53023}, {110, 37638, 15069}, {154, 61735, 1503}, {159, 58450, 47355}, {184, 37453, 26958}, {206, 5651, 15139}, {468, 61690, 61506}, {631, 5656, 23328}, {1495, 5094, 36990}, {1503, 10192, 35260}, {1503, 35260, 154}, {1503, 61735, 1853}, {1995, 15577, 56924}, {2883, 3523, 8567}, {3526, 6759, 40686}, {4232, 5480, 31860}, {5642, 61644, 6090}, {5656, 23328, 64}, {6090, 61644, 599}, {6353, 23292, 17810}, {6776, 52290, 47296}, {7493, 11064, 1350}, {10192, 58434, 2}, {11204, 46265, 15693}, {12315, 55863, 25563}, {14530, 46219, 20299}, {15066, 34117, 17847}, {15694, 32063, 23329}, {15701, 35450, 10193}, {16252, 23328, 5656}, {18580, 46817, 11472}, {26869, 37453, 61691}, {31152, 35268, 59411}, {31267, 58437, 6}, {32269, 37645, 11477}, {61506, 61683, 61685}, {61646, 61681, 3167}

X(61681) = CENTROID OF THE PEDAL TRIANGLE OF X(156)

Barycentrics    4*a^6-4*a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)-a^2*(b^4-4*b^2*c^2+c^4) : :
X(61681) = 2*X[156]+X[20299], 2*X[10020]+X[41597], -4*X[10125]+X[52104], X[12084]+2*X[14862], 2*X[13371]+X[45185], -X[14864]+4*X[32144], X[23335]+2*X[50414], -4*X[23336]+X[52102], 2*X[25563]+X[32139], 5*X[31267]+X[52016]

X(61681) lies on these lines: {2, 98}, {3, 59551}, {5, 59699}, {30, 5448}, {49, 61713}, {51, 61655}, {154, 29012}, {156, 20299}, {381, 11425}, {389, 44211}, {428, 35266}, {468, 34986}, {511, 10154}, {524, 41593}, {539, 47360}, {541, 25564}, {549, 5876}, {575, 6677}, {576, 6353}, {597, 9822}, {858, 44110}, {1147, 10201}, {1495, 34603}, {1568, 11464}, {1993, 32223}, {2030, 40326}, {3098, 37669}, {3167, 5965}, {3564, 58434}, {3589, 13361}, {3818, 8780}, {3819, 13394}, {5020, 25555}, {5055, 6288}, {5092, 7734}, {5449, 34330}, {5640, 41713}, {5654, 11202}, {5663, 10193}, {5943, 61690}, {6102, 16532}, {6676, 40107}, {6688, 61507}, {6759, 44441}, {7426, 21969}, {7505, 10112}, {7506, 12242}, {7552, 43572}, {7667, 11064}, {7764, 44347}, {9704, 43817}, {9705, 14940}, {9707, 31180}, {9730, 59648}, {9909, 19924}, {10018, 43844}, {10020, 41597}, {10116, 60780}, {10125, 52104}, {10182, 13754}, {10219, 38110}, {10254, 30714}, {10565, 52987}, {10990, 35493}, {11225, 61645}, {11402, 32068}, {11430, 51425}, {11449, 43831}, {12084, 14862}, {13334, 59656}, {13335, 59651}, {13367, 52069}, {13368, 58489}, {13371, 45185}, {13857, 52397}, {14070, 23358}, {14864, 32144}, {15063, 35473}, {15688, 18442}, {16072, 19357}, {16534, 18570}, {17809, 33749}, {18350, 48411}, {18388, 38321}, {18445, 44673}, {18928, 55710}, {19130, 23292}, {21849, 44084}, {23335, 50414}, {23336, 52102}, {25563, 32139}, {26881, 51360}, {29317, 34608}, {31267, 52016}, {32225, 41628}, {32330, 34725}, {32375, 34114}, {34148, 46451}, {35264, 61743}, {35481, 38791}, {36178, 55308}, {37672, 44492}, {41149, 47451}, {43586, 61619}, {44212, 44495}, {44458, 51394}, {45968, 61691}, {47316, 55718}, {48886, 59623}, {52348, 59708}, {52349, 59709}, {61506, 61677}

X(61681) = midpoint of X(i) and X(j) for these {i,j}: {156, 61736}, {1147, 10201}, {3167, 61646}, {5654, 11202}, {6759, 44441}, {10192, 59553}
X(61681) = reflection of X(i) in X(j) for these {i,j}: {20299, 61736}, {34330, 58435}, {5449, 34330}, {61736, 43839}
X(61681) = pole of line {511, 11440} with respect to the Stammler hyperbola
X(61681) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {156, 43839, 20299}, {3167, 61680, 61646}, {9306, 58447, 24206}, {10192, 59553, 511}

X(61682) = CENTROID OF THE PEDAL TRIANGLE OF X(157)

Barycentrics    a^8-a^6*(b^2+c^2)-3*a^2*(b^2-c^2)^2*(b^2+c^2)+2*a^4*(b^4+c^4)+(b^2-c^2)^2*(b^4+c^4) : :
X(61682) = -X[577]+4*X[58436]

X(61682) lies on these lines: {2, 2393}, {6, 47200}, {66, 53015}, {127, 33926}, {141, 13355}, {157, 2794}, {206, 45198}, {577, 58436}, {1632, 52247}, {2453, 9220}, {3054, 47449}, {3150, 34845}, {8263, 44389}, {9306, 44388}, {9753, 9969}, {9756, 61737}, {14120, 18424}, {14651, 41760}, {20208, 57332}, {34827, 54393}, {41584, 53414}, {47556, 58831}, {52251, 53569}, {61644, 61689}

X(61682) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 61683, 61684}

X(61683) = CENTROID OF THE PEDAL TRIANGLE OF X(159)

Barycentrics    a^8+2*a^6*(b^2+c^2)-2*a^2*(b^2-c^2)^2*(b^2+c^2)-2*a^4*(b^2+c^2)^2+(b^4-c^4)^2 : :
X(61683) = -4*X[140]+X[8549], -X[1853]+3*X[21358], X[2888]+2*X[32367], 5*X[3620]+X[5596], 2*X[3631]+X[34774], X[5656]+3*X[10519], X[5895]+5*X[55614], -X[5925]+7*X[55626], X[6759]+2*X[40107], -X[8548]+4*X[10020], 2*X[10282]+X[34507], -3*X[10516]+X[18405] and many others

X(61683) lies on the Thomson-Gibert-Moses hyperbola and on these lines: {2, 2393}, {3, 66}, {5, 23049}, {6, 468}, {20, 19510}, {25, 54347}, {49, 8262}, {69, 110}, {140, 8549}, {154, 599}, {182, 10182}, {193, 9716}, {235, 7716}, {376, 36201}, {392, 3827}, {394, 16789}, {511, 5654}, {524, 3167}, {542, 11202}, {549, 10249}, {577, 35282}, {597, 5644}, {924, 5652}, {935, 35902}, {1660, 7494}, {1843, 61743}, {1853, 21358}, {1992, 55038}, {2549, 16321}, {2777, 3098}, {2781, 5655}, {2888, 32367}, {2892, 7492}, {3147, 14912}, {3313, 28419}, {3542, 6403}, {3564, 23041}, {3589, 5544}, {3618, 5643}, {3619, 5888}, {3620, 5596}, {3631, 34774}, {3763, 5646}, {3818, 49669}, {4846, 47569}, {5645, 39125}, {5653, 47139}, {5656, 10519}, {5895, 55614}, {5925, 55626}, {5965, 10274}, {5972, 11511}, {6000, 50977}, {6030, 11206}, {6353, 19136}, {6467, 35371}, {6676, 8263}, {6759, 40107}, {6776, 11464}, {6816, 15435}, {7505, 15073}, {8548, 10020}, {8681, 61646}, {9813, 58447}, {9822, 38317}, {10168, 10250}, {10169, 17813}, {10201, 14984}, {10257, 54183}, {10282, 34507}, {10516, 18405}, {10602, 37453}, {11178, 18400}, {11179, 44214}, {11255, 58435}, {11331, 45279}, {11799, 31670}, {11898, 41729}, {12220, 28408}, {13383, 19139}, {13567, 32621}, {14023, 15257}, {14457, 43725}, {14561, 16776}, {14643, 18438}, {14924, 47355}, {15068, 16618}, {15069, 17821}, {15113, 16051}, {15116, 16063}, {15118, 18919}, {15131, 54334}, {15311, 54169}, {15583, 34573}, {16238, 38110}, {16511, 40132}, {17907, 61181}, {18325, 43621}, {18358, 34775}, {18376, 25561}, {18553, 34785}, {19132, 40341}, {19459, 26869}, {19596, 31383}, {20582, 23332}, {22802, 55606}, {23292, 41585}, {23325, 24206}, {25555, 34788}, {32225, 61692}, {32605, 41716}, {34177, 37636}, {34776, 43150}, {34817, 43695}, {35901, 47150}, {37645, 41583}, {38227, 41770}, {40330, 41171}, {40673, 61645}, {41735, 54050}, {44285, 47353}, {46262, 47200}, {51831, 60133}, {52283, 53569}, {58439, 59543}, {59778, 61739}, {61644, 61667}

X(61683) = midpoint of X(i) and X(j) for these {i,j}: {69, 41719}, {154, 599}, {159, 61737}, {23049, 34787}, {41735, 54050}
X(61683) = reflection of X(i) in X(j) for these {i,j}: {182, 10182}, {10249, 549}, {10250, 10168}, {11216, 597}, {17813, 10169}, {18376, 25561}, {19153, 10192}, {23049, 5}, {23325, 24206}, {23326, 3589}, {23327, 2}, {23332, 20582}, {31166, 154}, {34777, 23326}, {41719, 206}, {597, 58434}, {66, 61737}, {61664, 61676}, {61737, 141}
X(61683) = perspector of circumconic {{A, B, C, X(30247), X(44766)}}
X(61683) = pole of line {30209, 30474} with respect to the orthoptic circle of the Steiner inellipse
X(61683) = pole of line {3767, 5094} with respect to the Kiepert hyperbola
X(61683) = pole of line {1576, 4235} with respect to the Kiepert parabola
X(61683) = pole of line {22, 2393} with respect to the Stammler hyperbola
X(61683) = pole of line {315, 858} with respect to the Wallace hyperbola
X(61683) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(66), X(2373)}}, {{A, B, C, X(69), X(57466)}}, {{A, B, C, X(1177), X(2353)}}, {{A, B, C, X(5486), X(14376)}}, {{A, B, C, X(23327), X(46140)}}
X(61683) = barycentric product X(i)*X(j) for these (i, j): {3, 51260}
X(61683) = barycentric quotient X(i)/X(j) for these (i, j): {51260, 264}
X(61683) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 2393, 23327}, {6, 58437, 31267}, {69, 35260, 41719}, {141, 1503, 61737}, {141, 15585, 159}, {141, 159, 66}, {159, 61737, 1503}, {524, 10192, 19153}, {1352, 15577, 36989}, {3619, 36851, 6697}, {3763, 9924, 23300}, {15582, 34118, 9833}, {35260, 41719, 206}, {48876, 61610, 19149}, {61680, 61685, 61506}, {61682, 61684, 2}

X(61684) = CENTROID OF THE PEDAL TRIANGLE OF X(160)

Barycentrics    2*b^2*c^2*(b^2-c^2)^2+3*a^6*(b^2+c^2)+a^2*(b^2-c^2)^2*(b^2+c^2)-4*a^4*(b^4+b^2*c^2+c^4) : :
X(61684) = X[160]+2*X[14767]

X(61684) lies on these lines: {2, 2393}, {66, 7710}, {95, 35278}, {114, 141}, {159, 9756}, {160, 14767}, {216, 523}, {262, 9969}, {549, 2790}, {1632, 60700}, {1634, 59197}, {3055, 47449}, {3613, 22682}, {6676, 44389}, {7709, 41760}, {8589, 47326}, {9754, 41770}, {34986, 44376}, {35707, 58849}, {39663, 53477}, {41593, 56290}

X(61684) = midpoint of X(i) and X(j) for these {i,j}: {160, 61738}
X(61684) = reflection of X(i) in X(j) for these {i,j}: {61738, 14767}
X(61684) = pole of line {30209, 53331} with respect to the orthoptic circle of the Steiner inellipse
X(61684) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 61683, 61682}

X(61685) = CENTROID OF THE PEDAL TRIANGLE OF X(161)

Barycentrics    a^12+(b^2-c^2)^4*(b^2+c^2)^2+3*a^4*(b^2-c^2)^2*(b^4+c^4)+4*a^6*(b^2+c^2)*(b^4+c^4)-a^8*(5*b^4+4*b^2*c^2+5*c^4)-4*a^2*(b^2-c^2)^2*(b^6+c^6) : :
X(61685) = -X[64]+4*X[44683], -X[1993]+4*X[58439]

X(61685) lies on these lines: {2, 34751}, {6, 468}, {20, 11598}, {22, 161}, {64, 44683}, {68, 1658}, {69, 15139}, {154, 3564}, {206, 41586}, {550, 8567}, {569, 10182}, {1209, 23325}, {1350, 32125}, {1352, 56924}, {1368, 61735}, {1853, 7667}, {1993, 58439}, {2393, 61644}, {2777, 37478}, {3098, 41603}, {3580, 15577}, {5656, 6293}, {5972, 8538}, {6146, 32534}, {6515, 9544}, {7505, 11746}, {10192, 61658}, {10201, 61724}, {10316, 35282}, {11202, 61713}, {12605, 18405}, {14683, 15647}, {15131, 41673}, {18911, 35228}, {32263, 41674}, {33522, 34944}, {34787, 37638}, {42459, 47164}, {47328, 61743}, {59778, 61737}, {61646, 61666}

X(61685) = midpoint of X(i) and X(j) for these {i,j}: {161, 61739}
X(61685) = reflection of X(i) in X(j) for these {i,j}: {61739, 343}
X(61685) = pole of line {15577, 41614} with respect to the Stammler hyperbola
X(61685) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {161, 61739, 1503}, {343, 1503, 61739}, {61506, 61683, 61680}

X(61686) = CENTROID OF THE PEDAL TRIANGLE OF X(165)

Barycentrics    a*(-b^2-6*b*c-c^2+a*(b+c)) : :
X(61686) = 2*X[2]+X[210], 8*X[5]+X[7957], X[8]+2*X[10179], -X[65]+10*X[1698], X[72]+8*X[3634], X[165]+2*X[10157], 2*X[375]+X[3917], X[551]+2*X[3956], -10*X[631]+X[12680], 5*X[632]+4*X[58632], 4*X[942]+5*X[4005], 4*X[960]+5*X[3698] and many others

X(61686) lies on these lines: {1, 3711}, {2, 210}, {5, 7957}, {8, 10179}, {9, 1155}, {10, 11}, {37, 899}, {38, 16602}, {43, 37593}, {44, 750}, {55, 7308}, {57, 3715}, {65, 1698}, {72, 3634}, {75, 4009}, {100, 15254}, {140, 12757}, {141, 60423}, {165, 10157}, {192, 4706}, {200, 3748}, {226, 38204}, {244, 31197}, {312, 26038}, {321, 59506}, {373, 674}, {375, 3917}, {404, 5302}, {497, 59413}, {513, 6544}, {516, 46916}, {517, 4731}, {519, 3921}, {551, 3956}, {612, 37679}, {631, 12680}, {632, 58632}, {726, 42056}, {756, 3752}, {758, 53039}, {896, 15492}, {908, 3826}, {936, 2646}, {942, 4005}, {958, 35262}, {960, 3698}, {984, 4003}, {993, 35271}, {1001, 3689}, {1125, 3697}, {1212, 3119}, {1279, 17125}, {1319, 9708}, {1376, 3305}, {1385, 5531}, {1386, 5297}, {1656, 58630}, {1757, 37520}, {1836, 18228}, {1864, 5432}, {1898, 47742}, {2262, 38472}, {2550, 4679}, {2771, 5660}, {2801, 38101}, {2805, 17359}, {2810, 15082}, {3008, 17602}, {3011, 17337}, {3035, 5784}, {3059, 6666}, {3091, 58637}, {3175, 28522}, {3218, 15481}, {3219, 9342}, {3240, 15569}, {3241, 4711}, {3244, 4540}, {3294, 24052}, {3303, 3646}, {3306, 5220}, {3338, 16863}, {3452, 3925}, {3525, 12675}, {3555, 4015}, {3616, 4662}, {3617, 3893}, {3618, 58653}, {3620, 58694}, {3624, 17609}, {3666, 16569}, {3678, 5439}, {3679, 5919}, {3696, 4358}, {3699, 16823}, {3706, 18743}, {3712, 25101}, {3720, 4849}, {3739, 30958}, {3744, 17123}, {3745, 4383}, {3753, 3828}, {3763, 58633}, {3811, 16842}, {3812, 3876}, {3816, 25006}, {3823, 25760}, {3827, 61735}, {3833, 4134}, {3834, 33065}, {3838, 27131}, {3869, 3922}, {3870, 8167}, {3874, 4533}, {3878, 4002}, {3898, 4745}, {3900, 14476}, {3911, 8581}, {3912, 4023}, {3920, 37687}, {3935, 42819}, {3940, 44840}, {3952, 24589}, {3967, 4359}, {3971, 28516}, {3994, 4686}, {3999, 49448}, {4042, 30567}, {4096, 24165}, {4113, 10453}, {4407, 61176}, {4414, 16814}, {4420, 17536}, {4521, 44319}, {4640, 27065}, {4641, 17122}, {4663, 37633}, {4668, 31792}, {4682, 32911}, {4687, 58655}, {4689, 56009}, {4699, 58693}, {4850, 9330}, {4860, 5223}, {4863, 26105}, {4871, 49457}, {4883, 25502}, {4903, 42029}, {4914, 10327}, {4968, 59577}, {5045, 34595}, {5047, 56176}, {5048, 9623}, {5067, 13374}, {5087, 33108}, {5204, 5234}, {5205, 17277}, {5218, 14100}, {5231, 51380}, {5235, 18191}, {5251, 15015}, {5257, 61034}, {5260, 59691}, {5273, 10861}, {5326, 58699}, {5524, 16484}, {5550, 34791}, {5640, 9047}, {5650, 8679}, {5705, 31246}, {5745, 17612}, {5777, 31423}, {5791, 37566}, {5836, 46933}, {5880, 31018}, {5902, 19876}, {5904, 19872}, {5918, 5927}, {6048, 37548}, {6174, 60986}, {6684, 12688}, {6700, 24953}, {7174, 54390}, {7288, 9850}, {7292, 49465}, {7322, 17599}, {7354, 18250}, {7786, 58656}, {7964, 19541}, {7987, 9947}, {7989, 31793}, {7998, 9037}, {8166, 45776}, {8227, 58643}, {8582, 21677}, {8583, 20323}, {8758, 25067}, {8889, 41611}, {9004, 21358}, {9024, 49731}, {9347, 14997}, {9458, 16482}, {9588, 9856}, {9709, 37568}, {9710, 41012}, {9711, 24987}, {9817, 41339}, {9956, 14110}, {10165, 18908}, {10167, 15064}, {10175, 44847}, {10303, 58567}, {10404, 17582}, {10527, 46677}, {10582, 41711}, {10916, 17575}, {10950, 12447}, {11019, 38210}, {11108, 37080}, {11284, 12329}, {11375, 19855}, {12587, 54012}, {12607, 24564}, {13373, 46219}, {14061, 58662}, {14439, 44798}, {15017, 37562}, {15059, 58671}, {15104, 58688}, {15185, 58677}, {15568, 21471}, {15624, 16373}, {15726, 61023}, {15837, 60958}, {16187, 43146}, {16408, 32636}, {16604, 21893}, {16832, 20358}, {16857, 59337}, {17238, 25108}, {17259, 29828}, {17348, 17763}, {17355, 17635}, {17356, 32775}, {17362, 49990}, {17388, 49986}, {17392, 61652}, {17461, 56159}, {17495, 49523}, {17529, 21077}, {17592, 36634}, {17593, 51294}, {17613, 60911}, {17634, 18249}, {17641, 58689}, {17642, 20196}, {17660, 31235}, {17726, 50291}, {17749, 56237}, {18149, 25280}, {18229, 21334}, {19732, 20359}, {19804, 27538}, {19843, 24954}, {19998, 49475}, {20195, 58635}, {21060, 38054}, {21805, 30950}, {23155, 44299}, {24318, 40629}, {24386, 61032}, {24393, 51463}, {24620, 49447}, {24723, 26073}, {24798, 40615}, {24914, 54366}, {24988, 26580}, {25066, 46196}, {25107, 59633}, {25144, 43216}, {25615, 38375}, {26029, 31359}, {26037, 44417}, {27191, 58691}, {28257, 52541}, {29639, 51415}, {30700, 44902}, {30745, 58639}, {30827, 31245}, {30947, 49450}, {31035, 49462}, {31140, 38200}, {31142, 38052}, {31146, 59414}, {31238, 40607}, {31241, 58644}, {31249, 58696}, {31254, 58638}, {31260, 58636}, {31262, 58640}, {31263, 58641}, {31264, 58642}, {31266, 58651}, {31272, 58663}, {31273, 58664}, {31276, 58695}, {31493, 58645}, {31658, 44425}, {31993, 59511}, {32771, 59596}, {32860, 35652}, {33156, 41310}, {33174, 36482}, {33993, 44547}, {34612, 40998}, {35289, 52139}, {35445, 61152}, {37998, 45684}, {38191, 59684}, {44671, 53034}, {46934, 58609}, {48154, 58675}, {49471, 49988}, {51126, 58676}, {53663, 59686}, {55861, 58561}, {58646, 61640}, {60782, 60981}, {61662, 61672}

X(61686) = midpoint of X(i) and X(j) for these {i,j}: {165, 61740}
X(61686) = reflection of X(i) in X(j) for these {i,j}: {4731, 19875}, {61740, 10157}
X(61686) = perspector of circumconic {{A, B, C, X(24858), X(32041)}}
X(61686) = pole of line {390, 519} with respect to the Feuerbach hyperbola
X(61686) = pole of line {3762, 4762} with respect to the Steiner inellipse
X(61686) = pole of line {16610, 29571} with respect to the dual conic of Yff parabola
X(61686) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1001), X(51099)}}, {{A, B, C, X(1002), X(56163)}}, {{A, B, C, X(3742), X(57815)}}, {{A, B, C, X(3848), X(57785)}}, {{A, B, C, X(14554), X(27475)}}
X(61686) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3681, 3742}, {2, 3740, 210}, {2, 3873, 3848}, {9, 4413, 1155}, {10, 11814, 21242}, {10, 24003, 30818}, {10, 25917, 3057}, {10, 5316, 11}, {43, 44307, 37593}, {57, 30393, 3715}, {100, 35595, 15254}, {200, 4423, 3748}, {200, 51780, 4423}, {517, 19875, 4731}, {631, 58631, 12680}, {960, 9780, 3698}, {984, 16610, 4003}, {1698, 5044, 65}, {3452, 3925, 17605}, {3624, 34790, 17609}, {3678, 51073, 5439}, {3696, 4358, 4519}, {3740, 3742, 58629}, {3740, 58451, 2}, {3742, 58629, 3681}, {3812, 3876, 3962}, {3828, 10176, 3753}, {3833, 4134, 24473}, {3876, 19877, 3812}, {3952, 24589, 49483}, {4015, 19862, 3555}, {4383, 5268, 3745}, {4420, 17536, 51715}, {5220, 61158, 3306}, {5297, 37680, 1386}, {5927, 10164, 5918}, {7308, 8580, 55}, {7322, 23511, 17599}, {15064, 58441, 10167}, {16408, 41229, 32636}, {17718, 61660, 354}, {18228, 26040, 1836}, {18230, 58634, 14100}, {18743, 59296, 3706}, {20196, 58650, 17642}, {21805, 30950, 49478}, {31142, 38052, 61716}, {31197, 49515, 244}, {31235, 46694, 17660}, {58677, 61001, 15185}

X(61687) = CENTROID OF THE PEDAL TRIANGLE OF X(171)

Barycentrics    a*(a^2*b*c*(b+c)+b*(b-c)^2*c*(b+c)+a^3*(b^2+4*b*c+c^2)-a*(b^4-6*b^2*c^2+c^4)) : :
X(61687) = 2*X[181]+X[21334]

X(61687) lies on these lines: {1, 9567}, {2, 210}, {65, 17720}, {171, 15310}, {181, 21334}, {373, 61647}, {375, 61661}, {899, 28244}, {942, 17719}, {978, 3304}, {1100, 38472}, {1155, 1400}, {1193, 20323}, {1463, 37520}, {2269, 45881}, {3338, 19549}, {3713, 4413}, {3745, 45897}, {3748, 21321}, {6745, 52020}, {6784, 51408}, {13731, 37080}, {17602, 20358}, {19133, 33849}, {19513, 32636}, {20103, 53005}, {24210, 29309}, {25135, 33073}, {28275, 59305}, {61652, 61670}

X(61687) = perspector of circumconic {{A, B, C, X(32041), X(39631)}}
X(61687) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {61670, 61672, 61652}

X(61688) = CENTROID OF THE PEDAL TRIANGLE OF X(172)

Barycentrics    4*a^4+a^3*(b+c)-a*(b-c)^2*(b+c)+(b^2-c^2)^2+a^2*(b^2+4*b*c+c^2) : :

X(61688) lies on these lines: {6, 17728}, {44, 37634}, {172, 515}, {230, 61648}, {354, 5306}, {1210, 7296}, {1468, 61706}, {2243, 24210}, {2276, 10164}, {3338, 5319}, {3475, 7735}, {3509, 33152}, {3985, 59664}, {5332, 11019}, {5603, 54382}, {7755, 13407}, {9300, 61649}, {9596, 54447}, {16972, 26258}, {26446, 54416}, {33119, 49756}, {40869, 60697}, {51406, 61661}, {61643, 61650}, {61652, 61694}

X(61688) = midpoint of X(i) and X(j) for these {i,j}: {172, 61741}

X(61689) = CENTROID OF THE PEDAL TRIANGLE OF X(183)

Barycentrics    -(a^2*b^2*c^2*(b^4-6*b^2*c^2+c^4))-a^4*(b^2+c^2)*(b^4-4*b^2*c^2+c^4)+a^6*(b^4-b^2*c^2+c^4) : :

X(61689) lies on these lines: {2, 6784}, {6, 373}, {51, 8667}, {182, 9149}, {183, 511}, {290, 14937}, {385, 5640}, {599, 13240}, {2679, 6787}, {3111, 3734}, {3511, 11171}, {3917, 8556}, {5167, 12525}, {5201, 34417}, {5650, 15271}, {5943, 14614}, {7610, 47638}, {7697, 41330}, {7998, 13207}, {8177, 16776}, {9418, 35259}, {11159, 32442}, {12093, 33755}, {12188, 40280}, {16836, 39646}, {24256, 47211}, {32828, 40951}, {35268, 60514}, {61644, 61682}

X(61689) = midpoint of X(i) and X(j) for these {i,j}: {183, 61742}
X(61689) = pole of line {11059, 22712} with respect to the Wallace hyperbola
X(61689) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {183, 61742, 511}

X(61690) = CENTROID OF THE PEDAL TRIANGLE OF X(184)

Barycentrics    4*a^6-5*a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2) : :
X(61690) = 2*X[184]+X[427], -5*X[631]+2*X[44683], X[1993]+2*X[6676], -X[15760]+4*X[61619], X[18445]+2*X[52262], -4*X[18475]+X[44239]

X(61690) lies on these lines: {2, 3167}, {3, 37645}, {4, 14530}, {5, 49}, {6, 468}, {23, 21850}, {25, 11427}, {30, 6800}, {39, 35282}, {51, 10192}, {107, 42873}, {125, 8550}, {140, 7592}, {141, 3292}, {154, 428}, {156, 7403}, {182, 11064}, {184, 427}, {185, 15151}, {217, 35325}, {235, 578}, {275, 6755}, {323, 7495}, {343, 5965}, {373, 597}, {389, 10182}, {394, 7499}, {418, 16030}, {436, 14569}, {511, 13394}, {523, 14582}, {524, 61644}, {542, 45303}, {547, 61701}, {549, 5890}, {550, 15080}, {568, 34351}, {569, 9820}, {570, 47195}, {575, 5972}, {576, 32269}, {631, 44683}, {632, 11423}, {858, 11003}, {879, 47248}, {895, 32227}, {1112, 50649}, {1147, 7399}, {1199, 10018}, {1316, 6794}, {1351, 7493}, {1352, 37454}, {1353, 3580}, {1368, 5012}, {1495, 5480}, {1593, 5656}, {1594, 31804}, {1595, 1614}, {1596, 15033}, {1656, 54013}, {1885, 11425}, {1899, 17809}, {1906, 11424}, {1907, 6759}, {1970, 61206}, {1993, 6676}, {1994, 41588}, {1995, 18583}, {2452, 47146}, {2777, 11430}, {3060, 10154}, {3134, 15920}, {3147, 11432}, {3431, 10295}, {3516, 54050}, {3520, 13171}, {3526, 18916}, {3530, 21766}, {3541, 19347}, {3542, 11426}, {3574, 34782}, {3575, 19357}, {3589, 5651}, {3618, 11284}, {3628, 18912}, {3629, 41586}, {3796, 7667}, {3815, 47200}, {3917, 21167}, {5064, 11206}, {5085, 43957}, {5094, 6776}, {5097, 32223}, {5112, 18907}, {5133, 9544}, {5159, 18911}, {5169, 39884}, {5422, 6677}, {5449, 11232}, {5476, 35266}, {5576, 9704}, {5640, 44212}, {5654, 34664}, {5663, 44218}, {5943, 61681}, {5946, 44211}, {5967, 41939}, {6146, 23325}, {6353, 9777}, {6467, 23326}, {6639, 13292}, {6689, 41597}, {6723, 33749}, {6756, 9707}, {6793, 47202}, {6823, 34148}, {6997, 8780}, {7426, 11002}, {7483, 26637}, {7484, 37669}, {7488, 31802}, {7492, 48874}, {7503, 61607}, {7507, 18925}, {7515, 54349}, {7539, 14826}, {7542, 12161}, {7576, 61715}, {7605, 38079}, {7709, 40884}, {7712, 37900}, {7715, 26882}, {7745, 44116}, {7769, 57216}, {8369, 9155}, {8584, 32225}, {8887, 33549}, {8964, 55566}, {9143, 53843}, {9306, 35283}, {9545, 13160}, {9703, 37347}, {9717, 15000}, {9730, 38793}, {10024, 43595}, {10168, 15082}, {10282, 12242}, {10299, 40911}, {10303, 44833}, {10601, 59543}, {10619, 41362}, {11004, 52300}, {11179, 47097}, {11433, 37453}, {11464, 37458}, {11482, 21970}, {11585, 32046}, {12007, 47296}, {12017, 46336}, {12045, 46267}, {12107, 22051}, {12112, 35484}, {12233, 13367}, {12244, 35492}, {13198, 15131}, {13366, 13567}, {13383, 36749}, {13403, 46682}, {13416, 13630}, {13857, 51737}, {14561, 35259}, {14848, 26255}, {15018, 52124}, {15032, 15106}, {15035, 44273}, {15139, 23300}, {15448, 34417}, {15712, 41462}, {15739, 41725}, {15760, 61619}, {16238, 36753}, {16266, 34002}, {17330, 61694}, {17825, 59551}, {18405, 19467}, {18445, 52262}, {18475, 44239}, {18914, 37119}, {19125, 41719}, {20423, 37904}, {20775, 44886}, {21466, 32461}, {21467, 32460}, {21637, 46444}, {23042, 44077}, {23291, 52298}, {23606, 26906}, {25328, 32235}, {25406, 31152}, {26917, 55856}, {26926, 61737}, {27377, 41203}, {29181, 35268}, {31383, 52285}, {31670, 37899}, {32136, 58407}, {32220, 43697}, {32341, 56292}, {32366, 60774}, {34177, 54347}, {34211, 44891}, {34330, 45969}, {34397, 54381}, {34513, 44261}, {35237, 47092}, {35265, 38136}, {37070, 41371}, {37643, 52292}, {37672, 43653}, {37971, 39522}, {37974, 42118}, {37975, 42117}, {39242, 44285}, {39874, 52284}, {40132, 51171}, {40909, 47340}, {40981, 44890}, {41005, 44888}, {41202, 42459}, {41334, 61199}, {41587, 44516}, {41628, 55038}, {42215, 47631}, {42216, 47632}, {43273, 47311}, {43394, 44240}, {43602, 43607}, {43650, 53415}, {44413, 47093}, {44882, 51360}, {46064, 59241}, {46124, 46128}, {46264, 46517}, {46349, 54992}, {47095, 48905}, {47251, 58900}, {47312, 54131}, {47597, 59373}, {50679, 61714}, {53093, 54012}, {57586, 61207}, {58434, 61645}, {61646, 61658}

X(61690) = midpoint of X(i) and X(j) for these {i,j}: {184, 61743}
X(61690) = reflection of X(i) in X(j) for these {i,j}: {427, 61743}, {44210, 13394}, {44261, 34513}, {44285, 39242}, {61743, 23292}
X(61690) = inverse of X(29959) in Thomson-Gibert-Moses hyperbola
X(61690) = perspector of circumconic {{A, B, C, X(18316), X(30247)}}
X(61690) = pole of line {12007, 19161} with respect to the Jerabek hyperbola
X(61690) = pole of line {50, 5094} with respect to the Kiepert hyperbola
X(61690) = pole of line {1499, 50644} with respect to the orthic inconic
X(61690) = pole of line {1154, 1351} with respect to the Stammler hyperbola
X(61690) = pole of line {24978, 61656} with respect to the Steiner inellipse
X(61690) = pole of line {1007, 1273} with respect to the Wallace hyperbola
X(61690) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(523), X(4993)}}, {{A, B, C, X(1141), X(7612)}}, {{A, B, C, X(5486), X(56267)}}
X(61690) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14912, 26869}, {2, 61655, 59553}, {6, 5486, 47277}, {6, 61506, 61657}, {110, 14389, 5}, {125, 44109, 8550}, {182, 11064, 30739}, {184, 61743, 1503}, {323, 7495, 48876}, {373, 5642, 61507}, {436, 56297, 14569}, {468, 61657, 61506}, {511, 13394, 44210}, {575, 5972, 37648}, {597, 61507, 373}, {858, 11003, 48906}, {1351, 7493, 47582}, {1495, 5480, 10301}, {1503, 23292, 61743}, {1503, 61743, 427}, {3580, 11422, 1353}, {5169, 46818, 39884}, {5654, 37506, 34664}, {9306, 38317, 35283}, {10282, 12242, 45089}, {11003, 59771, 858}, {11402, 26869, 14912}, {11424, 16252, 1906}, {11427, 35260, 14853}, {14853, 35260, 25}, {14912, 26869, 11245}, {34986, 58447, 343}, {35283, 37649, 38317}, {35283, 38317, 37439}, {44212, 59399, 5640}, {53093, 59767, 54012}, {61506, 61680, 468}, {61691, 61712, 13567}

X(61691) = CENTROID OF THE PEDAL TRIANGLE OF X(186)

Barycentrics    2*a^6-3*a^2*(b^2-c^2)^2-a^4*(b^2+c^2)+2*(b^2-c^2)^2*(b^2+c^2) : :
X(61691) = -4*X[5]+X[1531], X[23]+5*X[15059], X[67]+5*X[47453], X[125]+2*X[468], -4*X[140]+X[10564], 2*X[141]+X[53777], 2*X[186]+X[13851], 2*X[547]+X[15361], -X[858]+4*X[6723], 2*X[1514]+X[10990], X[1533]+5*X[38729], -X[1568]+4*X[44911] and many others

X(61691) lies on these lines: {2, 51}, {3, 61127}, {4, 20421}, {5, 1531}, {6, 52292}, {23, 15059}, {24, 11572}, {25, 61735}, {30, 23515}, {49, 11232}, {52, 60780}, {67, 47453}, {125, 468}, {126, 59695}, {140, 10564}, {141, 53777}, {184, 26869}, {185, 7505}, {186, 13851}, {187, 15000}, {230, 6793}, {235, 23328}, {382, 40920}, {389, 14940}, {403, 2777}, {427, 44106}, {451, 58889}, {512, 47255}, {524, 47240}, {539, 59648}, {547, 15361}, {549, 61744}, {858, 6723}, {973, 32205}, {1514, 10990}, {1533, 38729}, {1568, 44911}, {1570, 41939}, {1648, 1692}, {1649, 55265}, {1656, 3581}, {1843, 35370}, {1853, 44082}, {1899, 35260}, {1974, 61737}, {2076, 39602}, {2393, 47450}, {2677, 47140}, {3154, 47327}, {3258, 11657}, {3292, 3580}, {3515, 18405}, {3518, 32767}, {3526, 11424}, {3527, 55866}, {3542, 11381}, {3564, 5642}, {3574, 3628}, {3589, 8262}, {3618, 41721}, {3763, 19510}, {3906, 9210}, {5034, 30516}, {5039, 9745}, {5054, 15362}, {5055, 32620}, {5092, 52300}, {5094, 34417}, {5095, 47457}, {5097, 59771}, {5159, 32269}, {5181, 32127}, {5462, 22815}, {5480, 52293}, {5651, 37638}, {5656, 26937}, {5663, 44282}, {5894, 45004}, {5946, 34330}, {6000, 37943}, {6070, 16319}, {6130, 32112}, {6143, 10110}, {6353, 11550}, {6467, 35371}, {6530, 47204}, {6622, 54050}, {6640, 45186}, {6677, 35283}, {6697, 44091}, {6698, 32217}, {6699, 11799}, {6741, 16332}, {6776, 53857}, {7426, 29012}, {7512, 43866}, {7552, 16836}, {7575, 20304}, {7687, 10295}, {7703, 14002}, {7886, 45284}, {9140, 35265}, {9181, 58448}, {9729, 58805}, {10011, 57431}, {10018, 10182}, {10020, 43817}, {10113, 18571}, {10117, 15126}, {10192, 44108}, {10282, 26917}, {10418, 53475}, {10510, 47355}, {10516, 47597}, {10546, 18553}, {10619, 12024}, {10733, 37952}, {10982, 37496}, {11064, 34380}, {11202, 61701}, {11225, 61655}, {11245, 58434}, {11433, 44111}, {11645, 37907}, {11704, 18383}, {11735, 47321}, {11793, 43581}, {11801, 22249}, {12041, 44961}, {12099, 44668}, {12295, 47335}, {13202, 37984}, {13366, 13567}, {13392, 14049}, {13417, 15131}, {13449, 46512}, {13474, 43608}, {13754, 14643}, {14639, 44579}, {14855, 44278}, {14912, 37643}, {14915, 15061}, {15025, 37957}, {15088, 18572}, {15107, 30745}, {15113, 37981}, {15118, 32113}, {15359, 47326}, {15471, 47456}, {16003, 46817}, {16080, 41204}, {16111, 47336}, {16194, 44270}, {16320, 51428}, {16532, 30522}, {16654, 21841}, {16658, 20299}, {17508, 47596}, {17702, 44214}, {17810, 52298}, {18325, 38728}, {19457, 37933}, {20192, 38136}, {20417, 32111}, {21167, 30739}, {21451, 44870}, {22104, 47348}, {22264, 47004}, {23292, 34565}, {23326, 41584}, {23329, 32062}, {25338, 40685}, {29181, 47097}, {30775, 51538}, {31282, 46728}, {31726, 38788}, {31857, 48895}, {31884, 32216}, {32220, 32257}, {32237, 37760}, {32423, 44234}, {32460, 44667}, {32461, 44666}, {32743, 45181}, {34147, 35442}, {34566, 61659}, {34786, 35479}, {35282, 44887}, {37648, 38110}, {37920, 56924}, {37942, 51403}, {37958, 58789}, {38397, 43150}, {38793, 44452}, {39663, 44576}, {39691, 40350}, {42736, 47219}, {43907, 44271}, {44077, 61739}, {44102, 47455}, {44145, 58261}, {44212, 45303}, {45089, 55856}, {45968, 61681}, {47149, 57423}, {47150, 57426}, {47166, 57424}, {47170, 57425}, {47187, 51434}, {47215, 57587}, {47347, 55319}, {51372, 57588}, {51548, 61548}

X(61691) = midpoint of X(i) and X(j) for these {i,j}: {186, 14644}, {5054, 15362}, {9140, 35265}, {31726, 38788}
X(61691) = reflection of X(i) in X(j) for these {i,j}: {13851, 14644}, {38793, 44452}, {44102, 47455}, {51394, 38793}
X(61691) = pole of line {512, 2394} with respect to the orthoptic circle of the Steiner inellipse
X(61691) = pole of line {2781, 6776} with respect to the Jerabek hyperbola
X(61691) = pole of line {3815, 6103} with respect to the Kiepert hyperbola
X(61691) = pole of line {182, 15036} with respect to the Stammler hyperbola
X(61691) = pole of line {19569, 23878} with respect to the Steiner circumellipse
X(61691) = pole of line {14537, 23878} with respect to the Steiner inellipse
X(61691) = intersection, other than A, B, C, of circumconics {{A, B, C, X(262), X(61127)}}, {{A, B, C, X(20421), X(54032)}}
X(61691) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 32225, 13857}, {2, 61506, 61743}, {2, 61644, 5650}, {2, 61645, 51}, {2, 61646, 3917}, {5, 32110, 1531}, {125, 468, 1495}, {403, 44673, 21663}, {468, 47296, 125}, {3580, 5972, 3292}, {5159, 32269, 51360}, {6723, 32223, 858}, {7703, 14002, 48889}, {10018, 12022, 10182}, {11704, 44879, 18383}, {18325, 38728, 58871}, {26869, 37453, 61680}, {26869, 61680, 184}, {61645, 61743, 61506}, {61690, 61712, 13366}

X(61692) = CENTROID OF THE PEDAL TRIANGLE OF X(193)

Barycentrics    a^2*(-b^6-16*a^2*b^2*c^2+5*b^4*c^2+5*b^2*c^4-c^6+a^4*(b^2+c^2)) : :
X(61692) = -4*X[6]+3*X[373], -2*X[69]+3*X[5650], -5*X[141]+6*X[61045], -5*X[3620]+6*X[15082], -3*X[5032]+2*X[5943], -X[5562]+4*X[32284], -3*X[5640]+2*X[14913], X[6144]+2*X[32366], -3*X[7998]+X[20080], -3*X[11002]+X[12272], X[11008]+2*X[11574], -3*X[14912]+2*X[16836] and many others

X(61692) lies on these lines: {6, 373}, {20, 185}, {51, 1992}, {52, 53778}, {69, 5650}, {141, 61045}, {155, 3527}, {184, 53019}, {524, 3917}, {542, 32062}, {568, 34382}, {576, 11441}, {800, 9155}, {1092, 5050}, {1112, 1843}, {1154, 50986}, {1353, 9730}, {1993, 21639}, {2393, 15534}, {3564, 15030}, {3620, 15082}, {3819, 11160}, {5032, 5943}, {5102, 11470}, {5562, 32284}, {5640, 14913}, {5921, 46847}, {6000, 50974}, {6144, 32366}, {7998, 20080}, {8584, 29959}, {8705, 16327}, {9004, 61678}, {9813, 34565}, {9970, 55716}, {10170, 11898}, {11002, 12272}, {11004, 11443}, {11008, 11574}, {11477, 12174}, {11820, 44456}, {13292, 15067}, {13366, 41614}, {14831, 14984}, {14912, 16836}, {14915, 39899}, {15063, 21850}, {15141, 39125}, {16776, 32455}, {17040, 18916}, {19459, 35268}, {19588, 35259}, {21637, 40318}, {22352, 32621}, {22829, 40341}, {32225, 61683}, {32226, 52699}, {32260, 45237}, {32285, 40316}, {34986, 37784}, {41617, 44109}, {43810, 55695}, {45187, 50649}, {51140, 52989}, {51179, 54041}

X(61692) = midpoint of X(i) and X(j) for these {i,j}: {193, 15531}, {6144, 54334}
X(61692) = reflection of X(i) in X(j) for these {i,j}: {11160, 3819}, {11898, 10170}, {16776, 32455}, {29959, 8584}, {3917, 40673}, {32260, 45237}, {51, 1992}, {5921, 46847}, {54334, 32366}, {6467, 15531}, {61667, 6}, {61679, 5095}, {9730, 1353}
X(61692) = perspector of circumconic {{A, B, C, X(1296), X(43188)}}
X(61692) = pole of line {22159, 30230} with respect to the cosine circle
X(61692) = pole of line {16229, 53365} with respect to the polar circle
X(61692) = pole of line {2524, 8644} with respect to the Brocard inellipse
X(61692) = pole of line {2, 8263} with respect to the Jerabek hyperbola
X(61692) = pole of line {1992, 9306} with respect to the Stammler hyperbola
X(61692) = pole of line {1975, 11059} with respect to the Wallace hyperbola
X(61692) = intersection, other than A, B, C, of circumconics {{A, B, C, X(9289), X(25322)}}, {{A, B, C, X(9292), X(39238)}}, {{A, B, C, X(9307), X(21448)}}, {{A, B, C, X(11059), X(11284)}}
X(61692) = barycentric product X(i)*X(j) for these (i, j): {59766, 6}
X(61692) = barycentric quotient X(i)/X(j) for these (i, j): {59766, 76}
X(61692) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 61667, 373}, {6, 9027, 61667}, {193, 15531, 511}, {511, 15531, 6467}, {524, 40673, 3917}, {1992, 8681, 51}, {2854, 5095, 61679}

X(61693) = CENTROID OF THE PEDAL TRIANGLE OF X(198)

Barycentrics    a^5+2*a^4*(b+c)-3*a^2*(b-c)^2*(b+c)+(b-c)^2*(b+c)^3-a^3*(b^2+6*b*c+c^2) : :

X(61693) lies on these lines: {2, 374}, {6, 17728}, {9, 119}, {44, 24914}, {45, 8756}, {198, 515}, {1213, 15487}, {1400, 61706}, {1699, 2270}, {1853, 61668}, {1903, 5658}, {2183, 46835}, {2262, 5603}, {4390, 17275}, {5848, 17330}, {5886, 61695}, {6735, 59221}, {7967, 53994}, {10164, 54322}, {17718, 61506}, {20324, 52962}, {21068, 28228}, {21871, 27508}, {24005, 61717}, {24328, 26001}, {28174, 54420}, {37828, 54389}, {46344, 51408}

X(61693) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {198, 20262, 54008}

X(61694) = CENTROID OF THE PEDAL TRIANGLE OF X(199)

Barycentrics    a^6+a^4*b*c+a^5*(b+c)+a*(b-c)^2*(b+c)^3-2*a^3*(b+c)*(b^2+c^2)+(b^2-c^2)^2*(b^2+b*c+c^2)-2*a^2*(b^4+b^3*c+b*c^3+c^4) : :

X(61694) lies on these lines: {2, 51}, {86, 41586}, {125, 6998}, {468, 1213}, {1654, 3292}, {4213, 22080}, {5112, 24275}, {5224, 5651}, {5642, 31144}, {6090, 17251}, {7380, 34417}, {7410, 37643}, {7474, 32223}, {11284, 17327}, {17330, 61690}, {24907, 48937}, {24932, 48882}, {25442, 48887}, {26244, 47200}, {32460, 37831}, {32461, 37834}, {33329, 37508}, {37158, 37823}, {61652, 61688}

X(61695) = X(6)X(1718)∩X(9)X(374)

Barycentrics    a*(a^3*(b+c)-(b^2-c^2)^2+a^2*(b^2-3*b*c+c^2)-a*(b+c)*(b^2-3*b*c+c^2)) : :
X(61695) = -3*X[5640]+X[30437], -X[42447]+4*X[58473]

X(61695) lies on these lines: {1, 37503}, {6, 1718}, {9, 374}, {44, 5903}, {45, 5697}, {65, 16670}, {165, 54420}, {169, 2323}, {198, 10246}, {354, 1449}, {610, 10202}, {758, 37654}, {966, 10176}, {1405, 1731}, {2173, 15016}, {2267, 5011}, {2270, 3576}, {2324, 11224}, {2325, 14923}, {2364, 30274}, {2772, 5890}, {2801, 5819}, {3057, 16676}, {3247, 5919}, {3681, 3686}, {3707, 3869}, {3817, 20262}, {3868, 4700}, {3885, 4029}, {3889, 4982}, {3918, 26039}, {3973, 21853}, {4266, 17451}, {4873, 10914}, {5131, 36743}, {5640, 30437}, {5692, 17330}, {5834, 26932}, {5886, 61693}, {5927, 9119}, {6173, 34371}, {7146, 53391}, {9004, 51194}, {14557, 25525}, {16438, 47057}, {16548, 55432}, {16666, 18398}, {16833, 34377}, {17810, 56317}, {17868, 29497}, {18202, 19733}, {18725, 60985}, {19297, 21842}, {23073, 50190}, {37571, 54409}, {37625, 54324}, {42447, 58473}, {53994, 59387}, {61699, 61706}, {61710, 61730}

X(61695) = midpoint of X(i) and X(j) for these {i,j}: {374, 2262}
X(61695) = reflection of X(i) in X(j) for these {i,j}: {9, 374}
X(61695) = pole of line {37783, 60994} with respect to the Stammler hyperbola
X(61695) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 61704, 5902}, {374, 2262, 517}, {374, 517, 9}, {5640, 61720, 61718}, {61704, 61708, 6}

X(61696) = X(1)X(12006)∩X(51)X(513)

Barycentrics    a^2*(a^5*(b^2+c^2)-a^4*(b+c)*(b^2+c^2)+2*a^2*(b-c)^2*(b+c)*(b^2+b*c+c^2)+2*a^3*(-b^4+b^3*c+b^2*c^2+b*c^3-c^4)+a*(b-c)^2*(b^4-3*b^2*c^2+c^4)-(b-c)^2*(b+c)*(b^4-b^2*c^2+c^4)) : :
X(61696) = 2*X[389]+X[31849], -X[38389]+4*X[58475]

X(61696) lies on these lines: {1, 12006}, {6, 46408}, {11, 2807}, {33, 35604}, {36, 5396}, {51, 513}, {57, 3025}, {79, 10095}, {143, 3336}, {389, 31849}, {511, 34583}, {517, 3058}, {1618, 20988}, {1718, 3028}, {2808, 33519}, {3567, 5221}, {3649, 5462}, {5131, 13391}, {5442, 10627}, {5640, 61716}, {5663, 37718}, {5876, 15079}, {5890, 61717}, {5902, 5946}, {6174, 34372}, {9729, 10543}, {10263, 37524}, {11544, 58531}, {13363, 37701}, {13364, 61703}, {13630, 37702}, {13756, 25415}, {15888, 58487}, {18838, 46017}, {31760, 32636}, {38389, 58475}, {41341, 56878}, {51682, 61397}

X(61696) = midpoint of X(i) and X(j) for these {i,j}: {5890, 61731}
X(61696) = pole of line {495, 51889} with respect to the Feuerbach hyperbola

X(61697) = X(6)X(3200)∩X(51)X(61)

Barycentrics    a^2*(-2*(b^2-c^2)^4+2*a^6*(b^2+c^2)-a^4*(6*b^4+b^2*c^2+6*c^4)+a^2*(6*b^6-9*b^4*c^2-9*b^2*c^4+6*c^6)-6*sqrt(3)*a^2*b^2*c^2*S) : :

X(61697) lies on circumconic {{A, B, C, X(3489), X(14579)}} and on these lines: {6, 3200}, {13, 5890}, {14, 13364}, {15, 51890}, {16, 5892}, {17, 1154}, {18, 11451}, {51, 61}, {143, 3412}, {381, 30439}, {389, 42992}, {396, 36981}, {511, 41943}, {568, 16267}, {1216, 42979}, {3060, 16962}, {3206, 11402}, {3411, 15024}, {3819, 42936}, {5891, 37832}, {5943, 16268}, {5946, 11624}, {6000, 42813}, {6688, 42489}, {8929, 48796}, {9730, 41107}, {9971, 36757}, {10095, 42991}, {10110, 41973}, {10645, 36987}, {11459, 49907}, {13321, 49947}, {13348, 42959}, {13363, 16963}, {13754, 41121}, {14855, 42431}, {15026, 61642}, {15043, 42990}, {15045, 41100}, {16241, 36978}, {16644, 36979}, {20791, 42158}, {21849, 42976}, {23302, 44324}, {34373, 50859}, {43238, 54047}, {52989, 59410}

X(61697) = reflection of X(i) in X(j) for these {i,j}: {17, 61641}
X(61697) = pole of line {6140, 57142} with respect to the circumcircle
X(61697) = pole of line {627, 37779} with respect to the Stammler hyperbola
X(61697) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1154, 61641, 17}, {5946, 11624, 61719}, {5946, 61719, 30440}

X(61698) = X(6)X(3200)∩X(51)X(62)

Barycentrics    a^2*(-2*(b^2-c^2)^4+2*a^6*(b^2+c^2)-a^4*(6*b^4+b^2*c^2+6*c^4)+a^2*(6*b^6-9*b^4*c^2-9*b^2*c^4+6*c^6)+6*sqrt(3)*a^2*b^2*c^2*S) : :

X(61698) lies on circumconic {{A, B, C, X(3490), X(14579)}} and on these lines: {6, 3200}, {13, 13364}, {14, 5890}, {15, 5892}, {16, 51891}, {17, 11451}, {18, 1154}, {51, 62}, {143, 3411}, {381, 30440}, {389, 42993}, {395, 36979}, {511, 41944}, {568, 16268}, {1216, 42978}, {3060, 16963}, {3205, 11402}, {3412, 15024}, {3819, 42937}, {5640, 61719}, {5891, 37835}, {5943, 16267}, {5946, 11626}, {6000, 42814}, {6688, 42488}, {8930, 48794}, {9730, 41108}, {9971, 36758}, {10095, 42990}, {10110, 41974}, {10646, 36987}, {11459, 49908}, {13321, 49948}, {13348, 42958}, {13363, 16962}, {13754, 41122}, {14855, 42432}, {15026, 61641}, {15043, 42991}, {15045, 41101}, {16242, 36980}, {16645, 36981}, {20791, 42157}, {21849, 42977}, {23303, 44324}, {34375, 50860}, {43239, 54047}

X(61698) = reflection of X(i) in X(j) for these {i,j}: {18, 61642}
X(61698) = pole of line {6140, 57143} with respect to the circumcircle
X(61698) = pole of line {628, 37779} with respect to the Stammler hyperbola
X(61698) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1154, 61642, 18}

X(61699) = X(2)X(392)∩X(4)X(34800)

Barycentrics    a*(-2*b*c*(b^2-c^2)^2+a^4*(b^2+b*c+c^2)+a^3*(b^3+b^2*c+b*c^2+c^3)+a^2*(-b^4+b^3*c+3*b^2*c^2+b*c^3-c^4)-a*(b^5+b^4*c-3*b^3*c^2-3*b^2*c^3+b*c^4+c^5)) : :
X(61699) = 2*X[442]+X[41723], -5*X[1698]+2*X[56894], X[2475]+2*X[18180], -2*X[22076]+5*X[31254]

X(61699) lies on these lines: {2, 392}, {4, 34800}, {21, 46623}, {51, 17577}, {65, 24883}, {110, 45923}, {381, 5640}, {389, 7548}, {442, 41723}, {511, 6175}, {942, 33150}, {1325, 37527}, {1698, 56894}, {2475, 18180}, {2979, 17528}, {3017, 5902}, {3057, 24936}, {3060, 17532}, {3580, 30444}, {3754, 25441}, {3794, 50171}, {3812, 24907}, {3822, 56878}, {3869, 25446}, {4185, 23059}, {4197, 10441}, {4682, 37080}, {5047, 15488}, {5177, 6045}, {5178, 5300}, {5690, 25444}, {5901, 24925}, {5903, 24880}, {5943, 37375}, {6000, 52269}, {6901, 39271}, {6985, 19771}, {7419, 48903}, {7998, 44217}, {10902, 16451}, {11451, 17556}, {14923, 25650}, {15049, 61703}, {16452, 59320}, {16453, 37621}, {17579, 53794}, {18178, 26131}, {22076, 31254}, {22791, 25648}, {24299, 37264}, {24881, 61541}, {24898, 50193}, {24904, 31870}, {24934, 61524}, {30437, 61717}, {30438, 61716}, {38508, 45924}, {44299, 57005}, {61695, 61706}, {61704, 61741}

X(61699) = midpoint of X(i) and X(j) for these {i,j}: {58889, 61643}
X(61699) = reflection of X(i) in X(j) for these {i,j}: {21, 61643}
X(61699) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3017, 5902, 61728}

X(61700) = X(2)X(154)∩X(4)X(3580)

Barycentrics    a^6-2*(b^2-c^2)^2*(b^2+c^2)+a^2*(b^4+c^4) : :
X(61700) = -4*X[5]+X[11456], X[22]+2*X[11550], -2*X[184]+5*X[31236], 2*X[343]+X[7391], -4*X[427]+X[1993], -3*X[5054]+2*X[34513], -X[18445]+4*X[39504], -4*X[44201]+X[44831]

X(61700) lies on these lines: {2, 154}, {3, 18432}, {4, 3580}, {5, 11456}, {6, 3448}, {22, 11550}, {23, 36990}, {25, 23293}, {64, 34007}, {68, 15559}, {69, 31099}, {110, 5094}, {125, 1995}, {141, 16063}, {155, 52295}, {184, 31236}, {193, 15431}, {265, 31861}, {323, 15069}, {343, 7391}, {378, 12827}, {381, 5640}, {382, 15062}, {389, 7566}, {394, 3410}, {399, 7579}, {427, 1993}, {468, 39884}, {511, 31133}, {524, 31105}, {542, 11187}, {599, 8705}, {858, 1352}, {1209, 10323}, {1350, 5189}, {1351, 41724}, {1370, 10519}, {1593, 58922}, {1594, 5654}, {1597, 50435}, {1656, 61134}, {1899, 5133}, {1907, 61544}, {2453, 17511}, {2781, 61739}, {2888, 37498}, {2979, 34609}, {3060, 5064}, {3066, 7533}, {3091, 18909}, {3516, 12278}, {3541, 14516}, {3549, 16659}, {3627, 47582}, {3763, 7496}, {3830, 15360}, {5020, 26913}, {5054, 34513}, {5072, 5643}, {5449, 10594}, {5476, 61712}, {5480, 37644}, {5576, 7592}, {5650, 11178}, {5651, 18553}, {5655, 39484}, {5891, 31180}, {5921, 37645}, {6288, 12084}, {6515, 7378}, {6636, 59411}, {6642, 23294}, {6644, 15061}, {6776, 14389}, {6792, 15538}, {6997, 23291}, {7394, 13567}, {7403, 18912}, {7492, 48905}, {7495, 46264}, {7503, 18381}, {7506, 13561}, {7507, 12111}, {7517, 34826}, {7519, 32269}, {7527, 18396}, {7528, 26879}, {7529, 26917}, {7547, 12162}, {7564, 34783}, {7570, 47355}, {7571, 43650}, {7577, 18451}, {7605, 10601}, {7699, 14094}, {7706, 16003}, {7998, 31152}, {8780, 52298}, {9306, 30744}, {9745, 11646}, {9818, 25739}, {9927, 18488}, {10539, 52296}, {10546, 15059}, {10984, 14864}, {10990, 41428}, {11002, 53023}, {11005, 15928}, {11179, 53843}, {11180, 40112}, {11188, 61737}, {11245, 59399}, {11422, 39899}, {11425, 34799}, {11439, 37197}, {11440, 12173}, {11454, 37196}, {11469, 50689}, {11477, 37779}, {11645, 35268}, {11898, 23061}, {12134, 37119}, {12293, 14865}, {13160, 14216}, {13203, 34778}, {13595, 26958}, {14683, 59771}, {14731, 47284}, {14918, 37200}, {15030, 23325}, {15043, 26944}, {15045, 56965}, {15078, 23329}, {15578, 37978}, {16051, 54013}, {16981, 44555}, {17810, 37349}, {17811, 31101}, {17928, 20299}, {18350, 31283}, {18356, 33332}, {18358, 30739}, {18392, 44438}, {18394, 43613}, {18445, 39504}, {18952, 50137}, {20191, 35479}, {22467, 40686}, {22804, 32138}, {23039, 31181}, {23300, 26206}, {24206, 40916}, {26096, 26542}, {26543, 31106}, {26864, 48662}, {30745, 59767}, {32125, 34118}, {32306, 52171}, {32423, 44287}, {32534, 45286}, {34417, 48889}, {34507, 51360}, {34780, 52525}, {35488, 44084}, {36753, 50138}, {37454, 48906}, {37471, 53999}, {37643, 51537}, {37760, 41424}, {38136, 61657}, {38444, 61139}, {40330, 46336}, {41586, 48901}, {41588, 52285}, {41603, 51756}, {43653, 52397}, {44201, 44831}, {44407, 44837}, {46517, 48876}, {47095, 48874}, {47314, 54173}, {47315, 61545}, {51941, 52191}, {57257, 57533}

X(61700) = midpoint of X(i) and X(j) for these {i,j}: {11550, 61644}
X(61700) = reflection of X(i) in X(j) for these {i,j}: {2, 45303}, {22, 61644}, {6800, 2}, {61644, 21243}
X(61700) = inverse of X(12824) in orthocentroidal circle
X(61700) = anticomplement of X(13394)
X(61700) = X(i)-Dao conjugate of X(j) for these {i, j}: {13394, 13394}
X(61700) = pole of line {526, 12824} with respect to the orthocentroidal circle
X(61700) = pole of line {48904, 52842} with respect to the Jerabek hyperbola
X(61700) = pole of line {23, 7735} with respect to the Kiepert hyperbola
X(61700) = pole of line {1350, 7502} with respect to the Stammler hyperbola
X(61700) = pole of line {6031, 37668} with respect to the Wallace hyperbola
X(61700) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3424), X(34213)}}, {{A, B, C, X(6800), X(35140)}}, {{A, B, C, X(18125), X(42287)}}
X(61700) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1503, 6800}, {2, 35265, 61680}, {110, 7703, 5094}, {125, 3818, 1995}, {141, 16063, 21766}, {381, 26869, 5640}, {381, 61702, 61701}, {1503, 45303, 2}, {1899, 5133, 5422}, {3448, 5169, 6}, {5094, 18440, 110}, {5640, 9140, 26869}, {9927, 18488, 35502}, {11550, 21243, 22}, {11550, 61644, 29012}, {14644, 16261, 381}, {18356, 33332, 36749}, {21243, 29012, 61644}, {36990, 37638, 23}, {47353, 61735, 35259}

X(61701) = X(4)X(64)∩X(6)X(2914)

Barycentrics    a^10-2*a^8*(b^2+c^2)-4*a^4*(b^2-c^2)^2*(b^2+c^2)-2*(b^2-c^2)^4*(b^2+c^2)+5*a^2*(b^2-c^2)^2*(b^4+c^4)+2*a^6*(b^4+b^2*c^2+c^4) : :
X(61701) = 2*X[235]+X[11457], -2*X[1092]+5*X[31282], 2*X[1204]+X[35490], X[37444]+2*X[41587]

X(61701) lies on circumconic {{A, B, C, X(459), X(33565)}} and on these lines: {2, 12022}, {3, 26913}, {4, 64}, {5, 5422}, {6, 2914}, {24, 18400}, {25, 25739}, {51, 23325}, {54, 1656}, {74, 44438}, {125, 378}, {154, 37943}, {185, 35488}, {186, 18396}, {235, 11457}, {265, 6644}, {376, 44569}, {381, 5640}, {382, 13445}, {389, 7547}, {403, 1899}, {468, 61612}, {511, 31180}, {547, 61690}, {578, 52296}, {597, 5071}, {1092, 31282}, {1181, 16868}, {1192, 34797}, {1204, 35490}, {1498, 44958}, {1593, 23294}, {1594, 39571}, {1993, 2072}, {1995, 18474}, {3089, 16659}, {3090, 14826}, {3091, 18916}, {3147, 18945}, {3153, 37489}, {3448, 18451}, {3515, 12289}, {3516, 43608}, {3527, 17711}, {3542, 11206}, {3545, 18950}, {3567, 7507}, {3580, 18531}, {3796, 7552}, {5020, 41171}, {5055, 11402}, {5079, 11423}, {5094, 15033}, {5449, 7503}, {5627, 15111}, {5654, 45968}, {6143, 11425}, {6146, 7505}, {6241, 26944}, {6623, 32111}, {6640, 12370}, {6642, 58922}, {6761, 52249}, {6794, 15538}, {6800, 10201}, {7517, 61299}, {7526, 43821}, {7576, 61506}, {7579, 15038}, {9818, 23293}, {9927, 17928}, {10018, 19467}, {10024, 18952}, {10193, 13403}, {10224, 36749}, {10255, 12161}, {10594, 18381}, {10982, 52295}, {11178, 40673}, {11202, 61691}, {11422, 15025}, {11424, 32767}, {11438, 13851}, {11451, 56965}, {11459, 16072}, {11464, 37453}, {11801, 44263}, {12024, 58434}, {12173, 18394}, {12241, 37119}, {12254, 17821}, {12293, 22467}, {13352, 30744}, {13619, 37487}, {14789, 17825}, {14865, 40686}, {14940, 19357}, {15027, 15121}, {15045, 43836}, {15053, 18392}, {15063, 18418}, {15078, 17702}, {15340, 59229}, {15361, 15681}, {15760, 18911}, {16657, 23332}, {16658, 32064}, {17845, 44879}, {18377, 37490}, {18405, 18559}, {18533, 18918}, {18560, 26937}, {19122, 39899}, {20299, 35502}, {21659, 32534}, {23327, 39588}, {23515, 61713}, {30771, 43574}, {31074, 44413}, {31101, 37483}, {31283, 37472}, {32138, 43865}, {32269, 44831}, {32339, 44056}, {33586, 46450}, {34117, 45181}, {34785, 35479}, {35472, 44673}, {35603, 45177}, {35921, 37638}, {36752, 43816}, {36990, 52294}, {37444, 41587}, {41724, 58891}, {42016, 45736}, {44076, 59648}, {44837, 61646}, {45179, 51734}, {45237, 61724}, {45970, 60780}, {49673, 50708}

X(61701) = reflection of X(i) in X(j) for these {i,j}: {24, 61645}
X(61701) = inverse of X(46430) in orthocentroidal circle
X(61701) = pole of line {526, 42731} with respect to the orthocentroidal circle
X(61701) = pole of line {8057, 24978} with respect to the polar circle
X(61701) = pole of line {11381, 34786} with respect to the Jerabek hyperbola
X(61701) = pole of line {186, 393} with respect to the Kiepert hyperbola
X(61701) = pole of line {6587, 45147} with respect to the orthic inconic
X(61701) = pole of line {16266, 35602} with respect to the Stammler hyperbola
X(61701) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 18912, 7592}, {5, 25738, 11441}, {54, 11704, 1656}, {125, 18390, 378}, {125, 61744, 23329}, {381, 26869, 5890}, {381, 38724, 61702}, {381, 61702, 61700}, {403, 1899, 11456}, {5890, 14644, 381}, {6146, 7505, 9707}, {11438, 13851, 35480}, {16868, 43808, 1181}, {18390, 23329, 61744}, {18400, 61645, 24}, {26913, 50435, 3}, {26944, 37197, 6241}

X(61702) = X(3)X(12278)∩X(5)X(1181)

Barycentrics    a^10-2*a^8*(b^2+c^2)-2*(b^2-c^2)^4*(b^2+c^2)+2*a^6*(b^4+c^4)+a^2*(b^2-c^2)^2*(5*b^4+4*b^2*c^2+5*c^4)+2*a^4*(-2*b^6+b^4*c^2+b^2*c^4-2*c^6) : :
X(61702) = -X[26]+4*X[5449], X[64]+2*X[44279], X[68]+2*X[13371], -X[155]+4*X[10224], -2*X[156]+5*X[1656], -X[382]+4*X[18379], -2*X[1147]+5*X[31283], -X[1498]+4*X[13406], -X[1657]+4*X[32210], -7*X[3090]+4*X[61608], -7*X[3526]+4*X[32171], -11*X[5070]+8*X[58435] and many others

X(61702) lies on these lines: {2, 59648}, {3, 12278}, {4, 34796}, {5, 1181}, {6, 39504}, {25, 34514}, {26, 5449}, {30, 1853}, {49, 52296}, {64, 44279}, {68, 13371}, {74, 18392}, {125, 6644}, {155, 10224}, {156, 1656}, {184, 45730}, {265, 378}, {343, 14791}, {381, 5640}, {382, 18379}, {389, 7564}, {394, 37938}, {427, 39522}, {511, 31181}, {547, 10516}, {567, 31236}, {599, 44324}, {1147, 31283}, {1192, 45971}, {1209, 7516}, {1498, 13406}, {1503, 10201}, {1594, 12161}, {1657, 32210}, {1995, 15027}, {2072, 11442}, {3090, 61608}, {3448, 7577}, {3526, 32171}, {3541, 12370}, {3564, 23327}, {3580, 31723}, {3581, 52842}, {5070, 58435}, {5094, 15114}, {5576, 18912}, {5622, 18440}, {6102, 7507}, {6143, 34799}, {6288, 17928}, {6639, 34224}, {6640, 14516}, {6696, 34350}, {6776, 61619}, {7502, 37638}, {7506, 26917}, {7514, 21243}, {7530, 11550}, {7547, 34783}, {7569, 13353}, {7579, 15087}, {7689, 18383}, {7703, 15033}, {8548, 34118}, {8976, 32169}, {9654, 32143}, {9669, 32168}, {9833, 10020}, {9909, 61299}, {9927, 12084}, {9932, 49108}, {10024, 11457}, {10113, 44438}, {10125, 17821}, {10254, 11456}, {10255, 11441}, {10264, 10605}, {10982, 33332}, {11003, 54000}, {11250, 12293}, {11416, 11898}, {11425, 45970}, {11440, 18394}, {11451, 43836}, {11472, 11801}, {11818, 13567}, {12106, 26958}, {12118, 23336}, {12163, 18377}, {12359, 18569}, {13363, 56965}, {13391, 34609}, {13451, 53023}, {13490, 61506}, {13630, 26944}, {13754, 23325}, {13951, 32170}, {14216, 15761}, {14984, 61737}, {15060, 16072}, {15061, 15078}, {15331, 17845}, {15538, 15547}, {17702, 23329}, {17814, 49673}, {18281, 23332}, {18324, 18400}, {18350, 45622}, {18390, 31861}, {18396, 18570}, {18420, 23291}, {18430, 35480}, {18439, 35488}, {18536, 33533}, {18568, 23324}, {18911, 37347}, {18918, 49669}, {19139, 20300}, {19347, 45732}, {19357, 45731}, {20191, 34785}, {22115, 30744}, {23039, 31180}, {23335, 61544}, {25337, 46264}, {26913, 41171}, {31152, 54042}, {31884, 60749}, {32207, 42132}, {32208, 42129}, {32345, 46939}, {32423, 47391}, {32539, 58726}, {34330, 61680}, {36749, 52295}, {36753, 43808}, {36989, 61612}, {37119, 44076}, {37489, 44288}, {37494, 46450}, {37672, 50708}, {39884, 44233}, {41362, 44158}, {44883, 46085}, {45303, 60763}, {51391, 58891}, {61713, 61743}, {61724, 61739}

X(61702) = midpoint of X(i) and X(j) for these {i,j}: {1853, 14852}, {18381, 61646}
X(61702) = reflection of X(i) in X(j) for these {i,j}: {18281, 23332}, {18568, 23324}, {26, 61646}, {47391, 61736}, {61646, 5449}
X(61702) = inverse of X(16222) in orthocentroidal circle
X(61702) = pole of line {526, 16222} with respect to the orthocentroidal circle
X(61702) = pole of line {45186, 52843} with respect to the Jerabek hyperbola
X(61702) = pole of line {1609, 2070} with respect to the Kiepert hyperbola
X(61702) = pole of line {1658, 37494} with respect to the Stammler hyperbola
X(61702) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 32140, 32139}, {381, 26869, 5946}, {381, 38724, 61701}, {1147, 32767, 31283}, {1594, 25738, 12161}, {1853, 14852, 30}, {2072, 11442, 15068}, {3448, 7577, 18445}, {5449, 44407, 61646}, {7689, 18383, 52843}, {9927, 20299, 12084}, {10224, 18356, 155}, {10264, 44263, 10605}, {12278, 43608, 3}, {12293, 40686, 11250}, {14644, 15305, 381}, {18379, 32138, 382}, {18381, 61646, 44407}, {23332, 44665, 18281}, {32423, 61736, 47391}, {44407, 61646, 26}, {47391, 61735, 61736}

X(61703) = X(1)X(4)∩X(5)X(79)

Barycentrics    a^4+a^3*(b+c)-a*(b-c)^2*(b+c)-2*(b^2-c^2)^2+a^2*(b^2+b*c+c^2) : :
X(61703) = -4*X[12]+X[11010], -7*X[3624]+4*X[5267], -2*X[3916]+5*X[31262], -X[4324]+4*X[13411], -X[6763]+4*X[25639], X[37005]+2*X[45065]

X(61703) lies on circumconic {{A, B, C, X(3467), X(6198)}} and on these lines: {1, 4}, {2, 5131}, {3, 16118}, {5, 79}, {10, 26792}, {12, 11010}, {30, 37701}, {35, 28146}, {36, 7489}, {46, 54447}, {65, 38140}, {80, 39542}, {115, 61741}, {191, 2476}, {381, 2771}, {382, 37571}, {484, 1836}, {498, 9778}, {516, 3584}, {517, 51518}, {518, 31159}, {546, 3649}, {758, 17577}, {993, 10129}, {1125, 4325}, {1482, 9656}, {1656, 37524}, {1698, 4338}, {1737, 11552}, {1768, 6830}, {1770, 10164}, {1781, 61710}, {2099, 9897}, {2646, 28168}, {2800, 59392}, {2829, 38039}, {3017, 61707}, {3065, 16128}, {3304, 45035}, {3337, 7741}, {3338, 18540}, {3582, 3817}, {3614, 5445}, {3624, 5267}, {3627, 5441}, {3628, 5442}, {3679, 4134}, {3746, 22793}, {3753, 31160}, {3814, 20292}, {3822, 5057}, {3824, 25542}, {3838, 5251}, {3850, 11544}, {3851, 5221}, {3853, 10543}, {3861, 16137}, {3892, 10707}, {3894, 31164}, {3916, 31262}, {4197, 5506}, {4292, 6884}, {4295, 18395}, {4299, 54445}, {4302, 5226}, {4312, 37787}, {4324, 13411}, {4330, 51118}, {4870, 28160}, {4995, 28178}, {5010, 5219}, {5046, 11263}, {5047, 6701}, {5298, 61269}, {5426, 11114}, {5432, 15228}, {5434, 16173}, {5443, 7354}, {5444, 15326}, {5531, 37820}, {5535, 6980}, {5536, 37826}, {5538, 6923}, {5540, 61706}, {5560, 15173}, {5563, 9955}, {5587, 14988}, {5692, 17532}, {5694, 5790}, {5697, 9654}, {5844, 11280}, {5883, 37375}, {6001, 52850}, {6175, 10176}, {6284, 37731}, {6327, 51285}, {6763, 25639}, {6831, 16767}, {6839, 21635}, {6858, 53056}, {6861, 15803}, {6895, 14526}, {6911, 15017}, {7173, 24470}, {7280, 9579}, {7548, 31803}, {7680, 34789}, {7743, 37602}, {8727, 16152}, {8818, 16547}, {9655, 21842}, {9657, 18493}, {9669, 50190}, {9779, 10072}, {9812, 10056}, {10039, 28228}, {10044, 16127}, {10404, 37720}, {10483, 11375}, {10573, 54448}, {10590, 59417}, {10593, 52783}, {10896, 18398}, {11113, 26725}, {11372, 17699}, {12102, 15174}, {12699, 37563}, {12943, 37525}, {13273, 45764}, {13364, 61696}, {13743, 14804}, {14035, 30123}, {14063, 30119}, {15015, 17579}, {15049, 61699}, {15888, 40273}, {15950, 36975}, {16842, 41862}, {17530, 17768}, {17549, 38062}, {18990, 37735}, {19872, 56203}, {19876, 38052}, {23708, 37587}, {24851, 37693}, {28190, 37737}, {30135, 33019}, {30139, 33018}, {30311, 51768}, {32423, 56402}, {36250, 55027}, {37005, 45065}, {37006, 50194}, {37356, 49178}, {37406, 49177}, {38150, 60932}, {38155, 41684}, {41812, 52258}, {43731, 61256}, {54648, 60116}

X(61703) = reflection of X(i) in X(j) for these {i,j}: {17549, 38062}, {35, 61648}
X(61703) = pole of line {1901, 50657} with respect to the Kiepert hyperbola
X(61703) = pole of line {283, 35195} with respect to the Stammler hyperbola
X(61703) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 79, 3336}, {381, 5902, 37718}, {381, 61716, 5902}, {1478, 18393, 1}, {1836, 7951, 484}, {5902, 61740, 61709}, {7741, 57282, 3337}, {9579, 37692, 7280}, {13407, 18483, 4857}, {61699, 61729, 15049}

X(61704) = X(6)X(1718)∩X(44)X(65)

Barycentrics    a*(a^3*(b+c)-(b^2-c^2)^2+a^2*(b^2+c^2)-a*(b+c)*(b^2-3*b*c+c^2)) : :

X(61704) lies on these lines: {1, 19297}, {2, 59265}, {6, 1718}, {9, 21863}, {37, 517}, {44, 65}, {45, 5903}, {48, 354}, {518, 50082}, {572, 2160}, {758, 17330}, {942, 16666}, {960, 52706}, {966, 21873}, {1213, 10176}, {1400, 17443}, {2178, 10246}, {2245, 17451}, {2278, 15586}, {2294, 4271}, {2650, 4285}, {2802, 50113}, {3681, 17275}, {3707, 4084}, {3723, 5919}, {3754, 17369}, {3817, 24005}, {3833, 17398}, {3873, 50131}, {3874, 4969}, {3880, 50123}, {3919, 50115}, {3924, 4290}, {4430, 5839}, {4688, 34377}, {4727, 10914}, {5109, 24443}, {5124, 5131}, {5697, 16672}, {6792, 61729}, {9957, 39260}, {11063, 14804}, {16590, 44663}, {16814, 21853}, {18202, 19731}, {21739, 60258}, {21858, 22278}, {26869, 61716}, {54420, 59337}, {58565, 61302}, {61699, 61741}, {61722, 61725}

X(61704) = reflection of X(i) in X(j) for these {i,j}: {37, 61650}
X(61704) = pole of line {650, 14438} with respect to the DeLongchamps ellipse
X(61704) = pole of line {4336, 9629} with respect to the Feuerbach hyperbola
X(61704) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(19297), X(60258)}}, {{A, B, C, X(21739), X(54409)}}, {{A, B, C, X(46018), X(59265)}}
X(61704) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 61695, 61708}, {45, 5903, 21864}, {517, 61650, 37}, {5902, 61695, 6}

X(61705) = X(1)X(1898)∩X(4)X(758)

Barycentrics    a*(a^5*(b+c)-(b-c)^2*(b+c)^4-a^4*(b^2-b*c+c^2)-a^3*(b+c)*(2*b^2-3*b*c+2*c^2)+a^2*(b+c)^2*(2*b^2-3*b*c+2*c^2)+a*(b-c)^2*(b^3+c^3)) : :
X(61705) = -8*X[5]+5*X[15016], -X[20]+4*X[20117], -2*X[65]+5*X[18492], 2*X[72]+X[41869], -2*X[354]+3*X[38021], X[382]+2*X[5694], -5*X[3091]+2*X[5884], X[3146]+2*X[31806], -3*X[3545]+2*X[5883], -7*X[3624]+4*X[13369], -4*X[3678]+X[6361], -7*X[3832]+4*X[31870] and many others

X(61705) lies on circumconic {{A, B, C, X(6598), X(38248)}} and on these lines: {1, 1898}, {3, 7701}, {4, 758}, {5, 15016}, {9, 7688}, {20, 20117}, {30, 5692}, {36, 7082}, {40, 210}, {65, 18492}, {72, 41869}, {79, 44229}, {80, 18516}, {84, 17616}, {90, 37583}, {191, 6985}, {354, 38021}, {355, 12679}, {376, 10176}, {377, 16127}, {381, 2771}, {382, 5694}, {392, 50811}, {405, 16132}, {442, 18243}, {443, 16120}, {474, 17653}, {484, 18491}, {500, 27785}, {515, 3877}, {516, 4134}, {517, 3830}, {518, 31162}, {581, 1962}, {912, 1699}, {942, 17604}, {944, 3898}, {946, 3873}, {952, 34697}, {962, 4661}, {971, 3576}, {999, 60884}, {1006, 60911}, {1012, 6326}, {1071, 3742}, {1147, 43609}, {1490, 4512}, {1706, 17646}, {1709, 2077}, {1749, 37251}, {1768, 6911}, {1836, 18397}, {1853, 3753}, {1858, 9612}, {1864, 11529}, {2093, 18529}, {2392, 11459}, {2772, 5890}, {2778, 61721}, {2779, 15305}, {2800, 59387}, {2801, 3892}, {2802, 34627}, {2836, 47353}, {2842, 16261}, {3062, 6282}, {3091, 5884}, {3146, 31806}, {3158, 12705}, {3358, 61115}, {3428, 5779}, {3485, 41562}, {3545, 5883}, {3560, 5426}, {3587, 41860}, {3624, 13369}, {3647, 6876}, {3649, 10399}, {3678, 6361}, {3681, 28194}, {3832, 31870}, {3833, 5071}, {3851, 5885}, {3868, 18483}, {3869, 31673}, {3876, 31730}, {3880, 5881}, {3899, 5691}, {3919, 19925}, {3921, 58631}, {3927, 24468}, {3940, 5696}, {3956, 5657}, {3968, 5818}, {4018, 16616}, {4245, 53252}, {4525, 51118}, {4711, 18908}, {4731, 31788}, {4863, 5904}, {4881, 5450}, {5044, 35242}, {5082, 12059}, {5119, 18528}, {5429, 9355}, {5531, 10679}, {5535, 19541}, {5697, 12953}, {5784, 58808}, {5836, 61256}, {5903, 18480}, {6245, 12666}, {6264, 17661}, {6642, 43805}, {6684, 9961}, {6830, 21635}, {6839, 9809}, {6854, 60896}, {6869, 16113}, {6900, 16116}, {6945, 10265}, {6990, 11263}, {7330, 11012}, {7680, 13257}, {7724, 32431}, {7982, 9856}, {7988, 10202}, {7989, 34339}, {7992, 59333}, {9624, 12675}, {9943, 31423}, {9955, 18398}, {10157, 50740}, {10165, 11220}, {10308, 37403}, {10539, 43610}, {10605, 16547}, {10855, 37526}, {10864, 18239}, {10914, 61250}, {11010, 18518}, {11372, 15733}, {12111, 31825}, {12511, 26878}, {12529, 21075}, {12664, 37224}, {12665, 14217}, {12702, 56762}, {13743, 37571}, {14110, 31821}, {15097, 39504}, {15104, 28174}, {17605, 30274}, {17625, 37704}, {18242, 38058}, {18412, 39542}, {18446, 54370}, {18493, 50190}, {18517, 41686}, {21669, 22836}, {21842, 26321}, {24725, 45924}, {25466, 41543}, {26333, 49176}, {29097, 36512}, {30326, 30503}, {34043, 37696}, {34789, 37820}, {34862, 59332}, {37562, 37714}, {41704, 45770}, {45776, 61296}

X(61705) = midpoint of X(i) and X(j) for these {i,j}: {210, 12688}, {962, 4661}, {3873, 12528}, {3899, 5691}, {4525, 51118}, {15305, 30438}
X(61705) = reflection of X(i) in X(j) for these {i,j}: {1071, 3742}, {11220, 10165}, {210, 5777}, {376, 10176}, {3873, 946}, {3899, 5887}, {3919, 19925}, {40, 210}, {5587, 5927}, {5657, 15064}, {50811, 392}, {5890, 15049}, {5902, 381}, {944, 3898}, {9943, 58451}
X(61705) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 31803, 5693}, {4, 5693, 37625}, {9, 50528, 7688}, {377, 16127, 49178}, {381, 2771, 5902}, {2772, 15049, 5890}, {5777, 12688, 40}, {5902, 61709, 61718}, {5902, 61740, 381}, {5927, 6001, 5587}, {9856, 14872, 7982}, {15305, 30438, 2779}, {18480, 40266, 5903}, {31803, 31871, 4}, {31937, 40263, 1}

X(61706) = X(2)X(35102)∩X(41)X(515)

Barycentrics    a^4+a^2*(b-c)^2-2*a^3*(b+c)-a*(b-c)^2*(b+c)+(b^2-c^2)^2 : :

X(61706) lies on these lines: {2, 35102}, {6, 21044}, {41, 515}, {218, 5790}, {604, 61654}, {672, 26446}, {1212, 61648}, {1400, 61693}, {1468, 61688}, {1475, 17728}, {1478, 2246}, {1699, 2082}, {2099, 4530}, {2170, 5603}, {2280, 5179}, {3475, 6554}, {3822, 21373}, {5309, 33128}, {5434, 51406}, {5540, 61703}, {5902, 61730}, {11230, 43065}, {14439, 45701}, {16572, 54447}, {21384, 27068}, {26869, 61707}, {33127, 49758}, {61695, 61699}

X(61706) = reflection of X(i) in X(j) for these {i,j}: {41, 61651}
X(61706) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {515, 61651, 41}

X(61707) = X(1)X(17484)∩X(6)X(3120)

Barycentrics    2*a^3+2*a^2*(b+c)-(b-c)^2*(b+c) : :
X(61707) = -2*X[4001]+5*X[31241]

X(61707) lies on these lines: {1, 17484}, {2, 17770}, {6, 3120}, {11, 7277}, {31, 17718}, {38, 5852}, {42, 516}, {58, 37701}, {63, 29688}, {65, 20962}, {81, 33096}, {226, 2308}, {244, 17365}, {320, 32944}, {321, 17772}, {329, 5311}, {527, 46901}, {597, 31177}, {614, 59372}, {752, 46897}, {894, 32843}, {896, 5718}, {899, 50307}, {1215, 28498}, {1386, 32856}, {1468, 5886}, {1647, 4644}, {1707, 29678}, {1757, 33112}, {1836, 61358}, {1961, 26792}, {2842, 5640}, {2886, 4722}, {3011, 21747}, {3017, 61703}, {3187, 48642}, {3219, 29682}, {3664, 30950}, {3751, 33104}, {3758, 25760}, {3821, 17491}, {3836, 41241}, {3923, 4062}, {3936, 4672}, {3944, 37685}, {3989, 17781}, {4001, 31241}, {4054, 50756}, {4138, 29867}, {4388, 29685}, {4414, 24695}, {4416, 30970}, {4425, 19717}, {4442, 49489}, {4641, 33105}, {4649, 5057}, {4663, 33136}, {4671, 49995}, {4675, 17125}, {4679, 9345}, {4697, 5741}, {4703, 6536}, {5256, 33098}, {5432, 9340}, {5587, 54421}, {5739, 8013}, {5846, 31161}, {5905, 17017}, {6535, 32852}, {6792, 61730}, {7988, 29662}, {8040, 19701}, {9779, 11269}, {10176, 49744}, {15523, 26223}, {16468, 31019}, {16475, 31164}, {16477, 33129}, {16704, 25385}, {17011, 33099}, {17012, 32857}, {17120, 29631}, {17127, 29689}, {17184, 29684}, {17350, 29643}, {17351, 32848}, {17364, 30942}, {17483, 29821}, {17721, 54352}, {17723, 36263}, {17768, 46904}, {17771, 46909}, {17777, 20090}, {17778, 32930}, {19740, 25354}, {20064, 29670}, {24295, 31017}, {24342, 37656}, {25496, 32859}, {26061, 48650}, {26098, 29690}, {26251, 50304}, {26580, 33682}, {26869, 61706}, {27064, 29687}, {27131, 37604}, {29675, 30653}, {29683, 31053}, {29686, 33064}, {31134, 38047}, {31136, 34379}, {32772, 33066}, {32846, 41242}, {32911, 33097}, {32913, 33107}, {32935, 33070}, {32938, 33073}, {32940, 33071}, {33122, 50300}, {33161, 50127}, {38389, 52020}, {49474, 49985}, {49996, 50289}, {61728, 61729}

X(61707) = midpoint of X(i) and X(j) for these {i,j}: {41011, 61652}
X(61707) = reflection of X(i) in X(j) for these {i,j}: {38, 17726}, {42, 61652}
X(61707) = pole of line {5195, 17729} with respect to the dual conic of Yff parabola
X(61707) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 61716, 33128}, {516, 61652, 42}, {3923, 31034, 4062}, {4054, 51196, 50756}, {4703, 19684, 6536}, {5852, 17726, 38}, {16475, 31164, 33143}, {24725, 33128, 61716}, {26098, 32912, 29690}, {26223, 32946, 15523}, {41011, 61652, 516}

X(61708) = X(1)X(3196)∩X(6)X(1718)

Barycentrics    a*(a^3*(b+c)-(b^2-c^2)^2+a^2*(b^2-6*b*c+c^2)-a*(b+c)*(b^2-3*b*c+c^2)) : :
X(61708) = 2*X[3271]+X[21889]

X(61708) lies on these lines: {1, 3196}, {6, 1718}, {9, 13143}, {37, 374}, {44, 517}, {101, 1100}, {354, 2246}, {392, 16590}, {513, 14442}, {909, 910}, {1635, 39982}, {2183, 56531}, {2262, 2265}, {2802, 4370}, {2805, 24482}, {3271, 21889}, {3681, 25048}, {3686, 4103}, {3707, 22029}, {3740, 4553}, {3880, 4908}, {4120, 8674}, {4145, 46457}, {5053, 15586}, {5131, 19302}, {7202, 53391}, {9004, 46149}, {10176, 17330}, {12653, 59239}, {17275, 26074}, {26744, 54409}

X(61708) = midpoint of X(i) and X(j) for these {i,j}: {3681, 25048}
X(61708) = reflection of X(i) in X(j) for these {i,j}: {4553, 3740}
X(61708) = X(i)-Dao conjugate of X(j) for these {i, j}: {21630, 30578}, {52537, 4358}
X(61708) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4638, 513}
X(61708) = pole of line {14431, 61716} with respect to the orthocentroidal circle
X(61708) = pole of line {1635, 9269} with respect to the DeLongchamps ellipse
X(61708) = pole of line {9629, 52371} with respect to the Feuerbach hyperbola
X(61708) = pole of line {17191, 37783} with respect to the Stammler hyperbola
X(61708) = intersection, other than A, B, C, of circumconics {{A, B, C, X(80), X(39148)}}, {{A, B, C, X(1168), X(13143)}}, {{A, B, C, X(3196), X(8046)}}, {{A, B, C, X(4120), X(21864)}}, {{A, B, C, X(4792), X(52537)}}, {{A, B, C, X(6126), X(8674)}}, {{A, B, C, X(56421), X(56426)}}
X(61708) = barycentric product X(i)*X(j) for these (i, j): {1, 21630}, {1320, 56421}, {52537, 80}
X(61708) = barycentric quotient X(i)/X(j) for these (i, j): {21630, 75}, {52537, 320}
X(61708) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 61695, 61704}, {2161, 2316, 44}, {2262, 16669, 21863}

X(61709) = X(1)X(1864)∩X(46)X(1898)

Barycentrics    a*(a^5*(b+c)-(b-c)^2*(b+c)^4-a^4*(b^2-b*c+c^2)+a*(b-c)^2*(b+c)*(b^2+b*c+c^2)-a^3*(b+c)*(2*b^2-b*c+2*c^2)+a^2*(2*b^4+b^3*c-4*b^2*c^2+b*c^3+2*c^4)) : :
X(61709) = X[46]+2*X[1898], 2*X[72]+X[41709], 2*X[1479]+X[41686], X[10085]+2*X[41560]

X(61709) lies on these lines: {1, 1864}, {21, 18233}, {35, 7082}, {46, 1898}, {65, 3843}, {72, 41709}, {80, 37820}, {381, 2771}, {499, 41562}, {1479, 41686}, {1532, 15071}, {1656, 17637}, {1717, 36754}, {1727, 11502}, {1737, 6932}, {1837, 14988}, {1858, 10826}, {2801, 10072}, {3303, 56762}, {3336, 19541}, {3338, 40263}, {3467, 15910}, {3583, 18397}, {3678, 4309}, {4857, 5904}, {5010, 31658}, {5221, 31828}, {5434, 33519}, {5570, 17604}, {5692, 11113}, {5693, 6929}, {5697, 9670}, {5884, 6968}, {5887, 37721}, {5903, 18514}, {5918, 58887}, {5919, 34748}, {6826, 16152}, {6896, 10044}, {6924, 16141}, {6957, 31803}, {6976, 20117}, {6980, 15016}, {6991, 14526}, {7489, 37571}, {8069, 60910}, {8226, 10399}, {10056, 15064}, {10085, 41560}, {10176, 31156}, {12691, 26333}, {15049, 61720}, {17605, 18398}, {18393, 18412}, {18549, 25413}, {30223, 32760}

X(61709) = midpoint of X(i) and X(j) for these {i,j}: {1898, 61653}
X(61709) = reflection of X(i) in X(j) for these {i,j}: {46, 61653}, {5902, 61717}
X(61709) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2771, 61717, 5902}, {5902, 61740, 61703}

X(61710) = X(2)X(8680)∩X(4)X(2173)

Barycentrics    a^5-a^4*(b+c)+(b-c)^2*(b+c)^3-a^3*(b^2+c^2) : :
X(61710) = -2*X[307]+5*X[31265], -X[17134]+4*X[58406]

X(61710) lies on these lines: {2, 8680}, {4, 2173}, {5, 7359}, {6, 21044}, {9, 3814}, {19, 1699}, {37, 29678}, {44, 17606}, {48, 515}, {71, 26446}, {219, 5790}, {281, 1953}, {307, 31265}, {355, 22356}, {381, 61725}, {573, 7110}, {857, 24315}, {946, 8756}, {965, 21675}, {1731, 7741}, {1781, 61703}, {1839, 59644}, {1901, 11246}, {2183, 46835}, {2260, 17728}, {2267, 5179}, {2294, 5747}, {2317, 54008}, {2345, 59511}, {2476, 50198}, {4466, 30808}, {5706, 21686}, {7967, 17438}, {8804, 10164}, {9028, 31163}, {10171, 59646}, {10175, 61668}, {11230, 40937}, {14543, 24682}, {16548, 24045}, {17134, 58406}, {17303, 59207}, {17861, 25651}, {18481, 22357}, {18525, 23073}, {21094, 30882}, {21801, 54283}, {24683, 31042}, {24684, 31015}, {26063, 27382}, {28174, 59671}, {38140, 59681}, {61695, 61730}, {61716, 61735}

X(61710) = midpoint of X(i) and X(j) for these {i,j}: {1826, 61654}
X(61710) = reflection of X(i) in X(j) for these {i,j}: {48, 61654}, {61654, 40942}
X(61710) = pole of line {14400, 30574} with respect to the orthocentroidal circle
X(61710) = pole of line {20277, 36195} with respect to the Kiepert hyperbola
X(61710) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 7359, 54324}, {515, 40942, 61654}, {1826, 40942, 48}, {1826, 61654, 515}, {14543, 31014, 24682}

X(61711) = X(2)X(568)∩X(3)X(18388)

Barycentrics    a^10-4*a^8*(b^2+c^2)+(b^2-c^2)^4*(b^2+c^2)+5*a^6*(b^4+b^2*c^2+c^4)-a^4*(b^6+c^6)-2*a^2*(b^8-b^6*c^2-b^2*c^6+c^8) : :
X(61711) = X[49]+2*X[1594], X[265]+2*X[3043], -X[1614]+4*X[15806], -X[2937]+4*X[44516], -X[7488]+4*X[58407], 2*X[10024]+X[37495], 2*X[13367]+X[31724], -4*X[23047]+X[52863], 2*X[34826]+X[56292]

X(61711) lies on circumconic {{A, B, C, X(9221), X(14938)}} and on these lines: {2, 568}, {3, 18388}, {4, 16665}, {5, 15033}, {49, 1594}, {54, 10224}, {110, 39504}, {125, 15087}, {140, 15053}, {143, 14940}, {156, 52295}, {195, 5449}, {265, 3043}, {323, 54000}, {378, 7728}, {381, 5642}, {394, 1656}, {427, 10540}, {547, 40112}, {567, 2072}, {578, 10255}, {599, 5093}, {858, 61619}, {1147, 6288}, {1368, 13339}, {1614, 15806}, {1658, 15800}, {2937, 44516}, {3518, 58435}, {3521, 11250}, {3526, 37490}, {3541, 18439}, {3548, 43841}, {3549, 37484}, {3567, 60780}, {3574, 43839}, {3628, 15019}, {5012, 37938}, {5070, 37493}, {5094, 18445}, {5448, 14130}, {5576, 9820}, {5654, 18435}, {5655, 15305}, {5890, 15061}, {5891, 48411}, {6102, 6143}, {6243, 6639}, {6640, 37481}, {6644, 38794}, {6800, 31181}, {7488, 58407}, {7540, 10192}, {7552, 13391}, {7574, 18475}, {7579, 9703}, {7592, 31283}, {7699, 12121}, {8254, 43651}, {9544, 34514}, {9704, 18381}, {9706, 45731}, {10024, 37495}, {10125, 20424}, {10182, 37922}, {10254, 13352}, {10263, 58805}, {11064, 37347}, {11422, 15027}, {11430, 18403}, {11464, 44288}, {11585, 13353}, {11597, 23306}, {12161, 52296}, {12242, 32068}, {13321, 61645}, {13367, 31724}, {13413, 40111}, {13434, 49673}, {13451, 44282}, {14561, 40670}, {14805, 18531}, {15068, 31236}, {15131, 20126}, {15559, 61608}, {15760, 37477}, {18449, 54347}, {18564, 39242}, {18912, 45622}, {18917, 52299}, {19130, 21308}, {21243, 50461}, {23047, 52863}, {32136, 43808}, {32447, 34897}, {34783, 37119}, {34826, 56292}, {35921, 51391}, {37452, 37471}, {38724, 55039}, {43573, 61659}, {43574, 46029}, {43598, 50138}, {43614, 50136}, {50137, 59659}, {51519, 61680}, {54048, 61644}

X(61711) = midpoint of X(i) and X(j) for these {i,j}: {1594, 61655}
X(61711) = reflection of X(i) in X(j) for these {i,j}: {49, 61655}
X(61711) = pole of line {567, 1199} with respect to the Stammler hyperbola
X(61711) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 61715, 5946}, {578, 10255, 43821}, {2072, 23292, 567}, {3574, 43839, 45735}, {5576, 9820, 18350}, {5890, 61736, 15061}, {7579, 9703, 18474}, {9703, 18474, 23236}, {13413, 40111, 41171}, {38724, 55039, 61713}, {51392, 58447, 3}

X(61712) = X(2)X(5965)∩X(6)X(67)

Barycentrics    2*a^6+3*a^2*(b^2-c^2)^2-4*a^4*(b^2+c^2)-(b^2-c^2)^2*(b^2+c^2) : :
X(61712) = -5*X[51]+2*X[428], 5*X[185]+4*X[13488], -10*X[389]+X[6240], X[568]+2*X[43573], -10*X[3567]+X[61139], X[3575]+2*X[12024], 2*X[3819]+X[41628], -5*X[3917]+8*X[7734], 2*X[5462]+X[11232], 2*X[5943]+X[45968], X[6241]+8*X[40240], -4*X[9729]+X[54040] and many others

X(61712) lies on circumconic {{A, B, C, X(8791), X(53104)}} and on these lines: {2, 5965}, {4, 14483}, {6, 67}, {51, 428}, {54, 10182}, {69, 22112}, {182, 37644}, {184, 6353}, {185, 13488}, {193, 54012}, {343, 38110}, {373, 3564}, {389, 6240}, {427, 34565}, {468, 12007}, {524, 5650}, {542, 5640}, {568, 43573}, {575, 3580}, {576, 18911}, {858, 5097}, {868, 5355}, {1075, 35717}, {1353, 3292}, {1495, 8550}, {1899, 7378}, {1995, 24981}, {2777, 5890}, {3060, 29317}, {3066, 39899}, {3410, 12834}, {3448, 15019}, {3567, 61139}, {3574, 18912}, {3575, 12024}, {3629, 30739}, {3819, 41628}, {3917, 7734}, {5008, 47526}, {5050, 61644}, {5102, 31152}, {5111, 59768}, {5422, 7571}, {5462, 11232}, {5476, 61700}, {5480, 44107}, {5943, 45968}, {5946, 16223}, {5972, 11422}, {6241, 40240}, {6329, 37454}, {6515, 43650}, {6723, 59771}, {6776, 34417}, {7495, 50664}, {7592, 34564}, {8546, 41583}, {8584, 13857}, {9729, 54040}, {9777, 11550}, {9935, 10619}, {10110, 16658}, {10112, 15043}, {10168, 44555}, {10263, 50476}, {10545, 14683}, {11002, 29012}, {11003, 32223}, {11179, 35268}, {11402, 61645}, {11424, 18916}, {11431, 32340}, {11750, 16881}, {12242, 26917}, {12585, 53092}, {13321, 44407}, {13366, 13567}, {13394, 32225}, {13490, 45730}, {13754, 45967}, {14389, 15516}, {14643, 15087}, {14644, 18388}, {15018, 24206}, {15026, 32165}, {15033, 43391}, {15069, 44300}, {16063, 37517}, {16226, 44665}, {16654, 18914}, {16981, 19924}, {18390, 44795}, {20583, 47097}, {21243, 34545}, {21849, 29323}, {22352, 41588}, {23292, 44111}, {26879, 37505}, {34396, 35282}, {34783, 58807}, {37481, 58806}, {37638, 53091}, {37779, 40107}, {38848, 45185}, {39571, 43831}, {45303, 59399}, {46084, 50136}, {51939, 60693}

X(61712) = midpoint of X(i) and X(j) for these {i,j}: {11245, 61657}
X(61712) = reflection of X(i) in X(j) for these {i,j}: {51, 61657}
X(61712) = pole of line {1596, 2393} with respect to the Jerabek hyperbola
X(61712) = pole of line {690, 3288} with respect to the orthic inconic
X(61712) = pole of line {5097, 22151} with respect to the Stammler hyperbola
X(61712) = pole of line {37647, 37804} with respect to the Wallace hyperbola
X(61712) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 26869, 61743}, {182, 37644, 41586}, {468, 12007, 44109}, {576, 18911, 51360}, {1503, 61657, 51}, {3448, 15019, 19130}, {5946, 45969, 61713}, {11225, 32068, 2}, {11245, 61657, 1503}, {11433, 14912, 61506}, {13366, 61691, 61690}, {13567, 61690, 61691}, {14912, 61506, 184}, {15018, 41724, 24206}, {26869, 61743, 125}, {32223, 33749, 11003}, {45298, 61658, 3917}

X(61713) = X(2)X(54)∩X(6)X(13)

Barycentrics    2*a^10-6*a^8*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)+3*a^2*(b^2-c^2)^2*(b^4+c^4)+a^6*(7*b^4+6*b^2*c^2+7*c^4)+a^4*(-5*b^6+3*b^4*c^2+3*b^2*c^4-5*c^6) : :
X(61713) = X[3]+2*X[10112], X[4]+2*X[10116], X[5]+2*X[11264], -X[20]+4*X[18128], -3*X[51]+2*X[13490], 2*X[143]+X[45731], -5*X[3091]+8*X[58807], 5*X[3567]+X[34799], X[3627]+2*X[45732], -5*X[3843]+8*X[40240], 2*X[5446]+X[34224], -4*X[5462]+X[14516] and many others

X(61713) lies on these lines: {2, 54}, {3, 10112}, {4, 10116}, {5, 11264}, {6, 13}, {20, 18128}, {30, 52}, {49, 61681}, {51, 13490}, {125, 61736}, {143, 45731}, {155, 16072}, {156, 44270}, {161, 51519}, {184, 10201}, {343, 549}, {376, 6515}, {378, 16003}, {389, 38321}, {524, 9967}, {541, 7722}, {547, 37649}, {567, 21243}, {568, 11225}, {575, 37347}, {576, 31723}, {578, 25738}, {973, 38322}, {1092, 18952}, {1199, 58922}, {1353, 21639}, {1493, 10224}, {1503, 45730}, {1614, 46451}, {1658, 10619}, {1899, 13352}, {1993, 31180}, {1994, 25739}, {2072, 34986}, {2904, 11536}, {2917, 37922}, {3060, 44407}, {3091, 58807}, {3448, 15033}, {3524, 51033}, {3534, 17834}, {3564, 5891}, {3567, 34799}, {3580, 18475}, {3627, 45732}, {3830, 12315}, {3843, 40240}, {3845, 18379}, {5054, 37476}, {5093, 23048}, {5446, 34224}, {5462, 14516}, {5562, 32358}, {5576, 37505}, {5663, 61744}, {5876, 43575}, {5890, 17702}, {5943, 45967}, {5946, 16223}, {5965, 23039}, {5972, 9703}, {6145, 15002}, {6241, 12897}, {6243, 44829}, {6644, 30714}, {6723, 11935}, {6816, 9936}, {7502, 41586}, {7540, 21849}, {7552, 40441}, {7574, 47466}, {7576, 47328}, {7577, 11422}, {7592, 9927}, {7667, 10625}, {8538, 18531}, {8550, 15760}, {9140, 15463}, {9706, 14940}, {9730, 11245}, {9937, 38405}, {10154, 31804}, {10539, 39571}, {10605, 16111}, {11179, 19131}, {11202, 61685}, {11232, 12022}, {11402, 14852}, {11424, 18488}, {11440, 43818}, {11550, 39522}, {11804, 32226}, {11818, 15004}, {12038, 26879}, {12118, 18916}, {12162, 12241}, {12235, 38323}, {12383, 15053}, {12429, 36752}, {12585, 15073}, {12893, 15078}, {12899, 21660}, {13293, 20126}, {13321, 61677}, {13358, 14708}, {13367, 34477}, {13403, 34783}, {13567, 44211}, {14118, 52104}, {14156, 26913}, {15032, 50435}, {15067, 50708}, {15115, 15121}, {15133, 15135}, {16194, 16657}, {16532, 32171}, {18378, 45185}, {18381, 36749}, {18553, 50135}, {18569, 32377}, {18951, 19467}, {20299, 37472}, {21651, 22663}, {23329, 61739}, {23515, 61701}, {26869, 38793}, {32225, 44213}, {32366, 45118}, {34148, 43808}, {34545, 41171}, {34609, 36747}, {34785, 37490}, {34786, 46027}, {35921, 41724}, {37488, 43273}, {38724, 55039}, {40107, 54006}, {40647, 44458}, {41729, 51136}, {43602, 50009}, {44109, 61619}, {45187, 52073}, {61702, 61743}

X(61713) = midpoint of X(i) and X(j) for these {i,j}: {6146, 61658}, {12022, 45968}, {34224, 34603}, {38321, 44076}
X(61713) = reflection of X(i) in X(j) for these {i,j}: {10625, 7667}, {16194, 16657}, {2, 43573}, {34603, 5446}, {38321, 389}, {44458, 40647}, {45968, 11232}, {52, 61658}, {568, 11225}, {5946, 45969}, {61658, 13292}, {7540, 21849}, {9730, 11245}
X(61713) = inverse of X(1879) in Kiepert hyperbola
X(61713) = pole of line {9185, 13224} with respect to the orthoptic circle of the Steiner inellipse
X(61713) = pole of line {30, 1879} with respect to the Kiepert hyperbola
X(61713) = pole of line {2623, 9033} with respect to the MacBeath circumconic
X(61713) = pole of line {30451, 55121} with respect to the orthic inconic
X(61713) = pole of line {52, 323} with respect to the Stammler hyperbola
X(61713) = pole of line {7799, 39113} with respect to the Wallace hyperbola
X(61713) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(96), X(1989)}}, {{A, B, C, X(265), X(54666)}}, {{A, B, C, X(1879), X(5627)}}, {{A, B, C, X(11060), X(41271)}}, {{A, B, C, X(39839), X(54738)}}
X(61713) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 14, 1879}, {30, 13292, 61658}, {30, 61658, 52}, {52, 6146, 11750}, {68, 569, 1209}, {143, 45731, 61139}, {1147, 18912, 43817}, {2888, 43838, 43651}, {3567, 34799, 45286}, {5946, 45969, 61712}, {6102, 45970, 21659}, {6146, 61658, 30}, {9545, 26917, 43839}, {10114, 19481, 265}, {10116, 58806, 4}, {11232, 13754, 45968}, {11424, 32140, 18488}, {12022, 45968, 13754}, {12227, 18390, 18388}, {12370, 43588, 185}, {15087, 18445, 12227}, {18390, 18445, 113}, {32165, 45970, 6102}, {32423, 45969, 5946}, {38724, 55039, 61711}, {43572, 43836, 2}

X(61714) = X(6)X(74)∩X(53)X(6000)

Barycentrics    a^2*(a^10*(b^2+c^2)-5*a^8*(b^4+c^4)-(b^2-c^2)^4*(b^4+b^2*c^2+c^4)-5*a^4*(b^2-c^2)^2*(2*b^4+3*b^2*c^2+2*c^4)+a^6*(b^2+c^2)*(10*b^4-13*b^2*c^2+10*c^4)+a^2*(b^2-c^2)^2*(5*b^6+4*b^4*c^2+4*b^2*c^4+5*c^6)) : :

X(61714) lies on these lines: {6, 74}, {51, 6748}, {53, 6000}, {54, 50660}, {185, 1990}, {389, 6749}, {577, 1154}, {2979, 36748}, {3284, 6102}, {5158, 13630}, {5892, 50671}, {5946, 32438}, {10574, 52703}, {11402, 52435}, {13491, 52945}, {14111, 18912}, {14533, 19209}, {14577, 41373}, {18439, 61315}, {20791, 36751}, {22052, 54042}, {26869, 61675}, {45959, 61327}, {50647, 53420}, {50679, 61690}

X(61714) = pole of line {53, 1495} with respect to the Jerabek hyperbola
X(61714) = pole of line {403, 6747} with respect to the Kiepert hyperbola
X(61714) = pole of line {526, 39201} with respect to the orthic inconic
X(61714) = pole of line {11064, 58408} with respect to the Stammler hyperbola

X(61715) = X(4)X(54)∩X(5)X(195)

Barycentrics    a^10-5*a^8*(b^2+c^2)-4*a^4*(b^2-c^2)^2*(b^2+c^2)+(b^2-c^2)^4*(b^2+c^2)-a^2*(b^2-c^2)^2*(b^4+3*b^2*c^2+c^4)+a^6*(8*b^4+5*b^2*c^2+8*c^4) : :
X(61715) = -X[3]+4*X[8254], X[4]+2*X[54], 2*X[5]+X[195], -X[20]+4*X[10610], 2*X[52]+X[32338], 2*X[125]+X[43580], -4*X[140]+X[12307], -X[146]+4*X[11805], X[265]+2*X[11702], 2*X[546]+X[36966], -5*X[631]+8*X[6689], -5*X[632]+2*X[54201] and many others

X(61715) lies on these lines: {2, 568}, {3, 8254}, {4, 54}, {5, 195}, {6, 2914}, {20, 10610}, {23, 61619}, {24, 32333}, {51, 7730}, {52, 32338}, {74, 38006}, {125, 43580}, {140, 12307}, {143, 58805}, {146, 11805}, {185, 22949}, {186, 23292}, {265, 11702}, {323, 37347}, {376, 39242}, {378, 12244}, {381, 9143}, {388, 10082}, {389, 6143}, {394, 14789}, {427, 15032}, {485, 12971}, {486, 12965}, {497, 10066}, {498, 6286}, {499, 7356}, {539, 3545}, {546, 36966}, {547, 7605}, {567, 3153}, {631, 6689}, {632, 54201}, {944, 12266}, {946, 9905}, {973, 6242}, {1138, 15111}, {1173, 13418}, {1199, 1594}, {1209, 3090}, {1352, 19150}, {1479, 47378}, {1493, 3091}, {1587, 44640}, {1588, 44639}, {1656, 11803}, {1853, 7592}, {1992, 5071}, {1995, 25714}, {2072, 34545}, {2917, 3518}, {3060, 7552}, {3085, 13079}, {3086, 18984}, {3089, 11576}, {3431, 18533}, {3448, 11804}, {3519, 5056}, {3520, 12233}, {3525, 32348}, {3526, 54202}, {3527, 18368}, {3541, 10937}, {3542, 6152}, {3547, 12363}, {3549, 12606}, {3567, 14940}, {3580, 54000}, {3832, 22804}, {3873, 5886}, {5012, 46450}, {5050, 31180}, {5067, 32396}, {5072, 20584}, {5169, 18445}, {5476, 11188}, {5480, 19596}, {5640, 61724}, {5818, 12785}, {5889, 10115}, {5890, 10628}, {5898, 7693}, {6145, 13472}, {6153, 12280}, {6243, 44056}, {6276, 7721}, {6277, 7720}, {6639, 22815}, {6644, 59771}, {7547, 11426}, {7550, 37649}, {7558, 41590}, {7564, 34799}, {7569, 12160}, {7576, 61690}, {7581, 19043}, {7582, 19044}, {7687, 14049}, {7699, 18390}, {7741, 35197}, {7951, 51803}, {7979, 10595}, {8154, 54034}, {9544, 11818}, {9545, 47360}, {9706, 45286}, {9781, 11808}, {9920, 10594}, {9971, 14853}, {10095, 13368}, {10110, 12291}, {10113, 47117}, {10201, 11002}, {10203, 43651}, {10224, 43816}, {10289, 16768}, {10531, 49192}, {10532, 49191}, {10540, 37349}, {10590, 12946}, {10591, 12956}, {10596, 13121}, {10597, 13122}, {10598, 12926}, {10599, 12936}, {10677, 18581}, {10678, 18582}, {10982, 44958}, {11003, 31723}, {11004, 15091}, {11422, 18474}, {11423, 18381}, {11425, 34797}, {11430, 13619}, {11432, 52296}, {11577, 11743}, {11597, 12383}, {11745, 47486}, {11802, 15043}, {12022, 23324}, {12234, 39571}, {12241, 54001}, {12380, 34417}, {13364, 14643}, {13366, 25739}, {13399, 43596}, {13490, 35265}, {13621, 15806}, {13622, 14491}, {14072, 16762}, {14076, 26917}, {14156, 43584}, {14389, 35254}, {14865, 15311}, {14912, 23327}, {15037, 37938}, {15068, 37353}, {15559, 48669}, {15739, 37119}, {16252, 26863}, {16554, 61725}, {16657, 22971}, {18583, 37784}, {18916, 49108}, {19130, 20125}, {19357, 52008}, {19468, 34484}, {19552, 27246}, {23358, 44879}, {32068, 43836}, {32401, 35475}, {34007, 37472}, {34986, 41171}, {37440, 44515}, {37990, 54434}, {38724, 45969}, {42059, 43891}, {44441, 61136}, {44802, 59648}, {45480, 49357}, {45481, 49358}, {45970, 54007}

X(61715) = midpoint of X(i) and X(j) for these {i,j}: {381, 55039}, {1853, 17824}, {3574, 61659}, {11206, 32346}
X(61715) = reflection of X(i) in X(j) for these {i,j}: {1853, 32351}, {11206, 32379}, {2917, 10192}, {21357, 547}, {32337, 1853}, {54, 61659}, {61659, 12242}, {7730, 51}
X(61715) = inverse of X(47065) in orthocentroidal circle
X(61715) = perspector of circumconic {{A, B, C, X(16813), X(52998)}}
X(61715) = pole of line {42731, 45147} with respect to the orthocentroidal circle
X(61715) = pole of line {6368, 24978} with respect to the polar circle
X(61715) = pole of line {389, 7730} with respect to the Jerabek hyperbola
X(61715) = pole of line {186, 6748} with respect to the Kiepert hyperbola
X(61715) = pole of line {930, 58975} with respect to the Kiepert parabola
X(61715) = pole of line {12077, 45147} with respect to the orthic inconic
X(61715) = pole of line {195, 567} with respect to the Stammler hyperbola
X(61715) = pole of line {20577, 44554} with respect to the Steiner circumellipse
X(61715) = pole of line {19553, 45799} with respect to the Wallace hyperbola
X(61715) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(275), X(33565)}}, {{A, B, C, X(3459), X(8884)}}, {{A, B, C, X(4994), X(6145)}}, {{A, B, C, X(13472), X(58079)}}, {{A, B, C, X(19553), X(45799)}}
X(61715) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 54, 12254}, {4, 578, 43818}, {5, 195, 2888}, {5, 22051, 195}, {140, 54157, 12307}, {195, 2888, 11271}, {381, 55039, 32423}, {389, 43581, 32339}, {546, 36966, 48675}, {1199, 1594, 43808}, {1209, 15801, 12325}, {3090, 12325, 1209}, {5946, 61711, 2}, {6689, 7691, 631}, {8254, 20424, 3}, {8254, 30531, 20424}, {9781, 13423, 11808}, {10610, 15800, 20}, {11206, 32346, 18400}, {11597, 36853, 12383}, {11803, 21230, 12316}, {11808, 21660, 13423}, {12242, 18400, 61659}, {15033, 18388, 4}, {15087, 39504, 3448}, {17824, 32351, 32337}, {18400, 32379, 11206}, {18400, 61659, 54}, {32352, 58489, 3567}

X(61716) = X(3)X(79)∩X(7)X(11)

Barycentrics    a^3+a^2*(b+c)-2*(b-c)^2*(b+c) : :
X(61716) = -X[55]+4*X[226], -X[63]+4*X[3838], X[3428]+2*X[37826], 2*X[3434]+X[41711], -X[4302]+4*X[5719], -2*X[4640]+5*X[31266], -4*X[6690]+X[44447], 2*X[8545]+X[36971], X[16465]+2*X[41871], 2*X[18446]+X[36999], X[42014]+2*X[61011]

X(61716) lies on these lines: {1, 382}, {2, 10032}, {3, 79}, {4, 3649}, {5, 5221}, {6, 3120}, {7, 11}, {12, 4295}, {36, 18541}, {46, 11231}, {55, 226}, {56, 3560}, {57, 7082}, {63, 3838}, {65, 5587}, {80, 1159}, {125, 8818}, {142, 4679}, {149, 42871}, {165, 61648}, {210, 28609}, {329, 3715}, {354, 971}, {355, 9656}, {381, 2771}, {388, 2098}, {390, 37703}, {405, 11263}, {484, 31479}, {495, 28212}, {497, 11038}, {499, 24470}, {514, 60083}, {517, 11237}, {518, 27479}, {553, 3817}, {554, 16038}, {581, 11553}, {599, 31177}, {758, 17532}, {896, 31187}, {908, 4413}, {940, 3944}, {942, 1898}, {944, 52837}, {946, 3304}, {948, 53014}, {952, 1478}, {962, 15888}, {999, 16173}, {1001, 5057}, {1004, 42843}, {1081, 51749}, {1125, 19526}, {1150, 17491}, {1155, 4312}, {1319, 61275}, {1376, 20292}, {1388, 10283}, {1420, 61274}, {1466, 7702}, {1479, 6147}, {1482, 5270}, {1656, 3336}, {1657, 16118}, {1659, 52806}, {1737, 61263}, {1770, 5217}, {1788, 3614}, {1837, 3671}, {1853, 53036}, {1864, 59389}, {1985, 53566}, {2306, 42156}, {2475, 12635}, {2476, 14450}, {2550, 3711}, {2635, 42289}, {2646, 9579}, {2829, 5434}, {2836, 61720}, {2886, 5852}, {3052, 33127}, {3057, 5290}, {3058, 3475}, {3086, 52783}, {3146, 10543}, {3187, 48645}, {3218, 10129}, {3242, 32856}, {3303, 12699}, {3306, 5087}, {3338, 9955}, {3339, 17606}, {3340, 37712}, {3361, 61271}, {3416, 4054}, {3428, 37826}, {3434, 41711}, {3474, 5226}, {3485, 5731}, {3487, 6284}, {3526, 37524}, {3550, 17783}, {3576, 4870}, {3579, 4338}, {3583, 15934}, {3586, 44840}, {3627, 16137}, {3663, 17723}, {3683, 25525}, {3712, 24280}, {3746, 48661}, {3748, 9580}, {3753, 31141}, {3772, 41011}, {3782, 17599}, {3826, 31018}, {3843, 37702}, {3873, 11235}, {3894, 31159}, {3911, 30424}, {3914, 61652}, {3923, 4892}, {3936, 5695}, {3951, 28645}, {3982, 11019}, {4003, 4862}, {4042, 33066}, {4138, 32777}, {4197, 27197}, {4292, 5204}, {4293, 15950}, {4298, 11376}, {4299, 37737}, {4302, 5719}, {4307, 17602}, {4313, 5556}, {4316, 37606}, {4317, 5901}, {4323, 37734}, {4355, 50443}, {4361, 32843}, {4362, 28498}, {4363, 25760}, {4383, 17889}, {4387, 18134}, {4423, 5249}, {4425, 19701}, {4427, 30834}, {4442, 31034}, {4519, 17296}, {4640, 31266}, {4641, 17064}, {4655, 25385}, {4683, 5737}, {4703, 19732}, {4713, 30969}, {4854, 5712}, {4942, 32862}, {4995, 9778}, {5054, 5131}, {5072, 15079}, {5073, 5441}, {5177, 21677}, {5183, 31434}, {5220, 17484}, {5225, 11036}, {5229, 10950}, {5231, 60933}, {5252, 28234}, {5425, 18513}, {5442, 46219}, {5506, 41862}, {5536, 60922}, {5563, 18493}, {5584, 5812}, {5640, 61696}, {5660, 37541}, {5692, 17528}, {5703, 15338}, {5707, 8614}, {5708, 7741}, {5715, 12688}, {5718, 24248}, {5722, 11551}, {5733, 6357}, {5761, 11826}, {5883, 17556}, {5903, 9654}, {5919, 31162}, {5927, 61663}, {6583, 11928}, {6690, 44447}, {6745, 61152}, {6763, 31493}, {6845, 16116}, {6872, 11281}, {6985, 16159}, {7073, 20277}, {7223, 38941}, {7232, 30942}, {7288, 59350}, {7706, 7986}, {7743, 51816}, {7951, 11552}, {8167, 27186}, {8227, 32636}, {8545, 36971}, {8581, 18839}, {9613, 11011}, {9614, 17609}, {9669, 18398}, {9671, 18483}, {10044, 37356}, {10056, 28174}, {10072, 38034}, {10157, 61653}, {10172, 24914}, {10176, 44217}, {10389, 50865}, {10573, 38138}, {10589, 21454}, {10590, 40663}, {10826, 31794}, {10827, 38176}, {11024, 50038}, {11269, 17365}, {11415, 25466}, {11495, 61013}, {11509, 37713}, {11522, 20323}, {11680, 17483}, {11929, 35004}, {12245, 31410}, {12373, 45924}, {12436, 24954}, {12609, 58798}, {12701, 21620}, {12702, 37719}, {13159, 60911}, {13390, 52809}, {15325, 61270}, {16127, 37447}, {16128, 33593}, {16133, 36002}, {16418, 26725}, {16465, 41871}, {16475, 50103}, {17070, 24597}, {17234, 17777}, {17235, 29826}, {17253, 30970}, {17262, 29643}, {17276, 29639}, {17290, 32944}, {17351, 29857}, {17579, 56177}, {17595, 17717}, {17597, 33103}, {17603, 31391}, {17702, 56402}, {17719, 37540}, {17720, 50307}, {17721, 24231}, {17772, 32946}, {18221, 50689}, {18421, 61254}, {18446, 36999}, {19749, 25354}, {19765, 24851}, {20182, 33154}, {20430, 45916}, {21060, 38201}, {21241, 32935}, {22836, 50239}, {24692, 30824}, {24695, 35466}, {24929, 28154}, {25453, 48649}, {25568, 34612}, {25959, 41242}, {26223, 48646}, {26869, 61704}, {28146, 59337}, {28472, 33088}, {28534, 35258}, {29020, 33152}, {30135, 33234}, {30438, 61699}, {30755, 56517}, {31142, 38052}, {31161, 59407}, {31179, 53372}, {31673, 37724}, {31776, 37618}, {32852, 48642}, {33070, 49453}, {33098, 33105}, {33099, 33111}, {33101, 33109}, {33107, 33146}, {33112, 33151}, {33122, 48805}, {33143, 38315}, {33161, 49721}, {33592, 37234}, {33654, 42153}, {33925, 34789}, {34753, 61267}, {34830, 36635}, {35016, 50242}, {35445, 52638}, {35801, 38235}, {37080, 41869}, {37374, 60896}, {37411, 49177}, {37578, 38031}, {37582, 37692}, {37710, 51515}, {38150, 61660}, {38357, 52023}, {38454, 61027}, {42014, 61011}, {44425, 52682}, {45287, 61287}, {46897, 48829}, {46901, 49747}, {46916, 51100}, {47522, 53280}, {53801, 60845}, {54366, 60883}, {54408, 60937}, {61710, 61735}

X(61716) = midpoint of X(i) and X(j) for these {i,j}: {1836, 17718}
X(61716) = reflection of X(i) in X(j) for these {i,j}: {17718, 226}, {55, 17718}
X(61716) = perspector of circumconic {{A, B, C, X(2690), X(60487)}}
X(61716) = pole of line {1638, 4777} with respect to the incircle
X(61716) = pole of line {4120, 8674} with respect to the orthocentroidal circle
X(61716) = pole of line {3586, 4312} with respect to the Feuerbach hyperbola
X(61716) = pole of line {16272, 33329} with respect to the Kiepert hyperbola
X(61716) = pole of line {4777, 47723} with respect to the Suppa-Cucoanes circle
X(61716) = pole of line {1323, 4031} with respect to the dual conic of Yff parabola
X(61716) = intersection, other than A, B, C, of circumconics {{A, B, C, X(658), X(60083)}}, {{A, B, C, X(5561), X(56144)}}
X(61716) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 22793, 9670}, {7, 11, 4860}, {12, 4295, 37567}, {57, 7988, 61649}, {63, 3838, 31245}, {65, 9612, 10895}, {226, 1836, 55}, {226, 516, 17718}, {329, 3925, 3715}, {381, 5902, 61717}, {553, 3817, 17728}, {908, 5880, 4413}, {946, 10404, 3304}, {1478, 39542, 2099}, {1699, 4654, 354}, {1836, 17718, 516}, {3120, 24725, 6}, {3120, 61707, 33128}, {3485, 7354, 34471}, {3782, 26098, 17599}, {3923, 4892, 30811}, {3944, 33097, 940}, {4292, 11375, 5204}, {4295, 5714, 12}, {4312, 5219, 1155}, {4442, 31034, 49486}, {4655, 25385, 37660}, {5057, 31019, 1001}, {5249, 24703, 4423}, {5902, 61703, 381}, {5902, 61705, 61722}, {5902, 61740, 61718}, {7951, 11552, 36279}, {9809, 10883, 16112}, {12047, 57282, 56}, {12699, 13407, 3303}, {16118, 37571, 1657}, {17605, 61649, 7988}, {17717, 32857, 17595}, {17889, 33096, 4383}, {24725, 33128, 61707}, {31142, 38052, 61686}, {32856, 33104, 3242}, {33103, 33106, 17597}

X(61717) = X(1)X(1656)∩X(12)X(938)

Barycentrics    a^4+a^2*(b-c)^2-2*a^3*(b+c)+2*a*(b-c)^2*(b+c)-2*(b^2-c^2)^2 : :
X(61717) = 2*X[46]+X[12953], -2*X[78]+5*X[31246], -4*X[496]+X[2098], 2*X[1329]+X[12649], -4*X[3825]+X[5730], 2*X[4848]+X[12701], 2*X[10395]+X[41710], 2*X[12053]+X[41687], X[12764]+2*X[12832], 2*X[24928]+X[37711], 2*X[36846]+X[36972]

X(61717) lies on these lines: {1, 1656}, {2, 44669}, {3, 5441}, {4, 5221}, {5, 16137}, {6, 21044}, {8, 1997}, {10, 3303}, {11, 2099}, {12, 938}, {40, 9670}, {46, 12953}, {55, 1737}, {56, 515}, {57, 12943}, {65, 1699}, {78, 31246}, {79, 3843}, {80, 999}, {145, 10584}, {354, 5587}, {355, 3304}, {381, 2771}, {382, 3336}, {388, 54448}, {405, 58449}, {484, 9668}, {496, 2098}, {497, 40663}, {498, 12433}, {499, 34471}, {517, 11238}, {518, 31141}, {631, 10543}, {632, 15174}, {758, 17556}, {940, 37717}, {942, 10826}, {950, 5217}, {952, 10072}, {1012, 10265}, {1125, 37724}, {1155, 3586}, {1159, 18393}, {1319, 5727}, {1329, 12649}, {1385, 37721}, {1388, 3086}, {1454, 10396}, {1470, 11219}, {1478, 4860}, {1479, 28174}, {1482, 37720}, {1657, 37524}, {1698, 37080}, {1788, 6284}, {1834, 27685}, {1864, 18838}, {2096, 52836}, {2136, 37829}, {2306, 5339}, {3036, 12648}, {3057, 58643}, {3058, 5657}, {3091, 3649}, {3241, 32558}, {3295, 18395}, {3296, 31410}, {3337, 9655}, {3338, 9657}, {3419, 4413}, {3421, 51463}, {3485, 7173}, {3486, 5433}, {3487, 3614}, {3488, 5432}, {3526, 37571}, {3534, 5131}, {3576, 61649}, {3582, 10246}, {3583, 36279}, {3585, 5708}, {3617, 45081}, {3679, 5919}, {3711, 3820}, {3748, 31434}, {3753, 31140}, {3811, 17619}, {3813, 5554}, {3825, 5730}, {3833, 44217}, {3858, 11544}, {3870, 5123}, {3873, 11236}, {3894, 31160}, {3913, 25005}, {4187, 49168}, {4193, 12635}, {4217, 59574}, {4299, 28190}, {4309, 61524}, {4312, 51792}, {4313, 52793}, {4848, 12701}, {4857, 12702}, {4870, 7988}, {5045, 10827}, {5046, 31888}, {5048, 37704}, {5055, 37701}, {5068, 18221}, {5076, 16118}, {5084, 21677}, {5086, 25524}, {5119, 18527}, {5154, 34195}, {5172, 11502}, {5183, 9580}, {5204, 10572}, {5219, 44840}, {5229, 52783}, {5252, 11019}, {5292, 25646}, {5298, 5731}, {5340, 33654}, {5434, 59387}, {5435, 15326}, {5563, 18525}, {5658, 57285}, {5691, 32636}, {5726, 44841}, {5818, 15888}, {5881, 20323}, {5883, 17532}, {5890, 61696}, {5903, 9669}, {6583, 11929}, {6598, 37244}, {6737, 24954}, {6738, 10171}, {6788, 61732}, {6933, 11281}, {6945, 9803}, {7373, 37710}, {7743, 25415}, {7887, 30139}, {7951, 15934}, {7962, 30286}, {7989, 11518}, {8069, 10073}, {8162, 31397}, {8164, 37703}, {9578, 17609}, {9588, 41864}, {9654, 18398}, {9656, 10404}, {9671, 12699}, {10056, 38042}, {10175, 17718}, {10247, 16173}, {10389, 19875}, {10395, 41710}, {10483, 37545}, {10589, 15950}, {10679, 12619}, {10944, 14986}, {11011, 50443}, {11231, 59337}, {11240, 38455}, {11529, 17605}, {11545, 12647}, {11928, 35004}, {12053, 41687}, {12764, 12832}, {13407, 61261}, {14584, 14629}, {14839, 22706}, {15016, 17637}, {15170, 38112}, {16140, 60911}, {16408, 47033}, {17054, 21935}, {17318, 25367}, {17597, 37716}, {17599, 37715}, {17757, 41711}, {18513, 18541}, {23708, 50194}, {24005, 61693}, {24477, 34606}, {24928, 37711}, {25681, 41575}, {28168, 37582}, {30437, 61699}, {31231, 37600}, {31245, 54318}, {31520, 37617}, {31795, 59316}, {33128, 61735}, {33152, 37549}, {33925, 49176}, {34122, 45701}, {35802, 38235}, {36846, 36972}, {37006, 37587}, {37708, 51788}, {37740, 44675}, {38454, 41712}, {46835, 61651}

X(61717) = midpoint of X(i) and X(j) for these {i,j}: {1837, 17728}, {5902, 61709}
X(61717) = reflection of X(i) in X(j) for these {i,j}: {17728, 1210}, {56, 17728}
X(61717) = pole of line {8674, 11125} with respect to the orthocentroidal circle
X(61717) = pole of line {5691, 5697} with respect to the Feuerbach hyperbola
X(61717) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 15079, 1656}, {1, 54447, 61648}, {11, 18391, 2099}, {65, 9581, 10896}, {354, 5587, 11237}, {381, 5902, 61716}, {496, 10573, 2098}, {499, 37730, 34471}, {515, 1210, 17728}, {938, 54361, 12}, {942, 10826, 10895}, {1210, 1837, 56}, {1698, 37723, 37080}, {1737, 5722, 55}, {1837, 17728, 515}, {3086, 10950, 1388}, {3338, 18480, 9657}, {3486, 5704, 5433}, {5902, 37718, 381}, {5902, 61709, 2771}, {5902, 61718, 61722}, {7962, 30286, 36920}, {10404, 19925, 9656}, {11502, 57278, 5172}, {17606, 61648, 54447}, {37716, 53619, 17597}

X(61718) = X(5)X(10399)∩X(9)X(1998)

Barycentrics    a*(a^4*(b+c)-(b-c)^2*(b+c)^3+a*(b-c)^2*(2*b+c)*(b+2*c)-a^3*(2*b^2+b*c+2*c^2)) : :
X(61718) = 2*X[5722]+X[18397], X[9580]+2*X[41539]

X(61718) lies on these lines: {5, 10399}, {6, 36197}, {9, 1998}, {11, 18412}, {33, 52423}, {55, 59381}, {57, 971}, {72, 37723}, {165, 61653}, {210, 10389}, {354, 7988}, {381, 2771}, {518, 31142}, {942, 3851}, {1005, 60994}, {1210, 6941}, {1699, 61663}, {1898, 3339}, {2078, 15299}, {2800, 18391}, {3058, 15104}, {3066, 16547}, {3090, 10122}, {3243, 17615}, {3256, 30223}, {3475, 15064}, {3911, 10394}, {4413, 5696}, {4654, 5927}, {5044, 16860}, {5083, 40269}, {5129, 40661}, {5173, 17604}, {5187, 39772}, {5219, 5728}, {5225, 12432}, {5316, 41228}, {5531, 33925}, {5640, 30437}, {5693, 6893}, {5715, 9581}, {5722, 18397}, {5777, 11518}, {5919, 34747}, {6842, 15016}, {6928, 16155}, {7004, 26742}, {7671, 60986}, {9580, 41539}, {9842, 12528}, {10382, 21153}, {10391, 31231}, {10396, 12875}, {10588, 12564}, {10601, 56317}, {12831, 39692}, {14100, 35445}, {15297, 58328}, {15733, 46917}, {16465, 30827}, {16554, 35259}, {16767, 37524}, {17718, 38108}, {33128, 61732}, {34790, 37556}, {37541, 60910}, {37736, 42884}

X(61718) = midpoint of X(i) and X(j) for these {i,j}: {1864, 61660}
X(61718) = reflection of X(i) in X(j) for these {i,j}: {57, 61660}
X(61718) = pole of line {5119, 11372} with respect to the Feuerbach hyperbola
X(61718) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {971, 61660, 57}, {1864, 61660, 971}, {5640, 61720, 61695}, {5902, 61709, 61705}, {5902, 61740, 61716}, {61717, 61722, 5902}

X(61719) = X(2)X(17)∩X(6)X(13)

Barycentrics    a^4-2*(b^2-c^2)^2+a^2*(b^2+c^2)+6*sqrt(3)*a^2*S : :

X(61719) lies on these lines: {2, 17}, {3, 3412}, {4, 12816}, {5, 16268}, {6, 13}, {15, 376}, {16, 396}, {18, 5055}, {20, 41974}, {30, 61}, {140, 43426}, {182, 20425}, {202, 10072}, {203, 5434}, {262, 54490}, {302, 6669}, {303, 11128}, {372, 35731}, {395, 547}, {398, 3845}, {485, 36467}, {486, 36450}, {524, 37352}, {530, 11299}, {531, 46854}, {533, 7760}, {548, 42791}, {550, 42612}, {576, 54141}, {597, 36758}, {598, 11603}, {619, 46709}, {623, 3181}, {631, 49862}, {632, 42979}, {732, 25157}, {1003, 9116}, {1080, 41021}, {1656, 3411}, {1992, 37170}, {2043, 51727}, {3058, 7005}, {3090, 49812}, {3091, 41120}, {3105, 36364}, {3106, 22696}, {3107, 5464}, {3146, 43252}, {3180, 3642}, {3364, 36449}, {3365, 36437}, {3389, 32787}, {3390, 32788}, {3391, 51853}, {3392, 50246}, {3523, 42994}, {3524, 5237}, {3529, 42588}, {3533, 42592}, {3534, 22236}, {3543, 5335}, {3544, 33604}, {3545, 40694}, {3584, 7127}, {3594, 35730}, {3627, 41973}, {3628, 43207}, {3830, 5340}, {3832, 49824}, {3839, 41113}, {5007, 37333}, {5032, 22491}, {5054, 22238}, {5066, 42166}, {5067, 42952}, {5070, 10187}, {5071, 16961}, {5072, 33606}, {5097, 20426}, {5238, 8703}, {5304, 43275}, {5318, 15687}, {5321, 14893}, {5334, 42905}, {5339, 12817}, {5344, 42160}, {5349, 43368}, {5350, 12101}, {5351, 12100}, {5352, 10304}, {5459, 22511}, {5463, 11301}, {5474, 5611}, {5615, 6771}, {5640, 61698}, {5858, 7759}, {5859, 11298}, {5868, 41028}, {5890, 30439}, {5946, 11624}, {6108, 47857}, {6109, 47864}, {6115, 22998}, {6419, 18587}, {6420, 18586}, {6772, 25156}, {6773, 7684}, {6775, 22997}, {7006, 10056}, {7426, 54363}, {7576, 8740}, {7583, 42562}, {7584, 42563}, {7765, 37007}, {7772, 37332}, {7829, 11306}, {7878, 11304}, {8014, 34395}, {8550, 41016}, {8584, 22496}, {8716, 36775}, {8741, 46925}, {9115, 36766}, {9300, 44219}, {9761, 22489}, {9763, 11302}, {10109, 42502}, {10124, 23302}, {10188, 55858}, {10645, 34200}, {10646, 15692}, {11001, 42150}, {11117, 34321}, {11179, 36757}, {11237, 54403}, {11238, 54402}, {11295, 35752}, {11296, 36329}, {11361, 12154}, {11480, 14093}, {11481, 15700}, {11485, 15681}, {11486, 15694}, {11488, 15702}, {11489, 42911}, {11539, 16773}, {11540, 42949}, {11543, 11737}, {11581, 36299}, {11626, 13364}, {11812, 42420}, {12102, 42908}, {12820, 54591}, {12821, 42133}, {13363, 61641}, {13846, 36438}, {13847, 36456}, {14139, 48314}, {14182, 25217}, {14188, 25151}, {14853, 41025}, {14912, 41036}, {15033, 46471}, {15048, 43274}, {15534, 22493}, {15640, 42965}, {15682, 42161}, {15683, 42086}, {15684, 19106}, {15685, 43194}, {15686, 34754}, {15688, 36836}, {15689, 42435}, {15690, 43018}, {15691, 42088}, {15693, 36843}, {15695, 42508}, {15699, 42489}, {15701, 42505}, {15703, 16645}, {15707, 42490}, {15710, 42798}, {15714, 43205}, {15715, 43250}, {15716, 42504}, {15718, 42115}, {15721, 42092}, {15723, 33416}, {17504, 42792}, {17578, 42909}, {18581, 42897}, {19053, 36454}, {19054, 36436}, {19709, 42153}, {22235, 54594}, {22492, 37171}, {22580, 43538}, {22846, 51487}, {22900, 53428}, {23004, 41746}, {23303, 42634}, {25154, 46855}, {25201, 35873}, {25202, 35874}, {25235, 41745}, {31709, 41621}, {31710, 47861}, {33458, 37341}, {33602, 43551}, {33699, 42164}, {35400, 42096}, {35403, 42094}, {35404, 42117}, {35434, 42126}, {35770, 54535}, {35771, 54534}, {36251, 47865}, {36382, 52649}, {36978, 36981}, {38071, 42163}, {39554, 45879}, {40579, 51274}, {41038, 59393}, {41099, 42159}, {41106, 42921}, {41945, 51728}, {41971, 42145}, {41972, 42928}, {41984, 42590}, {42085, 42629}, {42087, 42922}, {42089, 42986}, {42095, 43015}, {42097, 42430}, {42098, 43010}, {42101, 44018}, {42104, 43399}, {42106, 43032}, {42111, 43543}, {42116, 42625}, {42136, 43400}, {42137, 43308}, {42138, 43334}, {42141, 43482}, {42143, 42778}, {42146, 42497}, {42475, 43333}, {42494, 49810}, {42499, 42512}, {42580, 42989}, {42593, 48154}, {42596, 43023}, {42597, 43239}, {42689, 43305}, {42691, 43303}, {42794, 58190}, {42802, 45759}, {42907, 43472}, {42910, 42915}, {42914, 43104}, {42918, 43011}, {42920, 49873}, {42930, 43420}, {42940, 43007}, {42950, 43549}, {42954, 43029}, {42959, 44682}, {42969, 54592}, {42984, 43877}, {42997, 43304}, {43024, 43102}, {43028, 43200}, {43033, 43227}, {43198, 43249}, {43204, 43243}, {43236, 43774}, {43253, 43556}, {43295, 43372}, {43324, 43331}, {43373, 43554}, {43447, 56627}, {43550, 54479}, {43645, 43648}, {43769, 46333}, {44465, 54138}, {46466, 61744}, {47611, 52648}, {51140, 51208}

X(61719) = midpoint of X(i) and X(j) for these {i,j}: {61, 41107}, {397, 43228}, {16965, 41101}, {42431, 46335}
X(61719) = reflection of X(i) in X(j) for these {i,j}: {16965, 41107}, {41101, 61}, {41107, 397}, {42157, 41101}, {46335, 42147}, {61, 43228}
X(61719) = inverse of X(5469) in orthocentroidal circle
X(61719) = inverse of X(16808) in Kiepert hyperbola
X(61719) = perspector of circumconic {{A, B, C, X(476), X(32036)}}
X(61719) = pole of line {690, 5469} with respect to the orthocentroidal circle
X(61719) = pole of line {9185, 22934} with respect to the orthoptic circle of the Steiner inellipse
X(61719) = pole of line {30, 10645} with respect to the Kiepert hyperbola
X(61719) = pole of line {61, 323} with respect to the Stammler hyperbola
X(61719) = pole of line {1637, 23872} with respect to the Steiner inellipse
X(61719) = pole of line {302, 7799} with respect to the Wallace hyperbola
X(61719) = intersection, other than A, B, C, of circumconics {{A, B, C, X(13), X(19779)}}, {{A, B, C, X(14), X(41907)}}, {{A, B, C, X(17), X(1989)}}, {{A, B, C, X(265), X(12816)}}, {{A, B, C, X(11060), X(21461)}}, {{A, B, C, X(11144), X(33607)}}, {{A, B, C, X(54490), X(56401)}}
X(61719) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 22495, 22494}, {2, 34509, 21360}, {2, 62, 16963}, {3, 49947, 16962}, {4, 41112, 42973}, {4, 42973, 12816}, {6, 16809, 43031}, {6, 42815, 16809}, {6, 5475, 9113}, {6, 59410, 5476}, {13, 14, 16808}, {14, 43031, 42975}, {15, 10653, 36968}, {15, 36968, 42529}, {16, 396, 16241}, {16, 41943, 549}, {17, 16963, 2}, {17, 42506, 16267}, {18, 42156, 42581}, {18, 49907, 5055}, {30, 397, 41107}, {30, 41101, 42157}, {30, 41107, 16965}, {30, 42147, 46335}, {30, 43228, 61}, {30, 61, 41101}, {61, 42431, 42147}, {61, 43632, 42925}, {62, 16963, 42533}, {62, 42149, 42436}, {62, 42488, 42149}, {62, 42779, 40693}, {395, 11542, 37832}, {395, 37832, 16967}, {396, 549, 41943}, {398, 3845, 42972}, {3524, 42510, 5237}, {3524, 49813, 42152}, {3545, 40694, 41122}, {3839, 41113, 42814}, {3839, 42999, 41113}, {3839, 49825, 42162}, {5054, 42988, 49905}, {5055, 42156, 49907}, {5238, 43775, 42148}, {5335, 10654, 36969}, {5339, 14269, 12817}, {5344, 49827, 50687}, {5352, 42631, 10304}, {5355, 61319, 6}, {5858, 11305, 21359}, {5946, 11624, 61697}, {6772, 47859, 25156}, {10304, 42151, 42631}, {10304, 49875, 42151}, {10653, 42091, 43481}, {10654, 36969, 19107}, {11485, 42155, 36967}, {11486, 16644, 16242}, {11486, 16960, 33417}, {11489, 43542, 42911}, {13665, 13785, 42962}, {16242, 16960, 16644}, {16267, 40693, 42506}, {16267, 42977, 42488}, {16268, 41121, 5}, {16268, 42992, 41121}, {16772, 42924, 5351}, {16809, 42975, 14}, {16962, 41100, 3}, {16962, 42990, 41100}, {16962, 49947, 3412}, {16963, 40693, 49903}, {16963, 42436, 42977}, {16963, 42506, 17}, {16965, 41101, 30}, {18582, 37641, 37835}, {21360, 36366, 34509}, {22236, 42158, 42434}, {30440, 61697, 5946}, {31709, 41621, 47860}, {31862, 31863, 5469}, {34754, 43232, 42633}, {34755, 44017, 43006}, {35822, 35823, 13}, {36967, 42155, 42100}, {36970, 43418, 5318}, {37641, 37835, 16961}, {40693, 42998, 62}, {40694, 41119, 3545}, {41101, 43228, 42520}, {41108, 42973, 4}, {41112, 43201, 43424}, {41113, 42162, 3839}, {41121, 43229, 49908}, {42091, 43481, 43646}, {42118, 42633, 42942}, {42146, 42497, 43101}, {42152, 42510, 3524}, {42165, 42925, 43632}, {42496, 42913, 23302}, {42511, 49826, 46334}, {42633, 42942, 34754}, {42792, 42945, 17504}, {42813, 42972, 3845}, {42912, 42943, 10645}, {42974, 42975, 42815}, {43029, 43544, 43548}, {43424, 43476, 43201}, {49827, 50687, 42160}, {52214, 52215, 16}

X(61720) = X(2)X(10158)∩X(19)X(2000)

Barycentrics    a*(-(a^3*b*c)+a^4*(b+c)-(b-c)^2*(b+c)^3+a*b*c*(b^2+c^2)) : :
X(61720) = X[63]+2*X[1824], -X[3870]+4*X[40635], -4*X[5745]+X[20243], -2*X[17441]+5*X[31266]

X(61720) lies on these lines: {2, 10158}, {4, 14206}, {19, 2000}, {22, 56317}, {63, 1824}, {381, 61726}, {1699, 41717}, {1754, 21367}, {1995, 16547}, {2779, 15305}, {2817, 59387}, {2836, 61716}, {3017, 5902}, {3681, 29311}, {3870, 40635}, {4185, 52362}, {4414, 15076}, {4463, 11679}, {4523, 29828}, {5287, 43214}, {5640, 30437}, {5745, 20243}, {5903, 33136}, {7293, 21370}, {9895, 54392}, {10546, 41164}, {10896, 41591}, {11188, 61725}, {12723, 36277}, {15049, 61709}, {16585, 37400}, {17441, 31266}, {17616, 61671}, {18161, 61220}, {18210, 47522}, {20760, 21807}, {24597, 32118}, {31164, 34381}, {35258, 44670}, {37782, 51687}, {61729, 61740}

X(61720) = midpoint of X(i) and X(j) for these {i,j}: {1824, 61662}
X(61720) = reflection of X(i) in X(j) for these {i,j}: {63, 61662}
X(61720) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {61695, 61718, 5640}

X(61721) = X(4)X(64)∩X(30)X(154)

Barycentrics    5*a^10-14*a^6*(b^2-c^2)^2-4*a^8*(b^2+c^2)+16*a^4*(b^2-c^2)^2*(b^2+c^2)-4*(b^2-c^2)^4*(b^2+c^2)+a^2*(b^2-c^2)^2*(b^4-18*b^2*c^2+c^4) : :
X(61721) = -7*X[3]+8*X[46265], -4*X[4]+X[64], -4*X[5]+X[5925], -X[20]+4*X[5893], -2*X[376]+3*X[61680], -4*X[546]+X[20427], -4*X[1539]+X[2935], -5*X[1656]+4*X[10193], -2*X[1657]+5*X[17821], 2*X[2883]+X[3146], -5*X[3091]+2*X[5894], -2*X[3357]+5*X[3843] and many others

X(61721) lies on these lines: {3, 46265}, {4, 64}, {5, 5925}, {6, 1562}, {20, 5893}, {30, 154}, {51, 7729}, {66, 14490}, {195, 382}, {221, 12953}, {376, 61680}, {378, 7699}, {381, 2777}, {389, 10937}, {403, 37487}, {546, 20427}, {568, 3830}, {858, 58762}, {1181, 35490}, {1192, 37197}, {1350, 44440}, {1503, 1992}, {1514, 18533}, {1531, 21312}, {1539, 2935}, {1596, 31860}, {1656, 10193}, {1657, 17821}, {1885, 32602}, {1899, 13473}, {2192, 12943}, {2393, 51024}, {2778, 61705}, {2781, 11188}, {2883, 3146}, {3066, 13203}, {3091, 5894}, {3357, 3843}, {3426, 18434}, {3521, 36752}, {3529, 16252}, {3545, 23328}, {3567, 22949}, {3627, 5878}, {3832, 6696}, {3839, 23332}, {3853, 14216}, {5055, 11204}, {5064, 32395}, {5072, 25563}, {5073, 6759}, {5076, 18381}, {5085, 52069}, {5198, 46373}, {5656, 15682}, {5663, 61724}, {5691, 7973}, {5706, 52845}, {5786, 52846}, {5972, 60746}, {6145, 22334}, {6225, 17578}, {6241, 32329}, {6266, 7721}, {6267, 7720}, {6293, 11381}, {7396, 40196}, {7728, 17847}, {7730, 11455}, {9914, 11403}, {9919, 18550}, {9924, 48910}, {9971, 32062}, {10060, 18513}, {10076, 18514}, {10151, 26958}, {10152, 42854}, {10182, 15688}, {10249, 37077}, {10282, 17800}, {10296, 34117}, {10304, 58434}, {11202, 15681}, {11425, 18560}, {11472, 32316}, {12163, 44279}, {12173, 15811}, {12279, 41589}, {12315, 34786}, {12324, 50688}, {12379, 34417}, {12779, 51118}, {13093, 18383}, {13094, 41698}, {13598, 36982}, {14269, 23325}, {14530, 49134}, {14862, 49133}, {15683, 35260}, {15684, 32063}, {15686, 61606}, {17819, 42263}, {17820, 42264}, {17826, 42096}, {17827, 42097}, {17835, 38790}, {18376, 38335}, {18396, 57584}, {18534, 56924}, {19043, 19087}, {19044, 19088}, {19132, 48905}, {19149, 52842}, {23327, 51745}, {30443, 58492}, {31726, 37489}, {32064, 50687}, {32345, 35502}, {33586, 52403}, {33703, 34782}, {34725, 41580}, {34785, 49136}, {36990, 39871}, {37196, 51403}, {37444, 61150}, {37476, 52070}, {39879, 48904}, {40909, 44276}, {41735, 51163}, {43695, 52518}, {44241, 59767}, {44639, 49250}, {44640, 49251}, {44762, 50690}, {45480, 49349}, {45481, 49350}, {52843, 61299}

X(61721) = midpoint of X(i) and X(j) for these {i,j}: {1853, 5895}, {3146, 11206}, {5656, 15682}, {15684, 32063}
X(61721) = reflection of X(i) in X(j) for these {i,j}: {10192, 5893}, {10606, 381}, {1853, 4}, {11206, 2883}, {15681, 11202}, {15686, 61606}, {17813, 54131}, {17845, 11206}, {18405, 3830}, {20, 10192}, {35450, 23325}, {52028, 53023}, {54050, 23332}, {64, 1853}, {7729, 51}
X(61721) = pole of line {7729, 11381} with respect to the Jerabek hyperbola
X(61721) = pole of line {393, 10151} with respect to the Kiepert hyperbola
X(61721) = pole of line {6587, 9033} with respect to the orthic inconic
X(61721) = pole of line {8567, 35602} with respect to the Stammler hyperbola
X(61721) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(459), X(11744)}}, {{A, B, C, X(1853), X(10152)}}, {{A, B, C, X(6526), X(31361)}}, {{A, B, C, X(39268), X(52518)}}
X(61721) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 15005, 6526}, {4, 15311, 1853}, {4, 51491, 5895}, {5, 5925, 8567}, {381, 10606, 61735}, {381, 2777, 10606}, {382, 22802, 1498}, {1853, 15311, 64}, {1853, 5895, 15311}, {3830, 6000, 18405}, {5893, 50709, 10192}, {6225, 17578, 41362}, {10192, 50709, 20}, {13567, 51998, 4}

X(61722) = X(1)X(195)∩X(4)X(65)

Barycentrics    a*((a-b)^3*b*(a+b)^2+a^3*(a-b)*(a+b)*c-(a^4+a^3*b+4*a^2*b^2+a*b^3-b^4)*c^2-a*(2*a^2+b^2)*c^3+(2*a^2+b^2)*c^4+a*c^5-c^6) : :
X(61722) = X[3962]+2*X[14054], X[6284]+2*X[15556], -4*X[6738]+X[45288], X[7354]+2*X[41562]

X(61722) lies on these lines: {1, 195}, {3, 17637}, {4, 65}, {6, 10693}, {11, 18389}, {12, 15064}, {55, 18397}, {72, 3683}, {79, 31828}, {210, 45701}, {354, 912}, {381, 2771}, {405, 44782}, {411, 41697}, {517, 568}, {518, 1992}, {758, 11113}, {774, 2594}, {942, 7741}, {960, 16865}, {999, 17660}, {1006, 33857}, {1071, 32636}, {1203, 9630}, {1329, 20612}, {1532, 5884}, {1725, 5396}, {1854, 17823}, {2074, 2194}, {2099, 13253}, {2476, 8261}, {2778, 5890}, {2801, 5434}, {2836, 11188}, {3017, 61732}, {3057, 37739}, {3086, 13751}, {3295, 41686}, {3303, 5904}, {3476, 40269}, {3649, 8226}, {3827, 9971}, {3868, 24703}, {3869, 37724}, {3873, 34647}, {3874, 37722}, {3901, 37723}, {3962, 14054}, {5183, 41539}, {5221, 15071}, {5426, 5692}, {5494, 15033}, {5693, 6913}, {5728, 44840}, {5883, 17530}, {5885, 6980}, {5903, 12953}, {6284, 15556}, {6326, 33667}, {6583, 37720}, {6738, 45288}, {6884, 11375}, {6906, 16141}, {7354, 41562}, {7680, 12691}, {7699, 15904}, {8069, 41541}, {9627, 54301}, {10122, 20117}, {10176, 15670}, {10202, 61649}, {10391, 37106}, {10404, 12528}, {10543, 31806}, {12711, 37568}, {13375, 37705}, {13750, 17606}, {15049, 61726}, {15175, 24929}, {18977, 37468}, {37358, 39772}, {37564, 54432}, {37719, 56762}, {57666, 59282}, {61704, 61725}

X(61722) = midpoint of X(i) and X(j) for these {i,j}: {1858, 61663}
X(61722) = reflection of X(i) in X(j) for these {i,j}: {65, 61663}, {61663, 44547}, {61726, 15049}
X(61722) = perspector of circumconic {{A, B, C, X(2766), X(54240)}}
X(61722) = pole of line {4, 35} with respect to the Feuerbach hyperbola
X(61722) = pole of line {1865, 37982} with respect to the Kiepert hyperbola
X(61722) = pole of line {650, 8674} with respect to the orthic inconic
X(61722) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(158), X(3467)}}, {{A, B, C, X(10693), X(40149)}}
X(61722) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1858, 44547, 65}, {1858, 61663, 6001}, {5902, 61705, 61716}, {5902, 61709, 381}, {5902, 61718, 61717}, {6001, 44547, 61663}

X(61723) = X(4)X(66)∩X(23)X(206)

Barycentrics    a^2*(a^10*(b^2+c^2)-a^8*(b^4-b^2*c^2+c^4)-(b^4-c^4)^2*(b^4-b^2*c^2+c^4)-2*a^6*(b^6+c^6)+2*a^4*(b^8-b^6*c^2-b^2*c^6+c^8)+a^2*(b^10-b^8*c^2-b^2*c^8+c^10)) : :
X(61723) = -4*X[143]+X[8549], 2*X[10263]+X[34787], -X[12220]+4*X[41593]

X(61723) lies on circumconic {{A, B, C, X(1177), X(43678)}} and on these lines: {4, 66}, {6, 1112}, {23, 206}, {26, 23041}, {51, 23327}, {141, 10024}, {143, 8549}, {157, 53767}, {159, 195}, {235, 37473}, {381, 2781}, {428, 9971}, {511, 5654}, {542, 61724}, {568, 1503}, {1992, 2393}, {2777, 52989}, {3313, 7493}, {3818, 10628}, {5133, 34177}, {5169, 6697}, {5596, 7519}, {5890, 36201}, {5946, 10249}, {7530, 19149}, {9019, 9909}, {10263, 34787}, {11061, 12272}, {12220, 41593}, {15462, 44259}, {17823, 52028}, {18420, 54146}, {18449, 35707}, {31861, 34778}, {32395, 53023}, {35228, 37477}, {44210, 54334}, {52300, 58450}

X(61723) = reflection of X(i) in X(j) for these {i,j}: {10249, 5946}, {23327, 51}, {31166, 41580}, {66, 61664}, {61664, 9969}, {61737, 16776}
X(61723) = pole of line {11550, 23327} with respect to the Jerabek hyperbola
X(61723) = pole of line {27376, 37981} with respect to the Kiepert hyperbola
X(61723) = pole of line {2485, 9517} with respect to the orthic inconic
X(61723) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2393, 41580, 31166}, {2781, 16776, 61737}, {3313, 58547, 31267}, {9969, 34146, 61664}, {34146, 61664, 66}

X(61724) = X(4)X(52)∩X(6)X(1511)

Barycentrics    a^2*(a^2-b^2-c^2)*(a^10*(b^2+c^2)-3*a^2*(b^2-c^2)^4*(b^2+c^2)+2*a^6*(b^2+c^2)*(b^4+c^4)+(b^2-c^2)^4*(b^4-b^2*c^2+c^4)-3*a^8*(b^4+b^2*c^2+c^4)+2*a^4*(b^8-2*b^6*c^2-2*b^2*c^6+c^8)) : :
X(61724) = -4*X[143]+X[155], -4*X[389]+X[12118], -4*X[5448]+7*X[9781], -4*X[5449]+X[11412], -X[5562]+4*X[58496], 2*X[6102]+X[12293], X[6243]+2*X[12359], 2*X[6756]+X[12421], -X[9928]+4*X[31760], X[9936]+2*X[21651], 2*X[10263]+X[12163], X[11819]+2*X[22663] and many others

X(61724) lies on these lines: {2, 45780}, {3, 19361}, {4, 52}, {6, 1511}, {30, 7729}, {51, 5654}, {143, 155}, {195, 973}, {343, 2072}, {389, 12118}, {511, 23048}, {539, 7730}, {542, 61723}, {568, 38321}, {569, 15045}, {1112, 18451}, {1147, 1994}, {1154, 14852}, {1594, 33563}, {1992, 34382}, {2071, 37478}, {3548, 3917}, {3564, 9971}, {5448, 9781}, {5449, 11412}, {5462, 11427}, {5562, 58496}, {5640, 61715}, {5663, 61721}, {5890, 17702}, {6102, 12293}, {6146, 10937}, {6152, 19908}, {6243, 12359}, {6403, 37784}, {6642, 44752}, {6746, 36747}, {6756, 12421}, {7577, 46085}, {7592, 32048}, {7689, 12086}, {7699, 32263}, {7720, 9929}, {7721, 9930}, {8567, 12084}, {8681, 41714}, {9019, 37488}, {9306, 32411}, {9928, 31760}, {9932, 36749}, {9936, 21651}, {9938, 37490}, {10110, 18418}, {10201, 61685}, {10263, 12163}, {11557, 12272}, {11649, 34788}, {11750, 22949}, {11800, 18390}, {11819, 22663}, {12038, 15043}, {12271, 41597}, {12280, 52417}, {12282, 15083}, {12302, 13358}, {12310, 15087}, {12364, 34417}, {12420, 37122}, {13198, 44259}, {13451, 46030}, {14070, 44668}, {15024, 43839}, {15073, 18475}, {15078, 46430}, {15317, 40441}, {18438, 44201}, {18917, 54384}, {19043, 19061}, {19044, 19062}, {19131, 45170}, {27365, 52000}, {32166, 34224}, {34116, 59279}, {35264, 35603}, {35480, 53781}, {37484, 44158}, {37511, 41256}, {37513, 61128}, {37951, 44077}, {44439, 52262}, {44639, 49224}, {44640, 49225}, {45237, 61701}, {45480, 49321}, {45481, 49322}, {61702, 61739}

X(61724) = midpoint of X(i) and X(j) for these {i,j}: {52, 61666}
X(61724) = reflection of X(i) in X(j) for these {i,j}: {47391, 5946}, {5654, 51}, {68, 61666}, {61666, 12235}
X(61724) = perspector of circumconic {{A, B, C, X(10420), X(30450)}}
X(61724) = pole of line {924, 21646} with respect to the 1st DrozFarny circle
X(61724) = pole of line {5654, 43844} with respect to the Jerabek hyperbola
X(61724) = pole of line {526, 52317} with respect to the MacBeath circumconic
X(61724) = pole of line {1147, 3580} with respect to the Stammler hyperbola
X(61724) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(847), X(14910)}}, {{A, B, C, X(5392), X(5504)}}, {{A, B, C, X(5962), X(52557)}}
X(61724) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {52, 61666, 13754}, {5946, 14984, 47391}, {12235, 13754, 61666}, {13754, 61666, 68}

X(61725) = X(4)X(9)∩X(5)X(2173)

Barycentrics    2*a^5-(b-c)^2*(b+c)^3-2*a*(b^2-c^2)^2+a^2*(b+c)*(b^2+c^2) : :
X(61725) = -X[20291]+4*X[58410]

X(61725) lies on these lines: {4, 9}, {5, 2173}, {6, 3120}, {45, 12953}, {48, 5886}, {284, 37701}, {379, 4466}, {381, 61710}, {546, 7359}, {568, 916}, {610, 7988}, {674, 9971}, {946, 22356}, {952, 1953}, {1125, 22357}, {1213, 33329}, {1474, 57591}, {1731, 3585}, {1732, 9579}, {1781, 37718}, {1992, 9028}, {2772, 5890}, {3817, 61654}, {5046, 50198}, {5829, 5851}, {8053, 20989}, {10165, 22054}, {10283, 17438}, {11188, 61720}, {14953, 24317}, {16554, 61715}, {17220, 17484}, {17330, 21020}, {17379, 29833}, {18493, 23073}, {18594, 61264}, {20291, 58410}, {25359, 37076}, {28160, 40937}, {36026, 37508}, {42289, 57277}, {59671, 61262}, {61704, 61722}

X(61725) = midpoint of X(i) and X(j) for these {i,j}: {1839, 61668}
X(61725) = reflection of X(i) in X(j) for these {i,j}: {71, 61668}
X(61725) = perspector of circumconic {{A, B, C, X(1897), X(2690)}}
X(61725) = pole of line {1834, 33329} with respect to the Kiepert hyperbola
X(61725) = pole of line {3239, 47234} with respect to the Steiner inellipse
X(61725) = pole of line {4000, 4257} with respect to the dual conic of Yff parabola
X(61725) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(6), X(56747)}}, {{A, B, C, X(10), X(38535)}}
X(61725) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {516, 61668, 71}, {1839, 61668, 516}

X(61726) = X(4)X(8)∩X(6)X(1718)

Barycentrics    a*(a^5*(b+c)-a^3*b*c*(b+c)+a^4*(b^2+c^2)-(b^2-c^2)^2*(b^2+c^2)-a*(b^5-3*b^3*c^2-3*b^2*c^3+c^5)) : :
X(61726) = -X[1]+4*X[41591], -X[4018]+4*X[44545], -5*X[5439]+2*X[18732]

X(61726) lies on circumconic {{A, B, C, X(6), X(56877)}} and on these lines: {1, 41591}, {4, 8}, {6, 1718}, {165, 54305}, {195, 7562}, {381, 61720}, {392, 41581}, {518, 9971}, {568, 912}, {942, 37685}, {1211, 10176}, {1699, 22971}, {1763, 3576}, {1992, 24473}, {2771, 5890}, {2778, 61705}, {2838, 11355}, {3753, 3827}, {4018, 44545}, {4245, 18210}, {5049, 17024}, {5439, 18732}, {5587, 32395}, {6001, 7729}, {11113, 44661}, {15049, 61722}, {18180, 56439}

X(61726) = midpoint of X(i) and X(j) for these {i,j}: {1829, 61669}
X(61726) = reflection of X(i) in X(j) for these {i,j}: {392, 41581}, {61722, 15049}, {72, 61669}
X(61726) = perspector of circumconic {{A, B, C, X(1290), X(6335)}}
X(61726) = pole of line {42670, 48383} with respect to the circumcircle
X(61726) = pole of line {1837, 9629} with respect to the Feuerbach hyperbola
X(61726) = pole of line {30447, 53417} with respect to the Kiepert hyperbola
X(61726) = pole of line {1437, 37783} with respect to the Stammler hyperbola
X(61726) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {517, 61669, 72}, {1829, 61669, 517}

X(61727) = X(2)X(2387)∩X(32)X(2001)

Barycentrics    a^2*b^4*c^4-a^4*(b^2-c^2)^2*(b^2+c^2)+a^6*(b^4+c^4) : :
X(61727) = X[76]+2*X[40951], -2*X[4173]+5*X[7786], -3*X[5640]+2*X[7753], 2*X[7747]+X[32547], -X[7823]+4*X[27375], -5*X[7921]+8*X[58486]

X(61727) lies on these lines: {2, 2387}, {6, 13210}, {32, 2001}, {51, 7812}, {76, 40951}, {211, 7793}, {381, 6785}, {511, 7811}, {512, 11361}, {542, 5890}, {574, 61101}, {754, 3060}, {2882, 22486}, {2896, 41262}, {2979, 7810}, {3111, 33246}, {3314, 14962}, {3491, 7752}, {4173, 7786}, {5309, 46303}, {5640, 7753}, {6179, 27374}, {6644, 15920}, {7747, 32547}, {7757, 34383}, {7818, 33873}, {7823, 27375}, {7835, 35060}, {7921, 58486}, {7924, 13207}, {9996, 18322}, {10546, 46301}, {11196, 12150}, {13862, 31850}, {18474, 52190}, {31168, 52658}, {33008, 35704}, {37896, 54332}, {38664, 40254}

X(61727) = reflection of X(i) in X(j) for these {i,j}: {2979, 7810}, {61745, 7753}, {7812, 51}
X(61727) = pole of line {8149, 54332} with respect to the Stammler hyperbola
X(61727) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5640, 61745, 7753}

X(61728) = X(2)X(210)∩X(6)X(110)

Barycentrics    a^2*(-b^4+3*b^2*c^2-c^4+3*a*b*c*(b+c)+a^2*(b^2+3*b*c+c^2)) : :

X(61728) lies on these lines: {1, 56894}, {2, 210}, {6, 110}, {42, 19345}, {65, 37798}, {81, 511}, {100, 52020}, {209, 17019}, {373, 32911}, {386, 5563}, {579, 41423}, {899, 24923}, {940, 7998}, {942, 24883}, {1255, 3690}, {1290, 2711}, {1385, 19767}, {2194, 35265}, {2940, 3336}, {3017, 5902}, {3240, 24530}, {3699, 29559}, {3779, 9347}, {3874, 25441}, {3881, 25645}, {3889, 25650}, {3909, 20090}, {3920, 9049}, {3952, 25660}, {4239, 41610}, {4259, 14996}, {4260, 5650}, {4649, 56878}, {5045, 24936}, {5050, 44094}, {5132, 41341}, {5138, 35268}, {5297, 22277}, {5663, 45923}, {5706, 15072}, {5707, 11459}, {6800, 37538}, {9330, 24944}, {9342, 53005}, {11002, 37685}, {13363, 37509}, {13476, 33148}, {15067, 45931}, {16981, 37516}, {18164, 61220}, {18398, 24880}, {21813, 57397}, {24474, 51223}, {24916, 30329}, {24955, 25651}, {25689, 33119}, {33879, 37674}, {39561, 44104}, {39673, 40984}, {44671, 46918}, {46923, 53280}, {61707, 61729}

X(61728) = midpoint of X(i) and X(j) for these {i,j}: {40952, 61670}
X(61728) = reflection of X(i) in X(j) for these {i,j}: {81, 61670}
X(61728) = perspector of circumconic {{A, B, C, X(691), X(32041)}}
X(61728) = pole of line {3309, 19912} with respect to the orthoptic circle of the Steiner inellipse
X(61728) = pole of line {524, 15670} with respect to the Stammler hyperbola
X(61728) = pole of line {2492, 4762} with respect to the Steiner inellipse
X(61728) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {511, 61670, 81}, {3017, 5902, 61699}, {40952, 61670, 511}

X(61729) = X(2)X(513)∩X(4)X(8)

Barycentrics    a*(-(a^2*b*c*(b+c))+2*b*(b-c)^2*c*(b+c)+a^3*(b^2-b*c+c^2)-a*(b^4-3*b^2*c^2+c^4)) : :
X(61729) = -4*X[10]+X[38512], -X[149]+4*X[38390], -5*X[3091]+2*X[31849], -2*X[3937]+5*X[31272], -3*X[5640]+2*X[61696], -4*X[6667]+X[58893], X[9809]+2*X[34462], X[12532]+2*X[15906], X[16110]+2*X[47320], -X[20095]+4*X[61166], -3*X[59377]+2*X[61674]

X(61729) lies on the orthocentroidal circle and on these lines: {2, 513}, {4, 8}, {10, 38512}, {36, 748}, {55, 14513}, {59, 34048}, {81, 60698}, {88, 4014}, {100, 29349}, {149, 38390}, {354, 33107}, {381, 30438}, {901, 1376}, {908, 29353}, {953, 22758}, {958, 38568}, {2703, 24271}, {2810, 10707}, {2836, 10773}, {2841, 59415}, {2842, 37718}, {2957, 21367}, {3091, 31849}, {3259, 11680}, {3628, 46171}, {3648, 34466}, {3740, 33083}, {3814, 25957}, {3888, 30566}, {3909, 17777}, {3937, 31272}, {4080, 25048}, {4220, 59787}, {4383, 38530}, {4423, 59234}, {4430, 20042}, {4499, 51583}, {4553, 30578}, {4813, 24484}, {5091, 32911}, {5640, 61696}, {5701, 48026}, {5790, 53800}, {5902, 6788}, {6667, 58893}, {6792, 61704}, {6968, 46044}, {7336, 33146}, {8034, 24488}, {9016, 27493}, {9809, 34462}, {10176, 36154}, {10546, 51881}, {10584, 15635}, {10589, 14115}, {11499, 38569}, {11813, 33064}, {12532, 15906}, {15049, 61699}, {15632, 17784}, {16110, 47320}, {17592, 24429}, {18515, 38617}, {20095, 61166}, {23705, 45829}, {23838, 52031}, {24250, 32782}, {30953, 30981}, {31134, 31160}, {36216, 42721}, {36280, 52242}, {38042, 56750}, {46125, 48544}, {54370, 56411}, {59377, 61674}, {61707, 61728}, {61720, 61740}

X(61729) = midpoint of X(i) and X(j) for these {i,j}: {38389, 61672}
X(61729) = reflection of X(i) in X(j) for these {i,j}: {100, 61672}, {46171, 3628}, {61731, 381}
X(61729) = inverse of X(47803) in orthoptic circle of the Steiner inellipse
X(61729) = anticomplement of X(34583)
X(61729) = perspector of circumconic {{A, B, C, X(3227), X(6335)}}
X(61729) = X(i)-Dao conjugate of X(j) for these {i, j}: {34583, 34583}
X(61729) = pole of line {517, 47803} with respect to the orthoptic circle of the Steiner inellipse
X(61729) = pole of line {536, 4391} with respect to the Steiner circumellipse
X(61729) = pole of line {4552, 47776} with respect to the Yff parabola
X(61729) = pole of line {14431, 18210} with respect to the dual conic of Wallace hyperbola
X(61729) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(43928)}}, {{A, B, C, X(9081), X(44429)}}, {{A, B, C, X(35353), X(41013)}}
X(61729) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {15049, 61703, 61699}, {29349, 61672, 100}, {34151, 44013, 31512}, {38389, 61672, 29349}

X(61730) = X(2)X(514)∩X(4)X(9)

Barycentrics    a^4-a^3*(b+c)-2*a*(b-c)^2*(b+c)+(b^2-c^2)^2+a^2*(b^2-b*c+c^2) : :
X(61730) = 2*X[3]+X[18328], 2*X[116]+X[3732], -X[664]+4*X[6710], -2*X[1565]+5*X[31273], 5*X[1656]+X[18329], -5*X[3091]+2*X[31851]

X(61730) lies on the orthocentroidal circle and on these lines: {1, 4530}, {2, 514}, {3, 18328}, {4, 9}, {6, 6788}, {8, 1023}, {45, 14358}, {55, 5532}, {80, 2246}, {101, 952}, {110, 45747}, {116, 3732}, {220, 59503}, {346, 4169}, {664, 6710}, {910, 28160}, {996, 2726}, {1145, 4752}, {1212, 11231}, {1213, 36155}, {1308, 4413}, {1565, 31273}, {1566, 31841}, {1656, 18329}, {2170, 16173}, {2702, 2758}, {3015, 5972}, {3017, 61741}, {3091, 31851}, {3119, 5660}, {3570, 50024}, {4103, 27546}, {4370, 10713}, {4705, 24488}, {5074, 17292}, {5080, 21372}, {5088, 16815}, {5195, 29591}, {5205, 51280}, {5218, 60579}, {5252, 60060}, {5540, 10773}, {5845, 10708}, {5886, 46835}, {5902, 61706}, {6506, 23513}, {6785, 15049}, {6792, 61707}, {7434, 26244}, {7988, 33573}, {10165, 41006}, {11607, 59149}, {16549, 26793}, {16611, 19950}, {17277, 24279}, {17369, 40595}, {17451, 37701}, {17734, 49758}, {17747, 28212}, {20006, 33159}, {21201, 42462}, {24499, 48003}, {28234, 40869}, {28877, 50896}, {29535, 33944}, {30858, 51419}, {31192, 43057}, {34522, 55316}, {36158, 37508}, {37658, 56528}, {43065, 61649}, {45763, 50027}, {49778, 56807}, {51621, 59235}, {55161, 60065}, {59239, 61321}, {61695, 61710}

X(61730) = midpoint of X(i) and X(j) for these {i,j}: {1146, 51406}
X(61730) = reflection of X(i) in X(j) for these {i,j}: {101, 51406}
X(61730) = inverse of X(47766) in orthoptic circle of the Steiner inellipse
X(61730) = inverse of X(8756) in polar circle
X(61730) = complement of X(38941)
X(61730) = perspector of circumconic {{A, B, C, X(903), X(1897)}}
X(61730) = X(i)-complementary conjugate of X(j) for these {i, j}: {61425, 10}
X(61730) = pole of line {23854, 48387} with respect to the circumcircle
X(61730) = pole of line {516, 47766} with respect to the orthoptic circle of the Steiner inellipse
X(61730) = pole of line {514, 8756} with respect to the polar circle
X(61730) = pole of line {1834, 6788} with respect to the Kiepert hyperbola
X(61730) = pole of line {519, 25259} with respect to the Steiner circumellipse
X(61730) = pole of line {519, 3239} with respect to the Steiner inellipse
X(61730) = pole of line {101, 900} with respect to the Yff parabola
X(61730) = pole of line {3977, 30805} with respect to the dual conic of polar circle
X(61730) = pole of line {1647, 4000} with respect to the dual conic of Yff parabola
X(61730) = pole of line {4120, 4466} with respect to the dual conic of Wallace hyperbola
X(61730) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(6548)}}, {{A, B, C, X(19), X(1022)}}, {{A, B, C, X(281), X(60480)}}, {{A, B, C, X(514), X(8756)}}, {{A, B, C, X(1826), X(4049)}}, {{A, B, C, X(2183), X(15378)}}, {{A, B, C, X(2333), X(55263)}}, {{A, B, C, X(2690), X(16088)}}, {{A, B, C, X(2726), X(44435)}}, {{A, B, C, X(2758), X(17927)}}, {{A, B, C, X(38941), X(39444)}}
X(61730) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 61239, 3730}, {242, 31897, 41327}, {952, 51406, 101}, {1146, 51406, 952}, {1565, 40483, 31273}, {3732, 31640, 116}, {5011, 5179, 5134}, {5179, 8074, 5011}, {5199, 44897, 8074}, {5199, 8074, 5179}

X(61731) = X(2)X(392)∩X(4)X(513)

Barycentrics    a*(-3*a^6*b*c*(b+c)+4*a^4*b*(b-c)^2*c*(b+c)-2*b*(b-c)^4*c*(b+c)^3+a^7*(b^2+b*c+c^2)+a^2*b*(b-c)^2*c*(b+c)*(b^2+6*b*c+c^2)+a^3*(b-c)^4*(3*b^2+5*b*c+3*c^2)+a^5*(-3*b^4+2*b^3*c+5*b^2*c^2+2*b*c^3-3*c^4)-a*(b^2-c^2)^2*(b^4-4*b^3*c+9*b^2*c^2-4*b*c^3+c^4)) : :
X(61731) = -4*X[946]+X[38513], -5*X[3091]+2*X[31847], 2*X[3937]+X[10728], 2*X[12699]+X[38512], 2*X[18330]+X[56878], -X[38753]+4*X[46174]

X(61731) lies on the orthocentroidal circle, circumconic {{A, B, C, X(957), X(43933)}}, and on these lines: {2, 392}, {4, 513}, {30, 46171}, {59, 60691}, {104, 61674}, {376, 34583}, {381, 30438}, {946, 38513}, {953, 22753}, {2775, 10767}, {2779, 37718}, {2810, 10711}, {2818, 59391}, {3025, 12943}, {3091, 31847}, {3887, 18341}, {3937, 10728}, {4293, 14115}, {5091, 7425}, {5890, 61696}, {5902, 61732}, {11496, 38569}, {12699, 38512}, {14511, 47051}, {14513, 18491}, {18330, 56878}, {19245, 47081}, {22791, 56750}, {38753, 46174}, {61695, 61710}

X(61731) = reflection of X(i) in X(j) for these {i,j}: {104, 61674}, {376, 34583}, {5890, 61696}, {61729, 381}

X(61732) = X(1)X(4)∩X(2)X(522)

Barycentrics    a^6+a^4*b*c-a^5*(b+c)+a^3*(b-c)^2*(b+c)+4*a*b*(b-c)^2*c*(b+c)+(b-c)^4*(b+c)^2-a^2*(b-c)^2*(2*b+c)*(b+2*c) : :
X(61732) = -4*X[5]+X[18339], X[102]+2*X[21664], -X[109]+4*X[15252], 2*X[124]+X[1897], X[10732]+2*X[38554], -4*X[11734]+X[51565]

X(61732) lies on the orthocentroidal circle and on these lines: {1, 4}, {2, 522}, {5, 18339}, {55, 2222}, {102, 21664}, {109, 15252}, {124, 1897}, {1324, 20988}, {1647, 5573}, {1836, 60062}, {2006, 2310}, {2701, 53185}, {2716, 10269}, {3017, 61722}, {3109, 4653}, {3120, 10773}, {3676, 45276}, {3700, 45282}, {3939, 26611}, {4845, 5723}, {5790, 14629}, {5902, 61731}, {6788, 61717}, {7004, 11219}, {7046, 15633}, {9778, 23703}, {9809, 61225}, {10017, 50940}, {10732, 38554}, {11734, 51565}, {12831, 44858}, {17728, 53525}, {28146, 33649}, {33128, 61718}, {38028, 60687}, {42759, 52242}, {52659, 59458}

X(61732) = midpoint of X(i) and X(j) for these {i,j}: {38357, 51408}
X(61732) = reflection of X(i) in X(j) for these {i,j}: {109, 51408}, {51408, 15252}
X(61732) = inverse of X(47800) in orthoptic circle of the Steiner inellipse
X(61732) = inverse of X(23710) in polar circle
X(61732) = perspector of circumconic {{A, B, C, X(653), X(1121)}}
X(61732) = pole of line {522, 42763} with respect to the incircle
X(61732) = pole of line {515, 47800} with respect to the orthoptic circle of the Steiner inellipse
X(61732) = pole of line {522, 23710} with respect to the polar circle
X(61732) = pole of line {65, 38507} with respect to the Feuerbach hyperbola
X(61732) = pole of line {527, 14837} with respect to the Steiner inellipse
X(61732) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(34), X(35348)}}, {{A, B, C, X(522), X(23710)}}, {{A, B, C, X(1870), X(2717)}}, {{A, B, C, X(17985), X(53185)}}
X(61732) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 51889, 18340}, {1785, 16869, 45272}, {1785, 45272, 38945}, {15252, 38357, 109}

X(61733) = X(2)X(51)∩X(6)X(5941)

Barycentrics    a^2*(b^2*(a^2-b^2)^3*(a^4+b^4)+(a-b)*(a+b)*(a^8-a^6*b^2-2*a^4*b^4+4*a^2*b^6-4*b^8)*c^2-(3*a^8+a^6*b^2-3*a^2*b^6+9*b^8)*c^4+(4*a^6+6*a^4*b^2+3*a^2*b^4+12*b^6)*c^6-(4*a^4+8*a^2*b^2+9*b^4)*c^8+(3*a^2+4*b^2)*c^10-c^12) : :
X(61733) = 2*X[389]+X[31848], -4*X[5462]+X[31850], -4*X[11554]+7*X[15043], X[18321]+5*X[37481]

X(61733) lies on circumconic {{A, B, C, X(14565), X(46807)}} and on these lines: {2, 51}, {5, 33967}, {6, 5941}, {39, 47079}, {182, 37930}, {185, 52473}, {389, 31848}, {512, 9730}, {568, 7775}, {575, 13137}, {842, 15018}, {2871, 6055}, {3111, 5892}, {5462, 31850}, {5890, 6787}, {5946, 7753}, {6644, 32761}, {7706, 13449}, {9218, 43584}, {11554, 15043}, {13335, 61446}, {14389, 16760}, {14984, 61675}, {15032, 33803}, {15539, 37348}, {16188, 37648}, {18321, 37481}, {18583, 47570}, {18911, 58261}, {44221, 53494}, {59208, 59805}

X(61733) = midpoint of X(i) and X(j) for these {i,j}: {5890, 6787}, {5946, 15536}, {6785, 61734}
X(61733) = reflection of X(i) in X(j) for these {i,j}: {15544, 5946}, {3111, 5892}
X(61733) = pole of line {3815, 34349} with respect to the Kiepert hyperbola
X(61733) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5640, 61734, 6785}, {6785, 61734, 511}

X(61734) = X(2)X(51)∩X(3)X(9218)

Barycentrics    a^2*(b^2*(a^2-b^2)^3*(a^4+a^2*b^2+b^4)+(a^2-b^2)^2*(a^6+a^4*b^2+2*b^6)*c^2-(2*a^8+a^6*b^2-3*a^4*b^4+4*b^8)*c^4+(a^6+3*a^4*b^2+6*b^6)*c^6-(a^2+2*b^2)^2*c^8+2*(a^2+b^2)*c^10-c^12) : :
X(61734) = X[6241]+2*X[18321], -X[12111]+4*X[31848], -3*X[15045]+2*X[41330]

X(61734) lies on these lines: {2, 51}, {3, 9218}, {381, 15536}, {512, 15072}, {842, 15080}, {5889, 7759}, {5890, 61745}, {6241, 18321}, {6787, 15305}, {7878, 15043}, {7922, 11444}, {10349, 50437}, {12111, 31848}, {13137, 15073}, {14984, 46303}, {15045, 41330}, {15107, 15919}, {15915, 44114}, {16259, 41042}, {16260, 41043}, {22240, 59805}, {37930, 56980}, {47619, 51739}

X(61734) = reflection of X(i) in X(j) for these {i,j}: {15305, 6787}, {381, 15536}, {6785, 61733}
X(61734) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {511, 61733, 6785}, {6785, 61733, 5640}

X(61735) = X(2)X(154)∩X(5)X(64)

Barycentrics    a^6-3*a^2*(b^2-c^2)^2-2*a^4*(b^2+c^2)+4*(b^2-c^2)^2*(b^2+c^2) : :
X(61735) = -4*X[2]+X[154], 5*X[3]+4*X[18383], 4*X[4]+5*X[8567], 8*X[5]+X[64], 4*X[66]+5*X[19132], X[68]+8*X[32144], X[69]+2*X[23326], X[155]+8*X[13561], X[376]+2*X[23324], X[382]+8*X[25563], 8*X[546]+X[5925], 2*X[599]+X[17813] and many others

X(61735) lies on these lines: {2, 154}, {3, 18383}, {4, 8567}, {5, 64}, {6, 67}, {23, 15578}, {25, 61691}, {66, 19132}, {68, 32144}, {69, 23326}, {107, 42854}, {122, 20208}, {141, 16051}, {155, 13561}, {161, 7484}, {182, 15139}, {184, 52298}, {206, 22112}, {373, 34146}, {376, 23324}, {378, 14644}, {381, 2777}, {382, 25563}, {394, 23293}, {426, 56308}, {427, 17810}, {458, 53017}, {468, 36990}, {470, 41039}, {471, 41038}, {523, 52720}, {524, 30775}, {546, 5925}, {599, 17813}, {631, 17845}, {632, 9833}, {858, 1350}, {1181, 23294}, {1192, 7507}, {1352, 5159}, {1368, 61685}, {1495, 52292}, {1498, 1656}, {1594, 9786}, {1620, 12173}, {1854, 17606}, {1899, 17809}, {1995, 7703}, {2393, 5650}, {2453, 3154}, {2781, 5640}, {2883, 5056}, {2917, 7516}, {2935, 20304}, {3053, 14003}, {3066, 5169}, {3090, 5656}, {3091, 5895}, {3258, 47284}, {3357, 3851}, {3523, 41362}, {3525, 34782}, {3526, 10182}, {3534, 10193}, {3541, 16657}, {3542, 16654}, {3544, 12250}, {3545, 15311}, {3580, 11477}, {3589, 41719}, {3619, 15583}, {3628, 14216}, {3763, 5646}, {3818, 6723}, {3827, 61686}, {3830, 11204}, {3832, 5894}, {3850, 20427}, {3855, 51491}, {3917, 34751}, {5054, 18400}, {5055, 6000}, {5064, 61645}, {5067, 16252}, {5068, 5893}, {5070, 6759}, {5072, 22802}, {5210, 47526}, {5449, 37498}, {5480, 37643}, {5596, 51126}, {5965, 37672}, {5972, 18440}, {6001, 54447}, {6143, 19357}, {6146, 14528}, {6225, 15022}, {6644, 34128}, {6688, 41580}, {7386, 21167}, {7392, 34944}, {7486, 12324}, {7493, 48905}, {7495, 34775}, {7496, 35228}, {7505, 16658}, {7533, 13203}, {7547, 43608}, {7577, 10605}, {7579, 17835}, {7706, 20397}, {7716, 54381}, {7729, 15030}, {7736, 53496}, {7973, 8227}, {7989, 12262}, {7998, 44668}, {8252, 17820}, {8253, 17819}, {8889, 13567}, {8991, 42561}, {9909, 29323}, {10169, 15534}, {10224, 12163}, {10250, 50955}, {10282, 46219}, {10546, 15647}, {10601, 26913}, {10982, 26917}, {11064, 15069}, {11202, 15694}, {11216, 13857}, {11284, 15126}, {11410, 13851}, {11425, 12022}, {11550, 37453}, {11572, 15750}, {11704, 35502}, {12111, 32184}, {12293, 23336}, {13371, 17834}, {13568, 58378}, {13611, 37072}, {13980, 31412}, {14389, 55711}, {14516, 45248}, {14530, 14864}, {14643, 18451}, {14852, 18281}, {14912, 23291}, {15028, 41589}, {15066, 30745}, {15138, 37470}, {15274, 51358}, {15448, 52290}, {15576, 51939}, {15577, 40916}, {15579, 16042}, {15703, 32063}, {15720, 34785}, {16063, 18382}, {16177, 57346}, {17811, 21243}, {17824, 36752}, {17825, 38317}, {17826, 43029}, {17827, 43028}, {17928, 32345}, {18386, 21663}, {18396, 37118}, {18474, 38793}, {18494, 44673}, {18911, 34118}, {19087, 42265}, {19088, 42262}, {19709, 35450}, {21970, 48901}, {24206, 41603}, {24855, 33979}, {26543, 30776}, {29317, 34609}, {31074, 33586}, {31099, 32269}, {31152, 31884}, {31382, 34845}, {31383, 52297}, {31856, 34507}, {32225, 51024}, {32423, 47391}, {33128, 61717}, {34360, 37987}, {34573, 36851}, {34780, 55857}, {36201, 47597}, {37911, 39884}, {41586, 55722}, {44210, 59411}, {44439, 60774}, {44440, 58762}, {44569, 54131}, {44762, 46935}, {46034, 52283}, {46517, 48872}, {47315, 48873}, {47629, 48876}, {49674, 61136}, {50687, 50709}, {51360, 53097}, {51756, 53094}, {54334, 61664}, {61710, 61716}

X(61735) = midpoint of X(i) and X(j) for these {i,j}: {1853, 61680}
X(61735) = reflection of X(i) in X(j) for these {i,j}: {154, 61680}, {61680, 2}
X(61735) = complement of X(35260)
X(61735) = pole of line {9007, 52744} with respect to the nine-point circle
X(61735) = pole of line {1636, 1637} with respect to the orthocentroidal circle
X(61735) = pole of line {468, 2452} with respect to the Kiepert hyperbola
X(61735) = pole of line {690, 54259} with respect to the orthic inconic
X(61735) = pole of line {1350, 10298} with respect to the Stammler hyperbola
X(61735) = pole of line {37668, 37804} with respect to the Wallace hyperbola
X(61735) = intersection, other than A, B, C, of circumconics {{A, B, C, X(67), X(42287)}}, {{A, B, C, X(3424), X(8791)}}, {{A, B, C, X(4846), X(33702)}}, {{A, B, C, X(10192), X(41530)}}
X(61735) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11206, 58434}, {2, 1503, 61680}, {2, 23332, 1853}, {2, 32064, 10192}, {2, 45303, 10516}, {2, 61700, 35259}, {3, 23325, 18405}, {5, 40686, 64}, {66, 47355, 19132}, {122, 20208, 33924}, {125, 15113, 15131}, {125, 5094, 6}, {125, 61743, 26869}, {381, 10606, 61721}, {381, 23329, 10606}, {427, 26958, 17810}, {427, 61506, 53023}, {468, 36990, 41424}, {599, 23327, 17813}, {858, 37638, 1350}, {1352, 5159, 59767}, {1503, 61680, 154}, {1656, 20299, 1498}, {1853, 61680, 1503}, {1995, 44883, 10117}, {3091, 6696, 5895}, {3526, 18381, 17821}, {3763, 23300, 9924}, {5094, 26869, 61743}, {7703, 15059, 1995}, {10193, 18376, 3534}, {13561, 31283, 155}, {14852, 18281, 37497}, {21243, 30771, 17811}, {23294, 52296, 1181}, {26869, 61737, 61739}, {26913, 31236, 10601}, {26958, 53023, 61506}, {31099, 32269, 48910}, {31152, 61644, 31884}, {35259, 61700, 47353}, {37454, 54012, 47355}, {37643, 52284, 5480}, {61702, 61736, 47391}

X(61736) = X(2)X(3)∩X(6)X(40685)

Barycentrics    a^10-3*a^8*(b^2+c^2)+(b^2-c^2)^4*(b^2+c^2)+2*a^6*(b^4+3*b^2*c^2+c^4)+a^4*(2*b^6-3*b^4*c^2-3*b^2*c^4+2*c^6)-3*a^2*(b^8-b^6*c^2-b^2*c^6+c^8) : :
X(61736) = X[156]+2*X[20299], X[1147]+2*X[13561], X[5448]+2*X[25563], X[6247]+2*X[61608], -X[6759]+4*X[58435], X[11255]+2*X[40107], X[12038]+2*X[32767], X[18381]+2*X[32171], -X[19154]+4*X[58445], X[32139]+5*X[40686], X[47360]+2*X[49108]

X(61736) lies on these lines: {2, 3}, {6, 40685}, {49, 23294}, {125, 61713}, {156, 20299}, {394, 46114}, {539, 14076}, {542, 6697}, {567, 26913}, {1092, 34826}, {1147, 13561}, {1181, 15806}, {1511, 18474}, {3448, 9703}, {3818, 20773}, {5448, 25563}, {5655, 12270}, {5663, 23329}, {5890, 15061}, {5946, 34128}, {6247, 61608}, {6699, 18388}, {6759, 58435}, {7699, 38728}, {7703, 38794}, {8254, 36752}, {9140, 58881}, {10182, 44407}, {10264, 18445}, {10272, 18451}, {10605, 61548}, {11255, 40107}, {11267, 33417}, {11268, 33416}, {11425, 43575}, {11442, 40111}, {12038, 32767}, {12121, 18392}, {12281, 20126}, {13391, 61646}, {13392, 18440}, {13451, 61506}, {14156, 21243}, {14643, 15305}, {15033, 15059}, {15087, 59771}, {15111, 57306}, {16000, 16665}, {18381, 32171}, {18390, 20304}, {19154, 58445}, {20424, 37490}, {22115, 23293}, {23325, 30522}, {23515, 61744}, {26869, 45969}, {26917, 37472}, {26958, 39522}, {32139, 40686}, {32423, 47391}, {34514, 51393}, {34783, 43608}, {47360, 49108}, {51732, 53022}, {54042, 61644}

X(61736) = midpoint of X(i) and X(j) for these {i,j}: {2, 18281}, {376, 18568}, {20299, 61681}, {47391, 61702}
X(61736) = reflection of X(i) in X(j) for these {i,j}: {156, 61681}, {10154, 10020}, {14070, 15330}, {17714, 10154}, {61681, 43839}
X(61736) = complement of X(10201)
X(61736) = anticomplement of X(34330)
X(61736) = X(i)-Dao conjugate of X(j) for these {i, j}: {34330, 34330}
X(61736) = pole of line {6, 47192} with respect to the Kiepert hyperbola
X(61736) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1658), X(16665)}}, {{A, B, C, X(6662), X(10018)}}, {{A, B, C, X(18575), X(52296)}}, {{A, B, C, X(31846), X(50143)}}
X(61736) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14787, 15699}, {2, 18281, 30}, {3, 10224, 18377}, {5, 3627, 10019}, {26, 3526, 10125}, {30, 10020, 10154}, {30, 10154, 17714}, {30, 15330, 14070}, {140, 13371, 1658}, {631, 18569, 15331}, {1147, 13561, 18356}, {1344, 1345, 13861}, {1656, 12084, 13406}, {5448, 25563, 32138}, {10212, 15332, 3}, {15061, 61711, 5890}, {18586, 18587, 16868}, {20299, 43839, 156}, {47391, 61702, 32423}, {47391, 61735, 61702}

X(61737) = X(3)X(66)∩X(6)X(67)

Barycentrics    a^8-a^6*(b^2+c^2)+a^2*(b^2-c^2)^2*(b^2+c^2)+a^4*(b^2+c^2)^2-2*(b^4-c^4)^2 : :
X(61737) = -X[154]+3*X[21358], -2*X[206]+5*X[3763], -X[576]+4*X[32767], -X[1177]+4*X[6698], -X[1351]+4*X[20300], -5*X[1656]+2*X[34117], 2*X[3098]+X[34775], X[3357]+2*X[18553], -7*X[3619]+X[5596], 2*X[3631]+X[15583], -4*X[5449]+X[44492], -X[5656]+5*X[40330] and many others

X(61737) lies on these lines: {2, 19153}, {3, 66}, {6, 67}, {25, 34177}, {69, 858}, {70, 43725}, {154, 21358}, {206, 3763}, {338, 57533}, {381, 2781}, {382, 8262}, {511, 14852}, {524, 11216}, {542, 10249}, {576, 32767}, {599, 1853}, {1092, 15069}, {1177, 6698}, {1350, 18405}, {1351, 20300}, {1370, 16789}, {1594, 14853}, {1597, 54146}, {1656, 34117}, {1899, 32621}, {1974, 61691}, {1992, 10169}, {1995, 2892}, {2777, 3818}, {3098, 34775}, {3357, 18553}, {3564, 18281}, {3566, 18310}, {3589, 40920}, {3619, 5596}, {3620, 16063}, {3631, 15583}, {3827, 5692}, {5064, 9971}, {5449, 44492}, {5656, 40330}, {5965, 44469}, {6000, 11178}, {6144, 32127}, {6145, 34817}, {6776, 37118}, {7507, 9969}, {7574, 18382}, {7716, 12173}, {8542, 15126}, {8548, 13561}, {8549, 20299}, {8550, 26944}, {8889, 51744}, {9019, 34609}, {9140, 15531}, {9756, 61682}, {9925, 18356}, {10182, 23041}, {10192, 20582}, {10295, 47449}, {10510, 40341}, {10516, 15030}, {10606, 36201}, {10628, 52989}, {11188, 61700}, {11204, 11645}, {11443, 32244}, {11469, 15435}, {11579, 11935}, {13371, 34380}, {14277, 55121}, {14791, 48876}, {14912, 37119}, {14984, 61702}, {15311, 47354}, {15533, 17813}, {16774, 19119}, {18358, 50008}, {18374, 37453}, {18376, 19924}, {18381, 34787}, {18383, 52987}, {18400, 50977}, {18580, 48906}, {19118, 47455}, {19130, 52163}, {19132, 58450}, {19136, 26958}, {19149, 24206}, {20987, 21284}, {21356, 32064}, {22151, 30744}, {23042, 44491}, {23293, 41614}, {26156, 34207}, {26283, 37485}, {26926, 61690}, {28408, 46442}, {29181, 34725}, {31099, 47558}, {31267, 34573}, {31861, 61543}, {32903, 55644}, {34786, 55606}, {35219, 46448}, {35283, 40917}, {35370, 37197}, {36990, 37196}, {37638, 41613}, {38317, 44480}, {38323, 54050}, {41593, 47355}, {44134, 45279}, {44280, 51023}, {46444, 47459}, {50709, 51022}, {52251, 53575}, {56597, 56921}, {59778, 61685}

X(61737) = midpoint of X(i) and X(j) for these {i,j}: {66, 61683}, {67, 15131}, {599, 1853}, {1350, 18405}, {10606, 47353}, {15533, 17813}
X(61737) = reflection of X(i) in X(j) for these {i,j}: {159, 61683}, {10192, 20582}, {10249, 23329}, {1992, 10169}, {11216, 23327}, {15131, 15116}, {15141, 15131}, {18405, 51756}, {19153, 2}, {23049, 23325}, {23327, 23332}, {31166, 10192}, {61683, 141}, {61723, 16776}
X(61737) = complement of X(41719)
X(61737) = perspector of circumconic {{A, B, C, X(935), X(44766)}}
X(61737) = pole of line {525, 42659} with respect to the circumcircle
X(61737) = pole of line {1637, 9517} with respect to the orthocentroidal circle
X(61737) = pole of line {9979, 59932} with respect to the polar circle
X(61737) = pole of line {468, 3767} with respect to the Kiepert hyperbola
X(61737) = pole of line {22, 19153} with respect to the Stammler hyperbola
X(61737) = pole of line {3265, 47138} with respect to the Steiner inellipse
X(61737) = pole of line {315, 7493} with respect to the Wallace hyperbola
X(61737) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(6), X(54060)}}, {{A, B, C, X(66), X(8791)}}, {{A, B, C, X(67), X(14376)}}
X(61737) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {66, 61683, 1503}, {67, 15116, 15141}, {69, 23300, 34777}, {141, 1503, 61683}, {511, 23325, 23049}, {524, 23327, 11216}, {524, 23332, 23327}, {542, 23329, 10249}, {599, 1853, 2393}, {1503, 61683, 159}, {1899, 54347, 32621}, {2781, 16776, 61723}, {3619, 5596, 58437}, {10606, 47353, 36201}, {15131, 61735, 5094}, {18381, 40107, 34787}, {20299, 34507, 8549}, {34573, 34774, 31267}, {61735, 61739, 26869}

X(61738) = X(6)X(18575)∩X(264)X(523)

Barycentrics    a^4*(b^4+b^2*c^2+c^4)-2*b^2*c^2*(b^2-c^2)^2-a^2*(b^2-c^2)^2*(b^2+c^2) : :
X(61738) = -X[160]+4*X[14767]

X(61738) lies on these lines: {6, 18575}, {66, 7694}, {141, 7697}, {157, 9756}, {160, 14767}, {262, 3613}, {264, 523}, {338, 37988}, {381, 2781}, {458, 1576}, {868, 9220}, {1853, 11197}, {2493, 5094}, {3001, 44135}, {3095, 53474}, {5117, 34981}, {6697, 36412}, {7703, 9148}, {9969, 22682}, {10256, 59702}, {21445, 45838}, {37473, 54005}, {39486, 52989}, {40814, 59739}, {52247, 53575}

X(61738) = reflection of X(i) in X(j) for these {i,j}: {160, 61684}, {61684, 14767}
X(61738) = pole of line {297, 9420} with respect to the nine-point circle
X(61738) = pole of line {110, 112} with respect to the orthocentroidal circle
X(61738) = pole of line {5112, 16311} with respect to the Kiepert hyperbola

X(61739) = X(6)X(67)∩X(22)X(161)

Barycentrics    a^12-3*a^10*(b^2+c^2)-2*(b^2-c^2)^4*(b^2+c^2)^2-3*a^4*(b^2-c^2)^2*(b^4+c^4)-2*a^6*(b^2+c^2)*(b^4+c^4)+2*a^8*(2*b^4+b^2*c^2+2*c^4)+a^2*(b^2-c^2)^2*(5*b^6+3*b^4*c^2+3*b^2*c^4+5*c^6) : :
X(61739) = -2*X[13352]+5*X[40686], 2*X[18381]+X[37494]

X(61739) lies on these lines: {6, 67}, {22, 161}, {52, 23325}, {68, 12084}, {154, 61644}, {157, 35442}, {381, 10628}, {511, 1853}, {1657, 3357}, {2777, 18474}, {2781, 61700}, {3448, 44883}, {3580, 34118}, {5189, 61044}, {5894, 41428}, {6145, 9927}, {6146, 23328}, {6293, 12162}, {6515, 31074}, {9306, 19131}, {9937, 32539}, {10117, 18440}, {10606, 17702}, {11430, 26944}, {12429, 32345}, {13352, 40686}, {15139, 37638}, {18381, 37494}, {20300, 37644}, {23329, 61713}, {23332, 61658}, {32316, 40914}, {35260, 52300}, {36749, 49108}, {37488, 37972}, {41586, 51756}, {44077, 61691}, {59778, 61683}, {61702, 61724}

X(61739) = reflection of X(i) in X(j) for these {i,j}: {154, 61644}, {161, 61685}, {61685, 343}
X(61739) = pole of line {15577, 22151} with respect to the Stammler hyperbola
X(61739) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {343, 1503, 61685}, {1503, 61685, 161}, {26869, 61737, 61735}

X(61740) = X(4)X(5692)∩X(79)X(6849)

Barycentrics    a*(a^4*(b+c)+2*a^2*b*c*(b+c)+a*(b-c)^2*(2*b+c)*(b+2*c)+a^3*(-2*b^2+b*c-2*c^2)-(b-c)^2*(b+c)*(b^2+6*b*c+c^2)) : :
X(61740) = 2*X[4]+X[5692], -X[165]+4*X[10157], 2*X[210]+X[50865], -2*X[354]+5*X[30308], 2*X[392]+X[5691], 8*X[546]+X[5693], -5*X[3091]+2*X[5883], X[3543]+2*X[10176], 7*X[3832]+2*X[31803], -10*X[3843]+X[37625], -14*X[3851]+5*X[15016], -11*X[3855]+2*X[5884] and many others

X(61740) lies on these lines: {4, 5692}, {11, 60901}, {36, 18540}, {79, 6849}, {165, 10157}, {210, 50865}, {226, 41858}, {354, 30308}, {381, 2771}, {392, 5691}, {517, 14269}, {518, 1699}, {546, 5693}, {758, 3839}, {908, 5696}, {971, 7988}, {1012, 15015}, {1750, 13615}, {1768, 16112}, {2772, 5640}, {2779, 16261}, {2801, 9779}, {2802, 59387}, {3091, 5883}, {3305, 41853}, {3452, 41866}, {3543, 10176}, {3651, 41872}, {3832, 31803}, {3843, 37625}, {3851, 15016}, {3855, 5884}, {3873, 50802}, {3877, 34648}, {3898, 50864}, {3919, 50803}, {3956, 34632}, {4679, 31672}, {4860, 60884}, {5119, 18529}, {5252, 30294}, {5506, 37426}, {5533, 12831}, {5536, 5779}, {5537, 11372}, {5697, 18480}, {5903, 18492}, {5904, 18483}, {6896, 16127}, {6919, 16120}, {6945, 59419}, {7308, 41860}, {7701, 37524}, {7987, 16866}, {7989, 12688}, {7994, 10241}, {8165, 12446}, {9581, 30290}, {9589, 58631}, {9812, 15064}, {9856, 37714}, {9947, 11531}, {9955, 50190}, {10057, 18516}, {10171, 11220}, {10883, 21635}, {10980, 17604}, {11108, 16143}, {11424, 43609}, {12528, 12571}, {12684, 35010}, {13257, 42356}, {15049, 15305}, {18398, 40263}, {18761, 21842}, {25542, 41854}, {28451, 58221}, {30315, 31787}, {30326, 41338}, {30827, 41871}, {31318, 48897}, {35258, 44425}, {36002, 60911}, {36835, 58834}, {37234, 37571}, {38054, 41561}, {61720, 61729}

X(61740) = reflection of X(i) in X(j) for these {i,j}: {165, 61686}, {61686, 10157}
X(61740) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {381, 61705, 5902}, {3091, 31871, 15071}, {9812, 15064, 15104}, {18492, 31937, 5903}

X(61741) = X(1)X(7755)∩X(172)X(515)

Barycentrics    a^4+a^3*(b+c)-a*(b-c)^2*(b+c)+(b^2-c^2)^2+a^2*(b^2+b*c+c^2) : :

X(61741) lies on these lines: {1, 7755}, {6, 21044}, {115, 61703}, {172, 515}, {1699, 54382}, {1837, 7296}, {2275, 17728}, {2276, 26446}, {3017, 61730}, {3336, 7765}, {3496, 23903}, {3721, 33152}, {4124, 11269}, {5007, 37702}, {5179, 60697}, {5254, 11246}, {5309, 5902}, {5332, 5722}, {5441, 35007}, {5442, 31652}, {5790, 54416}, {7751, 30119}, {7753, 37718}, {7856, 30139}, {9598, 9778}, {17469, 21928}, {21331, 33133}, {21332, 33140}, {33142, 50014}, {61699, 61704}

X(61741) = reflection of X(i) in X(j) for these {i,j}: {172, 61688}
X(61741) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {515, 61688, 172}

X(61742) = X(2)X(13207)∩X(6)X(110)

Barycentrics    a^2*(-2*b^2*c^2*(b^4-3*b^2*c^2+c^4)+a^4*(2*b^4+b^2*c^2+2*c^4)+a^2*(-2*b^6+3*b^4*c^2+3*b^2*c^4-2*c^6)) : :
X(61742) =

X(61742) lies on circumconic {{A, B, C, X(111), X(54830)}} and on these lines: {2, 13207}, {6, 110}, {51, 14614}, {183, 511}, {263, 22329}, {373, 11174}, {381, 6785}, {385, 11002}, {512, 11317}, {599, 33873}, {1003, 3111}, {2387, 44543}, {2979, 8556}, {3060, 8667}, {3511, 32447}, {6800, 60514}, {7610, 11673}, {7998, 15271}, {8705, 9832}, {8860, 47638}, {9730, 39646}, {11163, 34383}, {11168, 34095}, {13137, 35930}, {31489, 61101}, {32819, 35687}, {61102, 61136}

X(61742) = reflection of X(i) in X(j) for these {i,j}: {183, 61689}, {34095, 11168}
X(61742) = pole of line {11634, 48961} with respect to the Kiepert parabola
X(61742) = pole of line {3266, 22712} with respect to the Wallace hyperbola
X(61742) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5640, 46303, 6}, {16776, 61675, 5640}

X(61743) = X(2)X(51)∩X(6)X(67)

Barycentrics    a^6-2*a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2) : :
X(61743) = -4*X[140]+X[37478], X[184]+2*X[427], -7*X[3526]+X[37494], -X[8541]+4*X[51744], X[11442]+2*X[34986], 2*X[18475]+X[31723], -4*X[25555]+X[44493], -X[54384]+4*X[58550]

X(61743) lies on these lines: {2, 51}, {3, 3574}, {4, 1495}, {5, 1092}, {6, 67}, {22, 29317}, {23, 48901}, {24, 10182}, {25, 53023}, {30, 13394}, {39, 14003}, {54, 18381}, {69, 11056}, {74, 55293}, {110, 3818}, {113, 31861}, {140, 37478}, {141, 30747}, {154, 5064}, {156, 33332}, {159, 38396}, {182, 858}, {184, 427}, {185, 3541}, {264, 46247}, {265, 7579}, {275, 52249}, {323, 34507}, {343, 34380}, {378, 2777}, {381, 5642}, {389, 37119}, {428, 10192}, {468, 5480}, {475, 58889}, {542, 11187}, {569, 13371}, {574, 47526}, {575, 18911}, {576, 3580}, {578, 1594}, {597, 47097}, {647, 54991}, {868, 5475}, {973, 6101}, {1147, 5576}, {1199, 23294}, {1204, 12233}, {1209, 16266}, {1316, 3258}, {1344, 14499}, {1345, 14500}, {1346, 13414}, {1347, 13415}, {1351, 37638}, {1352, 3292}, {1368, 19131}, {1370, 22352}, {1493, 18356}, {1531, 49669}, {1568, 9818}, {1593, 43831}, {1595, 16654}, {1597, 51403}, {1656, 10982}, {1692, 15820}, {1724, 27685}, {1843, 61683}, {1853, 11402}, {1899, 8889}, {1907, 16252}, {1970, 46243}, {1974, 54381}, {1989, 18575}, {1993, 5965}, {1994, 23293}, {1995, 5972}, {2452, 6070}, {2502, 18424}, {2549, 30516}, {2682, 57594}, {3079, 60137}, {3088, 5656}, {3098, 7495}, {3148, 35282}, {3231, 7746}, {3448, 7703}, {3526, 37494}, {3527, 5070}, {3549, 45186}, {3564, 45303}, {3567, 6143}, {3589, 22112}, {3613, 53577}, {3618, 15812}, {3690, 56366}, {3767, 40130}, {3781, 56464}, {3784, 56462}, {3796, 34609}, {3845, 35266}, {3937, 56445}, {3972, 35922}, {4993, 54062}, {5012, 31074}, {5085, 31152}, {5092, 16063}, {5097, 37644}, {5108, 15539}, {5133, 9306}, {5159, 18583}, {5189, 15080}, {5422, 30744}, {5446, 6639}, {5449, 36749}, {5462, 6640}, {5611, 40710}, {5615, 40709}, {5654, 15030}, {5663, 44287}, {5889, 43581}, {5890, 10628}, {5891, 60763}, {5925, 34563}, {5946, 34128}, {5967, 51943}, {6090, 10516}, {6102, 15739}, {6241, 35482}, {6353, 44106}, {6619, 56346}, {6644, 22109}, {6755, 53506}, {6759, 15559}, {6776, 44109}, {6800, 29012}, {6997, 59543}, {7378, 31383}, {7391, 29323}, {7399, 43652}, {7403, 9820}, {7492, 48880}, {7493, 31670}, {7499, 21167}, {7505, 10110}, {7506, 43839}, {7507, 11425}, {7514, 51392}, {7517, 44516}, {7519, 32237}, {7533, 10546}, {7539, 17811}, {7547, 13403}, {7558, 15644}, {7570, 42786}, {7574, 14805}, {7576, 11202}, {7577, 14644}, {7592, 12242}, {7752, 56430}, {7833, 35277}, {7834, 54332}, {7855, 52906}, {8371, 55265}, {8541, 51744}, {8901, 34845}, {9148, 14397}, {9707, 13419}, {9730, 18281}, {9777, 26958}, {9781, 14940}, {9822, 28408}, {9927, 37472}, {9971, 47450}, {10095, 60780}, {10170, 14787}, {10301, 15448}, {10545, 42785}, {10564, 50008}, {10601, 30771}, {10796, 11007}, {10984, 23335}, {11003, 31857}, {11004, 41724}, {11178, 40112}, {11206, 44108}, {11232, 25738}, {11245, 23332}, {11284, 59767}, {11412, 32352}, {11433, 34565}, {11438, 37118}, {11442, 34986}, {11472, 15063}, {11547, 42400}, {11572, 19467}, {11645, 31105}, {11818, 51393}, {11935, 23236}, {12039, 19510}, {13160, 13346}, {13451, 34330}, {13567, 15004}, {13860, 47200}, {14041, 35301}, {14791, 37513}, {14865, 22802}, {15018, 30745}, {15019, 15059}, {15066, 24206}, {15078, 48375}, {15107, 52300}, {15122, 37470}, {15139, 51756}, {16165, 44263}, {17810, 37453}, {17825, 31255}, {17845, 32340}, {18394, 43818}, {18420, 51394}, {18440, 24981}, {18474, 32423}, {18475, 31723}, {18488, 32139}, {18580, 32110}, {18653, 36685}, {18906, 37804}, {18912, 32767}, {18950, 34566}, {19136, 47455}, {19357, 61139}, {19577, 32451}, {19924, 47596}, {20191, 37490}, {20791, 44450}, {21460, 30786}, {21637, 41719}, {21850, 32269}, {22111, 24855}, {23039, 48411}, {23042, 44078}, {23291, 44111}, {23327, 40673}, {25555, 44493}, {26864, 36990}, {26913, 34545}, {27687, 43531}, {29181, 44210}, {30685, 39486}, {30769, 51171}, {30775, 59373}, {31099, 46264}, {31267, 44091}, {31283, 43817}, {32111, 35484}, {32216, 47352}, {32601, 54050}, {35235, 44127}, {35264, 61681}, {35278, 55008}, {35717, 45062}, {35930, 51389}, {36794, 57532}, {37242, 51372}, {37439, 53415}, {37440, 58407}, {37643, 44107}, {37779, 38397}, {37899, 51163}, {37900, 48904}, {37981, 44080}, {38072, 47597}, {38136, 44212}, {40250, 51430}, {40913, 52990}, {40916, 58445}, {41330, 57307}, {41585, 47447}, {42873, 51358}, {43462, 60693}, {43577, 47524}, {44265, 51993}, {44882, 46517}, {45544, 47632}, {45545, 47631}, {47296, 52293}, {47311, 51737}, {47328, 61685}, {47629, 51732}, {49671, 51391}, {50659, 59768}, {53017, 57533}, {54384, 58550}, {61702, 61713}

X(61743) = midpoint of X(i) and X(j) for these {i,j}: {427, 61690}, {6800, 31133}, {14644, 15463}
X(61743) = reflection of X(i) in X(j) for these {i,j}: {184, 61690}, {19131, 38110}, {22109, 38793}, {35268, 13394}, {54374, 21167}, {61644, 2}, {61690, 23292}
X(61743) = pole of line {1637, 1989} with respect to the orthocentroidal circle
X(61743) = pole of line {9979, 42651} with respect to the polar circle
X(61743) = pole of line {42659, 45907} with respect to the Brocard inellipse
X(61743) = pole of line {2393, 5890} with respect to the Jerabek hyperbola
X(61743) = pole of line {468, 3815} with respect to the Kiepert hyperbola
X(61743) = pole of line {182, 5890} with respect to the Stammler hyperbola
X(61743) = pole of line {23878, 47138} with respect to the Steiner inellipse
X(61743) = pole of line {183, 37804} with respect to the Wallace hyperbola
X(61743) = intersection, other than A, B, C, of circumconics {{A, B, C, X(67), X(42313)}}, {{A, B, C, X(262), X(8791)}}, {{A, B, C, X(3431), X(54032)}}, {{A, B, C, X(14165), X(18575)}}
X(61743) = barycentric product X(i)*X(j) for these (i, j): {141, 58852}
X(61743) = barycentric quotient X(i)/X(j) for these (i, j): {58852, 83}
X(61743) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14561, 373}, {2, 14853, 61506}, {2, 20423, 32225}, {2, 3060, 61646}, {2, 51, 61645}, {2, 511, 61644}, {2, 61506, 61691}, {5, 11064, 5651}, {6, 17847, 15135}, {6, 26869, 61712}, {30, 13394, 35268}, {54, 52295, 18381}, {110, 5169, 3818}, {125, 61712, 26869}, {184, 427, 11550}, {427, 61690, 1503}, {428, 10192, 44082}, {468, 5480, 34417}, {578, 23325, 12022}, {858, 14389, 182}, {1351, 37638, 41586}, {1352, 37645, 3292}, {1368, 37649, 43650}, {1503, 23292, 61690}, {1503, 61690, 184}, {1594, 12022, 23325}, {1899, 11427, 13366}, {1993, 31236, 21243}, {3589, 30739, 22112}, {3618, 16051, 54012}, {5094, 26869, 61735}, {5159, 18583, 37648}, {5169, 59771, 110}, {5189, 15080, 48898}, {5972, 19130, 1995}, {6800, 31133, 29012}, {7507, 11425, 21659}, {7577, 15033, 18390}, {7703, 11422, 3448}, {8889, 11427, 1899}, {9777, 52298, 26958}, {12242, 20299, 7592}, {14853, 61506, 51}, {26869, 61735, 125}, {32237, 48895, 7519}, {32767, 37505, 18912}, {40112, 53843, 11178}, {51744, 54347, 8541}, {53023, 61680, 25}

X(61744) = X(4)X(54)∩X(30)X(51)

Barycentrics    2*a^10-4*a^8*(b^2+c^2)+a^4*(b^2-c^2)^2*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)+a^2*(b^2-c^2)^2*(b^4-6*b^2*c^2+c^4)+a^6*(b^4+10*b^2*c^2+c^4) : :
X(61744) = X[3]+2*X[12897], -X[5]+4*X[15807], X[52]+2*X[52070], X[185]+2*X[1885], 2*X[389]+X[18560], -5*X[3522]+8*X[44862], -5*X[3567]+8*X[40240], 2*X[3627]+X[11750], -7*X[3832]+X[12278], -5*X[3843]+2*X[45286], 2*X[5446]+X[18563], 2*X[6146]+X[11381] and many others

X(61744) lies on circumconic {{A, B, C, X(275), X(11744)}} and on these lines: {3, 12897}, {4, 54}, {5, 15807}, {6, 1562}, {20, 15053}, {30, 51}, {52, 52070}, {115, 52438}, {125, 378}, {182, 44440}, {185, 1885}, {235, 10192}, {376, 61506}, {381, 5642}, {382, 10982}, {389, 18560}, {399, 14049}, {403, 11430}, {427, 13851}, {436, 34170}, {511, 52069}, {539, 18435}, {542, 15305}, {546, 51425}, {549, 61691}, {567, 31726}, {970, 52072}, {1204, 39571}, {1495, 1596}, {1503, 32062}, {1514, 44109}, {1533, 44276}, {1568, 13352}, {1593, 1853}, {1595, 11572}, {1597, 11550}, {1899, 13399}, {1906, 34782}, {1907, 41362}, {2777, 5890}, {3091, 59543}, {3146, 15019}, {3357, 18912}, {3520, 10193}, {3522, 44862}, {3527, 5073}, {3543, 11179}, {3567, 40240}, {3575, 44079}, {3627, 11750}, {3819, 54040}, {3830, 44407}, {3832, 12278}, {3843, 45286}, {3845, 30522}, {3917, 34664}, {5012, 52403}, {5064, 18405}, {5169, 18392}, {5198, 17845}, {5309, 6793}, {5446, 18563}, {5448, 37472}, {5449, 14130}, {5480, 44102}, {5651, 18537}, {5663, 61713}, {5876, 43581}, {5895, 34564}, {5943, 38323}, {6000, 12022}, {6146, 11381}, {6240, 10110}, {6644, 16163}, {6816, 43652}, {7527, 21243}, {7577, 7687}, {7592, 22802}, {7728, 15087}, {7731, 22950}, {9703, 16534}, {9729, 52071}, {9781, 34797}, {9825, 27355}, {10018, 46265}, {10112, 12111}, {10113, 39504}, {10116, 18439}, {10151, 23292}, {10182, 37943}, {10201, 39242}, {10224, 43865}, {10263, 32352}, {10298, 32223}, {10594, 34785}, {10605, 10990}, {10606, 26869}, {10625, 52073}, {10733, 15462}, {11064, 44920}, {11250, 43817}, {11410, 26958}, {11422, 38791}, {11425, 37197}, {11438, 35481}, {11439, 34799}, {11799, 18475}, {12038, 59648}, {12162, 12370}, {12225, 13598}, {12295, 44263}, {12605, 45186}, {12900, 61127}, {13142, 14531}, {13434, 50009}, {13474, 34224}, {13491, 43575}, {13567, 21663}, {13568, 50709}, {13596, 25739}, {14516, 44870}, {14865, 20299}, {15030, 44665}, {15063, 18445}, {15559, 18383}, {15739, 45959}, {16072, 37497}, {16836, 44458}, {16881, 34798}, {17712, 17800}, {17810, 37196}, {18379, 33332}, {18381, 35502}, {18382, 46026}, {18451, 24981}, {18474, 31861}, {18531, 51360}, {18533, 34417}, {18916, 20427}, {18950, 54050}, {19124, 23327}, {19153, 53023}, {23048, 39588}, {23515, 61736}, {25563, 26917}, {29181, 44935}, {32046, 44271}, {32137, 45731}, {32225, 44285}, {32621, 36990}, {34783, 58806}, {34796, 61677}, {35240, 46730}, {35473, 44673}, {35478, 43608}, {37458, 44106}, {37481, 43577}, {37643, 60765}, {37648, 44241}, {38789, 55039}, {41586, 49669}, {43394, 44235}, {43595, 43844}, {46030, 51393}, {46466, 61719}, {47336, 61619}, {48901, 52842}, {54012, 61113}, {54994, 61644}

X(61744) = midpoint of X(i) and X(j) for these {i,j}: {1885, 11245}
X(61744) = reflection of X(i) in X(j) for these {i,j}: {185, 11245}, {11245, 12241}, {3917, 34664}, {38323, 5943}, {44458, 16836}, {51, 16657}, {54040, 3819}
X(61744) = perspector of circumconic {{A, B, C, X(16813), X(22239)}}
X(61744) = pole of line {235, 389} with respect to the Jerabek hyperbola
X(61744) = pole of line {6748, 10151} with respect to the Kiepert hyperbola
X(61744) = pole of line {9033, 12077} with respect to the orthic inconic
X(61744) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 11424, 3574}, {4, 12289, 13419}, {4, 13403, 21659}, {4, 15033, 18388}, {4, 184, 51403}, {4, 19467, 26883}, {4, 21659, 61139}, {4, 34786, 32340}, {4, 43818, 1614}, {4, 578, 43831}, {30, 16657, 51}, {378, 61701, 23329}, {1597, 18396, 11550}, {1885, 11245, 15311}, {6146, 13488, 11381}, {11245, 15311, 185}, {18390, 23329, 61701}, {26917, 35475, 25563}

X(61745) = X(39)X(32547)∩X(754)X(2979)

Barycentrics    a^2*(a^4*(b^2-c^2)^2+b^2*c^2*(b^4-b^2*c^2+c^4)-a^2*(b^6+b^4*c^2+b^2*c^4+c^6)) : :
X(61745) = -4*X[39]+X[32547], 2*X[4173]+X[7823], -3*X[5640]+4*X[7753], -2*X[7811]+3*X[7998], -5*X[7921]+2*X[40951]

X(61745) lies on these lines: {39, 32547}, {110, 52438}, {381, 46303}, {512, 7757}, {542, 15305}, {754, 2979}, {2387, 3060}, {3491, 7787}, {3917, 9939}, {4173, 7823}, {5167, 7766}, {5309, 6787}, {5640, 7753}, {5890, 61734}, {5891, 34623}, {6786, 33246}, {7737, 61101}, {7811, 7998}, {7837, 55005}, {7921, 40951}, {7926, 14962}, {9517, 52693}, {10546, 13210}, {11361, 34383}, {13571, 58212}, {34734, 54042}

X(61745) = reflection of X(i) in X(j) for these {i,j}: {3060, 7812}, {34623, 5891}, {34734, 54042}, {61727, 7753}, {9939, 3917}
X(61745) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2387, 7812, 3060}, {7753, 61727, 5640}

X(61746) = X(944)X(1706) n X(3445)X(46946)

Barycentrics    a*(a^9-5*a^8*(b+c)-(b+c)*(b^2-c^2)^4-8*a^7*(b^2-8*b*c+c^2)+16*a^6*(b+c)*(b^2-6*b*c+c^2)+a*(b-c)^2*(b^2-c^2)^2*(5*b^2-6*b*c+5*c^2)+2*a^5*(b^2-6*b*c+c^2)*(9*b^2-34*b*c+9*c^2)-2*a^4*(b+c)*(9*b^4+9*c^4-10*b*c*(8*b^2-11*b*c+8*c^2))-16*a^3*(b^6+c^6-2*b*c*(4*b^4+4*c^4-b*c*(14*b^2-11*b*c+14*c^2)))+8*a^2*(b+c)*(b^6+c^6-b*c*(8*b^4+8*c^4-b*c*(25*b^2-28*b*c+25*c^2)))) : :

See Tran Viet Hung and César Lozada, Romantics of Geometry - Feb 27, 2024.

X(61746) lies on these lines: {944, 1706}, {3445, 46946}



leftri  Reflected-parallels circles: X(61747) - X(61761)  rightri

This preamble and centers X(61747)-X(61761) were contributed by César Eliud Lozada, February 27, 2024.

The following problem by C. Pohoata is published in AOPS:

Three parallel lines pa, pb, pc pass through the vertices of a triangle ABC. Their reflections in BC, CA, AB, respectively, form a triangle A'B'C'. Find the locus of the incenters of such triangles.

When ABC is acute, the required locus is a circle centered at the circumcenter X(3)-of-ABC and having radius ρ = 2*R. But, as a matter of fact, similar constructions with centers X(n), for 1 ≤ n ≤ 1000, result each in a circle as locus (conjectured and not formally proven yet, but numerically tested). The appearance of (i, j) in the following list means that the locus of centers X(i)-of-A'B'C' is a circle with center X(j) wrt ABC:

(1, 3), (2, 61747), (3, 156), (4, 9927), (5, 13406), (6, 61748), (7, 34507), (8, 22802), (9, 34117), (10, 61749), (11, 5), (12, 61750), (20, 61751), (21, 10274), (35, 1614), (36, 110), (40, 32139), (46, 11441), (55, 61752), (56, 61753), (57, 15068), (65, 5876), (79, 2888), (80, 4), (84, 58726), (90, 2904), (100, 6759), (101, 61754), (104, 1147), (105, 61755), (108, 61756), (109, 61757), (110, 61758), (113, 61759), (117, 61760), (118, 61761), (119, 15761), (149, 18381), (177, 5694), (191, 17824), (214, 10282), (238, 1576), (354, 15067), (355, 44279), (496, 49673), (551, 10182), (942, 11591), (946, 5449), (954, 19127), (960, 41589)

The locus of X(i)-of-A'B'C' is denoted here as the reflected-parallels circle of X(i). It must be taken in account that the given results are valid as long as ABC is acute.

underbar

X(61747) = CENTER OF THE REFLECTED-PARALLELS CIRCLE OF X(2)

Barycentrics    a^10-4*(b^2+c^2)*a^8+5*(b^4+c^4)*a^6-(b^4-c^4)*(b^2-c^2)*a^4-2*(b^2-c^2)^2*(b^4-b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2-c^2)^3 : :
X(61747) = 3*X(2)+X(5656) = 2*X(2)-X(23329) = 5*X(3)+X(5895) = 7*X(3)-X(5925) = X(3)-2*X(10182) = 2*X(3)+X(22802) = X(3)-3*X(61680) = X(3)+2*X(61749) = X(4)+2*X(10282) = 2*X(4)+X(34785) = X(4)+3*X(35260) = 2*X(5)+X(6759) = X(5)+2*X(16252) = 4*X(5)-X(18381) = 2*X(5)-X(23325) = X(26)+2*X(5448) = X(64)-7*X(3526) = X(64)-4*X(25563) = 2*X(113)+X(13289) = 2*X(140)+X(2883) = 4*X(140)-X(3357) = 10*X(140)-X(15105) = 2*X(140)-X(23328) = 2*X(206)+X(3818) = 4*X(206)-X(34776) = 7*X(3526)-4*X(25563) = 2*X(3818)+X(34776) = 2*X(5656)+3*X(23329) = 2*X(5895)-5*X(22802) = X(5895)-10*X(61749) = 2*X(5925)+7*X(22802) = 4*X(5972)-X(13293) = X(6759)-4*X(16252) = 2*X(6759)+X(18381) = 4*X(10182)+X(22802) = 2*X(10182)-3*X(61680) = 2*X(10192)-X(11202) = X(10192)-2*X(61606) = 4*X(10282)-X(34785) = 2*X(10282)-3*X(35260) = X(11202)-4*X(61606) = X(11744)+2*X(25564) = X(11744)+5*X(38794) = 3*X(14643)-X(15131) = 8*X(16252)+X(18381) = 4*X(16252)+X(23325) = X(18381)-2*X(23325) = X(22802)+6*X(61680) = X(22802)-4*X(61749) = X(23358)+2*X(32364)

X(61747) lies on these lines: {2, 5656}, {3, 113}, {4, 1495}, {5, 182}, {13, 11244}, {14, 11243}, {20, 1531}, {22, 1568}, {24, 43831}, {25, 18388}, {26, 5448}, {30, 10192}, {52, 61685}, {54, 44958}, {64, 3526}, {125, 11456}, {133, 41372}, {140, 2883}, {141, 34779}, {146, 11454}, {154, 381}, {155, 5965}, {156, 9927}, {159, 19130}, {184, 403}, {185, 7505}, {233, 17849}, {235, 578}, {378, 51403}, {382, 17821}, {389, 3542}, {427, 16654}, {468, 11438}, {511, 5654}, {541, 16219}, {542, 14852}, {546, 34782}, {547, 23332}, {548, 51491}, {549, 11204}, {550, 5893}, {576, 47581}, {597, 10250}, {631, 5878}, {632, 6696}, {1092, 54040}, {1147, 15761}, {1154, 44278}, {1181, 26869}, {1204, 10018}, {1209, 61739}, {1352, 41719}, {1498, 1656}, {1594, 16658}, {1596, 23292}, {1598, 20987}, {1614, 13198}, {1660, 46030}, {1843, 3089}, {1853, 5055}, {1971, 5475}, {2192, 31479}, {2393, 5476}, {2781, 15067}, {2790, 14640}, {2917, 18378}, {3016, 7746}, {3060, 46451}, {3090, 14216}, {3091, 9833}, {3098, 16618}, {3153, 26881}, {3462, 14249}, {3523, 20427}, {3524, 46265}, {3525, 6225}, {3529, 32903}, {3530, 5894}, {3534, 61721}, {3541, 13474}, {3545, 11206}, {3547, 11793}, {3548, 46850}, {3549, 5907}, {3574, 10594}, {3582, 32065}, {3584, 11189}, {3628, 6247}, {3734, 59706}, {3788, 59530}, {3796, 16072}, {3830, 61711}, {3843, 17845}, {3848, 6001}, {3850, 41362}, {3851, 14530}, {5054, 10193}, {5056, 14864}, {5066, 23324}, {5067, 12324}, {5070, 12315}, {5071, 32064}, {5079, 34780}, {5092, 31267}, {5167, 38227}, {5198, 38396}, {5449, 32139}, {5480, 61610}, {5655, 44751}, {5876, 41589}, {5890, 37943}, {5891, 41580}, {5946, 44270}, {6053, 37638}, {6143, 12290}, {6241, 14940}, {6564, 10534}, {6565, 10533}, {6622, 14912}, {6639, 12162}, {6640, 10575}, {6697, 42786}, {6793, 8743}, {6794, 39575}, {6800, 36518}, {6823, 59659}, {6842, 14925}, {7387, 29317}, {7395, 32321}, {7399, 35283}, {7503, 32401}, {7507, 13419}, {7516, 32600}, {7526, 44516}, {7530, 15577}, {7545, 56924}, {7547, 61139}, {7552, 10628}, {7576, 44082}, {7577, 11550}, {7592, 34564}, {7687, 18396}, {7689, 10020}, {7706, 12106}, {7729, 40280}, {7741, 26888}, {7951, 10535}, {8549, 25555}, {8550, 47457}, {8567, 15720}, {8918, 8919}, {9306, 15760}, {9544, 50435}, {9707, 12140}, {9737, 59869}, {9818, 58447}, {9820, 13346}, {9934, 32743}, {9955, 40660}, {9956, 40658}, {10024, 10539}, {10125, 32138}, {10168, 10249}, {10170, 34146}, {10181, 10197}, {10201, 13754}, {10254, 10540}, {10303, 12250}, {10576, 12970}, {10577, 12964}, {10605, 37453}, {10675, 16967}, {10676, 16966}, {10982, 12242}, {11064, 37480}, {11232, 41593}, {11241, 35823}, {11242, 35822}, {11250, 58435}, {11381, 37119}, {11426, 40240}, {11449, 50009}, {11477, 41583}, {11799, 13352}, {12024, 31804}, {12082, 51360}, {12083, 51392}, {12084, 43839}, {12111, 58805}, {12233, 21841}, {12241, 44960}, {12900, 15113}, {13093, 46219}, {13336, 50143}, {13383, 22660}, {13394, 34664}, {13403, 19357}, {13491, 34128}, {13567, 37942}, {13665, 17820}, {13785, 17819}, {13851, 44110}, {13997, 40557}, {14003, 44437}, {14076, 48669}, {14790, 29323}, {14791, 48898}, {14848, 17813}, {14915, 18281}, {15043, 21451}, {15062, 32415}, {15068, 16534}, {15069, 56565}, {15125, 43586}, {15340, 50718}, {15448, 37458}, {15585, 21850}, {15644, 59349}, {15647, 19506}, {15686, 50709}, {15694, 35450}, {15873, 51734}, {16197, 21167}, {16239, 61540}, {16808, 30403}, {16809, 30402}, {17826, 42125}, {17827, 42128}, {18338, 42426}, {18358, 34774}, {18377, 32391}, {18418, 18475}, {18440, 19132}, {18451, 21243}, {18491, 18621}, {18583, 23326}, {18931, 52290}, {19149, 24206}, {19479, 20773}, {20186, 45693}, {20417, 52292}, {23041, 29012}, {25561, 31166}, {32046, 44235}, {32111, 37118}, {32223, 37489}, {32351, 50136}, {32379, 40276}, {34224, 35487}, {34380, 61607}, {35018, 44762}, {35228, 48880}, {36989, 48889}, {37473, 47450}, {39170, 56397}, {40285, 49108}, {43394, 44271}, {44282, 45956}, {44440, 51394}, {44666, 46703}, {44667, 46702}, {44883, 58450}, {47391, 61681}, {51385, 56297}, {55857, 58795}, {61750, 61753}

X(61747) = midpoint of X(i) and X(j) for these (i, j): {154, 381}, {159, 23049}, {1352, 41719}, {1853, 32063}, {2883, 23328}, {3534, 61721}, {5878, 54050}, {5891, 41580}, {6759, 23325}, {10182, 61749}, {19149, 61737}
X(61747) = reflection of X(i) in X(j) for these (i, j): (3, 10182), (549, 58434), (3357, 23328), (10192, 61606), (10249, 10168), (10250, 597), (10606, 10193), (11202, 10192), (11204, 549), (15113, 12900), (18376, 381), (18381, 23325), (23048, 5476), (23049, 19130), (23324, 5066), (23325, 5), (23326, 18583), (23328, 140), (23329, 2), (23332, 547), (47391, 61681), (61646, 10201), (61737, 24206)
X(61747) = pole of the line {574, 53420} with respect to the Evans conic
X(61747) = pole of the line {5890, 35481} with respect to the Jerabek circumhyperbola
X(61747) = pole of the line {32, 6749} with respect to the Kiepert circumhyperbola
X(61747) = pole of the line {2071, 2979} with respect to the Stammler hyperbola
X(61747) = pole of the line {33294, 41077} with respect to the Steiner inellipse
X(61747) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {154, 381, 37926}, {399, 6069, 38577}
X(61747) = X(10182)-of-X3-ABC reflections triangle
X(61747) = X(18405)-of-Ehrmann-mid triangle
X(61747) = X(23325)-of-Johnson triangle
X(61747) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (3, 61680, 10182), (3, 61749, 22802), (4, 10282, 34785), (5, 6759, 18381), (5, 16252, 6759), (5, 46261, 3818), (5, 46817, 46261), (64, 3526, 25563), (140, 2883, 3357), (156, 9927, 61751), (156, 13406, 9927), (184, 403, 18390), (206, 3818, 34776), (206, 46261, 6759), (235, 61690, 16657), (546, 34782, 34786), (1498, 1656, 20299), (3090, 14216, 32767), (3091, 9833, 18383), (5054, 10606, 10193), (5055, 32063, 1853), (5070, 12315, 40686), (5890, 37943, 61645), (7552, 11459, 61644), (7577, 14157, 11550), (9707, 35488, 21659), (10254, 10540, 18474), (10605, 37453, 44673), (11744, 38794, 25564), (12315, 40686, 52102), (13383, 22660, 46730), (14862, 20299, 1498), (15647, 61574, 19506), (15720, 48672, 8567), (15760, 51425, 9306), (15761, 61608, 1147), (16657, 61690, 578), (18383, 50414, 9833), (19357, 37197, 13403)

X(61748) = CENTER OF THE REFLECTED-PARALLELS CIRCLE OF X(6)

Barycentrics    a^2*(a^10-4*(b^2+c^2)*a^8+6*(b^4+b^2*c^2+c^4)*a^6-(b^2+c^2)*(2*b^2-3*b*c+2*c^2)*(2*b^2+3*b*c+2*c^2)*a^4+(b^4-c^4)^2*a^2+(b^4-c^4)*(b^2-c^2)*b^2*c^2) : :

X(61748) lies on these lines: {3, 1177}, {4, 50}, {97, 154}, {112, 15274}, {156, 32438}, {157, 44668}, {511, 19156}, {571, 5480}, {577, 1503}, {1199, 13337}, {2965, 14853}, {3060, 56308}, {3357, 14634}, {4558, 15069}, {5063, 8550}, {5065, 12007}, {7592, 61714}, {7669, 15073}, {8883, 10982}, {9756, 10313}, {13749, 26916}, {14249, 16813}, {15582, 42671}, {18121, 43388}, {18374, 37114}, {19149, 36748}, {23200, 51739}, {38397, 47053}, {50649, 52144}

X(61749) = CENTER OF THE REFLECTED-PARALLELS CIRCLE OF X(10)

Barycentrics    2*(b^2+c^2)*a^8-(5*b^4-4*b^2*c^2+5*c^4)*a^6+3*(b^4-c^4)*(b^2-c^2)*a^4+(b^4-4*b^2*c^2+c^4)*(b^2-c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)^3 : :
X(61749) = 3*X(2)+X(5878) = 9*X(2)-X(12250) = 3*X(3)+X(5895) = 5*X(3)-X(5925) = 2*X(3)-3*X(10182) = 5*X(3)-9*X(61680) = X(3)-3*X(61747) = 3*X(4)+X(9833) = 5*X(4)+3*X(11206) = X(4)+2*X(14862) = 3*X(4)-X(34786) = 2*X(4)+X(45185) = 3*X(5)-X(6247) = 2*X(5)-X(20299) = 5*X(5)-3*X(23332) = 3*X(5)-2*X(32767) = 4*X(5)-X(52102) = 3*X(3357)-X(12250) = X(3357)-2*X(25563) = 5*X(3357)+X(54211) = X(3574)-3*X(32364) = 3*X(5878)+X(12250) = X(5878)+2*X(25563) = 5*X(5878)-X(54211) = 5*X(5895)+3*X(5925) = X(5895)-3*X(22802) = X(5895)+9*X(61747) = X(5925)+5*X(22802) = X(5925)-9*X(61680) = 2*X(5972)-X(25564) = 3*X(6759)-X(9833) = 5*X(6759)-3*X(11206) = X(6759)-2*X(14862) = 3*X(6759)+X(34786) = 2*X(6759)-X(45185) = 5*X(9833)-9*X(11206) = X(9833)-6*X(14862) = 2*X(9833)-3*X(45185) = X(10117)+3*X(38789) = 3*X(10182)+2*X(22802) = 5*X(10182)-6*X(61680) = X(10182)-2*X(61747) = 3*X(10274)-X(12254) = 3*X(11206)-10*X(14862) = 6*X(11206)-5*X(45185) = X(11744)+3*X(14643) = X(12250)-6*X(25563) = 5*X(12250)+3*X(54211) = X(13293)-3*X(14643) = 6*X(14862)+X(34786)

X(61749) lies on these lines: {2, 3357}, {3, 113}, {4, 54}, {5, 2883}, {6, 40240}, {20, 1568}, {30, 5448}, {49, 31726}, {52, 11799}, {64, 1656}, {74, 14940}, {110, 50009}, {115, 32445}, {125, 6241}, {133, 14249}, {140, 10193}, {141, 40247}, {146, 11440}, {154, 382}, {156, 17702}, {159, 48901}, {185, 403}, {206, 18569}, {221, 9669}, {235, 389}, {381, 1498}, {399, 17824}, {427, 13474}, {498, 12950}, {499, 12940}, {511, 22660}, {541, 20191}, {542, 8548}, {546, 575}, {547, 61540}, {548, 61606}, {549, 5894}, {550, 10192}, {626, 59530}, {631, 11204}, {632, 23328}, {1092, 44440}, {1181, 18390}, {1204, 7505}, {1209, 6293}, {1352, 34779}, {1495, 6240}, {1514, 1885}, {1531, 12225}, {1533, 3146}, {1539, 5944}, {1562, 39575}, {1594, 11381}, {1596, 10110}, {1657, 17821}, {1660, 44276}, {1853, 3851}, {1906, 45089}, {1971, 7747}, {2072, 10575}, {2192, 9654}, {2781, 11591}, {2917, 5899}, {2929, 43905}, {2937, 23358}, {2979, 45014}, {3090, 6225}, {3091, 5643}, {3521, 45735}, {3525, 54050}, {3526, 10606}, {3529, 35260}, {3530, 58434}, {3542, 11438}, {3545, 12324}, {3583, 26888}, {3585, 10535}, {3627, 34782}, {3628, 6696}, {3818, 19149}, {3830, 14530}, {3832, 34781}, {3843, 18376}, {3845, 41362}, {3850, 14864}, {3855, 32064}, {3858, 23324}, {4846, 22800}, {5054, 8567}, {5055, 13093}, {5070, 35450}, {5072, 58795}, {5079, 61735}, {5449, 5663}, {5462, 46030}, {5476, 8549}, {5480, 32366}, {5576, 16194}, {5654, 13346}, {5790, 7973}, {5876, 10628}, {5885, 6001}, {5886, 12779}, {5890, 44958}, {5907, 15760}, {5943, 41602}, {5965, 15083}, {6053, 11441}, {6102, 11563}, {6146, 10151}, {6285, 7951}, {6564, 12970}, {6565, 12964}, {6623, 22533}, {6699, 60780}, {6816, 37515}, {6823, 11793}, {6923, 14925}, {7355, 7741}, {7393, 9914}, {7403, 46847}, {7526, 58447}, {7547, 11550}, {7552, 10706}, {7575, 34798}, {7577, 12290}, {7687, 11456}, {7689, 10201}, {7706, 13861}, {7816, 59706}, {8976, 19088}, {9707, 35490}, {9730, 36982}, {9818, 32321}, {9899, 54447}, {9934, 19506}, {9968, 34118}, {10018, 21663}, {10024, 12162}, {10112, 18445}, {10113, 45731}, {10125, 32210}, {10226, 58435}, {10254, 18439}, {10263, 43893}, {10296, 41482}, {10533, 35821}, {10534, 35820}, {10576, 49250}, {10577, 49251}, {10675, 16809}, {10676, 16808}, {10990, 11468}, {11189, 37719}, {11230, 12262}, {11243, 16964}, {11244, 16965}, {11250, 43839}, {11449, 16163}, {11455, 52295}, {11464, 13202}, {11572, 16659}, {11585, 46850}, {11750, 18403}, {12111, 12827}, {12112, 54001}, {12163, 61646}, {12241, 44226}, {12293, 61751}, {12370, 47336}, {12897, 44271}, {13160, 15030}, {13352, 31725}, {13363, 32184}, {13367, 18560}, {13371, 14915}, {13382, 13567}, {13399, 23294}, {13487, 45298}, {13488, 23292}, {13565, 14076}, {13568, 21841}, {13630, 32050}, {13754, 15761}, {13851, 34224}, {13951, 19087}, {13997, 57336}, {14363, 51385}, {14561, 41735}, {14810, 58437}, {14855, 37452}, {15028, 54039}, {15053, 21451}, {15058, 41715}, {15060, 44544}, {15072, 18504}, {15105, 55856}, {15274, 51342}, {15532, 20424}, {15559, 32062}, {15575, 49123}, {15577, 29317}, {15578, 58450}, {15583, 38136}, {15704, 32903}, {15712, 46265}, {16198, 16656}, {16534, 61753}, {16655, 23047}, {16657, 37505}, {17508, 31267}, {17826, 42126}, {17827, 42127}, {18308, 20184}, {18325, 37495}, {18377, 44407}, {18404, 44829}, {18420, 44679}, {18475, 52070}, {18480, 40658}, {18570, 44516}, {18809, 35579}, {18914, 37984}, {19106, 30403}, {19107, 30402}, {19153, 32300}, {19357, 44438}, {19362, 22972}, {20423, 34788}, {22793, 40660}, {23041, 48898}, {23042, 46264}, {24206, 34146}, {26882, 34797}, {27371, 38297}, {29181, 61610}, {31101, 52093}, {31829, 59659}, {32065, 37720}, {32125, 50143}, {32137, 39504}, {32396, 60763}, {32601, 52290}, {32743, 49673}, {34114, 46686}, {34148, 52403}, {34170, 56298}, {34563, 44879}, {34577, 61598}, {34774, 39884}, {34776, 36990}, {35228, 48885}, {35502, 61743}, {36412, 41373}, {36989, 48884}, {37201, 37480}, {37481, 41603}, {37814, 43577}, {39879, 53023}, {40276, 44263}, {41367, 51363}, {41736, 43650}, {43604, 44452}, {43605, 50435}, {43898, 59648}, {44110, 57584}, {44883, 58445}, {45186, 47096}, {46728, 59349}, {51394, 52071}, {52172, 56297}, {52987, 61683}

X(61749) = midpoint of X(i) and X(j) for these (i, j): {3, 22802}, {4, 6759}, {5, 2883}, {156, 44279}, {159, 48901}, {382, 34785}, {550, 51491}, {1352, 34779}, {1498, 18381}, {1539, 15647}, {1660, 44276}, {3357, 5878}, {3627, 34782}, {3818, 19149}, {5656, 23325}, {5893, 16252}, {7728, 13289}, {9833, 34786}, {9927, 32139}, {9934, 19506}, {9968, 34118}, {11744, 13293}, {12162, 41725}, {12293, 61751}, {18376, 32063}, {18480, 40658}, {22793, 40660}, {34774, 39884}, {34776, 36990}, {36989, 48884}
X(61749) = reflection of X(i) in X(j) for these (i, j): (3357, 25563), (5449, 13406), (6247, 32767), (6696, 3628), (6759, 14862), (10182, 61747), (10226, 58435), (10282, 16252), (11250, 43839), (12038, 61608), (14810, 58437), (15578, 58450), (15704, 32903), (18383, 546), (20299, 5), (25564, 5972), (32138, 20191), (32210, 10125), (32743, 61574), (34782, 50414), (44883, 58445), (45185, 6759), (48885, 35228), (52102, 20299)
X(61749) = complement of X(3357)
X(61749) = anticomplement of X(25563)
X(61749) = cross-difference of every pair of points on the line X(17434)X(46425)
X(61749) = crosspoint of X(32230) and X(53957)
X(61749) = X(25563)-Dao conjugate of-X(25563)
X(61749) = perspector of the circumconic through X(16813) and X(48373)
X(61749) = pole of the line {9033, 23286} with respect to the circumcircle
X(61749) = pole of the line {520, 44918} with respect to the nine-point circle
X(61749) = pole of the line {389, 18560} with respect to the Jerabek circumhyperbola
X(61749) = pole of the line {800, 6748} with respect to the Kiepert circumhyperbola
X(61749) = pole of the line {2071, 5562} with respect to the Stammler hyperbola
X(61749) = (Euler)-isogonal conjugate-of-X(8798)
X(61749) = center of circle {{X(5), X(2883), X(43278)}}
X(61749) = X(6759)-of-Euler triangle
X(61749) = X(8666)-of-orthic triangle, when ABC is acute
X(61749) = X(18381)-of-Ehrmann-mid triangle
X(61749) = X(20299)-of-Johnson triangle
X(61749) = X(22802)-of-anti-X3-ABC reflections triangle
X(61749) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (2, 3357, 25563), (2, 5878, 3357), (4, 184, 13403), (4, 1614, 21659), (4, 9833, 34786), (4, 26883, 13419), (4, 43831, 18388), (5, 6247, 32767), (64, 1656, 23329), (146, 58805, 11440), (154, 382, 34785), (381, 1498, 18381), (631, 20427, 11204), (1181, 37197, 18390), (1204, 7505, 44673), (1594, 32111, 11381), (1596, 12233, 10110), (3091, 5656, 14216), (3091, 14216, 23325), (3526, 48672, 10606), (3830, 14530, 17845), (3851, 12315, 1853), (5055, 13093, 40686), (5925, 61680, 3), (6241, 16868, 125), (6247, 32767, 20299), (6759, 10274, 1614), (6759, 32364, 18388), (6759, 34786, 9833), (10024, 12162, 21243), (10192, 51491, 550), (11744, 14643, 13293), (12038, 61608, 61681), (12162, 41580, 41725), (14157, 32379, 6759), (17821, 61721, 1657), (22802, 61747, 3), (43831, 51403, 4)

X(61750) = CENTER OF THE REFLECTED-PARALLELS CIRCLE OF X(12)

Barycentrics    (b^2+c^2)*a^8-2*(b^2-c^2)^2*a^6-3*(b^2+c^2)*b^2*c^2*a^4+(2*b^4-b^2*c^2+2*c^4)*(b^2-c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)^3 : :
X(61750) = X(3)-3*X(7552) = X(3)-2*X(34577) = 7*X(3)-9*X(50007) = 3*X(5)-2*X(1594) = X(5)-2*X(10024) = 2*X(140)-X(3520) = 2*X(15806)-X(34148) = 4*X(20391)-3*X(23329) = X(43394)-2*X(44516)

X(61750) lies on these lines: {2, 3}, {113, 11591}, {184, 36966}, {265, 52525}, {399, 2888}, {1154, 43831}, {1209, 45959}, {1533, 18488}, {1568, 10627}, {1614, 32423}, {3613, 22335}, {5012, 43575}, {5448, 6101}, {5449, 10264}, {5876, 10628}, {5893, 44201}, {5944, 17702}, {6000, 34826}, {6102, 43392}, {6243, 54157}, {6288, 10203}, {7999, 18504}, {8254, 15033}, {9722, 18573}, {9927, 45731}, {10263, 18388}, {10575, 13561}, {10610, 13403}, {11440, 44753}, {11441, 46446}, {11456, 18356}, {11565, 23060}, {11572, 61299}, {11750, 18379}, {11804, 21659}, {11805, 13417}, {12041, 20191}, {12254, 12902}, {12316, 13418}, {12359, 45957}, {12897, 58447}, {13366, 18555}, {13399, 44866}, {13419, 22804}, {13470, 13851}, {14641, 32767}, {14677, 32210}, {15032, 32165}, {15088, 55286}, {15107, 15800}, {15644, 51391}, {15806, 34148}, {16105, 32142}, {18435, 21357}, {20391, 23329}, {25043, 43917}, {29495, 61757}, {32171, 34153}, {40111, 61608}, {41482, 52863}, {43394, 44516}, {43821, 61134}, {43845, 45969}, {45970, 50435}, {51394, 58435}, {61747, 61753}

X(61750) = midpoint of X(i) and X(j) for these (i, j): {3, 50009}, {4, 2937}, {12088, 31724}, {41482, 52863}
X(61750) = reflection of X(i) in X(j) for these (i, j): (3, 34577), (5, 10024), (3520, 140), (31724, 546), (33282, 10020), (34148, 15806), (43394, 44516)
X(61750) = complement of the circumperp conjugate of X(37938)
X(61750) = pole of the line {6, 43809} with respect to the Evans conic
X(61750) = X(2937)-of-Euler triangle
X(61750) = X(34577)-of-X3-ABC reflections triangle
X(61750) = X(50009)-of-anti-X3-ABC reflections triangle
X(61750) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (2, 44235, 5), (3, 13406, 5), (3, 14940, 140), (4, 46029, 5), (5, 43893, 4), (140, 403, 5), (546, 13160, 5), (1209, 51403, 45959), (3850, 37347, 5), (5066, 14788, 5), (5068, 60764, 5), (5449, 13491, 10264), (7399, 46030, 5), (7552, 50009, 3), (9927, 61752, 45731), (10224, 10254, 5), (10263, 18388, 20424), (15760, 15761, 5), (16868, 49673, 5)

X(61751) = CENTER OF THE REFLECTED-PARALLELS CIRCLE OF X(20)

Barycentrics    3*a^10-8*(b^2+c^2)*a^8+(7*b^4+8*b^2*c^2+7*c^4)*a^6-(b^2+c^2)*(3*b^4-2*b^2*c^2+3*c^4)*a^4+2*(b^6-c^6)*(b^2-c^2)*a^2-(b^4-c^4)*(b^2-c^2)^3 : :
X(61751) = X(68)-2*X(10282) = 2*X(68)-3*X(61646) = 3*X(154)-X(12429) = 2*X(156)-X(9927) = 3*X(156)-2*X(13406) = 4*X(156)-3*X(61747) = 3*X(1147)-2*X(13371) = 2*X(1147)-X(18381) = 5*X(1656)-6*X(61681) = 4*X(5448)-3*X(18376) = 3*X(5654)-2*X(18383) = 3*X(6193)+X(31305) = X(7387)-2*X(45185) = 4*X(9820)-3*X(23325) = 3*X(9833)-X(31305) = 3*X(9927)-4*X(13406) = 2*X(9927)-3*X(61747) = 3*X(10192)-2*X(61544) = 4*X(10282)-3*X(61646) = 3*X(11202)-2*X(12359) = 4*X(12038)-3*X(23329) = 2*X(12038)-X(32140) = X(12293)-2*X(61749) = 4*X(13371)-3*X(18381) = 8*X(13406)-9*X(61747) = 2*X(14864)-3*X(44441) = 3*X(18324)-2*X(52104) = X(18356)-2*X(32171) = X(18569)-2*X(41597) = 2*X(20299)-3*X(47391) = 2*X(22660)-X(34786) = X(22802)-2*X(32139) = 3*X(23329)-2*X(32140) = X(34780)-3*X(37497) = 2*X(34782)-X(46730) = X(41362)-2*X(61607) = 4*X(43839)-3*X(61702)

X(61751) lies on these lines: {3, 67}, {4, 34986}, {20, 45187}, {25, 10112}, {26, 539}, {30, 15083}, {49, 18474}, {68, 10282}, {110, 34799}, {154, 12429}, {155, 18400}, {156, 9927}, {182, 31804}, {184, 13160}, {381, 12242}, {389, 41714}, {394, 44829}, {511, 5596}, {569, 38317}, {575, 7401}, {576, 6756}, {578, 3818}, {1092, 34224}, {1147, 13371}, {1352, 18925}, {1353, 11745}, {1498, 17837}, {1503, 13346}, {1656, 61681}, {1993, 61139}, {2777, 12419}, {2854, 41589}, {2888, 61644}, {2904, 12140}, {3292, 37444}, {3448, 11449}, {3564, 34776}, {5189, 40241}, {5448, 18376}, {5476, 7528}, {5654, 18383}, {5907, 19467}, {5965, 17834}, {6000, 12118}, {6146, 9306}, {6241, 12383}, {6288, 9704}, {6644, 10116}, {6759, 44665}, {6776, 9729}, {6803, 11179}, {7387, 45185}, {7404, 18553}, {7487, 16625}, {7503, 10619}, {7506, 61713}, {7544, 13366}, {7577, 9705}, {7748, 39849}, {8550, 9813}, {9544, 58922}, {9545, 61743}, {9786, 39899}, {9815, 14912}, {9820, 23325}, {10192, 61544}, {10533, 35836}, {10534, 35837}, {10539, 18390}, {10625, 48880}, {11202, 12359}, {11264, 12106}, {11425, 18440}, {11426, 19130}, {11441, 21659}, {11442, 13367}, {11451, 43838}, {11457, 51394}, {11459, 12254}, {11468, 12317}, {11550, 34148}, {11645, 34938}, {12038, 23329}, {12111, 14683}, {12161, 45286}, {12164, 17845}, {12278, 43605}, {12293, 61749}, {12370, 46261}, {13347, 48906}, {13348, 46264}, {13403, 18451}, {13419, 36747}, {13598, 31383}, {13754, 34785}, {13861, 58806}, {14531, 31304}, {14864, 44441}, {15063, 35490}, {15644, 48898}, {16266, 44407}, {17702, 22802}, {17811, 44862}, {18324, 52104}, {18356, 32171}, {18569, 41597}, {18931, 25712}, {18952, 43586}, {19150, 36749}, {19357, 21243}, {20299, 47391}, {21230, 34513}, {21849, 37122}, {22660, 34786}, {24206, 37476}, {25738, 51393}, {26883, 46818}, {29012, 37498}, {34469, 37853}, {34780, 37497}, {35473, 43895}, {41362, 61607}, {43839, 61702}, {45731, 61753}, {53169, 56397}, {58465, 59699}

X(61751) = midpoint of X(i) and X(j) for these (i, j): {6193, 9833}, {12164, 17845}
X(61751) = reflection of X(i) in X(j) for these (i, j): (68, 10282), (7387, 45185), (9927, 156), (12293, 61749), (18356, 32171), (18381, 1147), (18569, 41597), (22802, 32139), (32140, 12038), (34786, 22660), (41362, 61607), (46730, 34782)
X(61751) = center of circle {{X(399), X(6069), X(13188)}}
X(61751) = X(10112)-of-Ara triangle
X(61751) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (68, 10282, 61646), (156, 9927, 61747), (578, 12134, 3818), (7528, 37505, 5476), (10539, 44076, 18390), (12038, 32140, 23329), (13419, 36747, 48901), (21659, 24981, 11441)

X(61752) = CENTER OF THE REFLECTED-PARALLELS CIRCLE OF X(55)

Barycentrics    a^2*(a^8-3*(b^2+c^2)*a^6+3*(b^4+c^4)*a^4-(b^4-3*b^2*c^2+c^4)*(b^2+c^2)*a^2+(b^2-c^2)^2*b^2*c^2) : :
X(61752) = X(3)-3*X(6800) = 2*X(3)-3*X(34513) = 2*X(5)-X(34514) = 3*X(22)-X(37494) = 2*X(140)-3*X(13394) = 3*X(184)-X(13352) = X(343)-2*X(25337) = X(427)-2*X(61619) = 5*X(1656)-3*X(61700) = 4*X(3628)-3*X(45303) = 3*X(6800)+X(11456) = 2*X(6800)-X(34513) = 2*X(7555)-3*X(35268) = 2*X(7555)-X(37478) = 3*X(18445)+X(37494) = 2*X(18475)-X(18570) = 3*X(35268)-X(37478) = 3*X(39588)-5*X(53091)

X(61752) lies on these lines: {2, 10540}, {3, 74}, {4, 567}, {5, 182}, {6, 7530}, {20, 49}, {22, 1154}, {23, 568}, {24, 13630}, {25, 5946}, {26, 1181}, {30, 184}, {35, 9652}, {36, 9667}, {52, 17714}, {54, 382}, {140, 5651}, {143, 7517}, {146, 11597}, {154, 6644}, {155, 1350}, {185, 1658}, {215, 4302}, {323, 13340}, {343, 25337}, {376, 9544}, {381, 5012}, {389, 32237}, {394, 54042}, {427, 61619}, {511, 35707}, {542, 19127}, {546, 569}, {547, 43650}, {548, 1092}, {549, 9306}, {550, 1147}, {576, 8705}, {578, 3627}, {631, 18350}, {632, 16187}, {974, 20773}, {1176, 18440}, {1204, 15331}, {1216, 14810}, {1351, 7387}, {1493, 36747}, {1495, 9730}, {1498, 7526}, {1539, 9934}, {1596, 44077}, {1598, 19118}, {1656, 61134}, {1657, 8718}, {1885, 52432}, {1899, 10201}, {1993, 12083}, {1994, 37925}, {1995, 13363}, {2070, 5890}, {2420, 14585}, {2477, 4299}, {2782, 54332}, {2854, 44493}, {2883, 52070}, {2937, 5889}, {2979, 50461}, {3043, 20127}, {3044, 38730}, {3047, 12121}, {3060, 5899}, {3066, 13861}, {3070, 9677}, {3090, 37471}, {3091, 13353}, {3146, 37472}, {3167, 35243}, {3200, 36968}, {3201, 36967}, {3205, 42158}, {3206, 42157}, {3448, 7552}, {3518, 37481}, {3521, 34797}, {3526, 43598}, {3529, 9545}, {3534, 9703}, {3542, 18952}, {3547, 5921}, {3549, 32140}, {3564, 16618}, {3567, 18378}, {3581, 7556}, {3628, 13336}, {3796, 7514}, {3830, 15033}, {3843, 13434}, {3851, 43651}, {3853, 11424}, {5070, 43614}, {5092, 10170}, {5097, 5446}, {5157, 18358}, {5422, 13364}, {5448, 44829}, {5562, 7525}, {5576, 16659}, {5640, 7545}, {5654, 14791}, {5656, 49669}, {5891, 22352}, {6000, 18475}, {6146, 15761}, {6243, 12088}, {6636, 23039}, {6639, 11457}, {6640, 58435}, {6642, 14530}, {6699, 10182}, {6723, 60780}, {6776, 19154}, {7488, 34783}, {7493, 18917}, {7496, 54434}, {7502, 13754}, {7503, 45959}, {7506, 12006}, {7509, 14128}, {7512, 18436}, {7516, 17814}, {7527, 12112}, {7550, 15052}, {7555, 35268}, {7575, 11438}, {7689, 45957}, {7706, 38322}, {7737, 9604}, {7746, 53493}, {7782, 10411}, {8547, 15074}, {8550, 16619}, {8703, 40111}, {9638, 18447}, {9653, 10483}, {9705, 15696}, {9706, 17800}, {9729, 50414}, {9818, 32063}, {9919, 11702}, {9920, 13368}, {9927, 45731}, {10024, 34224}, {10095, 10594}, {10096, 61645}, {10110, 15516}, {10113, 13198}, {10117, 38898}, {10192, 44452}, {10254, 25739}, {10274, 11805}, {10282, 37814}, {10323, 10627}, {10535, 37729}, {10541, 43811}, {10574, 26882}, {10575, 11250}, {10605, 18324}, {10625, 43844}, {10653, 11137}, {10654, 11134}, {11179, 18374}, {11202, 15646}, {11206, 18420}, {11245, 37971}, {11402, 18534}, {11412, 13564}, {11414, 16266}, {11422, 37924}, {11423, 14627}, {11430, 14915}, {11443, 12283}, {11451, 21308}, {11550, 39504}, {11563, 18390}, {11565, 35488}, {11572, 15432}, {11579, 14852}, {11585, 61608}, {11645, 51739}, {11750, 18377}, {11793, 55674}, {11799, 12022}, {11801, 13406}, {11818, 31383}, {11819, 12233}, {11820, 12085}, {12038, 46850}, {12039, 43130}, {12084, 19357}, {12254, 15089}, {12290, 14130}, {12295, 21659}, {12370, 31804}, {13323, 31649}, {13346, 15704}, {13347, 14869}, {13383, 18914}, {13403, 44271}, {13451, 15004}, {13470, 18404}, {13621, 15043}, {14118, 18439}, {14156, 61681}, {14254, 14560}, {14389, 16658}, {14708, 15647}, {14790, 14927}, {14855, 44108}, {14867, 35890}, {15024, 18369}, {15030, 37513}, {15058, 34864}, {15083, 46728}, {15139, 18580}, {15462, 43273}, {15463, 34584}, {15580, 41714}, {15581, 44480}, {15606, 55612}, {15644, 41597}, {15688, 43572}, {16003, 32235}, {16197, 31831}, {16836, 43586}, {16868, 44795}, {17809, 44413}, {18388, 44288}, {18400, 44263}, {18434, 40441}, {18435, 35921}, {18474, 46029}, {19121, 39899}, {19129, 39874}, {19136, 50979}, {20299, 40276}, {22146, 22240}, {22505, 39805}, {22515, 39834}, {22804, 32402}, {23240, 58048}, {25738, 45732}, {31074, 61711}, {31305, 31815}, {31723, 61299}, {31861, 37506}, {32136, 36749}, {32196, 32341}, {32227, 52300}, {32339, 44515}, {33532, 37483}, {33923, 43652}, {34114, 46686}, {34116, 52073}, {34128, 61680}, {34545, 52294}, {35237, 37497}, {35265, 40280}, {35481, 52416}, {37119, 58407}, {37197, 43865}, {37458, 44080}, {37484, 56292}, {37949, 55039}, {38741, 58058}, {38753, 58056}, {38765, 58057}, {38777, 58051}, {38797, 58059}, {40241, 54007}, {40330, 46448}, {41372, 52917}, {41587, 43588}, {43573, 51730}, {43821, 44958}, {44078, 46030}, {44110, 51393}, {44233, 45298}, {44911, 61606}, {45185, 45286}, {47334, 51733}

X(61752) = midpoint of X(i) and X(j) for these (i, j): {3, 11456}, {22, 18445}, {1993, 12083}, {14867, 35890}
X(61752) = reflection of X(i) in X(j) for these (i, j): (343, 25337), (427, 61619), (11550, 39504), (18474, 46029), (18570, 18475), (34513, 6800), (34514, 5), (37478, 7555), (44288, 18388)
X(61752) = inverse of X(11459) in Stammler hyperbola
X(61752) = pole of the line {574, 9722} with respect to the Evans conic
X(61752) = pole of the line {9730, 18570} with respect to the Jerabek circumhyperbola
X(61752) = pole of the line {30, 2979} with respect to the Stammler hyperbola
X(61752) = pole of the line {8552, 33294} with respect to the Steiner inellipse
X(61752) = pole of the line {3260, 7796} with respect to the Steiner-Wallace hyperbola
X(61752) = center of circle {{X(3), X(11456), X(18338)}}
X(61752) = X(11456)-of-anti-X3-ABC reflections triangle
X(61752) = X(34514)-of-Johnson triangle
X(61752) = X(44287)-of-anti-orthocentroidal triangle
X(61752) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (3, 399, 11459), (3, 1614, 156), (3, 10620, 11454), (3, 11441, 11591), (3, 32139, 5876), (4, 11003, 567), (23, 15032, 568), (26, 1181, 6102), (182, 6759, 46261), (182, 46261, 5), (376, 9544, 22115), (567, 11003, 32046), (569, 26883, 546), (1147, 8717, 37480), (1495, 9730, 12106), (1614, 52525, 3), (1657, 9704, 34148), (3529, 9545, 37495), (3534, 9703, 43574), (3549, 32140, 34826), (3796, 18451, 7514), (5012, 14157, 381), (5654, 14791, 51391), (5654, 46264, 14791), (5890, 26881, 2070), (5899, 15087, 3060), (5944, 13491, 3), (6241, 11454, 10620), (6639, 11457, 13561), (6800, 11456, 3), (7387, 12161, 10263), (7387, 19347, 12161), (7512, 43605, 18436), (7514, 18451, 15060), (7517, 7592, 143), (7545, 15037, 5640), (7575, 45956, 11438), (8550, 32217, 44490), (8717, 37480, 550), (8718, 34148, 1657), (9934, 12228, 1539), (10282, 40647, 37814), (10539, 10984, 140), (10594, 36753, 10095), (11459, 15080, 3), (11464, 15072, 3), (13861, 36752, 15026), (18378, 43845, 3567), (35268, 37478, 7555), (45731, 61750, 9927)

X(61753) = CENTER OF THE REFLECTED-PARALLELS CIRCLE OF X(56)

Barycentrics    a^2*(a^8-3*(b^2+c^2)*a^6+(3*b^4+4*b^2*c^2+3*c^4)*a^4-(b^4+b^2*c^2+c^4)*(b^2+c^2)*a^2+(b^2-c^2)^2*b^2*c^2) : :
X(61753) = X(5)-2*X(59659) = 3*X(1092)+X(26883) = X(1204)-2*X(43615) = 5*X(1656)-3*X(61701) = X(7517)-3*X(35264) = 3*X(10539)-X(26883)

X(61753) lies on these lines: {2, 49}, {3, 74}, {4, 18350}, {5, 578}, {6, 1493}, {17, 3200}, {18, 3201}, {20, 10540}, {22, 10627}, {23, 37484}, {24, 1154}, {25, 10263}, {26, 394}, {30, 1092}, {35, 9667}, {36, 9652}, {52, 3292}, {54, 1656}, {68, 59543}, {69, 19154}, {113, 44279}, {125, 18356}, {140, 184}, {141, 7568}, {143, 1993}, {154, 54042}, {155, 2929}, {182, 632}, {186, 18436}, {195, 3567}, {206, 48876}, {215, 499}, {249, 18321}, {323, 3518}, {343, 10020}, {378, 45959}, {381, 13482}, {382, 43574}, {389, 41597}, {468, 52432}, {498, 2477}, {511, 37440}, {546, 13352}, {548, 43652}, {549, 13347}, {550, 6759}, {567, 3090}, {568, 44802}, {569, 3628}, {575, 61676}, {631, 9544}, {1173, 10545}, {1204, 43615}, {1209, 47360}, {1216, 7502}, {1353, 44489}, {1495, 10625}, {1568, 18377}, {1595, 44080}, {1620, 12163}, {1657, 14157}, {1658, 5562}, {1660, 44679}, {1698, 9621}, {1974, 34380}, {1995, 10095}, {2070, 11412}, {2071, 18439}, {2072, 14516}, {2888, 11597}, {2937, 2979}, {3043, 14643}, {3044, 38224}, {3045, 57298}, {3046, 57297}, {3047, 15061}, {3048, 57331}, {3060, 13621}, {3071, 9676}, {3091, 37472}, {3098, 9968}, {3146, 37477}, {3147, 34397}, {3167, 5946}, {3202, 49111}, {3357, 34152}, {3410, 6143}, {3515, 58891}, {3519, 52417}, {3520, 18435}, {3525, 11003}, {3526, 5012}, {3530, 10984}, {3548, 32140}, {3564, 16238}, {3581, 44879}, {3624, 9622}, {3627, 13346}, {3767, 9603}, {3818, 33332}, {3850, 11424}, {3851, 15033}, {3917, 7525}, {5054, 61134}, {5055, 13434}, {5070, 9706}, {5079, 11935}, {5422, 32205}, {5448, 44263}, {5449, 5972}, {5462, 34986}, {5504, 10113}, {5640, 14627}, {5889, 45735}, {5890, 43809}, {5891, 13367}, {5907, 12038}, {5925, 9934}, {5965, 51730}, {6242, 15091}, {6247, 15122}, {6288, 7577}, {6403, 32196}, {6509, 37081}, {6638, 13855}, {6639, 58435}, {6640, 11442}, {6677, 13292}, {6689, 24206}, {7387, 8780}, {7399, 61619}, {7405, 61690}, {7487, 31815}, {7488, 23039}, {7503, 14128}, {7505, 52416}, {7507, 22804}, {7514, 10610}, {7516, 17811}, {7517, 13391}, {7526, 15060}, {7528, 37645}, {7529, 39522}, {7530, 37498}, {7540, 40112}, {7575, 46730}, {7592, 12006}, {7689, 15646}, {7741, 9666}, {7746, 9696}, {7951, 9653}, {8227, 9586}, {8548, 32245}, {8718, 15696}, {9587, 31423}, {9604, 31401}, {9697, 31455}, {9701, 26364}, {9702, 26363}, {9730, 43844}, {9781, 10546}, {9833, 14791}, {9937, 34966}, {10018, 59648}, {10125, 13392}, {10224, 18474}, {10255, 58922}, {10272, 13406}, {10274, 21230}, {10303, 13339}, {10510, 11663}, {10564, 11381}, {11064, 12134}, {11134, 42149}, {11137, 42152}, {11250, 12162}, {11255, 22151}, {11264, 18912}, {11402, 36153}, {11411, 41615}, {11422, 15024}, {11423, 15028}, {11438, 15083}, {11451, 22462}, {11458, 12272}, {11465, 15047}, {11550, 46114}, {11793, 18475}, {11898, 19128}, {12022, 50143}, {12084, 18451}, {12088, 13340}, {12107, 37478}, {12175, 13368}, {12228, 14852}, {12236, 58726}, {12278, 18403}, {12290, 18859}, {12359, 44452}, {13142, 44233}, {13198, 34128}, {13348, 50414}, {13363, 32136}, {13564, 26881}, {13567, 32358}, {13630, 17928}, {13754, 37814}, {13861, 35259}, {14130, 15058}, {14156, 20299}, {14530, 35243}, {14585, 35324}, {14786, 54013}, {14788, 61655}, {14790, 37669}, {14805, 54434}, {14865, 15052}, {14869, 37515}, {14984, 38851}, {15004, 58531}, {15043, 15087}, {15045, 43845}, {15069, 15462}, {15073, 15532}, {15081, 15089}, {15136, 34798}, {15233, 55540}, {15234, 55539}, {15331, 31834}, {15463, 35488}, {15561, 58058}, {15704, 37480}, {15760, 61608}, {15761, 51425}, {15800, 40113}, {15805, 17809}, {16187, 55861}, {16239, 43650}, {16534, 61749}, {17104, 50317}, {17821, 32379}, {18281, 58357}, {18381, 37938}, {18404, 30522}, {18553, 51739}, {18569, 51391}, {18572, 34786}, {19127, 40107}, {19131, 61545}, {19137, 59399}, {19468, 44325}, {20773, 41673}, {21243, 43839}, {21659, 30714}, {21663, 43898}, {22112, 55862}, {22467, 34783}, {22802, 46374}, {23236, 34799}, {24475, 42463}, {31833, 61607}, {32110, 45187}, {32423, 49673}, {34127, 39834}, {34224, 37452}, {34577, 61644}, {35473, 38942}, {36433, 46841}, {37068, 58468}, {38752, 58056}, {38764, 58057}, {38776, 58051}, {38796, 58059}, {39899, 43812}, {41587, 44232}, {43576, 49136}, {44078, 44213}, {44288, 45286}, {44516, 61681}, {44673, 52104}, {44911, 61544}, {45731, 61751}, {45970, 50140}, {50138, 61743}, {50708, 61645}, {51392, 61139}, {51872, 57011}, {57299, 58055}, {57300, 58054}, {57301, 58067}, {57302, 58063}, {57303, 58060}, {57304, 58064}, {57314, 58066}, {57316, 58068}, {57324, 58062}, {57327, 58053}, {57328, 58052}, {57329, 58048}, {57330, 58050}, {57332, 58049}, {57333, 58065}, {57334, 58061}, {57335, 58069}, {61747, 61750}

X(61753) = midpoint of X(i) and X(j) for these (i, j): {3, 11441}, {1092, 10539}
X(61753) = reflection of X(i) in X(j) for these (i, j): (5, 59659), (1204, 43615), (41587, 44232)
X(61753) = complement of X(25738)
X(61753) = cross-difference of every pair of points on the line X(1637)X(20184)
X(61753) = perspector of the circumconic through X(20185) and X(44769)
X(61753) = inverse of X(6241) in Stammler hyperbola
X(61753) = pole of the line {7748, 9722} with respect to the Evans conic
X(61753) = pole of the line {10625, 21663} with respect to the Jerabek circumhyperbola
X(61753) = pole of the line {577, 37452} with respect to the Kiepert circumhyperbola
X(61753) = pole of the line {1510, 1636} with respect to the MacBeath circumconic
X(61753) = pole of the line {30, 5889} with respect to the Stammler hyperbola
X(61753) = pole of the line {8552, 57065} with respect to the Steiner inellipse
X(61753) = pole of the line {52, 156} with respect to the Thomson-Gibert-Moses hyperbola
X(61753) = X(11441)-of-anti-X3-ABC reflections triangle
X(61753) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (2, 49, 32046), (3, 110, 156), (3, 399, 6241), (3, 15068, 5876), (3, 32139, 13491), (3, 32609, 11449), (5, 40111, 1147), (25, 16266, 10263), (26, 394, 6101), (110, 15132, 5609), (110, 58881, 399), (155, 6644, 6102), (323, 3518, 6243), (569, 5651, 3628), (1147, 9306, 5), (1216, 10282, 7502), (1493, 15026, 6), (1495, 10625, 17714), (1511, 5876, 3), (1656, 9703, 54), (1993, 7506, 143), (1995, 36749, 10095), (2979, 26882, 2937), (3090, 9545, 567), (3167, 6642, 12161), (3525, 11003, 37471), (3526, 9704, 5012), (5012, 9705, 9704), (5449, 5972, 60780), (5562, 51393, 1658), (5907, 12038, 18570), (5944, 15067, 3), (6640, 11442, 13561), (6642, 12161, 5946), (7514, 19357, 10610), (9707, 15066, 3), (11440, 15035, 3), (11444, 11464, 3), (11449, 11459, 3), (11591, 32171, 3), (13346, 46261, 3627), (15033, 43614, 3851), (15060, 43394, 7526), (17814, 47391, 7526), (18350, 22115, 4), (34148, 43598, 381), (41597, 43586, 389), (43572, 43598, 34148), (44802, 56292, 568), (45735, 50461, 5889)

X(61754) = CENTER OF THE REFLECTED-PARALLELS CIRCLE OF X(101)

Barycentrics    a^2*(a^12-4*(b^2+c^2)*a^10+(6*b^4+7*b^2*c^2+6*c^4)*a^8-(b^2+c^2)*(4*b^4+b^2*c^2+4*c^4)*a^6+(b^8+c^8+2*b^2*c^2*(b^4+c^4))*a^4-(b^4-c^4)*(b^2-c^2)*b^2*c^2*a^2+(b^2-c^2)^2*b^2*c^2*(b^4+c^4)) : :
X(61754) = X(9927)-2*X(61761)

X(61754) lies on these lines: {3, 61213}, {4, 14591}, {20, 249}, {26, 206}, {54, 6785}, {110, 53767}, {132, 61208}, {154, 37921}, {184, 21525}, {187, 11456}, {512, 6759}, {1513, 19627}, {1625, 14676}, {2715, 8721}, {2794, 32661}, {3111, 10984}, {7506, 61733}, {7592, 15544}, {9927, 61761}, {10539, 31848}, {10540, 18321}, {11457, 35605}, {14574, 52128}, {18396, 58312}, {33753, 44127}, {39857, 52170}

X(61754) = midpoint of X(39857) and X(52170)
X(61754) = reflection of X(9927) in X(61761)
X(61754) = pole of the line {11442, 18337} with respect to the Stammler hyperbola
X(61754) = center of circle {{X(110), X(2715), X(32661)}}
X(61754) = (X(3), X(61213))-harmonic conjugate of X(61755)

X(61755) = CENTER OF THE REFLECTED-PARALLELS CIRCLE OF X(105)

Barycentrics    a^2*(a^12-3*(b^2+c^2)*a^10+(4*b^4+3*b^2*c^2+4*c^4)*a^8-4*(b^6+c^6)*a^6+(3*b^8+3*c^8-b^2*c^2*(b^2+c^2)^2)*a^4-(b^8-c^8)*a^2*(b^2-c^2)-2*(b^2-c^2)^2*b^4*c^4) : :
X(61755) = 2*X(14574)-X(14676)

X(61755) lies on these lines: {3, 61213}, {4, 6328}, {5, 182}, {6, 33753}, {24, 2088}, {32, 2698}, {54, 6794}, {110, 14981}, {184, 1316}, {525, 1147}, {569, 7902}, {574, 11464}, {578, 43278}, {1092, 5118}, {1569, 9696}, {1614, 15920}, {1976, 11623}, {2794, 17974}, {2871, 15562}, {3269, 39854}, {3767, 39085}, {5028, 15073}, {5938, 11171}, {7862, 36471}, {10539, 43389}, {10991, 11653}, {14574, 14676}, {15067, 61758}, {15068, 61757}, {18335, 53935}, {19165, 22146}, {23583, 32734}, {26883, 43279}, {31850, 44127}, {39764, 41363}, {43586, 52036}

X(61755) = midpoint of X(19165) and X(22146)
X(61755) = reflection of X(14676) in X(14574)
X(61755) = Psi-transform of X(14652)
X(61755) = inverse of X(5) in 1st Brocard circle
X(61755) = pole of the line {5, 525} with respect to the 1st Brocard circle
X(61755) = pole of the line {31850, 54384} with respect to the Jerabek circumhyperbola
X(61755) = pole of the line {2979, 36163} with respect to the Stammler hyperbola
X(61755) = reflection of X(5) in the line X(525)X(9820)
X(61755) = center of circle {{X(110), X(2715), X(17974)}}
X(61755) = X(19165)-of-1st Brocard triangle
X(61755) = (X(3), X(61213))-harmonic conjugate of X(61754)

X(61756) = CENTER OF THE REFLECTED-PARALLELS CIRCLE OF X(108)

Barycentrics    a^2*(a^20-7*(b^2+c^2)*a^18+(22*b^4+35*b^2*c^2+22*c^4)*a^16-2*(b^2+c^2)*(21*b^4+17*b^2*c^2+21*c^4)*a^14+(56*b^8+56*c^8+(95*b^4+104*b^2*c^2+95*c^4)*b^2*c^2)*a^12-2*(b^2+c^2)*(28*b^8+28*c^8+(8*b^4+29*b^2*c^2+8*c^4)*b^2*c^2)*a^10+(42*b^12+42*c^12+(27*b^8+27*c^8+2*b^2*c^2*(4*b^2+5*b*c+4*c^2)*(4*b^2-5*b*c+4*c^2))*b^2*c^2)*a^8-2*(b^2+c^2)*(11*b^12+11*c^12-(11*b^8+11*c^8-b^2*c^2*(13*b^4-14*b^2*c^2+13*c^4))*b^2*c^2)*a^6+(7*b^12+7*c^12+(15*b^8+15*c^8+b^2*c^2*(3*b^4+14*b^2*c^2+3*c^4))*b^2*c^2)*(b^2-c^2)^2*a^4-(b^4-c^4)*(b^2-c^2)^3*(b^8+c^8+4*b^2*c^2*(2*b^4-b^2*c^2+2*c^4))*a^2+2*(b^4+b^2*c^2+c^4)*(b^2-c^2)^6*b^2*c^2) : :

X(61756) lies on these lines: {5, 578}, {110, 131}, {1092, 3258}, {12111, 54061}, {21268, 22115}, {60342, 61757}

X(61757) = CENTER OF THE REFLECTED-PARALLELS CIRCLE OF X(109)

Barycentrics    a^2*(-a^2+b^2+c^2)*(a^12-4*(b^2+c^2)*a^10+(6*b^4+7*b^2*c^2+6*c^4)*a^8-(b^2+c^2)*(4*b^4+b^2*c^2+4*c^4)*a^6+(b^8+c^8+4*b^2*c^2*(b^4-b^2*c^2+c^4))*a^4-(b^4-c^4)*(b^2-c^2)*b^2*c^2*a^2-(b^2-c^2)^4*b^2*c^2) : :
X(61757) = X(9927)-2*X(61760)

X(61757) lies on these lines: {3, 49}, {4, 52603}, {5, 24975}, {20, 477}, {68, 39170}, {924, 6759}, {1576, 16534}, {1614, 18770}, {3184, 38726}, {5467, 46261}, {5663, 13496}, {5962, 16868}, {7505, 16221}, {9927, 61760}, {10539, 15329}, {12161, 18114}, {15068, 61755}, {18404, 42424}, {21268, 35488}, {21844, 32710}, {29495, 61750}, {60342, 61756}

X(61757) = reflection of X(i) in X(j) for these (i, j): (9927, 61760), (14889, 13557)
X(61757) = isogonal conjugate of the antigonal conjugate of X(6344)
X(61757) = X(924)-vertex conjugate of-X(22115)
X(61757) = inverse of X(22115) in circumcircle
X(61757) = pole of the line {924, 22115} with respect to the circumcircle
X(61757) = pole of the line {9722, 32761} with respect to the Kiepert circumhyperbola
X(61757) = pole of the line {4, 15112} with respect to the Stammler hyperbola
X(61757) = reflection of X(3) in the line X(924)X(10282)
X(61757) = center of circle {{X(110), X(10420), X(15478)}}

X(61758) = CENTER OF THE REFLECTED-PARALLELS CIRCLE OF X(110)

Barycentrics    a^2*(a^20-7*(b^2+c^2)*a^18+(21*b^4+34*b^2*c^2+21*c^4)*a^16-(b^2+c^2)*(35*b^4+32*b^2*c^2+35*c^4)*a^14+(5*b^4+9*b^2*c^2+5*c^4)*(7*b^4+b^2*c^2+7*c^4)*a^12-3*(b^2+c^2)*(7*b^8+7*c^8+b^2*c^2*(5*b^4+9*b^2*c^2+5*c^4))*a^10+(b^4+b^2*c^2+c^4)*(7*b^8+4*b^4*c^4+7*c^8)*a^8-(b^4-c^4)*(b^2-c^2)*(b^8+3*b^4*c^4+c^8)*a^6+2*(b^2-c^2)^2*(b^8+c^8-b^2*c^2*(b^4-b^2*c^2+c^4))*b^2*c^2*a^4-(b^4-c^4)*(b^2-c^2)^3*b^2*c^2*(3*b^4-2*b^2*c^2+3*c^4)*a^2+(b^4+b^2*c^2+c^4)*(b^2-c^2)^6*b^2*c^2) : :
X(61758) = X(9927)-2*X(61759)

X(61758) lies on these lines: {110, 8157}, {1092, 43969}, {1147, 1154}, {1157, 1614}, {1510, 6759}, {6150, 13491}, {7506, 15537}, {9927, 61759}, {11750, 45180}, {14703, 32609}, {15067, 61755}, {15532, 27246}, {16337, 21659}

X(61758) = reflection of X(9927) in X(61759)
X(61758) = center of circle {{X(110), X(15958), X(46966)}}

X(61759) = CENTER OF THE REFLECTED-PARALLELS CIRCLE OF X(113)

Barycentrics    ((b^2+c^2)*a^2-(b^2-c^2)^2)*(a^18-4*(b^2+c^2)*a^16+4*(b^4+3*b^2*c^2+c^4)*a^14+(b^2+c^2)*(5*b^4-14*b^2*c^2+5*c^4)*a^12-(16*b^8+16*c^8+b^2*c^2*(5*b^4-7*b^2*c^2+5*c^4))*a^10+(b^2+c^2)*(19*b^8+19*c^8-14*(b^4-b^2*c^2+c^4)*b^2*c^2)*a^8-2*(8*b^12+8*c^12-(7*b^8+7*c^8-b^2*c^2*(6*b^4-5*b^2*c^2+6*c^4))*b^2*c^2)*a^6+(b^8-c^8)*a^4*(b^2-c^2)*(11*b^4-16*b^2*c^2+11*c^4)-(b^2-c^2)^4*(5*b^8+5*c^8+b^2*c^2*(b^4+b^2*c^2+c^4))*a^2+(b^2-c^2)^6*(b^2+c^2)*(b^4+c^4)) : :

X(61759) lies on these lines: {5, 51}, {1510, 15761}, {9927, 61758}

X(61759) = midpoint of X(9927) and X(61758)
X(61759) = reflection of X(5) in the line X(1510)X(13406)

X(61760) = CENTER OF THE REFLECTED-PARALLELS CIRCLE OF X(117)

Barycentrics    (-a^2+b^2+c^2)*((b^2+c^2)*a^18-(3*b^4+2*b^2*c^2+3*c^4)*a^16-(b^2+c^2)*(b^4-5*b^2*c^2+c^4)*a^14+2*(7*b^8+7*c^8-(7*b^4-6*b^2*c^2+7*c^4)*b^2*c^2)*a^12-(b^2+c^2)*(21*b^8+21*c^8-2*(19*b^4-22*b^2*c^2+19*c^4)*b^2*c^2)*a^10+(14*b^12+14*c^12-(b^8+c^8+18*(2*b^4-3*b^2*c^2+2*c^4)*b^2*c^2)*b^2*c^2)*a^8-(b^4-c^4)*(b^2-c^2)*(7*b^8+7*c^8+5*(b^2-c^2)^2*b^2*c^2)*a^6+2*(b^2-c^2)^4*(3*b^8+5*b^4*c^4+3*c^8)*a^4-4*(b^6+c^6)*(b^2-c^2)^6*a^2+(b^4+b^2*c^2+c^4)*(b^2-c^2)^8) : :

X(61760) lies on these lines: {5, 389}, {924, 15761}, {5562, 42424}, {7689, 35235}, {9927, 61757}

X(61760) = midpoint of X(9927) and X(61757)
X(61760) = reflection of X(5) in the line X(924)X(13406)

X(61761) = CENTER OF THE REFLECTED-PARALLELS CIRCLE OF X(118)

Barycentrics    (b^2+c^2)*a^12-2*(b^4+c^4)*a^10-(b^2+c^2)*b^2*c^2*a^8+(b^4-b^2*c^2+c^4)*(3*b^4+2*b^2*c^2+3*c^4)*a^6-2*(b^6+c^6)*(2*b^4-3*b^2*c^2+2*c^4)*a^4+(3*b^8+3*c^8-b^2*c^2*(3*b^4-2*b^2*c^2+3*c^4))*(b^2-c^2)^2*a^2-(b^6+c^6)*(b^2-c^2)^4 : :

X(61761) lies on these lines: {5, 141}, {403, 31848}, {512, 15761}, {868, 61646}, {6787, 44958}, {9927, 61754}, {10024, 31850}, {10575, 35605}, {15575, 36472}

X(61761) = midpoint of X(9927) and X(61754)
X(61761) = reflection of X(5) in the line X(512)X(13406)

X(61762) = X(1)X(3) ∩ X(2)X(5828)

Barycentrics    a*(3*a^3-(b+c)*a^2-(3*b-c)*(b-3*c)*a+(b^2-c^2)*(b-c)) : :
X(61762) = 3*X(1)+2*X(37545)

See Tran Viet Hung and César Lozada, Romantics of Geometry - Feb 28, 2024.

X(61762) lies on these lines: {1, 3}, {2, 5828}, {4, 4315}, {7, 13464}, {9, 8666}, {10, 31190}, {11, 9613}, {30, 51785}, {84, 1476}, {90, 15180}, {104, 7091}, {140, 51784}, {145, 26062}, {200, 17614}, {226, 9624}, {376, 12575}, {380, 37519}, {381, 50444}, {388, 6939}, {404, 36846}, {474, 4853}, {495, 3624}, {496, 5691}, {497, 4311}, {499, 9578}, {515, 4308}, {518, 17624}, {519, 5438}, {551, 3487}, {581, 4322}, {595, 54319}, {908, 3616}, {936, 4662}, {937, 1104}, {938, 5882}, {944, 11019}, {946, 3600}, {950, 50811}, {956, 8583}, {958, 3646}, {979, 1050}, {995, 1066}, {997, 6762}, {1000, 43174}, {1001, 60965}, {1056, 1125}, {1058, 4297}, {1167, 1451}, {1201, 1453}, {1210, 3476}, {1222, 51284}, {1376, 12629}, {1387, 11522}, {1449, 2183}, {1478, 50443}, {1490, 9844}, {1656, 5726}, {1698, 15325}, {1699, 11373}, {1706, 11525}, {1737, 37709}, {1870, 30148}, {2136, 25440}, {2242, 9575}, {2975, 31435}, {3086, 5587}, {3090, 51782}, {3157, 5315}, {3158, 3244}, {3241, 4855}, {3243, 22836}, {3296, 12563}, {3297, 9583}, {3306, 4861}, {3436, 25522}, {3485, 61275}, {3488, 21625}, {3529, 51783}, {3560, 60937}, {3582, 10827}, {3586, 37722}, {3622, 5905}, {3623, 4881}, {3632, 46917}, {3635, 11041}, {3636, 5542}, {3655, 12433}, {3656, 24470}, {3671, 10595}, {3680, 54286}, {3812, 39779}, {3872, 5253}, {3873, 56387}, {3876, 19861}, {3877, 54290}, {3878, 3928}, {3889, 46681}, {3890, 4652}, {3895, 4188}, {3897, 4666}, {3957, 8000}, {4252, 45219}, {4292, 31162}, {4293, 12053}, {4298, 5603}, {4299, 9580}, {4312, 22791}, {4313, 40270}, {4317, 9579}, {4321, 11372}, {4342, 6361}, {4355, 39542}, {4511, 41863}, {4512, 10569}, {4646, 8572}, {4679, 37737}, {4915, 9709}, {5044, 12128}, {5234, 11035}, {5247, 56630}, {5258, 7308}, {5265, 6684}, {5270, 23708}, {5274, 31673}, {5289, 54422}, {5290, 5886}, {5313, 5399}, {5426, 16137}, {5433, 31434}, {5434, 9612}, {5435, 11362}, {5609, 51793}, {5693, 17625}, {5734, 21454}, {5777, 9850}, {5836, 40726}, {6049, 13607}, {6147, 61276}, {6261, 10394}, {6264, 41554}, {6691, 32049}, {6736, 17567}, {6738, 7967}, {6765, 59691}, {6796, 7966}, {7191, 59285}, {7288, 31397}, {7354, 9614}, {7686, 17626}, {7743, 9655}, {7988, 9654}, {8164, 19862}, {9310, 16572}, {9581, 10072}, {9615, 35808}, {9623, 11260}, {9785, 31730}, {10039, 31231}, {10283, 59372}, {10390, 56027}, {10944, 17728}, {11036, 38314}, {11038, 41572}, {11194, 31424}, {11240, 57287}, {11374, 25055}, {11523, 30144}, {12573, 38036}, {12625, 49627}, {12645, 30286}, {12650, 22753}, {12735, 13996}, {12908, 55175}, {15170, 34630}, {15841, 43179}, {16485, 28011}, {16670, 22356}, {17098, 56036}, {17647, 24392}, {18391, 61296}, {18991, 35769}, {18992, 35768}, {19925, 47743}, {20076, 41012}, {24391, 36922}, {24982, 36977}, {30524, 51812}, {30525, 51813}, {31479, 34595}, {32577, 54418}, {34625, 57284}, {34711, 51071}, {34790, 35272}, {37817, 56804}, {45776, 52027}, {47623, 54386}, {49169, 58405}, {51522, 51794}, {51523, 51796}, {51524, 51795}, {51525, 51767}, {51526, 51766}, {51527, 51808}, {51528, 51809}, {51529, 51768}, {51530, 51770}, {51531, 51765}, {51535, 51814}, {54361, 61256}, {55176, 58616}, {56029, 56038}, {56177, 58609}

X(61762) = midpoint of X(i) and X(j) for these (i, j): {1, 3361}, {4308, 14986}
X(61762) = reflection of X(40) in X(10270)
X(61762) = isogonal conjugate of X(56038)
X(61762) = X(21)-beth conjugate of-X(1697)
X(61762) = X(56029)-Ceva conjugate of-X(1)
X(61762) = Cundy-Parry-Phi-transform of X(7962)
X(61762) = pole of the line {513, 57198} with respect to the mixtilinear incircles radical circle
X(61762) = pole of the line {21, 31393} with respect to the Stammler hyperbola
X(61762) = pole of the line {314, 56038} with respect to the Steiner-Wallace hyperbola
X(61762) = (anti-Aquila)-isogonal conjugate-of-X(3646)
X(61762) = X(3089)-of-2nd circumperp triangle, when ABC is acute
X(61762) = X(3361)-of-anti-Aquila triangle
X(61762) = X(3517)-of-incircle-circles triangle, when ABC is acute
X(61762) = X(3546)-of-hexyl triangle, when ABC is acute
X(61762) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 56, 40), (1, 5563, 57), (1, 13462, 3), (1, 37587, 46), (3, 31797, 165), (3, 51788, 1), (56, 20323, 1), (354, 1388, 1), (999, 24928, 1), (1319, 3304, 1), (1385, 7373, 1), (3057, 15803, 40), (5045, 10246, 1), (8171, 58577, 165), (15178, 15934, 1), (17609, 34471, 1), (21842, 37602, 1)

X(61763) = X(1)X(3) ∩ X(10)X(452)

Barycentrics    a*(3*a^3+(b+c)*a^2-3*(b+c)^2*a-(b^2-c^2)*(b-c)) : :

See Tran Viet Hung and César Lozada, Romantics of Geometry - Feb 28, 2024.

X(61763) lies on these lines: {1, 3}, {2, 9614}, {4, 31434}, {5, 9580}, {6, 31426}, {8, 3977}, {9, 3697}, {10, 452}, {11, 31423}, {12, 41869}, {19, 3731}, {20, 9613}, {21, 9623}, {30, 9578}, {32, 31433}, {33, 6197}, {63, 3871}, {71, 380}, {72, 3158}, {80, 6154}, {90, 4866}, {100, 936}, {140, 50443}, {145, 4652}, {191, 3174}, {200, 1005}, {226, 6361}, {329, 59722}, {372, 31432}, {376, 10106}, {388, 31730}, {390, 1210}, {392, 5438}, {405, 1706}, {495, 9579}, {496, 31231}, {497, 6684}, {498, 1699}, {499, 51785}, {516, 3085}, {518, 54290}, {519, 4305}, {528, 26066}, {549, 11373}, {580, 52428}, {595, 2999}, {612, 35988}, {631, 12053}, {846, 28029}, {902, 54418}, {944, 52027}, {946, 5218}, {950, 5657}, {956, 2136}, {960, 4421}, {962, 5281}, {993, 4853}, {1015, 31422}, {1058, 3911}, {1103, 1253}, {1104, 21000}, {1125, 30305}, {1158, 30304}, {1335, 9616}, {1376, 31435}, {1449, 21866}, {1453, 3052}, {1478, 51784}, {1479, 1698}, {1490, 7995}, {1497, 13329}, {1571, 2241}, {1572, 31451}, {1702, 5414}, {1703, 2066}, {1707, 50581}, {1722, 8616}, {1737, 4309}, {1742, 2956}, {1745, 8915}, {1750, 11500}, {1768, 9898}, {1770, 5290}, {1788, 10385}, {1802, 2301}, {1864, 58643}, {1914, 9593}, {2003, 7086}, {2067, 9582}, {2082, 41423}, {2177, 54421}, {2218, 56135}, {2264, 3973}, {2269, 54377}, {2275, 31421}, {2324, 36744}, {2650, 17782}, {2948, 10065}, {2951, 10045}, {2975, 3895}, {3035, 25522}, {3058, 24914}, {3062, 7162}, {3086, 10164}, {3091, 30332}, {3100, 9537}, {3189, 3632}, {3296, 4031}, {3434, 5705}, {3452, 59591}, {3474, 21620}, {3485, 28194}, {3486, 11362}, {3488, 4848}, {3522, 4311}, {3523, 9785}, {3526, 7743}, {3553, 21864}, {3555, 3928}, {3583, 6893}, {3584, 50865}, {3585, 5726}, {3624, 17567}, {3634, 10591}, {3646, 4413}, {3650, 60977}, {3654, 37730}, {3679, 5234}, {3680, 19535}, {3681, 41562}, {3727, 39255}, {3753, 5436}, {3784, 53002}, {3811, 4067}, {3812, 4428}, {3870, 54422}, {3872, 4189}, {3877, 4855}, {3885, 17549}, {3890, 35262}, {3913, 4640}, {3916, 6762}, {3918, 5248}, {3925, 7741}, {3929, 34790}, {3935, 3951}, {4258, 21872}, {4292, 9778}, {4293, 12512}, {4295, 5493}, {4298, 50808}, {4302, 5691}, {4308, 10304}, {4312, 13407}, {4313, 59417}, {4314, 18391}, {4326, 10398}, {4330, 6930}, {4333, 5270}, {4354, 9577}, {4668, 5441}, {4677, 37706}, {4882, 41229}, {4900, 15446}, {4915, 5258}, {4995, 11375}, {5044, 46917}, {5053, 16667}, {5082, 5745}, {5219, 12699}, {5225, 10175}, {5229, 28150}, {5252, 15338}, {5268, 33849}, {5288, 11519}, {5415, 19004}, {5416, 19003}, {5423, 59576}, {5432, 8227}, {5433, 37704}, {5439, 38316}, {5440, 15829}, {5531, 12665}, {5541, 10058}, {5587, 6284}, {5690, 5727}, {5698, 21075}, {5703, 20070}, {5720, 32141}, {5722, 10386}, {5732, 7676}, {5735, 36976}, {5744, 56936}, {6174, 24954}, {6253, 10827}, {6594, 51768}, {6734, 20075}, {6735, 6872}, {6906, 12650}, {6944, 7988}, {7031, 10315}, {7074, 54301}, {7080, 12572}, {7160, 37426}, {7161, 36599}, {7284, 45830}, {7308, 9709}, {7412, 40971}, {7672, 10122}, {7713, 11406}, {7951, 24644}, {7971, 33597}, {8274, 42042}, {8545, 33557}, {8583, 25440}, {9574, 16502}, {9575, 31448}, {9581, 15171}, {9589, 12047}, {9599, 31428}, {9654, 28146}, {9665, 31441}, {9668, 9956}, {9669, 11231}, {9670, 17606}, {9841, 17613}, {9843, 26062}, {9860, 10086}, {9904, 10088}, {10053, 13174}, {10382, 55104}, {10384, 31658}, {10399, 12710}, {10543, 41687}, {10588, 18483}, {10590, 51118}, {10826, 19875}, {10896, 54447}, {10914, 16370}, {10944, 50811}, {11372, 15837}, {11374, 28174}, {11376, 52793}, {11471, 41227}, {11496, 16616}, {11530, 19526}, {11683, 55998}, {12245, 21165}, {12408, 13311}, {12515, 37736}, {12527, 34619}, {12672, 52026}, {12700, 52265}, {12711, 18397}, {12758, 15015}, {12953, 18492}, {13116, 13221}, {15558, 34474}, {15624, 23844}, {16469, 21059}, {16569, 51504}, {16572, 42316}, {16673, 54424}, {16781, 31443}, {17524, 18163}, {17548, 38460}, {17564, 37735}, {18406, 18514}, {18446, 54156}, {18481, 37709}, {18518, 18540}, {19256, 56191}, {20196, 47742}, {22793, 31479}, {23708, 34595}, {24248, 28015}, {25006, 31446}, {25055, 28629}, {25264, 41831}, {28376, 59311}, {30286, 37721}, {31249, 58405}, {31425, 37722}, {31795, 50821}, {32195, 35348}, {34744, 51093}, {34772, 61157}, {35808, 51842}, {35809, 51841}, {36643, 51058}, {37006, 61252}, {37313, 54318}, {37703, 41870}, {38665, 41166}, {41230, 60846}, {42043, 50583}, {51284, 56311}, {51792, 61261}, {54386, 60714}, {54392, 61155}, {56176, 61153}

X(61763) = reflection of X(i) in X(j) for these (i, j): (1, 3601), (5175, 10), (9612, 3085)
X(61763) = cross-difference of every pair of points on the line X(650)X(48342)
X(61763) = crosssum of X(2310) and X(14300)
X(61763) = X(i)-beth conjugate of-X(j) for these (i, j): (8, 5175), (643, 936)
X(61763) = X(7160)-Ceva conjugate of-X(1)
X(61763) = X(3303)-zayin conjugate of-X(1)
X(61763) = pole of the line {1756, 3339} with respect to the 1st Evans circle
X(61763) = pole of the line {672, 10857} with respect to the Gheorghe circle
X(61763) = pole of the line {4978, 44426} with respect to the polar circle
X(61763) = pole of the line {910, 10857} with respect to the Stevanovic circle
X(61763) = pole of the line {314, 10462} with respect to the Steiner-Wallace hyperbola
X(61763) = X(3541)-of-excentral triangle, when ABC is acute
X(61763) = X(3549)-of-6th mixtilinear triangle, when ABC is acute
X(61763) = X(3601)-of-Aquila triangle
X(61763) = X(5175)-of-outer-Garcia triangle
X(61763) = X(59349)-of-1st circumperp triangle, when ABC is acute
X(61763) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 16192, 36), (1, 31508, 35), (3, 1697, 1), (35, 5119, 1), (40, 55, 1), (46, 3746, 1), (55, 37568, 40), (56, 31393, 1), (57, 3295, 1), (165, 53053, 1), (942, 10389, 1), (986, 3749, 1), (988, 37588, 1), (999, 37556, 1), (1385, 7962, 1), (1420, 9957, 1), (1482, 13384, 1), (1697, 35445, 3), (2646, 7982, 1), (3057, 3576, 1), (3303, 3333, 1), (3340, 24929, 1), (3612, 5697, 1), (3931, 5269, 1), (5010, 37563, 1), (5255, 17594, 1), (5711, 37553, 1), (5903, 59337, 1), (5919, 61762, 1), (7070, 37528, 1), (7373, 51779, 1), (7987, 9819, 1), (8726, 10388, 1), (11529, 37080, 1), (11531, 53054, 1), (13462, 30337, 1), (16192, 53052, 1), (16200, 34471, 1), (25415, 37571, 1), (26358, 59333, 1), (30323, 37525, 1), (34486, 54408, 1), (37548, 37554, 1), (37552, 37598, 1)

X(61764) = X(36)X(8056) ∩ X(58245)X(58793)

Barycentrics    a*(a+b-3*c)*(a-3*b+c)*(27*a^4-12*(b+c)*a^3-2*(9*b^2-14*b*c+9*c^2)*a^2+4*(b+c)*(3*b^2-5*b*c+3*c^2)*a-9*(b^2-c^2)^2) : :

See Tran Viet Hung and César Lozada, Romantics of Geometry - Feb 28, 2024.

X(61764) lies on these lines: {36, 8056}, {5204, 61765}, {58245, 58793}

X(61765) = X(4)X(519) ∩ X(5204)X(61764)

Barycentrics    a*(a+b-3*c)*(a-3*b+c)*(9*a^4-6*(b+c)*a^3+16*b*c*a^2+2*(b+c)*(3*b^2-8*b*c+3*c^2)*a-9*(b^2-c^2)^2) : :

See Tran Viet Hung and César Lozada, Romantics of Geometry - Feb 28, 2024.

X(61765) lies on these lines: {4, 519}, {5204, 61764}

X(61766) = (X(35)X(25430) ∩ X(5217)X(61767)

Barycentrics    a*(a+3*c+b)*(a+c+3*b)*(27*a^4+12*(b+c)*a^3-2*(9*b^2+10*b*c+9*c^2)*a^2-4*(b+c)*(3*b^2-b*c+3*c^2)*a-9*(b^2-c^2)^2) : :

See Tran Viet Hung and César Lozada, Romantics of Geometry - Feb 28, 2024.

X(61766) lies on these lines: {35, 25430}, {5217, 61767}

X(61767) = X(4)X(3679) ∩ X(5217)X(61766)

Barycentrics    a*(a+3*c+b)*(a+c+3*b)*(9*a^4+6*(b+c)*a^3-8*b*c*a^2-2*(b+c)*(3*b^2-4*b*c+3*c^2)*a-9*(b^2-c^2)^2) : :

See Tran Viet Hung and César Lozada, Romantics of Geometry - Feb 28, 2024.

X(61767) lies on these lines: {4, 3679}, {5217, 61766}

X(61768) = X(4)X(145) ∩ X(56)X(88)

Barycentrics    a*(a+c-2*b)*(a-2*c+b)*(a^4-(b+c)*a^3+3*b*c*a^2+(b+c)*(b^2-3*b*c+c^2)*a-(b^2-c^2)^2) : :

See Tran Viet Hung and César Lozada, Romantics of Geometry - Feb 28, 2024.

X(61768) lies on the cubic K619 and these lines: {1, 1168}, {4, 145}, {36, 61769}, {40, 901}, {56, 88}, {65, 40215}, {78, 52925}, {106, 3924}, {355, 36590}, {519, 52753}, {523, 1222}, {903, 34605}, {1385, 52478}, {1797, 4792}, {2099, 47058}, {3057, 14190}, {3257, 3869}, {3336, 4674}, {4188, 14193}, {4591, 37405}, {4861, 21307}, {4945, 11236}, {4997, 11681}, {5289, 40594}, {5697, 39148}, {7354, 19636}, {10106, 60578}, {19861, 52140}, {37614, 52900}, {38460, 42753}

X(61768) = X(1320)-beth conjugate of-X(16944)
X(61768) = X(1319)-Dao conjugate of-X(1317)
X(61768) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (5176, 4358), (39270, 14628)
X(61768) = Cundy-Parry-Psi-transform of X(48667)
X(61768) = barycentric product X(88)*X(5176)
X(61768) = trilinear product X(106)*X(5176)
X(61768) = trilinear quotient X(i)/X(j) for these (i, j): (5176, 519), (39270, 14584)

X(61769) = X(34)X(106) ∩ X(56)X(1168)

Barycentrics    a*(a+c-2*b)*(a-2*c+b)*(3*a^4-2*(b+c)*a^3-(2*b-c)*(b-2*c)*a^2+2*(b^2-c^2)*(b-c)*a-(b^2-c^2)^2) : :

See Tran Viet Hung and César Lozada, Romantics of Geometry - Feb 28, 2024.

X(61769) lies on these lines: {1, 39148}, {34, 106}, {36, 61768}, {46, 4792}, {56, 1168}, {65, 16944}, {901, 5697}, {1388, 14260}, {3257, 30144}, {14190, 24928}, {37618, 52031}

X(61770) = X(5225)X(5558) ∩ X(5229)X(7320)

Barycentrics    (9*a^2+2*a*b+9*b^2-9*c^2)*(9*a^2-9*b^2+2*a*c+9*c^2) : :

See Tran Viet Hung and César Lozada, Romantics of Geometry - March 1st, 2024.

X(61770) lies on the Feuerbach hyperbola and these lines: {1, 50688}, {1000, 22793}, {3296, 18527}, {5225, 5558}, {5229, 7320}, {6223, 61105}, {9785, 13602}, {18391, 33696}

X(61770) = cevapoint of X(31601) and X(31602)

X(61771) = THOMSON-ISOGONAL CONJUGATE OF X(3091)

Barycentrics    a^2*(27*a^4 - 12*a^2*b^2 - 15*b^4 - 12*a^2*c^2 + 2*b^2*c^2 - 15*c^4) : :

See X(5544) for context.

X(61771) lies on the Thomson-Gibert-Moses hyperbola and these lines: {2, 50957}, {6, 9909}, {22, 9716}, {23, 52719}, {25, 5643}, {30, 43841}, {110, 55629}, {154, 55649}, {376, 32605}, {3167, 35268}, {3534, 5654}, {3796, 5644}, {5020, 14924}, {5054, 16655}, {5544, 43650}, {5646, 55674}, {5648, 50989}, {5655, 15695}, {5656, 8703}, {5888, 26881}, {6800, 55038}, {7712, 8780}, {12164, 12307}, {15066, 55156}, {17811, 55661}, {37672, 55587}, {50991, 61683}, {55707, 58470}.

X(61771) = Thomson-isogonal conjugate of X(3091)
X(61771) = {X(44108),X(55593)}-harmonic conjugate of X(3167)

X(61772) = THOMSON-ISOGONAL CONJUGATE OF X(140)

Barycentrics    a^2*(3*a^4 + a^2*b^2 - 4*b^4 + a^2*c^2 - 13*b^2*c^2 - 4*c^4) : :
X(61772) = 5 X[3] + X[33539], 14 X[3] + X[57715], 14 X[33539] - 5 X[57715], 2 X[6] + 7 X[41435], X[14861] - 10 X[15712]

X(61772) lies on the Thomson-Gibert-Moses hyperbola and these lines: {2, 29317}, {3, 11439}, {6, 1627}, {22, 5646}, {35, 1201}, {51, 5643}, {110, 3819}, {354, 33852}, {392, 13587}, {549, 43804}, {1154, 43600}, {3060, 5644}, {3167, 7998}, {3523, 43841}, {3524, 5654}, {3917, 55038}, {5012, 9716}, {5544, 7484}, {5640, 55618}, {5645, 55587}, {5648, 50991}, {5650, 6030}, {5655, 12100}, {5656, 11204}, {5888, 6636}, {5943, 55621}, {6000, 45308}, {6688, 15107}, {7516, 54041}, {7712, 55665}, {10545, 16419}, {10627, 46865}, {11402, 21766}, {12163, 20791}, {13434, 54042}, {14861, 15712}, {14924, 40916}, {15019, 55580}, {15080, 55157}, {15131, 58434}, {15717, 32605}, {20188, 34291}, {23061, 55704}, {32064, 61683}, {33884, 55707}, {43650, 55721}, {43651, 54047}, {44324, 61134}, {53863, 55719}, {54006, 54044}.

X(61772) = Thomson-isogonal conjugate of X(140)
X(61772) = {X(3819),X(55674)}-harmonic conjugate of X(44108)

X(61773) = THOMSON-ISOGONAL CONJUGATE OF X(631)

Barycentrics    a^2*(3*a^4 + 2*a^2*b^2 - 5*b^4 + 2*a^2*c^2 - 22*b^2*c^2 - 5*c^4) : :
X(61773) = 4 X[3] - X[16936], 8 X[3] + X[22334], 2 X[3] + X[33537], 2 X[16936] + X[22334], X[16936] + 2 X[33537], X[22334] - 4 X[33537], X[6] - 4 X[31521], X[6] + 2 X[34817], 2 X[31521] + X[34817], 4 X[140] - X[9815], 5 X[631] + X[11821], 7 X[3523] - X[15740], 5 X[3763] - 2 X[15435], 13 X[10303] - X[15741], X[11469] + 11 X[15717]

X(61773) lies on the Thomson-Gibert-Moses hyperbola and these lines: {2, 21167}, {3, 13474}, {6, 3917}, {22, 5888}, {25, 5646}, {51, 55591}, {55, 1201}, {110, 3796}, {140, 9815}, {154, 5650}, {165, 392}, {184, 55684}, {394, 7496}, {511, 5644}, {549, 5654}, {631, 1192}, {1350, 5544}, {1853, 21358}, {2178, 42316}, {3060, 5643}, {3098, 10219}, {3167, 3819}, {3304, 33588}, {3523, 3532}, {3524, 5656}, {3530, 59543}, {3763, 7386}, {5020, 55646}, {5324, 37679}, {5645, 10601}, {5648, 50993}, {5655, 15041}, {6030, 35259}, {6688, 55610}, {7392, 48872}, {7396, 34573}, {7516, 10610}, {7712, 15246}, {7998, 37672}, {8667, 59564}, {8780, 55674}, {9306, 55157}, {9909, 15082}, {10303, 15741}, {10516, 10691}, {11245, 15533}, {11469, 15717}, {12045, 55624}, {12100, 32620}, {12316, 36752}, {13154, 13391}, {14096, 15815}, {14924, 17810}, {15080, 55156}, {15720, 58447}, {17265, 37107}, {20062, 59776}, {20850, 55653}, {23039, 37514}, {26898, 33924}, {33586, 41462}, {34986, 55699}, {35450, 55166}, {36751, 53852}, {37261, 37674}, {55593, 58470}.

X(61773) = Thomson-isogonal conjugate of X(631)
X(61773) = X(23051)-complementary conjugate of X(16254)
X(61773) = crossdifference of every pair of points on line {3800, 43061}
X(61773) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 33537, 16936}, {7485, 17811, 53094}, {16936, 33537, 22334}, {31521, 34817, 6}, {41462, 59777, 55607}

X(61774) = THOMSON-ISOGONAL CONJUGATE OF X(15692)

Barycentrics    a^2*(a^4 + 4*a^2*b^2 - 5*b^4 + 4*a^2*c^2 - 74*b^2*c^2 - 5*c^4) : :

X(61774) lies on the Thomson-Gibert-Moses hyperbola and these lines: {2, 21850}, {6, 15082}, {110, 12017}, {140, 5656}, {154, 5092}, {323, 52719}, {354, 5268}, {392, 12702}, {511, 14924}, {632, 43841}, {1351, 5643}, {3098, 5646}, {3167, 43650}, {3426, 5054}, {3525, 32605}, {3526, 5654}, {3763, 5648}, {5020, 55646}, {5050, 9716}, {5544, 5650}, {5644, 15004}, {5651, 55157}, {5655, 6699}, {5888, 11284}, {6030, 7484}, {6800, 55156}, {7712, 40916}, {9909, 55658}, {10545, 55610}, {12045, 55585}, {15041, 45019}, {15066, 55038}, {15583, 34573}, {15701, 18551}, {16042, 55643}, {16059, 35270}, {16187, 55676}, {17810, 55598}, {17811, 55710}, {17825, 55715}, {22260, 34291}, {30734, 55648}, {31860, 55636}, {37517, 59777}, {41424, 55665}, {44106, 55632}, {46219, 54202}.

X(61774) = Thomson-isogonal conjugate of X(15692)
X(61774) = {X(5888),X(11284)}-harmonic conjugate of X(55639)

X(61775) = THOMSON-ISOGONAL CONJUGATE OF X(548)

Barycentrics    a^2*(3*a^4 - 7*a^2*b^2 + 4*b^4 - 7*a^2*c^2 - 13*b^2*c^2 + 4*c^4) : :
X(61775) = 2 X[3] + 7 X[1173], X[3] - 7 X[15047], 13 X[3] - 7 X[33542], X[3] + 14 X[46084], X[1173] + 2 X[15047], 13 X[1173] + 2 X[33542], X[1173] - 4 X[46084], 13 X[15047] - X[33542], X[15047] + 2 X[46084], X[33542] + 26 X[46084], 13 X[5068] + 14 X[34564], 7 X[34483] - 22 X[55859], 20 X[48154] + 7 X[51885].

X(61775) lies on the Thomson-Gibert-Moses hyperbola and these lines: {2, 15520}, {3, 143}, {51, 6030}, {110, 5943}, {154, 5640}, {323, 10219}, {373, 55038}, {392, 16861}, {394, 14924}, {1201, 37602}, {1993, 5544}, {1994, 5643}, {3167, 11451}, {3839, 5656}, {3858, 43821}, {3917, 5888}, {5012, 7712}, {5066, 5655}, {5068, 11442}, {5071, 5654}, {5093, 44299}, {5646, 10601}, {5648, 61655}, {5652, 7927}, {6636, 55690}, {7486, 43841}, {7605, 11225}, {9140, 32068}, {9706, 15026}, {10545, 35264}, {10821, 45019}, {11002, 55693}, {11205, 39024}, {12013, 15699}, {13451, 61134}, {13595, 55156}, {15004, 55720}, {15107, 55696}, {15246, 44107}, {15682, 51993}, {16042, 44111}, {16981, 55630}, {21849, 55686}, {21969, 55615}, {23061, 34565}, {34483, 55859}, {35018, 41724}, {37636, 48154}, {43650, 55585}, {47328, 47486}, {59373, 61683}.

X(61775) = Thomson-isogonal conjugate of X(548)
X(61775) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {12834, 34545, 110}, {15047, 46084, 1173}.

X(61776) = X(3)X(351)∩X(74)X(526)

Barycentrics    a^2*(b^2 - c^2)*(4*a^6 - 7*a^4*b^2 + 2*a^2*b^4 + b^6 - 7*a^4*c^2 + 18*a^2*b^2*c^2 - 7*b^4*c^2 + 2*a^2*c^4 - 7*b^2*c^4 + c^6) : :
X(61776) = 3 X[3] - 2 X[9126], 5 X[3] - 2 X[11615], 3 X[351] - 4 X[9126], 5 X[351] - 4 X[11615], 5 X[9126] - 3 X[11615], X[9409] + 2 X[53247], X[684] - 4 X[44826], 3 X[2071] - X[9213], 3 X[3524] - 2 X[11176], 3 X[5085] - 2 X[9188], 3 X[8371] - 2 X[44203], X[9138] - 3 X[15055], X[9147] - 3 X[10304], X[9156] - 3 X[38716].

X(61776) lies on these lines: {3, 351}, {4, 45689}, {20, 53365}, {30, 9148}, {74, 526}, {376, 804}, {378, 17994}, {381, 16235}, {512, 684}, {523, 54995}, {549, 19912}, {669, 30230}, {686, 21663}, {1296, 6088}, {1350, 9023}, {2071, 9213}, {2793, 55271}, {3524, 11176}, {5085, 9188}, {7464, 20403}, {8371, 44203}, {8644, 20186}, {9134, 9529}, {9135, 9155}, {9138, 15055}, {9147, 10304}, {9156, 38716}, {11410, 47230}, {11634, 42743}, {12041, 19902}, {14420, 44202}, {17414, 30209}, {19901, 38623}, {21731, 44814}, {46997, 53567}.

X(61776) = midpoint of X(20) and X(53365)
X(61776) = reflection of X(i) in X(j) for these {i,j}: {4, 45689}, {351, 3}, {381, 16235}, {14420, 44202}, {19901, 38623}, {19902, 12041}, {19912, 549}, {21731, 44814}
X(61776) = crossdifference of every pair of points on line {3163, 7735}

X(61777) = X(2)X(3)∩X(40)X(51104)

Barycentrics    55*a^4+(b^2-c^2)^2-56*a^2*(b^2+c^2) : :
X(61777) = X[2]+18*X[3], 9*X[40]+10*X[51104], -X[1992]+20*X[55672], 15*X[3576]+4*X[50814], X[4677]+75*X[58217], -3*X[5032]+22*X[55678], 15*X[5085]+4*X[50970], 15*X[5657]+4*X[51082], 3*X[6361]+16*X[51108], 9*X[6776]+10*X[50989], 15*X[7967]+4*X[50817], -20*X[7987]+X[34631] and many others

X(61777) lies on these lines: {2, 3}, {40, 51104}, {1992, 55672}, {3576, 50814}, {4677, 58217}, {5032, 55678}, {5085, 50970}, {5657, 51082}, {6361, 51108}, {6482, 43524}, {6483, 43523}, {6560, 43536}, {6561, 54597}, {6776, 50989}, {7967, 50817}, {7987, 34631}, {8252, 43522}, {8253, 43521}, {8584, 55676}, {9541, 43387}, {9741, 46893}, {10164, 51080}, {10165, 50813}, {10519, 51136}, {10595, 41150}, {11179, 55666}, {11488, 42631}, {11489, 42632}, {13665, 60622}, {13785, 60623}, {14226, 43375}, {14241, 43374}, {14912, 50973}, {18581, 43331}, {18582, 43330}, {20423, 55660}, {21167, 51135}, {33604, 54593}, {33605, 54594}, {33750, 51189}, {34089, 42267}, {34091, 42266}, {34632, 61277}, {35242, 51103}, {38064, 55659}, {38737, 41154}, {39874, 50991}, {40693, 42504}, {40694, 42505}, {41100, 42930}, {41101, 42931}, {41112, 43646}, {41113, 43645}, {41119, 43554}, {41120, 43555}, {41149, 55671}, {41945, 42569}, {41946, 42568}, {42095, 51915}, {42098, 51916}, {42476, 43104}, {42477, 43101}, {42478, 42800}, {42479, 42799}, {42490, 42502}, {42491, 42503}, {42510, 43003}, {42511, 43002}, {42528, 42588}, {42529, 42589}, {42557, 43518}, {42558, 43517}, {42566, 43209}, {42567, 43210}, {42572, 43256}, {42573, 43257}, {42576, 42582}, {42577, 42583}, {42586, 42949}, {42587, 42948}, {42625, 43463}, {42626, 43464}, {42777, 43777}, {42778, 43778}, {43273, 51142}, {43314, 53131}, {43315, 53130}, {43420, 49947}, {43421, 49948}, {43481, 49905}, {43482, 49906}, {43489, 46334}, {43490, 46335}, {43493, 49813}, {43494, 49812}, {43548, 44015}, {43549, 44016}, {43787, 60307}, {43788, 60308}, {49875, 52080}, {49876, 52079}, {50808, 61275}, {50810, 51097}, {50811, 51067}, {50820, 58441}, {50872, 61280}, {50966, 55649}, {50967, 55673}, {50974, 55664}, {50987, 55624}, {50992, 55665}, {51028, 55643}, {51066, 58215}, {51069, 61256}, {51072, 61244}, {51079, 54447}, {51178, 51188}, {51185, 55656}, {51187, 54169}, {51705, 61294}, {54132, 55654}, {54170, 55655}, {54173, 55667}, {54174, 55682}, {54523, 60283}, {54612, 60277}, {54616, 54734}, {54637, 54644}, {54645, 60284}, {54707, 60238}, {54851, 60143}, {55653, 59373}, {58223, 61282}, {60150, 60641}, {60185, 60216}

X(61777) = pole of line {69, 61993} with respect to the Wallace hyperbola
X(61777) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(18317), X(55858)}}, {{A, B, C, X(46412), X(55861)}}, {{A, B, C, X(50691), X(54667)}}, {{A, B, C, X(52301), X(54851)}}
X(61777) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10304, 15690}, {3, 14891, 10304}, {3, 15692, 15710}, {3, 15705, 376}, {3, 15706, 15714}, {3, 15716, 15759}, {4, 5070, 3544}, {376, 3545, 1657}, {376, 631, 3839}, {547, 14890, 632}, {547, 8703, 3534}, {1657, 15718, 14890}, {1657, 3861, 3146}, {3522, 15700, 15709}, {3523, 4220, 15717}, {3524, 3528, 5071}, {3524, 5067, 549}, {3544, 12108, 3525}, {3830, 12100, 3523}, {3839, 15705, 17504}, {3839, 15718, 631}, {5054, 15681, 5}, {8703, 12100, 5054}, {10299, 10304, 15702}, {10299, 15682, 15693}, {10299, 15702, 3524}, {10299, 15710, 15681}, {10304, 14891, 10299}, {10304, 15693, 15682}, {10304, 15702, 17538}, {12100, 15705, 15698}, {12101, 15711, 6908}, {14093, 15708, 3529}, {14891, 15681, 15692}, {15640, 15713, 3090}, {15681, 15693, 11540}, {15682, 17538, 11001}, {15683, 15707, 3533}, {15688, 15713, 15640}, {15690, 15693, 2}, {15692, 15710, 4}, {15697, 15701, 3545}, {15697, 15717, 15701}, {15698, 15710, 15719}, {15702, 15715, 14891}, {15706, 15714, 20}, {15710, 15719, 8703}, {15711, 15759, 15716}, {15716, 15722, 12100}

X(61778) = X(2)X(3)∩X(8)X(58217)

Barycentrics    49*a^4+(b^2-c^2)^2-50*a^2*(b^2+c^2) : :
X(61778) = X[2]+16*X[3], X[8]+50*X[58217], 2*X[10]+49*X[58215], -X[1992]+18*X[55673], -X[3241]+18*X[58221], 16*X[3654]+X[20014], 4*X[3828]+81*X[58213], -15*X[5032]+32*X[51138], 16*X[5092]+X[54174], -25*X[7987]+8*X[51085], 7*X[7989]+10*X[51079], 7*X[9778]+10*X[61274] and many others

X(61778) lies on these lines: {2, 3}, {8, 58217}, {10, 58215}, {1992, 55673}, {3068, 43382}, {3069, 43383}, {3070, 60299}, {3071, 60300}, {3241, 58221}, {3654, 20014}, {3828, 58213}, {5032, 51138}, {5092, 54174}, {5210, 14930}, {5334, 43484}, {5335, 43483}, {5585, 37665}, {6452, 9542}, {6496, 42523}, {6497, 42522}, {7750, 32895}, {7771, 32869}, {7782, 32874}, {7809, 32873}, {7850, 32837}, {7987, 51085}, {7989, 51079}, {9543, 19053}, {9778, 61274}, {10519, 55664}, {11179, 55667}, {12007, 55671}, {14810, 51028}, {14831, 55166}, {14853, 55663}, {14927, 50984}, {16192, 38314}, {16772, 43495}, {16773, 43496}, {20049, 61291}, {20070, 50828}, {20080, 51737}, {20423, 55659}, {23253, 43558}, {23263, 43559}, {31663, 50872}, {32898, 48913}, {35814, 53130}, {35815, 53131}, {37640, 42687}, {37641, 42686}, {38064, 55658}, {42093, 51915}, {42094, 51916}, {42096, 43553}, {42097, 43552}, {42139, 51945}, {42142, 51944}, {42147, 43253}, {42148, 43252}, {42225, 42605}, {42226, 42604}, {42433, 49874}, {42434, 49873}, {42588, 43107}, {42589, 43100}, {42795, 43031}, {42796, 43030}, {43024, 43403}, {43025, 43404}, {43256, 43342}, {43257, 43343}, {43511, 52045}, {43512, 52046}, {46267, 55661}, {48872, 51139}, {50810, 61284}, {50863, 51088}, {50966, 55648}, {50967, 55674}, {50983, 61044}, {50987, 55616}, {50988, 51211}, {51107, 58229}, {51140, 55669}, {51141, 51216}, {51170, 55676}, {51171, 55656}, {54132, 55653}, {54170, 55654}, {54173, 55668}, {54639, 60331}, {54866, 60639}, {55651, 59373}, {58216, 61247}, {60102, 60625}, {60200, 60336}, {60293, 60295}, {60294, 60296}, {60333, 60650}

X(61778) = reflection of X(i) in X(j) for these {i,j}: {3533, 15722}, {3854, 2}
X(61778) = anticomplement of X(61927)
X(61778) = pole of line {185, 58186} with respect to the Jerabek hyperbola
X(61778) = pole of line {69, 51166} with respect to the Wallace hyperbola
X(61778) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1105), X(58186)}}, {{A, B, C, X(1494), X(3854)}}, {{A, B, C, X(3346), X(55858)}}, {{A, B, C, X(13623), X(38335)}}, {{A, B, C, X(46412), X(55860)}}
X(61778) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 30, 3854}, {3, 12100, 15710}, {3, 15698, 10304}, {3, 15700, 15714}, {3, 15706, 15759}, {3, 15715, 15692}, {4, 15698, 15706}, {4, 3528, 16434}, {20, 3523, 632}, {20, 3850, 3146}, {30, 15722, 3533}, {376, 15694, 3543}, {376, 15700, 15721}, {376, 15702, 15687}, {376, 15715, 14891}, {376, 3524, 15694}, {549, 15686, 3628}, {549, 3543, 17678}, {632, 17504, 12100}, {3146, 17564, 381}, {3522, 17678, 15683}, {3523, 10304, 15640}, {3523, 15640, 15709}, {3523, 3832, 17549}, {3524, 14269, 15708}, {3524, 3529, 11812}, {3524, 3533, 15722}, {3526, 3534, 14269}, {3528, 15693, 3839}, {3534, 10304, 3522}, {3534, 15720, 5055}, {5054, 15697, 3832}, {5071, 10299, 15718}, {6926, 15718, 15681}, {8703, 15718, 5071}, {10303, 10304, 3534}, {10304, 15640, 548}, {10304, 15692, 549}, {10304, 15698, 15717}, {10304, 15717, 2}, {11540, 17800, 3545}, {11812, 15709, 10303}, {12100, 14093, 15702}, {12100, 15710, 20}, {12100, 15720, 3524}, {14093, 15687, 376}, {14093, 15718, 3850}, {14891, 15714, 15700}, {15022, 15717, 3523}, {15640, 15709, 15022}, {15688, 15719, 3091}, {15692, 15715, 15705}, {15702, 15710, 14093}, {15705, 15717, 15698}, {15706, 15759, 4}

X(61779) = X(2)X(3)∩X(145)X(58220)

Barycentrics    46*a^4+(b^2-c^2)^2-47*a^2*(b^2+c^2) : :
X(61779) = X[2]+15*X[3], -X[145]+49*X[58220], X[597]+7*X[55658], -X[3629]+25*X[55672], -5*X[5092]+X[20583], X[6329]+5*X[55653], -X[8584]+9*X[17508], -X[11695]+4*X[55320], -X[15534]+33*X[55671], -9*X[17502]+X[51071], -X[18481]+49*X[58215], X[18583]+11*X[55662] and many others

X(61779) lies on these lines: {2, 3}, {145, 58220}, {395, 42505}, {396, 42504}, {519, 58219}, {524, 55668}, {597, 55658}, {3564, 55664}, {3629, 55672}, {4745, 28224}, {5092, 20583}, {6329, 55653}, {6411, 42644}, {6412, 42643}, {6425, 43524}, {6426, 43523}, {8584, 17508}, {9680, 43793}, {10645, 42533}, {10646, 42532}, {10653, 43207}, {10654, 43208}, {11542, 42631}, {11543, 42632}, {11695, 55320}, {12816, 42500}, {12817, 42501}, {15534, 55671}, {16241, 42502}, {16242, 42503}, {17502, 51071}, {18481, 58215}, {18583, 55662}, {19106, 51916}, {19107, 51915}, {28146, 51086}, {28174, 51108}, {28182, 50816}, {28186, 50829}, {28208, 58214}, {28212, 50828}, {29317, 51139}, {31662, 50814}, {31663, 51103}, {33750, 50990}, {34380, 55670}, {34641, 61524}, {34773, 58217}, {38034, 50812}, {38136, 50968}, {38138, 50819}, {38140, 51079}, {41100, 43111}, {41101, 43110}, {41107, 43871}, {41108, 43872}, {42108, 43231}, {42109, 43230}, {42121, 49859}, {42122, 43005}, {42123, 43004}, {42124, 49860}, {42135, 51945}, {42138, 51944}, {42274, 42577}, {42277, 42576}, {42415, 42507}, {42416, 42506}, {42419, 42977}, {42420, 42976}, {42496, 43109}, {42497, 43108}, {42524, 52045}, {42525, 52046}, {42608, 43791}, {42609, 43792}, {42625, 42627}, {42626, 42628}, {42635, 42798}, {42636, 42797}, {42791, 42897}, {42792, 42896}, {42902, 46335}, {42903, 46334}, {42946, 43026}, {42947, 43027}, {50818, 58218}, {50824, 51094}, {50965, 55660}, {50970, 55695}, {50979, 55673}, {50980, 51186}, {50983, 55657}, {50987, 55610}, {51132, 55685}, {51138, 55680}, {51181, 54174}, {51185, 55654}, {51732, 55655}, {51737, 55667}, {54044, 55166}, {54169, 55669}

X(61779) = midpoint of X(i) and X(j) for these {i,j}: {3, 14891}, {376, 3628}, {548, 10124}, {550, 11737}, {3534, 3860}, {3850, 15691}, {3861, 15686}, {8703, 11812}, {10109, 15690}, {12100, 15759}
X(61779) = reflection of X(i) in X(j) for these {i,j}: {12811, 10124}, {16239, 549}
X(61779) = complement of X(61997)
X(61779) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(265), X(41988)}}, {{A, B, C, X(16239), X(18317)}}, {{A, B, C, X(43970), X(49136)}}
X(61779) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12100, 3530}, {2, 15681, 3845}, {2, 15682, 3851}, {2, 15720, 15713}, {2, 3528, 3534}, {2, 3534, 15687}, {2, 546, 10109}, {3, 12100, 15759}, {3, 15700, 15710}, {3, 3524, 15714}, {30, 10124, 12811}, {30, 549, 16239}, {140, 3534, 3860}, {140, 548, 3146}, {376, 15713, 12101}, {548, 3524, 10124}, {549, 17504, 10299}, {549, 8703, 3830}, {550, 14869, 3855}, {550, 17504, 15700}, {1656, 15688, 15681}, {3146, 15692, 3524}, {3522, 15718, 15699}, {3524, 15714, 548}, {3528, 15692, 15707}, {3530, 3628, 15720}, {3534, 15707, 2}, {3545, 15687, 546}, {3830, 8703, 15690}, {3843, 5068, 3857}, {3845, 8703, 15697}, {5054, 15691, 3850}, {5066, 12100, 15693}, {5066, 15693, 11812}, {5068, 10304, 376}, {8703, 15693, 5066}, {8703, 15711, 15698}, {10109, 14891, 15716}, {10109, 15690, 30}, {10299, 15688, 549}, {10299, 15715, 15705}, {10304, 15712, 547}, {11539, 14093, 12103}, {11812, 15759, 8703}, {12100, 12103, 15722}, {12100, 15711, 14891}, {12101, 15713, 3628}, {12811, 16239, 1656}, {14093, 15717, 11539}, {14093, 15722, 15682}, {14891, 15759, 12100}, {15640, 15698, 15706}, {15686, 15713, 6959}, {15687, 15707, 140}, {15688, 15705, 17504}, {15688, 15707, 3545}, {15692, 15710, 5079}, {15695, 15706, 15719}, {15695, 15719, 5}, {15700, 15710, 550}, {15702, 15704, 14892}, {15714, 17504, 14869}

X(61780) = X(2)X(3)∩X(15)X(42517)

Barycentrics    43*a^4+(b^2-c^2)^2-44*a^2*(b^2+c^2) : :
X(61780) = X[2]+14*X[3], X[69]+44*X[55665], 8*X[141]+7*X[51177], 8*X[1125]+7*X[50813], -X[1992]+16*X[55674], 8*X[3589]+7*X[50969], X[3618]+8*X[55661], -X[3623]+10*X[58224], 8*X[3625]+7*X[50818], 8*X[3630]+7*X[50974], 8*X[3634]+7*X[50820], 14*X[3655]+X[20053] and many others

X(61780) lies on these lines: {2, 3}, {15, 42517}, {16, 42516}, {69, 55665}, {141, 51177}, {395, 43305}, {396, 43304}, {1125, 50813}, {1285, 5585}, {1992, 55674}, {3589, 50969}, {3618, 55661}, {3623, 58224}, {3625, 50818}, {3630, 50974}, {3634, 50820}, {3655, 20053}, {4668, 58217}, {4726, 51043}, {5032, 55682}, {5237, 42520}, {5238, 42521}, {5965, 55667}, {6144, 51179}, {6441, 43259}, {6442, 43258}, {6522, 9692}, {7750, 32889}, {8589, 46453}, {9680, 42524}, {9780, 58214}, {10576, 43521}, {10577, 43522}, {10653, 42928}, {10654, 42929}, {11179, 55668}, {11488, 43294}, {11489, 43295}, {11693, 15055}, {13624, 34631}, {14226, 42260}, {14241, 42261}, {14482, 53095}, {14912, 55670}, {14930, 15603}, {16267, 43481}, {16268, 43482}, {18492, 51079}, {19877, 51088}, {19878, 51083}, {20423, 55658}, {25055, 28232}, {25406, 55664}, {28234, 58221}, {31447, 51072}, {32455, 50967}, {32875, 37671}, {33602, 43769}, {33603, 43770}, {34573, 50976}, {35242, 50809}, {36427, 36751}, {36967, 42513}, {36968, 42512}, {37640, 44017}, {37641, 44018}, {38064, 55657}, {41869, 51086}, {42095, 43780}, {42096, 51915}, {42097, 51916}, {42098, 43779}, {42133, 51945}, {42134, 51944}, {42225, 43518}, {42226, 43517}, {42429, 42472}, {42430, 42473}, {42433, 43310}, {42434, 43311}, {42490, 49825}, {42491, 49824}, {42510, 42806}, {42511, 42805}, {42625, 43107}, {42626, 43100}, {42942, 42987}, {42943, 42986}, {42944, 49876}, {42945, 49875}, {43322, 53131}, {43323, 53130}, {43372, 43542}, {43373, 43543}, {43465, 43554}, {43466, 43555}, {43544, 43771}, {43545, 43772}, {43787, 43795}, {43788, 43796}, {46930, 50800}, {46934, 50833}, {48910, 51139}, {50966, 55646}, {50970, 55699}, {50983, 55656}, {50987, 55604}, {51028, 55639}, {51212, 55662}, {53620, 58216}, {54041, 55166}, {54132, 55651}, {54170, 55653}, {54173, 55669}, {55649, 59373}, {60131, 60325}, {60297, 60309}, {60298, 60310}, {61306, 61312}

X(61780) = midpoint of X(i) and X(j) for these {i,j}: {5055, 15696}, {15688, 15694}
X(61780) = reflection of X(i) in X(j) for these {i,j}: {12812, 14890}, {15697, 15688}, {3524, 15692}, {3839, 1656}, {5055, 15713}, {631, 3524}
X(61780) = pole of line {69, 14893} with respect to the Wallace hyperbola
X(61780) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(14893)}}, {{A, B, C, X(5072), X(36889)}}, {{A, B, C, X(12811), X(54763)}}, {{A, B, C, X(15696), X(54660)}}, {{A, B, C, X(15708), X(18852)}}, {{A, B, C, X(18851), X(44245)}}, {{A, B, C, X(33703), X(57822)}}, {{A, B, C, X(35404), X(54667)}}, {{A, B, C, X(46412), X(48154)}}
X(61780) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10304, 15689}, {2, 12108, 15702}, {2, 15692, 15712}, {2, 15708, 14890}, {2, 20, 14893}, {2, 3543, 5072}, {3, 15693, 15714}, {3, 15698, 376}, {3, 15700, 15759}, {3, 15715, 15698}, {3, 17504, 10304}, {3, 3524, 15710}, {20, 377, 12102}, {30, 14890, 12812}, {30, 15713, 5055}, {30, 1656, 3839}, {376, 15698, 10299}, {376, 15719, 3090}, {376, 3524, 15709}, {376, 3533, 15682}, {376, 3855, 11001}, {549, 15682, 3533}, {549, 8703, 3853}, {631, 15696, 3855}, {631, 3529, 1656}, {1656, 3853, 3091}, {1657, 14093, 15695}, {3522, 15692, 15693}, {3524, 10304, 3545}, {3524, 15702, 15707}, {3524, 15709, 15719}, {3524, 15715, 15705}, {3545, 15682, 14269}, {3627, 14891, 15716}, {8703, 15702, 3529}, {10124, 15640, 3544}, {10299, 15709, 3524}, {10304, 15705, 17504}, {11737, 15686, 15684}, {12100, 15688, 15708}, {12108, 15684, 2}, {12812, 14093, 15697}, {14093, 14891, 15692}, {14093, 15693, 3843}, {14093, 15694, 15686}, {14269, 15689, 1657}, {15683, 15701, 5067}, {15686, 15697, 17538}, {15688, 15694, 30}, {15688, 15707, 11737}, {15688, 15708, 4}, {15692, 15714, 5071}, {15693, 15714, 3522}, {15699, 17504, 12100}, {15700, 15759, 20}, {15711, 15712, 14891}, {15712, 17538, 631}, {15713, 16239, 15694}

X(61781) = X(2)X(3)∩X(165)X(50872)

Barycentrics    37*a^4+(b^2-c^2)^2-38*a^2*(b^2+c^2) : :
X(61781) = X[2]+12*X[3], 12*X[165]+X[50872], -X[193]+40*X[55672], 2*X[597]+11*X[55656], -3*X[962]+16*X[51108], -3*X[1699]+16*X[51086], -X[1992]+14*X[55676], X[2979]+12*X[55166], -15*X[3576]+2*X[51077], 12*X[3653]+X[20070], X[3679]+25*X[58217], 4*X[4669]+9*X[5731] and many others

X(61781) lies on these lines: {2, 3}, {165, 50872}, {193, 55672}, {597, 55656}, {962, 51108}, {1078, 32892}, {1699, 51086}, {1992, 55676}, {2979, 55166}, {3576, 51077}, {3593, 13798}, {3595, 13678}, {3653, 20070}, {3679, 58217}, {4669, 5731}, {5032, 5092}, {5085, 51132}, {5237, 43022}, {5238, 43023}, {5304, 8589}, {5334, 42632}, {5335, 42631}, {5351, 42532}, {5352, 42533}, {5476, 55663}, {5585, 9300}, {5657, 50804}, {5734, 51106}, {5886, 50813}, {5921, 50991}, {6396, 9542}, {6409, 42523}, {6410, 42522}, {6411, 19053}, {6412, 19054}, {6426, 9692}, {6776, 55666}, {7917, 32837}, {7987, 51071}, {7988, 50873}, {7991, 51104}, {8584, 53094}, {8588, 37665}, {9143, 15036}, {9588, 51070}, {9740, 46893}, {9812, 50812}, {10164, 50801}, {10168, 55662}, {10171, 51083}, {10175, 50820}, {10519, 50961}, {11055, 32522}, {11160, 55668}, {11179, 55669}, {14561, 50969}, {14853, 55660}, {14912, 51174}, {14930, 15655}, {15534, 55673}, {16192, 34632}, {16241, 49825}, {16242, 49824}, {17502, 50810}, {17508, 33748}, {19875, 58215}, {20014, 58220}, {20423, 55657}, {21167, 50958}, {22165, 25406}, {26446, 58216}, {28198, 46934}, {30308, 50816}, {30389, 51107}, {30392, 50814}, {31145, 58219}, {31884, 51028}, {32836, 43459}, {33606, 43645}, {33607, 43646}, {33750, 50977}, {34473, 36521}, {35242, 38314}, {36967, 49873}, {36968, 49874}, {37640, 42792}, {37641, 42791}, {38064, 55655}, {41119, 42528}, {41120, 42529}, {42089, 46335}, {42090, 43541}, {42091, 43540}, {42092, 46334}, {42104, 54580}, {42105, 54581}, {42111, 43478}, {42114, 43477}, {42121, 43778}, {42124, 43777}, {42140, 42501}, {42141, 42500}, {42149, 42505}, {42150, 42507}, {42151, 42506}, {42152, 42504}, {42270, 42577}, {42273, 42576}, {42275, 43567}, {42276, 43566}, {42417, 42638}, {42418, 42637}, {42502, 43238}, {42503, 43239}, {42510, 42976}, {42511, 42977}, {42524, 43511}, {42525, 43512}, {42588, 42625}, {42589, 42626}, {42604, 43517}, {42605, 43518}, {42639, 43374}, {42640, 43375}, {42942, 42983}, {42943, 42982}, {43242, 49811}, {43243, 49810}, {43254, 43407}, {43255, 43408}, {43273, 50994}, {43296, 49813}, {43297, 49812}, {43509, 52048}, {43510, 52047}, {43641, 54592}, {43642, 54591}, {44882, 51186}, {46932, 58214}, {47745, 51072}, {50808, 51110}, {50811, 51068}, {50829, 59387}, {50864, 51069}, {50867, 51081}, {50966, 55643}, {50968, 51538}, {50970, 55703}, {50972, 51213}, {50983, 55654}, {50987, 55593}, {50992, 51737}, {51023, 51143}, {51075, 51109}, {51093, 58221}, {51130, 51211}, {51139, 53023}, {51170, 55678}, {51171, 55653}, {51185, 54170}, {52711, 57822}, {54132, 55649}, {54169, 55671}, {54173, 55670}, {55646, 59373}

X(61781) = midpoint of X(i) and X(j) for these {i,j}: {376, 5067}
X(61781) = anticomplement of X(61926)
X(61781) = pole of line {69, 61989} with respect to the Wallace hyperbola
X(61781) = intersection, other than A, B, C, of circumconics {{A, B, C, X(253), X(5066)}}, {{A, B, C, X(1217), X(55862)}}, {{A, B, C, X(15640), X(57822)}}, {{A, B, C, X(18317), X(46219)}}, {{A, B, C, X(46412), X(55857)}}
X(61781) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10304, 15697}, {2, 11001, 3839}, {2, 15640, 3091}, {2, 15693, 15708}, {2, 15697, 3543}, {3, 15693, 15759}, {3, 5054, 15714}, {3, 549, 15710}, {20, 10303, 5068}, {20, 5056, 3627}, {140, 14891, 17504}, {140, 15699, 15723}, {140, 15708, 15721}, {140, 15759, 8703}, {140, 382, 3090}, {140, 8703, 15685}, {376, 5055, 5059}, {376, 5067, 30}, {548, 15707, 5071}, {549, 15710, 3522}, {550, 15718, 15709}, {3090, 11001, 12101}, {3090, 3524, 549}, {3524, 15682, 15701}, {3524, 15698, 15716}, {3524, 15710, 15689}, {3528, 5054, 15683}, {3530, 14093, 3545}, {3534, 10109, 15682}, {3534, 12100, 15719}, {3534, 15701, 10109}, {3627, 8703, 15690}, {3850, 15704, 382}, {5054, 15683, 5056}, {5054, 15714, 3528}, {5066, 15712, 15722}, {6891, 15698, 5154}, {6911, 16239, 1656}, {6926, 15693, 15704}, {8703, 10109, 3534}, {8703, 15691, 15695}, {8703, 15711, 14891}, {10304, 15692, 3523}, {10304, 15721, 20}, {11812, 15695, 4}, {12100, 15701, 3524}, {12100, 15759, 3845}, {12101, 15689, 11001}, {14891, 15716, 15698}, {15640, 15708, 2}, {15640, 15759, 10304}, {15685, 15693, 140}, {15688, 15702, 3146}, {15688, 15712, 15702}, {15688, 15722, 5066}, {15692, 15708, 15717}, {15693, 15759, 376}, {15695, 15700, 11812}, {15698, 15711, 15705}, {15698, 15715, 15711}, {15701, 15716, 12100}, {15717, 15759, 15640}, {15717, 17504, 15692}, {15759, 17504, 15693}, {37640, 43003, 42792}, {37641, 43002, 42791}, {42500, 51944, 42141}, {42501, 51945, 42140}

X(61782) = X(2)X(3)∩X(6)X(43258)

Barycentrics    34*a^4+(b^2-c^2)^2-35*a^2*(b^2+c^2) : :
X(61782) = X[2]+11*X[3], X[597]+5*X[55655], 5*X[3655]+X[50830], -5*X[4701]+11*X[50827], -5*X[5092]+2*X[51138], X[5476]+11*X[55662], -10*X[7987]+X[61597], -X[8584]+7*X[55681], -X[9143]+13*X[15042], -X[9955]+4*X[51086], X[10168]+5*X[55661], 2*X[10620]+7*X[22250] and many others

X(61782) lies on these lines: {2, 3}, {6, 43258}, {515, 58216}, {524, 55670}, {542, 55664}, {597, 55655}, {1154, 55166}, {3564, 55667}, {3653, 28212}, {3655, 50830}, {4701, 50827}, {5092, 51138}, {5318, 43330}, {5321, 43331}, {5476, 55662}, {5844, 58221}, {6409, 43526}, {6410, 43525}, {6496, 19053}, {6497, 19054}, {7987, 61597}, {8252, 43337}, {8253, 43336}, {8584, 55681}, {8981, 43338}, {9143, 15042}, {9955, 51086}, {10168, 55661}, {10620, 22250}, {10653, 43197}, {10654, 43198}, {11179, 50985}, {11180, 50981}, {11542, 43483}, {11543, 43484}, {11693, 12041}, {12007, 55674}, {12702, 50832}, {12816, 42949}, {12817, 42948}, {13624, 51085}, {13966, 43339}, {15170, 59325}, {16192, 51700}, {16644, 43328}, {16645, 43329}, {16962, 42796}, {16963, 42795}, {18357, 50829}, {18358, 50984}, {18481, 50825}, {18493, 50813}, {18510, 43383}, {18512, 43382}, {18526, 50822}, {18583, 55659}, {19130, 51139}, {19883, 28178}, {19924, 55663}, {20423, 55656}, {20583, 55688}, {28186, 38068}, {28190, 38083}, {28208, 61614}, {28216, 38022}, {31162, 50833}, {31454, 42524}, {31730, 51084}, {33697, 51079}, {33878, 50987}, {34380, 55673}, {34627, 50826}, {34628, 58215}, {34648, 51088}, {34748, 58220}, {35814, 41945}, {35815, 41946}, {36967, 42628}, {36968, 42627}, {38064, 55654}, {39899, 51184}, {41107, 43635}, {41108, 43634}, {41112, 42773}, {41113, 42774}, {41943, 43109}, {41944, 43108}, {42121, 43333}, {42124, 43332}, {42136, 42501}, {42137, 42500}, {42144, 51945}, {42145, 51944}, {42225, 43255}, {42226, 43254}, {42260, 43341}, {42261, 43340}, {42263, 43514}, {42264, 43513}, {42506, 42959}, {42507, 42958}, {42584, 43203}, {42585, 43204}, {42686, 42913}, {42687, 42912}, {42688, 43404}, {42689, 43403}, {42690, 43630}, {42691, 43631}, {42934, 42944}, {42935, 42945}, {42968, 43481}, {42969, 43482}, {42970, 43417}, {42971, 43416}, {42972, 43490}, {42973, 43489}, {42980, 43009}, {42981, 43008}, {42998, 43003}, {42999, 43002}, {43101, 43468}, {43104, 43467}, {43105, 43200}, {43106, 43199}, {43110, 43303}, {43111, 43302}, {43211, 43316}, {43212, 43317}, {43300, 43871}, {43301, 43872}, {46264, 50980}, {48881, 51137}, {48884, 51134}, {50664, 50970}, {50805, 58224}, {50811, 58217}, {50815, 58214}, {50820, 61261}, {50965, 55658}, {50967, 55678}, {50977, 55665}, {50979, 55676}, {50982, 55668}, {50983, 55653}, {50988, 54131}, {51028, 55632}, {51091, 58223}, {51132, 55691}, {51140, 54169}, {51732, 55651}, {51737, 55669}, {53094, 61624}, {54132, 55648}, {54173, 55671}, {54174, 55692}, {55643, 59373}

X(61782) = midpoint of X(i) and X(j) for these {i,j}: {3, 17504}, {5, 15689}, {376, 15699}, {549, 10304}, {550, 3545}, {5054, 8703}, {11539, 15688}, {11693, 12041}, {14269, 15686}
X(61782) = reflection of X(i) in X(j) for these {i,j}: {10304, 15759}, {12100, 17504}, {12101, 3545}, {14269, 10109}, {14892, 11539}, {15699, 11812}, {17504, 14891}, {3545, 10124}, {546, 15699}, {547, 5054}, {548, 10304}, {5054, 3530}, {5055, 14890}
X(61782) = complement of X(61995)
X(61782) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(15714)}}, {{A, B, C, X(1294), X(58187)}}, {{A, B, C, X(3861), X(34483)}}, {{A, B, C, X(5073), X(57822)}}, {{A, B, C, X(13623), X(15687)}}, {{A, B, C, X(18317), X(47598)}}
X(61782) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12811, 547}, {2, 16434, 15684}, {2, 3, 15714}, {2, 376, 5073}, {3, 15706, 10304}, {3, 15715, 15711}, {3, 15716, 376}, {3, 5054, 15710}, {3, 549, 15759}, {4, 10303, 5070}, {4, 15696, 15704}, {4, 15698, 15692}, {4, 548, 12103}, {4, 549, 11540}, {5, 550, 11541}, {20, 15713, 11737}, {20, 15718, 15713}, {20, 3528, 6961}, {30, 10109, 14269}, {30, 10124, 3545}, {30, 10304, 548}, {30, 11539, 14892}, {30, 11812, 15699}, {30, 14890, 5055}, {30, 15699, 546}, {30, 3545, 12101}, {140, 12103, 3859}, {140, 15690, 14893}, {376, 15716, 15712}, {549, 15684, 10124}, {549, 15704, 2}, {549, 3534, 3628}, {549, 5055, 14890}, {550, 10303, 3856}, {631, 15686, 10109}, {632, 15681, 3860}, {632, 8703, 15681}, {3522, 15701, 15687}, {3523, 14093, 3845}, {3524, 15688, 11539}, {3530, 12103, 140}, {3627, 6917, 3843}, {3857, 15686, 15640}, {5055, 15706, 3524}, {5079, 17800, 4}, {8703, 12811, 15691}, {10124, 12101, 12812}, {10303, 15693, 549}, {10304, 15698, 15706}, {10304, 15705, 15698}, {10304, 15708, 15683}, {10304, 15709, 3534}, {10304, 15717, 15709}, {11539, 15688, 30}, {11540, 15759, 8703}, {11812, 15716, 12100}, {12100, 12101, 15693}, {12100, 15714, 3853}, {12100, 15759, 5066}, {15681, 15719, 632}, {15684, 15693, 10303}, {15687, 15701, 16239}, {15689, 15700, 15708}, {15689, 15708, 5}, {15692, 15710, 5054}, {15695, 15702, 3627}, {15698, 15706, 17504}, {15699, 15707, 11812}, {15699, 15712, 15707}, {15705, 17504, 14891}, {15710, 17504, 3530}, {15711, 17504, 15705}, {43258, 43259, 6}

X(61783) = X(2)X(3)∩X(99)X(32888)

Barycentrics    29*a^4+(b^2-c^2)^2-30*a^2*(b^2+c^2) : :
X(61783) = 3*X[2]+28*X[3], -X[193]+32*X[55674], 5*X[3620]+88*X[55665], -4*X[3635]+35*X[7987], 10*X[4668]+21*X[5731], -9*X[5032]+40*X[55687], 4*X[5493]+27*X[54445], 28*X[5882]+3*X[20053], -X[6144]+63*X[55673], -X[6776]+32*X[55668], -2*X[8550]+33*X[55671], 3*X[10519]+28*X[55669] and many others

X(61783) lies on these lines: {2, 3}, {99, 32888}, {193, 55674}, {315, 32889}, {1078, 32878}, {1152, 9542}, {1587, 43382}, {1588, 43383}, {3068, 43338}, {3069, 43339}, {3070, 43438}, {3071, 43439}, {3590, 6560}, {3591, 6561}, {3594, 9692}, {3620, 55665}, {3635, 7987}, {4114, 5703}, {4668, 5731}, {5032, 55687}, {5265, 59325}, {5281, 59319}, {5304, 15515}, {5334, 43301}, {5335, 43300}, {5343, 42978}, {5344, 42979}, {5349, 43299}, {5350, 43298}, {5351, 42435}, {5352, 42436}, {5418, 43376}, {5420, 43377}, {5493, 54445}, {5882, 20053}, {6144, 55673}, {6200, 42523}, {6396, 42522}, {6496, 9543}, {6497, 43509}, {6776, 55668}, {7771, 32824}, {7850, 32825}, {8550, 55671}, {9541, 43431}, {10194, 43408}, {10195, 43407}, {10519, 55669}, {10541, 54174}, {10574, 55166}, {10576, 43336}, {10577, 43337}, {10653, 42959}, {10654, 42958}, {12007, 55676}, {13607, 59417}, {13665, 60303}, {13785, 60304}, {14853, 55658}, {14929, 32881}, {15105, 35260}, {15513, 37665}, {18581, 43492}, {18582, 43491}, {25555, 55660}, {32455, 33748}, {32877, 43459}, {33750, 34507}, {35770, 43523}, {35771, 43524}, {35820, 43513}, {35821, 43514}, {36836, 42793}, {36843, 42794}, {38064, 55652}, {42090, 42901}, {42091, 42900}, {42119, 42774}, {42120, 42773}, {42126, 43446}, {42127, 43447}, {42140, 42948}, {42141, 42949}, {42150, 42929}, {42151, 42928}, {42684, 42944}, {42685, 42945}, {42690, 43557}, {42691, 43556}, {42795, 42893}, {42796, 42892}, {42801, 42999}, {42802, 42998}, {42936, 43550}, {42937, 43551}, {42964, 43404}, {42965, 43403}, {42988, 43495}, {42989, 43496}, {43150, 55664}, {43364, 43467}, {43365, 43468}, {43537, 60250}, {46931, 58214}, {46933, 58216}, {50809, 61278}, {50967, 55681}, {51028, 55626}, {51138, 55684}, {51170, 55682}, {51171, 55649}, {53099, 60649}, {53859, 60630}, {54132, 55644}, {54866, 60640}, {55641, 59373}, {55653, 61044}, {58213, 58441}, {59418, 61020}, {60102, 60209}, {60146, 60333}, {60285, 60323}

X(61783) = pole of line {185, 62060} with respect to the Jerabek hyperbola
X(61783) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(58188)}}, {{A, B, C, X(1217), X(55859)}}, {{A, B, C, X(3524), X(51348)}}, {{A, B, C, X(3845), X(42021)}}, {{A, B, C, X(5076), X(13623)}}, {{A, B, C, X(7714), X(60323)}}, {{A, B, C, X(11403), X(43713)}}, {{A, B, C, X(12103), X(46168)}}, {{A, B, C, X(14861), X(38335)}}, {{A, B, C, X(15681), X(60618)}}, {{A, B, C, X(15710), X(40448)}}, {{A, B, C, X(31363), X(38071)}}
X(61783) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15689, 3543}, {2, 15705, 14891}, {2, 15712, 3523}, {2, 3522, 1657}, {2, 3832, 12812}, {3, 10299, 3522}, {3, 12100, 3528}, {3, 15716, 5}, {3, 17504, 631}, {3, 3526, 15759}, {3, 382, 15714}, {3, 5, 15710}, {4, 15709, 1656}, {4, 3533, 5055}, {4, 3534, 5059}, {140, 5071, 6675}, {376, 15720, 5068}, {376, 3524, 15713}, {548, 15684, 17538}, {548, 15704, 15689}, {548, 3534, 16434}, {548, 3627, 3534}, {548, 549, 5072}, {549, 10304, 15640}, {550, 15712, 12108}, {631, 3534, 15022}, {631, 3861, 6857}, {1656, 15704, 4}, {1657, 3851, 3627}, {3091, 3543, 3861}, {3146, 3530, 15721}, {3522, 3523, 5056}, {3524, 14093, 2}, {3524, 15696, 6931}, {3524, 15759, 15683}, {3528, 15700, 17549}, {3528, 15709, 15704}, {3534, 15706, 15718}, {3534, 15718, 14890}, {3628, 13633, 3855}, {3628, 15713, 3526}, {3839, 5056, 3851}, {3851, 17504, 10299}, {10303, 10304, 20}, {10303, 15640, 7486}, {10303, 15692, 15717}, {10304, 15698, 15692}, {10304, 15717, 10303}, {12101, 15720, 3533}, {12108, 15759, 548}, {14093, 15718, 547}, {14890, 17504, 15706}, {14891, 15706, 15698}, {15683, 15759, 10304}, {15695, 16239, 11541}, {15711, 15715, 15705}, {15717, 15759, 3091}, {42150, 43480, 42983}, {42151, 43479, 42982}, {42988, 52080, 43495}, {42989, 52079, 43496}

X(61784) = X(2)X(3)∩X(6)X(43523)

Barycentrics    26*a^4+(b^2-c^2)^2-27*a^2*(b^2+c^2) : :
X(61784) = 3*X[2]+25*X[3], 3*X[597]+11*X[55652], X[3589]+6*X[55663], X[3626]+20*X[58219], -X[3629]+15*X[17508], X[3631]+20*X[55668], 2*X[3636]+5*X[31663], 3*X[3819]+4*X[55286], -8*X[5092]+X[61624], 2*X[6329]+5*X[14810], -65*X[7987]+9*X[61285], -X[8550]+15*X[55672] and many others

X(61784) lies on these lines: {2, 3}, {6, 43523}, {15, 42793}, {16, 42794}, {17, 43106}, {18, 43105}, {397, 42959}, {398, 42958}, {597, 55652}, {3564, 55669}, {3589, 55663}, {3626, 58219}, {3629, 17508}, {3631, 55668}, {3636, 31663}, {3819, 55286}, {5092, 61624}, {5585, 31406}, {5663, 22250}, {6200, 42644}, {6329, 14810}, {6396, 42643}, {7987, 61285}, {8550, 55672}, {9624, 50833}, {10095, 55320}, {10187, 42143}, {10188, 42146}, {10194, 42225}, {10195, 42226}, {11592, 31834}, {13348, 13421}, {13624, 61597}, {15808, 28174}, {16192, 28212}, {16241, 43013}, {16242, 43012}, {17704, 54044}, {18583, 55657}, {20190, 20583}, {21167, 55665}, {23302, 43546}, {23303, 43547}, {25555, 55659}, {26446, 58217}, {26861, 57713}, {31423, 58215}, {34380, 55676}, {34507, 55667}, {35242, 51700}, {36967, 42946}, {36968, 42947}, {36987, 58531}, {38110, 55656}, {40341, 55671}, {41973, 43634}, {41974, 43635}, {42117, 42774}, {42118, 42773}, {42122, 43486}, {42123, 43485}, {42136, 42948}, {42137, 42949}, {42150, 42415}, {42151, 42416}, {42157, 42628}, {42158, 42627}, {42260, 43571}, {42261, 43570}, {42431, 43103}, {42432, 43102}, {42530, 43783}, {42531, 43784}, {42590, 43633}, {42591, 43632}, {42629, 42936}, {42630, 42937}, {42684, 43776}, {42685, 43775}, {42775, 43649}, {42776, 43644}, {42779, 42945}, {42780, 42944}, {42938, 43110}, {42939, 43111}, {42978, 43417}, {42979, 43416}, {42994, 44017}, {42995, 44018}, {43314, 43793}, {43315, 43794}, {43374, 60291}, {43375, 60292}, {43676, 60334}, {48378, 61598}, {50983, 55647}, {50987, 55724}, {51094, 58225}, {51732, 55646}, {53100, 60642}, {53102, 60332}, {54169, 55675}, {55648, 59399}, {55666, 61545}, {58216, 61614}, {58218, 59388}, {58224, 59417}

X(61784) = midpoint of X(i) and X(j) for these {i,j}: {550, 3851}, {3528, 14869}, {8703, 15702}
X(61784) = reflection of X(i) in X(j) for these {i,j}: {140, 3523}, {14869, 3530}, {15698, 14891}, {15703, 11812}, {3832, 3628}, {3853, 3857}
X(61784) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(546), X(26861)}}, {{A, B, C, X(12102), X(14861)}}, {{A, B, C, X(15759), X(40448)}}, {{A, B, C, X(26863), X(57713)}}, {{A, B, C, X(42021), X(50689)}}
X(61784) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 10299, 550}, {3, 12100, 548}, {3, 15692, 5}, {3, 15700, 3528}, {3, 15706, 20}, {3, 15716, 631}, {3, 15717, 8703}, {3, 20, 15714}, {3, 382, 15710}, {3, 5, 15759}, {5, 15723, 3628}, {20, 11812, 12812}, {30, 11812, 15703}, {30, 14891, 15698}, {30, 3530, 14869}, {30, 3628, 3832}, {30, 3857, 3853}, {140, 12103, 3850}, {140, 3853, 1656}, {140, 550, 546}, {382, 546, 12101}, {549, 8703, 3839}, {550, 15687, 1657}, {550, 15712, 15720}, {550, 17504, 10299}, {1010, 3628, 4208}, {1656, 12108, 140}, {3522, 3523, 3090}, {3522, 3850, 12103}, {3523, 10299, 15700}, {3523, 3528, 3851}, {3525, 15686, 3856}, {3528, 10299, 3523}, {3528, 14869, 30}, {3528, 15702, 3529}, {3528, 15707, 3857}, {3529, 15717, 15707}, {3529, 3839, 382}, {3530, 11737, 12108}, {3839, 11001, 15684}, {5066, 15716, 12100}, {8703, 15707, 11737}, {10124, 15704, 3859}, {10299, 15720, 15712}, {11539, 15696, 12102}, {14869, 15700, 3530}, {15688, 15700, 15701}, {15698, 15700, 17504}, {15705, 15711, 14891}, {15706, 15714, 11812}, {15711, 17504, 15715}, {43523, 43524, 6}

X(61785) = X(2)X(3)∩X(141)X(55664)

Barycentrics    24*a^4+(b^2-c^2)^2-25*a^2*(b^2+c^2) : :
X(61785) = 3*X[2]+23*X[3], X[141]+12*X[55664], 9*X[165]+4*X[61278], X[355]+25*X[58217], 3*X[597]+10*X[55650], -X[1353]+14*X[55676], 2*X[3589]+11*X[55662], 9*X[3654]+4*X[61290], X[5480]+12*X[55663], 3*X[5587]+49*X[58215], 10*X[5882]+3*X[50830], 4*X[6329]+9*X[55640] and many others

X(61785) lies on these lines: {2, 3}, {141, 55664}, {165, 61278}, {355, 58217}, {397, 43640}, {398, 43639}, {597, 55650}, {952, 31425}, {1353, 55676}, {3589, 55662}, {3654, 61290}, {5210, 31450}, {5237, 42633}, {5238, 42634}, {5480, 55663}, {5587, 58215}, {5882, 50830}, {6329, 55640}, {6411, 19116}, {6412, 9680}, {6418, 9692}, {6684, 61251}, {7583, 43338}, {7584, 43339}, {7982, 50832}, {7987, 61286}, {8550, 50985}, {8589, 9607}, {9606, 15513}, {9681, 35256}, {10283, 35242}, {10645, 42686}, {10646, 42687}, {11362, 32900}, {11477, 50987}, {11488, 43635}, {11489, 43634}, {12007, 17508}, {12245, 58224}, {13363, 55320}, {13607, 17502}, {13624, 61283}, {14677, 48375}, {16192, 61276}, {16772, 42685}, {16773, 42684}, {16808, 43648}, {16809, 43647}, {18583, 55656}, {18907, 31457}, {21167, 43150}, {21850, 55657}, {23251, 43513}, {23261, 43514}, {25555, 50988}, {31447, 34773}, {31666, 51085}, {33556, 34513}, {33749, 54169}, {36967, 43026}, {36968, 43027}, {37714, 61614}, {38042, 58216}, {38081, 61252}, {38110, 55655}, {40107, 55668}, {42087, 42954}, {42088, 42955}, {42096, 42493}, {42097, 42492}, {42099, 42694}, {42100, 42695}, {42101, 42597}, {42102, 42596}, {42117, 43005}, {42118, 43004}, {42122, 42491}, {42123, 42490}, {42258, 43341}, {42259, 43340}, {42262, 43337}, {42265, 43336}, {42459, 61312}, {42528, 42965}, {42529, 42964}, {42602, 43378}, {42603, 43379}, {42795, 42991}, {42796, 42990}, {42920, 51945}, {42921, 51944}, {42938, 43303}, {42939, 43302}, {43174, 51087}, {43197, 52080}, {43198, 52079}, {43442, 51915}, {43443, 51916}, {48874, 55658}, {48876, 55670}, {48906, 55669}, {50979, 55679}, {50983, 55644}, {51138, 55687}, {51140, 55675}, {51732, 55643}, {55646, 59399}, {58219, 61245}, {58220, 59503}, {61297, 61524}

X(61785) = midpoint of X(i) and X(j) for these {i,j}: {3, 10299}
X(61785) = reflection of X(i) in X(j) for these {i,j}: {5079, 140}
X(61785) = complement of X(61991)
X(61785) = pole of line {185, 15759} with respect to the Jerabek hyperbola
X(61785) = pole of line {6, 43638} with respect to the Kiepert hyperbola
X(61785) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1105), X(15759)}}, {{A, B, C, X(3845), X(34483)}}, {{A, B, C, X(3853), X(13623)}}
X(61785) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 10299, 30}, {3, 12100, 550}, {3, 15692, 140}, {3, 15700, 3522}, {3, 15716, 3523}, {3, 1657, 15710}, {3, 17504, 15712}, {3, 4, 15759}, {3, 550, 15714}, {5, 15686, 382}, {5, 548, 15704}, {20, 15710, 6868}, {20, 3526, 3856}, {30, 140, 5079}, {140, 15703, 632}, {140, 3534, 3857}, {382, 11357, 11737}, {548, 3628, 17800}, {548, 3856, 20}, {549, 3845, 15709}, {549, 550, 3628}, {550, 3627, 11001}, {631, 3528, 3146}, {1657, 17530, 3861}, {3146, 3843, 3853}, {3522, 12108, 3845}, {3522, 15700, 12108}, {3523, 15696, 16239}, {3523, 3627, 15713}, {3526, 15717, 3530}, {3526, 3534, 3843}, {3526, 3843, 7486}, {3528, 7486, 3534}, {3533, 15689, 12102}, {3627, 16239, 5}, {3628, 5066, 5056}, {3843, 3855, 3860}, {5067, 10303, 3526}, {6869, 12100, 6948}, {7486, 15692, 15717}, {8703, 15712, 14869}, {10304, 12100, 549}, {10304, 15717, 631}, {10304, 17800, 548}, {11001, 15716, 12100}, {11539, 15714, 8703}, {12100, 15714, 11539}, {12103, 15720, 15699}, {14891, 15705, 15711}, {14891, 15711, 17504}, {15674, 17530, 13741}, {15683, 15693, 14890}, {15686, 15703, 15687}, {15695, 15707, 15703}, {15696, 16239, 3627}, {15698, 15715, 10304}, {15709, 16434, 4}, {16772, 42685, 42935}, {16773, 42684, 42934}

X(61786) = X(2)X(3)∩X(8)X(58220)

Barycentrics    47*a^4+2*(b^2-c^2)^2-49*a^2*(b^2+c^2) : :
X(61786) = 2*X[2]+15*X[3], 2*X[8]+49*X[58220], X[599]+16*X[55668], -4*X[3629]+55*X[55678], X[3679]+16*X[58219], 16*X[6329]+35*X[55639], -75*X[7987]+7*X[51094], 3*X[9778]+14*X[50833], 8*X[11694]+9*X[38633], -25*X[12017]+8*X[20583], 12*X[14810]+5*X[51185], 3*X[14848]+14*X[55651] and many others

X(61786) lies on these lines: {2, 3}, {8, 58220}, {599, 55668}, {3629, 55678}, {3679, 58219}, {5237, 42635}, {5238, 42636}, {6329, 55639}, {6427, 43523}, {6428, 43524}, {6496, 52046}, {6497, 52045}, {7987, 51094}, {9778, 50833}, {10645, 42977}, {10646, 42976}, {10653, 42781}, {10654, 42782}, {11480, 43021}, {11481, 43020}, {11694, 38633}, {12017, 20583}, {14810, 51185}, {14848, 55651}, {15028, 55320}, {15300, 35021}, {15533, 55671}, {15534, 17508}, {16241, 54593}, {16242, 54594}, {17502, 51093}, {17810, 33544}, {18480, 58215}, {18525, 58217}, {20049, 58222}, {22236, 42797}, {22238, 42798}, {31663, 51105}, {32787, 43314}, {32788, 43315}, {33750, 50994}, {36836, 42533}, {36843, 42532}, {38064, 55648}, {40341, 55672}, {40995, 57894}, {41100, 43420}, {41101, 43421}, {41107, 43332}, {41108, 43333}, {41121, 43489}, {41122, 43490}, {41943, 42508}, {41944, 42509}, {42126, 43331}, {42127, 43330}, {42129, 46335}, {42130, 49908}, {42131, 49907}, {42132, 46334}, {42140, 42985}, {42141, 42984}, {42474, 43475}, {42475, 43476}, {42490, 43485}, {42491, 43486}, {42590, 43201}, {42591, 43202}, {42631, 43418}, {42632, 43419}, {42799, 42893}, {42800, 42892}, {42815, 49903}, {42816, 49904}, {42942, 49810}, {42943, 49811}, {42946, 43194}, {42947, 43193}, {43207, 43640}, {43208, 43639}, {43230, 43469}, {43231, 43470}, {43273, 55667}, {47352, 55658}, {50797, 51069}, {50800, 58441}, {50805, 51095}, {50954, 51143}, {50962, 55682}, {50983, 55643}, {51137, 55663}, {51141, 59411}, {51172, 55610}, {51175, 51737}, {54131, 55659}, {54644, 60626}, {54851, 60210}, {54920, 60283}, {54934, 60277}, {55632, 59373}, {60216, 60335}

X(61786) = midpoint of X(i) and X(j) for these {i,j}: {376, 7486}
X(61786) = reflection of X(i) in X(j) for these {i,j}: {3533, 549}
X(61786) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(3533), X(18317)}}, {{A, B, C, X(3830), X(57894)}}, {{A, B, C, X(15686), X(46168)}}
X(61786) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11001, 546}, {2, 15698, 17504}, {2, 15700, 15693}, {2, 15710, 8703}, {2, 550, 3830}, {2, 8703, 15681}, {3, 10299, 382}, {3, 15681, 15710}, {3, 15689, 15714}, {3, 15698, 15716}, {3, 15700, 15688}, {3, 15718, 10304}, {3, 3524, 14093}, {3, 3830, 15759}, {30, 549, 3533}, {376, 7486, 30}, {382, 15700, 15707}, {549, 8703, 3860}, {550, 3861, 3529}, {1657, 3526, 3091}, {3091, 3524, 549}, {3091, 3528, 550}, {3523, 15689, 15723}, {3523, 15714, 15689}, {3524, 14093, 3526}, {3524, 15683, 12108}, {3528, 3530, 5070}, {3530, 17504, 15692}, {3534, 15682, 1657}, {3627, 17567, 3851}, {5070, 15681, 14269}, {8703, 12100, 15719}, {10299, 15707, 15700}, {10304, 11812, 15685}, {10304, 15718, 1656}, {11540, 15701, 5054}, {11540, 15719, 15701}, {11812, 15687, 2}, {12100, 15713, 3524}, {12100, 15759, 15713}, {14891, 15705, 3}, {14891, 15711, 15698}, {15681, 15688, 15696}, {15682, 15695, 3534}, {15685, 15718, 11812}, {15688, 15700, 15720}, {15688, 15720, 381}, {15688, 17504, 15706}, {15689, 15723, 5076}, {15692, 15710, 3530}, {15692, 15719, 12100}, {15696, 15720, 5079}, {15698, 15705, 15711}

X(61787) = X(2)X(3)∩X(61)X(42517)

Barycentrics    23*a^4+(b^2-c^2)^2-24*a^2*(b^2+c^2) : :
X(61787) = 3*X[2]+22*X[3], X[69]+24*X[55670], X[1352]+24*X[55664], -3*X[1992]+28*X[55681], X[3618]+4*X[55655], -8*X[4701]+33*X[5657], 16*X[5447]+9*X[61136], X[5691]+49*X[58215], 2*X[5734]+3*X[50809], -2*X[5882]+27*X[58221], 16*X[7780]+9*X[9741], 9*X[7967]+16*X[43174] and many others

X(61787) lies on these lines: {2, 3}, {61, 42517}, {62, 42516}, {69, 55670}, {397, 52080}, {398, 52079}, {515, 58217}, {1056, 59319}, {1058, 59325}, {1285, 15513}, {1352, 55664}, {1992, 55681}, {3070, 43374}, {3071, 43375}, {3316, 43409}, {3317, 43410}, {3618, 55655}, {4701, 5657}, {5126, 7320}, {5318, 43447}, {5321, 43446}, {5334, 42774}, {5335, 42773}, {5339, 43464}, {5340, 43463}, {5343, 42970}, {5344, 42971}, {5346, 8589}, {5447, 61136}, {5691, 58215}, {5702, 36751}, {5734, 50809}, {5844, 58224}, {5882, 58221}, {5965, 55672}, {6409, 43510}, {6410, 43509}, {6411, 7582}, {6412, 7581}, {6428, 9692}, {6445, 42523}, {6446, 42522}, {6496, 7586}, {6497, 7585}, {6564, 34089}, {6565, 34091}, {7761, 39142}, {7780, 9741}, {7820, 60183}, {7967, 43174}, {7987, 28234}, {8550, 55673}, {8960, 42637}, {9693, 19053}, {10519, 55671}, {10595, 28228}, {10645, 42980}, {10646, 42981}, {10653, 43426}, {10654, 43427}, {11147, 55730}, {11488, 41974}, {11489, 41973}, {11522, 28232}, {12244, 48375}, {12245, 17502}, {12645, 58220}, {12815, 43619}, {13382, 55166}, {13464, 16192}, {13886, 43411}, {13939, 43412}, {14561, 55662}, {14641, 44299}, {14683, 15042}, {14853, 55656}, {14862, 54050}, {14912, 55676}, {15036, 20417}, {15815, 46453}, {16960, 42151}, {16961, 42150}, {16964, 42513}, {16965, 42512}, {16966, 43445}, {16967, 43444}, {17704, 54041}, {18840, 32459}, {20423, 55652}, {21167, 39874}, {22235, 42123}, {22236, 42793}, {22237, 42122}, {22238, 42794}, {23253, 43505}, {23263, 43506}, {25406, 55669}, {25555, 55658}, {30389, 34631}, {31412, 43517}, {31670, 55663}, {32817, 32890}, {32818, 32891}, {33416, 42776}, {33417, 42775}, {34507, 55668}, {34754, 42797}, {34755, 42798}, {35770, 43524}, {35771, 43523}, {36967, 43425}, {36968, 43424}, {37714, 50819}, {38064, 55647}, {40693, 42959}, {40694, 42958}, {42089, 43770}, {42090, 42495}, {42091, 42494}, {42092, 43769}, {42133, 42948}, {42134, 42949}, {42490, 43542}, {42491, 43543}, {42528, 42979}, {42529, 42978}, {42561, 43518}, {42582, 43564}, {42583, 43565}, {42638, 58866}, {42777, 43481}, {42778, 43482}, {42795, 42938}, {42796, 42939}, {42801, 42931}, {42802, 42930}, {42960, 43544}, {42961, 43545}, {42986, 43479}, {42987, 43480}, {43003, 61719}, {43403, 43422}, {43404, 43423}, {43681, 47287}, {50966, 55637}, {50967, 55684}, {51028, 55620}, {51171, 55643}, {51212, 55657}, {54132, 55641}, {54170, 55644}, {54173, 55675}, {54174, 55701}, {55631, 59373}, {58216, 59387}

X(61787) = anticomplement of X(61923)
X(61787) = pole of line {185, 62061} with respect to the Jerabek hyperbola
X(61787) = pole of line {3, 44871} with respect to the Stammler hyperbola
X(61787) = pole of line {69, 61984} with respect to the Wallace hyperbola
X(61787) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1294), X(58188)}}, {{A, B, C, X(3431), X(5198)}}, {{A, B, C, X(3519), X(14269)}}, {{A, B, C, X(3843), X(42021)}}, {{A, B, C, X(5076), X(15740)}}, {{A, B, C, X(11270), X(11403)}}, {{A, B, C, X(14528), X(18535)}}, {{A, B, C, X(14536), X(37942)}}, {{A, B, C, X(15697), X(54660)}}, {{A, B, C, X(20421), X(35502)}}
X(61787) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10304, 15691}, {3, 12100, 20}, {3, 15696, 15714}, {3, 15700, 548}, {3, 15706, 5}, {3, 15712, 3522}, {3, 15716, 3530}, {3, 17504, 15717}, {3, 20, 15710}, {3, 3524, 3528}, {3, 3530, 10304}, {3, 382, 15759}, {4, 140, 5067}, {20, 15702, 3544}, {140, 15712, 15693}, {140, 376, 4}, {376, 15698, 17504}, {376, 3545, 15685}, {376, 631, 3091}, {548, 15709, 6905}, {548, 15713, 5076}, {548, 16370, 15682}, {550, 3523, 3533}, {631, 3090, 15694}, {1656, 15696, 5073}, {1656, 15712, 3523}, {1656, 3523, 631}, {3091, 17538, 11541}, {3091, 17578, 3845}, {3091, 5067, 5071}, {3522, 15692, 15712}, {3522, 3523, 1656}, {3523, 5059, 140}, {3524, 3528, 3525}, {3525, 3528, 11001}, {3528, 5071, 17538}, {3843, 15697, 3529}, {5073, 15704, 5059}, {10299, 15710, 15720}, {12100, 15702, 3524}, {12100, 15710, 15702}, {12103, 15701, 7486}, {12108, 15688, 3832}, {14093, 15693, 5055}, {14813, 14814, 14269}, {14891, 15705, 15698}, {15685, 15693, 15713}, {15692, 15705, 15711}, {15692, 15712, 10299}, {15693, 17504, 15692}, {15694, 17578, 3090}, {15696, 15717, 13634}, {15698, 15705, 15715}, {15708, 15759, 376}, {15712, 15714, 3858}, {43505, 43787, 23253}, {43506, 43788, 23263}

X(61788) = X(2)X(3)∩X(6)X(9692)

Barycentrics    21*a^4+(b^2-c^2)^2-22*a^2*(b^2+c^2) : :
X(61788) = 3*X[2]+20*X[3], -3*X[8]+26*X[31425], X[69]+22*X[55671], -X[145]+24*X[17502], -X[146]+24*X[48375], 15*X[165]+8*X[3636], -X[193]+24*X[17508], 3*X[944]+20*X[31447], -5*X[962]+28*X[15808], X[1352]+22*X[55665], -2*X[1483]+25*X[58224], -2*X[3244]+25*X[7987] and many others

X(61788) lies on these lines: {2, 3}, {6, 9692}, {8, 31425}, {61, 42797}, {62, 42798}, {69, 55671}, {99, 32868}, {145, 17502}, {146, 48375}, {165, 3636}, {193, 17508}, {372, 9542}, {390, 59325}, {393, 61312}, {397, 43304}, {398, 43305}, {944, 31447}, {962, 15808}, {1151, 42523}, {1152, 42522}, {1352, 55665}, {1483, 58224}, {3244, 7987}, {3576, 20057}, {3579, 61279}, {3592, 43258}, {3594, 43259}, {3600, 31452}, {3617, 58219}, {3618, 55654}, {3620, 33750}, {3622, 31663}, {3626, 5731}, {3629, 53094}, {3631, 25406}, {3632, 58221}, {4031, 11036}, {4297, 58217}, {4301, 16192}, {4308, 31436}, {4325, 5261}, {4330, 5274}, {5010, 5265}, {5032, 20190}, {5092, 33748}, {5206, 31450}, {5210, 9606}, {5281, 7280}, {5304, 37512}, {5319, 15515}, {5343, 42529}, {5344, 42528}, {5349, 51945}, {5350, 51944}, {5351, 43232}, {5352, 43233}, {5585, 31492}, {5650, 52093}, {5921, 21167}, {6194, 32450}, {6329, 31884}, {6412, 31454}, {6419, 43523}, {6420, 43524}, {6445, 42644}, {6446, 42643}, {6451, 9543}, {6452, 43320}, {6455, 9693}, {6456, 43509}, {6496, 7582}, {6497, 7581}, {6776, 55670}, {7585, 9680}, {7765, 37689}, {8273, 61153}, {8588, 31400}, {9541, 35813}, {9624, 9778}, {9681, 13935}, {9706, 43652}, {10192, 54211}, {10519, 55672}, {10541, 20583}, {10574, 15606}, {10645, 43870}, {10646, 43869}, {10653, 43479}, {10654, 43480}, {10979, 61301}, {11008, 55676}, {11034, 53057}, {11362, 20050}, {11430, 11431}, {12006, 16981}, {12528, 33575}, {13474, 33879}, {13624, 61284}, {14531, 17704}, {14561, 55661}, {14810, 51171}, {14853, 55655}, {15023, 20417}, {15036, 16003}, {15051, 24981}, {15589, 43459}, {16241, 22235}, {16242, 22237}, {16964, 42531}, {16965, 42530}, {18538, 60305}, {18553, 50975}, {18762, 60306}, {19876, 50863}, {20049, 61290}, {20052, 61297}, {20054, 37727}, {20070, 61276}, {20423, 55650}, {21153, 60983}, {21166, 35021}, {22352, 38942}, {28160, 46931}, {31666, 50810}, {31670, 55662}, {34473, 35022}, {34747, 43174}, {35023, 38693}, {35024, 38692}, {38064, 55644}, {40107, 55669}, {40341, 55673}, {40680, 52711}, {42103, 42597}, {42106, 42596}, {42119, 42491}, {42120, 42490}, {42130, 43488}, {42131, 43487}, {42147, 42983}, {42148, 42982}, {42153, 43105}, {42156, 43106}, {42157, 42946}, {42158, 42947}, {42433, 43465}, {42434, 43466}, {42488, 42629}, {42489, 42630}, {42803, 42999}, {42804, 42998}, {42817, 43635}, {42818, 43634}, {42930, 43308}, {42931, 43309}, {42938, 42991}, {42939, 42990}, {42956, 43194}, {42957, 43193}, {42974, 43495}, {42975, 43496}, {42980, 43007}, {42981, 43006}, {43177, 60957}, {43242, 43294}, {43243, 43295}, {43256, 43376}, {43257, 43377}, {43372, 43418}, {43373, 43419}, {43374, 60620}, {43375, 60621}, {46264, 55664}, {46932, 58216}, {48873, 55663}, {50967, 55687}, {50983, 55641}, {51028, 55614}, {51093, 58225}, {51212, 55656}, {53093, 54174}, {54132, 55637}, {54173, 55677}, {55626, 59373}, {55649, 61044}, {58214, 61261}, {58222, 61293}, {59418, 60980}

X(61788) = anticomplement of X(61921)
X(61788) = pole of line {185, 62063} with respect to the Jerabek hyperbola
X(61788) = pole of line {69, 61982} with respect to the Wallace hyperbola
X(61788) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(68), X(14893)}}, {{A, B, C, X(253), X(3851)}}, {{A, B, C, X(1217), X(16239)}}, {{A, B, C, X(3346), X(3533)}}, {{A, B, C, X(5071), X(15318)}}, {{A, B, C, X(15704), X(60618)}}, {{A, B, C, X(15712), X(51348)}}, {{A, B, C, X(15740), X(50687)}}, {{A, B, C, X(45759), X(60007)}}, {{A, B, C, X(50688), X(57894)}}
X(61788) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11113, 17678}, {2, 11346, 4234}, {2, 11352, 16054}, {2, 15681, 3839}, {2, 15705, 15715}, {2, 15717, 3530}, {2, 15720, 10303}, {2, 17697, 11354}, {2, 3146, 3851}, {2, 3522, 3529}, {2, 3528, 20}, {2, 546, 5056}, {3, 15700, 550}, {3, 15706, 140}, {3, 15712, 376}, {3, 15716, 15712}, {3, 1657, 15759}, {3, 17504, 10299}, {3, 3523, 10304}, {3, 3524, 3522}, {3, 3530, 3528}, {3, 550, 15710}, {4, 15685, 3146}, {4, 15703, 7402}, {4, 3530, 17533}, {4, 631, 16239}, {5, 11812, 3526}, {5, 14269, 3855}, {20, 10303, 5}, {20, 15692, 15717}, {20, 15717, 3523}, {20, 5056, 17578}, {20, 631, 7486}, {140, 15681, 3544}, {376, 3524, 11812}, {382, 3851, 3861}, {405, 16296, 21}, {546, 15712, 15707}, {548, 631, 3832}, {549, 15696, 5067}, {550, 14869, 11737}, {631, 3528, 382}, {632, 11001, 3854}, {1657, 15702, 15022}, {2041, 2042, 5071}, {3090, 14869, 17571}, {3091, 3523, 15721}, {3522, 10303, 3543}, {3523, 10304, 3091}, {3523, 7486, 631}, {3524, 15710, 14269}, {3524, 3529, 15720}, {3525, 8703, 5059}, {3529, 3544, 5076}, {3529, 6967, 13725}, {3861, 16239, 12812}, {4234, 11346, 13735}, {5046, 14269, 16853}, {5054, 17538, 5068}, {5068, 17538, 15640}, {5068, 8703, 411}, {5192, 16859, 11110}, {6833, 11001, 15682}, {10299, 15715, 3}, {11108, 11354, 2}, {11108, 17697, 1010}, {11812, 15699, 15694}, {12100, 15694, 3524}, {12812, 15685, 4}, {14784, 14785, 14893}, {14891, 15698, 15705}, {15688, 15707, 15699}, {15692, 15708, 12100}, {15694, 15720, 14869}, {15698, 15705, 15692}, {15698, 15715, 17504}

X(61789) = X(2)X(3)∩X(17)X(43328)

Barycentrics    20*a^4+(b^2-c^2)^2-21*a^2*(b^2+c^2) : :
X(61789) = 3*X[2]+19*X[3], 5*X[40]+6*X[61280], X[141]+10*X[55666], 15*X[165]+7*X[61277], 5*X[576]+6*X[50970], 3*X[597]+8*X[55647], -X[1353]+12*X[17508], -X[1483]+12*X[17502], -15*X[3576]+4*X[61281], 2*X[3589]+9*X[55660], -X[3629]+12*X[55680], 15*X[3654]+7*X[61289] and many others

X(61789) lies on these lines: {2, 3}, {17, 43328}, {18, 43329}, {40, 61280}, {61, 42793}, {62, 42794}, {141, 55666}, {165, 61277}, {395, 42958}, {396, 42959}, {397, 42916}, {398, 42917}, {524, 55675}, {576, 50970}, {597, 55647}, {1353, 17508}, {1483, 17502}, {1503, 55665}, {3411, 42791}, {3412, 42792}, {3564, 55671}, {3576, 61281}, {3589, 55660}, {3629, 55680}, {3654, 61289}, {5351, 43008}, {5352, 43009}, {5418, 42578}, {5420, 42579}, {5446, 40284}, {5447, 45956}, {5480, 55661}, {5493, 38028}, {5891, 55286}, {6329, 55633}, {6361, 61273}, {6411, 42569}, {6412, 42568}, {6431, 43523}, {6432, 43524}, {7871, 14929}, {7967, 58224}, {7987, 61287}, {7989, 58213}, {8550, 55674}, {8588, 31406}, {9680, 52048}, {9690, 42523}, {10164, 37705}, {10187, 42501}, {10188, 42500}, {10222, 50814}, {10283, 31663}, {10386, 59325}, {10645, 42897}, {10646, 42896}, {11362, 50831}, {11542, 42773}, {11543, 42774}, {11693, 38626}, {11694, 15021}, {14810, 59399}, {15023, 20126}, {15055, 22251}, {16192, 61275}, {16808, 43779}, {16809, 43780}, {17704, 54042}, {18538, 43432}, {18583, 55654}, {18762, 43433}, {19106, 42492}, {19107, 42493}, {19116, 41964}, {19117, 41963}, {20190, 51181}, {21167, 55668}, {21850, 55655}, {23302, 42903}, {23303, 42902}, {23328, 45185}, {25555, 48874}, {26446, 61253}, {29181, 55662}, {31673, 58214}, {32820, 43459}, {33750, 61545}, {34380, 55678}, {34507, 55669}, {34773, 38127}, {35786, 43785}, {35787, 43786}, {36836, 42634}, {36843, 42633}, {36969, 43248}, {36970, 43249}, {38110, 55653}, {38112, 61246}, {40273, 61271}, {42108, 43470}, {42109, 43469}, {42117, 43011}, {42118, 43010}, {42121, 42993}, {42122, 43239}, {42123, 43238}, {42124, 42992}, {42135, 42948}, {42138, 42949}, {42150, 42923}, {42151, 42922}, {42164, 43331}, {42165, 43330}, {42225, 42567}, {42226, 42566}, {42431, 42693}, {42432, 42692}, {42433, 43033}, {42434, 43032}, {42522, 43415}, {42528, 43489}, {42529, 43490}, {42584, 42921}, {42585, 42920}, {42775, 42889}, {42776, 42888}, {42936, 44015}, {42937, 44016}, {42946, 43245}, {42947, 43244}, {42956, 43026}, {42957, 43027}, {42970, 43017}, {42971, 43016}, {42978, 43630}, {42979, 43631}, {43479, 52080}, {43480, 52079}, {43497, 43775}, {43498, 43776}, {43869, 56613}, {43870, 56612}, {44882, 55664}, {46265, 51491}, {48876, 55672}, {48881, 55663}, {48906, 55670}, {50822, 51082}, {50825, 51080}, {50973, 51180}, {50979, 55681}, {50980, 51135}, {50983, 55637}, {50986, 55677}, {51136, 51184}, {51705, 61297}, {51732, 55639}, {54169, 55679}, {58217, 61256}, {58221, 61296}, {58225, 61288}

X(61789) = midpoint of X(i) and X(j) for these {i,j}: {3, 15717}, {15715, 15716}
X(61789) = reflection of X(i) in X(j) for these {i,j}: {15718, 12100}, {5, 3525}, {5056, 140}
X(61789) = complement of X(61990)
X(61789) = pole of line {185, 62064} with respect to the Jerabek hyperbola
X(61789) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(58190)}}, {{A, B, C, X(3519), X(3861)}}, {{A, B, C, X(3839), X(42021)}}, {{A, B, C, X(3858), X(26861)}}, {{A, B, C, X(5055), X(52441)}}, {{A, B, C, X(14861), X(15687)}}, {{A, B, C, X(35381), X(46452)}}, {{A, B, C, X(40448), X(45759)}}, {{A, B, C, X(52294), X(57713)}}
X(61789) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 15246, 10226}, {3, 15693, 3528}, {3, 15696, 15710}, {3, 15700, 20}, {3, 15706, 631}, {3, 15712, 550}, {3, 15716, 15717}, {3, 20, 15759}, {3, 3530, 8703}, {3, 548, 15714}, {4, 1656, 12811}, {4, 5079, 3850}, {5, 14869, 10124}, {5, 15704, 3830}, {5, 8703, 12103}, {20, 11539, 3857}, {30, 12100, 15718}, {30, 140, 5056}, {140, 10299, 15712}, {140, 1657, 5}, {140, 550, 3858}, {376, 3854, 1657}, {376, 5054, 3860}, {548, 12811, 15681}, {631, 15704, 15699}, {631, 5079, 11540}, {1656, 15681, 4}, {1657, 3523, 140}, {3523, 3525, 15720}, {3524, 15714, 3845}, {3528, 15693, 3628}, {3528, 3628, 15686}, {3530, 12103, 5054}, {3530, 15681, 14869}, {3530, 3860, 12108}, {5054, 15692, 12100}, {5054, 15718, 15719}, {5054, 5070, 3525}, {5067, 8728, 5070}, {5070, 6980, 3526}, {8703, 17504, 15692}, {10124, 12100, 3524}, {10303, 15688, 3853}, {12100, 12103, 3530}, {12100, 14891, 15705}, {12103, 12811, 3146}, {12811, 14869, 632}, {14813, 14814, 3861}, {14869, 15714, 548}, {14891, 15698, 17504}, {14891, 17504, 15711}, {15700, 15759, 11539}, {15702, 17800, 12812}, {15711, 17504, 549}, {15712, 15714, 1656}, {15715, 15716, 30}, {15715, 15717, 3}, {15716, 15723, 15706}, {15718, 15720, 3523}

X(61790) = X(2)X(3)∩X(141)X(55667)

Barycentrics    18*a^4+(b^2-c^2)^2-19*a^2*(b^2+c^2) : :
X(61790) = 3*X[2]+17*X[3], X[141]+9*X[55667], 3*X[165]+2*X[51700], -2*X[399]+7*X[22250], 3*X[597]+7*X[55644], X[1216]+9*X[55166], -X[1353]+11*X[55678], -27*X[3576]+7*X[61282], 3*X[3579]+2*X[61278], X[3589]+4*X[55659], -X[3629]+11*X[55683], 3*X[4297]+2*X[61255] and many others

X(61790) lies on these lines: {2, 3}, {141, 55667}, {165, 51700}, {399, 22250}, {524, 55677}, {597, 55644}, {952, 31447}, {1216, 55166}, {1353, 55678}, {1503, 55666}, {3411, 42893}, {3412, 42892}, {3564, 55672}, {3576, 61282}, {3579, 61278}, {3589, 55659}, {3629, 55683}, {4297, 61255}, {4325, 52793}, {5023, 31450}, {5085, 61624}, {5206, 9606}, {5237, 43020}, {5238, 43021}, {5305, 8589}, {5319, 53095}, {5339, 42513}, {5340, 42512}, {5346, 9607}, {5351, 42912}, {5352, 42913}, {5368, 37512}, {5446, 55320}, {5480, 55660}, {5657, 61297}, {5690, 31425}, {5844, 7987}, {5892, 58533}, {5893, 46265}, {5907, 55286}, {5965, 54201}, {6329, 55627}, {6410, 9680}, {6417, 9692}, {6451, 19116}, {6452, 19117}, {6480, 42644}, {6481, 42643}, {6497, 31487}, {6684, 58219}, {7957, 58605}, {7998, 45957}, {8550, 55675}, {8588, 31457}, {9588, 34773}, {9681, 13966}, {9691, 42523}, {9729, 54044}, {9956, 58216}, {10164, 61510}, {10272, 48375}, {10576, 43789}, {10577, 43790}, {10627, 17704}, {11017, 15082}, {11362, 17502}, {11482, 50987}, {11542, 43635}, {11543, 43634}, {11592, 40647}, {12007, 55680}, {12045, 44871}, {12680, 58675}, {13348, 14449}, {13392, 15055}, {13624, 28234}, {13630, 15606}, {14531, 54042}, {15036, 23236}, {15057, 34153}, {15655, 31470}, {15888, 59319}, {16192, 38028}, {16960, 42148}, {16961, 42147}, {16964, 42628}, {16965, 42627}, {18553, 50984}, {18583, 55653}, {18907, 31492}, {19862, 28182}, {20396, 38726}, {21153, 61596}, {21154, 61601}, {21163, 61625}, {21167, 55669}, {21850, 55654}, {23238, 38710}, {26446, 61252}, {28186, 31399}, {28212, 35242}, {28224, 61248}, {28228, 31663}, {29181, 55661}, {31835, 33575}, {31884, 51732}, {32455, 55686}, {33749, 55679}, {33814, 35202}, {34380, 53094}, {36969, 42590}, {36970, 42591}, {37714, 58217}, {37722, 59325}, {38064, 55641}, {38110, 55651}, {38737, 61600}, {38748, 61599}, {38760, 61605}, {38772, 61604}, {38793, 61598}, {40107, 55670}, {40693, 43197}, {40694, 43198}, {41963, 52048}, {41964, 52047}, {42087, 42901}, {42088, 42900}, {42107, 42597}, {42110, 42596}, {42117, 42491}, {42118, 42490}, {42143, 42682}, {42146, 42683}, {42150, 42497}, {42151, 42496}, {42431, 42500}, {42432, 42501}, {42504, 42898}, {42505, 42899}, {42545, 43442}, {42546, 43443}, {42594, 43399}, {42595, 43400}, {42779, 42796}, {42780, 42795}, {42813, 43103}, {42814, 43102}, {42888, 43028}, {42889, 43029}, {42944, 42991}, {42945, 42990}, {42992, 43109}, {42993, 43108}, {42996, 43022}, {42997, 43023}, {43483, 43773}, {43484, 43774}, {44882, 55665}, {48874, 55656}, {48876, 55673}, {48881, 55662}, {48906, 55671}, {48920, 51127}, {50983, 55631}, {54169, 55681}, {55620, 59373}, {55639, 59399}, {58214, 61262}, {58220, 61245}

X(61790) = midpoint of X(i) and X(j) for these {i,j}: {3, 15712}, {5, 15696}, {550, 3091}, {632, 3522}, {3858, 17538}, {8703, 15694}, {14093, 15713}, {15692, 15711}, {15693, 15714}
X(61790) = reflection of X(i) in X(j) for these {i,j}: {12100, 15692}, {12812, 140}, {14093, 15759}, {15691, 15695}, {15711, 14891}, {3853, 3859}, {3858, 3628}, {546, 1656}, {547, 15713}, {5076, 3850}, {631, 3530}
X(61790) = complement of X(61988)
X(61790) = pole of line {185, 45759} with respect to the Jerabek hyperbola
X(61790) = intersection, other than A, B, C, of circumconics {{A, B, C, X(20), X(46168)}}, {{A, B, C, X(1105), X(45759)}}, {{A, B, C, X(5079), X(15318)}}, {{A, B, C, X(6662), X(15022)}}, {{A, B, C, X(19708), X(60007)}}, {{A, B, C, X(35400), X(60122)}}, {{A, B, C, X(40448), X(58190)}}
X(61790) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 12100, 140}, {3, 15693, 3522}, {3, 15706, 3523}, {3, 15716, 10299}, {3, 15717, 5}, {3, 15720, 10304}, {3, 3522, 15714}, {3, 3530, 548}, {3, 550, 15759}, {5, 15717, 3530}, {20, 13735, 4}, {20, 3545, 382}, {20, 548, 15690}, {20, 549, 16239}, {20, 631, 1656}, {30, 140, 12812}, {30, 14891, 15711}, {30, 15695, 15691}, {30, 15713, 547}, {30, 15759, 14093}, {30, 3530, 631}, {30, 3850, 5076}, {140, 12103, 5066}, {140, 14893, 3628}, {140, 15690, 546}, {140, 548, 3853}, {376, 14869, 3850}, {546, 548, 20}, {547, 12100, 3524}, {547, 15683, 14893}, {548, 3853, 12103}, {549, 15688, 10109}, {549, 17504, 15716}, {549, 8703, 3545}, {631, 3522, 3843}, {631, 3528, 17578}, {632, 15712, 15693}, {1656, 3830, 3091}, {1657, 11539, 12811}, {2041, 2042, 5079}, {3524, 14093, 15713}, {3528, 17578, 15696}, {3530, 15759, 3861}, {3533, 15681, 3857}, {3545, 15683, 3830}, {3627, 15720, 10124}, {3853, 12812, 3859}, {3858, 8703, 17538}, {3861, 12108, 3526}, {6988, 17504, 3856}, {7486, 17697, 5067}, {10299, 15705, 3}, {10304, 15720, 3627}, {12108, 15759, 550}, {14093, 15694, 15683}, {14093, 15712, 12108}, {14093, 15713, 30}, {14891, 17504, 12100}, {15686, 15707, 11540}, {15687, 15719, 14890}, {15692, 15715, 15694}, {15694, 17538, 3858}, {15698, 17504, 14891}, {15705, 15716, 549}, {15706, 15715, 8703}, {15706, 17538, 15712}, {15710, 15718, 3845}, {15711, 17504, 15692}, {15712, 15714, 632}

X(61791) = X(2)X(3)∩X(6)X(42793)

Barycentrics    17*a^4+(b^2-c^2)^2-18*a^2*(b^2+c^2) : :
X(61791) = 3*X[2]+16*X[3], X[8]+18*X[58221], X[69]+18*X[55673], -X[145]+20*X[7987], 12*X[165]+7*X[3622], -X[193]+20*X[53094], 16*X[575]+3*X[54174], X[1352]+18*X[55667], -3*X[1992]+22*X[55684], 3*X[2979]+16*X[17704], -24*X[3576]+5*X[3623], 15*X[3616]+4*X[5493] and many others

X(61791) lies on these lines: {2, 3}, {6, 42793}, {8, 58221}, {69, 55673}, {145, 7987}, {165, 3622}, {183, 32882}, {184, 43902}, {193, 53094}, {316, 32871}, {325, 32895}, {397, 43479}, {398, 43480}, {491, 51953}, {492, 51952}, {542, 15023}, {575, 54174}, {590, 43376}, {615, 43377}, {1078, 32824}, {1204, 41462}, {1352, 55667}, {1420, 7320}, {1620, 11427}, {1742, 27625}, {1975, 32894}, {1992, 55684}, {2979, 17704}, {3053, 14930}, {3070, 3590}, {3071, 3591}, {3312, 9542}, {3361, 5558}, {3431, 26861}, {3576, 3623}, {3616, 5493}, {3617, 10164}, {3618, 55651}, {3620, 21167}, {3621, 5882}, {3634, 58215}, {3785, 32841}, {3876, 33575}, {3889, 33574}, {4297, 46933}, {4430, 58637}, {4661, 58567}, {4678, 5731}, {5010, 14986}, {5023, 37665}, {5032, 10541}, {5085, 51170}, {5122, 11036}, {5204, 5281}, {5217, 5265}, {5286, 8589}, {5303, 56879}, {5304, 15815}, {5314, 55909}, {5343, 42089}, {5344, 42092}, {5355, 15515}, {5365, 42090}, {5366, 42091}, {5550, 12512}, {5562, 55166}, {5650, 12279}, {5657, 20052}, {5691, 46931}, {5734, 50828}, {5921, 33750}, {6053, 15055}, {6221, 42523}, {6329, 55622}, {6337, 32879}, {6398, 42522}, {6409, 7586}, {6410, 7585}, {6411, 43512}, {6412, 43511}, {6419, 9692}, {6449, 43510}, {6450, 43509}, {6451, 7582}, {6452, 7581}, {6776, 55672}, {7293, 55914}, {7768, 32831}, {7771, 32830}, {7782, 32834}, {7860, 32829}, {7917, 32825}, {8550, 20080}, {8567, 35260}, {8972, 42637}, {9541, 58866}, {9589, 51075}, {9778, 11522}, {9780, 58217}, {9841, 27065}, {10159, 60324}, {10187, 42432}, {10188, 42431}, {10194, 23259}, {10195, 23249}, {10248, 34595}, {10513, 32821}, {10519, 55674}, {10574, 33884}, {10645, 42995}, {10646, 42994}, {10857, 34772}, {10979, 40138}, {10990, 48375}, {10992, 35369}, {11003, 43652}, {11179, 55675}, {11362, 20049}, {11381, 44299}, {11480, 43870}, {11481, 43869}, {11488, 42773}, {11489, 42774}, {11542, 43777}, {11543, 43778}, {11623, 20094}, {12250, 14862}, {13382, 20791}, {13464, 20070}, {13624, 59417}, {13941, 42638}, {14561, 55659}, {14683, 15051}, {14853, 55653}, {14907, 32835}, {14912, 55678}, {15028, 36987}, {15036, 30714}, {15043, 16981}, {15108, 18909}, {15258, 20218}, {15513, 31400}, {15589, 32820}, {16990, 51579}, {17502, 20014}, {17508, 51033}, {18435, 55286}, {18480, 58216}, {18553, 55664}, {20095, 20418}, {20105, 32522}, {20190, 50967}, {20423, 55647}, {21153, 61006}, {22235, 42120}, {22237, 42119}, {22251, 38633}, {23302, 43769}, {23303, 43770}, {23958, 37526}, {25406, 55671}, {25555, 55655}, {26446, 58219}, {27003, 37551}, {27082, 37638}, {27525, 56880}, {30315, 46930}, {31423, 54448}, {31425, 51705}, {31670, 55660}, {31884, 51171}, {32789, 42414}, {32790, 42413}, {32826, 32897}, {32827, 32898}, {32840, 43459}, {32881, 37668}, {33522, 41427}, {33879, 44870}, {34506, 53141}, {34507, 55670}, {36413, 36751}, {37714, 50829}, {38064, 55637}, {38079, 51211}, {38083, 50863}, {38259, 53859}, {38808, 59183}, {41977, 43031}, {41978, 43030}, {42021, 57713}, {42087, 42495}, {42088, 42494}, {42095, 43474}, {42098, 43473}, {42121, 43243}, {42124, 43242}, {42125, 43446}, {42128, 43447}, {42139, 42948}, {42142, 42949}, {42149, 42958}, {42152, 42959}, {42263, 43561}, {42264, 43560}, {42433, 42979}, {42434, 42978}, {42582, 43507}, {42583, 43508}, {42610, 43401}, {42611, 43402}, {42775, 43029}, {42776, 43028}, {42785, 48873}, {42982, 52080}, {42983, 52079}, {43240, 43443}, {43241, 43442}, {43252, 49862}, {43253, 49861}, {43254, 43432}, {43255, 43433}, {43413, 43883}, {43414, 43884}, {43465, 43556}, {43466, 43557}, {43527, 60328}, {43537, 43681}, {46264, 55666}, {47586, 60285}, {50983, 55626}, {51028, 55606}, {51071, 58229}, {51073, 58213}, {51132, 53093}, {51212, 55654}, {51732, 55632}, {53099, 60145}, {54132, 55631}, {54170, 55641}, {54173, 55679}, {54706, 60182}, {55614, 59373}, {55646, 61044}, {60118, 60647}

X(61791) = reflection of X(i) in X(j) for these {i,j}: {44446, 3679}
X(61791) = anticomplement of X(15022)
X(61791) = pole of line {185, 62067} with respect to the Jerabek hyperbola
X(61791) = pole of line {3, 10219} with respect to the Stammler hyperbola
X(61791) = pole of line {69, 32894} with respect to the Wallace hyperbola
X(61791) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(50689)}}, {{A, B, C, X(95), X(21734)}}, {{A, B, C, X(381), X(26861)}}, {{A, B, C, X(428), X(60324)}}, {{A, B, C, X(546), X(42021)}}, {{A, B, C, X(1217), X(46219)}}, {{A, B, C, X(3091), X(52443)}}, {{A, B, C, X(3346), X(3526)}}, {{A, B, C, X(3431), X(26863)}}, {{A, B, C, X(3532), X(11403)}}, {{A, B, C, X(3851), X(46455)}}, {{A, B, C, X(3854), X(35510)}}, {{A, B, C, X(3855), X(15319)}}, {{A, B, C, X(4846), X(12102)}}, {{A, B, C, X(5064), X(60328)}}, {{A, B, C, X(5076), X(14861)}}, {{A, B, C, X(5198), X(14528)}}, {{A, B, C, X(6662), X(47478)}}, {{A, B, C, X(7714), X(47586)}}, {{A, B, C, X(10594), X(57713)}}, {{A, B, C, X(11001), X(60618)}}, {{A, B, C, X(14269), X(14841)}}, {{A, B, C, X(15703), X(46412)}}, {{A, B, C, X(15717), X(51348)}}, {{A, B, C, X(15740), X(50688)}}, {{A, B, C, X(19708), X(40448)}}, {{A, B, C, X(22270), X(55860)}}, {{A, B, C, X(31363), X(41106)}}, {{A, B, C, X(38282), X(53859)}}
X(61791) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11737, 11112}, {2, 3522, 5059}, {2, 3855, 16371}, {2, 5059, 3854}, {2, 5079, 17530}, {3, 12100, 631}, {3, 15693, 548}, {3, 15696, 15759}, {3, 15700, 5}, {3, 15706, 3530}, {3, 15712, 4}, {3, 16859, 16435}, {3, 3523, 3522}, {3, 548, 15710}, {3, 549, 3528}, {4, 10299, 15712}, {5, 15689, 11541}, {20, 11541, 15683}, {20, 140, 5068}, {20, 3091, 15682}, {20, 381, 3146}, {140, 15691, 3850}, {140, 3524, 3523}, {140, 3627, 1656}, {140, 5068, 2}, {140, 5070, 3533}, {140, 5073, 3090}, {140, 550, 381}, {140, 8703, 5073}, {376, 3530, 10303}, {381, 14891, 15715}, {381, 15701, 11539}, {381, 17800, 3627}, {548, 15693, 3525}, {549, 8703, 14892}, {631, 11001, 3628}, {631, 14893, 16866}, {631, 3528, 3853}, {1656, 15701, 140}, {1656, 1657, 14269}, {1656, 3544, 5056}, {1657, 3533, 3091}, {2045, 2046, 15702}, {3070, 3590, 60291}, {3071, 3591, 60292}, {3091, 14269, 3832}, {3523, 15692, 10299}, {3524, 15682, 549}, {3524, 15689, 15708}, {3524, 15698, 14891}, {3524, 15710, 15699}, {3524, 8703, 15721}, {3526, 15685, 12811}, {3526, 17538, 3839}, {3528, 3533, 1657}, {3529, 5054, 7486}, {3530, 3627, 15701}, {3534, 12108, 5067}, {3832, 17556, 16864}, {3854, 5059, 17578}, {3855, 12103, 15640}, {6409, 7586, 9543}, {10299, 15715, 550}, {10303, 10304, 17800}, {10303, 15706, 15717}, {10304, 15692, 12100}, {11001, 15714, 10304}, {11539, 17800, 3544}, {11541, 15689, 20}, {12100, 15714, 15707}, {12103, 15694, 3855}, {14869, 15696, 3545}, {14869, 15759, 15696}, {14891, 15716, 3524}, {14891, 17504, 15716}, {15692, 15698, 15705}, {15693, 15710, 3543}, {15696, 15718, 14869}, {15698, 17504, 15692}, {15705, 15717, 3}, {15706, 15711, 376}, {15707, 15714, 11001}, {15719, 17538, 3526}, {34595, 59420, 10248}, {35242, 54445, 20070}, {42090, 42937, 5365}, {42091, 42936, 5366}, {42119, 43239, 22237}, {42120, 43238, 22235}, {42793, 42794, 6}

X(61792) = X(2)X(3)∩X(15)X(42686)

Barycentrics    14*a^4+(b^2-c^2)^2-15*a^2*(b^2+c^2) : :
X(61792) = 3*X[2]+13*X[3], 7*X[40]+9*X[61279], X[141]+7*X[55669], X[185]+3*X[44324], X[389]+3*X[54044], 3*X[597]+5*X[55637], -X[1353]+9*X[55682], -21*X[3576]+5*X[61284], X[3589]+3*X[55657], 5*X[3618]+11*X[55648], -X[3629]+9*X[55685], 3*X[3655]+13*X[31425] and many others

X(61792) lies on these lines: {2, 3}, {15, 42686}, {16, 42687}, {17, 42123}, {18, 42122}, {40, 61279}, {61, 42794}, {62, 42793}, {141, 55669}, {185, 44324}, {389, 54044}, {395, 41971}, {396, 41972}, {397, 42685}, {398, 42684}, {515, 58219}, {517, 58605}, {524, 55679}, {597, 55637}, {952, 4746}, {1125, 28216}, {1154, 17704}, {1353, 55682}, {1503, 55668}, {3098, 51732}, {3564, 55674}, {3576, 61284}, {3579, 51700}, {3589, 55657}, {3618, 55648}, {3629, 55685}, {3634, 28190}, {3655, 31425}, {3793, 13571}, {4297, 61614}, {4816, 5690}, {5010, 15172}, {5092, 12007}, {5131, 16137}, {5210, 31406}, {5237, 42912}, {5238, 42913}, {5270, 52793}, {5305, 15515}, {5318, 42955}, {5321, 42954}, {5339, 42628}, {5340, 42627}, {5343, 42688}, {5344, 42689}, {5349, 33416}, {5350, 33417}, {5447, 13382}, {5480, 55658}, {5493, 5901}, {5585, 31401}, {5844, 13607}, {5882, 17502}, {5894, 61606}, {6000, 55286}, {6200, 41964}, {6329, 55612}, {6390, 43459}, {6396, 41963}, {6407, 43510}, {6408, 43509}, {6409, 43802}, {6410, 43801}, {6411, 13966}, {6412, 8981}, {6437, 42644}, {6438, 42643}, {6449, 43414}, {6450, 43413}, {6455, 19116}, {6456, 19117}, {6496, 13935}, {6497, 9540}, {6501, 9542}, {6560, 43340}, {6561, 43341}, {6684, 28224}, {6696, 45185}, {7755, 8589}, {7771, 32820}, {7987, 61291}, {7999, 45957}, {8550, 17508}, {8584, 55694}, {9589, 38022}, {9680, 43525}, {10159, 54891}, {10168, 55650}, {10187, 36970}, {10188, 36969}, {10193, 14864}, {10194, 43379}, {10195, 43378}, {10264, 15036}, {10272, 10990}, {10610, 13431}, {10627, 16836}, {10645, 42925}, {10646, 42924}, {10991, 61561}, {10992, 61560}, {10993, 61566}, {11202, 44762}, {11204, 15105}, {11362, 51087}, {11542, 41974}, {11543, 41973}, {11592, 13754}, {11694, 51522}, {11695, 12002}, {11803, 61659}, {12006, 13348}, {12017, 61624}, {12041, 13392}, {12512, 61272}, {12815, 53419}, {13391, 55320}, {13393, 30714}, {13421, 15644}, {13464, 28212}, {14692, 34473}, {14929, 32825}, {15026, 36987}, {15041, 22251}, {15325, 59325}, {16192, 22791}, {16534, 48375}, {16772, 42959}, {16773, 42958}, {16962, 42994}, {16963, 42995}, {16966, 42889}, {16967, 42888}, {18337, 46170}, {18358, 55665}, {18481, 61254}, {18553, 55666}, {18583, 55649}, {19106, 43467}, {19107, 43468}, {19878, 28154}, {20014, 58226}, {20190, 51138}, {21167, 34507}, {21850, 55651}, {23251, 43336}, {23261, 43337}, {25555, 55653}, {25565, 50972}, {26446, 61250}, {28168, 58214}, {28202, 51086}, {29181, 55659}, {31423, 58217}, {31447, 51705}, {31454, 52048}, {31662, 61281}, {31666, 61286}, {32455, 55690}, {33520, 61565}, {33521, 61563}, {33751, 34573}, {34483, 57713}, {34754, 42798}, {34755, 42797}, {34773, 58221}, {35242, 38028}, {35255, 35815}, {35256, 35814}, {35812, 41967}, {35813, 41968}, {36521, 38627}, {36967, 42978}, {36968, 42979}, {37727, 50830}, {38064, 55626}, {38110, 55646}, {38726, 40685}, {38739, 61600}, {38750, 61599}, {38762, 61605}, {38774, 61604}, {38794, 61598}, {40647, 55166}, {41953, 42258}, {41954, 42259}, {41977, 42980}, {41978, 42981}, {42087, 42937}, {42088, 42936}, {42089, 43423}, {42092, 43422}, {42099, 43442}, {42100, 43443}, {42117, 43239}, {42118, 43238}, {42121, 42150}, {42124, 42151}, {42129, 43770}, {42130, 42495}, {42131, 42494}, {42132, 43769}, {42143, 42432}, {42144, 42920}, {42145, 42921}, {42146, 42431}, {42147, 42497}, {42148, 42496}, {42157, 43425}, {42158, 43424}, {42215, 43339}, {42216, 43338}, {42262, 43514}, {42265, 43513}, {42433, 42965}, {42434, 42964}, {42490, 43635}, {42491, 43634}, {42500, 42590}, {42501, 42591}, {42528, 42598}, {42529, 42599}, {42596, 51916}, {42597, 51915}, {42637, 43411}, {42638, 43412}, {42791, 42991}, {42792, 42990}, {42914, 43641}, {42915, 43642}, {42916, 43479}, {42917, 43480}, {42922, 52080}, {42923, 52079}, {42942, 42993}, {42943, 42992}, {42986, 43495}, {42987, 43496}, {42988, 43197}, {42989, 43198}, {43028, 43644}, {43029, 43649}, {43150, 55670}, {44882, 55667}, {46893, 59546}, {48874, 55654}, {48876, 55676}, {48881, 55660}, {48896, 51128}, {48906, 55673}, {50828, 61278}, {50965, 55652}, {50979, 55684}, {50982, 55677}, {50983, 55606}, {50987, 53092}, {51140, 55681}, {51171, 55624}, {51737, 55675}, {54169, 55687}, {55602, 59373}, {55629, 59399}, {55663, 58445}, {55671, 61545}, {58216, 58441}, {58224, 61295}

X(61792) = midpoint of X(i) and X(j) for these {i,j}: {3, 3530}, {20, 12102}, {376, 10109}, {548, 3628}, {549, 15759}, {550, 3850}, {3098, 51732}, {3579, 51700}, {3860, 15691}, {3861, 12103}, {6329, 55612}, {8703, 10124}, {10304, 14890}, {11737, 15690}, {12006, 13348}, {12041, 13392}, {12100, 14891}, {12512, 61272}, {13393, 30714}, {15336, 15957}, {15644, 16881}, {25565, 50972}, {33751, 34573}, {38726, 40685}
X(61792) = reflection of X(i) in X(j) for these {i,j}: {11540, 549}, {12108, 3530}, {12811, 16239}, {16239, 12108}, {3856, 3628}
X(61792) = complement of X(3861)
X(61792) = pole of line {185, 54044} with respect to the Jerabek hyperbola
X(61792) = pole of line {3, 12046} with respect to the Stammler hyperbola
X(61792) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(95), X(46853)}}, {{A, B, C, X(382), X(43970)}}, {{A, B, C, X(428), X(54891)}}, {{A, B, C, X(546), X(34483)}}, {{A, B, C, X(1294), X(58190)}}, {{A, B, C, X(3519), X(3845)}}, {{A, B, C, X(3627), X(13623)}}, {{A, B, C, X(3832), X(42021)}}, {{A, B, C, X(3853), X(14861)}}, {{A, B, C, X(5071), X(6662)}}, {{A, B, C, X(11403), X(44763)}}, {{A, B, C, X(11540), X(18317)}}, {{A, B, C, X(14863), X(14892)}}, {{A, B, C, X(21735), X(60007)}}, {{A, B, C, X(34200), X(40448)}}, {{A, B, C, X(34484), X(57713)}}, {{A, B, C, X(35502), X(43713)}}
X(61792) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12103, 3861}, {2, 17800, 3857}, {2, 5076, 5}, {2, 6908, 15711}, {3, 15693, 20}, {3, 15700, 631}, {3, 15706, 15717}, {3, 15707, 15696}, {3, 15712, 140}, {3, 3523, 550}, {3, 3526, 10304}, {3, 3528, 15714}, {3, 5054, 3528}, {4, 5072, 3858}, {4, 7486, 3851}, {5, 3529, 12101}, {5, 3543, 546}, {5, 549, 10303}, {20, 14869, 547}, {20, 15693, 14869}, {20, 547, 12102}, {30, 12108, 16239}, {30, 16239, 12811}, {30, 3530, 12108}, {30, 3628, 3856}, {30, 549, 11540}, {140, 12100, 15712}, {140, 15712, 3530}, {140, 550, 3850}, {376, 632, 3853}, {382, 11539, 12812}, {546, 12103, 11541}, {549, 15714, 15683}, {549, 17504, 15698}, {549, 5066, 14890}, {549, 8703, 5055}, {631, 11001, 17697}, {631, 11541, 2}, {632, 3853, 10109}, {1657, 14093, 6928}, {3091, 10303, 17542}, {3146, 15699, 3859}, {3146, 17554, 5068}, {3522, 3523, 3533}, {3522, 3524, 15720}, {3522, 3533, 5073}, {3522, 5046, 3839}, {3524, 3533, 3523}, {3524, 3543, 15722}, {3526, 10304, 15704}, {3526, 15684, 15022}, {3526, 15704, 5066}, {3526, 5066, 3628}, {3528, 3627, 15690}, {3528, 5054, 3627}, {3534, 5055, 3543}, {3534, 5076, 17800}, {3628, 10109, 7486}, {3628, 14890, 3526}, {3839, 5129, 3090}, {3858, 15712, 15693}, {5054, 15690, 11737}, {5070, 17538, 15687}, {6825, 15711, 6989}, {7486, 10303, 17678}, {10299, 15698, 4}, {10299, 15712, 12100}, {10303, 15717, 3524}, {10304, 14890, 30}, {10304, 15704, 548}, {10645, 42944, 42925}, {10646, 42945, 42924}, {11539, 15691, 3860}, {11812, 15759, 3534}, {12100, 15698, 15759}, {12100, 15705, 10124}, {12100, 15711, 11812}, {12100, 17504, 14891}, {12812, 15691, 382}, {14093, 15719, 15699}, {14813, 14814, 3845}, {15688, 15713, 14893}, {15692, 15698, 15706}, {15692, 15716, 17504}, {15693, 15709, 549}, {15696, 15707, 3525}, {15698, 15709, 15715}, {15698, 15717, 3}, {15700, 15705, 8703}, {15701, 15710, 15686}, {15708, 17538, 5070}, {15711, 15712, 3522}, {15715, 15717, 5072}, {30714, 61548, 13393}, {42150, 42774, 42121}, {42151, 42773, 42124}, {42431, 42949, 42146}, {42432, 42948, 42143}, {42433, 43544, 42965}, {42434, 43545, 42964}, {42500, 42813, 42590}, {43338, 43430, 42216}, {43339, 43431, 42215}

X(61793) = X(2)X(3)∩X(599)X(55675)

Barycentrics    21*a^4+2*(b^2-c^2)^2-23*a^2*(b^2+c^2) : :
X(61793) = 6*X[2]+19*X[3], 3*X[599]+22*X[55675], X[3763]+4*X[55666], X[5925]+24*X[46265], -28*X[6684]+3*X[61247], 3*X[7987]+2*X[31447], -28*X[9588]+3*X[12645], 16*X[9729]+9*X[54047], 24*X[10164]+X[18526], 3*X[10516]+22*X[55665], -28*X[10541]+3*X[50962], X[10620]+24*X[48375] and many others

X(61793) lies on these lines: {2, 3}, {599, 55675}, {952, 58224}, {1384, 31450}, {3053, 31470}, {3411, 11480}, {3412, 11481}, {3763, 55666}, {5023, 31457}, {5204, 31480}, {5206, 31492}, {5210, 9698}, {5346, 15815}, {5925, 46265}, {5965, 53094}, {6396, 31487}, {6398, 9680}, {6411, 35813}, {6412, 35812}, {6447, 52046}, {6448, 52045}, {6450, 31454}, {6451, 13961}, {6452, 13903}, {6484, 42569}, {6485, 42568}, {6496, 9681}, {6497, 18512}, {6519, 41964}, {6522, 41963}, {6684, 61247}, {7987, 31447}, {8588, 31467}, {9588, 12645}, {9692, 43510}, {9693, 19116}, {9729, 54047}, {10164, 18526}, {10516, 55665}, {10541, 50962}, {10620, 48375}, {11522, 51084}, {11592, 20791}, {11898, 17508}, {12702, 61279}, {13321, 13348}, {13624, 31425}, {14531, 40280}, {14848, 55631}, {15036, 20379}, {15042, 38727}, {15069, 55674}, {18440, 55670}, {21167, 39899}, {28160, 58217}, {28228, 61276}, {28234, 61284}, {30389, 50805}, {31666, 61288}, {33749, 55684}, {35242, 61274}, {36990, 55664}, {38064, 55602}, {40107, 55676}, {40341, 55680}, {41977, 43007}, {41978, 43006}, {42096, 43241}, {42097, 43240}, {42099, 42611}, {42100, 42610}, {42129, 42434}, {42130, 42489}, {42131, 42488}, {42132, 42433}, {42150, 42778}, {42151, 42777}, {42154, 43025}, {42155, 43024}, {42490, 42817}, {42491, 42818}, {42682, 42963}, {42683, 42962}, {42773, 42974}, {42774, 42975}, {42813, 42950}, {42814, 42951}, {42918, 43641}, {42919, 43642}, {42928, 43334}, {42929, 43335}, {42946, 43645}, {42947, 43646}, {42958, 49948}, {42959, 49947}, {47352, 55647}, {47355, 55660}, {48910, 55663}, {50983, 55580}, {51137, 55650}, {51185, 55600}, {53023, 55662}, {54131, 55652}, {58222, 61245}

X(61793) = pole of line {185, 62073} with respect to the Jerabek hyperbola
X(61793) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(13599), X(41989)}}, {{A, B, C, X(14093), X(60007)}}, {{A, B, C, X(15318), X(35018)}}
X(61793) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 10299, 15706}, {3, 15693, 1656}, {3, 15694, 3522}, {3, 15701, 550}, {3, 15707, 4}, {3, 15712, 15693}, {3, 15718, 140}, {3, 15722, 5073}, {3, 3523, 381}, {3, 3530, 3526}, {3, 3851, 10304}, {3, 5070, 3528}, {3, 549, 1657}, {3, 631, 15696}, {4, 5177, 14892}, {5, 3533, 5070}, {5, 548, 3529}, {140, 15714, 17538}, {381, 3526, 5067}, {548, 15022, 17800}, {548, 632, 17578}, {631, 15717, 15712}, {1656, 15696, 382}, {1656, 3534, 5076}, {1657, 15720, 3533}, {3091, 3853, 3843}, {3523, 3529, 11812}, {3524, 15692, 15711}, {3524, 15698, 3543}, {3524, 15711, 15694}, {3524, 3529, 3523}, {3530, 3853, 549}, {3534, 15700, 3524}, {3855, 5067, 15022}, {3858, 14892, 3091}, {5070, 14269, 5}, {5070, 15702, 16067}, {5073, 15722, 10303}, {10299, 12100, 3}, {10303, 15722, 15720}, {10304, 12108, 3851}, {12100, 15706, 15700}, {14093, 15693, 5054}, {15692, 15700, 14093}, {15692, 15717, 631}, {15693, 15706, 15692}, {15693, 15711, 3534}, {15694, 15695, 14269}, {15698, 15718, 15688}, {15700, 15706, 15716}, {15712, 17504, 632}, {15712, 17538, 15718}

X(61794) = X(2)X(3)∩X(6)X(42930)

Barycentrics    19*a^4+2*(b^2-c^2)^2-21*a^2*(b^2+c^2) : :
X(61794) = 6*X[2]+17*X[3], -X[399]+24*X[48375], 12*X[597]+11*X[55620], 3*X[599]+20*X[55677], -2*X[944]+25*X[58224], 5*X[3763]+18*X[55667], -X[5895]+24*X[46265], 8*X[6053]+15*X[15041], -X[6144]+24*X[55686], 20*X[7987]+3*X[59503], -4*X[8550]+27*X[55682], 15*X[8567]+8*X[14862] and many others

X(61794) lies on these lines: {2, 3}, {6, 42930}, {399, 48375}, {597, 55620}, {599, 55677}, {944, 58224}, {3763, 55667}, {5237, 42959}, {5238, 42958}, {5351, 42800}, {5352, 42799}, {5355, 15815}, {5365, 43102}, {5366, 43103}, {5895, 46265}, {6053, 15041}, {6144, 55686}, {6221, 41964}, {6398, 41963}, {6409, 13961}, {6410, 13903}, {6411, 58866}, {6412, 8960}, {6448, 9680}, {6480, 42569}, {6481, 42568}, {6560, 43409}, {6561, 43410}, {7755, 53095}, {7987, 59503}, {8550, 55682}, {8567, 14862}, {9541, 43412}, {9624, 51084}, {10164, 12645}, {10168, 55641}, {10182, 48672}, {10193, 34780}, {10516, 55666}, {10610, 13432}, {10645, 42774}, {10646, 42773}, {11898, 21167}, {11935, 61134}, {12242, 37487}, {13421, 15045}, {14848, 55626}, {15023, 20379}, {15040, 20417}, {15042, 38728}, {15056, 55286}, {15069, 55675}, {16644, 43013}, {16645, 43012}, {17502, 18526}, {17508, 39899}, {18440, 55671}, {18553, 55669}, {21163, 32520}, {23269, 43881}, {23275, 43882}, {25555, 55646}, {30315, 58217}, {31423, 58219}, {31425, 31666}, {31470, 35007}, {32137, 33879}, {32821, 43459}, {34507, 55676}, {36836, 43009}, {36843, 43008}, {36990, 55665}, {38064, 55595}, {38110, 55632}, {40341, 55683}, {41973, 42816}, {41974, 42815}, {42090, 42948}, {42091, 42949}, {42095, 42908}, {42098, 42909}, {42115, 42945}, {42116, 42944}, {42119, 43329}, {42120, 43328}, {42126, 42937}, {42127, 42936}, {42150, 42818}, {42151, 42817}, {42154, 42978}, {42155, 42979}, {42431, 42962}, {42432, 42963}, {42488, 43330}, {42489, 43331}, {42490, 42992}, {42491, 42993}, {42528, 43548}, {42529, 43549}, {42557, 43379}, {42558, 43378}, {42584, 42775}, {42585, 42776}, {42785, 55656}, {42890, 43545}, {42891, 43544}, {42926, 42982}, {42927, 42983}, {42954, 43547}, {42955, 43546}, {42960, 42965}, {42961, 42964}, {42974, 43420}, {42975, 43421}, {42994, 49947}, {42995, 49948}, {43193, 43422}, {43194, 43423}, {43324, 43441}, {43325, 43440}, {43542, 43635}, {43543, 43634}, {46267, 55628}, {47352, 55644}, {47355, 55659}, {48872, 55663}, {48905, 55664}, {48910, 55662}, {50983, 55724}, {51132, 53092}, {51137, 55647}, {51172, 53097}, {51175, 55681}, {51185, 55597}, {53023, 55661}, {54131, 55650}, {54169, 55701}

X(61794) = pole of line {185, 62074} with respect to the Jerabek hyperbola
X(61794) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(3519), X(3839)}}, {{A, B, C, X(3855), X(42021)}}, {{A, B, C, X(5068), X(26861)}}, {{A, B, C, X(5198), X(44731)}}, {{A, B, C, X(13599), X(14892)}}, {{A, B, C, X(14093), X(40448)}}, {{A, B, C, X(14528), X(52294)}}, {{A, B, C, X(14861), X(17578)}}, {{A, B, C, X(58204), X(60618)}}
X(61794) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 15694, 548}, {3, 15701, 20}, {3, 15707, 5}, {3, 15717, 15700}, {3, 15718, 631}, {3, 3526, 15688}, {3, 3843, 10304}, {3, 5054, 15696}, {3, 5070, 8703}, {3, 549, 382}, {4, 10299, 15692}, {4, 140, 5070}, {4, 15710, 3522}, {4, 3522, 12103}, {4, 547, 3851}, {20, 3090, 12101}, {140, 15712, 3524}, {140, 5073, 1656}, {140, 550, 5068}, {140, 8703, 4}, {381, 15706, 15716}, {381, 15720, 140}, {381, 5070, 5079}, {382, 1656, 3850}, {632, 3530, 15719}, {1657, 15720, 3526}, {3524, 14891, 15701}, {3526, 15688, 5076}, {3528, 12108, 5055}, {3530, 12103, 549}, {3530, 14891, 12811}, {3534, 5054, 547}, {3627, 5059, 5073}, {3843, 15722, 14869}, {7491, 15722, 15694}, {10109, 11541, 3843}, {10299, 15700, 15720}, {10299, 15712, 3}, {10299, 15717, 15712}, {10304, 15722, 15723}, {10645, 42774, 42989}, {10646, 42773, 42988}, {12100, 15700, 15706}, {12100, 15712, 10299}, {12108, 15711, 3528}, {14093, 15721, 381}, {14813, 14814, 3839}, {15681, 15719, 5054}, {15685, 15707, 15721}, {15698, 15707, 14093}, {15700, 15706, 15693}, {15706, 15712, 1657}, {15718, 17504, 3534}, {31425, 31666, 34718}, {42930, 42931, 6}

X(61795) = X(2)X(3)∩X(61)X(42930)

Barycentrics    25*a^4+3*(b^2-c^2)^2-28*a^2*(b^2+c^2) : :
X(61795) = 9*X[2]+22*X[3], 3*X[69]+28*X[55681], -9*X[1992]+40*X[55698], 15*X[3618]+16*X[55631], 7*X[3619]+24*X[55670], -2*X[4701]+33*X[10164], -X[6102]+32*X[55320], 12*X[6699]+19*X[15023], -9*X[7967]+40*X[31666], 25*X[7987]+6*X[38127], 28*X[9588]+3*X[50818], 6*X[10175]+25*X[58217] and many others

X(61795) lies on these lines: {2, 3}, {61, 42930}, {62, 42931}, {69, 55681}, {371, 43315}, {372, 43314}, {397, 43420}, {398, 43421}, {1131, 43517}, {1132, 43518}, {1992, 55698}, {3316, 42570}, {3317, 42571}, {3618, 55631}, {3619, 55670}, {3785, 32891}, {4701, 10164}, {5585, 31404}, {6102, 55320}, {6411, 13939}, {6412, 13886}, {6419, 43510}, {6420, 43509}, {6425, 42569}, {6426, 42568}, {6447, 43884}, {6448, 43883}, {6488, 9693}, {6489, 32787}, {6496, 13941}, {6497, 8972}, {6519, 7586}, {6522, 7585}, {6699, 15023}, {7772, 46453}, {7967, 31666}, {7987, 38127}, {8164, 59319}, {9588, 50818}, {10175, 58217}, {10519, 55684}, {10645, 42987}, {10646, 42986}, {10653, 42926}, {10654, 42927}, {11008, 55688}, {11362, 58229}, {12245, 30389}, {12317, 15020}, {13464, 50809}, {14482, 53096}, {14561, 55652}, {14641, 33879}, {14853, 55641}, {14912, 55687}, {14927, 55668}, {15034, 48375}, {15036, 38729}, {16964, 43490}, {16965, 43489}, {17502, 61244}, {17852, 31454}, {20423, 55628}, {25406, 55677}, {31425, 50817}, {31730, 61271}, {32818, 43459}, {34507, 51176}, {35820, 43505}, {35821, 43506}, {37640, 43008}, {37641, 43009}, {38064, 55588}, {38074, 51080}, {38112, 58224}, {39874, 55674}, {40247, 55166}, {41977, 43021}, {41978, 43020}, {42103, 43325}, {42106, 43324}, {42111, 43470}, {42114, 43469}, {42119, 42531}, {42120, 42530}, {42147, 43333}, {42148, 43332}, {42149, 42799}, {42152, 42800}, {42160, 42593}, {42161, 42592}, {42260, 42557}, {42261, 42558}, {42268, 43788}, {42269, 43787}, {42494, 42528}, {42495, 42529}, {42512, 43485}, {42513, 43486}, {42598, 42971}, {42599, 42970}, {42775, 43203}, {42776, 43204}, {42954, 43772}, {42955, 43771}, {43205, 43497}, {43206, 43498}, {43334, 43777}, {43335, 43778}, {45187, 61136}, {47743, 59325}, {51171, 55595}, {51212, 55644}, {51538, 55658}, {51705, 58225}, {53620, 58223}, {54170, 55623}, {54173, 55694}, {55583, 59373}, {59417, 61281}

X(61795) = pole of line {69, 3858} with respect to the Wallace hyperbola
X(61795) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(3858)}}, {{A, B, C, X(3530), X(18852)}}, {{A, B, C, X(3861), X(15077)}}, {{A, B, C, X(5067), X(52441)}}, {{A, B, C, X(10109), X(46412)}}, {{A, B, C, X(15686), X(54660)}}, {{A, B, C, X(15687), X(31371)}}, {{A, B, C, X(18849), X(49137)}}, {{A, B, C, X(18853), X(46936)}}, {{A, B, C, X(18854), X(19709)}}
X(61795) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15696, 4}, {2, 20, 3858}, {3, 10303, 17538}, {3, 12108, 3146}, {3, 14869, 20}, {3, 15693, 14869}, {3, 15720, 3627}, {3, 3091, 3528}, {3, 3523, 3525}, {3, 3627, 10304}, {3, 3628, 3522}, {3, 5054, 12103}, {3, 5079, 8703}, {3, 549, 3091}, {3, 631, 3529}, {4, 3524, 3530}, {140, 15684, 6904}, {405, 3627, 5071}, {547, 12103, 12102}, {547, 15692, 15715}, {549, 3528, 3533}, {632, 15704, 12811}, {1657, 3528, 376}, {1657, 5054, 5070}, {1657, 5070, 3860}, {3091, 15022, 14892}, {3146, 3523, 12108}, {3146, 3839, 5076}, {3522, 15702, 3855}, {3522, 3628, 11541}, {3523, 15705, 5}, {3523, 15717, 12100}, {3523, 3854, 15720}, {3524, 10299, 631}, {3524, 15692, 15719}, {3524, 15715, 15693}, {3524, 15717, 10299}, {3525, 4192, 17578}, {3528, 3533, 15682}, {3529, 15698, 3}, {3530, 5054, 3523}, {3853, 3858, 14269}, {3855, 10299, 17504}, {5054, 12100, 15692}, {5054, 15703, 11540}, {5070, 15696, 3853}, {6996, 17697, 3854}, {10303, 15696, 7407}, {10303, 17538, 3090}, {10304, 15720, 5067}, {11541, 15702, 3628}, {12100, 15718, 15705}, {12103, 12108, 632}, {14269, 15693, 549}, {15681, 15722, 5054}, {15692, 15710, 15698}, {15692, 15719, 15710}, {15693, 15715, 15709}, {15700, 15712, 15717}, {15712, 15717, 3524}

X(61796) = X(2)X(3)∩X(6)X(42932)

Barycentrics    41*a^4+5*(b^2-c^2)^2-46*a^2*(b^2+c^2) : :
X(61796) = 5*X[2]+12*X[3], 9*X[165]+8*X[51108], -5*X[193]+56*X[55691], 10*X[597]+7*X[55607], -3*X[962]+20*X[51109], -5*X[1992]+22*X[55699], 5*X[3654]+12*X[31662], 2*X[4669]+15*X[7987], -X[4677]+18*X[10164], 8*X[4745]+9*X[5731], -15*X[5032]+32*X[50664], 16*X[5092]+X[11160] and many others

X(61796) lies on these lines: {2, 3}, {6, 42932}, {15, 42505}, {16, 42504}, {165, 51108}, {193, 55691}, {597, 55607}, {962, 51109}, {1131, 42608}, {1132, 42609}, {1587, 42524}, {1588, 42525}, {1992, 55699}, {3654, 31662}, {4669, 7987}, {4677, 10164}, {4745, 5731}, {5032, 50664}, {5092, 11160}, {5102, 50983}, {5281, 37587}, {5334, 43200}, {5335, 43199}, {5351, 43479}, {5352, 43480}, {5476, 55645}, {5569, 11148}, {5603, 51084}, {5734, 41150}, {5921, 50993}, {6411, 42417}, {6412, 42418}, {6431, 42523}, {6432, 42522}, {6433, 32788}, {6434, 32787}, {6437, 19053}, {6438, 19054}, {6480, 7586}, {6481, 7585}, {6486, 13935}, {6487, 9540}, {6496, 43212}, {6497, 43211}, {6684, 51068}, {7988, 50816}, {7991, 51106}, {8584, 51214}, {8972, 53131}, {9541, 43890}, {9692, 41964}, {10168, 55633}, {10519, 55685}, {10541, 41149}, {10645, 42507}, {10646, 42506}, {11055, 21163}, {11177, 55728}, {11179, 55683}, {11180, 55674}, {11231, 50819}, {11480, 49812}, {11481, 49813}, {11531, 51103}, {12117, 38735}, {13624, 31145}, {13941, 53130}, {14226, 42527}, {14241, 42526}, {14853, 51137}, {15533, 21167}, {15589, 32896}, {15602, 21843}, {16200, 50828}, {16241, 49826}, {16242, 49827}, {19570, 55819}, {20049, 61524}, {20423, 55627}, {21156, 35749}, {21157, 36327}, {21356, 55676}, {22165, 53094}, {23302, 42588}, {23303, 42589}, {25406, 50991}, {28208, 46932}, {30308, 51119}, {30389, 51091}, {30392, 51071}, {31884, 51166}, {32837, 43459}, {33602, 42132}, {33603, 42129}, {33748, 54173}, {34632, 51110}, {36346, 49878}, {36352, 49877}, {38028, 50809}, {38064, 55587}, {38079, 55648}, {38110, 50966}, {38155, 50829}, {39561, 50967}, {41107, 43242}, {41108, 43243}, {41121, 43465}, {41122, 43466}, {41135, 55812}, {42089, 42632}, {42092, 42631}, {42150, 49904}, {42151, 49903}, {42510, 42804}, {42511, 42803}, {42516, 42687}, {42517, 42686}, {42528, 43540}, {42529, 43541}, {42532, 43870}, {42533, 43869}, {42791, 49861}, {42792, 49862}, {42892, 43308}, {42893, 43309}, {42942, 43002}, {42943, 43003}, {42952, 43244}, {42953, 43245}, {42982, 43236}, {42983, 43237}, {43108, 52079}, {43109, 52080}, {43174, 51097}, {43505, 43560}, {43506, 43561}, {48310, 55656}, {50825, 59388}, {50872, 51105}, {50873, 59420}, {50969, 55657}, {50974, 55682}, {50977, 55680}, {50984, 51186}, {50988, 55610}, {50990, 51215}, {51028, 51185}, {51072, 51705}, {51085, 51094}, {51122, 55823}, {51171, 55594}, {51188, 55684}, {51216, 59411}, {54132, 55603}, {54169, 55711}, {54170, 55622}, {55582, 59373}

X(61796) = midpoint of X(i) and X(j) for these {i,j}: {376, 3544}
X(61796) = anticomplement of X(61915)
X(61796) = pole of line {69, 61966} with respect to the Wallace hyperbola
X(61796) = intersection, other than A, B, C, of circumconics {{A, B, C, X(253), X(19709)}}, {{A, B, C, X(5079), X(46412)}}, {{A, B, C, X(5481), X(30734)}}, {{A, B, C, X(16251), X(35409)}}, {{A, B, C, X(18317), X(55863)}}
X(61796) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15701, 10303}, {2, 15717, 12100}, {2, 15719, 15708}, {2, 3522, 15682}, {2, 3534, 3839}, {2, 3845, 5056}, {2, 8703, 15640}, {3, 15707, 15723}, {3, 15720, 3853}, {3, 3543, 10304}, {3, 3850, 3528}, {3, 5054, 15686}, {3, 549, 3545}, {3, 631, 5059}, {20, 15692, 15705}, {20, 3545, 3543}, {140, 15710, 15683}, {140, 3525, 4193}, {376, 3524, 3530}, {376, 3544, 30}, {546, 3522, 20}, {546, 549, 5054}, {547, 3545, 15022}, {549, 12100, 15716}, {549, 15688, 3525}, {549, 15710, 13735}, {631, 3524, 15718}, {1656, 17800, 546}, {1656, 3830, 5066}, {3523, 10304, 15721}, {3524, 10299, 549}, {3524, 15692, 3523}, {3524, 15698, 15693}, {3524, 15700, 15717}, {3530, 15711, 15701}, {3545, 15702, 16239}, {3627, 11539, 547}, {5054, 15686, 5067}, {5056, 15708, 15702}, {5066, 11812, 11539}, {6437, 43888, 19053}, {6438, 43887, 19054}, {10299, 15705, 15692}, {10304, 15721, 3091}, {11001, 11812, 2}, {11001, 15698, 3}, {11001, 15719, 11812}, {11540, 15685, 5071}, {11812, 15693, 15719}, {12100, 15693, 15698}, {12100, 15711, 15706}, {12100, 15716, 10299}, {13735, 17568, 1656}, {14891, 15707, 4}, {15682, 15715, 15759}, {15682, 15759, 3522}, {15685, 15720, 11540}, {15690, 16239, 3845}, {15692, 15693, 15697}, {15693, 15716, 3830}, {15698, 15719, 11001}, {15700, 15712, 3524}, {15701, 15706, 15711}, {15701, 15711, 376}, {15706, 15718, 3627}, {15707, 15710, 11113}, {15711, 15719, 3832}, {15718, 17504, 631}, {42089, 42632, 49873}, {42092, 42631, 49874}, {42932, 42933, 6}

X(61797) = X(2)X(3)∩X(141)X(33618)

Barycentrics    31*a^4+4*(b^2-c^2)^2-35*a^2*(b^2+c^2) : :
X(61797) = 4*X[2]+9*X[3], 3*X[165]+10*X[51084], 8*X[597]+5*X[55604], 2*X[599]+11*X[55678], -18*X[1385]+5*X[51097], -15*X[3576]+2*X[51087], 6*X[3579]+7*X[51110], -27*X[3653]+14*X[51106], 5*X[3654]+8*X[51085], 16*X[3828]+49*X[58220], X[4677]+12*X[13624], 16*X[4745]+75*X[58224] and many others

X(61797) lies on these lines: {2, 3}, {141, 33618}, {165, 51084}, {597, 55604}, {599, 55678}, {1327, 43513}, {1328, 43514}, {1385, 51097}, {3070, 42526}, {3071, 42527}, {3576, 51087}, {3579, 51110}, {3653, 51106}, {3654, 51085}, {3828, 58220}, {4677, 13624}, {4745, 58224}, {5085, 51140}, {5092, 15533}, {5093, 50983}, {5334, 43002}, {5335, 43003}, {5418, 42418}, {5420, 42417}, {5476, 55643}, {5569, 51122}, {5585, 14537}, {5655, 38633}, {5657, 50830}, {5731, 50825}, {5790, 50829}, {5886, 51086}, {6199, 43315}, {6395, 43314}, {6417, 52046}, {6418, 52045}, {6445, 32788}, {6446, 32787}, {6449, 35814}, {6450, 35815}, {6451, 13847}, {6452, 13846}, {6496, 35823}, {6497, 35822}, {6560, 60313}, {6561, 60314}, {6684, 51067}, {7585, 17851}, {7987, 38066}, {8148, 51103}, {8584, 55705}, {8724, 38634}, {8976, 43342}, {9541, 43317}, {9690, 35256}, {10164, 50827}, {10168, 55629}, {10247, 50828}, {10302, 54851}, {10519, 50985}, {10645, 43421}, {10646, 43420}, {11178, 55671}, {11480, 42799}, {11481, 42800}, {11485, 42930}, {11486, 42931}, {11542, 42968}, {11543, 42969}, {11632, 38635}, {12007, 55692}, {12017, 15534}, {12702, 51105}, {12816, 43029}, {12817, 43028}, {13607, 34718}, {13665, 43568}, {13785, 43569}, {13951, 43343}, {14561, 51139}, {14848, 55616}, {14912, 51182}, {15815, 39593}, {16241, 42796}, {16242, 42795}, {16644, 33607}, {16645, 33606}, {16962, 43008}, {16963, 43009}, {17502, 50798}, {17508, 50955}, {18435, 55166}, {18440, 51143}, {18525, 51069}, {18526, 51072}, {20126, 38638}, {20423, 55624}, {21167, 50982}, {21358, 55672}, {22236, 42977}, {22238, 42976}, {25406, 50980}, {25561, 55665}, {31662, 50817}, {31884, 51137}, {33878, 51185}, {34773, 51068}, {35255, 43415}, {36967, 42688}, {36968, 42689}, {37624, 51107}, {37832, 43330}, {37835, 43331}, {38034, 50813}, {38064, 55584}, {38072, 55655}, {38136, 50969}, {38140, 50820}, {39899, 50990}, {41149, 51138}, {41152, 51737}, {41153, 55593}, {41943, 42935}, {41944, 42934}, {41945, 43431}, {41946, 43430}, {42115, 43030}, {42116, 43031}, {42121, 49876}, {42122, 49873}, {42123, 49874}, {42124, 49875}, {42126, 42501}, {42127, 42500}, {42147, 49859}, {42148, 49860}, {42154, 42690}, {42155, 42691}, {42508, 43238}, {42509, 43239}, {42518, 43199}, {42519, 43200}, {42625, 43548}, {42626, 43549}, {42631, 43024}, {42632, 43025}, {42633, 43870}, {42634, 43869}, {42639, 60299}, {42640, 60300}, {42773, 61719}, {42791, 42975}, {42792, 42974}, {42815, 43109}, {42816, 43108}, {42817, 49826}, {42818, 49827}, {42950, 43246}, {42951, 43247}, {43150, 50993}, {43328, 49825}, {43329, 49824}, {43384, 43881}, {43385, 43882}, {46267, 55614}, {47352, 55639}, {47353, 51141}, {48906, 50994}, {49919, 49920}, {50807, 59420}, {50815, 58218}, {50821, 51515}, {50832, 59417}, {50863, 61260}, {50957, 59411}, {50968, 55660}, {50973, 55695}, {50977, 50989}, {50988, 54132}, {51024, 55657}, {51070, 51705}, {51189, 53094}, {53091, 54169}, {54131, 55648}, {54608, 60277}, {54643, 60238}, {54644, 60228}, {54645, 60282}, {54734, 60239}, {54866, 60641}, {60175, 60216}, {60192, 60283}

X(61797) = midpoint of X(i) and X(j) for these {i,j}: {376, 5068}
X(61797) = reflection of X(i) in X(j) for these {i,j}: {10303, 549}, {381, 5067}
X(61797) = inverse of X(61918) in orthocentroidal circle
X(61797) = inverse of X(61918) in Yff hyperbola
X(61797) = complement of X(61979)
X(61797) = pole of line {523, 61918} with respect to the orthocentroidal circle
X(61797) = pole of line {6, 61918} with respect to the Kiepert hyperbola
X(61797) = pole of line {523, 61918} with respect to the Yff hyperbola
X(61797) = pole of line {69, 61961} with respect to the Wallace hyperbola
X(61797) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(15695)}}, {{A, B, C, X(3855), X(34483)}}, {{A, B, C, X(10301), X(54851)}}, {{A, B, C, X(10303), X(18317)}}, {{A, B, C, X(12101), X(57822)}}, {{A, B, C, X(13623), X(15682)}}, {{A, B, C, X(15022), X(46412)}}
X(61797) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12100, 15716}, {2, 15693, 15722}, {2, 15698, 15759}, {2, 15722, 15701}, {2, 376, 12101}, {2, 6949, 3857}, {3, 15684, 10304}, {3, 15690, 6926}, {3, 15694, 15689}, {3, 15703, 15688}, {3, 15707, 15694}, {3, 15720, 3843}, {3, 3524, 15718}, {3, 5054, 15681}, {4, 7486, 12811}, {20, 382, 6971}, {30, 5067, 381}, {30, 549, 10303}, {140, 14093, 14269}, {140, 15705, 14093}, {376, 5068, 30}, {381, 3534, 15640}, {381, 5054, 632}, {547, 15710, 15696}, {548, 549, 15709}, {549, 10304, 3526}, {549, 15704, 14890}, {549, 17504, 548}, {549, 8703, 11540}, {632, 3530, 3523}, {3523, 15709, 549}, {3524, 15692, 3530}, {3524, 15712, 15700}, {3526, 10304, 15684}, {3526, 3534, 5066}, {3530, 10299, 5079}, {3530, 15692, 5054}, {3530, 8703, 15719}, {3534, 15706, 15698}, {3534, 3830, 17800}, {3845, 8703, 12103}, {5054, 12103, 15703}, {5054, 15681, 5070}, {5054, 15696, 547}, {5072, 15688, 15683}, {5072, 15706, 14891}, {8703, 12100, 15692}, {10109, 15697, 382}, {10303, 15717, 10299}, {11812, 12100, 17504}, {12100, 15693, 3}, {12100, 15698, 15706}, {12100, 15718, 3830}, {12101, 15713, 2}, {12108, 15714, 3545}, {13587, 16239, 1656}, {15688, 15703, 5073}, {15689, 15694, 3851}, {15692, 15719, 8703}, {15693, 15700, 12100}, {15693, 15701, 15707}, {15693, 15706, 3534}, {15694, 17800, 5055}, {15697, 15702, 10109}, {15698, 15719, 4}, {15700, 15706, 15717}, {15701, 15718, 15693}, {15716, 15722, 15695}, {42154, 43545, 42690}, {42155, 43544, 42691}, {42508, 43238, 49903}, {42509, 43239, 49904}, {51141, 55670, 47353}

X(61798) = X(2)X(3)∩X(165)X(15808)

Barycentrics    23*a^4+3*(b^2-c^2)^2-26*a^2*(b^2+c^2) : :
X(61798) = 9*X[2]+20*X[3], 15*X[165]+14*X[15808], -3*X[193]+32*X[20190], 3*X[3241]+26*X[31425], -6*X[3244]+35*X[30389], 5*X[3617]+24*X[17502], 15*X[3618]+14*X[55626], 7*X[3619]+22*X[55671], 5*X[3620]+24*X[17508], 4*X[3626]+25*X[7987], -6*X[3629]+35*X[10541], 4*X[3631]+25*X[53094] and many others

X(61798) lies on these lines: {2, 3}, {61, 43869}, {62, 43870}, {99, 32886}, {165, 15808}, {193, 20190}, {315, 32887}, {371, 43884}, {372, 43883}, {3241, 31425}, {3244, 30389}, {3576, 4917}, {3592, 9542}, {3617, 17502}, {3618, 55626}, {3619, 55671}, {3620, 17508}, {3626, 7987}, {3629, 10541}, {3631, 53094}, {3632, 10164}, {3679, 58225}, {3746, 5265}, {4031, 5703}, {5032, 55708}, {5085, 11008}, {5261, 59319}, {5274, 59325}, {5281, 5563}, {5304, 53096}, {5351, 42612}, {5352, 42613}, {5657, 20054}, {5921, 55676}, {6329, 53097}, {6417, 42644}, {6418, 42643}, {6419, 42523}, {6420, 42522}, {6427, 43510}, {6428, 43509}, {6453, 7586}, {6454, 7585}, {6496, 13939}, {6497, 13886}, {6519, 35256}, {6522, 35255}, {6776, 55679}, {9543, 13966}, {9545, 13347}, {9588, 34641}, {9692, 19053}, {10147, 32788}, {10148, 32787}, {10168, 55628}, {10519, 55687}, {10645, 42967}, {10646, 42966}, {10979, 61307}, {13346, 46865}, {14561, 55650}, {14853, 55637}, {15020, 24981}, {15021, 48378}, {15023, 38729}, {15036, 20397}, {16772, 43428}, {16773, 43429}, {19925, 58217}, {20057, 59417}, {20423, 55623}, {20791, 45187}, {21153, 60957}, {21167, 40341}, {22234, 50967}, {22235, 43013}, {22237, 43012}, {23235, 35021}, {28160, 46930}, {30315, 50815}, {31663, 46934}, {34747, 58229}, {35007, 37665}, {35022, 38664}, {35023, 38669}, {35024, 38668}, {36422, 61315}, {37512, 37689}, {37668, 43459}, {38064, 55583}, {38110, 55620}, {40107, 51215}, {40330, 55670}, {42130, 42591}, {42131, 42590}, {42140, 43327}, {42141, 43326}, {42160, 43371}, {42161, 43370}, {42415, 42818}, {42416, 42817}, {42488, 43540}, {42489, 43541}, {42494, 42500}, {42495, 42501}, {42637, 43879}, {42638, 43880}, {42779, 43479}, {42780, 43480}, {42797, 42939}, {42798, 42938}, {42932, 43022}, {42933, 43023}, {43102, 43488}, {43103, 43487}, {43507, 51910}, {43508, 51911}, {46931, 58219}, {50819, 61258}, {50983, 53858}, {51170, 55701}, {51171, 52987}, {54132, 55600}, {54173, 55698}, {55631, 61044}, {58224, 61510}

X(61798) = pole of line {185, 62078} with respect to the Jerabek hyperbola
X(61798) = intersection, other than A, B, C, of circumconics {{A, B, C, X(253), X(3544)}}, {{A, B, C, X(1217), X(11539)}}, {{A, B, C, X(3091), X(57823)}}, {{A, B, C, X(3346), X(15702)}}, {{A, B, C, X(3857), X(31363)}}, {{A, B, C, X(15740), X(50690)}}, {{A, B, C, X(17800), X(60618)}}
X(61798) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11319, 17535}, {2, 13741, 1010}, {2, 15717, 10299}, {2, 17536, 11110}, {2, 17697, 16408}, {2, 3146, 3544}, {2, 3522, 382}, {2, 3529, 3091}, {2, 3530, 3523}, {2, 3851, 7486}, {2, 4195, 16862}, {2, 632, 16857}, {3, 10303, 20}, {3, 12108, 4}, {3, 140, 17538}, {3, 14869, 3529}, {3, 15693, 12108}, {3, 15701, 5076}, {3, 15720, 546}, {3, 3090, 3522}, {3, 3523, 10303}, {3, 5054, 15704}, {3, 5072, 8703}, {3, 549, 3090}, {3, 631, 3146}, {3, 632, 376}, {4, 631, 11539}, {20, 15689, 6925}, {20, 3523, 15708}, {21, 5177, 8363}, {140, 15688, 3855}, {140, 15714, 17800}, {140, 17538, 15022}, {140, 3090, 16858}, {381, 6938, 3854}, {382, 550, 11001}, {546, 631, 16370}, {548, 15702, 5068}, {549, 12101, 5054}, {550, 14869, 3628}, {550, 3530, 15707}, {3091, 3628, 5056}, {3146, 17564, 13587}, {3522, 6910, 15687}, {3523, 10304, 631}, {3524, 10299, 3530}, {3524, 15698, 15718}, {3525, 3529, 5079}, {3528, 10299, 17504}, {3530, 15712, 15700}, {3530, 17504, 15720}, {3533, 8703, 17578}, {3855, 10299, 15698}, {3858, 6833, 3832}, {5079, 14869, 3525}, {6955, 15759, 5059}, {10299, 15700, 15717}, {10303, 15692, 3}, {10304, 12100, 15692}, {11001, 15715, 15710}, {11539, 15705, 10304}, {11737, 15709, 2}, {12100, 15707, 15715}, {14782, 14783, 15723}, {15022, 17538, 3543}, {15688, 17800, 550}, {15689, 15693, 549}, {15693, 15705, 15721}, {15700, 15707, 12100}, {15720, 17504, 3528}, {16343, 16357, 16347}, {17531, 17543, 16346}

X(61799) = X(2)X(3)∩X(13)X(43027)

Barycentrics    15*a^4+2*(b^2-c^2)^2-17*a^2*(b^2+c^2) : :
X(61799) = 6*X[2]+13*X[3], 12*X[597]+7*X[55602], 3*X[599]+16*X[55679], 6*X[1385]+13*X[31425], 9*X[3576]+10*X[31447], 10*X[3579]+9*X[61275], 8*X[3589]+11*X[55648], 10*X[3618]+9*X[55624], 15*X[3653]+4*X[50814], 5*X[3763]+14*X[55669], 10*X[4297]+9*X[61257], -32*X[4746]+13*X[12645] and many others

X(61799) lies on these lines: {2, 3}, {13, 43027}, {14, 43026}, {32, 31470}, {36, 31480}, {187, 31492}, {371, 42569}, {372, 42568}, {597, 55602}, {599, 55679}, {1131, 43881}, {1132, 43882}, {1152, 31487}, {1384, 9606}, {1385, 31425}, {3053, 31457}, {3312, 9680}, {3411, 36836}, {3412, 36843}, {3576, 31447}, {3579, 61275}, {3589, 55648}, {3618, 55624}, {3653, 50814}, {3763, 55669}, {4297, 61257}, {4317, 52793}, {4325, 31479}, {4746, 12645}, {4816, 9588}, {5013, 5368}, {5023, 9698}, {5085, 33749}, {5126, 31436}, {5210, 31467}, {5237, 42773}, {5238, 42774}, {5339, 43645}, {5340, 43646}, {5351, 42988}, {5352, 42989}, {5365, 42591}, {5366, 42590}, {5418, 6497}, {5420, 6496}, {5585, 31455}, {5587, 58219}, {5657, 61292}, {5731, 58224}, {5881, 17502}, {5890, 11592}, {6144, 55690}, {6200, 13961}, {6396, 13903}, {6398, 31454}, {6407, 35256}, {6408, 35255}, {6409, 18510}, {6410, 18512}, {6427, 52046}, {6428, 52045}, {6433, 35814}, {6434, 35815}, {6445, 13935}, {6446, 9540}, {6451, 9681}, {6500, 43510}, {6501, 43509}, {6684, 61244}, {7586, 9691}, {7765, 53095}, {7871, 43459}, {7987, 18526}, {8148, 61280}, {8550, 51175}, {9607, 21843}, {9624, 31663}, {9657, 59319}, {9670, 59325}, {9690, 19116}, {9729, 54048}, {10164, 37727}, {10168, 55626}, {10516, 55668}, {10541, 50973}, {10645, 42491}, {10646, 42490}, {11271, 20585}, {11362, 61287}, {11480, 42991}, {11481, 42990}, {11482, 50983}, {11898, 55682}, {12162, 55166}, {12307, 37475}, {12702, 61277}, {14848, 55614}, {15040, 16003}, {15041, 48378}, {15042, 15061}, {15043, 54044}, {15047, 37483}, {15051, 20379}, {15069, 17508}, {15305, 55286}, {15534, 55694}, {16192, 18493}, {16772, 42115}, {16773, 42116}, {17704, 23039}, {17821, 52102}, {18357, 58220}, {18440, 55673}, {18525, 58221}, {18553, 51141}, {18583, 55632}, {19106, 42610}, {19107, 42611}, {19117, 43415}, {23236, 38727}, {25440, 31494}, {25555, 55641}, {30389, 50817}, {30435, 31450}, {33416, 42963}, {33417, 42962}, {33542, 33586}, {33697, 58216}, {33750, 48662}, {33879, 45958}, {34718, 61288}, {36751, 59655}, {36990, 55667}, {37481, 54047}, {38064, 50970}, {38066, 51082}, {38068, 50797}, {38110, 55616}, {39899, 40107}, {40341, 55685}, {41945, 43794}, {41946, 43793}, {42087, 42951}, {42088, 42950}, {42090, 42692}, {42091, 42693}, {42099, 42597}, {42100, 42596}, {42125, 42434}, {42126, 42489}, {42127, 42488}, {42128, 42433}, {42129, 43194}, {42130, 44016}, {42131, 44015}, {42132, 43193}, {42147, 42818}, {42148, 42817}, {42160, 42501}, {42161, 42500}, {42258, 42567}, {42259, 42566}, {42260, 53520}, {42261, 53517}, {42586, 42909}, {42587, 42908}, {42625, 42936}, {42626, 42937}, {42631, 42979}, {42632, 42978}, {42637, 45384}, {42638, 45385}, {42694, 43241}, {42695, 43240}, {42815, 43004}, {42816, 43005}, {43028, 43632}, {43029, 43633}, {43174, 50805}, {43273, 55675}, {43503, 43785}, {43504, 43786}, {43511, 43797}, {43512, 43798}, {43898, 55674}, {46267, 55611}, {47352, 55637}, {47355, 55657}, {48872, 55661}, {48905, 55666}, {48910, 55660}, {50954, 51135}, {50962, 55701}, {51137, 55631}, {51139, 51173}, {51185, 55588}, {53023, 55659}, {53092, 54169}, {54131, 55647}, {54445, 61278}, {55656, 58445}, {55665, 59411}, {58222, 61251}, {58230, 61286}

X(61799) = pole of line {185, 14093} with respect to the Jerabek hyperbola
X(61799) = pole of line {6, 43644} with respect to the Kiepert hyperbola
X(61799) = intersection, other than A, B, C, of circumconics {{A, B, C, X(547), X(15318)}}, {{A, B, C, X(1105), X(14093)}}, {{A, B, C, X(3628), X(52441)}}, {{A, B, C, X(15688), X(60007)}}
X(61799) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15759, 6958}, {2, 6825, 15716}, {3, 15694, 550}, {3, 15701, 4}, {3, 15707, 140}, {3, 15712, 15700}, {3, 15718, 3523}, {3, 3843, 3528}, {3, 3851, 8703}, {3, 5054, 1657}, {3, 5070, 548}, {3, 5073, 10304}, {3, 549, 1656}, {3, 631, 382}, {4, 6846, 7413}, {5, 14893, 3855}, {5, 16239, 13735}, {5, 20, 3830}, {20, 15688, 15696}, {20, 15717, 10299}, {20, 4193, 5071}, {20, 631, 16239}, {140, 15692, 3}, {140, 3146, 15703}, {140, 3528, 3843}, {140, 3534, 5079}, {140, 3845, 13741}, {140, 3857, 2}, {376, 3523, 12108}, {376, 3525, 3854}, {382, 3861, 5076}, {548, 631, 5070}, {549, 16239, 631}, {549, 17504, 15690}, {550, 15694, 5072}, {631, 3528, 7486}, {631, 3859, 15694}, {632, 10304, 5073}, {1656, 5054, 3525}, {1656, 5072, 10109}, {1657, 3523, 15720}, {1657, 3526, 5}, {2041, 2042, 547}, {3091, 10303, 16858}, {3522, 15719, 14869}, {3523, 12108, 15722}, {3523, 15692, 3146}, {3524, 12100, 15718}, {3524, 15700, 15693}, {3524, 15717, 3530}, {3525, 10299, 15705}, {3528, 3530, 15707}, {3528, 3545, 20}, {3530, 15712, 15717}, {3533, 5071, 6856}, {3830, 15703, 3545}, {3843, 15689, 6971}, {3851, 10303, 15723}, {5054, 15700, 12100}, {5071, 17559, 3628}, {5076, 5079, 3857}, {7390, 15717, 3861}, {8703, 10303, 3851}, {10124, 12100, 17504}, {10124, 15701, 5054}, {11812, 15715, 15689}, {14093, 15690, 15688}, {14869, 14891, 3522}, {14891, 15719, 5055}, {15688, 15693, 549}, {15692, 15707, 3534}, {15693, 15700, 15706}, {15693, 15706, 381}, {15696, 15720, 3526}, {15701, 17504, 14093}, {15708, 15711, 15681}, {15709, 15714, 15685}, {15710, 15713, 15684}, {15721, 15759, 14269}

X(61800) = X(2)X(3)∩X(15)X(42481)

Barycentrics    52*a^4+7*(b^2-c^2)^2-59*a^2*(b^2+c^2) : :
X(61800) = 7*X[2]+15*X[3], 7*X[597]+4*X[55601], -7*X[1353]+40*X[55690], -15*X[1385]+4*X[51095], -12*X[3576]+X[50831], -7*X[3629]+40*X[55696], 15*X[3654]+7*X[51094], -4*X[4677]+15*X[50822], 2*X[4745]+9*X[17502], -12*X[5085]+X[50986], X[5562]+32*X[55320], 28*X[6329]+5*X[55585] and many others

X(61800) lies on circumconic {{A, B, C, X(3845), X(57894)}} and on these lines: {2, 3}, {15, 42481}, {16, 42480}, {524, 55689}, {597, 55601}, {1353, 55690}, {1385, 51095}, {3576, 50831}, {3629, 55696}, {3654, 51094}, {4677, 50822}, {4745, 17502}, {5085, 50986}, {5562, 55320}, {6329, 55585}, {6468, 35256}, {6469, 35255}, {6560, 51850}, {6561, 51849}, {8584, 50987}, {10164, 50823}, {10168, 55625}, {10283, 50833}, {10519, 51183}, {11480, 43110}, {11481, 43111}, {11542, 42508}, {11543, 42509}, {13624, 34641}, {15516, 54169}, {15520, 50983}, {15533, 51184}, {16241, 42922}, {16242, 42923}, {16772, 42797}, {16773, 42798}, {17508, 50980}, {20583, 55710}, {21167, 50978}, {23302, 43033}, {23303, 43032}, {31425, 51097}, {31663, 51109}, {34747, 61524}, {34773, 38098}, {35021, 36521}, {36836, 42419}, {36843, 42420}, {38042, 51088}, {38110, 55615}, {41151, 51524}, {41153, 52987}, {42085, 43872}, {42086, 43871}, {42087, 43247}, {42088, 43246}, {42117, 42503}, {42118, 42502}, {42121, 42507}, {42124, 42506}, {42415, 43639}, {42416, 43640}, {42490, 49811}, {42491, 49810}, {42492, 42941}, {42493, 42940}, {42498, 43366}, {42499, 43367}, {42500, 46334}, {42501, 46335}, {42504, 43228}, {42505, 43229}, {42526, 43256}, {42527, 43257}, {42528, 43248}, {42529, 43249}, {42631, 43106}, {42632, 43105}, {42918, 51915}, {42919, 51916}, {42930, 43235}, {42931, 43234}, {42942, 43011}, {42943, 43010}, {46932, 58220}, {50812, 61269}, {50826, 51705}, {50832, 51071}, {50959, 55660}, {50979, 55693}, {50981, 51737}, {50982, 55685}, {50988, 55596}, {51068, 61245}, {51084, 51108}, {51092, 58230}, {51136, 55680}, {51137, 55630}, {51139, 55649}, {51181, 54173}

X(61800) = midpoint of X(i) and X(j) for these {i,j}: {3, 15721}, {376, 5072}, {15715, 15720}, {15716, 15719}, {15717, 15718}
X(61800) = reflection of X(i) in X(j) for these {i,j}: {15687, 3855}, {15716, 12100}, {5, 15723}
X(61800) = complement of X(61977)
X(61800) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12100, 17504}, {2, 14269, 10109}, {2, 15710, 3534}, {2, 15719, 15720}, {2, 3534, 546}, {2, 550, 3845}, {3, 15709, 15691}, {3, 15720, 3855}, {3, 5054, 15683}, {3, 549, 15699}, {5, 8703, 11001}, {546, 3530, 3523}, {549, 12100, 15711}, {549, 3627, 5054}, {3523, 14891, 11539}, {3524, 15700, 3530}, {3524, 15717, 15718}, {3528, 3627, 550}, {3528, 5054, 11737}, {3530, 10299, 14869}, {5054, 15714, 3627}, {8703, 15713, 5066}, {11001, 15759, 8703}, {11539, 17504, 15710}, {11737, 15683, 15687}, {11812, 12100, 15698}, {12100, 15759, 15692}, {14869, 15707, 549}, {15687, 15713, 2}, {15687, 17504, 3}, {15688, 15720, 15723}, {15691, 15709, 5}, {15692, 15701, 15759}, {15693, 15698, 11812}, {15700, 15707, 10299}, {15700, 15718, 15715}, {15712, 17504, 15700}, {15715, 15720, 30}, {15716, 15717, 12100}, {15716, 15718, 15719}, {15717, 15719, 15716}

X(61801) = X(2)X(3)∩X(17)X(43635)

Barycentrics    22*a^4+3*(b^2-c^2)^2-25*a^2*(b^2+c^2) : :
X(61801) = 9*X[2]+19*X[3], 3*X[141]+11*X[55675], 9*X[597]+5*X[55600], 3*X[3589]+4*X[55647], X[3631]+6*X[55680], -X[4301]+15*X[51084], 3*X[5480]+11*X[55652], 11*X[5690]+3*X[61294], -X[5881]+15*X[50825], -9*X[5892]+2*X[16982], X[7991]+6*X[51700], 9*X[10164]+5*X[31666] and many others

X(61801) lies on these lines: {2, 3}, {17, 43635}, {18, 43634}, {61, 42687}, {62, 42686}, {141, 55675}, {397, 43483}, {398, 43484}, {597, 55600}, {3564, 55681}, {3589, 55647}, {3631, 55680}, {4301, 51084}, {5318, 42592}, {5321, 42593}, {5418, 43338}, {5420, 43339}, {5480, 55652}, {5690, 61294}, {5844, 30389}, {5881, 50825}, {5892, 16982}, {6409, 43431}, {6410, 43430}, {6453, 35256}, {6454, 35255}, {6470, 43315}, {6471, 43314}, {6519, 19116}, {6522, 19117}, {7991, 51700}, {10147, 43526}, {10148, 43525}, {10164, 31666}, {10168, 55623}, {10170, 55286}, {10541, 34380}, {10627, 15012}, {11480, 43198}, {11481, 43197}, {11542, 42685}, {11543, 42684}, {11592, 16836}, {11694, 38632}, {12007, 20190}, {13367, 44756}, {13392, 15054}, {13607, 61524}, {13886, 43382}, {13939, 43383}, {14449, 54044}, {15023, 15061}, {15039, 22250}, {15069, 50980}, {16192, 28216}, {16962, 42793}, {16963, 42794}, {17502, 61510}, {17508, 61545}, {18358, 55670}, {18583, 55631}, {21167, 55687}, {21850, 55641}, {22234, 54169}, {22330, 50983}, {22712, 32523}, {23251, 43558}, {23261, 43559}, {31447, 51087}, {33606, 43100}, {33607, 43107}, {34573, 55666}, {35770, 42643}, {35771, 42644}, {38068, 61255}, {38110, 55614}, {38136, 55656}, {38740, 61600}, {38751, 61599}, {38763, 61605}, {38775, 61604}, {38795, 61598}, {42087, 42904}, {42088, 42905}, {42101, 43638}, {42102, 43643}, {42140, 43644}, {42141, 43649}, {42147, 42795}, {42148, 42796}, {42164, 43102}, {42165, 43103}, {42476, 42889}, {42477, 42888}, {42490, 42496}, {42491, 42497}, {42584, 43467}, {42585, 43468}, {42598, 42955}, {42599, 42954}, {42912, 43018}, {42913, 43019}, {42958, 43229}, {42959, 43228}, {43150, 55677}, {43174, 58232}, {44324, 55320}, {48375, 61548}, {48876, 55684}, {50414, 61540}, {51085, 61286}, {51126, 55660}, {51137, 55628}, {51138, 55698}, {51732, 53097}, {53093, 61624}, {55595, 59399}, {58219, 58441}, {58223, 61249}, {58224, 59388}

X(61801) = midpoint of X(i) and X(j) for these {i,j}: {3, 14869}, {549, 15698}, {550, 3832}, {8703, 15703}
X(61801) = reflection of X(i) in X(j) for these {i,j}: {12100, 15700}, {3523, 3530}, {3857, 3628}, {546, 3090}
X(61801) = complement of X(61976)
X(61801) = pole of line {185, 62079} with respect to the Jerabek hyperbola
X(61801) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(15319), X(41990)}}, {{A, B, C, X(15687), X(43970)}}
X(61801) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 10303, 15704}, {3, 12108, 546}, {3, 140, 12103}, {3, 14869, 30}, {3, 15720, 3091}, {3, 3091, 8703}, {3, 3523, 14869}, {3, 3525, 550}, {3, 3628, 548}, {3, 5054, 3529}, {3, 5079, 3522}, {3, 631, 3627}, {4, 15717, 15706}, {5, 10299, 14891}, {30, 15700, 12100}, {30, 3530, 3523}, {30, 3628, 3857}, {140, 12103, 12812}, {140, 3859, 2}, {546, 5076, 14893}, {547, 12100, 17504}, {549, 10303, 12108}, {549, 10304, 11540}, {549, 15706, 15759}, {549, 15712, 15717}, {549, 17504, 3534}, {549, 3534, 14890}, {549, 5055, 11812}, {550, 3525, 12811}, {632, 15704, 5072}, {3090, 10303, 3526}, {3522, 11539, 3861}, {3523, 15692, 3832}, {3523, 15717, 15698}, {3523, 3528, 15701}, {3524, 15712, 3530}, {3525, 15692, 3}, {3526, 3534, 3851}, {3530, 12100, 140}, {3534, 14890, 547}, {3627, 15022, 3856}, {3628, 12108, 10303}, {3628, 3856, 15022}, {5072, 10303, 632}, {8703, 15720, 16239}, {10299, 15693, 5}, {10303, 15704, 3628}, {10304, 15693, 549}, {10304, 15717, 10299}, {10304, 17678, 15682}, {11540, 14891, 10304}, {11540, 15690, 5066}, {11812, 12811, 3525}, {12100, 15693, 15690}, {12103, 12812, 3853}, {12108, 14891, 17538}, {15682, 17678, 5055}, {15702, 17538, 3090}, {15707, 15711, 10124}, {15708, 15714, 10109}, {15715, 15722, 15699}, {15720, 17800, 15709}, {42954, 42964, 42599}, {42955, 42965, 42598}

X(61802) = X(2)X(3)∩X(141)X(55677)

Barycentrics    20*a^4+3*(b^2-c^2)^2-23*a^2*(b^2+c^2) : :
X(61802) = 9*X[2]+17*X[3], 3*X[141]+10*X[55677], 9*X[597]+4*X[55597], -3*X[1353]+16*X[20190], X[1483]+12*X[10164], -15*X[3576]+2*X[61292], 6*X[3589]+7*X[55644], 15*X[3618]+11*X[55620], X[3630]+12*X[55686], 2*X[3631]+11*X[55683], -27*X[3653]+X[58245], 12*X[3819]+X[45957] and many others

X(61802) lies on these lines: {2, 3}, {141, 55677}, {397, 41972}, {398, 41971}, {597, 55597}, {1353, 20190}, {1483, 10164}, {3411, 42794}, {3412, 42793}, {3576, 61292}, {3589, 55644}, {3592, 42569}, {3594, 42568}, {3618, 55620}, {3630, 55686}, {3631, 55683}, {3653, 58245}, {3819, 45957}, {5351, 42124}, {5352, 42121}, {5480, 55650}, {5690, 31666}, {5881, 58225}, {5894, 46265}, {6199, 43884}, {6395, 43883}, {6425, 35256}, {6426, 35255}, {6451, 13993}, {6452, 13925}, {6453, 19116}, {6454, 19117}, {6488, 52047}, {6489, 52048}, {6519, 13935}, {6522, 9540}, {6684, 59400}, {7982, 61280}, {7987, 38112}, {7991, 61277}, {8981, 41965}, {9588, 50822}, {9681, 43212}, {10168, 55617}, {10264, 48375}, {10645, 42923}, {10646, 42922}, {11480, 42917}, {11481, 42916}, {13348, 40284}, {13464, 51084}, {13624, 38127}, {13966, 41966}, {14094, 22251}, {14677, 38795}, {14929, 43459}, {15020, 61548}, {15027, 15036}, {16625, 54042}, {16881, 54041}, {17502, 37705}, {17704, 45956}, {18358, 55671}, {18583, 55626}, {21163, 32523}, {21850, 55637}, {22234, 50983}, {22330, 54169}, {23328, 50414}, {24475, 33575}, {26446, 61246}, {28182, 34595}, {30389, 61287}, {31423, 61257}, {31447, 50824}, {31730, 61270}, {33416, 42692}, {33417, 42693}, {34153, 38729}, {34507, 50980}, {34573, 55667}, {37495, 46865}, {38022, 51086}, {38079, 51139}, {38081, 50829}, {38110, 55606}, {38136, 55655}, {39884, 55670}, {40107, 50981}, {41973, 43100}, {41974, 43107}, {42085, 42591}, {42086, 42590}, {42107, 43636}, {42110, 43637}, {42144, 42493}, {42145, 42492}, {42160, 43102}, {42161, 43103}, {42163, 43630}, {42166, 43631}, {42258, 42557}, {42259, 42558}, {42433, 42500}, {42434, 42501}, {42528, 42949}, {42529, 42948}, {42791, 43237}, {42792, 43236}, {43324, 43643}, {43325, 43638}, {48378, 51522}, {48874, 55647}, {48876, 55687}, {48906, 55679}, {50814, 50833}, {50821, 61297}, {50826, 51082}, {50831, 58229}, {50832, 58232}, {50970, 50988}, {50973, 51181}, {50979, 55694}, {50987, 55704}, {51080, 51088}, {51126, 55659}, {51135, 51141}, {51137, 55611}, {51163, 55663}, {51732, 55580}, {52987, 59399}, {55678, 61545}, {58221, 61256}, {61253, 61614}

X(61802) = midpoint of X(i) and X(j) for these {i,j}: {3, 10303}
X(61802) = reflection of X(i) in X(j) for these {i,j}: {5067, 140}
X(61802) = complement of X(61975)
X(61802) = pole of line {6, 43012} with respect to the Kiepert hyperbola
X(61802) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(44245)}}, {{A, B, C, X(5070), X(52441)}}, {{A, B, C, X(12101), X(43970)}}
X(61802) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 10303, 30}, {3, 140, 15704}, {3, 14869, 3627}, {3, 15701, 5072}, {3, 15720, 3090}, {3, 3523, 12108}, {3, 3525, 12103}, {3, 3526, 17538}, {3, 5054, 3146}, {3, 5072, 3522}, {3, 5076, 3528}, {3, 549, 632}, {3, 631, 546}, {3, 632, 550}, {5, 15704, 12102}, {5, 3830, 3858}, {5, 8703, 1657}, {30, 140, 5067}, {140, 15717, 17504}, {140, 15759, 382}, {140, 3530, 15693}, {140, 376, 5}, {140, 3856, 2}, {140, 548, 11737}, {376, 3525, 3091}, {376, 3839, 15685}, {548, 11737, 5059}, {548, 15720, 11539}, {549, 15711, 15699}, {550, 632, 3857}, {631, 3523, 15722}, {1657, 15722, 631}, {3090, 15701, 6883}, {3090, 16417, 1656}, {3091, 3627, 3845}, {3091, 5067, 5079}, {3522, 15701, 16239}, {3522, 16239, 15687}, {3523, 15717, 376}, {3523, 15718, 3530}, {3524, 3530, 15712}, {3525, 12108, 14869}, {3526, 17538, 12811}, {3530, 12100, 3523}, {3533, 15688, 3861}, {3860, 12100, 15698}, {5059, 15717, 15692}, {10124, 12100, 15705}, {10124, 15705, 8703}, {10299, 10303, 3}, {11812, 15706, 15714}, {12102, 12108, 140}, {12103, 12108, 3525}, {14891, 15707, 15713}, {15685, 15693, 15719}, {15692, 15720, 548}, {15693, 15700, 5055}, {15693, 15723, 15707}, {15693, 17504, 549}, {15700, 15705, 12100}, {15705, 15722, 10124}, {15712, 17504, 15717}

X(61803) = X(2)X(3)∩X(15)X(42774)

Barycentrics    13*a^4+2*(b^2-c^2)^2-15*a^2*(b^2+c^2) : :
X(61803) = 6*X[2]+11*X[3], 4*X[125]+13*X[15042], 8*X[389]+9*X[54047], 12*X[597]+5*X[55595], 3*X[599]+14*X[55681], -26*X[1385]+9*X[61285], 5*X[3567]+12*X[54044], -21*X[3576]+4*X[32900], 8*X[3589]+9*X[55643], 10*X[3618]+7*X[55616], 2*X[3621]+49*X[58228], 5*X[3763]+12*X[55670] and many others

X(61803) lies on these lines: {2, 3}, {15, 42774}, {16, 42773}, {61, 42958}, {62, 42959}, {125, 15042}, {389, 54047}, {590, 6497}, {597, 55595}, {599, 55681}, {615, 6496}, {1151, 35814}, {1152, 35815}, {1192, 12242}, {1385, 61285}, {1506, 5585}, {1587, 42574}, {1588, 42575}, {3311, 41964}, {3312, 41963}, {3532, 13623}, {3567, 54044}, {3576, 32900}, {3589, 55643}, {3618, 55616}, {3621, 58228}, {3763, 55670}, {4701, 5882}, {5092, 11898}, {5206, 31467}, {5339, 42978}, {5340, 42979}, {5351, 42490}, {5352, 42491}, {5418, 6452}, {5420, 6451}, {5447, 40280}, {5476, 55641}, {5650, 18439}, {5691, 58219}, {5889, 11592}, {6144, 55693}, {6407, 13935}, {6408, 9540}, {6409, 58866}, {6410, 8960}, {6411, 13951}, {6412, 8976}, {6427, 52045}, {6428, 9680}, {6445, 13966}, {6446, 8981}, {6448, 31454}, {6449, 13961}, {6450, 13903}, {6454, 31487}, {6455, 18510}, {6456, 18512}, {6500, 43509}, {6501, 43510}, {6519, 32788}, {6522, 32787}, {6684, 18526}, {7581, 43415}, {7582, 9690}, {7666, 19357}, {7755, 15815}, {7767, 32891}, {7771, 32821}, {7780, 11165}, {7850, 43459}, {8567, 10182}, {8589, 44535}, {9588, 31666}, {9691, 19116}, {10164, 13607}, {10168, 55614}, {10187, 42529}, {10188, 42528}, {10193, 17821}, {10194, 42258}, {10195, 42259}, {10246, 43174}, {10272, 38633}, {10516, 55669}, {10519, 55692}, {10575, 55166}, {10606, 14862}, {10619, 26944}, {10620, 48378}, {10645, 42818}, {10646, 42817}, {10990, 38794}, {10991, 38750}, {10992, 38739}, {11149, 55734}, {11362, 51085}, {11480, 42980}, {11481, 42981}, {11482, 54169}, {11485, 42687}, {11486, 42686}, {11488, 56617}, {11489, 56616}, {11522, 31663}, {11591, 55320}, {11850, 11935}, {12002, 36987}, {12006, 54041}, {12007, 12017}, {12026, 38640}, {12290, 55286}, {12307, 61659}, {12355, 38740}, {12645, 13624}, {13321, 15644}, {13339, 43652}, {13347, 22115}, {13382, 23039}, {13421, 15043}, {13665, 43438}, {13785, 43439}, {14528, 34483}, {14530, 23328}, {14561, 55648}, {14848, 51137}, {14853, 55632}, {14861, 43713}, {15036, 38724}, {15040, 38727}, {15041, 16534}, {15046, 37853}, {15069, 55679}, {15178, 31425}, {15484, 15513}, {15534, 55698}, {15655, 31401}, {16644, 41974}, {16645, 41973}, {16772, 42793}, {16773, 42794}, {16808, 43443}, {16809, 43442}, {16962, 42480}, {16963, 42481}, {16964, 43545}, {16965, 43544}, {17508, 43150}, {17704, 18436}, {18440, 55674}, {18553, 55672}, {18581, 42688}, {18582, 42689}, {18583, 55624}, {19872, 28168}, {20190, 51140}, {20417, 32609}, {20423, 55620}, {20791, 32142}, {22235, 52080}, {22237, 52079}, {22331, 31457}, {22712, 55822}, {23302, 42691}, {23303, 42690}, {25555, 31884}, {28160, 30315}, {30389, 31447}, {30714, 38728}, {31479, 59319}, {32789, 43336}, {32790, 43337}, {33521, 38774}, {34507, 53094}, {36990, 55668}, {37727, 50827}, {38064, 55724}, {38110, 55604}, {38317, 55656}, {38634, 61561}, {38635, 61560}, {38636, 61566}, {38637, 61562}, {38638, 61548}, {38748, 52090}, {39899, 55682}, {40341, 55688}, {40912, 44109}, {41100, 43426}, {41101, 43427}, {41121, 43422}, {41122, 43423}, {42085, 42948}, {42086, 42949}, {42090, 42963}, {42091, 42962}, {42095, 43468}, {42098, 43467}, {42115, 42152}, {42116, 42149}, {42125, 42937}, {42128, 42936}, {42129, 42157}, {42130, 42951}, {42131, 42950}, {42132, 42158}, {42144, 42776}, {42145, 42775}, {42150, 42684}, {42151, 42685}, {42159, 42501}, {42162, 42500}, {42260, 43433}, {42261, 43432}, {42431, 43029}, {42432, 43028}, {42488, 42625}, {42489, 42626}, {42494, 43103}, {42495, 43102}, {42631, 43424}, {42632, 43425}, {42795, 42969}, {42796, 42968}, {42797, 43302}, {42798, 43303}, {42922, 43495}, {42923, 43496}, {42964, 43194}, {42965, 43193}, {43014, 43294}, {43015, 43295}, {43273, 55677}, {43342, 43879}, {43343, 43880}, {43446, 43466}, {43447, 43465}, {43568, 53513}, {43569, 53516}, {44299, 45959}, {45184, 47391}, {46267, 55600}, {47352, 55631}, {47355, 55655}, {48672, 61680}, {48872, 55660}, {48905, 55667}, {48910, 55659}, {50797, 51088}, {50833, 61278}, {50954, 51141}, {50962, 53093}, {50977, 55684}, {50983, 53092}, {50988, 51172}, {51173, 55647}, {51185, 55583}, {53023, 55658}, {54131, 55644}, {54173, 55701}, {54447, 58217}, {55654, 58445}, {55666, 59411}, {58226, 61245}, {58230, 61524}, {58233, 61597}

X(61803) = inverse of X(44904) in orthocentroidal circle
X(61803) = inverse of X(44904) in Yff hyperbola
X(61803) = pole of line {523, 44904} with respect to the orthocentroidal circle
X(61803) = pole of line {185, 54047} with respect to the Jerabek hyperbola
X(61803) = pole of line {6, 44904} with respect to the Kiepert hyperbola
X(61803) = pole of line {523, 44904} with respect to the Yff hyperbola
X(61803) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(15696)}}, {{A, B, C, X(264), X(44904)}}, {{A, B, C, X(3091), X(34483)}}, {{A, B, C, X(3146), X(13623)}}, {{A, B, C, X(3519), X(3832)}}, {{A, B, C, X(3532), X(13596)}}, {{A, B, C, X(3543), X(14861)}}, {{A, B, C, X(3545), X(42021)}}, {{A, B, C, X(5056), X(26861)}}, {{A, B, C, X(11737), X(13599)}}, {{A, B, C, X(14528), X(34484)}}, {{A, B, C, X(14865), X(43713)}}, {{A, B, C, X(15688), X(40448)}}, {{A, B, C, X(22270), X(46935)}}, {{A, B, C, X(35502), X(44763)}}, {{A, B, C, X(47485), X(57713)}}, {{A, B, C, X(47599), X(52441)}}
X(61803) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3, 15696}, {3, 140, 1657}, {3, 14869, 5076}, {3, 15701, 5}, {3, 15707, 631}, {3, 15717, 15706}, {3, 15718, 3530}, {3, 17800, 10304}, {3, 3523, 15720}, {3, 3530, 15693}, {3, 382, 14093}, {3, 3830, 3528}, {3, 3843, 8703}, {3, 3851, 3522}, {3, 5054, 382}, {3, 5070, 376}, {3, 549, 3526}, {3, 7393, 18859}, {3, 7484, 14130}, {4, 15022, 3850}, {4, 15704, 5073}, {4, 3533, 7486}, {4, 5068, 3856}, {20, 15694, 5079}, {20, 15719, 12108}, {140, 10299, 3}, {140, 15712, 10299}, {140, 1657, 1656}, {140, 3522, 3851}, {140, 3858, 2}, {140, 550, 5056}, {376, 14869, 5070}, {381, 15688, 11001}, {381, 15693, 15707}, {381, 3526, 3628}, {548, 11540, 3857}, {548, 3857, 15683}, {548, 549, 10303}, {549, 17504, 5066}, {549, 8703, 14890}, {550, 15712, 12100}, {631, 15715, 3146}, {631, 3146, 11539}, {1656, 3534, 4}, {1657, 15720, 140}, {2045, 2046, 14869}, {3523, 3524, 15712}, {3524, 15693, 15700}, {3525, 8703, 3843}, {3526, 3534, 5072}, {3528, 15708, 632}, {3529, 15721, 16239}, {3628, 10304, 17800}, {3830, 6827, 550}, {3854, 5056, 3544}, {5054, 15700, 15716}, {5067, 12103, 14269}, {5351, 42490, 42974}, {5351, 43483, 42935}, {5352, 42491, 42975}, {5352, 43484, 42934}, {9680, 52046, 6428}, {10124, 15710, 15685}, {10303, 15698, 548}, {10303, 15717, 15698}, {11539, 12100, 15715}, {11539, 15695, 381}, {11539, 15715, 15695}, {11540, 15683, 5055}, {11812, 15705, 15681}, {12103, 15713, 5067}, {12108, 17504, 20}, {12108, 17533, 15701}, {14813, 14814, 3832}, {14891, 15708, 3830}, {15684, 15688, 3534}, {15684, 15701, 15709}, {15684, 15759, 15688}, {15688, 15701, 15723}, {15692, 15709, 15759}, {15693, 15700, 5054}, {15693, 15706, 549}, {15693, 15720, 3523}, {15700, 15723, 15692}, {15702, 15711, 15689}, {15709, 15759, 15684}, {15719, 17504, 15694}, {30389, 31447, 34718}

X(61804) = X(2)X(3)∩X(15)X(43295)

Barycentrics    19*a^4+3*(b^2-c^2)^2-22*a^2*(b^2+c^2) : :
X(61804) = 9*X[2]+16*X[3], 3*X[69]+22*X[55684], 6*X[125]+19*X[15023], X[145]+24*X[10164], 12*X[165]+13*X[46934], -3*X[193]+28*X[10541], 3*X[1352]+22*X[55675], 9*X[2979]+16*X[15012], X[3448]+24*X[48375], 24*X[3576]+X[3621], X[3617]+4*X[7987], 3*X[3618]+2*X[55614] and many others

X(61804) lies on these lines: {2, 3}, {15, 43295}, {16, 43294}, {69, 55684}, {99, 32872}, {125, 15023}, {145, 10164}, {165, 46934}, {183, 32880}, {193, 10541}, {315, 32873}, {316, 32898}, {519, 58229}, {1078, 32840}, {1352, 55675}, {1621, 44846}, {2979, 15012}, {3069, 9543}, {3303, 5265}, {3304, 5281}, {3448, 48375}, {3576, 3621}, {3592, 43884}, {3593, 51952}, {3594, 43883}, {3595, 51953}, {3600, 52793}, {3616, 28228}, {3617, 7987}, {3618, 55614}, {3619, 55673}, {3620, 53094}, {3622, 7991}, {3623, 28234}, {3654, 58232}, {3868, 33575}, {4297, 46932}, {4678, 6684}, {5085, 20080}, {5304, 22332}, {5346, 21843}, {5351, 16960}, {5352, 16961}, {5365, 42529}, {5366, 42528}, {5368, 53096}, {5493, 51086}, {5550, 16192}, {5657, 20014}, {5691, 46930}, {5921, 17508}, {5965, 55687}, {5984, 38748}, {6409, 13941}, {6410, 8972}, {6411, 43880}, {6412, 43879}, {6425, 7586}, {6426, 7585}, {6427, 42523}, {6428, 42522}, {6447, 35256}, {6448, 35255}, {6449, 43321}, {6450, 43320}, {6451, 13939}, {6452, 13886}, {6453, 13935}, {6454, 9540}, {6482, 35814}, {6483, 35815}, {6496, 23273}, {6497, 23267}, {6519, 7582}, {6522, 7581}, {6527, 52712}, {6776, 55681}, {7583, 43797}, {7584, 43798}, {7771, 32831}, {7783, 55819}, {7982, 54445}, {7998, 17704}, {8588, 31404}, {8960, 43793}, {9588, 31145}, {9729, 33884}, {9740, 59546}, {9780, 58221}, {9841, 35595}, {10165, 20070}, {10168, 55611}, {10182, 12250}, {10193, 34781}, {10248, 19878}, {10513, 32881}, {10519, 20190}, {10653, 43372}, {10654, 43373}, {11002, 13348}, {11003, 13347}, {11004, 37514}, {11204, 54211}, {11381, 33879}, {11454, 32605}, {11592, 40280}, {14561, 55647}, {14683, 15020}, {14853, 55631}, {14997, 37501}, {15029, 37853}, {15036, 36253}, {15051, 38729}, {15054, 48378}, {15072, 40247}, {15178, 59417}, {15448, 22334}, {15589, 32879}, {15644, 16981}, {15815, 37689}, {17852, 32787}, {20052, 31666}, {20059, 21153}, {20081, 21163}, {20094, 38737}, {20095, 21154}, {20105, 22712}, {20214, 21164}, {20423, 55617}, {20427, 46265}, {21166, 35369}, {22235, 42943}, {22236, 43869}, {22237, 42942}, {22238, 43870}, {22330, 50967}, {22331, 37665}, {25565, 51213}, {28164, 58217}, {28224, 58224}, {28232, 35242}, {31400, 35007}, {31425, 50828}, {31670, 55652}, {32142, 61136}, {35260, 58795}, {36413, 52703}, {37640, 42773}, {37641, 42774}, {38064, 55721}, {38074, 51088}, {38110, 55602}, {38314, 58245}, {40138, 61312}, {40330, 55672}, {41121, 43310}, {41122, 43311}, {42154, 43557}, {42155, 43556}, {42159, 42593}, {42162, 42592}, {42262, 43520}, {42265, 43519}, {42417, 43412}, {42418, 43411}, {42474, 51916}, {42475, 51915}, {42494, 42625}, {42495, 42626}, {42518, 43107}, {42519, 43100}, {42598, 43465}, {42599, 43466}, {42610, 43552}, {42611, 43553}, {42637, 53513}, {42638, 53516}, {42682, 43028}, {42683, 43029}, {42777, 43238}, {42778, 43239}, {42793, 49947}, {42794, 49948}, {42912, 42933}, {42913, 42932}, {42978, 49873}, {42979, 49874}, {42986, 43306}, {42987, 43307}, {42996, 42998}, {42997, 42999}, {43242, 43463}, {43243, 43464}, {43416, 43447}, {43417, 43446}, {43621, 55663}, {43794, 58866}, {44299, 46850}, {44434, 61132}, {46931, 58441}, {51028, 55588}, {51084, 61276}, {51137, 55600}, {51170, 53093}, {51171, 53097}, {51212, 55641}, {51538, 55656}, {53620, 58225}, {53858, 54169}, {54132, 55597}, {54173, 55704}, {54174, 55718}, {55626, 61044}, {60131, 60324}, {60328, 60645}

X(61804) = anticomplement of X(61914)
X(61804) = pole of line {185, 62083} with respect to the Jerabek hyperbola
X(61804) = pole of line {69, 3854} with respect to the Wallace hyperbola
X(61804) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(3854)}}, {{A, B, C, X(95), X(50693)}}, {{A, B, C, X(1217), X(15694)}}, {{A, B, C, X(3346), X(5054)}}, {{A, B, C, X(5068), X(52443)}}, {{A, B, C, X(14893), X(32533)}}, {{A, B, C, X(15703), X(22270)}}, {{A, B, C, X(15740), X(50691)}}, {{A, B, C, X(19709), X(46412)}}, {{A, B, C, X(31371), X(50687)}}, {{A, B, C, X(49138), X(60618)}}
X(61804) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20, 3854}, {2, 3522, 17578}, {3, 12108, 3090}, {3, 13154, 7464}, {3, 140, 3529}, {3, 15701, 5079}, {3, 15720, 3628}, {3, 3525, 20}, {3, 3526, 12103}, {3, 3627, 3528}, {3, 3628, 376}, {3, 5054, 3627}, {3, 5079, 548}, {3, 549, 3525}, {3, 631, 3091}, {3, 632, 17538}, {20, 10299, 15705}, {20, 3523, 549}, {20, 546, 3146}, {140, 10304, 3832}, {140, 15696, 5071}, {140, 15711, 15696}, {140, 3832, 2}, {140, 3854, 17590}, {546, 632, 1656}, {548, 15701, 3533}, {548, 5079, 11541}, {549, 12100, 15688}, {549, 15690, 5054}, {549, 15716, 3545}, {549, 17504, 10109}, {631, 3524, 15712}, {631, 5071, 140}, {1656, 15694, 16239}, {1656, 15696, 3830}, {1656, 3091, 15022}, {3090, 12108, 10303}, {3090, 17538, 5076}, {3091, 10303, 632}, {3146, 15022, 546}, {3522, 15717, 15692}, {3524, 15719, 15700}, {3524, 3530, 3523}, {3525, 5068, 17535}, {3526, 12103, 3544}, {3526, 15695, 3858}, {3528, 5054, 5056}, {3528, 5056, 15683}, {3530, 15712, 15693}, {3544, 12103, 3543}, {3830, 15688, 15686}, {3843, 15720, 15713}, {3854, 11111, 13742}, {3854, 13745, 6921}, {5067, 11106, 13745}, {6175, 11111, 17677}, {10303, 10304, 5072}, {10304, 15692, 15711}, {10304, 15696, 3522}, {12100, 14869, 3}, {12100, 15685, 15698}, {12812, 14869, 15694}, {13168, 14869, 7486}, {14093, 15693, 15707}, {14891, 15722, 15709}, {15686, 15719, 15708}, {15688, 16239, 4}, {15692, 15708, 15697}, {15692, 15712, 15717}, {15692, 15721, 14093}, {15693, 15711, 15719}, {15693, 15712, 631}, {15698, 15707, 15721}, {15700, 15719, 10304}, {15701, 15715, 3839}, {15705, 15717, 10299}

X(61805) = X(2)X(3)∩X(165)X(51086)

Barycentrics    43*a^4+7*(b^2-c^2)^2-50*a^2*(b^2+c^2) : :
X(61805) = 7*X[2]+12*X[3], 3*X[165]+16*X[51086], -7*X[193]+64*X[55696], -24*X[1385]+5*X[51092], 15*X[3576]+4*X[50827], 4*X[4745]+15*X[7987], -21*X[5032]+40*X[55710], 15*X[5085]+4*X[50982], 7*X[5476]+12*X[55638], 15*X[5657]+4*X[51087], 3*X[5731]+16*X[50829], -24*X[6684]+5*X[51072] and many others

X(61805) lies on these lines: {2, 3}, {165, 51086}, {193, 55696}, {1078, 32896}, {1385, 51092}, {3576, 50827}, {4745, 7987}, {5032, 55710}, {5085, 50982}, {5281, 37602}, {5334, 33606}, {5335, 33607}, {5418, 42524}, {5420, 42525}, {5476, 55638}, {5657, 51087}, {5731, 50829}, {6468, 32788}, {6469, 32787}, {6684, 51072}, {7967, 50830}, {7991, 41150}, {8252, 43381}, {8253, 43380}, {8596, 38739}, {9542, 19053}, {9779, 50812}, {10164, 51085}, {10168, 55608}, {10171, 50873}, {10172, 50820}, {10175, 50863}, {10302, 54866}, {10519, 51140}, {10645, 49827}, {10646, 49826}, {11148, 13468}, {11160, 55689}, {11224, 51103}, {11230, 50813}, {11480, 49861}, {11481, 49862}, {11488, 42792}, {11489, 42791}, {14561, 51211}, {14711, 32522}, {14853, 55630}, {14912, 50985}, {15520, 50967}, {15534, 21167}, {16241, 41972}, {16242, 41971}, {16644, 42685}, {16645, 42684}, {16981, 54044}, {20423, 55615}, {21153, 60971}, {21156, 35750}, {21157, 36331}, {23235, 41151}, {23249, 43513}, {23259, 43514}, {25406, 50984}, {30389, 51096}, {30392, 51095}, {31884, 51139}, {32785, 41954}, {32786, 41953}, {34632, 51108}, {36324, 49829}, {36326, 49828}, {38064, 55720}, {38317, 50969}, {41100, 43483}, {41101, 43484}, {41107, 42796}, {41108, 42795}, {41119, 43544}, {41120, 43545}, {41121, 42955}, {41122, 42954}, {41153, 53097}, {42089, 49824}, {42092, 49825}, {42115, 42804}, {42116, 42803}, {42130, 43247}, {42131, 43246}, {42417, 43339}, {42418, 43338}, {42506, 42935}, {42507, 42934}, {42514, 51916}, {42515, 51915}, {42631, 43403}, {42632, 43404}, {42686, 43228}, {42687, 43229}, {42928, 43489}, {42929, 43490}, {42932, 42977}, {42933, 42976}, {43108, 43543}, {43109, 43542}, {43382, 53131}, {43383, 53130}, {43430, 43511}, {43431, 43512}, {43479, 61719}, {43540, 46334}, {43541, 46335}, {43568, 60299}, {43569, 60300}, {44299, 55166}, {46941, 60175}, {50819, 54448}, {50828, 59417}, {50864, 58221}, {50961, 55685}, {50975, 55670}, {50977, 55686}, {50980, 55682}, {50989, 55684}, {50991, 53094}, {50994, 51737}, {51023, 55673}, {51123, 55823}, {51137, 54132}, {51171, 55585}, {51179, 55697}, {53104, 60632}, {54173, 55706}, {54521, 60239}, {54639, 60192}, {55625, 61044}, {60102, 60228}, {60282, 60333}, {60293, 60313}, {60294, 60314}, {60336, 60637}

X(61805) = anticomplement of X(61913)
X(61805) = pole of line {69, 61958} with respect to the Wallace hyperbola
X(61805) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(15697)}}, {{A, B, C, X(5072), X(46412)}}, {{A, B, C, X(10301), X(54866)}}, {{A, B, C, X(18850), X(58202)}}, {{A, B, C, X(35408), X(46168)}}, {{A, B, C, X(49139), X(60618)}}
X(61805) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10304, 15640}, {2, 11001, 3091}, {2, 15683, 5066}, {2, 15693, 3523}, {2, 3, 15697}, {2, 3522, 3830}, {3, 15709, 15683}, {3, 15713, 15682}, {3, 5054, 15687}, {3, 549, 15709}, {3, 631, 5068}, {4, 15698, 15759}, {376, 15699, 17578}, {376, 3524, 15712}, {376, 5054, 13735}, {546, 10124, 15699}, {549, 11540, 15701}, {549, 12100, 3534}, {549, 15683, 15721}, {549, 15706, 4}, {549, 15715, 17678}, {549, 17504, 3628}, {549, 3524, 15717}, {549, 5055, 631}, {631, 15700, 15705}, {631, 3524, 15700}, {3091, 13735, 5056}, {3523, 10304, 549}, {3523, 15692, 15708}, {3524, 15719, 12100}, {3528, 14869, 17563}, {3530, 15718, 3524}, {3534, 15701, 11540}, {3543, 15721, 10124}, {5054, 15711, 11001}, {5056, 10303, 3526}, {5073, 15712, 10299}, {6987, 15720, 632}, {10109, 12100, 15711}, {10303, 15640, 2}, {10303, 15692, 10304}, {10304, 15709, 3839}, {10304, 15717, 15692}, {10304, 15721, 7486}, {11812, 15711, 5073}, {11812, 15712, 15716}, {11812, 15716, 376}, {12100, 15693, 15719}, {12100, 15713, 3}, {13634, 15715, 5054}, {14891, 15720, 3545}, {15688, 17697, 3543}, {15692, 15708, 20}, {15693, 15700, 15722}, {15693, 15716, 15707}, {15694, 15710, 3146}, {15700, 15707, 546}, {15700, 15722, 8703}, {15702, 17504, 3522}, {15706, 15759, 15698}, {15707, 15716, 11812}, {15709, 15721, 10303}

X(61806) = X(2)X(3)∩X(99)X(32893)

Barycentrics    29*a^4+5*(b^2-c^2)^2-34*a^2*(b^2+c^2) : :
X(61806) = 5*X[2]+8*X[3], -5*X[193]+44*X[55699], -X[355]+14*X[51088], 10*X[597]+3*X[55591], -X[1351]+14*X[50988], -X[1352]+14*X[51141], -X[1482]+14*X[50833], X[1992]+12*X[21167], X[3241]+12*X[10164], -10*X[3244]+49*X[58231], 12*X[3576]+X[31145], 5*X[3617]+8*X[51705] and many others

X(61806) lies on these lines: {2, 3}, {99, 32893}, {193, 55699}, {355, 51088}, {590, 43889}, {597, 55591}, {615, 43890}, {1351, 50988}, {1352, 51141}, {1482, 50833}, {1992, 21167}, {3068, 6434}, {3069, 6433}, {3241, 10164}, {3244, 58231}, {3576, 31145}, {3617, 51705}, {3618, 55607}, {3620, 51737}, {3621, 32900}, {3623, 3654}, {3636, 58248}, {3653, 11278}, {3828, 58221}, {4678, 13624}, {5008, 14930}, {5032, 50983}, {5085, 11160}, {5097, 50967}, {5102, 54169}, {5309, 15602}, {5343, 42890}, {5344, 42891}, {5351, 43252}, {5352, 43253}, {5476, 55636}, {5657, 20049}, {5892, 16981}, {5901, 50809}, {5984, 41134}, {6429, 32788}, {6430, 32787}, {6431, 43888}, {6432, 43887}, {6437, 7586}, {6438, 7585}, {6455, 43212}, {6456, 43211}, {6486, 9543}, {6776, 55683}, {7767, 32881}, {7771, 10513}, {7782, 32885}, {7987, 50829}, {8591, 38737}, {8596, 21166}, {8972, 41946}, {9140, 48375}, {9143, 38727}, {9542, 35256}, {9779, 34638}, {9956, 50819}, {10072, 51817}, {10165, 34632}, {10168, 55603}, {10519, 55695}, {10645, 43200}, {10646, 43199}, {11177, 38748}, {11178, 33750}, {11179, 55685}, {11180, 17508}, {11362, 51092}, {11485, 42932}, {11486, 42933}, {11531, 38314}, {11898, 50981}, {12645, 50826}, {13172, 26614}, {13846, 43511}, {13847, 43512}, {13941, 41945}, {14561, 55645}, {14831, 33884}, {14853, 55627}, {14927, 51025}, {15305, 55166}, {16192, 19883}, {16200, 54445}, {16964, 42953}, {16965, 42952}, {17502, 34627}, {17851, 42542}, {18583, 50966}, {20070, 25055}, {20080, 55691}, {20423, 55612}, {20582, 55673}, {21153, 60984}, {21356, 50984}, {22165, 55684}, {24206, 50975}, {24473, 33575}, {25565, 55660}, {28194, 46934}, {31423, 50864}, {32785, 41952}, {32786, 41951}, {32835, 43459}, {33179, 50810}, {33751, 50956}, {34628, 54448}, {34641, 58227}, {35369, 38739}, {36836, 43480}, {36843, 43479}, {37517, 38064}, {37640, 43870}, {37641, 43869}, {37749, 38804}, {38068, 46933}, {38079, 55639}, {41947, 42638}, {41948, 42637}, {42089, 42531}, {42092, 42530}, {42490, 49862}, {42491, 49861}, {42532, 42959}, {42533, 42958}, {42588, 42598}, {42589, 42599}, {42602, 42604}, {42603, 42605}, {42625, 43540}, {42626, 43541}, {42631, 43556}, {42632, 43557}, {42773, 43228}, {42774, 43229}, {42791, 43239}, {42792, 43238}, {42892, 43294}, {42893, 43295}, {43242, 43542}, {43243, 43543}, {43254, 43256}, {43255, 43257}, {44434, 44562}, {46267, 54132}, {47352, 51139}, {47354, 55671}, {48310, 55651}, {48872, 51165}, {48874, 51211}, {48898, 51216}, {50664, 51170}, {50872, 51084}, {50969, 55655}, {50971, 51537}, {50977, 55688}, {50978, 55692}, {50980, 51215}, {51028, 51137}, {51073, 58217}, {51171, 55582}, {51176, 61545}, {54170, 55618}, {55722, 59373}

X(61806) = reflection of X(i) in X(j) for these {i,j}: {2, 10303}, {5068, 2}
X(61806) = complement of X(61972)
X(61806) = anticomplement of X(61912)
X(61806) = pole of line {69, 50959} with respect to the Wallace hyperbola
X(61806) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1494), X(5068)}}, {{A, B, C, X(3346), X(14869)}}, {{A, B, C, X(3545), X(35510)}}, {{A, B, C, X(3851), X(46412)}}, {{A, B, C, X(5066), X(46455)}}, {{A, B, C, X(18850), X(44903)}}
X(61806) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10304, 3146}, {2, 15705, 3522}, {2, 15717, 15705}, {2, 30, 5068}, {2, 3524, 15717}, {2, 5055, 13735}, {3, 11001, 10304}, {3, 15719, 15708}, {3, 15720, 16239}, {3, 15723, 15686}, {3, 3533, 20}, {3, 5054, 3845}, {5, 15710, 15697}, {5, 15716, 15710}, {5, 15721, 11111}, {20, 10304, 15695}, {140, 17528, 17678}, {140, 3839, 2}, {376, 15702, 547}, {376, 15715, 15714}, {376, 3524, 15700}, {376, 5071, 15684}, {376, 549, 15721}, {381, 3628, 5071}, {549, 10124, 15701}, {549, 14891, 15694}, {549, 15686, 11812}, {549, 15717, 15683}, {549, 3530, 15718}, {631, 3524, 12100}, {2476, 15720, 11102}, {3090, 15688, 15640}, {3090, 17800, 15971}, {3146, 5056, 3832}, {3523, 11541, 15680}, {3523, 15708, 15719}, {3523, 3839, 15722}, {3524, 15693, 3523}, {3524, 15698, 15712}, {3530, 15693, 3524}, {3543, 15686, 5059}, {3545, 11001, 3853}, {3627, 6918, 546}, {3628, 5076, 3544}, {3845, 11539, 3628}, {3845, 5054, 3533}, {5055, 15711, 3528}, {8703, 15709, 3091}, {8703, 15720, 15709}, {10124, 14093, 4}, {10124, 17504, 14093}, {10304, 15692, 15715}, {10304, 15708, 11539}, {11001, 11539, 5056}, {11539, 12100, 3}, {11812, 15686, 15723}, {11812, 15723, 15702}, {12100, 15695, 15698}, {12100, 15707, 631}, {12100, 15715, 15692}, {12108, 15711, 5055}, {14093, 15701, 10124}, {14891, 15694, 376}, {15683, 17678, 15022}, {15686, 15723, 3545}, {15688, 15713, 3090}, {15692, 15708, 3543}, {15693, 15718, 549}, {15694, 15700, 14891}, {15702, 15715, 11001}, {15703, 17800, 381}, {15706, 15722, 140}, {43887, 52046, 6432}, {43888, 52045, 6431}, {47352, 55622, 51166}, {51214, 55711, 5032}

X(61807) = X(2)X(3)∩X(8)X(31666)

Barycentrics    17*a^4+3*(b^2-c^2)^2-20*a^2*(b^2+c^2) : :
X(61807) = 9*X[2]+14*X[3], 3*X[8]+20*X[31666], 3*X[69]+20*X[55687], 7*X[944]+16*X[4691], 3*X[1352]+20*X[55677], -9*X[1992]+32*X[55704], 3*X[3241]+20*X[31447], 21*X[3576]+2*X[3625], 12*X[3589]+11*X[55641], 15*X[3618]+8*X[55606], 7*X[3619]+16*X[55674], 5*X[3620]+18*X[55682] and many others

X(61807) lies on these lines: {2, 3}, {8, 31666}, {17, 43481}, {18, 43482}, {69, 55687}, {183, 32877}, {590, 43338}, {615, 43339}, {944, 4691}, {1056, 52793}, {1352, 55677}, {1620, 43841}, {1992, 55704}, {3241, 31447}, {3311, 43884}, {3312, 43883}, {3316, 42637}, {3317, 42638}, {3576, 3625}, {3589, 55641}, {3618, 55606}, {3619, 55674}, {3620, 55682}, {3630, 5085}, {3633, 5657}, {3635, 10164}, {3653, 58240}, {4114, 15803}, {4301, 50809}, {4668, 6684}, {5007, 46453}, {5010, 47743}, {5334, 42684}, {5335, 42685}, {5351, 11488}, {5352, 11489}, {5818, 58221}, {5878, 46265}, {5881, 50829}, {5921, 55678}, {6144, 10519}, {6200, 43431}, {6225, 10182}, {6396, 43430}, {6409, 13939}, {6410, 13886}, {6411, 53516}, {6412, 53513}, {6419, 43509}, {6420, 43510}, {6425, 13935}, {6426, 9540}, {6447, 7586}, {6448, 7585}, {6451, 43375}, {6452, 43374}, {6453, 7582}, {6454, 7581}, {6455, 13941}, {6456, 8972}, {6519, 13966}, {6522, 8981}, {6564, 43505}, {6565, 43506}, {7280, 8164}, {7612, 60250}, {7735, 31652}, {7771, 32818}, {7801, 55726}, {7967, 20053}, {7987, 59388}, {7999, 17704}, {9541, 43880}, {9588, 50827}, {9693, 10147}, {9862, 38751}, {10168, 55600}, {10193, 12324}, {10575, 44299}, {10645, 43005}, {10646, 43004}, {11008, 55695}, {11465, 36987}, {11480, 42987}, {11481, 42986}, {11592, 33884}, {11669, 18844}, {12244, 38795}, {12248, 38763}, {12317, 15034}, {12383, 38729}, {13172, 38740}, {13352, 46865}, {14094, 48378}, {14482, 22332}, {14494, 60649}, {14561, 55644}, {14853, 55626}, {14912, 20190}, {14927, 55670}, {15021, 38793}, {15023, 36253}, {15025, 38726}, {15051, 20397}, {15069, 50984}, {15482, 18841}, {16241, 42935}, {16242, 42934}, {17508, 39874}, {18581, 42964}, {18582, 42965}, {18583, 55620}, {18840, 60323}, {20050, 31662}, {20080, 55692}, {20081, 32523}, {20125, 51522}, {20423, 55611}, {20582, 51177}, {21151, 60977}, {21153, 60962}, {21167, 32455}, {21168, 60976}, {21843, 53096}, {22236, 42687}, {22238, 42686}, {22331, 31400}, {22615, 43788}, {22644, 43787}, {25406, 43150}, {25555, 55628}, {28186, 46931}, {31425, 50810}, {31450, 41940}, {31670, 55650}, {31859, 55819}, {33606, 41973}, {33607, 41974}, {36422, 61314}, {36751, 61307}, {36967, 42593}, {36968, 42592}, {36996, 61000}, {38064, 55718}, {38110, 55595}, {38664, 52886}, {40330, 55673}, {40693, 43483}, {40694, 43484}, {42089, 52079}, {42092, 52080}, {42112, 43472}, {42113, 43471}, {42119, 42929}, {42120, 42928}, {42122, 42690}, {42123, 42691}, {42126, 42591}, {42127, 42590}, {42140, 42580}, {42141, 42581}, {42147, 42927}, {42148, 42926}, {42150, 42795}, {42151, 42796}, {42260, 43514}, {42261, 43513}, {42433, 42494}, {42434, 42495}, {42488, 43769}, {42489, 43770}, {42500, 43193}, {42501, 43194}, {42528, 43550}, {42529, 43551}, {42596, 42695}, {42597, 42694}, {42625, 42949}, {42626, 42948}, {42805, 42944}, {42806, 42945}, {42946, 43778}, {42947, 43777}, {42978, 43002}, {42979, 43003}, {43340, 43517}, {43341, 43518}, {43376, 43536}, {43377, 54597}, {43568, 60303}, {43569, 60304}, {43621, 55662}, {50966, 51139}, {50967, 53858}, {51137, 55583}, {51138, 51179}, {51140, 55694}, {51171, 55580}, {51212, 55637}, {51538, 55655}, {51587, 55827}, {54170, 55617}, {54173, 55708}, {54211, 61606}, {54857, 60643}, {55652, 58445}, {55721, 59373}, {60123, 60630}, {60278, 60325}, {60289, 60293}, {60290, 60294}, {60329, 60646}

X(61807) = anticomplement of X(61911)
X(61807) = pole of line {185, 62084} with respect to the Jerabek hyperbola
X(61807) = pole of line {69, 3850} with respect to the Wallace hyperbola
X(61807) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(17538)}}, {{A, B, C, X(1217), X(15709)}}, {{A, B, C, X(1597), X(43691)}}, {{A, B, C, X(3346), X(15721)}}, {{A, B, C, X(3534), X(18851)}}, {{A, B, C, X(3628), X(18853)}}, {{A, B, C, X(3845), X(15077)}}, {{A, B, C, X(3851), X(34483)}}, {{A, B, C, X(3853), X(31371)}}, {{A, B, C, X(5066), X(46412)}}, {{A, B, C, X(5073), X(13623)}}, {{A, B, C, X(6995), X(60323)}}, {{A, B, C, X(15681), X(54660)}}, {{A, B, C, X(15699), X(22270)}}, {{A, B, C, X(15717), X(18852)}}, {{A, B, C, X(18849), X(49140)}}, {{A, B, C, X(20421), X(35478)}}, {{A, B, C, X(37174), X(60250)}}, {{A, B, C, X(38071), X(54763)}}, {{A, B, C, X(43713), X(55571)}}, {{A, B, C, X(44245), X(60007)}}
X(61807) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10304, 15684}, {2, 15718, 3524}, {2, 20, 3850}, {2, 3, 17538}, {3, 13154, 12086}, {3, 140, 3146}, {3, 14869, 3091}, {3, 15720, 632}, {3, 3525, 3529}, {3, 5054, 546}, {3, 5072, 548}, {3, 5076, 8703}, {3, 549, 10303}, {3, 631, 3090}, {4, 15717, 15698}, {4, 3525, 3628}, {4, 3528, 3534}, {20, 15720, 15702}, {20, 632, 3544}, {140, 15692, 3528}, {140, 3528, 3545}, {140, 3534, 7486}, {140, 3843, 2}, {376, 3533, 3855}, {376, 631, 3533}, {548, 15712, 15706}, {548, 17538, 16434}, {548, 3628, 3627}, {549, 12100, 5055}, {549, 15700, 15683}, {549, 17504, 11540}, {631, 3523, 15719}, {631, 3545, 140}, {3091, 14869, 3525}, {3146, 7486, 3857}, {3522, 5054, 5067}, {3522, 5067, 15682}, {3523, 15682, 13634}, {3524, 15702, 12100}, {3530, 15693, 3523}, {3530, 15712, 15718}, {3534, 3860, 15640}, {3534, 5055, 15687}, {3543, 10303, 17542}, {3627, 3628, 5072}, {3628, 3857, 5079}, {3843, 15712, 15692}, {3850, 15687, 3843}, {7999, 17704, 61136}, {10299, 13634, 5054}, {10299, 15719, 631}, {10303, 10304, 15022}, {10303, 15022, 3526}, {10303, 15717, 3}, {10304, 15022, 15704}, {11539, 15696, 5068}, {12100, 15702, 15710}, {12100, 15720, 20}, {12108, 14891, 12812}, {12108, 16434, 15709}, {14782, 14783, 10124}, {14890, 15706, 10304}, {15022, 15704, 4}, {15682, 15698, 15759}, {15698, 15709, 376}, {15698, 15717, 10299}, {15701, 15705, 5071}, {15706, 15712, 15717}, {15709, 15719, 549}, {15721, 17504, 11001}, {15722, 17504, 15721}, {15759, 17800, 3522}

X(61808) = X(2)X(3)∩X(6)X(43296)

Barycentrics    16*a^4+3*(b^2-c^2)^2-19*a^2*(b^2+c^2) : :
X(61808) = 9*X[2]+13*X[3], 3*X[141]+8*X[55679], 3*X[265]+19*X[15023], 2*X[575]+9*X[21167], 9*X[597]+2*X[55588], -3*X[1353]+14*X[10541], -3*X[1483]+14*X[30389], 9*X[2482]+2*X[38627], -X[2883]+12*X[46265], 39*X[3576]+5*X[4816], 6*X[3589]+5*X[55637], 15*X[3618]+7*X[55602] and many others

X(61808) lies on these lines: {2, 3}, {6, 43296}, {141, 55679}, {265, 15023}, {524, 55694}, {575, 21167}, {597, 55588}, {1353, 10541}, {1483, 30389}, {1503, 55675}, {2482, 38627}, {2883, 46265}, {3564, 55684}, {3576, 4816}, {3589, 55637}, {3592, 35256}, {3594, 35255}, {3618, 55602}, {3630, 55690}, {3631, 55685}, {3653, 16189}, {4746, 6684}, {5237, 42124}, {5238, 42121}, {5355, 31652}, {5480, 55647}, {5493, 38022}, {5550, 28216}, {5569, 59546}, {5609, 22251}, {5642, 38626}, {5690, 32900}, {6053, 51522}, {6055, 38628}, {6101, 15012}, {6174, 38631}, {6425, 19116}, {6426, 19117}, {6447, 13935}, {6448, 9540}, {6453, 13966}, {6454, 8981}, {6455, 13993}, {6456, 13925}, {7987, 37705}, {7991, 10283}, {8567, 61606}, {9588, 50823}, {9730, 11592}, {10147, 52047}, {10148, 52048}, {10168, 55597}, {10175, 58219}, {10187, 46335}, {10188, 46334}, {10193, 50414}, {10272, 15021}, {10574, 44324}, {10645, 43011}, {10646, 43010}, {11362, 58232}, {12162, 55320}, {13464, 51086}, {13491, 40247}, {13624, 38112}, {14449, 54041}, {15020, 38728}, {15029, 38788}, {15030, 55286}, {15034, 61548}, {15036, 40685}, {15067, 17704}, {16192, 61272}, {16241, 43775}, {16242, 43776}, {16644, 43640}, {16645, 43639}, {16982, 54044}, {18350, 30507}, {18357, 58221}, {18358, 55673}, {18583, 55614}, {20190, 48876}, {20397, 34153}, {20791, 31834}, {21843, 22332}, {21850, 55631}, {22330, 50988}, {25555, 55623}, {29181, 55652}, {31406, 35007}, {31423, 38138}, {31447, 50828}, {32142, 45187}, {32205, 36987}, {32523, 49111}, {33751, 51128}, {34380, 55701}, {34507, 50984}, {34573, 55669}, {34773, 38176}, {36422, 42459}, {37727, 58229}, {38110, 52987}, {38136, 55653}, {39884, 55672}, {40107, 50980}, {42115, 42916}, {42116, 42917}, {42135, 43782}, {42136, 42493}, {42137, 42492}, {42138, 43781}, {42157, 42501}, {42158, 42500}, {42159, 43102}, {42160, 42591}, {42161, 42590}, {42162, 43103}, {42163, 42593}, {42166, 42592}, {42433, 42949}, {42434, 42948}, {42488, 43248}, {42489, 43249}, {42490, 42924}, {42491, 42925}, {42612, 43483}, {42613, 43484}, {42633, 42945}, {42634, 42944}, {42773, 42912}, {42774, 42913}, {42785, 55649}, {42791, 42993}, {42792, 42992}, {42793, 61719}, {42894, 42956}, {42895, 42957}, {42954, 43105}, {42955, 43106}, {43330, 43550}, {43331, 43551}, {43509, 43884}, {43510, 43883}, {43513, 43885}, {43514, 43886}, {48874, 55644}, {48906, 55681}, {49812, 56614}, {49813, 56615}, {50801, 51088}, {50804, 50826}, {50832, 61286}, {50833, 51077}, {50958, 51141}, {50961, 50981}, {50979, 55698}, {50983, 55708}, {51126, 55657}, {51137, 55721}, {51139, 55600}, {51163, 55661}, {51174, 51181}, {51732, 55724}, {53097, 59399}, {54169, 55718}, {55650, 58445}, {55682, 61545}, {58225, 61249}, {58245, 61278}, {59649, 61307}, {61283, 61524}

X(61808) = midpoint of X(i) and X(j) for these {i,j}: {3, 3525}, {15716, 15721}, {15717, 15720}, {15718, 15719}
X(61808) = reflection of X(i) in X(j) for these {i,j}: {15715, 12100}, {549, 15719}, {5070, 140}
X(61808) = complement of X(61970)
X(61808) = pole of line {185, 62087} with respect to the Jerabek hyperbola
X(61808) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(12103)}}, {{A, B, C, X(5066), X(15319)}}, {{A, B, C, X(14893), X(43970)}}, {{A, B, C, X(22268), X(47599)}}, {{A, B, C, X(41106), X(46412)}}, {{A, B, C, X(50693), X(60007)}}, {{A, B, C, X(58208), X(60618)}}
X(61808) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12103, 3857}, {2, 3, 12103}, {3, 10303, 546}, {3, 15720, 3525}, {3, 3091, 548}, {3, 3526, 3529}, {3, 3628, 550}, {3, 5054, 3091}, {3, 5079, 376}, {3, 549, 14869}, {3, 631, 3628}, {3, 632, 15704}, {20, 15701, 140}, {30, 12100, 15715}, {140, 14891, 20}, {140, 14892, 16239}, {140, 3090, 632}, {140, 3530, 3524}, {140, 3861, 2}, {140, 548, 10109}, {140, 8703, 5}, {376, 16239, 3858}, {381, 3524, 12100}, {381, 5070, 5056}, {546, 12108, 10303}, {548, 10109, 5073}, {549, 12100, 11539}, {549, 15699, 15701}, {549, 15711, 5054}, {549, 17504, 15713}, {549, 3530, 15712}, {549, 550, 631}, {549, 632, 12108}, {631, 10299, 11001}, {631, 3523, 15707}, {632, 3534, 6981}, {3523, 15693, 3530}, {3523, 15717, 15719}, {3524, 15701, 14891}, {3524, 15719, 15721}, {3524, 15721, 15716}, {3525, 9840, 10299}, {3526, 15689, 5068}, {3526, 3529, 12812}, {3528, 15694, 3850}, {3529, 12812, 3845}, {3529, 16863, 3851}, {3533, 15696, 5066}, {3533, 15705, 15696}, {3627, 15699, 12811}, {3627, 3857, 3861}, {3628, 3853, 3544}, {3853, 14890, 16052}, {3861, 12103, 11541}, {5054, 15711, 15687}, {5059, 15703, 3859}, {5070, 5072, 3090}, {7987, 61614, 37705}, {10109, 15711, 8703}, {11001, 12100, 15711}, {11539, 12100, 15714}, {11812, 12100, 15695}, {12100, 12108, 3146}, {12100, 15707, 549}, {12100, 15714, 17504}, {12102, 12812, 13587}, {12102, 15682, 3627}, {14869, 15712, 3}, {14891, 15701, 15699}, {15713, 17504, 15686}, {15715, 15721, 381}, {15716, 15720, 5070}, {15716, 15721, 30}, {15717, 15719, 15720}, {15718, 15720, 15717}, {15765, 18585, 11540}, {43296, 43297, 6}

X(61809) = X(2)X(3)∩X(40)X(51086)

Barycentrics    37*a^4+7*(b^2-c^2)^2-44*a^2*(b^2+c^2) : :
X(61809) = 7*X[2]+10*X[3], X[40]+16*X[51086], 7*X[69]+44*X[55689], 16*X[182]+X[51179], 5*X[944]+12*X[38098], X[1350]+16*X[51139], -7*X[1992]+24*X[55706], 15*X[3576]+2*X[34641], 35*X[3618]+16*X[55601], 10*X[3654]+7*X[20057], 7*X[5476]+10*X[55634], 15*X[5657]+2*X[34747] and many others

X(61809) lies on these lines: {2, 3}, {40, 51086}, {69, 55689}, {182, 51179}, {944, 38098}, {1350, 51139}, {1992, 55706}, {3068, 43322}, {3069, 43323}, {3576, 34641}, {3618, 55601}, {3654, 20057}, {5237, 49862}, {5238, 49861}, {5334, 42956}, {5335, 42957}, {5476, 55634}, {5657, 34747}, {5702, 61312}, {6470, 52045}, {6471, 52046}, {6684, 50818}, {6776, 50984}, {8227, 50813}, {10168, 55596}, {10645, 43543}, {10646, 43542}, {11008, 55696}, {11179, 55686}, {11362, 51094}, {11485, 43494}, {11486, 43493}, {11488, 43372}, {11489, 43373}, {12245, 50828}, {12820, 42114}, {12821, 42111}, {13347, 43572}, {14226, 42638}, {14241, 42637}, {14482, 21843}, {14912, 55693}, {16241, 42986}, {16242, 42987}, {20049, 58230}, {20190, 50992}, {20423, 55608}, {20582, 33750}, {20583, 21167}, {21356, 51176}, {22235, 43109}, {22237, 43108}, {25055, 50809}, {31425, 51103}, {33602, 42158}, {33603, 42157}, {34631, 54445}, {36836, 42899}, {36843, 42898}, {38064, 55716}, {38314, 51084}, {40330, 51177}, {40693, 42797}, {40694, 42798}, {41121, 43447}, {41122, 43446}, {41951, 43257}, {41952, 43256}, {42089, 43419}, {42092, 43418}, {42115, 43111}, {42116, 43110}, {42117, 43555}, {42118, 43554}, {42150, 42946}, {42151, 42947}, {42510, 42779}, {42511, 42780}, {42586, 43104}, {42587, 43101}, {42629, 42911}, {42630, 42910}, {42641, 43407}, {42642, 43408}, {42996, 61719}, {43100, 49827}, {43105, 43404}, {43106, 43403}, {43107, 49826}, {43211, 43386}, {43212, 43387}, {43232, 43294}, {43233, 43295}, {43238, 49875}, {43239, 49876}, {46265, 54050}, {46267, 55590}, {47352, 50966}, {50961, 55688}, {50975, 55671}, {50977, 55690}, {51023, 55674}, {51137, 55720}, {51212, 55635}, {52519, 60645}, {54170, 55615}, {54173, 55710}, {54845, 60131}, {60287, 60330}, {60297, 60305}, {60298, 60306}, {60337, 60638}

X(61809) = reflection of X(i) in X(j) for these {i,j}: {3544, 2}
X(61809) = pole of line {69, 38071} with respect to the Wallace hyperbola
X(61809) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(38071)}}, {{A, B, C, X(1494), X(3544)}}, {{A, B, C, X(3545), X(57823)}}, {{A, B, C, X(4846), X(35434)}}, {{A, B, C, X(12100), X(18852)}}, {{A, B, C, X(14893), X(43699)}}, {{A, B, C, X(15704), X(54660)}}, {{A, B, C, X(15707), X(36948)}}
X(61809) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10299, 15710}, {2, 10304, 382}, {2, 15700, 15715}, {2, 15708, 14869}, {2, 15710, 3529}, {2, 17504, 3528}, {2, 30, 3544}, {2, 3523, 15707}, {2, 3529, 3545}, {3, 140, 17578}, {3, 15699, 15697}, {3, 15709, 15682}, {3, 15713, 3839}, {3, 5054, 5066}, {3, 549, 15721}, {4, 16239, 3090}, {4, 3524, 12100}, {140, 15705, 11001}, {376, 3090, 3543}, {547, 549, 15701}, {549, 14891, 5054}, {549, 15694, 15708}, {549, 15712, 547}, {549, 15714, 11812}, {631, 6936, 13634}, {3523, 3524, 15719}, {3524, 15702, 15692}, {3524, 15715, 15700}, {3524, 15719, 631}, {3524, 15722, 3533}, {3543, 15717, 14891}, {5054, 15685, 16239}, {5066, 16239, 15699}, {6863, 15701, 15693}, {10124, 15683, 5071}, {10124, 15702, 15709}, {10124, 15721, 15702}, {10299, 15710, 15698}, {10304, 15701, 3525}, {11001, 14093, 376}, {11539, 15716, 3522}, {11737, 14869, 15694}, {11737, 15694, 2}, {11812, 15706, 20}, {11812, 15714, 15703}, {12100, 14869, 15688}, {12100, 15699, 3}, {12100, 15708, 4}, {14869, 15720, 17533}, {15022, 17582, 11346}, {15681, 15700, 17504}, {15683, 15697, 15686}, {15683, 15721, 10124}, {15685, 15688, 550}, {15687, 15699, 11737}, {15692, 15718, 3524}, {15692, 15721, 15683}, {15693, 15707, 3530}, {15700, 15707, 549}, {15700, 15715, 10299}, {15700, 15720, 15681}, {15701, 15712, 10304}, {15703, 15706, 15714}, {15708, 15717, 15685}, {15715, 15721, 3855}, {42637, 43254, 14241}, {42638, 43255, 14226}, {43211, 43511, 43386}, {43212, 43512, 43387}

X(61810) = X(2)X(3)∩X(13)X(43635)

Barycentrics    14*a^4+3*(b^2-c^2)^2-17*a^2*(b^2+c^2) : :
X(61810) = 9*X[2]+11*X[3], 3*X[141]+7*X[55681], X[389]+4*X[11592], -8*X[575]+3*X[61624], X[576]+9*X[21167], 9*X[597]+X[55583], 2*X[1493]+3*X[54201], 3*X[3589]+2*X[55631], 3*X[3618]+X[55595], X[3630]+9*X[55693], X[3631]+4*X[55688], -6*X[3819]+X[31834] and many others

X(61810) lies on these lines: {2, 3}, {13, 43635}, {14, 43634}, {15, 43198}, {16, 43197}, {69, 32891}, {141, 55681}, {389, 11592}, {397, 42981}, {398, 42980}, {524, 55698}, {575, 61624}, {576, 21167}, {597, 55583}, {952, 31666}, {1493, 54201}, {1503, 55677}, {3068, 6522}, {3069, 6519}, {3564, 55687}, {3589, 55631}, {3618, 55595}, {3630, 55693}, {3631, 55688}, {3819, 31834}, {3828, 58223}, {4701, 6684}, {5092, 61545}, {5237, 16960}, {5238, 16961}, {5305, 31652}, {5318, 42590}, {5321, 42591}, {5346, 53096}, {5351, 11542}, {5352, 11543}, {5447, 15012}, {5462, 54044}, {5476, 55628}, {5480, 55644}, {5563, 52793}, {5609, 38727}, {5650, 13491}, {5690, 30389}, {5844, 61284}, {5892, 14449}, {5901, 28228}, {5965, 20190}, {6200, 13993}, {6337, 32890}, {6396, 13925}, {6417, 43884}, {6418, 43883}, {6419, 35256}, {6420, 35255}, {6425, 13966}, {6426, 8981}, {6433, 43431}, {6434, 43430}, {6447, 19116}, {6448, 19117}, {6470, 43314}, {6471, 43315}, {6488, 13847}, {6489, 13846}, {6496, 32786}, {6497, 32785}, {6696, 50414}, {7982, 51700}, {7987, 28224}, {7991, 38028}, {7999, 45956}, {9588, 50824}, {10164, 10222}, {10168, 55588}, {10193, 61540}, {10264, 15020}, {10519, 55701}, {10541, 48876}, {10627, 16625}, {10645, 42628}, {10646, 42627}, {10992, 26614}, {11477, 51732}, {11591, 17704}, {11694, 20417}, {11695, 13451}, {12040, 14023}, {12512, 61269}, {13348, 13363}, {13392, 14094}, {13393, 15057}, {13624, 28236}, {13630, 44324}, {14561, 55641}, {14641, 15082}, {14853, 55620}, {15021, 38794}, {15025, 38723}, {15027, 15051}, {15034, 38728}, {15178, 28234}, {15515, 43291}, {15579, 61610}, {15644, 16982}, {15860, 61312}, {16192, 38034}, {16241, 42924}, {16242, 42925}, {16252, 46265}, {16836, 32142}, {16881, 54042}, {16962, 42958}, {16963, 42959}, {16964, 42501}, {16965, 42500}, {16966, 42683}, {16967, 42682}, {18357, 58441}, {18358, 55674}, {18439, 44299}, {18583, 55606}, {19862, 28178}, {19925, 58219}, {20070, 61273}, {20398, 61600}, {20399, 61599}, {20400, 61605}, {20401, 61604}, {21154, 51525}, {21850, 55626}, {22234, 51137}, {22250, 48378}, {22253, 55819}, {22331, 31406}, {22712, 55818}, {25555, 55617}, {28168, 31253}, {28212, 61274}, {28216, 35242}, {28232, 31663}, {29181, 55650}, {31423, 61254}, {31425, 58245}, {31447, 51084}, {31662, 61292}, {32423, 38729}, {33416, 42164}, {33417, 42165}, {34380, 53093}, {34507, 51141}, {34573, 55670}, {34773, 61247}, {35770, 42644}, {35771, 42643}, {35812, 52048}, {35813, 52047}, {36253, 48375}, {36836, 42121}, {36843, 42124}, {36967, 42948}, {36968, 42949}, {37472, 46865}, {38064, 53858}, {38066, 61297}, {38110, 53097}, {38136, 55651}, {38317, 55652}, {38737, 51524}, {38748, 51523}, {38760, 51529}, {38772, 51528}, {38784, 51534}, {38793, 51522}, {39884, 55673}, {40107, 50984}, {42122, 42599}, {42123, 42598}, {42133, 42493}, {42134, 42492}, {42136, 42580}, {42137, 42581}, {42150, 42513}, {42151, 42512}, {42157, 42593}, {42158, 42592}, {42163, 42970}, {42166, 42971}, {42263, 43796}, {42264, 43795}, {42496, 43238}, {42497, 43239}, {42584, 43240}, {42585, 43241}, {42594, 51916}, {42595, 51915}, {42596, 43104}, {42597, 43101}, {42793, 42990}, {42794, 42991}, {42797, 42935}, {42798, 42934}, {42898, 42994}, {42899, 42995}, {42902, 43371}, {42903, 43370}, {42912, 42944}, {42913, 42945}, {42922, 43463}, {42923, 43464}, {42936, 43416}, {42937, 43417}, {42956, 43011}, {42957, 43010}, {42992, 43107}, {42993, 43100}, {43110, 43484}, {43111, 43483}, {43199, 43773}, {43200, 43774}, {43378, 43570}, {43379, 43571}, {43467, 43871}, {43468, 43872}, {43485, 43544}, {43486, 43545}, {44158, 44756}, {46850, 55320}, {48885, 51127}, {50805, 58235}, {50811, 58225}, {50825, 58229}, {50828, 58232}, {50830, 61289}, {50977, 55694}, {50983, 55704}, {51086, 58240}, {51126, 55655}, {51139, 55718}, {51163, 55660}, {54169, 55721}, {55166, 55286}, {55580, 59399}, {55647, 58445}, {61551, 61596}

X(61810) = midpoint of X(i) and X(j) for these {i,j}: {2, 15714}, {3, 632}, {5, 3522}, {549, 15693}, {550, 3843}, {631, 15712}, {3858, 15696}, {5071, 8703}, {15692, 15713}, {15694, 15711}, {51126, 55655}
X(61810) = reflection of X(i) in X(j) for these {i,j}: {140, 631}, {12812, 632}, {15690, 14093}, {15694, 11812}, {15712, 3530}, {3091, 3628}, {3853, 3858}, {3859, 1656}, {546, 12812}
X(61810) = complement of X(3858)
X(61810) = pole of line {185, 62091} with respect to the Jerabek hyperbola
X(61810) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(15704)}}, {{A, B, C, X(3845), X(43970)}}, {{A, B, C, X(6662), X(7486)}}, {{A, B, C, X(14938), X(47598)}}, {{A, B, C, X(17538), X(60007)}}, {{A, B, C, X(18848), X(35400)}}, {{A, B, C, X(40448), X(44245)}}, {{A, B, C, X(41099), X(46412)}}, {{A, B, C, X(46168), X(50690)}}
X(61810) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15696, 3858}, {2, 15704, 12811}, {2, 3, 15704}, {2, 5073, 5}, {3, 12108, 140}, {3, 140, 546}, {3, 15694, 5076}, {3, 15720, 10303}, {3, 1656, 17538}, {3, 3525, 3627}, {3, 3526, 3146}, {3, 3628, 12103}, {3, 5072, 376}, {3, 5076, 3522}, {3, 549, 12108}, {5, 15720, 11812}, {5, 549, 15720}, {5, 550, 3543}, {30, 11812, 15694}, {30, 1656, 3859}, {30, 3530, 15712}, {30, 3628, 3091}, {140, 12100, 548}, {140, 12103, 3628}, {140, 12812, 632}, {140, 3530, 12100}, {140, 3853, 2}, {140, 5066, 16239}, {140, 548, 547}, {549, 17504, 15701}, {549, 8703, 15708}, {631, 10299, 5071}, {631, 15692, 1656}, {631, 15717, 3843}, {631, 1656, 15713}, {631, 3523, 15693}, {1656, 15695, 17578}, {1657, 15699, 3856}, {1657, 6981, 12102}, {3090, 12102, 5066}, {3091, 3522, 3529}, {3524, 15694, 15711}, {3524, 15708, 14269}, {3526, 15718, 10299}, {3526, 8703, 3850}, {3529, 15720, 14869}, {3530, 16239, 15717}, {3627, 14869, 3525}, {3843, 15712, 14891}, {3858, 15714, 15696}, {5072, 11108, 15699}, {10124, 15690, 14892}, {10124, 17504, 15690}, {10299, 15708, 3526}, {10303, 17542, 15709}, {11539, 15700, 15759}, {11539, 15759, 14893}, {11812, 12100, 12101}, {12102, 12108, 5054}, {12102, 16239, 3090}, {12108, 15712, 12812}, {12811, 15704, 3853}, {13624, 61614, 61510}, {14891, 16239, 550}, {15692, 15713, 30}, {15692, 17538, 3}, {15693, 15694, 3524}, {15693, 15712, 3530}, {15694, 15720, 631}, {15701, 17504, 10124}, {15706, 15721, 3845}, {15707, 15719, 549}, {15708, 15718, 8703}, {15709, 15716, 15686}, {42133, 42493, 43644}, {42134, 42492, 43649}

X(61811) = X(1)X(31447)∩X(2)X(3)

Barycentrics    9*a^4+2*(b^2-c^2)^2-11*a^2*(b^2+c^2) : :
X(61811) = 3*X[1]+10*X[31447], 6*X[2]+7*X[3], -18*X[10]+5*X[61248], 4*X[52]+9*X[54047], X[64]+12*X[10182], 2*X[69]+11*X[55692], 4*X[141]+9*X[55682], 4*X[143]+9*X[54041], 9*X[154]+4*X[52102], -14*X[182]+X[6144], X[265]+12*X[48375], X[399]+12*X[38727] and many others

X(61811) lies on these lines: {1, 31447}, {2, 3}, {6, 31457}, {10, 61248}, {15, 42491}, {16, 42490}, {32, 31492}, {52, 54047}, {56, 31480}, {61, 42773}, {62, 42774}, {64, 10182}, {69, 55692}, {141, 55682}, {143, 54041}, {154, 52102}, {182, 6144}, {187, 31467}, {195, 37514}, {265, 48375}, {372, 31487}, {399, 38727}, {485, 6452}, {486, 6451}, {517, 31425}, {575, 50962}, {590, 6456}, {597, 55580}, {599, 51141}, {615, 6455}, {944, 61614}, {999, 31452}, {1092, 11935}, {1151, 35813}, {1152, 35812}, {1216, 40280}, {1263, 38640}, {1351, 21167}, {1352, 55678}, {1376, 31494}, {1385, 3633}, {1482, 10164}, {1484, 38636}, {1498, 10193}, {1511, 15057}, {1992, 50988}, {2548, 15655}, {2782, 52886}, {2979, 11592}, {3053, 9698}, {3066, 33543}, {3068, 6408}, {3069, 6407}, {3070, 6497}, {3071, 6496}, {3241, 50833}, {3311, 9680}, {3312, 31454}, {3357, 46265}, {3411, 22236}, {3412, 22238}, {3576, 4668}, {3579, 9624}, {3589, 55629}, {3618, 55593}, {3619, 48662}, {3624, 48661}, {3625, 6684}, {3630, 12017}, {3632, 31662}, {3635, 10246}, {3653, 43174}, {3679, 31666}, {3763, 55674}, {3785, 32889}, {3818, 55671}, {3819, 34783}, {3933, 32876}, {4114, 13411}, {4309, 5433}, {4317, 5432}, {4325, 9654}, {4330, 9669}, {4691, 18526}, {5010, 9670}, {5013, 5355}, {5024, 5319}, {5050, 32455}, {5085, 11898}, {5092, 15069}, {5204, 37719}, {5206, 15484}, {5210, 31455}, {5217, 37720}, {5237, 42974}, {5238, 42975}, {5351, 16644}, {5352, 16645}, {5418, 6450}, {5420, 6449}, {5447, 14531}, {5476, 55626}, {5480, 55643}, {5585, 7747}, {5644, 33522}, {5646, 33539}, {5657, 61286}, {5690, 20053}, {5731, 61249}, {5734, 38028}, {5790, 7987}, {5881, 13624}, {5882, 38066}, {5892, 37484}, {6053, 10620}, {6199, 13935}, {6221, 13961}, {6337, 32877}, {6390, 32875}, {6395, 9540}, {6398, 13903}, {6409, 13951}, {6410, 8976}, {6417, 35256}, {6418, 35255}, {6427, 41963}, {6428, 41964}, {6437, 35814}, {6438, 35815}, {6445, 7584}, {6446, 7583}, {6447, 32788}, {6448, 32787}, {6519, 43323}, {6522, 43322}, {6683, 22728}, {6696, 14530}, {6699, 15040}, {7280, 9657}, {7582, 9692}, {7749, 53095}, {7751, 11165}, {7765, 15815}, {7771, 7917}, {7814, 43459}, {7998, 13630}, {8148, 61278}, {8550, 50961}, {8589, 13881}, {9589, 18493}, {9605, 21843}, {9606, 30435}, {9655, 59319}, {9668, 59325}, {9703, 61134}, {9709, 31458}, {9730, 15606}, {9780, 58224}, {9936, 44158}, {9956, 58221}, {10156, 37585}, {10165, 12702}, {10168, 53097}, {10192, 13093}, {10264, 38638}, {10267, 61154}, {10516, 55672}, {10519, 55705}, {10541, 33749}, {10574, 32142}, {10625, 13321}, {10627, 15045}, {10645, 42153}, {10646, 42156}, {10653, 43773}, {10654, 43774}, {11160, 50981}, {11178, 55677}, {11202, 34780}, {11204, 48672}, {11230, 16192}, {11231, 37714}, {11480, 42818}, {11481, 42817}, {11482, 38064}, {11485, 16773}, {11486, 16772}, {11591, 20791}, {11698, 38637}, {11849, 61159}, {12054, 52770}, {12188, 38748}, {12250, 61606}, {12290, 33879}, {12315, 23328}, {12331, 21154}, {12355, 20398}, {12525, 14135}, {12773, 38760}, {12902, 20396}, {13108, 21163}, {13188, 38737}, {13334, 32519}, {13353, 43652}, {13391, 15028}, {13925, 43511}, {13993, 43512}, {14128, 44299}, {14561, 55639}, {14830, 38751}, {14848, 52987}, {14853, 55616}, {14926, 33540}, {14929, 32835}, {14981, 38750}, {15035, 20379}, {15036, 34128}, {15038, 15805}, {15039, 20126}, {15041, 15063}, {15042, 17702}, {15043, 54042}, {15046, 16111}, {15051, 38724}, {15178, 50805}, {15513, 31489}, {15515, 37637}, {15534, 55704}, {15851, 61301}, {16003, 32609}, {16241, 36843}, {16242, 36836}, {16808, 42596}, {16809, 42597}, {16836, 18436}, {16964, 42129}, {16965, 42132}, {17502, 18525}, {17508, 18440}, {17821, 25563}, {18358, 33750}, {18481, 31399}, {18543, 38121}, {18553, 55675}, {18583, 55604}, {18907, 31407}, {19130, 55654}, {19877, 28186}, {20423, 55602}, {20427, 58434}, {21153, 60922}, {21309, 31400}, {21850, 55624}, {22115, 37515}, {22712, 32520}, {23241, 61583}, {24206, 55673}, {24474, 33575}, {24928, 31436}, {25555, 55614}, {25565, 50968}, {26864, 43607}, {28146, 34595}, {28212, 46934}, {30389, 50821}, {31145, 50826}, {31235, 38754}, {31274, 38742}, {31414, 45384}, {31475, 31499}, {31483, 61337}, {31657, 60976}, {31658, 60977}, {31670, 55648}, {31834, 61136}, {33416, 42126}, {33417, 42127}, {33533, 43601}, {34507, 55684}, {34754, 42938}, {34755, 42939}, {35251, 38031}, {35260, 61540}, {35770, 42569}, {35771, 42568}, {36422, 36751}, {36990, 55670}, {37495, 43650}, {37512, 44535}, {37600, 37721}, {37606, 37724}, {37624, 54445}, {37725, 38762}, {37832, 43491}, {37835, 43492}, {38068, 50801}, {38110, 55584}, {38317, 55651}, {38574, 38772}, {38579, 38784}, {38593, 38804}, {38634, 51872}, {39565, 44541}, {40341, 55695}, {40693, 42115}, {40694, 42116}, {41462, 43597}, {42087, 42963}, {42088, 42962}, {42089, 42147}, {42092, 42148}, {42095, 43632}, {42098, 43633}, {42125, 42489}, {42128, 42488}, {42130, 42814}, {42131, 42813}, {42154, 42937}, {42155, 42936}, {42159, 42948}, {42162, 42949}, {42494, 42590}, {42495, 42591}, {42498, 43226}, {42499, 43227}, {42510, 42793}, {42511, 42794}, {42592, 42631}, {42593, 42632}, {42627, 43777}, {42628, 43778}, {42639, 43376}, {42640, 43377}, {42779, 43483}, {42780, 43484}, {42785, 55646}, {42918, 43472}, {42919, 43471}, {42926, 43640}, {42927, 43639}, {42946, 42969}, {42947, 42968}, {43102, 43772}, {43103, 43771}, {43150, 55683}, {43177, 59381}, {43254, 53513}, {43255, 53516}, {43273, 55679}, {43634, 52079}, {43635, 52080}, {43879, 53131}, {43880, 53130}, {45958, 52093}, {46267, 55583}, {47352, 55606}, {47355, 55649}, {47391, 52104}, {48673, 61132}, {48872, 55658}, {48876, 55697}, {48884, 55664}, {48889, 55665}, {48895, 55662}, {48901, 55656}, {48904, 55663}, {48905, 55669}, {48910, 55657}, {50980, 51175}, {50983, 51174}, {51093, 58232}, {51173, 55641}, {51185, 55721}, {51212, 55632}, {53023, 55655}, {53092, 54173}, {54044, 58533}, {54131, 55637}, {54169, 55724}, {54857, 60131}, {55668, 59411}, {58220, 61259}, {58233, 61283}, {59380, 60962}, {60329, 60645}

X(61811) = midpoint of X(i) and X(j) for these {i,j}: {10299, 10303}
X(61811) = reflection of X(i) in X(j) for these {i,j}: {3, 10299}, {7491, 15710}
X(61811) = inverse of X(12812) in orthocentroidal circle
X(61811) = inverse of X(12812) in Yff hyperbola
X(61811) = complement of X(61964)
X(61811) = anticomplement of X(61907)
X(61811) = pole of line {523, 12812} with respect to the orthocentroidal circle
X(61811) = pole of line {185, 15688} with respect to the Jerabek hyperbola
X(61811) = pole of line {6, 12812} with respect to the Kiepert hyperbola
X(61811) = pole of line {523, 12812} with respect to the Yff hyperbola
X(61811) = pole of line {69, 55719} with respect to the Wallace hyperbola
X(61811) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(68), X(41099)}}, {{A, B, C, X(95), X(1657)}}, {{A, B, C, X(264), X(12812)}}, {{A, B, C, X(1105), X(15688)}}, {{A, B, C, X(3519), X(3854)}}, {{A, B, C, X(3521), X(50687)}}, {{A, B, C, X(3534), X(60007)}}, {{A, B, C, X(3628), X(15318)}}, {{A, B, C, X(3839), X(46412)}}, {{A, B, C, X(3851), X(15319)}}, {{A, B, C, X(7486), X(22270)}}, {{A, B, C, X(12811), X(13599)}}, {{A, B, C, X(13623), X(50692)}}, {{A, B, C, X(14861), X(50691)}}, {{A, B, C, X(14893), X(21400)}}, {{A, B, C, X(15696), X(40448)}}, {{A, B, C, X(23046), X(57822)}}, {{A, B, C, X(26861), X(46935)}}, {{A, B, C, X(35404), X(60122)}}, {{A, B, C, X(52441), X(55862)}}
X(61811) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15706, 14093}, {2, 15718, 15706}, {2, 16434, 3858}, {2, 17538, 3850}, {2, 3524, 14891}, {2, 4, 12812}, {2, 5072, 1656}, {2, 548, 3843}, {3, 10303, 5079}, {3, 15707, 3523}, {3, 15718, 15712}, {3, 1656, 3534}, {3, 17800, 3528}, {3, 3525, 5076}, {3, 3830, 3522}, {3, 3843, 548}, {3, 5, 15696}, {3, 5070, 20}, {3, 549, 15720}, {3, 7393, 14130}, {3, 7395, 18859}, {5, 3528, 17800}, {5, 3530, 15717}, {6, 31457, 31470}, {20, 140, 5070}, {20, 3090, 3861}, {20, 3832, 15682}, {20, 3861, 5073}, {30, 15710, 7491}, {140, 10109, 632}, {140, 14891, 3627}, {140, 15691, 3628}, {140, 17504, 11541}, {140, 3524, 3}, {140, 5070, 3526}, {140, 8703, 3090}, {376, 632, 3851}, {376, 7486, 3853}, {381, 15688, 15685}, {381, 15693, 3524}, {381, 5079, 5068}, {546, 15713, 3533}, {547, 15705, 15695}, {549, 12100, 15708}, {549, 15712, 12108}, {549, 15719, 15707}, {549, 3524, 15701}, {550, 11812, 3525}, {550, 4205, 3855}, {631, 10299, 5067}, {631, 3523, 3530}, {631, 3855, 15702}, {631, 5067, 10303}, {632, 3853, 7486}, {1657, 3843, 382}, {3522, 11541, 15691}, {3524, 15682, 15692}, {3526, 15696, 5}, {3526, 15720, 631}, {3530, 13634, 6842}, {3530, 16239, 12100}, {3533, 10304, 546}, {3534, 5054, 15723}, {3850, 17538, 15684}, {5056, 15704, 14269}, {5076, 15720, 11812}, {5237, 43238, 42974}, {5238, 43239, 42975}, {5418, 6450, 18512}, {5420, 6449, 18510}, {5447, 37481, 54048}, {6929, 15704, 3845}, {10124, 15704, 5056}, {10299, 10303, 30}, {10304, 15713, 15703}, {11539, 15698, 15681}, {11540, 15714, 3839}, {11812, 12811, 140}, {11812, 15692, 5055}, {12100, 14869, 4}, {12100, 14890, 15686}, {12100, 15694, 15688}, {12100, 15708, 15694}, {12108, 12812, 14869}, {12108, 15712, 2}, {12108, 15718, 1657}, {13587, 15710, 550}, {14093, 15718, 15700}, {14813, 14814, 3854}, {14891, 14892, 8703}, {14891, 15706, 15716}, {15685, 15694, 15699}, {15685, 15699, 381}, {15688, 15708, 5054}, {15692, 17678, 376}, {15693, 15706, 15718}, {15697, 17677, 3545}, {15701, 15718, 15689}, {15702, 17504, 3830}, {15707, 15722, 549}, {15712, 15759, 4220}, {15718, 15720, 5072}, {15719, 15722, 15693}, {15765, 18585, 15709}, {16241, 36843, 42988}, {16242, 36836, 42989}, {16808, 42596, 42610}, {16809, 42597, 42611}, {17502, 31423, 18525}, {33416, 42126, 42951}, {33417, 42127, 42950}, {38728, 48378, 32609}, {42435, 42436, 6}, {42488, 43193, 42128}, {42489, 43194, 42125}, {54445, 61524, 37624}

X(61812) = X(1)X(51086)∩X(2)X(3)

Barycentrics    31*a^4+7*(b^2-c^2)^2-38*a^2*(b^2+c^2) : :
X(61812) = -X[1]+16*X[51086], 7*X[2]+8*X[3], -X[6]+16*X[51139], -X[8]+16*X[50829], -X[69]+16*X[50984], -X[145]+16*X[50828], -X[193]+16*X[50983], -X[1278]+16*X[51049], -16*X[1385]+X[20049], -X[3621]+16*X[50821], -X[3623]+16*X[51084], 4*X[3653]+X[59417] and many others

X(61812) lies on these lines: {1, 51086}, {2, 3}, {6, 51139}, {8, 50829}, {69, 50984}, {145, 50828}, {193, 50983}, {395, 43869}, {396, 43870}, {1278, 51049}, {1385, 20049}, {3068, 6469}, {3069, 6468}, {3621, 50821}, {3623, 51084}, {3653, 59417}, {3655, 4678}, {4788, 51045}, {4995, 5265}, {5281, 5298}, {5334, 42513}, {5335, 42512}, {5343, 42632}, {5344, 42631}, {5351, 43495}, {5352, 43496}, {5420, 9543}, {5476, 55625}, {5550, 50808}, {5656, 46265}, {5731, 38068}, {5965, 55693}, {6036, 8596}, {6470, 19053}, {6471, 19054}, {6684, 31145}, {7585, 52046}, {7586, 52045}, {7811, 32835}, {8252, 42605}, {8253, 42604}, {9143, 48378}, {9541, 43255}, {9778, 19883}, {9955, 50813}, {10164, 11224}, {10168, 51028}, {10519, 55706}, {10541, 50992}, {11008, 51138}, {11057, 32839}, {11179, 51141}, {11480, 42778}, {11481, 42777}, {12017, 50980}, {14561, 55638}, {14853, 55615}, {15516, 54173}, {15520, 38064}, {16267, 43252}, {16268, 43253}, {16981, 54041}, {17502, 38074}, {18358, 51177}, {19130, 50969}, {19872, 50862}, {19877, 34628}, {20014, 50824}, {20050, 51085}, {20052, 50825}, {20054, 50827}, {20080, 50977}, {20423, 55601}, {21153, 59375}, {21167, 59373}, {25055, 28228}, {28234, 54445}, {28236, 53620}, {31253, 58217}, {32841, 37671}, {34595, 34638}, {34632, 46934}, {34718, 50833}, {34748, 50826}, {35369, 49102}, {36836, 49861}, {36843, 49862}, {38737, 52695}, {41121, 43556}, {41122, 43557}, {41150, 58245}, {41963, 43884}, {41964, 43883}, {42087, 43202}, {42088, 43201}, {42119, 42501}, {42120, 42500}, {42413, 43567}, {42414, 43566}, {42472, 43477}, {42473, 43478}, {42490, 49813}, {42491, 49812}, {42516, 43296}, {42517, 43297}, {42518, 42792}, {42519, 42791}, {42570, 60293}, {42571, 60294}, {42572, 43338}, {42573, 43339}, {42773, 43229}, {42774, 43228}, {43240, 43473}, {43241, 43474}, {43479, 49947}, {43480, 49948}, {46931, 50796}, {46932, 50864}, {46933, 50811}, {48880, 51213}, {50797, 58224}, {50863, 61261}, {50959, 55656}, {50961, 55691}, {50967, 55716}, {50975, 55672}, {50982, 55699}, {50991, 55684}, {51023, 55676}, {51137, 51170}, {51171, 54169}, {51179, 55705}, {54132, 55590}, {54174, 55720}, {54448, 58221}

X(61812) = midpoint of X(i) and X(j) for these {i,j}: {631, 3524}, {3839, 15697}, {5055, 14093}, {11539, 15711}
X(61812) = reflection of X(i) in X(j) for these {i,j}: {1656, 11539}, {15688, 15714}, {15692, 3524}, {17538, 15688}, {17578, 3839}, {3524, 15693}, {3839, 5071}, {5055, 632}
X(61812) = complement of X(61962)
X(61812) = anticomplement of X(61906)
X(61812) = pole of line {69, 61944} with respect to the Wallace hyperbola
X(61812) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(15683)}}, {{A, B, C, X(3346), X(12108)}}, {{A, B, C, X(3832), X(57822)}}, {{A, B, C, X(3843), X(46412)}}, {{A, B, C, X(12102), X(54552)}}, {{A, B, C, X(15022), X(36889)}}, {{A, B, C, X(35381), X(46921)}}
X(61812) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15683, 5068}, {2, 15692, 3522}, {2, 3524, 15705}, {2, 3543, 15022}, {2, 376, 3832}, {2, 3854, 547}, {3, 10124, 15682}, {3, 140, 3855}, {3, 15709, 3839}, {3, 5054, 15699}, {3, 5071, 15697}, {20, 140, 17697}, {30, 11539, 1656}, {30, 15688, 17538}, {30, 15693, 3524}, {30, 3524, 15692}, {140, 15698, 3543}, {140, 15718, 15698}, {140, 3543, 2}, {376, 15701, 10303}, {547, 15640, 3854}, {547, 15716, 3528}, {547, 3528, 15640}, {549, 12100, 15720}, {549, 15693, 631}, {549, 3524, 15708}, {549, 3530, 15701}, {631, 15712, 3091}, {631, 17538, 140}, {631, 5071, 15713}, {631, 7390, 548}, {3523, 10303, 3530}, {3523, 15692, 15693}, {3524, 15702, 15710}, {3524, 15705, 15717}, {3524, 15707, 3523}, {3524, 15710, 12100}, {3524, 15719, 15707}, {3524, 3545, 17504}, {3524, 5054, 10304}, {3526, 14891, 11001}, {3530, 11539, 15706}, {3530, 15720, 3544}, {3839, 15708, 15721}, {3839, 15721, 15709}, {3858, 15713, 10124}, {5054, 15706, 14269}, {5054, 17504, 3545}, {5071, 15682, 3858}, {10124, 15682, 7486}, {10304, 15708, 5054}, {11539, 15706, 376}, {11539, 15711, 30}, {11812, 15700, 4}, {12100, 15687, 3}, {12100, 15702, 20}, {12100, 15720, 15702}, {15022, 15705, 15688}, {15687, 15713, 632}, {15692, 15713, 17578}, {15692, 15721, 5071}, {15693, 15694, 15712}, {15693, 15701, 15711}, {15693, 15720, 14093}, {15697, 17578, 15683}, {15698, 17538, 15714}, {15701, 15706, 11539}, {15701, 15718, 17800}, {15702, 15710, 5055}, {15703, 15759, 3529}, {15711, 15713, 5066}

X(61813) = X(2)X(3)∩X(141)X(55683)

Barycentrics    22*a^4+5*(b^2-c^2)^2-27*a^2*(b^2+c^2) : :
X(61813) = 15*X[2]+17*X[3], 5*X[141]+11*X[55683], 3*X[1511]+X[13393], 5*X[3589]+3*X[55627], 5*X[5480]+11*X[55642], -9*X[5892]+X[13421], 5*X[6684]+3*X[31662], -5*X[8550]+21*X[55691], 15*X[10164]+X[11278], X[11362]+15*X[51084], -X[12002]+3*X[32205], X[12317]+7*X[22250] and many others

X(61813) lies on these lines: {2, 3}, {141, 55683}, {395, 42995}, {396, 42994}, {1511, 13393}, {1990, 36422}, {3564, 55688}, {3589, 55627}, {5237, 42496}, {5238, 42497}, {5318, 10188}, {5321, 10187}, {5418, 6434}, {5420, 6433}, {5480, 55642}, {5892, 13421}, {6411, 10194}, {6412, 10195}, {6427, 43413}, {6428, 43414}, {6437, 13966}, {6438, 8981}, {6482, 35813}, {6483, 35812}, {6484, 7584}, {6485, 7583}, {6486, 58866}, {6487, 8960}, {6684, 31662}, {8550, 55691}, {10164, 11278}, {11362, 51084}, {12002, 32205}, {12317, 22250}, {13348, 58531}, {13382, 32142}, {13392, 38727}, {14862, 46265}, {15003, 18874}, {15082, 32137}, {15172, 51817}, {18583, 55603}, {19878, 28182}, {20190, 50984}, {20582, 55677}, {21167, 37517}, {21850, 55622}, {25555, 55612}, {25565, 51165}, {26861, 34567}, {28190, 58219}, {33179, 43174}, {34380, 50664}, {34507, 55685}, {34754, 42897}, {34755, 42896}, {35255, 35770}, {35256, 35771}, {36967, 42591}, {36968, 42590}, {37727, 50825}, {38068, 61249}, {38079, 55626}, {38110, 55582}, {40685, 48375}, {42090, 42477}, {42091, 42476}, {42122, 42937}, {42123, 42936}, {42143, 42904}, {42146, 42905}, {42150, 42628}, {42151, 42627}, {42157, 42902}, {42158, 42903}, {42163, 42890}, {42166, 42891}, {42494, 43631}, {42495, 43630}, {42568, 42643}, {42569, 42644}, {42596, 42941}, {42597, 42940}, {42682, 43468}, {42683, 43467}, {42793, 42924}, {42794, 42925}, {42906, 42920}, {42907, 42921}, {42908, 43101}, {42909, 43104}, {42916, 43870}, {42917, 43869}, {42942, 42978}, {42943, 42979}, {42944, 43018}, {42945, 43019}, {42954, 43486}, {42955, 43485}, {42992, 43199}, {42993, 43200}, {42998, 43197}, {42999, 43198}, {44158, 45184}, {48310, 55644}, {48876, 55699}, {50988, 53093}, {51127, 55659}, {51128, 55667}, {51214, 53092}, {54201, 55038}, {54445, 61597}, {55645, 58445}, {58234, 61281}, {58567, 58675}, {58605, 58637}

X(61813) = midpoint of X(i) and X(j) for these {i,j}: {3, 16239}, {548, 12811}, {3530, 12108}, {11540, 14891}, {13348, 58531}, {51127, 55659}, {58567, 58675}, {58605, 58637}
X(61813) = complement of X(3856)
X(61813) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(3519), X(3857)}}, {{A, B, C, X(3628), X(26861)}}, {{A, B, C, X(3843), X(43970)}}, {{A, B, C, X(15022), X(42021)}}, {{A, B, C, X(15690), X(40448)}}, {{A, B, C, X(26863), X(34567)}}
X(61813) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 11539, 3853}, {3, 140, 3850}, {3, 15702, 5}, {3, 3526, 3543}, {3, 3845, 548}, {3, 5, 15690}, {3, 5054, 5067}, {3, 5067, 15686}, {3, 631, 11539}, {3, 6842, 15722}, {5, 15682, 546}, {140, 12100, 550}, {140, 1656, 10124}, {140, 3523, 3530}, {140, 3850, 16239}, {140, 547, 3533}, {140, 548, 1656}, {140, 550, 3628}, {549, 15712, 15720}, {549, 3530, 12108}, {631, 3524, 3146}, {2045, 2046, 15701}, {3146, 3628, 12811}, {3523, 10299, 15693}, {3523, 15720, 15712}, {3524, 15714, 12100}, {3526, 12103, 10109}, {3526, 15695, 3544}, {3526, 17504, 12103}, {3530, 11812, 3}, {3530, 3861, 15717}, {3533, 11001, 5056}, {3628, 15759, 17800}, {6846, 17504, 14093}, {10124, 14891, 15681}, {10299, 15702, 5059}, {10304, 12100, 14891}, {11001, 11539, 547}, {11539, 15714, 3845}, {11540, 14891, 30}, {11812, 15690, 11540}, {12108, 12811, 14869}, {12108, 16239, 11812}, {14813, 14814, 3857}, {15681, 15693, 3524}, {15682, 15715, 10304}, {15701, 15717, 632}, {15712, 15720, 140}

X(61814) = X(2)X(3)∩X(40)X(15808)

Barycentrics    13*a^4+3*(b^2-c^2)^2-16*a^2*(b^2+c^2) : :
X(61814) = 9*X[2]+10*X[3], 5*X[40]+14*X[15808], 3*X[69]+16*X[20190], -20*X[182]+X[11008], -3*X[193]+22*X[55701], 3*X[568]+16*X[11592], -20*X[1153]+X[53143], 3*X[1352]+16*X[55679], -20*X[1385]+X[20050], -X[1992]+20*X[51137], 4*X[3244]+15*X[5657], 15*X[3576]+4*X[3626] and many others

X(61814) lies on these lines: {2, 3}, {40, 15808}, {69, 20190}, {182, 11008}, {193, 55701}, {325, 32887}, {568, 11592}, {575, 53860}, {1007, 43459}, {1153, 53143}, {1249, 61307}, {1285, 31401}, {1352, 55679}, {1385, 20050}, {1975, 32886}, {1992, 51137}, {3068, 6454}, {3069, 6453}, {3244, 5657}, {3304, 52793}, {3316, 41948}, {3317, 9541}, {3411, 42481}, {3412, 42480}, {3487, 4031}, {3576, 3626}, {3589, 55626}, {3592, 13935}, {3594, 9540}, {3617, 61614}, {3618, 52987}, {3619, 17508}, {3621, 58230}, {3629, 10519}, {3631, 5085}, {3632, 6684}, {3636, 7982}, {3653, 31447}, {3746, 7288}, {3763, 33750}, {3982, 15803}, {5204, 8164}, {5210, 31404}, {5217, 47743}, {5218, 5563}, {5237, 11488}, {5238, 11489}, {5339, 42501}, {5340, 42500}, {5351, 42092}, {5352, 42089}, {5365, 42626}, {5366, 42625}, {5476, 55623}, {5550, 31663}, {5569, 7758}, {5650, 6241}, {5690, 20054}, {5818, 58441}, {5882, 58229}, {5921, 55682}, {6200, 13939}, {6329, 11477}, {6396, 13886}, {6409, 23273}, {6410, 23267}, {6417, 42643}, {6418, 42644}, {6425, 7582}, {6426, 7581}, {6427, 35256}, {6428, 35255}, {6447, 13966}, {6448, 8981}, {6449, 13941}, {6450, 8972}, {6484, 43431}, {6485, 43430}, {6699, 15020}, {6776, 55684}, {7612, 60636}, {7622, 14023}, {7735, 53096}, {7736, 35007}, {7754, 55819}, {7772, 21843}, {7863, 42850}, {7991, 10165}, {7999, 16836}, {8252, 23275}, {8253, 23269}, {8960, 43386}, {9542, 19116}, {9543, 18510}, {9545, 13339}, {9588, 34747}, {9680, 19053}, {9741, 34506}, {9751, 39142}, {9755, 55827}, {9780, 17502}, {9862, 20399}, {10147, 13847}, {10148, 13846}, {10155, 18843}, {10168, 55583}, {10517, 26339}, {10518, 26340}, {10541, 14912}, {10588, 59319}, {10589, 59325}, {11160, 50980}, {11206, 25563}, {11381, 55166}, {11412, 15012}, {11444, 61136}, {11459, 17704}, {11480, 43464}, {11481, 43463}, {11491, 61152}, {11530, 59675}, {12162, 44299}, {12245, 15178}, {12248, 20400}, {12250, 61680}, {12317, 38728}, {12324, 50414}, {12383, 20397}, {12818, 42267}, {12819, 42266}, {13172, 20398}, {13348, 15024}, {13624, 59388}, {14094, 38727}, {14561, 55637}, {14843, 57713}, {14853, 55614}, {14927, 55672}, {15023, 17702}, {15029, 16111}, {15034, 24981}, {15035, 38729}, {15036, 15081}, {15039, 61548}, {15044, 38726}, {15045, 16625}, {15051, 36253}, {15054, 20125}, {15055, 38795}, {15482, 55774}, {16189, 50810}, {16241, 42779}, {16242, 42780}, {16772, 42774}, {16773, 42773}, {18581, 42593}, {18582, 42592}, {18583, 55602}, {18840, 60322}, {19875, 58225}, {19876, 50819}, {20049, 50832}, {20080, 55697}, {20421, 31371}, {20423, 55600}, {20583, 51139}, {21151, 60942}, {21153, 60980}, {21154, 35023}, {21166, 38740}, {21168, 60933}, {21445, 50771}, {22234, 54173}, {22235, 42926}, {22237, 42927}, {22330, 38064}, {22712, 32450}, {23235, 35022}, {23302, 52080}, {23303, 52079}, {23328, 58795}, {25406, 55681}, {25555, 54170}, {26446, 31666}, {26877, 61122}, {26878, 37526}, {31145, 50825}, {31400, 46453}, {31414, 53131}, {31457, 41940}, {31658, 60957}, {31670, 55647}, {32000, 52712}, {32789, 43407}, {32790, 43408}, {32815, 52718}, {32822, 37688}, {33416, 42160}, {33417, 42161}, {33630, 36751}, {33749, 50992}, {33884, 37481}, {34089, 42259}, {34091, 42258}, {34473, 38751}, {34511, 55823}, {34573, 55671}, {34631, 43174}, {34641, 50829}, {35021, 38664}, {35024, 38666}, {35369, 38635}, {35786, 42600}, {35787, 42601}, {36422, 36431}, {36948, 46724}, {36967, 42495}, {36968, 42494}, {36996, 60983}, {37487, 43841}, {37640, 42939}, {37641, 42938}, {37832, 43769}, {37835, 43770}, {38110, 55580}, {38314, 58240}, {38317, 55650}, {38628, 52695}, {38668, 38772}, {38669, 38760}, {38674, 38784}, {38688, 38804}, {38692, 38775}, {38693, 38763}, {38697, 38787}, {38716, 38807}, {39874, 53094}, {40107, 50974}, {40330, 55676}, {40693, 42612}, {40694, 42613}, {42090, 42580}, {42091, 42581}, {42111, 43196}, {42114, 43195}, {42115, 42986}, {42116, 42987}, {42121, 43869}, {42124, 43870}, {42136, 43872}, {42137, 43871}, {42139, 42630}, {42142, 42629}, {42147, 43543}, {42148, 43542}, {42150, 43419}, {42151, 43418}, {42153, 43482}, {42156, 43481}, {42164, 43488}, {42165, 43487}, {42262, 43506}, {42265, 43505}, {42271, 43788}, {42272, 43787}, {42415, 42816}, {42416, 42815}, {42488, 43546}, {42489, 43547}, {42490, 42998}, {42491, 42999}, {42598, 43106}, {42599, 43105}, {42610, 42941}, {42611, 42940}, {42627, 43242}, {42628, 43243}, {42633, 42806}, {42634, 42805}, {42775, 43633}, {42776, 43632}, {42785, 55645}, {42786, 55664}, {42944, 43493}, {42945, 43494}, {42948, 43194}, {42949, 43193}, {42964, 43772}, {42965, 43771}, {42988, 43111}, {42989, 43110}, {42990, 49862}, {42991, 49861}, {43022, 43233}, {43023, 43232}, {43100, 49876}, {43102, 43466}, {43103, 43465}, {43107, 49875}, {43256, 51850}, {43257, 51849}, {43334, 43499}, {43335, 43500}, {43387, 58866}, {43403, 43447}, {43404, 43446}, {43621, 55660}, {46264, 55675}, {48873, 55652}, {50818, 51088}, {50827, 61289}, {50833, 61286}, {50966, 55617}, {50977, 55698}, {50988, 51179}, {51126, 55654}, {51171, 55724}, {51212, 55631}, {51538, 55653}, {53100, 60629}, {53103, 60219}, {54616, 60330}, {54845, 60183}, {55620, 61044}, {55644, 58445}, {55718, 59373}, {60123, 60631}, {60142, 60616}, {60143, 60337}, {60334, 60627}

X(61814) = anticomplement of X(61905)
X(61814) = pole of line {185, 62092} with respect to the Jerabek hyperbola
X(61814) = pole of line {3, 12002} with respect to the Stammler hyperbola
X(61814) = pole of line {69, 3851} with respect to the Wallace hyperbola
X(61814) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(3851)}}, {{A, B, C, X(95), X(3529)}}, {{A, B, C, X(546), X(14843)}}, {{A, B, C, X(547), X(22270)}}, {{A, B, C, X(1173), X(18535)}}, {{A, B, C, X(1217), X(15702)}}, {{A, B, C, X(1597), X(13452)}}, {{A, B, C, X(3346), X(15708)}}, {{A, B, C, X(3431), X(3517)}}, {{A, B, C, X(3516), X(20421)}}, {{A, B, C, X(3530), X(36948)}}, {{A, B, C, X(3544), X(57823)}}, {{A, B, C, X(3830), X(31371)}}, {{A, B, C, X(3843), X(15077)}}, {{A, B, C, X(3845), X(46412)}}, {{A, B, C, X(3855), X(57894)}}, {{A, B, C, X(5056), X(14863)}}, {{A, B, C, X(5073), X(15740)}}, {{A, B, C, X(6995), X(60322)}}, {{A, B, C, X(7408), X(54845)}}, {{A, B, C, X(7409), X(52519)}}, {{A, B, C, X(7529), X(55976)}}, {{A, B, C, X(11270), X(55571)}}, {{A, B, C, X(12103), X(60007)}}, {{A, B, C, X(14269), X(32533)}}, {{A, B, C, X(14938), X(15723)}}, {{A, B, C, X(15683), X(54660)}}, {{A, B, C, X(18852), X(61138)}}, {{A, B, C, X(36889), X(47478)}}, {{A, B, C, X(37174), X(60636)}}, {{A, B, C, X(40448), X(50693)}}, {{A, B, C, X(45758), X(46452)}}, {{A, B, C, X(50692), X(60618)}}, {{A, B, C, X(52301), X(60337)}}
X(61814) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10299, 3528}, {2, 10304, 15687}, {2, 13741, 16863}, {2, 15692, 15688}, {2, 15700, 15710}, {2, 16854, 16844}, {2, 17546, 16343}, {2, 20, 3851}, {2, 3, 3529}, {2, 3524, 15715}, {2, 3528, 4}, {2, 5192, 16864}, {2, 550, 3855}, {3, 12108, 10303}, {3, 13154, 7527}, {3, 140, 3091}, {3, 15720, 14869}, {3, 1656, 12103}, {3, 3090, 17538}, {3, 3526, 3627}, {3, 3627, 3522}, {3, 3628, 20}, {3, 5054, 3628}, {3, 5079, 550}, {3, 631, 3525}, {3, 632, 3146}, {4, 15684, 1532}, {4, 631, 15702}, {5, 140, 15723}, {20, 15712, 15698}, {20, 3533, 5071}, {20, 5054, 3533}, {140, 15693, 15717}, {140, 15759, 5}, {140, 17504, 382}, {140, 3530, 17504}, {140, 376, 5067}, {140, 5079, 16418}, {376, 3091, 11541}, {376, 3545, 15640}, {381, 17538, 6969}, {382, 3851, 3845}, {548, 15694, 5056}, {549, 15693, 15708}, {549, 3530, 15720}, {550, 3530, 15700}, {1656, 15685, 3856}, {1657, 11539, 7486}, {3090, 3529, 546}, {3091, 15717, 3}, {3091, 16859, 15699}, {3091, 5059, 12102}, {3146, 10303, 632}, {3522, 15721, 3526}, {3523, 15717, 15693}, {3524, 11001, 15692}, {3526, 3628, 17542}, {3530, 10299, 3524}, {3530, 15707, 3523}, {3534, 16239, 5068}, {5056, 15705, 548}, {5071, 17538, 5076}, {6427, 35256, 43884}, {6428, 35255, 43883}, {7407, 17578, 6879}, {10299, 14869, 3544}, {10303, 12108, 631}, {10303, 15717, 15704}, {10304, 15685, 376}, {11354, 16845, 2}, {11812, 15718, 10304}, {12100, 15721, 3545}, {12811, 17697, 3090}, {14782, 14783, 11539}, {15640, 15708, 15721}, {15684, 15701, 5054}, {15692, 15701, 15709}, {15692, 15709, 11001}, {15693, 15701, 15759}, {15694, 15705, 15682}, {15698, 15709, 15684}, {15699, 17800, 3854}, {15706, 15713, 3543}, {15707, 15720, 3530}, {15708, 15717, 140}, {15717, 17504, 10299}

X(61815) = X(2)X(3)∩X(17)X(43334)

Barycentrics    17*a^4+4*(b^2-c^2)^2-21*a^2*(b^2+c^2) : :
X(61815) = 12*X[2]+13*X[3], X[64]+24*X[46265], 16*X[620]+9*X[38634], 16*X[3035]+9*X[38637], 16*X[3589]+9*X[55624], 12*X[4746]+13*X[5882], 16*X[5972]+9*X[38633], 16*X[6036]+9*X[38635], 16*X[6699]+9*X[38638], 16*X[6713]+9*X[38636], X[8148]+24*X[10164], -8*X[8550]+33*X[55692] and many others

X(61815) lies on these lines: {2, 3}, {17, 43334}, {18, 43335}, {61, 42893}, {62, 42892}, {64, 46265}, {515, 58224}, {620, 38634}, {3035, 38637}, {3069, 9691}, {3070, 43881}, {3071, 43882}, {3589, 55624}, {4746, 5882}, {5024, 5346}, {5343, 43102}, {5344, 43103}, {5351, 43420}, {5352, 43421}, {5418, 6446}, {5420, 6445}, {5844, 58233}, {5965, 12017}, {5972, 38633}, {6036, 38635}, {6199, 43314}, {6395, 43315}, {6409, 45385}, {6410, 45384}, {6417, 41963}, {6418, 41964}, {6449, 58866}, {6450, 8960}, {6459, 43317}, {6460, 43316}, {6500, 35256}, {6501, 35255}, {6519, 35813}, {6522, 35812}, {6699, 38638}, {6713, 38636}, {7373, 52793}, {7745, 15603}, {8148, 10164}, {8550, 55692}, {10168, 55580}, {10182, 13093}, {10187, 36967}, {10188, 36968}, {10193, 12315}, {10247, 43174}, {10645, 42978}, {10646, 42979}, {11362, 51086}, {11480, 42993}, {11481, 42992}, {11485, 42773}, {11486, 42774}, {11592, 15045}, {12006, 54047}, {12308, 38727}, {12815, 44526}, {12902, 48375}, {14862, 35450}, {15028, 54044}, {15042, 34128}, {15533, 55694}, {15805, 37496}, {16960, 42115}, {16961, 42116}, {17508, 48662}, {18493, 28232}, {18526, 61614}, {18553, 55676}, {19106, 43441}, {19107, 43440}, {20190, 51141}, {21167, 44456}, {21358, 55679}, {22115, 44749}, {22236, 42959}, {22238, 42958}, {25555, 55610}, {28168, 58217}, {28234, 37624}, {30389, 34748}, {31487, 52046}, {34837, 38640}, {34841, 38639}, {36836, 42799}, {36843, 42800}, {37727, 50829}, {38066, 51088}, {38072, 55647}, {40693, 42793}, {40694, 42794}, {41943, 42994}, {41944, 42995}, {41973, 43490}, {41974, 43489}, {42021, 44731}, {42125, 42948}, {42128, 42949}, {42154, 43549}, {42155, 43548}, {42258, 43433}, {42259, 43432}, {42490, 43008}, {42491, 43009}, {42682, 42920}, {42683, 42921}, {42688, 43547}, {42689, 43546}, {42813, 43330}, {42814, 43331}, {46933, 58226}, {47352, 55602}, {47353, 55675}, {47355, 55648}, {50955, 55684}, {51024, 55652}, {51071, 58235}, {51137, 53093}, {54447, 58219}, {55643, 58445}

X(61815) = pole of line {185, 62093} with respect to the Jerabek hyperbola
X(61815) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(17800)}}, {{A, B, C, X(1294), X(58192)}}, {{A, B, C, X(3519), X(3855)}}, {{A, B, C, X(3627), X(46168)}}, {{A, B, C, X(3858), X(14841)}}, {{A, B, C, X(5071), X(42021)}}, {{A, B, C, X(10594), X(44731)}}, {{A, B, C, X(14861), X(15682)}}, {{A, B, C, X(15689), X(40448)}}, {{A, B, C, X(43908), X(52294)}}
X(61815) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11541, 5}, {2, 3, 17800}, {3, 140, 3851}, {3, 14269, 548}, {3, 15685, 3528}, {3, 15694, 3843}, {3, 3526, 3830}, {3, 5, 15689}, {3, 5054, 5070}, {3, 631, 15694}, {4, 15681, 5073}, {4, 15719, 3523}, {4, 3523, 3530}, {140, 10299, 1657}, {140, 15712, 3522}, {140, 3522, 1656}, {381, 5054, 11540}, {547, 12103, 3861}, {549, 15707, 15701}, {549, 15722, 15707}, {549, 3523, 15720}, {631, 3091, 15713}, {631, 3522, 140}, {631, 3530, 15696}, {631, 5071, 10303}, {632, 8703, 3859}, {1656, 15693, 15712}, {1656, 15696, 4}, {1656, 1657, 3858}, {2045, 2046, 12108}, {3090, 3525, 17542}, {3091, 15713, 3526}, {3524, 15713, 14093}, {3526, 14093, 3091}, {3528, 11539, 5072}, {3528, 5072, 15685}, {3530, 12108, 547}, {3530, 12811, 12100}, {3530, 14869, 15710}, {3830, 15689, 15683}, {5054, 15693, 15692}, {5054, 15696, 632}, {10303, 12100, 382}, {11540, 15710, 381}, {11812, 15706, 15703}, {12103, 17800, 15681}, {12108, 15713, 631}, {12811, 17533, 5054}, {12812, 15714, 20}, {14093, 15693, 3524}, {14813, 14814, 3855}, {15692, 15696, 3}, {15692, 15710, 15711}, {15693, 15701, 15695}, {15694, 15695, 5055}, {15694, 15707, 15693}, {15701, 15707, 15718}, {15702, 15716, 14269}, {15712, 15713, 550}

X(61816) = X(2)X(3)∩X(145)X(9588)

Barycentrics    21*a^4+5*(b^2-c^2)^2-26*a^2*(b^2+c^2) : :
X(61816) = 15*X[2]+16*X[3], 3*X[145]+28*X[9588], -5*X[193]+36*X[55703], -32*X[1385]+X[20014], -X[1992]+32*X[51139], -X[3241]+32*X[51086], 24*X[3576]+7*X[4678], 20*X[3589]+11*X[55622], 25*X[3618]+6*X[55591], -X[3621]+32*X[6684], 7*X[3622]+24*X[10164], 15*X[3623]+16*X[11362] and many others

X(61816) lies on these lines: {2, 3}, {69, 32881}, {95, 52443}, {145, 9588}, {187, 31407}, {193, 55703}, {1078, 32841}, {1131, 6412}, {1132, 6411}, {1385, 20014}, {1587, 6487}, {1588, 6486}, {1992, 51139}, {3068, 6430}, {3069, 6429}, {3086, 51817}, {3241, 51086}, {3316, 6452}, {3317, 6451}, {3411, 34754}, {3412, 34755}, {3576, 4678}, {3589, 55622}, {3618, 55591}, {3621, 6684}, {3622, 10164}, {3623, 11362}, {3636, 58241}, {3767, 15602}, {4297, 46931}, {4300, 27645}, {4301, 46934}, {5008, 31400}, {5041, 21843}, {5265, 52793}, {5343, 43245}, {5344, 43244}, {5418, 6485}, {5420, 6484}, {5550, 9589}, {5657, 61284}, {5731, 61250}, {5734, 10165}, {5921, 55683}, {6036, 35369}, {6337, 32880}, {6410, 31414}, {6432, 31454}, {6433, 9543}, {6434, 8972}, {6459, 43890}, {6460, 43889}, {6480, 35813}, {6481, 35812}, {6776, 55685}, {7280, 31410}, {7584, 9693}, {7771, 32835}, {7782, 32870}, {7850, 32887}, {7987, 38155}, {8273, 61156}, {9542, 13966}, {9544, 13347}, {9606, 14930}, {9607, 37689}, {9624, 20070}, {9680, 13935}, {9706, 37515}, {9780, 61254}, {10194, 43257}, {10195, 43256}, {10519, 50664}, {10541, 11160}, {11180, 55681}, {11278, 61279}, {11439, 15082}, {13334, 20105}, {13624, 61247}, {14531, 33884}, {14561, 55636}, {14683, 15057}, {14853, 55612}, {14907, 32871}, {15023, 45311}, {15513, 31417}, {18581, 43371}, {18582, 43370}, {19876, 50868}, {19877, 58221}, {20049, 50828}, {20050, 58231}, {20052, 31662}, {20054, 61289}, {20080, 55699}, {21167, 51171}, {21356, 55684}, {22236, 43429}, {22238, 43428}, {23269, 42604}, {23275, 42605}, {30389, 31145}, {31447, 33179}, {31492, 37665}, {32805, 51952}, {32806, 51953}, {32895, 37668}, {33879, 46850}, {35255, 42523}, {35256, 42522}, {37640, 42774}, {37641, 42773}, {37714, 46932}, {38138, 58224}, {40107, 55691}, {42089, 43005}, {42092, 43004}, {42150, 43026}, {42151, 43027}, {42488, 42891}, {42489, 42890}, {42598, 43556}, {42599, 43557}, {42610, 43326}, {42611, 43327}, {42793, 49905}, {42794, 49906}, {42892, 43023}, {42893, 43022}, {42966, 43199}, {42967, 43200}, {42978, 49824}, {42979, 49825}, {43177, 61006}, {43883, 43888}, {43884, 43887}, {50988, 55701}, {51166, 55614}, {51170, 55711}, {52093, 55166}, {55618, 61044}, {55642, 58445}, {58244, 61277}, {60279, 60324}

X(61816) = pole of line {185, 62094} with respect to the Jerabek hyperbola
X(61816) = intersection, other than A, B, C, of circumconics {{A, B, C, X(5), X(52443)}}, {{A, B, C, X(68), X(23046)}}, {{A, B, C, X(95), X(5059)}}, {{A, B, C, X(1217), X(55863)}}, {{A, B, C, X(3346), X(15720)}}, {{A, B, C, X(5481), X(20850)}}, {{A, B, C, X(11541), X(60618)}}, {{A, B, C, X(14269), X(46412)}}, {{A, B, C, X(15640), X(15740)}}, {{A, B, C, X(15686), X(60007)}}, {{A, B, C, X(18850), X(58203)}}, {{A, B, C, X(42021), X(44904)}}
X(61816) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1656, 17697}, {2, 3, 5059}, {3, 11812, 3533}, {3, 140, 3545}, {3, 15702, 5056}, {3, 15719, 3523}, {3, 15720, 11812}, {3, 1656, 15686}, {3, 17928, 13620}, {3, 3526, 3853}, {3, 3533, 3543}, {3, 3543, 3522}, {3, 3850, 376}, {3, 5067, 20}, {4, 10109, 3091}, {4, 10303, 17678}, {4, 12108, 15721}, {5, 15711, 548}, {5, 15720, 631}, {5, 548, 5073}, {20, 3523, 3530}, {20, 3530, 15717}, {20, 5067, 3832}, {20, 7486, 3843}, {140, 15692, 3146}, {140, 3146, 2}, {140, 3528, 7486}, {549, 15719, 15708}, {631, 3528, 140}, {3091, 15709, 17554}, {3146, 3522, 3534}, {3523, 10303, 3524}, {3524, 15720, 10303}, {3524, 3534, 15692}, {3525, 10304, 5068}, {3525, 15712, 10304}, {3526, 3853, 5067}, {3529, 15703, 6839}, {3529, 6949, 1657}, {3530, 3856, 12100}, {3545, 11001, 15687}, {3832, 5059, 17578}, {5070, 5076, 5}, {7486, 15692, 3528}, {10165, 31425, 5734}, {10299, 11001, 3}, {11812, 15722, 15719}, {12108, 15693, 4}, {15692, 15721, 15703}, {15693, 15721, 15705}, {15701, 15712, 3525}, {15703, 15707, 15693}, {15705, 17582, 17538}, {16370, 17578, 5070}

X(61817) = X(2)X(3)∩X(8)X(31662)

Barycentrics    19*a^4+5*(b^2-c^2)^2-24*a^2*(b^2+c^2) : :
X(61817) = 15*X[2]+14*X[3], 5*X[8]+24*X[31662], 5*X[69]+24*X[55695], 5*X[1352]+24*X[55680], 28*X[1385]+X[20053], X[1992]+28*X[51141], X[3241]+28*X[51088], 21*X[3576]+8*X[4691], 20*X[3589]+9*X[55618], 25*X[3618]+4*X[55587], 8*X[3625]+21*X[7967], 8*X[3630]+21*X[14912] and many others

X(61817) lies on these lines: {2, 3}, {8, 31662}, {69, 55695}, {183, 32875}, {397, 43463}, {398, 43464}, {485, 43517}, {486, 43518}, {620, 55732}, {1131, 6497}, {1132, 6496}, {1352, 55680}, {1385, 20053}, {1587, 6434}, {1588, 6433}, {1992, 51141}, {3068, 43801}, {3069, 43802}, {3241, 51088}, {3316, 6410}, {3317, 6409}, {3576, 4691}, {3589, 55618}, {3618, 55587}, {3625, 7967}, {3630, 14912}, {3633, 6684}, {3635, 5657}, {4668, 5882}, {5237, 43199}, {5238, 43200}, {5339, 43446}, {5340, 43447}, {5343, 42948}, {5344, 42949}, {5365, 43028}, {5366, 43029}, {5418, 6481}, {5420, 6480}, {6144, 55703}, {6411, 23275}, {6412, 23269}, {6419, 43413}, {6420, 43414}, {6431, 13935}, {6432, 9540}, {6437, 7582}, {6438, 7581}, {6484, 58866}, {6485, 8960}, {6486, 13939}, {6487, 13886}, {6519, 43212}, {6522, 43211}, {7780, 55823}, {7800, 39142}, {7999, 13382}, {8976, 43889}, {9542, 13961}, {9543, 13993}, {9624, 51120}, {9862, 38746}, {10141, 13847}, {10142, 13846}, {10155, 60146}, {10164, 10595}, {10165, 11531}, {10187, 42159}, {10188, 42162}, {10194, 60290}, {10195, 60289}, {10519, 32455}, {10575, 33879}, {10576, 43432}, {10577, 43433}, {11160, 50988}, {11451, 12002}, {11485, 43480}, {11486, 43479}, {12244, 38792}, {12248, 38758}, {12383, 38725}, {13172, 38735}, {13607, 58231}, {13951, 43890}, {14226, 43410}, {14241, 43409}, {14561, 55633}, {14853, 55607}, {14929, 32873}, {15081, 48375}, {15105, 61680}, {16200, 43174}, {16241, 42958}, {16242, 42959}, {18581, 42929}, {18582, 42928}, {18844, 53098}, {20049, 50826}, {20125, 38727}, {20190, 50974}, {21151, 61000}, {21167, 55582}, {21168, 60962}, {21356, 55687}, {23249, 43505}, {23259, 43506}, {25406, 55683}, {25555, 55603}, {28186, 46930}, {31145, 50833}, {31412, 34089}, {31414, 43254}, {31423, 38155}, {31447, 38314}, {31454, 43888}, {31658, 60976}, {31666, 53620}, {31670, 55645}, {32817, 32878}, {32820, 32877}, {32824, 32888}, {32825, 32889}, {33416, 42495}, {33417, 42494}, {34091, 42561}, {34507, 55688}, {34754, 42149}, {34755, 42152}, {37727, 51084}, {38064, 51214}, {38068, 50871}, {38079, 55620}, {38748, 52886}, {41973, 43555}, {41974, 43554}, {42085, 43444}, {42086, 43445}, {42089, 42993}, {42090, 42776}, {42091, 42775}, {42092, 42992}, {42119, 42937}, {42120, 42936}, {42150, 42978}, {42151, 42979}, {42435, 43494}, {42436, 43493}, {42488, 43244}, {42489, 43245}, {42500, 43481}, {42501, 43482}, {42600, 51910}, {42601, 51911}, {42773, 42999}, {42774, 42998}, {42815, 43495}, {42816, 43496}, {42924, 42986}, {42925, 42987}, {42972, 43002}, {42973, 43003}, {43255, 54597}, {43491, 43769}, {43492, 43770}, {43564, 60309}, {43565, 60310}, {48310, 55641}, {50984, 53093}, {51027, 55684}, {51212, 55627}, {51537, 55670}, {53103, 60209}, {54857, 60183}, {55640, 58445}, {60185, 60640}

X(61817) = anticomplement of X(61903)
X(61817) = pole of line {185, 62096} with respect to the Jerabek hyperbola
X(61817) = pole of line {69, 5072} with respect to the Wallace hyperbola
X(61817) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(5072)}}, {{A, B, C, X(95), X(33703)}}, {{A, B, C, X(3431), X(55578)}}, {{A, B, C, X(3532), X(35501)}}, {{A, B, C, X(5055), X(42021)}}, {{A, B, C, X(7408), X(54857)}}, {{A, B, C, X(7409), X(60329)}}, {{A, B, C, X(11403), X(11738)}}, {{A, B, C, X(14861), X(15684)}}, {{A, B, C, X(15687), X(46412)}}, {{A, B, C, X(15712), X(36948)}}, {{A, B, C, X(15740), X(49136)}}, {{A, B, C, X(22270), X(35018)}}, {{A, B, C, X(26861), X(55860)}}, {{A, B, C, X(55569), X(60304)}}, {{A, B, C, X(55572), X(57713)}}, {{A, B, C, X(55573), X(60303)}}
X(61817) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10304, 14893}, {2, 15686, 3545}, {2, 15692, 15689}, {2, 15706, 376}, {2, 15721, 14890}, {2, 20, 5072}, {2, 3523, 15712}, {2, 3843, 3090}, {2, 4220, 15696}, {3, 11001, 3528}, {3, 11539, 3832}, {3, 140, 5056}, {3, 15702, 5067}, {3, 15723, 3853}, {3, 16239, 3543}, {3, 3526, 3845}, {3, 5054, 16239}, {3, 5067, 11001}, {4, 1656, 3544}, {5, 15694, 17542}, {20, 14869, 15709}, {20, 16457, 11737}, {140, 10299, 4}, {140, 15712, 1657}, {140, 1657, 2}, {140, 3523, 10299}, {140, 5056, 3533}, {382, 3530, 5154}, {549, 15708, 15719}, {549, 15720, 3523}, {550, 15712, 14891}, {631, 15709, 14869}, {631, 3090, 5054}, {632, 10304, 3855}, {1656, 15720, 15701}, {3523, 5046, 15714}, {3524, 5067, 3}, {3525, 3528, 5071}, {3526, 15689, 12812}, {3526, 15692, 3529}, {3528, 5071, 11541}, {3530, 14869, 14269}, {3530, 15701, 10303}, {3530, 3627, 15706}, {3543, 5056, 3854}, {3544, 10303, 3525}, {3544, 17538, 3627}, {3627, 5066, 3843}, {3832, 10303, 11539}, {3851, 14869, 17576}, {3858, 14869, 140}, {5055, 15713, 17679}, {10124, 15696, 15022}, {10303, 15701, 631}, {10303, 15717, 5066}, {12102, 15693, 15717}, {12102, 16239, 547}, {13735, 15640, 12811}, {14869, 15693, 20}, {15693, 15709, 15715}, {15693, 15715, 3524}, {15694, 15704, 2476}, {15707, 15721, 15698}, {15708, 15719, 15702}, {43446, 52079, 5339}, {43447, 52080, 5340}

X(61818) = X(2)X(3)∩X(1384)X(9698)

Barycentrics    15*a^4+4*(b^2-c^2)^2-19*a^2*(b^2+c^2) : :
X(61818) = 12*X[2]+11*X[3], 20*X[575]+3*X[50973], -30*X[1385]+7*X[61289], 3*X[1482]+20*X[31447], -X[1498]+24*X[46265], 16*X[3589]+7*X[55616], 20*X[3617]+49*X[58228], 12*X[4701]+11*X[37727], 12*X[5476]+11*X[55620], 15*X[5657]+8*X[61281], 15*X[5731]+8*X[61253], -X[5882]+24*X[51086] and many others

X(61818) lies on these lines: {2, 3}, {485, 42566}, {486, 42567}, {575, 50973}, {1384, 9698}, {1385, 61289}, {1482, 31447}, {1498, 46265}, {3311, 42568}, {3312, 42569}, {3411, 11485}, {3412, 11486}, {3589, 55616}, {3617, 58228}, {4701, 37727}, {5418, 6408}, {5420, 6407}, {5476, 55620}, {5657, 61281}, {5731, 61253}, {5882, 51086}, {6199, 9680}, {6221, 35813}, {6395, 31487}, {6398, 35812}, {6418, 31454}, {6451, 43882}, {6452, 43881}, {6455, 45385}, {6456, 45384}, {6474, 9692}, {6496, 8252}, {6497, 8253}, {6500, 35255}, {6501, 35256}, {6519, 13847}, {6522, 13846}, {6684, 61287}, {6767, 52793}, {7373, 31452}, {7583, 43415}, {7584, 9690}, {7765, 44535}, {7989, 58219}, {8148, 10165}, {8550, 51139}, {9543, 43375}, {9588, 10246}, {9605, 31457}, {9606, 21843}, {9656, 59319}, {9671, 59325}, {9681, 13951}, {9693, 13941}, {9703, 37515}, {10137, 43431}, {10138, 43430}, {10164, 61276}, {10168, 55724}, {10182, 12315}, {10193, 13093}, {10283, 58247}, {10541, 51137}, {11231, 61256}, {11362, 37624}, {11439, 55320}, {11592, 15043}, {12017, 40107}, {12307, 21766}, {12308, 38793}, {12645, 61614}, {12702, 31425}, {13491, 44299}, {13624, 37712}, {14530, 52102}, {14561, 55632}, {14848, 50970}, {15024, 54044}, {15028, 58533}, {15040, 20379}, {15042, 15059}, {15051, 20396}, {15057, 32609}, {15178, 50817}, {15533, 55698}, {15606, 37481}, {15655, 31455}, {15905, 61312}, {16241, 42774}, {16242, 42773}, {16644, 42981}, {16645, 42980}, {17502, 37714}, {18525, 58441}, {21167, 55584}, {21358, 55681}, {22712, 55815}, {23236, 38638}, {25555, 55602}, {30389, 38066}, {30435, 31492}, {31253, 58218}, {31399, 58224}, {31666, 50798}, {33416, 43194}, {33417, 43193}, {33879, 45959}, {34718, 61282}, {35242, 61271}, {36967, 42985}, {36968, 42984}, {37484, 40284}, {38072, 55644}, {38317, 55648}, {41943, 42958}, {41944, 42959}, {42095, 42597}, {42098, 42596}, {42125, 42970}, {42128, 42971}, {42130, 42692}, {42131, 42693}, {42150, 42501}, {42151, 42500}, {42271, 42601}, {42272, 42600}, {42433, 43029}, {42434, 43028}, {42488, 42903}, {42489, 42902}, {42572, 43254}, {42573, 43255}, {42610, 43633}, {42611, 43632}, {42688, 42890}, {42689, 42891}, {42793, 43107}, {42794, 43100}, {42914, 43636}, {42915, 43637}, {42990, 43238}, {42991, 43239}, {43554, 43640}, {43555, 43639}, {47352, 55595}, {47353, 55677}, {47355, 55643}, {48662, 55678}, {48672, 58434}, {50955, 55687}, {50977, 55701}, {50988, 51178}, {51024, 55650}, {51103, 58236}, {51515, 61296}, {51700, 58238}, {51705, 61248}, {54445, 61286}, {55639, 58445}, {58220, 61261}, {59503, 61292}

X(61818) = pole of line {185, 15695} with respect to the Jerabek hyperbola
X(61818) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(5073)}}, {{A, B, C, X(632), X(52441)}}, {{A, B, C, X(1105), X(15695)}}, {{A, B, C, X(15318), X(55856)}}, {{A, B, C, X(15681), X(60007)}}, {{A, B, C, X(22268), X(46935)}}, {{A, B, C, X(46412), X(50687)}}
X(61818) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12811, 1656}, {2, 16434, 3850}, {2, 3, 5073}, {2, 3524, 15714}, {3, 15684, 3522}, {3, 15694, 3851}, {3, 15703, 1657}, {3, 15720, 15701}, {3, 15722, 3523}, {3, 1656, 15681}, {3, 3523, 15718}, {3, 3526, 3843}, {3, 3851, 15689}, {3, 4, 15695}, {3, 5070, 17800}, {5, 548, 3146}, {20, 5067, 3856}, {140, 12100, 12102}, {140, 15693, 3}, {140, 15704, 2}, {140, 15712, 5059}, {140, 15717, 382}, {140, 17504, 3091}, {140, 3091, 15723}, {140, 5067, 3526}, {376, 15705, 15759}, {376, 5059, 12103}, {382, 15693, 15717}, {382, 15696, 15704}, {382, 3526, 5067}, {549, 5054, 15722}, {631, 3528, 10303}, {632, 10299, 3534}, {1657, 3525, 15703}, {1657, 5054, 3525}, {3146, 3523, 3524}, {3522, 11539, 5079}, {3523, 3525, 12100}, {3528, 10303, 16239}, {3528, 15697, 548}, {3530, 14869, 3855}, {3533, 8703, 5072}, {3832, 17533, 15721}, {3843, 5073, 3853}, {3845, 15759, 15697}, {5054, 15693, 376}, {5054, 15720, 12108}, {5055, 15681, 3845}, {6908, 15694, 14269}, {10299, 15721, 632}, {10303, 15712, 381}, {10303, 15719, 15712}, {11539, 15716, 15684}, {11541, 15721, 140}, {11592, 15043, 54047}, {12103, 15712, 15705}, {12103, 16239, 5}, {15022, 17577, 5056}, {15685, 15723, 5055}, {15693, 15723, 17504}, {15694, 17800, 5070}, {15695, 15701, 11812}, {15701, 15707, 15694}, {15701, 15718, 5054}, {15701, 15722, 3830}, {15708, 15717, 631}, {15712, 16239, 3528}, {15718, 15722, 15707}, {15719, 15759, 15693}, {15723, 17504, 15685}

X(61819) = X(2)X(3)∩X(182)X(51188)

Barycentrics    37*a^4+10*(b^2-c^2)^2-47*a^2*(b^2+c^2) : :
X(61819) = 10*X[2]+9*X[3], 18*X[182]+X[51188], 5*X[599]+14*X[55691], -9*X[1482]+28*X[51106], -27*X[3653]+8*X[51107], 9*X[3654]+10*X[51104], 9*X[3655]+10*X[51067], 7*X[4677]+12*X[32900], 16*X[4745]+3*X[18526], -27*X[5050]+8*X[41149], 12*X[5092]+7*X[51186], 10*X[5476]+9*X[55618] and many others

X(61819) lies on these lines: {2, 3}, {182, 51188}, {599, 55691}, {1482, 51106}, {3653, 51107}, {3654, 51104}, {3655, 51067}, {4677, 32900}, {4745, 18526}, {5050, 41149}, {5092, 51186}, {5351, 42508}, {5352, 42509}, {5476, 55618}, {6407, 43212}, {6408, 43211}, {6455, 42417}, {6456, 42418}, {6480, 13847}, {6481, 13846}, {6496, 42603}, {6497, 42602}, {6684, 51096}, {7583, 10138}, {7584, 10137}, {10165, 41150}, {10168, 55722}, {10246, 50829}, {10645, 42953}, {10646, 42952}, {11179, 51142}, {11231, 50797}, {11278, 51105}, {11898, 51189}, {12017, 22165}, {12355, 38735}, {12702, 51108}, {13903, 52046}, {13961, 52045}, {14226, 43882}, {14241, 43881}, {14848, 55587}, {15533, 55699}, {15534, 50664}, {16241, 43020}, {16242, 43021}, {20582, 55678}, {22236, 42504}, {22238, 42505}, {25565, 55656}, {26446, 51070}, {30392, 50821}, {31662, 51084}, {31884, 51173}, {33616, 33620}, {33617, 33621}, {33748, 51184}, {34718, 51097}, {34754, 49948}, {34755, 49947}, {36521, 38739}, {36836, 42507}, {36843, 42506}, {36967, 42951}, {36968, 42950}, {37517, 51185}, {38079, 55616}, {38110, 51172}, {38224, 41147}, {38737, 41151}, {39561, 50962}, {39899, 50991}, {41100, 42817}, {41101, 42818}, {41112, 42500}, {41113, 42501}, {41152, 51139}, {41943, 42774}, {41944, 42773}, {42121, 42419}, {42124, 42420}, {42125, 42632}, {42128, 42631}, {42566, 43568}, {42567, 43569}, {42900, 43029}, {42901, 43028}, {43100, 49810}, {43107, 49811}, {43244, 49907}, {43245, 49908}, {43273, 55680}, {47352, 55594}, {47355, 55642}, {48310, 55639}, {49877, 49959}, {49878, 49960}, {50805, 51088}, {50813, 61269}, {50828, 59503}, {50833, 58230}, {50873, 61267}, {50977, 51187}, {50988, 51175}, {50989, 51137}, {51027, 55685}, {51166, 55610}, {54131, 55633}

X(61819) = intersection, other than A, B, C, of circumconics {{A, B, C, X(15687), X(46168)}}, {{A, B, C, X(15722), X(57895)}}, {{A, B, C, X(46412), X(50688)}}
X(61819) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12100, 15695}, {2, 12101, 5055}, {2, 15693, 15716}, {2, 15711, 15685}, {2, 15716, 3534}, {2, 15759, 3830}, {2, 3524, 15759}, {2, 549, 15722}, {3, 15694, 3545}, {3, 5054, 15723}, {3, 5055, 15686}, {3, 5067, 1657}, {3, 5070, 5059}, {140, 15718, 15688}, {381, 15688, 17800}, {381, 15693, 12100}, {382, 5054, 15694}, {547, 11812, 15713}, {549, 11812, 15719}, {549, 631, 15707}, {550, 11539, 547}, {550, 12108, 631}, {631, 3523, 3628}, {632, 15705, 15684}, {3523, 15683, 3524}, {3525, 14891, 14269}, {3526, 15706, 15683}, {3526, 15720, 12108}, {3534, 15693, 15700}, {3545, 17538, 3543}, {3627, 11353, 5072}, {3628, 12100, 8703}, {3830, 15713, 3526}, {3845, 11812, 15702}, {5054, 15700, 1656}, {5056, 11001, 3845}, {6958, 15695, 15690}, {8703, 12100, 15715}, {10124, 15689, 5079}, {10124, 15717, 15689}, {10303, 17504, 15703}, {11001, 12100, 3}, {11001, 15690, 6958}, {11539, 12100, 11001}, {11812, 12100, 11539}, {11812, 15708, 15701}, {12100, 15707, 15693}, {12100, 15714, 15698}, {14890, 15714, 16408}, {15693, 15701, 5054}, {15693, 15713, 14093}, {15694, 15706, 382}, {15694, 15715, 381}, {15701, 15722, 2}, {15703, 17504, 15696}, {15707, 17800, 15718}, {15708, 15719, 11812}, {15709, 15712, 15681}, {15718, 17538, 15706}

X(61820) = X(2)X(3)∩X(8)X(30389)

Barycentrics    11*a^4+3*(b^2-c^2)^2-14*a^2*(b^2+c^2) : :
X(61820) = 9*X[2]+8*X[3], 3*X[8]+14*X[30389], 4*X[40]+13*X[46934], 3*X[69]+14*X[10541], 6*X[141]+11*X[55684], X[145]+16*X[6684], -3*X[146]+20*X[38795], -3*X[147]+20*X[38751], -3*X[148]+20*X[38740], -3*X[152]+20*X[38775], -3*X[153]+20*X[38763], 6*X[165]+11*X[5550] and many others

X(61820) lies on these lines: {2, 3}, {6, 43883}, {8, 30389}, {17, 43489}, {18, 43490}, {40, 46934}, {69, 10541}, {76, 54921}, {84, 35595}, {95, 35510}, {110, 13347}, {141, 55684}, {144, 27385}, {145, 6684}, {146, 38795}, {147, 38751}, {148, 38740}, {152, 38775}, {153, 38763}, {165, 5550}, {182, 20080}, {183, 32840}, {193, 53093}, {216, 61307}, {323, 37514}, {325, 32873}, {371, 43314}, {372, 43315}, {385, 55819}, {389, 33884}, {390, 5433}, {395, 42479}, {396, 42478}, {397, 43332}, {398, 43333}, {485, 60311}, {486, 60312}, {515, 46932}, {551, 58245}, {575, 10519}, {578, 46865}, {590, 43511}, {599, 51139}, {615, 43512}, {620, 5984}, {944, 31666}, {950, 31188}, {1001, 44846}, {1078, 32831}, {1125, 20070}, {1131, 8253}, {1132, 8252}, {1151, 13941}, {1152, 8972}, {1153, 53141}, {1285, 31467}, {1352, 55681}, {1385, 3621}, {1588, 9543}, {1742, 28257}, {1975, 32872}, {1992, 50984}, {2975, 27525}, {2979, 16625}, {3019, 24936}, {3068, 6426}, {3069, 6425}, {3218, 61122}, {3219, 37526}, {3241, 9588}, {3303, 5281}, {3304, 5218}, {3329, 55797}, {3346, 55982}, {3448, 15020}, {3576, 3617}, {3589, 55614}, {3590, 31414}, {3591, 60623}, {3592, 7586}, {3594, 7585}, {3600, 5432}, {3616, 7991}, {3618, 21167}, {3619, 53094}, {3620, 5085}, {3622, 7982}, {3623, 5657}, {3624, 9778}, {3634, 58221}, {3653, 51088}, {3679, 51086}, {3697, 33574}, {3746, 14986}, {3785, 7917}, {3819, 10574}, {3828, 58225}, {3876, 11227}, {3917, 15012}, {3951, 11407}, {3984, 5744}, {4297, 19877}, {4300, 27625}, {4313, 31231}, {4678, 26446}, {5007, 14930}, {5013, 37689}, {5092, 5921}, {5158, 36413}, {5204, 5261}, {5206, 31404}, {5217, 5274}, {5225, 7294}, {5229, 5326}, {5237, 42092}, {5238, 42089}, {5286, 31652}, {5334, 5352}, {5335, 5351}, {5343, 42489}, {5344, 42488}, {5349, 42611}, {5350, 42610}, {5355, 53096}, {5365, 42434}, {5366, 42433}, {5418, 6454}, {5420, 6453}, {5435, 11518}, {5439, 33575}, {5447, 15045}, {5462, 54041}, {5476, 55617}, {5480, 55641}, {5493, 51075}, {5569, 14023}, {5587, 46930}, {5609, 38728}, {5640, 13348}, {5650, 12111}, {5690, 20014}, {5704, 30282}, {5731, 31423}, {5818, 17502}, {5881, 38068}, {5888, 11440}, {5907, 44299}, {5972, 15021}, {6036, 20094}, {6053, 15054}, {6193, 20191}, {6194, 61132}, {6225, 61680}, {6243, 11592}, {6409, 32786}, {6410, 32785}, {6411, 42561}, {6412, 31412}, {6419, 13935}, {6420, 9540}, {6427, 35255}, {6428, 35256}, {6445, 13993}, {6446, 13925}, {6447, 7582}, {6448, 7581}, {6449, 13939}, {6450, 13886}, {6455, 23273}, {6456, 23267}, {6459, 43880}, {6460, 43879}, {6480, 43431}, {6481, 43430}, {6496, 18762}, {6497, 18538}, {6519, 7584}, {6522, 7583}, {6560, 42604}, {6561, 42605}, {6564, 43519}, {6565, 43520}, {6696, 35260}, {6699, 14683}, {6712, 20096}, {6713, 20095}, {6723, 15044}, {6776, 55687}, {7607, 60635}, {7616, 40925}, {7622, 7758}, {7735, 22332}, {7736, 22331}, {7738, 44535}, {7752, 32898}, {7763, 10513}, {7767, 32895}, {7771, 32829}, {7782, 32838}, {7786, 44434}, {7793, 52770}, {7856, 51237}, {7967, 20052}, {7987, 9780}, {7998, 9729}, {8567, 58434}, {8859, 55812}, {8976, 43316}, {8981, 43510}, {9143, 15057}, {9545, 13336}, {9589, 19883}, {9624, 34632}, {9692, 35813}, {9779, 12512}, {9786, 21766}, {9812, 16192}, {10168, 54174}, {10171, 10248}, {10192, 58795}, {10222, 59417}, {10529, 34486}, {10590, 59319}, {10591, 59325}, {10625, 16981}, {10979, 61314}, {11002, 15028}, {11003, 37515}, {11004, 36752}, {11008, 55703}, {11160, 50983}, {11185, 32897}, {11381, 15082}, {11444, 16836}, {11477, 51171}, {11488, 36843}, {11489, 36836}, {11591, 61136}, {11623, 52695}, {11668, 38259}, {11793, 20791}, {11801, 15042}, {12243, 38628}, {12278, 44862}, {12317, 15039}, {13334, 20081}, {13340, 16982}, {13367, 58378}, {13411, 21454}, {13464, 31425}, {13607, 20054}, {13846, 17852}, {13951, 43317}, {13966, 43509}, {14094, 38793}, {14389, 40911}, {14561, 55631}, {14810, 42785}, {14853, 55606}, {14907, 32839}, {14927, 34573}, {14996, 36745}, {14997, 36746}, {15018, 37498}, {15023, 15059}, {15025, 16163}, {15035, 20397}, {15515, 43448}, {15589, 32841}, {15819, 32522}, {15860, 61301}, {16189, 38314}, {16241, 42998}, {16242, 42999}, {16644, 43773}, {16645, 43774}, {16881, 54047}, {16960, 42612}, {16961, 42613}, {16964, 42593}, {16965, 42592}, {17128, 51579}, {17131, 51587}, {17508, 40330}, {17811, 43605}, {18220, 37568}, {18231, 59691}, {18583, 55595}, {18845, 53108}, {19053, 41963}, {19054, 41964}, {19130, 55652}, {19872, 28164}, {20007, 59491}, {20049, 50821}, {20059, 31658}, {20099, 40556}, {20105, 49111}, {20398, 21166}, {20399, 34473}, {20400, 38693}, {20401, 38692}, {20423, 55597}, {20477, 36948}, {20992, 44849}, {21151, 61006}, {21154, 38669}, {21163, 31276}, {21850, 55620}, {22234, 38064}, {22235, 42148}, {22237, 42147}, {22330, 54173}, {22712, 55814}, {23235, 38748}, {23958, 55104}, {24206, 33750}, {25555, 55600}, {25563, 34781}, {27812, 58389}, {31399, 50864}, {31401, 35007}, {31406, 46453}, {31447, 50810}, {31670, 55644}, {32137, 55320}, {32142, 40280}, {32814, 45508}, {32815, 32870}, {32816, 32871}, {32817, 32882}, {32824, 32874}, {33416, 42159}, {33417, 42162}, {33650, 38787}, {33748, 48876}, {33813, 35369}, {35010, 60912}, {37501, 37680}, {37638, 53050}, {37640, 42490}, {37641, 42491}, {38022, 50809}, {38066, 50833}, {38079, 50966}, {38083, 50819}, {38110, 55724}, {38136, 55648}, {38317, 55647}, {38664, 38737}, {38665, 38760}, {38666, 38772}, {38667, 38784}, {38675, 38804}, {38739, 51524}, {38750, 51523}, {38762, 51529}, {38774, 51528}, {38786, 51534}, {38794, 51522}, {39874, 55682}, {40107, 50961}, {40680, 52712}, {40693, 42800}, {40694, 42799}, {41100, 43252}, {41101, 43253}, {41112, 42979}, {41113, 42978}, {41150, 58242}, {41462, 46730}, {41971, 42980}, {41972, 42981}, {42085, 42904}, {42086, 42905}, {42087, 42477}, {42088, 42476}, {42104, 43325}, {42105, 43324}, {42115, 42982}, {42116, 42983}, {42119, 42599}, {42120, 42598}, {42125, 42591}, {42128, 42590}, {42129, 52079}, {42132, 52080}, {42133, 42580}, {42134, 42581}, {42153, 42501}, {42154, 42948}, {42155, 42949}, {42156, 42500}, {42163, 43466}, {42164, 43028}, {42165, 43029}, {42166, 43465}, {42431, 42596}, {42432, 42597}, {42492, 42962}, {42493, 42963}, {42494, 43193}, {42495, 43194}, {42528, 42921}, {42529, 42920}, {42537, 43786}, {42538, 43785}, {42566, 43382}, {42567, 43383}, {42629, 43467}, {42630, 43468}, {42633, 43494}, {42634, 43493}, {42786, 55666}, {42934, 43200}, {42935, 43199}, {42936, 43403}, {42937, 43404}, {42950, 43631}, {42951, 43630}, {42958, 61719}, {42992, 49875}, {42993, 49876}, {43242, 43328}, {43243, 43329}, {43292, 43642}, {43293, 43641}, {43440, 43553}, {43441, 43552}, {43469, 43473}, {43470, 43474}, {43537, 60628}, {43540, 43769}, {43541, 43770}, {43584, 46728}, {43621, 55659}, {43681, 54644}, {43951, 60644}, {46264, 55677}, {46931, 59387}, {47586, 60277}, {48872, 51127}, {48873, 55650}, {49826, 54593}, {49827, 54594}, {50804, 51084}, {50825, 61286}, {50967, 55718}, {50977, 55704}, {50980, 51174}, {51028, 55583}, {51069, 61252}, {51085, 61289}, {51126, 51538}, {51128, 59411}, {51132, 53858}, {51212, 55626}, {53099, 60648}, {54132, 55588}, {54522, 60647}, {54645, 60145}, {55637, 58445}, {56059, 60147}, {58223, 61258}, {60118, 60238}, {60210, 60336}, {60335, 60639}

X(61820) = reflection of X(i) in X(j) for these {i,j}: {15722, 549}, {3854, 7486}, {7486, 3533}
X(61820) = inverse of X(61914) in orthocentroidal circle
X(61820) = inverse of X(61914) in Yff hyperbola
X(61820) = complement of X(3854)
X(61820) = anticomplement of X(7486)
X(61820) = pole of line {523, 61914} with respect to the orthocentroidal circle
X(61820) = pole of line {185, 62097} with respect to the Jerabek hyperbola
X(61820) = pole of line {6, 61914} with respect to the Kiepert hyperbola
X(61820) = pole of line {3, 58470} with respect to the Stammler hyperbola
X(61820) = pole of line {523, 61914} with respect to the Yff hyperbola
X(61820) = pole of line {69, 5068} with respect to the Wallace hyperbola
X(61820) = intersection, other than A, B, C, of circumconics {{A, B, C, X(5), X(35510)}}, {{A, B, C, X(25), X(54921)}}, {{A, B, C, X(68), X(3858)}}, {{A, B, C, X(69), X(5068)}}, {{A, B, C, X(95), X(3146)}}, {{A, B, C, X(253), X(15022)}}, {{A, B, C, X(549), X(3346)}}, {{A, B, C, X(1217), X(5054)}}, {{A, B, C, X(1585), X(60311)}}, {{A, B, C, X(1586), X(60312)}}, {{A, B, C, X(3431), X(47486)}}, {{A, B, C, X(3526), X(46921)}}, {{A, B, C, X(3545), X(15319)}}, {{A, B, C, X(3830), X(46412)}}, {{A, B, C, X(3839), X(15077)}}, {{A, B, C, X(3860), X(43970)}}, {{A, B, C, X(3861), X(32533)}}, {{A, B, C, X(5055), X(22270)}}, {{A, B, C, X(5481), X(9909)}}, {{A, B, C, X(6617), X(55982)}}, {{A, B, C, X(11668), X(38282)}}, {{A, B, C, X(12811), X(18855)}}, {{A, B, C, X(13472), X(52294)}}, {{A, B, C, X(14893), X(54923)}}, {{A, B, C, X(15703), X(22268)}}, {{A, B, C, X(15704), X(60007)}}, {{A, B, C, X(15717), X(36948)}}, {{A, B, C, X(15722), X(18317)}}, {{A, B, C, X(15740), X(49135)}}, {{A, B, C, X(16251), X(49136)}}, {{A, B, C, X(17538), X(40448)}}, {{A, B, C, X(17578), X(31371)}}, {{A, B, C, X(33703), X(60618)}}, {{A, B, C, X(35018), X(42021)}}, {{A, B, C, X(38335), X(54552)}}, {{A, B, C, X(52282), X(60635)}}, {{A, B, C, X(52299), X(53108)}}
X(61820) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15705, 15683}, {2, 15717, 3522}, {2, 17578, 5056}, {2, 3, 3146}, {2, 3523, 15717}, {2, 3854, 7486}, {2, 5056, 13735}, {3, 140, 3090}, {3, 14869, 3525}, {3, 15694, 5072}, {3, 15720, 12108}, {3, 1656, 15704}, {3, 1995, 16661}, {3, 3525, 3091}, {3, 3526, 546}, {3, 3628, 3529}, {3, 5, 17538}, {3, 5072, 550}, {3, 5076, 548}, {3, 5079, 12103}, {3, 631, 10303}, {3, 632, 4}, {4, 15708, 17533}, {4, 15710, 15696}, {4, 3090, 12811}, {4, 631, 5054}, {20, 15682, 5059}, {20, 15721, 140}, {30, 549, 15722}, {30, 7486, 3854}, {140, 12100, 3861}, {140, 12101, 16239}, {140, 12811, 632}, {140, 15701, 631}, {140, 15712, 5073}, {140, 3524, 20}, {140, 3530, 8703}, {140, 631, 15721}, {140, 8703, 5070}, {376, 3524, 15716}, {549, 11812, 15707}, {549, 5054, 15719}, {550, 15694, 5067}, {631, 15720, 15708}, {631, 3525, 14869}, {632, 7486, 16864}, {1656, 12100, 3528}, {1657, 16239, 5071}, {3090, 11541, 381}, {3091, 16454, 17573}, {3523, 11812, 17578}, {3523, 15692, 3530}, {3523, 5056, 15712}, {3524, 15682, 14891}, {3524, 15702, 15682}, {3524, 15709, 15689}, {3524, 8703, 15692}, {3525, 3529, 3628}, {3526, 5073, 15699}, {3528, 15709, 1656}, {3530, 14869, 5079}, {3530, 15681, 10299}, {3530, 15719, 3523}, {3545, 10303, 16370}, {4297, 19877, 54448}, {5054, 11540, 15702}, {5054, 15681, 11540}, {5054, 15693, 15681}, {5054, 15718, 3860}, {5055, 15704, 1012}, {5055, 15715, 15697}, {5076, 6913, 3855}, {5650, 17704, 12111}, {5731, 31423, 46933}, {6684, 54445, 145}, {7288, 52793, 5281}, {7987, 58441, 9780}, {8252, 42638, 1132}, {8253, 42637, 1131}, {8703, 10303, 16858}, {10124, 15706, 11001}, {10299, 15702, 5}, {10299, 17538, 3}, {10303, 13168, 5084}, {10303, 15717, 15022}, {10304, 15702, 2}, {11541, 17697, 5068}, {11812, 15707, 376}, {11812, 15712, 3526}, {12100, 15709, 3543}, {12103, 12811, 3627}, {12512, 34595, 9779}, {14093, 17559, 3832}, {14782, 14783, 15694}, {14784, 14785, 3858}, {14890, 15711, 15703}, {14891, 15682, 10304}, {14891, 15693, 3524}, {15020, 38729, 3448}, {15028, 15644, 11002}, {15693, 17678, 15705}, {15694, 15698, 3839}, {15700, 15713, 3545}, {15701, 15716, 11812}, {15702, 15704, 16866}, {15708, 15721, 15701}, {16192, 19862, 9812}, {16239, 17504, 1657}, {16417, 17571, 16861}, {34573, 55673, 14927}, {37640, 42490, 43479}, {37641, 42491, 43480}, {38729, 48378, 15020}, {42115, 43463, 42982}, {42116, 43464, 42983}, {42433, 42911, 5366}, {42434, 42910, 5365}, {42490, 42944, 37640}, {42491, 42945, 37641}, {43883, 43884, 6}, {51126, 55651, 51538}

X(61821) = X(2)X(3)∩X(590)X(6487)

Barycentrics    18*a^4+5*(b^2-c^2)^2-23*a^2*(b^2+c^2) : :
X(61821) = 15*X[2]+13*X[3], 5*X[141]+9*X[55685], X[575]+6*X[50984], -9*X[1385]+2*X[61290], 5*X[3589]+2*X[55612], 10*X[4746]+39*X[31662], 15*X[4816]+13*X[37727], -3*X[5102]+10*X[51732], 5*X[5480]+9*X[55640], 5*X[5690]+9*X[30392], -X[5882]+15*X[51084], 3*X[5892]+4*X[11592] and many others

X(61821) lies on these lines: {2, 3}, {141, 55685}, {397, 43199}, {398, 43200}, {575, 50984}, {590, 6487}, {615, 6486}, {1385, 61290}, {3411, 42945}, {3412, 42944}, {3564, 55691}, {3589, 55612}, {3624, 28216}, {4746, 31662}, {4816, 37727}, {5102, 51732}, {5210, 31417}, {5351, 42500}, {5352, 42501}, {5418, 6430}, {5420, 6429}, {5433, 51817}, {5480, 55640}, {5690, 30392}, {5844, 9588}, {5882, 51084}, {5892, 11592}, {6419, 43887}, {6420, 43888}, {6453, 43212}, {6454, 43211}, {6456, 31414}, {6480, 7584}, {6481, 7583}, {6482, 52047}, {6483, 52048}, {6484, 13993}, {6485, 13925}, {6684, 61286}, {6696, 46265}, {7749, 15602}, {8550, 51137}, {9624, 28212}, {9680, 13966}, {9693, 18510}, {9706, 13339}, {9729, 44324}, {10139, 43431}, {10140, 43430}, {10165, 11278}, {10172, 58219}, {10182, 61540}, {10187, 42632}, {10188, 42631}, {10541, 50988}, {10645, 43634}, {10646, 43635}, {11231, 61255}, {11362, 61597}, {11531, 38028}, {11695, 54044}, {11801, 48375}, {13348, 13451}, {13392, 38728}, {13393, 15034}, {13624, 61249}, {15057, 22250}, {15082, 45958}, {15178, 50829}, {15644, 58533}, {16200, 51700}, {16267, 42793}, {16268, 42794}, {16836, 31834}, {16964, 43102}, {16965, 43103}, {17502, 31399}, {18583, 55594}, {20379, 48378}, {20582, 55679}, {21167, 55587}, {21843, 31492}, {21850, 55618}, {22165, 55694}, {28190, 51073}, {28224, 31423}, {30389, 50833}, {31454, 35256}, {31666, 38068}, {33179, 61524}, {33416, 42890}, {33417, 42891}, {33749, 50983}, {34380, 55711}, {34754, 43198}, {34755, 43197}, {34773, 61248}, {35255, 35771}, {35812, 41962}, {35813, 41961}, {36836, 42497}, {36843, 42496}, {38079, 55614}, {38110, 55722}, {38735, 61600}, {38746, 61599}, {38758, 61605}, {38770, 61604}, {38792, 61598}, {39561, 61624}, {40107, 55695}, {41947, 41957}, {41948, 41958}, {41977, 42913}, {41978, 42912}, {42090, 42611}, {42091, 42610}, {42099, 43638}, {42100, 43643}, {42122, 42489}, {42123, 42488}, {42130, 42493}, {42131, 42492}, {42143, 42434}, {42146, 42433}, {42147, 42628}, {42148, 42627}, {42157, 42591}, {42158, 42590}, {42163, 43245}, {42166, 43244}, {42692, 43468}, {42693, 43467}, {42946, 43774}, {42947, 43773}, {42948, 43417}, {42949, 43416}, {43177, 61596}, {47354, 55675}, {48310, 55637}, {48876, 55703}, {50978, 55701}, {51127, 55657}, {51128, 55669}, {55166, 55320}, {55636, 58445}, {55688, 61545}, {58231, 61289}, {58237, 61280}

X(61821) = midpoint of X(i) and X(j) for these {i,j}: {5, 3528}, {549, 15701}, {3523, 14869}, {51128, 55669}
X(61821) = reflection of X(i) in X(j) for these {i,j}: {140, 14869}, {15702, 11812}, {3851, 3628}, {3853, 3832}, {5066, 15703}
X(61821) = complement of X(3857)
X(61821) = pole of line {185, 62098} with respect to the Jerabek hyperbola
X(61821) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(3858), X(43970)}}, {{A, B, C, X(6662), X(46936)}}, {{A, B, C, X(11001), X(60007)}}, {{A, B, C, X(14863), X(35018)}}, {{A, B, C, X(15318), X(55857)}}
X(61821) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17800, 5}, {3, 11539, 3850}, {3, 15720, 15708}, {3, 15723, 4}, {3, 16239, 3853}, {3, 1656, 11001}, {3, 3526, 3832}, {3, 3533, 3845}, {3, 5054, 3533}, {3, 5056, 15686}, {3, 5059, 8703}, {5, 17578, 3856}, {5, 17800, 3861}, {5, 550, 17578}, {20, 3628, 3859}, {20, 631, 5054}, {30, 11812, 15702}, {30, 15703, 5066}, {30, 3628, 3851}, {140, 12100, 546}, {140, 12103, 2}, {140, 12812, 10124}, {140, 3530, 548}, {140, 3853, 16239}, {140, 5066, 632}, {382, 15695, 20}, {382, 3526, 15703}, {547, 12101, 3545}, {547, 3845, 14892}, {549, 11539, 15719}, {549, 14869, 3523}, {549, 15708, 11812}, {549, 15713, 15707}, {549, 15720, 12108}, {549, 17504, 15722}, {549, 631, 3530}, {550, 12812, 12101}, {631, 15680, 15685}, {632, 15686, 5056}, {632, 15712, 15695}, {3090, 17566, 5055}, {3090, 3523, 15700}, {3090, 3525, 16857}, {3091, 10303, 16370}, {3522, 15699, 12102}, {3523, 14869, 30}, {3523, 15701, 14869}, {3523, 15702, 3}, {3523, 3851, 15712}, {3526, 15701, 631}, {3533, 3845, 3628}, {3627, 10299, 15759}, {3832, 15702, 3526}, {3850, 16239, 5067}, {3856, 10124, 5070}, {3856, 5070, 12812}, {5054, 15693, 15684}, {10124, 10303, 140}, {10165, 31447, 61278}, {10299, 15694, 3627}, {10303, 15693, 550}, {11539, 15690, 547}, {11540, 17504, 14893}, {11812, 15719, 15690}, {12101, 15693, 12100}, {15702, 15708, 15701}, {15707, 15713, 14891}, {15709, 15711, 11737}, {15721, 15722, 17504}, {15721, 17504, 11540}

X(61822) = X(2)X(3)∩X(6)X(43493)

Barycentrics    25*a^4+7*(b^2-c^2)^2-32*a^2*(b^2+c^2) : :
X(61822) = 7*X[2]+6*X[3], 3*X[40]+10*X[51109], 7*X[69]+32*X[55696], 12*X[182]+X[50992], X[944]+12*X[38068], 6*X[1699]+7*X[50813], -7*X[1992]+20*X[55710], -25*X[3567]+64*X[40284], 9*X[3576]+4*X[4745], 35*X[3618]+4*X[55585], 12*X[3653]+X[12245], -X[3654]+14*X[51088] and many others

X(61822) lies on these lines: {2, 3}, {6, 43493}, {15, 49861}, {16, 49862}, {40, 51109}, {69, 55696}, {182, 50992}, {183, 32896}, {485, 42524}, {486, 42525}, {618, 33615}, {619, 33614}, {944, 38068}, {1699, 50813}, {1992, 55710}, {3567, 40284}, {3576, 4745}, {3618, 55585}, {3653, 12245}, {3654, 51088}, {3655, 51068}, {3828, 61256}, {4669, 61296}, {4677, 7967}, {4995, 8162}, {5050, 50980}, {5085, 50991}, {5218, 37602}, {5237, 49903}, {5238, 49904}, {5334, 33605}, {5335, 33604}, {5365, 43444}, {5366, 43445}, {5476, 50966}, {5657, 50817}, {5862, 13083}, {5863, 13084}, {6361, 19883}, {6409, 42607}, {6410, 42606}, {6411, 53520}, {6412, 53517}, {6459, 43255}, {6460, 43254}, {6468, 13847}, {6469, 13846}, {6470, 42568}, {6471, 42569}, {6684, 51093}, {6770, 36767}, {6771, 35750}, {6774, 36331}, {6776, 50993}, {7581, 52046}, {7582, 52045}, {7612, 60627}, {7619, 47102}, {7622, 55823}, {7709, 14711}, {7805, 55816}, {7880, 55732}, {7982, 41150}, {7987, 38074}, {8252, 43257}, {8253, 43256}, {8550, 51189}, {8556, 60143}, {8584, 10519}, {8591, 26614}, {8972, 52048}, {9167, 9862}, {9300, 46453}, {9541, 14226}, {9588, 51097}, {9693, 58866}, {10155, 60284}, {10165, 11224}, {10168, 55720}, {10246, 50825}, {10541, 50989}, {10595, 51110}, {10645, 41120}, {10646, 41119}, {10653, 43004}, {10654, 43005}, {11057, 34803}, {11179, 50994}, {11180, 51143}, {11455, 55166}, {11477, 41153}, {11480, 43543}, {11481, 43542}, {11488, 42506}, {11489, 42507}, {11693, 15057}, {12243, 38748}, {13199, 38069}, {13941, 52047}, {14561, 55630}, {14651, 15300}, {14912, 15533}, {15482, 55178}, {15516, 38064}, {15520, 51141}, {16241, 42505}, {16242, 42504}, {16644, 49875}, {16645, 49876}, {17502, 50864}, {17508, 51023}, {18581, 43645}, {18582, 43646}, {19877, 28208}, {20070, 38022}, {20423, 55596}, {21156, 36768}, {21166, 36523}, {21167, 50970}, {21168, 60963}, {21356, 55689}, {21358, 39874}, {21849, 54041}, {22236, 56612}, {22238, 56613}, {23267, 42418}, {23269, 34089}, {23273, 42417}, {23275, 34091}, {23302, 43481}, {23303, 43482}, {26446, 50818}, {30392, 50827}, {31145, 61292}, {31423, 34627}, {31658, 60971}, {31662, 50804}, {32785, 53131}, {32786, 53130}, {32787, 43510}, {32788, 43509}, {32817, 32892}, {32822, 32885}, {33416, 42632}, {33417, 42631}, {33602, 42155}, {33603, 42154}, {33606, 42513}, {33607, 42512}, {33622, 49106}, {33624, 49105}, {33748, 50978}, {33750, 47354}, {34631, 51103}, {34718, 61281}, {35260, 46265}, {36836, 43100}, {36843, 43107}, {36996, 38067}, {37515, 43572}, {37690, 40344}, {37712, 51705}, {38079, 61044}, {38110, 54174}, {38664, 41151}, {38739, 52695}, {41100, 42092}, {41101, 42089}, {41121, 42120}, {41122, 42119}, {42126, 43247}, {42127, 43246}, {42258, 43506}, {42259, 43505}, {42274, 43796}, {42277, 43795}, {42588, 49907}, {42589, 49908}, {42602, 42637}, {42603, 42638}, {42910, 44016}, {42911, 44015}, {42942, 49873}, {42943, 49874}, {42974, 43870}, {42975, 43869}, {43174, 51106}, {43244, 43771}, {43245, 43772}, {43374, 43386}, {43375, 43387}, {43403, 52080}, {43404, 52079}, {46933, 61253}, {47353, 51135}, {50571, 60150}, {50809, 51709}, {50811, 58441}, {50815, 54447}, {50819, 58221}, {50821, 54445}, {50832, 59503}, {50833, 61614}, {50959, 55654}, {50961, 55695}, {50967, 51185}, {50969, 53023}, {50974, 50990}, {50975, 55673}, {50977, 55706}, {50982, 55703}, {51186, 51737}, {51212, 55625}, {53103, 54637}, {53620, 61244}, {54170, 55608}, {54523, 54616}, {54612, 60183}, {55635, 58445}, {55716, 59373}, {59417, 61280}, {60127, 60616}, {60307, 60315}, {60308, 60316}

X(61822) = inverse of X(61913) in orthocentroidal circle
X(61822) = inverse of X(61913) in Yff hyperbola
X(61822) = complement of X(61958)
X(61822) = anticomplement of X(61901)
X(61822) = pole of line {523, 61913} with respect to the orthocentroidal circle
X(61822) = pole of line {6, 43536} with respect to the Kiepert hyperbola
X(61822) = pole of line {523, 61913} with respect to the Yff hyperbola
X(61822) = pole of line {69, 19709} with respect to the Wallace hyperbola
X(61822) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(19709)}}, {{A, B, C, X(95), X(15682)}}, {{A, B, C, X(3533), X(52441)}}, {{A, B, C, X(3627), X(46412)}}, {{A, B, C, X(3854), X(54763)}}, {{A, B, C, X(5059), X(54660)}}, {{A, B, C, X(7408), X(54612)}}, {{A, B, C, X(7409), X(54707)}}, {{A, B, C, X(10109), X(36889)}}, {{A, B, C, X(12100), X(36948)}}, {{A, B, C, X(12812), X(22270)}}, {{A, B, C, X(14269), X(43699)}}, {{A, B, C, X(14491), X(18535)}}, {{A, B, C, X(15715), X(18852)}}, {{A, B, C, X(15719), X(57895)}}, {{A, B, C, X(15740), X(49134)}}, {{A, B, C, X(17578), X(54667)}}, {{A, B, C, X(37174), X(60627)}}, {{A, B, C, X(41106), X(57822)}}, {{A, B, C, X(50689), X(54838)}}, {{A, B, C, X(50690), X(60122)}}, {{A, B, C, X(52301), X(60185)}}
X(61822) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15682, 5071}, {2, 15692, 3534}, {2, 15693, 15698}, {2, 15701, 631}, {2, 15708, 15701}, {2, 15713, 15709}, {2, 15721, 15713}, {2, 3, 15682}, {2, 3523, 12100}, {2, 3543, 10109}, {2, 549, 15719}, {3, 10124, 3839}, {3, 140, 7486}, {3, 15691, 10304}, {3, 15699, 15683}, {3, 3526, 3858}, {3, 5054, 10124}, {4, 3524, 15715}, {5, 15718, 15705}, {140, 12100, 3860}, {140, 15707, 15692}, {140, 549, 15707}, {381, 15717, 15710}, {547, 15706, 3522}, {549, 12100, 15722}, {549, 15720, 15708}, {550, 14890, 15723}, {631, 10299, 10303}, {631, 15709, 15721}, {631, 3533, 14869}, {1657, 5054, 15694}, {3146, 3839, 15687}, {3522, 11540, 6832}, {3523, 15705, 15718}, {3523, 3854, 15712}, {3524, 11541, 14891}, {3524, 15702, 4}, {3524, 5071, 3}, {3530, 3845, 15716}, {3533, 15717, 17538}, {3534, 3860, 3146}, {3545, 15692, 3528}, {5054, 15693, 3830}, {5054, 15703, 140}, {5054, 15718, 5}, {5068, 7486, 5079}, {10109, 15695, 3543}, {10109, 17504, 15695}, {10124, 15687, 15703}, {10124, 15709, 3525}, {10299, 10303, 5067}, {10304, 15694, 3090}, {10304, 17578, 15691}, {10304, 17677, 3850}, {11001, 11812, 15702}, {11539, 15700, 20}, {11540, 15711, 381}, {11812, 15693, 2}, {11812, 15719, 11001}, {12100, 14893, 15759}, {12100, 15722, 3523}, {13741, 15681, 3545}, {14869, 15711, 11540}, {14869, 15717, 3533}, {15683, 15699, 3855}, {15692, 15703, 376}, {15693, 15698, 3524}, {15693, 15701, 11812}, {15693, 15713, 15697}, {15694, 15716, 3845}, {15698, 15709, 5066}, {15698, 15719, 15693}, {15701, 15722, 5054}, {15714, 16239, 14269}, {42502, 42508, 5335}, {42502, 42792, 42508}, {42503, 42509, 5334}, {42503, 42791, 42509}, {43493, 43494, 6}

X(61823) = X(2)X(3)∩X(13)X(43873)

Barycentrics    38*a^4+11*(b^2-c^2)^2-49*a^2*(b^2+c^2) : :
X(61823) = 11*X[2]+9*X[3], -11*X[597]+X[55723], 11*X[3589]+4*X[55609], -6*X[3653]+X[61597], 3*X[5050]+7*X[50981], 3*X[5092]+2*X[51143], 11*X[5476]+9*X[55613], 9*X[6684]+X[51091], -11*X[8584]+21*X[55712], -2*X[9143]+7*X[22250], -6*X[9167]+X[61599], 3*X[10165]+7*X[51088] and many others

X(61823) lies on these lines: {2, 3}, {13, 43873}, {14, 43874}, {395, 42419}, {396, 42420}, {524, 55702}, {597, 55723}, {952, 51067}, {3564, 51137}, {3589, 55609}, {3653, 61597}, {5050, 50981}, {5092, 51143}, {5476, 55613}, {5844, 50825}, {5965, 50983}, {6200, 43317}, {6396, 43316}, {6411, 43385}, {6412, 43384}, {6435, 35255}, {6436, 35256}, {6455, 42527}, {6456, 42526}, {6684, 51091}, {8584, 55712}, {9143, 22250}, {9167, 61599}, {10165, 51088}, {10168, 41153}, {10246, 50826}, {10653, 42518}, {10654, 42519}, {11480, 42513}, {11481, 42512}, {11488, 43207}, {11489, 43208}, {11542, 42931}, {11543, 42930}, {12017, 50990}, {13624, 51069}, {14641, 55320}, {15300, 26614}, {16772, 42533}, {16773, 42532}, {16960, 42800}, {16961, 42799}, {16966, 43330}, {16967, 43331}, {18583, 55592}, {21167, 55589}, {23267, 60622}, {23273, 60623}, {23302, 43109}, {23303, 43108}, {26446, 50833}, {28234, 50829}, {28236, 51086}, {30392, 50830}, {33748, 51183}, {34380, 50980}, {36521, 61560}, {36836, 49810}, {36843, 49811}, {38064, 61624}, {38067, 61596}, {38068, 61510}, {38069, 61601}, {41100, 42777}, {41101, 42778}, {41107, 42500}, {41108, 42501}, {41112, 43328}, {41113, 43329}, {41121, 43103}, {41122, 43102}, {41149, 55709}, {41943, 42505}, {41944, 42504}, {42089, 43333}, {42092, 43332}, {42122, 42902}, {42123, 42903}, {42143, 46335}, {42146, 46334}, {42496, 42510}, {42497, 42511}, {42506, 42924}, {42507, 42925}, {42520, 42912}, {42521, 42913}, {42528, 42683}, {42529, 42682}, {42590, 42973}, {42591, 42972}, {42643, 43887}, {42644, 43888}, {42936, 43635}, {42937, 43634}, {42940, 43241}, {42941, 43240}, {43028, 43247}, {43029, 43246}, {43197, 49947}, {43198, 49948}, {43489, 54593}, {43490, 54594}, {48876, 51187}, {48906, 51186}, {50815, 61262}, {50823, 54445}, {50828, 61614}, {50977, 55707}, {50979, 51188}, {50984, 55713}, {50985, 55703}, {50988, 51189}, {51022, 55667}, {51103, 61524}, {51130, 55627}, {51141, 55717}, {54044, 58470}, {54169, 55581}, {54644, 60216}, {54645, 60283}, {54734, 60238}, {54851, 60277}

X(61823) = midpoint of X(i) and X(j) for these {i,j}: {2, 15711}, {5, 14093}, {376, 3858}, {549, 631}, {632, 15692}, {1656, 15714}, {3845, 15697}, {5076, 15686}, {15693, 15713}, {15694, 15712}
X(61823) = reflection of X(i) in X(j) for these {i,j}: {1656, 10124}, {12100, 15693}, {15691, 3522}, {15692, 3530}, {15695, 15759}, {15713, 11812}, {3859, 547}, {546, 5071}, {547, 632}, {548, 15714}
X(61823) = complement of X(61956)
X(61823) = pole of line {6, 54593} with respect to the Kiepert hyperbola
X(61823) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(33699)}}, {{A, B, C, X(41991), X(43970)}}, {{A, B, C, X(44580), X(57895)}}
X(61823) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15693, 15711}, {2, 15698, 15685}, {2, 8703, 3860}, {3, 3526, 3854}, {5, 15721, 14890}, {5, 549, 15707}, {30, 10124, 1656}, {30, 11812, 15713}, {30, 15714, 548}, {30, 15759, 15695}, {30, 3522, 15691}, {30, 3530, 15692}, {30, 547, 3859}, {140, 15690, 2}, {140, 3530, 12103}, {140, 3859, 632}, {376, 16239, 14892}, {549, 11539, 3523}, {549, 14869, 3524}, {549, 15701, 11812}, {549, 15708, 12108}, {549, 5054, 3530}, {549, 8703, 15719}, {631, 1656, 14869}, {632, 12103, 12812}, {632, 15712, 15696}, {1656, 15697, 3845}, {3523, 11539, 14891}, {3524, 15702, 3855}, {3525, 13168, 3090}, {3525, 15706, 15687}, {3530, 11540, 8703}, {3530, 11812, 11540}, {3533, 6962, 5079}, {3845, 15714, 15697}, {3845, 8703, 15681}, {5054, 15696, 15694}, {5054, 15710, 11539}, {10109, 14893, 5066}, {10124, 15681, 547}, {10303, 15700, 15699}, {11114, 15708, 15709}, {11539, 14891, 546}, {11540, 11812, 5054}, {11540, 15719, 12100}, {11812, 12100, 140}, {11812, 12108, 15701}, {11812, 15722, 12101}, {12100, 12101, 15759}, {12101, 15759, 15690}, {15681, 15692, 15714}, {15692, 15719, 15693}, {15693, 15701, 631}, {15693, 15713, 30}, {15697, 15713, 10124}, {15702, 17504, 3628}, {15705, 15723, 3627}, {15707, 15721, 5}, {15708, 15720, 549}, {15709, 15718, 550}

X(61824) = X(2)X(3)∩X(15)X(43427)

Barycentrics    16*a^4+5*(b^2-c^2)^2-21*a^2*(b^2+c^2) : :
X(61824) = 15*X[2]+11*X[3], 4*X[40]+9*X[61273], 5*X[141]+8*X[55688], X[576]+12*X[50984], -5*X[1353]+18*X[55703], 11*X[1385]+2*X[4701], -5*X[1483]+18*X[30392], -5*X[3244]+18*X[58234], 12*X[3576]+X[61245], 10*X[3589]+3*X[55603], 6*X[3653]+7*X[50826], 5*X[5480]+8*X[55636] and many others

X(61824) lies on these lines: {2, 3}, {15, 43427}, {16, 43426}, {17, 42931}, {18, 42930}, {40, 61273}, {141, 55688}, {395, 43009}, {396, 43008}, {496, 51817}, {576, 50984}, {590, 6485}, {615, 6484}, {1353, 55703}, {1385, 4701}, {1483, 30392}, {3244, 58234}, {3311, 43413}, {3312, 43414}, {3576, 61245}, {3589, 55603}, {3653, 50826}, {5008, 31406}, {5237, 42500}, {5238, 42501}, {5254, 15602}, {5339, 43102}, {5340, 43103}, {5418, 6438}, {5420, 6437}, {5480, 55636}, {5882, 31662}, {6247, 46265}, {6409, 10194}, {6410, 10195}, {6425, 43212}, {6426, 43211}, {6429, 7584}, {6430, 7583}, {6431, 35255}, {6432, 35256}, {6480, 58866}, {6481, 8960}, {6486, 42215}, {6487, 42216}, {6699, 22251}, {7780, 12040}, {7987, 38138}, {8550, 55695}, {8589, 12815}, {8976, 43411}, {8981, 41964}, {10137, 18510}, {10138, 18512}, {10141, 52047}, {10142, 52048}, {10165, 33179}, {10187, 42163}, {10188, 42166}, {10222, 50829}, {10283, 11531}, {10619, 21357}, {10645, 42948}, {10646, 42949}, {11278, 38028}, {11362, 50825}, {11592, 13421}, {11694, 15057}, {13382, 15067}, {13393, 32609}, {13624, 38155}, {13951, 43412}, {13966, 41963}, {14561, 55622}, {14862, 23328}, {16192, 61269}, {16200, 61524}, {16772, 42634}, {16773, 42633}, {16808, 43469}, {16809, 43470}, {16964, 42961}, {16965, 42960}, {18439, 33879}, {18581, 43423}, {18582, 43422}, {18583, 55591}, {20190, 50988}, {20582, 55681}, {21167, 25555}, {21850, 55612}, {22165, 55698}, {22712, 55809}, {23302, 41974}, {23303, 41973}, {25563, 44762}, {26446, 61295}, {28178, 34595}, {30389, 61297}, {31423, 37705}, {34507, 55691}, {34754, 42121}, {34755, 42124}, {34773, 58441}, {36836, 43333}, {36843, 43332}, {37515, 40111}, {37517, 38110}, {37727, 50832}, {37832, 42891}, {37835, 42890}, {38022, 51120}, {38064, 50981}, {38068, 50833}, {38079, 51166}, {38081, 50871}, {38083, 50868}, {38136, 55645}, {38317, 55642}, {38725, 48378}, {41955, 43410}, {41956, 43409}, {42085, 42493}, {42086, 42492}, {42087, 42906}, {42088, 42907}, {42089, 42773}, {42092, 42774}, {42117, 42937}, {42118, 42936}, {42144, 42908}, {42145, 42909}, {42147, 42978}, {42148, 42979}, {42153, 43421}, {42154, 42591}, {42155, 42590}, {42156, 43420}, {42157, 42970}, {42158, 42971}, {42490, 42913}, {42491, 42912}, {42557, 43341}, {42558, 43340}, {42596, 43330}, {42597, 43331}, {42598, 43548}, {42599, 43549}, {42602, 43885}, {42603, 43886}, {42629, 43443}, {42630, 43442}, {42684, 43486}, {42685, 43485}, {42777, 42947}, {42778, 42946}, {42793, 42992}, {42794, 42993}, {42797, 42955}, {42798, 42954}, {42799, 42959}, {42800, 42958}, {42916, 42998}, {42917, 42999}, {42918, 43325}, {42919, 43324}, {42990, 43107}, {42991, 43100}, {43028, 43630}, {43029, 43631}, {43384, 43432}, {43385, 43433}, {43403, 43635}, {43404, 43634}, {43430, 43524}, {43431, 43523}, {47354, 55677}, {48310, 55631}, {48874, 55640}, {48876, 50664}, {48906, 55685}, {50978, 53093}, {51127, 55655}, {51128, 55670}, {55627, 58445}, {55722, 59399}, {58221, 61259}, {58227, 61246}, {58231, 61292}, {58241, 61277}

X(61824) = midpoint of X(i) and X(j) for these {i,j}: {3, 5067}
X(61824) = complement of X(61953)
X(61824) = pole of line {185, 41981} with respect to the Jerabek hyperbola
X(61824) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(3853)}}, {{A, B, C, X(1105), X(41981)}}, {{A, B, C, X(3519), X(5066)}}, {{A, B, C, X(3533), X(46921)}}, {{A, B, C, X(3859), X(43970)}}, {{A, B, C, X(5059), X(60007)}}, {{A, B, C, X(6662), X(15703)}}, {{A, B, C, X(7486), X(42021)}}, {{A, B, C, X(12812), X(60171)}}, {{A, B, C, X(15686), X(40448)}}, {{A, B, C, X(26861), X(55859)}}, {{A, B, C, X(34567), X(52294)}}, {{A, B, C, X(44880), X(57713)}}
X(61824) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15696, 12811}, {2, 3, 3853}, {3, 15702, 16239}, {3, 15719, 3530}, {3, 15723, 3832}, {3, 16239, 3845}, {3, 1656, 5059}, {3, 3526, 3545}, {3, 3543, 548}, {3, 3832, 15690}, {3, 5, 15686}, {3, 5067, 30}, {3, 631, 11812}, {4, 12811, 3858}, {4, 3522, 15681}, {4, 3851, 3860}, {5, 14869, 15713}, {5, 15714, 15704}, {140, 12108, 15720}, {140, 15712, 5}, {140, 3523, 550}, {140, 3530, 4}, {140, 3850, 3533}, {140, 549, 15712}, {547, 11812, 5054}, {548, 3525, 15699}, {549, 15699, 15693}, {549, 15711, 15707}, {549, 15713, 17504}, {549, 5054, 8703}, {549, 550, 3523}, {549, 631, 14869}, {550, 3858, 5073}, {631, 15701, 12108}, {1656, 5059, 3850}, {3523, 10303, 5068}, {3523, 5068, 10299}, {3526, 12100, 3627}, {3526, 15640, 3628}, {3530, 11540, 12103}, {3530, 12103, 15692}, {3530, 5054, 632}, {3533, 5059, 1656}, {3858, 15712, 15714}, {5054, 15692, 11540}, {5054, 15719, 547}, {7486, 15688, 12102}, {8703, 15704, 15696}, {10124, 15707, 15711}, {11001, 15717, 3}, {11540, 12103, 5070}, {11812, 15708, 549}, {13741, 15709, 3526}, {14813, 14814, 5066}, {14869, 15712, 140}, {15686, 15713, 11539}, {15694, 15717, 546}, {15703, 17538, 3856}, {15709, 15722, 14891}, {42089, 42773, 42925}, {42092, 42774, 42924}

X(61825) = X(2)X(3)∩X(182)X(51178)

Barycentrics    35*a^4+11*(b^2-c^2)^2-46*a^2*(b^2+c^2) : :
X(61825) = 11*X[2]+8*X[3], -20*X[182]+X[51178], -X[944]+20*X[51084], -5*X[3617]+24*X[38068], -5*X[3623]+24*X[3653], -28*X[3828]+9*X[61254], 15*X[5032]+4*X[50973], 11*X[5476]+8*X[55609], -20*X[6684]+X[50817], -X[6776]+20*X[51137], 5*X[9778]+14*X[61271], 14*X[10164]+5*X[61274] and many others

X(61825) lies on these lines: {2, 3}, {182, 51178}, {944, 51084}, {3617, 38068}, {3623, 3653}, {3828, 61254}, {5032, 50973}, {5351, 49825}, {5352, 49824}, {5476, 55609}, {6409, 41951}, {6410, 41952}, {6459, 42573}, {6460, 42572}, {6494, 13966}, {6495, 8981}, {6496, 43506}, {6497, 43505}, {6684, 50817}, {6776, 51137}, {7809, 32871}, {9541, 42557}, {9778, 61271}, {10164, 61274}, {10168, 55717}, {10519, 55713}, {10541, 50990}, {12245, 50825}, {14075, 14930}, {14561, 55621}, {14853, 55599}, {16644, 43870}, {16645, 43869}, {19875, 51086}, {19876, 54448}, {20049, 61287}, {20052, 38066}, {20080, 55702}, {20423, 55592}, {21356, 51136}, {21358, 51139}, {25055, 50814}, {30389, 51072}, {31145, 38127}, {31400, 34571}, {32787, 42569}, {32788, 42568}, {32884, 48913}, {32898, 43459}, {33416, 43645}, {33417, 43646}, {34631, 61280}, {36836, 43237}, {36843, 43236}, {37624, 50826}, {37712, 58441}, {38064, 51170}, {38067, 61006}, {38314, 50829}, {41107, 43495}, {41108, 43496}, {41945, 42567}, {41946, 42566}, {42506, 42958}, {42507, 42959}, {42625, 42693}, {42626, 42692}, {42803, 42987}, {42804, 42986}, {42898, 43238}, {42899, 43239}, {42936, 49874}, {42937, 49873}, {42944, 49813}, {42945, 49812}, {43002, 43194}, {43003, 43193}, {43006, 43295}, {43007, 43294}, {43028, 43541}, {43029, 43540}, {43228, 43479}, {43229, 43480}, {43507, 43799}, {43508, 43800}, {46267, 50967}, {46932, 61256}, {46933, 51705}, {47352, 50970}, {50810, 61277}, {50821, 61284}, {50828, 61296}, {50872, 51088}, {50956, 55669}, {50977, 55709}, {50981, 53091}, {50984, 59373}, {50988, 51215}, {51028, 51141}, {51130, 55622}, {51143, 55684}, {54132, 55586}, {54173, 55715}, {54174, 55723}, {59417, 61279}

X(61825) = reflection of X(i) in X(j) for these {i,j}: {15022, 2}
X(61825) = complement of X(61952)
X(61825) = pole of line {69, 61930} with respect to the Wallace hyperbola
X(61825) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(50687)}}, {{A, B, C, X(1494), X(15022)}}, {{A, B, C, X(5073), X(46412)}}, {{A, B, C, X(15705), X(36948)}}, {{A, B, C, X(16251), X(35400)}}
X(61825) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10304, 3832}, {2, 15692, 15683}, {2, 15694, 17678}, {2, 15705, 3146}, {2, 17578, 5055}, {2, 30, 15022}, {2, 3523, 15705}, {2, 3524, 3522}, {5, 11812, 5054}, {5, 12108, 15720}, {140, 10304, 2}, {140, 15700, 5071}, {140, 15719, 10304}, {140, 549, 15700}, {376, 15702, 10124}, {376, 15718, 15692}, {376, 3525, 15703}, {376, 5071, 3830}, {547, 15693, 15715}, {547, 549, 15693}, {549, 14891, 15707}, {549, 15700, 15719}, {549, 631, 15721}, {631, 15701, 15708}, {631, 3524, 11812}, {632, 15706, 15682}, {1656, 15710, 15640}, {3090, 17504, 15697}, {3146, 13735, 5068}, {3146, 3523, 15717}, {3522, 3832, 3529}, {3523, 10303, 5}, {3523, 15692, 15718}, {3523, 3839, 12100}, {3524, 11812, 10303}, {3524, 15694, 3543}, {3524, 15709, 14269}, {3524, 15722, 3523}, {3524, 3529, 15711}, {3524, 3533, 3534}, {3525, 12100, 3839}, {3543, 10303, 15694}, {3830, 5054, 140}, {5054, 12100, 3525}, {5054, 15701, 12108}, {5054, 15720, 15722}, {6943, 7486, 3855}, {10124, 15718, 376}, {11539, 15698, 3091}, {11540, 15688, 5067}, {11812, 15720, 3524}, {14869, 15693, 15709}, {14891, 15713, 15723}, {14891, 15723, 4}, {15692, 15721, 15702}, {15693, 15709, 20}, {15694, 15720, 549}, {15702, 15719, 15686}, {15707, 15723, 14891}, {15709, 15715, 547}, {15717, 16418, 5059}

X(61826) = X(2)X(3)∩X(1385)X(4816)

Barycentrics    19*a^4+6*(b^2-c^2)^2-25*a^2*(b^2+c^2) : :
X(61826) = 18*X[2]+13*X[3], 9*X[599]+22*X[55694], 26*X[1385]+5*X[4816], -18*X[3241]+49*X[58235], 24*X[3589]+7*X[55602], 15*X[3763]+16*X[55679], -8*X[4746]+39*X[26446], X[5881]+30*X[51084], 24*X[6699]+7*X[15039], 28*X[9588]+3*X[50805], 9*X[10516]+22*X[55675], 28*X[10541]+3*X[11898] and many others

X(61826) lies on these lines: {2, 3}, {599, 55694}, {1385, 4816}, {3070, 43513}, {3071, 43514}, {3241, 58235}, {3589, 55602}, {3592, 35814}, {3594, 35815}, {3763, 55679}, {4746, 26446}, {5339, 42593}, {5340, 42592}, {5418, 6448}, {5420, 6447}, {5881, 51084}, {6221, 43431}, {6398, 43430}, {6455, 53516}, {6456, 53513}, {6488, 35823}, {6489, 35822}, {6500, 43883}, {6501, 43884}, {6519, 18510}, {6522, 18512}, {6699, 15039}, {7894, 55813}, {8960, 17852}, {9541, 43341}, {9588, 50805}, {9681, 43569}, {9690, 13993}, {9691, 13941}, {10516, 55675}, {10541, 11898}, {11480, 42894}, {11481, 42895}, {11935, 37471}, {12007, 55701}, {12645, 30389}, {13607, 59503}, {13623, 43691}, {13665, 43338}, {13785, 43339}, {13925, 43415}, {14692, 38737}, {14848, 51141}, {15023, 20304}, {15028, 16982}, {15040, 20397}, {15069, 51137}, {16644, 42935}, {16645, 42934}, {17810, 33542}, {17851, 43374}, {18440, 55681}, {21167, 55595}, {22234, 50962}, {22236, 43031}, {22238, 43030}, {31423, 31666}, {31447, 58245}, {31467, 35007}, {31652, 44535}, {36836, 42818}, {36843, 42817}, {38066, 51085}, {38627, 41134}, {41977, 43232}, {41978, 43233}, {42089, 42687}, {42092, 42686}, {42125, 42964}, {42128, 42965}, {42153, 43025}, {42156, 43024}, {42159, 42688}, {42162, 42689}, {42270, 43337}, {42273, 43336}, {42494, 42984}, {42495, 42985}, {42528, 42610}, {42529, 42611}, {42596, 43443}, {42597, 43442}, {42598, 42685}, {42599, 42684}, {42773, 42975}, {42774, 42974}, {43150, 55687}, {43495, 43554}, {43496, 43555}, {47352, 55588}, {47355, 55637}, {51087, 58232}, {51126, 55648}, {51140, 55704}, {53023, 55652}, {54131, 55628}, {54891, 60278}, {55626, 58445}, {58224, 59387}

X(61826) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(5076)}}, {{A, B, C, X(5056), X(34483)}}, {{A, B, C, X(5059), X(13623)}}, {{A, B, C, X(13596), X(43691)}}, {{A, B, C, X(15640), X(46412)}}, {{A, B, C, X(35478), X(43713)}}, {{A, B, C, X(49137), X(60007)}}
X(61826) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3, 5076}, {3, 12108, 15720}, {3, 15694, 3090}, {3, 15701, 12108}, {3, 3090, 1657}, {3, 3525, 5079}, {3, 3526, 5072}, {3, 3851, 17538}, {3, 5055, 15704}, {3, 5070, 3146}, {3, 5072, 3534}, {3, 546, 15696}, {3, 632, 381}, {4, 15717, 15759}, {140, 12102, 632}, {140, 15693, 382}, {140, 15717, 5055}, {140, 17504, 5067}, {140, 3530, 3845}, {140, 382, 15723}, {140, 5055, 3526}, {140, 549, 15717}, {381, 11812, 5054}, {381, 1657, 17578}, {382, 5054, 140}, {548, 549, 3523}, {549, 11540, 3524}, {549, 14869, 3628}, {549, 14890, 15698}, {549, 15698, 15707}, {549, 5055, 15693}, {631, 3523, 11812}, {1657, 3530, 15716}, {3090, 16434, 4}, {3091, 3529, 12102}, {3523, 10303, 15022}, {3523, 15709, 548}, {3523, 5067, 17504}, {3524, 11540, 15684}, {3526, 15696, 7486}, {3526, 15720, 549}, {3526, 3534, 1656}, {3529, 5067, 3091}, {3534, 5079, 2050}, {3628, 12103, 3857}, {3628, 14869, 10303}, {5054, 15716, 15694}, {5070, 15722, 15712}, {10299, 11539, 3843}, {10303, 15022, 15709}, {11541, 15704, 17800}, {12100, 17538, 3}, {12102, 15704, 15640}, {15678, 15708, 5071}, {15692, 16239, 5073}, {15698, 15721, 14890}, {15702, 15712, 5070}, {15702, 15722, 15688}

X(61827) = X(1)X(50825)∩X(2)X(3)

Barycentrics    22*a^4+7*(b^2-c^2)^2-29*a^2*(b^2+c^2) : :
X(61827) = X[1]+5*X[50825], 7*X[2]+5*X[3], X[6]+5*X[50980], X[8]+5*X[50832], X[10]+5*X[51084], X[69]+5*X[50987], X[141]+5*X[51137], X[145]+5*X[50822], X[193]+5*X[51184], -7*X[597]+X[55720], 5*X[1385]+X[34641], X[3244]+5*X[50821] and many others

X(61827) lies on these lines: {1, 50825}, {2, 3}, {6, 50980}, {8, 50832}, {10, 51084}, {15, 43100}, {16, 43107}, {69, 50987}, {141, 51137}, {145, 50822}, {193, 51184}, {395, 43007}, {396, 43006}, {397, 42947}, {398, 42946}, {519, 61614}, {524, 55706}, {542, 55686}, {597, 55720}, {952, 38068}, {1385, 34641}, {3244, 50821}, {3564, 55693}, {3589, 55601}, {3626, 50828}, {3629, 50977}, {3631, 50983}, {3632, 50824}, {3636, 50829}, {3644, 51048}, {3653, 5844}, {3654, 51700}, {3655, 50833}, {4681, 51049}, {4686, 51045}, {5092, 51139}, {5298, 37602}, {5351, 43109}, {5352, 43108}, {5476, 55608}, {5480, 55635}, {5690, 34747}, {5843, 38067}, {6329, 10168}, {6459, 42640}, {6460, 42639}, {6470, 13966}, {6471, 8981}, {6684, 61597}, {6699, 11694}, {10193, 61606}, {11008, 50978}, {11179, 50988}, {11224, 38028}, {11480, 42415}, {11481, 42416}, {11542, 42500}, {11543, 42501}, {11592, 14449}, {11693, 22250}, {12820, 42110}, {12821, 42107}, {13339, 43572}, {13392, 20126}, {13451, 54044}, {13624, 51086}, {13925, 52048}, {13993, 52047}, {15170, 52793}, {15178, 51095}, {15516, 20583}, {15808, 51088}, {16241, 43197}, {16242, 43198}, {16772, 43018}, {16773, 43019}, {16962, 42636}, {16963, 42635}, {18583, 55590}, {19872, 50799}, {19875, 28224}, {19883, 28174}, {19924, 55638}, {20050, 50823}, {20054, 50831}, {20057, 34718}, {20080, 51180}, {20190, 50991}, {21167, 55596}, {23302, 43418}, {23303, 43419}, {26446, 61294}, {26614, 38748}, {28186, 38083}, {28190, 38076}, {28202, 61269}, {28204, 58441}, {28212, 38022}, {28216, 38021}, {31253, 58219}, {31414, 42526}, {33416, 43105}, {33417, 43106}, {34380, 38064}, {35021, 61561}, {35022, 61560}, {35023, 61566}, {35024, 61565}, {35255, 42643}, {35256, 42644}, {36431, 59649}, {38066, 54445}, {38627, 41151}, {40341, 50979}, {41121, 42949}, {41122, 42948}, {41150, 58240}, {41153, 55718}, {41943, 42944}, {41944, 42945}, {42089, 42497}, {42092, 42496}, {42108, 42595}, {42109, 42594}, {42122, 42972}, {42123, 42973}, {42130, 43202}, {42131, 43201}, {42147, 42798}, {42148, 42797}, {42160, 43247}, {42161, 43246}, {42215, 43255}, {42216, 43254}, {42225, 42642}, {42226, 42641}, {42419, 42899}, {42420, 42898}, {42476, 42625}, {42477, 42626}, {42502, 42979}, {42503, 42978}, {42506, 42612}, {42507, 42613}, {42510, 42774}, {42511, 42773}, {42524, 53513}, {42525, 53516}, {42590, 49907}, {42591, 49908}, {42598, 43485}, {42599, 43486}, {42686, 42781}, {42687, 42782}, {42786, 51022}, {42932, 42987}, {42933, 42986}, {42938, 43229}, {42939, 43228}, {42942, 43102}, {42943, 43103}, {43211, 52046}, {43212, 52045}, {46932, 50797}, {48310, 55630}, {48879, 51129}, {48943, 51131}, {50664, 50982}, {50808, 61272}, {50959, 55653}, {50961, 55699}, {50972, 55661}, {50986, 55705}, {50992, 55701}, {51023, 55678}, {51069, 61249}, {51072, 61297}, {51085, 61292}, {51136, 55691}, {51141, 54169}, {51732, 54173}, {55625, 58445}, {55690, 61545}

X(61827) = midpoint of X(i) and X(j) for these {i,j}: {2, 17504}, {3, 15699}, {5, 10304}, {549, 5054}, {550, 14269}, {3524, 11539}, {3545, 8703}, {3845, 15689}, {26614, 38748}
X(61827) = reflection of X(i) in X(j) for these {i,j}: {140, 5054}, {10304, 14891}, {11539, 14890}, {14269, 11737}, {14893, 3545}, {15690, 10304}, {15699, 10124}, {17504, 3530}, {3545, 3628}, {5054, 11812}, {5066, 15699}
X(61827) = complement of X(38071)
X(61827) = pole of line {69, 61928} with respect to the Wallace hyperbola
X(61827) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(15687)}}, {{A, B, C, X(265), X(41987)}}, {{A, B, C, X(1494), X(47478)}}, {{A, B, C, X(3530), X(57895)}}, {{A, B, C, X(3851), X(57822)}}, {{A, B, C, X(3857), X(43970)}}, {{A, B, C, X(6662), X(46935)}}, {{A, B, C, X(11737), X(57894)}}, {{A, B, C, X(15715), X(36948)}}, {{A, B, C, X(18317), X(41983)}}, {{A, B, C, X(33703), X(46412)}}, {{A, B, C, X(49138), X(60007)}}
X(61827) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11106, 17677}, {2, 15692, 3529}, {2, 15710, 14269}, {2, 15715, 382}, {2, 17504, 30}, {2, 17576, 17679}, {2, 3, 15687}, {2, 3523, 15715}, {2, 3524, 15688}, {2, 376, 3851}, {2, 550, 11737}, {3, 10124, 5066}, {3, 15683, 8703}, {3, 15709, 15699}, {3, 3526, 5068}, {3, 381, 15697}, {4, 15718, 15711}, {5, 15693, 14891}, {5, 549, 15693}, {30, 14890, 11539}, {30, 14891, 10304}, {30, 3545, 14893}, {140, 12812, 3526}, {140, 3524, 14892}, {140, 3530, 546}, {140, 3853, 632}, {140, 5066, 10124}, {140, 549, 12100}, {376, 10109, 3853}, {376, 15702, 17678}, {376, 632, 10109}, {381, 15712, 15759}, {381, 15719, 15712}, {547, 12100, 548}, {547, 548, 12101}, {549, 15701, 12108}, {549, 15712, 15719}, {549, 631, 11812}, {549, 8703, 3523}, {631, 15720, 14869}, {1656, 15686, 3860}, {1656, 15698, 15686}, {3523, 3545, 15706}, {3524, 15709, 3839}, {3526, 15692, 3845}, {3526, 15722, 15692}, {3530, 12108, 15720}, {3530, 16239, 3528}, {3830, 15717, 15714}, {3832, 15721, 6853}, {3858, 15713, 15694}, {5054, 15701, 15708}, {5054, 15720, 15707}, {5066, 14893, 3858}, {5066, 15690, 15682}, {8703, 15694, 3628}, {10124, 15691, 547}, {10124, 15713, 140}, {10299, 15702, 2}, {10303, 15712, 16239}, {10303, 15719, 381}, {11540, 14891, 5}, {11540, 15693, 15690}, {11812, 12108, 549}, {12100, 15691, 3}, {12103, 15697, 15691}, {14269, 15700, 15710}, {14269, 15707, 15700}, {14269, 15710, 550}, {14869, 15687, 15713}, {14869, 15688, 14890}, {14869, 15720, 3530}, {15681, 15693, 10299}, {15682, 15713, 11540}, {15682, 17538, 15683}, {15688, 15707, 3524}, {15693, 15694, 17538}, {15694, 15706, 3545}, {15697, 15721, 10303}, {15698, 16417, 15681}, {15699, 15713, 15709}, {15700, 15710, 17504}, {15702, 15719, 5059}, {15709, 15721, 5054}, {15712, 16239, 12103}

X(61828) = X(2)X(3)∩X(182)X(50989)

Barycentrics    41*a^4+14*(b^2-c^2)^2-55*a^2*(b^2+c^2) : :
X(61828) = 14*X[2]+9*X[3], 18*X[182]+5*X[50989], 7*X[599]+16*X[55696], -9*X[1351]+32*X[41153], -9*X[1482]+32*X[41150], -27*X[3653]+4*X[51091], 9*X[3654]+14*X[51106], 15*X[5050]+8*X[50982], 3*X[5093]+20*X[50980], 3*X[5790]+20*X[51084], -9*X[6321]+32*X[41148], 18*X[6684]+5*X[51104] and many others

X(61828) lies on circumconic {{A, B, C, X(46412), X(49140)}} and on these lines: {2, 3}, {182, 50989}, {590, 43525}, {599, 55696}, {615, 43526}, {1351, 41153}, {1482, 41150}, {3653, 51091}, {3654, 51106}, {5050, 50982}, {5093, 50980}, {5790, 51084}, {6321, 41148}, {6468, 18510}, {6469, 18512}, {6470, 35814}, {6471, 35815}, {6684, 51104}, {10165, 50805}, {10246, 50827}, {10247, 50825}, {11480, 43545}, {11481, 43544}, {11898, 41152}, {12017, 50991}, {12188, 41151}, {12355, 41154}, {12645, 38068}, {12702, 51109}, {13607, 38066}, {13665, 42524}, {13785, 42525}, {15534, 55710}, {18526, 51066}, {20049, 58233}, {26446, 51085}, {33416, 42795}, {33417, 42796}, {33606, 42816}, {33607, 42815}, {33614, 33620}, {33615, 33621}, {36836, 49904}, {36843, 49903}, {38064, 41149}, {39593, 44535}, {39899, 50993}, {41100, 42996}, {41101, 42997}, {41107, 43304}, {41108, 43305}, {42104, 42595}, {42105, 42594}, {42122, 42985}, {42123, 42984}, {42126, 43468}, {42127, 43467}, {42417, 43343}, {42418, 43342}, {42419, 49861}, {42420, 49862}, {42433, 43443}, {42434, 43442}, {42490, 42976}, {42491, 42977}, {42500, 42510}, {42501, 42511}, {42631, 43029}, {42632, 43028}, {42688, 42951}, {42689, 42950}, {42690, 42942}, {42691, 42943}, {42773, 42934}, {42774, 42935}, {43102, 49873}, {43103, 49874}, {43150, 51186}, {43294, 49906}, {43295, 49905}, {43372, 44017}, {43373, 44018}, {43382, 43881}, {43383, 43882}, {43430, 52046}, {43431, 52045}, {43483, 49947}, {43484, 49948}, {43513, 53131}, {43514, 53130}, {47352, 55585}, {47355, 55634}, {49828, 49959}, {49829, 49960}, {50797, 51086}, {50798, 58441}, {50816, 61266}, {50821, 51097}, {50828, 51067}, {50832, 51515}, {50954, 51139}, {50983, 51142}, {50984, 51172}, {50992, 55705}, {51087, 59503}, {51137, 55686}, {51138, 51175}, {51140, 51188}, {51141, 55596}, {51185, 55716}, {54131, 55625}, {54608, 60131}, {54643, 60645}, {60175, 60638}, {60192, 60287}, {60297, 60313}, {60298, 60314}

X(61828) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12100, 15685}, {2, 15719, 15711}, {2, 15722, 15716}, {2, 3524, 15690}, {3, 15694, 15699}, {3, 5055, 15683}, {3, 5066, 3534}, {4, 10304, 15686}, {140, 15711, 2}, {140, 15719, 3830}, {140, 5072, 3526}, {140, 549, 10304}, {549, 11540, 15698}, {549, 14869, 14890}, {549, 14890, 4}, {549, 15702, 15684}, {549, 15713, 5066}, {549, 3628, 3524}, {631, 11812, 15701}, {1656, 5054, 15702}, {1657, 15701, 13632}, {1657, 3526, 3628}, {3524, 15723, 1657}, {3526, 15706, 381}, {3529, 15707, 15700}, {3529, 5071, 3839}, {3534, 15693, 15706}, {3534, 15716, 15759}, {5054, 15700, 140}, {5054, 15708, 15688}, {5055, 15684, 3857}, {7486, 15709, 10124}, {10303, 15683, 15709}, {10303, 15698, 11540}, {11539, 15718, 382}, {11540, 15698, 5055}, {11737, 12100, 8703}, {11737, 15702, 15694}, {11812, 12100, 14869}, {11812, 15701, 5054}, {11812, 15713, 15721}, {12100, 15697, 3}, {12100, 15699, 15697}, {12108, 15702, 15707}, {15684, 15707, 15717}, {15686, 15688, 15696}, {15688, 15693, 12100}, {15693, 15701, 15720}, {15700, 15719, 15693}, {15702, 15707, 1656}, {15706, 15720, 549}

X(61829) = X(2)X(3)∩X(6)X(42892)

Barycentrics    23*a^4+8*(b^2-c^2)^2-31*a^2*(b^2+c^2) : :
X(61829) = 8*X[2]+5*X[3], -X[40]+14*X[51088], 4*X[599]+9*X[55697], 4*X[671]+9*X[38635], -X[944]+14*X[50833], 12*X[1153]+X[8716], -X[1350]+14*X[51141], -3*X[1351]+16*X[46267], X[3241]+12*X[61614], -2*X[3244]+15*X[3653], -40*X[3616]+X[58247], -2*X[3626]+15*X[38068] and many others

X(61829) lies on these lines: {2, 3}, {6, 42892}, {40, 51088}, {590, 43415}, {599, 55697}, {615, 9690}, {671, 38635}, {944, 50833}, {1153, 8716}, {1350, 51141}, {1351, 46267}, {3241, 61614}, {3244, 3653}, {3616, 58247}, {3626, 38068}, {3629, 38064}, {3632, 38066}, {3636, 3654}, {3655, 58441}, {3679, 58230}, {5093, 10168}, {5215, 47618}, {5476, 55604}, {6054, 38634}, {6329, 54173}, {6445, 35823}, {6446, 35822}, {6474, 7584}, {6475, 7583}, {6776, 50988}, {7585, 42644}, {7586, 42643}, {7767, 32887}, {8724, 35021}, {9140, 38638}, {10145, 52047}, {10146, 52048}, {10165, 34718}, {10246, 34747}, {10706, 38633}, {10707, 38636}, {10711, 38637}, {10718, 38639}, {11178, 55682}, {11480, 43419}, {11481, 43418}, {11485, 41944}, {11486, 41943}, {11488, 43111}, {11489, 43110}, {11632, 35022}, {12245, 50826}, {12820, 42097}, {12821, 42096}, {13188, 26614}, {14810, 50963}, {15178, 51094}, {15533, 55701}, {16267, 42947}, {16268, 42946}, {16962, 42491}, {16963, 42490}, {17502, 19876}, {17851, 18512}, {19872, 58220}, {19875, 51084}, {20050, 58233}, {20190, 50993}, {21358, 51137}, {22247, 38743}, {25561, 55673}, {26446, 34641}, {28202, 34595}, {31423, 50798}, {31663, 50806}, {33749, 50989}, {37624, 50821}, {38028, 58238}, {38065, 60933}, {38067, 60942}, {38072, 55639}, {38098, 50828}, {38314, 50825}, {38737, 48657}, {38794, 56567}, {40341, 55705}, {40912, 44201}, {41100, 42774}, {41101, 42773}, {41119, 42949}, {41120, 42948}, {41121, 43485}, {41122, 43486}, {41945, 45385}, {41946, 45384}, {41951, 53130}, {41952, 53131}, {42125, 42985}, {42128, 42984}, {42492, 43487}, {42493, 43488}, {42500, 42974}, {42501, 42975}, {42504, 42991}, {42505, 42990}, {42625, 42629}, {42626, 42630}, {42635, 42938}, {42636, 42939}, {42779, 49905}, {42780, 49906}, {42894, 43305}, {42895, 43304}, {42898, 42944}, {42899, 42945}, {42918, 51945}, {42919, 51944}, {42988, 43107}, {42989, 43100}, {43002, 43247}, {43003, 43246}, {43006, 43372}, {43007, 43373}, {43020, 61719}, {43209, 43515}, {43210, 43516}, {47352, 55584}, {47353, 55678}, {47355, 55632}, {48662, 51139}, {50819, 61259}, {50955, 55692}, {50976, 55666}, {50977, 53091}, {50980, 59373}, {51024, 55648}, {51174, 55711}, {51187, 55708}, {51515, 54445}, {54131, 55624}, {55616, 58445}

X(61829) = midpoint of X(i) and X(j) for these {i,j}: {2, 10299}
X(61829) = reflection of X(i) in X(j) for these {i,j}: {5079, 2}
X(61829) = inverse of X(61909) in orthocentroidal circle
X(61829) = inverse of X(61909) in Yff hyperbola
X(61829) = complement of X(61947)
X(61829) = pole of line {523, 61909} with respect to the orthocentroidal circle
X(61829) = pole of line {6, 61909} with respect to the Kiepert hyperbola
X(61829) = pole of line {523, 61909} with respect to the Yff hyperbola
X(61829) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(14269)}}, {{A, B, C, X(1494), X(5079)}}, {{A, B, C, X(3845), X(46168)}}, {{A, B, C, X(5055), X(57897)}}, {{A, B, C, X(5059), X(46412)}}, {{A, B, C, X(11737), X(57822)}}, {{A, B, C, X(15700), X(57895)}}, {{A, B, C, X(15710), X(36948)}}, {{A, B, C, X(47478), X(57823)}}, {{A, B, C, X(49134), X(60007)}}
X(61829) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10299, 30}, {2, 10304, 3855}, {2, 14869, 5054}, {2, 15688, 3851}, {2, 15710, 546}, {2, 15715, 15687}, {2, 15720, 15707}, {2, 3, 14269}, {2, 30, 5079}, {2, 3523, 15710}, {2, 3524, 550}, {2, 3544, 15699}, {2, 376, 11737}, {3, 15694, 15703}, {3, 5055, 15685}, {5, 15706, 15695}, {5, 15719, 15706}, {140, 15693, 5055}, {140, 15708, 15693}, {140, 15723, 15694}, {140, 17504, 2}, {140, 3091, 3526}, {140, 376, 15723}, {376, 15759, 14093}, {376, 3543, 15704}, {381, 14093, 15683}, {381, 5054, 15702}, {381, 549, 15718}, {382, 15693, 17504}, {549, 10124, 15692}, {549, 11812, 15721}, {549, 14891, 3523}, {549, 15687, 3530}, {631, 5054, 15701}, {1656, 12100, 15689}, {3091, 3524, 15759}, {3523, 11539, 3534}, {3523, 5071, 14891}, {3524, 3526, 3830}, {3526, 14093, 547}, {3526, 5054, 15713}, {3533, 15705, 5066}, {3534, 11539, 5070}, {3830, 5055, 3091}, {3861, 15713, 15709}, {5054, 15693, 140}, {5055, 6926, 5073}, {5066, 15705, 15696}, {8703, 14890, 3525}, {10124, 15692, 381}, {11539, 14891, 5071}, {11540, 15712, 3545}, {11737, 17504, 376}, {12100, 15689, 3}, {12100, 15709, 1656}, {12108, 15713, 3524}, {14269, 15681, 15684}, {14269, 15685, 382}, {14269, 15720, 15722}, {15681, 15707, 15700}, {15687, 15688, 15681}, {15687, 15715, 15688}, {15688, 15700, 15715}, {15692, 15702, 10124}, {15694, 15701, 549}, {15698, 15699, 1657}, {15701, 15707, 15720}, {15711, 16239, 3839}, {42892, 42893, 6}

X(61830) = X(2)X(3)∩X(8)X(51085)

Barycentrics    37*a^4+13*(b^2-c^2)^2-50*a^2*(b^2+c^2) : :
X(61830) = 13*X[2]+8*X[3], 5*X[8]+16*X[51085], 5*X[69]+16*X[51138], 5*X[145]+16*X[50827], 5*X[193]+16*X[50982], 5*X[1698]+16*X[51086], 5*X[3616]+16*X[50829], 5*X[3617]+16*X[50828], 5*X[3618]+16*X[50984], 5*X[3620]+16*X[50983], 5*X[3621]+16*X[51087], 5*X[3623]+16*X[50821] and many others

X(61830) lies on these lines: {2, 3}, {8, 51085}, {69, 51138}, {145, 50827}, {193, 50982}, {590, 6440}, {615, 6439}, {1587, 43525}, {1588, 43526}, {1698, 51086}, {3590, 43378}, {3591, 43379}, {3616, 50829}, {3617, 50828}, {3618, 50984}, {3620, 50983}, {3621, 51087}, {3623, 50821}, {3763, 51139}, {4704, 51049}, {4821, 51045}, {5237, 33607}, {5238, 33606}, {5334, 43545}, {5335, 43544}, {5351, 49874}, {5352, 49873}, {5365, 42597}, {5366, 42596}, {6200, 43343}, {6396, 43342}, {6407, 43387}, {6408, 43386}, {6441, 7586}, {6442, 7585}, {6445, 43518}, {6446, 43517}, {6455, 14226}, {6456, 14241}, {6488, 43412}, {6489, 43411}, {7837, 55819}, {8972, 52046}, {9543, 35823}, {10194, 42525}, {10195, 42524}, {10256, 41136}, {10302, 60336}, {10541, 50994}, {10653, 42955}, {10654, 42954}, {11160, 12007}, {11180, 51137}, {11669, 60650}, {11693, 14683}, {12017, 51215}, {13607, 31145}, {13941, 52045}, {16226, 33884}, {16644, 42686}, {16645, 42687}, {18581, 42795}, {18582, 42796}, {19872, 50815}, {20014, 50830}, {20052, 50824}, {20080, 51140}, {30389, 51068}, {34627, 51084}, {34631, 50825}, {36967, 43468}, {36968, 43467}, {38068, 54445}, {41119, 43783}, {41120, 43784}, {42417, 43377}, {42418, 43376}, {42488, 43556}, {42489, 43557}, {42490, 43480}, {42491, 43479}, {42496, 42804}, {42497, 42803}, {42600, 43336}, {42601, 43337}, {42625, 43201}, {42626, 43202}, {42932, 42975}, {42933, 42974}, {42936, 49825}, {42937, 49824}, {42944, 49862}, {42945, 49861}, {42958, 49903}, {42959, 49904}, {43102, 43482}, {43103, 43481}, {43211, 43510}, {43212, 43509}, {43558, 60295}, {43559, 60296}, {43869, 43878}, {43870, 43877}, {46930, 50796}, {46931, 50864}, {46932, 50811}, {50813, 61268}, {50964, 55658}, {50977, 51170}, {53104, 60625}, {53620, 58441}, {54639, 60333}, {60102, 60200}, {60175, 60639}, {60239, 60331}, {60293, 60299}, {60294, 60300}

X(61830) = midpoint of X(i) and X(j) for these {i,j}: {3528, 3545}, {5054, 15701}
X(61830) = reflection of X(i) in X(j) for these {i,j}: {10304, 15698}, {15702, 5054}, {3545, 15703}, {3851, 15699}, {5054, 14869}
X(61830) = anticomplement of X(61897)
X(61830) = pole of line {69, 61927} with respect to the Wallace hyperbola
X(61830) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(5068), X(57822)}}, {{A, B, C, X(5071), X(35510)}}, {{A, B, C, X(10301), X(60336)}}, {{A, B, C, X(14861), X(35405)}}, {{A, B, C, X(15717), X(57895)}}, {{A, B, C, X(15740), X(58208)}}, {{A, B, C, X(17800), X(46412)}}
X(61830) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15683, 15022}, {2, 15692, 3146}, {2, 15717, 15683}, {2, 376, 5068}, {2, 5059, 5071}, {2, 5071, 13735}, {2, 549, 15717}, {4, 16434, 17800}, {20, 631, 17533}, {30, 15699, 3851}, {140, 15707, 3545}, {140, 15717, 13741}, {140, 3857, 3526}, {140, 549, 3534}, {547, 10299, 15697}, {547, 15722, 10299}, {548, 549, 15693}, {549, 11540, 3}, {549, 15713, 3628}, {549, 3526, 15698}, {549, 5055, 3524}, {631, 11812, 15721}, {631, 15702, 15701}, {631, 5054, 15708}, {632, 15718, 11001}, {3146, 5068, 3843}, {3524, 11539, 3839}, {3524, 15709, 5055}, {3525, 15710, 15699}, {3526, 15717, 3832}, {3526, 3528, 7486}, {3526, 3534, 15703}, {3528, 3545, 30}, {3534, 11737, 3149}, {3534, 15703, 3857}, {3545, 15707, 15692}, {5054, 15707, 140}, {5054, 15709, 10303}, {5054, 5055, 14890}, {5079, 15707, 17504}, {10303, 10304, 15709}, {10303, 15708, 10304}, {10304, 15708, 549}, {10304, 15709, 2}, {10304, 15717, 15705}, {12108, 15694, 15719}, {14869, 15701, 15702}, {15022, 15717, 3522}, {15684, 17678, 17528}, {15693, 15699, 15710}, {15694, 15719, 20}, {15699, 15710, 3543}, {15701, 15702, 3523}, {15708, 15721, 5054}, {15712, 15723, 15682}, {15713, 15720, 376}, {16370, 16371, 17543}

X(61831) = X(2)X(3)∩X(590)X(6522)

Barycentrics    17*a^4+6*(b^2-c^2)^2-23*a^2*(b^2+c^2) : :
X(61831) = 18*X[2]+11*X[3], 9*X[599]+20*X[55698], 24*X[3589]+5*X[55595], 15*X[3763]+14*X[55681], -4*X[4701]+33*X[26446], -30*X[5734]+X[58249], 9*X[5790]+20*X[31666], 4*X[6053]+25*X[38728], 16*X[6723]+13*X[15042], -36*X[10168]+7*X[53858], 9*X[10516]+20*X[55677], 17*X[11465]+12*X[54044] and many others

X(61831) lies on these lines: {2, 3}, {590, 6522}, {599, 55698}, {615, 6519}, {3589, 55595}, {3592, 13961}, {3594, 13903}, {3763, 55681}, {3933, 32891}, {4701, 26446}, {5237, 42815}, {5238, 42816}, {5351, 42132}, {5352, 42129}, {5355, 22332}, {5734, 58249}, {5790, 31666}, {6053, 38728}, {6390, 32890}, {6449, 43880}, {6450, 43879}, {6451, 43792}, {6452, 43791}, {6453, 18510}, {6454, 18512}, {6496, 32790}, {6497, 32789}, {6723, 15042}, {9543, 43518}, {9690, 13939}, {9691, 13993}, {10147, 35823}, {10148, 35822}, {10168, 53858}, {10516, 55677}, {11465, 54044}, {11592, 15028}, {13491, 33879}, {13886, 43415}, {14561, 55620}, {15027, 48378}, {15039, 38793}, {15041, 38795}, {16644, 43775}, {16645, 43776}, {18526, 31423}, {20190, 39899}, {21167, 55602}, {22331, 31467}, {22712, 55808}, {26614, 38628}, {31399, 51086}, {31425, 51088}, {31492, 41940}, {31884, 42785}, {32609, 38729}, {34754, 43206}, {34755, 43205}, {37624, 61614}, {38064, 51174}, {38068, 50804}, {38314, 58236}, {38317, 55641}, {40107, 51175}, {40280, 45187}, {40686, 46265}, {41949, 53516}, {41950, 53513}, {41971, 43012}, {41972, 43013}, {42119, 42591}, {42120, 42590}, {42130, 42580}, {42131, 42581}, {42159, 42951}, {42162, 42950}, {42260, 43790}, {42261, 43789}, {42510, 43236}, {42511, 43237}, {42557, 43339}, {42558, 43338}, {42633, 43480}, {42634, 43479}, {42892, 43019}, {42893, 43018}, {43024, 43304}, {43025, 43305}, {43558, 53517}, {43559, 53520}, {44535, 53096}, {47352, 55583}, {47355, 55631}, {47745, 58441}, {50829, 61276}, {51126, 55643}, {51141, 55600}, {51172, 55721}, {53023, 55650}, {54131, 55623}, {55614, 58445}

X(61831) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(15319), X(19709)}}, {{A, B, C, X(49136), X(60007)}}
X(61831) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3524, 15691}, {3, 15694, 3628}, {3, 3091, 3534}, {3, 3525, 1656}, {3, 3526, 5079}, {3, 3628, 382}, {3, 3851, 12103}, {3, 5055, 3529}, {3, 5079, 1657}, {3, 632, 5072}, {20, 3090, 546}, {140, 3524, 5070}, {140, 3530, 15699}, {140, 381, 3526}, {140, 549, 20}, {140, 631, 15701}, {381, 15696, 5073}, {381, 15706, 8703}, {382, 1656, 3545}, {382, 3523, 15706}, {546, 12108, 549}, {549, 10109, 3524}, {549, 16239, 10299}, {631, 10303, 12108}, {631, 5046, 15686}, {631, 5054, 15720}, {3090, 10303, 140}, {3091, 17697, 3090}, {3525, 10299, 15022}, {3525, 15022, 16239}, {3525, 9840, 3855}, {3526, 15720, 15693}, {3533, 12100, 3843}, {3534, 5054, 15702}, {3545, 15706, 15688}, {3851, 15722, 15717}, {5054, 15723, 15713}, {5070, 15685, 5068}, {6908, 15707, 15718}, {8703, 15683, 15689}, {8703, 15699, 14893}, {10299, 16239, 3830}, {10303, 12108, 3}, {10303, 15720, 5076}, {11539, 15717, 3851}, {11539, 15722, 14093}, {12108, 14869, 10303}, {12811, 15691, 3627}, {14891, 15723, 381}, {14893, 15702, 15694}, {15701, 15721, 5054}, {15707, 15713, 15723}, {15717, 16397, 15697}

X(61832) = X(2)X(3)∩X(6)X(42801)

Barycentrics    11*a^4+4*(b^2-c^2)^2-15*a^2*(b^2+c^2) : :
X(61832) = 12*X[2]+7*X[3], 8*X[141]+11*X[55692], -27*X[373]+8*X[12002], -20*X[620]+X[14692], 18*X[1153]+X[7781], 14*X[1385]+5*X[4668], 3*X[3060]+16*X[11592], 3*X[3167]+16*X[20191], 10*X[3567]+9*X[54047], 16*X[3589]+3*X[55593], -28*X[3622]+9*X[58238], 5*X[3625]+14*X[13607] and many others

X(61832) lies on these lines: {2, 3}, {6, 42801}, {17, 42115}, {18, 42116}, {61, 43484}, {62, 43483}, {69, 32889}, {141, 55692}, {373, 12002}, {397, 42686}, {398, 42687}, {590, 6408}, {615, 6407}, {620, 14692}, {1153, 7781}, {1385, 4668}, {1506, 15655}, {1587, 43415}, {1588, 9690}, {3055, 15603}, {3060, 11592}, {3167, 20191}, {3311, 35814}, {3312, 35815}, {3567, 54047}, {3589, 55593}, {3622, 58238}, {3625, 13607}, {3630, 12007}, {3633, 10246}, {3634, 58224}, {3635, 10165}, {3653, 50827}, {3763, 48662}, {4114, 11374}, {4677, 58232}, {4691, 5882}, {5024, 7755}, {5050, 6144}, {5085, 43150}, {5237, 42979}, {5238, 42978}, {5298, 31480}, {5306, 31470}, {5326, 9655}, {5339, 33416}, {5340, 33417}, {5418, 6395}, {5420, 6199}, {5476, 55602}, {5480, 55632}, {5493, 18493}, {5650, 34783}, {5876, 44299}, {6200, 43882}, {6221, 58866}, {6337, 32888}, {6390, 32877}, {6396, 43881}, {6398, 8960}, {6445, 13951}, {6446, 8976}, {6447, 13847}, {6448, 13846}, {6449, 43379}, {6450, 43378}, {6451, 10577}, {6452, 10576}, {6455, 8252}, {6456, 8253}, {6472, 13993}, {6473, 13925}, {6496, 42262}, {6497, 42265}, {6500, 9540}, {6501, 13935}, {6560, 43558}, {6561, 43559}, {6684, 10247}, {7294, 9668}, {7607, 60250}, {7608, 60649}, {7878, 51237}, {8148, 43174}, {8550, 55697}, {9681, 43343}, {9691, 18510}, {9703, 13336}, {9704, 13339}, {9781, 54044}, {10145, 13939}, {10146, 13886}, {10159, 60323}, {10168, 11482}, {10182, 14530}, {10185, 60630}, {10187, 16964}, {10188, 16965}, {10194, 13785}, {10195, 13665}, {10575, 15082}, {10595, 58247}, {10653, 42793}, {10654, 42794}, {10990, 38633}, {10991, 38634}, {10992, 38635}, {10993, 38636}, {11426, 44673}, {11455, 55286}, {11480, 41973}, {11481, 41974}, {11485, 43239}, {11486, 43238}, {11623, 38750}, {11669, 60146}, {11695, 13340}, {12006, 54048}, {12017, 34507}, {12242, 54202}, {12308, 20417}, {12316, 61659}, {12645, 54445}, {12815, 44518}, {13093, 14862}, {13188, 52886}, {13321, 13421}, {13347, 18350}, {13382, 40280}, {13393, 22251}, {13431, 32348}, {13623, 43719}, {13903, 35256}, {13961, 35255}, {14128, 33879}, {14561, 55616}, {14644, 15042}, {14848, 50984}, {14861, 44763}, {14864, 17821}, {14900, 38639}, {15026, 54041}, {15028, 54042}, {15105, 58434}, {15533, 55704}, {16241, 42436}, {16242, 42435}, {16534, 38728}, {16966, 42476}, {16967, 42477}, {17704, 18435}, {18553, 53094}, {18581, 42684}, {18582, 42685}, {19130, 55648}, {19862, 48661}, {19875, 31666}, {20053, 59503}, {20190, 50955}, {20418, 38762}, {21167, 55604}, {21309, 31401}, {21358, 55687}, {21843, 31467}, {22236, 43007}, {22238, 43006}, {22712, 55806}, {23235, 26614}, {24206, 55678}, {24844, 52885}, {25055, 31447}, {25555, 33878}, {25563, 32063}, {30714, 38638}, {31235, 38756}, {31274, 38744}, {31425, 51709}, {31658, 51514}, {31673, 58220}, {32455, 53091}, {32878, 34229}, {34483, 34564}, {36836, 42934}, {36843, 42935}, {36967, 42597}, {36968, 42596}, {36969, 42610}, {36970, 42611}, {37621, 61154}, {37705, 58228}, {37727, 38068}, {37832, 42965}, {37835, 42964}, {38064, 50982}, {38072, 55637}, {38122, 60962}, {38317, 55639}, {38724, 48378}, {38737, 52090}, {40107, 55701}, {40686, 45185}, {40693, 42500}, {40694, 42501}, {41945, 43569}, {41946, 43568}, {42089, 42945}, {42092, 42944}, {42122, 42495}, {42123, 42494}, {42129, 42150}, {42130, 42920}, {42131, 42921}, {42132, 42151}, {42143, 43770}, {42146, 43769}, {42153, 43545}, {42154, 42985}, {42155, 42984}, {42156, 43544}, {42157, 42688}, {42158, 42689}, {42215, 43412}, {42216, 43411}, {42270, 42601}, {42273, 42600}, {42488, 43424}, {42489, 43425}, {42580, 42626}, {42581, 42625}, {42627, 43870}, {42628, 43869}, {42817, 42924}, {42818, 42925}, {42894, 42980}, {42895, 42981}, {43010, 43027}, {43011, 43026}, {43014, 43023}, {43015, 43022}, {43254, 43525}, {43255, 43526}, {43376, 60293}, {43377, 60294}, {43380, 43432}, {43381, 43433}, {43467, 43491}, {43468, 43492}, {47352, 55580}, {47353, 55679}, {47355, 55629}, {50825, 61278}, {50977, 53092}, {51024, 55647}, {51069, 61248}, {51108, 58249}, {51137, 55684}, {51140, 53093}, {51141, 55606}, {53104, 60209}, {54857, 60278}, {55610, 58445}, {59380, 60976}, {59381, 60977}, {60100, 60329}, {60175, 60640}

X(61832) = inverse of X(61907) in orthocentroidal circle
X(61832) = inverse of X(61907) in Yff hyperbola
X(61832) = complement of X(61945)
X(61832) = pole of line {523, 61907} with respect to the orthocentroidal circle
X(61832) = pole of line {185, 62107} with respect to the Jerabek hyperbola
X(61832) = pole of line {6, 61907} with respect to the Kiepert hyperbola
X(61832) = pole of line {523, 61907} with respect to the Yff hyperbola
X(61832) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(3843)}}, {{A, B, C, X(428), X(60323)}}, {{A, B, C, X(3090), X(34483)}}, {{A, B, C, X(3519), X(3545)}}, {{A, B, C, X(3529), X(13623)}}, {{A, B, C, X(3533), X(26861)}}, {{A, B, C, X(5067), X(42021)}}, {{A, B, C, X(5068), X(22270)}}, {{A, B, C, X(5073), X(60007)}}, {{A, B, C, X(5079), X(60171)}}, {{A, B, C, X(7486), X(22268)}}, {{A, B, C, X(13596), X(43719)}}, {{A, B, C, X(13599), X(38071)}}, {{A, B, C, X(14528), X(47485)}}, {{A, B, C, X(14861), X(33703)}}, {{A, B, C, X(14865), X(44763)}}, {{A, B, C, X(14892), X(57822)}}, {{A, B, C, X(15681), X(40448)}}, {{A, B, C, X(15683), X(46412)}}, {{A, B, C, X(15706), X(57895)}}, {{A, B, C, X(21735), X(36948)}}, {{A, B, C, X(34484), X(43908)}}, {{A, B, C, X(35475), X(43713)}}, {{A, B, C, X(52282), X(60250)}}, {{A, B, C, X(52285), X(60329)}}
X(61832) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15684, 5055}, {2, 15706, 15684}, {2, 15712, 1657}, {2, 17538, 5}, {2, 3, 3843}, {2, 3524, 15686}, {2, 376, 14892}, {2, 549, 15706}, {2, 631, 12108}, {3, 14269, 15696}, {3, 15694, 5070}, {3, 15703, 382}, {3, 1656, 5073}, {3, 382, 15695}, {3, 5, 15681}, {3, 631, 15701}, {4, 10299, 10304}, {4, 10303, 140}, {4, 3522, 15704}, {4, 5056, 5066}, {5, 14891, 17538}, {17, 42774, 42115}, {18, 42773, 42116}, {140, 12108, 15712}, {140, 3523, 1656}, {140, 549, 4}, {140, 550, 3533}, {140, 631, 15720}, {376, 16239, 5079}, {381, 5054, 15713}, {382, 632, 15703}, {547, 3528, 5076}, {549, 10304, 15693}, {549, 11539, 15759}, {549, 15684, 15718}, {549, 3628, 15717}, {631, 15721, 14869}, {631, 3525, 15708}, {1656, 15720, 3523}, {1656, 1657, 3850}, {1656, 5073, 3851}, {2045, 2046, 3530}, {3090, 15683, 3856}, {3522, 15720, 15722}, {3523, 3533, 550}, {3526, 15700, 3857}, {3526, 5054, 10303}, {3530, 15704, 15698}, {3530, 15713, 3525}, {3628, 15709, 3526}, {3628, 15717, 3534}, {3763, 55682, 48662}, {3857, 15759, 20}, {5054, 15693, 15702}, {5054, 15706, 14890}, {5073, 15681, 5059}, {5076, 15716, 3528}, {10124, 15719, 15688}, {10303, 12108, 5072}, {10303, 15701, 17800}, {10303, 15708, 7486}, {10303, 15717, 15709}, {10304, 15702, 11540}, {10304, 17538, 548}, {11539, 14893, 2}, {11812, 14869, 631}, {11812, 15721, 5054}, {12100, 15696, 3}, {12100, 15723, 14269}, {12812, 15712, 3522}, {13632, 15723, 3524}, {14813, 14814, 3545}, {14891, 15712, 10299}, {15681, 15702, 15694}, {15681, 15718, 14891}, {15686, 15695, 15689}, {15694, 15701, 15707}, {15694, 15707, 3830}, {15696, 15723, 3090}, {15698, 15708, 549}, {15702, 15708, 15690}, {15708, 15713, 381}, {15709, 15717, 3628}, {15765, 18585, 15721}, {42089, 42945, 42989}, {42092, 42944, 42988}, {42150, 42948, 42129}, {42151, 42949, 42132}, {42801, 42802, 6}, {42958, 42992, 36843}, {42959, 42993, 36836}

X(61833) = X(2)X(3)∩X(6)X(41965)

Barycentrics    29*a^4+11*(b^2-c^2)^2-40*a^2*(b^2+c^2) : :
X(61833) = 11*X[2]+6*X[3], 11*X[69]+40*X[55702], 12*X[182]+5*X[50990], 16*X[1153]+X[9741], 12*X[1385]+5*X[51072], -11*X[1992]+28*X[55712], 9*X[3576]+8*X[51069], -55*X[3618]+4*X[55723], 8*X[4669]+9*X[7967], 5*X[4677]+12*X[13607], -4*X[4745]+21*X[31423], 15*X[5050]+2*X[50985] and many others

X(61833) lies on these lines: {2, 3}, {6, 41965}, {15, 49810}, {16, 49811}, {69, 55702}, {182, 50990}, {590, 43386}, {615, 43387}, {1153, 9741}, {1385, 51072}, {1992, 55712}, {3316, 41946}, {3317, 41945}, {3576, 51069}, {3618, 55723}, {4669, 7967}, {4677, 13607}, {4745, 31423}, {5050, 50985}, {5085, 51143}, {5093, 50981}, {5334, 43874}, {5335, 43873}, {5476, 55599}, {5657, 51103}, {5690, 51092}, {5731, 51084}, {5886, 50809}, {6200, 43514}, {6396, 43513}, {6409, 43506}, {6410, 43505}, {6435, 19053}, {6436, 19054}, {6449, 42527}, {6450, 42526}, {6455, 43341}, {6456, 43340}, {6459, 43343}, {6460, 43342}, {6468, 43798}, {6469, 43797}, {6684, 34631}, {6776, 51186}, {7612, 60637}, {7880, 39142}, {8252, 14226}, {8253, 14241}, {9862, 22247}, {10155, 60282}, {10165, 50827}, {10168, 55714}, {10171, 50812}, {10175, 50819}, {10246, 50830}, {10247, 50826}, {10302, 60185}, {10357, 51237}, {10595, 51108}, {10653, 33607}, {10654, 33606}, {11480, 49824}, {11481, 49825}, {11669, 60284}, {12007, 15533}, {12156, 55810}, {13665, 43382}, {13701, 26362}, {13785, 43383}, {13821, 26361}, {13846, 43374}, {13847, 43375}, {13886, 43254}, {13939, 43255}, {14561, 50966}, {14651, 36521}, {14912, 22165}, {15534, 50982}, {16241, 42977}, {16242, 42976}, {16267, 42505}, {16268, 42504}, {17508, 51177}, {20423, 55589}, {20582, 39874}, {21156, 36318}, {21157, 36320}, {23302, 49826}, {23303, 49827}, {25406, 51137}, {26446, 51087}, {30308, 50813}, {31412, 43558}, {32064, 46265}, {32785, 43536}, {32786, 43569}, {32789, 43380}, {32790, 43381}, {33416, 41120}, {33417, 41119}, {33602, 52080}, {33603, 52079}, {33604, 41107}, {33605, 41108}, {34089, 42602}, {34091, 42603}, {36967, 43002}, {36968, 43003}, {37640, 43483}, {37641, 43484}, {37832, 42588}, {37835, 42589}, {38064, 55709}, {38122, 60971}, {41100, 42955}, {41101, 42954}, {42089, 49861}, {42092, 49862}, {42119, 42795}, {42120, 42796}, {42129, 43108}, {42132, 43109}, {42139, 46335}, {42142, 46334}, {42149, 42532}, {42152, 42533}, {42157, 43444}, {42158, 43445}, {42419, 42989}, {42420, 42988}, {42494, 42965}, {42495, 42964}, {42500, 43463}, {42501, 43464}, {42508, 43447}, {42509, 43446}, {42510, 49903}, {42511, 49904}, {42530, 56617}, {42531, 56616}, {42561, 43559}, {42580, 43202}, {42581, 43201}, {42631, 42911}, {42632, 42910}, {42791, 43482}, {42792, 43481}, {42930, 43500}, {42931, 43499}, {42998, 43107}, {42999, 43100}, {43000, 54593}, {43001, 54594}, {43246, 43540}, {43247, 43541}, {43378, 43879}, {43379, 43880}, {43517, 43525}, {43518, 43526}, {43542, 49875}, {43543, 49876}, {43645, 43772}, {43646, 43771}, {44299, 61136}, {47353, 51139}, {50810, 51110}, {50818, 51068}, {50825, 59417}, {50828, 51066}, {50829, 51109}, {50869, 61265}, {50956, 55670}, {50974, 50994}, {50977, 55713}, {50983, 50993}, {50984, 54132}, {50988, 51176}, {50992, 51140}, {51130, 55618}, {51178, 55703}, {51212, 55619}, {53103, 60228}, {53104, 54637}, {54041, 58470}, {54170, 55605}, {54173, 55717}, {54521, 60616}, {54523, 60239}, {54608, 60183}, {54612, 60278}, {54616, 60192}, {54707, 60100}, {54866, 60629}, {55715, 59373}, {60102, 60627}, {60127, 60646}, {60143, 60175}, {60150, 60643}

X(61833) = inverse of X(61904) in orthocentroidal circle
X(61833) = inverse of X(61904) in Yff hyperbola
X(61833) = complement of X(61943)
X(61833) = anticomplement of X(61893)
X(61833) = pole of line {523, 61904} with respect to the orthocentroidal circle
X(61833) = pole of line {6, 61904} with respect to the Kiepert hyperbola
X(61833) = pole of line {523, 61904} with respect to the Yff hyperbola
X(61833) = pole of line {69, 61920} with respect to the Wallace hyperbola
X(61833) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(41099)}}, {{A, B, C, X(7408), X(54608)}}, {{A, B, C, X(7409), X(54643)}}, {{A, B, C, X(8703), X(36948)}}, {{A, B, C, X(10301), X(60185)}}, {{A, B, C, X(12811), X(22270)}}, {{A, B, C, X(13623), X(15685)}}, {{A, B, C, X(15698), X(57895)}}, {{A, B, C, X(15704), X(46412)}}, {{A, B, C, X(37174), X(60637)}}, {{A, B, C, X(41984), X(46921)}}, {{A, B, C, X(49135), X(54660)}}, {{A, B, C, X(50688), X(54667)}}, {{A, B, C, X(52285), X(54707)}}, {{A, B, C, X(52301), X(60175)}}
X(61833) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10304, 5066}, {2, 11001, 5071}, {2, 11812, 631}, {2, 12100, 15682}, {2, 15692, 3830}, {2, 15697, 5}, {2, 15701, 15719}, {2, 15708, 15693}, {2, 15717, 15640}, {2, 15721, 11812}, {2, 3523, 8703}, {2, 3524, 11001}, {2, 8703, 3545}, {4, 7486, 3544}, {5, 15716, 15697}, {140, 11737, 11539}, {140, 15693, 2}, {140, 15704, 3526}, {140, 17504, 15723}, {140, 5067, 3525}, {140, 549, 5055}, {376, 3545, 382}, {376, 5066, 6834}, {376, 631, 15708}, {547, 15705, 3529}, {548, 3628, 3858}, {549, 11539, 548}, {549, 15713, 11540}, {549, 3526, 10304}, {549, 5054, 10303}, {631, 10299, 12108}, {631, 3090, 15720}, {632, 15700, 3839}, {3523, 15683, 15706}, {3523, 15715, 3524}, {3523, 3545, 15715}, {3524, 5071, 3528}, {3534, 5055, 3845}, {3545, 15715, 17538}, {3628, 15706, 15683}, {3845, 15759, 3534}, {3858, 15720, 3523}, {5046, 15705, 15721}, {5054, 15701, 15713}, {5066, 15759, 15704}, {10124, 15707, 20}, {10303, 15709, 15702}, {10303, 15717, 140}, {10304, 14890, 15709}, {10304, 15022, 15684}, {10304, 15704, 376}, {11539, 15692, 3090}, {11539, 15720, 15692}, {11540, 15719, 4}, {11812, 15713, 15701}, {13741, 15717, 5059}, {15640, 15693, 15698}, {15640, 15717, 15759}, {15682, 15719, 12100}, {15685, 15693, 17504}, {15693, 15723, 15685}, {15693, 15759, 15717}, {15694, 15706, 3628}, {15697, 15716, 15710}, {15699, 15718, 3522}, {15702, 15708, 5067}, {15702, 15715, 15694}, {15705, 16857, 381}, {15708, 15717, 549}, {15723, 17504, 3091}, {41965, 41966, 6}, {42791, 49873, 43482}, {42792, 49874, 43481}

X(61834) = X(2)X(3)∩X(8)X(30392)

Barycentrics    13*a^4+5*(b^2-c^2)^2-18*a^2*(b^2+c^2) : :
X(61834) = 15*X[2]+8*X[3], 5*X[8]+18*X[30392], 5*X[69]+18*X[55703], -X[145]+24*X[10165], 2*X[185]+21*X[44299], -5*X[193]+28*X[55711], 5*X[1352]+18*X[55685], 16*X[1385]+7*X[4678], 12*X[3576]+11*X[46933], 20*X[3589]+3*X[55591], -25*X[3616]+2*X[11531], 15*X[3617]+8*X[5882] and many others

X(61834) lies on these lines: {2, 3}, {6, 43479}, {8, 30392}, {17, 42958}, {18, 42959}, {69, 55703}, {99, 32870}, {145, 10165}, {183, 32841}, {185, 44299}, {193, 55711}, {315, 32871}, {316, 32884}, {390, 52793}, {485, 6487}, {486, 6486}, {499, 51817}, {515, 46931}, {590, 6430}, {615, 6429}, {1064, 27645}, {1078, 10513}, {1131, 6410}, {1132, 6409}, {1352, 55685}, {1385, 4678}, {1587, 6481}, {1588, 6480}, {2996, 17006}, {3068, 41964}, {3069, 41963}, {3085, 37587}, {3087, 36422}, {3316, 6450}, {3317, 6449}, {3424, 16988}, {3576, 46933}, {3589, 55591}, {3590, 6434}, {3591, 6433}, {3592, 43413}, {3594, 43414}, {3601, 31188}, {3616, 11531}, {3617, 5882}, {3618, 55722}, {3620, 8550}, {3621, 26446}, {3622, 6684}, {3624, 5493}, {3626, 58231}, {3634, 54448}, {3653, 20049}, {3868, 10156}, {3933, 32881}, {4297, 30315}, {4652, 46873}, {5008, 31401}, {5041, 31400}, {5097, 10519}, {5102, 51171}, {5265, 5432}, {5281, 5433}, {5334, 42937}, {5335, 42936}, {5343, 10645}, {5344, 10646}, {5351, 43403}, {5352, 43404}, {5365, 16967}, {5366, 16966}, {5462, 16981}, {5550, 10164}, {5558, 13405}, {5650, 10574}, {5657, 33179}, {5731, 46932}, {5907, 33879}, {5921, 55688}, {5984, 38737}, {6200, 10194}, {6225, 58434}, {6390, 32880}, {6396, 10195}, {6431, 7586}, {6432, 7585}, {6437, 13941}, {6438, 8972}, {6451, 23275}, {6452, 23269}, {6453, 43255}, {6454, 43254}, {6459, 43377}, {6460, 43376}, {6484, 9543}, {6496, 42539}, {6497, 42540}, {6776, 55691}, {7584, 9542}, {7607, 43681}, {7608, 60145}, {7746, 15602}, {7768, 32829}, {7771, 32839}, {7774, 55819}, {7779, 10256}, {7782, 32867}, {7787, 52770}, {7871, 32887}, {7987, 19877}, {7991, 50829}, {8273, 9342}, {8591, 38740}, {8981, 42523}, {9143, 38729}, {9540, 35771}, {9544, 37515}, {9588, 38314}, {9778, 19862}, {9779, 16192}, {9780, 38155}, {9812, 34595}, {9833, 46265}, {10137, 43518}, {10138, 43517}, {10159, 47586}, {10182, 34781}, {10185, 38259}, {10187, 18581}, {10188, 18582}, {10193, 12250}, {10246, 20014}, {10541, 21356}, {10576, 43791}, {10577, 43792}, {10619, 23291}, {10653, 42979}, {10654, 42978}, {10990, 38792}, {10991, 38746}, {10992, 38735}, {11002, 11695}, {11160, 53093}, {11171, 20105}, {11177, 38751}, {11180, 55687}, {11278, 59417}, {11444, 13382}, {11451, 13348}, {11480, 42948}, {11481, 42949}, {11488, 42944}, {11489, 42945}, {12245, 61614}, {12815, 15515}, {13464, 46934}, {13886, 43797}, {13935, 35770}, {13939, 43798}, {13966, 42522}, {14561, 55612}, {14683, 38793}, {14853, 55594}, {15043, 33884}, {15056, 17704}, {15108, 18916}, {15589, 32821}, {15808, 58248}, {15819, 20081}, {16241, 42893}, {16242, 42892}, {16989, 55797}, {18538, 43505}, {18553, 55680}, {18762, 43506}, {18845, 60144}, {19053, 43883}, {19054, 43884}, {19876, 51086}, {20054, 38127}, {20059, 38122}, {20080, 50664}, {20085, 38133}, {20094, 38748}, {20095, 38760}, {20096, 38772}, {20099, 38804}, {20582, 55684}, {21167, 55607}, {22235, 23302}, {22236, 42501}, {22237, 23303}, {22238, 42500}, {22712, 55803}, {25555, 55587}, {25565, 50969}, {27003, 61122}, {27065, 37526}, {27525, 56879}, {30389, 53620}, {30714, 38725}, {31145, 38068}, {31407, 35007}, {31425, 34632}, {31467, 46453}, {31666, 34627}, {31670, 55640}, {32348, 55038}, {32789, 42637}, {32790, 42638}, {32814, 45509}, {32815, 32897}, {32816, 32898}, {32817, 32894}, {32818, 32895}, {32820, 34229}, {32824, 32834}, {32872, 37688}, {32873, 37668}, {33416, 42150}, {33417, 42151}, {33521, 38770}, {34507, 55695}, {34567, 42021}, {34754, 42089}, {34755, 42092}, {35260, 44762}, {35369, 38224}, {35820, 42600}, {35821, 42601}, {36948, 52710}, {37501, 37687}, {37513, 38942}, {37640, 42491}, {37641, 42490}, {37689, 44535}, {37749, 38807}, {38074, 51084}, {38079, 55595}, {38317, 55636}, {39561, 51170}, {40330, 55683}, {40693, 42994}, {40694, 42995}, {42087, 42776}, {42088, 42775}, {42129, 43243}, {42132, 43242}, {42159, 43245}, {42162, 43244}, {42260, 43520}, {42261, 43519}, {42494, 43029}, {42495, 43028}, {42592, 42952}, {42593, 42953}, {42596, 42911}, {42597, 42910}, {42686, 43773}, {42687, 43774}, {42805, 43197}, {42806, 43198}, {42924, 42982}, {42925, 42983}, {42988, 43463}, {42989, 43464}, {43022, 43309}, {43023, 43308}, {43102, 43446}, {43103, 43447}, {43193, 43540}, {43194, 43541}, {43407, 43560}, {43408, 43561}, {43411, 43879}, {43412, 43880}, {43442, 44016}, {43443, 44015}, {43527, 60118}, {43537, 60285}, {43951, 60182}, {46930, 59387}, {47355, 55622}, {48310, 55614}, {50833, 61249}, {50984, 53097}, {51073, 58221}, {51127, 55651}, {51128, 51537}, {51212, 55618}, {53099, 60647}, {54921, 60640}, {55603, 58445}, {60334, 60639}, {60336, 60642}

X(61834) = anticomplement of X(46936)
X(61834) = pole of line {185, 62110} with respect to the Jerabek hyperbola
X(61834) = pole of line {6, 3590} with respect to the Kiepert hyperbola
X(61834) = pole of line {69, 15022} with respect to the Wallace hyperbola
X(61834) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(68), X(3857)}}, {{A, B, C, X(69), X(15022)}}, {{A, B, C, X(95), X(3832)}}, {{A, B, C, X(428), X(47586)}}, {{A, B, C, X(546), X(46168)}}, {{A, B, C, X(1217), X(15720)}}, {{A, B, C, X(3346), X(3530)}}, {{A, B, C, X(3519), X(5072)}}, {{A, B, C, X(3522), X(36948)}}, {{A, B, C, X(3526), X(26861)}}, {{A, B, C, X(3628), X(42021)}}, {{A, B, C, X(3851), X(22270)}}, {{A, B, C, X(5056), X(35510)}}, {{A, B, C, X(5064), X(60118)}}, {{A, B, C, X(5071), X(60171)}}, {{A, B, C, X(6353), X(53859)}}, {{A, B, C, X(6662), X(47599)}}, {{A, B, C, X(7714), X(43537)}}, {{A, B, C, X(10185), X(38282)}}, {{A, B, C, X(10594), X(34567)}}, {{A, B, C, X(11001), X(40448)}}, {{A, B, C, X(12101), X(54552)}}, {{A, B, C, X(13599), X(41106)}}, {{A, B, C, X(14528), X(55578)}}, {{A, B, C, X(14861), X(49136)}}, {{A, B, C, X(15681), X(46412)}}, {{A, B, C, X(15682), X(60618)}}, {{A, B, C, X(15705), X(57895)}}, {{A, B, C, X(15740), X(49140)}}, {{A, B, C, X(15749), X(50689)}}, {{A, B, C, X(16251), X(49134)}}, {{A, B, C, X(21734), X(51348)}}, {{A, B, C, X(31363), X(41099)}}, {{A, B, C, X(33270), X(57857)}}, {{A, B, C, X(35479), X(57713)}}, {{A, B, C, X(43681), X(52282)}}, {{A, B, C, X(52281), X(60145)}}, {{A, B, C, X(52299), X(60144)}}
X(61834) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15022, 13735}, {2, 17578, 3090}, {2, 3, 3832}, {2, 3522, 5068}, {2, 3523, 3522}, {2, 3524, 15683}, {2, 5070, 13741}, {2, 549, 15705}, {3, 11539, 5067}, {3, 140, 3533}, {3, 15686, 3528}, {3, 15723, 5}, {3, 16239, 3545}, {3, 3526, 547}, {3, 3853, 376}, {3, 5, 11001}, {4, 631, 15720}, {20, 1656, 3854}, {20, 3091, 3830}, {20, 3523, 10299}, {140, 12108, 550}, {140, 15708, 5059}, {140, 15720, 4}, {140, 1656, 3525}, {140, 3850, 11539}, {140, 549, 1656}, {140, 631, 3523}, {376, 632, 7486}, {549, 11539, 15690}, {631, 14869, 15721}, {631, 3524, 12108}, {631, 5054, 10303}, {1078, 32835, 10513}, {1656, 15716, 1657}, {1656, 3545, 5056}, {1656, 3854, 15022}, {2045, 2046, 3524}, {3090, 10304, 17578}, {3090, 3530, 10304}, {3522, 3523, 15717}, {3523, 10303, 140}, {3523, 5056, 3}, {3524, 3526, 3091}, {3525, 3545, 16239}, {3528, 3628, 3839}, {3533, 15716, 7379}, {3533, 3854, 13742}, {3543, 15708, 15719}, {3543, 5056, 3850}, {3856, 6924, 381}, {4193, 5154, 17529}, {5054, 11812, 15702}, {5070, 12100, 3529}, {5070, 17504, 6969}, {5550, 10164, 20070}, {6433, 32786, 43890}, {6434, 32785, 43889}, {10303, 15721, 631}, {10304, 15694, 2}, {11001, 15702, 15709}, {11001, 15709, 15723}, {11539, 15719, 3543}, {11812, 15702, 15708}, {12108, 15713, 3526}, {13735, 15705, 3146}, {13735, 15717, 20}, {14784, 14785, 3857}, {14813, 14814, 5072}, {15688, 15701, 549}, {15699, 15715, 15640}, {15699, 15722, 15715}, {15701, 15709, 15692}, {15705, 17678, 10109}, {15708, 15721, 11812}, {16192, 19878, 9779}, {43479, 43480, 6}, {51128, 55673, 51537}

X(61835) = X(2)X(3)∩X(17)X(43000)

Barycentrics    18*a^4+7*(b^2-c^2)^2-25*a^2*(b^2+c^2) : :
X(61835) = 21*X[2]+11*X[3], 7*X[141]+9*X[55693], 5*X[575]+3*X[50982], 27*X[3576]+5*X[61248], 7*X[3589]+X[55590], 15*X[3653]+X[50830], 5*X[4701]+11*X[13607], 7*X[5480]+9*X[55630], -9*X[5650]+X[31834], 9*X[5690]+7*X[61282], 3*X[5901]+5*X[31447], 3*X[6684]+X[61278] and many others

X(61835) lies on these lines: {2, 3}, {17, 43000}, {18, 43001}, {141, 55693}, {575, 50982}, {3411, 42912}, {3412, 42913}, {3564, 55696}, {3576, 61248}, {3589, 55590}, {3653, 50830}, {4325, 5326}, {4330, 7294}, {4701, 13607}, {5237, 43544}, {5238, 43545}, {5305, 31457}, {5318, 42596}, {5321, 42597}, {5418, 6471}, {5420, 6470}, {5480, 55630}, {5650, 31834}, {5690, 61282}, {5901, 31447}, {6684, 61278}, {7877, 55821}, {7982, 50825}, {8162, 31452}, {9588, 38028}, {9680, 43431}, {9681, 43514}, {9692, 18510}, {9705, 13339}, {10165, 61286}, {11231, 61249}, {11362, 51700}, {11477, 50980}, {11542, 42686}, {11543, 42687}, {11592, 11695}, {11694, 13393}, {12006, 15606}, {12007, 40107}, {13392, 16003}, {13624, 61255}, {15082, 45959}, {15178, 50827}, {15516, 34380}, {15520, 51732}, {16964, 42684}, {16965, 42685}, {18581, 43634}, {18582, 43635}, {18583, 55585}, {19878, 28178}, {20396, 48378}, {21167, 55608}, {22712, 55802}, {22791, 31425}, {23267, 60293}, {23273, 60294}, {25555, 50984}, {26446, 61288}, {31450, 44535}, {33606, 42978}, {33607, 42979}, {33749, 51138}, {34483, 57714}, {34773, 61252}, {35255, 35813}, {35256, 35812}, {36967, 43442}, {36968, 43443}, {38064, 50985}, {38068, 51087}, {38317, 55635}, {41963, 43212}, {41964, 43211}, {42085, 43644}, {42086, 43649}, {42108, 42499}, {42109, 42498}, {42121, 42490}, {42122, 42970}, {42123, 42971}, {42124, 42491}, {42135, 42611}, {42138, 42610}, {42147, 43102}, {42148, 43103}, {42496, 42990}, {42497, 42991}, {42590, 42943}, {42591, 42942}, {42795, 43417}, {42796, 43416}, {42936, 42981}, {42937, 42980}, {42996, 43027}, {42997, 43026}, {43150, 55690}, {43338, 43340}, {43339, 43341}, {50959, 55650}, {50991, 55698}, {51139, 55679}, {55601, 58445}

X(61835) = midpoint of X(i) and X(j) for these {i,j}: {140, 12108}, {548, 3856}, {549, 11540}, {3530, 16239}, {11592, 11695}
X(61835) = complement of X(12811)
X(61835) = pole of line {185, 62111} with respect to the Jerabek hyperbola
X(61835) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(3858)}}, {{A, B, C, X(547), X(34483)}}, {{A, B, C, X(3851), X(43970)}}, {{A, B, C, X(14938), X(45760)}}, {{A, B, C, X(15318), X(55858)}}, {{A, B, C, X(15682), X(60007)}}, {{A, B, C, X(34484), X(57714)}}, {{A, B, C, X(46333), X(46412)}}
X(61835) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15696, 5}, {2, 3, 3858}, {3, 140, 10124}, {3, 15713, 140}, {3, 1656, 15682}, {3, 3526, 7486}, {3, 3839, 550}, {3, 3858, 15691}, {5, 15696, 3853}, {5, 549, 15717}, {20, 631, 15720}, {140, 10303, 14890}, {140, 11812, 12108}, {140, 12100, 632}, {140, 12108, 30}, {140, 14869, 11812}, {140, 15708, 12102}, {140, 15720, 3850}, {140, 3530, 16239}, {140, 546, 11539}, {140, 547, 3525}, {140, 549, 3628}, {548, 3853, 15704}, {549, 11539, 3534}, {549, 15713, 15709}, {549, 5055, 12100}, {550, 5067, 3859}, {631, 15702, 20}, {3523, 11539, 546}, {3523, 5071, 3}, {3525, 15701, 15712}, {3525, 15712, 547}, {3526, 3530, 3856}, {3526, 3534, 5070}, {3530, 10124, 3861}, {3530, 11812, 631}, {3530, 3628, 548}, {3533, 15693, 3627}, {3628, 15704, 12811}, {3628, 15759, 4}, {3628, 3850, 5055}, {3857, 15712, 10304}, {3859, 5067, 10109}, {5054, 15721, 15713}, {7486, 15683, 3855}, {10124, 14891, 5071}, {10124, 15709, 11540}, {10304, 15701, 549}, {11540, 16239, 3526}, {11694, 38729, 13393}, {12100, 15710, 14891}, {12108, 16239, 3530}, {15683, 15699, 5066}, {15711, 15723, 14892}, {42686, 42955, 11542}, {42687, 42954, 11543}

X(61836) = X(2)X(3)∩X(61)X(43493)

Barycentrics    17*a^4+7*(b^2-c^2)^2-24*a^2*(b^2+c^2) : :
X(61836) = 21*X[2]+10*X[3], 7*X[69]+24*X[55706], 7*X[1352]+24*X[55686], X[3244]+30*X[58441], -35*X[3618]+4*X[55720], 49*X[3619]+44*X[55689], 7*X[3622]+24*X[61614], 16*X[3626]+15*X[7967], 16*X[3631]+15*X[14912], X[3632]+30*X[10165], 16*X[3636]+15*X[5657], 27*X[5650]+4*X[13382] and many others

X(61836) lies on these lines: {2, 3}, {61, 43493}, {62, 43494}, {69, 55706}, {1285, 31455}, {1352, 55686}, {1587, 6469}, {1588, 6468}, {3068, 43414}, {3069, 43413}, {3070, 43505}, {3071, 43506}, {3244, 58441}, {3411, 42635}, {3412, 42636}, {3590, 42216}, {3591, 42215}, {3618, 55720}, {3619, 55689}, {3622, 61614}, {3626, 7967}, {3631, 14912}, {3632, 10165}, {3636, 5657}, {5334, 42773}, {5335, 42774}, {5343, 43028}, {5344, 43029}, {5351, 10188}, {5352, 10187}, {5365, 43488}, {5366, 43487}, {5650, 13382}, {6329, 10519}, {6459, 10194}, {6460, 10195}, {6684, 11224}, {7288, 37602}, {7581, 41964}, {7582, 41963}, {7607, 60636}, {7860, 34803}, {7869, 55732}, {8252, 43410}, {8253, 43409}, {8718, 16187}, {9542, 13993}, {9543, 45385}, {9588, 34631}, {9624, 50829}, {9693, 35823}, {10155, 53102}, {10159, 60322}, {10185, 60631}, {10246, 20054}, {10256, 50251}, {10595, 15808}, {10645, 42495}, {10646, 42494}, {10653, 42958}, {10654, 42959}, {11008, 55710}, {11488, 42779}, {11489, 42780}, {13886, 43517}, {13939, 43518}, {14561, 55608}, {14651, 35022}, {15058, 15082}, {16241, 42938}, {16242, 42939}, {16966, 43769}, {16967, 43770}, {18581, 43425}, {18582, 43424}, {18840, 60337}, {18841, 60330}, {18843, 53098}, {19883, 31425}, {20050, 26446}, {20125, 20417}, {21168, 60980}, {22235, 42115}, {22237, 42116}, {22712, 55800}, {23269, 32789}, {23275, 32790}, {25555, 55585}, {31487, 43884}, {31670, 55638}, {32000, 36948}, {32450, 61132}, {32785, 43411}, {32786, 43412}, {32817, 32868}, {32824, 32886}, {32825, 32887}, {33416, 41973}, {33417, 41974}, {33749, 50990}, {33879, 40647}, {34089, 43570}, {34091, 43571}, {34507, 55696}, {34747, 38068}, {36836, 43543}, {36843, 43542}, {38122, 60957}, {38317, 55634}, {40693, 42947}, {40694, 42946}, {41112, 42592}, {41113, 42593}, {41977, 43014}, {41978, 43015}, {42089, 43022}, {42090, 42908}, {42091, 42909}, {42092, 43023}, {42104, 42499}, {42105, 42498}, {42117, 42927}, {42118, 42926}, {42150, 42798}, {42151, 42797}, {42153, 42794}, {42156, 42793}, {42159, 42597}, {42162, 42596}, {42415, 43496}, {42416, 43495}, {42490, 42501}, {42491, 42500}, {42512, 42935}, {42513, 42934}, {42586, 43501}, {42587, 43502}, {42598, 43481}, {42599, 43482}, {42629, 42921}, {42630, 42920}, {42954, 43776}, {42955, 43775}, {42978, 43012}, {42979, 43013}, {42998, 43463}, {42999, 43464}, {43102, 43869}, {43103, 43870}, {43386, 52046}, {43387, 52045}, {43564, 60305}, {43565, 60306}, {43676, 53103}, {47743, 52793}, {50980, 55724}, {50992, 55708}, {51023, 55681}, {51179, 53092}, {51212, 55615}, {53100, 60183}, {54616, 60332}, {55596, 58445}, {60123, 60219}, {60143, 60334}, {60185, 60642}

X(61836) = anticomplement of X(61892)
X(61836) = pole of line {69, 5079} with respect to the Wallace hyperbola
X(61836) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(5079)}}, {{A, B, C, X(95), X(3855)}}, {{A, B, C, X(428), X(60322)}}, {{A, B, C, X(550), X(36948)}}, {{A, B, C, X(3090), X(57897)}}, {{A, B, C, X(3519), X(19709)}}, {{A, B, C, X(5070), X(42021)}}, {{A, B, C, X(5198), X(14491)}}, {{A, B, C, X(6995), X(60337)}}, {{A, B, C, X(7378), X(60330)}}, {{A, B, C, X(7408), X(53100)}}, {{A, B, C, X(7409), X(60142)}}, {{A, B, C, X(14861), X(49134)}}, {{A, B, C, X(15022), X(60171)}}, {{A, B, C, X(15640), X(54660)}}, {{A, B, C, X(15683), X(40448)}}, {{A, B, C, X(15686), X(46412)}}, {{A, B, C, X(15710), X(57895)}}, {{A, B, C, X(15740), X(49137)}}, {{A, B, C, X(52282), X(60636)}}, {{A, B, C, X(52301), X(60334)}}, {{A, B, C, X(55570), X(57713)}}
X(61836) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10304, 11737}, {2, 14869, 631}, {2, 15692, 14269}, {2, 15707, 376}, {2, 15708, 15700}, {2, 15720, 10299}, {2, 20, 5079}, {2, 3, 3855}, {2, 3523, 550}, {2, 3528, 3544}, {2, 3530, 3529}, {2, 3544, 5067}, {2, 382, 3090}, {2, 549, 15710}, {3, 10124, 7486}, {3, 15699, 17578}, {3, 3526, 15699}, {3, 3861, 15697}, {3, 5, 15683}, {3, 7486, 15682}, {4, 140, 3525}, {4, 15702, 140}, {4, 3522, 11001}, {4, 548, 13635}, {20, 12108, 15719}, {140, 11812, 15712}, {140, 14869, 15720}, {140, 15712, 3526}, {140, 3523, 3533}, {140, 631, 4}, {546, 550, 5073}, {549, 11001, 3524}, {549, 11539, 12101}, {550, 15720, 3523}, {631, 15719, 12108}, {631, 3090, 549}, {632, 15717, 3545}, {2045, 2046, 15717}, {3090, 15710, 382}, {3091, 11114, 3530}, {3524, 5067, 17538}, {3526, 15707, 546}, {3526, 15712, 5056}, {3529, 3530, 15715}, {3529, 3855, 15687}, {3628, 15698, 6927}, {3839, 5068, 3850}, {5054, 15713, 15721}, {5071, 11001, 3839}, {5073, 15699, 5068}, {5335, 42949, 43447}, {10303, 15717, 14890}, {11539, 15681, 2}, {12108, 15694, 20}, {14869, 15694, 17533}, {14869, 15702, 3528}, {15682, 15709, 10124}, {15693, 16239, 3146}, {15697, 15717, 3}, {15702, 15721, 5071}, {15709, 15713, 15702}, {15713, 15721, 15709}, {42773, 42948, 5334}, {42774, 42949, 5335}

X(61837) = X(2)X(3)∩X(10)X(31662)

Barycentrics    12*a^4+5*(b^2-c^2)^2-17*a^2*(b^2+c^2) : :
X(61837) = 15*X[2]+7*X[3], 5*X[10]+6*X[31662], 3*X[51]+8*X[11592], 5*X[141]+6*X[55695], 4*X[551]+7*X[50826], 8*X[575]+3*X[50978], 4*X[597]+7*X[50981], 4*X[599]+7*X[51181], 6*X[1125]+5*X[31447], 7*X[1353]+4*X[3630], 7*X[1385]+4*X[4691], 7*X[1483]+4*X[3625] and many others

X(61837) lies on these lines: {2, 3}, {10, 31662}, {51, 11592}, {61, 42501}, {62, 42500}, {141, 55695}, {230, 31457}, {485, 6434}, {486, 6433}, {551, 50826}, {575, 50978}, {597, 50981}, {599, 51181}, {1125, 31447}, {1151, 42579}, {1152, 42578}, {1353, 3630}, {1384, 31407}, {1385, 4691}, {1483, 3625}, {1503, 55683}, {1511, 38725}, {1698, 61255}, {3054, 15602}, {3316, 6446}, {3317, 6445}, {3411, 16772}, {3412, 16773}, {3564, 55699}, {3576, 61249}, {3589, 55587}, {3592, 43212}, {3594, 43211}, {3633, 26446}, {3635, 5690}, {3653, 50831}, {3828, 31666}, {4325, 10592}, {4330, 10593}, {4668, 30392}, {4669, 58232}, {4726, 51046}, {5008, 9698}, {5023, 31417}, {5041, 9606}, {5097, 38110}, {5237, 42949}, {5238, 42948}, {5305, 31450}, {5318, 42492}, {5319, 44535}, {5321, 42493}, {5339, 42591}, {5340, 42590}, {5418, 6432}, {5420, 6431}, {5480, 55627}, {5550, 28212}, {5650, 13630}, {5882, 50832}, {5886, 31425}, {5888, 43597}, {5892, 15606}, {6144, 55711}, {6425, 43255}, {6426, 43254}, {6429, 43318}, {6430, 43319}, {6437, 7584}, {6438, 7583}, {6450, 31414}, {6482, 35823}, {6483, 35822}, {6484, 42215}, {6485, 42216}, {6684, 10283}, {7288, 31480}, {7735, 31470}, {7749, 9607}, {7751, 12040}, {7769, 14929}, {7987, 61258}, {8252, 9681}, {8550, 50987}, {8981, 35770}, {9466, 32523}, {9588, 16200}, {9589, 61272}, {9692, 13939}, {9706, 37471}, {9780, 61251}, {10156, 24475}, {10192, 52102}, {10246, 20053}, {10256, 15480}, {10386, 37720}, {10625, 58533}, {10645, 42597}, {10646, 42596}, {11231, 37705}, {11362, 33179}, {11465, 13451}, {11482, 51214}, {11531, 61276}, {11695, 54042}, {11793, 45956}, {12006, 14531}, {12041, 38792}, {12042, 38746}, {12702, 61273}, {13336, 40111}, {13340, 58531}, {13372, 23238}, {13393, 15039}, {13935, 31487}, {13966, 31454}, {14449, 15028}, {14561, 55607}, {15057, 38794}, {15060, 17704}, {15061, 22251}, {15178, 38068}, {15325, 31452}, {15808, 58244}, {15888, 37587}, {16194, 55286}, {16241, 42802}, {16242, 42801}, {16836, 45957}, {16960, 43250}, {16961, 43251}, {16966, 43631}, {16967, 43630}, {17814, 51959}, {18583, 55582}, {18874, 36987}, {19116, 35813}, {19117, 35812}, {19130, 55645}, {19661, 51237}, {19862, 61270}, {19872, 61262}, {19875, 61248}, {20191, 59553}, {20379, 38793}, {20396, 34153}, {20582, 50988}, {21167, 55612}, {21850, 55603}, {22165, 55704}, {22712, 55799}, {23251, 42600}, {23261, 42601}, {23302, 42922}, {23303, 42923}, {24206, 55680}, {25565, 55650}, {29181, 55642}, {31458, 47742}, {31494, 59572}, {31657, 61000}, {31834, 40280}, {32134, 52770}, {32455, 39561}, {32877, 34229}, {33416, 42147}, {33417, 42148}, {33813, 38735}, {34595, 40273}, {34773, 38155}, {34782, 46265}, {34783, 44299}, {35242, 61269}, {36422, 52704}, {37481, 44324}, {37517, 59399}, {38064, 50986}, {38079, 50984}, {38081, 50828}, {38083, 51086}, {38111, 61020}, {38113, 43177}, {38122, 60977}, {38127, 58234}, {38136, 55640}, {38170, 52769}, {38317, 55633}, {38601, 38770}, {38602, 38758}, {38607, 38782}, {38623, 38802}, {38750, 52886}, {41107, 42793}, {41108, 42794}, {41973, 42953}, {41974, 42952}, {42085, 42611}, {42086, 42610}, {42089, 42490}, {42092, 42491}, {42117, 42489}, {42118, 42488}, {42135, 42434}, {42138, 42433}, {42143, 43194}, {42146, 43193}, {42149, 42633}, {42152, 42634}, {42153, 43102}, {42156, 43103}, {42164, 43551}, {42165, 43550}, {42568, 43431}, {42569, 43430}, {42894, 43874}, {42895, 43873}, {42912, 43239}, {42913, 43238}, {42942, 43032}, {42943, 43033}, {42944, 42990}, {42945, 42991}, {42950, 52080}, {42951, 52079}, {42996, 43024}, {42997, 43025}, {43174, 50825}, {43378, 43525}, {43379, 43526}, {46849, 55166}, {47354, 55679}, {47355, 55618}, {48310, 55606}, {48874, 51126}, {48906, 55688}, {51127, 55649}, {51128, 55674}, {54445, 61510}, {55594, 58445}, {58231, 61296}, {58248, 61275}, {59381, 60976}, {61540, 61680}

X(61837) = midpoint of X(i) and X(j) for these {i,j}: {2, 15718}, {3, 5056}, {3525, 15720}, {5070, 15717}, {15719, 15723}
X(61837) = reflection of X(i) in X(j) for these {i,j}: {3525, 140}, {5, 5070}, {8703, 15715}
X(61837) = inverse of X(61903) in orthocentroidal circle
X(61837) = inverse of X(61903) in Yff hyperbola
X(61837) = complement of X(5072)
X(61837) = pole of line {523, 61903} with respect to the orthocentroidal circle
X(61837) = pole of line {185, 15690} with respect to the Jerabek hyperbola
X(61837) = pole of line {6, 61903} with respect to the Kiepert hyperbola
X(61837) = pole of line {523, 61903} with respect to the Yff hyperbola
X(61837) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1105), X(15690)}}, {{A, B, C, X(3543), X(60007)}}, {{A, B, C, X(3855), X(22270)}}, {{A, B, C, X(6662), X(55857)}}, {{A, B, C, X(15318), X(46219)}}, {{A, B, C, X(15723), X(46452)}}, {{A, B, C, X(17538), X(36948)}}, {{A, B, C, X(22268), X(35018)}}, {{A, B, C, X(35409), X(54660)}}, {{A, B, C, X(35434), X(60122)}}, {{A, B, C, X(41987), X(60121)}}, {{A, B, C, X(45759), X(57895)}}
X(61837) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12108, 15712}, {2, 14093, 14892}, {2, 15706, 14893}, {2, 15712, 3627}, {2, 1657, 12812}, {2, 3, 3850}, {2, 3523, 17538}, {2, 3524, 15684}, {3, 15720, 15719}, {3, 15723, 5056}, {3, 1656, 3543}, {3, 3526, 5067}, {3, 3533, 547}, {3, 3845, 550}, {3, 3850, 15686}, {3, 4, 15690}, {3, 5067, 3853}, {3, 6923, 15722}, {5, 8703, 382}, {30, 140, 3525}, {140, 10303, 15713}, {140, 11812, 3}, {140, 3530, 3526}, {140, 3628, 15694}, {140, 5054, 14869}, {140, 546, 11540}, {140, 549, 632}, {140, 631, 5}, {547, 11812, 15708}, {549, 15699, 15711}, {550, 15699, 3857}, {550, 632, 15699}, {632, 15716, 6939}, {1656, 12100, 15704}, {1656, 3528, 3861}, {3090, 17800, 3859}, {3146, 17568, 3091}, {3523, 15694, 3628}, {3523, 17538, 15706}, {3524, 7486, 15696}, {3525, 15717, 5070}, {3525, 15721, 15720}, {3526, 5067, 16239}, {3528, 15689, 548}, {3545, 15719, 15715}, {3627, 3850, 3845}, {3628, 8703, 3858}, {3843, 5072, 3855}, {3850, 11812, 12108}, {3850, 3853, 3843}, {3855, 15720, 3530}, {3856, 5066, 6938}, {3859, 17800, 15687}, {3859, 5070, 6892}, {3861, 12100, 3528}, {5054, 15702, 11812}, {5055, 10299, 12103}, {5070, 15720, 15717}, {5072, 15720, 15718}, {7486, 15696, 546}, {10124, 14892, 2}, {10124, 15701, 17504}, {10299, 12103, 15714}, {11539, 11812, 549}, {11539, 15713, 15702}, {11812, 15690, 15701}, {11812, 15702, 11539}, {12108, 14890, 140}, {12108, 14893, 3523}, {12812, 14891, 1657}, {14893, 15706, 8703}, {15702, 15721, 15723}, {15717, 15721, 631}, {15719, 15723, 30}, {61278, 61614, 9588}

X(61838) = X(2)X(3)∩X(13)X(43777)

Barycentrics    31*a^4+13*(b^2-c^2)^2-44*a^2*(b^2+c^2) : :
X(61838) = 13*X[2]+6*X[3], 12*X[182]+7*X[50994], 3*X[944]+16*X[51069], 12*X[1385]+7*X[51068], 15*X[3576]+4*X[50801], 12*X[3817]+7*X[50813], -2*X[4669]+21*X[31423], X[4677]+18*X[10165], 16*X[4745]+3*X[50818], 15*X[5085]+4*X[50958], 3*X[5587]+16*X[51086], 3*X[5603]+16*X[50829] and many others

X(61838) lies on these lines: {2, 3}, {13, 43777}, {14, 43778}, {15, 49859}, {16, 49860}, {182, 50994}, {371, 43323}, {372, 43322}, {944, 51069}, {1385, 51068}, {3576, 50801}, {3817, 50813}, {4669, 31423}, {4677, 10165}, {4745, 50818}, {5085, 50958}, {5237, 43447}, {5238, 43446}, {5334, 43305}, {5335, 43304}, {5587, 51086}, {5603, 50829}, {5657, 51077}, {6200, 14226}, {6221, 43387}, {6396, 14241}, {6398, 43386}, {6411, 43790}, {6412, 43789}, {6433, 42573}, {6434, 42572}, {6441, 32788}, {6442, 32787}, {6445, 42640}, {6446, 42639}, {6476, 43798}, {6477, 43797}, {6486, 43343}, {6487, 43342}, {6684, 51110}, {6776, 51143}, {7612, 60638}, {7967, 50804}, {8252, 42417}, {8253, 42418}, {8584, 51179}, {9766, 55823}, {10141, 43379}, {10142, 43378}, {10164, 50809}, {10516, 51139}, {10519, 51132}, {10645, 42589}, {10646, 42588}, {10653, 42996}, {10654, 42997}, {11055, 15819}, {11480, 49873}, {11481, 49874}, {12245, 51103}, {13886, 52046}, {13939, 52045}, {14494, 60287}, {14853, 50984}, {14912, 50961}, {16241, 43233}, {16242, 43232}, {21156, 36344}, {21157, 36319}, {21167, 50966}, {23302, 49875}, {23303, 49876}, {32789, 43256}, {32790, 43257}, {33416, 41113}, {33417, 41112}, {33602, 42120}, {33603, 42119}, {33604, 43103}, {33605, 43102}, {35255, 43375}, {35256, 43374}, {35820, 60307}, {35821, 60308}, {37640, 42533}, {37641, 42532}, {37832, 43771}, {37835, 43772}, {38064, 50992}, {38067, 60971}, {38068, 51093}, {41100, 43542}, {41101, 43543}, {41119, 43481}, {41120, 43482}, {41945, 42607}, {41946, 42606}, {42089, 43309}, {42092, 43308}, {42117, 43876}, {42118, 43875}, {42139, 43002}, {42142, 43003}, {42149, 42976}, {42152, 42977}, {42215, 42527}, {42216, 42526}, {42274, 43522}, {42277, 43521}, {42433, 43201}, {42434, 43202}, {42490, 43100}, {42491, 43107}, {42494, 42596}, {42495, 42597}, {42500, 49947}, {42501, 49948}, {42502, 49826}, {42503, 49827}, {42504, 42511}, {42505, 42510}, {42508, 49825}, {42509, 49824}, {42520, 43484}, {42521, 43483}, {42524, 42602}, {42525, 42603}, {42608, 53131}, {42609, 53130}, {42791, 43404}, {42792, 43403}, {42805, 43238}, {42806, 43239}, {42956, 42987}, {42957, 42986}, {43244, 43467}, {43245, 43468}, {43463, 49862}, {43464, 49861}, {47745, 51066}, {50810, 51108}, {50827, 51094}, {50828, 59388}, {50863, 61262}, {50964, 55657}, {50974, 50991}, {50980, 54174}, {50983, 51186}, {51071, 58441}, {51215, 55697}, {60127, 60645}, {60131, 60150}

X(61838) = inverse of X(61902) in orthocentroidal circle
X(61838) = inverse of X(61902) in Yff hyperbola
X(61838) = complement of X(61938)
X(61838) = anticomplement of X(61891)
X(61838) = pole of line {523, 61902} with respect to the orthocentroidal circle
X(61838) = pole of line {6, 61902} with respect to the Kiepert hyperbola
X(61838) = pole of line {523, 61902} with respect to the Yff hyperbola
X(61838) = pole of line {69, 10109} with respect to the Wallace hyperbola
X(61838) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(10109)}}, {{A, B, C, X(95), X(41106)}}, {{A, B, C, X(3534), X(36948)}}, {{A, B, C, X(3853), X(54667)}}, {{A, B, C, X(3857), X(22270)}}, {{A, B, C, X(3858), X(54763)}}, {{A, B, C, X(5073), X(54660)}}, {{A, B, C, X(12103), X(46412)}}, {{A, B, C, X(16239), X(18853)}}, {{A, B, C, X(19708), X(57895)}}, {{A, B, C, X(37174), X(60638)}}
X(61838) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10303, 15713}, {2, 15692, 3845}, {2, 15693, 11001}, {2, 15708, 12100}, {2, 15713, 15702}, {2, 15719, 376}, {2, 15721, 15701}, {2, 20, 10109}, {2, 3523, 3534}, {2, 3524, 15682}, {2, 3534, 5071}, {3, 17542, 3544}, {20, 140, 3525}, {20, 3854, 3627}, {140, 11812, 8703}, {140, 12101, 11540}, {140, 14891, 11539}, {140, 15699, 15694}, {140, 15721, 3524}, {140, 5054, 15721}, {140, 631, 3090}, {140, 7508, 3859}, {376, 15709, 3533}, {546, 5071, 3545}, {549, 10109, 15716}, {549, 11539, 546}, {549, 16239, 15688}, {549, 1656, 15705}, {549, 3545, 10299}, {631, 15702, 15709}, {632, 15707, 3543}, {3523, 5071, 15710}, {3524, 15702, 140}, {3524, 15721, 631}, {3530, 15723, 3839}, {3543, 6931, 5054}, {3845, 15722, 15692}, {5054, 15694, 14869}, {5068, 15692, 15689}, {5084, 15717, 3091}, {6931, 10303, 632}, {6956, 17538, 3146}, {8703, 10109, 3830}, {8703, 15685, 15697}, {10109, 15716, 20}, {10124, 10304, 5067}, {10124, 15720, 10304}, {10304, 17697, 381}, {11001, 15693, 15698}, {11539, 14891, 5070}, {12100, 15694, 2}, {12100, 15699, 15685}, {14869, 15694, 15708}, {15682, 15701, 15719}, {15688, 15694, 16239}, {15689, 15701, 15722}, {15694, 15708, 4}, {15701, 15716, 549}

X(61839) = X(2)X(3)∩X(3632)X(3653)

Barycentrics    26*a^4+11*(b^2-c^2)^2-37*a^2*(b^2+c^2) : :
X(61839) = 11*X[2]+5*X[3], X[355]+7*X[50833], X[551]+3*X[61614], -11*X[597]+3*X[55717], X[946]+7*X[51088], X[1351]+7*X[50981], X[1352]+7*X[50988], 5*X[1385]+3*X[38098], X[1482]+7*X[50826], X[3244]+15*X[38068], 11*X[3589]+X[55586], 7*X[3626]+5*X[32900] and many others

X(61839) lies on these lines: {2, 3}, {355, 50833}, {524, 55709}, {551, 61614}, {597, 55717}, {946, 51088}, {1351, 50981}, {1352, 50988}, {1385, 38098}, {1482, 50826}, {3244, 38068}, {3564, 55700}, {3589, 55586}, {3626, 32900}, {3629, 55712}, {3631, 55702}, {3632, 3653}, {3828, 28224}, {5032, 51184}, {5476, 55598}, {5480, 51141}, {5844, 58441}, {6154, 38069}, {6200, 41951}, {6329, 46267}, {6396, 41952}, {6433, 43514}, {6434, 43513}, {6494, 19116}, {6495, 19117}, {9543, 54597}, {10165, 34641}, {10168, 20583}, {11592, 58531}, {11645, 51139}, {11694, 24981}, {11898, 51181}, {12820, 42594}, {12821, 42595}, {13925, 43254}, {13993, 43255}, {14831, 44324}, {15808, 61524}, {16772, 42635}, {16773, 42636}, {16962, 42938}, {16963, 42939}, {18583, 55581}, {19878, 28202}, {20050, 38066}, {20190, 51143}, {21167, 55613}, {21356, 50987}, {25055, 50825}, {26614, 61561}, {28208, 51086}, {31423, 50824}, {33416, 42415}, {33417, 42416}, {33749, 41152}, {33751, 50960}, {37832, 43106}, {37835, 43105}, {38064, 40341}, {38065, 60957}, {38067, 60933}, {41107, 42949}, {41108, 42948}, {41112, 42774}, {41113, 42773}, {41121, 42590}, {41122, 42591}, {41943, 42500}, {41944, 42501}, {42225, 42601}, {42226, 42600}, {42260, 42642}, {42261, 42641}, {42480, 43107}, {42481, 43100}, {42488, 42792}, {42489, 42791}, {42496, 43111}, {42497, 43110}, {42504, 42993}, {42505, 42992}, {42596, 42973}, {42597, 42972}, {42598, 43109}, {42599, 43108}, {42633, 43198}, {42634, 43197}, {42777, 42955}, {42778, 42954}, {42956, 43251}, {42957, 43250}, {43102, 43874}, {43103, 43873}, {44299, 45956}, {47352, 50980}, {48310, 55605}, {50821, 51700}, {50827, 61281}, {50832, 53620}, {50956, 55671}, {50977, 51732}, {50984, 55592}, {50985, 55711}, {50990, 55701}, {51022, 55669}, {51068, 61297}, {51130, 55612}, {51849, 53130}, {51850, 53131}, {54169, 55589}, {56567, 61548}

X(61839) = midpoint of X(i) and X(j) for these {i,j}: {2, 3530}, {3, 10109}, {5, 15759}, {140, 11812}, {547, 14891}, {548, 3860}, {549, 10124}, {3534, 12102}, {3628, 12100}, {3850, 8703}, {3861, 15690}, {5054, 14890}, {11540, 12108}, {20190, 51143}, {33749, 41152}, {33751, 50960}, {50821, 51700}, {50827, 61281}, {50977, 51732}, {50984, 58445}, {51130, 55612}
X(61839) = reflection of X(i) in X(j) for these {i,j}: {11540, 140}, {12108, 11812}, {16239, 11540}, {3856, 10109}
X(61839) = complement of X(11737)
X(61839) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(38071)}}, {{A, B, C, X(1494), X(35018)}}, {{A, B, C, X(5055), X(57823)}}, {{A, B, C, X(5072), X(43970)}}, {{A, B, C, X(34200), X(57895)}}, {{A, B, C, X(47478), X(57894)}}
X(61839) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10299, 14269}, {2, 10304, 3544}, {2, 15700, 15687}, {2, 15708, 10299}, {2, 15710, 3851}, {2, 15720, 17504}, {2, 17504, 546}, {2, 3524, 382}, {2, 3529, 5055}, {2, 3851, 15699}, {2, 5054, 14869}, {5, 15692, 15691}, {30, 10109, 3856}, {30, 11812, 12108}, {30, 140, 11540}, {140, 12100, 11539}, {140, 12108, 16239}, {140, 15713, 14890}, {140, 5054, 11812}, {140, 547, 15694}, {140, 548, 3525}, {140, 549, 10124}, {381, 14093, 17800}, {381, 15703, 5056}, {381, 15707, 15715}, {381, 549, 12100}, {548, 15699, 3860}, {549, 15686, 3524}, {549, 15713, 15702}, {550, 14869, 631}, {550, 3544, 3853}, {631, 15694, 15714}, {631, 15709, 11001}, {632, 15686, 15703}, {3524, 15703, 15686}, {3524, 5056, 15695}, {3526, 15718, 5071}, {3530, 10124, 11737}, {3530, 14891, 15700}, {3530, 3860, 15710}, {3534, 14892, 12102}, {3545, 15711, 12103}, {3850, 11812, 15708}, {3853, 12100, 10304}, {5054, 10303, 15713}, {5054, 15694, 15721}, {5055, 15690, 3861}, {5055, 15712, 15690}, {5071, 15708, 15718}, {10124, 11737, 2}, {10124, 11812, 549}, {10124, 14891, 547}, {10299, 14269, 8703}, {11001, 12100, 15759}, {11001, 15688, 550}, {11114, 15710, 15707}, {11539, 12100, 3628}, {11540, 12108, 30}, {11812, 14890, 140}, {11812, 15759, 15701}, {12100, 15707, 3530}, {12100, 15714, 14891}, {15684, 15694, 15723}, {15686, 15703, 5066}, {15692, 15723, 5}, {15693, 15699, 548}, {15694, 15701, 15684}, {15695, 15703, 381}, {15701, 15723, 15692}

X(61840) = X(2)X(3)∩X(15)X(43296)

Barycentrics    13*a^4+6*(b^2-c^2)^2-19*a^2*(b^2+c^2) : :
X(61840) = 18*X[2]+7*X[3], -28*X[575]+3*X[6144], 9*X[599]+16*X[55704], X[1482]+24*X[58441], 3*X[1698]+2*X[31666], 24*X[3589]+X[55580], 14*X[3619]+11*X[55692], 4*X[3625]+21*X[10246], 4*X[3630]+21*X[5050], -3*X[3633]+28*X[15178], 9*X[3679]+16*X[58232], 3*X[3763]+2*X[55687] and many others

X(61840) lies on these lines: {2, 3}, {15, 43296}, {16, 43297}, {397, 42512}, {398, 42513}, {575, 6144}, {590, 6448}, {599, 55704}, {615, 6447}, {1482, 58441}, {1698, 31666}, {3411, 42520}, {3412, 42521}, {3589, 55580}, {3591, 9693}, {3619, 55692}, {3625, 10246}, {3630, 5050}, {3633, 15178}, {3679, 58232}, {3763, 55687}, {4114, 37545}, {4691, 10165}, {5237, 42132}, {5238, 42129}, {5351, 43029}, {5352, 43028}, {5418, 6428}, {5420, 6427}, {5447, 13321}, {5462, 54047}, {5640, 11592}, {5876, 33879}, {6390, 32878}, {6407, 32786}, {6408, 32785}, {6419, 13961}, {6420, 13903}, {6425, 18510}, {6426, 18512}, {6445, 42575}, {6446, 42574}, {6449, 53516}, {6450, 53513}, {6453, 13951}, {6454, 8976}, {6455, 32790}, {6456, 32789}, {6486, 43886}, {6487, 43885}, {6496, 42583}, {6497, 42582}, {6519, 43880}, {6522, 43879}, {7749, 22332}, {7772, 44535}, {7909, 55730}, {8148, 61614}, {9588, 58240}, {10113, 15023}, {10182, 34780}, {10193, 48672}, {10516, 55679}, {10541, 39899}, {11231, 18526}, {11898, 55701}, {13093, 58434}, {13630, 44299}, {14561, 55602}, {14924, 32223}, {14929, 32871}, {15012, 23039}, {15020, 34128}, {15024, 16982}, {15027, 15040}, {15039, 15061}, {15042, 23515}, {15057, 38632}, {15069, 55694}, {15819, 32520}, {15851, 61307}, {16241, 42435}, {16242, 42436}, {16261, 55286}, {16625, 54048}, {16960, 22238}, {16961, 22236}, {16966, 42928}, {16967, 42929}, {17852, 35822}, {18440, 55684}, {19862, 28232}, {20397, 32609}, {21167, 55620}, {22112, 37495}, {22115, 44787}, {22331, 31455}, {22712, 55793}, {25563, 58795}, {26614, 38627}, {28186, 58224}, {28204, 58229}, {30315, 58225}, {31276, 32523}, {31399, 50797}, {31652, 37637}, {32205, 54041}, {32455, 53092}, {32519, 61132}, {32875, 34229}, {33416, 36836}, {33417, 36843}, {34573, 55682}, {34595, 48661}, {34754, 42946}, {34755, 42947}, {36751, 61314}, {36967, 42611}, {36968, 42610}, {36990, 55675}, {38064, 51175}, {38068, 50805}, {38122, 61000}, {38317, 55626}, {38638, 40685}, {38728, 38795}, {38729, 38794}, {38739, 38751}, {38740, 38750}, {40995, 52712}, {41112, 42793}, {41113, 42794}, {41963, 43255}, {41964, 43254}, {42149, 42500}, {42152, 42501}, {42153, 42593}, {42156, 42592}, {42163, 42951}, {42166, 42950}, {42258, 42601}, {42259, 42600}, {42488, 42774}, {42489, 42773}, {42490, 42989}, {42491, 42988}, {42492, 43465}, {42493, 43466}, {42518, 42992}, {42519, 42993}, {42566, 43430}, {42567, 43431}, {42580, 42963}, {42581, 42962}, {42777, 42944}, {42778, 42945}, {42785, 55622}, {42786, 55671}, {42795, 43547}, {42796, 43546}, {42801, 43238}, {42802, 43239}, {42936, 43013}, {42937, 43012}, {42938, 43483}, {42939, 43484}, {43010, 43295}, {43011, 43294}, {43193, 43491}, {43194, 43492}, {47352, 55721}, {47355, 55606}, {48910, 55652}, {50833, 61255}, {50977, 53858}, {51126, 55629}, {51524, 52886}, {52703, 59655}, {53023, 55647}, {53097, 58445}, {54131, 55617}, {58235, 61286}, {59380, 60977}, {59381, 60962}

X(61840) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(5072)}}, {{A, B, C, X(3839), X(22270)}}, {{A, B, C, X(3859), X(13599)}}, {{A, B, C, X(5071), X(22268)}}, {{A, B, C, X(5076), X(60007)}}, {{A, B, C, X(14938), X(15709)}}, {{A, B, C, X(15689), X(57895)}}, {{A, B, C, X(15697), X(46412)}}, {{A, B, C, X(33703), X(36948)}}, {{A, B, C, X(40448), X(49137)}}
X(61840) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15686, 5055}, {2, 15702, 14890}, {2, 3, 5072}, {2, 3524, 14893}, {2, 3843, 1656}, {2, 549, 15689}, {3, 15694, 632}, {3, 3090, 382}, {3, 3851, 15704}, {3, 5055, 3146}, {3, 5070, 546}, {3, 546, 3534}, {5, 140, 15709}, {5, 15691, 4}, {140, 10303, 3}, {140, 14869, 3525}, {140, 15713, 631}, {140, 5054, 3526}, {140, 631, 15694}, {546, 4221, 15681}, {547, 10299, 17800}, {631, 3522, 549}, {631, 5071, 3523}, {1656, 15693, 15696}, {1656, 15696, 381}, {1656, 15712, 1657}, {1656, 3091, 5079}, {1656, 5072, 12812}, {3091, 17538, 3627}, {3523, 11539, 5070}, {3524, 16239, 3851}, {3525, 10303, 14869}, {3526, 5054, 15720}, {3533, 15721, 3530}, {3627, 12812, 3091}, {3627, 14869, 12108}, {3850, 15712, 3522}, {5054, 15700, 11812}, {5054, 15723, 15701}, {5067, 12100, 5073}, {10124, 15704, 16408}, {11539, 14891, 2}, {11540, 15708, 15703}, {12108, 12812, 15712}, {12812, 14093, 5076}, {12812, 15712, 17538}, {12812, 17538, 3843}, {14093, 15693, 15706}, {14782, 14783, 15721}, {15683, 16418, 17697}, {15684, 15689, 11001}, {15684, 15692, 14093}, {15688, 15693, 15692}, {15692, 15694, 15723}, {15694, 15713, 5054}, {15696, 15720, 15693}, {15701, 15723, 15688}, {15703, 15708, 15716}, {15708, 17528, 15698}, {15722, 17800, 10299}, {16434, 17538, 15697}

X(61841) = X(1)X(50822)∩X(2)X(3)

Barycentrics    28*a^4+13*(b^2-c^2)^2-41*a^2*(b^2+c^2) : :
X(61841) = 4*X[1]+5*X[50822], 13*X[2]+5*X[3], 4*X[6]+5*X[51184], 4*X[10]+5*X[50832], 4*X[69]+5*X[51180], 4*X[141]+5*X[50987], 4*X[1125]+5*X[50825], 5*X[1483]+4*X[34641], 4*X[3244]+5*X[50823], 4*X[3589]+5*X[50980], 4*X[3626]+5*X[50824], -X[3629]+10*X[10168] and many others

X(61841) lies on these lines: {1, 50822}, {2, 3}, {6, 51184}, {10, 50832}, {69, 51180}, {141, 50987}, {1125, 50825}, {1151, 42640}, {1152, 42639}, {1483, 34641}, {3068, 42644}, {3069, 42643}, {3244, 50823}, {3589, 50980}, {3626, 50824}, {3629, 10168}, {3631, 50979}, {3632, 50831}, {3634, 51084}, {3636, 50821}, {3653, 38112}, {3818, 51139}, {4681, 51048}, {4686, 51047}, {4739, 51045}, {4745, 61297}, {6200, 41953}, {6329, 50977}, {6396, 41954}, {6411, 42642}, {6412, 42641}, {6433, 43343}, {6434, 43342}, {6441, 43212}, {6442, 43211}, {6476, 52045}, {6477, 52046}, {6484, 42573}, {6485, 42572}, {8981, 41967}, {10165, 38098}, {10283, 58441}, {11008, 51183}, {11178, 50988}, {11231, 38081}, {11542, 43877}, {11543, 43878}, {13966, 41968}, {15808, 50826}, {16241, 42635}, {16242, 42636}, {16644, 43111}, {16645, 43110}, {16962, 42121}, {16963, 42124}, {18480, 51086}, {19875, 61247}, {20583, 48876}, {21850, 50984}, {22791, 50829}, {25055, 61614}, {28198, 61270}, {31423, 34747}, {33416, 42923}, {33417, 42922}, {33749, 51142}, {34573, 51137}, {35022, 49102}, {35255, 43255}, {35256, 43254}, {37705, 50828}, {38028, 38068}, {38066, 61283}, {38067, 38111}, {40341, 50986}, {41100, 42949}, {41101, 42948}, {41119, 42590}, {41120, 42591}, {42089, 42633}, {42092, 42634}, {42129, 42415}, {42132, 42416}, {42157, 43247}, {42158, 43246}, {42472, 43648}, {42473, 43647}, {42596, 42797}, {42597, 42798}, {42786, 50971}, {42912, 42917}, {42913, 42916}, {42947, 61719}, {42972, 43105}, {42973, 43106}, {43020, 43250}, {43021, 43251}, {43230, 43642}, {43231, 43641}, {43403, 43640}, {43404, 43639}, {43485, 49907}, {43486, 49908}, {46931, 50797}, {50958, 55691}, {50964, 55656}, {50994, 55701}, {57895, 57897}

X(61841) = midpoint of X(i) and X(j) for these {i,j}: {2, 15707}, {5054, 15709}, {5055, 15705}
X(61841) = reflection of X(i) in X(j) for these {i,j}: {11539, 15709}, {15709, 140}, {17504, 15707}, {8703, 15705}
X(61841) = complement of X(61933)
X(61841) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(11737)}}, {{A, B, C, X(547), X(57897)}}, {{A, B, C, X(550), X(57895)}}, {{A, B, C, X(5079), X(57822)}}, {{A, B, C, X(46452), X(55858)}}
X(61841) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10299, 381}, {2, 15692, 3855}, {2, 15700, 546}, {2, 15707, 30}, {2, 15708, 15710}, {2, 15715, 3851}, {2, 3, 11737}, {2, 3524, 14269}, {2, 3530, 15687}, {2, 3544, 15703}, {2, 376, 5079}, {2, 382, 547}, {2, 549, 550}, {2, 631, 15700}, {3, 13742, 3850}, {5, 14869, 15720}, {5, 3522, 3627}, {5, 549, 15711}, {5, 8703, 3543}, {30, 140, 15709}, {140, 11812, 15694}, {140, 15702, 15713}, {140, 15713, 549}, {140, 5054, 11539}, {381, 15694, 17678}, {547, 15701, 15712}, {549, 11539, 15699}, {549, 632, 3845}, {550, 3857, 382}, {631, 3525, 5068}, {3090, 15718, 15690}, {3523, 15723, 5066}, {3523, 5066, 15714}, {3524, 3545, 3522}, {3526, 15721, 12100}, {3528, 16849, 5056}, {3529, 15720, 3530}, {3534, 15693, 6908}, {3534, 15694, 3533}, {3543, 15694, 10124}, {3628, 15693, 15686}, {3830, 15701, 6863}, {4189, 15681, 11540}, {5054, 15702, 14890}, {5054, 5055, 631}, {5067, 14093, 3860}, {5070, 15698, 14893}, {10109, 15692, 15704}, {10124, 15722, 5}, {10303, 15694, 11812}, {11114, 15715, 15707}, {11539, 14869, 17504}, {11539, 15699, 632}, {11539, 15713, 5054}, {11539, 17504, 2}, {11540, 11812, 12101}, {11541, 14891, 8703}, {14269, 15688, 3529}, {14269, 15720, 3524}, {15673, 15705, 11112}, {15687, 17504, 15688}, {15700, 15720, 15722}, {15703, 15719, 548}, {16417, 17542, 16863}, {16418, 17535, 16857}

X(61842) = X(2)X(3)∩X(8)X(61289)

Barycentrics    15*a^4+7*(b^2-c^2)^2-22*a^2*(b^2+c^2) : :
X(61842) = 21*X[2]+8*X[3], 15*X[8]+14*X[61289], X[145]+28*X[31423], 2*X[185]+27*X[33879], 3*X[962]+26*X[31425], 7*X[1352]+22*X[55689], 12*X[3576]+17*X[46932], 15*X[3616]+14*X[9588], 5*X[3617]+24*X[10165], 5*X[3621]+24*X[61287], 21*X[3622]+8*X[11362], 5*X[3623]+24*X[26446] and many others

X(61842) lies on these lines: {2, 3}, {8, 61289}, {69, 32873}, {99, 32897}, {145, 31423}, {185, 33879}, {315, 32898}, {486, 9543}, {515, 46930}, {590, 42569}, {615, 42568}, {962, 31425}, {1131, 32789}, {1132, 32790}, {1352, 55689}, {1588, 9692}, {3068, 6471}, {3069, 6470}, {3087, 61312}, {3314, 55729}, {3316, 43320}, {3317, 9693}, {3411, 42089}, {3412, 42092}, {3576, 46932}, {3616, 9588}, {3617, 10165}, {3621, 61287}, {3622, 11362}, {3623, 26446}, {3624, 20070}, {3785, 32871}, {3828, 61252}, {3876, 10156}, {4301, 5550}, {4678, 37727}, {5237, 43495}, {5238, 43496}, {5265, 15888}, {5274, 52793}, {5281, 37722}, {5286, 31457}, {5304, 9606}, {5326, 9657}, {5433, 8162}, {5603, 31447}, {5657, 61277}, {5731, 31399}, {5734, 6684}, {5881, 46933}, {5921, 55690}, {6337, 32872}, {6390, 32882}, {6409, 53520}, {6410, 53517}, {6468, 32786}, {6469, 32785}, {6683, 44434}, {6776, 55693}, {7294, 9670}, {7585, 41966}, {7586, 31454}, {7735, 31492}, {7749, 31450}, {7777, 55819}, {7782, 32883}, {7796, 32835}, {7806, 55797}, {7814, 32839}, {7871, 10513}, {7875, 55780}, {7987, 54448}, {7998, 14531}, {8252, 43512}, {8253, 31414}, {8596, 20398}, {8972, 42566}, {9540, 35813}, {9542, 13939}, {9589, 19862}, {9705, 13336}, {9729, 44299}, {9778, 34595}, {9780, 37712}, {9812, 19878}, {10187, 41120}, {10188, 41119}, {10246, 20052}, {10519, 55716}, {10541, 51136}, {10576, 42604}, {10577, 42605}, {10595, 61614}, {11231, 61244}, {11488, 42491}, {11489, 42490}, {11522, 50829}, {12245, 61280}, {13624, 61257}, {13665, 43505}, {13785, 43506}, {13925, 43517}, {13935, 35812}, {13941, 42567}, {13993, 43518}, {14561, 55601}, {14853, 55590}, {14907, 32884}, {14927, 51128}, {14930, 31401}, {14986, 31452}, {15043, 15606}, {15056, 15082}, {15178, 20049}, {15516, 51170}, {16241, 43373}, {16242, 43372}, {18581, 42597}, {18582, 42596}, {19116, 43375}, {19117, 43374}, {19877, 37714}, {20014, 61286}, {20080, 40107}, {20081, 61132}, {22235, 36843}, {22237, 36836}, {22712, 55792}, {25555, 51028}, {30389, 51082}, {31145, 61288}, {31253, 58221}, {31407, 31455}, {31465, 61322}, {31666, 38074}, {31670, 55635}, {32787, 43884}, {32788, 43883}, {32824, 32893}, {32840, 34229}, {33416, 43294}, {33417, 43295}, {35510, 36948}, {35595, 37526}, {37640, 43480}, {37641, 43479}, {38064, 51178}, {38068, 50817}, {38122, 61006}, {38317, 55625}, {38740, 52695}, {41945, 43377}, {41946, 43376}, {41957, 42571}, {41958, 42570}, {42090, 43474}, {42091, 43473}, {42103, 42499}, {42106, 42498}, {42139, 42611}, {42142, 42610}, {42147, 43869}, {42148, 43870}, {42149, 43233}, {42152, 43232}, {42159, 43645}, {42162, 43646}, {42274, 43561}, {42277, 43560}, {42474, 43477}, {42475, 43478}, {42500, 43239}, {42501, 43238}, {42510, 42979}, {42511, 42978}, {42512, 43775}, {42513, 43776}, {42625, 42775}, {42626, 42776}, {42684, 43772}, {42685, 43771}, {42817, 43306}, {42818, 43307}, {42926, 42984}, {42927, 42985}, {42992, 43252}, {42993, 43253}, {42994, 49811}, {42995, 49810}, {43244, 43443}, {43245, 43442}, {43254, 43322}, {43255, 43323}, {43889, 60293}, {43890, 60294}, {47355, 61044}, {47586, 60131}, {50975, 55675}, {50980, 55580}, {51109, 58245}, {51127, 51538}, {55585, 58445}, {59417, 61276}, {60118, 60645}, {60291, 60297}, {60292, 60298}

X(61842) = anticomplement of X(46935)
X(61842) = pole of line {185, 15697} with respect to the Jerabek hyperbola
X(61842) = pole of line {69, 61914} with respect to the Wallace hyperbola
X(61842) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(68), X(38071)}}, {{A, B, C, X(95), X(5068)}}, {{A, B, C, X(1105), X(15697)}}, {{A, B, C, X(3090), X(35510)}}, {{A, B, C, X(3146), X(36948)}}, {{A, B, C, X(3346), X(15712)}}, {{A, B, C, X(3521), X(35434)}}, {{A, B, C, X(3533), X(15318)}}, {{A, B, C, X(3843), X(22270)}}, {{A, B, C, X(5079), X(46921)}}, {{A, B, C, X(10303), X(52441)}}, {{A, B, C, X(11737), X(18855)}}, {{A, B, C, X(15687), X(60007)}}, {{A, B, C, X(15689), X(46412)}}, {{A, B, C, X(16251), X(49133)}}, {{A, B, C, X(35403), X(54552)}}, {{A, B, C, X(40448), X(49138)}}
X(61842) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15717, 3832}, {2, 17578, 7486}, {2, 3, 5068}, {2, 3522, 15022}, {2, 5, 13735}, {2, 5141, 16393}, {2, 631, 15717}, {3, 140, 15709}, {3, 15683, 3522}, {3, 1656, 15687}, {3, 3855, 20}, {3, 4, 15697}, {3, 5068, 15683}, {4, 3090, 11737}, {5, 5054, 631}, {5, 548, 3830}, {20, 3091, 3853}, {20, 3855, 17578}, {20, 7486, 3855}, {140, 14869, 15694}, {140, 14890, 14869}, {140, 15702, 10303}, {140, 15713, 3}, {140, 5054, 3525}, {549, 15695, 3524}, {549, 5070, 3528}, {631, 15708, 17533}, {631, 5067, 3530}, {632, 3524, 5056}, {1656, 15718, 12103}, {2041, 2042, 3533}, {3090, 13741, 16417}, {3090, 15692, 5059}, {3090, 15720, 15692}, {3091, 3860, 3854}, {3146, 3523, 15705}, {3146, 5068, 3839}, {3525, 5054, 3523}, {3526, 3530, 5067}, {3528, 3533, 5070}, {3528, 5070, 3091}, {3628, 10299, 3543}, {3628, 15701, 10299}, {3853, 14892, 3856}, {5054, 15694, 12100}, {5054, 15718, 11812}, {5066, 15695, 15682}, {10124, 12100, 15699}, {10124, 15713, 5054}, {11539, 15692, 2}, {11539, 15720, 3090}, {11737, 14869, 15720}, {11812, 14892, 549}, {12100, 16239, 5}, {12812, 15688, 4}, {13735, 15717, 3146}, {15686, 15699, 5066}, {15692, 15702, 17556}, {15697, 15721, 15708}, {15702, 15709, 15713}, {15709, 15713, 15721}

X(61843) = X(2)X(3)∩X(6)X(43483)

Barycentrics    17*a^4+8*(b^2-c^2)^2-25*a^2*(b^2+c^2) : :
X(61843) = 8*X[2]+3*X[3], 8*X[8]+25*X[58233], 6*X[165]+5*X[50806], 6*X[182]+5*X[50993], -12*X[575]+X[51187], 4*X[599]+7*X[55705], -12*X[1153]+X[8667], 6*X[1385]+5*X[51066], -3*X[1482]+14*X[51110], 9*X[3653]+2*X[4669], 3*X[3654]+8*X[51108], 3*X[3655]+8*X[51069] and many others

X(61843) lies on these lines: {2, 3}, {6, 43483}, {8, 58233}, {13, 42508}, {14, 42509}, {165, 50806}, {182, 50993}, {485, 42606}, {486, 42607}, {542, 55692}, {575, 51187}, {599, 55705}, {1153, 8667}, {1327, 42600}, {1328, 42601}, {1385, 51066}, {1482, 51110}, {1587, 6473}, {1588, 6472}, {3070, 42608}, {3071, 42609}, {3653, 4669}, {3654, 51108}, {3655, 51069}, {3679, 32900}, {4677, 10246}, {4745, 10165}, {5024, 39593}, {5050, 15533}, {5093, 50977}, {5215, 9301}, {5306, 22246}, {5339, 42597}, {5340, 42596}, {5418, 6501}, {5420, 6500}, {5475, 15603}, {5476, 55593}, {5657, 58238}, {5731, 50797}, {5790, 50828}, {5886, 50829}, {6055, 14692}, {6199, 13847}, {6390, 32892}, {6395, 13846}, {6407, 35823}, {6408, 35822}, {6417, 35814}, {6418, 35815}, {6433, 42557}, {6434, 42558}, {6445, 8252}, {6446, 8253}, {6560, 43380}, {6561, 43381}, {6684, 51109}, {6771, 36767}, {7619, 9766}, {7622, 51122}, {7987, 38083}, {8148, 25055}, {8584, 50982}, {8976, 52046}, {9167, 38739}, {9540, 43212}, {9542, 43387}, {9681, 41951}, {9690, 42527}, {9691, 13951}, {10168, 15534}, {10175, 51086}, {10247, 50821}, {10302, 60175}, {10576, 42524}, {10577, 42525}, {10645, 42688}, {10646, 42689}, {10653, 42502}, {10654, 42503}, {10992, 41154}, {11171, 14711}, {11179, 51143}, {11231, 50798}, {11362, 41150}, {11402, 44751}, {11465, 11592}, {11480, 41122}, {11481, 41121}, {11482, 46267}, {11485, 49906}, {11486, 49905}, {11645, 55678}, {11669, 60282}, {11898, 50994}, {12007, 22165}, {12017, 21358}, {12188, 26614}, {12355, 34127}, {12645, 51068}, {12816, 42625}, {12817, 42626}, {13340, 58470}, {13363, 54047}, {13624, 19876}, {13665, 42418}, {13785, 42417}, {13935, 43211}, {14537, 15655}, {14561, 50984}, {14830, 31274}, {14971, 38733}, {14981, 41151}, {15037, 37672}, {15082, 18435}, {15300, 38224}, {16241, 42532}, {16242, 42533}, {16644, 42506}, {16645, 42507}, {16962, 43239}, {16963, 43238}, {17825, 37496}, {17851, 32785}, {18362, 53095}, {18480, 58224}, {18581, 42791}, {18582, 42792}, {19924, 55632}, {22712, 55791}, {23267, 60299}, {23273, 60300}, {23302, 42510}, {23303, 42511}, {25406, 50954}, {25561, 55676}, {26446, 50827}, {31423, 37624}, {31884, 50963}, {32027, 55727}, {32786, 52047}, {32789, 53131}, {32790, 53130}, {32896, 34229}, {33416, 33606}, {33417, 33607}, {34126, 38636}, {34128, 38638}, {34718, 38068}, {34773, 58228}, {35751, 59383}, {36329, 59384}, {36386, 49959}, {36388, 49960}, {36521, 38750}, {36523, 38748}, {36948, 40995}, {37727, 51070}, {37832, 42903}, {37835, 42902}, {38028, 50805}, {38069, 38762}, {38072, 55629}, {38110, 50962}, {39561, 51174}, {40107, 51188}, {41107, 42115}, {41108, 42116}, {41112, 42132}, {41113, 42129}, {41943, 42977}, {41944, 42976}, {41945, 43343}, {41946, 43342}, {42089, 42500}, {42092, 42501}, {42096, 42499}, {42097, 42498}, {42099, 42475}, {42100, 42474}, {42122, 43247}, {42123, 43246}, {42125, 42684}, {42128, 42685}, {42130, 43101}, {42131, 43104}, {42154, 42795}, {42155, 42796}, {42215, 43882}, {42216, 43881}, {42491, 61719}, {42492, 52080}, {42493, 52079}, {42526, 43415}, {42566, 43888}, {42567, 43887}, {42815, 49875}, {42816, 49876}, {42912, 49812}, {42913, 49813}, {42934, 42937}, {42935, 42936}, {42950, 43416}, {42951, 43417}, {42952, 43418}, {42953, 43419}, {42968, 49826}, {42969, 49827}, {42974, 49860}, {42975, 49859}, {43028, 43032}, {43029, 43033}, {43108, 43404}, {43109, 43403}, {43199, 43302}, {43200, 43303}, {43254, 43430}, {43255, 43431}, {44456, 47352}, {46265, 61735}, {47353, 51137}, {47355, 55604}, {48680, 59376}, {50800, 54447}, {50810, 61614}, {50820, 61264}, {50823, 51092}, {50824, 51072}, {50826, 59417}, {50830, 59503}, {50955, 51186}, {50976, 55667}, {50979, 50990}, {50980, 54132}, {50981, 51172}, {50991, 51138}, {51024, 55643}, {51189, 53093}, {53104, 60228}, {54131, 55616}, {54521, 60646}, {54608, 60278}, {54643, 60100}, {54866, 60643}, {55584, 58445}, {58247, 61524}, {59381, 60963}, {60102, 60637}, {60192, 60239}

X(61843) = midpoint of X(i) and X(j) for these {i,j}: {2, 15719}, {3525, 15721}, {5056, 15715}, {5070, 15718}, {15720, 15723}
X(61843) = reflection of X(i) in X(j) for these {i,j}: {15716, 15719}, {15717, 549}, {15718, 15720}, {15720, 15721}, {15723, 3525}, {3, 15718}, {381, 5056}, {5070, 15723}
X(61843) = inverse of X(61898) in orthocentroidal circle
X(61843) = inverse of X(61898) in Yff hyperbola
X(61843) = complement of X(61932)
X(61843) = anticomplement of X(61890)
X(61843) = pole of line {523, 61898} with respect to the orthocentroidal circle
X(61843) = pole of line {6, 43568} with respect to the Kiepert hyperbola
X(61843) = pole of line {523, 61898} with respect to the Yff hyperbola
X(61843) = pole of line {69, 61913} with respect to the Wallace hyperbola
X(61843) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(95), X(19709)}}, {{A, B, C, X(3534), X(57895)}}, {{A, B, C, X(5067), X(34483)}}, {{A, B, C, X(10109), X(57822)}}, {{A, B, C, X(10301), X(60175)}}, {{A, B, C, X(11001), X(13623)}}, {{A, B, C, X(15022), X(22268)}}, {{A, B, C, X(15682), X(36948)}}, {{A, B, C, X(15717), X(18317)}}, {{A, B, C, X(22270), X(50689)}}, {{A, B, C, X(40448), X(49139)}}, {{A, B, C, X(46412), X(50693)}}, {{A, B, C, X(46452), X(55859)}}, {{A, B, C, X(52285), X(54643)}}
X(61843) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11812, 15693}, {2, 12100, 381}, {2, 15682, 547}, {2, 15693, 3830}, {2, 15702, 15713}, {2, 15709, 11540}, {2, 15722, 15685}, {2, 3523, 15682}, {2, 3524, 3845}, {2, 376, 10109}, {2, 3845, 1656}, {3, 15701, 15722}, {3, 15703, 14269}, {3, 5055, 15684}, {4, 549, 15706}, {5, 15700, 15689}, {5, 15708, 15700}, {30, 15721, 15720}, {30, 15723, 5070}, {30, 549, 15717}, {140, 10303, 3526}, {140, 15702, 5054}, {140, 5054, 15694}, {140, 549, 15709}, {381, 10304, 17800}, {381, 5054, 631}, {382, 15701, 6863}, {547, 15688, 3843}, {549, 11539, 3628}, {549, 3857, 17504}, {631, 3525, 5056}, {631, 3544, 3523}, {1656, 15693, 15697}, {1656, 3524, 15681}, {2478, 5067, 632}, {3146, 5056, 3855}, {3523, 15682, 15711}, {3526, 15720, 5072}, {3530, 3545, 14093}, {3533, 15692, 15699}, {3534, 10304, 15695}, {3534, 15693, 15698}, {3534, 15706, 15759}, {3545, 14093, 5073}, {3628, 15704, 3544}, {3839, 14891, 15696}, {3855, 15717, 548}, {5054, 15693, 11812}, {5054, 15720, 15721}, {5066, 8703, 15640}, {5067, 15705, 15687}, {5071, 17504, 1657}, {9167, 38739, 48657}, {10124, 14869, 3524}, {10303, 15702, 14890}, {10303, 15709, 549}, {10304, 15709, 11539}, {10304, 15717, 15715}, {11001, 15698, 10304}, {11539, 11812, 11001}, {11539, 12100, 2}, {11539, 14869, 15714}, {11540, 11812, 5066}, {11812, 15693, 15701}, {12100, 15695, 3}, {12100, 15715, 15716}, {12108, 15699, 15692}, {15640, 15698, 8703}, {15681, 15694, 10124}, {15682, 15711, 15688}, {15692, 15699, 382}, {15694, 15718, 15723}, {15695, 15701, 15707}, {15695, 15707, 12100}, {15695, 17800, 3534}, {15702, 15709, 10303}, {15716, 15719, 15718}, {15716, 15720, 15719}, {15717, 15723, 5055}, {15720, 15723, 30}, {16239, 17504, 5071}, {41100, 43544, 33607}, {41101, 43545, 33606}, {43483, 43484, 6}, {43513, 43525, 43568}, {43514, 43526, 43569}, {47353, 51137, 55682}

X(61844) = X(2)X(3)∩X(13)X(43870)

Barycentrics    23*a^4+11*(b^2-c^2)^2-34*a^2*(b^2+c^2) : :
X(61844) = 11*X[2]+4*X[3], -16*X[141]+X[51215], -X[147]+16*X[22247], -X[193]+16*X[10168], -16*X[1125]+X[50872], -16*X[1153]+X[9740], X[3241]+14*X[31423], X[3448]+4*X[11693], -16*X[3589]+X[51028], 7*X[3619]+8*X[50983], 11*X[3620]+16*X[55702], 7*X[3622]+8*X[50821] and many others

X(61844) lies on these lines: {2, 3}, {13, 43870}, {14, 43869}, {15, 42513}, {16, 42512}, {141, 51215}, {147, 22247}, {193, 10168}, {253, 57895}, {395, 42516}, {396, 42517}, {397, 42518}, {398, 42519}, {1125, 50872}, {1131, 53131}, {1132, 53130}, {1153, 9740}, {3241, 31423}, {3448, 11693}, {3582, 5281}, {3584, 5265}, {3589, 51028}, {3619, 50983}, {3620, 55702}, {3622, 50821}, {3624, 34632}, {3634, 50864}, {3655, 46933}, {4678, 50824}, {4698, 51064}, {4772, 51045}, {5032, 55713}, {5237, 49825}, {5238, 49824}, {5368, 31400}, {5476, 55592}, {5734, 51109}, {5921, 20582}, {5965, 33748}, {6221, 43798}, {6329, 51214}, {6337, 32893}, {6398, 43797}, {6435, 7586}, {6436, 7585}, {6449, 43506}, {6450, 43505}, {6480, 43514}, {6481, 43513}, {6488, 43410}, {6489, 43409}, {6498, 13966}, {6499, 8981}, {6519, 42527}, {6522, 42526}, {7622, 11148}, {7811, 32839}, {7998, 16226}, {8148, 50826}, {8859, 10256}, {8972, 43254}, {9541, 43792}, {9588, 51108}, {9780, 50828}, {10165, 53620}, {10519, 55717}, {10541, 51143}, {11160, 55709}, {11542, 43252}, {11543, 43253}, {12699, 51088}, {13624, 46930}, {13941, 43255}, {14075, 37665}, {14561, 55599}, {14853, 55589}, {15082, 20791}, {15933, 31231}, {16772, 49812}, {16773, 49813}, {16962, 42089}, {16963, 42092}, {16966, 43540}, {16967, 43541}, {18440, 50988}, {18493, 50809}, {18525, 50833}, {19872, 34648}, {19875, 28236}, {19877, 50811}, {19878, 50865}, {19883, 28228}, {20057, 50827}, {20423, 55586}, {22235, 49875}, {22237, 49876}, {22712, 55788}, {23249, 42600}, {23259, 42601}, {25055, 58441}, {27268, 51049}, {28232, 38021}, {28234, 38068}, {30389, 51069}, {31253, 50863}, {31401, 34571}, {31670, 51141}, {32785, 43259}, {32786, 43258}, {32787, 42523}, {32788, 42522}, {32835, 37671}, {32874, 37688}, {34573, 51023}, {34595, 50808}, {34627, 46932}, {34628, 51073}, {35812, 43884}, {35813, 43883}, {37640, 42501}, {37641, 42500}, {38067, 59375}, {38076, 58221}, {38081, 58230}, {38083, 54448}, {38317, 55621}, {38748, 41135}, {41121, 42596}, {41122, 42597}, {41943, 42521}, {41944, 42520}, {42095, 43202}, {42098, 43201}, {42099, 43478}, {42100, 43477}, {42488, 49874}, {42489, 49873}, {42510, 42936}, {42511, 42937}, {42557, 43343}, {42558, 43342}, {42610, 43769}, {42611, 43770}, {42625, 42683}, {42626, 42682}, {42777, 42804}, {42778, 42803}, {42910, 43466}, {42911, 43465}, {42912, 43464}, {42913, 43463}, {42932, 43874}, {42933, 43873}, {43024, 43248}, {43025, 43249}, {43102, 43543}, {43103, 43542}, {43242, 43403}, {43243, 43404}, {44456, 50981}, {46934, 50810}, {47355, 50984}, {50664, 51178}, {50819, 61261}, {50956, 55672}, {50967, 55723}, {50977, 51171}, {50990, 53093}, {51024, 51127}, {51079, 58217}, {51126, 51211}, {51128, 51139}, {51130, 55607}, {51177, 55678}, {52703, 52707}, {52711, 52712}, {54132, 55581}, {54173, 55719}, {55605, 61044}

X(61844) = midpoint of X(i) and X(j) for these {i,j}: {3091, 10304}, {5054, 15694}, {14269, 15696}, {15699, 15712}
X(61844) = reflection of X(i) in X(j) for these {i,j}: {10304, 15692}, {14093, 17504}, {15697, 10304}, {3545, 1656}, {5054, 15713}, {631, 5054}
X(61844) = complement of X(61930)
X(61844) = anticomplement of X(61889)
X(61844) = pole of line {69, 61912} with respect to the Wallace hyperbola
X(61844) = intersection, other than A, B, C, of circumconics {{A, B, C, X(20), X(57895)}}, {{A, B, C, X(253), X(547)}}, {{A, B, C, X(3543), X(36948)}}, {{A, B, C, X(5056), X(57822)}}, {{A, B, C, X(7486), X(36889)}}, {{A, B, C, X(15696), X(46412)}}, {{A, B, C, X(19709), X(46921)}}, {{A, B, C, X(46452), X(55862)}}, {{A, B, C, X(46936), X(55958)}}
X(61844) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10303, 15721}, {2, 15692, 3091}, {2, 15702, 10303}, {2, 15705, 3545}, {2, 15719, 15640}, {2, 3146, 547}, {2, 3522, 5071}, {2, 3523, 3543}, {2, 3524, 3839}, {2, 3543, 7486}, {2, 376, 5056}, {2, 5068, 15703}, {20, 5056, 546}, {30, 10304, 15697}, {30, 17504, 14093}, {140, 14890, 11539}, {140, 15702, 2}, {140, 15713, 15694}, {140, 5054, 15709}, {381, 15711, 17538}, {546, 11812, 549}, {546, 549, 15716}, {547, 15698, 3146}, {547, 15720, 15698}, {549, 10109, 3}, {549, 16239, 3830}, {549, 3830, 10299}, {631, 15702, 15713}, {631, 3525, 1656}, {631, 3526, 17578}, {631, 5071, 15693}, {3090, 12100, 15683}, {3523, 16857, 3832}, {3524, 15688, 15705}, {3524, 3545, 15688}, {3525, 10299, 16239}, {3525, 15684, 15673}, {3525, 15720, 13742}, {3526, 15707, 15699}, {3530, 15703, 11001}, {3533, 14869, 15717}, {3545, 15709, 3525}, {3624, 50829, 34632}, {3628, 15700, 15682}, {3843, 15693, 15714}, {5054, 11540, 15710}, {5054, 15707, 11812}, {5066, 15718, 3528}, {5071, 15693, 3522}, {10124, 15701, 4}, {10299, 15022, 20}, {10299, 16239, 15022}, {10303, 15708, 5054}, {10303, 15709, 10304}, {10304, 15708, 3523}, {10304, 15721, 15708}, {11001, 15703, 5068}, {11540, 14869, 381}, {11812, 15699, 15707}, {12100, 15723, 3090}, {14093, 15694, 10124}, {14269, 15696, 30}, {14892, 15701, 3524}, {15693, 15694, 632}, {15694, 15711, 3533}, {15694, 15713, 631}, {15699, 15707, 376}, {15711, 15717, 15692}, {47355, 50984, 54170}, {51073, 51086, 34628}

X(61845) = X(2)X(3)∩X(395)X(42481)

Barycentrics    52*a^4+25*(b^2-c^2)^2-77*a^2*(b^2+c^2) : :
X(61845) = 25*X[2]+9*X[3], -25*X[551]+8*X[58237], 25*X[3654]+9*X[58241], 9*X[5690]+8*X[51107], 12*X[11231]+5*X[50832], -3*X[11278]+20*X[51108], 15*X[17502]+2*X[50868], 15*X[17508]+2*X[51025], 10*X[20582]+7*X[55691], 5*X[22165]+12*X[50664], 12*X[30392]+5*X[59400], 63*X[31423]+5*X[51097] and many others

X(61845) lies on these lines: {2, 3}, {395, 42481}, {396, 42480}, {551, 58237}, {3316, 10138}, {3317, 10137}, {3654, 58241}, {5690, 51107}, {6431, 43212}, {6432, 43211}, {6433, 60298}, {6434, 60297}, {6486, 42417}, {6487, 42418}, {9690, 54597}, {10645, 43247}, {10646, 43246}, {11231, 50832}, {11278, 51108}, {16241, 42917}, {16242, 42916}, {17502, 50868}, {17508, 51025}, {18538, 51850}, {18762, 51849}, {20582, 55691}, {22165, 50664}, {23302, 54593}, {23303, 54594}, {30392, 59400}, {31423, 51097}, {32789, 42524}, {32790, 42525}, {33179, 38068}, {33813, 41154}, {34754, 43490}, {34755, 43489}, {38028, 50822}, {38034, 51088}, {38064, 51189}, {38079, 55587}, {38110, 51184}, {38136, 51141}, {38138, 50833}, {38735, 41147}, {39561, 41149}, {41107, 42996}, {41108, 42997}, {41112, 43304}, {41113, 43305}, {41150, 50821}, {41152, 50979}, {41153, 50977}, {42121, 43233}, {42124, 43232}, {42500, 43373}, {42501, 43372}, {42510, 43103}, {42511, 43102}, {42600, 43384}, {42601, 43385}, {42639, 43316}, {42640, 43317}, {42686, 43334}, {42687, 43335}, {42791, 42930}, {42792, 42931}, {42906, 43101}, {42907, 43104}, {42956, 43200}, {42957, 43199}, {42976, 43100}, {42977, 43107}, {43108, 43421}, {43109, 43420}, {43306, 43332}, {43307, 43333}, {43314, 52047}, {43315, 52048}, {43415, 43536}, {43469, 43631}, {43470, 43630}, {47354, 55680}, {48310, 55594}, {50812, 61267}, {50823, 51091}, {50824, 51070}, {50826, 58441}, {50831, 58234}, {50984, 55603}, {50988, 55685}, {50989, 51180}, {51066, 58231}, {51068, 61295}, {51109, 58244}, {51127, 55642}, {51183, 51187}, {51186, 55699}, {51188, 55711}, {54644, 60638}, {54645, 60287}, {54734, 60645}, {54851, 60131}, {58248, 61524}

X(61845) = midpoint of X(i) and X(j) for these {i,j}: {2, 15722}
X(61845) = complement of X(61929)
X(61845) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3545), X(46921)}}, {{A, B, C, X(19710), X(57895)}}
X(61845) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15693, 12101}, {2, 15695, 10109}, {2, 15701, 15759}, {2, 15716, 5066}, {2, 15722, 30}, {2, 15759, 5}, {2, 5046, 4194}, {2, 631, 15716}, {4, 12100, 8703}, {4, 15692, 15688}, {4, 5070, 12812}, {5, 11539, 15723}, {140, 14890, 15694}, {140, 15702, 11539}, {547, 11539, 632}, {547, 11812, 15719}, {547, 15690, 3860}, {549, 3858, 17504}, {550, 632, 5070}, {3545, 15702, 10303}, {3545, 6825, 15690}, {5054, 15681, 631}, {5054, 15694, 4}, {5055, 16370, 10124}, {6930, 15712, 15704}, {6987, 17697, 3850}, {8703, 15713, 5054}, {10124, 12101, 2}, {10303, 12812, 14869}, {10303, 15709, 15684}, {11001, 15719, 15692}, {11539, 11812, 3845}, {11539, 14869, 15686}, {11539, 15686, 16239}, {11539, 15708, 15699}, {11539, 15713, 11812}, {11540, 11812, 547}, {11737, 12100, 15697}, {11812, 12100, 15708}, {11812, 15702, 15713}, {11812, 16239, 12100}, {14869, 15699, 549}, {15684, 15701, 15693}, {15701, 15723, 11001}

X(61846) = X(2)X(3)∩X(182)X(51215)

Barycentrics    25*a^4+13*(b^2-c^2)^2-38*a^2*(b^2+c^2) : :
X(61846) = 13*X[2]+4*X[3], 16*X[182]+X[51215], 8*X[599]+9*X[33748], X[962]+16*X[50829], 5*X[3241]+12*X[38127], 16*X[3589]+X[54174], 5*X[3616]+12*X[38068], 5*X[3617]+12*X[3653], 5*X[3620]+12*X[38064], 5*X[3623]+12*X[38066], 4*X[3654]+13*X[46934], -20*X[3828]+3*X[37712] and many others

X(61846) lies on these lines: {2, 3}, {182, 51215}, {599, 33748}, {962, 50829}, {1151, 42573}, {1152, 42572}, {1587, 6479}, {1588, 6478}, {3068, 6442}, {3069, 6441}, {3241, 38127}, {3316, 52048}, {3317, 52047}, {3589, 54174}, {3590, 6454}, {3591, 6453}, {3616, 38068}, {3617, 3653}, {3620, 38064}, {3623, 38066}, {3654, 46934}, {3828, 37712}, {4669, 61289}, {5237, 49874}, {5238, 49873}, {5365, 42632}, {5366, 42631}, {5691, 51086}, {5731, 19876}, {5921, 50983}, {6199, 43518}, {6395, 43517}, {6407, 42640}, {6408, 42639}, {6439, 8252}, {6440, 8253}, {6449, 14226}, {6450, 14241}, {6459, 41951}, {6460, 41952}, {6476, 35823}, {6477, 35822}, {6484, 43343}, {6485, 43342}, {6486, 43559}, {6487, 43558}, {6496, 43520}, {6497, 43519}, {6684, 50872}, {7619, 9740}, {7987, 51080}, {9540, 43255}, {9541, 42601}, {9542, 32786}, {9588, 51109}, {9692, 43880}, {10164, 61271}, {10168, 11160}, {10248, 50812}, {10645, 43541}, {10646, 43540}, {10653, 42933}, {10654, 42932}, {11148, 15597}, {11177, 22247}, {11488, 42501}, {11489, 42500}, {13935, 43254}, {16226, 40284}, {16772, 49861}, {16773, 49862}, {17852, 43411}, {19875, 51082}, {19877, 51705}, {19883, 50814}, {21358, 51136}, {22235, 41100}, {22237, 41101}, {23302, 43877}, {23303, 43878}, {25561, 33750}, {28204, 46932}, {31145, 61287}, {31423, 38314}, {32869, 37688}, {33416, 42983}, {33417, 42982}, {34718, 61280}, {36990, 51139}, {38065, 61006}, {38074, 46931}, {41107, 42596}, {41108, 42597}, {41943, 42089}, {41944, 42092}, {41971, 43294}, {41972, 43295}, {42107, 42587}, {42110, 42586}, {42115, 43875}, {42116, 43876}, {42144, 43553}, {42145, 43552}, {42266, 43567}, {42267, 43566}, {42488, 49825}, {42489, 49824}, {42508, 42793}, {42509, 42794}, {42803, 43102}, {42804, 43103}, {42918, 43478}, {42919, 43477}, {42924, 43252}, {42925, 43253}, {43028, 43243}, {43029, 43242}, {43100, 43238}, {43107, 43239}, {43403, 43870}, {43404, 43869}, {43465, 43646}, {43466, 43645}, {46933, 61244}, {48310, 50970}, {50821, 61277}, {50964, 55655}, {50967, 58445}, {50973, 59373}, {50984, 51212}, {50994, 53093}, {51135, 53094}, {51176, 55692}, {51179, 51732}, {53620, 61296}, {59417, 61275}

X(61846) = reflection of X(i) in X(j) for these {i,j}: {2, 3533}, {7486, 2}
X(61846) = inverse of X(61897) in orthocentroidal circle
X(61846) = inverse of X(61897) in Yff hyperbola
X(61846) = complement of X(61927)
X(61846) = anticomplement of X(61888)
X(61846) = pole of line {523, 61897} with respect to the orthocentroidal circle
X(61846) = pole of line {6, 61897} with respect to the Kiepert hyperbola
X(61846) = pole of line {523, 61897} with respect to the Yff hyperbola
X(61846) = pole of line {69, 61906} with respect to the Wallace hyperbola
X(61846) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1494), X(7486)}}, {{A, B, C, X(3543), X(57895)}}, {{A, B, C, X(3839), X(36948)}}, {{A, B, C, X(5066), X(46168)}}, {{A, B, C, X(5076), X(22270)}}, {{A, B, C, X(15681), X(46921)}}, {{A, B, C, X(41106), X(46455)}}, {{A, B, C, X(46452), X(48154)}}
X(61846) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10304, 5056}, {2, 15701, 15697}, {2, 15708, 20}, {2, 15717, 3545}, {2, 15721, 15692}, {2, 17678, 15723}, {2, 30, 7486}, {2, 3522, 5055}, {2, 3524, 3091}, {2, 3832, 15699}, {2, 5054, 3523}, {2, 549, 3543}, {2, 631, 10304}, {3, 3533, 13742}, {20, 11541, 6840}, {20, 6960, 15689}, {140, 15694, 15702}, {140, 15709, 2}, {376, 15718, 15705}, {376, 3525, 10124}, {376, 381, 3146}, {376, 3830, 15683}, {376, 5071, 14893}, {381, 15700, 15695}, {381, 15707, 15714}, {381, 17800, 15687}, {381, 549, 15715}, {547, 549, 14093}, {549, 10124, 15703}, {549, 11737, 3}, {549, 15691, 15700}, {631, 11001, 15707}, {631, 3533, 3544}, {1657, 5054, 15701}, {3523, 10304, 12100}, {3525, 14893, 17678}, {3525, 15702, 376}, {3526, 15713, 3524}, {3526, 5054, 3830}, {3533, 3859, 17534}, {3545, 15701, 15717}, {3628, 15707, 11001}, {3628, 15714, 381}, {3830, 5054, 12108}, {5054, 12100, 631}, {5055, 14869, 15719}, {5055, 15719, 3522}, {5066, 15710, 5059}, {10109, 15706, 3529}, {10124, 12108, 547}, {10124, 15694, 3525}, {10124, 15721, 3839}, {10303, 15692, 15721}, {11539, 15713, 550}, {11812, 15691, 549}, {12108, 15713, 5054}, {14893, 15703, 5071}, {15692, 15721, 15708}, {15702, 15709, 15694}, {15702, 15721, 10303}, {15717, 16351, 5}, {16370, 17549, 16408}, {17678, 17679, 11539}

X(61847) = X(2)X(3)∩X(1327)X(6452)

Barycentrics    19*a^4+10*(b^2-c^2)^2-29*a^2*(b^2+c^2) : :
X(61847) = 10*X[2]+3*X[3], 6*X[182]+7*X[51186], 12*X[575]+X[51188], 5*X[599]+8*X[50664], 12*X[1153]+X[9766], X[1482]+12*X[38068], 9*X[3653]+4*X[4745], 3*X[3654]+10*X[51109], X[3656]+12*X[58441], 25*X[3763]+14*X[55691], 4*X[4669]+9*X[10246], 9*X[5050]+4*X[22165] and many others

X(61847) lies on these lines: {2, 3}, {182, 51186}, {485, 41970}, {486, 41969}, {575, 51188}, {590, 43888}, {599, 50664}, {615, 43887}, {1153, 9766}, {1327, 6452}, {1328, 6451}, {1482, 38068}, {3311, 43255}, {3312, 43254}, {3317, 9691}, {3642, 33618}, {3643, 33619}, {3653, 4745}, {3654, 51109}, {3656, 58441}, {3763, 55691}, {4669, 10246}, {5050, 22165}, {5093, 51214}, {5097, 51185}, {5102, 50977}, {5237, 42508}, {5238, 42509}, {5418, 41967}, {5420, 41968}, {5476, 55591}, {5587, 51084}, {5603, 50825}, {5790, 31662}, {5886, 51120}, {6417, 43212}, {6418, 43211}, {6429, 35823}, {6430, 35822}, {6433, 13785}, {6434, 13665}, {6437, 18510}, {6438, 18512}, {6449, 42417}, {6450, 42418}, {6480, 8252}, {6481, 8253}, {6519, 10194}, {6522, 10195}, {7619, 8667}, {9167, 12188}, {9690, 43890}, {10165, 50798}, {10168, 15533}, {10171, 51119}, {10175, 50868}, {10516, 51137}, {11178, 55688}, {11180, 55692}, {11231, 30392}, {11238, 51817}, {11278, 25055}, {11480, 49908}, {11481, 49907}, {11485, 42500}, {11486, 42501}, {11614, 44526}, {11648, 15602}, {11898, 38064}, {12017, 20582}, {12331, 38069}, {12355, 38748}, {12702, 19883}, {12816, 42131}, {12817, 42130}, {13903, 35770}, {13961, 35771}, {14561, 51166}, {14848, 55722}, {14853, 50980}, {15040, 45311}, {15041, 38792}, {15300, 38750}, {15534, 39561}, {15597, 51122}, {16200, 50821}, {16241, 43200}, {16242, 43199}, {16267, 42491}, {16268, 42490}, {16644, 34755}, {16645, 34754}, {16966, 43244}, {16967, 43245}, {17851, 43536}, {18525, 19876}, {18526, 19875}, {21356, 55705}, {21358, 39899}, {21969, 54047}, {22236, 42507}, {22238, 42506}, {22247, 38739}, {22712, 55786}, {25565, 55646}, {26446, 50805}, {26614, 48657}, {28198, 34595}, {31423, 33179}, {32609, 38725}, {32789, 41954}, {32790, 41953}, {33416, 42975}, {33417, 42974}, {33602, 42492}, {33603, 42493}, {33612, 49960}, {33613, 49959}, {33813, 55807}, {33878, 48310}, {34748, 51072}, {35786, 42576}, {35787, 42577}, {36521, 38224}, {36769, 59383}, {36836, 42504}, {36843, 42505}, {36967, 42963}, {36968, 42962}, {37517, 47352}, {37727, 51067}, {38066, 51071}, {38067, 60922}, {38072, 55622}, {38079, 55584}, {38127, 51095}, {38155, 50828}, {38317, 55618}, {40107, 51187}, {41100, 42815}, {41101, 42816}, {41107, 41972}, {41108, 41971}, {41112, 42115}, {41113, 42116}, {41121, 43029}, {41122, 43028}, {41149, 53092}, {41943, 43239}, {41944, 43238}, {42087, 42595}, {42088, 42594}, {42089, 43228}, {42092, 43229}, {42095, 46335}, {42098, 46334}, {42126, 42632}, {42127, 42631}, {42149, 43107}, {42152, 43100}, {42600, 43791}, {42601, 43792}, {42608, 43793}, {42609, 43794}, {42610, 42891}, {42611, 42890}, {42633, 43464}, {42634, 43463}, {42639, 43881}, {42640, 43882}, {42791, 42951}, {42792, 42950}, {42817, 49811}, {42818, 49810}, {42912, 49861}, {42913, 49862}, {42976, 49948}, {42977, 49947}, {42984, 43403}, {42985, 43404}, {43273, 55685}, {43415, 43889}, {45384, 52048}, {45385, 52047}, {47354, 55682}, {47355, 55594}, {47867, 59384}, {49855, 49877}, {49858, 49878}, {50797, 51705}, {50800, 51086}, {50815, 61263}, {50824, 51068}, {50832, 59388}, {50954, 51737}, {50955, 51143}, {50957, 51139}, {50979, 50994}, {50981, 54174}, {50984, 51173}, {50993, 55703}, {51027, 55695}, {51087, 58234}, {51093, 59503}, {51127, 55639}, {51128, 55678}, {51141, 55640}, {51172, 54173}, {52712, 57895}, {53023, 55645}, {54131, 55612}

X(61847) = reflection of X(i) in X(j) for these {i,j}: {10299, 549}, {381, 5079}
X(61847) = inverse of X(61896) in orthocentroidal circle
X(61847) = inverse of X(61896) in Yff hyperbola
X(61847) = complement of X(61926)
X(61847) = pole of line {523, 61896} with respect to the orthocentroidal circle
X(61847) = pole of line {6, 61896} with respect to the Kiepert hyperbola
X(61847) = pole of line {523, 61896} with respect to the Yff hyperbola
X(61847) = pole of line {69, 61904} with respect to the Wallace hyperbola
X(61847) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3544), X(22268)}}, {{A, B, C, X(3830), X(57895)}}, {{A, B, C, X(10299), X(18317)}}, {{A, B, C, X(18850), X(58205)}}, {{A, B, C, X(22270), X(50688)}}, {{A, B, C, X(36948), X(41099)}}, {{A, B, C, X(40448), X(49133)}}, {{A, B, C, X(46452), X(55856)}}
X(61847) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11001, 547}, {2, 15697, 3090}, {2, 15698, 5}, {2, 15701, 3534}, {2, 15702, 11812}, {2, 15708, 11001}, {2, 3830, 1656}, {2, 5066, 15703}, {2, 631, 8703}, {3, 15694, 11539}, {3, 15701, 15719}, {3, 5055, 3543}, {3, 5056, 382}, {3, 5070, 3850}, {5, 14890, 15721}, {5, 15698, 15685}, {5, 15721, 15707}, {5, 16239, 13742}, {30, 549, 10299}, {140, 11539, 15702}, {140, 11540, 15713}, {140, 15694, 5054}, {140, 15709, 15694}, {381, 15706, 15696}, {381, 15720, 15706}, {381, 5054, 15720}, {547, 11539, 3533}, {549, 11001, 6825}, {549, 11539, 16239}, {631, 5055, 15700}, {1656, 15688, 381}, {1656, 15716, 3830}, {3090, 15697, 3860}, {3090, 17504, 15684}, {3523, 15699, 15681}, {3524, 5056, 15686}, {3524, 5066, 15695}, {3525, 15702, 3545}, {3525, 15705, 10124}, {3530, 5071, 15689}, {3533, 15702, 15708}, {3543, 11812, 15722}, {3543, 3545, 546}, {3628, 15692, 14269}, {3830, 15716, 15688}, {3830, 15722, 15705}, {3860, 17504, 15697}, {5054, 10124, 1657}, {5054, 15700, 631}, {5187, 15717, 3523}, {6824, 8703, 15687}, {7486, 15710, 14893}, {10109, 15690, 3845}, {10109, 15701, 15716}, {11539, 11812, 2}, {11539, 15686, 632}, {11539, 15702, 3}, {11539, 15723, 3526}, {11812, 15690, 549}, {11812, 15719, 15701}, {11812, 16239, 15690}, {15681, 15699, 5072}, {15685, 15698, 14093}, {15685, 15707, 15698}, {15687, 17697, 5055}, {15694, 15702, 15723}, {15695, 15703, 5066}, {15700, 15722, 15693}

X(61848) = X(2)X(3)∩X(13)X(43495)

Barycentrics    17*a^4+9*(b^2-c^2)^2-26*a^2*(b^2+c^2) : :
X(61848) = 27*X[2]+8*X[3], 32*X[575]+3*X[20080], -36*X[1125]+X[58245], -36*X[1153]+X[14023], 9*X[1698]+5*X[58229], 12*X[3576]+23*X[46931], -9*X[3616]+2*X[16189], 3*X[3619]+2*X[10541], 3*X[3621]+32*X[15178], 33*X[5550]+2*X[7991], 27*X[5650]+8*X[15012], 27*X[5657]+8*X[58240] and many others

X(61848) lies on these lines: {2, 3}, {13, 43495}, {14, 43496}, {15, 43371}, {16, 43370}, {395, 43479}, {396, 43480}, {575, 20080}, {1078, 32871}, {1092, 46865}, {1125, 58245}, {1153, 14023}, {1698, 58229}, {3068, 43884}, {3069, 43883}, {3070, 42604}, {3071, 42605}, {3576, 46931}, {3592, 13941}, {3594, 8972}, {3616, 16189}, {3619, 10541}, {3620, 44787}, {3621, 15178}, {3622, 28234}, {3624, 28228}, {3785, 32898}, {3933, 32895}, {5261, 5326}, {5274, 7294}, {5346, 31400}, {5349, 42595}, {5350, 42594}, {5550, 7991}, {5650, 15012}, {5657, 58240}, {5731, 46930}, {5818, 31666}, {5888, 46730}, {5921, 20190}, {5965, 55708}, {5984, 20399}, {6247, 59776}, {6390, 32894}, {6417, 43375}, {6418, 43374}, {6425, 32786}, {6426, 32785}, {6431, 42567}, {6432, 42566}, {6447, 13939}, {6448, 13886}, {6459, 6488}, {6460, 6489}, {6776, 55694}, {7619, 7758}, {7771, 32884}, {7982, 46934}, {7998, 16625}, {8167, 44846}, {8252, 41947}, {8253, 17852}, {9542, 13951}, {9692, 35823}, {9729, 33879}, {9778, 19878}, {9780, 28236}, {10141, 43890}, {10142, 43889}, {10147, 43512}, {10148, 43511}, {10165, 46933}, {10187, 41113}, {10188, 41112}, {10519, 55718}, {10653, 42596}, {10654, 42597}, {11231, 58232}, {12111, 15082}, {14561, 55597}, {14651, 38628}, {14683, 20397}, {14853, 55588}, {15024, 16981}, {15025, 48378}, {15028, 33884}, {15589, 32873}, {15860, 36413}, {16772, 42516}, {16773, 42517}, {20094, 20398}, {22234, 51170}, {22712, 55785}, {25555, 54174}, {31260, 40333}, {31401, 41940}, {32841, 34229}, {34573, 55684}, {37665, 44535}, {38317, 55617}, {40330, 55687}, {41961, 43880}, {41962, 43879}, {41977, 42998}, {41978, 42999}, {42090, 42499}, {42091, 42498}, {42111, 43474}, {42114, 43473}, {42115, 42590}, {42116, 42591}, {42133, 43241}, {42134, 43240}, {42215, 43506}, {42216, 43505}, {42260, 43561}, {42261, 43560}, {42512, 42936}, {42513, 42937}, {42777, 42949}, {42778, 42948}, {42982, 43103}, {42983, 43102}, {42994, 49860}, {42995, 49859}, {43028, 43869}, {43029, 43870}, {43238, 43429}, {43239, 43428}, {43326, 43364}, {43327, 43365}, {43440, 43492}, {43441, 43491}, {43523, 43569}, {43524, 43568}, {46932, 54445}, {47586, 60279}, {51073, 58225}, {51109, 58242}, {51126, 55614}, {51171, 53858}, {55721, 58445}, {58434, 58795}

X(61848) = midpoint of X(i) and X(j) for these {i,j}: {632, 14869}, {3522, 3832}, {5071, 15698}, {15693, 15703}
X(61848) = reflection of X(i) in X(j) for these {i,j}: {3091, 3090}, {3523, 631}, {3857, 12812}
X(61848) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(15022)}}, {{A, B, C, X(1217), X(15693)}}, {{A, B, C, X(3346), X(12100)}}, {{A, B, C, X(3830), X(22270)}}, {{A, B, C, X(3832), X(36948)}}, {{A, B, C, X(7486), X(35510)}}, {{A, B, C, X(11541), X(40448)}}, {{A, B, C, X(14843), X(41106)}}, {{A, B, C, X(15695), X(46412)}}, {{A, B, C, X(15696), X(46921)}}, {{A, B, C, X(19709), X(22268)}}, {{A, B, C, X(31371), X(50690)}}, {{A, B, C, X(46452), X(47599)}}, {{A, B, C, X(50687), X(57895)}}
X(61848) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11539, 17678}, {2, 15708, 15683}, {2, 15717, 5068}, {2, 15721, 15705}, {2, 17533, 550}, {2, 17578, 1656}, {2, 3, 15022}, {2, 3523, 3832}, {2, 3544, 16417}, {2, 5059, 7486}, {2, 5068, 13735}, {3, 15022, 3146}, {3, 5, 11541}, {4, 631, 15693}, {5, 15689, 4}, {20, 15684, 5059}, {20, 3091, 5076}, {20, 3523, 15698}, {30, 12812, 3857}, {30, 631, 3523}, {140, 15694, 631}, {140, 3525, 10303}, {140, 3526, 15702}, {452, 15715, 16052}, {631, 1656, 15692}, {631, 3525, 632}, {631, 5071, 15712}, {632, 15694, 3525}, {632, 15712, 3628}, {1656, 15692, 17578}, {1656, 15695, 3859}, {1656, 17538, 3091}, {1656, 3859, 5071}, {2478, 5154, 17677}, {3090, 15702, 14869}, {3090, 3525, 3526}, {3090, 6968, 3850}, {3091, 15692, 17538}, {3525, 15702, 3090}, {3526, 5054, 3851}, {3533, 5054, 20}, {3859, 15712, 15695}, {5056, 15697, 3843}, {5067, 10304, 3854}, {5067, 15720, 10304}, {5070, 10299, 3839}, {5070, 11812, 10299}, {6918, 12811, 5072}, {7841, 17680, 17671}, {10124, 10304, 2}, {10124, 15720, 5067}, {11102, 16418, 3529}, {11284, 16199, 1995}, {13735, 15022, 17573}, {14782, 14783, 15701}, {15022, 16866, 16456}, {15692, 17578, 3522}, {15693, 15694, 11539}, {15693, 15703, 30}, {15698, 15702, 5054}, {15702, 15703, 15721}, {15765, 18585, 15722}, {16370, 16857, 17571}, {16370, 17549, 16857}, {16408, 16860, 17534}, {16411, 16862, 17531}, {16864, 17548, 3}

X(61849) = X(2)X(3)∩X(486)X(9690)

Barycentrics    15*a^4+8*(b^2-c^2)^2-23*a^2*(b^2+c^2) : :
X(61849) = 24*X[2]+7*X[3], 10*X[3579]+21*X[61271], -40*X[3616]+9*X[58238], 21*X[3624]+10*X[31447], 10*X[3625]+21*X[61287], -4*X[3633]+35*X[37624], -40*X[3634]+9*X[61257], 20*X[3763]+11*X[55692], 15*X[3819]+16*X[40284], -36*X[3828]+5*X[61248], 10*X[4668]+21*X[10246], 4*X[5881]+27*X[58230] and many others

X(61849) lies on these lines: {2, 3}, {230, 31470}, {485, 43415}, {486, 9690}, {1151, 42557}, {1152, 42558}, {1587, 6475}, {1588, 6474}, {3035, 31494}, {3317, 9692}, {3411, 43238}, {3412, 43239}, {3579, 61271}, {3616, 58238}, {3624, 31447}, {3625, 61287}, {3633, 37624}, {3634, 61257}, {3763, 55692}, {3819, 40284}, {3828, 61248}, {3933, 32889}, {4309, 7294}, {4317, 5326}, {4668, 10246}, {5418, 6500}, {5420, 6501}, {5433, 31480}, {5881, 58230}, {5901, 58247}, {6144, 40107}, {6390, 32888}, {6407, 8252}, {6408, 8253}, {6417, 35813}, {6418, 35812}, {7749, 31492}, {8148, 9588}, {9543, 34091}, {9606, 22246}, {9680, 13951}, {9681, 32790}, {9691, 45385}, {9693, 43506}, {9698, 43136}, {9780, 61246}, {10165, 61244}, {10247, 31423}, {10645, 42611}, {10646, 42610}, {11230, 31425}, {11231, 61296}, {11362, 61277}, {11451, 11592}, {11482, 50973}, {12308, 15057}, {13630, 33879}, {14929, 32898}, {15024, 54047}, {15040, 20396}, {15069, 55697}, {17851, 43881}, {19872, 58224}, {19876, 31666}, {19877, 61255}, {19878, 48661}, {20053, 61286}, {21309, 31455}, {22712, 55784}, {31454, 42567}, {31457, 37637}, {32876, 34229}, {33416, 42490}, {33417, 42491}, {33749, 55705}, {34573, 48662}, {37832, 43016}, {37835, 43017}, {38317, 55616}, {41119, 42793}, {41120, 42794}, {42093, 42499}, {42094, 42498}, {42115, 42488}, {42116, 42489}, {42153, 42597}, {42156, 42596}, {42435, 43015}, {42436, 43014}, {42580, 43551}, {42581, 43550}, {42928, 43193}, {42929, 43194}, {42948, 42975}, {42949, 42974}, {44456, 58445}, {47355, 55593}, {50963, 55631}, {50993, 55704}, {51066, 58232}, {51141, 55641}, {51515, 58233}, {52102, 61680}, {54445, 61249}, {58219, 61264}, {58222, 61262}, {59381, 61020}, {59503, 61281}

X(61849) = pole of line {185, 62116} with respect to the Jerabek hyperbola
X(61849) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1656), X(57896)}}, {{A, B, C, X(5068), X(22268)}}, {{A, B, C, X(6662), X(41992)}}, {{A, B, C, X(11539), X(15318)}}, {{A, B, C, X(13599), X(41991)}}, {{A, B, C, X(14269), X(60007)}}, {{A, B, C, X(14869), X(52441)}}, {{A, B, C, X(17578), X(22270)}}, {{A, B, C, X(38335), X(57895)}}, {{A, B, C, X(40448), X(49134)}}, {{A, B, C, X(45757), X(57822)}}
X(61849) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12108, 1657}, {2, 15712, 5072}, {2, 631, 548}, {3, 1656, 14269}, {3, 3851, 15685}, {5, 12100, 20}, {5, 12102, 3855}, {5, 3530, 376}, {5, 3853, 3854}, {20, 15717, 15710}, {140, 11539, 10303}, {140, 11540, 14869}, {140, 15694, 3}, {140, 632, 15702}, {382, 16239, 5070}, {382, 3526, 16239}, {548, 12812, 3861}, {549, 5067, 15696}, {631, 16239, 382}, {1656, 10303, 15701}, {1656, 15706, 3627}, {1656, 3530, 17800}, {1656, 3544, 5055}, {1657, 12108, 15718}, {1657, 5054, 12108}, {1657, 5072, 14893}, {3146, 5067, 5}, {3523, 3525, 10124}, {3530, 15711, 15717}, {3533, 10303, 15711}, {3533, 14869, 381}, {3533, 17538, 2}, {3628, 15693, 5073}, {3832, 10303, 631}, {3850, 12108, 12100}, {5054, 10124, 3830}, {5054, 15703, 15722}, {5070, 6865, 6977}, {5072, 15712, 15689}, {10299, 15699, 5076}, {10303, 11539, 1656}, {11540, 14869, 3533}, {11540, 15717, 3526}, {12100, 15702, 5054}, {12108, 14893, 15712}, {12812, 15696, 3843}, {14869, 15710, 15720}, {15688, 16417, 3851}, {15694, 15701, 11539}, {15701, 17800, 3530}, {15703, 15718, 15684}, {15713, 15723, 15707}

X(61850) = X(2)X(3)∩X(15)X(42593)

Barycentrics    11*a^4+6*(b^2-c^2)^2-17*a^2*(b^2+c^2) : :
X(61850) = 18*X[2]+5*X[3], 12*X[141]+11*X[55701], 3*X[399]+20*X[38729], 20*X[575]+3*X[40341], 9*X[599]+14*X[55708], -5*X[1482]+28*X[15808], 8*X[3244]+15*X[59503], -24*X[3589]+X[55724], 14*X[3619]+9*X[55697], 8*X[3626]+15*X[10246], -12*X[3629]+35*X[53092], 8*X[3631]+15*X[5050] and many others

X(61850) lies on these lines: {2, 3}, {15, 42593}, {16, 42592}, {61, 42946}, {62, 42947}, {141, 55701}, {399, 38729}, {485, 6522}, {486, 6519}, {575, 40341}, {599, 55708}, {1482, 15808}, {3070, 42600}, {3071, 42601}, {3244, 59503}, {3589, 55724}, {3619, 55697}, {3626, 10246}, {3629, 53092}, {3631, 5050}, {3632, 15178}, {3636, 26446}, {3763, 20190}, {3982, 37545}, {5007, 31467}, {5237, 43029}, {5238, 43028}, {5334, 42591}, {5335, 42590}, {5351, 42128}, {5352, 42125}, {5418, 6427}, {5420, 6428}, {5480, 55620}, {5550, 61614}, {5650, 37481}, {5790, 30389}, {6102, 44299}, {6154, 38762}, {6221, 43880}, {6329, 11482}, {6390, 32868}, {6398, 43879}, {6425, 13951}, {6426, 8976}, {6447, 18510}, {6448, 18512}, {6449, 32790}, {6450, 32789}, {6451, 42583}, {6452, 42582}, {6453, 8252}, {6454, 8253}, {6482, 42557}, {6483, 42558}, {6496, 42274}, {6497, 42277}, {7755, 31470}, {8972, 42644}, {9543, 60621}, {9681, 43571}, {9691, 43882}, {9780, 58230}, {9781, 11592}, {10165, 18526}, {10194, 52045}, {10195, 52046}, {10222, 31423}, {10516, 55681}, {10620, 38795}, {11008, 53091}, {11231, 12645}, {11465, 54042}, {11477, 58445}, {11480, 42951}, {11481, 42950}, {11591, 33879}, {11614, 15515}, {11695, 13321}, {11898, 53093}, {11935, 13353}, {12188, 38751}, {12315, 58434}, {12702, 58441}, {12773, 38763}, {13188, 38740}, {13941, 42643}, {14561, 55595}, {14848, 55721}, {15020, 38724}, {15027, 38793}, {15029, 38790}, {15034, 34128}, {15039, 20397}, {15040, 36253}, {15069, 55698}, {15082, 40247}, {15561, 35021}, {16189, 50821}, {16241, 42989}, {16242, 42988}, {16644, 42779}, {16645, 42780}, {16964, 42798}, {16965, 42797}, {17502, 19872}, {17811, 43845}, {17845, 46265}, {18440, 55687}, {18501, 52770}, {18525, 31666}, {19116, 43883}, {19117, 43884}, {19130, 55641}, {19876, 50797}, {20050, 37624}, {20057, 38028}, {20398, 38750}, {20399, 38739}, {22112, 37472}, {22236, 33416}, {22238, 33417}, {22247, 52090}, {22330, 50962}, {22712, 55782}, {24206, 55684}, {25055, 58240}, {28224, 46931}, {31454, 43255}, {31489, 35007}, {32520, 40108}, {33749, 50993}, {35022, 38224}, {35023, 57298}, {35024, 57297}, {36836, 42129}, {36843, 42132}, {36990, 55677}, {37637, 53096}, {37727, 38098}, {37832, 42774}, {37835, 42773}, {38068, 61276}, {38113, 60983}, {38136, 55632}, {38138, 46930}, {38317, 55614}, {38574, 38775}, {38579, 38787}, {38593, 38807}, {38628, 41134}, {40686, 50414}, {40693, 42501}, {40694, 42500}, {41121, 42958}, {41122, 42959}, {42115, 42598}, {42116, 42599}, {42126, 42580}, {42127, 42581}, {42157, 42611}, {42158, 42610}, {42159, 43105}, {42162, 43106}, {42164, 42963}, {42165, 42962}, {42488, 43418}, {42489, 43419}, {42490, 42613}, {42491, 42612}, {42785, 55618}, {42786, 55673}, {42938, 43019}, {42939, 43018}, {43487, 43631}, {43488, 43630}, {47352, 55718}, {47355, 52987}, {48910, 55650}, {51072, 61290}, {51126, 55610}, {53023, 55644}, {54131, 55611}, {58236, 61278}, {59380, 60942}, {59381, 60980}

X(61850) = inverse of X(61894) in orthocentroidal circle
X(61850) = inverse of X(61894) in Yff hyperbola
X(61850) = complement of X(61921)
X(61850) = pole of line {523, 61894} with respect to the orthocentroidal circle
X(61850) = pole of line {185, 62119} with respect to the Jerabek hyperbola
X(61850) = pole of line {6, 61894} with respect to the Kiepert hyperbola
X(61850) = pole of line {523, 61894} with respect to the Yff hyperbola
X(61850) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(5079)}}, {{A, B, C, X(1656), X(57897)}}, {{A, B, C, X(3543), X(22270)}}, {{A, B, C, X(3545), X(22268)}}, {{A, B, C, X(3855), X(36948)}}, {{A, B, C, X(3856), X(13599)}}, {{A, B, C, X(14269), X(57895)}}, {{A, B, C, X(14938), X(15702)}}, {{A, B, C, X(15318), X(45760)}}, {{A, B, C, X(15699), X(46452)}}, {{A, B, C, X(21734), X(46921)}}, {{A, B, C, X(40448), X(49136)}}
X(61850) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15721, 15710}, {2, 3, 5079}, {2, 3523, 3855}, {2, 3524, 11737}, {2, 3530, 3851}, {2, 5054, 15700}, {2, 549, 14269}, {2, 631, 550}, {3, 14869, 15720}, {3, 3090, 5076}, {3, 3091, 1657}, {3, 3529, 15688}, {3, 3627, 15696}, {3, 3843, 12103}, {3, 3851, 3529}, {3, 5055, 3627}, {3, 5070, 3091}, {5, 10299, 15681}, {5, 140, 15702}, {5, 14891, 5059}, {5, 15690, 4}, {140, 11539, 631}, {140, 11540, 5}, {140, 15694, 3526}, {140, 16239, 15713}, {140, 3525, 3}, {140, 3526, 5054}, {140, 632, 10303}, {381, 15693, 10304}, {381, 1657, 3853}, {381, 5079, 3544}, {546, 550, 3146}, {547, 15717, 5073}, {549, 3533, 5070}, {550, 3528, 15695}, {550, 3530, 15715}, {631, 5056, 12100}, {632, 12100, 17697}, {632, 12108, 3090}, {1656, 15700, 382}, {1656, 3526, 15723}, {3090, 10303, 12108}, {3090, 5076, 5072}, {3146, 10304, 17538}, {3146, 17697, 5056}, {3146, 3544, 546}, {3523, 15696, 15716}, {3523, 16239, 5055}, {3525, 10303, 632}, {3526, 15696, 16239}, {3544, 14869, 15707}, {3853, 11539, 3533}, {5054, 14093, 15701}, {5054, 15723, 3534}, {5056, 12100, 17800}, {5067, 15712, 3830}, {5067, 15721, 15712}, {10124, 17504, 2}, {10299, 15682, 3528}, {10299, 16866, 3628}, {11812, 15703, 15706}, {12103, 15022, 3843}, {14269, 15681, 15682}, {14782, 14783, 15708}, {15688, 15720, 3530}, {15690, 15701, 15693}, {15702, 17678, 14891}, {15703, 15714, 381}, {15713, 16239, 3523}, {15716, 16239, 1656}, {15721, 17567, 10299}, {15765, 18585, 15719}, {16853, 17525, 3525}, {16858, 17578, 13741}, {20397, 38794, 15039}, {42490, 42937, 42975}, {42491, 42936, 42974}

X(61851) = X(2)X(3)∩X(15)X(43874)

Barycentrics    20*a^4+11*(b^2-c^2)^2-31*a^2*(b^2+c^2) : :
X(61851) = 11*X[2]+3*X[3], 11*X[141]+10*X[55702], 3*X[182]+4*X[51143], -11*X[597]+4*X[55715], 5*X[1216]+16*X[40284], -X[1353]+8*X[10168], 4*X[1385]+3*X[38081], 3*X[1483]+4*X[4669], -25*X[1698]+4*X[61253], -22*X[3589]+X[55723], 9*X[3653]+5*X[51066], 5*X[3654]+9*X[61275] and many others

X(61851) lies on these lines: {2, 3}, {15, 43874}, {16, 43873}, {141, 55702}, {182, 51143}, {395, 42532}, {396, 42533}, {511, 50981}, {515, 50833}, {516, 51088}, {517, 50826}, {524, 55712}, {597, 55715}, {1216, 40284}, {1353, 10168}, {1385, 38081}, {1483, 4669}, {1503, 50988}, {1698, 61253}, {3564, 51181}, {3589, 55723}, {3653, 51066}, {3654, 61275}, {3655, 61246}, {3656, 61614}, {3679, 61292}, {3828, 37705}, {4677, 38112}, {4745, 11231}, {5050, 50990}, {5418, 43212}, {5420, 43211}, {5476, 50970}, {5480, 55619}, {5690, 51103}, {6221, 42527}, {6398, 42526}, {6407, 43506}, {6408, 43505}, {6435, 32788}, {6436, 32787}, {6437, 43514}, {6438, 43513}, {6449, 42571}, {6450, 42570}, {6468, 43317}, {6469, 43316}, {6486, 43341}, {6487, 43340}, {6494, 9540}, {6495, 13935}, {6684, 38022}, {7294, 10386}, {7619, 13468}, {8252, 42640}, {8253, 42639}, {8584, 38110}, {9140, 22251}, {9300, 14075}, {10164, 61270}, {10165, 50832}, {10172, 51086}, {10246, 51072}, {10283, 50821}, {11168, 54964}, {11230, 50829}, {11645, 51128}, {12816, 42594}, {12817, 42595}, {15533, 50986}, {15597, 51123}, {16226, 32142}, {16267, 42949}, {16268, 42948}, {16966, 43246}, {16967, 43247}, {17502, 61260}, {18538, 42600}, {18581, 43108}, {18582, 43109}, {18762, 42601}, {19875, 61244}, {19876, 61256}, {21167, 55621}, {21850, 55598}, {22236, 49810}, {22238, 49811}, {22247, 26614}, {22712, 55781}, {26446, 50817}, {28174, 61271}, {28182, 50807}, {28208, 51073}, {29181, 51141}, {31423, 51110}, {31658, 38080}, {32789, 42418}, {32790, 42417}, {33416, 42500}, {33417, 42501}, {34127, 36523}, {36363, 36770}, {36967, 42692}, {36968, 42693}, {37832, 42492}, {37835, 42493}, {38028, 38127}, {38042, 50828}, {38064, 50993}, {38066, 51700}, {38068, 51109}, {38079, 55581}, {38111, 60963}, {38138, 51705}, {38176, 51085}, {38317, 50984}, {39561, 50985}, {40693, 42420}, {40694, 42419}, {41100, 42502}, {41101, 42503}, {41107, 42505}, {41108, 42504}, {41119, 42508}, {41120, 42509}, {41943, 43100}, {41944, 43107}, {42089, 42634}, {42092, 42633}, {42115, 49825}, {42116, 49824}, {42117, 49908}, {42118, 49907}, {42121, 43228}, {42124, 43229}, {42129, 49827}, {42132, 49826}, {42135, 46335}, {42138, 46334}, {42215, 42557}, {42216, 42558}, {42520, 43483}, {42521, 43484}, {42596, 42944}, {42597, 42945}, {42606, 52046}, {42607, 52045}, {42631, 43631}, {42632, 43630}, {42686, 43418}, {42687, 43419}, {42817, 43207}, {42818, 43208}, {42912, 49906}, {42913, 49905}, {42936, 49903}, {42937, 49904}, {43102, 49859}, {43103, 49860}, {43320, 60297}, {43321, 60298}, {43368, 51916}, {43369, 51915}, {43536, 43881}, {43882, 54597}, {48310, 55586}, {48876, 55714}, {50799, 58221}, {50811, 61257}, {50814, 50825}, {50956, 55673}, {50973, 51184}, {50977, 55717}, {50979, 50991}, {50987, 51136}, {51022, 55670}, {51080, 51084}, {51092, 59503}, {51093, 61281}, {51126, 55609}, {51130, 55603}, {51134, 55664}, {51135, 51137}, {53620, 61295}, {54042, 58470}, {54169, 55592}, {54445, 61251}, {55719, 58445}

X(61851) = midpoint of X(i) and X(j) for these {i,j}: {2, 15701}, {381, 3528}, {3090, 15700}, {3523, 15703}, {3526, 15702}
X(61851) = reflection of X(i) in X(j) for these {i,j}: {14869, 15702}, {15687, 3832}, {15702, 140}, {3851, 547}, {5, 15703}, {549, 14869}, {8703, 15698}
X(61851) = inverse of X(61893) in orthocentroidal circle
X(61851) = inverse of X(61893) in Yff hyperbola
X(61851) = complement of X(61920)
X(61851) = pole of line {523, 61893} with respect to the orthocentroidal circle
X(61851) = pole of line {6, 61893} with respect to the Kiepert hyperbola
X(61851) = pole of line {523, 61893} with respect to the Yff hyperbola
X(61851) = pole of line {69, 61902} with respect to the Wallace hyperbola
X(61851) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(10109)}}, {{A, B, C, X(1656), X(46452)}}, {{A, B, C, X(3845), X(57895)}}, {{A, B, C, X(12811), X(22268)}}, {{A, B, C, X(15710), X(46921)}}, {{A, B, C, X(18317), X(44682)}}, {{A, B, C, X(36948), X(41106)}}, {{A, B, C, X(41988), X(54924)}}
X(61851) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10303, 15719}, {2, 140, 15713}, {2, 15682, 1656}, {2, 15693, 5066}, {2, 15694, 11540}, {2, 15701, 30}, {2, 15702, 15701}, {2, 15708, 15682}, {2, 15719, 381}, {2, 15722, 3860}, {2, 3, 10109}, {2, 3534, 547}, {2, 3845, 15699}, {2, 5054, 12100}, {2, 631, 3534}, {5, 14869, 3523}, {5, 3146, 3858}, {5, 3544, 6864}, {5, 8703, 3830}, {30, 140, 15702}, {30, 3832, 15687}, {30, 547, 3851}, {140, 10124, 5054}, {140, 11539, 549}, {140, 15694, 11539}, {140, 16239, 10303}, {140, 3525, 5}, {140, 3526, 14869}, {140, 547, 14890}, {376, 5054, 12108}, {381, 15705, 12103}, {547, 17504, 3627}, {547, 631, 17504}, {549, 11539, 632}, {549, 3845, 15711}, {631, 3839, 15718}, {632, 14869, 3857}, {1657, 3830, 15640}, {3091, 15706, 15691}, {3523, 3525, 3526}, {3524, 15723, 3628}, {3525, 5054, 10124}, {3526, 3528, 16239}, {3526, 5054, 15703}, {3530, 5055, 15686}, {3533, 15721, 5055}, {3545, 14891, 15704}, {3545, 15720, 14891}, {3845, 15711, 550}, {3856, 14893, 3839}, {3860, 12100, 376}, {4193, 15692, 15709}, {5054, 15694, 3525}, {5054, 15718, 631}, {5054, 15723, 1657}, {5055, 14893, 6981}, {5055, 15721, 3530}, {5066, 11812, 15693}, {5067, 15681, 14892}, {5070, 10304, 11737}, {5071, 15707, 548}, {8252, 52047, 42640}, {8253, 52048, 42639}, {8703, 15713, 11812}, {10124, 12100, 2}, {10303, 16239, 15712}, {11539, 15686, 3533}, {12100, 12103, 15759}, {12100, 12108, 15722}, {12100, 15759, 15705}, {15694, 15709, 140}, {15697, 15759, 8703}, {15699, 15711, 3845}, {22247, 26614, 51872}, {51709, 58441, 50825}

X(61852) = X(2)X(3)∩X(10)X(58232)

Barycentrics    16*a^4+9*(b^2-c^2)^2-25*a^2*(b^2+c^2) : :
X(61852) = 27*X[2]+7*X[3], 9*X[10]+8*X[58232], 9*X[141]+8*X[55704], 9*X[355]+25*X[58229], 9*X[373]+8*X[11592], 14*X[575]+3*X[3630], 7*X[1483]+10*X[4668], -20*X[1698]+3*X[61251], -18*X[3589]+X[55721], 3*X[3625]+14*X[15178], -4*X[3633]+21*X[61283], 12*X[3634]+5*X[31666] and many others

X(61852) lies on these lines: {2, 3}, {10, 58232}, {61, 42954}, {62, 42955}, {141, 55704}, {355, 58229}, {373, 11592}, {395, 42435}, {396, 42436}, {397, 42592}, {398, 42593}, {485, 17852}, {575, 3630}, {1483, 4668}, {1698, 61251}, {3054, 31652}, {3411, 43107}, {3412, 43100}, {3589, 55721}, {3592, 43431}, {3594, 43430}, {3625, 15178}, {3633, 61283}, {3634, 31666}, {3653, 61297}, {3934, 32523}, {4301, 50825}, {4691, 11231}, {5237, 43467}, {5238, 43468}, {5339, 43639}, {5340, 43640}, {5480, 55617}, {5690, 17051}, {5876, 15082}, {5901, 58245}, {6447, 32786}, {6448, 32785}, {6488, 42601}, {6489, 42600}, {6500, 43375}, {6501, 43374}, {7991, 61614}, {8981, 35814}, {10147, 43559}, {10148, 43558}, {10194, 52047}, {10195, 52048}, {10283, 16189}, {10576, 41954}, {10577, 41953}, {11480, 42493}, {11481, 42492}, {11669, 60649}, {12007, 55708}, {12245, 58236}, {13966, 35815}, {15012, 15067}, {15034, 40685}, {15069, 50987}, {16966, 42685}, {16967, 42684}, {18358, 55684}, {19872, 28186}, {19876, 61255}, {21167, 55623}, {21850, 55597}, {22234, 32455}, {22236, 43102}, {22238, 43103}, {22251, 34128}, {22330, 48876}, {22712, 55779}, {30389, 37705}, {31406, 41940}, {34507, 51138}, {34573, 55687}, {34595, 61270}, {35255, 43514}, {35256, 43513}, {35770, 42566}, {35771, 42567}, {35812, 41968}, {35813, 41967}, {36836, 42591}, {36843, 42590}, {37832, 43443}, {37835, 43442}, {38111, 60962}, {38113, 61000}, {38136, 55631}, {38224, 52886}, {38317, 55611}, {38626, 38795}, {38627, 38751}, {38628, 38740}, {38631, 38763}, {38632, 38729}, {39884, 55681}, {40107, 50985}, {41121, 42793}, {41122, 42794}, {41949, 41969}, {41950, 41970}, {41971, 42489}, {41972, 42488}, {42087, 42499}, {42088, 42498}, {42099, 56628}, {42100, 56627}, {42103, 43647}, {42106, 43648}, {42494, 43635}, {42495, 43634}, {42500, 42937}, {42501, 42936}, {42580, 42929}, {42581, 42928}, {42598, 42686}, {42599, 42687}, {42612, 42777}, {42613, 42778}, {42633, 42802}, {42634, 42801}, {42773, 43417}, {42774, 43416}, {42906, 43241}, {42907, 43240}, {42934, 42945}, {42935, 42944}, {43150, 55698}, {43197, 43464}, {43198, 43463}, {45384, 60293}, {45385, 60294}, {48874, 51127}, {51126, 55606}, {53104, 60250}, {55701, 61545}, {55718, 58445}, {58225, 61259}, {58795, 61606}, {60278, 60323}, {61273, 61524}

X(61852) = midpoint of X(i) and X(j) for these {i,j}: {3, 3544}
X(61852) = complement of X(61919)
X(61852) = pole of line {185, 58196} with respect to the Jerabek hyperbola
X(61852) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(12812)}}, {{A, B, C, X(1105), X(58196)}}, {{A, B, C, X(5055), X(46452)}}, {{A, B, C, X(5066), X(22268)}}, {{A, B, C, X(6662), X(55866)}}, {{A, B, C, X(14938), X(15713)}}, {{A, B, C, X(15682), X(22270)}}, {{A, B, C, X(23046), X(57895)}}, {{A, B, C, X(34483), X(55856)}}, {{A, B, C, X(43970), X(47478)}}, {{A, B, C, X(50689), X(60007)}}
X(61852) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12108, 3627}, {2, 14893, 15699}, {2, 15689, 547}, {2, 15718, 14892}, {2, 3, 12812}, {2, 5054, 14891}, {2, 5072, 3628}, {2, 631, 1657}, {3, 12102, 550}, {3, 16417, 3859}, {3, 3090, 12102}, {3, 3628, 3857}, {3, 3857, 15704}, {5, 140, 15713}, {140, 10124, 631}, {140, 11539, 5}, {140, 11540, 3526}, {140, 16239, 5054}, {140, 3530, 15702}, {140, 3628, 10303}, {140, 548, 14890}, {140, 632, 14869}, {376, 6923, 3530}, {546, 3628, 5055}, {548, 3628, 5072}, {548, 3850, 15684}, {549, 11540, 11539}, {549, 15699, 3534}, {549, 5055, 8703}, {549, 550, 15717}, {631, 5068, 15700}, {632, 3627, 2}, {1656, 10304, 3856}, {1657, 3843, 3543}, {2050, 5072, 381}, {3526, 15709, 140}, {3526, 15717, 16239}, {3543, 5055, 5066}, {3545, 7380, 5056}, {3627, 12108, 15712}, {3628, 12108, 548}, {3628, 5066, 3090}, {5070, 12100, 3858}, {8703, 11539, 10124}, {8703, 15705, 15714}, {10299, 15703, 3861}, {10304, 11812, 549}, {11539, 14869, 632}, {11812, 14892, 15718}, {12108, 12812, 3}, {13742, 15720, 30}, {14869, 15712, 12108}, {14891, 14892, 15685}, {14893, 15714, 15686}, {15694, 15709, 11540}, {15705, 17697, 3091}

X(61853) = X(2)X(3)∩X(10)X(61297)

Barycentrics    12*a^4+7*(b^2-c^2)^2-19*a^2*(b^2+c^2) : :
X(61853) = 21*X[2]+5*X[3], 12*X[10]+X[61297], 9*X[141]+4*X[33749], 8*X[551]+5*X[50822], -16*X[575]+3*X[50986], 8*X[597]+5*X[51184], 8*X[599]+5*X[51180], 5*X[1353]+8*X[3631], 5*X[1483]+8*X[3626], 5*X[1484]+8*X[35023], -15*X[1698]+2*X[61249], -2*X[3244]+15*X[38028] and many others

X(61853) lies on these lines: {2, 3}, {10, 61297}, {17, 42501}, {18, 42500}, {141, 33749}, {395, 42946}, {396, 42947}, {485, 6469}, {486, 6468}, {551, 50822}, {575, 50986}, {597, 51184}, {599, 51180}, {1151, 42601}, {1152, 42600}, {1353, 3631}, {1483, 3626}, {1484, 35023}, {1698, 61249}, {3054, 7765}, {3244, 38028}, {3576, 61255}, {3579, 61270}, {3589, 55720}, {3617, 61293}, {3624, 61614}, {3629, 15516}, {3632, 38112}, {3634, 38138}, {3636, 5690}, {3679, 61290}, {3828, 50832}, {4297, 61260}, {4739, 51046}, {5305, 31492}, {5326, 37719}, {5351, 43546}, {5352, 43547}, {5433, 37602}, {5480, 55615}, {5550, 61273}, {5650, 12006}, {5882, 38081}, {5901, 9588}, {5946, 15606}, {6329, 15520}, {7294, 37720}, {7749, 9606}, {7814, 14929}, {7998, 16881}, {8252, 9680}, {8550, 51181}, {8981, 35813}, {9540, 42643}, {9624, 61524}, {9681, 18762}, {9705, 37471}, {9780, 61245}, {10165, 37705}, {10170, 45957}, {10194, 42640}, {10195, 42639}, {10272, 15057}, {10279, 34752}, {10283, 11362}, {10653, 42590}, {10654, 42591}, {11224, 31423}, {11542, 42491}, {11543, 42490}, {13935, 42644}, {13966, 35812}, {14135, 20326}, {14531, 32142}, {15043, 44324}, {15048, 31457}, {15082, 45956}, {15178, 34641}, {16241, 41978}, {16242, 41977}, {16772, 33416}, {16773, 33417}, {16966, 43106}, {16967, 43105}, {17502, 31253}, {18436, 33879}, {19116, 31454}, {19130, 55638}, {19872, 61259}, {19877, 28224}, {19878, 38034}, {20050, 61283}, {20054, 37624}, {20057, 51700}, {20379, 24981}, {20396, 38793}, {20399, 26614}, {20582, 50987}, {20583, 50978}, {21167, 55625}, {21850, 55596}, {22236, 43110}, {22238, 43111}, {22247, 51523}, {22251, 23236}, {22712, 55776}, {22791, 31447}, {23238, 34837}, {23302, 42596}, {23303, 42597}, {24206, 55686}, {26446, 61278}, {28174, 31425}, {30389, 61248}, {31399, 34773}, {31450, 37637}, {32450, 40108}, {34573, 55689}, {34747, 61282}, {35021, 51872}, {35814, 42567}, {35815, 42566}, {36967, 42595}, {36968, 42594}, {37481, 44299}, {37727, 59400}, {38022, 43174}, {38079, 50981}, {38083, 50833}, {38111, 60933}, {38113, 60942}, {38136, 51127}, {38137, 58433}, {38317, 55608}, {39884, 51128}, {40693, 43103}, {40694, 43102}, {41362, 46265}, {41947, 41961}, {41948, 41962}, {42115, 42416}, {42116, 42415}, {42117, 42493}, {42118, 42492}, {42121, 42916}, {42124, 42917}, {42125, 43634}, {42128, 43635}, {42143, 42611}, {42146, 42610}, {42153, 42923}, {42156, 42922}, {42163, 43486}, {42166, 43485}, {42433, 42498}, {42434, 42499}, {42522, 43518}, {42523, 43517}, {42545, 43402}, {42546, 43401}, {42598, 43418}, {42599, 43419}, {42612, 42979}, {42613, 42978}, {42633, 43238}, {42634, 43239}, {42773, 42910}, {42774, 42911}, {42797, 42943}, {42798, 42942}, {42813, 43631}, {42814, 43630}, {42950, 43870}, {42951, 43869}, {42956, 43015}, {42957, 43014}, {42958, 49907}, {42959, 49908}, {43000, 43775}, {43001, 43776}, {43444, 43496}, {43445, 43495}, {43505, 45384}, {43506, 45385}, {43523, 52047}, {43524, 52048}, {43544, 43773}, {43545, 43774}, {46852, 55166}, {46932, 58230}, {48874, 55634}, {48906, 55690}, {50959, 55644}, {50980, 52987}, {50991, 55708}, {51109, 58240}, {51126, 55601}, {51139, 55675}, {52104, 59553}, {55716, 58445}

X(61853) = midpoint of X(i) and X(j) for these {i,j}: {3, 5068}, {5079, 10299}
X(61853) = reflection of X(i) in X(j) for these {i,j}: {10303, 140}, {5, 5067}
X(61853) = inverse of X(61892) in orthocentroidal circle
X(61853) = inverse of X(61892) in Yff hyperbola
X(61853) = complement of X(5079)
X(61853) = pole of line {523, 61892} with respect to the orthocentroidal circle
X(61853) = pole of line {185, 15691} with respect to the Jerabek hyperbola
X(61853) = pole of line {6, 61892} with respect to the Kiepert hyperbola
X(61853) = pole of line {523, 61892} with respect to the Yff hyperbola
X(61853) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(35018)}}, {{A, B, C, X(381), X(46452)}}, {{A, B, C, X(1105), X(15691)}}, {{A, B, C, X(1656), X(57823)}}, {{A, B, C, X(3544), X(36948)}}, {{A, B, C, X(3839), X(60007)}}, {{A, B, C, X(6662), X(55858)}}, {{A, B, C, X(14863), X(55856)}}, {{A, B, C, X(15318), X(15694)}}, {{A, B, C, X(22270), X(33703)}}, {{A, B, C, X(38071), X(57895)}}, {{A, B, C, X(43970), X(44904)}}
X(61853) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10299, 5079}, {2, 10303, 10299}, {2, 140, 14869}, {2, 15688, 547}, {2, 15702, 15707}, {2, 15715, 5055}, {2, 15720, 546}, {2, 3523, 3544}, {2, 3529, 1656}, {2, 631, 382}, {3, 15699, 3858}, {3, 15709, 140}, {3, 1656, 3839}, {3, 4, 15691}, {3, 5068, 30}, {3, 7486, 3861}, {5, 11539, 3526}, {5, 15687, 3855}, {5, 15704, 3843}, {5, 15712, 20}, {30, 140, 10303}, {140, 10124, 3}, {140, 11539, 632}, {140, 11540, 3525}, {140, 12108, 15702}, {140, 16239, 631}, {140, 3526, 5}, {140, 3628, 5054}, {140, 632, 549}, {381, 3851, 13587}, {382, 17567, 12812}, {382, 3861, 15687}, {546, 3530, 3528}, {547, 3523, 15704}, {548, 16239, 5070}, {631, 5070, 548}, {1656, 15702, 12108}, {1656, 15707, 3529}, {1656, 15717, 3853}, {1656, 3529, 11737}, {1656, 8703, 3857}, {2041, 2042, 15694}, {3090, 15696, 3856}, {3522, 15703, 12811}, {3523, 15704, 15711}, {3523, 3544, 15688}, {3524, 16408, 3851}, {3526, 15696, 15723}, {3528, 3530, 17504}, {3628, 15712, 3845}, {3845, 15699, 5071}, {3845, 6846, 5066}, {3853, 12108, 15717}, {3856, 12100, 15696}, {3861, 10124, 16239}, {5056, 15693, 12103}, {10109, 15708, 15714}, {10124, 15709, 15713}, {10124, 15713, 15699}, {11106, 17549, 2}, {11539, 15713, 10124}, {11540, 15694, 11539}, {11737, 15707, 8703}, {12108, 15684, 15712}, {14869, 17504, 15720}, {15681, 17533, 3530}, {15681, 17559, 3628}, {15688, 15704, 550}

X(61854) = X(2)X(3)∩X(13)X(42505)

Barycentrics    23*a^4+14*(b^2-c^2)^2-37*a^2*(b^2+c^2) : :
X(61854) = 14*X[2]+3*X[3], 12*X[575]+5*X[50989], 7*X[599]+10*X[55710], -3*X[1482]+20*X[51109], 3*X[1699]+14*X[51088], 12*X[3576]+5*X[50797], 15*X[3653]+2*X[47745], 35*X[3763]+16*X[55696], 16*X[3828]+X[18526], -X[4677]+18*X[11231], 8*X[4745]+9*X[10246], 15*X[5050]+2*X[50961] and many others

X(61854) lies on these lines: {2, 3}, {13, 42505}, {14, 42504}, {575, 50989}, {599, 55710}, {1482, 51109}, {1699, 51088}, {3576, 50797}, {3653, 47745}, {3763, 55696}, {3828, 18526}, {4677, 11231}, {4745, 10246}, {5050, 50961}, {5085, 50954}, {5334, 42985}, {5335, 42984}, {6221, 42601}, {6398, 42600}, {6449, 42609}, {6450, 42608}, {8252, 42527}, {8253, 42526}, {8584, 51174}, {9542, 54597}, {10164, 50806}, {10165, 50801}, {10168, 11898}, {10172, 50800}, {10519, 51172}, {11055, 40108}, {11178, 55690}, {11224, 50821}, {11482, 41153}, {11614, 18362}, {11935, 43650}, {12188, 22247}, {12645, 51066}, {13903, 43254}, {13961, 43255}, {14711, 32519}, {14848, 55720}, {15516, 15534}, {15520, 50962}, {16241, 42507}, {16242, 42506}, {18440, 55689}, {19872, 28208}, {20582, 39899}, {21167, 50963}, {21849, 54047}, {22236, 49904}, {22238, 49903}, {23302, 49860}, {23303, 49859}, {26446, 51077}, {33416, 42532}, {33417, 42533}, {33608, 49829}, {33609, 49828}, {34718, 51110}, {36768, 59383}, {36967, 42499}, {36968, 42498}, {37637, 39593}, {38064, 51143}, {38066, 51103}, {38317, 51173}, {41100, 42132}, {41101, 42129}, {41107, 43029}, {41108, 43028}, {41119, 42115}, {41120, 42116}, {41121, 42508}, {41122, 42509}, {42095, 42632}, {42098, 42631}, {42121, 49813}, {42124, 49812}, {42143, 42589}, {42146, 42588}, {42490, 43012}, {42491, 43013}, {42502, 42510}, {42503, 42511}, {42520, 42954}, {42521, 42955}, {42596, 43023}, {42597, 43022}, {42773, 42972}, {42774, 42973}, {42791, 42910}, {42792, 42911}, {42950, 49907}, {42951, 49908}, {42976, 43238}, {42977, 43239}, {43273, 55686}, {43418, 43467}, {43419, 43468}, {43509, 43882}, {43510, 43881}, {47352, 55716}, {47355, 55585}, {50805, 51105}, {50819, 61262}, {50833, 59387}, {50959, 55643}, {50980, 55593}, {50990, 51175}, {50992, 53091}, {51071, 59503}, {51075, 58441}, {51141, 53023}, {51186, 55706}, {54131, 55608}, {54479, 56623}, {54480, 56624}

X(61854) = complement of X(61915)
X(61854) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(550), X(46452)}}, {{A, B, C, X(4846), X(35409)}}, {{A, B, C, X(18317), X(61138)}}, {{A, B, C, X(19709), X(57895)}}, {{A, B, C, X(22270), X(49140)}}
X(61854) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10109, 5070}, {2, 11540, 15694}, {2, 11812, 3830}, {2, 12100, 5055}, {2, 15702, 12100}, {2, 15709, 15713}, {2, 15719, 5}, {2, 15721, 15682}, {2, 3524, 10109}, {2, 3525, 11540}, {2, 3534, 1656}, {2, 3845, 15703}, {2, 5054, 3534}, {2, 631, 3845}, {3, 15683, 15688}, {3, 15694, 15709}, {3, 3830, 15697}, {3, 3855, 1657}, {3, 5055, 15687}, {5, 15719, 15695}, {20, 3090, 3850}, {140, 10124, 15699}, {140, 15699, 15721}, {140, 381, 5054}, {140, 632, 20}, {381, 15688, 5073}, {381, 15689, 382}, {381, 15693, 8703}, {381, 15701, 15716}, {381, 5079, 14892}, {382, 5054, 549}, {547, 10303, 15707}, {549, 3090, 15689}, {549, 3850, 15710}, {1656, 5054, 15700}, {3524, 5068, 15691}, {3526, 15720, 632}, {3526, 5054, 15723}, {3534, 6881, 6959}, {3545, 14869, 15718}, {3545, 15718, 15696}, {3628, 15708, 15681}, {3830, 11812, 15693}, {3839, 15682, 12101}, {3850, 15687, 3839}, {3861, 15699, 5071}, {5054, 14093, 15720}, {5055, 15720, 14093}, {7486, 15713, 15722}, {8703, 12101, 11001}, {8703, 15699, 5066}, {10109, 15685, 381}, {10124, 15709, 3}, {10124, 15713, 2}, {11539, 15694, 3526}, {11737, 15705, 17800}, {13742, 17578, 7486}, {15682, 15691, 15685}, {15682, 15713, 15701}, {15685, 15701, 3524}, {15688, 15703, 5072}, {15691, 15699, 5068}, {15695, 15719, 15706}, {15709, 15721, 140}

X(61855) = X(2)X(3)∩X(486)X(9691)

Barycentrics    13*a^4+8*(b^2-c^2)^2-21*a^2*(b^2+c^2) : :
X(61855) = 24*X[2]+5*X[3], 20*X[1698]+9*X[58230], -X[3632]+30*X[11231], 20*X[3763]+9*X[55697], -3*X[5093]+32*X[58445], -88*X[5550]+X[58247], 4*X[5691]+25*X[58224], 2*X[6102]+27*X[33879], X[8148]+28*X[31423], -X[11008]+30*X[38110], 8*X[12006]+21*X[44299], 4*X[12645]+25*X[58233] and many others

X(61855) lies on these lines: {2, 3}, {485, 43524}, {486, 9691}, {1587, 43881}, {1588, 43882}, {1698, 58230}, {3519, 44731}, {3590, 43510}, {3591, 43509}, {3632, 11231}, {3763, 55697}, {3933, 32887}, {5093, 58445}, {5351, 42610}, {5352, 42611}, {5550, 58247}, {5691, 58224}, {6102, 33879}, {6199, 58866}, {6390, 32886}, {6395, 8960}, {6429, 42557}, {6430, 42558}, {6445, 10577}, {6446, 10576}, {6472, 43317}, {6473, 43316}, {7581, 42644}, {7582, 42643}, {7607, 60210}, {8148, 31423}, {8976, 41964}, {9690, 32790}, {10143, 42573}, {10144, 42572}, {10145, 42215}, {10146, 42216}, {10159, 60335}, {10185, 60626}, {10187, 42153}, {10188, 42156}, {10194, 42601}, {10195, 42600}, {11008, 38110}, {11480, 43470}, {11481, 43469}, {11485, 42780}, {11486, 42779}, {11668, 43676}, {12006, 44299}, {12645, 58233}, {13382, 15082}, {13421, 15024}, {13624, 30315}, {13951, 41963}, {14061, 38635}, {15026, 54047}, {15028, 54048}, {15042, 15088}, {15059, 38638}, {15808, 26446}, {16241, 43009}, {16242, 43008}, {16644, 42596}, {16645, 42597}, {16966, 42774}, {16967, 42773}, {18493, 58441}, {20050, 38028}, {20054, 38112}, {20057, 59503}, {21309, 44535}, {21358, 55701}, {22236, 42978}, {22238, 42979}, {22246, 31401}, {22712, 55772}, {23302, 42781}, {23303, 42782}, {25555, 44456}, {28224, 46930}, {31272, 38636}, {31274, 35021}, {31455, 43136}, {31487, 43254}, {32785, 43414}, {32786, 43413}, {32789, 41970}, {33416, 43238}, {33417, 43239}, {33749, 51186}, {34507, 55705}, {34748, 38098}, {36836, 41971}, {36843, 41972}, {37621, 61152}, {37832, 42958}, {37835, 42959}, {38072, 55620}, {38113, 60957}, {38317, 55604}, {40341, 53091}, {41953, 43571}, {41954, 43570}, {41973, 42116}, {41974, 42115}, {42089, 42949}, {42092, 42948}, {42095, 42499}, {42098, 42498}, {42129, 42945}, {42132, 42944}, {42490, 43549}, {42491, 43548}, {42592, 42612}, {42593, 42613}, {42598, 42984}, {42599, 42985}, {42635, 49906}, {42636, 49905}, {42799, 42993}, {42800, 42992}, {42938, 42947}, {42939, 42946}, {42962, 43769}, {42963, 43770}, {42998, 43103}, {42999, 43102}, {43527, 54920}, {47355, 55584}, {50963, 55626}, {50993, 55708}, {51068, 61290}, {53100, 56059}, {53102, 53108}, {54644, 60642}, {58226, 61259}, {58235, 61288}, {59380, 60983}, {60142, 60644}, {60238, 60332}, {60277, 60334}

X(61855) = intersection, other than A, B, C, of circumconics {{A, B, C, X(428), X(60335)}}, {{A, B, C, X(1656), X(57894)}}, {{A, B, C, X(3518), X(44731)}}, {{A, B, C, X(3519), X(5071)}}, {{A, B, C, X(3523), X(46921)}}, {{A, B, C, X(3832), X(22268)}}, {{A, B, C, X(5059), X(22270)}}, {{A, B, C, X(5064), X(54920)}}, {{A, B, C, X(5068), X(14841)}}, {{A, B, C, X(5072), X(60171)}}, {{A, B, C, X(8703), X(46452)}}, {{A, B, C, X(13599), X(23046)}}, {{A, B, C, X(14861), X(49138)}}, {{A, B, C, X(15684), X(40448)}}, {{A, B, C, X(52282), X(60210)}}
X(61855) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10303, 3528}, {2, 11346, 6856}, {2, 14269, 15703}, {2, 14869, 382}, {2, 15702, 17504}, {2, 15710, 547}, {2, 15720, 3851}, {2, 17558, 16052}, {2, 17568, 17580}, {2, 3855, 3628}, {2, 5054, 15681}, {2, 5079, 5070}, {2, 631, 546}, {3, 5, 15684}, {3, 631, 15722}, {4, 140, 5054}, {4, 5056, 12811}, {4, 8703, 1657}, {140, 15712, 10303}, {140, 16239, 15712}, {140, 3533, 1656}, {140, 632, 4}, {381, 5054, 15719}, {382, 15720, 10299}, {546, 3530, 8703}, {547, 6914, 7486}, {632, 17504, 4205}, {1010, 14869, 3529}, {1656, 1657, 5068}, {1656, 3523, 5073}, {1656, 3526, 3533}, {1656, 5068, 5055}, {1657, 15720, 15700}, {2045, 2046, 548}, {2478, 6919, 11106}, {3090, 15693, 17800}, {3525, 11539, 3526}, {3525, 3526, 15694}, {3526, 5054, 632}, {3528, 3529, 15697}, {3533, 5059, 16239}, {3628, 15691, 5}, {3628, 17504, 3855}, {3855, 5067, 4190}, {5054, 5079, 3530}, {5067, 12108, 3534}, {5068, 15705, 5059}, {5141, 17575, 8728}, {7486, 12100, 5076}, {10299, 14869, 15720}, {10299, 15720, 15707}, {10303, 13725, 550}, {10303, 15705, 631}, {10303, 16239, 381}, {11108, 12108, 5079}, {14813, 14814, 5071}, {15688, 15723, 2}, {15693, 17800, 3}, {15694, 15701, 15709}, {15709, 15723, 15701}, {16966, 42797, 43546}, {16967, 42798, 43547}, {42089, 42949, 42988}, {42092, 42948, 42989}

X(61856) = X(2)X(3)∩X(15)X(10187)

Barycentrics    11*a^4+7*(b^2-c^2)^2-18*a^2*(b^2+c^2) : :
X(61856) = 21*X[2]+4*X[3], 16*X[141]+9*X[33748], X[145]+24*X[11231], -7*X[193]+32*X[15516], -4*X[355]+29*X[46930], 4*X[389]+21*X[44299], 2*X[944]+23*X[46931], -X[962]+26*X[34595], -28*X[1125]+3*X[11224], 7*X[1352]+18*X[55693], 8*X[1385]+17*X[46932], 21*X[3619]+4*X[8550] and many others

X(61856) lies on these lines: {2, 3}, {13, 42933}, {14, 42932}, {15, 10187}, {16, 10188}, {17, 42982}, {18, 42983}, {69, 32871}, {76, 53859}, {99, 32883}, {141, 33748}, {145, 11231}, {147, 55743}, {193, 15516}, {315, 32884}, {323, 15805}, {325, 32898}, {355, 46930}, {371, 42601}, {372, 42600}, {389, 44299}, {590, 6471}, {615, 6470}, {944, 46931}, {962, 34595}, {1125, 11224}, {1352, 55693}, {1385, 46932}, {1587, 3590}, {1588, 3591}, {1698, 28236}, {1975, 32897}, {2549, 12815}, {2996, 10185}, {3085, 37602}, {3316, 35256}, {3317, 35255}, {3616, 28234}, {3619, 8550}, {3620, 5965}, {3621, 38028}, {3624, 43174}, {3634, 54445}, {3819, 15028}, {3933, 32873}, {5032, 40107}, {5218, 7294}, {5304, 7749}, {5326, 7288}, {5339, 42477}, {5340, 42476}, {5343, 16967}, {5344, 16966}, {5346, 31401}, {5365, 10645}, {5366, 10646}, {5395, 60144}, {5418, 13941}, {5420, 8972}, {5447, 11002}, {5462, 33884}, {5493, 19878}, {5550, 13464}, {5562, 33879}, {5650, 15043}, {5882, 9780}, {6337, 32870}, {6390, 32872}, {6392, 17006}, {6468, 32790}, {6469, 32789}, {6776, 55696}, {7320, 44675}, {7607, 7836}, {7608, 10583}, {7755, 31400}, {7764, 9740}, {7769, 15589}, {7785, 55819}, {7797, 55797}, {7868, 9742}, {7987, 31253}, {7998, 11695}, {8162, 14986}, {8227, 28232}, {8252, 41963}, {8253, 41964}, {8960, 13935}, {8976, 43505}, {9540, 58866}, {9543, 13785}, {9545, 43650}, {9588, 19883}, {9589, 50829}, {9624, 38068}, {10156, 12528}, {10159, 43537}, {10165, 19877}, {10279, 44010}, {10519, 25555}, {10576, 43511}, {10577, 43512}, {10627, 16981}, {11230, 20070}, {11480, 42495}, {11481, 42494}, {11488, 42949}, {11489, 42948}, {11522, 19862}, {11542, 43447}, {11543, 43446}, {11614, 43448}, {12045, 27355}, {12324, 58434}, {13347, 43614}, {13411, 31188}, {13571, 37667}, {13624, 54448}, {13903, 42542}, {13951, 43506}, {13961, 42541}, {14128, 61136}, {14156, 42021}, {14484, 60182}, {14491, 26861}, {14561, 55590}, {14683, 34128}, {14853, 55585}, {14930, 31467}, {15258, 53025}, {15520, 51171}, {16189, 51109}, {16241, 42513}, {16242, 42512}, {16644, 42517}, {16645, 42516}, {16772, 42479}, {16773, 42478}, {16960, 42089}, {16961, 42092}, {18553, 55686}, {19130, 55635}, {20014, 38112}, {20052, 37624}, {20059, 38113}, {20080, 38110}, {20081, 40108}, {20094, 34127}, {20095, 34126}, {20398, 52695}, {22112, 34148}, {22236, 42778}, {22238, 42777}, {22247, 38664}, {22712, 55770}, {23267, 43564}, {23273, 43565}, {23328, 54211}, {24206, 55689}, {26446, 46934}, {30315, 51073}, {31239, 32522}, {31363, 60138}, {31414, 43409}, {31455, 37665}, {31487, 43212}, {31670, 55630}, {32820, 32834}, {32821, 32835}, {32824, 32832}, {32831, 37688}, {32839, 37668}, {33416, 42152}, {33417, 42149}, {34507, 55706}, {35595, 37534}, {35812, 43255}, {35813, 43254}, {38064, 51215}, {38098, 61289}, {38317, 55601}, {40330, 55690}, {40693, 43006}, {40694, 43007}, {41973, 43404}, {41974, 43403}, {42085, 43241}, {42086, 43240}, {42095, 43770}, {42098, 43769}, {42115, 43495}, {42116, 43496}, {42117, 43557}, {42118, 43556}, {42119, 42773}, {42120, 42774}, {42150, 42959}, {42151, 42958}, {42153, 42500}, {42154, 42595}, {42155, 42594}, {42156, 42501}, {42157, 42499}, {42158, 42498}, {42610, 42943}, {42611, 42942}, {42690, 43778}, {42691, 43777}, {42803, 43543}, {42804, 43542}, {42914, 43365}, {42915, 43364}, {42938, 43199}, {42939, 43200}, {42944, 43029}, {42945, 43028}, {42988, 43103}, {42989, 43102}, {43100, 49862}, {43107, 49861}, {43410, 52045}, {43523, 43890}, {43524, 43889}, {43527, 53099}, {43681, 60123}, {43841, 44673}, {44762, 61680}, {48310, 54174}, {50975, 55677}, {50980, 55595}, {51023, 55684}, {51072, 61288}, {53098, 60145}, {54047, 58531}, {60102, 60642}, {60171, 60193}

X(61856) = inverse of X(46935) in orthocentroidal circle
X(61856) = inverse of X(46935) in Yff hyperbola
X(61856) = complement of X(61914)
X(61856) = anticomplement of X(60781)
X(61856) = pole of line {523, 46935} with respect to the orthocentroidal circle
X(61856) = pole of line {185, 62124} with respect to the Jerabek hyperbola
X(61856) = pole of line {6, 46935} with respect to the Kiepert hyperbola
X(61856) = pole of line {523, 46935} with respect to the Yff hyperbola
X(61856) = pole of line {69, 32897} with respect to the Wallace hyperbola
X(61856) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(25), X(53859)}}, {{A, B, C, X(68), X(12811)}}, {{A, B, C, X(69), X(46936)}}, {{A, B, C, X(95), X(7486)}}, {{A, B, C, X(253), X(5067)}}, {{A, B, C, X(264), X(46935)}}, {{A, B, C, X(428), X(43537)}}, {{A, B, C, X(632), X(42021)}}, {{A, B, C, X(1217), X(15712)}}, {{A, B, C, X(1657), X(22270)}}, {{A, B, C, X(3346), X(61138)}}, {{A, B, C, X(3519), X(5079)}}, {{A, B, C, X(3528), X(51348)}}, {{A, B, C, X(3545), X(60171)}}, {{A, B, C, X(3830), X(60618)}}, {{A, B, C, X(3843), X(22268)}}, {{A, B, C, X(3845), X(31363)}}, {{A, B, C, X(3858), X(60007)}}, {{A, B, C, X(5054), X(26861)}}, {{A, B, C, X(5056), X(36948)}}, {{A, B, C, X(5064), X(53099)}}, {{A, B, C, X(6353), X(10185)}}, {{A, B, C, X(6662), X(47598)}}, {{A, B, C, X(7607), X(7714)}}, {{A, B, C, X(8889), X(60144)}}, {{A, B, C, X(10594), X(57730)}}, {{A, B, C, X(12100), X(46452)}}, {{A, B, C, X(13599), X(41099)}}, {{A, B, C, X(14093), X(46412)}}, {{A, B, C, X(14491), X(26863)}}, {{A, B, C, X(14841), X(19709)}}, {{A, B, C, X(14861), X(49137)}}, {{A, B, C, X(15682), X(40448)}}, {{A, B, C, X(18850), X(49139)}}, {{A, B, C, X(32999), X(56360)}}, {{A, B, C, X(43699), X(50689)}}, {{A, B, C, X(52281), X(60647)}}, {{A, B, C, X(52282), X(60285)}}, {{A, B, C, X(52288), X(60182)}}
X(61856) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 140, 3523}, {2, 15022, 5070}, {2, 15683, 15699}, {2, 15705, 547}, {2, 15713, 15697}, {2, 15717, 3090}, {2, 15721, 3839}, {2, 3, 7486}, {2, 3146, 5067}, {2, 3832, 3628}, {2, 5054, 3543}, {2, 6921, 4208}, {2, 7483, 17554}, {2, 7504, 16394}, {3, 15691, 3528}, {3, 15699, 3855}, {3, 1656, 3858}, {3, 3526, 10124}, {3, 3855, 15683}, {3, 5, 15682}, {3, 5071, 17578}, {4, 631, 15712}, {5, 10299, 5059}, {20, 10303, 15708}, {140, 16239, 550}, {140, 3523, 10303}, {140, 3526, 3533}, {140, 3850, 14869}, {140, 5068, 15721}, {140, 550, 5054}, {140, 632, 1656}, {376, 5070, 15022}, {548, 15703, 3544}, {549, 12812, 15696}, {549, 3861, 3}, {549, 5067, 3146}, {550, 3090, 3854}, {631, 17538, 15693}, {631, 3525, 15694}, {1587, 10195, 3590}, {1588, 10194, 3591}, {1656, 15694, 140}, {1656, 15696, 3851}, {1656, 15712, 4}, {1656, 3091, 5056}, {1656, 3851, 12812}, {2045, 2046, 376}, {3090, 5054, 15717}, {3091, 3523, 3522}, {3091, 3543, 3843}, {3149, 15723, 16351}, {3522, 5059, 17538}, {3523, 10304, 10299}, {3524, 3628, 3832}, {3526, 11539, 3525}, {3526, 15694, 632}, {3526, 17536, 7559}, {3544, 15719, 548}, {3628, 15690, 5}, {3839, 15640, 15687}, {3839, 5056, 5068}, {3854, 5068, 5066}, {3859, 12108, 15711}, {3861, 15723, 16849}, {5054, 15685, 549}, {5071, 15709, 15713}, {5418, 13941, 42522}, {5420, 8972, 42523}, {5447, 11465, 11002}, {5550, 31423, 59417}, {6390, 52718, 32872}, {10124, 15687, 15723}, {10124, 15694, 5071}, {10124, 15709, 2}, {10303, 15692, 631}, {10304, 15693, 15692}, {11540, 17678, 10304}, {13735, 15022, 11112}, {13735, 15711, 3091}, {14784, 14785, 12811}, {14813, 14814, 5079}, {14890, 16853, 20}, {15682, 15709, 15702}, {15694, 15713, 15709}, {15765, 18585, 15718}, {34595, 58441, 962}, {42089, 42936, 42998}, {42089, 42998, 43480}, {42092, 42937, 42999}, {42092, 42999, 43479}, {42948, 43238, 11489}, {42949, 43239, 11488}

X(61857) = X(2)X(3)∩X(10)X(58233)

Barycentrics    25*a^4+16*(b^2-c^2)^2-41*a^2*(b^2+c^2) : :
X(61857) = 16*X[2]+3*X[3], 32*X[10]+25*X[58233], 12*X[575]+7*X[51189], -20*X[3828]+X[61244], 10*X[4669]+9*X[61287], 16*X[4745]+3*X[34748], 9*X[5050]+10*X[50993], 15*X[5093]+4*X[50973], 15*X[5790]+4*X[51082], 15*X[5886]+4*X[50814], 12*X[10168]+7*X[51186], 15*X[10175]+4*X[51080] and many others

X(61857) lies on these lines: {2, 3}, {10, 58233}, {485, 6473}, {486, 6472}, {575, 51189}, {3828, 61244}, {4669, 61287}, {4745, 34748}, {5050, 50993}, {5093, 50973}, {5790, 51082}, {5886, 50814}, {6221, 42557}, {6398, 42558}, {7603, 15603}, {10145, 52045}, {10146, 52046}, {10168, 51186}, {10175, 51080}, {10246, 51066}, {10247, 50817}, {10653, 42984}, {10654, 42985}, {10992, 41148}, {11178, 55692}, {11231, 51093}, {11485, 44018}, {11486, 44017}, {11614, 11648}, {13903, 43212}, {13961, 43211}, {14561, 50970}, {15533, 53091}, {16241, 49904}, {16242, 49903}, {16644, 43030}, {16645, 43031}, {16962, 42597}, {16963, 42596}, {17502, 50800}, {17508, 50957}, {17851, 32789}, {18525, 58228}, {19877, 61253}, {19883, 58247}, {21358, 55705}, {23302, 49811}, {23303, 49810}, {25561, 55678}, {26446, 51109}, {30308, 51088}, {31274, 48657}, {32787, 42567}, {32788, 42566}, {32790, 42573}, {33416, 49948}, {33417, 49947}, {33604, 42922}, {33605, 42923}, {33697, 58220}, {34718, 51108}, {35255, 43882}, {35256, 43881}, {35822, 42569}, {35823, 42568}, {36523, 38750}, {36767, 59383}, {37712, 58230}, {38066, 51105}, {38072, 55616}, {38110, 50992}, {38113, 60971}, {38127, 51103}, {41100, 42895}, {41101, 42894}, {41121, 42115}, {41122, 42116}, {41151, 52090}, {42119, 43247}, {42120, 43246}, {42121, 49862}, {42124, 49861}, {42125, 42791}, {42128, 42792}, {42129, 42500}, {42132, 42501}, {42262, 42525}, {42265, 42524}, {42518, 43544}, {42519, 43545}, {42520, 43200}, {42521, 43199}, {42532, 43238}, {42533, 43239}, {42610, 42973}, {42611, 42972}, {42639, 43510}, {42640, 43509}, {42976, 49906}, {42977, 49905}, {49952, 49960}, {49953, 49959}, {50805, 61280}, {50821, 61275}, {50963, 55624}, {50994, 51178}, {51068, 51515}, {51084, 54447}, {51092, 51700}, {51141, 55643}, {51185, 58445}, {51187, 53092}, {51705, 61257}, {53130, 53520}, {53131, 53517}, {53620, 61292}

X(61857) = reflection of X(i) in X(j) for these {i,j}: {381, 15022}
X(61857) = inverse of X(61890) in orthocentroidal circle
X(61857) = inverse of X(61890) in Yff hyperbola
X(61857) = complement of X(61913)
X(61857) = pole of line {523, 61890} with respect to the orthocentroidal circle
X(61857) = pole of line {185, 58198} with respect to the Jerabek hyperbola
X(61857) = pole of line {6, 61890} with respect to the Kiepert hyperbola
X(61857) = pole of line {523, 61890} with respect to the Yff hyperbola
X(61857) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1105), X(58198)}}, {{A, B, C, X(15712), X(46452)}}, {{A, B, C, X(22268), X(50689)}}
X(61857) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10303, 11001}, {2, 11001, 15699}, {2, 11812, 381}, {2, 15698, 547}, {2, 15702, 8703}, {2, 15709, 11812}, {2, 15719, 10109}, {2, 631, 5066}, {2, 8703, 1656}, {5, 5054, 15718}, {140, 15723, 5055}, {140, 16239, 15704}, {140, 3856, 14869}, {140, 632, 5067}, {376, 10124, 15723}, {376, 3523, 17504}, {376, 3830, 15685}, {381, 5054, 3523}, {382, 15693, 15759}, {547, 15720, 15689}, {549, 14892, 3528}, {631, 5066, 15716}, {1656, 15702, 15707}, {1656, 15707, 15684}, {1657, 5054, 549}, {3091, 15682, 3845}, {3091, 15693, 15695}, {3523, 5067, 12102}, {3525, 5054, 15694}, {3526, 5054, 10124}, {3529, 15709, 15702}, {3533, 15694, 14269}, {3534, 15713, 15701}, {3628, 15721, 15688}, {3830, 15695, 1657}, {3839, 15702, 12108}, {5055, 15694, 140}, {5066, 15716, 15681}, {5070, 15701, 15682}, {5071, 14869, 15706}, {5071, 15706, 5073}, {6948, 16239, 7405}, {10109, 15713, 15719}, {10109, 15719, 3534}, {10124, 11539, 3525}, {10124, 11540, 12100}, {10124, 15694, 15703}, {10303, 15699, 15700}, {11737, 17504, 3529}, {11812, 15640, 15693}, {12100, 15701, 15722}, {12102, 17504, 376}, {12108, 15702, 5054}, {14269, 15684, 3853}, {15684, 15707, 3}, {15693, 15723, 2}, {15699, 15700, 3843}, {15703, 15722, 3830}

X(61858) = X(2)X(3)∩X(15)X(42591)

Barycentrics    14*a^4+9*(b^2-c^2)^2-23*a^2*(b^2+c^2) : :
X(61858) = 27*X[2]+5*X[3], 9*X[141]+7*X[55708], 5*X[575]+3*X[3631], -9*X[620]+X[38628], -9*X[1125]+X[58240], -35*X[1698]+3*X[61247], -9*X[3035]+X[38629], X[3244]+15*X[11231], -9*X[3589]+X[55718], 21*X[3619]+11*X[55701], 3*X[3626]+5*X[15178], -9*X[3629]+25*X[22234] and many others

X(61858) lies on these lines: {2, 3}, {15, 42591}, {16, 42590}, {17, 42612}, {18, 42613}, {61, 43102}, {62, 43103}, {141, 55708}, {395, 42597}, {396, 42596}, {397, 43013}, {398, 43012}, {575, 3631}, {620, 38628}, {952, 58232}, {1125, 58240}, {1698, 61247}, {3035, 38629}, {3054, 53096}, {3055, 35007}, {3244, 11231}, {3564, 55704}, {3589, 55718}, {3592, 13993}, {3594, 13925}, {3619, 55701}, {3626, 15178}, {3629, 22234}, {3632, 38028}, {3634, 28224}, {3636, 5844}, {3746, 7294}, {3819, 16881}, {4745, 61290}, {5318, 42498}, {5321, 42499}, {5326, 5563}, {5351, 42146}, {5352, 42143}, {5447, 16982}, {5480, 55611}, {5642, 13393}, {5690, 61279}, {5972, 38632}, {6036, 38627}, {6154, 34126}, {6329, 22330}, {6453, 32790}, {6454, 32789}, {6500, 43374}, {6501, 43375}, {6699, 38626}, {6710, 38630}, {6713, 38631}, {7619, 59546}, {7749, 41940}, {9542, 34091}, {9588, 38022}, {9693, 43565}, {10219, 18874}, {10222, 15808}, {10272, 38729}, {11008, 53092}, {11591, 15082}, {12512, 61267}, {13373, 58675}, {13392, 24981}, {14677, 15029}, {15021, 61598}, {16189, 26446}, {16241, 42593}, {16242, 42592}, {16625, 32142}, {16772, 42497}, {16773, 42496}, {17852, 42216}, {18357, 31666}, {18358, 55687}, {18510, 43506}, {18512, 43505}, {18583, 55721}, {19878, 28174}, {20050, 38112}, {20054, 61283}, {20190, 34573}, {20398, 35022}, {20399, 35021}, {20583, 40107}, {21167, 55628}, {22115, 46865}, {22236, 42628}, {22238, 42627}, {22712, 55769}, {28160, 58223}, {30389, 38042}, {30531, 32348}, {31235, 51529}, {31253, 61259}, {31274, 51523}, {31423, 58245}, {31652, 43291}, {31662, 61253}, {32523, 61132}, {32887, 34229}, {33416, 42946}, {33417, 42947}, {33749, 51143}, {33879, 37481}, {34641, 61286}, {34754, 42782}, {34755, 42781}, {34773, 58229}, {35255, 43880}, {35256, 43879}, {35770, 42567}, {35771, 42566}, {35812, 43212}, {35813, 43211}, {38110, 40341}, {38111, 60957}, {38113, 60933}, {38136, 55626}, {38317, 55600}, {38740, 61561}, {38751, 61560}, {38763, 61566}, {38775, 61565}, {38787, 61571}, {38795, 61548}, {42101, 43872}, {42102, 43871}, {42115, 42492}, {42116, 42493}, {42122, 42580}, {42123, 42581}, {42488, 42501}, {42489, 42500}, {42568, 43886}, {42569, 43885}, {42584, 43195}, {42585, 43196}, {42594, 42797}, {42595, 42798}, {42610, 43635}, {42611, 43634}, {42786, 55675}, {42793, 43109}, {42794, 43108}, {42888, 42914}, {42889, 42915}, {42912, 42937}, {42913, 42936}, {42916, 43464}, {42917, 43463}, {42942, 43547}, {42943, 43546}, {42962, 43487}, {42963, 43488}, {43416, 43485}, {43417, 43486}, {46931, 58230}, {46932, 61245}, {48876, 53858}, {50828, 61255}, {51126, 52987}, {51127, 55617}, {52984, 55080}, {53093, 61545}, {58249, 61273}, {58441, 61272}, {58605, 58630}

X(61858) = midpoint of X(i) and X(j) for these {i,j}: {3, 12811}, {140, 16239}, {3628, 12108}, {5447, 58531}, {10124, 11540}, {13373, 58675}, {58605, 58630}
X(61858) = complement of X(35018)
X(61858) = pole of line {6, 42530} with respect to the Kiepert hyperbola
X(61858) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3524), X(46452)}}, {{A, B, C, X(3845), X(22268)}}, {{A, B, C, X(5055), X(43970)}}, {{A, B, C, X(11001), X(22270)}}, {{A, B, C, X(11812), X(14938)}}, {{A, B, C, X(47478), X(57895)}}
X(61858) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10303, 3529}, {2, 140, 3530}, {2, 14869, 546}, {2, 15681, 15699}, {2, 15702, 15688}, {2, 17504, 547}, {2, 17533, 5068}, {2, 3528, 1656}, {2, 5054, 15687}, {2, 631, 3851}, {3, 12812, 12102}, {3, 15022, 3627}, {3, 5072, 11541}, {5, 140, 11812}, {5, 15711, 5073}, {5, 3522, 12101}, {5, 549, 3522}, {5, 550, 14269}, {21, 16370, 16417}, {140, 10124, 16239}, {140, 3526, 10124}, {140, 3628, 12108}, {140, 547, 631}, {140, 548, 5054}, {140, 631, 14890}, {382, 3851, 3839}, {474, 16860, 16853}, {546, 12103, 382}, {546, 12812, 3544}, {546, 16239, 1010}, {546, 5079, 11737}, {549, 15689, 12100}, {631, 3851, 17504}, {631, 5059, 15718}, {632, 11539, 3525}, {1656, 12100, 3861}, {1656, 3543, 5}, {2049, 14869, 14893}, {3090, 11001, 3091}, {3090, 12103, 3850}, {3091, 13735, 3090}, {3523, 15699, 3853}, {3523, 3524, 6948}, {3523, 3853, 15759}, {3525, 10303, 15694}, {3525, 17678, 5076}, {3525, 3526, 632}, {3525, 3533, 10303}, {3526, 15694, 3533}, {3529, 10303, 15720}, {3530, 11737, 550}, {3628, 12102, 12812}, {3628, 15759, 5072}, {3839, 3850, 3856}, {3851, 15723, 16845}, {3858, 15717, 15690}, {5054, 11001, 549}, {5070, 15702, 15712}, {5070, 15712, 5066}, {5073, 15720, 10299}, {6931, 16861, 17568}, {10109, 11812, 15711}, {10124, 11539, 11540}, {10124, 11540, 30}, {10124, 14891, 15723}, {10299, 15687, 548}, {10303, 15720, 14869}, {11540, 16239, 140}, {12102, 12812, 12811}, {12108, 12811, 3}, {12108, 16239, 3628}, {13587, 16418, 16857}, {14782, 14783, 15719}, {15689, 15704, 12103}, {15703, 15717, 3858}, {15707, 15723, 2}, {15721, 16397, 3528}

X(61859) = X(2)X(3)∩X(40)X(51075)

Barycentrics    17*a^4+11*(b^2-c^2)^2-28*a^2*(b^2+c^2) : :
X(61859) = 11*X[2]+2*X[3], 5*X[40]+8*X[51075], 11*X[69]+28*X[55712], X[147]+12*X[26614], 8*X[575]+5*X[50990], 5*X[944]+8*X[50801], 8*X[946]+5*X[50809], 5*X[1350]+8*X[51130], 8*X[1352]+5*X[51176], -3*X[1992]+16*X[46267], X[3241]+12*X[11231], -55*X[3618]+16*X[55715] and many others

X(61859) lies on these lines: {2, 3}, {40, 51075}, {69, 55712}, {147, 26614}, {371, 43506}, {372, 43505}, {575, 50990}, {944, 50801}, {946, 50809}, {1056, 5326}, {1058, 7294}, {1151, 41951}, {1152, 41952}, {1285, 3055}, {1350, 51130}, {1352, 51176}, {1992, 46267}, {2549, 11614}, {3068, 6436}, {3069, 6435}, {3241, 11231}, {3618, 55715}, {3619, 38064}, {3622, 38066}, {3624, 38068}, {3634, 38074}, {3653, 9780}, {3654, 5550}, {3828, 59388}, {5032, 51174}, {5343, 42611}, {5344, 42610}, {5355, 14482}, {5476, 55586}, {5480, 50966}, {5485, 11668}, {5818, 50828}, {5890, 15082}, {5892, 33879}, {6221, 43317}, {6390, 32893}, {6398, 43316}, {6409, 43385}, {6410, 43384}, {6447, 42527}, {6448, 42526}, {6484, 42571}, {6485, 42570}, {6498, 43211}, {6499, 43212}, {6519, 43377}, {6522, 43376}, {6776, 50958}, {7585, 43375}, {7586, 43374}, {7607, 60641}, {7612, 60277}, {7736, 14075}, {7753, 46453}, {7757, 23053}, {7788, 32839}, {7811, 34803}, {7967, 38176}, {7999, 16226}, {8227, 50829}, {8591, 34127}, {8976, 43386}, {9143, 34128}, {9167, 12243}, {9693, 53516}, {9771, 55823}, {10155, 60648}, {10165, 19876}, {10168, 14912}, {10172, 34628}, {10576, 14241}, {10577, 14226}, {10595, 50821}, {11160, 38110}, {11179, 55700}, {11230, 34632}, {11465, 21849}, {11480, 56610}, {11481, 56611}, {12045, 36987}, {12245, 25055}, {12571, 50812}, {13172, 14971}, {13199, 59376}, {13951, 43387}, {14494, 60238}, {14561, 55589}, {15178, 51072}, {16267, 43008}, {16268, 43009}, {16644, 42898}, {16645, 42899}, {16808, 43330}, {16809, 43331}, {16962, 49861}, {16963, 49862}, {16964, 42927}, {16965, 42926}, {16966, 43771}, {16967, 43772}, {17852, 43409}, {18581, 43778}, {18582, 43777}, {18840, 54644}, {18841, 54645}, {18842, 53108}, {19053, 43254}, {19054, 43255}, {19875, 47745}, {19877, 28204}, {19878, 38021}, {19883, 31423}, {19925, 50819}, {20049, 38112}, {20423, 55581}, {21356, 50961}, {21358, 50974}, {22110, 55726}, {22235, 42590}, {22237, 42591}, {22712, 55768}, {23267, 42602}, {23269, 53131}, {23273, 42603}, {23275, 53130}, {23302, 43332}, {23303, 43333}, {25565, 51538}, {26446, 34631}, {28194, 34595}, {31145, 38028}, {31162, 58441}, {31455, 34571}, {32785, 42600}, {32786, 42601}, {32837, 37688}, {32838, 59634}, {33416, 37641}, {33417, 37640}, {33602, 42494}, {33603, 42495}, {34089, 60622}, {34091, 60623}, {34754, 42513}, {34755, 42512}, {35822, 43510}, {35823, 43509}, {36836, 49824}, {36843, 49825}, {37832, 43469}, {37835, 43470}, {38067, 60996}, {38072, 51127}, {38073, 58433}, {38079, 54174}, {38113, 60984}, {38317, 54170}, {38750, 41135}, {40330, 50983}, {41973, 42504}, {41974, 42505}, {42085, 43782}, {42086, 43781}, {42089, 42986}, {42092, 42987}, {42119, 42930}, {42120, 42931}, {42149, 42596}, {42152, 42597}, {42260, 43522}, {42261, 43521}, {42433, 43003}, {42434, 43002}, {42488, 42510}, {42489, 42511}, {42500, 43028}, {42501, 43029}, {42592, 49903}, {42593, 49904}, {42594, 42943}, {42595, 42942}, {42598, 49826}, {42599, 49827}, {42631, 42921}, {42632, 42920}, {42785, 55609}, {42799, 43543}, {42800, 43542}, {42944, 49875}, {42945, 49876}, {42948, 43107}, {42949, 43100}, {42974, 43554}, {42975, 43555}, {42978, 49859}, {42979, 49860}, {43030, 43248}, {43031, 43249}, {43334, 43467}, {43335, 43468}, {43446, 54594}, {43447, 54593}, {44401, 55794}, {47352, 51132}, {47353, 51128}, {47355, 54132}, {48310, 50967}, {48873, 51141}, {48885, 51029}, {49810, 56614}, {49811, 56615}, {50804, 53620}, {50956, 55674}, {50977, 55719}, {50981, 55584}, {51022, 55671}, {51070, 61288}, {51143, 53093}, {51177, 53094}, {51178, 55711}, {51179, 55714}, {51212, 55605}, {53098, 60283}, {53103, 60628}, {54173, 55723}, {54920, 60646}, {54921, 60629}, {56059, 60150}, {59386, 60999}, {60123, 60216}, {60127, 60644}, {60335, 60643}

X(61859) = midpoint of X(i) and X(j) for these {i,j}: {2, 10303}
X(61859) = reflection of X(i) in X(j) for these {i,j}: {5067, 2}
X(61859) = inverse of X(61889) in orthocentroidal circle
X(61859) = inverse of X(61889) in Yff hyperbola
X(61859) = complement of X(61912)
X(61859) = anticomplement of X(61883)
X(61859) = pole of line {523, 61889} with respect to the orthocentroidal circle
X(61859) = pole of line {6, 61889} with respect to the Kiepert hyperbola
X(61859) = pole of line {523, 61889} with respect to the Yff hyperbola
X(61859) = pole of line {69, 15699} with respect to the Wallace hyperbola
X(61859) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(15699)}}, {{A, B, C, X(549), X(46921)}}, {{A, B, C, X(1494), X(5067)}}, {{A, B, C, X(3530), X(46452)}}, {{A, B, C, X(3627), X(54660)}}, {{A, B, C, X(3843), X(54763)}}, {{A, B, C, X(3856), X(60007)}}, {{A, B, C, X(4232), X(11668)}}, {{A, B, C, X(5055), X(36948)}}, {{A, B, C, X(5071), X(57895)}}, {{A, B, C, X(5079), X(18854)}}, {{A, B, C, X(6995), X(54644)}}, {{A, B, C, X(7378), X(54645)}}, {{A, B, C, X(7409), X(54522)}}, {{A, B, C, X(8703), X(18852)}}, {{A, B, C, X(14893), X(54838)}}, {{A, B, C, X(15022), X(15319)}}, {{A, B, C, X(15703), X(36889)}}, {{A, B, C, X(15704), X(22270)}}, {{A, B, C, X(18849), X(49134)}}, {{A, B, C, X(18853), X(55864)}}, {{A, B, C, X(33923), X(46412)}}, {{A, B, C, X(37174), X(60277)}}, {{A, B, C, X(38335), X(54667)}}, {{A, B, C, X(40448), X(50691)}}, {{A, B, C, X(52282), X(60641)}}, {{A, B, C, X(52284), X(53108)}}
X(61859) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10303, 30}, {2, 11539, 3525}, {2, 14890, 17538}, {2, 15702, 376}, {2, 15705, 7486}, {2, 15708, 5}, {2, 15713, 11001}, {2, 20, 15699}, {2, 30, 5067}, {2, 3524, 3090}, {2, 3543, 15703}, {2, 3839, 3628}, {2, 5054, 4}, {2, 631, 3545}, {3, 1656, 3856}, {4, 3524, 8703}, {4, 3544, 3859}, {4, 5054, 15719}, {4, 5067, 5079}, {5, 15700, 15683}, {140, 14892, 11812}, {140, 15699, 15701}, {140, 15721, 15702}, {140, 16239, 3627}, {140, 381, 15721}, {140, 3861, 14869}, {140, 632, 5070}, {140, 8703, 5054}, {376, 15719, 15692}, {381, 15694, 140}, {381, 15700, 15689}, {381, 15701, 14891}, {546, 15706, 15697}, {547, 10124, 632}, {547, 549, 15681}, {549, 10124, 15723}, {549, 11737, 14093}, {549, 14893, 3}, {549, 3526, 17678}, {549, 3543, 15715}, {631, 3545, 15698}, {632, 11539, 11540}, {1656, 15685, 14892}, {1656, 15718, 15687}, {3090, 3524, 15682}, {3525, 3526, 3533}, {3526, 15694, 10124}, {3533, 11540, 15710}, {3545, 15693, 16434}, {3545, 15698, 3529}, {3628, 15693, 3839}, {3839, 15693, 3528}, {3845, 14890, 15720}, {3845, 15720, 15705}, {3855, 15709, 15713}, {3860, 5054, 3523}, {5055, 11001, 3855}, {5055, 15696, 3860}, {5055, 15717, 6834}, {5066, 15707, 3522}, {5067, 10303, 10299}, {6922, 16239, 13742}, {7486, 15705, 3845}, {8703, 15699, 12811}, {10124, 11539, 15694}, {10124, 11540, 547}, {10124, 15694, 2}, {10165, 19876, 34627}, {10299, 10303, 631}, {11737, 14093, 3543}, {11812, 15687, 15718}, {14093, 15703, 11737}, {14891, 15699, 381}, {15683, 15708, 15700}, {15687, 15718, 10304}, {15689, 15708, 3524}, {15694, 15702, 15709}, {15694, 15723, 549}, {15699, 15701, 20}, {15704, 16401, 5071}, {15713, 16239, 5055}, {15717, 16853, 1656}, {19883, 31423, 50810}, {42948, 43107, 49906}, {42949, 43100, 49905}, {43374, 43518, 7586}, {43375, 43517, 7585}

X(61860) = X(2)X(3)∩X(15)X(42503)

Barycentrics    26*a^4+17*(b^2-c^2)^2-43*a^2*(b^2+c^2) : :
X(61860) = 17*X[2]+3*X[3], 8*X[125]+7*X[22250], 3*X[575]+2*X[41152], 3*X[1353]+7*X[50994], 3*X[1483]+7*X[51068], 3*X[3817]+7*X[51088], X[4677]+9*X[38028], 3*X[5587]+7*X[50833], 3*X[5603]+7*X[50826], 3*X[5690]+7*X[51110], 3*X[10168]+2*X[51143], 4*X[10219]+X[54044] and many others

X(61860) lies on these lines: {2, 3}, {15, 42503}, {16, 42502}, {125, 22250}, {395, 42520}, {396, 42521}, {575, 41152}, {1353, 50994}, {1483, 51068}, {3817, 51088}, {4677, 38028}, {5587, 50833}, {5603, 50826}, {5690, 51110}, {5844, 51105}, {5965, 50991}, {6437, 43569}, {6438, 43568}, {7294, 15170}, {10168, 51143}, {10219, 54044}, {10516, 50988}, {11231, 51071}, {13665, 42574}, {13785, 42575}, {14711, 40108}, {14853, 50981}, {15178, 51070}, {15300, 34127}, {15533, 38110}, {15534, 51732}, {16191, 26446}, {16241, 42628}, {16242, 42627}, {16267, 41977}, {16268, 41978}, {16960, 42913}, {16961, 42912}, {16962, 42948}, {16963, 42949}, {16966, 42594}, {16967, 42595}, {18538, 42418}, {18581, 42509}, {18582, 42508}, {18762, 42417}, {20399, 41151}, {22247, 61560}, {23302, 42506}, {23303, 42507}, {28186, 51084}, {28208, 31253}, {28212, 50825}, {28228, 61614}, {28232, 50829}, {28234, 51108}, {31423, 38022}, {32789, 41950}, {32790, 41949}, {33416, 43229}, {33417, 43228}, {34380, 51185}, {35822, 41948}, {35823, 41947}, {37832, 43109}, {37835, 43108}, {38113, 60963}, {41100, 42501}, {41101, 42500}, {41121, 42505}, {41122, 42504}, {41149, 46267}, {41943, 42597}, {41944, 42596}, {42089, 42496}, {42092, 42497}, {42121, 49905}, {42124, 49906}, {42130, 43002}, {42131, 43003}, {42143, 42499}, {42146, 42498}, {42480, 42533}, {42481, 42532}, {42492, 43403}, {42493, 43404}, {42510, 43029}, {42511, 43028}, {42512, 49860}, {42513, 49859}, {42631, 43104}, {42632, 43101}, {42633, 49861}, {42634, 49862}, {42952, 43467}, {42953, 43468}, {42972, 43634}, {42973, 43635}, {42976, 43107}, {42977, 43100}, {43240, 46334}, {43241, 46335}, {43797, 45384}, {43798, 45385}, {50812, 61266}, {50827, 61280}, {50830, 51094}, {50960, 55670}, {50979, 51186}, {51069, 61510}, {51081, 58216}, {51093, 51700}, {51103, 61597}, {58445, 61624}

X(61860) = midpoint of X(i) and X(j) for these {i,j}: {2, 15713}, {5, 15692}, {549, 1656}, {632, 15694}, {3091, 15714}, {3845, 15695}, {3858, 14093}, {5071, 15712}, {15686, 17578}, {15687, 17538}
X(61860) = reflection of X(i) in X(j) for these {i,j}: {140, 15694}, {14893, 3091}, {15693, 11812}, {15714, 3530}, {3522, 14891}, {3843, 11737}, {3859, 5071}, {5071, 3628}, {632, 10124}
X(61860) = complement of X(61910)
X(61860) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3523), X(46452)}}, {{A, B, C, X(10109), X(57895)}}
X(61860) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10303, 15682}, {2, 11539, 11540}, {2, 11812, 5066}, {2, 12100, 547}, {2, 140, 12100}, {2, 15682, 15703}, {2, 15694, 15713}, {2, 15702, 3534}, {2, 15709, 15701}, {2, 15719, 5055}, {2, 3534, 15699}, {2, 3845, 3628}, {2, 5054, 3845}, {2, 549, 10109}, {5, 549, 15688}, {20, 5054, 549}, {30, 10124, 632}, {30, 11737, 3843}, {30, 11812, 15693}, {30, 14891, 3522}, {30, 3091, 14893}, {30, 3530, 15714}, {30, 3628, 5071}, {30, 5071, 3859}, {140, 12812, 631}, {140, 3853, 14869}, {140, 5066, 11812}, {376, 15682, 6949}, {382, 3090, 6917}, {452, 5067, 3526}, {546, 12100, 15690}, {547, 12100, 12101}, {549, 11539, 3525}, {632, 11539, 15694}, {632, 1656, 16239}, {1656, 15693, 3830}, {1656, 3843, 15022}, {3522, 7402, 17578}, {3524, 11737, 12103}, {3526, 11539, 10124}, {3534, 6891, 376}, {3628, 5076, 12812}, {3830, 15688, 11001}, {3845, 15712, 15695}, {3859, 5071, 14892}, {5055, 14869, 14891}, {5055, 14891, 3853}, {5070, 15708, 15687}, {5071, 15692, 15684}, {6953, 15719, 14093}, {6989, 12100, 14890}, {10109, 15690, 546}, {10109, 16239, 2}, {10124, 11539, 140}, {10303, 15703, 17504}, {11539, 17678, 12108}, {11540, 15759, 15709}, {12100, 12101, 548}, {12100, 15691, 15759}, {15684, 15688, 20}, {15686, 17578, 30}, {15693, 15695, 15698}, {15693, 15697, 15711}, {15693, 15698, 15712}, {15694, 15723, 15692}, {15699, 15702, 3530}, {15699, 15714, 3091}, {15703, 17504, 3850}, {15709, 15723, 5}

X(61861) = X(2)X(3)∩X(6)X(43517)

Barycentrics    19*a^4+13*(b^2-c^2)^2-32*a^2*(b^2+c^2) : :
X(61861) = 13*X[2]+2*X[3], 8*X[575]+7*X[50994], X[944]+14*X[19876], -16*X[1125]+X[34631], -X[1992]+16*X[58445], 7*X[3619]+8*X[10168], 14*X[3624]+X[50810], -16*X[3634]+X[34627], 4*X[3653]+X[59388], 2*X[3655]+13*X[19877], 8*X[3818]+7*X[51177], 14*X[4751]+X[51043] and many others

X(61861) lies on these lines: {2, 3}, {6, 43517}, {371, 43387}, {372, 43386}, {395, 43463}, {396, 43464}, {485, 6479}, {486, 6478}, {575, 50994}, {590, 6442}, {615, 6441}, {754, 55823}, {944, 19876}, {1125, 34631}, {1151, 14226}, {1152, 14241}, {1587, 34089}, {1588, 34091}, {1992, 58445}, {3055, 46453}, {3068, 42600}, {3069, 42601}, {3590, 6448}, {3591, 6447}, {3619, 10168}, {3624, 50810}, {3634, 34627}, {3653, 59388}, {3655, 19877}, {3818, 51177}, {4751, 51043}, {4995, 47743}, {5298, 8164}, {5334, 42500}, {5335, 42501}, {5343, 42791}, {5344, 42792}, {5351, 42588}, {5352, 42589}, {5550, 50821}, {5603, 38068}, {5657, 19883}, {5731, 38083}, {5965, 21356}, {6361, 50829}, {6429, 42573}, {6430, 42572}, {6439, 23273}, {6440, 23267}, {6480, 43343}, {6481, 43342}, {7585, 43212}, {7586, 43211}, {7612, 60629}, {7619, 9741}, {7967, 19875}, {9167, 14651}, {9540, 43506}, {9780, 50818}, {10155, 54616}, {10165, 38074}, {10519, 48310}, {11180, 34573}, {11231, 38314}, {11465, 21969}, {11488, 16963}, {11489, 16962}, {12017, 51176}, {13935, 43505}, {14494, 60616}, {14912, 21358}, {15045, 15082}, {15178, 51068}, {15808, 50817}, {16267, 42089}, {16268, 42092}, {16644, 43100}, {16645, 43107}, {16960, 42517}, {16961, 42516}, {18483, 50813}, {18493, 50825}, {19872, 50796}, {19878, 31162}, {20049, 51700}, {21168, 38093}, {22236, 42519}, {22238, 42518}, {25055, 28234}, {26516, 49092}, {26521, 49093}, {32789, 43510}, {32790, 43509}, {32817, 32885}, {32822, 32883}, {32823, 32884}, {32839, 37671}, {33416, 37640}, {33417, 37641}, {33602, 42610}, {33603, 42611}, {33604, 42491}, {33605, 42490}, {34127, 52695}, {34718, 46934}, {36836, 49873}, {36843, 49874}, {36948, 57895}, {36967, 43202}, {36968, 43201}, {37832, 42498}, {37835, 42499}, {38021, 58441}, {38022, 59417}, {38067, 59386}, {38113, 59375}, {39874, 50983}, {40693, 43023}, {40694, 43022}, {41943, 42596}, {41944, 42597}, {42149, 42521}, {42152, 42520}, {42270, 43522}, {42273, 43521}, {42506, 42592}, {42507, 42593}, {42582, 43256}, {42583, 43257}, {42598, 49875}, {42599, 49876}, {42686, 43777}, {42687, 43778}, {42777, 43494}, {42778, 43493}, {42912, 42987}, {42913, 42986}, {42944, 49826}, {42945, 49827}, {42948, 49948}, {42949, 49947}, {42978, 49810}, {42979, 49811}, {43014, 43373}, {43015, 43372}, {43020, 43024}, {43021, 43025}, {43209, 56622}, {43210, 56621}, {43273, 51128}, {43416, 43870}, {43417, 43869}, {43572, 43650}, {46932, 50798}, {46933, 50824}, {46951, 52718}, {47355, 50967}, {48891, 51217}, {48905, 51139}, {50811, 51073}, {50866, 58217}, {50958, 55699}, {50964, 55653}, {51084, 61261}, {51127, 54131}, {51171, 51179}, {51215, 55705}, {53103, 60143}, {54500, 60237}, {60123, 60627}, {60183, 60185}

X(61861) = midpoint of X(i) and X(j) for these {i,j}: {632, 11539}, {3522, 3839}, {3524, 5071}, {3843, 15688}, {5055, 15693}
X(61861) = reflection of X(i) in X(j) for these {i,j}: {15688, 15711}, {15694, 11539}, {3091, 5055}, {3524, 631}
X(61861) = inverse of X(61888) in orthocentroidal circle
X(61861) = inverse of X(61888) in Yff hyperbola
X(61861) = complement of X(61906)
X(61861) = anticomplement of X(61882)
X(61861) = pole of line {523, 61888} with respect to the orthocentroidal circle
X(61861) = pole of line {6, 43554} with respect to the Kiepert hyperbola
X(61861) = pole of line {523, 61888} with respect to the Yff hyperbola
X(61861) = pole of line {69, 15703} with respect to the Wallace hyperbola
X(61861) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(15703)}}, {{A, B, C, X(547), X(36948)}}, {{A, B, C, X(3090), X(57895)}}, {{A, B, C, X(3628), X(36889)}}, {{A, B, C, X(3859), X(60007)}}, {{A, B, C, X(5067), X(57822)}}, {{A, B, C, X(5076), X(22268)}}, {{A, B, C, X(7408), X(60185)}}, {{A, B, C, X(7409), X(54523)}}, {{A, B, C, X(12103), X(22270)}}, {{A, B, C, X(12108), X(46452)}}, {{A, B, C, X(17578), X(54660)}}, {{A, B, C, X(37174), X(60629)}}, {{A, B, C, X(40448), X(50690)}}, {{A, B, C, X(41986), X(46168)}}, {{A, B, C, X(46412), X(46853)}}, {{A, B, C, X(50689), X(54763)}}, {{A, B, C, X(52301), X(53103)}}
X(61861) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10124, 3533}, {2, 10303, 381}, {2, 10304, 15699}, {2, 11539, 15709}, {2, 140, 376}, {2, 15692, 1656}, {2, 15702, 4}, {2, 15708, 5055}, {2, 15721, 5}, {2, 20, 15703}, {2, 3523, 547}, {2, 3525, 15702}, {2, 3543, 3628}, {2, 376, 5067}, {2, 549, 3090}, {2, 631, 5071}, {3, 11737, 15640}, {3, 1656, 3859}, {4, 3857, 6830}, {4, 6949, 15684}, {5, 14890, 15707}, {5, 15721, 15698}, {30, 11539, 15694}, {30, 15711, 15688}, {30, 5055, 3091}, {140, 15685, 15721}, {140, 15723, 2}, {140, 17504, 5054}, {376, 15682, 15704}, {376, 15759, 3528}, {376, 382, 11001}, {376, 3845, 11541}, {376, 631, 15693}, {381, 10303, 15719}, {381, 15759, 5059}, {547, 15682, 3544}, {547, 15711, 3843}, {547, 3523, 15682}, {549, 12101, 3}, {631, 1656, 17538}, {631, 3090, 3522}, {631, 3533, 632}, {632, 15712, 16239}, {1656, 15694, 15713}, {1656, 15713, 15692}, {1995, 4189, 17548}, {3090, 15710, 3839}, {3091, 3522, 382}, {3522, 3839, 30}, {3523, 7402, 15696}, {3524, 11001, 15710}, {3524, 3528, 15705}, {3543, 15701, 10299}, {3619, 10168, 50974}, {3628, 15701, 3543}, {3839, 15705, 12103}, {3839, 7486, 17579}, {4223, 16856, 17531}, {5054, 15689, 549}, {5054, 15699, 10304}, {5054, 5055, 17504}, {5055, 15707, 15685}, {5079, 15722, 15686}, {10109, 15700, 3146}, {10303, 15712, 631}, {10304, 15699, 3545}, {11539, 15709, 3525}, {11539, 15723, 15708}, {11540, 11737, 140}, {11812, 12812, 15714}, {11812, 15703, 20}, {15692, 15719, 7390}, {15692, 17578, 15695}, {15694, 16239, 15697}, {15698, 15707, 3524}, {15698, 15709, 14890}, {16370, 16418, 16863}, {16417, 16418, 17543}, {16418, 17547, 16866}, {43517, 43518, 6}

X(61862) = X(2)X(3)∩X(6)X(43489)

Barycentrics    29*a^4+20*(b^2-c^2)^2-49*a^2*(b^2+c^2) : :
X(61862) = 20*X[2]+3*X[3], 8*X[4669]+15*X[37624], -32*X[4745]+9*X[51515], 9*X[5050]+14*X[51186], -24*X[7619]+X[51122], 9*X[7988]+14*X[51088], -X[8148]+24*X[19883], -9*X[10247]+32*X[51108], 18*X[11231]+5*X[51105], 5*X[15300]+18*X[38735], 5*X[15533]+18*X[39561], -X[15534]+24*X[58445] and many others

X(61862) lies on these lines: {2, 3}, {6, 43489}, {15, 42953}, {16, 42952}, {4669, 37624}, {4745, 51515}, {5050, 51186}, {5339, 43440}, {5340, 43441}, {6407, 42603}, {6408, 42602}, {6417, 43254}, {6418, 43255}, {6437, 45385}, {6438, 45384}, {6445, 42417}, {6446, 42418}, {6447, 43886}, {6448, 43885}, {6500, 43211}, {6501, 43212}, {6564, 43384}, {6565, 43385}, {7619, 51122}, {7988, 51088}, {8148, 19883}, {10137, 52045}, {10138, 52046}, {10247, 51108}, {11231, 51105}, {11485, 42507}, {11486, 42506}, {11668, 60216}, {13665, 43315}, {13785, 43314}, {15300, 38735}, {15533, 39561}, {15534, 58445}, {15602, 18362}, {16241, 43005}, {16242, 43004}, {16644, 42533}, {16645, 42532}, {16772, 49810}, {16773, 49811}, {18581, 42595}, {18582, 42594}, {20582, 55705}, {21358, 50664}, {22165, 53091}, {25565, 55639}, {30392, 50798}, {32787, 42600}, {32788, 42601}, {33179, 38066}, {33416, 43199}, {33417, 43200}, {33602, 43870}, {33603, 43869}, {34718, 51109}, {34748, 51066}, {38028, 51072}, {38072, 55612}, {38110, 50990}, {38112, 51092}, {38155, 58230}, {41112, 42501}, {41113, 42500}, {41121, 43469}, {41122, 43470}, {42089, 49860}, {42092, 49859}, {42115, 42498}, {42116, 42499}, {42129, 42503}, {42132, 42502}, {42154, 42930}, {42155, 42931}, {42433, 56627}, {42434, 56628}, {42526, 43881}, {42527, 43882}, {42566, 43514}, {42567, 43513}, {42936, 42977}, {42937, 42976}, {42988, 43100}, {42989, 43107}, {43008, 43027}, {43009, 43026}, {43102, 49861}, {43103, 49862}, {44456, 48310}, {46267, 51187}, {46933, 58233}, {47353, 55685}, {48662, 55688}, {50797, 54445}, {50809, 61270}, {50955, 55703}, {50984, 55624}, {50993, 55711}, {51024, 55640}, {51127, 55604}, {51141, 55645}, {51166, 55593}, {51188, 53092}, {53108, 60283}, {54644, 60277}, {54645, 60238}, {54734, 60644}, {54851, 56059}

X(61862) = complement of X(61904)
X(61862) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(15708), X(46921)}}, {{A, B, C, X(22268), X(50688)}}
X(61862) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12100, 1656}, {2, 140, 3534}, {2, 15682, 3628}, {2, 15694, 15701}, {2, 15701, 5055}, {2, 15702, 3845}, {2, 15709, 12100}, {2, 15713, 381}, {2, 15719, 547}, {2, 3525, 15713}, {2, 3534, 15703}, {2, 631, 10109}, {3, 10299, 6988}, {3, 11539, 15694}, {3, 12100, 6908}, {3, 14269, 15686}, {3, 15703, 3545}, {3, 15717, 6916}, {3, 3543, 15689}, {3, 3850, 17800}, {3, 5067, 3851}, {140, 15692, 5054}, {140, 15703, 15707}, {140, 3857, 631}, {381, 15713, 15722}, {381, 5054, 3530}, {547, 3545, 5079}, {3146, 3534, 15685}, {3526, 15723, 11539}, {3528, 3545, 3543}, {3530, 8703, 15698}, {3533, 11539, 15723}, {3534, 5079, 3860}, {3830, 8703, 15681}, {3845, 16239, 2}, {3845, 5054, 6863}, {5054, 15696, 549}, {5054, 5079, 15692}, {5055, 15701, 15695}, {5055, 15718, 5073}, {5076, 5079, 13743}, {6919, 15721, 15709}, {8703, 11812, 15719}, {10124, 11539, 3533}, {11001, 11812, 15693}, {11001, 15693, 3}, {11539, 16239, 15702}, {14269, 15640, 3830}, {15690, 15713, 15708}, {15694, 15707, 140}, {15695, 15701, 15718}, {15697, 15710, 8703}, {15699, 15720, 15684}, {15703, 15707, 3843}, {42504, 42509, 42116}, {42504, 49908, 42509}, {42505, 42508, 42115}, {42505, 49907, 42508}, {43489, 43490, 6}

X(61863) = X(2)X(3)∩X(6)X(42956)

Barycentrics    13*a^4+9*(b^2-c^2)^2-22*a^2*(b^2+c^2) : :
X(61863) = 27*X[2]+4*X[3], 13*X[8]+18*X[61285], -9*X[193]+40*X[22234], 4*X[389]+27*X[33879], 16*X[575]+15*X[3620], 2*X[944]+29*X[46930], -X[962]+32*X[19878], -36*X[1125]+5*X[16189], 9*X[1352]+22*X[55694], 8*X[1385]+23*X[46931], -18*X[1483]+49*X[58235], 15*X[3617]+16*X[15178] and many others

X(61863) lies on these lines: {2, 3}, {6, 42956}, {8, 61285}, {69, 32898}, {183, 32871}, {193, 22234}, {389, 33879}, {397, 42804}, {398, 42803}, {486, 9542}, {575, 3620}, {590, 42523}, {615, 42522}, {944, 46930}, {962, 19878}, {1078, 32884}, {1125, 16189}, {1151, 42575}, {1152, 42574}, {1352, 55694}, {1385, 46931}, {1483, 58235}, {2888, 54012}, {3054, 22332}, {3055, 22331}, {3070, 6489}, {3071, 6488}, {3303, 7294}, {3304, 5326}, {3590, 60297}, {3591, 60298}, {3592, 32786}, {3594, 32785}, {3617, 15178}, {3618, 53858}, {3619, 53093}, {3622, 11231}, {3624, 58245}, {3634, 30389}, {4297, 58225}, {4678, 38028}, {5158, 45245}, {5237, 43242}, {5238, 43243}, {5304, 31455}, {5351, 43465}, {5352, 43466}, {5355, 31400}, {5418, 43883}, {5420, 43884}, {5550, 7982}, {5650, 15028}, {5731, 51073}, {5734, 19883}, {5888, 46728}, {5921, 10541}, {6053, 38729}, {6337, 32897}, {6417, 43374}, {6418, 43375}, {6419, 13941}, {6420, 8972}, {6425, 32790}, {6426, 32789}, {6431, 42566}, {6432, 42567}, {6459, 10147}, {6460, 10148}, {6486, 43383}, {6487, 43382}, {6519, 23273}, {6522, 23267}, {6723, 15020}, {6776, 55698}, {7583, 43505}, {7584, 43506}, {7585, 42600}, {7586, 42601}, {7619, 11148}, {7687, 15023}, {7749, 37665}, {7772, 37689}, {7991, 19862}, {8960, 43322}, {9588, 50872}, {9742, 55739}, {9780, 47745}, {10222, 46934}, {10519, 55721}, {10574, 40247}, {11036, 31231}, {11444, 15012}, {11480, 43772}, {11481, 43771}, {11614, 31652}, {13903, 43517}, {13961, 43518}, {14561, 55588}, {14643, 38626}, {14853, 55583}, {15024, 33884}, {15026, 16981}, {15029, 38727}, {15039, 40685}, {15044, 48378}, {15061, 38632}, {15561, 38627}, {15589, 32839}, {16187, 52525}, {16808, 56627}, {16809, 56628}, {16966, 43870}, {16967, 43869}, {17852, 53513}, {18581, 42499}, {18582, 42498}, {19872, 59387}, {19876, 50801}, {20014, 51700}, {20080, 53092}, {20190, 40330}, {20582, 51215}, {22235, 42488}, {22236, 42983}, {22237, 42489}, {22238, 42982}, {22330, 51171}, {22712, 55765}, {25406, 51128}, {26446, 58240}, {30315, 50864}, {31235, 38669}, {31274, 38664}, {31404, 35007}, {31670, 55628}, {32820, 32893}, {32835, 37688}, {32900, 38176}, {33748, 55708}, {34089, 45384}, {34091, 45385}, {37640, 42949}, {37641, 42948}, {38224, 38628}, {38317, 55597}, {38629, 57298}, {38630, 57297}, {38631, 38752}, {40693, 42592}, {40694, 42593}, {42115, 43777}, {42116, 43778}, {42149, 42597}, {42152, 42596}, {42494, 42610}, {42495, 42611}, {42594, 42933}, {42595, 42932}, {42602, 43376}, {42603, 43377}, {42627, 43306}, {42628, 43307}, {42785, 55606}, {42786, 55677}, {42974, 43447}, {42975, 43446}, {42984, 43445}, {42985, 43444}, {43101, 43770}, {43102, 43463}, {43103, 43464}, {43104, 43769}, {43323, 58866}, {43481, 43556}, {43482, 43557}, {43537, 60131}, {46932, 58232}, {51068, 61288}, {51126, 53097}, {51127, 51212}, {51538, 55641}, {53099, 60645}, {53859, 60638}, {54445, 58229}, {55600, 61044}

X(61863) = anticomplement of X(61881)
X(61863) = pole of line {185, 62125} with respect to the Jerabek hyperbola
X(61863) = pole of line {69, 46935} with respect to the Wallace hyperbola
X(61863) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(46935)}}, {{A, B, C, X(95), X(46936)}}, {{A, B, C, X(253), X(3628)}}, {{A, B, C, X(1217), X(12100)}}, {{A, B, C, X(3346), X(15698)}}, {{A, B, C, X(3534), X(22270)}}, {{A, B, C, X(3830), X(22268)}}, {{A, B, C, X(3853), X(60618)}}, {{A, B, C, X(3854), X(15077)}}, {{A, B, C, X(3855), X(46455)}}, {{A, B, C, X(3857), X(60007)}}, {{A, B, C, X(5071), X(15319)}}, {{A, B, C, X(7486), X(36948)}}, {{A, B, C, X(14938), X(15701)}}, {{A, B, C, X(15684), X(31361)}}, {{A, B, C, X(16922), X(56360)}}, {{A, B, C, X(31371), X(50691)}}, {{A, B, C, X(43970), X(45757)}}
X(61863) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10303, 3091}, {2, 140, 20}, {2, 15694, 15708}, {2, 15709, 15692}, {2, 15717, 1656}, {2, 17566, 17580}, {2, 3146, 3628}, {2, 3522, 5067}, {2, 3523, 7486}, {2, 439, 16922}, {2, 5059, 13735}, {2, 5068, 5070}, {2, 631, 5056}, {3, 12102, 17538}, {3, 12811, 11541}, {3, 1656, 3857}, {3, 3544, 3146}, {3, 3628, 3544}, {3, 5079, 12102}, {4, 631, 12100}, {5, 140, 15701}, {20, 140, 15721}, {20, 15721, 3523}, {140, 16239, 15699}, {140, 381, 631}, {140, 5070, 3524}, {381, 15707, 8703}, {547, 3528, 3854}, {631, 5067, 17800}, {632, 14869, 16239}, {632, 3526, 3525}, {1656, 12108, 3529}, {1656, 15684, 5}, {1656, 15702, 15717}, {1656, 15707, 3853}, {1656, 15717, 3839}, {3090, 11541, 12811}, {3090, 12811, 15022}, {3090, 3524, 3627}, {3090, 3525, 140}, {3090, 3627, 5068}, {3146, 17697, 3090}, {3522, 11346, 3545}, {3523, 7486, 3543}, {3525, 3533, 632}, {3526, 10124, 3533}, {3528, 3854, 15640}, {3529, 15702, 12108}, {3530, 5071, 5059}, {3545, 5055, 17579}, {5055, 10299, 17578}, {5055, 6850, 382}, {5059, 13735, 5071}, {5079, 17538, 3832}, {8703, 15699, 11737}, {10303, 15708, 14869}, {11001, 15692, 10304}, {11539, 12100, 15694}, {11539, 15723, 11001}, {11540, 13741, 10303}, {11737, 15694, 15702}, {12100, 15699, 381}, {12812, 14869, 3}, {14782, 14783, 15693}, {15022, 16371, 12812}, {15685, 15688, 15691}, {15686, 15759, 15688}, {15694, 16239, 4}, {15699, 15721, 15697}, {15703, 15712, 3855}, {15709, 15723, 2}, {15715, 17800, 3522}, {16410, 16862, 17531}, {16418, 17571, 16371}, {42956, 42957, 6}

X(61864) = X(2)X(3)∩X(6)X(51174)

Barycentrics    11*a^4+8*(b^2-c^2)^2-19*a^2*(b^2+c^2) : :
X(61864) = 8*X[2]+X[3], -10*X[6]+X[51174], 8*X[10]+X[34748], -10*X[141]+X[50961], 4*X[575]+5*X[50993], 4*X[599]+5*X[53091], 8*X[1125]+X[34718], 2*X[1385]+7*X[19876], -10*X[1698]+X[50798], 4*X[3098]+5*X[50963], X[3576]+2*X[38083], 4*X[3579]+5*X[50806] and many others

X(61864) lies on these lines: {2, 3}, {6, 51174}, {10, 34748}, {13, 42476}, {14, 42477}, {141, 50961}, {216, 61306}, {230, 22246}, {542, 55697}, {575, 50993}, {590, 42601}, {599, 53091}, {615, 42600}, {633, 33612}, {634, 33613}, {1125, 34718}, {1154, 33879}, {1385, 19876}, {1698, 50798}, {3054, 7739}, {3068, 43212}, {3069, 43211}, {3098, 50963}, {3576, 38083}, {3579, 50806}, {3582, 6767}, {3584, 7373}, {3589, 51132}, {3616, 50805}, {3618, 50962}, {3619, 50979}, {3620, 51175}, {3622, 50823}, {3624, 8148}, {3634, 3655}, {3653, 5790}, {3656, 19862}, {3679, 37624}, {3763, 10168}, {3828, 47745}, {4678, 50831}, {4687, 51039}, {4751, 51045}, {4772, 51047}, {5024, 11614}, {5050, 21358}, {5093, 47352}, {5237, 42610}, {5238, 42611}, {5298, 31479}, {5306, 31467}, {5326, 10056}, {5355, 37637}, {5368, 31455}, {5461, 38750}, {5476, 55584}, {5544, 32225}, {5640, 54047}, {5657, 38022}, {5886, 38068}, {5946, 44299}, {6036, 48657}, {6053, 20126}, {6199, 8252}, {6390, 32885}, {6395, 8253}, {6407, 10577}, {6408, 10576}, {6417, 13847}, {6418, 13846}, {6437, 42557}, {6438, 42558}, {6472, 52047}, {6473, 52048}, {6500, 32788}, {6501, 32787}, {6688, 13340}, {6721, 14830}, {7294, 10072}, {7603, 15655}, {7619, 40727}, {7749, 43136}, {7753, 44535}, {7767, 32884}, {7967, 38081}, {7988, 28202}, {7998, 13321}, {8724, 31274}, {9143, 40685}, {9167, 38224}, {9690, 13785}, {9691, 42603}, {9703, 43650}, {9780, 50824}, {10194, 42527}, {10195, 42526}, {10246, 19875}, {10247, 11231}, {10519, 38079}, {10540, 16187}, {11160, 51732}, {11178, 12017}, {11179, 34573}, {11480, 42972}, {11481, 42973}, {11485, 16268}, {11486, 16267}, {11632, 22247}, {11645, 55682}, {11693, 38794}, {12045, 14845}, {12355, 14061}, {12699, 50829}, {12702, 34595}, {13363, 54048}, {13665, 43415}, {13903, 19053}, {13925, 43505}, {13961, 19054}, {13993, 43506}, {14535, 58448}, {14666, 58427}, {14848, 48310}, {14971, 38732}, {15037, 17811}, {15046, 38633}, {15178, 51066}, {15533, 46267}, {15808, 50827}, {15815, 18362}, {16226, 23039}, {16241, 42499}, {16242, 42498}, {16644, 16963}, {16645, 16962}, {17006, 22253}, {17851, 42216}, {18357, 58228}, {18405, 46265}, {18440, 50983}, {18493, 19878}, {18510, 43882}, {18512, 43881}, {18524, 61158}, {18525, 50828}, {18526, 19877}, {18581, 42500}, {18582, 42501}, {19106, 42474}, {19107, 42475}, {19130, 55632}, {19872, 50811}, {19883, 26446}, {19924, 55624}, {20057, 50830}, {20415, 36767}, {20423, 51126}, {20477, 55958}, {21151, 38082}, {21168, 38080}, {21309, 31489}, {21356, 38110}, {22112, 22115}, {22234, 51187}, {22268, 36609}, {22712, 55761}, {23234, 26614}, {23251, 56622}, {23261, 56621}, {23302, 43100}, {23303, 43107}, {24206, 55692}, {25561, 53094}, {27268, 51048}, {27742, 44414}, {28186, 58226}, {28204, 58230}, {28208, 54447}, {30308, 31663}, {30315, 31666}, {31145, 51700}, {31238, 51040}, {31253, 50796}, {31423, 51709}, {31670, 50984}, {31673, 51086}, {32789, 45384}, {32790, 45385}, {32869, 52718}, {34127, 41134}, {34474, 38084}, {34628, 50800}, {34632, 50825}, {34638, 50807}, {34773, 50797}, {35242, 51088}, {36430, 36751}, {36650, 43843}, {36836, 41122}, {36843, 41121}, {37484, 58470}, {37496, 59777}, {37640, 43103}, {37641, 43102}, {37705, 46930}, {37727, 51069}, {37832, 42115}, {37835, 42116}, {38025, 38121}, {38028, 51515}, {38030, 38101}, {38065, 51516}, {38067, 38107}, {38069, 38752}, {38072, 55610}, {38093, 59381}, {38098, 61287}, {38113, 51514}, {38314, 59503}, {38317, 55593}, {38762, 45310}, {39563, 53095}, {40107, 51185}, {41100, 42491}, {41101, 42490}, {41112, 42944}, {41113, 42945}, {41943, 42937}, {41944, 42936}, {42089, 42974}, {42092, 42975}, {42095, 42904}, {42098, 42905}, {42126, 43101}, {42127, 43104}, {42129, 42595}, {42132, 42594}, {42159, 42791}, {42162, 42792}, {42274, 43790}, {42277, 43789}, {42478, 42817}, {42479, 42818}, {42488, 43775}, {42489, 43776}, {42510, 42598}, {42511, 42599}, {42580, 42773}, {42581, 42774}, {42582, 53131}, {42583, 53130}, {42596, 43238}, {42597, 43239}, {42633, 43463}, {42634, 43464}, {42688, 43645}, {42689, 43646}, {42785, 54131}, {42795, 44016}, {42796, 44015}, {42948, 43228}, {42949, 43229}, {42950, 43403}, {42951, 43404}, {42982, 43494}, {42983, 43493}, {43004, 43020}, {43005, 43021}, {43193, 56627}, {43194, 56628}, {43308, 43373}, {43309, 43372}, {44401, 51588}, {44456, 47355}, {46932, 50818}, {48662, 51737}, {48895, 50968}, {48906, 50954}, {50808, 61268}, {50810, 58247}, {50820, 58219}, {50957, 51137}, {50976, 55668}, {50978, 51171}, {50980, 51173}, {51024, 55639}, {51072, 61286}, {51085, 61244}, {51127, 51130}, {51141, 55646}, {51517, 59376}, {59380, 61023}

X(61864) = midpoint of X(i) and X(j) for these {i,j}: {2, 15709}, {3545, 15705}, {5055, 15707}
X(61864) = reflection of X(i) in X(j) for these {i,j}: {15688, 15705}, {15705, 549}, {15706, 15708}, {15707, 5054}, {15709, 11539}, {3, 15707}, {5054, 15709}
X(61864) = inverse of X(61885) in orthocentroidal circle
X(61864) = inverse of X(61885) in Yff hyperbola
X(61864) = complement of X(61899)
X(61864) = anticomplement of X(61879)
X(61864) = pole of line {523, 61885} with respect to the orthocentroidal circle
X(61864) = pole of line {185, 62128} with respect to the Jerabek hyperbola
X(61864) = pole of line {6, 42512} with respect to the Kiepert hyperbola
X(61864) = pole of line {523, 61885} with respect to the Yff hyperbola
X(61864) = pole of line {69, 61888} with respect to the Wallace hyperbola
X(61864) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(15703)}}, {{A, B, C, X(1656), X(57895)}}, {{A, B, C, X(3146), X(22268)}}, {{A, B, C, X(3628), X(57822)}}, {{A, B, C, X(5070), X(55958)}}, {{A, B, C, X(5079), X(15319)}}, {{A, B, C, X(12102), X(60122)}}, {{A, B, C, X(14869), X(46452)}}, {{A, B, C, X(15705), X(18317)}}, {{A, B, C, X(21734), X(46412)}}, {{A, B, C, X(22270), X(50693)}}, {{A, B, C, X(31846), X(44904)}}
X(61864) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10303, 5071}, {2, 11540, 15693}, {2, 15692, 5067}, {2, 15702, 5}, {2, 15709, 30}, {2, 3, 15703}, {2, 3524, 15699}, {2, 3533, 10124}, {2, 376, 3628}, {2, 381, 5070}, {2, 549, 1656}, {2, 631, 547}, {2, 632, 15723}, {3, 15686, 6891}, {3, 381, 15685}, {3, 5055, 14269}, {3, 5059, 6961}, {4, 11812, 15700}, {4, 15700, 15695}, {5, 14891, 15682}, {5, 549, 15690}, {20, 15688, 15689}, {30, 11539, 15709}, {30, 15708, 15706}, {30, 549, 15705}, {140, 10109, 549}, {140, 15691, 11812}, {140, 15699, 3524}, {140, 3524, 5054}, {140, 3627, 631}, {140, 381, 15701}, {140, 5068, 15720}, {140, 5070, 3}, {140, 8703, 15721}, {376, 5068, 12101}, {381, 15700, 15691}, {381, 1656, 10109}, {381, 3534, 3627}, {381, 8703, 5073}, {547, 14890, 17504}, {547, 17504, 3839}, {547, 3534, 3851}, {549, 15690, 10299}, {1656, 15716, 381}, {1656, 3526, 3525}, {2043, 2044, 12102}, {3090, 15721, 8703}, {3523, 3845, 14093}, {3523, 5079, 17800}, {3524, 10304, 14891}, {3524, 15682, 10304}, {3524, 3545, 20}, {3526, 15723, 2}, {3526, 5054, 11539}, {3628, 15713, 376}, {3628, 15720, 3843}, {3763, 10168, 50955}, {3839, 10304, 5059}, {3839, 17504, 3534}, {3839, 5054, 15718}, {3843, 15694, 15713}, {3850, 15711, 15683}, {3854, 6921, 15022}, {3860, 15714, 3529}, {5054, 15706, 15708}, {5056, 15698, 15687}, {5066, 14869, 15692}, {5066, 15692, 1657}, {5067, 15692, 5066}, {5071, 10303, 12100}, {5071, 12100, 382}, {5079, 14093, 3845}, {7486, 11001, 11737}, {8703, 15699, 14892}, {10109, 15716, 3830}, {10124, 15723, 15694}, {10168, 50955, 55705}, {10299, 14891, 15716}, {10304, 15690, 15688}, {11231, 25055, 38066}, {11297, 11298, 5077}, {11539, 15699, 140}, {11539, 16239, 3545}, {11540, 17678, 3526}, {11737, 15712, 11001}, {12108, 15687, 15698}, {14269, 15703, 5055}, {14892, 15699, 3090}, {15533, 46267, 53092}, {15681, 15694, 15702}, {15687, 15698, 15696}, {15706, 15708, 15707}, {15723, 17678, 15681}, {15765, 18585, 15717}, {25055, 38066, 10247}, {41943, 42937, 49906}, {41944, 42936, 49905}, {50825, 61272, 34632}

X(61865) = X(2)X(3)∩X(69)X(46267)

Barycentrics    23*a^4+17*(b^2-c^2)^2-40*a^2*(b^2+c^2) : :
X(61865) = 17*X[2]+2*X[3], 3*X[69]+16*X[46267], 6*X[3653]+13*X[19877], 16*X[3828]+3*X[7967], 15*X[5032]+4*X[50985], 14*X[7989]+5*X[50819], 49*X[9780]+8*X[32900], 16*X[10219]+3*X[54041], -5*X[10595]+24*X[19883], 4*X[12007]+15*X[21358], 4*X[13607]+15*X[19875], 3*X[14651]+16*X[22247] and many others

X(61865) lies on these lines: {2, 3}, {69, 46267}, {371, 34091}, {372, 34089}, {590, 43375}, {615, 43374}, {3068, 43513}, {3069, 43514}, {3316, 43386}, {3317, 43387}, {3653, 19877}, {3828, 7967}, {5032, 50985}, {5309, 11614}, {7612, 60643}, {7850, 34803}, {7874, 60175}, {7989, 50819}, {9780, 32900}, {10155, 60239}, {10219, 54041}, {10302, 53103}, {10576, 43342}, {10577, 43343}, {10595, 19883}, {11488, 41944}, {11489, 41943}, {11669, 54616}, {12007, 21358}, {13607, 19875}, {14226, 52045}, {14241, 52046}, {14494, 60646}, {14651, 22247}, {14831, 15082}, {14912, 20582}, {14927, 51137}, {16191, 34631}, {16267, 42597}, {16268, 42596}, {16644, 43464}, {16645, 43463}, {16772, 43446}, {16773, 43447}, {19053, 35815}, {19054, 35814}, {19872, 51705}, {20070, 50825}, {21168, 60999}, {21356, 51140}, {23267, 41952}, {23269, 43338}, {23273, 41951}, {23275, 43339}, {32785, 42601}, {32786, 42600}, {32836, 52718}, {32867, 59634}, {33604, 42935}, {33605, 42934}, {33606, 42489}, {33607, 42488}, {34595, 38068}, {38064, 43150}, {38066, 46934}, {39874, 51128}, {42089, 43004}, {42092, 43005}, {42472, 42528}, {42473, 42529}, {42490, 49876}, {42491, 49875}, {42498, 43544}, {42499, 43545}, {42594, 43029}, {42595, 43028}, {42631, 43201}, {42632, 43202}, {42688, 43541}, {42689, 43540}, {42775, 46334}, {42776, 46335}, {42926, 43246}, {42927, 43247}, {42936, 49862}, {42937, 49861}, {42944, 49825}, {42945, 49824}, {42948, 49947}, {42949, 49948}, {42998, 43100}, {42999, 43107}, {43254, 43431}, {43255, 43430}, {43340, 43511}, {43341, 43512}, {43484, 61719}, {43536, 43558}, {43559, 54597}, {47352, 50982}, {50960, 55671}, {50980, 61044}, {51087, 53620}, {51126, 54132}, {51182, 51732}, {51211, 55616}, {52047, 60300}, {52048, 60299}, {53104, 60143}, {54523, 60100}, {60102, 60629}, {60123, 60637}, {60185, 60278}, {60333, 60616}

X(61865) = pole of line {69, 61887} with respect to the Wallace hyperbola
X(61865) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(4846), X(35400)}}, {{A, B, C, X(7408), X(60175)}}, {{A, B, C, X(7409), X(60192)}}, {{A, B, C, X(8797), X(47599)}}, {{A, B, C, X(10301), X(53103)}}, {{A, B, C, X(15699), X(36948)}}, {{A, B, C, X(22268), X(49136)}}, {{A, B, C, X(22270), X(44245)}}, {{A, B, C, X(34483), X(55866)}}, {{A, B, C, X(37174), X(60643)}}, {{A, B, C, X(50688), X(54660)}}, {{A, B, C, X(52285), X(54523)}}, {{A, B, C, X(52301), X(53104)}}
X(61865) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10303, 5055}, {2, 10304, 3628}, {2, 11540, 15698}, {2, 15692, 15703}, {2, 15702, 5071}, {2, 15708, 1656}, {2, 15709, 4}, {2, 15721, 547}, {2, 3523, 15699}, {2, 3524, 5067}, {2, 3525, 3524}, {2, 3839, 5070}, {2, 5054, 3090}, {4, 3526, 3525}, {5, 15706, 15640}, {140, 15703, 15692}, {140, 3146, 631}, {376, 3545, 15687}, {381, 15681, 3853}, {381, 5071, 3544}, {381, 550, 3543}, {381, 631, 15715}, {547, 15694, 15721}, {547, 549, 15684}, {549, 10124, 3526}, {549, 5055, 15683}, {550, 3843, 3146}, {631, 3090, 550}, {632, 10124, 15723}, {1656, 15708, 15682}, {3091, 15701, 15710}, {3146, 10304, 3534}, {3524, 3544, 11001}, {3525, 3528, 140}, {3525, 5071, 15702}, {3526, 10124, 17678}, {3526, 16239, 15717}, {3526, 5055, 11540}, {3628, 17800, 5056}, {3839, 11812, 10299}, {5070, 11812, 3839}, {7486, 15717, 3843}, {10124, 15723, 2}, {10303, 11540, 15709}, {10303, 13741, 3857}, {10303, 15683, 549}, {11737, 15713, 15718}, {11737, 15718, 20}, {12100, 17800, 10304}, {15687, 15692, 376}, {15692, 15703, 3545}, {15698, 15709, 10303}, {15699, 15759, 5072}, {15702, 15703, 3528}, {15703, 15707, 381}

X(61866) = X(2)X(3)∩X(141)X(51178)

Barycentrics    25*a^4+19*(b^2-c^2)^2-44*a^2*(b^2+c^2) : :
X(61866) = 19*X[2]+2*X[3], 20*X[141]+X[51178], 20*X[1125]+X[50817], 20*X[1698]+X[50818], 20*X[3589]+X[50973], 20*X[3618]+X[51179], 20*X[3634]+X[51082], 20*X[3763]+X[50974], 20*X[3828]+X[61296], -22*X[5550]+X[34631], 16*X[11178]+5*X[51176], 2*X[11693]+5*X[15059] and many others

X(61866) lies on these lines: {2, 3}, {141, 51178}, {395, 42957}, {396, 42956}, {1125, 50817}, {1698, 50818}, {3316, 60297}, {3317, 60298}, {3589, 50973}, {3618, 51179}, {3634, 51082}, {3763, 50974}, {3828, 61296}, {5550, 34631}, {7581, 43322}, {7582, 43323}, {7612, 60131}, {8252, 42566}, {8253, 42567}, {8972, 43212}, {11178, 51176}, {11485, 43555}, {11486, 43554}, {11488, 42498}, {11489, 42499}, {11542, 43494}, {11543, 43493}, {11614, 14482}, {11693, 15059}, {12243, 31274}, {13665, 43320}, {13785, 43321}, {13941, 43211}, {14494, 60645}, {15082, 16226}, {16962, 43372}, {16963, 43373}, {16966, 43481}, {16967, 43482}, {18492, 51086}, {19862, 50810}, {19872, 50828}, {19877, 61244}, {19878, 50814}, {19883, 61275}, {25055, 38127}, {28194, 61271}, {31145, 61281}, {31238, 51043}, {31253, 50811}, {32785, 43255}, {32786, 43254}, {32833, 52718}, {33416, 42986}, {33417, 42987}, {33602, 42151}, {33603, 42150}, {34089, 43386}, {34091, 43387}, {34573, 51136}, {37640, 43233}, {37641, 43232}, {38083, 54445}, {38223, 52691}, {42089, 43542}, {42092, 43543}, {42159, 42927}, {42162, 42926}, {42490, 49827}, {42491, 49826}, {42512, 43484}, {42513, 43483}, {42532, 42593}, {42533, 42592}, {42568, 42573}, {42569, 42572}, {42594, 43100}, {42595, 43107}, {42910, 42997}, {42911, 42996}, {42936, 49813}, {42937, 49812}, {42944, 49874}, {42945, 49873}, {42948, 49905}, {42949, 49906}, {42984, 43252}, {42985, 43253}, {44015, 52080}, {44016, 52079}, {46267, 50990}, {46931, 50798}, {46932, 50824}, {46933, 61292}, {50967, 51126}, {50970, 51127}, {51073, 61256}, {51129, 55656}, {53098, 60287}, {53620, 61287}, {60123, 60638}

X(61866) = midpoint of X(i) and X(j) for these {i,j}: {3545, 15698}, {3832, 10304}, {5054, 15703}, {14869, 15699}
X(61866) = reflection of X(i) in X(j) for these {i,j}: {10304, 15700}, {3523, 5054}, {3545, 3090}
X(61866) = inverse of X(61884) in orthocentroidal circle
X(61866) = inverse of X(61884) in Yff hyperbola
X(61866) = complement of X(61897)
X(61866) = pole of line {523, 61884} with respect to the orthocentroidal circle
X(61866) = pole of line {6, 61884} with respect to the Kiepert hyperbola
X(61866) = pole of line {523, 61884} with respect to the Yff hyperbola
X(61866) = pole of line {69, 61885} with respect to the Wallace hyperbola
X(61866) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3853), X(54660)}}, {{A, B, C, X(5067), X(57895)}}, {{A, B, C, X(5070), X(36889)}}, {{A, B, C, X(12812), X(18854)}}, {{A, B, C, X(15688), X(18852)}}, {{A, B, C, X(15703), X(36948)}}, {{A, B, C, X(22268), X(49137)}}, {{A, B, C, X(35403), X(54667)}}, {{A, B, C, X(37174), X(60131)}}, {{A, B, C, X(46412), X(58190)}}, {{A, B, C, X(55569), X(60298)}}, {{A, B, C, X(55573), X(60297)}}
X(61866) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10124, 3525}, {2, 10303, 547}, {2, 140, 5071}, {2, 15692, 3628}, {2, 15702, 3090}, {2, 15708, 15699}, {2, 15709, 3545}, {2, 15721, 1656}, {2, 3523, 15703}, {2, 3526, 15702}, {2, 3543, 5070}, {2, 549, 5067}, {4, 5067, 12812}, {5, 5054, 15705}, {30, 15700, 10304}, {30, 5054, 3523}, {140, 3529, 631}, {140, 5071, 15719}, {376, 15709, 5054}, {376, 3830, 3529}, {549, 12812, 15685}, {631, 3545, 15710}, {1656, 11540, 15721}, {1656, 15721, 11001}, {1656, 15722, 14893}, {1657, 5054, 15707}, {3090, 15702, 15698}, {3090, 3533, 3526}, {3091, 11812, 15715}, {3524, 11539, 15709}, {3528, 15702, 15701}, {3545, 15710, 15682}, {5070, 15713, 3543}, {5071, 15702, 15700}, {10124, 16239, 12100}, {10303, 13735, 1657}, {11539, 14890, 15694}, {11539, 15699, 14890}, {11737, 15697, 4}, {14869, 15699, 30}, {14890, 15688, 15708}, {14890, 15699, 15688}, {15685, 15696, 15686}, {15688, 15708, 3524}, {15694, 16239, 2}, {15702, 15703, 376}

X(61867) = X(2)X(3)∩X(8)X(61282)

Barycentrics    9*a^4+7*(b^2-c^2)^2-16*a^2*(b^2+c^2) : :
X(61867) = 21*X[2]+2*X[3], 9*X[8]+14*X[61282], 18*X[10]+5*X[61288], 2*X[52]+21*X[44299], 7*X[69]+16*X[15516], 20*X[575]+3*X[50961], 3*X[944]+20*X[31399], 3*X[962]+20*X[31447], -4*X[1216]+27*X[33879], 7*X[1352]+16*X[55696], 18*X[1385]+5*X[61248], 20*X[1698]+3*X[7967] and many others

X(61867) lies on these lines: {2, 3}, {8, 61282}, {10, 61288}, {52, 44299}, {54, 22112}, {69, 15516}, {182, 9705}, {325, 32884}, {371, 42600}, {372, 42601}, {485, 60315}, {486, 60316}, {498, 37602}, {575, 50961}, {590, 43505}, {615, 43506}, {944, 31399}, {952, 46931}, {962, 31447}, {1007, 7917}, {1058, 31452}, {1199, 17811}, {1216, 33879}, {1285, 1506}, {1352, 55696}, {1385, 61248}, {1698, 7967}, {1975, 32883}, {3054, 31400}, {3068, 35813}, {3069, 35812}, {3085, 7294}, {3086, 5326}, {3296, 61648}, {3316, 13935}, {3317, 9540}, {3411, 37640}, {3412, 37641}, {3567, 5650}, {3576, 31253}, {3618, 15520}, {3619, 55710}, {3624, 10595}, {3634, 5881}, {3763, 14912}, {3819, 15024}, {3917, 11465}, {3926, 52718}, {3933, 32871}, {4301, 19878}, {4309, 10589}, {4317, 10588}, {4678, 51700}, {5218, 37720}, {5237, 42494}, {5238, 42495}, {5286, 31492}, {5319, 11614}, {5334, 42490}, {5335, 42491}, {5339, 42500}, {5340, 42501}, {5349, 56623}, {5350, 56624}, {5355, 31401}, {5365, 43101}, {5366, 43104}, {5418, 13939}, {5420, 13886}, {5432, 47743}, {5433, 8164}, {5437, 26878}, {5447, 11451}, {5550, 11231}, {5603, 9588}, {5657, 9624}, {5731, 61258}, {5734, 26446}, {5735, 58433}, {5790, 46930}, {5818, 51073}, {5882, 19876}, {6361, 31425}, {6390, 32870}, {6468, 23273}, {6469, 23267}, {6470, 7582}, {6471, 7581}, {6689, 11271}, {7288, 37719}, {7308, 26877}, {7586, 31487}, {7607, 60629}, {7608, 60616}, {7612, 60183}, {7709, 31239}, {7735, 9698}, {7738, 31457}, {7746, 31450}, {7775, 55823}, {7796, 34229}, {7814, 34803}, {7817, 55794}, {7849, 37690}, {7879, 55729}, {7888, 42850}, {7999, 11695}, {8960, 43255}, {9606, 37637}, {9671, 52793}, {9680, 10577}, {9681, 42561}, {9692, 42215}, {9716, 36153}, {9780, 37727}, {9936, 43839}, {10155, 15491}, {10165, 19872}, {10185, 60627}, {10219, 45186}, {10246, 46932}, {10248, 61266}, {10519, 51126}, {10576, 31414}, {11002, 32205}, {11004, 15047}, {11374, 31188}, {11431, 23292}, {11482, 51179}, {11488, 42499}, {11489, 42498}, {11522, 38068}, {12243, 38751}, {12317, 34128}, {13925, 42523}, {13993, 42522}, {14491, 61644}, {14561, 55585}, {14651, 31274}, {14986, 31480}, {15056, 61136}, {15069, 34573}, {15178, 50804}, {15805, 56292}, {16003, 20125}, {16187, 43598}, {16241, 43776}, {16242, 43775}, {16644, 42594}, {16645, 42595}, {16772, 43028}, {16773, 43029}, {16962, 42593}, {16963, 42592}, {16964, 43772}, {16965, 43771}, {16981, 58531}, {18840, 53103}, {19130, 55630}, {19855, 31235}, {19877, 59388}, {19883, 34631}, {20070, 61614}, {20107, 26105}, {20195, 21168}, {20396, 38794}, {21151, 61001}, {22234, 50992}, {22236, 43444}, {22238, 43445}, {22247, 23235}, {22712, 55757}, {23269, 42582}, {23275, 42583}, {23302, 43464}, {23303, 43463}, {24206, 55693}, {25406, 55689}, {25561, 51177}, {26929, 56469}, {26939, 56468}, {30315, 51705}, {30389, 38074}, {31404, 44535}, {31407, 31489}, {31467, 37689}, {31666, 50864}, {31670, 55625}, {32785, 43375}, {32786, 43374}, {32817, 32838}, {32818, 32839}, {32820, 32885}, {32823, 37647}, {33416, 40693}, {33417, 40694}, {33556, 51033}, {33602, 42793}, {33603, 42794}, {33749, 50974}, {34781, 58434}, {35595, 37612}, {36967, 42776}, {36968, 42775}, {38028, 46933}, {38317, 55590}, {40330, 51128}, {42089, 42488}, {42092, 42489}, {42095, 52079}, {42098, 52080}, {42111, 42434}, {42114, 42433}, {42121, 42986}, {42124, 42987}, {42143, 43869}, {42146, 43870}, {42147, 42611}, {42148, 42610}, {42163, 43482}, {42166, 43481}, {42492, 42815}, {42493, 42816}, {42512, 42779}, {42513, 42780}, {42590, 42974}, {42591, 42975}, {42692, 43488}, {42693, 43487}, {42785, 51212}, {42786, 51537}, {42938, 42954}, {42939, 42955}, {42944, 43403}, {42945, 43404}, {42976, 43427}, {42977, 43426}, {43238, 43446}, {43239, 43447}, {43254, 58866}, {43338, 60305}, {43339, 60306}, {43342, 43524}, {43343, 43523}, {43536, 43564}, {43565, 54597}, {43666, 60114}, {43808, 54012}, {46266, 59371}, {46267, 50994}, {46934, 61278}, {50959, 55641}, {50980, 55602}, {51023, 55687}, {51538, 55638}, {53098, 54616}, {60123, 60143}, {60160, 60237}

X(61867) = reflection of X(i) in X(j) for these {i,j}: {3533, 16418}
X(61867) = inverse of X(60781) in orthocentroidal circle
X(61867) = inverse of X(60781) in Yff hyperbola
X(61867) = complement of X(46936)
X(61867) = anticomplement of X(55860)
X(61867) = pole of line {523, 60781} with respect to the orthocentroidal circle
X(61867) = pole of line {185, 62130} with respect to the Jerabek hyperbola
X(61867) = pole of line {6, 60781} with respect to the Kiepert hyperbola
X(61867) = pole of line {523, 60781} with respect to the Yff hyperbola
X(61867) = pole of line {69, 5070} with respect to the Wallace hyperbola
X(61867) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(68), X(19709)}}, {{A, B, C, X(69), X(5070)}}, {{A, B, C, X(548), X(22270)}}, {{A, B, C, X(1217), X(61138)}}, {{A, B, C, X(1585), X(60315)}}, {{A, B, C, X(1586), X(60316)}}, {{A, B, C, X(1657), X(22268)}}, {{A, B, C, X(3089), X(43666)}}, {{A, B, C, X(3431), X(55570)}}, {{A, B, C, X(3628), X(36948)}}, {{A, B, C, X(3843), X(43699)}}, {{A, B, C, X(3854), X(60171)}}, {{A, B, C, X(4846), X(49134)}}, {{A, B, C, X(5056), X(15319)}}, {{A, B, C, X(5066), X(60007)}}, {{A, B, C, X(6995), X(53103)}}, {{A, B, C, X(7378), X(10155)}}, {{A, B, C, X(7408), X(7612)}}, {{A, B, C, X(7409), X(14494)}}, {{A, B, C, X(8797), X(55856)}}, {{A, B, C, X(10303), X(15318)}}, {{A, B, C, X(12811), X(14843)}}, {{A, B, C, X(13599), X(50689)}}, {{A, B, C, X(15681), X(15740)}}, {{A, B, C, X(15702), X(18853)}}, {{A, B, C, X(17578), X(40448)}}, {{A, B, C, X(34089), X(55573)}}, {{A, B, C, X(34091), X(55569)}}, {{A, B, C, X(36889), X(47599)}}, {{A, B, C, X(37174), X(60183)}}, {{A, B, C, X(45759), X(46412)}}, {{A, B, C, X(50687), X(54660)}}, {{A, B, C, X(52281), X(60616)}}, {{A, B, C, X(52282), X(60629)}}, {{A, B, C, X(52301), X(60123)}}
X(61867) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10124, 15709}, {2, 140, 3090}, {2, 15694, 3545}, {2, 15708, 15703}, {2, 15721, 15699}, {2, 16923, 14001}, {2, 17566, 6856}, {2, 20, 5070}, {2, 3523, 3628}, {2, 3525, 4}, {2, 3526, 631}, {2, 3533, 3525}, {2, 631, 5067}, {2, 632, 3533}, {3, 1656, 5066}, {3, 3858, 15683}, {3, 5, 17578}, {3, 7486, 3855}, {5, 3530, 17800}, {5, 631, 3528}, {20, 5068, 3861}, {20, 7486, 5068}, {140, 12101, 12108}, {140, 12811, 549}, {140, 14891, 14869}, {140, 15699, 3}, {140, 15701, 10303}, {140, 3090, 3524}, {140, 3627, 15701}, {140, 3628, 8703}, {140, 5070, 20}, {376, 631, 3530}, {382, 3526, 15694}, {547, 15720, 3146}, {548, 3530, 15711}, {549, 5056, 3529}, {550, 15703, 15022}, {631, 3533, 3526}, {1656, 10303, 376}, {1656, 15701, 3627}, {1656, 15711, 3091}, {1656, 17800, 5}, {1656, 3530, 3832}, {2045, 2046, 5059}, {3090, 3529, 12811}, {3090, 3627, 3544}, {3091, 10299, 11001}, {3091, 5054, 10299}, {3091, 5129, 16239}, {3146, 15720, 15698}, {3146, 17580, 7486}, {3316, 32789, 34089}, {3317, 32790, 34091}, {3522, 13747, 5056}, {3522, 14869, 15719}, {3523, 17538, 15715}, {3523, 3545, 17538}, {3524, 3525, 140}, {3526, 16239, 2}, {3534, 12812, 3854}, {3851, 12108, 10304}, {4234, 10303, 3843}, {5055, 14869, 3522}, {5066, 10124, 11539}, {5071, 17538, 3858}, {5079, 15712, 3543}, {5550, 11231, 12245}, {11110, 17575, 17553}, {11311, 11312, 8360}, {11313, 11314, 8355}, {11540, 15703, 15708}, {13935, 32789, 3316}, {14782, 14783, 15712}, {15022, 15708, 550}, {15682, 15699, 5071}, {15682, 15709, 15721}, {15687, 15699, 10109}, {15694, 15715, 15702}, {15699, 15713, 15691}, {15699, 15721, 15682}, {15703, 15716, 14892}, {15708, 16864, 1656}, {15765, 18585, 15706}, {16347, 17678, 3523}, {31404, 44535, 46453}, {42488, 42597, 42089}, {42489, 42596, 42092}

X(61868) = X(2)X(3)∩X(372)X(43536)

Barycentrics    31*a^4+25*(b^2-c^2)^2-56*a^2*(b^2+c^2) : :
X(61868) = 25*X[2]+2*X[3], -28*X[3624]+X[34631], -X[5102]+10*X[48310], -275*X[5550]+32*X[58237], -X[11180]+28*X[51128], 8*X[12045]+X[54041], -X[16200]+10*X[19883], 26*X[19877]+X[50818], 20*X[20582]+7*X[55711], 5*X[21356]+4*X[39561], 20*X[25565]+7*X[55633], 26*X[34595]+X[50810] and many others

X(61868) lies on these lines: {2, 3}, {371, 54597}, {372, 43536}, {515, 58227}, {1587, 43888}, {1588, 43887}, {3624, 34631}, {5102, 48310}, {5418, 34091}, {5420, 34089}, {5550, 58237}, {6429, 56621}, {6430, 56622}, {7581, 41968}, {7582, 41967}, {7736, 11614}, {8252, 43374}, {8253, 43375}, {9540, 43387}, {9690, 42605}, {10139, 14226}, {10140, 14241}, {10155, 60238}, {10645, 43202}, {10646, 43201}, {11180, 51128}, {11668, 60143}, {12045, 54041}, {13846, 43505}, {13847, 43506}, {13935, 43386}, {16200, 19883}, {16267, 42530}, {16268, 42531}, {16644, 42595}, {16645, 42594}, {18581, 41971}, {18582, 41972}, {19877, 50818}, {20582, 55711}, {21356, 39561}, {22112, 43572}, {23267, 43259}, {23273, 43258}, {25565, 55633}, {32785, 43518}, {32786, 43517}, {32837, 52718}, {32884, 37671}, {33604, 43441}, {33605, 43440}, {34595, 50810}, {34627, 51073}, {34754, 42498}, {34755, 42499}, {35255, 43890}, {35256, 43889}, {37640, 43200}, {37641, 43199}, {38735, 41134}, {41953, 52045}, {41954, 52046}, {42089, 42800}, {42092, 42799}, {42139, 42930}, {42142, 42931}, {42490, 49873}, {42491, 49874}, {42500, 43482}, {42501, 43481}, {42510, 56627}, {42511, 56628}, {42512, 43467}, {42513, 43468}, {42604, 43415}, {42631, 42775}, {42632, 42776}, {42635, 42955}, {42636, 42954}, {43028, 43107}, {43029, 43100}, {43101, 52079}, {43104, 52080}, {43444, 54594}, {43445, 54593}, {43469, 43494}, {43470, 43493}, {43564, 43879}, {43565, 43880}, {46930, 50798}, {46931, 50824}, {50664, 50974}, {50821, 58244}, {50871, 58231}, {51127, 55582}, {53103, 60277}, {53108, 54616}, {54523, 60644}, {54644, 60183}, {56059, 60185}, {60123, 60641}, {60315, 60622}, {60316, 60623}

X(61868) = pole of line {69, 61883} with respect to the Wallace hyperbola
X(61868) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1294), X(58194)}}, {{A, B, C, X(7408), X(54644)}}, {{A, B, C, X(7409), X(54645)}}, {{A, B, C, X(11668), X(52301)}}, {{A, B, C, X(11812), X(46921)}}, {{A, B, C, X(36889), X(55856)}}
X(61868) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10124, 631}, {2, 10303, 15703}, {2, 11539, 3545}, {2, 15692, 5070}, {2, 15694, 3090}, {2, 15702, 5067}, {2, 15721, 3628}, {2, 15723, 3533}, {2, 3525, 5071}, {4, 15702, 15719}, {546, 15699, 5055}, {546, 1657, 17578}, {547, 15690, 12811}, {547, 3530, 3845}, {631, 3090, 1657}, {632, 8703, 10124}, {1656, 3628, 17530}, {1657, 3845, 3543}, {3090, 16434, 3091}, {3090, 3530, 4}, {3524, 3545, 11001}, {3526, 15716, 15694}, {3533, 3545, 11539}, {3533, 5067, 3525}, {3543, 11001, 11541}, {3543, 15708, 15705}, {3545, 15702, 3524}, {3845, 11812, 15716}, {5054, 5055, 8703}, {5070, 11540, 15692}, {8703, 15705, 15710}, {10303, 15703, 15682}, {11539, 15699, 11812}, {11539, 15708, 15709}, {11812, 15707, 15708}, {14269, 14890, 3523}, {15708, 15709, 15702}, {15709, 15710, 5054}, {15716, 17578, 376}, {15723, 16239, 2}

X(61869) = X(2)X(3)∩X(17)X(43100)

Barycentrics    16*a^4+13*(b^2-c^2)^2-29*a^2*(b^2+c^2) : :
X(61869) = 13*X[2]+X[3], 3*X[141]+4*X[46267], 5*X[182]+2*X[50958], 2*X[355]+5*X[50832], 4*X[551]+3*X[38112], 2*X[946]+5*X[50825], 2*X[1351]+5*X[51184], 2*X[1352]+5*X[50987], X[1353]+6*X[21358], 5*X[1385]+2*X[50801], 2*X[1482]+5*X[50822], X[1483]+6*X[19875] and many others

X(61869) lies on these lines: {2, 3}, {17, 43100}, {18, 43107}, {141, 46267}, {182, 50958}, {355, 50832}, {371, 41947}, {372, 41948}, {542, 51128}, {551, 38112}, {946, 50825}, {952, 19876}, {1351, 51184}, {1352, 50987}, {1353, 21358}, {1385, 50801}, {1482, 50822}, {1483, 19875}, {1698, 38081}, {3054, 5355}, {3653, 37705}, {3654, 34595}, {3655, 61251}, {3679, 61283}, {3815, 11614}, {3828, 38028}, {5032, 51183}, {5476, 51127}, {5480, 50980}, {5550, 38066}, {5690, 19883}, {5946, 15082}, {6407, 14226}, {6408, 14241}, {6429, 43343}, {6430, 43342}, {6439, 18762}, {6440, 18538}, {6441, 8252}, {6442, 8253}, {6476, 41951}, {6477, 41952}, {6478, 10577}, {6479, 10576}, {6684, 51075}, {6721, 26614}, {6723, 22251}, {7583, 43255}, {7584, 43254}, {7915, 54964}, {11645, 50988}, {11693, 20396}, {11694, 15059}, {11698, 38069}, {11898, 51180}, {13903, 43506}, {13961, 43505}, {16192, 50807}, {16644, 43102}, {16645, 43103}, {16962, 42899}, {16963, 42898}, {16964, 43247}, {16965, 43246}, {19116, 43211}, {19117, 43212}, {19862, 38022}, {19878, 51709}, {19925, 51084}, {20195, 38080}, {20582, 38110}, {21167, 25565}, {21356, 50986}, {21969, 32205}, {22247, 34127}, {22791, 38068}, {23302, 41944}, {23303, 41943}, {25055, 50823}, {26446, 61273}, {28204, 51073}, {28208, 50833}, {31162, 61270}, {31253, 34773}, {31423, 50826}, {33879, 44324}, {34628, 61262}, {35255, 42600}, {35256, 42601}, {37640, 42917}, {37641, 42916}, {38079, 51126}, {38082, 61001}, {38111, 60986}, {38113, 60999}, {41119, 42491}, {41120, 42490}, {41977, 42488}, {41978, 42489}, {42089, 42492}, {42092, 42493}, {42103, 42587}, {42106, 42586}, {42117, 42500}, {42118, 42501}, {42121, 61719}, {42160, 56623}, {42161, 56624}, {42532, 42978}, {42533, 42979}, {42590, 43239}, {42591, 43238}, {42596, 42599}, {42597, 42598}, {42912, 43028}, {42913, 43029}, {42936, 43229}, {42937, 43228}, {42944, 49907}, {42945, 49908}, {42984, 43542}, {42985, 43543}, {43030, 43373}, {43031, 43372}, {43416, 43640}, {43417, 43639}, {47352, 50978}, {47745, 50824}, {48310, 48876}, {48874, 50984}, {48885, 51129}, {48898, 51139}, {48942, 51134}, {50831, 51700}, {50964, 55651}, {50979, 58445}, {50994, 53092}, {51066, 61286}, {51135, 55683}, {51174, 59373}

X(61869) = midpoint of X(i) and X(j) for these {i,j}: {2, 3526}, {3090, 15701}, {3851, 15698}, {15702, 15703}, {16192, 50807}, {50964, 55651}, {50994, 53092}
X(61869) = reflection of X(i) in X(j) for these {i,j}: {15701, 140}, {3528, 12100}, {3845, 3851}, {549, 15702}, {50826, 31423}
X(61869) = inverse of X(61882) in orthocentroidal circle
X(61869) = inverse of X(61882) in Yff hyperbola
X(61869) = complement of X(15703)
X(61869) = pole of line {523, 61882} with respect to the orthocentroidal circle
X(61869) = pole of line {6, 61882} with respect to the Kiepert hyperbola
X(61869) = pole of line {523, 61882} with respect to the Yff hyperbola
X(61869) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(47599)}}, {{A, B, C, X(1494), X(55856)}}, {{A, B, C, X(12103), X(22268)}}, {{A, B, C, X(12812), X(15319)}}, {{A, B, C, X(14863), X(55859)}}, {{A, B, C, X(15022), X(31846)}}, {{A, B, C, X(41985), X(57927)}}, {{A, B, C, X(46452), X(55863)}}
X(61869) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 140, 15699}, {2, 15694, 547}, {2, 15702, 15703}, {2, 15709, 1656}, {2, 15723, 10124}, {2, 3524, 5070}, {2, 3525, 5055}, {2, 5054, 3628}, {2, 632, 11539}, {5, 15713, 17504}, {20, 14892, 3845}, {20, 3090, 3851}, {21, 11284, 4189}, {30, 12100, 3528}, {30, 140, 15701}, {140, 10109, 3524}, {140, 14891, 15721}, {140, 15699, 8703}, {140, 3628, 20}, {140, 5070, 3627}, {140, 547, 14891}, {381, 14093, 5073}, {381, 15682, 14893}, {381, 15689, 3543}, {381, 15703, 3090}, {381, 15716, 15681}, {381, 3524, 15691}, {381, 3543, 3861}, {381, 5071, 14892}, {546, 14890, 15693}, {549, 15687, 15714}, {549, 15702, 14869}, {549, 15711, 15718}, {1656, 15704, 5}, {1656, 15709, 12100}, {3091, 15707, 15690}, {3524, 5068, 15685}, {3524, 5070, 10109}, {3525, 5055, 11812}, {3526, 15700, 15694}, {3839, 15720, 15759}, {3845, 5054, 15712}, {3851, 5054, 15698}, {3851, 5076, 3832}, {3861, 12100, 15689}, {5054, 18587, 15764}, {5055, 15682, 12811}, {5056, 15688, 3860}, {5067, 12108, 3858}, {5071, 15692, 5076}, {6905, 9840, 4192}, {7486, 15719, 14269}, {9840, 13725, 13742}, {10109, 15691, 381}, {10124, 11737, 11540}, {10124, 14893, 3525}, {10124, 15723, 632}, {11812, 14893, 15692}, {11812, 15692, 549}, {12101, 14892, 3859}, {12812, 15759, 3839}, {13587, 16859, 17542}, {14869, 15687, 15700}, {14891, 14892, 15684}, {14893, 15692, 550}, {15684, 15694, 5054}, {15687, 15714, 15686}, {15694, 15700, 15702}, {15694, 15714, 15713}, {15694, 15721, 140}, {15699, 15721, 15687}, {15702, 15703, 30}, {16854, 16858, 16418}, {16855, 16861, 16857}, {16857, 16866, 17549}, {21356, 51732, 50986}, {42912, 43876, 43878}, {42913, 43875, 43877}, {51700, 53620, 50831}

X(61870) = X(2)X(3)∩X(17)X(43006)

Barycentrics    11*a^4+9*(b^2-c^2)^2-20*a^2*(b^2+c^2) : :
X(61870) = 27*X[2]+2*X[3], 2*X[52]+27*X[33879], 9*X[69]+20*X[22234], 8*X[575]+21*X[3619], X[944]+28*X[51073], 9*X[1352]+20*X[55698], 25*X[1698]+4*X[13607], -36*X[3589]+7*X[53858], -45*X[3618]+16*X[22330], 15*X[3620]+14*X[53092], 28*X[3624]+X[12245], -32*X[3634]+3*X[59388] and many others

X(61870) lies on these lines: {2, 3}, {15, 56616}, {16, 56617}, {17, 43006}, {18, 43007}, {52, 33879}, {61, 42955}, {62, 42954}, {69, 22234}, {183, 32884}, {575, 3619}, {944, 51073}, {952, 46930}, {1147, 46865}, {1285, 44535}, {1352, 55698}, {1506, 46453}, {1614, 16187}, {1698, 13607}, {3068, 35814}, {3069, 35815}, {3070, 10148}, {3071, 10147}, {3303, 5326}, {3304, 7294}, {3311, 43374}, {3312, 43375}, {3316, 5420}, {3317, 5418}, {3411, 49813}, {3412, 49812}, {3589, 53858}, {3592, 13939}, {3594, 13886}, {3618, 22330}, {3620, 53092}, {3624, 12245}, {3634, 59388}, {3746, 47743}, {3763, 12007}, {3819, 11465}, {3933, 32898}, {5007, 11614}, {5237, 42903}, {5238, 42902}, {5351, 42142}, {5352, 42139}, {5462, 44299}, {5550, 10222}, {5563, 8164}, {5603, 19878}, {5650, 15024}, {5657, 34595}, {5691, 58225}, {5818, 19872}, {5881, 51085}, {6390, 32897}, {6419, 32786}, {6420, 32785}, {6427, 13941}, {6428, 8972}, {6449, 43383}, {6450, 43382}, {6453, 23273}, {6454, 23267}, {6488, 42262}, {6489, 42265}, {6519, 18762}, {6522, 18538}, {6723, 15034}, {6776, 51128}, {7583, 43884}, {7584, 43883}, {7607, 60643}, {7608, 60646}, {7612, 60278}, {7735, 41940}, {7763, 52718}, {7850, 32823}, {7967, 19877}, {7982, 19862}, {7999, 15082}, {8617, 43843}, {8976, 34089}, {8981, 43517}, {9540, 43880}, {9680, 43343}, {9780, 15178}, {10165, 58229}, {10185, 60637}, {10246, 46931}, {10283, 58236}, {10302, 60123}, {10541, 40330}, {10576, 42601}, {10577, 42600}, {10595, 11231}, {11477, 51126}, {11485, 42591}, {11486, 42590}, {11488, 42896}, {11489, 42897}, {11491, 61158}, {11669, 18841}, {12244, 15029}, {12317, 20397}, {12325, 61659}, {12645, 58235}, {12900, 15021}, {13846, 43379}, {13847, 43378}, {13935, 43879}, {13951, 34091}, {13966, 43518}, {14482, 31401}, {14494, 60100}, {14561, 55583}, {14651, 38751}, {14692, 38627}, {14853, 51127}, {14912, 55708}, {14927, 42786}, {15020, 15081}, {15025, 38793}, {15026, 33884}, {15045, 45187}, {15069, 51138}, {15576, 20200}, {18840, 53104}, {19130, 55628}, {19876, 50818}, {20125, 34128}, {20190, 39874}, {22331, 31404}, {22712, 55754}, {23235, 31274}, {24206, 55694}, {30315, 50828}, {31235, 38665}, {31666, 59387}, {31670, 55623}, {32867, 52713}, {34126, 38629}, {34127, 38628}, {34573, 53093}, {37505, 37643}, {37514, 54434}, {37640, 42937}, {37641, 42936}, {37832, 43783}, {37835, 43784}, {38028, 46932}, {38136, 55620}, {38317, 55588}, {40107, 51179}, {40693, 42478}, {40694, 42479}, {41139, 55783}, {41951, 43439}, {41952, 43438}, {42089, 42499}, {42092, 42498}, {42095, 42684}, {42098, 42685}, {42119, 42580}, {42120, 42581}, {42133, 43299}, {42134, 43298}, {42160, 42904}, {42161, 42905}, {42163, 42687}, {42166, 42686}, {42476, 42598}, {42477, 42599}, {42488, 43443}, {42489, 43442}, {42490, 43404}, {42491, 43403}, {42494, 43481}, {42495, 43482}, {42516, 42780}, {42517, 42779}, {42592, 43019}, {42593, 43018}, {42594, 42949}, {42595, 42948}, {42596, 42934}, {42597, 42935}, {42610, 42944}, {42611, 42945}, {42773, 43101}, {42774, 43104}, {42795, 42814}, {42796, 42813}, {42805, 43554}, {42806, 43555}, {42974, 43480}, {42975, 43479}, {43012, 43021}, {43013, 43020}, {43150, 55704}, {43240, 43487}, {43241, 43488}, {43376, 52048}, {43377, 52047}, {43564, 43568}, {43565, 43569}, {44377, 55732}, {51072, 61282}, {51212, 55600}, {51538, 55637}, {53098, 60239}, {58223, 61263}, {58433, 59386}, {60102, 60183}

X(61870) = inverse of X(61881) in orthocentroidal circle
X(61870) = inverse of X(61881) in Yff hyperbola
X(61870) = complement of X(46935)
X(61870) = anticomplement of X(61878)
X(61870) = pole of line {523, 61881} with respect to the orthocentroidal circle
X(61870) = pole of line {185, 62133} with respect to the Jerabek hyperbola
X(61870) = pole of line {6, 43873} with respect to the Kiepert hyperbola
X(61870) = pole of line {523, 61881} with respect to the Yff hyperbola
X(61870) = pole of line {69, 55856} with respect to the Wallace hyperbola
X(61870) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(55856)}}, {{A, B, C, X(548), X(18852)}}, {{A, B, C, X(1217), X(15698)}}, {{A, B, C, X(3534), X(22268)}}, {{A, B, C, X(3545), X(14843)}}, {{A, B, C, X(3845), X(18296)}}, {{A, B, C, X(4846), X(49133)}}, {{A, B, C, X(5055), X(18854)}}, {{A, B, C, X(5070), X(36948)}}, {{A, B, C, X(6662), X(45760)}}, {{A, B, C, X(6995), X(53104)}}, {{A, B, C, X(7378), X(11669)}}, {{A, B, C, X(7408), X(60102)}}, {{A, B, C, X(7409), X(60333)}}, {{A, B, C, X(8703), X(22270)}}, {{A, B, C, X(8797), X(55857)}}, {{A, B, C, X(10301), X(60123)}}, {{A, B, C, X(10303), X(18853)}}, {{A, B, C, X(12811), X(60007)}}, {{A, B, C, X(14269), X(54763)}}, {{A, B, C, X(14494), X(52285)}}, {{A, B, C, X(14890), X(46452)}}, {{A, B, C, X(14938), X(15693)}}, {{A, B, C, X(15683), X(18851)}}, {{A, B, C, X(15687), X(54660)}}, {{A, B, C, X(15759), X(46412)}}, {{A, B, C, X(18849), X(49136)}}, {{A, B, C, X(34483), X(46219)}}, {{A, B, C, X(37174), X(60278)}}, {{A, B, C, X(40448), X(50688)}}, {{A, B, C, X(43558), X(55573)}}, {{A, B, C, X(43559), X(55569)}}, {{A, B, C, X(43691), X(55571)}}, {{A, B, C, X(52281), X(60646)}}, {{A, B, C, X(52282), X(60643)}}
X(61870) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10124, 3524}, {2, 10303, 3628}, {2, 11539, 5071}, {2, 17678, 10304}, {2, 3523, 5070}, {2, 3525, 3090}, {2, 3526, 4}, {2, 632, 3525}, {3, 1656, 12811}, {3, 3091, 11541}, {3, 3628, 15022}, {4, 3524, 548}, {4, 3528, 15683}, {4, 3544, 3857}, {4, 631, 15698}, {5, 10299, 15682}, {5, 140, 15693}, {5, 15693, 5059}, {5, 15702, 10299}, {140, 3628, 15704}, {140, 382, 15708}, {140, 3856, 549}, {140, 5055, 15717}, {140, 5067, 376}, {376, 15719, 17504}, {376, 3090, 3091}, {474, 17542, 13745}, {547, 15703, 17532}, {549, 3628, 5072}, {549, 5055, 15640}, {631, 15022, 16434}, {632, 14869, 10124}, {1656, 14869, 3146}, {1656, 15681, 5}, {1656, 3524, 3855}, {3090, 3529, 3545}, {3091, 15693, 17538}, {3091, 3146, 3845}, {3526, 3628, 10303}, {3526, 5055, 140}, {3530, 15703, 5068}, {3530, 5068, 11001}, {3533, 15709, 3526}, {3628, 12108, 5066}, {3628, 5072, 7486}, {3855, 10299, 15681}, {3857, 15022, 3544}, {3857, 15704, 12102}, {5054, 5056, 3528}, {5067, 15723, 3533}, {5070, 11539, 3523}, {5071, 15702, 14891}, {5079, 12108, 20}, {5079, 15694, 12108}, {6842, 15703, 3851}, {6906, 17542, 13725}, {7486, 15717, 3856}, {10299, 15702, 631}, {10303, 13741, 5055}, {10303, 15022, 3}, {10304, 11540, 15702}, {10304, 15683, 15690}, {10304, 17678, 11540}, {11540, 15702, 15709}, {13741, 15694, 6956}, {13741, 15704, 5067}, {14782, 14783, 12100}, {15682, 17538, 3529}, {15699, 15720, 3832}, {15765, 18585, 15716}, {16417, 16861, 16857}, {16857, 16866, 16417}

X(61871) = X(2)X(3)∩X(141)X(51175)

Barycentrics    17*a^4+14*(b^2-c^2)^2-31*a^2*(b^2+c^2) : :
X(61871) = 14*X[2]+X[3], -16*X[141]+X[51175], 4*X[373]+X[54047], 7*X[599]+8*X[15516], -16*X[1125]+X[50805], -16*X[3589]+X[50962], 14*X[3624]+X[34718], -16*X[3634]+X[50798], X[3655]+14*X[51073], -X[3656]+16*X[19878], 7*X[3763]+2*X[55710], -16*X[3828]+X[12645] and many others

X(61871) lies on these lines: {2, 3}, {141, 51175}, {371, 56621}, {372, 56622}, {373, 54047}, {599, 15516}, {1125, 50805}, {3582, 8162}, {3589, 50962}, {3624, 34718}, {3634, 50798}, {3653, 28236}, {3655, 51073}, {3656, 19878}, {3763, 55710}, {3828, 12645}, {4698, 51039}, {5346, 31467}, {5650, 13321}, {5965, 21358}, {6221, 42600}, {6329, 51174}, {6398, 42601}, {6468, 13785}, {6469, 13665}, {6722, 12355}, {6723, 11693}, {9680, 41951}, {9780, 34748}, {10150, 38225}, {10168, 39899}, {10187, 49904}, {10188, 49903}, {10516, 55686}, {10653, 42950}, {10654, 42951}, {11178, 55696}, {11179, 51128}, {11224, 11231}, {11485, 42778}, {11486, 42777}, {11542, 42984}, {11543, 42985}, {11614, 31489}, {11898, 20582}, {12017, 50954}, {13188, 22247}, {13846, 13961}, {13847, 13903}, {15047, 37672}, {15520, 47352}, {16241, 42498}, {16242, 42499}, {16267, 43029}, {16268, 43028}, {16960, 16963}, {16961, 16962}, {19877, 50824}, {19883, 28234}, {20423, 51127}, {22234, 50989}, {22236, 56628}, {22238, 56627}, {25055, 59503}, {26614, 38743}, {28228, 38068}, {31253, 50797}, {31470, 39593}, {32520, 44562}, {32785, 43212}, {32786, 43211}, {32789, 43255}, {32790, 43254}, {33416, 42974}, {33417, 42975}, {34573, 50955}, {34595, 50821}, {38074, 58230}, {38223, 55801}, {41121, 42491}, {41122, 42490}, {41869, 51088}, {41943, 42989}, {41944, 42988}, {41977, 43013}, {41978, 43012}, {42121, 42517}, {42124, 42516}, {42126, 43241}, {42127, 43240}, {42494, 43109}, {42495, 43108}, {42496, 43464}, {42497, 43463}, {42512, 42595}, {42513, 42594}, {42518, 43239}, {42519, 43238}, {42610, 49907}, {42611, 49908}, {42635, 43468}, {42636, 43467}, {42936, 49948}, {42937, 49947}, {42952, 43775}, {42953, 43776}, {42976, 42978}, {42977, 42979}, {42996, 43033}, {42997, 43032}, {43014, 43249}, {43015, 43248}, {43027, 61719}, {43273, 55689}, {46267, 51186}, {46930, 50818}, {46934, 50823}, {47355, 55716}, {48910, 51141}, {50819, 58224}, {50829, 61268}, {50959, 55639}, {50980, 55604}, {50991, 53092}, {51070, 61282}, {51126, 51172}, {51173, 54169}, {53023, 55638}, {54131, 55601}, {60922, 60999}

X(61871) = midpoint of X(i) and X(j) for these {i,j}: {1656, 5054}, {3545, 15692}, {14269, 15695}, {15699, 15713}
X(61871) = reflection of X(i) in X(j) for these {i,j}: {10304, 15712}, {14269, 3091}, {15693, 5054}, {3522, 17504}, {3843, 3545}, {5054, 15694}, {5071, 15699}
X(61871) = inverse of X(61880) in orthocentroidal circle
X(61871) = inverse of X(61880) in Yff hyperbola
X(61871) = complement of X(61889)
X(61871) = pole of line {523, 61880} with respect to the orthocentroidal circle
X(61871) = pole of line {6, 61880} with respect to the Kiepert hyperbola
X(61871) = pole of line {523, 61880} with respect to the Yff hyperbola
X(61871) = intersection, other than A, B, C, of circumconics {{A, B, C, X(5070), X(57895)}}, {{A, B, C, X(17538), X(22268)}}, {{A, B, C, X(41988), X(54585)}}, {{A, B, C, X(46412), X(58188)}}, {{A, B, C, X(55856), X(57822)}}, {{A, B, C, X(55857), X(55958)}}
X(61871) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11539, 5055}, {2, 140, 15703}, {2, 15694, 1656}, {2, 15702, 3628}, {2, 15709, 15699}, {2, 15723, 3526}, {2, 17678, 20}, {2, 3525, 547}, {2, 549, 5070}, {2, 632, 15694}, {3, 15694, 15713}, {3, 15697, 14093}, {3, 3830, 15691}, {3, 5055, 3839}, {3, 5068, 382}, {5, 15708, 15689}, {30, 15699, 5071}, {30, 15712, 10304}, {30, 17504, 3522}, {30, 3091, 14269}, {30, 3545, 3843}, {140, 15703, 3534}, {140, 15707, 5054}, {140, 3545, 15707}, {140, 3860, 549}, {140, 7486, 3}, {381, 15693, 15696}, {381, 5054, 15706}, {547, 3525, 15701}, {631, 1656, 5076}, {631, 5071, 15697}, {632, 15713, 10124}, {1656, 15693, 381}, {1656, 15694, 15693}, {1656, 3843, 5079}, {3090, 11812, 15681}, {3523, 10109, 15684}, {3525, 17535, 546}, {3526, 5079, 140}, {3628, 15702, 3830}, {3845, 10303, 15718}, {3861, 10124, 11540}, {5054, 15700, 15708}, {5054, 15706, 15720}, {5054, 5055, 15688}, {5055, 14269, 14892}, {5070, 15694, 15695}, {5071, 15682, 3091}, {5071, 15692, 15687}, {5071, 15697, 3858}, {5071, 17578, 5066}, {6825, 15689, 15710}, {10124, 15699, 15709}, {11541, 15708, 17504}, {11737, 15698, 5073}, {14269, 15695, 30}, {14269, 15707, 3528}, {15022, 15715, 12101}, {15689, 15708, 15700}, {15690, 15699, 17579}, {15694, 15703, 15692}, {15701, 15703, 3857}, {15703, 15707, 3545}

X(61872) = X(2)X(3)∩X(13)X(42499)

Barycentrics    19*a^4+16*(b^2-c^2)^2-35*a^2*(b^2+c^2) : :
X(61872) = 16*X[2]+X[3], 14*X[3624]+3*X[38066], 128*X[3634]+25*X[58233], 3*X[3653]+14*X[51073], X[3654]+16*X[19878], 10*X[7987]+7*X[50800], 7*X[7989]+10*X[51084], -X[8148]+52*X[34595], 16*X[10219]+X[13340], 3*X[10246]+14*X[19876], 8*X[11178]+9*X[55697], 3*X[13321]+14*X[44299] and many others

X(61872) lies on these lines: {2, 3}, {13, 42499}, {14, 42498}, {590, 43514}, {615, 43513}, {3624, 38066}, {3634, 58233}, {3653, 51073}, {3654, 19878}, {5418, 43569}, {5420, 43568}, {6472, 41951}, {6473, 41952}, {6500, 13847}, {6501, 13846}, {7987, 50800}, {7989, 51084}, {8148, 34595}, {8252, 56621}, {8253, 56622}, {8976, 43255}, {9703, 22112}, {10145, 43526}, {10146, 43525}, {10187, 42507}, {10188, 42506}, {10219, 13340}, {10246, 19876}, {10302, 11668}, {11178, 55697}, {11485, 43470}, {11486, 43469}, {11614, 21309}, {11669, 60238}, {13321, 44299}, {13665, 17851}, {13785, 42600}, {13951, 43254}, {14848, 51126}, {16644, 43014}, {16645, 43015}, {16962, 56628}, {16963, 56627}, {18493, 38068}, {19872, 28204}, {19875, 37624}, {19883, 50827}, {21358, 46267}, {22234, 51189}, {22246, 37637}, {22566, 38634}, {25561, 55682}, {31673, 58222}, {32907, 36770}, {33606, 43440}, {33607, 43441}, {33879, 54048}, {34638, 61266}, {34718, 58238}, {35812, 43378}, {35813, 43379}, {37832, 42691}, {37835, 42690}, {38064, 51128}, {38072, 55604}, {38081, 46931}, {38314, 50830}, {41100, 42597}, {41101, 42596}, {41121, 42610}, {41122, 42611}, {41943, 43468}, {41944, 43467}, {41945, 43314}, {41946, 43315}, {42095, 42930}, {42098, 42931}, {42125, 42500}, {42128, 42501}, {42149, 42898}, {42152, 42899}, {42490, 49908}, {42491, 49907}, {42594, 42975}, {42595, 42974}, {42684, 43101}, {42685, 43104}, {42896, 43429}, {42897, 43428}, {42914, 43331}, {42915, 43330}, {42936, 49906}, {42937, 49905}, {42950, 42968}, {42951, 42969}, {42954, 43029}, {42955, 43028}, {43008, 43239}, {43009, 43238}, {43016, 56624}, {43017, 56623}, {43150, 55705}, {48310, 50982}, {48661, 50829}, {48662, 50983}, {50955, 58445}, {50957, 53094}, {50963, 55616}, {50985, 59373}, {50993, 53092}, {51067, 61282}, {51127, 54173}, {51141, 55648}, {51175, 51732}, {51705, 58228}, {53104, 60277}, {53108, 60239}, {54644, 60278}, {54645, 60100}, {56059, 60175}, {60192, 60644}

X(61872) = midpoint of X(i) and X(j) for these {i,j}: {2, 3533}
X(61872) = reflection of X(i) in X(j) for these {i,j}: {3, 15722}
X(61872) = inverse of X(61879) in orthocentroidal circle
X(61872) = inverse of X(61879) in Yff hyperbola
X(61872) = complement of X(61888)
X(61872) = pole of line {523, 61879} with respect to the orthocentroidal circle
X(61872) = pole of line {6, 51182} with respect to the Kiepert hyperbola
X(61872) = pole of line {523, 61879} with respect to the Yff hyperbola
X(61872) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1494), X(55857)}}, {{A, B, C, X(10301), X(11668)}}, {{A, B, C, X(15721), X(46921)}}, {{A, B, C, X(22268), X(50693)}}, {{A, B, C, X(44731), X(47485)}}, {{A, B, C, X(52285), X(54645)}}
X(61872) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10124, 381}, {2, 11539, 1656}, {2, 15694, 15703}, {2, 15709, 3628}, {2, 15723, 15694}, {2, 3525, 15699}, {2, 3533, 30}, {2, 5054, 5070}, {3, 11001, 7491}, {4, 15681, 15684}, {4, 15719, 10304}, {4, 632, 3526}, {5, 14890, 15698}, {5, 15707, 15685}, {5, 15721, 14093}, {140, 15719, 5054}, {140, 5071, 15700}, {376, 5071, 3832}, {381, 15686, 3830}, {381, 15692, 15681}, {381, 15700, 15686}, {381, 15702, 15718}, {381, 15723, 10124}, {381, 5054, 15692}, {547, 12103, 11737}, {549, 14890, 15721}, {549, 15687, 15759}, {549, 15704, 14891}, {549, 5066, 376}, {632, 4205, 3523}, {1656, 10303, 17800}, {1656, 15701, 14269}, {1656, 15706, 5066}, {1656, 3526, 10303}, {3090, 15713, 15688}, {3525, 15699, 15693}, {3525, 16858, 632}, {3526, 3534, 15709}, {3526, 5054, 11540}, {3530, 3832, 15696}, {3533, 16864, 3530}, {3545, 15720, 15695}, {3628, 15709, 3534}, {3830, 15701, 15711}, {3830, 5055, 5072}, {3839, 14869, 15716}, {5054, 15696, 15719}, {5054, 5079, 8703}, {5070, 15681, 547}, {5072, 15696, 4}, {10109, 15708, 1657}, {10303, 15706, 15701}, {11539, 15711, 140}, {14093, 15721, 15707}, {14269, 15701, 3}, {15683, 15702, 549}, {15684, 15703, 5055}, {15693, 15699, 3851}, {15694, 15718, 15702}, {15701, 17800, 15706}, {43028, 43333, 43549}, {43029, 43332, 43548}

X(61873) = X(2)X(3)∩X(6)X(43505)

Barycentrics    13*a^4+11*(b^2-c^2)^2-24*a^2*(b^2+c^2) : :
X(61873) = 33*X[2]+2*X[3], 26*X[10]+9*X[61285], 11*X[69]+24*X[55713], X[944]+34*X[19872], 11*X[1352]+24*X[55700], -11*X[3618]+4*X[55714], 32*X[3634]+3*X[7967], 8*X[5462]+27*X[33879], 18*X[5650]+17*X[11465], 3*X[5657]+32*X[19878], -X[5818]+8*X[31253], 18*X[10165]+17*X[30315] and many others

X(61873) lies on these lines: {2, 3}, {6, 43505}, {10, 61285}, {17, 43445}, {18, 43444}, {61, 42513}, {62, 42512}, {69, 55713}, {944, 19872}, {1352, 55700}, {3316, 43564}, {3317, 43565}, {3411, 49862}, {3412, 49861}, {3590, 60315}, {3591, 60316}, {3618, 55714}, {3619, 5965}, {3624, 28234}, {3634, 7967}, {5339, 56623}, {5340, 56624}, {5365, 42773}, {5366, 42774}, {5462, 33879}, {5650, 11465}, {5657, 19878}, {5818, 31253}, {6221, 43377}, {6398, 43376}, {6425, 43410}, {6426, 43409}, {6435, 32786}, {6436, 32785}, {6480, 42571}, {6481, 42570}, {6494, 7584}, {6495, 7583}, {6498, 7586}, {6499, 7585}, {7581, 32789}, {7582, 32790}, {7607, 60183}, {7736, 34571}, {7760, 23053}, {7768, 34803}, {8960, 43518}, {10155, 43527}, {10159, 53103}, {10165, 30315}, {10185, 60143}, {10187, 40694}, {10188, 40693}, {10194, 13939}, {10195, 13886}, {10246, 46930}, {10519, 51127}, {10595, 19862}, {10645, 42776}, {10646, 42775}, {10653, 42597}, {10654, 42596}, {11412, 15082}, {11488, 42937}, {11489, 42936}, {11542, 43480}, {11543, 43479}, {12045, 45186}, {12359, 59776}, {13421, 33884}, {13464, 34595}, {14561, 55581}, {14864, 35260}, {14912, 34573}, {16187, 61134}, {16772, 42594}, {16773, 42595}, {16960, 42149}, {16961, 42152}, {18581, 42498}, {18582, 42499}, {18840, 60123}, {18841, 53098}, {21168, 58433}, {22234, 50990}, {22712, 55752}, {25555, 55717}, {26877, 51780}, {28236, 51073}, {31670, 55621}, {32817, 32867}, {32820, 32838}, {32821, 32839}, {32824, 32883}, {32825, 32884}, {32829, 52718}, {33416, 42992}, {33417, 42993}, {34507, 55709}, {35770, 43514}, {35771, 43513}, {38028, 46931}, {38317, 55586}, {41943, 42481}, {41944, 42480}, {41945, 51849}, {41946, 51850}, {41973, 42910}, {41974, 42911}, {42087, 43780}, {42088, 43779}, {42431, 43643}, {42432, 43638}, {42580, 42959}, {42581, 42958}, {42610, 43403}, {42611, 43404}, {42779, 42954}, {42780, 42955}, {42920, 43241}, {42921, 43240}, {42926, 43870}, {42927, 43869}, {42948, 42998}, {42949, 42999}, {42988, 43102}, {42989, 43103}, {43386, 43879}, {43387, 43880}, {43485, 43771}, {43486, 43772}, {43517, 58866}, {50956, 55677}, {51068, 61282}, {51177, 55681}, {51212, 55599}, {53859, 60629}, {54523, 60182}, {54616, 60144}, {55707, 58445}, {60137, 60171}

X(61873) = midpoint of X(i) and X(j) for these {i,j}: {631, 3090}
X(61873) = reflection of X(i) in X(j) for these {i,j}: {15692, 15701}, {17538, 3528}, {3526, 632}
X(61873) = pole of line {6, 42476} with respect to the Kiepert hyperbola
X(61873) = pole of line {69, 55857} with respect to the Wallace hyperbola
X(61873) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(55857)}}, {{A, B, C, X(428), X(53103)}}, {{A, B, C, X(3832), X(60171)}}, {{A, B, C, X(5064), X(10155)}}, {{A, B, C, X(6662), X(11540)}}, {{A, B, C, X(6995), X(60123)}}, {{A, B, C, X(7378), X(53098)}}, {{A, B, C, X(7408), X(7607)}}, {{A, B, C, X(7409), X(7608)}}, {{A, B, C, X(8797), X(48154)}}, {{A, B, C, X(10185), X(52301)}}, {{A, B, C, X(14536), X(37935)}}, {{A, B, C, X(14861), X(15685)}}, {{A, B, C, X(15694), X(42021)}}, {{A, B, C, X(15696), X(22268)}}, {{A, B, C, X(15714), X(46412)}}, {{A, B, C, X(22270), X(33923)}}, {{A, B, C, X(36948), X(55856)}}, {{A, B, C, X(40448), X(50687)}}, {{A, B, C, X(43564), X(55573)}}, {{A, B, C, X(43565), X(55569)}}, {{A, B, C, X(52282), X(60183)}}
X(61873) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10303, 5070}, {2, 15723, 15709}, {2, 3525, 5067}, {2, 3526, 3090}, {2, 3533, 4}, {4, 1656, 5071}, {4, 550, 11541}, {30, 15701, 15692}, {30, 3528, 17538}, {30, 632, 3526}, {140, 1656, 3522}, {140, 3851, 3523}, {140, 5056, 10299}, {376, 3545, 12101}, {382, 6954, 548}, {631, 3090, 30}, {1012, 15715, 20}, {1656, 15694, 15712}, {1656, 15712, 3091}, {1656, 15720, 3843}, {1656, 3858, 5056}, {2045, 2046, 3146}, {3090, 15702, 3528}, {3522, 5056, 3858}, {3524, 5067, 3544}, {3525, 11541, 10303}, {3525, 5067, 3524}, {3526, 15702, 3525}, {3526, 15703, 14869}, {3526, 3851, 140}, {3530, 15022, 15682}, {3628, 15720, 5068}, {3832, 14869, 15698}, {5054, 7486, 3529}, {5068, 15720, 376}, {5070, 15693, 12812}, {5154, 10303, 15701}, {5365, 42773, 52079}, {5366, 42774, 52080}, {7375, 7376, 7841}, {10303, 15693, 631}, {10303, 17578, 15693}, {10304, 13735, 5079}, {10304, 15694, 6853}, {12812, 15693, 17578}, {12812, 17578, 3545}, {14869, 15703, 3832}, {15684, 15723, 10124}, {15701, 15709, 15702}, {42948, 42998, 43464}, {42948, 43029, 42998}, {42949, 42999, 43463}, {42949, 43028, 42999}, {42998, 43029, 43447}, {42999, 43028, 43446}, {43505, 43506, 6}

X(61874) = X(2)X(3)∩X(6)X(51183)

Barycentrics    20*a^4+17*(b^2-c^2)^2-37*a^2*(b^2+c^2) : :
X(61874) = 17*X[2]+X[3], 8*X[6]+X[51183], 8*X[10]+X[50831], 8*X[141]+X[50986], 8*X[1125]+X[50823], X[1353]+8*X[20582], X[1483]+8*X[3828], 25*X[1698]+2*X[61292], 8*X[3589]+X[50978], 35*X[3619]+X[51178], 35*X[3624]+X[50817], 8*X[3631]+X[51182] and many others

X(61874) lies on these lines: {2, 3}, {6, 51183}, {10, 50831}, {141, 50986}, {395, 42916}, {396, 42917}, {1125, 50823}, {1353, 20582}, {1483, 3828}, {1698, 61292}, {3589, 50978}, {3619, 51178}, {3624, 50817}, {3631, 51182}, {3634, 50824}, {3636, 50830}, {3653, 37712}, {3655, 19872}, {3679, 61281}, {3739, 51047}, {3763, 51180}, {3818, 50988}, {4698, 51048}, {6102, 40284}, {6329, 50985}, {8252, 43211}, {8253, 43212}, {10141, 43571}, {10142, 43570}, {10168, 51128}, {10219, 54042}, {10283, 19883}, {10576, 42572}, {10577, 42573}, {11178, 50987}, {11231, 38022}, {13846, 56622}, {13847, 56621}, {16191, 61275}, {16267, 42121}, {16268, 42124}, {18480, 50833}, {18483, 51088}, {18538, 42601}, {18762, 42600}, {19862, 50822}, {19875, 59400}, {19876, 61296}, {19877, 61295}, {19878, 50821}, {21850, 50970}, {22112, 40111}, {22234, 41152}, {22791, 50814}, {25055, 38112}, {25565, 48874}, {28194, 61270}, {28208, 61260}, {31253, 50832}, {33416, 42492}, {33417, 42493}, {34573, 50979}, {34748, 46932}, {36836, 56623}, {36843, 56624}, {37705, 51073}, {37832, 42499}, {37835, 42498}, {38021, 61614}, {38028, 38081}, {38080, 38113}, {38083, 38138}, {41107, 42597}, {41108, 42596}, {41119, 42610}, {41120, 42611}, {42125, 43639}, {42128, 43640}, {42262, 43437}, {42265, 43436}, {42520, 42947}, {42521, 42946}, {42557, 42566}, {42558, 42567}, {42568, 52047}, {42569, 52048}, {42580, 42791}, {42581, 42792}, {42633, 43103}, {42634, 43102}, {42692, 42901}, {42693, 42900}, {42795, 43241}, {42796, 43240}, {42898, 42979}, {42899, 42978}, {42948, 61719}, {43101, 44016}, {43104, 44015}, {43644, 43869}, {43649, 43870}, {47355, 50973}, {48310, 59399}, {48891, 51133}, {50960, 55672}, {50977, 51127}, {51126, 51184}, {53620, 61283}

X(61874) = midpoint of X(i) and X(j) for these {i,j}: {381, 15710}, {3545, 15706}, {5055, 15708}
X(61874) = reflection of X(i) in X(j) for these {i,j}: {15708, 140}, {17504, 15708}, {8703, 15706}
X(61874) = complement of X(61887)
X(61874) = pole of line {6, 42984} with respect to the Kiepert hyperbola
X(61874) = intersection, other than A, B, C, of circumconics {{A, B, C, X(5055), X(46168)}}, {{A, B, C, X(22268), X(44245)}}, {{A, B, C, X(48154), X(55958)}}, {{A, B, C, X(55856), X(57895)}}, {{A, B, C, X(55857), X(57822)}}
X(61874) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11539, 15699}, {2, 15694, 3628}, {2, 15702, 5070}, {2, 17678, 5056}, {2, 3525, 15703}, {2, 3526, 547}, {2, 3533, 381}, {5, 12108, 550}, {5, 15712, 3146}, {5, 8703, 14893}, {30, 140, 15708}, {30, 15706, 8703}, {140, 11737, 15693}, {140, 15717, 14869}, {140, 3628, 382}, {140, 5055, 17504}, {140, 547, 15759}, {376, 15685, 12103}, {376, 15723, 10124}, {376, 3091, 3830}, {381, 14869, 15711}, {381, 3533, 11540}, {382, 5055, 3545}, {546, 15701, 15714}, {547, 15759, 3091}, {547, 3526, 15713}, {550, 632, 3526}, {631, 10109, 15686}, {1656, 10304, 14892}, {3146, 15702, 15722}, {3524, 3545, 15683}, {3524, 5054, 12108}, {3525, 15703, 12100}, {3544, 6973, 6855}, {3545, 15706, 30}, {3830, 5054, 3524}, {3845, 15699, 5055}, {3851, 15719, 15691}, {5054, 10124, 11539}, {5054, 15703, 3839}, {5055, 10304, 3856}, {5056, 15700, 12101}, {5066, 15702, 15712}, {5067, 15693, 11737}, {5070, 15702, 5066}, {10109, 15686, 3857}, {10124, 12100, 3525}, {10124, 14893, 15694}, {10304, 14892, 15687}, {11539, 15699, 549}, {11539, 17504, 140}, {11737, 15693, 15704}, {11737, 15704, 3845}, {11812, 12103, 15718}, {11812, 14892, 10304}, {12100, 12102, 376}, {12100, 15703, 5}, {15705, 15709, 5054}

X(61875) = X(2)X(3)∩X(17)X(43441)

Barycentrics    11*a^4+10*(b^2-c^2)^2-21*a^2*(b^2+c^2) : :
X(61875) = 30*X[2]+X[3], 4*X[143]+27*X[33879], -X[1351]+32*X[51127], -X[1482]+32*X[19878], 2*X[1483]+29*X[46930], -35*X[3624]+4*X[33179], -32*X[3634]+X[12645], 25*X[3763]+6*X[39561], 3*X[5050]+28*X[51128], -4*X[5097]+35*X[47355], -9*X[5102]+40*X[25555], -3*X[5790]+34*X[19872] and many others

X(61875) lies on these lines: {2, 3}, {17, 43441}, {18, 43440}, {61, 43333}, {62, 43332}, {143, 33879}, {1351, 51127}, {1482, 19878}, {1483, 46930}, {3070, 43315}, {3071, 43314}, {3311, 10194}, {3312, 10195}, {3624, 33179}, {3634, 12645}, {3763, 39561}, {5013, 12815}, {5041, 37637}, {5050, 51128}, {5097, 47355}, {5102, 25555}, {5790, 19872}, {5882, 31253}, {6429, 13785}, {6430, 13665}, {6431, 58866}, {6432, 8960}, {6437, 10577}, {6438, 10576}, {6447, 42603}, {6448, 42602}, {6453, 56622}, {6454, 56621}, {6474, 60292}, {6475, 60291}, {6484, 42262}, {6485, 42265}, {6683, 32520}, {7581, 43881}, {7582, 43882}, {7607, 56059}, {7608, 60644}, {7755, 31467}, {7998, 13421}, {8252, 13903}, {8253, 13961}, {9669, 51817}, {10159, 11668}, {10185, 60277}, {10187, 43549}, {10188, 43548}, {10246, 51073}, {10516, 55688}, {10990, 15046}, {11231, 11531}, {11480, 42498}, {11481, 42499}, {11482, 48310}, {11485, 42949}, {11486, 42948}, {11614, 44535}, {11898, 34573}, {11935, 43651}, {13432, 55038}, {14864, 61680}, {15026, 44299}, {15039, 45311}, {15047, 17811}, {15602, 44518}, {16200, 34595}, {16241, 42611}, {16242, 42610}, {16964, 43421}, {16965, 43420}, {18525, 30315}, {18526, 30392}, {18553, 55691}, {19130, 55622}, {19877, 37624}, {20582, 51175}, {22234, 51186}, {24206, 55699}, {25565, 55626}, {31274, 38735}, {33416, 42815}, {33417, 42816}, {34507, 55711}, {34754, 42129}, {34755, 42132}, {36836, 42596}, {36843, 42597}, {37621, 61158}, {38317, 55582}, {38746, 52090}, {39899, 55703}, {41973, 42490}, {41974, 42491}, {42089, 42950}, {42092, 42951}, {42126, 42773}, {42127, 42774}, {42149, 42817}, {42152, 42818}, {42153, 42799}, {42154, 42959}, {42155, 42958}, {42156, 42800}, {42157, 42904}, {42158, 42905}, {42159, 42794}, {42162, 42793}, {42474, 43633}, {42475, 43632}, {42488, 43006}, {42489, 43007}, {42582, 42601}, {42583, 42600}, {42592, 49947}, {42593, 49948}, {42625, 42909}, {42626, 42908}, {42797, 44015}, {42798, 44016}, {42896, 43371}, {42897, 43370}, {42924, 43328}, {42925, 43329}, {42936, 42978}, {42937, 42979}, {42956, 43873}, {42957, 43874}, {42974, 43008}, {42975, 43009}, {42986, 43445}, {42987, 43444}, {42998, 43102}, {42999, 43103}, {43004, 43023}, {43005, 43022}, {43026, 43031}, {43027, 43030}, {43527, 53108}, {45185, 61735}, {46931, 51700}, {46932, 51515}, {51069, 61282}, {51173, 55595}, {53023, 55636}, {54645, 60182}, {58234, 61296}, {58433, 60922}, {60144, 60238}

X(61875) = inverse of X(61877) in orthocentroidal circle
X(61875) = inverse of X(61877) in Yff hyperbola
X(61875) = complement of X(61881)
X(61875) = pole of line {523, 61877} with respect to the orthocentroidal circle
X(61875) = pole of line {6, 61877} with respect to the Kiepert hyperbola
X(61875) = pole of line {523, 61877} with respect to the Yff hyperbola
X(61875) = intersection, other than A, B, C, of circumconics {{A, B, C, X(428), X(11668)}}, {{A, B, C, X(3519), X(7486)}}, {{A, B, C, X(3528), X(22268)}}, {{A, B, C, X(3843), X(60171)}}, {{A, B, C, X(5064), X(53108)}}, {{A, B, C, X(10299), X(14938)}}, {{A, B, C, X(13599), X(14893)}}, {{A, B, C, X(14528), X(44880)}}, {{A, B, C, X(14861), X(15683)}}, {{A, B, C, X(15709), X(42021)}}, {{A, B, C, X(38335), X(40448)}}, {{A, B, C, X(44731), X(55578)}}, {{A, B, C, X(52281), X(60644)}}, {{A, B, C, X(52282), X(56059)}}
X(61875) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 632, 5070}, {3, 15723, 3526}, {3, 16239, 15723}, {3, 3545, 382}, {3, 3843, 11001}, {3, 3853, 3534}, {3, 5055, 3832}, {3, 5070, 547}, {4, 12103, 5073}, {4, 15692, 550}, {4, 1656, 5079}, {4, 3523, 8703}, {4, 5068, 3859}, {4, 5070, 1656}, {5, 140, 10299}, {5, 632, 11540}, {140, 1656, 1657}, {140, 1657, 15720}, {140, 3628, 3858}, {140, 3858, 3523}, {140, 5056, 3}, {382, 14893, 5076}, {547, 11539, 15719}, {547, 15702, 15681}, {547, 16239, 632}, {547, 8703, 3545}, {631, 15703, 5072}, {631, 5072, 15688}, {632, 12811, 3525}, {1656, 15720, 381}, {1656, 5054, 4}, {1657, 3526, 140}, {2045, 2046, 3627}, {3090, 15708, 3853}, {3090, 17578, 6964}, {3523, 15715, 15712}, {3525, 3832, 11812}, {3526, 3628, 15706}, {3545, 15683, 3845}, {3843, 10303, 15700}, {5054, 15681, 15693}, {5070, 15722, 16371}, {5071, 12108, 17800}, {5076, 5079, 12811}, {7486, 14869, 3830}, {10124, 15715, 15694}, {10303, 15699, 3843}, {11539, 15690, 15702}, {11540, 15681, 5054}, {12103, 15688, 15696}, {12108, 17800, 15716}, {12812, 15717, 14269}, {14813, 14814, 7486}, {15688, 15693, 14891}, {15694, 15703, 15683}, {15765, 18585, 15715}, {42936, 43028, 42989}, {42937, 43029, 42988}

X(61876) = X(2)X(3)∩X(13)X(56628)

Barycentrics    12*a^4+11*(b^2-c^2)^2-23*a^2*(b^2+c^2) : :
X(61876) = 33*X[2]+X[3], 11*X[141]+6*X[55713], -32*X[575]+15*X[51180], 16*X[597]+X[51183], X[1353]+16*X[34573], X[1483]+16*X[3634], -20*X[1698]+3*X[59400], -22*X[3589]+5*X[55714], 14*X[3624]+3*X[38112], 27*X[3653]+7*X[61252], 9*X[3917]+8*X[58533], -X[5446]+18*X[12045] and many others

X(61876) lies on these lines: {2, 3}, {13, 56628}, {14, 56627}, {141, 55713}, {302, 33405}, {303, 33404}, {575, 51180}, {597, 51183}, {952, 19872}, {1353, 34573}, {1483, 3634}, {1698, 59400}, {3054, 9698}, {3055, 14075}, {3068, 6499}, {3069, 6498}, {3411, 23302}, {3412, 23303}, {3589, 55714}, {3624, 38112}, {3653, 61252}, {3815, 34571}, {3917, 58533}, {5318, 42499}, {5321, 42498}, {5326, 37720}, {5355, 9606}, {5446, 12045}, {5480, 55599}, {5650, 32205}, {5690, 19878}, {5734, 61273}, {6053, 34128}, {6101, 15082}, {6417, 43505}, {6418, 43506}, {6431, 43513}, {6432, 43514}, {6435, 19116}, {6436, 19117}, {6480, 43341}, {6481, 43340}, {6494, 13951}, {6495, 8976}, {6684, 61270}, {7294, 37719}, {7917, 37647}, {7998, 58531}, {9589, 61269}, {9680, 18762}, {9681, 42600}, {9780, 61283}, {10283, 19862}, {11592, 14845}, {13363, 14531}, {13624, 61260}, {15024, 44324}, {15178, 38081}, {19130, 55621}, {19875, 61282}, {19876, 50804}, {19877, 51700}, {20326, 58211}, {20582, 50986}, {21850, 55589}, {22234, 51143}, {24206, 55700}, {25555, 51132}, {27355, 54044}, {31253, 38042}, {31376, 38429}, {31399, 37705}, {31417, 44535}, {31425, 61268}, {31450, 43291}, {31487, 32786}, {32900, 38028}, {34595, 61276}, {35242, 61267}, {37624, 46930}, {38022, 50822}, {38079, 51184}, {38083, 50832}, {38110, 51128}, {38136, 55613}, {38317, 55581}, {40107, 51126}, {40693, 43102}, {40694, 43103}, {42089, 42610}, {42092, 42611}, {42117, 42902}, {42118, 42903}, {42121, 42488}, {42124, 42489}, {42147, 42596}, {42148, 42597}, {42149, 42590}, {42152, 42591}, {42500, 42580}, {42501, 42581}, {42592, 43228}, {42593, 43229}, {42594, 42945}, {42595, 42944}, {42598, 43775}, {42599, 43776}, {42639, 43255}, {42640, 43254}, {42684, 43241}, {42685, 43240}, {42692, 42890}, {42693, 42891}, {42785, 55598}, {42956, 43030}, {42957, 43031}, {42990, 43773}, {42991, 43774}, {42992, 43100}, {42993, 43107}, {43238, 56624}, {43239, 56623}, {45184, 59553}, {48876, 51127}, {50958, 51181}, {50981, 51130}, {55702, 58445}

X(61876) = midpoint of X(i) and X(j) for these {i,j}: {3, 3854}
X(61876) = reflection of X(i) in X(j) for these {i,j}: {5, 7486}
X(61876) = complement of X(55857)
X(61876) = pole of line {185, 62138} with respect to the Jerabek hyperbola
X(61876) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(14938), X(44682)}}, {{A, B, C, X(15319), X(35018)}}, {{A, B, C, X(22268), X(33923)}}
X(61876) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3854, 30}, {5, 11539, 631}, {5, 14869, 548}, {5, 15704, 3832}, {5, 15712, 382}, {5, 16239, 632}, {5, 382, 3857}, {5, 5070, 15699}, {5, 8703, 3861}, {20, 381, 3853}, {140, 10109, 3}, {140, 12811, 3524}, {140, 15691, 12108}, {140, 15699, 3627}, {140, 3090, 8703}, {140, 3524, 14869}, {140, 3627, 549}, {140, 3628, 381}, {140, 5068, 15712}, {381, 15701, 10304}, {550, 3845, 3146}, {550, 632, 11539}, {631, 11001, 15717}, {631, 17800, 12100}, {631, 5056, 17800}, {632, 3857, 3525}, {1656, 14869, 3845}, {1656, 3524, 12811}, {3090, 15721, 5073}, {3090, 5073, 14892}, {3146, 15714, 550}, {3523, 12812, 15687}, {3524, 3855, 20}, {3525, 5068, 15701}, {3526, 5067, 3530}, {3528, 13735, 5055}, {3528, 5055, 3859}, {3628, 12100, 5056}, {3850, 10303, 17504}, {3851, 15716, 11541}, {3859, 12108, 3528}, {6913, 17504, 4}, {10124, 12811, 140}, {10303, 15703, 3850}, {11540, 12812, 3523}, {12108, 13735, 5}

X(61877) = X(2)X(3)∩X(10)X(61280)

Barycentrics    10*a^4+11*(b^2-c^2)^2-21*a^2*(b^2+c^2) : :
X(61877) = -33*X[2]+X[3], 5*X[10]+3*X[61280], 11*X[141]+5*X[55714], -9*X[373]+X[14449], -5*X[1125]+X[61281], 25*X[1698]+7*X[61277], -11*X[3589]+3*X[55713], 7*X[3619]+X[61624], -35*X[3624]+3*X[61287], -3*X[3848]+X[58605], 7*X[4751]+X[61623], -X[5462]+9*X[12045] and many others

X(61877) lies on these lines: {2, 3}, {10, 61280}, {17, 43440}, {18, 43441}, {141, 55714}, {230, 34571}, {371, 41965}, {372, 41966}, {373, 14449}, {395, 10187}, {396, 10188}, {397, 43102}, {398, 43103}, {952, 19878}, {1125, 61281}, {1698, 61277}, {3054, 14075}, {3055, 7755}, {3068, 6498}, {3069, 6499}, {3564, 51127}, {3589, 55713}, {3619, 61624}, {3624, 61287}, {3634, 5844}, {3848, 58605}, {4751, 61623}, {4857, 5326}, {5270, 7294}, {5462, 12045}, {5480, 55598}, {5493, 61614}, {5690, 19872}, {5843, 58433}, {5882, 61246}, {5901, 38127}, {5943, 13421}, {6199, 43505}, {6221, 42571}, {6395, 43506}, {6398, 42570}, {6429, 43341}, {6430, 43340}, {6435, 32789}, {6436, 8960}, {6688, 32142}, {6689, 20585}, {7583, 42558}, {7584, 42557}, {7607, 60644}, {7608, 56059}, {7871, 37647}, {8252, 10195}, {8253, 10194}, {8254, 13431}, {8550, 55707}, {9540, 43412}, {9589, 50825}, {9680, 43258}, {9780, 61597}, {9956, 61253}, {10159, 53108}, {10185, 60238}, {10219, 32205}, {10247, 46930}, {10272, 13393}, {10283, 19877}, {10627, 15082}, {11017, 17704}, {11488, 42493}, {11489, 42492}, {11542, 42937}, {11543, 42936}, {11592, 15003}, {11668, 43527}, {12002, 18874}, {12242, 47296}, {12815, 43291}, {13382, 14128}, {13464, 31253}, {13754, 40284}, {13935, 43411}, {15026, 44324}, {16187, 32046}, {16534, 40685}, {16772, 42799}, {16773, 42800}, {16960, 43442}, {16961, 43443}, {16966, 42924}, {16967, 42925}, {18538, 41964}, {18583, 51128}, {18762, 41963}, {19130, 55619}, {19862, 51700}, {19883, 61286}, {22235, 42950}, {22237, 42951}, {22330, 51143}, {22791, 61271}, {23302, 43874}, {23303, 43873}, {24206, 55702}, {25555, 34380}, {30315, 61256}, {31663, 61267}, {33416, 41974}, {33417, 41973}, {34507, 51126}, {34595, 38042}, {36836, 43423}, {36843, 43422}, {38022, 50817}, {38028, 61244}, {38079, 50973}, {38083, 51082}, {38317, 55723}, {41943, 54594}, {41944, 54593}, {42087, 42498}, {42088, 42499}, {42103, 56624}, {42106, 56623}, {42107, 42908}, {42110, 42909}, {42111, 42773}, {42114, 42774}, {42117, 43644}, {42118, 43649}, {42122, 42930}, {42123, 42931}, {42129, 43197}, {42132, 43198}, {42143, 42945}, {42146, 42944}, {42147, 43425}, {42148, 43424}, {42157, 42692}, {42158, 42693}, {42433, 56628}, {42434, 56627}, {42488, 42496}, {42489, 42497}, {42500, 42959}, {42501, 42958}, {42596, 42942}, {42597, 42943}, {42627, 43028}, {42628, 43029}, {42686, 43485}, {42687, 43486}, {42777, 42938}, {42778, 42939}, {42793, 43104}, {42794, 43101}, {42815, 43480}, {42816, 43479}, {42912, 42993}, {42913, 42992}, {42928, 43643}, {42929, 43638}, {42954, 43775}, {42955, 43776}, {43174, 61272}, {43211, 43880}, {43212, 43879}, {43238, 43329}, {43239, 43328}, {44762, 61606}, {45185, 58434}, {46852, 55286}, {46934, 59400}, {47355, 61545}, {50981, 55595}, {51178, 53092}, {54644, 60182}, {55700, 58435}, {58451, 58561}, {60144, 60277}, {60996, 61596}

X(61877) = midpoint of X(i) and X(j) for these {i,j}: {3, 3856}, {5, 12108}, {547, 11540}, {3530, 12811}, {3628, 16239}, {11017, 17704}, {12056, 12057}, {32142, 58531}, {46852, 55286}, {58561, 58675}, {58605, 58632}
X(61877) = inverse of X(61875) in orthocentroidal circle
X(61877) = inverse of X(61875) in Yff hyperbola
X(61877) = complement of X(16239)
X(61877) = pole of line {523, 61875} with respect to the orthocentroidal circle
X(61877) = pole of line {6, 61875} with respect to the Kiepert hyperbola
X(61877) = pole of line {523, 61875} with respect to the Yff hyperbola
X(61877) = intersection, other than A, B, C, of circumconics {{A, B, C, X(428), X(53108)}}, {{A, B, C, X(3519), X(15699)}}, {{A, B, C, X(3627), X(60171)}}, {{A, B, C, X(5064), X(11668)}}, {{A, B, C, X(5070), X(43970)}}, {{A, B, C, X(6662), X(15702)}}, {{A, B, C, X(13599), X(38335)}}, {{A, B, C, X(14893), X(40448)}}, {{A, B, C, X(14938), X(33923)}}, {{A, B, C, X(15693), X(52441)}}, {{A, B, C, X(22268), X(44682)}}, {{A, B, C, X(40410), X(55862)}}, {{A, B, C, X(52281), X(56059)}}, {{A, B, C, X(52282), X(60644)}}, {{A, B, C, X(55859), X(57927)}}
X(61877) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 16394, 17582}, {2, 3628, 16239}, {3, 10109, 3856}, {3, 5, 14893}, {4, 15719, 3522}, {5, 12100, 12102}, {5, 12103, 3860}, {5, 3525, 12100}, {5, 3860, 12811}, {5, 549, 3146}, {140, 15712, 11812}, {140, 1656, 3850}, {140, 546, 15712}, {140, 547, 4}, {140, 548, 15720}, {547, 15692, 11737}, {547, 3859, 5079}, {547, 5070, 3628}, {549, 12812, 3861}, {549, 5067, 12812}, {1656, 3523, 5}, {1656, 3526, 5073}, {1656, 3533, 550}, {2045, 2046, 3843}, {3090, 11539, 548}, {3090, 15720, 3858}, {3525, 12102, 12108}, {3526, 15699, 546}, {3530, 3628, 547}, {3530, 3861, 15696}, {3628, 15759, 7486}, {3628, 3850, 1656}, {3830, 5054, 15692}, {3848, 58632, 58605}, {3853, 14869, 14891}, {3860, 10124, 5054}, {5055, 14869, 3853}, {5070, 15696, 5067}, {5079, 8703, 3859}, {6688, 32142, 58531}, {7385, 15721, 3523}, {7486, 15694, 3627}, {10187, 42979, 395}, {10188, 42978, 396}, {11539, 15711, 17556}, {11539, 15720, 140}, {11540, 12811, 3530}, {11540, 16239, 632}, {12056, 12057, 30}, {12108, 12811, 12103}, {12108, 16239, 10124}, {12811, 16239, 11540}, {14813, 14814, 15699}, {15699, 15712, 5056}, {15765, 18585, 15714}, {16966, 42948, 42924}, {16967, 42949, 42925}

X(61878) = X(2)X(3)∩X(17)X(43200)

Barycentrics    9*a^4+10*(b^2-c^2)^2-19*a^2*(b^2+c^2) : :
X(61878) = -30*X[2]+X[3], 5*X[399]+24*X[38725], -36*X[1125]+7*X[61282], X[1351]+28*X[51128], X[1482]+28*X[51073], 25*X[1698]+4*X[33179], 28*X[3624]+X[12645], -32*X[3634]+3*X[59503], 25*X[3763]+4*X[5097], -3*X[5050]+32*X[51127], 9*X[5102]+20*X[40107], -33*X[5550]+4*X[61286] and many others

X(61878) lies on these lines: {2, 3}, {17, 43200}, {18, 43199}, {49, 16187}, {195, 17825}, {399, 38725}, {1125, 61282}, {1131, 43415}, {1132, 9690}, {1351, 51128}, {1384, 31417}, {1482, 51073}, {1698, 33179}, {3055, 5319}, {3411, 42988}, {3412, 42989}, {3624, 12645}, {3634, 59503}, {3763, 5097}, {4309, 5326}, {4317, 7294}, {5041, 31489}, {5050, 51127}, {5102, 40107}, {5550, 61286}, {5790, 32900}, {5844, 46930}, {6427, 10194}, {6428, 10195}, {6431, 13951}, {6432, 8976}, {6447, 43254}, {6448, 43255}, {6480, 42262}, {6481, 42265}, {6683, 32519}, {8252, 35770}, {8253, 31487}, {9588, 18493}, {9624, 11278}, {9670, 51817}, {9680, 42583}, {9780, 61278}, {9956, 30392}, {10095, 44299}, {10137, 42561}, {10138, 31412}, {10172, 61258}, {10187, 49906}, {10188, 49905}, {10219, 13321}, {10246, 19878}, {10247, 19877}, {10263, 33879}, {10283, 46931}, {10516, 55691}, {10620, 38792}, {11230, 11531}, {11362, 31253}, {11451, 58533}, {11480, 42596}, {11481, 42597}, {11482, 20582}, {11849, 61158}, {11898, 39561}, {12188, 38746}, {12773, 38758}, {12815, 22332}, {13188, 38735}, {13846, 43886}, {13847, 43885}, {13903, 32789}, {13961, 32790}, {15069, 50664}, {16772, 42816}, {16773, 42815}, {18350, 22112}, {18440, 55695}, {18510, 31454}, {18525, 31662}, {18526, 38155}, {19116, 43882}, {19117, 43881}, {19130, 55618}, {19862, 37727}, {19876, 50805}, {21970, 44300}, {22330, 51186}, {24206, 55703}, {25555, 50962}, {25565, 55614}, {31407, 43136}, {31425, 48661}, {31455, 31470}, {34754, 42153}, {34755, 42156}, {36990, 55680}, {37640, 42591}, {37641, 42590}, {38079, 51214}, {38083, 50871}, {38317, 55722}, {38574, 38770}, {38579, 38782}, {38593, 38802}, {42125, 42490}, {42126, 42890}, {42127, 42891}, {42128, 42491}, {42129, 42611}, {42132, 42610}, {42270, 42600}, {42273, 42601}, {42431, 42474}, {42432, 42475}, {42488, 42817}, {42489, 42818}, {42500, 42920}, {42501, 42921}, {42508, 43424}, {42509, 43425}, {42518, 42636}, {42519, 42635}, {42528, 56623}, {42529, 56624}, {42910, 42949}, {42911, 42948}, {42914, 43194}, {42915, 43193}, {42936, 42975}, {42937, 42974}, {42952, 42992}, {42953, 42993}, {42978, 49947}, {42979, 49948}, {43382, 60305}, {43383, 60306}, {43887, 53516}, {43888, 53513}, {46934, 51515}, {48310, 53092}, {48910, 55645}, {51173, 52987}, {53023, 55633}, {55699, 58445}, {58233, 61245}, {58237, 61275}, {58433, 59380}

X(61878) = inverse of X(55862) in orthocentroidal circle
X(61878) = inverse of X(55862) in Yff hyperbola
X(61878) = complement of X(61870)
X(61878) = pole of line {523, 55862} with respect to the orthocentroidal circle
X(61878) = pole of line {185, 62140} with respect to the Jerabek hyperbola
X(61878) = pole of line {6, 55862} with respect to the Kiepert hyperbola
X(61878) = pole of line {523, 55862} with respect to the Yff hyperbola
X(61878) = intersection, other than A, B, C, of circumconics {{A, B, C, X(264), X(55862)}}, {{A, B, C, X(3528), X(14938)}}, {{A, B, C, X(10299), X(22268)}}, {{A, B, C, X(12102), X(13599)}}, {{A, B, C, X(12108), X(15318)}}, {{A, B, C, X(40410), X(55866)}}, {{A, B, C, X(55858), X(57927)}}
X(61878) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5067, 16239}, {2, 5070, 3526}, {3, 15702, 15720}, {3, 3845, 1657}, {3, 3851, 3543}, {3, 5055, 3850}, {3, 5056, 381}, {3, 5070, 5067}, {3, 5073, 15690}, {5, 140, 3528}, {5, 3530, 17578}, {5, 631, 17800}, {20, 15710, 548}, {20, 631, 12100}, {140, 15703, 5079}, {140, 3146, 15707}, {140, 3545, 3}, {140, 3857, 15692}, {140, 5079, 3534}, {140, 7486, 3843}, {381, 3526, 631}, {382, 14093, 20}, {547, 11539, 11001}, {631, 10304, 3530}, {632, 15687, 140}, {632, 1656, 14093}, {632, 3628, 3544}, {1656, 3526, 382}, {1656, 5054, 5072}, {2041, 2042, 12108}, {3146, 4188, 3091}, {3146, 5056, 3545}, {3149, 3529, 3146}, {3525, 15699, 3851}, {3525, 3851, 15693}, {3526, 16239, 15723}, {3526, 5070, 1656}, {3533, 5067, 3832}, {3543, 3545, 3860}, {3544, 17697, 3628}, {3545, 5067, 7486}, {3628, 11539, 5056}, {3628, 16239, 3853}, {3832, 5067, 547}, {3843, 5070, 15703}, {3845, 12812, 7379}, {3853, 16239, 11539}, {5068, 12108, 15681}, {5071, 14869, 5073}, {5073, 14869, 15706}, {5079, 15720, 15687}, {10299, 12811, 15684}, {10304, 15691, 15695}, {11539, 12100, 15702}, {15022, 15712, 14269}, {15679, 15713, 15685}, {15694, 15716, 5054}, {15699, 15710, 5055}, {15709, 17530, 5}, {15765, 18585, 15710}

X(61879) = X(2)X(3)∩X(6)X(51182)

Barycentrics    16*a^4+19*(b^2-c^2)^2-35*a^2*(b^2+c^2) : :
X(61879) = -19*X[2]+X[3], -10*X[6]+X[51182], -10*X[10]+X[50830], -10*X[141]+X[50985], -10*X[1125]+X[51087], -10*X[1698]+X[50823], -10*X[3589]+X[51140], -10*X[3616]+X[50831], -10*X[3618]+X[50986], -10*X[3620]+X[51183], -28*X[3624]+X[61295], -10*X[3634]+X[50827] and many others

X(61879) lies on these lines: {2, 3}, {6, 51182}, {10, 50830}, {61, 43443}, {62, 43442}, {141, 50985}, {395, 42896}, {396, 42897}, {1125, 51087}, {1327, 43338}, {1328, 43339}, {1698, 50823}, {3589, 51140}, {3616, 50831}, {3618, 50986}, {3620, 51183}, {3624, 61295}, {3634, 50827}, {3653, 38138}, {3656, 19872}, {3763, 50978}, {4687, 51047}, {5901, 19876}, {6490, 35255}, {6491, 35256}, {7583, 43568}, {7584, 43569}, {7827, 38223}, {8981, 42640}, {9167, 38229}, {9955, 50825}, {10219, 15067}, {10283, 19875}, {10302, 53108}, {11178, 51127}, {11180, 51181}, {11668, 60239}, {11669, 60277}, {11693, 20304}, {13451, 44299}, {13846, 43431}, {13847, 43430}, {13966, 42639}, {16187, 40111}, {16267, 42634}, {16268, 42633}, {16644, 42492}, {16645, 42493}, {16962, 43005}, {16963, 43004}, {16966, 42800}, {16967, 42799}, {18357, 50832}, {18358, 50987}, {18538, 43255}, {18762, 43254}, {19116, 43558}, {19117, 43559}, {19130, 50980}, {19862, 50824}, {19878, 51085}, {19883, 38042}, {21357, 61659}, {21358, 59399}, {22330, 51142}, {25055, 38081}, {31162, 50826}, {31238, 51048}, {31253, 50821}, {32002, 57895}, {33416, 42903}, {33417, 42902}, {33606, 42599}, {33607, 42598}, {33697, 51086}, {34573, 50982}, {34595, 37705}, {34648, 50833}, {37832, 42954}, {37835, 42955}, {38022, 38112}, {38025, 38170}, {38028, 38083}, {38034, 38068}, {38041, 38101}, {38067, 38137}, {38082, 38111}, {38314, 59400}, {41107, 42948}, {41108, 42949}, {42095, 43421}, {42098, 43420}, {42121, 43468}, {42124, 43467}, {42135, 42500}, {42136, 42475}, {42137, 42474}, {42138, 42501}, {42147, 43247}, {42148, 43246}, {42490, 43108}, {42491, 43109}, {42496, 42917}, {42497, 42916}, {42582, 43340}, {42583, 43341}, {42590, 49905}, {42591, 49906}, {42684, 42914}, {42685, 42915}, {42686, 43104}, {42687, 43101}, {42785, 50970}, {42786, 50983}, {42892, 42957}, {42893, 42956}, {42910, 43103}, {42911, 43102}, {42934, 49908}, {42935, 49907}, {42946, 42952}, {42947, 42953}, {43010, 43373}, {43011, 43372}, {43150, 50979}, {43316, 43514}, {43317, 43513}, {46932, 50805}, {48879, 51131}, {48884, 51139}, {50981, 54131}, {51026, 55658}, {51066, 61278}, {51129, 55653}, {53104, 60238}, {54644, 60100}, {54645, 60278}, {56059, 60192}, {60175, 60644}

X(61879) = midpoint of X(i) and X(j) for these {i,j}: {381, 15705}, {3545, 15707}, {5055, 15709}
X(61879) = reflection of X(i) in X(j) for these {i,j}: {15707, 140}, {549, 15709}
X(61879) = inverse of X(61872) in orthocentroidal circle
X(61879) = inverse of X(61872) in Yff hyperbola
X(61879) = complement of X(61864)
X(61879) = pole of line {523, 61872} with respect to the orthocentroidal circle
X(61879) = pole of line {6, 61872} with respect to the Kiepert hyperbola
X(61879) = pole of line {523, 61872} with respect to the Yff hyperbola
X(61879) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(5068), X(31846)}}, {{A, B, C, X(10124), X(57927)}}, {{A, B, C, X(10301), X(53108)}}, {{A, B, C, X(13623), X(15691)}}, {{A, B, C, X(16239), X(55958)}}, {{A, B, C, X(52285), X(54644)}}, {{A, B, C, X(55858), X(57822)}}, {{A, B, C, X(55859), X(57895)}}
X(61879) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 13735, 15721}, {2, 15699, 11539}, {2, 15703, 140}, {2, 1656, 10124}, {2, 3090, 15723}, {2, 381, 16239}, {2, 5067, 15694}, {2, 547, 632}, {4, 15692, 3534}, {4, 5070, 3628}, {4, 5072, 3859}, {4, 549, 8703}, {4, 7486, 5079}, {5, 14893, 6959}, {5, 15713, 15686}, {30, 140, 15707}, {140, 3628, 7486}, {140, 3860, 15692}, {140, 547, 3860}, {140, 7486, 3857}, {381, 10303, 15759}, {546, 15702, 15711}, {547, 10124, 15681}, {547, 16239, 15719}, {548, 3628, 1656}, {549, 15759, 15712}, {549, 3845, 548}, {549, 5066, 15704}, {549, 632, 11540}, {2049, 5070, 5056}, {3090, 15723, 12100}, {3146, 3845, 15687}, {3146, 5079, 12811}, {3524, 15714, 17504}, {3524, 3545, 3146}, {3526, 10304, 14890}, {3526, 5055, 10304}, {3534, 5055, 3545}, {3545, 15707, 30}, {3545, 7486, 5055}, {3628, 5055, 15699}, {3845, 10124, 14869}, {3851, 15721, 15690}, {3856, 12100, 15683}, {5054, 15681, 3524}, {5054, 5055, 4}, {5056, 15701, 14893}, {5067, 15694, 10109}, {5071, 11812, 3627}, {5072, 15694, 15698}, {8703, 11539, 5054}, {10109, 15694, 550}, {10303, 15759, 549}, {11539, 15699, 5}, {11539, 17504, 15713}, {12811, 15681, 3845}, {14893, 15759, 13635}, {15022, 15684, 5066}, {15681, 15697, 12103}, {15692, 15703, 547}, {15697, 15712, 15714}, {25055, 38081, 61283}

X(61880) = X(2)X(3)∩X(1154)X(10219)

Barycentrics    14*a^4+17*(b^2-c^2)^2-31*a^2*(b^2+c^2) : :
X(61880) = -17*X[2]+X[3], 3*X[373]+X[44324], 5*X[551]+3*X[38176], X[962]+7*X[50826], 5*X[1698]+3*X[38022], 5*X[3616]+3*X[38081], -X[3654]+17*X[19872], 7*X[3655]+9*X[61254], 7*X[3679]+9*X[61279], 5*X[3763]+3*X[38079], X[5476]+7*X[51128], 3*X[5650]+X[13451] and many others

X(61880) lies on these lines: {2, 3}, {373, 44324}, {395, 43014}, {396, 43015}, {542, 51127}, {551, 38176}, {962, 50826}, {1154, 10219}, {1698, 38022}, {3055, 5355}, {3564, 46267}, {3616, 38081}, {3654, 19872}, {3655, 61254}, {3679, 61279}, {3763, 38079}, {3828, 5844}, {4745, 61278}, {5476, 51128}, {5650, 13451}, {5691, 50833}, {5843, 60999}, {5901, 51077}, {5921, 51181}, {6053, 40685}, {6431, 43569}, {6432, 43568}, {6500, 34089}, {6501, 34091}, {9956, 50801}, {10150, 14693}, {10171, 28216}, {10172, 28224}, {10576, 43212}, {10577, 43211}, {11542, 41944}, {11543, 41943}, {13364, 15082}, {13393, 38795}, {13846, 13993}, {13847, 13925}, {14971, 61561}, {16191, 19876}, {16644, 42628}, {16645, 42627}, {18230, 38080}, {18583, 51132}, {19862, 38083}, {19878, 28204}, {19883, 47745}, {20195, 38082}, {20582, 34380}, {21356, 51174}, {22330, 41152}, {23302, 42497}, {23303, 42496}, {24206, 50958}, {25055, 50804}, {25555, 51143}, {31235, 38084}, {31253, 61272}, {31260, 38085}, {32142, 58470}, {32907, 48311}, {32909, 48312}, {33416, 43416}, {33417, 43417}, {34595, 61250}, {34631, 61273}, {34641, 61280}, {36990, 50988}, {37832, 43102}, {37835, 43103}, {38028, 61247}, {38042, 61291}, {41100, 42948}, {41101, 42949}, {41134, 61600}, {42147, 43017}, {42148, 43016}, {42225, 42600}, {42226, 42601}, {42419, 42993}, {42420, 42992}, {42488, 42591}, {42489, 42590}, {42500, 42914}, {42501, 42915}, {42532, 42592}, {42533, 42593}, {42582, 52048}, {42583, 52047}, {42777, 43200}, {42778, 43199}, {42786, 51737}, {42894, 43248}, {42895, 43249}, {42924, 43100}, {42925, 43107}, {42938, 43442}, {42939, 43443}, {42974, 43198}, {42975, 43197}, {47352, 50961}, {48310, 51732}, {48896, 51133}, {50828, 61259}, {50830, 61277}, {50960, 55674}, {50981, 51212}, {51073, 51709}, {51088, 51118}, {51109, 61286}, {51141, 51163}, {53620, 61597}, {58441, 61267}, {58560, 58632}, {58561, 58629}, {59374, 61596}, {59376, 61562}

X(61880) = midpoint of X(i) and X(j) for these {i,j}: {2, 3628}, {3, 3860}, {5, 11812}, {140, 10109}, {381, 14891}, {546, 15759}, {547, 10124}, {549, 11737}, {3530, 5066}, {3850, 12100}, {3861, 8703}, {4745, 61278}, {12102, 15690}, {22330, 41152}, {25555, 51143}, {32142, 58470}, {50828, 61259}, {50960, 55674}, {58441, 61267}, {58560, 58632}, {58561, 58629}
X(61880) = reflection of X(i) in X(j) for these {i,j}: {11540, 16239}, {12108, 11540}, {12811, 10109}, {16239, 2}
X(61880) = inverse of X(61871) in orthocentroidal circle
X(61880) = inverse of X(61871) in Yff hyperbola
X(61880) = complement of X(10124)
X(61880) = pole of line {523, 61871} with respect to the orthocentroidal circle
X(61880) = pole of line {6, 61871} with respect to the Kiepert hyperbola
X(61880) = pole of line {523, 61871} with respect to the Yff hyperbola
X(61880) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1494), X(16239)}}, {{A, B, C, X(5072), X(31846)}}, {{A, B, C, X(11539), X(57927)}}, {{A, B, C, X(14938), X(44245)}}, {{A, B, C, X(40410), X(47598)}}, {{A, B, C, X(40512), X(44651)}}, {{A, B, C, X(41988), X(54512)}}, {{A, B, C, X(43970), X(55857)}}
X(61880) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 13735, 10304}, {2, 1656, 11539}, {2, 5055, 632}, {2, 5067, 5054}, {2, 5070, 15699}, {2, 5071, 15723}, {2, 547, 10124}, {5, 15711, 14269}, {5, 3522, 546}, {5, 549, 3543}, {5, 632, 15720}, {20, 381, 15687}, {30, 10109, 12811}, {30, 11540, 12108}, {30, 16239, 11540}, {140, 12101, 3524}, {140, 14892, 8703}, {140, 15699, 10109}, {140, 3090, 3861}, {140, 3524, 11812}, {140, 3627, 3530}, {140, 5070, 3628}, {376, 17800, 15686}, {376, 381, 3627}, {381, 15700, 15685}, {381, 549, 15691}, {382, 11106, 14869}, {546, 5054, 15759}, {549, 15686, 15715}, {549, 15687, 14093}, {549, 5071, 14893}, {1010, 1656, 16239}, {1656, 10303, 5}, {1656, 11539, 5066}, {3090, 8703, 14892}, {3524, 10303, 15701}, {3530, 3628, 1656}, {3544, 15702, 376}, {3545, 15713, 548}, {3628, 10124, 547}, {3860, 14890, 3}, {3861, 10124, 15721}, {5055, 12100, 3850}, {5068, 15689, 3845}, {5071, 14893, 11737}, {8703, 15699, 3090}, {10109, 10124, 14891}, {10109, 11812, 12101}, {10109, 14891, 381}, {10124, 11737, 549}, {10124, 11812, 15694}, {10124, 14891, 140}, {10303, 14269, 15711}, {11346, 17542, 3522}, {11539, 15711, 10303}, {12102, 15690, 30}, {15687, 15702, 12100}, {15694, 15720, 15702}, {15694, 15723, 17678}, {15703, 15723, 5071}, {43100, 49907, 42924}, {43107, 49908, 42925}

X(61881) = X(2)X(3)∩X(6)X(43873)

Barycentrics    9*a^4+11*(b^2-c^2)^2-20*a^2*(b^2+c^2) : :
X(61881) = -33*X[2]+2*X[3], 11*X[69]+20*X[55714], 27*X[373]+4*X[15606], -X[944]+32*X[19878], -36*X[1125]+5*X[61288], 11*X[1352]+20*X[55702], 2*X[1482]+29*X[46930], -45*X[3616]+14*X[61282], 15*X[3617]+16*X[61278], -55*X[3618]+24*X[55713], 77*X[3619]+16*X[55715], -35*X[3624]+4*X[13607] and many others

X(61881) lies on these lines: {2, 3}, {6, 43873}, {54, 16187}, {69, 55714}, {230, 31407}, {371, 43505}, {372, 43506}, {373, 15606}, {944, 19878}, {1007, 52718}, {1125, 61288}, {1151, 41957}, {1152, 41958}, {1352, 55702}, {1482, 46930}, {3035, 31420}, {3068, 43431}, {3069, 43430}, {3071, 9693}, {3316, 6436}, {3317, 6435}, {3616, 61282}, {3617, 61278}, {3618, 55713}, {3619, 55715}, {3624, 13607}, {3634, 9624}, {3817, 31425}, {4301, 31253}, {5326, 9670}, {5351, 42775}, {5352, 42776}, {5368, 7736}, {5420, 31414}, {5433, 31410}, {5446, 33879}, {5550, 37727}, {5603, 51073}, {5651, 9705}, {5657, 19872}, {5734, 11230}, {5735, 61001}, {5818, 34595}, {5881, 19862}, {5901, 46931}, {6118, 49049}, {6119, 49048}, {6179, 23053}, {6221, 43341}, {6398, 43340}, {6447, 43377}, {6448, 43376}, {6459, 43792}, {6460, 43791}, {6494, 8981}, {6495, 13966}, {6496, 43508}, {6497, 43507}, {6498, 7585}, {6499, 7586}, {6688, 7999}, {6723, 12317}, {6776, 51127}, {7294, 9657}, {7581, 35813}, {7582, 35812}, {7607, 60646}, {7608, 60643}, {7612, 60100}, {7735, 34571}, {7749, 31417}, {7796, 34803}, {7814, 34229}, {8252, 13886}, {8253, 13939}, {8972, 34089}, {9606, 14482}, {9680, 42561}, {9681, 23275}, {9780, 61276}, {9956, 61248}, {10172, 37714}, {10194, 19054}, {10195, 19053}, {10219, 11465}, {10302, 53098}, {10589, 31452}, {10595, 19877}, {11271, 15605}, {11431, 26958}, {11482, 50985}, {11488, 42489}, {11489, 42488}, {11669, 18840}, {12007, 47355}, {12900, 15057}, {13941, 34091}, {14226, 43254}, {14241, 43255}, {14494, 60278}, {14531, 15024}, {14561, 55723}, {14692, 34127}, {14853, 51128}, {14912, 43150}, {15069, 51126}, {16241, 42495}, {16242, 42494}, {16966, 43464}, {16967, 43463}, {17825, 56292}, {18581, 42934}, {18582, 42935}, {18841, 53104}, {19130, 55613}, {19876, 50827}, {20125, 20379}, {20582, 51179}, {22112, 43598}, {22330, 50990}, {23249, 43338}, {23259, 43339}, {23302, 42611}, {23303, 42610}, {24206, 55707}, {25406, 42786}, {27355, 54041}, {30315, 34627}, {31447, 61268}, {31454, 41949}, {31457, 43620}, {31470, 43291}, {31670, 55619}, {32822, 53127}, {32839, 52713}, {32867, 37647}, {32884, 59635}, {35786, 43336}, {35787, 43337}, {36996, 58433}, {37640, 43447}, {37641, 43446}, {37650, 45942}, {38042, 61290}, {38074, 51085}, {38317, 55719}, {39874, 58445}, {40107, 55717}, {42090, 42498}, {42091, 42499}, {42095, 42687}, {42098, 42686}, {42111, 52079}, {42114, 52080}, {42149, 43442}, {42152, 43443}, {42154, 42927}, {42155, 42926}, {42433, 42695}, {42434, 42694}, {42492, 42818}, {42493, 42817}, {42528, 56628}, {42529, 56627}, {42590, 42989}, {42591, 42988}, {42596, 42914}, {42597, 42915}, {42598, 42805}, {42599, 42806}, {42910, 43483}, {42911, 43484}, {42924, 43494}, {42925, 43493}, {42978, 49812}, {42979, 49813}, {43211, 43387}, {43212, 43386}, {43564, 43569}, {43565, 43568}, {43889, 60620}, {43890, 60621}, {46934, 61286}, {50956, 55679}, {51143, 53858}, {51212, 55598}, {54434, 59777}, {60123, 60239}, {60144, 60637}, {60183, 60333}

X(61881) = inverse of X(61870) in orthocentroidal circle
X(61881) = inverse of X(61870) in Yff hyperbola
X(61881) = complement of X(61863)
X(61881) = anticomplement of X(61875)
X(61881) = pole of line {523, 61870} with respect to the orthocentroidal circle
X(61881) = pole of line {185, 46333} with respect to the Jerabek hyperbola
X(61881) = pole of line {6, 61870} with respect to the Kiepert hyperbola
X(61881) = pole of line {3, 34566} with respect to the Stammler hyperbola
X(61881) = pole of line {523, 61870} with respect to the Yff hyperbola
X(61881) = pole of line {69, 16239} with respect to the Wallace hyperbola
X(61881) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(16239)}}, {{A, B, C, X(549), X(18853)}}, {{A, B, C, X(1105), X(46333)}}, {{A, B, C, X(3525), X(57927)}}, {{A, B, C, X(6995), X(11669)}}, {{A, B, C, X(7378), X(53104)}}, {{A, B, C, X(7408), X(60333)}}, {{A, B, C, X(7409), X(60102)}}, {{A, B, C, X(7486), X(18854)}}, {{A, B, C, X(7612), X(52285)}}, {{A, B, C, X(8797), X(46219)}}, {{A, B, C, X(10109), X(60007)}}, {{A, B, C, X(10301), X(53098)}}, {{A, B, C, X(13599), X(50688)}}, {{A, B, C, X(14269), X(54660)}}, {{A, B, C, X(14938), X(15696)}}, {{A, B, C, X(15640), X(18849)}}, {{A, B, C, X(15686), X(15740)}}, {{A, B, C, X(15687), X(54763)}}, {{A, B, C, X(15694), X(34483)}}, {{A, B, C, X(17800), X(18851)}}, {{A, B, C, X(18852), X(50693)}}, {{A, B, C, X(22270), X(44682)}}, {{A, B, C, X(36948), X(55858)}}, {{A, B, C, X(37174), X(60100)}}, {{A, B, C, X(43558), X(55569)}}, {{A, B, C, X(43559), X(55573)}}, {{A, B, C, X(49135), X(60171)}}, {{A, B, C, X(52281), X(60643)}}, {{A, B, C, X(52282), X(60646)}}
X(61881) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15699, 15702}, {2, 15703, 3524}, {2, 16393, 17580}, {2, 1656, 3525}, {2, 20, 16239}, {2, 3090, 3533}, {2, 3628, 4}, {2, 5056, 632}, {2, 5067, 631}, {2, 7486, 3526}, {3, 10109, 3854}, {3, 1656, 10109}, {4, 10303, 15698}, {4, 17538, 15640}, {4, 3525, 549}, {4, 3528, 17800}, {4, 5071, 5072}, {5, 140, 15696}, {5, 15696, 3832}, {5, 15723, 17533}, {5, 3526, 15717}, {20, 13735, 1656}, {20, 3832, 3830}, {20, 631, 10299}, {20, 7486, 15022}, {140, 3529, 15719}, {140, 5071, 3529}, {140, 5072, 10304}, {547, 3523, 3544}, {548, 3526, 10303}, {549, 3534, 15705}, {631, 3090, 3855}, {631, 3526, 15709}, {632, 15686, 140}, {632, 15703, 5056}, {1656, 13735, 5067}, {1656, 15716, 5079}, {1656, 16239, 20}, {1656, 3525, 3545}, {1656, 3545, 3090}, {3090, 3533, 376}, {3523, 17580, 5070}, {3523, 3544, 15682}, {3526, 3628, 7486}, {3526, 5055, 548}, {3526, 5070, 3628}, {3560, 11539, 550}, {3850, 15692, 11541}, {3857, 15022, 6950}, {5054, 11539, 11113}, {5054, 5068, 17538}, {5055, 11540, 15683}, {5055, 15692, 6952}, {5059, 12108, 15715}, {5070, 16239, 13735}, {5079, 11539, 3522}, {6827, 15720, 15712}, {7486, 15717, 5}, {7486, 17678, 3853}, {11311, 11312, 8367}, {12812, 15720, 3839}, {13735, 13742, 2}, {15640, 17678, 5054}, {15717, 17800, 3528}, {35815, 43558, 32785}, {43873, 43874, 6}

X(61882) = X(2)X(3)∩X(17)X(42480)

Barycentrics    13*a^4+16*(b^2-c^2)^2-29*a^2*(b^2+c^2) : :
X(61882) = -16*X[2]+X[3], -X[568]+16*X[10219], -16*X[1125]+X[34748], X[1482]+14*X[19876], 14*X[3619]+X[50962], -49*X[3624]+4*X[32900], -16*X[3634]+X[34718], X[3653]+4*X[10172], -X[3655]+16*X[19878], X[3656]+14*X[51073], 14*X[4751]+X[51039], 8*X[5092]+7*X[50957] and many others

X(61882) lies on these lines: {2, 3}, {17, 42480}, {18, 42481}, {395, 42512}, {396, 42513}, {568, 10219}, {1125, 34748}, {1482, 19876}, {3068, 43882}, {3069, 43881}, {3070, 10146}, {3071, 10145}, {3619, 50962}, {3624, 32900}, {3634, 34718}, {3653, 10172}, {3655, 19878}, {3656, 51073}, {4751, 51039}, {5092, 50957}, {5093, 21358}, {5790, 19883}, {5965, 47352}, {6474, 42583}, {6475, 42582}, {6500, 13846}, {6501, 13847}, {6721, 48657}, {9167, 38732}, {9691, 42262}, {9780, 50805}, {10246, 38083}, {10247, 19875}, {11178, 55705}, {11179, 51127}, {11230, 38066}, {11482, 50993}, {11485, 42892}, {11486, 42893}, {11542, 42517}, {11543, 42516}, {11614, 15603}, {13624, 50800}, {13665, 43255}, {13785, 43254}, {15808, 50804}, {16644, 16961}, {16645, 16960}, {16962, 43029}, {16963, 43028}, {16966, 43020}, {16967, 43021}, {18492, 51084}, {18493, 31253}, {18510, 43211}, {18512, 43212}, {18581, 43107}, {18582, 43100}, {19862, 58233}, {19872, 50821}, {20423, 51128}, {22246, 31489}, {22330, 51189}, {25555, 51186}, {26614, 38634}, {28234, 58238}, {32789, 45385}, {32790, 45384}, {33879, 54047}, {34631, 46930}, {38022, 59503}, {38065, 38318}, {38069, 38755}, {38072, 55593}, {38082, 59380}, {38093, 51516}, {38314, 51515}, {42107, 42594}, {42110, 42595}, {42115, 42973}, {42116, 42972}, {42122, 43202}, {42123, 43201}, {42126, 42500}, {42127, 42501}, {42129, 42778}, {42132, 42777}, {42265, 51850}, {42488, 49906}, {42489, 49905}, {42492, 42497}, {42493, 42496}, {42498, 42529}, {42499, 42528}, {42510, 42948}, {42511, 42949}, {42518, 61719}, {42592, 42976}, {42593, 42977}, {42786, 43273}, {42900, 42915}, {42901, 42914}, {42922, 43494}, {42923, 43493}, {43024, 43233}, {43025, 43232}, {43032, 43305}, {43033, 43304}, {43238, 49908}, {43239, 49907}, {46932, 50823}, {47353, 55692}, {47355, 50955}, {50828, 58228}, {50872, 58250}, {50963, 55604}, {51024, 55632}, {51068, 61278}, {51171, 51175}, {51514, 61023}, {52703, 61306}, {54447, 58230}, {58226, 61263}

X(61882) = midpoint of X(i) and X(j) for these {i,j}: {3091, 3524}, {5055, 15694}
X(61882) = reflection of X(i) in X(j) for these {i,j}: {14093, 3524}, {15688, 15692}, {3524, 15713}, {3858, 14892}, {5055, 1656}, {5076, 3839}, {631, 11539}
X(61882) = inverse of X(61869) in orthocentroidal circle
X(61882) = inverse of X(61869) in Yff hyperbola
X(61882) = complement of X(61861)
X(61882) = pole of line {523, 61869} with respect to the orthocentroidal circle
X(61882) = pole of line {6, 61869} with respect to the Kiepert hyperbola
X(61882) = pole of line {523, 61869} with respect to the Yff hyperbola
X(61882) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(14938), X(50693)}}, {{A, B, C, X(15694), X(57927)}}, {{A, B, C, X(15699), X(46168)}}, {{A, B, C, X(15723), X(40410)}}, {{A, B, C, X(16239), X(57822)}}, {{A, B, C, X(46219), X(55958)}}, {{A, B, C, X(49133), X(60171)}}, {{A, B, C, X(55858), X(57895)}}
X(61882) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 13735, 3543}, {2, 3090, 10124}, {2, 3628, 381}, {2, 376, 16239}, {2, 5, 15723}, {2, 5067, 549}, {2, 5070, 15703}, {2, 5071, 632}, {2, 547, 3526}, {5, 15701, 15684}, {30, 14892, 3858}, {30, 15692, 15688}, {30, 15713, 3524}, {30, 1656, 5055}, {30, 3524, 14093}, {30, 3839, 5076}, {140, 15681, 15722}, {140, 3839, 15706}, {381, 11539, 15707}, {381, 12100, 17800}, {381, 3534, 3853}, {381, 5054, 10304}, {381, 631, 15695}, {547, 15759, 5}, {550, 3861, 3146}, {631, 11001, 15692}, {1656, 15693, 5071}, {1656, 15696, 12812}, {1656, 3526, 3091}, {3090, 10124, 3534}, {3091, 14093, 3830}, {3091, 3524, 30}, {3524, 3533, 11113}, {3525, 5066, 15700}, {3526, 14093, 15713}, {3545, 15689, 14269}, {3545, 5054, 15689}, {3830, 15701, 15759}, {3839, 15706, 15681}, {3843, 15694, 15693}, {3845, 14890, 15705}, {3853, 11539, 15708}, {5055, 15689, 3545}, {5066, 15700, 5073}, {5067, 12812, 1656}, {5067, 16854, 550}, {5071, 15693, 3843}, {6964, 10124, 3523}, {10109, 15702, 382}, {10303, 15687, 15716}, {10304, 11539, 5054}, {11539, 12101, 11114}, {12812, 15694, 15685}, {12812, 15696, 3851}, {14890, 15705, 15720}, {15022, 15719, 14893}, {15681, 15722, 3}, {15688, 15709, 15701}, {15688, 15723, 15709}, {15692, 15723, 15694}, {15694, 15695, 631}

X(61883) = X(2)X(3)∩X(6)X(43544)

Barycentrics    11*a^4+14*(b^2-c^2)^2-25*a^2*(b^2+c^2) : :
X(61883) = -14*X[2]+X[3], 8*X[182]+5*X[50954], 5*X[355]+8*X[51085], 12*X[373]+X[54048], 7*X[599]+6*X[15520], 5*X[1351]+8*X[50982], 5*X[1352]+8*X[51138], 8*X[1385]+5*X[50797], 5*X[1482]+8*X[50827], X[2080]+12*X[10150], 7*X[3619]+6*X[38079], 7*X[3622]+6*X[38081] and many others

X(61883) lies on these lines: {2, 3}, {6, 43544}, {13, 42954}, {14, 42955}, {182, 50954}, {355, 51085}, {373, 54048}, {599, 15520}, {1351, 50982}, {1352, 51138}, {1385, 50797}, {1482, 50827}, {2080, 10150}, {3070, 43525}, {3071, 43526}, {3584, 8162}, {3619, 38079}, {3622, 38081}, {3624, 38083}, {3634, 38066}, {3653, 19878}, {3654, 51073}, {3655, 10172}, {3763, 14848}, {3828, 59503}, {5032, 51182}, {5418, 43343}, {5420, 43342}, {5790, 61294}, {5891, 12045}, {6451, 42600}, {6452, 42601}, {6470, 10577}, {6471, 10576}, {6684, 50806}, {6688, 13321}, {6721, 14692}, {6723, 56567}, {7585, 43882}, {7586, 43881}, {8976, 35814}, {9167, 12355}, {9780, 38022}, {10187, 49903}, {10188, 49904}, {10302, 11669}, {10516, 55693}, {10605, 14926}, {10645, 42475}, {10646, 42474}, {10653, 42691}, {10654, 42690}, {11178, 55706}, {11224, 11230}, {11480, 42904}, {11481, 42905}, {11482, 50991}, {11488, 42984}, {11489, 42985}, {11898, 15516}, {11935, 16187}, {12007, 48310}, {12331, 59376}, {12645, 25055}, {12702, 31253}, {13188, 14971}, {13364, 33879}, {13607, 19883}, {13903, 43558}, {13925, 60293}, {13951, 35815}, {13961, 43559}, {13993, 60294}, {14927, 50988}, {16267, 43019}, {16268, 43018}, {16644, 42476}, {16645, 42477}, {16808, 42796}, {16809, 42795}, {18440, 55696}, {18445, 59777}, {18493, 19872}, {18510, 32789}, {18512, 32790}, {18526, 19862}, {19875, 50805}, {20070, 50826}, {21356, 50985}, {21358, 50962}, {22330, 50989}, {25555, 50993}, {25561, 55686}, {26614, 38744}, {28204, 34595}, {31479, 37602}, {31487, 42527}, {32519, 44562}, {32787, 43431}, {32788, 43430}, {33606, 43443}, {33607, 43442}, {34127, 48657}, {34632, 61269}, {34748, 38042}, {37832, 43468}, {37835, 43467}, {38064, 51127}, {38065, 58433}, {38068, 61268}, {38082, 60996}, {38098, 61277}, {39899, 51126}, {41119, 43100}, {41120, 43107}, {41121, 42935}, {41122, 42934}, {41943, 42951}, {41944, 42950}, {41951, 41965}, {41952, 41966}, {42111, 42500}, {42114, 42501}, {42115, 43104}, {42116, 43101}, {42132, 61719}, {42488, 49948}, {42489, 49947}, {42490, 42972}, {42491, 42973}, {42518, 42779}, {42519, 42780}, {42522, 54597}, {42523, 43536}, {42582, 43255}, {42583, 43254}, {42594, 42940}, {42595, 42941}, {42610, 42988}, {42611, 42989}, {42688, 42942}, {42689, 42943}, {42773, 46335}, {42774, 46334}, {42786, 47353}, {42791, 42920}, {42792, 42921}, {42815, 42911}, {42816, 42910}, {43102, 43403}, {43103, 43404}, {43150, 46267}, {43226, 51944}, {43227, 51945}, {43273, 55690}, {43340, 52048}, {43341, 52047}, {43380, 52046}, {43381, 52045}, {48872, 51141}, {48876, 51172}, {49814, 49828}, {49815, 49829}, {50830, 53620}, {50959, 55629}, {50980, 55616}, {50981, 61044}, {51023, 55692}, {51069, 61276}, {51072, 61278}, {51128, 54173}, {51173, 55590}, {51175, 59373}, {51915, 56608}, {51916, 56609}, {53023, 55630}, {53104, 60239}, {54131, 55596}, {59380, 60999}, {60100, 60175}, {60102, 60646}, {60192, 60278}, {60333, 60643}

X(61883) = midpoint of X(i) and X(j) for these {i,j}: {2, 5067}
X(61883) = inverse of X(47598) in orthocentroidal circle
X(61883) = inverse of X(47598) in Yff hyperbola
X(61883) = complement of X(61859)
X(61883) = pole of line {523, 47598} with respect to the orthocentroidal circle
X(61883) = pole of line {6, 43513} with respect to the Kiepert hyperbola
X(61883) = pole of line {523, 47598} with respect to the Yff hyperbola
X(61883) = pole of line {69, 61868} with respect to the Wallace hyperbola
X(61883) = intersection, other than A, B, C, of circumconics {{A, B, C, X(264), X(47598)}}, {{A, B, C, X(1494), X(46219)}}, {{A, B, C, X(5054), X(57927)}}, {{A, B, C, X(10301), X(11669)}}, {{A, B, C, X(12811), X(31846)}}, {{A, B, C, X(14938), X(17538)}}, {{A, B, C, X(15723), X(55958)}}, {{A, B, C, X(34483), X(55864)}}, {{A, B, C, X(47485), X(57714)}}, {{A, B, C, X(49139), X(60171)}}, {{A, B, C, X(52285), X(60175)}}
X(61883) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3090, 11539}, {2, 3524, 16239}, {2, 3545, 632}, {2, 381, 15723}, {2, 5055, 3526}, {2, 5067, 30}, {2, 5071, 10124}, {2, 7486, 15709}, {3, 3851, 17578}, {3, 3861, 1657}, {3, 5055, 5066}, {5, 140, 17538}, {140, 15022, 17800}, {140, 17697, 5070}, {140, 3543, 15718}, {140, 3855, 3}, {381, 14093, 382}, {381, 15688, 3543}, {381, 15693, 15681}, {381, 5054, 14093}, {382, 5054, 15716}, {546, 15708, 15695}, {549, 3857, 15686}, {1656, 15723, 381}, {1656, 3526, 5072}, {3090, 15692, 11737}, {3090, 17536, 14869}, {3090, 5059, 5}, {3091, 11812, 15689}, {3524, 6824, 3843}, {3525, 3845, 15707}, {3526, 3628, 1656}, {3544, 15705, 12101}, {3545, 15697, 3861}, {3628, 5066, 15699}, {3830, 11539, 15720}, {3845, 15707, 15696}, {3855, 15709, 15698}, {3857, 15640, 14269}, {5056, 11539, 6958}, {5066, 15699, 7486}, {5071, 15692, 3858}, {5071, 15702, 15682}, {5071, 15709, 15683}, {5071, 15721, 15687}, {6891, 15718, 15715}, {7486, 10303, 5068}, {10124, 15687, 15721}, {10124, 15691, 15713}, {10124, 15699, 5071}, {10124, 15721, 15694}, {10304, 15702, 549}, {10304, 17678, 15702}, {11230, 19876, 34718}, {11539, 11737, 15692}, {11737, 15692, 3830}, {13735, 17529, 20}, {14869, 14892, 11001}, {14890, 15717, 15701}, {14891, 15693, 15700}, {15681, 15702, 15693}, {15682, 15721, 14891}, {15683, 15687, 15684}, {15687, 15699, 547}, {15688, 17800, 3534}, {15694, 15700, 5054}, {15698, 17538, 10304}, {15698, 17800, 15688}, {15699, 15709, 5055}, {15702, 17678, 11540}, {37832, 43468, 43484}, {43544, 43545, 6}

X(61884) = X(2)X(3)∩X(1327)X(6487)

Barycentrics    19*a^4+25*(b^2-c^2)^2-44*a^2*(b^2+c^2) : :
X(61884) = -25*X[2]+2*X[3], 20*X[3828]+3*X[16200], 8*X[5097]+15*X[21356], 3*X[5102]+20*X[20582], -77*X[5550]+8*X[32900], -25*X[5818]+2*X[50871], -X[5890]+24*X[12045], -25*X[7967]+48*X[58234], -25*X[8227]+2*X[51120], 175*X[9780]+32*X[58237], -50*X[10165]+27*X[58227], 20*X[10172]+3*X[30392] and many others

X(61884) lies on these lines: {2, 3}, {1327, 6487}, {1328, 6486}, {3055, 14482}, {3070, 10140}, {3071, 10139}, {3311, 54597}, {3312, 43536}, {3316, 35770}, {3317, 35771}, {3828, 16200}, {5097, 21356}, {5102, 20582}, {5351, 43201}, {5352, 43202}, {5418, 14226}, {5420, 14241}, {5550, 32900}, {5818, 50871}, {5890, 12045}, {6484, 23275}, {6485, 23269}, {7612, 60645}, {7788, 32883}, {7818, 55726}, {7967, 58234}, {8227, 51120}, {8976, 34091}, {8981, 43387}, {9780, 58237}, {10141, 42417}, {10142, 42418}, {10165, 58227}, {10172, 30392}, {10219, 14831}, {11180, 55703}, {11230, 34631}, {11278, 19877}, {11488, 43232}, {11489, 43233}, {12571, 50813}, {13951, 34089}, {13966, 43386}, {14494, 60131}, {14912, 46267}, {16644, 42899}, {16645, 42898}, {16962, 42953}, {16963, 42952}, {18538, 43518}, {18762, 43517}, {19862, 38074}, {19876, 58241}, {19883, 50818}, {21358, 51179}, {25555, 50994}, {25565, 55603}, {31253, 38021}, {31423, 50809}, {32785, 43323}, {32786, 43322}, {32884, 59634}, {33179, 53620}, {33751, 51217}, {34595, 58231}, {34638, 61265}, {34754, 42910}, {34755, 42911}, {37640, 42897}, {37641, 42896}, {37832, 43464}, {37835, 43463}, {38022, 46933}, {38066, 46930}, {38073, 61001}, {38725, 56567}, {40330, 51027}, {42089, 42903}, {42092, 42902}, {42496, 42985}, {42497, 42984}, {42512, 43545}, {42513, 43544}, {42582, 43888}, {42583, 43887}, {42594, 42626}, {42595, 42625}, {42596, 43770}, {42597, 43769}, {42610, 43229}, {42611, 43228}, {42914, 43245}, {42915, 43244}, {43002, 43502}, {43003, 43501}, {43100, 49825}, {43107, 49824}, {43199, 43543}, {43200, 43542}, {43238, 49873}, {43239, 49874}, {43374, 43890}, {43375, 43889}, {43446, 49861}, {43447, 49862}, {48310, 50974}, {51127, 55699}, {51128, 55582}, {51537, 55683}, {51709, 58244}, {53098, 60638}, {60123, 60287}

X(61884) = inverse of X(61866) in orthocentroidal circle
X(61884) = inverse of X(61866) in Yff hyperbola
X(61884) = pole of line {523, 61866} with respect to the orthocentroidal circle
X(61884) = pole of line {6, 61866} with respect to the Kiepert hyperbola
X(61884) = pole of line {523, 61866} with respect to the Yff hyperbola
X(61884) = pole of line {69, 47598} with respect to the Wallace hyperbola
X(61884) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(47598)}}, {{A, B, C, X(3524), X(57927)}}, {{A, B, C, X(3853), X(54763)}}, {{A, B, C, X(3856), X(15749)}}, {{A, B, C, X(15697), X(18852)}}, {{A, B, C, X(15723), X(36889)}}, {{A, B, C, X(35403), X(54838)}}, {{A, B, C, X(37174), X(60645)}}, {{A, B, C, X(55569), X(60297)}}, {{A, B, C, X(55573), X(60298)}}
X(61884) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15699, 4}, {2, 15703, 5071}, {2, 15708, 16239}, {2, 16401, 17564}, {2, 17568, 11113}, {2, 3090, 15709}, {2, 3543, 15723}, {2, 3545, 3533}, {2, 3839, 632}, {2, 4217, 16401}, {2, 5055, 3525}, {2, 5067, 3545}, {2, 7486, 5054}, {4, 14890, 15698}, {4, 3524, 15697}, {4, 5071, 11737}, {5, 14890, 15685}, {381, 15694, 12100}, {381, 15700, 17800}, {381, 15714, 3146}, {381, 547, 5056}, {547, 10124, 3845}, {547, 16239, 15686}, {631, 15698, 15707}, {1656, 3855, 3090}, {3524, 12811, 15682}, {3533, 3545, 15719}, {3543, 17678, 11812}, {3543, 3832, 14893}, {3545, 15682, 3832}, {3545, 3845, 3855}, {3628, 12100, 15699}, {3628, 5056, 5067}, {3845, 15681, 3543}, {3851, 11540, 15705}, {3853, 10304, 11001}, {3853, 5056, 3544}, {5056, 15723, 15715}, {5071, 15715, 381}, {10124, 14869, 15694}, {11001, 11539, 631}, {11737, 14869, 15681}, {11737, 15723, 15708}, {12100, 16239, 11539}, {14869, 15697, 3524}, {14892, 15720, 15640}, {15681, 15703, 1656}, {15682, 15692, 376}, {15686, 15699, 547}, {15694, 15708, 15702}

X(61885) = X(1)X(38081)∩X(2)X(3)

Barycentrics    8*a^4+11*(b^2-c^2)^2-19*a^2*(b^2+c^2) : :
X(61885) = 2*X[1]+3*X[38081], -11*X[2]+X[3], 2*X[9]+3*X[38080], 2*X[10]+3*X[38022], -2*X[40]+7*X[50826], 2*X[141]+3*X[38079], 2*X[142]+3*X[38082], X[165]+4*X[61267], 2*X[551]+3*X[38042], X[576]+4*X[51143], 2*X[599]+3*X[59399], 2*X[1125]+3*X[38083] and many others

X(61885) lies on these lines: {1, 38081}, {2, 3}, {6, 42512}, {9, 38080}, {10, 38022}, {17, 42898}, {18, 42899}, {40, 50826}, {141, 38079}, {142, 38082}, {165, 61267}, {230, 14075}, {371, 41951}, {372, 41952}, {395, 16960}, {396, 16961}, {485, 43212}, {486, 43211}, {524, 55714}, {542, 51126}, {551, 38042}, {576, 51143}, {590, 6435}, {597, 5965}, {599, 59399}, {615, 6436}, {1125, 38083}, {1350, 50981}, {1353, 47352}, {1483, 25055}, {1484, 59376}, {1494, 57927}, {2482, 38229}, {3035, 38084}, {3054, 7753}, {3055, 5309}, {3241, 59400}, {3576, 61260}, {3589, 55712}, {3619, 14848}, {3624, 37705}, {3634, 51709}, {3653, 18357}, {3654, 61272}, {3655, 38138}, {3679, 10283}, {3828, 11230}, {4297, 50833}, {4677, 61278}, {4995, 10593}, {4999, 38085}, {5097, 50985}, {5298, 10592}, {5306, 34571}, {5346, 9300}, {5349, 42632}, {5350, 42631}, {5476, 34573}, {5480, 55592}, {5640, 44324}, {5650, 13364}, {5655, 40685}, {5790, 61293}, {5886, 19876}, {5892, 12045}, {5901, 19875}, {6101, 58470}, {6427, 42527}, {6428, 42526}, {6437, 43513}, {6438, 43514}, {6498, 13993}, {6499, 13925}, {6669, 32907}, {6670, 32909}, {6688, 15067}, {6721, 49102}, {6776, 51181}, {7987, 50799}, {7988, 61614}, {7998, 13451}, {7999, 58531}, {8148, 46930}, {8252, 42602}, {8253, 42603}, {9166, 61561}, {9167, 61576}, {9606, 12815}, {9955, 38068}, {9956, 19883}, {10168, 55700}, {10170, 10219}, {10171, 28232}, {10172, 28236}, {10173, 31840}, {10222, 51069}, {10264, 56567}, {10576, 42639}, {10577, 42640}, {10653, 43102}, {10654, 43103}, {11178, 38110}, {11231, 28228}, {11482, 50990}, {11488, 42497}, {11489, 42496}, {11542, 42493}, {11543, 42492}, {11591, 16226}, {12046, 45186}, {12512, 51088}, {12816, 42597}, {12817, 42596}, {13363, 14831}, {13624, 38076}, {13846, 19116}, {13847, 19117}, {14073, 58429}, {15028, 31834}, {15082, 54042}, {16267, 42521}, {16268, 42520}, {16772, 41122}, {16773, 41121}, {16808, 42501}, {16809, 42500}, {16962, 42599}, {16963, 42598}, {16966, 41944}, {16967, 41943}, {18358, 38064}, {18583, 21358}, {19130, 55609}, {19862, 28204}, {19872, 38021}, {19877, 38066}, {19878, 34773}, {19924, 50980}, {20582, 38317}, {21850, 51128}, {21969, 32142}, {22165, 25555}, {22791, 51073}, {22793, 50829}, {23234, 61560}, {23302, 42633}, {23303, 42634}, {24206, 46267}, {25565, 38136}, {26446, 61270}, {28178, 61266}, {28190, 61264}, {28194, 31253}, {28198, 50825}, {30315, 61249}, {31162, 61269}, {31173, 38230}, {31399, 51109}, {32396, 54157}, {32789, 35823}, {32790, 35822}, {33179, 38098}, {33416, 43240}, {33417, 43241}, {34628, 61263}, {34747, 61280}, {36967, 42682}, {36968, 42683}, {37640, 42628}, {37641, 42627}, {37832, 42121}, {37835, 42124}, {38069, 61580}, {38093, 61511}, {38111, 38318}, {38170, 47357}, {38171, 60986}, {38223, 55085}, {38314, 50831}, {39884, 50983}, {40693, 42518}, {40694, 42519}, {41107, 43100}, {41108, 43107}, {41112, 43239}, {41113, 43238}, {41119, 42924}, {41120, 42925}, {41945, 41955}, {41946, 41956}, {42085, 42475}, {42086, 42474}, {42089, 43416}, {42092, 43417}, {42095, 43296}, {42098, 43297}, {42117, 43101}, {42118, 43104}, {42129, 42916}, {42132, 42917}, {42144, 42594}, {42145, 42595}, {42159, 43108}, {42162, 43109}, {42262, 43254}, {42265, 43255}, {42488, 43228}, {42489, 43229}, {42502, 42990}, {42503, 42991}, {42516, 42975}, {42517, 42974}, {42580, 42949}, {42581, 42948}, {42588, 43635}, {42589, 43634}, {42610, 49947}, {42611, 49948}, {42635, 42953}, {42636, 42952}, {42692, 43245}, {42693, 43244}, {42786, 48906}, {42791, 42814}, {42792, 42813}, {42910, 42912}, {42911, 42913}, {42914, 42942}, {42915, 42943}, {42922, 43403}, {42923, 43404}, {42936, 49908}, {42937, 49907}, {42938, 43773}, {42939, 43774}, {42944, 42973}, {42945, 42972}, {42950, 43542}, {42951, 43543}, {42970, 43311}, {42971, 43310}, {42988, 49812}, {42989, 49813}, {43014, 43024}, {43015, 43025}, {43020, 43373}, {43021, 43372}, {43334, 43490}, {43335, 43489}, {43401, 43648}, {43402, 43647}, {43418, 43468}, {43419, 43467}, {44882, 50988}, {45939, 48861}, {47354, 58445}, {48874, 50959}, {48876, 55719}, {48898, 50960}, {48901, 50984}, {50798, 51700}, {50804, 61281}, {50811, 61259}, {50955, 51732}, {50956, 53094}, {50977, 55581}, {50986, 59373}, {51022, 55674}, {51047, 51488}, {51048, 61522}, {51066, 61276}, {51110, 61286}, {51130, 55587}, {51134, 55666}, {51180, 53091}, {51183, 61624}, {52695, 61600}, {58722, 61613}, {59375, 61596}, {59377, 61562}, {61023, 61509}, {61606, 61735}

X(61885) = midpoint of X(i) and X(j) for these {i,j}: {2, 1656}, {4, 15695}, {5, 15713}, {381, 15692}, {3091, 15693}, {3534, 17578}, {3830, 17538}, {3858, 15711}, {3859, 12100}, {5071, 15694}, {5076, 15697}, {7987, 50799}, {11482, 50990}, {31399, 51109}, {50956, 53094}, {51066, 61276}
X(61885) = reflection of X(i) in X(j) for these {i,j}: {15693, 140}, {15711, 631}, {15712, 15713}, {15713, 632}, {15714, 549}, {3522, 12100}, {3843, 5066}, {3845, 3091}, {549, 15694}, {5071, 547}, {51134, 55666}, {51180, 53091}, {632, 2}, {8703, 15712}
X(61885) = inverse of X(61864) in orthocentroidal circle
X(61885) = inverse of X(61864) in Yff hyperbola
X(61885) = complement of X(15694)
X(61885) = pole of line {523, 61864} with respect to the orthocentroidal circle
X(61885) = pole of line {6, 51174} with respect to the Kiepert hyperbola
X(61885) = pole of line {525, 44554} with respect to the Steiner inellipse
X(61885) = pole of line {523, 61864} with respect to the Yff hyperbola
X(61885) = pole of line {69, 61866} with respect to the Wallace hyperbola
X(61885) = intersection, other than A, B, C, of circumconics {{A, B, C, X(30), X(57927)}}, {{A, B, C, X(95), X(47598)}}, {{A, B, C, X(632), X(1494)}}, {{A, B, C, X(3091), X(31846)}}, {{A, B, C, X(10124), X(55958)}}, {{A, B, C, X(11539), X(40410)}}, {{A, B, C, X(12102), X(60121)}}, {{A, B, C, X(14938), X(15704)}}, {{A, B, C, X(15714), X(18317)}}, {{A, B, C, X(15723), X(57822)}}
X(61885) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15699, 5}, {2, 1656, 30}, {2, 30, 632}, {2, 3090, 5054}, {2, 3545, 3526}, {2, 376, 15723}, {2, 381, 10124}, {2, 3839, 3533}, {2, 5, 11539}, {2, 5054, 16239}, {2, 5056, 15709}, {2, 7486, 3524}, {4, 15700, 15691}, {5, 15686, 381}, {5, 3854, 6981}, {30, 12100, 3522}, {30, 140, 15693}, {30, 5066, 3843}, {30, 631, 15711}, {140, 12102, 15717}, {140, 15759, 15708}, {140, 3628, 5067}, {140, 3845, 17504}, {140, 3856, 3}, {140, 5055, 3845}, {140, 547, 11737}, {376, 3543, 15685}, {376, 5071, 3091}, {381, 15694, 15692}, {381, 15718, 15683}, {381, 549, 15686}, {382, 15708, 15759}, {547, 14893, 10109}, {547, 3628, 15703}, {631, 12812, 3858}, {631, 1656, 12812}, {1656, 15693, 5055}, {1656, 15694, 5071}, {1656, 3843, 3090}, {1656, 5071, 547}, {3090, 5054, 5066}, {3522, 3859, 3627}, {3526, 15681, 15721}, {3526, 5055, 15640}, {3530, 14892, 3830}, {3530, 5056, 3857}, {3533, 3839, 15701}, {3533, 5079, 548}, {3543, 5054, 14891}, {3545, 15721, 15681}, {3830, 15709, 3530}, {3830, 5056, 14892}, {3845, 17504, 15704}, {3851, 10304, 12101}, {5066, 14891, 3543}, {5070, 13747, 12103}, {5072, 15707, 15682}, {5079, 15701, 3839}, {5901, 19875, 50823}, {6891, 15709, 12108}, {8703, 11539, 14869}, {9956, 19883, 50824}, {11230, 38112, 61273}, {11539, 15687, 549}, {11539, 15712, 15713}, {11541, 15715, 376}, {11737, 14891, 12102}, {11737, 17504, 15687}, {11812, 13735, 15699}, {11812, 15691, 15700}, {12101, 12108, 10304}, {12102, 15717, 550}, {12102, 16239, 140}, {12811, 14890, 15690}, {12811, 15690, 14269}, {14093, 15694, 631}, {14093, 15711, 15714}, {14890, 15690, 3523}, {15022, 15720, 3861}, {15681, 15721, 12100}, {15683, 15702, 15718}, {15693, 15723, 15694}, {15693, 17504, 15712}, {15694, 15703, 1656}, {15704, 17504, 8703}, {18583, 21358, 50978}, {18586, 18587, 15022}, {24206, 48310, 50979}, {25565, 54169, 38136}, {33179, 38098, 50830}, {38314, 61510, 50831}, {42262, 43254, 52047}, {42265, 43255, 52048}, {42512, 42513, 6}, {42786, 51127, 48906}, {42911, 43028, 42913}, {51488, 61549, 51047}, {59373, 61545, 50986}

X(61886) = X(2)X(3)∩X(17)X(11489)

Barycentrics    5*a^4+7*(b^2-c^2)^2-12*a^2*(b^2+c^2) : :
X(61886) = -21*X[2]+2*X[3], 5*X[8]+14*X[61277], 10*X[10]+9*X[61275], -X[40]+20*X[31253], 7*X[69]+12*X[15520], -5*X[145]+24*X[61280], 18*X[373]+X[11412], 16*X[576]+3*X[51179], -20*X[597]+X[51178], -X[944]+20*X[19862], 4*X[1216]+15*X[11451], 7*X[1352]+12*X[55706] and many others

X(61886) lies on these lines: {2, 3}, {8, 61277}, {10, 61275}, {15, 42495}, {16, 42494}, {17, 11489}, {18, 11488}, {40, 31253}, {61, 10188}, {62, 10187}, {69, 15520}, {76, 53098}, {83, 60123}, {145, 61280}, {183, 32883}, {233, 40065}, {325, 32867}, {373, 11412}, {395, 42611}, {396, 42610}, {397, 43028}, {398, 43029}, {459, 3462}, {485, 43565}, {486, 43564}, {498, 47743}, {499, 8164}, {576, 51179}, {590, 13939}, {597, 51178}, {615, 13886}, {944, 19862}, {1007, 7871}, {1131, 35256}, {1132, 35255}, {1151, 53520}, {1152, 53517}, {1181, 59777}, {1216, 11451}, {1352, 55706}, {1385, 61257}, {1482, 46932}, {1487, 56738}, {1587, 32790}, {1588, 32789}, {1698, 11224}, {3055, 5286}, {3068, 3317}, {3069, 3316}, {3070, 6469}, {3071, 6468}, {3085, 8162}, {3567, 6688}, {3590, 7583}, {3591, 7584}, {3616, 61287}, {3618, 15516}, {3619, 38317}, {3622, 38042}, {3624, 5818}, {3634, 5603}, {3767, 12815}, {3818, 55686}, {3819, 9781}, {3828, 9624}, {3933, 32870}, {4293, 7294}, {4294, 5326}, {4430, 58632}, {4661, 58561}, {4678, 10283}, {4857, 5218}, {5265, 10592}, {5270, 7288}, {5281, 10593}, {5298, 31410}, {5306, 31407}, {5334, 43238}, {5335, 43239}, {5339, 42949}, {5340, 42948}, {5343, 42095}, {5344, 42098}, {5349, 42773}, {5350, 42774}, {5365, 11480}, {5366, 11481}, {5418, 23273}, {5420, 23267}, {5447, 33879}, {5485, 60144}, {5493, 10171}, {5544, 12160}, {5550, 7967}, {5562, 11465}, {5587, 19878}, {5651, 43651}, {5657, 11522}, {5690, 46931}, {5707, 37687}, {5714, 31231}, {5759, 61001}, {5790, 46934}, {5817, 58433}, {5881, 19883}, {5886, 19877}, {5891, 15028}, {5892, 15056}, {5901, 46933}, {5907, 12045}, {5943, 7999}, {6090, 43908}, {6118, 6279}, {6119, 6280}, {6337, 53127}, {6361, 7988}, {6390, 32871}, {6470, 8253}, {6471, 8252}, {6666, 59386}, {6721, 14651}, {6776, 51126}, {7320, 11373}, {7581, 10576}, {7582, 10577}, {7592, 54434}, {7607, 18841}, {7608, 7869}, {7612, 43527}, {7736, 7755}, {7749, 46453}, {7768, 32823}, {7769, 32817}, {7821, 42850}, {7827, 15850}, {7881, 10155}, {7914, 9754}, {7920, 61618}, {8167, 11491}, {8227, 43174}, {8550, 40330}, {8972, 13951}, {8976, 13941}, {9143, 20396}, {9166, 38751}, {9540, 42583}, {9589, 38068}, {9780, 10595}, {10159, 14494}, {10170, 15043}, {10175, 34595}, {10185, 18842}, {10246, 61246}, {10516, 51127}, {10601, 56292}, {10625, 44299}, {10645, 42473}, {10646, 42472}, {10993, 38319}, {11002, 13421}, {11206, 32767}, {11433, 12242}, {11455, 17704}, {11459, 11695}, {11485, 22237}, {11486, 22235}, {11793, 15024}, {12002, 14845}, {12046, 54042}, {12243, 20399}, {12251, 31239}, {12317, 15059}, {12324, 14862}, {13172, 31274}, {13199, 31235}, {13336, 43614}, {13340, 18874}, {13382, 15045}, {13432, 21357}, {13665, 43518}, {13785, 43517}, {13935, 42582}, {14226, 43413}, {14241, 43414}, {14491, 42021}, {14561, 55720}, {14853, 34573}, {14912, 24206}, {14971, 23235}, {14997, 45931}, {15032, 15805}, {15058, 61136}, {15069, 48310}, {15081, 30714}, {15082, 45186}, {15274, 20200}, {15491, 55774}, {16772, 43404}, {16773, 43403}, {16808, 43769}, {16809, 43770}, {16966, 42149}, {16967, 42152}, {18538, 43375}, {18553, 39874}, {18581, 42936}, {18582, 42937}, {18762, 43374}, {19130, 55608}, {20053, 61279}, {20190, 51023}, {20195, 36996}, {20582, 50973}, {21168, 61595}, {22112, 61134}, {22330, 50992}, {23039, 32205}, {23234, 38740}, {23269, 42277}, {23275, 42274}, {23302, 42999}, {23303, 42998}, {24558, 38058}, {25406, 55690}, {26040, 31262}, {26958, 43841}, {31145, 61278}, {31188, 57282}, {31404, 37637}, {31412, 43510}, {31418, 52795}, {31454, 43410}, {31663, 61266}, {31670, 55615}, {32002, 36948}, {32805, 43145}, {32806, 43143}, {32818, 32832}, {32820, 32829}, {32821, 32828}, {32824, 32839}, {32825, 32838}, {33416, 42142}, {33417, 42139}, {34127, 52090}, {34224, 35283}, {34781, 61735}, {35260, 45185}, {35595, 37532}, {35812, 42603}, {35813, 42602}, {36836, 43101}, {36843, 43104}, {36969, 42597}, {36970, 42596}, {37640, 42488}, {37641, 42489}, {37727, 38083}, {37832, 43020}, {37835, 43021}, {38021, 50814}, {38028, 61253}, {38064, 51176}, {38072, 50970}, {38074, 51082}, {38076, 51080}, {38318, 60996}, {38665, 59376}, {38763, 59377}, {40331, 40897}, {41963, 42262}, {41964, 42265}, {41973, 42580}, {41974, 42581}, {42111, 42157}, {42114, 42158}, {42119, 42914}, {42120, 42915}, {42135, 43869}, {42138, 43870}, {42154, 42794}, {42155, 42793}, {42159, 43482}, {42160, 43645}, {42161, 43646}, {42162, 43481}, {42492, 42983}, {42493, 42982}, {42500, 43194}, {42501, 43193}, {42516, 42939}, {42517, 42938}, {42561, 43509}, {42592, 42991}, {42593, 42990}, {42892, 42910}, {42893, 42911}, {42924, 43480}, {42925, 43479}, {43000, 43200}, {43001, 43199}, {43100, 49826}, {43107, 49827}, {43211, 43883}, {43212, 43884}, {43240, 43485}, {43241, 43486}, {43426, 49812}, {43427, 49813}, {43442, 43775}, {43443, 43776}, {43598, 43650}, {43699, 57713}, {47065, 58429}, {48901, 55638}, {50959, 55626}, {50980, 55620}, {50991, 53858}, {51108, 61288}, {51118, 61265}, {51136, 53093}, {51212, 55596}, {51538, 55630}, {53099, 60183}, {53103, 60647}, {53620, 61276}, {53859, 54616}, {54048, 58531}, {54445, 61261}, {54660, 60138}, {55693, 58445}, {55732, 58446}, {59417, 61272}, {60100, 60337}, {60150, 60182}, {60169, 60173}, {60278, 60330}, {60291, 60316}, {60292, 60315}, {60332, 60643}, {60334, 60646}

X(61886) = inverse of X(3533) in orthocentroidal circle
X(61886) = inverse of X(3533) in Yff hyperbola
X(61886) = complement of X(55864)
X(61886) = anticomplement of X(55858)
X(61886) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 54892}
X(61886) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 54892}
X(61886) = pole of line {523, 3533} with respect to the orthocentroidal circle
X(61886) = pole of line {185, 62147} with respect to the Jerabek hyperbola
X(61886) = pole of line {6, 3533} with respect to the Kiepert hyperbola
X(61886) = pole of line {3, 44111} with respect to the Stammler hyperbola
X(61886) = pole of line {523, 3533} with respect to the Yff hyperbola
X(61886) = pole of line {69, 632} with respect to the Wallace hyperbola
X(61886) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(4), X(57927)}}, {{A, B, C, X(20), X(60171)}}, {{A, B, C, X(25), X(53098)}}, {{A, B, C, X(68), X(5079)}}, {{A, B, C, X(69), X(632)}}, {{A, B, C, X(264), X(3533)}}, {{A, B, C, X(427), X(60123)}}, {{A, B, C, X(428), X(14494)}}, {{A, B, C, X(546), X(43699)}}, {{A, B, C, X(550), X(18852)}}, {{A, B, C, X(1217), X(21735)}}, {{A, B, C, X(1585), X(43565)}}, {{A, B, C, X(1586), X(43564)}}, {{A, B, C, X(1656), X(18854)}}, {{A, B, C, X(1657), X(14938)}}, {{A, B, C, X(3346), X(58188)}}, {{A, B, C, X(3519), X(5070)}}, {{A, B, C, X(3523), X(18853)}}, {{A, B, C, X(3524), X(52441)}}, {{A, B, C, X(3525), X(40410)}}, {{A, B, C, X(3526), X(8797)}}, {{A, B, C, X(3543), X(13599)}}, {{A, B, C, X(3628), X(46168)}}, {{A, B, C, X(3830), X(54763)}}, {{A, B, C, X(3839), X(40448)}}, {{A, B, C, X(3845), X(54660)}}, {{A, B, C, X(4232), X(60144)}}, {{A, B, C, X(4846), X(49137)}}, {{A, B, C, X(5054), X(42021)}}, {{A, B, C, X(5059), X(18851)}}, {{A, B, C, X(5064), X(7612)}}, {{A, B, C, X(5073), X(18849)}}, {{A, B, C, X(6662), X(11812)}}, {{A, B, C, X(6995), X(7608)}}, {{A, B, C, X(7378), X(7607)}}, {{A, B, C, X(7408), X(53099)}}, {{A, B, C, X(7409), X(43537)}}, {{A, B, C, X(7714), X(10155)}}, {{A, B, C, X(10185), X(52284)}}, {{A, B, C, X(10194), X(55573)}}, {{A, B, C, X(10195), X(55569)}}, {{A, B, C, X(10594), X(14491)}}, {{A, B, C, X(11403), X(13603)}}, {{A, B, C, X(12101), X(54838)}}, {{A, B, C, X(12103), X(15740)}}, {{A, B, C, X(12811), X(15077)}}, {{A, B, C, X(14528), X(55570)}}, {{A, B, C, X(14861), X(15681)}}, {{A, B, C, X(14891), X(46412)}}, {{A, B, C, X(15712), X(22270)}}, {{A, B, C, X(15749), X(41991)}}, {{A, B, C, X(16251), X(58208)}}, {{A, B, C, X(18840), X(52281)}}, {{A, B, C, X(18841), X(52282)}}, {{A, B, C, X(18847), X(50691)}}, {{A, B, C, X(31363), X(50687)}}, {{A, B, C, X(31846), X(38071)}}, {{A, B, C, X(35018), X(60007)}}, {{A, B, C, X(36948), X(46219)}}, {{A, B, C, X(37174), X(43527)}}, {{A, B, C, X(52285), X(60337)}}, {{A, B, C, X(55576), X(57713)}}, {{A, B, C, X(55578), X(57714)}}
X(61886) = barycentric quotient X(i)/X(j) for these (i, j): {4, 54892}
X(61886) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10303, 16239}, {2, 10304, 15723}, {2, 14786, 6143}, {2, 15699, 5071}, {2, 17568, 17533}, {2, 20, 632}, {2, 3091, 3526}, {2, 3628, 5067}, {2, 3839, 10124}, {2, 4, 3533}, {2, 5055, 15702}, {2, 5056, 140}, {2, 5067, 3090}, {2, 5071, 15709}, {2, 6858, 6880}, {2, 6859, 6878}, {2, 6887, 6952}, {2, 6931, 6857}, {2, 6933, 17567}, {2, 6983, 6853}, {2, 7504, 443}, {2, 7571, 7386}, {3, 15687, 20}, {3, 15699, 7486}, {3, 3526, 15713}, {3, 382, 15691}, {3, 3855, 15682}, {3, 5, 3839}, {3, 5066, 17578}, {3, 5071, 3855}, {4, 17538, 5073}, {4, 3524, 550}, {4, 3544, 3850}, {4, 5067, 1656}, {4, 5071, 5068}, {5, 3628, 15703}, {5, 5054, 3146}, {5, 549, 12102}, {5, 632, 12100}, {20, 5055, 3544}, {140, 1656, 5056}, {140, 3851, 3522}, {140, 3858, 3}, {140, 5056, 4}, {376, 12100, 15710}, {376, 15719, 15705}, {376, 3090, 5}, {381, 15712, 5059}, {546, 13727, 6950}, {546, 15694, 15717}, {546, 15717, 11001}, {549, 3832, 17538}, {549, 5079, 3832}, {550, 15712, 15759}, {631, 3529, 15698}, {631, 3545, 3529}, {632, 14892, 6948}, {632, 3850, 15720}, {1656, 15720, 5055}, {2045, 2046, 3091}, {3070, 42567, 42569}, {3071, 42566, 42568}, {3090, 13725, 15712}, {3091, 15683, 3861}, {3091, 16857, 10303}, {3522, 5056, 3851}, {3523, 3854, 1657}, {3523, 5056, 3854}, {3524, 3830, 376}, {3525, 3854, 10299}, {3526, 3830, 12108}, {3526, 8703, 6931}, {3528, 10303, 15719}, {3530, 5072, 3543}, {3530, 6918, 3830}, {3624, 10172, 5818}, {3624, 30315, 5882}, {3628, 15703, 13735}, {3628, 5070, 2}, {3839, 3854, 3858}, {3843, 10304, 11541}, {3843, 15723, 14869}, {3856, 14869, 7491}, {3857, 11812, 15696}, {3860, 11539, 15718}, {5055, 15710, 3545}, {5056, 17566, 10109}, {5071, 15702, 15687}, {5072, 15717, 6848}, {5550, 9956, 7967}, {5882, 10172, 30315}, {6854, 17559, 6902}, {6898, 17582, 6951}, {6946, 11108, 6875}, {8960, 10194, 3069}, {9780, 11230, 10595}, {10109, 14869, 3843}, {10109, 15723, 10304}, {10195, 58866, 3068}, {10303, 15719, 631}, {10576, 32786, 7581}, {10577, 32785, 7582}, {11539, 12812, 382}, {11737, 15973, 15022}, {12100, 15720, 3523}, {12103, 15705, 3528}, {13727, 15717, 381}, {14093, 15687, 15683}, {14782, 14783, 548}, {14784, 14785, 5079}, {14813, 14814, 5070}, {15683, 15713, 3524}, {15699, 15713, 547}, {15705, 16239, 3525}, {15765, 18585, 14093}, {19862, 54447, 944}, {23267, 43506, 5420}, {23273, 43505, 5418}, {42095, 42945, 5343}, {42098, 42944, 5344}, {42111, 42157, 42776}, {42114, 42158, 42775}

X(61887) = X(2)X(3)∩X(6)X(51175)

Barycentrics    7*a^4+10*(b^2-c^2)^2-17*a^2*(b^2+c^2) : :
X(61887) = -10*X[2]+X[3], 8*X[6]+X[51175], 8*X[10]+X[50805], 8*X[141]+X[50962], X[265]+2*X[11693], -4*X[373]+X[13321], X[399]+8*X[45311], 8*X[551]+X[12645], 2*X[576]+7*X[51186], 8*X[597]+X[11898], 5*X[599]+4*X[5097], 8*X[620]+X[12355] and many others

X(61887) lies on these lines: {2, 3}, {6, 51175}, {10, 50805}, {17, 42611}, {18, 42610}, {61, 42953}, {62, 42952}, {141, 50962}, {265, 11693}, {373, 13321}, {395, 42817}, {396, 42818}, {399, 45311}, {541, 15046}, {542, 55703}, {551, 12645}, {576, 51186}, {597, 11898}, {599, 5097}, {620, 12355}, {1125, 50798}, {1132, 9691}, {1327, 6450}, {1328, 6449}, {1350, 25565}, {1351, 20582}, {1482, 3828}, {1698, 11278}, {3055, 7739}, {3311, 42603}, {3312, 42602}, {3316, 6501}, {3317, 6500}, {3411, 49903}, {3412, 49904}, {3582, 31479}, {3589, 50955}, {3616, 34748}, {3619, 51214}, {3624, 18526}, {3631, 51174}, {3634, 3656}, {3636, 50804}, {3653, 10175}, {3655, 19862}, {3679, 33179}, {3739, 51039}, {3763, 37517}, {4698, 51040}, {4745, 61276}, {5008, 37637}, {5050, 48310}, {5093, 21356}, {5102, 14848}, {5309, 31467}, {5418, 43887}, {5420, 43888}, {5461, 13188}, {5476, 55722}, {5544, 44569}, {5550, 50824}, {5587, 31662}, {5645, 44555}, {5650, 54047}, {5655, 6723}, {5779, 60999}, {5790, 25055}, {5886, 38066}, {5891, 10219}, {5943, 54048}, {6199, 43211}, {6221, 43254}, {6321, 22247}, {6329, 50961}, {6361, 50825}, {6395, 43212}, {6398, 43255}, {6419, 43885}, {6420, 43886}, {6427, 10195}, {6428, 10194}, {6431, 10577}, {6432, 10576}, {6433, 6565}, {6434, 6564}, {6437, 13785}, {6438, 13665}, {6459, 10137}, {6460, 10138}, {6480, 43318}, {6481, 43319}, {6496, 43210}, {6497, 43209}, {6519, 42417}, {6522, 42418}, {6688, 23039}, {6721, 11632}, {6722, 8724}, {7581, 42639}, {7582, 42640}, {7585, 43881}, {7586, 43882}, {7988, 28198}, {8148, 19877}, {8252, 18512}, {8253, 18510}, {8960, 42526}, {8976, 13847}, {9466, 32520}, {9778, 61267}, {10168, 18440}, {10170, 16226}, {10171, 38068}, {10172, 10246}, {10187, 42533}, {10188, 42532}, {10247, 38022}, {10516, 55695}, {10540, 22112}, {10653, 43100}, {10654, 43107}, {11178, 39899}, {11179, 50954}, {11180, 55705}, {11230, 16200}, {11231, 38021}, {11237, 37587}, {11480, 43245}, {11481, 43244}, {11482, 22165}, {11485, 42910}, {11486, 42911}, {11531, 19876}, {11645, 55685}, {11694, 15081}, {11935, 43572}, {12017, 47354}, {12117, 15092}, {12331, 45310}, {12702, 51073}, {12900, 20126}, {13108, 44562}, {13391, 33879}, {13690, 26341}, {13811, 26348}, {13846, 13951}, {14535, 44381}, {14537, 44535}, {14643, 38725}, {14845, 15082}, {14971, 15561}, {15038, 17811}, {15061, 38792}, {15069, 46267}, {15087, 17825}, {15533, 25555}, {15602, 39563}, {16187, 22115}, {16241, 42125}, {16242, 42128}, {16267, 16645}, {16268, 16644}, {16772, 41120}, {16773, 41119}, {16960, 43545}, {16961, 43544}, {16962, 16967}, {16963, 16966}, {18481, 50800}, {18487, 61340}, {18493, 50821}, {18525, 34595}, {19130, 55607}, {19872, 31162}, {19878, 50796}, {19924, 55618}, {20423, 34573}, {22236, 49908}, {22238, 49907}, {22330, 51188}, {23061, 53124}, {23234, 34127}, {23302, 42951}, {23303, 42950}, {24206, 55711}, {25561, 55688}, {28204, 30392}, {30308, 48661}, {31253, 50806}, {31399, 51108}, {31730, 50807}, {32785, 45385}, {32786, 45384}, {32885, 34803}, {33540, 37490}, {33878, 51128}, {34631, 46932}, {34641, 61277}, {34754, 37835}, {34755, 37832}, {35000, 61158}, {36969, 42474}, {36970, 42475}, {36990, 55683}, {37727, 51109}, {38024, 38179}, {38028, 38074}, {38042, 38314}, {38043, 38092}, {38065, 38108}, {38072, 55591}, {38073, 38113}, {38080, 51514}, {38081, 51515}, {38082, 51516}, {38084, 51517}, {38085, 51518}, {38093, 38318}, {38171, 61023}, {38224, 38746}, {38229, 52695}, {38732, 41134}, {38752, 59376}, {38758, 57298}, {38770, 57297}, {38782, 57303}, {38802, 57331}, {39561, 47352}, {39874, 50987}, {41107, 43239}, {41108, 43238}, {41121, 42937}, {41122, 42936}, {41150, 61282}, {41943, 42153}, {41944, 42156}, {42089, 43104}, {42092, 43101}, {42095, 42972}, {42098, 42973}, {42154, 42914}, {42155, 42915}, {42274, 52045}, {42277, 52046}, {42283, 42600}, {42284, 42601}, {42488, 42989}, {42489, 42988}, {42527, 58866}, {42590, 42999}, {42591, 42998}, {42625, 42919}, {42626, 42918}, {42631, 42774}, {42632, 42773}, {42924, 49874}, {42925, 49873}, {43273, 55691}, {43621, 51129}, {46264, 50957}, {46933, 50823}, {47353, 58445}, {48311, 59383}, {48312, 59384}, {48881, 50964}, {48895, 51141}, {48905, 51137}, {48910, 55642}, {50810, 61272}, {50828, 61261}, {50963, 54169}, {50977, 55582}, {50984, 55639}, {53023, 55627}, {53127, 59634}, {54131, 55594}, {57822, 57927}, {58238, 61273}, {58441, 61266}, {60922, 60986}

X(61887) = midpoint of X(i) and X(j) for these {i,j}: {381, 15706}, {3545, 15708}, {3839, 15710}
X(61887) = reflection of X(i) in X(j) for these {i,j}: {15688, 15706}, {15689, 15710}, {15706, 5054}, {15707, 15709}, {15708, 11539}, {15710, 549}, {3, 15708}
X(61887) = inverse of X(10124) in orthocentroidal circle
X(61887) = inverse of X(10124) in Yff hyperbola
X(61887) = complement of X(15709)
X(61887) = anticomplement of X(61874)
X(61887) = pole of line {523, 10124} with respect to the orthocentroidal circle
X(61887) = pole of line {6, 10124} with respect to the Kiepert hyperbola
X(61887) = pole of line {523, 10124} with respect to the Yff hyperbola
X(61887) = pole of line {69, 46267} with respect to the Wallace hyperbola
X(61887) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(95), X(15723)}}, {{A, B, C, X(264), X(10124)}}, {{A, B, C, X(381), X(57927)}}, {{A, B, C, X(632), X(57822)}}, {{A, B, C, X(3526), X(55958)}}, {{A, B, C, X(3529), X(14938)}}, {{A, B, C, X(3533), X(36889)}}, {{A, B, C, X(15694), X(40410)}}, {{A, B, C, X(15710), X(18317)}}, {{A, B, C, X(46219), X(57895)}}
X(61887) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15702, 16239}, {2, 15703, 1656}, {2, 1656, 381}, {2, 3, 15723}, {2, 3090, 549}, {2, 3543, 3533}, {2, 3545, 11539}, {2, 3628, 15703}, {2, 376, 632}, {2, 381, 3526}, {2, 4, 10124}, {2, 5, 15694}, {2, 5056, 15702}, {2, 5071, 140}, {2, 6931, 15670}, {2, 7486, 376}, {3, 15690, 14093}, {3, 15694, 11812}, {3, 3543, 3534}, {3, 3830, 15686}, {3, 3843, 5059}, {3, 3850, 382}, {3, 3851, 3853}, {3, 5055, 3545}, {4, 10124, 15701}, {5, 10303, 5073}, {5, 140, 3529}, {5, 549, 12101}, {20, 15713, 15718}, {30, 11539, 15708}, {30, 15709, 15707}, {30, 15710, 15689}, {30, 5054, 15706}, {30, 549, 15710}, {140, 3830, 15700}, {140, 3832, 3}, {140, 5071, 3830}, {140, 5072, 15696}, {376, 10109, 3851}, {376, 3843, 13633}, {376, 7486, 10109}, {381, 3526, 15693}, {381, 3534, 5076}, {382, 1656, 3090}, {546, 15692, 15685}, {547, 15686, 5071}, {547, 3845, 5056}, {549, 12101, 3522}, {631, 15681, 15716}, {631, 5066, 15681}, {1656, 3526, 5079}, {1656, 5054, 5055}, {3090, 16858, 3627}, {3090, 3522, 5}, {3091, 12100, 15684}, {3522, 3543, 11001}, {3523, 15687, 15695}, {3524, 10304, 15711}, {3524, 3529, 10304}, {3524, 3545, 3543}, {3524, 5054, 15720}, {3526, 5079, 1657}, {3528, 15703, 6861}, {3544, 15683, 3860}, {3545, 11001, 3839}, {3545, 15708, 30}, {3545, 3839, 3850}, {3830, 5071, 5072}, {3839, 12101, 14269}, {3860, 15712, 15683}, {5055, 15703, 15699}, {5056, 15702, 3845}, {5068, 14869, 17800}, {5070, 15703, 2}, {5071, 15719, 3832}, {5073, 15694, 15722}, {10124, 14892, 17504}, {10304, 15696, 15688}, {11178, 50664, 51027}, {11297, 11298, 11159}, {11539, 15699, 547}, {11540, 12812, 15687}, {11540, 15687, 3523}, {11737, 15713, 20}, {11812, 15711, 15719}, {14269, 15694, 3524}, {14892, 17504, 4}, {15694, 15722, 10303}, {15707, 15709, 5054}, {15765, 18585, 3528}, {21356, 38079, 5093}, {21358, 38317, 14848}, {25055, 38083, 5790}, {38022, 53620, 10247}

X(61888) = X(2)X(3)∩X(6)X(43554)

Barycentrics    13*a^4+19*(b^2-c^2)^2-32*a^2*(b^2+c^2) : :
X(61888) = -19*X[2]+2*X[3], -26*X[551]+9*X[61285], 5*X[3241]+12*X[38176], 5*X[3616]+12*X[38083], 5*X[3617]+12*X[38022], 5*X[3620]+12*X[38079], 5*X[3623]+12*X[38081], 14*X[3624]+3*X[38074], 16*X[3828]+X[34631], 3*X[5603]+14*X[19876], 5*X[5818]+12*X[19883], 16*X[6721]+X[12243] and many others

X(61888) lies on these lines: {2, 3}, {6, 43554}, {17, 49861}, {18, 49862}, {397, 33604}, {398, 33605}, {551, 61285}, {3241, 38176}, {3316, 32788}, {3317, 32787}, {3411, 49860}, {3412, 49859}, {3616, 38083}, {3617, 38022}, {3620, 38079}, {3623, 38081}, {3624, 38074}, {3828, 34631}, {5334, 43493}, {5335, 43494}, {5365, 42791}, {5366, 42792}, {5603, 19876}, {5818, 19883}, {6490, 43509}, {6491, 43510}, {6492, 42262}, {6493, 42265}, {6721, 12243}, {7581, 34091}, {7582, 34089}, {7612, 60616}, {7788, 32867}, {7856, 38223}, {7967, 10172}, {8227, 51075}, {9540, 14226}, {9541, 43790}, {9956, 50818}, {10155, 60143}, {10187, 42977}, {10188, 42976}, {10219, 11459}, {10595, 19875}, {11693, 15025}, {13903, 42640}, {13935, 14241}, {13961, 42639}, {14494, 60629}, {15059, 56567}, {16192, 51074}, {16267, 42480}, {16268, 42481}, {16772, 49873}, {16773, 49874}, {18583, 51179}, {19872, 28194}, {19877, 51709}, {21358, 51132}, {23267, 41954}, {23269, 52046}, {23273, 41953}, {23275, 52045}, {23302, 43543}, {23303, 43542}, {24206, 50974}, {25055, 47745}, {25555, 50992}, {25565, 54170}, {31399, 51110}, {31412, 43255}, {32785, 42603}, {32786, 42602}, {32789, 41951}, {32790, 41952}, {32818, 32885}, {32822, 32884}, {32823, 32883}, {33602, 42148}, {33603, 42147}, {33606, 42939}, {33607, 42938}, {34573, 54132}, {34627, 54447}, {37647, 46951}, {37671, 52718}, {38021, 51073}, {38064, 42786}, {38066, 46931}, {38072, 51128}, {38080, 61006}, {38314, 50804}, {40330, 48310}, {41119, 42937}, {41120, 42936}, {41943, 42910}, {41944, 42911}, {42089, 43771}, {42092, 43772}, {42095, 43482}, {42098, 43481}, {42133, 42475}, {42134, 42474}, {42417, 60302}, {42418, 60301}, {42488, 49813}, {42489, 49812}, {42494, 42510}, {42495, 42511}, {42516, 43199}, {42517, 43200}, {42561, 43254}, {42572, 60620}, {42573, 60621}, {42574, 43791}, {42575, 43792}, {42596, 46335}, {42597, 46334}, {42600, 52666}, {42601, 52667}, {42610, 43447}, {42611, 43446}, {42633, 42951}, {42634, 42950}, {42894, 43372}, {42895, 43373}, {42898, 49906}, {42899, 49905}, {42978, 49903}, {42979, 49904}, {43100, 49875}, {43107, 49876}, {43238, 49827}, {43239, 49826}, {43403, 43464}, {43404, 43463}, {43775, 49907}, {43776, 49908}, {47353, 51127}, {50961, 59373}, {51023, 58445}, {51068, 61276}, {51129, 55651}, {51142, 53858}, {51177, 51537}, {51215, 51732}, {53098, 60627}, {53103, 54616}, {54523, 60183}

X(61888) = midpoint of X(i) and X(j) for these {i,j}: {2, 7486}
X(61888) = reflection of X(i) in X(j) for these {i,j}: {3533, 2}
X(61888) = inverse of X(61861) in orthocentroidal circle
X(61888) = inverse of X(61861) in Yff hyperbola
X(61888) = complement of X(61846)
X(61888) = anticomplement of X(61872)
X(61888) = pole of line {523, 61861} with respect to the orthocentroidal circle
X(61888) = pole of line {6, 43517} with respect to the Kiepert hyperbola
X(61888) = pole of line {523, 61861} with respect to the Yff hyperbola
X(61888) = pole of line {69, 61864} with respect to the Wallace hyperbola
X(61888) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1494), X(3533)}}, {{A, B, C, X(3545), X(57927)}}, {{A, B, C, X(3857), X(31846)}}, {{A, B, C, X(7408), X(54523)}}, {{A, B, C, X(7409), X(60185)}}, {{A, B, C, X(8797), X(11539)}}, {{A, B, C, X(10124), X(36889)}}, {{A, B, C, X(10155), X(52301)}}, {{A, B, C, X(13599), X(50690)}}, {{A, B, C, X(14938), X(49137)}}, {{A, B, C, X(15319), X(46936)}}, {{A, B, C, X(15709), X(40410)}}, {{A, B, C, X(17578), X(54763)}}, {{A, B, C, X(31371), X(35407)}}, {{A, B, C, X(36948), X(47598)}}, {{A, B, C, X(37174), X(60616)}}, {{A, B, C, X(50689), X(54660)}}
X(61888) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10304, 632}, {2, 15692, 15723}, {2, 15699, 3090}, {2, 16401, 17528}, {2, 1656, 3545}, {2, 30, 3533}, {2, 3091, 11539}, {2, 3543, 10124}, {2, 3839, 3526}, {2, 5055, 631}, {2, 5056, 5054}, {2, 6931, 17561}, {2, 7486, 30}, {4, 15702, 15715}, {4, 17800, 6905}, {20, 15705, 8703}, {20, 5068, 546}, {140, 15682, 3524}, {376, 15684, 11001}, {376, 15714, 3528}, {376, 547, 5071}, {376, 631, 15700}, {381, 15681, 12101}, {381, 15694, 14891}, {381, 15701, 15691}, {381, 15703, 15699}, {381, 15723, 15701}, {381, 5073, 14893}, {381, 549, 20}, {381, 8703, 3543}, {546, 10124, 549}, {631, 5068, 11541}, {1010, 1656, 3832}, {1656, 16239, 15022}, {1656, 3628, 13735}, {3090, 3545, 10109}, {3091, 11539, 15698}, {3524, 5071, 381}, {3526, 3839, 15719}, {3533, 7486, 3544}, {3544, 16852, 16418}, {3545, 10299, 3830}, {3545, 15709, 15688}, {3839, 15719, 17538}, {3845, 10303, 15710}, {3860, 15706, 5059}, {5054, 11737, 15683}, {5055, 8703, 5068}, {5056, 15683, 11737}, {5056, 7397, 12811}, {5066, 15708, 3529}, {5070, 15699, 2}, {5071, 15702, 4}, {7486, 13740, 15712}, {10109, 15699, 1656}, {10299, 16239, 3525}, {11001, 15723, 15702}, {12811, 15685, 3839}, {14891, 15694, 15721}, {15022, 16239, 10299}, {15683, 15714, 376}, {15691, 15701, 15692}, {15692, 15723, 15709}, {42474, 42501, 42134}, {42475, 42500, 42133}, {42950, 42985, 42634}, {42951, 42984, 42633}, {43554, 43555, 6}

X(61889) = X(2)X(3)∩X(13)X(43464)

Barycentrics    11*a^4+17*(b^2-c^2)^2-28*a^2*(b^2+c^2) : :
X(61889) = -17*X[2]+2*X[3], -16*X[141]+X[51179], -16*X[1125]+X[50818], -16*X[3589]+X[50974], 14*X[3624]+X[34627], -16*X[3634]+X[50810], 2*X[3656]+13*X[19877], -16*X[3828]+X[12245], -16*X[4698]+X[51043], -X[5890]+16*X[10219], -16*X[6329]+X[51178], -16*X[6722]+X[12243] and many others

X(61889) lies on these lines: {2, 3}, {13, 43464}, {14, 43463}, {17, 49812}, {18, 49813}, {141, 51179}, {395, 42986}, {396, 42987}, {1125, 50818}, {3311, 34089}, {3312, 34091}, {3316, 19053}, {3317, 19054}, {3411, 49811}, {3412, 49810}, {3582, 8164}, {3584, 47743}, {3589, 50974}, {3591, 31487}, {3624, 34627}, {3634, 50810}, {3656, 19877}, {3828, 12245}, {4698, 51043}, {5318, 43420}, {5321, 43421}, {5485, 53108}, {5702, 52704}, {5890, 10219}, {5965, 38223}, {6329, 51178}, {6564, 43315}, {6565, 43314}, {6722, 12243}, {7581, 42602}, {7582, 42603}, {7603, 46453}, {7608, 60641}, {7612, 60238}, {7852, 55762}, {7867, 55741}, {7988, 28232}, {7999, 58470}, {9624, 51069}, {9693, 42417}, {9780, 34631}, {10150, 38227}, {10155, 60628}, {10168, 39874}, {10172, 25055}, {11179, 42786}, {11180, 47355}, {11230, 53620}, {11465, 14831}, {11488, 16268}, {11489, 16267}, {11668, 18842}, {12045, 61136}, {12317, 45311}, {13172, 22247}, {13665, 43375}, {13785, 43374}, {13846, 13939}, {13847, 13886}, {14482, 31489}, {14494, 60277}, {14845, 33879}, {16191, 19875}, {16644, 42778}, {16645, 42777}, {16772, 49824}, {16773, 49825}, {16960, 37641}, {16961, 37640}, {16962, 42516}, {16963, 42517}, {16966, 42478}, {16967, 42479}, {17825, 54434}, {18492, 50819}, {18581, 42799}, {18582, 42800}, {18840, 54645}, {18841, 54644}, {19116, 60312}, {19117, 60311}, {19878, 50811}, {19883, 28236}, {21356, 38317}, {25565, 51212}, {28202, 61266}, {28228, 38021}, {31162, 51073}, {31253, 50809}, {31399, 51105}, {31412, 43506}, {32836, 37647}, {32867, 37671}, {33602, 43440}, {33603, 43441}, {34573, 50967}, {34595, 50796}, {34632, 61268}, {34718, 46932}, {35770, 43568}, {35771, 43569}, {36967, 42473}, {36968, 42472}, {36969, 42931}, {36970, 42930}, {36996, 60999}, {38082, 59375}, {38098, 61275}, {38318, 59374}, {40693, 42521}, {40694, 42520}, {41100, 42494}, {41101, 42495}, {41112, 42937}, {41113, 42936}, {41152, 53858}, {41943, 43009}, {41944, 43008}, {42089, 42973}, {42092, 42972}, {42119, 42904}, {42120, 42905}, {42215, 43517}, {42216, 43518}, {42488, 49862}, {42489, 49861}, {42492, 43253}, {42493, 43252}, {42506, 42978}, {42507, 42979}, {42510, 42581}, {42511, 42580}, {42561, 43505}, {42584, 43477}, {42585, 43478}, {42588, 42921}, {42589, 42920}, {42596, 42632}, {42597, 42631}, {42608, 43414}, {42609, 43413}, {42610, 42999}, {42611, 42998}, {42637, 43521}, {42638, 43522}, {42725, 43623}, {42726, 43622}, {42912, 43329}, {42913, 43328}, {43014, 43025}, {43015, 43024}, {43019, 61719}, {43028, 43403}, {43029, 43404}, {43211, 43317}, {43212, 43316}, {43238, 49876}, {43239, 49875}, {43254, 43509}, {43255, 43510}, {43273, 51127}, {43621, 51141}, {46930, 50872}, {46934, 50798}, {50960, 55676}, {51072, 61276}, {51085, 61256}, {51126, 51176}, {51128, 54131}, {51211, 55604}, {53098, 60216}, {53103, 60648}, {54522, 60183}, {54920, 60643}, {54921, 60616}, {56059, 60127}, {60123, 60283}, {60150, 60644}, {60335, 60646}

X(61889) = midpoint of X(i) and X(j) for these {i,j}: {631, 3545}, {3858, 17504}, {5076, 15689}, {14093, 14269}
X(61889) = reflection of X(i) in X(j) for these {i,j}: {10304, 15693}, {1656, 15699}, {15689, 15714}, {15692, 5054}, {15695, 17504}, {17538, 10304}, {17578, 14269}, {3545, 5071}, {5054, 632}
X(61889) = inverse of X(61859) in orthocentroidal circle
X(61889) = inverse of X(61859) in Yff hyperbola
X(61889) = complement of X(61844)
X(61889) = anticomplement of X(61871)
X(61889) = pole of line {523, 61859} with respect to the orthocentroidal circle
X(61889) = pole of line {6, 61859} with respect to the Kiepert hyperbola
X(61889) = pole of line {523, 61859} with respect to the Yff hyperbola
X(61889) = pole of line {69, 10124} with respect to the Wallace hyperbola
X(61889) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(10124)}}, {{A, B, C, X(3525), X(55958)}}, {{A, B, C, X(3526), X(36889)}}, {{A, B, C, X(3530), X(18853)}}, {{A, B, C, X(3533), X(57822)}}, {{A, B, C, X(3627), X(54763)}}, {{A, B, C, X(3843), X(54660)}}, {{A, B, C, X(3858), X(31846)}}, {{A, B, C, X(4232), X(53108)}}, {{A, B, C, X(5071), X(57927)}}, {{A, B, C, X(6995), X(54645)}}, {{A, B, C, X(7378), X(54644)}}, {{A, B, C, X(7408), X(54522)}}, {{A, B, C, X(8797), X(15694)}}, {{A, B, C, X(11668), X(52284)}}, {{A, B, C, X(13599), X(50691)}}, {{A, B, C, X(14893), X(54667)}}, {{A, B, C, X(14938), X(49136)}}, {{A, B, C, X(15702), X(40410)}}, {{A, B, C, X(15713), X(46921)}}, {{A, B, C, X(15723), X(36948)}}, {{A, B, C, X(18847), X(35404)}}, {{A, B, C, X(18851), X(49137)}}, {{A, B, C, X(18854), X(46936)}}, {{A, B, C, X(37174), X(60238)}}, {{A, B, C, X(38335), X(54838)}}, {{A, B, C, X(52281), X(60641)}}
X(61889) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15022, 15721}, {2, 15703, 5067}, {2, 1656, 5071}, {2, 20, 10124}, {2, 3091, 15694}, {2, 3523, 15723}, {2, 3543, 3526}, {2, 3545, 15709}, {2, 376, 3533}, {2, 381, 3525}, {2, 3839, 11539}, {2, 5055, 3524}, {2, 5056, 549}, {2, 5059, 17678}, {4, 15681, 15682}, {4, 3525, 3530}, {4, 5054, 15710}, {5, 11540, 15681}, {30, 10304, 17538}, {30, 14269, 17578}, {30, 15693, 10304}, {30, 15699, 1656}, {30, 15714, 15689}, {30, 17504, 15695}, {30, 5054, 15692}, {30, 5071, 3545}, {140, 14269, 15705}, {381, 15713, 3522}, {381, 15722, 15704}, {381, 3525, 15698}, {547, 12103, 10109}, {547, 8703, 5079}, {549, 15022, 6833}, {549, 3843, 15697}, {631, 1656, 3090}, {1656, 12812, 7486}, {1656, 5070, 632}, {3090, 10299, 5}, {3090, 3533, 3855}, {3522, 7486, 12812}, {3526, 10109, 3543}, {3530, 5054, 15708}, {3543, 10109, 3544}, {3628, 15703, 2}, {3830, 10303, 15715}, {3845, 15721, 3528}, {3850, 15700, 15640}, {3851, 11812, 15683}, {5055, 15688, 14892}, {5066, 15714, 5076}, {5066, 15723, 3523}, {10299, 15682, 376}, {11539, 14892, 15688}, {11540, 15682, 15719}, {11737, 15701, 3146}, {12812, 15713, 381}, {14093, 14269, 30}, {14093, 17578, 11001}, {14891, 17678, 15702}, {14892, 15688, 3839}, {15022, 15721, 3845}, {15682, 15698, 15690}, {15682, 15702, 10299}, {15690, 15713, 15693}, {15693, 15702, 631}, {15709, 15719, 5054}, {16239, 16371, 4}, {16960, 42513, 37641}, {16961, 42512, 37640}, {17538, 17678, 6889}, {19883, 54447, 38074}

X(61890) = X(2)X(3)∩X(10)X(58237)

Barycentrics    16*a^4+25*(b^2-c^2)^2-41*a^2*(b^2+c^2) : :
X(61890) = -25*X[2]+3*X[3], 25*X[10]+8*X[58237], -3*X[1483]+14*X[51110], 2*X[3654]+9*X[61270], 6*X[3817]+5*X[50825], 10*X[3828]+X[11278], 5*X[4669]+6*X[33179], 2*X[4677]+9*X[10283], 2*X[4745]+9*X[11230], 6*X[5097]+5*X[22165], 6*X[5102]+5*X[50978], 6*X[5587]+5*X[50832] and many others

X(61890) lies on these lines: {2, 3}, {10, 58237}, {15, 43247}, {16, 43246}, {590, 42640}, {615, 42639}, {1327, 6434}, {1328, 6433}, {1483, 51110}, {3654, 61270}, {3817, 50825}, {3828, 11278}, {4669, 33179}, {4677, 10283}, {4745, 11230}, {5097, 22165}, {5102, 50978}, {5587, 50832}, {5603, 50822}, {5886, 58241}, {5901, 51066}, {6429, 43254}, {6430, 43255}, {6431, 42579}, {6432, 42578}, {6437, 42609}, {6438, 42608}, {6480, 42417}, {6481, 42418}, {9956, 51109}, {10172, 51108}, {10516, 50987}, {14853, 51184}, {15300, 38229}, {16200, 50823}, {16966, 42634}, {16967, 42633}, {18357, 58231}, {18583, 50993}, {19053, 42526}, {19054, 42527}, {19876, 58248}, {20252, 36767}, {20582, 37517}, {23302, 42532}, {23303, 42533}, {25055, 61295}, {25565, 51128}, {30308, 61614}, {30392, 38138}, {31399, 51106}, {31662, 50796}, {34507, 41153}, {34754, 49908}, {34755, 49907}, {35255, 43792}, {35256, 43791}, {35770, 42606}, {35771, 42607}, {38042, 51071}, {38081, 51093}, {38083, 51103}, {38155, 50824}, {38317, 50991}, {38746, 49102}, {41119, 43028}, {41120, 43029}, {41121, 42121}, {41122, 42124}, {41154, 51524}, {42089, 43109}, {42092, 43108}, {42122, 42475}, {42123, 42474}, {42129, 49862}, {42132, 49861}, {42135, 42791}, {42138, 42792}, {42143, 42511}, {42146, 42510}, {42149, 42420}, {42152, 42419}, {42215, 43887}, {42216, 43888}, {42270, 42525}, {42273, 42524}, {42488, 49904}, {42489, 49903}, {42492, 42912}, {42493, 42913}, {42496, 49812}, {42497, 49813}, {42498, 43293}, {42499, 43292}, {42502, 43010}, {42503, 43011}, {42508, 43416}, {42509, 43417}, {42528, 42595}, {42529, 42594}, {42566, 43381}, {42567, 43380}, {42580, 43107}, {42581, 43100}, {42635, 43774}, {42636, 43773}, {42922, 49874}, {42923, 49873}, {43797, 43889}, {43798, 43890}, {47354, 55695}, {48310, 50664}, {49859, 49905}, {49860, 49906}, {50811, 61260}, {50865, 61267}, {50984, 55640}, {50988, 55680}, {51025, 55685}, {51105, 61283}, {51127, 55691}, {54479, 56627}, {54480, 56628}, {58227, 61262}

X(61890) = midpoint of X(i) and X(j) for these {i,j}: {381, 15717}, {3855, 15718}, {5056, 15723}, {5072, 15721}
X(61890) = reflection of X(i) in X(j) for these {i,j}: {15718, 140}, {549, 3525}, {5056, 547}
X(61890) = inverse of X(61857) in orthocentroidal circle
X(61890) = inverse of X(61857) in Yff hyperbola
X(61890) = complement of X(61843)
X(61890) = pole of line {523, 61857} with respect to the orthocentroidal circle
X(61890) = pole of line {185, 58201} with respect to the Jerabek hyperbola
X(61890) = pole of line {6, 61857} with respect to the Kiepert hyperbola
X(61890) = pole of line {523, 61857} with respect to the Yff hyperbola
X(61890) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1105), X(58201)}}, {{A, B, C, X(3832), X(31846)}}, {{A, B, C, X(10109), X(57927)}}, {{A, B, C, X(11540), X(55958)}}, {{A, B, C, X(15713), X(40410)}}
X(61890) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12100, 632}, {2, 15682, 3526}, {2, 15719, 15723}, {2, 1656, 10109}, {2, 3090, 3534}, {2, 3534, 10124}, {2, 381, 11540}, {2, 3845, 11539}, {2, 5, 15713}, {2, 5055, 12100}, {2, 5056, 15719}, {2, 5071, 15701}, {2, 547, 3845}, {20, 3525, 15720}, {30, 140, 15718}, {30, 547, 5056}, {140, 15688, 549}, {381, 15717, 30}, {547, 3850, 5055}, {549, 15699, 1656}, {549, 550, 15705}, {632, 5055, 15687}, {1656, 13735, 3628}, {1656, 3545, 547}, {1656, 5070, 3525}, {3090, 15712, 5}, {3533, 15710, 15702}, {3543, 15714, 15686}, {3543, 15719, 6891}, {3545, 15702, 20}, {3628, 15703, 15699}, {3845, 11812, 8703}, {3853, 10124, 15708}, {3860, 15701, 550}, {5055, 14093, 3544}, {5055, 15702, 3850}, {5066, 11812, 11001}, {5070, 11346, 548}, {5071, 15701, 3860}, {5079, 15709, 14893}, {8703, 11539, 11812}, {8703, 15698, 15714}, {8703, 15704, 15697}, {10109, 15690, 3545}, {10109, 16239, 15690}, {11540, 15711, 14869}, {12100, 15710, 15711}, {14869, 15687, 15710}

X(61891) = X(2)X(3)∩X(6)X(42526)

Barycentrics    13*a^4+22*(b^2-c^2)^2-35*a^2*(b^2+c^2) : :
X(61891) = -22*X[2]+3*X[3], 11*X[599]+8*X[55715], 3*X[1351]+16*X[51143], 3*X[1482]+16*X[51069], 55*X[3763]+2*X[55723], X[4677]+18*X[11230], 16*X[4745]+3*X[50805], 15*X[5093]+4*X[50985], 15*X[5790]+4*X[51087], 15*X[5886]+4*X[50827], 12*X[5901]+7*X[51068], 16*X[8584]+3*X[51175] and many others

X(61891) lies on these lines: {2, 3}, {6, 42526}, {395, 42950}, {396, 42951}, {485, 6495}, {486, 6494}, {599, 55715}, {1327, 43315}, {1328, 43314}, {1351, 51143}, {1482, 51069}, {3763, 55723}, {4677, 11230}, {4745, 50805}, {5093, 50985}, {5790, 51087}, {5886, 50827}, {5901, 51068}, {6199, 43317}, {6200, 43385}, {6221, 43513}, {6395, 43316}, {6396, 43384}, {6398, 43514}, {6435, 13846}, {6436, 13847}, {6498, 43430}, {6499, 43431}, {7878, 38223}, {8584, 51175}, {8972, 42640}, {9691, 43505}, {9779, 50825}, {9956, 51110}, {10165, 50800}, {10171, 50806}, {10172, 51071}, {10175, 50797}, {10302, 54645}, {10516, 55700}, {11178, 55709}, {11668, 60282}, {11669, 60216}, {12645, 51103}, {13607, 51109}, {13886, 60294}, {13939, 60293}, {13941, 42639}, {14561, 50982}, {14848, 50993}, {15533, 38317}, {15534, 55714}, {16962, 42610}, {16963, 42611}, {16964, 43441}, {16965, 43440}, {16966, 42480}, {16967, 42481}, {18493, 19876}, {18583, 50994}, {23302, 42503}, {23303, 42502}, {31399, 51107}, {31489, 39593}, {32787, 42607}, {32788, 42606}, {32892, 34803}, {33416, 42505}, {33417, 42504}, {33606, 42532}, {33607, 42533}, {35255, 42575}, {35256, 42574}, {36362, 48312}, {36363, 48311}, {38079, 50992}, {38082, 60971}, {38083, 51093}, {38318, 60963}, {38751, 41147}, {39899, 42786}, {41107, 43028}, {41108, 43029}, {41112, 42691}, {41113, 42690}, {41121, 42800}, {41122, 42799}, {42093, 43331}, {42094, 43330}, {42095, 42509}, {42098, 42508}, {42111, 42688}, {42114, 42689}, {42121, 49874}, {42124, 49873}, {42125, 42955}, {42126, 42475}, {42127, 42474}, {42128, 42954}, {42129, 43333}, {42132, 43332}, {42143, 49876}, {42146, 49875}, {42153, 42976}, {42156, 42977}, {42274, 42417}, {42277, 42418}, {42419, 42590}, {42420, 42591}, {42490, 42964}, {42491, 42965}, {42498, 43325}, {42499, 43324}, {42600, 43337}, {42601, 43336}, {42795, 42930}, {42796, 42931}, {42815, 49907}, {42816, 49908}, {42817, 43229}, {42818, 43228}, {42914, 43301}, {42915, 43300}, {42962, 43420}, {42963, 43421}, {43150, 47352}, {47355, 55702}, {50798, 51108}, {50807, 58441}, {50832, 54448}, {50954, 51138}, {50956, 55682}, {50962, 50991}, {51092, 51515}, {51140, 51185}, {51186, 55717}, {53023, 55621}, {53104, 60283}, {53108, 60228}, {54048, 58470}, {54131, 55592}, {54522, 60643}, {54608, 60644}, {54643, 56059}, {54644, 60239}, {54734, 60278}, {54851, 60100}, {60175, 60238}, {60192, 60277}, {60333, 60641}

X(61891) = inverse of X(11540) in orthocentroidal circle
X(61891) = inverse of X(11540) in Yff hyperbola
X(61891) = complement of X(61838)
X(61891) = pole of line {523, 11540} with respect to the orthocentroidal circle
X(61891) = pole of line {6, 11540} with respect to the Kiepert hyperbola
X(61891) = pole of line {523, 11540} with respect to the Yff hyperbola
X(61891) = intersection, other than A, B, C, of circumconics {{A, B, C, X(264), X(11540)}}, {{A, B, C, X(3861), X(31846)}}, {{A, B, C, X(10301), X(54645)}}, {{A, B, C, X(13623), X(15697)}}, {{A, B, C, X(15701), X(40410)}}, {{A, B, C, X(52285), X(54851)}}
X(61891) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10109, 3}, {2, 15682, 11539}, {2, 15701, 15723}, {2, 15719, 632}, {2, 3090, 3845}, {2, 3545, 15713}, {2, 3845, 15694}, {2, 4, 11540}, {2, 5071, 12100}, {3, 3854, 382}, {4, 15709, 15692}, {4, 15710, 15683}, {4, 15717, 12103}, {4, 3628, 5070}, {4, 547, 5055}, {5, 15709, 15684}, {381, 3526, 15706}, {381, 5054, 15696}, {549, 5055, 5072}, {549, 5066, 15640}, {632, 3860, 15719}, {1656, 5054, 547}, {1656, 5070, 5079}, {1656, 5072, 7486}, {1657, 15688, 15691}, {3525, 11737, 15689}, {3525, 3533, 452}, {3526, 5055, 381}, {3526, 5079, 4}, {3530, 15694, 5054}, {3534, 15716, 10304}, {3534, 15759, 15688}, {3545, 15700, 5076}, {3545, 15713, 15685}, {3845, 15716, 1657}, {3850, 15713, 6838}, {3851, 15722, 15682}, {3857, 14890, 376}, {3860, 15719, 15681}, {4190, 15721, 3545}, {5054, 8703, 15693}, {5055, 15684, 5}, {5055, 15703, 3628}, {5056, 10124, 14269}, {5056, 16408, 631}, {5066, 15698, 3830}, {5067, 15699, 15703}, {11001, 15692, 8703}, {11539, 15682, 15722}, {13735, 14019, 20}, {15682, 15722, 14093}, {15683, 15695, 3534}, {15684, 15701, 15759}, {15685, 15713, 15700}, {15691, 15701, 15716}, {15699, 15703, 1656}, {15709, 15723, 3526}, {15709, 15759, 15701}, {42274, 43526, 43381}, {42277, 43525, 43380}, {42526, 42527, 6}

X(61892) = X(2)X(3)∩X(3631)X(5093)

Barycentrics    7*a^4+12*(b^2-c^2)^2-19*a^2*(b^2+c^2) : :
X(61892) = -36*X[2]+5*X[3], 28*X[1125]+3*X[61247], X[3244]+30*X[10172], 16*X[3626]+15*X[10247], 16*X[3631]+15*X[5093], X[3632]+30*X[11230], 16*X[3636]+15*X[5790], 30*X[3763]+X[55724], 3*X[5050]+28*X[42786], X[6154]+30*X[38319], 21*X[7989]+10*X[31666], 27*X[9166]+4*X[38628] and many others

X(61892) lies on these lines: {2, 3}, {1125, 61247}, {3244, 10172}, {3626, 10247}, {3631, 5093}, {3632, 11230}, {3636, 5790}, {3763, 55724}, {5050, 42786}, {6154, 38319}, {6199, 42583}, {6395, 42582}, {6407, 42274}, {6408, 42277}, {6417, 43880}, {6418, 43879}, {6419, 45385}, {6420, 45384}, {6427, 10577}, {6428, 10576}, {6447, 42262}, {6448, 42265}, {7603, 22331}, {7989, 31666}, {9166, 38628}, {9956, 61291}, {10187, 49907}, {10188, 49908}, {10222, 61274}, {10246, 61250}, {10283, 20054}, {10541, 48662}, {11480, 42901}, {11481, 42900}, {11482, 38317}, {12308, 12900}, {12316, 32396}, {15020, 15088}, {15025, 32609}, {15027, 24981}, {15029, 34128}, {15039, 20304}, {15046, 51522}, {15178, 54447}, {15808, 37624}, {16187, 37472}, {16241, 43547}, {16242, 43546}, {19130, 55602}, {19862, 58230}, {19875, 58240}, {20050, 38042}, {21358, 55718}, {22236, 42592}, {22238, 42593}, {23234, 38627}, {24206, 53092}, {30315, 50798}, {31274, 38635}, {31487, 42603}, {34573, 55584}, {34641, 61276}, {34747, 38083}, {35021, 38743}, {35022, 38732}, {35023, 51517}, {36836, 42914}, {36843, 42915}, {37481, 40247}, {37714, 58232}, {37832, 42611}, {37835, 42610}, {38072, 55588}, {38098, 58236}, {38171, 60957}, {38318, 60933}, {38629, 59377}, {42111, 43105}, {42114, 43106}, {42115, 43297}, {42116, 43296}, {42157, 42475}, {42158, 42474}, {42435, 43548}, {42436, 43549}, {42488, 42780}, {42489, 42779}, {42580, 43029}, {42581, 43028}, {42598, 42781}, {42599, 42782}, {42633, 43447}, {42634, 43446}, {42635, 42993}, {42636, 42992}, {42797, 43193}, {42798, 43194}, {43012, 43018}, {43013, 43019}, {43240, 43468}, {43241, 43467}, {43254, 43523}, {43255, 43524}, {43511, 60305}, {43512, 60306}, {46931, 58247}, {47353, 55694}, {47355, 55701}, {51024, 55628}, {51126, 55697}, {51514, 60942}, {51516, 60980}

X(61892) = inverse of X(61853) in orthocentroidal circle
X(61892) = inverse of X(61853) in Yff hyperbola
X(61892) = complement of X(61836)
X(61892) = pole of line {523, 61853} with respect to the orthocentroidal circle
X(61892) = pole of line {6, 61853} with respect to the Kiepert hyperbola
X(61892) = pole of line {523, 61853} with respect to the Yff hyperbola
X(61892) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3526), X(57894)}}, {{A, B, C, X(3543), X(14938)}}, {{A, B, C, X(14893), X(31846)}}, {{A, B, C, X(15708), X(22268)}}, {{A, B, C, X(15720), X(40410)}}, {{A, B, C, X(46168), X(55856)}}
X(61892) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11737, 5054}, {2, 14269, 15694}, {2, 15710, 10124}, {2, 3090, 546}, {2, 3544, 14869}, {2, 3855, 140}, {2, 5, 15720}, {2, 5055, 15681}, {2, 5056, 3528}, {2, 5071, 17504}, {3, 14269, 3529}, {3, 14869, 15707}, {3, 15703, 3628}, {3, 3091, 3830}, {3, 5079, 3851}, {3, 6982, 15719}, {5, 10303, 5076}, {5, 11812, 4}, {5, 140, 3543}, {5, 15720, 14269}, {140, 17800, 15718}, {140, 3855, 15688}, {381, 1656, 7486}, {381, 5054, 15690}, {382, 5079, 3544}, {546, 3090, 5079}, {546, 3530, 15704}, {550, 15713, 3530}, {632, 3090, 5072}, {1010, 16371, 382}, {1656, 15703, 5070}, {1656, 3526, 547}, {1656, 3628, 3}, {1656, 5067, 15703}, {1656, 5070, 5055}, {3090, 10303, 5}, {3090, 17538, 15022}, {3524, 10303, 12108}, {3525, 12812, 381}, {3525, 7486, 12812}, {3528, 15683, 550}, {3528, 5056, 11737}, {3530, 15720, 15722}, {3543, 17800, 5073}, {3830, 15694, 3524}, {3830, 6908, 3534}, {3851, 15681, 3843}, {3851, 5070, 2}, {5056, 16342, 17538}, {5066, 16402, 15700}, {5067, 15699, 1656}, {5068, 11539, 15696}, {5071, 16239, 1657}, {12812, 15713, 3091}, {14869, 16857, 3526}

X(61893) = X(2)X(3)∩X(13)X(42477)

Barycentrics    11*a^4+20*(b^2-c^2)^2-31*a^2*(b^2+c^2) : :
X(61893) = -20*X[2]+3*X[3], 3*X[1351]+14*X[51186], 16*X[3828]+X[8148], -X[4669]+18*X[10172], 5*X[4677]+12*X[33179], 15*X[5050]+2*X[51027], 9*X[5093]+8*X[22165], 12*X[5097]+5*X[15533], 9*X[5102]+25*X[50993], 5*X[5655]+12*X[38725], 9*X[5790]+8*X[51103], 9*X[5886]+8*X[51069] and many others

X(61893) lies on these lines: {2, 3}, {13, 42477}, {14, 42476}, {395, 49811}, {396, 49810}, {1131, 6475}, {1132, 6474}, {1327, 6446}, {1328, 6445}, {1351, 51186}, {3828, 8148}, {4669, 10172}, {4677, 33179}, {5050, 51027}, {5093, 22165}, {5097, 15533}, {5102, 50993}, {5655, 38725}, {5790, 51103}, {5886, 51069}, {5901, 51072}, {6407, 42417}, {6408, 42418}, {6417, 42603}, {6418, 42602}, {6722, 48657}, {8724, 38735}, {8976, 42527}, {9880, 38635}, {9956, 34748}, {10137, 41945}, {10138, 41946}, {10165, 50868}, {10168, 48662}, {10219, 18435}, {10246, 50871}, {11178, 55711}, {11230, 51093}, {11231, 50806}, {11278, 19875}, {11482, 51188}, {11485, 42984}, {11486, 42985}, {11531, 38066}, {11542, 42478}, {11543, 42479}, {11632, 38746}, {12188, 55771}, {12308, 45311}, {13846, 43881}, {13847, 43882}, {13951, 42526}, {14561, 51143}, {14848, 50991}, {15534, 38317}, {16200, 51066}, {16966, 49903}, {16967, 49904}, {18583, 50990}, {19872, 28198}, {20126, 38792}, {20582, 44456}, {21358, 37517}, {22247, 38733}, {24206, 51185}, {25055, 32900}, {25561, 55691}, {25565, 33878}, {26446, 51120}, {31399, 51091}, {32789, 43887}, {32790, 43888}, {33416, 42474}, {33417, 42475}, {34754, 41122}, {34755, 41121}, {35812, 43885}, {35813, 43886}, {36382, 48312}, {36383, 48311}, {36521, 38732}, {37624, 51108}, {37640, 42951}, {37641, 42950}, {37712, 58234}, {37832, 42977}, {37835, 42976}, {38028, 50797}, {38072, 55587}, {38110, 50954}, {38155, 51109}, {38171, 60971}, {38318, 51514}, {39561, 50955}, {41100, 43028}, {41101, 43029}, {41943, 42610}, {41944, 42611}, {42121, 49825}, {42124, 49824}, {42129, 43228}, {42132, 43229}, {42139, 43108}, {42142, 43109}, {42143, 49827}, {42146, 49826}, {42153, 42532}, {42154, 42904}, {42155, 42905}, {42156, 42533}, {42488, 43018}, {42489, 43019}, {42510, 43104}, {42511, 43101}, {42520, 43544}, {42521, 43545}, {42786, 47352}, {42896, 43877}, {42897, 43878}, {42952, 49906}, {42953, 49905}, {43246, 49875}, {43247, 49876}, {43248, 43305}, {43249, 43304}, {43525, 53517}, {43526, 53520}, {47353, 55695}, {47354, 55697}, {48310, 55705}, {49945, 49959}, {49946, 49960}, {50796, 58230}, {50798, 51110}, {50805, 51068}, {50808, 61266}, {50823, 58238}, {50825, 61267}, {50872, 61270}, {50962, 50994}, {51024, 55627}, {51085, 61257}, {51092, 61510}, {51119, 58441}, {51128, 55604}, {60884, 60999}

X(61893) = reflection of X(i) in X(j) for these {i,j}: {15723, 13742}, {381, 3544}
X(61893) = inverse of X(61851) in orthocentroidal circle
X(61893) = inverse of X(61851) in Yff hyperbola
X(61893) = complement of X(61833)
X(61893) = pole of line {523, 61851} with respect to the orthocentroidal circle
X(61893) = pole of line {6, 61851} with respect to the Kiepert hyperbola
X(61893) = pole of line {523, 61851} with respect to the Yff hyperbola
X(61893) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3853), X(31846)}}, {{A, B, C, X(14938), X(50688)}}, {{A, B, C, X(15693), X(40410)}}
X(61893) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10109, 3534}, {2, 11001, 11539}, {2, 11812, 15723}, {2, 15640, 3525}, {2, 15682, 11540}, {2, 15698, 10124}, {2, 3090, 5066}, {2, 3545, 11812}, {2, 3830, 15694}, {2, 5055, 3830}, {2, 5056, 11001}, {2, 5066, 5054}, {2, 5071, 8703}, {2, 8703, 3526}, {3, 11001, 15695}, {3, 15708, 15718}, {3, 3528, 6865}, {3, 3832, 5073}, {3, 6825, 15698}, {3, 6948, 10299}, {3, 8703, 6926}, {30, 3544, 381}, {381, 11812, 6958}, {381, 15707, 17800}, {381, 15715, 15684}, {381, 5054, 550}, {547, 11539, 5056}, {547, 15699, 5067}, {550, 14891, 10304}, {1656, 15699, 15703}, {1656, 15703, 5055}, {3090, 12102, 5079}, {3526, 5071, 14269}, {3543, 15702, 14891}, {3545, 15702, 5059}, {3830, 5070, 2}, {3843, 5073, 12102}, {3845, 15690, 15682}, {3851, 15694, 15689}, {3854, 7486, 3090}, {5054, 5066, 15685}, {5055, 15681, 5}, {5055, 15694, 3851}, {5055, 15703, 5070}, {5056, 5067, 3628}, {5066, 15685, 3843}, {5071, 15708, 3850}, {6918, 12812, 15022}, {10299, 14269, 15681}, {10299, 15702, 15708}, {10304, 11001, 15690}, {11540, 15682, 15693}, {11737, 15709, 1657}, {12100, 15701, 15707}, {15690, 15693, 3}, {15695, 15701, 12100}

X(61894) = X(2)X(3)∩X(13)X(42946)

Barycentrics    6*a^4+11*(b^2-c^2)^2-17*a^2*(b^2+c^2) : :
X(61894) = -33*X[2]+5*X[3], 11*X[141]+3*X[55717], -9*X[373]+2*X[16881], -9*X[551]+2*X[61290], 6*X[1125]+X[61249], 3*X[1216]+4*X[58533], -X[3244]+15*X[11230], X[3579]+6*X[61267], -15*X[3616]+X[61297], 5*X[3617]+9*X[61273], 2*X[3626]+5*X[5901], -X[3629]+15*X[38317] and many others

X(61894) lies on these lines: {2, 3}, {13, 42946}, {14, 42947}, {141, 55717}, {373, 16881}, {397, 42591}, {398, 42590}, {551, 61290}, {952, 15808}, {1125, 61249}, {1216, 58533}, {1506, 34571}, {3055, 7765}, {3244, 11230}, {3411, 42598}, {3412, 42599}, {3564, 42786}, {3579, 61267}, {3589, 15806}, {3616, 61297}, {3617, 61273}, {3626, 5901}, {3629, 38317}, {3631, 18583}, {3632, 38042}, {3634, 61269}, {3636, 9956}, {3817, 31447}, {3819, 18874}, {3982, 34753}, {4325, 7294}, {4330, 5326}, {4681, 61549}, {4686, 61623}, {4739, 61522}, {5334, 42492}, {5335, 42493}, {5446, 12046}, {5480, 55589}, {5550, 38138}, {5734, 38112}, {5844, 9624}, {5881, 51700}, {6154, 61601}, {6329, 24206}, {6407, 43505}, {6408, 43506}, {6409, 43516}, {6410, 43515}, {6429, 43513}, {6430, 43514}, {6435, 7584}, {6436, 7583}, {6437, 43341}, {6438, 43340}, {6478, 43435}, {6479, 43434}, {6498, 13951}, {6499, 8976}, {6688, 11591}, {9300, 12815}, {9588, 28212}, {9606, 43291}, {9680, 43318}, {10095, 44324}, {10170, 32205}, {10171, 61524}, {10175, 61255}, {10187, 41121}, {10188, 41122}, {10222, 38098}, {10272, 20396}, {10283, 20050}, {10576, 13993}, {10577, 13925}, {10589, 31480}, {10593, 31452}, {11008, 59399}, {11017, 16836}, {11362, 61272}, {11542, 42489}, {11543, 42488}, {12818, 42226}, {12819, 42225}, {12900, 20379}, {13363, 31834}, {13451, 32142}, {14449, 15606}, {14531, 15026}, {15047, 54434}, {15063, 40685}, {15067, 58531}, {15069, 51732}, {15425, 23337}, {16772, 42143}, {16773, 42146}, {16962, 42613}, {16963, 42612}, {16966, 42628}, {16967, 42627}, {18358, 55702}, {18538, 42644}, {18581, 42610}, {18582, 42611}, {18762, 31454}, {19130, 55599}, {19862, 61259}, {20054, 59400}, {20414, 46266}, {20583, 25555}, {22051, 32396}, {23302, 42939}, {23303, 42938}, {27355, 54042}, {28174, 51073}, {28216, 31423}, {30315, 61288}, {31253, 61614}, {31262, 34501}, {31417, 37637}, {31492, 43620}, {31666, 38076}, {32450, 61550}, {32767, 61606}, {34126, 61605}, {34127, 61599}, {34128, 61598}, {34573, 55586}, {34641, 38083}, {34747, 38022}, {35021, 61575}, {35022, 61576}, {35023, 60759}, {35024, 61577}, {35812, 42583}, {35813, 42582}, {36431, 61340}, {36969, 42797}, {36970, 42798}, {37714, 38028}, {37727, 54447}, {37832, 43111}, {37835, 43110}, {38084, 38763}, {38171, 60933}, {38231, 43676}, {38318, 60942}, {38319, 61562}, {40107, 55719}, {40341, 61624}, {40342, 61543}, {41973, 43107}, {41974, 43100}, {42095, 42415}, {42098, 42416}, {42111, 42490}, {42114, 42491}, {42147, 42914}, {42148, 42915}, {42160, 42475}, {42161, 42474}, {42472, 43631}, {42473, 43630}, {42580, 42925}, {42581, 42924}, {42596, 42918}, {42597, 42919}, {42801, 43549}, {42802, 43548}, {42813, 43106}, {42814, 43105}, {42936, 43101}, {42937, 43104}, {42948, 43485}, {42949, 43486}, {43026, 43233}, {43027, 43232}, {43211, 53516}, {43212, 53513}, {44863, 54044}, {46934, 61245}, {47742, 52795}, {50824, 61248}, {50981, 55602}, {51022, 55675}, {51069, 58240}, {51128, 55605}, {51143, 55718}, {58446, 61555}, {58715, 61613}, {60980, 61511}

X(61894) = midpoint of X(i) and X(j) for these {i,j}: {5, 3526}, {3523, 3857}, {3851, 14869}
X(61894) = reflection of X(i) in X(j) for these {i,j}: {12100, 15702}, {15701, 10124}, {3528, 3530}, {546, 3851}
X(61894) = inverse of X(61850) in orthocentroidal circle
X(61894) = inverse of X(61850) in Yff hyperbola
X(61894) = complement of X(14869)
X(61894) = pole of line {523, 61850} with respect to the orthocentroidal circle
X(61894) = pole of line {185, 44903} with respect to the Jerabek hyperbola
X(61894) = pole of line {6, 61850} with respect to the Kiepert hyperbola
X(61894) = pole of line {523, 61850} with respect to the Yff hyperbola
X(61894) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1105), X(44903)}}, {{A, B, C, X(3530), X(40410)}}, {{A, B, C, X(3830), X(31846)}}, {{A, B, C, X(3853), X(14938)}}, {{A, B, C, X(3856), X(40448)}}, {{A, B, C, X(13599), X(49136)}}, {{A, B, C, X(14890), X(34483)}}, {{A, B, C, X(15318), X(15693)}}, {{A, B, C, X(43970), X(55859)}}
X(61894) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15681, 11539}, {2, 15720, 632}, {2, 16052, 16853}, {2, 17504, 10124}, {2, 17674, 16351}, {2, 3528, 3526}, {2, 3544, 15720}, {2, 5, 3530}, {2, 5055, 15687}, {2, 5056, 3529}, {2, 5071, 15688}, {2, 5079, 550}, {2, 546, 140}, {3, 5, 3856}, {5, 13742, 14890}, {5, 140, 3853}, {5, 15699, 5067}, {5, 3843, 12811}, {5, 3855, 11737}, {5, 5070, 16239}, {5, 548, 3859}, {5, 549, 3843}, {5, 550, 3855}, {5, 631, 3861}, {5, 632, 20}, {30, 10124, 15701}, {30, 15702, 12100}, {30, 3530, 3528}, {30, 3851, 546}, {140, 12812, 5066}, {140, 14893, 3}, {140, 3859, 548}, {140, 5066, 12103}, {140, 547, 12812}, {382, 3851, 3832}, {382, 5070, 2}, {547, 12100, 5055}, {550, 14869, 15700}, {631, 5067, 13735}, {1656, 11001, 6914}, {1656, 15699, 3628}, {1656, 15703, 3090}, {1656, 3628, 547}, {1656, 5067, 5}, {1656, 5070, 7486}, {2041, 2042, 15693}, {3523, 3857, 30}, {3528, 3832, 382}, {3533, 5072, 8703}, {3544, 15687, 3850}, {3545, 15712, 12102}, {3628, 16239, 5070}, {3839, 15674, 631}, {3839, 15692, 6890}, {5054, 15022, 3858}, {5055, 15720, 3544}, {5068, 15694, 15704}, {5068, 15704, 3860}, {10124, 14892, 15690}, {10299, 17566, 3851}, {11230, 31399, 61278}, {11540, 12102, 15712}, {12102, 15712, 15691}, {15702, 15720, 14869}, {31399, 61278, 61510}

X(61895) = X(2)X(3)∩X(6)X(43877)

Barycentrics    7*a^4+13*(b^2-c^2)^2-20*a^2*(b^2+c^2) : :
X(61895) = -13*X[2]+2*X[3], -X[8]+12*X[38083], -X[144]+12*X[38082], -X[145]+12*X[38022], -X[149]+12*X[38084], -16*X[182]+5*X[51176], -X[193]+12*X[38079], 2*X[551]+9*X[54447], 4*X[576]+7*X[50994], -X[944]+12*X[19883], 8*X[1125]+3*X[38074], 3*X[1352]+8*X[46267] and many others

X(61895) lies on these lines: {2, 3}, {6, 43877}, {8, 38083}, {15, 43032}, {16, 43033}, {61, 33606}, {62, 33607}, {98, 60646}, {144, 38082}, {145, 38022}, {149, 38084}, {182, 51176}, {193, 38079}, {262, 60643}, {371, 14226}, {372, 14241}, {551, 54447}, {576, 50994}, {590, 6441}, {615, 6442}, {944, 19883}, {1125, 38074}, {1131, 52048}, {1132, 52047}, {1285, 3054}, {1352, 46267}, {1587, 41952}, {1588, 41951}, {1992, 38317}, {3068, 42603}, {3069, 42602}, {3241, 11230}, {3311, 43387}, {3312, 43386}, {3316, 10577}, {3317, 10576}, {3582, 10588}, {3584, 10589}, {3590, 6428}, {3591, 6427}, {3618, 42786}, {3619, 5476}, {3620, 14848}, {3621, 38081}, {3634, 38021}, {3654, 19877}, {3679, 10172}, {3828, 5603}, {4745, 9624}, {5237, 42588}, {5238, 42589}, {5309, 14482}, {5339, 43107}, {5340, 43100}, {5418, 6478}, {5420, 6479}, {5485, 11669}, {5550, 28204}, {5657, 19876}, {5817, 60999}, {5818, 13607}, {5881, 51109}, {5886, 34631}, {5901, 50830}, {6172, 38318}, {6221, 43517}, {6361, 19872}, {6398, 43518}, {6407, 60296}, {6408, 60295}, {6417, 42640}, {6418, 42639}, {6425, 43378}, {6426, 43379}, {6435, 43323}, {6436, 43322}, {6439, 41945}, {6440, 41946}, {6459, 43254}, {6460, 43255}, {6476, 42274}, {6477, 42277}, {6666, 38073}, {6684, 50809}, {6688, 14831}, {6721, 9166}, {6722, 23234}, {6770, 48311}, {6773, 48312}, {6776, 48310}, {7581, 35814}, {7582, 35815}, {7583, 43536}, {7584, 54597}, {7608, 60637}, {7612, 60239}, {7738, 18362}, {7752, 52718}, {7788, 32838}, {7850, 34229}, {7862, 18840}, {7886, 18841}, {7967, 61247}, {7989, 50828}, {7999, 21849}, {8164, 10072}, {8227, 50810}, {8596, 38229}, {8981, 34089}, {9167, 13172}, {9778, 61266}, {9780, 51709}, {9956, 38314}, {10056, 47743}, {10155, 60200}, {10171, 31162}, {10173, 31961}, {10175, 34627}, {10222, 51068}, {10283, 20049}, {10302, 14494}, {10595, 53620}, {10601, 54434}, {10653, 43464}, {10654, 43463}, {10707, 38319}, {11177, 34127}, {11178, 14912}, {11231, 34632}, {11465, 16226}, {11488, 42910}, {11489, 42911}, {12007, 40330}, {12046, 37484}, {12243, 14971}, {12245, 19875}, {12247, 38104}, {12248, 38069}, {12317, 12900}, {12325, 32396}, {12816, 43769}, {12817, 43770}, {13364, 33884}, {13846, 42579}, {13847, 42578}, {13886, 32788}, {13939, 32787}, {13966, 34091}, {14639, 22247}, {14692, 49102}, {14810, 50964}, {14853, 20582}, {14927, 50956}, {15033, 16187}, {15850, 53098}, {16241, 42139}, {16242, 42142}, {16267, 49812}, {16268, 49813}, {16772, 49827}, {16773, 49826}, {16966, 37641}, {16967, 37640}, {16981, 44324}, {18581, 41943}, {18582, 41944}, {18583, 50985}, {18842, 53104}, {19878, 38076}, {20059, 38080}, {20060, 38085}, {20070, 50806}, {21356, 51179}, {21358, 50982}, {22236, 49873}, {22238, 49874}, {22791, 46930}, {24206, 51140}, {25406, 25561}, {30315, 51105}, {31145, 38042}, {31399, 51093}, {31415, 46453}, {31423, 50802}, {31663, 50807}, {32785, 35823}, {32786, 35822}, {32817, 53127}, {32833, 34803}, {32837, 37647}, {32839, 59634}, {33602, 43442}, {33603, 43443}, {34573, 38072}, {34595, 51705}, {34641, 61275}, {36969, 42472}, {36970, 42473}, {36990, 51177}, {36993, 48313}, {36995, 48314}, {36996, 38093}, {37832, 43010}, {37835, 43011}, {38064, 39874}, {38066, 46932}, {38075, 58433}, {38171, 60984}, {40693, 49861}, {40694, 49862}, {41107, 42494}, {41108, 42495}, {41112, 42581}, {41113, 42580}, {41150, 61288}, {41957, 43318}, {41958, 43319}, {42085, 42795}, {42086, 42796}, {42101, 42587}, {42102, 42586}, {42112, 42498}, {42113, 42499}, {42115, 43540}, {42116, 43541}, {42121, 42691}, {42124, 42690}, {42133, 42684}, {42134, 42685}, {42149, 49907}, {42152, 49908}, {42154, 42687}, {42155, 42686}, {42157, 43202}, {42158, 43201}, {42163, 49876}, {42166, 49875}, {42215, 43374}, {42216, 43375}, {42268, 43522}, {42269, 43521}, {42270, 43257}, {42273, 43256}, {42474, 42943}, {42475, 42942}, {42488, 56612}, {42489, 56613}, {42496, 42950}, {42497, 42951}, {42510, 42937}, {42511, 42936}, {42537, 51911}, {42538, 51910}, {42590, 42806}, {42591, 42805}, {42598, 49906}, {42599, 49905}, {42775, 42926}, {42776, 42927}, {42815, 42985}, {42816, 42984}, {42892, 42894}, {42893, 42895}, {42898, 49948}, {42899, 49947}, {42912, 43875}, {42913, 43876}, {42914, 42955}, {42915, 42954}, {42920, 42964}, {42921, 42965}, {43028, 43104}, {43029, 43101}, {43240, 43777}, {43241, 43778}, {43246, 43444}, {43247, 43445}, {43564, 60314}, {43565, 60313}, {47353, 51126}, {48661, 50825}, {48662, 50987}, {48872, 51129}, {48896, 51217}, {50813, 51118}, {50833, 50863}, {50873, 51088}, {50958, 55711}, {50963, 61044}, {50969, 51163}, {50981, 51211}, {50988, 51216}, {51029, 51141}, {51092, 61278}, {51182, 61545}, {51215, 53091}, {52695, 61576}, {53103, 54639}, {54521, 60183}, {54616, 60102}, {58421, 59377}, {58441, 61265}, {59375, 61511}, {59386, 60986}, {60100, 60150}, {60123, 60282}, {60127, 60278}, {60143, 60333}, {60331, 60629}, {60336, 60616}, {61023, 61595}

X(61895) = midpoint of X(i) and X(j) for these {i,j}: {2, 5056}, {381, 15718}, {3855, 15719}
X(61895) = reflection of X(i) in X(j) for these {i,j}: {15715, 15721}, {15719, 3525}, {15721, 15723}, {2, 5070}, {376, 15715}, {3525, 2}
X(61895) = inverse of X(15709) in orthocentroidal circle
X(61895) = inverse of X(15709) in Yff hyperbola
X(61895) = complement of X(15721)
X(61895) = anticomplement of X(15723)
X(61895) = pole of line {523, 15709} with respect to the orthocentroidal circle
X(61895) = pole of line {6, 15709} with respect to the Kiepert hyperbola
X(61895) = pole of line {523, 15709} with respect to the Yff hyperbola
X(61895) = pole of line {69, 11539} with respect to the Wallace hyperbola
X(61895) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(11539)}}, {{A, B, C, X(264), X(15709)}}, {{A, B, C, X(297), X(60646)}}, {{A, B, C, X(382), X(54763)}}, {{A, B, C, X(458), X(60643)}}, {{A, B, C, X(546), X(54660)}}, {{A, B, C, X(1494), X(3525)}}, {{A, B, C, X(3524), X(40410)}}, {{A, B, C, X(3534), X(18852)}}, {{A, B, C, X(3627), X(31846)}}, {{A, B, C, X(3628), X(18854)}}, {{A, B, C, X(4232), X(11669)}}, {{A, B, C, X(5054), X(8797)}}, {{A, B, C, X(5076), X(14938)}}, {{A, B, C, X(6995), X(60192)}}, {{A, B, C, X(7378), X(60175)}}, {{A, B, C, X(7408), X(54521)}}, {{A, B, C, X(7409), X(54866)}}, {{A, B, C, X(10301), X(14494)}}, {{A, B, C, X(13599), X(49135)}}, {{A, B, C, X(13623), X(15689)}}, {{A, B, C, X(14269), X(54667)}}, {{A, B, C, X(15687), X(54838)}}, {{A, B, C, X(15694), X(36889)}}, {{A, B, C, X(15702), X(55958)}}, {{A, B, C, X(15717), X(18853)}}, {{A, B, C, X(18851), X(49140)}}, {{A, B, C, X(19307), X(53098)}}, {{A, B, C, X(34483), X(55863)}}, {{A, B, C, X(37174), X(60239)}}, {{A, B, C, X(50688), X(60121)}}, {{A, B, C, X(52281), X(60637)}}, {{A, B, C, X(52284), X(53104)}}, {{A, B, C, X(52285), X(60150)}}, {{A, B, C, X(52301), X(60333)}}
X(61895) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10109, 11001}, {2, 10304, 3526}, {2, 15022, 10304}, {2, 15640, 11540}, {2, 15692, 10124}, {2, 15699, 5067}, {2, 15708, 632}, {2, 15721, 15723}, {2, 20, 11539}, {2, 3091, 5054}, {2, 3524, 3533}, {2, 3839, 140}, {2, 4, 15709}, {2, 4193, 17561}, {2, 5, 3524}, {2, 5055, 4}, {2, 5068, 15708}, {2, 5071, 376}, {2, 547, 5071}, {2, 7486, 5055}, {4, 3524, 3534}, {4, 3525, 15717}, {4, 5067, 3628}, {5, 11812, 14269}, {5, 140, 5076}, {5, 15694, 3543}, {5, 15722, 3839}, {5, 5073, 3091}, {30, 15721, 15715}, {376, 3543, 3529}, {376, 549, 15698}, {381, 10124, 15692}, {381, 15723, 15718}, {381, 549, 15683}, {382, 15713, 15705}, {547, 15699, 15703}, {549, 15687, 548}, {549, 15694, 10303}, {549, 5066, 15684}, {631, 15682, 15710}, {631, 3545, 15682}, {1656, 15699, 2}, {1656, 15703, 547}, {1656, 3628, 7486}, {1656, 5067, 3090}, {3090, 3533, 5}, {3090, 3855, 5056}, {3524, 15711, 10299}, {3525, 13742, 13725}, {3525, 5056, 3855}, {3529, 16239, 6897}, {3530, 3854, 11541}, {3534, 12101, 15640}, {3830, 15708, 3528}, {3857, 11539, 15759}, {3860, 10304, 6927}, {3860, 14869, 15689}, {3860, 15689, 17578}, {5054, 5073, 15711}, {5055, 5066, 15022}, {5056, 13742, 3}, {5056, 15717, 5072}, {5066, 14890, 15704}, {5068, 15708, 3830}, {5071, 15702, 381}, {5818, 25055, 50818}, {10109, 10299, 3545}, {10124, 15692, 15702}, {10303, 15717, 15720}, {10303, 17678, 15694}, {10304, 15022, 5066}, {11488, 42910, 43543}, {11489, 42911, 43542}, {11539, 14893, 15700}, {11812, 14269, 3522}, {13442, 14636, 30}, {14782, 14783, 12103}, {14892, 15713, 382}, {14893, 15700, 20}, {15681, 15694, 15722}, {15698, 15709, 631}, {15705, 17679, 15721}, {15715, 15721, 15719}, {15717, 15721, 549}, {15721, 15723, 3525}, {16241, 42139, 43482}, {16242, 42142, 43481}, {16371, 16417, 16853}, {18586, 18587, 12812}, {19872, 30308, 38068}, {30308, 38068, 6361}, {40330, 47352, 50974}, {43877, 43878, 6}

X(61896) = X(2)X(3)∩X(395)X(42506)

Barycentrics    10*a^4+19*(b^2-c^2)^2-29*a^2*(b^2+c^2) : :
X(61896) = -19*X[2]+3*X[3], -5*X[551]+X[61292], 3*X[576]+5*X[51142], X[597]+7*X[42786], 5*X[1125]+X[61253], 3*X[1699]+5*X[50825], -5*X[3656]+21*X[61271], X[4669]+3*X[5901], -X[4677]+9*X[38042], 15*X[5886]+X[50817], -X[8584]+9*X[38317], 3*X[9956]+X[51103] and many others

X(61896) lies on these lines: {2, 3}, {395, 42506}, {396, 42507}, {551, 61292}, {576, 51142}, {597, 42786}, {952, 51108}, {1125, 61253}, {1699, 50825}, {3068, 42640}, {3069, 42639}, {3656, 61271}, {3828, 61272}, {4669, 5901}, {4677, 38042}, {4745, 5844}, {5663, 10219}, {5886, 50817}, {6490, 42274}, {6491, 42277}, {6564, 42567}, {6565, 42566}, {8584, 38317}, {9956, 51103}, {10171, 28212}, {10175, 51082}, {10222, 51067}, {10576, 42606}, {10577, 42607}, {10653, 43246}, {10654, 43247}, {11178, 51732}, {11230, 51071}, {11645, 51127}, {11694, 23515}, {12816, 42123}, {12817, 42122}, {13393, 56567}, {13565, 20585}, {14561, 50973}, {14848, 50994}, {15092, 22247}, {15534, 38079}, {16226, 31834}, {16241, 43108}, {16242, 43109}, {16962, 42419}, {16963, 42420}, {16966, 42496}, {16967, 42497}, {18357, 19883}, {18358, 48310}, {18538, 42572}, {18583, 22165}, {18762, 42573}, {19053, 42527}, {19054, 42526}, {19876, 22791}, {19878, 28208}, {20252, 36769}, {20253, 47867}, {21969, 44324}, {23302, 49908}, {23303, 49907}, {25055, 61244}, {25565, 34573}, {28154, 51076}, {28168, 51086}, {28178, 50829}, {28186, 51080}, {28190, 50803}, {28216, 50802}, {29323, 51139}, {31399, 51096}, {32787, 42558}, {32788, 42557}, {32789, 52047}, {32790, 52048}, {32896, 34803}, {33416, 42792}, {33417, 42791}, {34380, 50991}, {35255, 42417}, {35256, 42418}, {36521, 61576}, {37712, 50824}, {37832, 42502}, {37835, 42503}, {38022, 51093}, {38028, 61257}, {38068, 40273}, {38080, 60971}, {38081, 61597}, {38082, 61509}, {38084, 61562}, {38127, 51709}, {38171, 60963}, {39593, 43291}, {41100, 43104}, {41101, 43101}, {41107, 42146}, {41108, 42143}, {41112, 42121}, {41113, 42124}, {41121, 42913}, {41122, 42912}, {41943, 42590}, {41944, 42591}, {42107, 46335}, {42110, 46334}, {42135, 42475}, {42136, 42500}, {42137, 42501}, {42138, 42474}, {42262, 42609}, {42265, 42608}, {42478, 43306}, {42479, 43307}, {42492, 49827}, {42493, 49826}, {42504, 42942}, {42505, 42943}, {42510, 43028}, {42511, 43029}, {42568, 43254}, {42569, 43255}, {42627, 49859}, {42628, 49860}, {42682, 42795}, {42683, 42796}, {42777, 42952}, {42778, 42953}, {42910, 43208}, {42911, 43207}, {42914, 43417}, {42915, 43416}, {43013, 61719}, {43540, 43640}, {43541, 43639}, {49952, 50855}, {49953, 50858}, {50800, 54445}, {50805, 61273}, {50821, 61269}, {50832, 59387}, {50864, 61260}, {50980, 53023}, {50992, 61624}, {51026, 55657}, {51091, 61278}, {51105, 54447}, {51106, 61286}, {51109, 51700}, {51110, 61296}, {51129, 55649}, {51705, 61262}

X(61896) = midpoint of X(i) and X(j) for these {i,j}: {2, 10109}, {5, 10124}, {140, 11737}, {376, 12102}, {381, 3530}, {546, 14891}, {547, 3628}, {549, 3850}, {3545, 14890}, {3828, 61272}, {3845, 15759}, {3860, 12100}, {5066, 11812}, {11178, 51732}, {13393, 56567}, {15092, 22247}, {15333, 15957}, {25565, 34573}
X(61896) = reflection of X(i) in X(j) for these {i,j}: {11540, 2}, {12108, 10124}, {3856, 11737}
X(61896) = inverse of X(61847) in orthocentroidal circle
X(61896) = inverse of X(61847) in Yff hyperbola
X(61896) = complement of X(11812)
X(61896) = pole of line {523, 61847} with respect to the orthocentroidal circle
X(61896) = pole of line {6, 61847} with respect to the Kiepert hyperbola
X(61896) = pole of line {523, 61847} with respect to the Yff hyperbola
X(61896) = intersection, other than A, B, C, of circumconics {{A, B, C, X(382), X(31846)}}, {{A, B, C, X(1217), X(58193)}}, {{A, B, C, X(1494), X(11540)}}, {{A, B, C, X(12100), X(40410)}}, {{A, B, C, X(12102), X(14938)}}, {{A, B, C, X(13599), X(49133)}}, {{A, B, C, X(15713), X(55958)}}, {{A, B, C, X(18317), X(58190)}}, {{A, B, C, X(43970), X(55858)}}
X(61896) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11540, 16239}, {2, 12100, 10124}, {2, 15682, 15694}, {2, 15701, 632}, {2, 17533, 15673}, {2, 30, 11540}, {2, 3534, 11539}, {2, 3545, 15701}, {2, 381, 15713}, {2, 5056, 15682}, {2, 5071, 3534}, {2, 547, 10109}, {5, 12103, 3850}, {5, 140, 12102}, {5, 15699, 15703}, {5, 3523, 546}, {5, 5054, 14893}, {5, 549, 3839}, {5, 632, 1657}, {30, 10124, 12108}, {30, 11737, 3856}, {140, 11737, 30}, {140, 15693, 11812}, {140, 3845, 15759}, {140, 5067, 3628}, {140, 547, 5055}, {376, 3839, 382}, {376, 5055, 5}, {381, 15708, 15704}, {381, 15713, 15690}, {382, 3845, 12101}, {546, 11539, 14891}, {1656, 15699, 547}, {3090, 15710, 5071}, {3091, 15723, 17504}, {3522, 7486, 3090}, {3534, 5070, 2}, {3839, 11001, 3830}, {3845, 17504, 15685}, {3845, 8703, 15640}, {3850, 11812, 11001}, {3851, 15709, 15686}, {4190, 15022, 5056}, {5055, 15723, 3091}, {5066, 15697, 3861}, {5071, 11354, 15706}, {7491, 15694, 15720}, {10109, 10124, 3860}, {10109, 11812, 5066}, {10109, 15759, 11737}, {10124, 11737, 376}, {11001, 15698, 3522}, {11737, 15759, 3845}, {11812, 15759, 15693}, {12100, 12101, 12103}, {12100, 15722, 3530}, {15640, 15693, 8703}, {15711, 15718, 12100}, {15717, 17556, 15708}, {15723, 17504, 140}, {37832, 42533, 42502}, {37835, 42532, 42503}

X(61897) = X(2)X(3)∩X(13)X(42804)

Barycentrics    13*a^4+25*(b^2-c^2)^2-38*a^2*(b^2+c^2) : :
X(61897) = -25*X[2]+4*X[3], 20*X[141]+X[51214], 20*X[1125]+X[50871], 20*X[1698]+X[50872], 20*X[3589]+X[51027], 125*X[3617]+64*X[58237], 20*X[3618]+X[51215], -25*X[3624]+7*X[58231], 20*X[3634]+X[51120], 4*X[3653]+3*X[54448], 4*X[3656]+17*X[46932], 20*X[3763]+X[51028] and many others

X(61897) lies on these lines: {2, 3}, {13, 42804}, {14, 42803}, {141, 51214}, {1125, 50871}, {1327, 6485}, {1328, 6484}, {1698, 50872}, {3589, 51027}, {3617, 58237}, {3618, 51215}, {3624, 58231}, {3634, 51120}, {3653, 54448}, {3656, 46932}, {3763, 51028}, {3828, 11531}, {5032, 38317}, {5097, 11160}, {5102, 21356}, {5318, 43297}, {5321, 43296}, {6199, 42605}, {6395, 42604}, {6417, 54597}, {6418, 43536}, {6445, 42539}, {6446, 42540}, {6459, 10139}, {6460, 10140}, {6480, 43254}, {6481, 43255}, {6486, 43257}, {6487, 43256}, {7811, 32883}, {9542, 42274}, {9779, 38068}, {10172, 16200}, {11180, 50664}, {11278, 46933}, {11480, 43202}, {11481, 43201}, {11485, 43253}, {11486, 43252}, {12045, 20791}, {12815, 31407}, {13903, 43387}, {13961, 43386}, {14971, 38746}, {16241, 43243}, {16242, 43242}, {16644, 42983}, {16645, 42982}, {18581, 43199}, {18582, 43200}, {19569, 55819}, {19862, 50864}, {19872, 50802}, {19875, 58241}, {19878, 50868}, {19883, 30392}, {20582, 55722}, {25055, 38155}, {25565, 55587}, {30315, 51103}, {31145, 33179}, {31238, 51064}, {31253, 50865}, {31412, 51850}, {32787, 41947}, {32788, 41948}, {32897, 37671}, {34573, 51166}, {34754, 43404}, {34755, 43403}, {35770, 42602}, {35771, 42603}, {38074, 58234}, {38076, 54445}, {38314, 54447}, {38758, 59376}, {40680, 55958}, {40693, 42480}, {40694, 42481}, {41961, 42575}, {41962, 42574}, {41977, 49826}, {41978, 49827}, {42089, 43540}, {42092, 43541}, {42095, 43107}, {42098, 43100}, {42119, 42475}, {42120, 42474}, {42130, 43553}, {42131, 43552}, {42260, 43567}, {42261, 43566}, {42490, 42589}, {42491, 42588}, {42522, 42583}, {42523, 42582}, {42561, 51849}, {42580, 49824}, {42581, 49825}, {42592, 42961}, {42593, 42960}, {42598, 49861}, {42599, 49862}, {42786, 51171}, {43465, 43643}, {43466, 43638}, {43479, 49876}, {43480, 49875}, {46930, 50821}, {46931, 50810}, {47354, 55699}, {48310, 55703}, {51023, 51126}, {51025, 51127}, {51128, 55607}, {51211, 54169}, {52704, 52707}

X(61897) = midpoint of X(i) and X(j) for these {i,j}: {3545, 15702}, {3851, 5054}
X(61897) = reflection of X(i) in X(j) for these {i,j}: {10304, 3523}, {14269, 3857}, {15698, 5054}, {15703, 15699}, {3832, 3545}
X(61897) = inverse of X(61846) in orthocentroidal circle
X(61897) = inverse of X(61846) in Yff hyperbola
X(61897) = complement of X(61830)
X(61897) = anticomplement of X(61866)
X(61897) = pole of line {523, 61846} with respect to the orthocentroidal circle
X(61897) = pole of line {6, 61846} with respect to the Kiepert hyperbola
X(61897) = pole of line {523, 61846} with respect to the Yff hyperbola
X(61897) = intersection, other than A, B, C, of circumconics {{A, B, C, X(253), X(15694)}}, {{A, B, C, X(8797), X(15721)}}, {{A, B, C, X(10303), X(55958)}}, {{A, B, C, X(15692), X(40410)}}, {{A, B, C, X(36889), X(55864)}}
X(61897) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10109, 15640}, {2, 15022, 376}, {2, 15683, 3525}, {2, 15717, 10124}, {2, 3091, 15721}, {2, 3146, 15694}, {2, 3545, 15708}, {2, 381, 10303}, {2, 3832, 15702}, {2, 5, 15692}, {2, 5055, 3839}, {2, 5056, 3543}, {2, 5068, 549}, {2, 5071, 20}, {2, 547, 5056}, {5, 15759, 381}, {20, 10303, 15712}, {30, 15699, 15703}, {30, 3545, 3832}, {30, 3857, 14269}, {30, 5054, 15698}, {376, 15701, 5154}, {381, 10303, 15697}, {547, 11539, 5055}, {3090, 14869, 15022}, {3090, 15698, 5071}, {3090, 15703, 2}, {3523, 7486, 3090}, {3528, 15702, 15719}, {3533, 5067, 3628}, {3533, 5071, 3845}, {3543, 15697, 5059}, {3545, 15702, 30}, {3545, 15709, 11001}, {3545, 16239, 15705}, {3843, 11540, 15715}, {3845, 11812, 15695}, {3851, 15701, 15684}, {5054, 5055, 14892}, {5055, 11539, 3545}, {5055, 15688, 5}, {5071, 15698, 3851}, {11001, 15719, 15759}, {15692, 15701, 3523}, {15697, 15705, 10304}

X(61898) = X(2)X(3)∩X(6)X(43568)

Barycentrics    8*a^4+17*(b^2-c^2)^2-25*a^2*(b^2+c^2) : :
X(61898) = -17*X[2]+3*X[3], -8*X[551]+X[61295], 3*X[576]+4*X[41152], 5*X[597]+2*X[43150], -3*X[1353]+10*X[51185], -3*X[1483]+10*X[51105], 3*X[3653]+4*X[61259], X[3654]+6*X[61269], -2*X[3656]+9*X[61270], -2*X[4669]+9*X[38042], X[4677]+6*X[5901], -2*X[4745]+9*X[38083] and many others

X(61898) lies on these lines: {2, 3}, {6, 43568}, {61, 42503}, {62, 42502}, {395, 43025}, {396, 43024}, {524, 42786}, {551, 61295}, {576, 41152}, {597, 43150}, {1353, 51185}, {1483, 51105}, {3055, 18362}, {3653, 61259}, {3654, 61269}, {3656, 61270}, {4669, 38042}, {4677, 5901}, {4745, 38083}, {5093, 51183}, {5318, 43468}, {5321, 43467}, {5476, 50982}, {5790, 50831}, {5844, 51068}, {5886, 16191}, {6721, 36523}, {7581, 60294}, {7582, 60293}, {7617, 51123}, {8584, 24206}, {8960, 42606}, {9167, 15092}, {9956, 38022}, {10171, 50821}, {10172, 38112}, {10175, 50824}, {10222, 51070}, {10283, 51093}, {10302, 60192}, {11055, 61550}, {11178, 12007}, {11230, 51087}, {11272, 14711}, {11542, 49906}, {11543, 49905}, {11669, 60228}, {11698, 59376}, {13157, 31846}, {13607, 51108}, {13925, 42526}, {13993, 42527}, {14128, 16226}, {14561, 50978}, {14692, 23234}, {14831, 32205}, {14848, 50990}, {14971, 51872}, {15067, 58470}, {15088, 22251}, {15300, 61576}, {15533, 18583}, {15534, 51182}, {16808, 42792}, {16809, 42791}, {16966, 43228}, {16967, 43229}, {17502, 50803}, {17508, 50960}, {19116, 42603}, {19117, 42602}, {19875, 61272}, {19876, 61268}, {19924, 51128}, {20252, 35751}, {20253, 36329}, {20399, 41148}, {21850, 25565}, {22165, 50985}, {23302, 41122}, {23303, 41121}, {25055, 37705}, {25561, 51126}, {28150, 51088}, {28160, 50833}, {28168, 51078}, {28174, 50826}, {28178, 50807}, {28198, 51073}, {29012, 50988}, {29323, 51133}, {30308, 61267}, {30315, 51097}, {31406, 39593}, {32787, 42640}, {32788, 42639}, {32789, 43381}, {32790, 43380}, {33606, 37835}, {33607, 37832}, {34380, 50994}, {35255, 43513}, {35256, 43514}, {35812, 41951}, {35813, 41952}, {35814, 42582}, {35815, 42583}, {35885, 46266}, {36386, 61515}, {36388, 61516}, {36767, 59401}, {36969, 42685}, {36970, 42684}, {38028, 51085}, {38074, 51700}, {38080, 60963}, {38082, 61595}, {38084, 58421}, {38110, 51138}, {38317, 51140}, {38745, 41151}, {41100, 42915}, {41101, 42914}, {41107, 42121}, {41108, 42124}, {41112, 42146}, {41113, 42143}, {41119, 42913}, {41120, 42912}, {41147, 51524}, {42089, 42474}, {42092, 42475}, {42095, 42492}, {42098, 42493}, {42117, 42955}, {42118, 42954}, {42129, 42496}, {42132, 42497}, {42135, 42687}, {42138, 42686}, {42159, 42509}, {42162, 42508}, {42262, 43211}, {42265, 43212}, {42274, 52047}, {42277, 52048}, {42488, 42532}, {42489, 42533}, {42500, 42918}, {42501, 42919}, {42506, 42598}, {42507, 42599}, {42578, 43322}, {42579, 43323}, {42600, 43504}, {42601, 43503}, {42607, 58866}, {42610, 42925}, {42611, 42924}, {42627, 49813}, {42628, 49812}, {42690, 42923}, {42691, 42922}, {42775, 43635}, {42776, 43634}, {42777, 43302}, {42778, 43303}, {42795, 46335}, {42796, 46334}, {42910, 49810}, {42911, 49811}, {42916, 42975}, {42917, 42974}, {42944, 42965}, {42945, 42964}, {42976, 49908}, {42977, 49907}, {42984, 43644}, {42985, 43649}, {43010, 43874}, {43011, 43873}, {43028, 43416}, {43029, 43417}, {43102, 43109}, {43103, 43108}, {43207, 43542}, {43208, 43543}, {43558, 60314}, {43559, 60313}, {47353, 50987}, {50798, 61293}, {50804, 61280}, {50811, 61262}, {50832, 61260}, {50865, 61266}, {51094, 61277}, {51184, 54132}, {53104, 60282}, {54521, 60643}, {54608, 60100}, {54643, 60278}, {54866, 60646}, {60175, 60239}, {60333, 60637}

X(61898) = midpoint of X(i) and X(j) for these {i,j}: {381, 3523}, {549, 3857}, {3090, 15703}, {3832, 15700}, {3851, 15702}, {19876, 61268}
X(61898) = reflection of X(i) in X(j) for these {i,j}: {15700, 140}, {3090, 547}, {549, 3526}
X(61898) = inverse of X(61843) in orthocentroidal circle
X(61898) = inverse of X(61843) in Yff hyperbola
X(61898) = complement of X(15701)
X(61898) = pole of line {523, 61843} with respect to the orthocentroidal circle
X(61898) = pole of line {6, 43483} with respect to the Kiepert hyperbola
X(61898) = pole of line {523, 61843} with respect to the Yff hyperbola
X(61898) = intersection, other than A, B, C, of circumconics {{A, B, C, X(20), X(31846)}}, {{A, B, C, X(4846), X(58204)}}, {{A, B, C, X(8703), X(40410)}}, {{A, B, C, X(10301), X(60192)}}, {{A, B, C, X(11812), X(55958)}}, {{A, B, C, X(13599), X(49139)}}, {{A, B, C, X(13623), X(15690)}}, {{A, B, C, X(52285), X(54608)}}
X(61898) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10109, 3845}, {2, 11001, 15694}, {2, 11812, 632}, {2, 15022, 15640}, {2, 15640, 15709}, {2, 15693, 10124}, {2, 15697, 3525}, {2, 15698, 3526}, {2, 3534, 11540}, {2, 381, 11812}, {2, 3830, 140}, {2, 3845, 15713}, {2, 5071, 3830}, {2, 8703, 11539}, {5, 11539, 15687}, {30, 140, 15700}, {30, 547, 3090}, {140, 3830, 15711}, {376, 14892, 3858}, {376, 5079, 14892}, {377, 3525, 5070}, {381, 15709, 548}, {381, 5055, 15022}, {381, 632, 17504}, {547, 1656, 15699}, {547, 3628, 5055}, {548, 3856, 17578}, {1656, 7486, 3628}, {3090, 15701, 10109}, {3090, 15703, 30}, {3090, 3528, 5056}, {3090, 3628, 3857}, {3090, 5067, 3523}, {3523, 3832, 3529}, {3525, 14269, 14891}, {3526, 3534, 15701}, {3529, 15022, 5072}, {3534, 15701, 15698}, {3545, 10303, 15684}, {3545, 15684, 3856}, {3545, 15693, 12101}, {3627, 5054, 15714}, {3627, 5056, 5}, {3628, 12103, 13741}, {3628, 12812, 10303}, {3628, 5066, 2}, {3830, 15711, 15686}, {3839, 15723, 3530}, {3843, 15708, 15691}, {3857, 14869, 15704}, {5054, 11737, 3627}, {5054, 5056, 11737}, {5055, 5072, 5071}, {5055, 7486, 547}, {5056, 15717, 6950}, {5066, 11540, 3534}, {5066, 15759, 4}, {6825, 15693, 3524}, {10109, 11540, 5066}, {10124, 12101, 15693}, {10124, 12812, 3545}, {10124, 15684, 549}, {11539, 15687, 15712}, {12101, 15693, 550}, {14892, 16239, 376}, {15022, 15709, 381}, {15684, 15706, 16434}, {15686, 15711, 8703}, {15700, 15701, 15719}, {15701, 15713, 14869}, {41107, 43104, 43246}, {41108, 43101, 43247}, {42121, 43246, 41107}, {42124, 43247, 41108}, {43024, 43031, 396}, {43025, 43030, 395}, {43568, 43569, 6}

X(61899) = X(2)X(3)∩X(6)X(51178)

Barycentrics    5*a^4+11*(b^2-c^2)^2-16*a^2*(b^2+c^2) : :
X(61899) = -11*X[2]+2*X[3], -10*X[6]+X[51178], 8*X[10]+X[34631], -X[69]+28*X[42786], -10*X[141]+X[50973], -5*X[185]+32*X[40284], 4*X[551]+5*X[5818], 4*X[576]+5*X[50990], 4*X[597]+5*X[40330], X[671]+8*X[6721], 2*X[946]+7*X[19876], 8*X[1125]+X[34627] and many others

X(61899) lies on these lines: {2, 3}, {6, 51178}, {10, 34631}, {69, 42786}, {98, 60616}, {141, 50973}, {185, 40284}, {262, 60629}, {325, 32885}, {371, 42571}, {372, 42570}, {395, 43542}, {396, 43543}, {485, 43386}, {486, 43387}, {519, 54447}, {542, 55707}, {551, 5818}, {576, 50990}, {597, 40330}, {671, 6721}, {946, 19876}, {1056, 3582}, {1058, 3584}, {1125, 34627}, {1151, 43505}, {1152, 43506}, {1285, 31415}, {1327, 60316}, {1328, 60315}, {1352, 55709}, {1587, 42572}, {1588, 42573}, {1698, 50810}, {1699, 38068}, {1992, 24206}, {3054, 46453}, {3068, 6435}, {3069, 6436}, {3163, 61340}, {3241, 9956}, {3316, 32787}, {3317, 32788}, {3576, 38076}, {3589, 11180}, {3592, 41951}, {3594, 41952}, {3616, 32900}, {3618, 11178}, {3619, 20423}, {3620, 51179}, {3622, 50798}, {3624, 50796}, {3634, 31162}, {3653, 59387}, {3655, 5550}, {3656, 9780}, {3679, 10595}, {3763, 50967}, {3828, 8227}, {3933, 32893}, {4669, 9624}, {4677, 31399}, {4678, 50805}, {4687, 51043}, {4740, 61522}, {4751, 51038}, {4772, 51039}, {4995, 10591}, {5032, 38079}, {5092, 50956}, {5237, 42775}, {5238, 42776}, {5298, 10590}, {5306, 31404}, {5318, 42474}, {5321, 42475}, {5334, 43101}, {5335, 43104}, {5365, 42490}, {5366, 42491}, {5422, 54434}, {5476, 55719}, {5485, 9771}, {5587, 19883}, {5603, 10172}, {5642, 15081}, {5651, 43572}, {5657, 10171}, {5790, 38022}, {5817, 38093}, {5881, 51108}, {5886, 38083}, {5901, 31145}, {6054, 6722}, {6172, 61595}, {6361, 50802}, {6427, 42526}, {6428, 42527}, {6451, 43508}, {6452, 43507}, {6480, 43513}, {6481, 43514}, {6498, 8976}, {6499, 13951}, {6564, 43255}, {6565, 43254}, {6667, 10711}, {6684, 30308}, {6688, 11459}, {6723, 10706}, {7581, 13847}, {7582, 13846}, {7608, 60627}, {7612, 54616}, {7617, 9741}, {7735, 14075}, {7741, 10385}, {7746, 34571}, {7773, 32883}, {7776, 32897}, {7799, 34803}, {7809, 34229}, {7967, 10175}, {7982, 51069}, {7988, 28194}, {7989, 51705}, {7998, 14845}, {7999, 21969}, {8252, 23267}, {8253, 23273}, {8591, 61576}, {8596, 61561}, {8797, 55958}, {9140, 12900}, {9143, 20304}, {9167, 14639}, {9779, 28198}, {9812, 61266}, {9955, 34632}, {10056, 10589}, {10072, 10588}, {10164, 61265}, {10168, 51023}, {10170, 11451}, {10219, 15030}, {10222, 51072}, {10247, 38081}, {10516, 48310}, {10519, 38072}, {10576, 13939}, {10577, 13886}, {10653, 42915}, {10654, 42914}, {10707, 58421}, {10708, 58420}, {10709, 58426}, {10710, 58418}, {10714, 58431}, {10716, 58419}, {10718, 58430}, {11160, 18583}, {11177, 61575}, {11179, 55702}, {11230, 38314}, {11412, 58470}, {11477, 51143}, {11488, 37835}, {11489, 37832}, {11693, 12383}, {12045, 16261}, {12112, 59777}, {12117, 31274}, {12150, 38223}, {12243, 14061}, {12245, 51709}, {12699, 50809}, {12702, 46930}, {13464, 51066}, {13624, 50799}, {13665, 43212}, {13692, 26469}, {13785, 43211}, {13812, 26468}, {13925, 42640}, {13993, 42639}, {14157, 22112}, {14226, 34089}, {14241, 34091}, {14482, 43291}, {14494, 22110}, {14561, 21356}, {14651, 14971}, {14831, 15024}, {14853, 21358}, {14912, 47352}, {15032, 17825}, {15082, 54041}, {15561, 41135}, {15808, 50801}, {16187, 43574}, {16200, 38098}, {16241, 42111}, {16242, 42114}, {16267, 16967}, {16268, 16966}, {16644, 43873}, {16645, 43874}, {16772, 49876}, {16773, 49875}, {16808, 43201}, {16809, 43202}, {16962, 18581}, {16963, 18582}, {18362, 31401}, {18440, 51176}, {18493, 46932}, {18840, 54523}, {18841, 60185}, {18842, 44401}, {19130, 54170}, {19862, 50811}, {19872, 50865}, {19877, 50821}, {19878, 34648}, {19924, 55613}, {20049, 61510}, {20057, 50804}, {20582, 54132}, {21151, 38075}, {21168, 38073}, {21445, 41139}, {22236, 49824}, {22238, 49825}, {22791, 46931}, {23249, 42567}, {23259, 42566}, {23269, 41946}, {23275, 41945}, {23302, 43404}, {23303, 43403}, {23514, 41134}, {25565, 54173}, {27268, 51040}, {28204, 61257}, {28208, 54445}, {30315, 51093}, {31238, 51044}, {31239, 33706}, {31253, 50808}, {31670, 50966}, {31673, 50819}, {32001, 57822}, {32789, 43509}, {32790, 43510}, {32816, 52718}, {32817, 37647}, {32818, 46951}, {32819, 32884}, {32821, 32892}, {32822, 32839}, {32823, 32838}, {32837, 59635}, {33416, 42472}, {33417, 42473}, {33602, 43239}, {33603, 43238}, {33604, 43446}, {33605, 43447}, {34474, 38077}, {34573, 50970}, {34595, 50828}, {34718, 46933}, {36427, 40065}, {36765, 48311}, {36889, 40410}, {36948, 54105}, {38025, 38149}, {38036, 38101}, {38064, 55700}, {38067, 59385}, {38080, 51516}, {38082, 38107}, {38084, 38752}, {38108, 59374}, {38171, 59375}, {38253, 54763}, {38317, 55713}, {38318, 59386}, {38319, 59377}, {39874, 47354}, {40693, 49812}, {40694, 49813}, {41107, 43783}, {41108, 43784}, {41112, 42494}, {41113, 42495}, {41119, 41944}, {41120, 41943}, {41121, 42149}, {41122, 42152}, {41869, 50829}, {41963, 43564}, {41964, 43565}, {42089, 44015}, {42092, 44016}, {42093, 42500}, {42094, 42501}, {42095, 43463}, {42098, 43464}, {42107, 52079}, {42110, 52080}, {42129, 42986}, {42132, 42987}, {42139, 42972}, {42142, 42973}, {42154, 42692}, {42155, 42693}, {42163, 42610}, {42166, 42611}, {42258, 43522}, {42259, 43521}, {42274, 43374}, {42277, 43375}, {42413, 43504}, {42414, 43503}, {42488, 49908}, {42489, 49907}, {42496, 42818}, {42497, 42817}, {42532, 42979}, {42533, 42978}, {42588, 42813}, {42589, 42814}, {42598, 49948}, {42599, 49947}, {42633, 42983}, {42634, 42982}, {42803, 42923}, {42804, 42922}, {42815, 43252}, {42816, 43253}, {42904, 42997}, {42905, 42996}, {42924, 43246}, {42925, 43247}, {42998, 49906}, {42999, 49905}, {43004, 43233}, {43005, 43232}, {43028, 43100}, {43029, 43107}, {43240, 43484}, {43241, 43483}, {43273, 51126}, {43666, 54797}, {43787, 53518}, {43788, 53519}, {46934, 50824}, {48880, 51029}, {48905, 50960}, {48910, 50984}, {49861, 61719}, {50806, 61524}, {50813, 51074}, {50955, 51171}, {50959, 51128}, {50969, 51129}, {50977, 55586}, {50981, 55604}, {51022, 55676}, {51105, 61289}, {51106, 61288}, {51127, 51135}, {51130, 55582}, {51212, 55592}, {51538, 55621}, {53098, 54637}, {54660, 60137}, {54788, 60173}, {58230, 61260}, {59417, 61269}, {60123, 60284}, {60126, 60240}, {60127, 60183}, {60322, 60646}, {60984, 61511}

X(61899) = midpoint of X(i) and X(j) for these {i,j}: {381, 15707}, {3545, 15709}, {3839, 15705}
X(61899) = reflection of X(i) in X(j) for these {i,j}: {10304, 15707}, {15705, 5054}, {15707, 11539}, {15709, 2}, {15710, 15708}, {376, 15705}, {3524, 15709}
X(61899) = inverse of X(15702) in orthocentroidal circle
X(61899) = inverse of X(15702) in Yff hyperbola
X(61899) = complement of X(15708)
X(61899) = anticomplement of X(61864)
X(61899) = pole of line {523, 15702} with respect to the orthocentroidal circle
X(61899) = pole of line {6, 15702} with respect to the Kiepert hyperbola
X(61899) = pole of line {523, 15702} with respect to the Yff hyperbola
X(61899) = pole of line {69, 15694} with respect to the Wallace hyperbola
X(61899) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(15694)}}, {{A, B, C, X(140), X(36889)}}, {{A, B, C, X(264), X(15702)}}, {{A, B, C, X(297), X(60616)}}, {{A, B, C, X(376), X(40410)}}, {{A, B, C, X(458), X(60629)}}, {{A, B, C, X(549), X(8797)}}, {{A, B, C, X(550), X(31846)}}, {{A, B, C, X(631), X(55958)}}, {{A, B, C, X(1138), X(37934)}}, {{A, B, C, X(1494), X(15709)}}, {{A, B, C, X(3088), X(54500)}}, {{A, B, C, X(3146), X(54763)}}, {{A, B, C, X(3525), X(57822)}}, {{A, B, C, X(3533), X(57895)}}, {{A, B, C, X(3832), X(54660)}}, {{A, B, C, X(3839), X(46455)}}, {{A, B, C, X(3854), X(40448)}}, {{A, B, C, X(4232), X(10155)}}, {{A, B, C, X(4846), X(15685)}}, {{A, B, C, X(5059), X(13599)}}, {{A, B, C, X(6995), X(54523)}}, {{A, B, C, X(7378), X(60185)}}, {{A, B, C, X(7408), X(60127)}}, {{A, B, C, X(7409), X(60150)}}, {{A, B, C, X(10124), X(36948)}}, {{A, B, C, X(10299), X(52441)}}, {{A, B, C, X(12812), X(14843)}}, {{A, B, C, X(14487), X(18535)}}, {{A, B, C, X(14494), X(52301)}}, {{A, B, C, X(17578), X(60121)}}, {{A, B, C, X(18853), X(61138)}}, {{A, B, C, X(31363), X(50690)}}, {{A, B, C, X(37174), X(54616)}}, {{A, B, C, X(43536), X(55569)}}, {{A, B, C, X(44682), X(46412)}}, {{A, B, C, X(50687), X(54838)}}, {{A, B, C, X(50689), X(60122)}}, {{A, B, C, X(52281), X(60627)}}, {{A, B, C, X(52284), X(53103)}}, {{A, B, C, X(54097), X(54682)}}, {{A, B, C, X(54597), X(55573)}}
X(61899) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10303, 15723}, {2, 10304, 11539}, {2, 11737, 10299}, {2, 15022, 3543}, {2, 15692, 3526}, {2, 15697, 11540}, {2, 15721, 632}, {2, 20, 15694}, {2, 30, 15709}, {2, 3090, 5071}, {2, 3091, 549}, {2, 3523, 10124}, {2, 3543, 140}, {2, 3544, 15715}, {2, 376, 3525}, {2, 3832, 15721}, {2, 4, 15702}, {2, 5, 376}, {2, 5056, 381}, {2, 5066, 15719}, {2, 5068, 15692}, {2, 5071, 4}, {2, 549, 3533}, {2, 6175, 17567}, {2, 6919, 15670}, {2, 7486, 547}, {3, 5, 3854}, {4, 15684, 6848}, {5, 10124, 3830}, {5, 12102, 3851}, {5, 549, 3860}, {30, 11539, 15707}, {30, 15708, 15710}, {30, 5054, 15705}, {140, 15022, 3855}, {140, 3543, 15698}, {140, 3855, 17538}, {376, 15682, 1657}, {376, 3545, 3839}, {376, 631, 12100}, {381, 15695, 3853}, {381, 3628, 2}, {546, 15693, 15683}, {549, 3091, 15682}, {549, 3853, 15695}, {631, 3090, 5056}, {1656, 3090, 5067}, {1656, 5055, 15699}, {1656, 7486, 3090}, {1657, 3853, 3146}, {3090, 3529, 12812}, {3090, 3545, 5055}, {3090, 3628, 3544}, {3091, 3533, 3528}, {3522, 15694, 6967}, {3526, 12812, 5068}, {3526, 5068, 3529}, {3534, 11737, 3832}, {3545, 15709, 30}, {3618, 11178, 50974}, {3627, 11540, 15700}, {3627, 15700, 15697}, {3830, 10124, 3523}, {3832, 10299, 11541}, {3832, 15721, 3534}, {3832, 17533, 20}, {3850, 15713, 15681}, {3851, 15723, 8703}, {5054, 15688, 15718}, {5055, 5070, 14269}, {5056, 17697, 17800}, {5068, 15692, 3845}, {5072, 15701, 15687}, {5079, 15694, 5066}, {8703, 15723, 10303}, {10109, 14893, 5}, {10175, 25055, 38074}, {10304, 11539, 631}, {10576, 42603, 19054}, {10577, 42602, 19053}, {11539, 12100, 5054}, {11539, 15699, 3628}, {12101, 14093, 5059}, {12101, 14869, 14093}, {12811, 15720, 17578}, {14269, 14892, 3091}, {14782, 14783, 15704}, {14892, 15699, 5070}, {14971, 23234, 14651}, {15022, 15688, 3545}, {15681, 15713, 15717}, {15682, 15695, 11001}, {15687, 15701, 3522}, {15687, 16239, 15701}, {15688, 15714, 10304}, {15708, 15710, 3524}, {15709, 15710, 15708}, {15765, 18585, 15696}, {16966, 42910, 37640}, {16967, 42911, 37641}, {19053, 42602, 13886}, {19054, 42603, 13939}, {25055, 38074, 7967}, {32789, 43509, 43517}, {32790, 43510, 43518}, {34803, 53127, 52713}, {38127, 61271, 5603}, {41943, 42580, 41120}, {41944, 42581, 41119}, {51082, 61256, 34627}

X(61900) = X(2)X(3)∩X(11)X(38629)

Barycentrics    4*a^4+9*(b^2-c^2)^2-13*a^2*(b^2+c^2) : :
X(61900) = -27*X[2]+5*X[3], 2*X[8]+9*X[61273], 9*X[10]+2*X[58240], 9*X[11]+2*X[38629], 9*X[113]+2*X[38626], 9*X[114]+2*X[38627], 9*X[115]+2*X[38628], 9*X[116]+2*X[38630], 9*X[119]+2*X[38631], 9*X[125]+2*X[38632], 9*X[141]+2*X[55718], 9*X[373]+2*X[11591] and many others

X(61900) lies on these lines: {2, 3}, {8, 61273}, {10, 58240}, {11, 38629}, {15, 42492}, {16, 42493}, {61, 42916}, {62, 42917}, {113, 38626}, {114, 38627}, {115, 38628}, {116, 38630}, {119, 38631}, {125, 38632}, {141, 55718}, {233, 15860}, {373, 11591}, {395, 42779}, {396, 42780}, {397, 42938}, {398, 42939}, {551, 61297}, {576, 3631}, {597, 51180}, {1007, 32886}, {1125, 38138}, {1353, 6329}, {1483, 3636}, {1484, 20400}, {1493, 16254}, {1503, 55694}, {1506, 41940}, {1698, 61269}, {3054, 35007}, {3055, 53096}, {3244, 9956}, {3316, 45385}, {3317, 45384}, {3589, 55708}, {3592, 18762}, {3594, 18538}, {3616, 61245}, {3619, 55724}, {3622, 61293}, {3624, 61259}, {3629, 22330}, {3632, 5901}, {3644, 61549}, {3746, 10593}, {3828, 50822}, {3917, 18874}, {4686, 61522}, {5237, 42138}, {5238, 42135}, {5306, 12815}, {5349, 42798}, {5350, 42797}, {5351, 42110}, {5352, 42107}, {5365, 43634}, {5366, 43635}, {5480, 55588}, {5563, 10592}, {5609, 12900}, {5690, 10172}, {5790, 20057}, {5818, 61295}, {5876, 15012}, {5886, 16189}, {5891, 32205}, {5892, 45957}, {6102, 6688}, {6154, 38763}, {6248, 32523}, {6419, 42583}, {6420, 42582}, {6425, 42274}, {6426, 42277}, {6427, 13925}, {6428, 13993}, {6447, 42561}, {6448, 31412}, {6453, 32789}, {6454, 32790}, {6484, 42566}, {6485, 42567}, {6488, 6561}, {6489, 6560}, {6666, 38137}, {6667, 51529}, {6721, 38229}, {6722, 51523}, {6723, 51522}, {7583, 42578}, {7584, 42579}, {7617, 59546}, {7843, 15597}, {7967, 58235}, {7982, 38112}, {7988, 61524}, {7989, 58229}, {7991, 61268}, {8227, 58245}, {8981, 53516}, {10170, 15026}, {10171, 22791}, {10175, 15178}, {10187, 41107}, {10188, 41108}, {10219, 40647}, {10272, 15027}, {10576, 19116}, {10577, 19117}, {10627, 14845}, {10653, 42611}, {10654, 42610}, {11008, 11482}, {11451, 16881}, {11695, 15060}, {11704, 61690}, {11801, 15034}, {12046, 16982}, {12699, 61267}, {12820, 43633}, {12821, 43632}, {13391, 27355}, {13464, 38083}, {13966, 53513}, {14128, 45187}, {14644, 22251}, {15025, 32423}, {15029, 15061}, {15039, 15081}, {15044, 38794}, {15054, 40685}, {15801, 21357}, {15806, 43837}, {15850, 51587}, {16241, 43486}, {16242, 43485}, {16644, 43110}, {16645, 43111}, {16772, 42592}, {16773, 42593}, {16964, 43248}, {16965, 43249}, {16966, 42599}, {16967, 42598}, {17005, 50570}, {17852, 35256}, {18358, 53093}, {18553, 48310}, {18583, 40341}, {19130, 55597}, {19872, 61614}, {19878, 38140}, {19925, 31666}, {20050, 61510}, {20054, 61597}, {20190, 39884}, {20304, 24981}, {20398, 51872}, {20583, 34507}, {21850, 55583}, {22236, 42143}, {22238, 42146}, {22331, 31415}, {22332, 43620}, {22793, 31253}, {22844, 61515}, {22845, 61516}, {23039, 58531}, {23237, 58432}, {23302, 42580}, {23303, 42581}, {25055, 61249}, {25147, 58429}, {25339, 57316}, {29181, 55628}, {30315, 34747}, {30389, 61261}, {31399, 34641}, {31419, 52795}, {31423, 61266}, {31447, 50802}, {32785, 42643}, {32786, 42644}, {33416, 42165}, {33417, 42164}, {34126, 38757}, {34127, 35021}, {34128, 38791}, {34573, 38136}, {34595, 61263}, {34773, 61260}, {35022, 38734}, {36836, 42111}, {36843, 42114}, {37688, 61555}, {38022, 50831}, {38028, 58232}, {38107, 60983}, {38110, 55704}, {38139, 58433}, {38171, 60980}, {38729, 61574}, {38740, 61575}, {38751, 61576}, {38775, 61577}, {38787, 61578}, {38807, 40340}, {40330, 53092}, {40410, 41005}, {42112, 43872}, {42113, 43871}, {42121, 42166}, {42124, 42163}, {42144, 43196}, {42145, 43195}, {42147, 43547}, {42148, 43546}, {42153, 42633}, {42156, 42634}, {42159, 43029}, {42162, 43028}, {42431, 42501}, {42432, 42500}, {42474, 42921}, {42475, 42920}, {42488, 42613}, {42489, 42612}, {42496, 42989}, {42497, 42988}, {42539, 60315}, {42540, 60316}, {42568, 43513}, {42569, 43514}, {42635, 42979}, {42636, 42978}, {42813, 42948}, {42814, 42949}, {43101, 43419}, {43104, 43418}, {43197, 43644}, {43198, 43649}, {43238, 43417}, {43239, 43416}, {43467, 44016}, {43468, 44015}, {43598, 46865}, {46932, 58249}, {48874, 55623}, {48876, 55721}, {48906, 55698}, {51105, 61290}, {51128, 55617}, {51163, 55647}, {51525, 58421}, {51526, 58420}, {51527, 58426}, {51528, 58418}, {51532, 58431}, {51534, 58419}, {51536, 58430}, {51700, 61251}, {58710, 61613}, {60142, 60279}, {60286, 60332}, {60933, 61511}, {60942, 61595}, {60957, 61509}

X(61900) = midpoint of X(i) and X(j) for these {i,j}: {381, 15719}, {3525, 5072}, {3855, 15720}, {5056, 5070}
X(61900) = reflection of X(i) in X(j) for these {i,j}: {15717, 140}, {5, 5056}, {8703, 15718}
X(61900) = inverse of X(55863) in orthocentroidal circle
X(61900) = inverse of X(55863) in Yff hyperbola
X(61900) = complement of X(15720)
X(61900) = pole of line {523, 55863} with respect to the orthocentroidal circle
X(61900) = pole of line {185, 58203} with respect to the Jerabek hyperbola
X(61900) = pole of line {6, 42938} with respect to the Kiepert hyperbola
X(61900) = pole of line {523, 55863} with respect to the Yff hyperbola
X(61900) = intersection, other than A, B, C, of circumconics {{A, B, C, X(140), X(57897)}}, {{A, B, C, X(264), X(55863)}}, {{A, B, C, X(376), X(31846)}}, {{A, B, C, X(550), X(40410)}}, {{A, B, C, X(1105), X(58203)}}, {{A, B, C, X(3845), X(14938)}}, {{A, B, C, X(3857), X(40448)}}, {{A, B, C, X(11812), X(22268)}}, {{A, B, C, X(13599), X(17800)}}, {{A, B, C, X(15719), X(22270)}}, {{A, B, C, X(43970), X(47598)}}, {{A, B, C, X(46936), X(60007)}}
X(61900) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10299, 3526}, {2, 14869, 632}, {2, 15707, 10124}, {2, 3090, 5079}, {2, 3545, 15700}, {2, 3855, 15720}, {2, 5, 550}, {2, 5055, 11737}, {2, 5056, 3855}, {2, 5071, 14269}, {2, 546, 14869}, {3, 15022, 12811}, {3, 3090, 12812}, {3, 3091, 12102}, {3, 3857, 3627}, {3, 5, 3857}, {3, 5079, 3544}, {5, 11539, 4}, {5, 15687, 3851}, {5, 15712, 381}, {5, 1656, 15699}, {5, 549, 3858}, {30, 140, 15717}, {30, 15718, 8703}, {140, 11737, 382}, {140, 12102, 3}, {140, 12811, 11541}, {140, 3091, 15704}, {140, 382, 17504}, {140, 3856, 376}, {381, 10303, 12103}, {404, 16371, 16418}, {546, 3530, 3529}, {547, 3628, 3090}, {632, 3627, 549}, {1010, 10109, 546}, {1656, 3090, 3628}, {1656, 7486, 547}, {3090, 3091, 5055}, {3090, 3525, 5056}, {3090, 5067, 3091}, {3091, 10303, 5059}, {3091, 15708, 3146}, {3146, 3525, 15718}, {3523, 3861, 15686}, {3525, 5056, 5072}, {3525, 5072, 30}, {3526, 14269, 10299}, {3526, 5071, 3850}, {3529, 11319, 15723}, {3530, 3851, 15687}, {3533, 3843, 12100}, {3544, 16408, 15707}, {3544, 17571, 5073}, {3545, 12812, 6913}, {3628, 10109, 12108}, {3839, 11540, 15714}, {3854, 15696, 12101}, {3854, 15709, 15696}, {3859, 11812, 1657}, {5054, 5068, 3853}, {5055, 15703, 15693}, {5067, 15717, 5070}, {5070, 15720, 2}, {5070, 5072, 3525}, {10109, 15703, 11539}, {10303, 12103, 15712}, {11346, 11357, 5067}, {11737, 17504, 3845}, {12103, 12108, 15705}, {12103, 16239, 10303}, {12811, 12812, 15022}, {12811, 15022, 5}, {14782, 14783, 11001}, {15705, 15721, 15719}, {15715, 15720, 3530}, {15717, 15723, 140}, {15765, 18585, 15690}, {16370, 17526, 11108}, {42146, 42591, 22238}

X(61901) = X(2)X(3)∩X(17)X(49904)

Barycentrics    7*a^4+16*(b^2-c^2)^2-23*a^2*(b^2+c^2) : :
X(61901) = -16*X[2]+3*X[3], 3*X[355]+10*X[51109], 6*X[576]+7*X[51189], -X[599]+14*X[42786], -64*X[1125]+25*X[58233], 3*X[1351]+10*X[50993], X[1482]+12*X[38083], 6*X[3576]+7*X[50800], X[3654]+12*X[10171], X[3656]+12*X[10172], 5*X[3763]+8*X[25565], 8*X[3828]+5*X[18493] and many others

X(61901) lies on these lines: {2, 3}, {17, 49904}, {18, 49903}, {355, 51109}, {576, 51189}, {599, 42786}, {1125, 58233}, {1351, 50993}, {1482, 38083}, {3070, 6475}, {3071, 6474}, {3576, 50800}, {3654, 10171}, {3656, 10172}, {3763, 25565}, {3828, 18493}, {4677, 10247}, {4745, 5886}, {5024, 18362}, {5085, 50957}, {5093, 15533}, {5334, 43247}, {5335, 43246}, {5355, 22246}, {5418, 6472}, {5420, 6473}, {5476, 51186}, {5790, 50804}, {6500, 10576}, {6501, 10577}, {6564, 43415}, {6565, 9690}, {6669, 36363}, {6670, 36362}, {7585, 42640}, {7586, 42639}, {7603, 21309}, {7617, 51122}, {7988, 50806}, {7999, 12046}, {8148, 19875}, {8227, 38066}, {8584, 50961}, {8976, 41947}, {9167, 38733}, {9812, 50825}, {9956, 51093}, {10145, 41945}, {10146, 41946}, {10164, 50807}, {10175, 50801}, {10219, 40280}, {10246, 61254}, {10283, 51092}, {10519, 51173}, {11178, 53091}, {11230, 50798}, {11482, 51187}, {11485, 41122}, {11486, 41121}, {11542, 49861}, {11543, 49862}, {11898, 38079}, {12017, 25561}, {12045, 16194}, {12331, 38084}, {12645, 38022}, {12702, 19876}, {12816, 33416}, {12817, 33417}, {13103, 36767}, {13665, 42608}, {13785, 42609}, {13951, 41948}, {14561, 50991}, {14711, 32447}, {14762, 55007}, {14848, 22165}, {14971, 48657}, {15300, 38732}, {15534, 24206}, {15561, 36523}, {16241, 42475}, {16242, 42474}, {16644, 42532}, {16645, 42533}, {16808, 42505}, {16809, 42504}, {16966, 42507}, {16967, 42506}, {17851, 32790}, {18440, 48310}, {18510, 43881}, {18512, 43882}, {18525, 19883}, {18583, 50992}, {20252, 35750}, {20253, 36331}, {21167, 50964}, {21358, 44456}, {23251, 42524}, {23261, 42525}, {23302, 41120}, {23303, 41119}, {25055, 61250}, {28208, 34595}, {32787, 42526}, {32788, 42527}, {32789, 41955}, {33602, 42493}, {33603, 42492}, {33622, 61515}, {33624, 61516}, {34718, 51069}, {34748, 47745}, {36768, 59401}, {37624, 51110}, {37640, 42950}, {37641, 42951}, {37727, 41150}, {37832, 49906}, {37835, 49905}, {38042, 50805}, {38064, 48662}, {38068, 48661}, {38069, 38756}, {38072, 55584}, {38082, 60922}, {38093, 60884}, {38104, 48667}, {38317, 50955}, {41100, 42098}, {41101, 42095}, {41107, 42915}, {41108, 42914}, {41112, 42985}, {41113, 42984}, {41943, 43776}, {41944, 43775}, {41977, 42611}, {41978, 42610}, {42108, 42594}, {42109, 42595}, {42121, 49826}, {42124, 49827}, {42125, 42511}, {42126, 42791}, {42127, 42792}, {42128, 42510}, {42129, 42911}, {42130, 42500}, {42131, 42501}, {42132, 42910}, {42143, 49824}, {42146, 49825}, {42159, 43107}, {42162, 43100}, {42488, 42976}, {42489, 42977}, {42494, 42591}, {42495, 42590}, {42502, 42974}, {42503, 42975}, {42508, 43028}, {42509, 43029}, {42598, 49811}, {42599, 49810}, {42627, 43543}, {42628, 43542}, {42631, 42919}, {42632, 42918}, {42912, 49873}, {42913, 49874}, {43314, 43790}, {43315, 43789}, {46932, 58250}, {47353, 55697}, {48311, 48655}, {48312, 48656}, {49912, 49920}, {49913, 49919}, {49939, 49941}, {49940, 49942}, {50810, 61269}, {50828, 61263}, {50962, 50990}, {50963, 55593}, {50980, 51538}, {51024, 55624}, {51095, 61277}, {51096, 61276}, {51130, 54173}, {51175, 59399}, {51516, 60963}, {60971, 61511}

X(61901) = reflection of X(i) in X(j) for these {i,j}: {381, 5068}
X(61901) = inverse of X(15713) in orthocentroidal circle
X(61901) = inverse of X(15713) in Yff hyperbola
X(61901) = complement of X(61822)
X(61901) = pole of line {523, 15713} with respect to the orthocentroidal circle
X(61901) = pole of line {6, 15713} with respect to the Kiepert hyperbola
X(61901) = pole of line {523, 15713} with respect to the Yff hyperbola
X(61901) = intersection, other than A, B, C, of circumconics {{A, B, C, X(264), X(15713)}}, {{A, B, C, X(548), X(31846)}}, {{A, B, C, X(3534), X(40410)}}, {{A, B, C, X(8797), X(15719)}}, {{A, B, C, X(11540), X(57822)}}, {{A, B, C, X(14938), X(50689)}}, {{A, B, C, X(15319), X(55857)}}, {{A, B, C, X(15701), X(55958)}}, {{A, B, C, X(18317), X(21734)}}
X(61901) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10109, 381}, {2, 12100, 3526}, {2, 15682, 140}, {2, 15713, 15723}, {2, 15719, 10124}, {2, 3090, 10109}, {2, 3091, 15719}, {2, 3534, 15694}, {2, 3545, 12100}, {2, 376, 11540}, {2, 3845, 5054}, {2, 4, 15713}, {2, 5066, 15693}, {2, 5071, 3845}, {4, 15723, 15707}, {5, 3628, 3533}, {20, 5071, 14892}, {20, 5076, 5073}, {140, 15682, 15716}, {140, 15716, 15701}, {140, 381, 15689}, {381, 14892, 3851}, {381, 15716, 15682}, {381, 15723, 14891}, {381, 1656, 15699}, {381, 3090, 5055}, {381, 3534, 12101}, {381, 5054, 20}, {381, 5073, 14269}, {381, 8703, 3830}, {382, 11539, 15718}, {546, 15709, 14093}, {547, 15699, 3090}, {632, 3839, 15700}, {1656, 3090, 5070}, {1656, 5055, 15703}, {1656, 5079, 5067}, {3090, 5067, 5068}, {3091, 10124, 15688}, {3522, 15721, 3524}, {3524, 15701, 15722}, {3525, 15687, 15706}, {3526, 3545, 15681}, {3534, 15720, 15711}, {3544, 15708, 14893}, {3545, 15721, 3627}, {3628, 5055, 15684}, {3830, 15681, 15640}, {3839, 15700, 17800}, {3845, 5054, 15695}, {3851, 5055, 5071}, {6837, 11540, 1657}, {10109, 12101, 5}, {10109, 15699, 2}, {11812, 12101, 8703}, {14269, 15684, 5076}, {14269, 15694, 3}, {14269, 15722, 3534}, {14893, 15708, 15696}, {15682, 15689, 15685}

X(61902) = X(2)X(3)∩X(15)X(33603)

Barycentrics    13*a^4+31*(b^2-c^2)^2-44*a^2*(b^2+c^2) : :
X(61902) = -31*X[2]+6*X[3], -2*X[4669]+27*X[54447], 9*X[5603]+16*X[51069], 3*X[5818]+2*X[51105], 18*X[5886]+7*X[51068], 24*X[10150]+X[43453], 24*X[10171]+X[50810], 24*X[10175]+X[50818], 3*X[10595]+2*X[51072], X[11455]+24*X[12045], 18*X[14561]+7*X[50994], 9*X[14853]+16*X[51143] and many others

X(61902) lies on these lines: {2, 3}, {15, 33603}, {16, 33602}, {17, 49859}, {18, 49860}, {3316, 43323}, {3317, 43322}, {4669, 54447}, {5603, 51069}, {5702, 61340}, {5818, 51105}, {5886, 51068}, {6669, 36344}, {6670, 36319}, {7583, 42527}, {7584, 42526}, {7585, 54597}, {7586, 43536}, {7612, 60287}, {7809, 52718}, {8252, 51850}, {8253, 51849}, {8972, 43387}, {10150, 43453}, {10171, 50810}, {10175, 50818}, {10595, 51072}, {10653, 43240}, {10654, 43241}, {11455, 12045}, {11542, 43555}, {11543, 43554}, {13941, 43386}, {14226, 32785}, {14241, 32786}, {14494, 60638}, {14561, 50994}, {14853, 51143}, {16960, 42910}, {16961, 42911}, {16962, 43447}, {16963, 43446}, {16966, 42481}, {16967, 42480}, {18581, 42516}, {18582, 42517}, {18928, 44834}, {21356, 42786}, {23302, 49873}, {23303, 49874}, {28232, 30308}, {28234, 51066}, {28236, 51109}, {32789, 41957}, {32790, 41958}, {33750, 50960}, {34089, 43211}, {34091, 43212}, {34631, 38083}, {36346, 61516}, {36352, 61515}, {36969, 43295}, {36970, 43294}, {37640, 49810}, {37641, 49811}, {37832, 42513}, {37835, 42512}, {38074, 51108}, {40330, 51185}, {41112, 42915}, {41113, 42914}, {42089, 42588}, {42092, 42589}, {42095, 42957}, {42098, 42956}, {42103, 43502}, {42106, 43501}, {42111, 43482}, {42114, 43481}, {42125, 43493}, {42128, 43494}, {42508, 43100}, {42509, 43107}, {42510, 43464}, {42511, 43463}, {42518, 43229}, {42519, 43228}, {42574, 43510}, {42575, 43509}, {42606, 43880}, {42607, 43879}, {42777, 49948}, {42778, 49947}, {42813, 43310}, {42814, 43311}, {43101, 49824}, {43102, 43540}, {43103, 43541}, {43104, 49825}, {43308, 54593}, {43309, 54594}, {43320, 43518}, {43321, 43517}, {43374, 52047}, {43375, 52048}, {43487, 43646}, {43488, 43645}, {50827, 61271}, {51131, 55654}, {51213, 55643}, {60127, 60131}, {60150, 60645}

X(61902) = inverse of X(61838) in orthocentroidal circle
X(61902) = inverse of X(61838) in Yff hyperbola
X(61902) = pole of line {523, 61838} with respect to the orthocentroidal circle
X(61902) = pole of line {6, 61838} with respect to the Kiepert hyperbola
X(61902) = pole of line {523, 61838} with respect to the Yff hyperbola
X(61902) = pole of line {69, 61851} with respect to the Wallace hyperbola
X(61902) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3853), X(54838)}}, {{A, B, C, X(3858), X(54660)}}, {{A, B, C, X(5073), X(54763)}}, {{A, B, C, X(8797), X(15693)}}, {{A, B, C, X(11001), X(40410)}}, {{A, B, C, X(15686), X(18852)}}, {{A, B, C, X(18854), X(55857)}}, {{A, B, C, X(31846), X(46853)}}, {{A, B, C, X(37174), X(60287)}}
X(61902) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11001, 15709}, {2, 15640, 140}, {2, 3545, 15698}, {2, 3839, 11812}, {2, 5, 11001}, {2, 5056, 5066}, {2, 5066, 3524}, {2, 8703, 3525}, {4, 3524, 15686}, {376, 15717, 15710}, {376, 3090, 5055}, {376, 3845, 15682}, {382, 15693, 15695}, {443, 15022, 20}, {631, 5071, 3545}, {1656, 15694, 15699}, {1656, 3091, 5067}, {3091, 5055, 5071}, {3091, 5059, 3843}, {3628, 3830, 2}, {3839, 6921, 547}, {3845, 12100, 15685}, {3855, 15709, 15691}, {5055, 15699, 15708}, {5055, 15703, 382}, {5055, 15723, 5}, {6921, 7486, 5070}, {11001, 15759, 376}, {11540, 12100, 14869}, {11541, 15702, 17504}, {11737, 12100, 3845}, {11737, 15708, 4}, {12812, 15699, 15694}, {15674, 15689, 15702}, {15685, 15694, 15693}, {15686, 15695, 15697}, {15688, 15701, 12100}, {15692, 15709, 631}, {15693, 15711, 15717}, {15693, 15759, 15692}, {42512, 42520, 49862}, {42513, 42521, 49861}

X(61903) = X(2)X(3)∩X(156)X(46865)

Barycentrics    5*a^4+12*(b^2-c^2)^2-17*a^2*(b^2+c^2) : :
X(61903) = -36*X[2]+7*X[3], 20*X[1125]+9*X[61257], X[1351]+28*X[42786], -3*X[3060]+32*X[12046], 25*X[3616]+4*X[61246], 20*X[3617]+9*X[58238], 8*X[3625]+21*X[10247], 8*X[3630]+21*X[5093], X[3633]+28*X[9956], 8*X[3635]+21*X[5790], -30*X[3763]+X[55580], 144*X[3828]+X[58249] and many others

X(61903) lies on these lines: {2, 3}, {156, 46865}, {1125, 61257}, {1351, 42786}, {3060, 12046}, {3311, 43881}, {3312, 43882}, {3616, 61246}, {3617, 58238}, {3625, 10247}, {3630, 5093}, {3633, 9956}, {3635, 5790}, {3763, 55580}, {3828, 58249}, {4668, 10222}, {4691, 5886}, {4764, 61522}, {5334, 42590}, {5335, 42591}, {5418, 53520}, {5420, 53517}, {5818, 61292}, {5901, 20053}, {6144, 11482}, {6199, 53516}, {6395, 53513}, {6407, 32789}, {6408, 32790}, {6417, 42583}, {6418, 42582}, {6419, 42558}, {6420, 42557}, {6427, 10576}, {6428, 10577}, {6445, 42270}, {6446, 42273}, {6447, 8253}, {6448, 8252}, {6519, 6565}, {6522, 6564}, {7999, 16982}, {8148, 38127}, {8976, 43880}, {9588, 50806}, {10172, 18493}, {10175, 37624}, {10246, 61256}, {10516, 55701}, {10620, 15029}, {11230, 61296}, {11485, 42580}, {11486, 42581}, {12645, 61280}, {12900, 15027}, {13951, 43879}, {15025, 15039}, {15034, 15088}, {15040, 15044}, {15046, 15054}, {15178, 37712}, {15860, 61340}, {16187, 37495}, {16644, 42435}, {16645, 42436}, {16964, 42475}, {16965, 42474}, {16966, 42530}, {16967, 42531}, {19130, 55595}, {21358, 55721}, {22234, 50955}, {22236, 42914}, {22238, 42915}, {25561, 55694}, {28212, 46930}, {31399, 58236}, {31666, 34595}, {32396, 55039}, {33414, 33415}, {33537, 43807}, {34573, 55593}, {37832, 43025}, {37835, 43024}, {38066, 58245}, {38072, 55583}, {38079, 51178}, {38083, 50817}, {38084, 38629}, {38107, 61000}, {38317, 53092}, {38724, 38795}, {38729, 38789}, {38732, 38751}, {38740, 38743}, {38763, 51517}, {42089, 42693}, {42092, 42692}, {42093, 42929}, {42094, 42928}, {42115, 44015}, {42116, 44016}, {42129, 42598}, {42132, 42599}, {42154, 43551}, {42155, 43550}, {42488, 42802}, {42489, 42801}, {42592, 42610}, {42593, 42611}, {42596, 42626}, {42597, 42625}, {42910, 42988}, {42911, 42989}, {42946, 43240}, {42947, 43241}, {42962, 43102}, {42963, 43103}, {43012, 43232}, {43013, 43233}, {43426, 49904}, {43427, 49903}, {46933, 61270}, {47353, 55698}, {48661, 51073}, {50798, 61289}, {50973, 55718}, {51024, 55623}, {51108, 61248}, {51126, 55692}, {51514, 60977}, {51516, 60962}, {53023, 55620}, {60976, 61511}

X(61903) = inverse of X(61837) in orthocentroidal circle
X(61903) = inverse of X(61837) in Yff hyperbola
X(61903) = complement of X(61817)
X(61903) = pole of line {523, 61837} with respect to the orthocentroidal circle
X(61903) = pole of line {6, 61837} with respect to the Kiepert hyperbola
X(61903) = pole of line {523, 61837} with respect to the Yff hyperbola
X(61903) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1657), X(40410)}}, {{A, B, C, X(3839), X(14938)}}, {{A, B, C, X(15721), X(22268)}}, {{A, B, C, X(31846), X(34200)}}, {{A, B, C, X(35409), X(54763)}}, {{A, B, C, X(35434), X(60121)}}, {{A, B, C, X(41987), X(60122)}}, {{A, B, C, X(44682), X(52441)}}
X(61903) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12812, 5072}, {2, 14890, 15723}, {2, 14892, 14093}, {2, 14893, 5054}, {2, 15689, 15694}, {2, 15712, 3526}, {2, 3090, 12812}, {2, 3545, 14891}, {2, 5, 1657}, {3, 15684, 17538}, {3, 15704, 15695}, {3, 3090, 5055}, {3, 5072, 3843}, {3, 5076, 15681}, {3, 546, 5073}, {5, 10124, 4}, {5, 12100, 3854}, {5, 12103, 3091}, {5, 140, 3839}, {5, 1656, 15703}, {5, 3523, 381}, {5, 3628, 3525}, {5, 3830, 3851}, {5, 632, 12102}, {140, 3544, 5076}, {140, 5076, 3}, {381, 15640, 14269}, {381, 1656, 5067}, {547, 7486, 1656}, {548, 11812, 15712}, {548, 3627, 3529}, {549, 3628, 13741}, {1656, 3526, 15699}, {1656, 5055, 5070}, {1656, 5079, 3628}, {1657, 3843, 3830}, {3090, 3628, 5079}, {3090, 5067, 15022}, {3091, 3525, 12103}, {3523, 17578, 376}, {3525, 3529, 3523}, {3526, 5073, 15707}, {3533, 5066, 15696}, {3627, 3628, 2}, {3628, 12812, 3627}, {3830, 15718, 15689}, {3851, 15694, 17800}, {5056, 5067, 11812}, {5067, 15022, 632}, {5068, 16239, 3534}, {5071, 10303, 12811}, {10303, 12811, 382}, {12102, 12108, 548}, {12108, 12812, 5}, {14782, 14783, 15683}, {15706, 15722, 15718}, {15765, 18585, 15697}, {33414, 33415, 47355}, {51073, 61266, 48661}

X(61904) = X(2)X(3)∩X(17)X(49810)

Barycentrics    11*a^4+29*(b^2-c^2)^2-40*a^2*(b^2+c^2) : :
X(61904) = -29*X[2]+6*X[3], 7*X[3619]+16*X[25565], 8*X[4669]+15*X[10595], -4*X[4745]+27*X[54447], 15*X[5587]+8*X[51085], 15*X[5603]+8*X[50827], 18*X[5790]+5*X[51092], 15*X[5818]+8*X[51103], 18*X[5886]+5*X[51072], -9*X[7967]+32*X[51108], 15*X[8227]+8*X[51069], 18*X[9779]+5*X[50809] and many others

X(61904) lies on these lines: {2, 3}, {17, 49810}, {18, 49811}, {1327, 43514}, {1328, 43513}, {3311, 60293}, {3312, 60294}, {3619, 25565}, {4669, 10595}, {4745, 54447}, {5343, 43107}, {5344, 43100}, {5587, 51085}, {5603, 50827}, {5790, 51092}, {5818, 51103}, {5886, 51072}, {6429, 60306}, {6430, 60305}, {6564, 43518}, {6565, 43517}, {6669, 36318}, {6670, 36320}, {7967, 51108}, {8227, 51069}, {9779, 50809}, {10155, 60228}, {10172, 50810}, {10175, 51105}, {10302, 54523}, {10516, 51138}, {11230, 50818}, {11488, 49908}, {11489, 49907}, {11669, 54637}, {12245, 38083}, {13607, 38074}, {13846, 43387}, {13847, 43386}, {13886, 42603}, {13939, 42602}, {14226, 43798}, {14241, 43797}, {14494, 60637}, {14561, 50990}, {14853, 50982}, {16960, 42953}, {16961, 42952}, {16966, 33606}, {16967, 33607}, {18538, 60299}, {18581, 33605}, {18582, 33604}, {18762, 60300}, {19053, 43536}, {19054, 43568}, {23269, 43259}, {23275, 43258}, {23302, 49824}, {23303, 49825}, {24206, 50992}, {31412, 34091}, {33602, 43464}, {33603, 43463}, {34089, 42561}, {34627, 51109}, {34631, 51066}, {36324, 61516}, {36326, 61515}, {37640, 42507}, {37641, 42506}, {37832, 49812}, {37835, 49813}, {38317, 50974}, {39874, 48310}, {41119, 42915}, {41120, 42914}, {41943, 42495}, {41944, 42494}, {42095, 49827}, {42098, 49826}, {42119, 43467}, {42120, 43468}, {42417, 43509}, {42418, 43510}, {42474, 42477}, {42475, 42476}, {42502, 49906}, {42503, 49905}, {42510, 43484}, {42511, 43483}, {42580, 42976}, {42581, 42977}, {42582, 42607}, {42583, 42606}, {42608, 43342}, {42609, 43343}, {42690, 42912}, {42691, 42913}, {42795, 42918}, {42796, 42919}, {42813, 43442}, {42814, 43443}, {42910, 49860}, {42911, 49859}, {43028, 43481}, {43029, 43482}, {43101, 49873}, {43104, 49874}, {43150, 59373}, {43211, 43341}, {43212, 43340}, {43374, 43381}, {43375, 43380}, {43505, 52045}, {43506, 52046}, {43542, 49948}, {43543, 49947}, {43558, 60302}, {43559, 60301}, {50808, 61265}, {50872, 61269}, {51078, 58221}, {51087, 59388}, {51133, 55673}, {51216, 55682}, {53103, 60282}, {53104, 60284}, {54521, 60629}, {54612, 60100}, {54616, 60175}, {54643, 60183}, {54707, 60278}, {54866, 60616}, {60127, 60643}, {60143, 60192}, {60150, 60646}, {60185, 60239}, {60333, 60627}, {60971, 61595}

X(61904) = inverse of X(61833) in orthocentroidal circle
X(61904) = inverse of X(61833) in Yff hyperbola
X(61904) = anticomplement of X(61862)
X(61904) = pole of line {523, 61833} with respect to the orthocentroidal circle
X(61904) = pole of line {6, 41965} with respect to the Kiepert hyperbola
X(61904) = pole of line {523, 61833} with respect to the Yff hyperbola
X(61904) = pole of line {69, 61847} with respect to the Wallace hyperbola
X(61904) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7408), X(54643)}}, {{A, B, C, X(7409), X(54608)}}, {{A, B, C, X(8797), X(12100)}}, {{A, B, C, X(10301), X(54523)}}, {{A, B, C, X(15682), X(40410)}}, {{A, B, C, X(15713), X(36889)}}, {{A, B, C, X(15719), X(55958)}}, {{A, B, C, X(31846), X(44682)}}, {{A, B, C, X(49135), X(54763)}}, {{A, B, C, X(50688), X(54838)}}, {{A, B, C, X(52285), X(54612)}}, {{A, B, C, X(52301), X(60192)}}
X(61904) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10109, 3545}, {2, 10304, 11540}, {2, 15682, 15702}, {2, 15701, 3533}, {2, 3091, 12100}, {2, 3534, 15709}, {2, 3543, 15713}, {2, 3839, 15701}, {2, 3845, 631}, {2, 5, 15682}, {4, 10303, 3528}, {4, 15698, 11001}, {4, 15702, 10304}, {4, 5055, 5071}, {376, 3545, 546}, {381, 16239, 15705}, {546, 16239, 15712}, {546, 1656, 13735}, {547, 5055, 7486}, {549, 10304, 10299}, {549, 5055, 15022}, {549, 5066, 3830}, {1656, 10109, 2}, {1656, 15688, 15703}, {1656, 3525, 5067}, {3090, 7486, 4}, {3524, 5071, 3544}, {3526, 15712, 10303}, {3526, 5072, 5073}, {3528, 11001, 15697}, {3528, 5059, 17538}, {3533, 3839, 15715}, {3534, 3545, 6833}, {3832, 10124, 15710}, {3839, 15715, 11541}, {3857, 15706, 3543}, {5055, 15703, 5072}, {7486, 15022, 1656}, {10109, 15690, 5}, {10109, 15699, 15716}, {10299, 15682, 15690}, {10303, 15705, 549}, {10303, 15759, 15719}, {10304, 15693, 15698}, {14890, 17800, 15692}, {14892, 15723, 3146}, {15702, 17538, 3524}, {15707, 17578, 376}

X(61905) = X(2)X(3)∩X(11)X(31480)

Barycentrics    3*a^4+8*(b^2-c^2)^2-11*a^2*(b^2+c^2) : :
X(61905) = -24*X[2]+5*X[3], 5*X[355]+14*X[15808], 18*X[373]+X[18436], 3*X[399]+16*X[20396], 12*X[1125]+7*X[61258], X[1482]+18*X[54447], 9*X[1699]+10*X[31447], 3*X[2979]+16*X[18874], 4*X[3244]+15*X[5790], 15*X[3616]+4*X[61249], X[3621]+18*X[61273], -21*X[3622]+2*X[61297] and many others

X(61905) lies on these lines: {2, 3}, {6, 61340}, {11, 31480}, {15, 42610}, {16, 42611}, {115, 31492}, {230, 31417}, {233, 15851}, {355, 15808}, {373, 18436}, {399, 20396}, {486, 31487}, {1007, 32868}, {1125, 61258}, {1159, 37692}, {1329, 31494}, {1482, 54447}, {1699, 31447}, {2979, 18874}, {3055, 31450}, {3066, 33540}, {3244, 5790}, {3411, 16967}, {3412, 16966}, {3614, 4317}, {3616, 61249}, {3621, 61273}, {3622, 61297}, {3624, 58230}, {3626, 5886}, {3631, 14561}, {3632, 9624}, {3636, 10175}, {3644, 61522}, {3763, 55584}, {3767, 22246}, {3818, 55692}, {3933, 32886}, {4301, 10172}, {4309, 7173}, {5093, 24206}, {5254, 31470}, {5305, 31407}, {5418, 9691}, {5550, 61259}, {5734, 59503}, {5735, 38318}, {5818, 61286}, {5876, 11465}, {5881, 11230}, {5901, 20050}, {6154, 51517}, {6199, 35812}, {6390, 32887}, {6395, 35813}, {6407, 6565}, {6408, 6564}, {6417, 10576}, {6418, 10577}, {6431, 42558}, {6432, 42557}, {6451, 35787}, {6452, 35786}, {6459, 43321}, {6460, 17851}, {6500, 8976}, {6501, 13951}, {6667, 38755}, {6683, 48663}, {6684, 61266}, {6688, 37481}, {6721, 38732}, {6722, 38743}, {6723, 38789}, {6767, 37720}, {7373, 37719}, {7603, 30435}, {7697, 32450}, {7743, 31436}, {7746, 43136}, {7749, 18584}, {7765, 31489}, {7886, 14535}, {7982, 38083}, {7988, 12702}, {7999, 13364}, {8148, 8227}, {9588, 9955}, {9589, 11231}, {9607, 31467}, {9669, 31452}, {9680, 9690}, {9681, 42270}, {9692, 23275}, {9698, 13881}, {9711, 31493}, {9780, 58247}, {10095, 54048}, {10137, 42568}, {10138, 42569}, {10145, 35255}, {10146, 35256}, {10170, 14531}, {10171, 11362}, {10187, 41100}, {10188, 41101}, {10194, 53513}, {10195, 53516}, {10222, 30315}, {10246, 37714}, {10516, 55705}, {10541, 25561}, {10653, 42985}, {10654, 42984}, {11008, 18583}, {11017, 15072}, {11178, 53092}, {11278, 61271}, {11402, 11704}, {11412, 58533}, {11444, 13321}, {11451, 11591}, {11459, 32205}, {11485, 42488}, {11486, 42489}, {11522, 38066}, {11542, 42951}, {11543, 42950}, {11695, 18435}, {11849, 61152}, {12045, 13474}, {12046, 15067}, {12245, 61270}, {12308, 20379}, {12315, 61735}, {12645, 20057}, {12818, 42259}, {12819, 42258}, {12900, 24981}, {13363, 15056}, {13464, 38098}, {13565, 55039}, {13624, 61264}, {13785, 31454}, {13903, 18762}, {13961, 18538}, {13966, 31414}, {14128, 15024}, {14226, 43883}, {14241, 43884}, {14845, 37484}, {14929, 52718}, {14971, 52090}, {15028, 15060}, {15037, 17814}, {15046, 15059}, {15047, 15068}, {15057, 61574}, {15069, 38317}, {15088, 32609}, {15178, 61252}, {15325, 31410}, {15603, 43457}, {15655, 39590}, {15815, 39601}, {16644, 42580}, {16645, 42581}, {16772, 42125}, {16773, 42128}, {16808, 42491}, {16809, 42490}, {16964, 43029}, {16965, 43028}, {17004, 61555}, {18357, 58233}, {18362, 22332}, {18526, 61255}, {18553, 55701}, {19106, 42597}, {19107, 42596}, {19130, 55593}, {19862, 61263}, {19872, 22793}, {19877, 38034}, {20054, 61510}, {20398, 48657}, {21358, 55724}, {22235, 42634}, {22236, 43419}, {22237, 42633}, {22238, 43418}, {23236, 23515}, {23513, 35023}, {23514, 35022}, {25555, 50955}, {31275, 47618}, {31420, 47742}, {31457, 44518}, {31479, 37722}, {32063, 32767}, {32787, 43323}, {32788, 43322}, {32790, 43415}, {33416, 42629}, {33417, 42630}, {33749, 47352}, {34595, 38140}, {34748, 61282}, {34754, 42690}, {34755, 42691}, {35021, 36519}, {35283, 44076}, {36836, 43486}, {36843, 43485}, {37638, 44300}, {37725, 38319}, {37832, 42779}, {37835, 42780}, {38042, 58238}, {38072, 55580}, {38084, 38665}, {38107, 60942}, {38108, 60980}, {38138, 46934}, {38314, 61290}, {38767, 58418}, {38779, 58419}, {38799, 58427}, {40107, 42786}, {40410, 57823}, {40693, 42129}, {40694, 42132}, {41121, 42978}, {41122, 42979}, {41973, 42592}, {41974, 42593}, {42089, 43106}, {42092, 43105}, {42096, 42545}, {42097, 42546}, {42111, 42147}, {42114, 42148}, {42115, 42813}, {42116, 42814}, {42149, 43104}, {42152, 43101}, {42154, 42997}, {42155, 42996}, {42160, 42949}, {42161, 42948}, {42417, 43433}, {42418, 43432}, {42474, 43239}, {42475, 43238}, {42494, 42913}, {42495, 42912}, {42598, 42910}, {42599, 42911}, {42602, 43880}, {42603, 43879}, {42612, 42636}, {42613, 42635}, {42627, 43307}, {42628, 43306}, {42934, 43241}, {42935, 43240}, {42946, 43373}, {42947, 43372}, {42992, 49906}, {42993, 49905}, {43195, 43633}, {43196, 43632}, {43230, 51944}, {43231, 51945}, {43570, 60298}, {43571, 60297}, {47355, 55697}, {48889, 55678}, {48895, 55648}, {48901, 55632}, {50798, 61288}, {50963, 52987}, {50993, 55718}, {51066, 58240}, {51514, 60957}, {51516, 60933}, {53023, 55616}, {53100, 60645}, {60131, 60142}, {60287, 60334}, {60332, 60638}, {60922, 60983}

X(61905) = inverse of X(14869) in orthocentroidal circle
X(61905) = inverse of X(14869) in Yff hyperbola
X(61905) = complement of X(61814)
X(61905) = pole of line {523, 14869} with respect to the orthocentroidal circle
X(61905) = pole of line {185, 15685} with respect to the Jerabek hyperbola
X(61905) = pole of line {6, 14869} with respect to the Kiepert hyperbola
X(61905) = pole of line {523, 14869} with respect to the Yff hyperbola
X(61905) = pole of line {69, 55709} with respect to the Wallace hyperbola
X(61905) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(140), X(57823)}}, {{A, B, C, X(264), X(14869)}}, {{A, B, C, X(382), X(40410)}}, {{A, B, C, X(1105), X(15685)}}, {{A, B, C, X(3832), X(14938)}}, {{A, B, C, X(8797), X(10299)}}, {{A, B, C, X(12100), X(31846)}}, {{A, B, C, X(13599), X(15704)}}, {{A, B, C, X(14489), X(37913)}}, {{A, B, C, X(14841), X(46935)}}, {{A, B, C, X(15318), X(15712)}}, {{A, B, C, X(15703), X(60007)}}, {{A, B, C, X(15707), X(55958)}}, {{A, B, C, X(21400), X(41099)}}, {{A, B, C, X(46455), X(50689)}}, {{A, B, C, X(55863), X(57897)}}
X(61905) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11737, 15688}, {2, 15687, 5054}, {2, 15715, 11539}, {2, 17679, 17561}, {2, 3091, 10299}, {2, 3529, 140}, {2, 3530, 3526}, {2, 3544, 550}, {2, 381, 15707}, {2, 3855, 3530}, {2, 4, 14869}, {2, 4208, 11354}, {2, 5, 382}, {2, 5056, 3544}, {2, 5079, 3851}, {2, 546, 15720}, {3, 1656, 15703}, {3, 3851, 14269}, {3, 4, 15685}, {5, 140, 3832}, {5, 15699, 16239}, {5, 3628, 631}, {5, 3859, 5068}, {5, 3861, 3545}, {5, 547, 7486}, {5, 548, 3091}, {5, 549, 3859}, {5, 7486, 1656}, {140, 3529, 15700}, {140, 3830, 3}, {140, 3832, 15696}, {140, 5071, 5072}, {140, 5072, 3830}, {381, 11539, 15695}, {381, 15723, 15714}, {381, 1656, 3628}, {381, 3853, 3843}, {381, 5054, 11001}, {381, 631, 17800}, {382, 15696, 3529}, {382, 15720, 3528}, {382, 3528, 15681}, {550, 14869, 12100}, {631, 6907, 15722}, {632, 1657, 15701}, {632, 3861, 15717}, {1656, 12812, 15694}, {1656, 3090, 5055}, {1656, 3526, 5067}, {2041, 2042, 15712}, {3091, 10299, 15687}, {3091, 5054, 5073}, {3523, 15717, 7390}, {3523, 5066, 5076}, {3523, 5076, 15689}, {3525, 17542, 632}, {3525, 3850, 3534}, {3526, 5067, 5070}, {3533, 3627, 15693}, {3545, 15717, 3861}, {3545, 16351, 548}, {3628, 5056, 381}, {3830, 5055, 5071}, {3843, 17800, 3853}, {3843, 3851, 3855}, {3851, 15681, 546}, {3851, 5055, 5079}, {3854, 15702, 15704}, {3857, 10124, 3522}, {3861, 15717, 1657}, {5076, 15723, 3523}, {6904, 15680, 17580}, {8976, 42583, 45385}, {8976, 45385, 6500}, {11737, 14869, 4}, {11737, 15699, 2}, {12100, 15686, 10304}, {12812, 16239, 5}, {13951, 42582, 45384}, {13951, 45384, 6501}, {14782, 14783, 5059}, {14892, 15704, 3854}, {15694, 15701, 14890}, {15695, 15707, 15715}, {19872, 61265, 22793}, {42598, 42910, 42989}, {42599, 42911, 42988}

X(61906) = X(2)X(3)∩X(962)X(19876)

Barycentrics    7*a^4+19*(b^2-c^2)^2-26*a^2*(b^2+c^2) : :
X(61906) = -19*X[2]+4*X[3], X[962]+14*X[19876], 7*X[3616]+2*X[61250], 14*X[3619]+X[51028], 14*X[3624]+X[50864], -16*X[3634]+X[34632], 4*X[3656]+11*X[46933], -2*X[4669]+17*X[30315], 14*X[4751]+X[51064], 11*X[5550]+4*X[50796], X[5603]+4*X[38083], X[5731]+4*X[38076] and many others

X(61906) lies on these lines: {2, 3}, {519, 61274}, {962, 19876}, {1007, 32874}, {3070, 6493}, {3071, 6492}, {3616, 61250}, {3619, 51028}, {3624, 50864}, {3634, 34632}, {3656, 46933}, {4669, 30315}, {4751, 51064}, {5032, 5965}, {5334, 43241}, {5335, 43240}, {5346, 31404}, {5550, 50796}, {5603, 38083}, {5731, 38076}, {5734, 51066}, {5818, 61284}, {5901, 20049}, {6490, 9542}, {6721, 8591}, {6722, 11177}, {7603, 37689}, {7811, 32867}, {7938, 55735}, {7988, 28228}, {8596, 61576}, {8981, 14226}, {9143, 12900}, {9693, 43564}, {9771, 11148}, {9778, 61265}, {9779, 28232}, {9780, 50872}, {9812, 38068}, {9955, 46930}, {9956, 31145}, {10171, 19875}, {10172, 38021}, {10175, 38314}, {10219, 15072}, {11160, 24206}, {11178, 51171}, {11230, 38074}, {11488, 43428}, {11489, 43429}, {11693, 14644}, {13464, 51068}, {13966, 14241}, {14484, 60279}, {14845, 33884}, {15808, 50871}, {16189, 51067}, {16267, 16961}, {16268, 16960}, {16644, 42516}, {16645, 42517}, {16962, 42894}, {16963, 42895}, {16966, 42512}, {16967, 42513}, {18362, 31400}, {18492, 50863}, {18510, 42542}, {18512, 42541}, {19053, 42582}, {19054, 42583}, {19116, 54597}, {19117, 43536}, {19872, 50808}, {19877, 31162}, {19878, 34628}, {20423, 42786}, {20582, 54174}, {22235, 49907}, {22237, 49908}, {23249, 43255}, {23259, 43254}, {23267, 43212}, {23273, 43211}, {23514, 52695}, {25055, 28236}, {25565, 54132}, {28198, 61266}, {28234, 53620}, {31263, 40333}, {31399, 51072}, {32836, 53127}, {32870, 37671}, {32885, 37668}, {33748, 47352}, {34573, 54170}, {34595, 34648}, {34627, 46934}, {34631, 61272}, {35242, 51074}, {35812, 43377}, {35813, 43376}, {35822, 42523}, {35823, 42522}, {36967, 43365}, {36968, 43364}, {36969, 43870}, {36970, 43869}, {37640, 42778}, {37641, 42777}, {37714, 51109}, {37749, 58427}, {37832, 43030}, {37835, 43031}, {38022, 59388}, {38066, 61269}, {38073, 38318}, {38082, 59386}, {38108, 59375}, {41119, 42489}, {41120, 42488}, {41943, 49824}, {41944, 49825}, {42089, 42933}, {42092, 42932}, {42111, 42972}, {42114, 42973}, {42129, 43542}, {42132, 43543}, {42139, 42475}, {42140, 42500}, {42141, 42501}, {42142, 42474}, {42149, 49874}, {42152, 49873}, {42153, 49862}, {42156, 49861}, {42472, 42943}, {42473, 42942}, {42496, 42987}, {42497, 42986}, {42510, 43480}, {42511, 43479}, {42518, 42598}, {42519, 42599}, {42520, 42999}, {42521, 42998}, {42588, 42944}, {42589, 42945}, {42635, 43544}, {42636, 43545}, {42966, 49826}, {42967, 49827}, {43028, 43242}, {43029, 43243}, {43407, 43566}, {43408, 43567}, {43416, 43464}, {43417, 43463}, {46931, 50821}, {46932, 50810}, {47355, 51023}, {48881, 51213}, {48895, 50969}, {50865, 51073}, {51024, 51128}, {51026, 55656}, {51092, 61276}, {51129, 55646}, {53099, 60286}, {60984, 61595}

X(61906) = midpoint of X(i) and X(j) for these {i,j}: {1656, 5055}, {3839, 15692}
X(61906) = reflection of X(i) in X(j) for these {i,j}: {15688, 15712}, {15693, 11539}, {3522, 3524}, {3524, 15694}, {3839, 3091}, {5071, 5055}
X(61906) = inverse of X(15721) in orthocentroidal circle
X(61906) = inverse of X(15721) in Yff hyperbola
X(61906) = complement of X(61812)
X(61906) = anticomplement of X(61861)
X(61906) = pole of line {523, 15721} with respect to the orthocentroidal circle
X(61906) = pole of line {6, 15721} with respect to the Kiepert hyperbola
X(61906) = pole of line {523, 15721} with respect to the Yff hyperbola
X(61906) = pole of line {69, 61846} with respect to the Wallace hyperbola
X(61906) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(253), X(15702)}}, {{A, B, C, X(264), X(15721)}}, {{A, B, C, X(3523), X(55958)}}, {{A, B, C, X(3543), X(40410)}}, {{A, B, C, X(8797), X(15692)}}, {{A, B, C, X(10303), X(36889)}}, {{A, B, C, X(11541), X(54763)}}, {{A, B, C, X(15712), X(31846)}}, {{A, B, C, X(52288), X(60279)}}, {{A, B, C, X(55864), X(57822)}}
X(61906) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15022, 381}, {2, 15683, 140}, {2, 15705, 11539}, {2, 3091, 15692}, {2, 3146, 15702}, {2, 3522, 15694}, {2, 3543, 10303}, {2, 381, 3523}, {2, 3832, 549}, {2, 3839, 15708}, {2, 5, 3543}, {2, 5071, 3091}, {2, 547, 7486}, {4, 11539, 15705}, {4, 14869, 7397}, {5, 14269, 3545}, {5, 3628, 15720}, {30, 11539, 15693}, {30, 15712, 15688}, {30, 3091, 3839}, {30, 3524, 3522}, {30, 5055, 5071}, {376, 11540, 5187}, {546, 15723, 15698}, {632, 1656, 5067}, {1656, 15693, 15703}, {1656, 3843, 3628}, {1656, 5055, 30}, {3090, 7486, 5056}, {3091, 3523, 17578}, {3091, 7486, 1656}, {3523, 10304, 17504}, {3524, 15709, 11812}, {3524, 3545, 14269}, {3526, 11737, 15682}, {3529, 3543, 15640}, {3839, 15708, 20}, {3851, 10124, 11001}, {3859, 15714, 3830}, {5055, 15709, 15022}, {5056, 10303, 5}, {5066, 15702, 3146}, {5067, 12811, 16052}, {5070, 7380, 5141}, {5071, 15713, 5068}, {5076, 15694, 15711}, {10109, 15699, 15689}, {10109, 15703, 4}, {11113, 15683, 3524}, {11178, 51171, 51215}, {11539, 15705, 15721}, {11737, 15682, 3854}, {12101, 15720, 376}, {13442, 15692, 11541}, {13735, 15683, 2}, {14269, 17504, 3529}, {15022, 17549, 12811}, {15689, 15705, 10304}, {15694, 15711, 631}, {15694, 15720, 15713}

X(61907) = X(2)X(3)∩X(10)X(61270)

Barycentrics    4*a^4+11*(b^2-c^2)^2-15*a^2*(b^2+c^2) : :
X(61907) = -33*X[2]+7*X[3], 4*X[10]+9*X[61270], X[40]+12*X[61267], -3*X[51]+16*X[12046], 11*X[141]+2*X[55719], 9*X[373]+4*X[14128], 10*X[576]+3*X[50985], -3*X[1353]+16*X[25555], 4*X[1385]+9*X[61260], X[1483]+12*X[10175], -22*X[3589]+9*X[55707], 10*X[3616]+3*X[61251] and many others

X(61907) lies on these lines: {2, 3}, {10, 61270}, {40, 61267}, {51, 12046}, {141, 55719}, {371, 43341}, {372, 43340}, {373, 14128}, {397, 42801}, {398, 42802}, {576, 50985}, {1007, 32888}, {1151, 43513}, {1152, 43514}, {1353, 25555}, {1385, 61260}, {1483, 10175}, {3589, 55707}, {3590, 13939}, {3591, 13886}, {3616, 61251}, {3624, 61262}, {3625, 9956}, {3630, 24206}, {3633, 5901}, {3635, 10283}, {3819, 12002}, {3820, 52795}, {4668, 5886}, {4691, 13464}, {4718, 61522}, {4764, 61549}, {5318, 42954}, {5321, 42955}, {5349, 33417}, {5350, 33416}, {5365, 42688}, {5366, 42689}, {5418, 43378}, {5420, 43379}, {5480, 55586}, {5690, 10171}, {5876, 6688}, {5882, 38138}, {6144, 18583}, {6199, 43377}, {6395, 43376}, {6419, 43410}, {6420, 43409}, {6435, 10576}, {6436, 10577}, {6445, 43505}, {6446, 43506}, {6470, 43317}, {6471, 43316}, {7173, 10386}, {7583, 43431}, {7584, 43430}, {7603, 12815}, {7604, 40634}, {7607, 60649}, {7608, 60250}, {7746, 14075}, {7755, 34571}, {7764, 16509}, {7999, 13451}, {8227, 38112}, {8550, 55709}, {8960, 19116}, {9781, 44324}, {10172, 22791}, {10187, 16773}, {10188, 16772}, {10194, 42265}, {10195, 42262}, {10222, 38081}, {10627, 27355}, {10653, 42591}, {10654, 42590}, {10992, 15092}, {11230, 13607}, {11444, 58531}, {11522, 61269}, {11669, 60209}, {11695, 45956}, {11698, 38319}, {11803, 21357}, {12007, 38317}, {13382, 15060}, {13565, 61659}, {14061, 14692}, {14845, 32142}, {14848, 51183}, {14862, 23332}, {15024, 31834}, {15082, 44863}, {15088, 30714}, {16241, 42964}, {16242, 42965}, {16267, 43427}, {16268, 43426}, {16808, 42686}, {16809, 42687}, {16966, 42993}, {16967, 42992}, {18553, 38110}, {18581, 42916}, {18582, 42917}, {19117, 42582}, {19130, 55592}, {19877, 28212}, {20053, 61273}, {20400, 38084}, {21850, 55581}, {23302, 42923}, {23303, 42922}, {25055, 61255}, {25561, 50987}, {28186, 34595}, {32455, 34507}, {32767, 44762}, {32821, 53127}, {34573, 55598}, {34597, 35888}, {36967, 42694}, {36968, 42695}, {38022, 51087}, {38034, 43174}, {38079, 51140}, {38083, 50827}, {38108, 61020}, {38136, 55589}, {40273, 61266}, {41943, 43247}, {41944, 43246}, {41973, 43483}, {41974, 43484}, {42095, 42925}, {42098, 42924}, {42103, 42773}, {42106, 42774}, {42111, 43238}, {42114, 43239}, {42115, 42775}, {42116, 42776}, {42117, 42492}, {42118, 42493}, {42135, 42945}, {42138, 42944}, {42143, 42152}, {42146, 42149}, {42150, 43103}, {42151, 43102}, {42159, 42475}, {42162, 42474}, {42163, 42934}, {42166, 42935}, {42415, 43772}, {42416, 43771}, {42431, 42928}, {42432, 42929}, {42435, 42580}, {42436, 42581}, {42488, 43101}, {42489, 43104}, {42494, 42691}, {42495, 42690}, {42522, 43881}, {42523, 43882}, {42602, 42640}, {42603, 42639}, {42627, 42999}, {42628, 42998}, {42786, 48876}, {42815, 43649}, {42816, 43644}, {42920, 43029}, {42921, 43028}, {42956, 43016}, {42957, 43017}, {43010, 43019}, {43011, 43018}, {43527, 60323}, {48874, 51128}, {48906, 55700}, {50831, 61278}, {50956, 55684}, {50981, 55606}, {51022, 55677}, {51110, 61248}, {51143, 55721}, {51180, 53092}, {53104, 60146}, {54447, 61272}, {54852, 60182}, {54857, 60100}, {60144, 60630}, {60192, 60640}, {60278, 60329}, {60293, 60304}, {60294, 60303}, {60962, 61595}, {60976, 61509}, {60977, 61511}

X(61907) = midpoint of X(i) and X(j) for these {i,j}: {5067, 5079}
X(61907) = reflection of X(i) in X(j) for these {i,j}: {10299, 140}, {5, 5079}
X(61907) = inverse of X(61832) in orthocentroidal circle
X(61907) = inverse of X(61832) in Yff hyperbola
X(61907) = complement of X(61811)
X(61907) = pole of line {523, 61832} with respect to the orthocentroidal circle
X(61907) = pole of line {185, 62156} with respect to the Jerabek hyperbola
X(61907) = pole of line {6, 42801} with respect to the Kiepert hyperbola
X(61907) = pole of line {523, 61832} with respect to the Yff hyperbola
X(61907) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(45760)}}, {{A, B, C, X(3519), X(16239)}}, {{A, B, C, X(3524), X(31846)}}, {{A, B, C, X(3530), X(60171)}}, {{A, B, C, X(3627), X(40410)}}, {{A, B, C, X(3858), X(14938)}}, {{A, B, C, X(5064), X(60323)}}, {{A, B, C, X(6662), X(15693)}}, {{A, B, C, X(8797), X(61138)}}, {{A, B, C, X(13599), X(15681)}}, {{A, B, C, X(13623), X(44245)}}, {{A, B, C, X(14861), X(15686)}}, {{A, B, C, X(14869), X(34483)}}, {{A, B, C, X(15708), X(42021)}}, {{A, B, C, X(38071), X(40448)}}, {{A, B, C, X(41983), X(55958)}}, {{A, B, C, X(46935), X(60007)}}, {{A, B, C, X(52281), X(60250)}}, {{A, B, C, X(52285), X(54857)}}
X(61907) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14891, 11539}, {2, 14892, 15686}, {2, 15684, 14890}, {2, 3545, 14093}, {2, 3843, 12108}, {2, 5, 3627}, {2, 5072, 548}, {4, 1656, 3628}, {4, 3523, 3534}, {4, 3533, 15717}, {4, 5072, 3850}, {4, 7486, 1656}, {5, 11539, 546}, {5, 140, 3858}, {5, 14869, 381}, {5, 15687, 12811}, {5, 632, 3845}, {5, 8703, 3091}, {30, 140, 10299}, {140, 1657, 15712}, {140, 3850, 1657}, {140, 3858, 550}, {140, 5056, 5}, {547, 3628, 7486}, {548, 12108, 15706}, {548, 3628, 2}, {631, 12811, 15687}, {1656, 15720, 15703}, {1656, 5055, 4}, {1656, 5056, 140}, {1657, 3854, 14893}, {2045, 2046, 5079}, {3090, 7486, 5055}, {3091, 15709, 17800}, {3091, 16239, 8703}, {3525, 3853, 17504}, {3526, 15022, 5066}, {3526, 5055, 15022}, {3526, 5066, 15704}, {3526, 5072, 15684}, {3534, 5055, 5071}, {3544, 5054, 3861}, {3627, 5072, 3857}, {3628, 10109, 3856}, {3628, 12812, 5072}, {3628, 3857, 632}, {3628, 5066, 3526}, {3855, 15694, 12103}, {5067, 5079, 30}, {11540, 15717, 14869}, {12108, 14892, 3843}, {14813, 14814, 16239}, {14869, 15717, 549}, {15765, 18585, 15691}, {16808, 43468, 42686}, {16809, 43467, 42687}, {42474, 42611, 42162}, {42475, 42610, 42159}, {43010, 43026, 43019}, {43011, 43027, 43018}

X(61908) = X(2)X(3)∩X(6)X(49903)

Barycentrics    5*a^4+14*(b^2-c^2)^2-19*a^2*(b^2+c^2) : :
X(61908) = -14*X[2]+3*X[3], 3*X[355]+8*X[51108], 10*X[551]+X[61244], 6*X[576]+5*X[50989], 7*X[599]+4*X[55716], 3*X[1351]+8*X[50991], 3*X[1482]+8*X[4745], 25*X[3616]+8*X[61253], -X[3654]+12*X[10172], -X[3656]+12*X[10171], -35*X[3763]+2*X[55585], 4*X[3828]+7*X[61268] and many others

X(61908) lies on these lines: {2, 3}, {6, 49903}, {15, 42475}, {16, 42474}, {17, 42507}, {18, 42506}, {355, 51108}, {395, 42951}, {396, 42950}, {399, 17825}, {551, 61244}, {576, 50989}, {590, 42573}, {599, 55716}, {615, 42572}, {1327, 32790}, {1328, 32789}, {1351, 50991}, {1482, 4745}, {3616, 61253}, {3654, 10172}, {3656, 10171}, {3763, 55585}, {3828, 61268}, {4669, 5886}, {4677, 9956}, {5050, 50954}, {5418, 42417}, {5420, 42418}, {5476, 50973}, {5790, 51093}, {5818, 34748}, {6221, 53520}, {6398, 53517}, {6427, 42606}, {6428, 42607}, {6468, 6565}, {6469, 6564}, {6470, 13903}, {6471, 13961}, {6560, 42567}, {6561, 42566}, {6669, 36383}, {6670, 36382}, {6721, 15300}, {7988, 50821}, {8162, 31479}, {8227, 34718}, {8584, 11898}, {8976, 42579}, {9771, 51122}, {9955, 19876}, {10150, 35002}, {10165, 50799}, {10170, 13321}, {10175, 50798}, {10246, 50797}, {10516, 55706}, {10576, 42526}, {10577, 42527}, {10595, 38081}, {11055, 11272}, {11178, 15516}, {11224, 50817}, {11230, 37712}, {11231, 30308}, {11412, 12046}, {11480, 12817}, {11481, 12816}, {11485, 41120}, {11486, 41119}, {11542, 49812}, {11543, 49813}, {11645, 55689}, {11999, 43597}, {12045, 14855}, {12188, 14971}, {12355, 23514}, {12645, 51071}, {12773, 59376}, {13103, 36768}, {13188, 36523}, {13464, 51067}, {13846, 18510}, {13847, 18512}, {13881, 39593}, {13951, 42578}, {14061, 48657}, {14537, 18584}, {14561, 22165}, {14711, 32520}, {14848, 15533}, {15038, 37672}, {15046, 20126}, {15092, 41134}, {15520, 15534}, {16241, 43248}, {16242, 43249}, {16267, 42989}, {16268, 42988}, {16644, 41122}, {16645, 41121}, {16966, 42975}, {16967, 42974}, {18362, 31489}, {18493, 19875}, {18526, 25055}, {19053, 45384}, {19054, 45385}, {19883, 61261}, {20252, 35749}, {20253, 36327}, {20423, 51143}, {21358, 25565}, {21849, 54048}, {23039, 58470}, {23302, 41113}, {23303, 41112}, {24844, 36525}, {25561, 47355}, {26446, 50806}, {31399, 51070}, {31412, 43212}, {33604, 42917}, {33605, 42916}, {33606, 42520}, {33607, 42521}, {33626, 61515}, {33627, 61516}, {36362, 59384}, {36363, 59383}, {36769, 59401}, {37624, 38074}, {37727, 51106}, {37832, 42129}, {37835, 42132}, {38042, 51068}, {38077, 38762}, {38079, 40330}, {38314, 61292}, {39899, 47352}, {41100, 42128}, {41101, 42125}, {41107, 42098}, {41108, 42095}, {41153, 53092}, {42093, 42632}, {42094, 42631}, {42103, 42500}, {42106, 42501}, {42115, 42693}, {42116, 42692}, {42121, 42985}, {42124, 42984}, {42126, 43645}, {42127, 43646}, {42135, 42589}, {42138, 42588}, {42143, 49873}, {42146, 49874}, {42154, 43296}, {42155, 43297}, {42157, 42504}, {42158, 42505}, {42270, 43254}, {42271, 43563}, {42272, 43562}, {42273, 43255}, {42508, 42973}, {42509, 42972}, {42518, 42952}, {42519, 42953}, {42532, 42580}, {42533, 42581}, {42561, 43211}, {42582, 42603}, {42583, 42602}, {42598, 49860}, {42599, 49859}, {42817, 42911}, {42818, 42910}, {42888, 43502}, {42889, 43501}, {42912, 43247}, {42913, 43246}, {42918, 46335}, {42919, 46334}, {42962, 43028}, {42963, 43029}, {42982, 43555}, {42983, 43554}, {43234, 54593}, {43235, 54594}, {43240, 43418}, {43241, 43419}, {43273, 55693}, {43380, 43888}, {43381, 43887}, {47867, 59402}, {49951, 49959}, {49954, 49960}, {50800, 51705}, {50802, 61266}, {50804, 51095}, {50864, 58230}, {50956, 51135}, {50957, 51737}, {50959, 55610}, {50963, 50970}, {50980, 55624}, {51023, 55697}, {51074, 58441}, {51091, 61276}, {51105, 61296}, {51173, 54173}, {51186, 55720}, {51516, 60971}, {53023, 55615}, {53124, 53863}, {53620, 61272}, {54131, 55590}, {60963, 61595}

X(61908) = midpoint of X(i) and X(j) for these {i,j}: {381, 15720}, {3855, 15721}, {5072, 15723}
X(61908) = reflection of X(i) in X(j) for these {i,j}: {15718, 3525}, {15720, 15723}, {15723, 5070}, {3, 15721}, {381, 5072}
X(61908) = inverse of X(11812) in orthocentroidal circle
X(61908) = inverse of X(11812) in Yff hyperbola
X(61908) = complement of X(15719)
X(61908) = pole of line {523, 11812} with respect to the orthocentroidal circle
X(61908) = pole of line {6, 11812} with respect to the Kiepert hyperbola
X(61908) = pole of line {523, 11812} with respect to the Yff hyperbola
X(61908) = intersection, other than A, B, C, of circumconics {{A, B, C, X(264), X(11812)}}, {{A, B, C, X(3530), X(31846)}}, {{A, B, C, X(3830), X(40410)}}, {{A, B, C, X(8797), X(15698)}}, {{A, B, C, X(12102), X(54585)}}, {{A, B, C, X(15693), X(55958)}}, {{A, B, C, X(18317), X(21735)}}
X(61908) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11001, 140}, {2, 15640, 15702}, {2, 15697, 15709}, {2, 15698, 11539}, {2, 3545, 8703}, {2, 3830, 5054}, {2, 3845, 15701}, {2, 3860, 15722}, {2, 4, 11812}, {2, 5, 3830}, {2, 5068, 15697}, {2, 5071, 5066}, {2, 8703, 15694}, {3, 15682, 3534}, {3, 3851, 3861}, {3, 3858, 382}, {3, 5055, 5071}, {3, 7486, 1656}, {4, 11812, 15695}, {4, 16858, 3530}, {5, 12108, 3854}, {5, 14893, 3545}, {5, 15699, 10124}, {5, 3146, 3851}, {5, 3628, 3523}, {30, 5070, 15723}, {140, 14269, 14093}, {140, 17578, 3}, {381, 15688, 5076}, {381, 15720, 30}, {381, 3526, 15688}, {381, 5055, 5079}, {382, 15694, 15706}, {382, 1656, 3628}, {546, 15711, 15640}, {547, 15699, 7486}, {547, 3090, 5055}, {632, 14892, 3543}, {632, 3543, 15707}, {1656, 12812, 15696}, {1656, 5054, 15703}, {1656, 5055, 381}, {1656, 5056, 15720}, {1656, 5079, 3526}, {3091, 15698, 12101}, {3523, 3545, 14893}, {3523, 3839, 15683}, {3524, 11737, 3843}, {3524, 15022, 11737}, {3525, 3830, 15716}, {3533, 12811, 17800}, {3534, 5054, 12100}, {3544, 16239, 5073}, {3545, 15683, 3858}, {3628, 8703, 2}, {3830, 15685, 3146}, {3830, 15722, 376}, {3858, 14893, 3839}, {4217, 7379, 3524}, {5054, 15723, 3525}, {5056, 5070, 5072}, {5068, 15709, 15687}, {5071, 15709, 5068}, {5071, 7486, 15699}, {5818, 38022, 34748}, {8227, 38083, 34718}, {10109, 12100, 5}, {10109, 15699, 15682}, {10124, 12100, 15713}, {11539, 12101, 15698}, {11812, 15695, 15700}, {12100, 15719, 15718}, {12101, 15698, 15681}, {14893, 15706, 1657}, {15640, 15702, 15711}, {15640, 15711, 15689}, {15683, 15721, 15715}, {15699, 15721, 5070}, {15716, 15720, 15693}, {15765, 18585, 17538}, {16966, 49908, 49905}, {16967, 49907, 49906}, {42912, 43247, 49824}, {42913, 43246, 49825}, {49903, 49904, 6}, {49905, 49908, 42975}, {49906, 49907, 42974}, {50817, 61271, 51709}, {51705, 61263, 50800}

X(61909) = X(2)X(3)∩X(395)X(42531)

Barycentrics    8*a^4+23*(b^2-c^2)^2-31*a^2*(b^2+c^2) : :
X(61909) = -23*X[2]+5*X[3], 8*X[551]+X[61245], -14*X[3619]+5*X[51184], -14*X[3624]+5*X[50832], -32*X[3636]+5*X[61295], X[3653]+2*X[61262], 2*X[5886]+X[38081], -10*X[5901]+X[34747], 4*X[6329]+5*X[11178], -14*X[9780]+5*X[50822], -10*X[9956]+X[34641], 2*X[10171]+X[38083] and many others

X(61909) lies on these lines: {2, 3}, {395, 42531}, {396, 42530}, {519, 61273}, {551, 61245}, {3411, 42502}, {3412, 42503}, {3619, 51184}, {3624, 50832}, {3636, 61295}, {3653, 61262}, {5886, 38081}, {5901, 34747}, {6329, 11178}, {6447, 56618}, {6448, 56619}, {6564, 41958}, {6565, 41957}, {8252, 43791}, {8253, 43792}, {9780, 50822}, {9956, 34641}, {10171, 38083}, {10175, 38022}, {11230, 61251}, {12040, 53144}, {12699, 50826}, {12820, 42088}, {12821, 42087}, {13665, 42644}, {13785, 42643}, {15808, 50824}, {16241, 43639}, {16242, 43640}, {16962, 43101}, {16963, 43104}, {16966, 42633}, {16967, 42634}, {18440, 51181}, {18581, 43110}, {18582, 43111}, {19116, 42602}, {19117, 42603}, {19875, 61269}, {19877, 50806}, {20057, 50831}, {22566, 35021}, {23302, 43419}, {23303, 43418}, {25055, 38138}, {25565, 48876}, {31670, 50981}, {31673, 50833}, {33602, 43480}, {33603, 43479}, {34595, 50799}, {36431, 61306}, {38042, 38098}, {38080, 38108}, {38314, 61293}, {41100, 41977}, {41101, 41978}, {41947, 42582}, {41948, 42583}, {42117, 43107}, {42118, 43100}, {42139, 42415}, {42142, 42416}, {42274, 43211}, {42277, 43212}, {42474, 43416}, {42475, 43417}, {42520, 43774}, {42521, 43773}, {42522, 60621}, {42523, 60620}, {42532, 42613}, {42533, 42612}, {42635, 42914}, {42636, 42915}, {42797, 46334}, {42798, 46335}, {42904, 43248}, {42905, 43249}, {42920, 43108}, {42921, 43109}, {43010, 43025}, {43011, 43024}, {43032, 43372}, {43033, 43373}, {43199, 43241}, {43200, 43240}, {43244, 43468}, {43245, 43467}, {43489, 43638}, {43490, 43643}, {43789, 52046}, {43790, 52045}, {46934, 50797}, {47355, 50987}, {48892, 51133}, {50823, 61272}, {50825, 51073}, {50980, 51128}, {51105, 61297}, {51171, 51180}, {54447, 61270}, {61265, 61614}

X(61909) = midpoint of X(i) and X(j) for these {i,j}: {381, 15708}, {3839, 15706}, {14269, 15710}
X(61909) = reflection of X(i) in X(j) for these {i,j}: {15706, 140}, {550, 15710}
X(61909) = inverse of X(61829) in orthocentroidal circle
X(61909) = inverse of X(61829) in Yff hyperbola
X(61909) = complement of X(15707)
X(61909) = pole of line {523, 61829} with respect to the orthocentroidal circle
X(61909) = pole of line {6, 42892} with respect to the Kiepert hyperbola
X(61909) = pole of line {523, 61829} with respect to the Yff hyperbola
X(61909) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3523), X(31846)}}, {{A, B, C, X(3530), X(55958)}}, {{A, B, C, X(8797), X(15715)}}, {{A, B, C, X(14938), X(41991)}}, {{A, B, C, X(15687), X(40410)}}
X(61909) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11359, 16853}, {2, 11737, 550}, {2, 15681, 140}, {2, 15720, 10124}, {2, 17504, 11539}, {2, 3091, 15715}, {2, 3528, 15694}, {2, 3544, 15681}, {2, 3545, 15688}, {2, 381, 3530}, {2, 3855, 15700}, {2, 5, 15687}, {2, 5071, 3851}, {2, 5079, 11737}, {3, 1656, 13735}, {5, 15686, 5066}, {5, 15713, 381}, {5, 3628, 15712}, {20, 1656, 3628}, {20, 3851, 546}, {30, 140, 15706}, {381, 15713, 15704}, {381, 3525, 15690}, {382, 15703, 2}, {546, 16239, 10299}, {547, 5055, 15699}, {549, 3525, 15713}, {549, 3845, 20}, {549, 6964, 3858}, {632, 5066, 15686}, {1656, 10109, 549}, {1656, 15022, 16239}, {3091, 6891, 14893}, {3525, 7486, 1656}, {3526, 14893, 15711}, {3544, 17528, 15722}, {3545, 5055, 10109}, {3628, 3859, 3533}, {3628, 5071, 3845}, {3830, 6825, 3534}, {3845, 5071, 5}, {5054, 15695, 3524}, {5054, 5055, 5071}, {5054, 5071, 14892}, {5055, 14269, 5079}, {5066, 15703, 632}, {5072, 15702, 12101}, {11539, 15687, 17504}, {11539, 15712, 5054}, {11539, 17504, 14869}, {13727, 13745, 3545}, {14269, 15710, 30}, {14869, 15687, 8703}, {15688, 15707, 15705}

X(61910) = X(2)X(3)∩X(6)X(42518)

Barycentrics    4*a^4+13*(b^2-c^2)^2-17*a^2*(b^2+c^2) : :
X(61910) = -13*X[2]+3*X[3], -X[52]+16*X[12046], X[141]+4*X[25565], 3*X[165]+7*X[50807], 3*X[355]+7*X[51110], -7*X[551]+2*X[32900], 3*X[1351]+7*X[50994], X[1353]+4*X[11178], -X[1483]+6*X[38022], -X[1484]+6*X[38084], X[2482]+4*X[15092], 3*X[3653]+7*X[7989] and many others

X(61910) lies on these lines: {2, 3}, {6, 42518}, {13, 43240}, {14, 43241}, {52, 12046}, {61, 43027}, {62, 43026}, {141, 25565}, {165, 50807}, {355, 51110}, {395, 42502}, {396, 42503}, {397, 42977}, {398, 42976}, {511, 51184}, {515, 50832}, {516, 50825}, {517, 50822}, {551, 32900}, {952, 51105}, {1007, 32892}, {1327, 6440}, {1328, 6439}, {1351, 50994}, {1353, 11178}, {1483, 38022}, {1484, 38084}, {1503, 50987}, {2482, 15092}, {3054, 14537}, {3055, 11648}, {3068, 42526}, {3069, 42527}, {3564, 51180}, {3582, 10592}, {3584, 10593}, {3653, 7989}, {3654, 7988}, {3655, 61259}, {3656, 38112}, {3679, 61272}, {3815, 39593}, {3828, 22791}, {4669, 9956}, {4677, 5886}, {4745, 10171}, {5306, 7603}, {5318, 42493}, {5321, 42492}, {5339, 42590}, {5340, 42591}, {5461, 51872}, {5476, 50978}, {5642, 15088}, {5690, 38083}, {5731, 50800}, {5790, 61273}, {5844, 51072}, {5901, 51093}, {5965, 8584}, {6199, 14226}, {6395, 14241}, {6411, 42577}, {6412, 42576}, {6429, 43558}, {6430, 43559}, {6441, 13846}, {6442, 13847}, {6476, 6565}, {6477, 6564}, {6688, 15060}, {6721, 36521}, {6722, 22566}, {7583, 42603}, {7584, 42602}, {7604, 46454}, {7697, 11055}, {8227, 51066}, {8252, 52048}, {8253, 52047}, {9690, 43517}, {9771, 51123}, {10168, 39884}, {10170, 58470}, {10172, 28228}, {10175, 10283}, {10653, 42474}, {10654, 42475}, {10706, 40685}, {11180, 51732}, {11230, 28236}, {11231, 28232}, {11485, 49873}, {11486, 49874}, {11542, 42910}, {11543, 42911}, {11645, 51126}, {11694, 14644}, {11695, 45957}, {11698, 45310}, {12040, 18546}, {12156, 61555}, {12816, 42110}, {12817, 42107}, {13364, 21969}, {13464, 51070}, {14128, 14831}, {14561, 15533}, {14971, 61575}, {15048, 18362}, {15067, 21849}, {15300, 23514}, {15534, 18583}, {16226, 32205}, {16241, 42135}, {16242, 42138}, {16267, 42599}, {16268, 42598}, {16644, 41120}, {16645, 41119}, {16960, 37835}, {16961, 37832}, {16964, 43107}, {16965, 43100}, {16966, 41122}, {16967, 41121}, {18357, 25055}, {18358, 47352}, {18581, 42512}, {18582, 42513}, {19116, 42582}, {19117, 42583}, {19862, 28208}, {19875, 61268}, {19876, 61524}, {19883, 34773}, {20252, 35752}, {20253, 36330}, {20396, 56567}, {20399, 41154}, {20423, 51186}, {20582, 21850}, {22165, 24206}, {22247, 22515}, {22489, 36363}, {22490, 36362}, {23302, 41108}, {23303, 41107}, {25406, 50957}, {25561, 48310}, {26446, 61267}, {27355, 32142}, {28146, 51074}, {28164, 51084}, {28174, 30308}, {28186, 50799}, {28204, 51109}, {28212, 50806}, {29181, 50980}, {29317, 51129}, {31399, 51067}, {31884, 50964}, {32396, 36966}, {32787, 42606}, {32788, 42607}, {33406, 49940}, {33407, 49939}, {33416, 46334}, {33417, 46335}, {33602, 42985}, {33603, 42984}, {34380, 50990}, {34507, 41149}, {34627, 51700}, {35751, 59401}, {36319, 59384}, {36329, 59402}, {36344, 59383}, {36366, 61515}, {36368, 61516}, {36383, 36765}, {36523, 38229}, {38028, 50796}, {38074, 61245}, {38080, 61595}, {38108, 60963}, {38110, 47354}, {38136, 50977}, {38137, 38318}, {38140, 50828}, {38176, 50830}, {38314, 61295}, {38317, 50979}, {39561, 50958}, {41100, 42121}, {41101, 42124}, {41112, 42098}, {41113, 42095}, {41943, 42163}, {41944, 42166}, {42108, 43476}, {42109, 43475}, {42111, 42511}, {42114, 42510}, {42115, 42588}, {42116, 42589}, {42125, 49876}, {42128, 49875}, {42129, 49812}, {42132, 49813}, {42154, 43103}, {42155, 43102}, {42516, 43404}, {42517, 43403}, {42610, 42920}, {42611, 42921}, {42627, 42975}, {42628, 42974}, {42682, 42918}, {42683, 42919}, {42686, 43244}, {42687, 43245}, {42692, 42955}, {42693, 42954}, {42817, 43543}, {42818, 43542}, {42906, 43467}, {42907, 43468}, {42962, 43481}, {42963, 43482}, {43415, 43518}, {43887, 53520}, {43888, 53517}, {47610, 48311}, {47611, 48312}, {48876, 51143}, {50798, 61283}, {50803, 50833}, {50811, 61263}, {50865, 61265}, {50959, 50981}, {50960, 50988}, {51076, 51088}, {51097, 61276}, {51106, 61297}, {51131, 51141}, {51135, 55685}, {59376, 61580}, {60901, 60999}, {60971, 61509}

X(61910) = midpoint of X(i) and X(j) for these {i,j}: {4, 14093}, {376, 5076}, {381, 631}, {547, 12812}, {549, 3858}, {1656, 5071}, {3091, 15694}, {3830, 15697}, {3843, 15692}, {3845, 15711}
X(61910) = reflection of X(i) in X(j) for these {i,j}: {1656, 547}, {15686, 3522}, {15687, 3843}, {15692, 140}, {15695, 12100}, {15711, 15713}, {15712, 15694}, {15713, 2}, {15714, 631}, {17578, 14893}, {3859, 11737}, {5, 5071}, {549, 632}, {550, 15714}, {5071, 12812}, {8703, 15693}
X(61910) = inverse of X(15701) in orthocentroidal circle
X(61910) = inverse of X(15701) in Yff hyperbola
X(61910) = complement of X(15693)
X(61910) = anticomplement of X(61860)
X(61910) = pole of line {523, 15701} with respect to the orthocentroidal circle
X(61910) = pole of line {6, 15701} with respect to the Kiepert hyperbola
X(61910) = pole of line {523, 15701} with respect to the Yff hyperbola
X(61910) = intersection, other than A, B, C, of circumconics {{A, B, C, X(95), X(11540)}}, {{A, B, C, X(264), X(15701)}}, {{A, B, C, X(631), X(31846)}}, {{A, B, C, X(1217), X(58195)}}, {{A, B, C, X(1494), X(15713)}}, {{A, B, C, X(3845), X(40410)}}, {{A, B, C, X(3857), X(14938)}}, {{A, B, C, X(8797), X(19708)}}, {{A, B, C, X(12100), X(55958)}}, {{A, B, C, X(18317), X(46853)}}
X(61910) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12100, 11539}, {2, 15682, 5054}, {2, 15701, 10124}, {2, 15713, 632}, {2, 15719, 3526}, {2, 17556, 15673}, {2, 3, 11540}, {2, 30, 15713}, {2, 3534, 140}, {2, 381, 12100}, {2, 3830, 11812}, {2, 3839, 15719}, {2, 5, 3845}, {2, 5055, 10109}, {4, 15701, 15690}, {5, 14869, 3850}, {5, 15687, 3545}, {5, 15704, 3851}, {5, 15712, 3091}, {5, 547, 15699}, {5, 8703, 5066}, {30, 11737, 3859}, {30, 12100, 15695}, {30, 140, 15692}, {30, 14893, 17578}, {30, 15694, 15712}, {30, 547, 1656}, {140, 3545, 15687}, {140, 3860, 3534}, {140, 5079, 5}, {381, 10304, 3853}, {381, 15707, 3146}, {381, 5054, 17800}, {381, 5055, 5056}, {382, 15709, 14891}, {546, 15759, 15682}, {631, 15692, 15707}, {631, 1656, 3628}, {1656, 5055, 5071}, {1656, 5071, 30}, {1656, 5076, 5070}, {1656, 5079, 3843}, {3090, 5055, 547}, {3146, 3545, 381}, {3523, 3529, 6868}, {3523, 6871, 5067}, {3524, 14893, 15704}, {3524, 3851, 14893}, {3525, 6927, 10299}, {3533, 15700, 14890}, {3534, 15703, 2}, {3534, 3545, 3860}, {3545, 15687, 3857}, {3545, 7486, 15703}, {3830, 15693, 15697}, {3839, 15719, 15685}, {3843, 3857, 3858}, {3845, 6846, 14892}, {3850, 5070, 14869}, {3851, 10109, 6824}, {3855, 15708, 15684}, {4188, 15707, 11737}, {5054, 15682, 15759}, {5055, 15703, 5079}, {5055, 5071, 12812}, {5066, 11540, 15640}, {5066, 11812, 3830}, {5068, 15702, 14269}, {5079, 12811, 6859}, {6848, 15682, 3543}, {6862, 12100, 6939}, {8703, 15713, 15693}, {10109, 17504, 6846}, {10124, 14892, 4}, {10124, 15690, 15701}, {10171, 38042, 61270}, {11001, 12100, 8703}, {11178, 38079, 1353}, {11539, 15714, 631}, {11540, 11737, 12101}, {11540, 12101, 3}, {12100, 15695, 15714}, {12100, 15714, 15711}, {12100, 15759, 15715}, {12103, 14890, 15700}, {14269, 15702, 548}, {14782, 14783, 11541}, {14893, 16239, 3524}, {15682, 15759, 15686}, {15687, 15707, 550}, {15690, 15701, 17504}, {15711, 15713, 549}, {15765, 18585, 12103}, {16960, 37835, 42778}, {16961, 37832, 42777}, {18586, 18587, 7486}, {25561, 48310, 48906}, {38042, 51709, 50823}, {42107, 42791, 12817}, {42110, 42792, 12816}, {42518, 42519, 6}, {50823, 61270, 51709}

X(61911) = X(2)X(3)∩X(6)X(44019)

Barycentrics    3*a^4+10*(b^2-c^2)^2-13*a^2*(b^2+c^2) : :
X(61911) = -30*X[2]+7*X[3], 18*X[551]+5*X[61248], 20*X[575]+3*X[51027], -X[962]+24*X[61267], 7*X[1482]+16*X[4691], 2*X[3579]+21*X[61265], 15*X[3616]+8*X[61255], 5*X[3617]+18*X[61270], -35*X[3624]+12*X[31662], 2*X[3625]+21*X[5886], 2*X[3630]+21*X[14561], 2*X[3633]+21*X[5790] and many others

X(61911) lies on these lines: {2, 3}, {6, 44019}, {61, 43428}, {62, 43429}, {551, 61248}, {575, 51027}, {962, 61267}, {1007, 32878}, {1327, 6522}, {1328, 6519}, {1482, 4691}, {3411, 42581}, {3412, 42580}, {3579, 61265}, {3616, 61255}, {3617, 61270}, {3624, 31662}, {3625, 5886}, {3630, 14561}, {3633, 5790}, {3634, 61266}, {3635, 10175}, {3763, 55587}, {4668, 9956}, {5097, 6144}, {5102, 24206}, {5237, 43491}, {5238, 43492}, {5339, 41978}, {5340, 41977}, {5418, 41961}, {5420, 41962}, {5550, 61262}, {5640, 12046}, {5734, 38042}, {5818, 61278}, {5882, 50797}, {6395, 31414}, {6427, 42602}, {6428, 42603}, {6429, 6565}, {6430, 6564}, {6431, 10576}, {6432, 10577}, {6486, 23261}, {6487, 23251}, {6688, 34783}, {7173, 31452}, {7765, 31467}, {7999, 18874}, {8148, 61269}, {8227, 11278}, {8550, 50954}, {8976, 35771}, {9606, 43620}, {9654, 37587}, {9680, 42270}, {9681, 32789}, {9691, 23275}, {9708, 52795}, {10137, 35255}, {10138, 35256}, {10172, 12702}, {10219, 10575}, {10246, 61258}, {10247, 20053}, {10516, 50664}, {10896, 51817}, {11230, 18526}, {11362, 61268}, {11451, 14128}, {11465, 15060}, {11477, 25565}, {11480, 42890}, {11481, 42891}, {11482, 51175}, {11522, 38083}, {11531, 18493}, {11898, 32455}, {11935, 13434}, {12355, 38751}, {12773, 38319}, {12900, 23236}, {13321, 14531}, {13565, 55038}, {13665, 35813}, {13785, 35812}, {13903, 42262}, {13951, 35770}, {13961, 42265}, {14929, 32897}, {14981, 38735}, {15046, 15063}, {15047, 17814}, {15056, 32205}, {15057, 38789}, {15069, 39561}, {15092, 52886}, {15178, 50871}, {15808, 61257}, {16003, 38792}, {16241, 43551}, {16242, 43550}, {16267, 42953}, {16268, 42952}, {16644, 42802}, {16645, 42801}, {16772, 42111}, {16773, 42114}, {16964, 42610}, {16965, 42611}, {16966, 42435}, {16967, 42436}, {18440, 55703}, {18525, 30392}, {18581, 42950}, {18582, 42951}, {19130, 55591}, {20582, 51173}, {22236, 43199}, {22238, 43200}, {22728, 31239}, {27355, 37484}, {28212, 46931}, {30315, 51709}, {30435, 31417}, {31447, 48661}, {31454, 42274}, {31470, 31489}, {31479, 37720}, {32889, 34803}, {33539, 40920}, {33540, 37494}, {33749, 38317}, {34754, 42095}, {34755, 42098}, {34794, 35017}, {36990, 55685}, {37624, 61249}, {37726, 38758}, {37727, 38155}, {37832, 42989}, {37835, 42988}, {38022, 61290}, {38107, 60977}, {38108, 60962}, {38176, 58237}, {40107, 55722}, {40693, 42818}, {40694, 42817}, {41947, 41950}, {41948, 41949}, {42096, 43472}, {42097, 43471}, {42126, 42490}, {42127, 42491}, {42129, 42156}, {42130, 42929}, {42131, 42928}, {42132, 42153}, {42215, 43435}, {42216, 43434}, {42472, 43102}, {42473, 43103}, {42474, 42966}, {42475, 42967}, {42506, 43427}, {42507, 43426}, {42528, 54591}, {42529, 54592}, {42592, 42972}, {42593, 42973}, {42786, 55582}, {42813, 43028}, {42814, 43029}, {42918, 43194}, {42919, 43193}, {42938, 43240}, {42939, 43241}, {42984, 43417}, {42985, 43416}, {43014, 43235}, {43015, 43234}, {43174, 50806}, {43613, 52055}, {43881, 43890}, {43882, 43889}, {47354, 55701}, {47355, 55695}, {48910, 55640}, {50798, 61282}, {51127, 55682}, {51128, 55629}, {51186, 55721}, {51516, 60976}, {52102, 61735}, {53023, 55612}, {60279, 60329}, {60922, 61000}, {61020, 61595}

X(61911) = inverse of X(12108) in orthocentroidal circle
X(61911) = inverse of X(12108) in Yff hyperbola
X(61911) = complement of X(61807)
X(61911) = pole of line {523, 12108} with respect to the orthocentroidal circle
X(61911) = pole of line {185, 62158} with respect to the Jerabek hyperbola
X(61911) = pole of line {6, 12108} with respect to the Kiepert hyperbola
X(61911) = pole of line {523, 12108} with respect to the Yff hyperbola
X(61911) = intersection, other than A, B, C, of circumconics {{A, B, C, X(264), X(12108)}}, {{A, B, C, X(3521), X(15640)}}, {{A, B, C, X(3843), X(40410)}}, {{A, B, C, X(3855), X(14938)}}, {{A, B, C, X(8797), X(21735)}}, {{A, B, C, X(11812), X(31846)}}, {{A, B, C, X(12100), X(15318)}}, {{A, B, C, X(12103), X(13599)}}, {{A, B, C, X(14863), X(15720)}}, {{A, B, C, X(15706), X(55958)}}, {{A, B, C, X(15749), X(41106)}}, {{A, B, C, X(21400), X(23046)}}
X(61911) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15684, 5054}, {2, 17538, 140}, {2, 3545, 15686}, {2, 381, 15706}, {2, 4, 12108}, {2, 5, 3843}, {2, 5071, 14892}, {2, 5072, 1657}, {3, 3832, 382}, {3, 3851, 3845}, {3, 5055, 5056}, {3, 5070, 16239}, {3, 547, 1656}, {4, 12108, 15689}, {5, 140, 3855}, {5, 15699, 3530}, {5, 3628, 20}, {5, 3853, 3545}, {5, 3856, 5068}, {20, 5071, 5}, {140, 15699, 17697}, {140, 17538, 15718}, {140, 3543, 3}, {140, 3855, 17800}, {381, 3526, 15696}, {382, 1656, 5070}, {382, 5070, 3526}, {547, 10109, 11539}, {547, 12812, 3850}, {548, 14892, 3859}, {632, 3856, 3528}, {1656, 15022, 15688}, {1656, 5054, 3628}, {1656, 5055, 5079}, {1656, 5071, 5076}, {1656, 5079, 381}, {1657, 15688, 17538}, {1657, 5076, 15684}, {2041, 2042, 12100}, {2045, 3090, 18586}, {2046, 3090, 18587}, {3090, 5056, 547}, {3091, 15705, 4}, {3091, 16371, 3090}, {3523, 12811, 14269}, {3525, 5066, 5073}, {3525, 5073, 15700}, {3526, 15696, 15720}, {3528, 3856, 3830}, {3528, 5068, 3856}, {3543, 15702, 15714}, {3543, 5056, 15022}, {3628, 14892, 15712}, {3628, 15704, 17542}, {3628, 3845, 3533}, {3628, 5071, 3851}, {3832, 7486, 5067}, {3839, 13745, 3524}, {3845, 3859, 3832}, {3850, 16239, 548}, {3851, 14892, 5072}, {3854, 6880, 3861}, {3858, 10303, 15681}, {5055, 15703, 10109}, {6849, 15693, 3146}, {12812, 15712, 5071}, {14893, 15699, 2}, {15022, 17697, 3091}, {44019, 44020, 6}

X(61912) = X(2)X(3)∩X(147)X(14971)

Barycentrics    5*a^4+17*(b^2-c^2)^2-22*a^2*(b^2+c^2) : :
X(61912) = -17*X[2]+4*X[3], X[147]+12*X[14971], X[153]+12*X[59376], 10*X[551]+3*X[37712], 5*X[962]+8*X[50814], 8*X[1350]+5*X[51211], X[3241]+12*X[10175], 25*X[3616]+14*X[61256], 5*X[3617]+8*X[51709], 7*X[3619]+6*X[38072], 5*X[3620]+8*X[5476], 7*X[3622]+6*X[38074] and many others

X(61912) lies on these lines: {2, 3}, {147, 14971}, {153, 59376}, {325, 32893}, {395, 42982}, {396, 42983}, {551, 37712}, {962, 50814}, {1007, 32869}, {1131, 60298}, {1132, 60297}, {1327, 43511}, {1328, 43512}, {1350, 51211}, {3241, 10175}, {3424, 60645}, {3582, 5261}, {3584, 5274}, {3616, 61256}, {3617, 51709}, {3619, 38072}, {3620, 5476}, {3622, 38074}, {3624, 38076}, {3634, 30308}, {3654, 46932}, {3655, 54448}, {3679, 10171}, {3817, 19876}, {3828, 7988}, {4297, 50863}, {4745, 5734}, {5032, 40330}, {5304, 7603}, {5334, 41943}, {5335, 41944}, {5691, 51080}, {5790, 20049}, {5818, 61277}, {5886, 31145}, {5921, 47352}, {6449, 43561}, {6450, 43560}, {6565, 9542}, {6721, 52695}, {6776, 46267}, {7173, 10385}, {7585, 42602}, {7586, 42603}, {7752, 32885}, {7753, 37689}, {7809, 32838}, {7987, 50803}, {7989, 19883}, {8227, 50817}, {8252, 53517}, {8253, 53520}, {8591, 23514}, {8596, 15561}, {8972, 35823}, {9143, 23515}, {9780, 38021}, {9812, 61265}, {9955, 46931}, {10172, 31162}, {10194, 43884}, {10195, 43883}, {10219, 20791}, {10248, 51074}, {10574, 40284}, {10711, 38319}, {11160, 14561}, {11177, 36519}, {11180, 33748}, {11230, 34627}, {11444, 58470}, {11451, 14831}, {11488, 43101}, {11489, 43104}, {11522, 51069}, {12045, 32062}, {12512, 50873}, {13364, 16981}, {13464, 51072}, {13665, 43797}, {13785, 43798}, {13846, 41951}, {13847, 41952}, {13941, 35822}, {14484, 60131}, {14848, 20080}, {14853, 25565}, {15031, 32884}, {15052, 17825}, {15056, 16226}, {16189, 51070}, {16241, 43311}, {16242, 43310}, {16808, 42996}, {16809, 42997}, {16962, 49873}, {16963, 49874}, {16966, 43404}, {16967, 43403}, {18510, 42605}, {18512, 42604}, {19053, 42583}, {19054, 42582}, {19875, 50872}, {19877, 28194}, {21356, 50973}, {21358, 51028}, {22235, 42581}, {22237, 42580}, {23302, 42475}, {23303, 42474}, {25055, 51082}, {28204, 46934}, {31399, 51068}, {32789, 43790}, {32790, 43789}, {33416, 43364}, {33417, 43365}, {33602, 42591}, {33603, 42590}, {34631, 38042}, {34648, 54445}, {34718, 61269}, {35770, 43569}, {35771, 43568}, {35814, 60299}, {35815, 60300}, {36990, 51135}, {37714, 51108}, {37832, 43308}, {37835, 43309}, {38022, 61292}, {38075, 60996}, {38083, 46933}, {38108, 60984}, {38127, 54447}, {38314, 61296}, {40273, 50809}, {41112, 42489}, {41113, 42488}, {41975, 54634}, {41976, 54635}, {42085, 43294}, {42086, 43295}, {42111, 43372}, {42114, 43373}, {42119, 42932}, {42120, 42933}, {42139, 42957}, {42142, 42956}, {42149, 49825}, {42152, 49824}, {42153, 49813}, {42154, 42473}, {42155, 42472}, {42156, 49812}, {42159, 43479}, {42162, 43480}, {42262, 42522}, {42265, 42523}, {42270, 42568}, {42273, 42569}, {42539, 43517}, {42540, 43518}, {42598, 42899}, {42599, 42898}, {42606, 43410}, {42607, 43409}, {42610, 43107}, {42611, 43100}, {42633, 42950}, {42634, 42951}, {42639, 54597}, {42640, 43536}, {42692, 43029}, {42693, 43028}, {42694, 42798}, {42695, 42797}, {42786, 54173}, {42910, 42915}, {42911, 42914}, {42918, 43869}, {42919, 43870}, {42998, 49907}, {42999, 49908}, {43242, 43540}, {43243, 43541}, {43320, 43510}, {43321, 43509}, {43405, 56621}, {43406, 56622}, {43537, 60287}, {44882, 51216}, {46951, 53127}, {48310, 51023}, {48889, 50975}, {50797, 51700}, {50798, 61281}, {50818, 61246}, {50867, 51086}, {50954, 51732}, {50956, 58445}, {50960, 53094}, {50970, 51212}, {50983, 51537}, {50984, 51213}, {51103, 61289}, {51139, 51217}, {51215, 59373}, {53099, 60638}, {59375, 61595}, {59388, 61280}

X(61912) = midpoint of X(i) and X(j) for these {i,j}: {2, 5068}
X(61912) = reflection of X(i) in X(j) for these {i,j}: {10303, 2}, {2, 5067}
X(61912) = inverse of X(15708) in orthocentroidal circle
X(61912) = inverse of X(15708) in Yff hyperbola
X(61912) = complement of X(61806)
X(61912) = anticomplement of X(61859)
X(61912) = pole of line {523, 15708} with respect to the orthocentroidal circle
X(61912) = pole of line {6, 15708} with respect to the Kiepert hyperbola
X(61912) = pole of line {523, 15708} with respect to the Yff hyperbola
X(61912) = pole of line {69, 61844} with respect to the Wallace hyperbola
X(61912) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(253), X(5054)}}, {{A, B, C, X(264), X(15708)}}, {{A, B, C, X(1217), X(44245)}}, {{A, B, C, X(1494), X(10303)}}, {{A, B, C, X(3535), X(60298)}}, {{A, B, C, X(3536), X(60297)}}, {{A, B, C, X(3839), X(40410)}}, {{A, B, C, X(3858), X(60618)}}, {{A, B, C, X(4846), X(44903)}}, {{A, B, C, X(5073), X(31363)}}, {{A, B, C, X(8797), X(10304)}}, {{A, B, C, X(14869), X(31846)}}, {{A, B, C, X(15692), X(55958)}}, {{A, B, C, X(15721), X(36889)}}, {{A, B, C, X(41981), X(51348)}}, {{A, B, C, X(49138), X(54763)}}, {{A, B, C, X(52283), X(60645)}}, {{A, B, C, X(52288), X(60131)}}
X(61912) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15705, 3525}, {2, 15717, 11539}, {2, 30, 10303}, {2, 3091, 10304}, {2, 3146, 5054}, {2, 3522, 15709}, {2, 3543, 15721}, {2, 3854, 15705}, {2, 4, 15708}, {2, 5, 3839}, {2, 5055, 5056}, {2, 5068, 30}, {5, 12103, 3851}, {5, 15699, 12100}, {5, 3523, 3091}, {5, 3628, 1657}, {5, 547, 15703}, {20, 10303, 10299}, {20, 15688, 15697}, {20, 3839, 3830}, {20, 5056, 15022}, {140, 15684, 15715}, {376, 14893, 3146}, {376, 15702, 15718}, {376, 5071, 5}, {381, 15694, 15686}, {381, 15702, 15683}, {381, 15703, 10124}, {547, 11737, 15699}, {547, 12812, 11737}, {547, 549, 1656}, {549, 15687, 15690}, {632, 14269, 15698}, {1656, 10109, 3545}, {1656, 15022, 20}, {1656, 3525, 13735}, {1656, 5055, 10109}, {3090, 17800, 2475}, {3090, 5056, 7486}, {3090, 5071, 547}, {3524, 3832, 15640}, {3533, 5072, 17578}, {3534, 14892, 3855}, {3544, 15709, 3845}, {3544, 5070, 3522}, {3545, 15690, 3832}, {3619, 38072, 54174}, {3628, 15687, 15723}, {3817, 19876, 34632}, {3851, 11539, 15682}, {3858, 11540, 15689}, {5067, 5079, 5068}, {7989, 19883, 50864}, {10124, 15718, 15702}, {11539, 12103, 15722}, {11539, 15682, 15717}, {11737, 15686, 381}, {11737, 15694, 4}, {11737, 15699, 15694}, {12100, 15708, 3523}, {12101, 15707, 17538}, {12103, 14093, 376}, {12812, 15694, 5071}, {13735, 15022, 3854}, {13735, 15705, 2}, {14269, 15698, 5059}, {15640, 15687, 3543}, {15683, 15702, 15692}, {15687, 15723, 3524}, {15688, 15694, 549}, {42633, 42950, 43554}

X(61913) = X(2)X(3)∩X(6)X(43536)

Barycentrics    7*a^4+25*(b^2-c^2)^2-32*a^2*(b^2+c^2) : :
X(61913) = -25*X[2]+6*X[3], 25*X[8]+32*X[58237], 14*X[551]+5*X[61250], 15*X[3576]+4*X[50868], X[4669]+18*X[10171], 4*X[4677]+15*X[10595], 4*X[4745]+15*X[8227], 15*X[5085]+4*X[51025], 9*X[5102]+10*X[22165], 12*X[5476]+7*X[50994], 9*X[5587]+10*X[51109], 9*X[5603]+10*X[51066] and many others

X(61913) lies on these lines: {2, 3}, {6, 43536}, {8, 58237}, {551, 61250}, {590, 14226}, {615, 14241}, {1131, 43212}, {1132, 43211}, {1327, 6481}, {1328, 6480}, {3068, 43387}, {3069, 43386}, {3070, 34091}, {3071, 34089}, {3316, 6431}, {3317, 6432}, {3576, 50868}, {4669, 10171}, {4677, 10595}, {4745, 8227}, {5085, 51025}, {5102, 22165}, {5237, 43201}, {5238, 43202}, {5334, 42475}, {5335, 42474}, {5343, 42509}, {5344, 42508}, {5476, 50994}, {5587, 51109}, {5603, 51066}, {5657, 51120}, {5818, 51071}, {5881, 41150}, {5901, 51092}, {6429, 23275}, {6430, 23269}, {6433, 43257}, {6434, 43256}, {6484, 43254}, {6485, 43255}, {6564, 43375}, {6565, 43374}, {7967, 50871}, {7988, 50810}, {8252, 43888}, {8253, 43887}, {8584, 40330}, {9624, 51096}, {9690, 42539}, {9956, 51072}, {10139, 41945}, {10140, 41946}, {10155, 54637}, {10164, 51119}, {10175, 51093}, {10219, 16261}, {10519, 51166}, {11180, 55711}, {11230, 58234}, {11231, 50809}, {11278, 53620}, {11485, 43247}, {11486, 43246}, {11488, 41122}, {11489, 41121}, {12243, 38735}, {14494, 60627}, {14561, 50992}, {14853, 50993}, {14912, 51027}, {14981, 41148}, {15069, 41153}, {15092, 52695}, {16241, 42473}, {16242, 42472}, {16267, 49859}, {16268, 49860}, {16644, 49873}, {16645, 49874}, {16962, 42495}, {16963, 42494}, {16966, 41120}, {16967, 41119}, {18581, 49862}, {18582, 49861}, {18584, 46453}, {19875, 58248}, {20582, 55582}, {21167, 51165}, {21356, 25565}, {22489, 36344}, {22490, 36319}, {23235, 41154}, {23249, 43518}, {23259, 43517}, {23302, 49827}, {23303, 49826}, {24206, 50990}, {30392, 50796}, {31414, 42608}, {31662, 61263}, {32818, 32892}, {32823, 32885}, {32896, 59635}, {33406, 49800}, {33407, 49801}, {33604, 43104}, {33605, 43101}, {33748, 50954}, {34627, 51108}, {34754, 41113}, {34755, 41112}, {35750, 59401}, {35770, 42603}, {35771, 42602}, {36318, 36765}, {36331, 59402}, {36767, 59394}, {37640, 42914}, {37641, 42915}, {37832, 42953}, {37835, 42952}, {38074, 51105}, {38108, 60971}, {38110, 51176}, {38155, 51103}, {39561, 50974}, {41100, 42114}, {41101, 42111}, {41107, 43200}, {41108, 43199}, {42089, 43244}, {42092, 43245}, {42095, 49824}, {42098, 49825}, {42133, 42791}, {42134, 42792}, {42139, 42511}, {42142, 42510}, {42163, 43447}, {42166, 43446}, {42268, 42525}, {42269, 42524}, {42498, 43400}, {42499, 43399}, {42502, 42998}, {42503, 42999}, {42540, 43415}, {42639, 45385}, {42640, 45384}, {42686, 43487}, {42687, 43488}, {42803, 43197}, {42804, 43198}, {42910, 49812}, {42911, 49813}, {43108, 43541}, {43109, 43540}, {43228, 43543}, {43229, 43542}, {43240, 43545}, {43241, 43544}, {44678, 55823}, {47354, 55703}, {48310, 55699}, {50799, 54445}, {50806, 61267}, {50818, 61247}, {50828, 58227}, {51068, 51709}, {51069, 54447}, {51077, 61271}, {51095, 61275}, {51143, 54132}, {51186, 55722}, {51537, 55688}, {53103, 60284}, {54523, 60143}, {54616, 60185}, {54707, 60183}, {54827, 60237}, {58244, 61268}, {60127, 60629}, {60150, 60616}, {60307, 60316}, {60308, 60315}

X(61913) = inverse of X(61822) in orthocentroidal circle
X(61913) = inverse of X(61822) in Yff hyperbola
X(61913) = complement of X(61805)
X(61913) = anticomplement of X(61857)
X(61913) = pole of line {523, 61822} with respect to the orthocentroidal circle
X(61913) = pole of line {6, 43493} with respect to the Kiepert hyperbola
X(61913) = pole of line {523, 61822} with respect to the Yff hyperbola
X(61913) = pole of line {69, 61843} with respect to the Wallace hyperbola
X(61913) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(3854), X(54660)}}, {{A, B, C, X(4846), X(58202)}}, {{A, B, C, X(5059), X(54763)}}, {{A, B, C, X(7408), X(54707)}}, {{A, B, C, X(7409), X(54612)}}, {{A, B, C, X(8703), X(8797)}}, {{A, B, C, X(11738), X(35501)}}, {{A, B, C, X(11812), X(36889)}}, {{A, B, C, X(15698), X(55958)}}, {{A, B, C, X(17578), X(54838)}}, {{A, B, C, X(40410), X(41099)}}, {{A, B, C, X(50689), X(54667)}}, {{A, B, C, X(50690), X(60121)}}, {{A, B, C, X(52301), X(54523)}}
X(61913) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11001, 15702}, {2, 11812, 3533}, {2, 15640, 5054}, {2, 15697, 140}, {2, 15698, 3525}, {2, 3091, 8703}, {2, 3545, 11001}, {2, 3830, 631}, {2, 3839, 15693}, {2, 3845, 15719}, {2, 5068, 15640}, {2, 8703, 15709}, {5, 15711, 5066}, {5, 15720, 3091}, {5, 1656, 10303}, {5, 3543, 3545}, {5, 3628, 5073}, {376, 3545, 3832}, {376, 631, 15706}, {381, 5055, 12812}, {547, 11539, 1656}, {547, 3850, 15699}, {547, 5055, 5056}, {1656, 5066, 2}, {3090, 3545, 547}, {3090, 5055, 5071}, {3090, 5056, 5067}, {3522, 10303, 3530}, {3524, 5071, 5}, {3530, 15713, 15701}, {3533, 3545, 3543}, {3534, 15701, 15711}, {3543, 15708, 3522}, {3543, 3832, 14269}, {3545, 15702, 4}, {3545, 15719, 3845}, {3845, 15713, 15690}, {3850, 15699, 15723}, {5070, 11737, 10304}, {10303, 14269, 376}, {11539, 15711, 11812}, {11812, 15686, 6908}, {11812, 15722, 15708}, {12812, 15704, 5079}, {14269, 15701, 3534}, {15690, 15708, 15698}, {15698, 15722, 3524}, {37832, 49904, 49811}, {37835, 49903, 49810}, {42910, 49907, 49812}, {42911, 49908, 49813}, {43536, 54597, 6}

X(61914) = X(2)X(3)∩X(8)X(10171)

Barycentrics    3*a^4+11*(b^2-c^2)^2-14*a^2*(b^2+c^2) : :
X(61914) = -33*X[2]+8*X[3], X[8]+24*X[10171], -4*X[40]+29*X[46930], -3*X[145]+28*X[9624], X[153]+24*X[38319], 18*X[373]+7*X[15056], 18*X[551]+7*X[61252], 8*X[946]+17*X[46932], X[962]+24*X[10172], 16*X[1125]+9*X[54448], 16*X[1216]+9*X[16981], 11*X[1352]+14*X[55712] and many others

X(61914) lies on these lines: {2, 3}, {8, 10171}, {40, 46930}, {61, 42512}, {62, 42513}, {83, 54921}, {99, 32898}, {145, 9624}, {153, 38319}, {315, 32897}, {316, 32883}, {325, 32872}, {373, 15056}, {390, 7173}, {393, 52704}, {395, 22235}, {396, 22237}, {397, 42517}, {398, 42516}, {485, 6436}, {486, 6435}, {499, 31410}, {551, 61252}, {615, 31414}, {621, 33405}, {622, 33404}, {946, 46932}, {962, 10172}, {1125, 54448}, {1131, 32786}, {1132, 32785}, {1216, 16981}, {1352, 55712}, {1698, 28228}, {1975, 32873}, {2548, 14075}, {2551, 52795}, {2979, 27355}, {2996, 17005}, {3068, 42605}, {3069, 42604}, {3311, 43317}, {3312, 43316}, {3316, 18762}, {3317, 18538}, {3411, 18582}, {3412, 18581}, {3424, 16987}, {3590, 19054}, {3591, 19053}, {3592, 43377}, {3594, 43376}, {3600, 3614}, {3616, 28236}, {3617, 5734}, {3621, 5886}, {3622, 5881}, {3623, 5818}, {3626, 61271}, {3634, 9589}, {3767, 31407}, {3817, 9588}, {3829, 12632}, {4301, 7988}, {4678, 9956}, {5087, 18231}, {5218, 9671}, {5265, 9657}, {5281, 9670}, {5318, 42611}, {5319, 14930}, {5321, 42610}, {5334, 42488}, {5335, 42489}, {5346, 7603}, {5365, 16241}, {5366, 16242}, {5418, 9692}, {5550, 7989}, {5587, 46934}, {5640, 14531}, {5790, 20014}, {5921, 38317}, {5965, 40330}, {5984, 36519}, {6409, 43508}, {6410, 43507}, {6449, 43505}, {6450, 43506}, {6484, 43513}, {6485, 43514}, {6492, 41965}, {6493, 41966}, {6494, 42522}, {6495, 42523}, {6498, 13886}, {6499, 13939}, {6684, 61265}, {6688, 12111}, {6776, 55707}, {7288, 9656}, {7585, 42582}, {7586, 42583}, {7608, 60635}, {7697, 20105}, {7746, 31417}, {7752, 10513}, {7796, 32834}, {7814, 32828}, {7871, 32886}, {7967, 61255}, {7999, 14845}, {8888, 51358}, {8972, 42262}, {9143, 15025}, {9542, 23275}, {9543, 9680}, {9698, 43620}, {9778, 51073}, {10110, 33884}, {10187, 42973}, {10188, 42972}, {10219, 11381}, {10519, 42786}, {10588, 37722}, {10589, 15888}, {10591, 31452}, {10593, 31480}, {10595, 20052}, {10653, 43549}, {10654, 43548}, {11002, 11793}, {11003, 43614}, {11017, 40280}, {11180, 33749}, {11230, 61258}, {11271, 13565}, {11362, 46933}, {11487, 37779}, {11668, 18845}, {11680, 27525}, {12245, 61269}, {12571, 19872}, {12702, 61267}, {13598, 44299}, {13941, 42265}, {14561, 20080}, {14683, 23515}, {14853, 55719}, {14986, 37719}, {15018, 17814}, {15029, 45311}, {15057, 36518}, {15069, 51171}, {15088, 23236}, {15561, 35369}, {15851, 52707}, {16189, 51072}, {16267, 54594}, {16268, 54593}, {16644, 42495}, {16645, 42494}, {16772, 42139}, {16773, 42142}, {16960, 40694}, {16961, 40693}, {16966, 43009}, {16967, 43008}, {18358, 33748}, {18387, 43821}, {18483, 31425}, {19130, 55589}, {19862, 61264}, {20059, 38108}, {20094, 23514}, {20095, 23513}, {20399, 41135}, {23039, 58533}, {23238, 25339}, {23293, 32605}, {23329, 54211}, {24206, 55717}, {26364, 31420}, {28092, 33127}, {30315, 53620}, {30389, 38076}, {31246, 40333}, {31450, 43448}, {31454, 42561}, {31666, 50799}, {31670, 55605}, {32815, 32871}, {32816, 32870}, {32818, 32882}, {32825, 32874}, {32840, 59635}, {32879, 52713}, {35255, 42539}, {35256, 42540}, {35812, 42274}, {35813, 42277}, {36836, 42776}, {36843, 42775}, {36967, 43441}, {36968, 43440}, {38079, 51215}, {38083, 50872}, {38155, 61289}, {38259, 53108}, {40107, 55723}, {41817, 45100}, {42095, 43873}, {42098, 43874}, {42107, 42490}, {42110, 42491}, {42129, 42982}, {42132, 42983}, {42149, 42800}, {42152, 42799}, {42163, 42475}, {42166, 42474}, {42268, 43520}, {42269, 43519}, {42270, 43512}, {42273, 43511}, {42472, 43028}, {42473, 43029}, {42520, 42993}, {42521, 42992}, {42566, 43339}, {42567, 43338}, {42580, 42911}, {42581, 42910}, {42598, 42778}, {42599, 42777}, {42682, 43194}, {42683, 43193}, {42912, 43447}, {42913, 43446}, {42920, 43489}, {42921, 43490}, {42930, 43469}, {42931, 43470}, {42944, 43420}, {42945, 43421}, {42984, 43493}, {42985, 43494}, {42988, 43543}, {42989, 43542}, {42990, 43403}, {42991, 43404}, {43014, 43206}, {43015, 43205}, {43314, 43561}, {43315, 43560}, {43483, 43547}, {43484, 43546}, {43537, 60648}, {43681, 54645}, {43889, 60294}, {43890, 60293}, {43951, 56059}, {43981, 43982}, {44863, 54041}, {45958, 61136}, {47586, 60238}, {50956, 55687}, {51069, 58245}, {51126, 51537}, {53099, 60628}, {54522, 60285}, {54644, 60145}, {54920, 60639}, {59388, 61278}, {60118, 60277}, {60147, 60644}, {60210, 60331}

X(61914) = inverse of X(61820) in orthocentroidal circle
X(61914) = inverse of X(61820) in Yff hyperbola
X(61914) = complement of X(61804)
X(61914) = anticomplement of X(61856)
X(61914) = pole of line {523, 61820} with respect to the orthocentroidal circle
X(61914) = pole of line {185, 62160} with respect to the Jerabek hyperbola
X(61914) = pole of line {6, 43883} with respect to the Kiepert hyperbola
X(61914) = pole of line {523, 61820} with respect to the Yff hyperbola
X(61914) = pole of line {69, 32873} with respect to the Wallace hyperbola
X(61914) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(68), X(15699)}}, {{A, B, C, X(427), X(54921)}}, {{A, B, C, X(547), X(18855)}}, {{A, B, C, X(1217), X(15696)}}, {{A, B, C, X(1585), X(60312)}}, {{A, B, C, X(1586), X(60311)}}, {{A, B, C, X(3346), X(33923)}}, {{A, B, C, X(3522), X(8797)}}, {{A, B, C, X(3832), X(40410)}}, {{A, B, C, X(7714), X(54522)}}, {{A, B, C, X(10299), X(15318)}}, {{A, B, C, X(10303), X(35510)}}, {{A, B, C, X(11668), X(52299)}}, {{A, B, C, X(13599), X(17538)}}, {{A, B, C, X(14893), X(54552)}}, {{A, B, C, X(15697), X(15740)}}, {{A, B, C, X(15705), X(55958)}}, {{A, B, C, X(15710), X(18853)}}, {{A, B, C, X(15713), X(31846)}}, {{A, B, C, X(16251), X(49139)}}, {{A, B, C, X(31363), X(33703)}}, {{A, B, C, X(33012), X(57857)}}, {{A, B, C, X(38282), X(53108)}}, {{A, B, C, X(38335), X(54923)}}, {{A, B, C, X(52281), X(60635)}}
X(61914) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15022, 5068}, {2, 15708, 17678}, {2, 16397, 6933}, {2, 17578, 631}, {2, 3091, 3522}, {2, 3545, 15683}, {2, 381, 15705}, {2, 3832, 15717}, {2, 3854, 3}, {2, 5, 3832}, {2, 5056, 15022}, {2, 5059, 10303}, {2, 5187, 11106}, {4, 15719, 12103}, {4, 3090, 547}, {4, 3525, 15710}, {4, 631, 15696}, {5, 15699, 548}, {5, 16239, 381}, {5, 17575, 10883}, {5, 3090, 7486}, {5, 3526, 3855}, {5, 3628, 382}, {5, 382, 3545}, {5, 548, 3851}, {5, 632, 3859}, {20, 3091, 3843}, {20, 3843, 17578}, {20, 7486, 5067}, {140, 3544, 3839}, {376, 7486, 17530}, {381, 10303, 5059}, {381, 16239, 3528}, {546, 15703, 3533}, {546, 3533, 10304}, {632, 12812, 5079}, {962, 10172, 46931}, {1656, 12812, 5071}, {1656, 15694, 3628}, {1656, 15696, 5070}, {1656, 5055, 12812}, {1656, 5071, 3091}, {2041, 2042, 10299}, {3090, 5055, 5056}, {3090, 5071, 1656}, {3091, 15692, 4}, {3522, 15683, 17538}, {3525, 3851, 3543}, {3526, 3855, 20}, {3545, 17538, 3858}, {3628, 3858, 15694}, {3817, 19877, 20070}, {3832, 15022, 5}, {3832, 7486, 13735}, {3851, 15699, 3525}, {3855, 5067, 3526}, {3857, 15720, 15682}, {3861, 6907, 3529}, {5070, 15696, 632}, {8227, 31399, 5734}, {10303, 15697, 15712}, {10304, 15703, 2}, {13741, 15022, 5072}, {14782, 14783, 5073}, {14784, 14785, 15699}, {14892, 17582, 3146}, {15681, 15706, 8703}, {15693, 15710, 15692}, {15694, 17538, 3523}, {42472, 43028, 43465}, {42473, 43029, 43466}, {42581, 42910, 42998}

X(61915) = X(2)X(3)∩X(6)X(41949)

Barycentrics    5*a^4+23*(b^2-c^2)^2-28*a^2*(b^2+c^2) : :
X(61915) = -23*X[2]+6*X[3], X[69]+16*X[25565], 10*X[551]+7*X[61256], -3*X[944]+20*X[51109], 12*X[1699]+5*X[50809], 35*X[3622]+16*X[61253], 15*X[3817]+2*X[50814], 2*X[4669]+15*X[8227], -X[4677]+18*X[10175], 8*X[4745]+9*X[5603], 12*X[5476]+5*X[50990], 15*X[5587]+2*X[51082] and many others

X(61915) lies on these lines: {2, 3}, {6, 41949}, {69, 25565}, {262, 60641}, {551, 61256}, {944, 51109}, {1285, 18584}, {1327, 43510}, {1328, 43509}, {1699, 50809}, {3316, 35823}, {3317, 35822}, {3622, 61253}, {3817, 50814}, {4669, 8227}, {4677, 10175}, {4745, 5603}, {5365, 42610}, {5366, 42611}, {5476, 50990}, {5485, 54645}, {5587, 51082}, {5881, 51106}, {6200, 43522}, {6396, 43521}, {6437, 43381}, {6438, 43380}, {7581, 42603}, {7582, 42602}, {7612, 60283}, {7811, 52718}, {7967, 61257}, {7988, 38127}, {8252, 42418}, {8253, 42417}, {8584, 51178}, {8591, 15092}, {9143, 15088}, {9541, 42566}, {9624, 51091}, {9778, 50807}, {9956, 34631}, {10171, 51071}, {10172, 30308}, {10219, 11455}, {10516, 51136}, {10653, 42903}, {10654, 42902}, {11433, 44834}, {11488, 41120}, {11489, 41119}, {11668, 60281}, {12245, 51066}, {12816, 42089}, {12817, 42092}, {13846, 42573}, {13847, 42572}, {13925, 60311}, {13993, 60312}, {14226, 42274}, {14241, 42277}, {14482, 39593}, {14494, 60216}, {14853, 50973}, {15534, 40330}, {16267, 49810}, {16268, 49811}, {16644, 49824}, {16645, 49825}, {16808, 42588}, {16809, 42589}, {16966, 41113}, {16967, 41112}, {18538, 43386}, {18581, 49813}, {18582, 49812}, {18762, 43387}, {18840, 54734}, {18841, 54851}, {18842, 54644}, {22489, 36318}, {22490, 36320}, {23302, 49876}, {23303, 49875}, {24206, 50994}, {25561, 39874}, {31145, 61272}, {32532, 53108}, {32789, 43257}, {32790, 43256}, {32896, 52713}, {33406, 49849}, {33407, 49850}, {33602, 41100}, {33603, 41101}, {33604, 42129}, {33605, 42132}, {34627, 51110}, {35749, 59401}, {36327, 59402}, {36344, 36765}, {36768, 59394}, {36969, 42505}, {36970, 42504}, {37640, 42915}, {37641, 42914}, {37712, 50818}, {37832, 42507}, {37835, 42506}, {38021, 51069}, {38022, 61246}, {38072, 51143}, {38074, 51103}, {38314, 61244}, {40693, 49904}, {40694, 49903}, {41107, 42114}, {41108, 42111}, {41121, 42910}, {41122, 42911}, {41943, 43447}, {41944, 43446}, {42095, 49873}, {42098, 49874}, {42103, 42632}, {42106, 42631}, {42140, 43331}, {42141, 43330}, {42266, 43563}, {42267, 43562}, {42268, 43505}, {42269, 43506}, {42472, 44015}, {42473, 44016}, {42474, 43403}, {42475, 43404}, {42478, 43010}, {42479, 43011}, {42502, 43104}, {42503, 43101}, {42516, 43335}, {42517, 43334}, {42526, 43317}, {42527, 43316}, {42537, 43788}, {42538, 43787}, {42567, 43384}, {42582, 42606}, {42583, 42607}, {42976, 43009}, {42977, 43008}, {43028, 43420}, {43029, 43421}, {43228, 43332}, {43229, 43333}, {43244, 43487}, {43245, 43488}, {43475, 43637}, {43476, 43636}, {43481, 43490}, {43482, 43489}, {43536, 60623}, {43622, 54635}, {43623, 54634}, {46334, 52080}, {46335, 52079}, {50798, 61280}, {50802, 61265}, {50805, 61270}, {50810, 54447}, {50813, 58441}, {50821, 61266}, {50864, 61263}, {50966, 53023}, {50974, 51185}, {51029, 55649}, {51072, 51709}, {51133, 59411}, {51186, 54132}, {51705, 61264}, {53620, 61268}, {54522, 60143}, {54523, 60628}, {54597, 60622}, {54920, 60637}, {54934, 60646}, {59417, 61267}, {60127, 60277}, {60150, 60238}, {60185, 60648}

X(61915) = inverse of X(15719) in orthocentroidal circle
X(61915) = inverse of X(15719) in Yff hyperbola
X(61915) = complement of X(61796)
X(61915) = anticomplement of X(61854)
X(61915) = pole of line {523, 15719} with respect to the orthocentroidal circle
X(61915) = pole of line {6, 15719} with respect to the Kiepert hyperbola
X(61915) = pole of line {523, 15719} with respect to the Yff hyperbola
X(61915) = pole of line {69, 15713} with respect to the Wallace hyperbola
X(61915) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(15713)}}, {{A, B, C, X(264), X(15719)}}, {{A, B, C, X(458), X(60641)}}, {{A, B, C, X(632), X(18854)}}, {{A, B, C, X(1657), X(54763)}}, {{A, B, C, X(3534), X(8797)}}, {{A, B, C, X(3627), X(54838)}}, {{A, B, C, X(3843), X(54667)}}, {{A, B, C, X(4232), X(54645)}}, {{A, B, C, X(6995), X(54734)}}, {{A, B, C, X(7378), X(54851)}}, {{A, B, C, X(15681), X(18852)}}, {{A, B, C, X(15701), X(36889)}}, {{A, B, C, X(18850), X(35409)}}, {{A, B, C, X(18853), X(21734)}}, {{A, B, C, X(19708), X(55958)}}, {{A, B, C, X(40410), X(41106)}}, {{A, B, C, X(50691), X(60121)}}, {{A, B, C, X(52284), X(54644)}}, {{A, B, C, X(52301), X(54522)}}, {{A, B, C, X(53108), X(53857)}}
X(61915) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10109, 5071}, {2, 12100, 3525}, {2, 15640, 11812}, {2, 15682, 631}, {2, 15692, 11540}, {2, 20, 15713}, {2, 3091, 3534}, {2, 3534, 15702}, {2, 3543, 15701}, {2, 3545, 15682}, {2, 3839, 12100}, {2, 3845, 3524}, {2, 4, 15719}, {2, 5056, 10109}, {2, 5066, 11001}, {4, 12811, 3855}, {4, 3524, 15681}, {5, 12108, 3851}, {5, 1656, 3146}, {5, 3854, 3544}, {5, 547, 5054}, {140, 13635, 10299}, {140, 4205, 632}, {376, 15709, 3523}, {381, 11812, 15640}, {381, 12102, 3839}, {381, 17504, 17578}, {381, 5067, 15709}, {547, 3530, 15699}, {1006, 15682, 6891}, {3090, 15022, 3529}, {3090, 3533, 7486}, {3090, 3855, 1656}, {3090, 5071, 3545}, {3091, 15705, 14893}, {3091, 17697, 3}, {3091, 3530, 4}, {3146, 3523, 548}, {3523, 15022, 5}, {3529, 3545, 381}, {3544, 7486, 3533}, {3628, 5070, 13747}, {3830, 5054, 8703}, {3860, 11540, 12103}, {3860, 8703, 3830}, {3861, 5055, 17577}, {5054, 12103, 15692}, {5055, 5071, 3090}, {5055, 5079, 547}, {8703, 15681, 15697}, {8703, 15698, 15710}, {10124, 14893, 15714}, {12100, 15703, 2}, {14269, 15721, 17538}, {14892, 15694, 3832}, {14893, 15702, 376}, {15640, 15709, 15698}, {17566, 17578, 15022}, {37832, 42507, 49860}, {37832, 43543, 42986}, {37835, 42506, 49859}, {37835, 43542, 42987}, {41100, 42142, 33602}, {41101, 42139, 33603}, {41121, 42910, 49861}, {41122, 42911, 49862}, {41949, 41950, 6}

X(61916) = X(2)X(3)∩X(397)X(42636)

Barycentrics    4*a^4+19*(b^2-c^2)^2-23*a^2*(b^2+c^2) : :
X(61916) = -19*X[2]+5*X[3], 4*X[551]+3*X[38138], -2*X[3241]+9*X[61273], -8*X[3626]+15*X[38081], 2*X[3631]+5*X[5476], X[3632]+20*X[61272], 16*X[3636]+5*X[37705], X[3655]+6*X[61262], X[3679]+6*X[61269], 4*X[3828]+3*X[38034], -8*X[5097]+X[51182], -15*X[5886]+X[34747] and many others

X(61916) lies on these lines: {2, 3}, {397, 42636}, {398, 42635}, {551, 38138}, {3241, 61273}, {3626, 38081}, {3631, 5476}, {3632, 61272}, {3636, 37705}, {3655, 61262}, {3679, 61269}, {3828, 38034}, {5097, 51182}, {5886, 34747}, {5901, 50831}, {6329, 38079}, {6490, 8253}, {6491, 8252}, {6492, 52047}, {6493, 52048}, {6688, 45956}, {7583, 42640}, {7584, 42639}, {7988, 38112}, {9624, 51094}, {9771, 53144}, {9956, 38098}, {10171, 10283}, {10175, 34641}, {10645, 12821}, {10646, 12820}, {11008, 14848}, {11178, 20583}, {11230, 61260}, {11698, 38084}, {13903, 14226}, {13961, 14241}, {14810, 51129}, {15088, 24981}, {15808, 28204}, {16241, 42492}, {16242, 42493}, {16267, 42899}, {16268, 42898}, {16772, 43547}, {16773, 43546}, {16960, 42782}, {16961, 42781}, {16966, 42923}, {16967, 42922}, {18362, 31406}, {18538, 42603}, {18583, 50986}, {18762, 42602}, {18874, 21969}, {19875, 50822}, {19876, 28174}, {19883, 50832}, {19924, 50981}, {20304, 56567}, {20582, 38136}, {21358, 51184}, {22791, 38083}, {22793, 50825}, {24206, 50978}, {25055, 61259}, {25561, 38110}, {28198, 50826}, {28202, 51073}, {30308, 61524}, {31162, 61266}, {31423, 50807}, {31663, 51074}, {32907, 35019}, {32909, 35020}, {34773, 38076}, {35814, 42572}, {35815, 42573}, {37832, 43014}, {37835, 43015}, {38074, 61295}, {38080, 60980}, {38137, 60986}, {38139, 60999}, {38314, 61245}, {39884, 48310}, {41945, 41959}, {41946, 41960}, {41951, 42582}, {41952, 42583}, {42095, 42916}, {42098, 42917}, {42111, 42912}, {42114, 42913}, {42143, 42475}, {42144, 42500}, {42145, 42501}, {42146, 42474}, {42163, 42939}, {42166, 42938}, {42268, 42642}, {42269, 42641}, {42580, 43228}, {42581, 43229}, {42590, 42920}, {42591, 42921}, {42598, 42780}, {42599, 42779}, {42627, 43404}, {42628, 43403}, {42682, 43467}, {42683, 43468}, {42813, 43100}, {42814, 43107}, {42817, 43644}, {42818, 43649}, {42900, 42996}, {42901, 42997}, {42914, 43104}, {42915, 43101}, {42946, 42973}, {42947, 42972}, {42962, 42985}, {42963, 42984}, {43108, 43238}, {43109, 43239}, {46267, 47354}, {48896, 51139}, {48901, 50980}, {48904, 51131}, {51026, 55655}, {51047, 61522}, {51067, 58240}, {51103, 61297}, {51105, 61249}, {51110, 61258}, {51142, 55718}, {51180, 59373}, {51183, 61545}, {54447, 61267}

X(61916) = midpoint of X(i) and X(j) for these {i,j}: {2, 3851}, {381, 15702}, {3832, 15701}, {31423, 50807}, {51110, 61258}
X(61916) = reflection of X(i) in X(j) for these {i,j}: {14869, 2}, {15698, 140}, {15703, 547}, {3832, 5066}, {3845, 3857}, {8703, 3523}
X(61916) = inverse of X(15707) in orthocentroidal circle
X(61916) = inverse of X(15707) in Yff hyperbola
X(61916) = complement of X(15700)
X(61916) = pole of line {523, 15707} with respect to the orthocentroidal circle
X(61916) = pole of line {6, 15707} with respect to the Kiepert hyperbola
X(61916) = pole of line {523, 15707} with respect to the Yff hyperbola
X(61916) = intersection, other than A, B, C, of circumconics {{A, B, C, X(264), X(15707)}}, {{A, B, C, X(1494), X(14869)}}, {{A, B, C, X(3525), X(31846)}}, {{A, B, C, X(5054), X(57823)}}, {{A, B, C, X(34200), X(55958)}}, {{A, B, C, X(38071), X(40410)}}
X(61916) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11737, 15687}, {2, 15688, 140}, {2, 15715, 15694}, {2, 30, 14869}, {2, 3529, 5054}, {2, 3544, 14269}, {2, 3545, 382}, {2, 3839, 10299}, {2, 3851, 30}, {2, 3855, 15688}, {2, 4, 15707}, {2, 546, 17504}, {4, 15723, 14891}, {5, 15687, 11737}, {5, 15712, 12811}, {5, 1656, 3627}, {5, 8703, 3545}, {30, 140, 15698}, {30, 3857, 3845}, {30, 5066, 3832}, {30, 547, 15703}, {140, 15022, 5}, {140, 3543, 15714}, {376, 3543, 17800}, {381, 10124, 15686}, {381, 15694, 15683}, {381, 15703, 15702}, {381, 15718, 3543}, {382, 15694, 15715}, {547, 10109, 5071}, {547, 14893, 3628}, {547, 549, 15699}, {549, 3627, 376}, {1656, 3544, 3530}, {1656, 5066, 11539}, {3090, 15703, 547}, {3090, 3832, 1656}, {3523, 15715, 15700}, {3524, 5072, 3860}, {3528, 3851, 546}, {3529, 5067, 16052}, {3530, 3627, 550}, {3544, 14269, 5066}, {3544, 3832, 3851}, {3545, 15683, 381}, {3545, 15694, 14893}, {3545, 8703, 3858}, {3627, 11539, 15711}, {3628, 5066, 15706}, {3839, 11812, 15704}, {3839, 5070, 11812}, {3843, 15709, 15690}, {3845, 15699, 632}, {5055, 5056, 10109}, {5067, 12811, 15712}, {10109, 12812, 5055}, {10124, 15686, 549}, {10175, 61270, 59400}, {14784, 14785, 13735}, {14891, 15723, 15713}, {14893, 15694, 8703}, {15681, 15700, 3528}, {15687, 17504, 15681}, {15688, 15701, 5154}, {15700, 15703, 2}, {15701, 15706, 3523}, {39884, 48310, 50987}, {42143, 42911, 42633}, {42146, 42910, 42634}, {42474, 42910, 42146}, {42475, 42911, 42143}

X(61917) = X(2)X(3)∩X(13)X(42917)

Barycentrics    4*a^4+25*(b^2-c^2)^2-29*a^2*(b^2+c^2) : :
X(61917) = -25*X[2]+7*X[3], 25*X[10]+2*X[58244], -16*X[3589]+7*X[51181], 25*X[3625]+56*X[58237], -16*X[3630]+7*X[51183], -X[3633]+28*X[61272], -16*X[3634]+7*X[50826], X[3653]+5*X[61264], 4*X[3818]+5*X[50987], 5*X[4668]+49*X[61268], 20*X[4691]+7*X[11278], -X[5097]+10*X[25565] and many others

X(61917) lies on these lines: {2, 3}, {10, 58244}, {13, 42917}, {14, 42916}, {61, 43247}, {62, 43246}, {395, 44017}, {396, 44018}, {485, 42640}, {486, 42639}, {519, 61270}, {1327, 6430}, {1328, 6429}, {3589, 51181}, {3625, 58237}, {3630, 51183}, {3633, 61272}, {3634, 50826}, {3653, 61264}, {3818, 50987}, {4668, 61268}, {4691, 11278}, {5097, 25565}, {5550, 50800}, {6431, 42602}, {6432, 42603}, {6433, 43254}, {6434, 43255}, {6437, 43211}, {6438, 43212}, {6500, 43536}, {6501, 54597}, {7988, 58241}, {9955, 51120}, {10171, 38022}, {10175, 38081}, {10283, 38155}, {11178, 32455}, {11542, 42474}, {11543, 42475}, {16267, 43101}, {16268, 43104}, {16644, 42923}, {16645, 42922}, {16808, 43100}, {16809, 43107}, {17851, 42540}, {18357, 50871}, {18358, 51027}, {18480, 50832}, {18483, 50825}, {19130, 51166}, {19875, 61266}, {19876, 40273}, {19878, 50833}, {19883, 31662}, {20582, 55587}, {21850, 51184}, {22791, 50822}, {25055, 61262}, {28186, 58227}, {28204, 58234}, {30392, 61263}, {34573, 50981}, {37517, 50978}, {37832, 43031}, {37835, 43030}, {38021, 38112}, {38028, 38076}, {38034, 38083}, {38074, 61283}, {38075, 38111}, {38079, 39561}, {38082, 38137}, {38229, 38746}, {38314, 61251}, {41005, 55958}, {42095, 42633}, {42098, 42634}, {42115, 43201}, {42116, 43202}, {42121, 42973}, {42124, 42972}, {42163, 42802}, {42166, 42801}, {42270, 43887}, {42273, 43888}, {42492, 42906}, {42493, 42907}, {42516, 42690}, {42517, 42691}, {42785, 50982}, {42786, 50959}, {42791, 42890}, {42792, 42891}, {42892, 43873}, {42893, 43874}, {42894, 42915}, {42895, 42914}, {42953, 61719}, {42984, 43482}, {42985, 43481}, {43401, 54591}, {43402, 54592}, {47354, 50664}, {48310, 55695}, {48880, 51131}, {50984, 55642}, {50988, 51127}, {51025, 55691}, {51105, 61255}, {51128, 55636}

X(61917) = midpoint of X(i) and X(j) for these {i,j}: {381, 15709}, {3839, 15707}, {14269, 15705}
X(61917) = reflection of X(i) in X(j) for these {i,j}: {15705, 140}, {17504, 15709}, {8703, 15707}
X(61917) = inverse of X(15718) in orthocentroidal circle
X(61917) = inverse of X(15718) in Yff hyperbola
X(61917) = complement of X(15706)
X(61917) = pole of line {523, 15718} with respect to the orthocentroidal circle
X(61917) = pole of line {185, 58206} with respect to the Jerabek hyperbola
X(61917) = pole of line {6, 15718} with respect to the Kiepert hyperbola
X(61917) = pole of line {523, 15718} with respect to the Yff hyperbola
X(61917) = intersection, other than A, B, C, of circumconics {{A, B, C, X(264), X(15718)}}, {{A, B, C, X(548), X(55958)}}, {{A, B, C, X(549), X(57896)}}, {{A, B, C, X(1105), X(58206)}}, {{A, B, C, X(3533), X(31846)}}, {{A, B, C, X(35401), X(54585)}}
X(61917) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14093, 140}, {2, 15684, 12108}, {2, 15689, 14890}, {2, 3627, 549}, {2, 381, 548}, {2, 3843, 14891}, {2, 4, 15718}, {2, 5072, 14893}, {5, 15704, 5068}, {5, 15712, 5072}, {5, 1656, 3857}, {5, 3090, 550}, {5, 5055, 15699}, {5, 8703, 11737}, {30, 140, 15705}, {30, 15709, 17504}, {546, 15703, 15713}, {546, 16417, 14869}, {547, 10109, 5056}, {547, 11737, 15702}, {547, 15690, 3628}, {547, 5066, 16239}, {632, 3857, 3529}, {1656, 15684, 2}, {1657, 15690, 15686}, {3090, 15717, 1656}, {3524, 3545, 3832}, {3526, 12101, 15714}, {3545, 11539, 3845}, {3545, 15702, 3839}, {3545, 5055, 547}, {3545, 5056, 5055}, {3628, 15690, 15723}, {3628, 5079, 6973}, {3832, 15690, 15687}, {3832, 15723, 15690}, {3845, 15699, 11539}, {3850, 12108, 3853}, {3850, 14892, 3545}, {3853, 16239, 15717}, {3860, 15694, 15704}, {5054, 5055, 3090}, {5056, 15022, 5067}, {5066, 12102, 381}, {5066, 14891, 3843}, {5066, 16239, 3543}, {5068, 15694, 3860}, {5071, 10109, 5}, {5071, 5079, 10109}, {11539, 17504, 11812}, {12108, 15684, 8703}, {14269, 15705, 30}, {14890, 14893, 15689}, {14890, 15689, 15712}, {14892, 15699, 3627}

X(61918) = X(2)X(3)∩X(395)X(43246)

Barycentrics    4*a^4+31*(b^2-c^2)^2-35*a^2*(b^2+c^2) : :
X(61918) = -31*X[2]+9*X[3], -9*X[1483]+20*X[51104], X[3654]+21*X[61265], -X[3656]+12*X[61267], X[4677]+21*X[61268], 10*X[5476]+X[50985], -12*X[5886]+X[50831], -X[8584]+12*X[25565], -12*X[10171]+X[50824], -12*X[10175]+X[50823], -15*X[10283]+4*X[51087], 9*X[11178]+2*X[41149] and many others

X(61918) lies on these lines: {2, 3}, {395, 43246}, {396, 43247}, {1483, 51104}, {1587, 42527}, {1588, 42526}, {3654, 61265}, {3656, 61267}, {4677, 61268}, {5476, 50985}, {5886, 50831}, {7583, 42579}, {7584, 42578}, {8252, 43525}, {8253, 43526}, {8584, 25565}, {9681, 43378}, {10171, 50824}, {10175, 50823}, {10283, 51087}, {10302, 54734}, {10576, 43341}, {10577, 43340}, {11178, 41149}, {11230, 51085}, {11542, 42475}, {11543, 42474}, {12007, 38079}, {12816, 42954}, {12817, 42955}, {13607, 38022}, {14561, 50986}, {16808, 43490}, {16809, 43489}, {18357, 51105}, {18358, 51185}, {18493, 51068}, {18510, 60300}, {18512, 60299}, {18538, 42640}, {18581, 43332}, {18582, 43333}, {18762, 42639}, {21850, 51143}, {22791, 51069}, {33416, 43330}, {33417, 43331}, {33606, 43228}, {33607, 43229}, {37705, 51103}, {37832, 43011}, {37835, 43010}, {38042, 50827}, {38081, 51070}, {38112, 61266}, {38138, 51106}, {38229, 41154}, {38317, 51138}, {41107, 43545}, {41108, 43544}, {41119, 42634}, {41120, 42633}, {41121, 43328}, {41122, 43329}, {41955, 41965}, {41956, 41966}, {42087, 43469}, {42088, 43470}, {42111, 42419}, {42114, 42420}, {42117, 43483}, {42118, 43484}, {42121, 43549}, {42124, 43548}, {42129, 49874}, {42132, 49873}, {42143, 49947}, {42146, 49948}, {42153, 49860}, {42156, 49859}, {42163, 42976}, {42166, 42977}, {42215, 43381}, {42216, 43380}, {42274, 43317}, {42277, 43316}, {42492, 42942}, {42493, 42943}, {42502, 49904}, {42503, 49903}, {42588, 43640}, {42589, 43639}, {42606, 53516}, {42607, 53513}, {42627, 42690}, {42628, 42691}, {42684, 46335}, {42685, 46334}, {42686, 43249}, {42687, 43248}, {42799, 42923}, {42800, 42922}, {42910, 42917}, {42911, 42916}, {43101, 49907}, {43104, 49908}, {43254, 43339}, {43255, 43338}, {43314, 43385}, {43315, 43384}, {43336, 43562}, {43337, 43563}, {43542, 43649}, {43543, 43644}, {47353, 51181}, {50798, 61273}, {50804, 61271}, {50830, 51709}, {50978, 51142}, {51093, 61272}, {51096, 61270}, {51110, 61261}, {51131, 55649}, {51140, 59399}, {54521, 60641}, {54522, 60637}, {54608, 60238}, {54643, 60277}, {54644, 60282}, {54645, 60228}, {54851, 60239}, {60175, 60283}, {60192, 60216}

X(61918) = midpoint of X(i) and X(j) for these {i,j}: {381, 3525}, {3855, 15723}
X(61918) = reflection of X(i) in X(j) for these {i,j}: {15715, 140}, {5070, 547}, {8703, 15719}
X(61918) = inverse of X(61797) in orthocentroidal circle
X(61918) = inverse of X(61797) in Yff hyperbola
X(61918) = complement of X(15716)
X(61918) = pole of line {523, 61797} with respect to the orthocentroidal circle
X(61918) = pole of line {6, 61797} with respect to the Kiepert hyperbola
X(61918) = pole of line {523, 61797} with respect to the Yff hyperbola
X(61918) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(10301), X(54734)}}, {{A, B, C, X(15690), X(55958)}}
X(61918) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15685, 11812}, {2, 15690, 15713}, {2, 381, 15690}, {2, 3845, 15711}, {2, 6952, 17800}, {4, 10303, 15696}, {4, 3530, 15704}, {4, 5055, 547}, {5, 11539, 11737}, {5, 14869, 5068}, {5, 15687, 14892}, {30, 140, 15715}, {30, 547, 5070}, {381, 3525, 30}, {381, 5055, 7486}, {546, 14890, 15683}, {546, 3091, 6924}, {547, 11737, 15692}, {547, 12811, 5054}, {547, 14892, 12103}, {547, 5066, 11540}, {547, 632, 15699}, {1656, 14892, 15687}, {3090, 11737, 11539}, {3091, 6950, 5072}, {3522, 3545, 381}, {3526, 15640, 12100}, {3545, 15681, 3859}, {3628, 5066, 3534}, {3830, 3858, 3845}, {3845, 5066, 3857}, {3850, 15703, 17504}, {3856, 12103, 4}, {3859, 11540, 15640}, {5056, 12811, 6892}, {5056, 6939, 550}, {5066, 10109, 5055}, {5070, 5079, 5056}, {6849, 15707, 3543}, {8703, 15713, 3530}, {10303, 17504, 549}, {11539, 11737, 3858}, {12100, 15681, 8703}, {14269, 16239, 15714}, {15699, 15711, 2}, {15704, 15713, 15698}

X(61919) = X(2)X(3)∩X(6)X(14840)

Barycentrics    a^4+8*(b^2-c^2)^2-9*a^2*(b^2+c^2) : :
X(61919) = -24*X[2]+7*X[3], 8*X[8]+9*X[58238], 2*X[10]+15*X[61266], -X[145]+18*X[61270], -18*X[373]+X[34783], X[399]+16*X[15088], -20*X[576]+3*X[51174], -8*X[944]+25*X[58233], 2*X[1385]+15*X[61264], 8*X[1539]+9*X[38633], 9*X[1853]+8*X[14862], 16*X[3589]+X[48662] and many others

X(61919) lies on these lines: {2, 3}, {6, 14840}, {8, 58238}, {10, 61266}, {13, 42436}, {14, 42435}, {17, 42095}, {18, 42098}, {145, 61270}, {262, 60640}, {373, 34783}, {397, 42114}, {398, 42111}, {399, 15088}, {485, 6501}, {486, 6500}, {517, 30315}, {576, 51174}, {944, 58233}, {1007, 32875}, {1159, 17606}, {1385, 61264}, {1482, 3711}, {1539, 38633}, {1853, 14862}, {3070, 10194}, {3071, 10195}, {3531, 26861}, {3589, 48662}, {3590, 7582}, {3591, 7581}, {3616, 61262}, {3625, 5790}, {3633, 8227}, {3634, 48661}, {3635, 5886}, {3636, 61257}, {3763, 55593}, {3818, 55697}, {3917, 12002}, {3933, 32888}, {4691, 10175}, {5013, 39601}, {5024, 39565}, {5050, 18553}, {5093, 6144}, {5237, 42611}, {5238, 42610}, {5334, 42950}, {5335, 42951}, {5339, 16966}, {5340, 16967}, {5343, 42124}, {5344, 42121}, {5349, 42092}, {5350, 42089}, {5351, 42909}, {5352, 42908}, {5355, 13881}, {5418, 9690}, {5420, 43415}, {5475, 12815}, {5493, 10172}, {5544, 45622}, {5587, 37624}, {5640, 14128}, {5650, 44863}, {5663, 11465}, {5690, 58247}, {5779, 61020}, {5818, 20053}, {5876, 11451}, {5882, 10171}, {6053, 23515}, {6199, 10576}, {6241, 11017}, {6243, 14845}, {6390, 32889}, {6395, 10577}, {6407, 8253}, {6408, 8252}, {6417, 8960}, {6418, 42265}, {6445, 23261}, {6446, 23251}, {6455, 35787}, {6456, 35786}, {6459, 6472}, {6460, 6473}, {6474, 9540}, {6475, 13935}, {6667, 38756}, {6721, 38733}, {6722, 38744}, {6723, 38790}, {6749, 33636}, {6767, 7741}, {7173, 31479}, {7373, 7951}, {7603, 9605}, {7607, 60146}, {7608, 60209}, {7746, 18584}, {7755, 43136}, {7764, 40727}, {7776, 53127}, {7989, 10246}, {7991, 38083}, {8148, 9956}, {8797, 40995}, {8976, 42274}, {8981, 43881}, {9542, 34089}, {9624, 50798}, {9691, 41963}, {9777, 12316}, {9781, 13421}, {9955, 61265}, {10113, 38638}, {10143, 43526}, {10144, 43525}, {10159, 60329}, {10170, 27355}, {10185, 53107}, {10187, 16808}, {10188, 16809}, {10516, 25555}, {10546, 10610}, {11178, 11482}, {11362, 51075}, {11412, 18874}, {11441, 15047}, {11444, 13364}, {11485, 42802}, {11486, 42801}, {11499, 61159}, {11591, 13321}, {11623, 38743}, {11695, 18439}, {12111, 32205}, {12308, 15046}, {12315, 32767}, {12645, 61272}, {12702, 54447}, {12900, 12902}, {13093, 61735}, {13188, 15092}, {13363, 15058}, {13382, 18435}, {13432, 61715}, {13665, 42583}, {13785, 42582}, {13903, 42561}, {13951, 42277}, {13961, 31412}, {13966, 43882}, {14530, 23325}, {14561, 32455}, {14639, 52886}, {14848, 50961}, {14864, 32063}, {14929, 32870}, {15024, 15060}, {15026, 15056}, {15028, 45959}, {15029, 20379}, {15045, 45958}, {16534, 38724}, {16644, 43021}, {16645, 43020}, {17851, 23249}, {18525, 61263}, {18526, 61259}, {18581, 42988}, {18582, 42989}, {18844, 53859}, {19106, 42774}, {19107, 42773}, {19130, 55584}, {19163, 38639}, {19872, 28146}, {19877, 40273}, {20417, 38789}, {20418, 38755}, {21358, 55580}, {22236, 42892}, {22238, 42893}, {22246, 43620}, {22505, 38634}, {22515, 38635}, {22799, 38637}, {22938, 38636}, {23302, 42920}, {23303, 42921}, {24206, 42785}, {25043, 34599}, {25561, 53093}, {25565, 50955}, {28212, 46932}, {31399, 34718}, {31487, 42602}, {32396, 48675}, {32825, 32878}, {33179, 61271}, {33416, 42928}, {33417, 42929}, {33533, 38848}, {34748, 61276}, {36519, 52090}, {37727, 50801}, {37832, 42993}, {37835, 42992}, {38022, 50797}, {38072, 55724}, {38074, 61278}, {38079, 50954}, {38084, 38669}, {38107, 60962}, {38108, 61000}, {38314, 61255}, {38317, 55705}, {38768, 58418}, {38780, 58419}, {38800, 58427}, {40280, 44870}, {40693, 43101}, {40694, 43104}, {41943, 43425}, {41944, 43424}, {41973, 42488}, {41974, 42489}, {42085, 42949}, {42086, 42948}, {42107, 42150}, {42110, 42151}, {42115, 42900}, {42116, 42901}, {42117, 42776}, {42118, 42775}, {42125, 42152}, {42126, 42945}, {42127, 42944}, {42128, 42149}, {42139, 42925}, {42142, 42924}, {42143, 42817}, {42146, 42818}, {42153, 42474}, {42156, 42475}, {42157, 43029}, {42158, 43028}, {42163, 42911}, {42166, 42910}, {42431, 42958}, {42432, 42959}, {42494, 42815}, {42495, 42816}, {42598, 42975}, {42599, 42974}, {42603, 53513}, {42690, 42961}, {42691, 42960}, {42779, 43240}, {42780, 43241}, {42786, 53023}, {43004, 43235}, {43005, 43234}, {43413, 52047}, {43414, 52048}, {43427, 61719}, {43457, 44535}, {43527, 54857}, {47353, 55701}, {47355, 55692}, {48658, 58428}, {48680, 58421}, {48681, 58430}, {48889, 55682}, {48895, 55643}, {48901, 55624}, {50963, 53097}, {50993, 55721}, {51024, 55620}, {51103, 61248}, {51514, 60976}, {51516, 60977}, {51700, 54448}, {53106, 60144}, {59503, 61267}, {60182, 60326}, {60250, 60332}, {60334, 60649}, {60884, 61595}

X(61919) = midpoint of X(i) and X(j) for these {i,j}: {3533, 3854}, {3544, 7486}
X(61919) = reflection of X(i) in X(j) for these {i,j}: {3544, 5}
X(61919) = inverse of X(15712) in orthocentroidal circle
X(61919) = inverse of X(15712) in Yff hyperbola
X(61919) = complement of X(61138)
X(61919) = anticomplement of X(61852)
X(61919) = X(i)-complementary conjugate of X(j) for these {i, j}: {61137, 10}
X(61919) = pole of line {523, 15712} with respect to the orthocentroidal circle
X(61919) = pole of line {185, 49139} with respect to the Jerabek hyperbola
X(61919) = pole of line {6, 15712} with respect to the Kiepert hyperbola
X(61919) = pole of line {523, 15712} with respect to the Yff hyperbola
X(61919) = pole of line {69, 55704} with respect to the Wallace hyperbola
X(61919) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(14841)}}, {{A, B, C, X(4), X(14840)}}, {{A, B, C, X(264), X(15712)}}, {{A, B, C, X(265), X(3544)}}, {{A, B, C, X(428), X(60329)}}, {{A, B, C, X(458), X(60640)}}, {{A, B, C, X(632), X(46168)}}, {{A, B, C, X(1105), X(49139)}}, {{A, B, C, X(3519), X(3525)}}, {{A, B, C, X(3521), X(11541)}}, {{A, B, C, X(3524), X(26861)}}, {{A, B, C, X(3526), X(15319)}}, {{A, B, C, X(3531), X(26863)}}, {{A, B, C, X(3860), X(60122)}}, {{A, B, C, X(5054), X(60171)}}, {{A, B, C, X(5064), X(54857)}}, {{A, B, C, X(5068), X(14938)}}, {{A, B, C, X(5072), X(40410)}}, {{A, B, C, X(6662), X(17504)}}, {{A, B, C, X(8703), X(13599)}}, {{A, B, C, X(8797), X(33703)}}, {{A, B, C, X(10185), X(52298)}}, {{A, B, C, X(14861), X(17538)}}, {{A, B, C, X(14890), X(57822)}}, {{A, B, C, X(15689), X(55958)}}, {{A, B, C, X(18855), X(46935)}}, {{A, B, C, X(19709), X(40448)}}, {{A, B, C, X(31846), X(47598)}}, {{A, B, C, X(35475), X(43719)}}, {{A, B, C, X(43908), X(44879)}}, {{A, B, C, X(52281), X(60209)}}, {{A, B, C, X(52282), X(60146)}}, {{A, B, C, X(52297), X(60144)}}, {{A, B, C, X(55860), X(60007)}}
X(61919) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12108, 3526}, {2, 14893, 15706}, {2, 15686, 5054}, {2, 3545, 14893}, {2, 376, 14890}, {2, 381, 15689}, {2, 4, 15712}, {2, 5, 5072}, {3, 3843, 15684}, {5, 140, 5068}, {5, 15699, 12811}, {5, 30, 3544}, {5, 3627, 14892}, {5, 3628, 3545}, {5, 5071, 5079}, {5, 547, 3091}, {5, 632, 11737}, {20, 3090, 15699}, {140, 14892, 3850}, {140, 1656, 5070}, {140, 3090, 1656}, {140, 381, 5073}, {140, 3850, 3627}, {140, 3861, 550}, {140, 5073, 3}, {140, 550, 3524}, {140, 8703, 3523}, {381, 15685, 14269}, {381, 15699, 15701}, {381, 5054, 15682}, {381, 5068, 3851}, {382, 15706, 17538}, {485, 45385, 6501}, {486, 45384, 6500}, {546, 5054, 17800}, {549, 3855, 5076}, {549, 5067, 2049}, {550, 15759, 3522}, {632, 11737, 3832}, {632, 3832, 3534}, {1006, 15705, 3530}, {1656, 3858, 15694}, {1656, 5056, 5055}, {1656, 5072, 1657}, {1656, 5079, 5056}, {1657, 3850, 3843}, {2043, 2044, 3860}, {2045, 2046, 547}, {3090, 15682, 5067}, {3090, 5068, 140}, {3091, 3524, 3861}, {3091, 3526, 3830}, {3091, 5067, 15759}, {3146, 16239, 15693}, {3522, 3523, 15715}, {3523, 3545, 3858}, {3524, 15683, 8703}, {3525, 15696, 15707}, {3525, 3845, 15696}, {3526, 14093, 12108}, {3533, 3544, 3854}, {3533, 3854, 30}, {3543, 6938, 546}, {3627, 12812, 3090}, {3832, 15721, 11541}, {3839, 15723, 15695}, {3850, 15712, 4}, {3853, 10303, 15688}, {3854, 7486, 3533}, {3856, 11539, 3529}, {3859, 14869, 3543}, {5059, 17590, 17533}, {5071, 15022, 5}, {5072, 5079, 12812}, {5876, 12046, 11451}, {7407, 7486, 10109}, {11737, 15721, 381}, {12811, 15699, 20}, {14782, 14783, 17578}, {14813, 14814, 3525}, {14891, 15699, 2}, {14893, 17538, 382}, {15046, 20304, 12308}, {15684, 15689, 15685}, {15689, 15701, 14891}, {15765, 18585, 15683}, {42121, 42472, 42962}, {42124, 42473, 42963}, {42153, 42474, 42581}, {42156, 42475, 42580}, {42602, 53516, 31487}

X(61920) = X(2)X(3)∩X(6)X(25565)

Barycentrics    a^4+10*(b^2-c^2)^2-11*a^2*(b^2+c^2) : :
X(61920) = -10*X[2]+3*X[3], -X[6]+8*X[25565], 3*X[355]+4*X[51103], 6*X[373]+X[18435], -8*X[551]+X[18526], 6*X[576]+X[51188], -8*X[597]+X[39899], 5*X[599]+2*X[37517], -X[671]+8*X[15092], 4*X[946]+3*X[38066], 3*X[1351]+4*X[22165], 3*X[1482]+4*X[4669] and many others

X(61920) lies on these lines: {2, 3}, {6, 25565}, {13, 42129}, {14, 42132}, {15, 42509}, {16, 42508}, {98, 60287}, {262, 60638}, {355, 51103}, {373, 18435}, {395, 41119}, {396, 41120}, {399, 10601}, {485, 43322}, {486, 43323}, {511, 51173}, {515, 50800}, {516, 50807}, {517, 61265}, {519, 61268}, {542, 55711}, {551, 18526}, {576, 51188}, {597, 39899}, {599, 37517}, {671, 15092}, {946, 38066}, {1007, 32896}, {1327, 6398}, {1328, 6221}, {1351, 22165}, {1482, 4669}, {1503, 50957}, {3066, 14926}, {3241, 61272}, {3311, 42602}, {3312, 42603}, {3582, 9654}, {3584, 9669}, {3614, 10072}, {3624, 28208}, {3632, 58237}, {3653, 19925}, {3654, 3817}, {3655, 38076}, {3656, 4745}, {3679, 11278}, {3763, 55594}, {3818, 55699}, {3828, 12702}, {4677, 5790}, {5008, 15484}, {5041, 13881}, {5050, 47354}, {5093, 51175}, {5097, 11178}, {5102, 5476}, {5306, 31415}, {5318, 42956}, {5321, 42957}, {5339, 41943}, {5340, 41944}, {5459, 36363}, {5460, 36362}, {5461, 12188}, {5480, 51143}, {5587, 50797}, {5603, 51072}, {5655, 15046}, {5886, 38155}, {5891, 13321}, {5901, 34748}, {6033, 14971}, {6243, 27355}, {6321, 36521}, {6431, 8976}, {6432, 13951}, {6437, 6565}, {6438, 6564}, {6445, 43257}, {6446, 43256}, {6447, 10195}, {6448, 10194}, {6449, 43254}, {6450, 43255}, {6451, 43210}, {6452, 43209}, {6480, 8253}, {6481, 8252}, {6484, 23261}, {6485, 23251}, {6722, 14830}, {7173, 10056}, {7585, 42639}, {7586, 42640}, {7603, 18362}, {7615, 51122}, {7617, 9766}, {7697, 14711}, {7942, 34681}, {7967, 61260}, {7989, 28204}, {8148, 53620}, {8176, 8667}, {8227, 12645}, {8584, 14561}, {8724, 23514}, {9140, 15088}, {9166, 48657}, {9300, 43620}, {9306, 11935}, {9668, 51817}, {9692, 10143}, {9704, 43614}, {9778, 50825}, {9955, 19875}, {9956, 11531}, {10165, 50803}, {10170, 21969}, {10171, 10246}, {10219, 14855}, {10247, 61269}, {10516, 39561}, {10574, 11017}, {10588, 15170}, {10620, 45311}, {10711, 38084}, {10722, 26614}, {10742, 59376}, {11055, 32447}, {11123, 39492}, {11165, 18546}, {11180, 38079}, {11230, 30392}, {11231, 50865}, {11238, 31479}, {11444, 18874}, {11451, 15060}, {11465, 45959}, {11480, 42504}, {11481, 42505}, {11482, 41149}, {11485, 41113}, {11486, 41112}, {11488, 49824}, {11489, 49825}, {11632, 36519}, {11645, 47355}, {11648, 31489}, {12017, 48310}, {12046, 15024}, {12355, 15300}, {12571, 38068}, {12773, 45310}, {12815, 22331}, {12816, 16242}, {12817, 16241}, {13102, 47867}, {13103, 36769}, {13665, 13847}, {13690, 26336}, {13691, 26348}, {13785, 13846}, {13810, 26341}, {13811, 26346}, {13903, 42582}, {13961, 42583}, {14061, 22566}, {14226, 43890}, {14241, 43889}, {14458, 60645}, {14492, 60131}, {14537, 37637}, {14845, 21849}, {14853, 50990}, {15004, 53124}, {15027, 56567}, {15028, 45958}, {15029, 20396}, {15058, 32205}, {15597, 44678}, {15602, 44526}, {16267, 42153}, {16268, 42156}, {16644, 34754}, {16645, 34755}, {16966, 41101}, {16967, 41100}, {17006, 19569}, {18357, 38314}, {18358, 59373}, {18440, 25561}, {18510, 32787}, {18512, 32788}, {18525, 25055}, {18538, 19053}, {18581, 42503}, {18582, 42502}, {18762, 19054}, {19130, 21358}, {19876, 28198}, {19924, 42786}, {20126, 36518}, {20423, 50991}, {20582, 33878}, {21356, 44456}, {22247, 38730}, {22489, 48655}, {22490, 48656}, {23234, 61576}, {23249, 43320}, {23259, 43321}, {23302, 42511}, {23303, 42510}, {23513, 38758}, {24206, 38072}, {24833, 36522}, {25154, 36768}, {26446, 50802}, {28154, 51088}, {28164, 51078}, {28182, 50813}, {28190, 50833}, {28202, 31423}, {28216, 50826}, {29181, 50964}, {30308, 50821}, {31162, 38083}, {31467, 39565}, {31662, 38140}, {32620, 53780}, {32785, 52047}, {32786, 52048}, {32789, 53130}, {32790, 53131}, {32823, 32893}, {33618, 49920}, {33619, 49919}, {34507, 51187}, {34627, 37624}, {34631, 38081}, {35770, 42265}, {35771, 42262}, {36382, 59384}, {36383, 59383}, {36430, 52704}, {36836, 43311}, {36843, 43310}, {36967, 43294}, {36968, 43295}, {36969, 43028}, {36970, 43029}, {36990, 55688}, {37640, 42143}, {37641, 42146}, {37671, 53127}, {37727, 51104}, {37832, 41122}, {37835, 41121}, {38028, 50864}, {38034, 50810}, {38044, 50907}, {38073, 61511}, {38075, 61595}, {38077, 58421}, {38107, 60963}, {38110, 51023}, {38112, 50872}, {38127, 51075}, {38136, 50967}, {38138, 50818}, {38177, 50910}, {38182, 50908}, {38317, 47353}, {38733, 41134}, {38740, 41151}, {38743, 49102}, {40330, 50992}, {40693, 49810}, {40694, 49811}, {40920, 44747}, {41148, 52090}, {41951, 43879}, {41952, 43880}, {42089, 42792}, {42092, 42791}, {42093, 46335}, {42094, 46334}, {42119, 42906}, {42120, 42907}, {42130, 42632}, {42131, 42631}, {42135, 43108}, {42138, 43109}, {42139, 42912}, {42142, 42913}, {42150, 43107}, {42151, 43100}, {42154, 42918}, {42155, 42919}, {42157, 42610}, {42158, 42611}, {42268, 52045}, {42269, 52046}, {42429, 43368}, {42430, 43369}, {42488, 42972}, {42489, 42973}, {42496, 43307}, {42497, 43306}, {42572, 43569}, {42573, 43568}, {42580, 42989}, {42581, 42988}, {42641, 43338}, {42642, 43339}, {42916, 43554}, {42917, 43555}, {43207, 43644}, {43208, 43649}, {43246, 43403}, {43247, 43404}, {43273, 55695}, {43416, 49875}, {43417, 49876}, {45410, 48778}, {45411, 48779}, {47745, 51095}, {47865, 59401}, {47866, 59402}, {48889, 55683}, {48895, 55642}, {48901, 55622}, {48910, 55636}, {49861, 49874}, {49862, 49873}, {50799, 50868}, {50801, 61287}, {50817, 58241}, {50824, 61262}, {50956, 51025}, {50963, 51166}, {50977, 55591}, {50984, 55643}, {51024, 55618}, {51074, 51119}, {51076, 58441}, {51087, 61275}, {51092, 59388}, {51094, 61271}, {51106, 61258}, {51107, 61276}, {51127, 55678}, {51128, 55639}, {51129, 51165}, {51137, 59411}, {51537, 55692}, {53023, 55603}, {54131, 55587}, {58238, 59400}, {59374, 60884}, {59377, 61580}

X(61920) = midpoint of X(i) and X(j) for these {i,j}: {381, 3526}, {3832, 15702}, {3851, 15703}
X(61920) = reflection of X(i) in X(j) for these {i,j}: {15700, 3526}, {15701, 2}, {15703, 3090}, {3, 15702}, {381, 3851}, {3526, 15703}, {3528, 549}, {6891, 15719}
X(61920) = inverse of X(12100) in orthocentroidal circle
X(61920) = inverse of X(12100) in Yff hyperbola
X(61920) = complement of X(15698)
X(61920) = anticomplement of X(61851)
X(61920) = pole of line {523, 12100} with respect to the orthocentroidal circle
X(61920) = pole of line {185, 62170} with respect to the Jerabek hyperbola
X(61920) = pole of line {6, 12100} with respect to the Kiepert hyperbola
X(61920) = pole of line {523, 12100} with respect to the Yff hyperbola
X(61920) = pole of line {69, 55702} with respect to the Wallace hyperbola
X(61920) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(264), X(12100)}}, {{A, B, C, X(297), X(60287)}}, {{A, B, C, X(458), X(60638)}}, {{A, B, C, X(1494), X(15701)}}, {{A, B, C, X(3521), X(50692)}}, {{A, B, C, X(3528), X(18317)}}, {{A, B, C, X(3534), X(55958)}}, {{A, B, C, X(3544), X(14938)}}, {{A, B, C, X(3853), X(54585)}}, {{A, B, C, X(3856), X(21400)}}, {{A, B, C, X(3858), X(60122)}}, {{A, B, C, X(4846), X(46333)}}, {{A, B, C, X(5073), X(60121)}}, {{A, B, C, X(8797), X(15682)}}, {{A, B, C, X(11331), X(60645)}}, {{A, B, C, X(13599), X(33923)}}, {{A, B, C, X(15713), X(57822)}}, {{A, B, C, X(15719), X(36889)}}, {{A, B, C, X(16239), X(31846)}}, {{A, B, C, X(18550), X(33699)}}, {{A, B, C, X(19709), X(40410)}}, {{A, B, C, X(35403), X(54924)}}, {{A, B, C, X(52289), X(60131)}}
X(61920) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10109, 5055}, {2, 11001, 11812}, {2, 15682, 549}, {2, 15701, 3526}, {2, 15719, 11539}, {2, 30, 15701}, {2, 3524, 11540}, {2, 3534, 5054}, {2, 3545, 3845}, {2, 376, 15713}, {2, 3860, 15695}, {2, 5066, 3830}, {2, 5071, 10109}, {3, 3830, 11001}, {3, 3851, 3832}, {3, 5055, 547}, {3, 5059, 15696}, {3, 5070, 3533}, {4, 17533, 12103}, {5, 140, 3544}, {5, 15699, 11737}, {5, 1656, 5072}, {5, 3090, 3851}, {5, 3628, 5068}, {5, 547, 3545}, {5, 549, 14892}, {20, 10124, 15707}, {30, 15719, 6891}, {30, 3090, 15703}, {30, 549, 3528}, {140, 15681, 15706}, {140, 3839, 15681}, {381, 15706, 5076}, {381, 1657, 14269}, {381, 3526, 30}, {381, 5076, 3839}, {381, 547, 15723}, {546, 3524, 15684}, {547, 11539, 5067}, {549, 14892, 3091}, {550, 15709, 15718}, {631, 15687, 15689}, {632, 14893, 10304}, {1656, 5072, 382}, {2043, 2044, 3858}, {3090, 3526, 1656}, {3091, 15682, 3860}, {3091, 3533, 3853}, {3525, 3858, 17800}, {3534, 15716, 14093}, {3534, 5054, 15716}, {3534, 6983, 6858}, {3543, 15719, 15690}, {3543, 3545, 3850}, {3545, 5067, 3543}, {3545, 5071, 5056}, {3628, 3843, 15720}, {3628, 5068, 3843}, {3654, 3817, 50806}, {3845, 15708, 15685}, {3855, 10304, 14893}, {3861, 5067, 6980}, {5055, 15684, 7486}, {5055, 5071, 5079}, {5066, 15699, 15697}, {5071, 17579, 3861}, {5073, 12811, 6841}, {5790, 51709, 50805}, {6916, 15701, 6863}, {9166, 61575, 48657}, {9956, 38021, 34718}, {10304, 14893, 5073}, {11001, 11812, 3}, {11001, 15697, 15686}, {11001, 15702, 15698}, {11178, 14848, 11898}, {11539, 15690, 15719}, {11737, 12812, 15699}, {11737, 15694, 381}, {11737, 15699, 4}, {12100, 15685, 15688}, {12100, 15699, 2}, {12101, 15713, 376}, {12101, 15720, 3534}, {12812, 14869, 3090}, {14269, 15695, 15682}, {14869, 15688, 15700}, {15682, 15695, 1657}, {15685, 15694, 12100}, {15686, 15699, 16239}, {15686, 16239, 15708}, {15694, 15697, 15693}, {15700, 15723, 15702}, {15702, 15708, 14869}, {15708, 16239, 15694}, {15765, 18585, 3529}, {18586, 18587, 5070}, {25561, 47352, 18440}, {37832, 41122, 49947}, {37832, 42975, 42817}, {37835, 41121, 49948}, {37835, 42098, 42974}, {37835, 42974, 42818}, {38022, 61259, 34627}, {42095, 42474, 37832}, {42095, 49947, 41122}, {42098, 42475, 37835}, {42098, 49948, 41121}, {42125, 42915, 42950}, {42128, 42914, 42951}, {42506, 42507, 6}, {42507, 49907, 42506}, {42606, 42609, 3311}, {42607, 42608, 3312}

X(61921) = X(2)X(3)∩X(6)X(43409)

Barycentrics    a^4+11*(b^2-c^2)^2-12*a^2*(b^2+c^2) : :
X(61921) = -33*X[2]+10*X[3], 2*X[10]+21*X[61265], 11*X[69]+12*X[55717], -X[145]+24*X[61269], -27*X[373]+4*X[13382], -X[944]+24*X[10171], 6*X[946]+17*X[30315], 11*X[1352]+12*X[55713], -X[1482]+24*X[61267], -2*X[3244]+25*X[8227], 5*X[3616]+18*X[61263], 15*X[3618]+8*X[18553] and many others

X(61921) lies on these lines: {2, 3}, {6, 43409}, {10, 61265}, {15, 42776}, {16, 42775}, {17, 42111}, {18, 42114}, {69, 55717}, {76, 60330}, {83, 60337}, {145, 61269}, {325, 32868}, {373, 13382}, {944, 10171}, {946, 30315}, {1056, 3614}, {1058, 7173}, {1352, 55713}, {1482, 61267}, {2548, 34571}, {3068, 43412}, {3069, 43411}, {3244, 8227}, {3311, 43377}, {3312, 43376}, {3316, 42561}, {3317, 31412}, {3411, 42612}, {3412, 42613}, {3590, 60621}, {3591, 60620}, {3616, 61263}, {3618, 18553}, {3619, 55586}, {3622, 61259}, {3626, 5603}, {3631, 14853}, {3632, 5818}, {3636, 5587}, {3818, 55700}, {5339, 43873}, {5340, 43874}, {5343, 23302}, {5344, 23303}, {5349, 43029}, {5350, 43028}, {5365, 42107}, {5366, 42110}, {5485, 60332}, {5550, 38140}, {5817, 60980}, {5882, 7989}, {5886, 20057}, {6200, 43505}, {6241, 6688}, {6329, 10516}, {6361, 10172}, {6396, 43506}, {6435, 7582}, {6436, 7581}, {6455, 43508}, {6456, 43507}, {6486, 43513}, {6487, 43514}, {6494, 13785}, {6495, 13665}, {6498, 7584}, {6499, 7583}, {6564, 10194}, {6565, 10195}, {6704, 60132}, {7603, 14482}, {7607, 18843}, {7608, 60219}, {7612, 53102}, {7741, 8164}, {7755, 14075}, {7768, 53127}, {7781, 53144}, {7860, 34229}, {7951, 47743}, {7967, 61261}, {7982, 38098}, {8718, 22112}, {8797, 44134}, {9624, 38074}, {10159, 52519}, {10175, 11522}, {10576, 23273}, {10577, 23267}, {10595, 20050}, {10619, 18918}, {10653, 42978}, {10654, 42979}, {11002, 18874}, {11008, 34507}, {11412, 27355}, {11444, 14845}, {11465, 15030}, {11695, 61136}, {12248, 38319}, {12317, 23515}, {12818, 43565}, {12819, 43564}, {12834, 15083}, {13431, 61715}, {13886, 42262}, {13939, 42265}, {14226, 42602}, {14241, 42603}, {14494, 43676}, {14561, 55714}, {14639, 35022}, {14912, 25555}, {15081, 16534}, {16808, 43464}, {16809, 43463}, {16964, 42947}, {16965, 42946}, {16966, 41973}, {16967, 41974}, {18581, 42780}, {18582, 42779}, {18840, 60142}, {18841, 53100}, {18842, 60334}, {19130, 55581}, {19876, 50809}, {20190, 50956}, {22235, 42146}, {22236, 43423}, {22237, 42143}, {22238, 43422}, {23249, 41964}, {23253, 32790}, {23259, 41963}, {23263, 32789}, {23269, 32786}, {23275, 32785}, {24206, 55723}, {28174, 46931}, {31670, 55599}, {32006, 52718}, {32601, 43608}, {32821, 52713}, {32822, 34803}, {32825, 59635}, {33416, 43195}, {33417, 43196}, {33750, 51127}, {35019, 36765}, {35023, 59391}, {37624, 61260}, {37640, 42581}, {37641, 42580}, {37714, 50818}, {38034, 46933}, {38108, 60983}, {38314, 61258}, {38317, 39874}, {40330, 40341}, {40693, 43543}, {40694, 43542}, {41112, 42994}, {41113, 42995}, {42089, 42629}, {42092, 42630}, {42093, 42949}, {42094, 42948}, {42095, 42999}, {42098, 42998}, {42101, 42773}, {42102, 42774}, {42103, 42908}, {42106, 42909}, {42117, 43479}, {42118, 43480}, {42119, 42936}, {42120, 42937}, {42125, 42806}, {42128, 42805}, {42133, 42945}, {42134, 42944}, {42139, 42152}, {42142, 42149}, {42150, 42918}, {42151, 42919}, {42157, 42927}, {42158, 42926}, {42164, 42610}, {42165, 42611}, {42431, 42797}, {42432, 42798}, {42474, 42598}, {42475, 42599}, {42786, 55609}, {42813, 43481}, {42814, 43482}, {42894, 43018}, {42895, 43019}, {42910, 43418}, {42911, 43419}, {42950, 43557}, {42951, 43556}, {42990, 49861}, {42991, 49862}, {43174, 54447}, {43374, 43512}, {43375, 43511}, {43493, 43541}, {43494, 43540}, {43509, 43523}, {43510, 43524}, {43527, 54845}, {47745, 61271}, {48901, 55621}, {50990, 55718}, {51072, 58240}, {51177, 55684}, {51212, 55589}, {51538, 55613}, {53098, 53105}, {53099, 60636}, {53109, 60123}, {54720, 60144}, {59386, 60942}, {60127, 60642}, {60322, 60647}

X(61921) = inverse of X(10299) in orthocentroidal circle
X(61921) = inverse of X(10299) in Yff hyperbola
X(61921) = complement of X(61788)
X(61921) = anticomplement of X(61850)
X(61921) = pole of line {523, 10299} with respect to the orthocentroidal circle
X(61921) = pole of line {185, 62171} with respect to the Jerabek hyperbola
X(61921) = pole of line {6, 10299} with respect to the Kiepert hyperbola
X(61921) = pole of line {523, 10299} with respect to the Yff hyperbola
X(61921) = pole of line {69, 14869} with respect to the Wallace hyperbola
X(61921) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(25), X(60330)}}, {{A, B, C, X(68), X(55857)}}, {{A, B, C, X(69), X(14869)}}, {{A, B, C, X(140), X(18854)}}, {{A, B, C, X(264), X(10299)}}, {{A, B, C, X(382), X(8797)}}, {{A, B, C, X(427), X(60337)}}, {{A, B, C, X(428), X(52519)}}, {{A, B, C, X(631), X(57823)}}, {{A, B, C, X(1657), X(18852)}}, {{A, B, C, X(1907), X(16837)}}, {{A, B, C, X(3519), X(15694)}}, {{A, B, C, X(3522), X(18853)}}, {{A, B, C, X(3534), X(54763)}}, {{A, B, C, X(3544), X(40410)}}, {{A, B, C, X(4232), X(60332)}}, {{A, B, C, X(5064), X(54845)}}, {{A, B, C, X(5066), X(54660)}}, {{A, B, C, X(5198), X(14487)}}, {{A, B, C, X(6662), X(14891)}}, {{A, B, C, X(6995), X(60142)}}, {{A, B, C, X(7378), X(53100)}}, {{A, B, C, X(10303), X(60171)}}, {{A, B, C, X(10304), X(13599)}}, {{A, B, C, X(11403), X(46851)}}, {{A, B, C, X(12812), X(15077)}}, {{A, B, C, X(15640), X(60121)}}, {{A, B, C, X(15683), X(31363)}}, {{A, B, C, X(15707), X(36889)}}, {{A, B, C, X(15740), X(44245)}}, {{A, B, C, X(18843), X(52282)}}, {{A, B, C, X(18847), X(50690)}}, {{A, B, C, X(18851), X(49135)}}, {{A, B, C, X(33699), X(54838)}}, {{A, B, C, X(37174), X(53102)}}, {{A, B, C, X(37453), X(53098)}}, {{A, B, C, X(43570), X(55569)}}, {{A, B, C, X(43571), X(55573)}}, {{A, B, C, X(51348), X(58195)}}, {{A, B, C, X(52281), X(60219)}}, {{A, B, C, X(52284), X(60334)}}
X(61921) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14269, 15715}, {2, 15688, 15702}, {2, 15715, 15709}, {2, 20, 14869}, {2, 3091, 382}, {2, 3529, 631}, {2, 3530, 3525}, {2, 3543, 15707}, {2, 3544, 3855}, {2, 3855, 3529}, {2, 4, 10299}, {2, 443, 11354}, {2, 5, 3544}, {2, 546, 3528}, {4, 1656, 3533}, {4, 3524, 1657}, {4, 3525, 3522}, {4, 3544, 3851}, {4, 5067, 140}, {5, 10109, 3}, {5, 15022, 5071}, {5, 1656, 5068}, {5, 547, 5072}, {5, 632, 14892}, {5, 6975, 6873}, {17, 42111, 42495}, {18, 42114, 42494}, {140, 17504, 15720}, {140, 3091, 4}, {376, 15708, 15698}, {376, 15709, 15693}, {382, 11737, 3091}, {382, 5079, 5055}, {382, 550, 5059}, {631, 3529, 15710}, {1012, 11541, 12102}, {1656, 3850, 3523}, {1656, 3851, 550}, {2045, 2046, 7486}, {3090, 3533, 1656}, {3091, 15640, 3832}, {3091, 15717, 3845}, {3091, 5055, 5067}, {3523, 5068, 3850}, {3525, 12812, 3090}, {3526, 12811, 3839}, {3526, 17538, 15719}, {3526, 3839, 17538}, {3544, 3855, 3545}, {3545, 15698, 381}, {3830, 6863, 3534}, {3843, 10303, 11001}, {3843, 15699, 10303}, {3845, 15717, 11541}, {3851, 15720, 546}, {3857, 5054, 17578}, {5055, 15693, 547}, {5066, 10303, 6831}, {5066, 5070, 3146}, {5067, 6956, 15701}, {6963, 15682, 16434}, {11541, 15717, 376}, {12102, 15693, 20}, {14782, 14783, 3853}, {14813, 14814, 15694}, {15640, 15723, 3524}, {15679, 17582, 5056}, {15690, 15723, 15708}, {15699, 15700, 2}, {42107, 43238, 5365}, {42110, 43239, 5366}, {42143, 42988, 22237}, {42146, 42989, 22235}, {43409, 43410, 6}

X(61922) = X(2)X(3)∩X(371)X(43381)

Barycentrics    2*a^4+23*(b^2-c^2)^2-25*a^2*(b^2+c^2) : :
X(61922) = -23*X[2]+7*X[3], X[551]+3*X[61262], -X[3241]+9*X[61270], X[3625]+7*X[51709], X[3630]+7*X[5476], -X[3633]+49*X[61268], X[3655]+15*X[61264], X[3679]+15*X[61266], -5*X[5901]+X[51087], 7*X[7989]+X[50824], 15*X[9166]+X[14692], -5*X[9956]+X[50827] and many others

X(61922) lies on these lines: {2, 3}, {371, 43381}, {372, 43380}, {551, 61262}, {3241, 61270}, {3564, 25565}, {3625, 51709}, {3630, 5476}, {3633, 61268}, {3655, 61264}, {3679, 61266}, {3828, 28212}, {5318, 43484}, {5321, 43483}, {5844, 61267}, {5901, 51087}, {7581, 60299}, {7582, 60300}, {7989, 50824}, {9166, 14692}, {9956, 50827}, {10171, 28224}, {10172, 28216}, {11542, 43005}, {11543, 43004}, {11669, 60630}, {13607, 61259}, {13846, 43343}, {13847, 43342}, {13925, 43568}, {13993, 43569}, {14128, 58470}, {16267, 33606}, {16268, 33607}, {18493, 38081}, {18581, 43649}, {18582, 43644}, {18583, 51140}, {23251, 43559}, {23261, 43558}, {24206, 50982}, {32455, 43150}, {34599, 44028}, {34627, 61260}, {34748, 61273}, {36967, 43467}, {36968, 43468}, {36969, 42686}, {36970, 42687}, {38022, 61261}, {38042, 61265}, {41943, 43417}, {41944, 43416}, {42111, 42474}, {42114, 42475}, {42143, 42496}, {42146, 42497}, {42153, 43208}, {42156, 43207}, {42163, 42435}, {42166, 42436}, {42270, 43211}, {42273, 43212}, {42590, 42964}, {42591, 42965}, {42692, 43301}, {42693, 43300}, {42795, 42940}, {42796, 42941}, {42801, 43026}, {42802, 43027}, {42898, 49907}, {42899, 49908}, {42904, 42957}, {42905, 42956}, {42912, 42915}, {42913, 42914}, {42942, 42955}, {42943, 42954}, {42948, 46334}, {42949, 46335}, {43258, 43526}, {43259, 43525}, {43401, 43471}, {43402, 43472}, {43511, 60309}, {43512, 60310}, {46267, 51138}, {47354, 51732}, {48661, 50826}, {48662, 51181}, {48874, 50964}, {48898, 51133}, {50796, 51700}, {50801, 61281}, {50830, 61510}, {50960, 58445}, {50985, 61545}, {51029, 55648}, {51103, 61255}, {51182, 61624}, {54852, 60100}, {60175, 60649}, {60192, 60250}, {60239, 60323}

X(61922) = midpoint of X(i) and X(j) for these {i,j}: {2, 3850}, {4, 15759}, {5, 10109}, {140, 3860}, {381, 10124}, {546, 11812}, {547, 11737}, {3530, 3845}, {3628, 5066}, {3856, 11540}, {3861, 12100}, {8703, 12102}, {14128, 58470}, {14891, 14893}, {47354, 51732}, {50796, 51700}, {50801, 61281}, {50960, 58445}, {51103, 61255}
X(61922) = reflection of X(i) in X(j) for these {i,j}: {11540, 3628}, {12108, 2}, {3856, 5066}
X(61922) = inverse of X(15706) in orthocentroidal circle
X(61922) = inverse of X(15706) in Yff hyperbola
X(61922) = complement of X(14891)
X(61922) = pole of line {523, 15706} with respect to the orthocentroidal circle
X(61922) = pole of line {6, 15706} with respect to the Kiepert hyperbola
X(61922) = pole of line {523, 15706} with respect to the Yff hyperbola
X(61922) = intersection, other than A, B, C, of circumconics {{A, B, C, X(264), X(15706)}}, {{A, B, C, X(1494), X(12108)}}, {{A, B, C, X(14892), X(40410)}}, {{A, B, C, X(14938), X(41989)}}, {{A, B, C, X(15686), X(55958)}}, {{A, B, C, X(31846), X(55858)}}, {{A, B, C, X(41983), X(57896)}}, {{A, B, C, X(52285), X(54852)}}
X(61922) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14893, 14891}, {2, 17538, 5054}, {2, 30, 12108}, {2, 3545, 3843}, {2, 381, 15686}, {2, 4, 15706}, {2, 5, 14892}, {5, 5056, 546}, {5, 547, 11737}, {20, 16351, 631}, {30, 3628, 11540}, {30, 5066, 3856}, {140, 15707, 11812}, {140, 3545, 3860}, {140, 3860, 30}, {140, 547, 15703}, {140, 7486, 3628}, {376, 5071, 5056}, {381, 15686, 14893}, {381, 15703, 15692}, {381, 547, 10124}, {547, 5071, 10109}, {548, 14893, 15684}, {548, 15706, 15759}, {549, 15714, 15717}, {632, 3839, 15690}, {3090, 15716, 15699}, {3091, 11539, 12101}, {3526, 3534, 15707}, {3534, 3545, 3857}, {3534, 5055, 7486}, {3534, 5079, 5055}, {3545, 15703, 15687}, {3545, 3857, 5066}, {3545, 7486, 3534}, {3628, 12102, 10303}, {3628, 3850, 548}, {3845, 15694, 15691}, {5056, 17578, 3090}, {5066, 14892, 5072}, {5066, 15709, 3861}, {5067, 14269, 15713}, {10109, 11737, 547}, {10124, 11737, 381}, {10304, 15694, 549}, {11540, 12108, 14890}, {11737, 14891, 3850}, {12812, 14892, 2}, {14269, 15713, 12103}, {15687, 15703, 140}, {15691, 15694, 3530}, {15704, 15709, 12100}, {42143, 43104, 42496}, {42146, 43101, 42497}

X(61923) = X(2)X(3)∩X(6)X(43205)

Barycentrics    a^4+12*(b^2-c^2)^2-13*a^2*(b^2+c^2) : :
X(61923) = -36*X[2]+11*X[3], X[8]+24*X[61267], 3*X[399]+22*X[15025], 9*X[568]+16*X[40247], 7*X[3622]+18*X[61260], -6*X[3763]+X[55595], -8*X[4701]+33*X[5790], 21*X[5587]+4*X[32900], -24*X[5882]+49*X[58235], 24*X[6688]+X[18439], 16*X[7687]+9*X[38638], -27*X[7988]+2*X[10222] and many others

X(61923) lies on these lines: {2, 3}, {6, 43205}, {8, 61267}, {13, 43429}, {14, 43428}, {17, 42474}, {18, 42475}, {371, 43881}, {372, 43882}, {399, 15025}, {519, 58236}, {568, 40247}, {3614, 7373}, {3622, 61260}, {3763, 55595}, {4701, 5790}, {5587, 32900}, {5882, 58235}, {5965, 11482}, {6199, 42582}, {6395, 42583}, {6417, 42274}, {6418, 42277}, {6427, 42262}, {6428, 42265}, {6445, 42268}, {6446, 42269}, {6447, 6565}, {6448, 6564}, {6500, 18762}, {6501, 18538}, {6519, 8253}, {6522, 8252}, {6688, 18439}, {6767, 7173}, {7687, 38638}, {7902, 51588}, {7988, 10222}, {7989, 15178}, {8148, 10175}, {8797, 40996}, {8976, 53516}, {9624, 34748}, {9691, 23259}, {9956, 61265}, {10171, 18525}, {10172, 48661}, {10247, 61268}, {10516, 53092}, {11017, 15045}, {11178, 53858}, {11362, 58249}, {11465, 45958}, {12046, 15043}, {12308, 23515}, {12645, 61269}, {12818, 43514}, {12819, 43513}, {13321, 14128}, {13951, 53513}, {14094, 15046}, {14644, 15039}, {14852, 45184}, {15012, 18435}, {15029, 20304}, {15069, 25565}, {15092, 23235}, {16241, 42980}, {16242, 42981}, {16960, 42095}, {16961, 42098}, {16982, 54048}, {18492, 31666}, {18493, 28234}, {18526, 61262}, {18584, 30435}, {19130, 55580}, {19925, 58230}, {20397, 38789}, {20398, 38743}, {20399, 38732}, {20400, 51517}, {21358, 55583}, {22235, 42497}, {22236, 42915}, {22237, 42496}, {22238, 42914}, {22246, 31404}, {22253, 50570}, {22330, 50955}, {22332, 39565}, {23039, 27355}, {24206, 55724}, {25561, 55708}, {28164, 58224}, {28208, 58229}, {28224, 58233}, {28236, 37624}, {30315, 38066}, {30389, 38140}, {31415, 43136}, {32767, 58795}, {34573, 55616}, {36836, 42592}, {36843, 42593}, {36969, 42611}, {36970, 42610}, {38072, 55721}, {38084, 38631}, {38112, 58247}, {38317, 48662}, {38319, 38756}, {38633, 46686}, {39601, 53096}, {40693, 42778}, {40694, 42777}, {42089, 42683}, {42092, 42682}, {42107, 42970}, {42110, 42971}, {42111, 42598}, {42114, 42599}, {42115, 43371}, {42116, 43370}, {42129, 42166}, {42132, 42163}, {42139, 42950}, {42142, 42951}, {42519, 61719}, {42786, 55610}, {42984, 43238}, {42985, 43239}, {42986, 43649}, {42987, 43644}, {42988, 43104}, {42989, 43101}, {43199, 43547}, {43200, 43546}, {47353, 55704}, {51024, 55617}, {53023, 55602}, {58238, 61510}

X(61923) = inverse of X(44682) in orthocentroidal circle
X(61923) = inverse of X(44682) in Yff hyperbola
X(61923) = complement of X(61787)
X(61923) = pole of line {523, 44682} with respect to the orthocentroidal circle
X(61923) = pole of line {6, 44682} with respect to the Kiepert hyperbola
X(61923) = pole of line {523, 44682} with respect to the Yff hyperbola
X(61923) = intersection, other than A, B, C, of circumconics {{A, B, C, X(264), X(44682)}}, {{A, B, C, X(13599), X(46853)}}, {{A, B, C, X(17578), X(46455)}}, {{A, B, C, X(18550), X(50690)}}, {{A, B, C, X(32533), X(41106)}}
X(61923) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15691, 5054}, {2, 3858, 15696}, {3, 15684, 12103}, {3, 3091, 3843}, {3, 3525, 15701}, {3, 3627, 15681}, {5, 10109, 4}, {5, 15022, 5079}, {5, 3090, 5072}, {5, 3628, 3544}, {5, 5055, 3851}, {5, 547, 5068}, {140, 17578, 14093}, {381, 11001, 14269}, {381, 15707, 3830}, {381, 1656, 631}, {546, 632, 17538}, {547, 3857, 3525}, {631, 10304, 15712}, {631, 3522, 12100}, {631, 3843, 17800}, {631, 5071, 5056}, {632, 3858, 15704}, {1656, 15694, 5070}, {1656, 15696, 2}, {1656, 3843, 15694}, {1656, 5072, 5076}, {1656, 5076, 632}, {1656, 5079, 12812}, {3090, 3146, 3628}, {3090, 3544, 3146}, {3091, 12812, 1656}, {3091, 15022, 5071}, {3091, 17538, 546}, {3146, 17697, 10303}, {3146, 5056, 3090}, {3522, 3545, 3859}, {3525, 3857, 382}, {3525, 5068, 3857}, {3533, 3861, 15688}, {3544, 3628, 381}, {3628, 12811, 3853}, {3628, 3857, 10304}, {3832, 15699, 15720}, {3832, 15720, 15684}, {3855, 15703, 6865}, {3858, 12811, 3091}, {5055, 15701, 547}, {5066, 5067, 1657}, {10109, 15703, 5055}, {11539, 12100, 15721}, {11539, 15689, 15707}, {12103, 15720, 3}, {14093, 15693, 15705}, {15689, 15694, 15693}, {43205, 43206, 6}

X(61924) = X(1)X(50801)∩X(2)X(3)

Barycentrics    a^4+13*(b^2-c^2)^2-14*a^2*(b^2+c^2) : :
X(61924) = 5*X[1]+4*X[50801], -13*X[2]+4*X[3], 5*X[6]+4*X[50958], 5*X[8]+4*X[51077], 8*X[10]+X[50872], 5*X[69]+4*X[51132], 8*X[141]+X[51028], 5*X[145]+4*X[50804], X[146]+8*X[45311], X[147]+8*X[5461], X[153]+8*X[45310], X[193]+8*X[11178] and many others

X(61924) lies on these lines: {1, 50801}, {2, 3}, {6, 50958}, {8, 51077}, {10, 50872}, {15, 43541}, {16, 43540}, {17, 41120}, {18, 41119}, {61, 49873}, {62, 49874}, {69, 51132}, {76, 54522}, {98, 60648}, {141, 51028}, {145, 50804}, {146, 45311}, {147, 5461}, {153, 45310}, {193, 11178}, {233, 36430}, {253, 55958}, {262, 60628}, {325, 32874}, {395, 42475}, {396, 42474}, {397, 49861}, {398, 49862}, {485, 60623}, {486, 60622}, {519, 7988}, {542, 33748}, {551, 7989}, {597, 5921}, {962, 3828}, {1125, 50864}, {1131, 10577}, {1132, 10576}, {1327, 6479}, {1328, 6478}, {1352, 25565}, {1587, 42603}, {1588, 42602}, {1698, 34632}, {2996, 54645}, {3019, 37681}, {3068, 6441}, {3069, 6442}, {3098, 50964}, {3241, 8227}, {3311, 14226}, {3312, 14241}, {3424, 60238}, {3579, 50807}, {3582, 10590}, {3584, 10591}, {3589, 51023}, {3590, 6419}, {3591, 6420}, {3614, 14986}, {3616, 50796}, {3617, 3656}, {3618, 47354}, {3619, 54131}, {3620, 20423}, {3622, 34627}, {3623, 50798}, {3624, 34648}, {3631, 51214}, {3634, 50865}, {3636, 50871}, {3653, 38140}, {3655, 46934}, {3739, 51064}, {3763, 50959}, {3785, 48913}, {3817, 19875}, {4654, 5704}, {4669, 5734}, {4678, 18493}, {4687, 51041}, {4698, 51065}, {4699, 51038}, {4704, 51040}, {4745, 11522}, {4821, 51039}, {4870, 54361}, {5032, 14561}, {5219, 15933}, {5261, 10072}, {5274, 10056}, {5286, 18362}, {5304, 31415}, {5309, 31404}, {5334, 16962}, {5335, 16963}, {5343, 42488}, {5344, 42489}, {5349, 42610}, {5350, 42611}, {5355, 37665}, {5395, 10356}, {5400, 48855}, {5476, 11160}, {5480, 54174}, {5550, 50811}, {5587, 38314}, {5603, 38176}, {5655, 15088}, {5657, 38083}, {5731, 19883}, {5790, 61267}, {5817, 59375}, {5818, 31145}, {5886, 38074}, {5984, 22566}, {6053, 9140}, {6329, 51027}, {6361, 46930}, {6417, 42639}, {6418, 42640}, {6431, 42573}, {6432, 42572}, {6433, 42642}, {6434, 42641}, {6439, 8253}, {6440, 8252}, {6445, 43517}, {6446, 43518}, {6449, 43520}, {6450, 43519}, {6468, 43790}, {6469, 43789}, {6476, 9542}, {6477, 23249}, {6484, 43558}, {6485, 43559}, {6486, 12819}, {6487, 12818}, {6688, 15305}, {6776, 25561}, {7585, 42274}, {7586, 42277}, {7603, 7739}, {7615, 11148}, {7735, 18584}, {7752, 46951}, {7773, 32870}, {7788, 32893}, {7809, 15589}, {7811, 32838}, {7917, 32828}, {7967, 38022}, {8176, 9740}, {8724, 15092}, {9166, 36519}, {9541, 43254}, {9778, 38068}, {9779, 28194}, {9780, 31162}, {9812, 10172}, {9955, 46933}, {10168, 50956}, {10171, 25055}, {10175, 38021}, {10219, 32062}, {10516, 59373}, {10588, 11238}, {10589, 11237}, {10595, 20049}, {10601, 15052}, {10653, 42914}, {10654, 42915}, {10723, 22247}, {11002, 14845}, {11177, 14061}, {11180, 51171}, {11444, 21849}, {11451, 16226}, {11477, 50994}, {11542, 43543}, {11543, 43542}, {11668, 13449}, {11693, 12900}, {12046, 37481}, {12243, 61575}, {12699, 46931}, {12816, 42937}, {12817, 42936}, {13846, 42522}, {13847, 31412}, {14484, 60277}, {14494, 60635}, {14639, 52695}, {14831, 15056}, {14912, 38079}, {14930, 43291}, {15031, 32839}, {16241, 42133}, {16242, 42134}, {16267, 18581}, {16268, 18582}, {16644, 42139}, {16645, 42142}, {16772, 42776}, {16773, 42775}, {16808, 43242}, {16809, 43243}, {16964, 43479}, {16965, 43480}, {16966, 42972}, {16967, 42973}, {18357, 50818}, {18358, 50974}, {18842, 54921}, {19053, 42265}, {19054, 42262}, {19130, 50967}, {19862, 34628}, {19872, 50829}, {19878, 50862}, {20052, 50805}, {20080, 51174}, {20112, 53141}, {20415, 36344}, {20416, 36319}, {20582, 51212}, {21168, 38082}, {21356, 38072}, {22235, 54594}, {22237, 54593}, {23234, 23514}, {23253, 53131}, {23263, 53130}, {23269, 52048}, {23275, 52047}, {24206, 54132}, {24898, 56402}, {25406, 48310}, {28204, 54448}, {30315, 51069}, {31253, 34638}, {31276, 44422}, {32006, 32897}, {32819, 32871}, {32822, 32873}, {32823, 32872}, {32869, 59635}, {34573, 51024}, {34773, 50800}, {34803, 59634}, {35820, 43566}, {35821, 43567}, {36765, 59378}, {36836, 42589}, {36843, 42588}, {36889, 45198}, {36991, 60999}, {37640, 42095}, {37641, 42098}, {37714, 51103}, {37832, 42111}, {37835, 42114}, {38024, 38158}, {38034, 38066}, {38037, 38092}, {38065, 38139}, {38073, 38108}, {38075, 59374}, {38150, 61023}, {39492, 44010}, {39601, 43448}, {40693, 49908}, {40694, 49907}, {41100, 42921}, {41101, 42920}, {41112, 43775}, {41113, 43776}, {41121, 42580}, {41122, 42581}, {41869, 51074}, {41895, 53108}, {41943, 42159}, {41944, 42162}, {42089, 43364}, {42092, 43365}, {42103, 43869}, {42106, 43870}, {42119, 43421}, {42120, 43420}, {42135, 43482}, {42136, 43553}, {42137, 43552}, {42138, 43481}, {42149, 43016}, {42152, 43017}, {42154, 43107}, {42155, 43100}, {42163, 49905}, {42166, 49906}, {42268, 43257}, {42269, 43256}, {42472, 43771}, {42473, 43772}, {42494, 42599}, {42495, 42598}, {42791, 43770}, {42792, 43769}, {42918, 43466}, {42919, 43465}, {42930, 43331}, {42931, 43330}, {42932, 42942}, {42933, 42943}, {42954, 43646}, {42955, 43645}, {42974, 43328}, {42975, 43329}, {42992, 49904}, {42993, 49903}, {43008, 49825}, {43009, 49824}, {43150, 51178}, {43228, 43774}, {43229, 43773}, {43255, 43315}, {43440, 54581}, {43441, 54580}, {43469, 43478}, {43470, 43477}, {43473, 52080}, {43474, 52079}, {43483, 44016}, {43484, 44015}, {43537, 60283}, {43621, 50969}, {46932, 50821}, {48906, 50957}, {48910, 51129}, {50955, 51170}, {50960, 51126}, {51022, 51127}, {51029, 51131}, {51128, 51213}, {51176, 55705}, {51537, 51737}, {53099, 60216}, {54519, 60644}, {54520, 56059}, {54521, 60210}, {54639, 60335}, {54734, 60285}, {54851, 60647}, {54920, 60200}, {59388, 61269}, {60118, 60641}, {60333, 60626}, {61307, 61340}

X(61924) = midpoint of X(i) and X(j) for these {i,j}: {4, 15710}, {3839, 15708}, {14269, 15706}
X(61924) = reflection of X(i) in X(j) for these {i,j}: {10304, 15708}, {15705, 15709}, {15706, 11539}, {15708, 2}, {15710, 5054}, {376, 15706}
X(61924) = inverse of X(15692) in orthocentroidal circle
X(61924) = inverse of X(15692) in Yff hyperbola
X(61924) = complement of X(15705)
X(61924) = anticomplement of X(15709)
X(61924) = pole of line {523, 15692} with respect to the orthocentroidal circle
X(61924) = pole of line {6, 9542} with respect to the Kiepert hyperbola
X(61924) = pole of line {523, 15692} with respect to the Yff hyperbola
X(61924) = pole of line {69, 15721} with respect to the Wallace hyperbola
X(61924) = intersection, other than A, B, C, of circumconics {{A, B, C, X(20), X(55958)}}, {{A, B, C, X(25), X(54522)}}, {{A, B, C, X(68), X(48154)}}, {{A, B, C, X(69), X(15721)}}, {{A, B, C, X(253), X(549)}}, {{A, B, C, X(264), X(15692)}}, {{A, B, C, X(297), X(60648)}}, {{A, B, C, X(458), X(60628)}}, {{A, B, C, X(1217), X(12103)}}, {{A, B, C, X(1494), X(15708)}}, {{A, B, C, X(1657), X(31363)}}, {{A, B, C, X(3523), X(36889)}}, {{A, B, C, X(3525), X(15319)}}, {{A, B, C, X(3543), X(8797)}}, {{A, B, C, X(4846), X(19710)}}, {{A, B, C, X(5070), X(18855)}}, {{A, B, C, X(6353), X(54645)}}, {{A, B, C, X(7714), X(54734)}}, {{A, B, C, X(8889), X(54644)}}, {{A, B, C, X(10303), X(57822)}}, {{A, B, C, X(13599), X(21735)}}, {{A, B, C, X(17538), X(54763)}}, {{A, B, C, X(31361), X(49136)}}, {{A, B, C, X(31846), X(55859)}}, {{A, B, C, X(33703), X(60121)}}, {{A, B, C, X(52283), X(60238)}}, {{A, B, C, X(52284), X(54921)}}, {{A, B, C, X(52288), X(60277)}}, {{A, B, C, X(52290), X(53108)}}
X(61924) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15022, 5071}, {2, 15683, 631}, {2, 15705, 15709}, {2, 3091, 3543}, {2, 3146, 549}, {2, 3522, 15702}, {2, 3543, 3523}, {2, 3545, 3839}, {2, 381, 20}, {2, 3839, 10304}, {2, 3854, 15683}, {2, 4, 15692}, {2, 5071, 5056}, {2, 6175, 17580}, {3, 381, 12101}, {3, 3859, 4}, {4, 15719, 15681}, {4, 3090, 5070}, {4, 631, 12103}, {5, 12812, 3851}, {5, 15699, 14892}, {5, 1656, 3544}, {20, 5056, 3090}, {30, 11539, 15706}, {30, 15709, 15705}, {30, 5054, 15710}, {140, 381, 15682}, {376, 3544, 5066}, {381, 14892, 3545}, {381, 15685, 3861}, {381, 15703, 14891}, {381, 1656, 15701}, {381, 5073, 3845}, {382, 10124, 15698}, {546, 15022, 13727}, {546, 15694, 11001}, {547, 3859, 11540}, {547, 3860, 632}, {547, 5066, 3530}, {549, 3861, 15685}, {632, 15681, 15719}, {1656, 14269, 11539}, {1656, 3544, 3832}, {1656, 3832, 10303}, {1657, 15713, 15715}, {1698, 50802, 34632}, {3090, 11541, 3628}, {3090, 3544, 3627}, {3090, 5071, 10109}, {3091, 5056, 7486}, {3523, 3543, 15697}, {3524, 15682, 15689}, {3524, 15699, 2}, {3525, 3850, 17578}, {3530, 11539, 5054}, {3545, 14892, 5068}, {3545, 15688, 3854}, {3628, 3855, 3522}, {3763, 50959, 54170}, {3828, 30308, 962}, {3830, 15691, 11541}, {3845, 14891, 5073}, {3850, 15694, 6848}, {3851, 12812, 5067}, {3851, 5067, 3146}, {3855, 15702, 3830}, {3858, 11812, 15684}, {4189, 17531, 17545}, {5055, 14269, 1656}, {5066, 11539, 14269}, {7809, 32885, 15589}, {7809, 53127, 32885}, {10109, 12811, 547}, {10109, 14892, 15699}, {10109, 15699, 5055}, {10171, 61264, 59387}, {10303, 15701, 15721}, {10304, 15721, 3524}, {11001, 15694, 15717}, {11539, 14269, 376}, {11540, 11737, 3859}, {11540, 12101, 8703}, {11540, 15702, 4189}, {11737, 15640, 3091}, {11812, 15684, 3528}, {13587, 16371, 11108}, {14269, 15706, 30}, {14782, 14783, 5076}, {14892, 15699, 381}, {14893, 15693, 3529}, {15683, 16401, 15694}, {15696, 16402, 15708}, {15765, 18585, 17800}, {19862, 50803, 34628}, {25055, 61264, 38076}, {31253, 51076, 34638}, {37832, 42111, 43404}, {37835, 42114, 43403}, {41943, 42159, 49876}, {41944, 42162, 49875}, {42095, 43104, 37640}, {42098, 43101, 37641}

X(61925) = X(2)X(3)∩X(13)X(42475)

Barycentrics    a^4+16*(b^2-c^2)^2-17*a^2*(b^2+c^2) : :
X(61925) = -16*X[2]+5*X[3], 32*X[10]+X[58247], 4*X[182]+7*X[50957], 2*X[551]+9*X[61263], 4*X[1385]+7*X[50800], -X[3241]+12*X[61269], -2*X[3244]+35*X[61268], 8*X[3626]+25*X[18493], -4*X[3629]+15*X[14848], X[3632]+10*X[51709], 8*X[3636]+25*X[61261], -X[3655]+12*X[10171] and many others

X(61925) lies on these lines: {2, 3}, {10, 58247}, {13, 42475}, {14, 42474}, {182, 50957}, {551, 61263}, {590, 43792}, {615, 43791}, {1327, 6475}, {1328, 6474}, {1385, 50800}, {3241, 61269}, {3244, 61268}, {3626, 18493}, {3629, 14848}, {3632, 51709}, {3636, 61261}, {3655, 10171}, {3656, 38098}, {3679, 61265}, {5024, 39601}, {5050, 25561}, {5093, 11178}, {5309, 22246}, {5365, 42590}, {5366, 42591}, {5461, 38743}, {5476, 40341}, {5790, 34641}, {5818, 50805}, {5886, 34748}, {6500, 42262}, {6501, 42265}, {6684, 50807}, {7581, 42640}, {7582, 42639}, {7753, 18584}, {7988, 10247}, {7989, 37624}, {8148, 38021}, {8227, 50798}, {8252, 43319}, {8253, 9690}, {8972, 43798}, {9140, 15046}, {9605, 18362}, {9771, 53143}, {9955, 38066}, {10175, 34718}, {10246, 61264}, {10516, 25565}, {11017, 11465}, {11485, 43419}, {11486, 43418}, {11645, 55692}, {12046, 12111}, {12308, 15088}, {12702, 30308}, {12773, 38084}, {12818, 43255}, {12819, 43254}, {13665, 42603}, {13785, 42602}, {13941, 43797}, {14561, 20583}, {14971, 35021}, {15092, 23234}, {15808, 18525}, {16267, 42780}, {16268, 42779}, {16644, 43032}, {16645, 43033}, {17851, 41946}, {18481, 58228}, {18526, 38022}, {18581, 42782}, {18582, 42781}, {19875, 50806}, {19883, 50799}, {20057, 38074}, {21358, 50963}, {32907, 36765}, {33697, 58224}, {36519, 48657}, {37832, 43251}, {37835, 43250}, {38072, 44456}, {38073, 60983}, {38075, 60884}, {38077, 48680}, {38079, 39899}, {38140, 58230}, {38141, 38636}, {38314, 50797}, {38755, 45310}, {38789, 45311}, {40330, 50962}, {40693, 42899}, {40694, 42898}, {41100, 43546}, {41101, 43547}, {41107, 42938}, {41108, 42939}, {41119, 42599}, {41120, 42598}, {41943, 42915}, {41944, 42914}, {41945, 43790}, {41949, 41952}, {41950, 41951}, {42095, 43011}, {42096, 43293}, {42097, 43292}, {42098, 43010}, {42111, 42975}, {42114, 42974}, {42125, 42911}, {42128, 42910}, {42153, 49907}, {42156, 49908}, {42160, 43107}, {42161, 43100}, {42215, 43881}, {42216, 43882}, {42472, 43416}, {42473, 43417}, {42580, 49948}, {42581, 49947}, {42629, 43028}, {42630, 43029}, {42635, 49905}, {42636, 49906}, {42813, 42946}, {42814, 42947}, {42815, 43111}, {42816, 43110}, {42817, 43404}, {42818, 43403}, {42912, 42950}, {42913, 42951}, {43230, 43366}, {43231, 43367}, {43399, 51944}, {43400, 51945}, {44562, 48663}, {46267, 47353}, {48310, 50956}, {48873, 51129}, {48876, 51173}, {48942, 50976}, {50801, 61277}, {50954, 59373}, {50993, 55724}, {51024, 55616}, {51189, 55718}, {51515, 61267}

X(61925) = midpoint of X(i) and X(j) for these {i,j}: {2, 3855}, {381, 15723}
X(61925) = reflection of X(i) in X(j) for these {i,j}: {15716, 3525}, {15718, 15723}, {15720, 2}
X(61925) = inverse of X(17504) in orthocentroidal circle
X(61925) = inverse of X(17504) in Yff hyperbola
X(61925) = complement of X(15715)
X(61925) = pole of line {523, 17504} with respect to the orthocentroidal circle
X(61925) = pole of line {185, 58207} with respect to the Jerabek hyperbola
X(61925) = pole of line {6, 17504} with respect to the Kiepert hyperbola
X(61925) = pole of line {523, 17504} with respect to the Yff hyperbola
X(61925) = intersection, other than A, B, C, of circumconics {{A, B, C, X(264), X(17504)}}, {{A, B, C, X(1105), X(58207)}}, {{A, B, C, X(1494), X(15720)}}, {{A, B, C, X(3856), X(60122)}}, {{A, B, C, X(5054), X(57894)}}, {{A, B, C, X(15681), X(55958)}}, {{A, B, C, X(15707), X(57897)}}, {{A, B, C, X(16251), X(35414)}}, {{A, B, C, X(31846), X(55862)}}, {{A, B, C, X(49136), X(60121)}}
X(61925) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11737, 381}, {2, 15710, 140}, {2, 30, 15720}, {2, 3545, 546}, {2, 382, 15707}, {2, 3839, 3528}, {2, 3851, 14269}, {2, 3855, 30}, {2, 4, 17504}, {2, 546, 15688}, {2, 550, 5054}, {4, 10124, 14093}, {5, 12812, 5068}, {5, 5056, 5072}, {140, 6964, 3545}, {381, 11737, 3851}, {381, 14093, 4}, {381, 3543, 3843}, {381, 5054, 3543}, {381, 5055, 15703}, {546, 10299, 382}, {546, 15022, 5079}, {546, 16239, 550}, {547, 5066, 14891}, {632, 15682, 15706}, {1656, 10109, 5055}, {1656, 15688, 2}, {1656, 3525, 5070}, {1656, 3545, 3830}, {2043, 2044, 3856}, {2049, 15720, 3526}, {3090, 16239, 1656}, {3090, 3854, 16239}, {3091, 15702, 14893}, {3526, 15689, 15722}, {3526, 3845, 15689}, {3545, 15022, 10109}, {3545, 3854, 5066}, {3628, 3839, 15693}, {3830, 15701, 15690}, {3839, 15693, 5073}, {3843, 5054, 15685}, {3843, 5070, 15717}, {3860, 10304, 5076}, {5055, 15694, 547}, {5056, 15717, 3090}, {5070, 15718, 15723}, {5071, 15692, 12812}, {5072, 15720, 3855}, {7486, 12811, 1657}, {10124, 14093, 15701}, {10124, 15690, 549}, {14269, 15684, 15687}, {14269, 15722, 3529}, {14893, 15699, 15702}, {14893, 15702, 3534}, {15681, 15687, 15684}, {15681, 15694, 15700}, {15684, 15694, 3}, {15684, 15703, 15694}, {15687, 15700, 15681}, {15688, 15720, 15716}, {15694, 15718, 15721}, {15715, 15720, 15718}, {15765, 18585, 5059}, {21358, 50963, 55584}, {30308, 38083, 12702}, {38314, 61259, 50797}, {42114, 43101, 42974}

X(61926) = X(2)X(3)∩X(13)X(49861)

Barycentrics    a^4+19*(b^2-c^2)^2-20*a^2*(b^2+c^2) : :
X(61926) = -19*X[2]+6*X[3], X[153]+12*X[38084], 3*X[165]+10*X[51074], X[944]+12*X[38076], X[962]+12*X[38083], 5*X[1992]+8*X[43150], -X[3241]+14*X[61268], 5*X[3618]+8*X[25561], 6*X[3656]+7*X[51068], 12*X[3817]+X[50810], 4*X[4669]+9*X[5603], -2*X[4677]+15*X[5818] and many others

X(61926) lies on these lines: {2, 3}, {13, 49861}, {14, 49862}, {153, 38084}, {165, 51074}, {262, 60637}, {395, 49874}, {396, 49873}, {590, 43381}, {615, 43380}, {944, 38076}, {962, 38083}, {1327, 32786}, {1328, 32785}, {1992, 43150}, {3068, 14226}, {3069, 14241}, {3241, 61268}, {3316, 60314}, {3317, 60313}, {3618, 25561}, {3656, 51068}, {3817, 50810}, {4669, 5603}, {4677, 5818}, {4745, 12245}, {5093, 51182}, {5306, 18584}, {5351, 43442}, {5352, 43443}, {5459, 36344}, {5460, 36319}, {5476, 50992}, {5480, 51186}, {5485, 60192}, {5587, 50818}, {5651, 13482}, {5657, 30308}, {5731, 50799}, {5790, 50830}, {5881, 51104}, {5886, 51087}, {5921, 38079}, {6361, 19876}, {6490, 23259}, {6491, 23249}, {6515, 44834}, {6688, 61136}, {7585, 43387}, {7586, 43386}, {7612, 60282}, {7736, 18362}, {7850, 53127}, {7884, 39143}, {7967, 61263}, {7982, 51067}, {7988, 51093}, {7989, 13607}, {8227, 38074}, {8981, 60293}, {9540, 42417}, {9624, 51107}, {9779, 50821}, {10155, 60632}, {10168, 51537}, {10171, 51085}, {10172, 50865}, {10175, 50827}, {10302, 60127}, {10516, 50974}, {10653, 33602}, {10654, 33603}, {11180, 12007}, {11230, 50864}, {11231, 50807}, {11477, 51142}, {11485, 43554}, {11486, 43555}, {11488, 41113}, {11489, 41112}, {11669, 32532}, {11693, 15044}, {12243, 36519}, {12317, 18928}, {12816, 42120}, {12817, 42119}, {13199, 38077}, {13935, 42418}, {13966, 60294}, {14458, 14762}, {14492, 60643}, {14494, 60228}, {14537, 46453}, {14561, 51140}, {14639, 36521}, {14853, 22165}, {15025, 56567}, {15092, 41135}, {15533, 40330}, {16644, 49827}, {16645, 49826}, {16772, 42509}, {16773, 42508}, {16808, 43300}, {16809, 43301}, {16966, 42511}, {16967, 42510}, {18510, 42639}, {18512, 42640}, {18581, 33606}, {18582, 33607}, {18840, 54643}, {18841, 54608}, {18842, 60175}, {19053, 42277}, {19054, 42274}, {19877, 28198}, {20423, 50994}, {23234, 36523}, {25406, 50956}, {25565, 59373}, {31173, 55726}, {31412, 35814}, {31884, 51129}, {32892, 59635}, {32900, 38314}, {33604, 42974}, {33605, 42975}, {33750, 51022}, {34089, 43512}, {34091, 43511}, {34229, 48913}, {34631, 51072}, {35255, 43383}, {35256, 43382}, {35815, 42561}, {35820, 43506}, {35821, 43505}, {35822, 43431}, {35823, 43430}, {36769, 59394}, {36969, 42954}, {36970, 42955}, {36996, 38075}, {37640, 41122}, {37641, 41121}, {37672, 54434}, {37832, 41120}, {37835, 41119}, {38028, 50800}, {38042, 50872}, {38072, 50991}, {38110, 50957}, {38136, 54174}, {38155, 51095}, {38317, 51023}, {40693, 42507}, {40694, 42506}, {41100, 42914}, {41101, 42915}, {41107, 42142}, {41108, 42139}, {41943, 42920}, {41944, 42921}, {42095, 42986}, {42098, 42987}, {42103, 46335}, {42106, 46334}, {42117, 43493}, {42118, 43494}, {42121, 43540}, {42124, 43541}, {42140, 42632}, {42141, 42631}, {42150, 43202}, {42151, 43201}, {42154, 43299}, {42155, 43298}, {42164, 42927}, {42165, 42926}, {42225, 43567}, {42226, 43566}, {42474, 49824}, {42475, 49825}, {42488, 42776}, {42489, 42775}, {42494, 42580}, {42495, 42581}, {42496, 42983}, {42497, 42982}, {42512, 43419}, {42513, 43418}, {42520, 42952}, {42521, 42953}, {42526, 43341}, {42527, 43340}, {42791, 43029}, {42792, 43028}, {42795, 43467}, {42796, 43468}, {42918, 43463}, {42919, 43464}, {43000, 43643}, {43001, 43638}, {43101, 43403}, {43104, 43404}, {43336, 43503}, {43337, 43504}, {43509, 43526}, {43510, 43525}, {43513, 43522}, {43514, 43521}, {43558, 60308}, {43559, 60307}, {47353, 51138}, {47745, 51094}, {47867, 59396}, {49859, 61719}, {50796, 51110}, {50797, 61260}, {50798, 61269}, {50801, 61275}, {50802, 54447}, {50806, 59417}, {50813, 51076}, {50824, 54448}, {50960, 51177}, {50967, 51143}, {50969, 51131}, {50982, 50993}, {51026, 55654}, {51215, 59399}, {51709, 61266}, {52710, 55958}, {53104, 60281}, {54521, 60143}, {54523, 60200}, {54616, 54866}, {54637, 60333}, {54639, 60185}, {60102, 60284}, {60150, 60239}, {60331, 60627}

X(61926) = reflection of X(i) in X(j) for these {i,j}: {376, 10299}
X(61926) = inverse of X(15698) in orthocentroidal circle
X(61926) = inverse of X(15698) in Yff hyperbola
X(61926) = complement of X(61781)
X(61926) = anticomplement of X(61847)
X(61926) = pole of line {523, 15698} with respect to the orthocentroidal circle
X(61926) = pole of line {6, 15698} with respect to the Kiepert hyperbola
X(61926) = pole of line {523, 15698} with respect to the Yff hyperbola
X(61926) = pole of line {69, 11812} with respect to the Wallace hyperbola
X(61926) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(11812)}}, {{A, B, C, X(264), X(15698)}}, {{A, B, C, X(382), X(54838)}}, {{A, B, C, X(458), X(60637)}}, {{A, B, C, X(546), X(54667)}}, {{A, B, C, X(548), X(18853)}}, {{A, B, C, X(550), X(54763)}}, {{A, B, C, X(3346), X(58193)}}, {{A, B, C, X(3543), X(46455)}}, {{A, B, C, X(3830), X(8797)}}, {{A, B, C, X(3851), X(54660)}}, {{A, B, C, X(4232), X(60192)}}, {{A, B, C, X(6995), X(54643)}}, {{A, B, C, X(7378), X(54608)}}, {{A, B, C, X(10124), X(46168)}}, {{A, B, C, X(10301), X(60127)}}, {{A, B, C, X(10303), X(18854)}}, {{A, B, C, X(11001), X(55958)}}, {{A, B, C, X(11331), X(60646)}}, {{A, B, C, X(11669), X(53857)}}, {{A, B, C, X(13623), X(15695)}}, {{A, B, C, X(15683), X(18852)}}, {{A, B, C, X(15693), X(36889)}}, {{A, B, C, X(16251), X(58205)}}, {{A, B, C, X(18847), X(33699)}}, {{A, B, C, X(18851), X(49136)}}, {{A, B, C, X(49135), X(60121)}}, {{A, B, C, X(50688), X(54585)}}, {{A, B, C, X(52284), X(60175)}}, {{A, B, C, X(52289), X(60643)}}, {{A, B, C, X(52301), X(54521)}}, {{A, B, C, X(55569), X(60313)}}, {{A, B, C, X(55573), X(60314)}}
X(61926) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15640, 549}, {2, 15682, 15719}, {2, 15693, 3525}, {2, 15697, 5054}, {2, 15698, 15709}, {2, 20, 11812}, {2, 3091, 3830}, {2, 3543, 15693}, {2, 381, 11001}, {2, 3830, 3524}, {2, 3832, 15697}, {2, 3839, 8703}, {2, 4, 15698}, {2, 5066, 4}, {4, 3525, 548}, {4, 3534, 15682}, {4, 5067, 10303}, {4, 5071, 5055}, {5, 5056, 3544}, {5, 5079, 5068}, {376, 3545, 3855}, {381, 11539, 3146}, {381, 15640, 6847}, {381, 15703, 15714}, {381, 15707, 3853}, {381, 1656, 15707}, {381, 3544, 3545}, {381, 5055, 3628}, {549, 5055, 7486}, {550, 15713, 12100}, {550, 3628, 3526}, {631, 3545, 381}, {1656, 11737, 3839}, {1656, 3839, 15702}, {1656, 3857, 15717}, {3090, 10299, 5067}, {3090, 3855, 3533}, {3146, 11539, 15715}, {3523, 17678, 14890}, {3524, 15702, 12108}, {3525, 3543, 15710}, {3526, 3830, 15759}, {3526, 5055, 547}, {3534, 12100, 10304}, {3627, 15723, 15705}, {3830, 15759, 15683}, {3830, 6908, 15681}, {3832, 15697, 12101}, {3839, 15702, 3529}, {3839, 15717, 15684}, {3839, 4234, 14891}, {3851, 15693, 3860}, {3851, 15699, 3543}, {3854, 15708, 15687}, {5055, 12811, 17678}, {5055, 15022, 5071}, {5055, 15684, 1656}, {5066, 11540, 3845}, {5070, 15687, 15708}, {10109, 15682, 3090}, {10303, 15022, 5079}, {10304, 15683, 550}, {11001, 15715, 15695}, {11539, 15715, 631}, {11812, 15703, 2}, {14782, 14783, 12102}, {15682, 15698, 3534}, {15682, 15719, 376}, {15687, 15708, 17538}, {37832, 41120, 49813}, {37835, 41119, 49812}, {42602, 43343, 35815}, {42603, 43342, 35814}, {43386, 54597, 7586}, {43387, 43536, 7585}

X(61927) = X(2)X(3)∩X(6)X(42604)

Barycentrics    a^4+25*(b^2-c^2)^2-26*a^2*(b^2+c^2) : :
X(61927) = -25*X[2]+8*X[3], 50*X[10]+X[58248], 8*X[551]+9*X[54448], 5*X[671]+12*X[38746], -100*X[1125]+49*X[58231], -X[3241]+18*X[7988], 5*X[3616]+12*X[38076], 5*X[3617]+12*X[38021], 5*X[3620]+12*X[38072], X[3621]+16*X[51709], 5*X[3623]+12*X[38074], 25*X[3679]+9*X[58241] and many others

X(61927) lies on these lines: {2, 3}, {6, 42604}, {10, 58248}, {17, 49873}, {18, 49874}, {61, 43253}, {62, 43252}, {551, 54448}, {671, 38746}, {1125, 58231}, {3068, 43890}, {3069, 43889}, {3241, 7988}, {3411, 42960}, {3412, 42961}, {3590, 53516}, {3591, 53513}, {3616, 38076}, {3617, 38021}, {3620, 38072}, {3621, 51709}, {3623, 38074}, {3679, 58241}, {3828, 9779}, {4678, 11278}, {5102, 11160}, {5304, 18584}, {5418, 43561}, {5420, 43560}, {5476, 20080}, {6054, 38735}, {6221, 42539}, {6398, 42540}, {6417, 43536}, {6418, 54597}, {6419, 60292}, {6420, 60291}, {6459, 43887}, {6460, 43888}, {6484, 43257}, {6485, 43256}, {6486, 23263}, {6487, 23253}, {7752, 32874}, {7788, 32872}, {7989, 38314}, {8976, 14226}, {9140, 38792}, {9780, 30308}, {9812, 19876}, {9956, 50872}, {10139, 43512}, {10140, 43511}, {10171, 30392}, {10513, 32893}, {10706, 38725}, {10707, 38758}, {10708, 38770}, {10709, 38782}, {10717, 38802}, {11180, 25565}, {11488, 42474}, {11489, 42475}, {11522, 51068}, {11531, 53620}, {13570, 33879}, {13951, 14241}, {14927, 50960}, {14930, 43620}, {15031, 32871}, {16200, 31145}, {16644, 42473}, {16645, 42472}, {18362, 31404}, {18583, 51215}, {19053, 41952}, {19054, 41951}, {19130, 54174}, {19875, 51120}, {19883, 50868}, {20049, 61266}, {20070, 50802}, {20582, 55591}, {21356, 55722}, {21358, 51166}, {22235, 43229}, {22237, 43228}, {23269, 43212}, {23275, 43211}, {23302, 43541}, {23303, 43540}, {24206, 51028}, {28194, 46932}, {31423, 51074}, {32838, 48913}, {32873, 59634}, {33602, 42924}, {33603, 42925}, {34627, 61263}, {34632, 54447}, {34748, 61270}, {34754, 42911}, {34755, 42910}, {36836, 43202}, {36843, 43201}, {38073, 61006}, {41107, 43023}, {41108, 43022}, {41112, 43783}, {41113, 43784}, {41119, 42580}, {41120, 42581}, {41963, 43885}, {41964, 43886}, {42085, 43553}, {42086, 43552}, {42114, 61719}, {42133, 43245}, {42134, 43244}, {42143, 43542}, {42146, 43543}, {42149, 42966}, {42152, 42967}, {42153, 42898}, {42156, 42899}, {42163, 49862}, {42166, 49861}, {42258, 43567}, {42259, 43566}, {42494, 49948}, {42495, 49947}, {42588, 43239}, {42589, 43238}, {42610, 42791}, {42611, 42792}, {42813, 43495}, {42814, 43496}, {42914, 43200}, {42915, 43199}, {42920, 49876}, {42921, 49875}, {42992, 49859}, {42993, 49860}, {43012, 49908}, {43013, 49907}, {43951, 60279}, {47354, 55711}, {48310, 51025}, {48872, 51131}, {50818, 61259}, {50959, 61044}, {51027, 59373}, {51104, 61252}, {59388, 61267}, {60118, 60286}

X(61927) = midpoint of X(i) and X(j) for these {i,j}: {2, 3854}
X(61927) = reflection of X(i) in X(j) for these {i,j}: {2, 7486}
X(61927) = inverse of X(15705) in orthocentroidal circle
X(61927) = inverse of X(15705) in Yff hyperbola
X(61927) = complement of X(61778)
X(61927) = anticomplement of X(61846)
X(61927) = pole of line {523, 15705} with respect to the orthocentroidal circle
X(61927) = pole of line {185, 58208} with respect to the Jerabek hyperbola
X(61927) = pole of line {6, 15705} with respect to the Kiepert hyperbola
X(61927) = pole of line {523, 15705} with respect to the Yff hyperbola
X(61927) = pole of line {69, 51138} with respect to the Wallace hyperbola
X(61927) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(264), X(15705)}}, {{A, B, C, X(1105), X(58208)}}, {{A, B, C, X(3861), X(54552)}}, {{A, B, C, X(5076), X(54923)}}, {{A, B, C, X(8797), X(50687)}}, {{A, B, C, X(11541), X(60121)}}, {{A, B, C, X(15683), X(55958)}}, {{A, B, C, X(15708), X(35510)}}, {{A, B, C, X(18855), X(48154)}}, {{A, B, C, X(31846), X(41992)}}, {{A, B, C, X(33699), X(46455)}}
X(61927) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15721, 17678}, {2, 17578, 3524}, {2, 3545, 3832}, {2, 381, 15683}, {2, 3839, 3522}, {2, 3854, 30}, {2, 4, 15705}, {2, 5059, 15708}, {4, 12108, 20}, {5, 15022, 5068}, {376, 11541, 15681}, {376, 3845, 3543}, {376, 5067, 15723}, {376, 5071, 5055}, {381, 15718, 15687}, {381, 1656, 15718}, {381, 547, 15702}, {382, 15693, 15689}, {547, 11539, 15703}, {547, 14893, 16239}, {547, 3850, 549}, {549, 15687, 12103}, {3090, 3522, 13735}, {3090, 3523, 17530}, {3090, 3545, 11001}, {3091, 15708, 3845}, {3091, 5056, 5067}, {3091, 5067, 5059}, {3525, 14269, 15697}, {3543, 15692, 15686}, {3543, 5056, 547}, {3544, 7486, 3854}, {3545, 11001, 3850}, {3545, 15702, 381}, {3545, 3845, 3091}, {3832, 15022, 5056}, {3845, 11812, 15685}, {3850, 11001, 3839}, {3851, 7407, 7486}, {3860, 6914, 5054}, {5055, 15685, 1656}, {5055, 5072, 15759}, {5079, 15712, 6829}, {10109, 15689, 3090}, {11111, 16401, 2}, {12108, 17504, 15693}, {15022, 15705, 10109}, {15681, 15759, 376}, {15686, 15702, 15692}, {15693, 15705, 15717}, {15705, 17678, 15721}, {42604, 42605, 6}

X(61928) = X(2)X(3)∩X(371)X(60306)

Barycentrics    a^4-29*(b^2-c^2)^2+28*a^2*(b^2+c^2) : :
X(61928) = -29*X[2]+10*X[3], -2*X[551]+21*X[61265], X[3241]+18*X[61263], 4*X[3244]+15*X[38074], 4*X[3626]+15*X[38021], 4*X[3631]+15*X[38072], 4*X[3636]+15*X[38076], -20*X[5476]+X[11008], 15*X[5603]+4*X[34641], -X[7967]+20*X[61266], 5*X[7987]+14*X[51078], -20*X[8227]+X[50818] and many others

X(61928) lies on these lines: {2, 3}, {371, 60306}, {372, 60305}, {551, 61265}, {3241, 61263}, {3244, 38074}, {3626, 38021}, {3631, 38072}, {3636, 38076}, {5476, 11008}, {5485, 54920}, {5603, 34641}, {7585, 43317}, {7586, 43316}, {7788, 32886}, {7967, 61266}, {7987, 51078}, {8227, 50818}, {10516, 20583}, {11488, 42799}, {11489, 42800}, {12245, 38098}, {14494, 60626}, {14912, 25561}, {15081, 56567}, {16267, 42495}, {16268, 42494}, {16808, 41972}, {16809, 41971}, {16966, 43482}, {16967, 43481}, {18841, 54934}, {18842, 60335}, {18843, 54644}, {20050, 51709}, {20057, 61261}, {22235, 43246}, {22237, 43247}, {23249, 41958}, {23259, 41957}, {23267, 42603}, {23273, 42602}, {32887, 59634}, {33602, 42805}, {33603, 42806}, {34747, 59388}, {34748, 61260}, {35023, 38077}, {37832, 42473}, {37835, 42472}, {38073, 60942}, {38075, 60980}, {40330, 51179}, {41100, 42775}, {41101, 42776}, {41112, 42636}, {41113, 42635}, {41119, 54594}, {41120, 54593}, {41951, 42265}, {41952, 42262}, {42111, 43543}, {42114, 43542}, {42139, 43419}, {42142, 43418}, {42429, 43366}, {42430, 43367}, {42431, 43501}, {42432, 43502}, {42500, 42587}, {42501, 42586}, {42504, 42908}, {42505, 42909}, {42522, 60311}, {42523, 60312}, {42580, 49861}, {42581, 49862}, {42598, 49824}, {42599, 49825}, {42813, 43446}, {42814, 43447}, {42914, 43549}, {42915, 43548}, {42986, 43404}, {42987, 43403}, {43108, 43479}, {43109, 43480}, {43254, 43516}, {43255, 43515}, {43384, 52046}, {43385, 52045}, {43386, 60620}, {43387, 60621}, {43487, 43490}, {43488, 43489}, {46267, 51023}, {47352, 51176}, {51133, 53094}, {52519, 60277}, {53108, 54720}, {54448, 61267}, {54522, 60636}, {54645, 60219}, {54845, 60238}, {60127, 60210}, {60142, 60641}, {60216, 60330}, {60283, 60337}, {60322, 60648}

X(61928) = inverse of X(15710) in orthocentroidal circle
X(61928) = inverse of X(15710) in Yff hyperbola
X(61928) = pole of line {523, 15710} with respect to the orthocentroidal circle
X(61928) = pole of line {6, 15710} with respect to the Kiepert hyperbola
X(61928) = pole of line {523, 15710} with respect to the Yff hyperbola
X(61928) = pole of line {69, 50987} with respect to the Wallace hyperbola
X(61928) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(264), X(15710)}}, {{A, B, C, X(548), X(54763)}}, {{A, B, C, X(3524), X(57897)}}, {{A, B, C, X(4232), X(54920)}}, {{A, B, C, X(5072), X(54660)}}, {{A, B, C, X(7378), X(54934)}}, {{A, B, C, X(8797), X(14269)}}, {{A, B, C, X(15684), X(54838)}}, {{A, B, C, X(15696), X(18853)}}, {{A, B, C, X(15700), X(36889)}}, {{A, B, C, X(23046), X(54667)}}, {{A, B, C, X(49140), X(60121)}}, {{A, B, C, X(52284), X(60335)}}
X(61928) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10299, 15709}, {2, 14269, 3528}, {2, 15687, 15715}, {2, 15707, 3525}, {2, 3091, 14269}, {2, 3543, 15700}, {2, 3544, 3545}, {2, 3545, 3855}, {2, 382, 3524}, {2, 3839, 550}, {2, 4, 15710}, {4, 3525, 15696}, {4, 5071, 547}, {376, 3533, 549}, {376, 5071, 3090}, {381, 10124, 3543}, {381, 15703, 15686}, {381, 5055, 10124}, {381, 547, 15692}, {547, 14893, 11540}, {547, 549, 5070}, {547, 632, 15703}, {632, 5079, 16371}, {1656, 14893, 15721}, {3091, 17564, 15687}, {3091, 5070, 4}, {3528, 14269, 15682}, {3530, 15687, 15681}, {3545, 15682, 3091}, {3839, 10109, 5067}, {3839, 5067, 15698}, {3851, 5079, 3530}, {3861, 5067, 6963}, {5055, 15722, 1656}, {5066, 15686, 381}, {5068, 12812, 6938}, {5072, 10109, 3839}, {8703, 11540, 15722}, {11737, 15687, 3851}, {13587, 17549, 13738}, {14269, 15695, 382}, {14893, 15721, 11001}, {15681, 15700, 8703}, {15681, 15710, 376}, {15687, 15715, 3529}, {15699, 15720, 2}, {15710, 15719, 10299}

X(61929) = X(2)X(3)∩X(6)X(33606)

Barycentrics    a^4-26*(b^2-c^2)^2+25*a^2*(b^2+c^2) : :
X(61929) = -26*X[2]+9*X[3], 9*X[114]+8*X[41154], 9*X[355]+8*X[51107], 9*X[3656]+8*X[51070], 15*X[3817]+2*X[50827], 2*X[4677]+15*X[18493], 16*X[5476]+X[51175], 15*X[5587]+2*X[51087], 15*X[5603]+2*X[50830], 12*X[5886]+5*X[50797], 63*X[7989]+5*X[51097], 3*X[8148]+14*X[51068] and many others

X(61929) lies on these lines: {2, 3}, {6, 33606}, {114, 41154}, {302, 33613}, {303, 33612}, {355, 51107}, {3311, 41948}, {3312, 41947}, {3656, 51070}, {3817, 50827}, {4677, 18493}, {5476, 51175}, {5587, 51087}, {5603, 50830}, {5886, 50797}, {6221, 43790}, {6398, 43789}, {6441, 13785}, {6442, 13665}, {6449, 43558}, {6450, 43559}, {6451, 43504}, {6452, 43503}, {6484, 42642}, {6485, 42641}, {6498, 43323}, {6499, 43322}, {7989, 51097}, {8148, 51068}, {8724, 41147}, {9955, 51066}, {10171, 50799}, {10175, 50806}, {10302, 54643}, {10516, 51140}, {11178, 51188}, {11485, 42969}, {11486, 42968}, {13607, 38076}, {13903, 42526}, {13961, 42527}, {14226, 42639}, {14241, 42640}, {14561, 50954}, {14853, 50985}, {14926, 17810}, {15092, 48657}, {15534, 43150}, {16644, 42963}, {16645, 42962}, {18362, 18584}, {18440, 25565}, {18525, 51110}, {18526, 51105}, {19130, 50993}, {20423, 41152}, {25561, 39899}, {34748, 61259}, {37832, 43877}, {37835, 43878}, {38072, 51189}, {40693, 42503}, {40694, 42502}, {41100, 43545}, {41101, 43544}, {41107, 42129}, {41108, 42132}, {41112, 43101}, {41113, 43104}, {41121, 42095}, {41122, 42098}, {41149, 50955}, {41150, 50796}, {41153, 47354}, {41959, 41961}, {41960, 41962}, {41977, 42508}, {41978, 42509}, {42103, 42791}, {42106, 42792}, {42107, 42511}, {42110, 42510}, {42111, 43229}, {42114, 43228}, {42119, 42984}, {42120, 42985}, {42125, 49905}, {42128, 49906}, {42130, 42795}, {42131, 42796}, {42133, 43875}, {42134, 43876}, {42143, 43246}, {42146, 43247}, {42283, 43513}, {42284, 43514}, {42419, 42473}, {42420, 42472}, {42474, 42918}, {42475, 42919}, {42528, 54480}, {42529, 54479}, {42532, 42581}, {42533, 42580}, {42584, 43003}, {42585, 43002}, {42690, 42817}, {42691, 42818}, {42694, 42936}, {42695, 42937}, {42815, 49948}, {42816, 49947}, {42914, 43484}, {42915, 43483}, {42974, 49908}, {42975, 49907}, {43028, 46334}, {43029, 46335}, {43209, 43562}, {43210, 43563}, {43312, 54598}, {43313, 54599}, {43380, 43791}, {43381, 43792}, {43568, 60314}, {43569, 60313}, {44456, 50994}, {50798, 51091}, {50800, 51085}, {50818, 61270}, {50957, 51138}, {50964, 55610}, {50982, 51173}, {50989, 51172}, {51071, 61261}, {51103, 61268}, {51167, 55670}, {51709, 61264}, {54521, 60637}, {54608, 60239}, {60175, 60282}, {60192, 60228}

X(61929) = reflection of X(i) in X(j) for these {i,j}: {15722, 2}
X(61929) = inverse of X(15759) in orthocentroidal circle
X(61929) = inverse of X(15759) in Yff hyperbola
X(61929) = complement of X(62055)
X(61929) = anticomplement of X(61845)
X(61929) = pole of line {523, 15759} with respect to the orthocentroidal circle
X(61929) = pole of line {6, 15759} with respect to the Kiepert hyperbola
X(61929) = pole of line {523, 15759} with respect to the Yff hyperbola
X(61929) = intersection, other than A, B, C, of circumconics {{A, B, C, X(264), X(15759)}}, {{A, B, C, X(1494), X(15722)}}, {{A, B, C, X(3521), X(58208)}}, {{A, B, C, X(10301), X(54643)}}, {{A, B, C, X(49139), X(60121)}}
X(61929) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15695, 5054}, {2, 30, 15722}, {2, 3830, 15716}, {2, 3845, 15695}, {2, 3860, 15685}, {2, 3861, 6891}, {2, 4, 15759}, {3, 3851, 3859}, {5, 14892, 5071}, {20, 3525, 15712}, {20, 3845, 3830}, {381, 15696, 14269}, {381, 15706, 4}, {381, 1656, 15688}, {381, 5054, 5076}, {381, 5055, 3526}, {382, 1656, 3525}, {547, 3857, 10304}, {548, 549, 15705}, {1656, 15716, 2}, {1656, 3545, 381}, {3090, 14269, 15723}, {3525, 10304, 549}, {3526, 3534, 15693}, {3533, 7486, 3628}, {3534, 5054, 15698}, {3545, 5071, 20}, {3560, 3859, 3533}, {3628, 5066, 3845}, {3628, 5071, 5055}, {3830, 10109, 1656}, {3839, 5070, 14093}, {3843, 15699, 15700}, {3845, 15698, 15684}, {3854, 15022, 7486}, {3859, 14892, 11737}, {5055, 17800, 15703}, {5066, 12100, 3856}, {5067, 14893, 15707}, {5068, 15712, 3851}, {11540, 11737, 5066}, {11540, 15640, 3}, {14269, 15723, 15696}, {14892, 15684, 5072}, {15684, 15698, 3534}, {15703, 17800, 15709}, {15765, 18585, 11541}, {33606, 33607, 6}

X(61930) = X(2)X(3)∩X(13)X(43241)

Barycentrics    a^4-23*(b^2-c^2)^2+22*a^2*(b^2+c^2) : :
X(61930) = -23*X[2]+8*X[3], X[3241]+14*X[7989], 7*X[3619]+8*X[50959], 7*X[3622]+8*X[50796], X[3623]+8*X[61261], 7*X[3624]+8*X[50803], 8*X[3656]+7*X[4678], 4*X[3817]+X[53620], -16*X[3828]+X[20070], 7*X[4772]+8*X[51038], X[5032]+4*X[10516], -16*X[5461]+X[5984] and many others

X(61930) lies on these lines: {2, 3}, {13, 43241}, {14, 43240}, {17, 49824}, {18, 49825}, {395, 42472}, {396, 42473}, {485, 43323}, {486, 43322}, {519, 61264}, {1131, 13847}, {1132, 13846}, {3241, 7989}, {3591, 31414}, {3619, 50959}, {3622, 50796}, {3623, 61261}, {3624, 50803}, {3656, 4678}, {3817, 53620}, {3828, 20070}, {4772, 51038}, {5032, 10516}, {5318, 43304}, {5321, 43305}, {5343, 41943}, {5344, 41944}, {5461, 5984}, {5550, 34648}, {5921, 25561}, {6361, 50807}, {6449, 43522}, {6450, 43521}, {6776, 25565}, {7739, 39601}, {7752, 32869}, {7811, 32870}, {7814, 32892}, {7967, 61267}, {7988, 28236}, {9542, 43321}, {9543, 42268}, {9779, 19875}, {9780, 50802}, {9955, 50872}, {11057, 32867}, {11178, 20080}, {11522, 51072}, {12243, 15092}, {12571, 19876}, {13570, 44299}, {14930, 31415}, {15056, 58470}, {16267, 42114}, {16268, 42111}, {16960, 43232}, {16961, 43233}, {16962, 42512}, {16963, 42513}, {16966, 43372}, {16967, 43373}, {18358, 51215}, {18483, 46930}, {18493, 20052}, {18584, 37665}, {19130, 51028}, {19872, 34638}, {19877, 50865}, {20049, 51709}, {20057, 50801}, {20582, 61044}, {24206, 54174}, {27268, 51041}, {28204, 61266}, {28232, 54447}, {28234, 38021}, {31162, 46933}, {31407, 39593}, {32789, 43508}, {32790, 43507}, {32816, 32893}, {32900, 34627}, {33748, 38079}, {34595, 50862}, {34632, 46932}, {35242, 50873}, {35510, 55958}, {36519, 41135}, {36969, 42996}, {36970, 42997}, {38074, 61263}, {38075, 59375}, {39663, 41136}, {39874, 50957}, {40138, 61306}, {41112, 42580}, {41113, 42581}, {42087, 43478}, {42088, 43477}, {42089, 43473}, {42092, 43474}, {42095, 42778}, {42098, 42777}, {42103, 43553}, {42106, 43552}, {42107, 42474}, {42110, 42475}, {42119, 43107}, {42120, 43100}, {42139, 42516}, {42142, 42517}, {42163, 49813}, {42166, 49812}, {42274, 42605}, {42277, 42604}, {42494, 43229}, {42495, 43228}, {42520, 49873}, {42521, 49874}, {42539, 43211}, {42540, 43212}, {42910, 42973}, {42911, 42972}, {42920, 49827}, {42921, 49826}, {42940, 43869}, {42941, 43870}, {42942, 43365}, {42943, 43364}, {42956, 43201}, {42957, 43202}, {42982, 43543}, {42983, 43542}, {42992, 49810}, {42993, 49811}, {42998, 49908}, {42999, 49907}, {43334, 43638}, {43335, 43643}, {43376, 43880}, {43377, 43879}, {43560, 60298}, {43561, 60297}, {43951, 60131}, {46455, 46808}, {46934, 50864}, {47354, 51171}, {47355, 50960}, {47586, 60287}, {48905, 51133}, {50818, 61272}, {51029, 55646}, {51073, 51076}, {51107, 61252}, {51128, 51131}, {59387, 61265}, {60118, 60638}, {60147, 60645}

X(61930) = midpoint of X(i) and X(j) for these {i,j}: {3545, 5071}, {3843, 5054}, {14269, 15693}
X(61930) = reflection of X(i) in X(j) for these {i,j}: {10304, 631}, {14269, 3858}, {15689, 15711}, {15694, 15699}, {15696, 17504}, {15699, 12812}, {3091, 3545}
X(61930) = inverse of X(62063) in orthocentroidal circle
X(61930) = inverse of X(62063) in Yff hyperbola
X(61930) = complement of X(62056)
X(61930) = anticomplement of X(61844)
X(61930) = pole of line {523, 62063} with respect to the orthocentroidal circle
X(61930) = pole of line {6, 62063} with respect to the Kiepert hyperbola
X(61930) = pole of line {523, 62063} with respect to the Yff hyperbola
X(61930) = pole of line {69, 61825} with respect to the Wallace hyperbola
X(61930) = intersection, other than A, B, C, of circumconics {{A, B, C, X(30), X(46455)}}, {{A, B, C, X(549), X(35510)}}, {{A, B, C, X(3146), X(55958)}}, {{A, B, C, X(3853), X(54923)}}, {{A, B, C, X(15717), X(36889)}}, {{A, B, C, X(16239), X(18855)}}, {{A, B, C, X(49138), X(60121)}}
X(61930) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3543, 15717}, {2, 381, 3146}, {2, 3832, 15683}, {2, 3854, 3543}, {2, 5059, 549}, {4, 15694, 15697}, {4, 3090, 16239}, {5, 14892, 5055}, {5, 3544, 5056}, {5, 5068, 15022}, {20, 3091, 3858}, {30, 12812, 15699}, {30, 15699, 15694}, {30, 15711, 15689}, {30, 17504, 15696}, {30, 3545, 3091}, {30, 3858, 14269}, {376, 10109, 7486}, {381, 12100, 4}, {381, 1656, 15695}, {381, 17800, 3845}, {381, 3628, 11001}, {381, 5055, 11539}, {381, 547, 15715}, {546, 15702, 15640}, {547, 14269, 15709}, {547, 3858, 15693}, {547, 5066, 12102}, {550, 5066, 381}, {631, 11001, 15714}, {631, 3146, 3522}, {1656, 3091, 17578}, {1656, 3859, 17538}, {3091, 3522, 3832}, {3091, 3843, 3854}, {3146, 15717, 550}, {3524, 14890, 15708}, {3545, 15022, 15705}, {3545, 5055, 3839}, {3830, 5067, 15721}, {3843, 15694, 15685}, {3850, 15703, 15682}, {3851, 10109, 376}, {3858, 12102, 3843}, {5055, 14892, 3545}, {5070, 14893, 15698}, {7988, 38076, 38314}, {10303, 15703, 2}, {10304, 15708, 12100}, {11001, 15707, 10304}, {11737, 16239, 5066}, {12100, 15694, 631}, {12101, 15723, 3528}, {14269, 15693, 30}, {14269, 15709, 20}, {14890, 15688, 3524}, {15682, 15703, 10303}, {15693, 15694, 14869}, {15713, 17538, 15692}, {38076, 38314, 54448}

X(61931) = X(2)X(3)∩X(61)X(42952)

Barycentrics    a^4-20*(b^2-c^2)^2+19*a^2*(b^2+c^2) : :
X(61931) = -20*X[2]+7*X[3], -2*X[551]+15*X[61266], X[3241]+12*X[61262], 4*X[3625]+35*X[18493], -X[3633]+14*X[51709], 12*X[3817]+X[34718], 25*X[4668]+14*X[11278], 32*X[4691]+7*X[8148], -3*X[5050]+16*X[25565], 8*X[5097]+5*X[50955], 3*X[5102]+10*X[11178], -14*X[5476]+X[6144] and many others

X(61931) lies on these lines: {2, 3}, {61, 42952}, {62, 42953}, {485, 41951}, {486, 41952}, {551, 61266}, {3241, 61262}, {3625, 18493}, {3633, 51709}, {3817, 34718}, {4668, 11278}, {4691, 8148}, {5041, 18362}, {5050, 25565}, {5097, 50955}, {5102, 11178}, {5309, 18584}, {5476, 6144}, {5587, 34748}, {5901, 50797}, {6199, 42602}, {6395, 42603}, {6437, 43881}, {6438, 43882}, {6519, 43885}, {6522, 43886}, {7989, 33179}, {8227, 50871}, {9956, 50806}, {10137, 42268}, {10138, 42269}, {10171, 58230}, {10194, 42418}, {10195, 42417}, {10246, 61265}, {10247, 38155}, {12816, 43239}, {12817, 43238}, {14848, 32455}, {14971, 38744}, {16200, 51515}, {16241, 43296}, {16242, 43297}, {16808, 42475}, {16809, 42474}, {18581, 42899}, {18582, 42898}, {18583, 50954}, {19878, 58224}, {20582, 55593}, {21356, 51173}, {21358, 55587}, {23514, 48657}, {24206, 50963}, {25055, 50800}, {25561, 39561}, {30308, 38066}, {30392, 38140}, {31145, 58238}, {33751, 51167}, {34627, 61269}, {35822, 45385}, {35823, 45384}, {36836, 43492}, {36843, 43491}, {37517, 38072}, {37624, 50796}, {38075, 61020}, {38076, 61268}, {38176, 58241}, {38319, 38637}, {38724, 38792}, {38725, 38789}, {38732, 38746}, {38735, 38743}, {38756, 59376}, {38758, 51517}, {40330, 51214}, {41107, 42801}, {41108, 42802}, {41119, 42989}, {41120, 42988}, {41943, 42918}, {41944, 42919}, {42095, 43015}, {42098, 43014}, {42111, 42974}, {42114, 42975}, {42115, 42985}, {42116, 42984}, {42125, 43104}, {42128, 43101}, {42435, 42581}, {42436, 42580}, {42625, 54591}, {42626, 54592}, {42912, 42963}, {42913, 42962}, {46267, 55703}, {47352, 48662}, {47353, 50664}, {47354, 53091}, {48310, 55692}, {48661, 50807}, {48873, 51165}, {51024, 55612}, {51107, 61248}, {51166, 55584}, {51172, 61545}, {51186, 55580}

X(61931) = inverse of X(45759) in orthocentroidal circle
X(61931) = inverse of X(45759) in Yff hyperbola
X(61931) = complement of X(62058)
X(61931) = pole of line {523, 45759} with respect to the orthocentroidal circle
X(61931) = pole of line {6, 45759} with respect to the Kiepert hyperbola
X(61931) = pole of line {523, 45759} with respect to the Yff hyperbola
X(61931) = intersection, other than A, B, C, of circumconics {{A, B, C, X(264), X(45759)}}, {{A, B, C, X(3859), X(60122)}}, {{A, B, C, X(15684), X(55958)}}, {{A, B, C, X(15706), X(57896)}}, {{A, B, C, X(49137), X(60121)}}
X(61931) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14892, 5072}, {2, 3545, 3850}, {2, 3627, 15706}, {2, 3839, 17538}, {2, 548, 5054}, {3, 15684, 15686}, {3, 15703, 15723}, {3, 3850, 3843}, {5, 11737, 5071}, {5, 3544, 1656}, {5, 5068, 5079}, {381, 14093, 14893}, {381, 1656, 376}, {381, 5054, 15687}, {381, 5071, 15703}, {547, 3845, 15702}, {547, 3853, 10124}, {1656, 14269, 15701}, {1656, 3832, 3}, {1656, 5066, 14269}, {2043, 2044, 3859}, {3091, 13735, 4}, {3091, 15687, 381}, {3526, 3839, 15685}, {3543, 5071, 547}, {3545, 11001, 3091}, {3545, 15022, 15690}, {3545, 3832, 5066}, {3545, 5056, 3845}, {3627, 3850, 3832}, {3627, 6924, 546}, {3830, 5055, 5070}, {3830, 5070, 15707}, {3853, 15708, 3534}, {3854, 15709, 12101}, {5066, 10109, 15711}, {5071, 15703, 5055}, {5071, 15715, 3090}, {11737, 15681, 3851}, {12101, 15709, 15696}, {12108, 15699, 2}, {14093, 14893, 15684}, {14093, 15681, 15689}, {14093, 15684, 15681}, {14269, 15701, 17800}, {14269, 15711, 5073}, {14269, 17800, 3830}, {14892, 14893, 11737}, {14893, 15686, 3543}, {14893, 15703, 15718}, {15681, 15695, 15691}, {15681, 15703, 15694}, {15681, 15718, 14093}, {15690, 15699, 3533}, {47352, 50957, 48662}

X(61932) = X(2)X(3)∩X(6)X(42502)

Barycentrics    a^4-17*(b^2-c^2)^2+16*a^2*(b^2+c^2) : :
X(61932) = -17*X[2]+6*X[3], 5*X[69]+28*X[42785], 9*X[262]+2*X[14711], -3*X[944]+14*X[51110], 6*X[946]+5*X[51066], X[3241]+10*X[61261], 3*X[3576]+8*X[50803], -5*X[3618]+16*X[25565], 2*X[3654]+9*X[9779], 5*X[3656]+6*X[38176], 9*X[3817]+2*X[4745], -4*X[4669]+15*X[5818] and many others

X(61932) lies on these lines: {2, 3}, {6, 42502}, {13, 42472}, {14, 42473}, {69, 42785}, {262, 14711}, {325, 32892}, {395, 49825}, {396, 49824}, {944, 51110}, {946, 51066}, {1151, 34089}, {1152, 34091}, {3241, 61261}, {3316, 42270}, {3317, 42273}, {3576, 50803}, {3618, 25565}, {3654, 9779}, {3656, 38176}, {3817, 4745}, {4669, 5818}, {4677, 5603}, {5032, 18358}, {5085, 50960}, {5318, 42475}, {5321, 42474}, {5334, 43104}, {5335, 43101}, {5355, 18362}, {5459, 36318}, {5460, 36320}, {5476, 50961}, {5478, 36767}, {5480, 50993}, {5485, 54523}, {5587, 50801}, {5657, 50802}, {5817, 60963}, {5881, 51107}, {5886, 50818}, {6053, 15081}, {6407, 43561}, {6408, 43560}, {6560, 43375}, {6561, 43374}, {6688, 16261}, {7581, 42579}, {7582, 42578}, {7612, 60284}, {7736, 39593}, {7773, 32885}, {7776, 32893}, {7967, 7988}, {7982, 51070}, {7989, 10595}, {8164, 11238}, {8227, 34627}, {8252, 43256}, {8253, 43257}, {8584, 10516}, {8972, 42526}, {9300, 18584}, {9541, 43517}, {9624, 51104}, {9741, 18546}, {9812, 50807}, {9862, 14971}, {9955, 53620}, {10155, 32532}, {10164, 51076}, {10171, 50811}, {10172, 51074}, {10175, 30308}, {10283, 50797}, {10519, 50959}, {10653, 43771}, {10654, 43772}, {11178, 50992}, {11230, 50799}, {11237, 47743}, {11459, 58470}, {11477, 41152}, {11488, 41108}, {11489, 41107}, {11542, 43247}, {11543, 43246}, {12046, 18439}, {12112, 17825}, {12243, 23514}, {12245, 51068}, {12248, 59376}, {13570, 54041}, {13846, 23273}, {13847, 23267}, {13886, 35823}, {13939, 35822}, {13941, 42527}, {14226, 32787}, {14241, 32788}, {14458, 60616}, {14492, 60629}, {14494, 54637}, {14561, 50974}, {14639, 15300}, {14762, 55177}, {14853, 15533}, {14912, 47354}, {14981, 41154}, {15029, 56567}, {15058, 16226}, {16644, 49876}, {16645, 49875}, {16808, 42510}, {16809, 42511}, {16960, 43251}, {16961, 43250}, {16962, 42920}, {16963, 42921}, {18483, 19876}, {18492, 19883}, {18493, 31145}, {18581, 41121}, {18582, 41122}, {18840, 54707}, {18841, 54612}, {18842, 60185}, {19053, 42274}, {19054, 42277}, {19130, 21356}, {19925, 51109}, {20423, 50990}, {21167, 51131}, {22165, 38072}, {23235, 41147}, {23249, 42418}, {23253, 52046}, {23259, 42417}, {23263, 52045}, {23269, 42583}, {23275, 42582}, {23302, 43482}, {23303, 43481}, {25561, 59373}, {31162, 51069}, {32823, 46951}, {33602, 43555}, {33603, 43554}, {33604, 42095}, {33605, 42098}, {34632, 38083}, {35751, 59394}, {35786, 42524}, {35787, 42525}, {36329, 59396}, {36362, 59379}, {36363, 59378}, {36519, 36523}, {36765, 47865}, {37640, 41120}, {37641, 41119}, {37832, 41113}, {37835, 41112}, {38034, 50872}, {38042, 50806}, {38064, 51537}, {38136, 51028}, {38140, 50864}, {38253, 54838}, {38314, 61268}, {38317, 50956}, {38745, 41148}, {39874, 47352}, {41100, 42910}, {41101, 42911}, {41135, 61575}, {41971, 42904}, {41972, 42905}, {42089, 42505}, {42090, 43002}, {42091, 43003}, {42092, 42504}, {42093, 42791}, {42094, 42792}, {42107, 43778}, {42110, 43777}, {42144, 43478}, {42145, 43477}, {42147, 43447}, {42148, 43446}, {42153, 43773}, {42154, 43463}, {42155, 43464}, {42156, 43774}, {42494, 49810}, {42495, 49811}, {42516, 43419}, {42517, 43418}, {42528, 43475}, {42529, 43476}, {42570, 43431}, {42571, 43430}, {42580, 43775}, {42581, 43776}, {42588, 42914}, {42589, 42915}, {42643, 60296}, {42644, 60295}, {42690, 43110}, {42691, 43111}, {42775, 42973}, {42776, 42972}, {42795, 43196}, {42796, 43195}, {42940, 43502}, {42941, 43501}, {42952, 43240}, {42953, 43241}, {42974, 42987}, {42975, 42986}, {43407, 43506}, {43408, 43505}, {43518, 43521}, {43562, 60316}, {43563, 60315}, {44834, 45794}, {47102, 55823}, {48913, 53127}, {49873, 49947}, {49874, 49948}, {50798, 51092}, {50804, 51709}, {50819, 51078}, {50824, 61267}, {50871, 61271}, {50954, 59399}, {50957, 51176}, {50963, 54174}, {50964, 50966}, {50967, 51186}, {50975, 51133}, {50991, 51130}, {51087, 61257}, {51108, 61265}, {51143, 54131}, {51211, 55593}, {53103, 60281}, {54500, 54797}, {54616, 60150}, {54667, 60137}, {54710, 54763}, {54727, 54788}, {54827, 60114}, {59387, 61266}, {60127, 60143}

X(61932) = midpoint of X(i) and X(j) for these {i,j}: {4, 15715}, {381, 5070}
X(61932) = reflection of X(i) in X(j) for these {i,j}: {15715, 3525}, {15717, 15723}, {15719, 2}, {15721, 5070}, {376, 15717}
X(61932) = inverse of X(19708) in orthocentroidal circle
X(61932) = inverse of X(19708) in Yff hyperbola
X(61932) = complement of X(62059)
X(61932) = anticomplement of X(61843)
X(61932) = pole of line {523, 19708} with respect to the orthocentroidal circle
X(61932) = pole of line {6, 19708} with respect to the Kiepert hyperbola
X(61932) = pole of line {523, 19708} with respect to the Yff hyperbola
X(61932) = pole of line {69, 15701} with respect to the Wallace hyperbola
X(61932) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(68), X(55866)}}, {{A, B, C, X(69), X(15701)}}, {{A, B, C, X(264), X(19708)}}, {{A, B, C, X(458), X(60627)}}, {{A, B, C, X(1494), X(15719)}}, {{A, B, C, X(3089), X(54827)}}, {{A, B, C, X(3146), X(54838)}}, {{A, B, C, X(3521), X(58207)}}, {{A, B, C, X(3522), X(54763)}}, {{A, B, C, X(3832), X(54667)}}, {{A, B, C, X(3845), X(8797)}}, {{A, B, C, X(3854), X(60122)}}, {{A, B, C, X(4232), X(54523)}}, {{A, B, C, X(5059), X(60121)}}, {{A, B, C, X(5068), X(54660)}}, {{A, B, C, X(6995), X(54707)}}, {{A, B, C, X(7378), X(54612)}}, {{A, B, C, X(10155), X(53857)}}, {{A, B, C, X(10303), X(15319)}}, {{A, B, C, X(11331), X(60616)}}, {{A, B, C, X(11540), X(36948)}}, {{A, B, C, X(12100), X(36889)}}, {{A, B, C, X(14843), X(55861)}}, {{A, B, C, X(15318), X(58186)}}, {{A, B, C, X(15682), X(55958)}}, {{A, B, C, X(17578), X(54585)}}, {{A, B, C, X(49670), X(54681)}}, {{A, B, C, X(50689), X(54512)}}, {{A, B, C, X(52284), X(60185)}}, {{A, B, C, X(52289), X(60629)}}, {{A, B, C, X(52301), X(60127)}}, {{A, B, C, X(55569), X(60301)}}, {{A, B, C, X(55573), X(60302)}}
X(61932) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10109, 3090}, {2, 10304, 15713}, {2, 15697, 11812}, {2, 3091, 3845}, {2, 3523, 11540}, {2, 3534, 631}, {2, 3543, 12100}, {2, 381, 15682}, {2, 3839, 3534}, {5, 11737, 5055}, {5, 3545, 5071}, {5, 3851, 15022}, {5, 5072, 5056}, {20, 5068, 12811}, {30, 3525, 15715}, {30, 5070, 15721}, {140, 14892, 11737}, {140, 3090, 5067}, {140, 376, 3524}, {140, 3845, 15685}, {140, 3856, 3627}, {140, 3861, 15704}, {140, 8703, 15693}, {376, 15640, 11001}, {376, 3545, 3091}, {376, 631, 17504}, {381, 14892, 5068}, {381, 15689, 3861}, {381, 1656, 15689}, {381, 3627, 3839}, {381, 5055, 140}, {381, 5070, 30}, {546, 15703, 10304}, {546, 5079, 16417}, {632, 15684, 15705}, {1656, 3543, 15709}, {2043, 2044, 3854}, {3091, 11737, 3545}, {3091, 5059, 3856}, {3091, 5067, 4}, {3146, 15694, 15710}, {3525, 3544, 5072}, {3543, 15709, 3528}, {3628, 14269, 15692}, {3830, 11812, 15697}, {3839, 15022, 547}, {3843, 11539, 15683}, {3845, 15693, 15640}, {3845, 15759, 382}, {3850, 7486, 3529}, {3854, 15692, 14269}, {3861, 15689, 3543}, {4190, 10303, 1656}, {5056, 15701, 6852}, {5056, 5072, 3855}, {5818, 38021, 34631}, {8227, 38076, 34627}, {10109, 12101, 15699}, {10109, 12811, 12101}, {10175, 30308, 50810}, {10299, 13742, 3525}, {10304, 15703, 3533}, {11539, 15683, 10299}, {11540, 15687, 15695}, {11540, 15695, 3523}, {11737, 17504, 3851}, {11812, 15697, 15698}, {12101, 15699, 15701}, {12101, 15701, 20}, {12811, 15699, 381}, {15640, 15693, 376}, {15682, 15685, 11541}, {15685, 15693, 8703}, {15699, 15701, 2}, {15716, 15721, 15719}, {15718, 17504, 15717}, {18586, 18587, 16239}, {23303, 43481, 43494}, {37832, 41113, 49862}, {37835, 41112, 49861}, {41119, 42111, 49908}, {41119, 49908, 37641}, {41120, 42114, 49907}, {41120, 49907, 37640}, {42095, 43403, 43543}, {42098, 43404, 43542}, {42139, 49862, 41113}, {42142, 49861, 41112}, {42502, 42503, 6}

X(61933) = X(1)X(50797)∩X(2)X(3)

Barycentrics    a^4-14*(b^2-c^2)^2+13*a^2*(b^2+c^2) : :
X(61933) = 4*X[1]+5*X[50797], -14*X[2]+5*X[3], 4*X[6]+5*X[50954], 4*X[10]+5*X[50806], 4*X[69]+5*X[51172], 4*X[141]+5*X[50963], 7*X[599]+2*X[55720], 4*X[1125]+5*X[50799], 5*X[1352]+4*X[20583], 5*X[1482]+4*X[34641], X[1699]+2*X[38083], 4*X[3244]+5*X[50798] and many others

X(61933) lies on these lines: {1, 50797}, {2, 3}, {6, 50954}, {10, 50806}, {13, 42818}, {14, 42817}, {15, 42474}, {16, 42475}, {69, 51172}, {141, 50963}, {519, 61263}, {542, 15046}, {599, 55720}, {1125, 50799}, {1327, 42583}, {1328, 42582}, {1352, 20583}, {1482, 34641}, {1699, 38083}, {3066, 32608}, {3244, 50798}, {3589, 50956}, {3626, 3656}, {3629, 50955}, {3631, 20423}, {3632, 18493}, {3634, 51074}, {3636, 18526}, {3653, 10171}, {3655, 15808}, {3763, 55601}, {3817, 38098}, {4681, 51040}, {4686, 51039}, {4739, 51038}, {5339, 42939}, {5340, 42938}, {5365, 43108}, {5366, 43109}, {5476, 11898}, {5790, 11224}, {5886, 38076}, {6054, 15092}, {6329, 39899}, {6470, 8976}, {6471, 13951}, {7687, 11693}, {7951, 8162}, {7988, 28204}, {7989, 12645}, {8252, 42641}, {8253, 42642}, {8556, 13111}, {9166, 38743}, {9880, 35022}, {9955, 34718}, {9956, 30308}, {10175, 38066}, {10246, 61266}, {10247, 38074}, {10516, 14848}, {10574, 12046}, {10653, 42962}, {10654, 42963}, {10706, 15088}, {11008, 51175}, {11017, 15024}, {11178, 40341}, {11179, 50957}, {11184, 53144}, {11237, 37602}, {11485, 43104}, {11486, 43101}, {11645, 55693}, {11648, 31467}, {12702, 50802}, {12816, 36843}, {12817, 36836}, {12820, 36968}, {12821, 36967}, {13321, 14845}, {13903, 42270}, {13961, 42273}, {14488, 60279}, {15516, 25561}, {16226, 18435}, {16241, 42630}, {16242, 42629}, {16267, 42098}, {16268, 42095}, {16644, 42892}, {16645, 42893}, {16808, 42951}, {16809, 42950}, {16962, 42132}, {16963, 42129}, {18357, 20057}, {18436, 58470}, {18440, 55710}, {18481, 50803}, {18510, 42277}, {18512, 42274}, {18553, 51185}, {18584, 39601}, {19130, 51173}, {19876, 22793}, {20112, 53143}, {21356, 38136}, {22236, 43547}, {22238, 43546}, {23234, 38732}, {23249, 43212}, {23259, 43211}, {25055, 38140}, {25565, 47353}, {28198, 54447}, {31489, 39563}, {31730, 51076}, {33878, 50959}, {34573, 51129}, {34627, 61272}, {36990, 55690}, {37832, 42125}, {37835, 42128}, {38022, 59387}, {38034, 53620}, {38073, 51516}, {38075, 38107}, {38077, 38752}, {38082, 59385}, {38139, 59374}, {38314, 61269}, {38755, 59377}, {41112, 42599}, {41113, 42598}, {41121, 42153}, {41122, 42156}, {42104, 42500}, {42105, 42501}, {42107, 42911}, {42110, 42910}, {42111, 42815}, {42114, 42816}, {42115, 43100}, {42116, 43107}, {42130, 43196}, {42131, 43195}, {42143, 43403}, {42146, 43404}, {42154, 42901}, {42155, 42900}, {42283, 43254}, {42284, 43255}, {42472, 43111}, {42473, 43110}, {42488, 43486}, {42489, 43485}, {42490, 46335}, {42491, 46334}, {42580, 49906}, {42581, 49905}, {42625, 43326}, {42626, 43327}, {42647, 42726}, {42648, 42725}, {42775, 49875}, {42776, 49876}, {42988, 49907}, {42989, 49908}, {43199, 44016}, {43200, 44015}, {43230, 43399}, {43231, 43400}, {43232, 43251}, {43233, 43250}, {43273, 55696}, {43515, 53131}, {43516, 53130}, {43621, 50984}, {46264, 50960}, {46931, 50809}, {47352, 55706}, {47355, 55689}, {48657, 61576}, {48881, 51131}, {48891, 51167}, {48910, 55634}, {50964, 54169}, {50980, 55632}, {50989, 55718}, {50991, 55724}, {51023, 55705}, {51071, 61258}, {51087, 61256}, {53023, 55596}, {54131, 55585}, {54448, 61270}, {55958, 57823}, {60142, 60286}

X(61933) = midpoint of X(i) and X(j) for these {i,j}: {4, 15705}, {3839, 15709}, {14269, 15707}
X(61933) = reflection of X(i) in X(j) for these {i,j}: {15688, 15707}, {15689, 15705}, {15705, 11539}, {15707, 2}, {15709, 15699}, {3, 15709}
X(61933) = inverse of X(34200) in orthocentroidal circle
X(61933) = inverse of X(34200) in Yff hyperbola
X(61933) = complement of X(15710)
X(61933) = anticomplement of X(61841)
X(61933) = pole of line {523, 34200} with respect to the orthocentroidal circle
X(61933) = pole of line {6, 34200} with respect to the Kiepert hyperbola
X(61933) = pole of line {523, 34200} with respect to the Yff hyperbola
X(61933) = intersection, other than A, B, C, of circumconics {{A, B, C, X(264), X(34200)}}, {{A, B, C, X(382), X(55958)}}, {{A, B, C, X(549), X(57823)}}, {{A, B, C, X(1494), X(15707)}}, {{A, B, C, X(3857), X(60122)}}, {{A, B, C, X(3859), X(21400)}}, {{A, B, C, X(10299), X(36889)}}, {{A, B, C, X(11539), X(46168)}}, {{A, B, C, X(14869), X(57822)}}, {{A, B, C, X(15700), X(57897)}}, {{A, B, C, X(17800), X(60121)}}, {{A, B, C, X(18550), X(35404)}}, {{A, B, C, X(41106), X(43699)}}
X(61933) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11737, 3851}, {2, 15681, 15720}, {2, 15715, 140}, {2, 17677, 17559}, {2, 17679, 5084}, {2, 30, 15707}, {2, 3529, 549}, {2, 3530, 15694}, {2, 3543, 10299}, {2, 3544, 11737}, {2, 376, 14869}, {2, 382, 15700}, {2, 3851, 381}, {2, 3855, 15687}, {2, 546, 15681}, {3, 17578, 1657}, {3, 3830, 15683}, {3, 3851, 3855}, {3, 5055, 15699}, {4, 10109, 15703}, {5, 12811, 5056}, {5, 3545, 5055}, {5, 3850, 15022}, {5, 3851, 5079}, {30, 11539, 15705}, {30, 15699, 15709}, {30, 15705, 15689}, {381, 15688, 14269}, {381, 15693, 4}, {381, 1656, 3534}, {381, 1657, 3845}, {381, 3526, 3830}, {382, 5079, 1656}, {547, 3830, 3526}, {547, 5066, 3861}, {631, 14893, 15685}, {632, 11001, 15718}, {1656, 15700, 2}, {1656, 3534, 15723}, {1657, 15694, 15716}, {2043, 2044, 3857}, {2049, 5079, 16371}, {3091, 5071, 15713}, {3524, 3545, 3091}, {3526, 3830, 14093}, {3533, 15640, 14891}, {3543, 15701, 15696}, {3543, 3628, 15701}, {3544, 5079, 5072}, {3545, 3839, 5066}, {3545, 5071, 3839}, {3627, 15702, 15695}, {3628, 6846, 5071}, {3830, 15703, 12108}, {3839, 10304, 17578}, {3839, 5068, 3545}, {3850, 15022, 5070}, {3850, 5070, 5076}, {3857, 5067, 5073}, {3858, 10124, 15682}, {3861, 15699, 3524}, {5056, 12811, 3843}, {5066, 10124, 3858}, {5071, 15682, 7486}, {5071, 6952, 3533}, {7486, 15682, 10124}, {10109, 12108, 547}, {10124, 15682, 3}, {11539, 15689, 15693}, {11539, 15693, 5054}, {12101, 15692, 17800}, {12108, 15713, 15721}, {14269, 15688, 382}, {14269, 15707, 30}, {14892, 15699, 5068}, {15681, 17504, 15688}, {15687, 15713, 550}, {15688, 15706, 15710}, {15688, 15720, 17504}, {15689, 15703, 11539}, {15707, 15710, 15706}

X(61934) = X(2)X(3)∩X(6)X(43207)

Barycentrics    2*a^4-25*(b^2-c^2)^2+23*a^2*(b^2+c^2) : :
X(61934) = -25*X[2]+9*X[3], -25*X[3656]+9*X[58241], 27*X[3817]+5*X[51067], 5*X[4669]+3*X[11278], X[4745]+3*X[9955], -9*X[5097]+5*X[41149], 27*X[5102]+5*X[51188], 27*X[5587]+5*X[51097], 15*X[5886]+X[50871], X[5901]+3*X[38076], -9*X[7988]+X[50824], X[8584]+3*X[18358] and many others

X(61934) lies on these lines: {2, 3}, {6, 43207}, {395, 42420}, {396, 42419}, {519, 58237}, {542, 41148}, {952, 51107}, {1327, 6438}, {1328, 6437}, {2782, 41154}, {3656, 58241}, {3817, 51067}, {4669, 11278}, {4745, 9955}, {5097, 41149}, {5102, 51188}, {5318, 41972}, {5321, 41971}, {5587, 51097}, {5886, 50871}, {5901, 38076}, {7988, 50824}, {8584, 18358}, {9166, 61599}, {9300, 39601}, {10139, 42268}, {10140, 42269}, {10171, 31662}, {10175, 51120}, {11231, 51074}, {11542, 41122}, {11543, 41121}, {11592, 44871}, {12816, 42914}, {12817, 42915}, {13665, 42640}, {13785, 42639}, {14226, 45384}, {14241, 45385}, {14561, 51027}, {16200, 61263}, {18357, 51071}, {18480, 51109}, {19130, 50991}, {20423, 51189}, {20582, 55594}, {21850, 50993}, {22165, 37517}, {22791, 51066}, {23234, 61600}, {23302, 43108}, {23303, 43109}, {25565, 50664}, {27355, 31834}, {28146, 51076}, {28178, 51119}, {28182, 50829}, {28186, 50803}, {28204, 41150}, {28212, 50802}, {28224, 58234}, {29317, 51131}, {30308, 38042}, {30392, 61265}, {32787, 41950}, {32788, 41949}, {32900, 51103}, {33179, 51091}, {34754, 43417}, {34755, 43416}, {34773, 58231}, {36523, 61575}, {37785, 49858}, {37786, 49855}, {38021, 61510}, {38028, 50799}, {38072, 50989}, {38073, 61596}, {38074, 61597}, {38075, 61509}, {38077, 61562}, {38079, 55711}, {38083, 40273}, {38110, 50956}, {38112, 50806}, {38155, 51096}, {39561, 47354}, {40996, 55958}, {41100, 42110}, {41101, 42107}, {41107, 43101}, {41108, 43104}, {41112, 43644}, {41113, 43649}, {41119, 42095}, {41120, 42098}, {42111, 49948}, {42114, 49947}, {42121, 42475}, {42124, 42474}, {42125, 49862}, {42128, 49861}, {42129, 49826}, {42132, 49827}, {42135, 42511}, {42136, 42791}, {42137, 42792}, {42138, 42510}, {42143, 43229}, {42146, 43228}, {42154, 42906}, {42155, 42907}, {42283, 42525}, {42284, 42524}, {42417, 43211}, {42418, 43212}, {42472, 49874}, {42473, 49873}, {42496, 49907}, {42497, 49908}, {42520, 43110}, {42521, 43111}, {42532, 42598}, {42533, 42599}, {42580, 42977}, {42581, 42976}, {42633, 49824}, {42634, 49825}, {42904, 43873}, {42905, 43874}, {42912, 42918}, {42913, 42919}, {43463, 43639}, {43464, 43640}, {48310, 55691}, {50796, 51106}, {50797, 61283}, {50798, 61260}, {50807, 54447}, {50818, 61273}, {50984, 55645}, {51025, 55695}, {51093, 61261}, {51105, 61268}, {51128, 55642}, {51186, 55582}, {59377, 61605}

X(61934) = midpoint of X(i) and X(j) for these {i,j}: {2, 3860}, {4, 14891}, {5, 11737}, {381, 3628}, {546, 10124}, {547, 3850}, {549, 3861}, {3530, 14893}, {3845, 11812}, {5066, 10109}, {12101, 15759}
X(61934) = reflection of X(i) in X(j) for these {i,j}: {12811, 11737}, {16239, 547}
X(61934) = inverse of X(62073) in orthocentroidal circle
X(61934) = inverse of X(62073) in Yff hyperbola
X(61934) = complement of X(15759)
X(61934) = pole of line {523, 62073} with respect to the orthocentroidal circle
X(61934) = pole of line {6, 42524} with respect to the Kiepert hyperbola
X(61934) = pole of line {523, 62073} with respect to the Yff hyperbola
X(61934) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1494), X(44580)}}, {{A, B, C, X(15683), X(46455)}}, {{A, B, C, X(33699), X(55958)}}
X(61934) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15685, 549}, {2, 15711, 140}, {2, 3830, 15711}, {2, 3845, 15690}, {2, 4188, 4200}, {2, 5066, 3860}, {2, 6979, 11541}, {5, 14892, 11737}, {5, 3851, 12812}, {5, 3858, 15022}, {5, 5066, 10109}, {5, 5068, 546}, {30, 11737, 12811}, {30, 547, 16239}, {381, 11001, 3845}, {381, 15707, 4}, {381, 5055, 631}, {381, 5056, 11539}, {546, 5055, 10124}, {547, 14893, 15702}, {631, 10304, 15700}, {631, 3544, 5068}, {632, 14269, 15691}, {3091, 15699, 14893}, {3146, 12812, 3628}, {3146, 5056, 5067}, {3543, 15700, 15686}, {3543, 5068, 3545}, {3545, 15702, 3091}, {3545, 5056, 381}, {3545, 5071, 3832}, {3628, 3850, 3853}, {3832, 15719, 3830}, {3832, 5067, 15696}, {3845, 11539, 11001}, {3845, 8703, 3543}, {3851, 12812, 3861}, {3860, 10109, 2}, {3860, 15759, 12101}, {5066, 11540, 3856}, {5072, 15696, 3851}, {10109, 11737, 5066}, {10109, 11812, 547}, {11001, 11539, 12100}, {11001, 15719, 10304}, {11539, 12100, 11812}, {11541, 15701, 8703}, {11812, 16239, 11540}, {12100, 15695, 15759}, {12101, 15759, 30}, {12811, 16239, 3850}, {14893, 15699, 3530}, {15694, 16371, 15699}, {43207, 43208, 6}

X(61935) = X(2)X(3)∩X(6)X(43308)

Barycentrics    a^4-12*(b^2-c^2)^2+11*a^2*(b^2+c^2) : :
X(61935) = -36*X[2]+13*X[3], -3*X[399]+26*X[15029], -72*X[551]+49*X[58235], -X[944]+24*X[61267], -5*X[1351]+28*X[42785], 13*X[1482]+10*X[4816], -30*X[3763]+7*X[55602], -24*X[3817]+X[8148], 12*X[3818]+11*X[55701], -24*X[4301]+X[58249], -16*X[4746]+39*X[5790], 2*X[5493]+21*X[50807] and many others

X(61935) lies on these lines: {2, 3}, {6, 43308}, {399, 15029}, {551, 58235}, {944, 61267}, {1131, 43797}, {1132, 43798}, {1351, 42785}, {1482, 4816}, {3614, 6767}, {3763, 55602}, {3817, 8148}, {3818, 55701}, {4301, 58249}, {4746, 5790}, {5368, 13881}, {5493, 50807}, {5609, 15046}, {6053, 38724}, {6199, 42270}, {6395, 42273}, {6407, 42268}, {6408, 42269}, {6417, 42277}, {6418, 42274}, {6419, 45384}, {6420, 45385}, {6427, 42265}, {6428, 42262}, {6447, 10576}, {6448, 10577}, {6500, 18538}, {6501, 18762}, {6519, 23261}, {6522, 23251}, {6667, 38637}, {6721, 38635}, {6722, 38634}, {6723, 38633}, {7173, 7373}, {7603, 22332}, {7772, 39601}, {7982, 38176}, {7988, 15178}, {7989, 10222}, {9166, 38627}, {9605, 18584}, {9691, 32785}, {10247, 47745}, {10516, 11482}, {10595, 61260}, {11017, 15043}, {11444, 16982}, {11451, 45958}, {11485, 42581}, {11486, 42580}, {12046, 15045}, {12308, 15027}, {12316, 15605}, {12645, 61262}, {12900, 38638}, {12902, 38795}, {13321, 15056}, {13464, 50804}, {13665, 43880}, {13785, 43879}, {14845, 16625}, {14848, 50958}, {15025, 61574}, {15044, 32609}, {15054, 15088}, {15092, 38664}, {16960, 42690}, {16961, 42691}, {16964, 43305}, {16965, 43304}, {18362, 41940}, {18436, 27355}, {18480, 61265}, {18493, 51515}, {18526, 61269}, {19130, 55724}, {21358, 55588}, {22234, 25561}, {22236, 42918}, {22238, 42919}, {23234, 38628}, {24206, 55580}, {25565, 50957}, {28216, 46931}, {32786, 43320}, {33887, 37475}, {34507, 51174}, {34573, 55624}, {34748, 37714}, {36836, 42915}, {36843, 42914}, {36969, 42593}, {36970, 42592}, {37624, 61268}, {37832, 43776}, {37835, 43775}, {38021, 58240}, {38072, 55718}, {38076, 61276}, {38631, 59377}, {38636, 58421}, {38639, 58430}, {38640, 58429}, {38729, 38790}, {38733, 38751}, {38740, 38744}, {38763, 48680}, {40107, 50963}, {40693, 43774}, {40694, 43773}, {41957, 43790}, {41958, 43789}, {42111, 42166}, {42114, 42163}, {42119, 42590}, {42120, 42591}, {42125, 42598}, {42128, 42599}, {42129, 42162}, {42132, 42159}, {42135, 42950}, {42138, 42951}, {42157, 42997}, {42158, 42996}, {42160, 42957}, {42161, 42956}, {42431, 42611}, {42432, 42610}, {42472, 42815}, {42473, 42816}, {42488, 43372}, {42489, 43373}, {42582, 43881}, {42583, 43882}, {42694, 43645}, {42695, 43646}, {42775, 42913}, {42776, 42912}, {42786, 55629}, {42920, 43104}, {42921, 43101}, {42946, 43781}, {42947, 43782}, {42962, 43771}, {42963, 43772}, {43136, 43620}, {43515, 43559}, {43516, 43558}, {43793, 52046}, {43794, 52045}, {47353, 55708}, {48662, 53093}, {48889, 55684}, {48895, 55641}, {48901, 55620}, {50797, 61286}, {50801, 61258}, {50955, 53858}, {51024, 55611}, {53023, 55595}

X(61935) = inverse of X(46853) in orthocentroidal circle
X(61935) = inverse of X(46853) in Yff hyperbola
X(61935) = complement of X(62061)
X(61935) = pole of line {523, 46853} with respect to the orthocentroidal circle
X(61935) = pole of line {185, 62053} with respect to the Jerabek hyperbola
X(61935) = pole of line {6, 43320} with respect to the Kiepert hyperbola
X(61935) = pole of line {523, 46853} with respect to the Yff hyperbola
X(61935) = pole of line {69, 55700} with respect to the Wallace hyperbola
X(61935) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(264), X(46853)}}, {{A, B, C, X(3854), X(21400)}}, {{A, B, C, X(5054), X(15319)}}, {{A, B, C, X(13599), X(44682)}}, {{A, B, C, X(17505), X(41099)}}, {{A, B, C, X(18550), X(50691)}}
X(61935) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3857, 5076}, {2, 6848, 15711}, {3, 10303, 15707}, {3, 14269, 3146}, {3, 15703, 632}, {3, 3090, 5070}, {3, 5072, 3851}, {3, 5076, 17800}, {3, 546, 3830}, {4, 15686, 382}, {4, 7486, 14890}, {5, 3091, 5079}, {5, 3544, 5072}, {5, 3850, 5071}, {5, 3851, 5055}, {5, 5066, 5056}, {5, 546, 15022}, {20, 10109, 1656}, {20, 10299, 8703}, {20, 140, 15716}, {20, 3830, 5073}, {20, 5068, 3545}, {381, 15699, 15685}, {381, 1656, 20}, {381, 5054, 12101}, {381, 5055, 15701}, {381, 5073, 3843}, {382, 5056, 15703}, {546, 15690, 12102}, {546, 17573, 15700}, {547, 3855, 1657}, {1656, 15688, 16239}, {3090, 11541, 2}, {3090, 12811, 381}, {3090, 15022, 10109}, {3090, 3091, 3627}, {3090, 3544, 5068}, {3090, 5068, 12811}, {3525, 3545, 3091}, {3526, 3850, 14269}, {3627, 12103, 11541}, {3627, 15699, 14869}, {3830, 15694, 15688}, {3832, 15697, 4}, {3845, 7486, 15720}, {3850, 15713, 6831}, {3850, 5071, 3526}, {3851, 15707, 3855}, {3858, 5067, 3534}, {5070, 15689, 140}, {6957, 7486, 3839}, {10109, 12811, 546}, {11812, 17556, 5054}, {12812, 15699, 3090}, {14869, 16239, 3525}, {15685, 15699, 15694}, {15720, 17538, 3}, {15765, 18585, 15640}, {18586, 18587, 15723}, {43308, 43309, 6}

X(61936) = X(1)X(38076)∩X(2)X(3)

Barycentrics    a^4-11*(b^2-c^2)^2+10*a^2*(b^2+c^2) : :
X(61936) = X[1]+6*X[38076], -11*X[2]+4*X[3], X[7]+6*X[38075], X[8]+6*X[38021], 2*X[10]+5*X[30308], X[100]+6*X[38077], 4*X[114]+3*X[41135], -8*X[141]+X[54174], X[144]+6*X[38073], X[145]+6*X[38074], X[147]+6*X[9166], X[148]+6*X[23234] and many others

X(61936) lies on these lines: {1, 38076}, {2, 3}, {6, 41951}, {7, 38075}, {8, 38021}, {10, 30308}, {13, 42111}, {14, 42114}, {17, 41113}, {18, 41112}, {61, 49824}, {62, 49825}, {69, 32893}, {76, 54521}, {83, 54866}, {98, 54639}, {100, 38077}, {114, 41135}, {141, 54174}, {144, 38073}, {145, 38074}, {147, 9166}, {148, 23234}, {153, 59377}, {182, 50956}, {193, 5476}, {262, 60200}, {315, 32885}, {325, 32869}, {355, 51087}, {373, 15305}, {390, 3584}, {395, 42142}, {396, 42139}, {397, 49812}, {398, 49813}, {485, 60300}, {486, 60299}, {515, 61265}, {516, 19876}, {519, 7989}, {542, 51171}, {551, 7988}, {553, 5704}, {597, 33748}, {598, 60102}, {671, 36519}, {946, 50827}, {962, 19875}, {1131, 35814}, {1132, 35815}, {1327, 10577}, {1328, 10576}, {1351, 50985}, {1352, 5032}, {1353, 50954}, {1385, 50799}, {1482, 50830}, {1483, 50797}, {1587, 43342}, {1588, 43343}, {1699, 3828}, {1992, 10516}, {2548, 18362}, {2975, 38078}, {2996, 60192}, {3058, 10588}, {3062, 38094}, {3241, 5587}, {3311, 43341}, {3312, 43340}, {3316, 60296}, {3317, 60295}, {3424, 60239}, {3448, 56567}, {3579, 46930}, {3582, 3600}, {3590, 60314}, {3591, 60313}, {3614, 11238}, {3617, 9955}, {3618, 47353}, {3620, 19130}, {3621, 18493}, {3622, 28204}, {3623, 18357}, {3654, 46933}, {3655, 38140}, {3656, 5818}, {3679, 3817}, {3767, 34571}, {3818, 46267}, {3833, 61740}, {4301, 51066}, {4669, 11522}, {4677, 5734}, {4995, 5225}, {5097, 51178}, {5229, 5298}, {5261, 7741}, {5274, 7951}, {5304, 7753}, {5309, 31415}, {5318, 43874}, {5321, 43873}, {5334, 37832}, {5335, 37835}, {5343, 41101}, {5344, 41100}, {5349, 43107}, {5350, 43100}, {5365, 42964}, {5366, 42965}, {5395, 60175}, {5418, 43257}, {5420, 43256}, {5422, 15052}, {5434, 10589}, {5461, 11177}, {5475, 37689}, {5480, 21356}, {5485, 60331}, {5550, 18492}, {5603, 31145}, {5640, 14831}, {5650, 13570}, {5655, 15081}, {5690, 50806}, {5691, 19883}, {5731, 10171}, {5790, 34631}, {5817, 60984}, {5886, 34627}, {5889, 27355}, {5891, 11002}, {5892, 16261}, {5901, 50818}, {5921, 12007}, {5984, 49102}, {6054, 23514}, {6172, 38150}, {6200, 43508}, {6248, 51238}, {6361, 46931}, {6396, 43507}, {6419, 43377}, {6420, 43376}, {6431, 42571}, {6432, 42570}, {6435, 7585}, {6436, 7586}, {6455, 43505}, {6456, 43506}, {6486, 43516}, {6487, 43515}, {6490, 41965}, {6491, 41966}, {6494, 8976}, {6495, 13951}, {6498, 7583}, {6499, 7584}, {6560, 43382}, {6561, 43383}, {6564, 13941}, {6565, 8972}, {6684, 51074}, {6688, 15072}, {6721, 12117}, {6776, 55709}, {7173, 11237}, {7603, 43448}, {7608, 60632}, {7612, 60650}, {7617, 9740}, {7736, 18584}, {7739, 31404}, {7750, 32897}, {7752, 32836}, {7776, 32872}, {7788, 32834}, {7796, 32892}, {7802, 32883}, {7809, 32828}, {7811, 32827}, {7840, 39663}, {7850, 15589}, {7917, 32886}, {7967, 61269}, {7982, 51072}, {7987, 50862}, {7991, 51069}, {8148, 38081}, {8164, 15170}, {8165, 25639}, {8227, 13607}, {8591, 14639}, {8716, 20112}, {9140, 36518}, {9143, 14644}, {9167, 10723}, {9542, 32785}, {9545, 43614}, {9581, 15933}, {9742, 11163}, {9771, 53141}, {9778, 10172}, {9779, 10175}, {9780, 28194}, {9812, 54447}, {9880, 52695}, {9956, 50810}, {10056, 10591}, {10072, 10590}, {10157, 24473}, {10246, 61267}, {10247, 61260}, {10248, 31423}, {10302, 14484}, {10385, 10896}, {10519, 55589}, {10584, 34697}, {10585, 34746}, {10595, 50798}, {10653, 42919}, {10654, 42918}, {10706, 23515}, {10711, 23513}, {10728, 38069}, {10742, 38084}, {10827, 18220}, {11017, 37481}, {11148, 11184}, {11160, 11178}, {11179, 25565}, {11180, 14561}, {11185, 32837}, {11439, 11695}, {11444, 21969}, {11451, 15030}, {11459, 14845}, {11477, 50990}, {11488, 43104}, {11489, 43101}, {11531, 38098}, {11632, 15092}, {11648, 31400}, {11669, 41895}, {11898, 51182}, {12111, 16226}, {12243, 14692}, {12571, 50865}, {12699, 38083}, {12816, 42151}, {12817, 42150}, {13606, 45035}, {13846, 42270}, {13847, 42273}, {13886, 14226}, {13939, 14241}, {14494, 60625}, {14651, 22566}, {14848, 18358}, {14927, 50983}, {15017, 50889}, {15018, 18451}, {15028, 44870}, {15031, 32829}, {15088, 20126}, {15431, 54012}, {16241, 42103}, {16242, 42106}, {16267, 41120}, {16268, 41119}, {16644, 42107}, {16645, 42110}, {16808, 41944}, {16809, 41943}, {16962, 42159}, {16963, 42162}, {16966, 43466}, {16967, 43465}, {16981, 23039}, {18387, 18390}, {18440, 38079}, {18480, 46934}, {18483, 19877}, {18510, 42604}, {18512, 42605}, {18525, 38022}, {18581, 42897}, {18582, 42896}, {18583, 50974}, {18842, 60336}, {19053, 42262}, {19054, 42265}, {19106, 43468}, {19107, 43467}, {19924, 50964}, {19925, 25055}, {20049, 59388}, {20057, 61256}, {20070, 50821}, {20415, 36318}, {20416, 36320}, {20423, 40330}, {20582, 53023}, {20791, 46847}, {21358, 50959}, {22235, 33606}, {22236, 42776}, {22237, 33607}, {22238, 42775}, {23302, 42474}, {23303, 42475}, {23324, 35260}, {24206, 50967}, {28198, 50807}, {28236, 61271}, {31159, 38037}, {31401, 39563}, {31412, 32788}, {31414, 43880}, {31670, 55598}, {31671, 38082}, {32006, 32870}, {32786, 41946}, {32787, 42561}, {32789, 52666}, {32790, 52667}, {32832, 48913}, {32835, 59634}, {32874, 59635}, {32907, 59401}, {32909, 59402}, {33879, 36987}, {34628, 54445}, {34718, 38034}, {34747, 38155}, {34748, 38138}, {34754, 42512}, {34755, 42513}, {34789, 38104}, {35786, 43559}, {35787, 43558}, {35820, 43255}, {35821, 43254}, {36765, 51482}, {36961, 48311}, {36962, 48312}, {36967, 43869}, {36968, 43870}, {36969, 43364}, {36970, 43365}, {36990, 48310}, {36991, 38093}, {36992, 48313}, {36994, 48314}, {37640, 42098}, {37641, 42095}, {37668, 46951}, {37714, 51071}, {38061, 47357}, {38068, 41869}, {38080, 60884}, {38229, 48657}, {38317, 55700}, {39522, 54434}, {40686, 54211}, {41107, 42580}, {41108, 42581}, {42085, 42955}, {42086, 42954}, {42093, 42687}, {42094, 42686}, {42096, 42500}, {42097, 42501}, {42121, 43481}, {42122, 43474}, {42123, 43473}, {42124, 43482}, {42129, 42804}, {42132, 42803}, {42133, 42915}, {42134, 42914}, {42143, 42974}, {42146, 42975}, {42149, 42973}, {42152, 42972}, {42153, 42494}, {42156, 42495}, {42157, 42694}, {42158, 42695}, {42163, 49947}, {42166, 49948}, {42268, 43512}, {42269, 43511}, {42488, 43479}, {42489, 43480}, {42496, 42816}, {42497, 42815}, {42506, 42993}, {42507, 42992}, {42510, 42813}, {42511, 42814}, {42598, 49862}, {42599, 49861}, {42684, 42940}, {42685, 42941}, {42725, 42784}, {42726, 42783}, {42894, 43232}, {42895, 43233}, {42962, 43555}, {42963, 43554}, {43240, 43419}, {43241, 43418}, {43273, 51537}, {43338, 52046}, {43339, 52045}, {43442, 54581}, {43443, 54580}, {43446, 43495}, {43447, 43496}, {43537, 60282}, {43951, 60643}, {44134, 55958}, {47352, 51023}, {48661, 50809}, {48662, 51176}, {48872, 50984}, {48876, 50963}, {48901, 55619}, {49873, 49907}, {49874, 49908}, {50828, 50863}, {50829, 50873}, {50866, 51086}, {50977, 51211}, {50981, 55616}, {51022, 53094}, {51041, 51488}, {51043, 61522}, {51076, 51118}, {51130, 55722}, {51131, 51163}, {51139, 51167}, {51143, 53097}, {51179, 61545}, {51538, 54169}, {53099, 60228}, {53101, 53104}, {54173, 55586}, {54519, 60100}, {54520, 60278}, {54522, 60250}, {54608, 60647}, {54643, 60285}, {59385, 60986}, {59389, 60999}, {60118, 60637}, {60127, 60639}, {60147, 60646}, {60323, 60648}

X(61936) = midpoint of X(i) and X(j) for these {i,j}: {2, 3832}, {4, 15698}, {381, 15703}, {3845, 14869}
X(61936) = reflection of X(i) in X(j) for these {i,j}: {15698, 3526}, {15702, 15703}, {2, 3090}, {376, 15700}, {3523, 2}, {3528, 15701}, {3857, 5066}, {55616, 50981}
X(61936) = inverse of X(10304) in orthocentroidal circle
X(61936) = inverse of X(10304) in Yff hyperbola
X(61936) = complement of X(62063)
X(61936) = anticomplement of X(15702)
X(61936) = pole of line {523, 10304} with respect to the orthocentroidal circle
X(61936) = pole of line {185, 16981} with respect to the Jerabek hyperbola
X(61936) = pole of line {6, 10304} with respect to the Kiepert hyperbola
X(61936) = pole of line {523, 10304} with respect to the Yff hyperbola
X(61936) = pole of line {69, 15708} with respect to the Wallace hyperbola
X(61936) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(25), X(54521)}}, {{A, B, C, X(68), X(16239)}}, {{A, B, C, X(69), X(15708)}}, {{A, B, C, X(253), X(3524)}}, {{A, B, C, X(264), X(10304)}}, {{A, B, C, X(297), X(54639)}}, {{A, B, C, X(427), X(54866)}}, {{A, B, C, X(458), X(60200)}}, {{A, B, C, X(468), X(60333)}}, {{A, B, C, X(550), X(31363)}}, {{A, B, C, X(1105), X(50692)}}, {{A, B, C, X(1217), X(15704)}}, {{A, B, C, X(1494), X(3523)}}, {{A, B, C, X(1585), X(60300)}}, {{A, B, C, X(1586), X(60299)}}, {{A, B, C, X(3526), X(18855)}}, {{A, B, C, X(3528), X(54763)}}, {{A, B, C, X(3529), X(60121)}}, {{A, B, C, X(3543), X(55958)}}, {{A, B, C, X(3544), X(54660)}}, {{A, B, C, X(3839), X(8797)}}, {{A, B, C, X(3851), X(60618)}}, {{A, B, C, X(3855), X(60122)}}, {{A, B, C, X(4232), X(60331)}}, {{A, B, C, X(4846), X(15686)}}, {{A, B, C, X(5094), X(60102)}}, {{A, B, C, X(6353), X(60192)}}, {{A, B, C, X(7714), X(54643)}}, {{A, B, C, X(8889), X(60175)}}, {{A, B, C, X(10299), X(13599)}}, {{A, B, C, X(10301), X(14484)}}, {{A, B, C, X(10302), X(52288)}}, {{A, B, C, X(11001), X(46455)}}, {{A, B, C, X(11541), X(31361)}}, {{A, B, C, X(11669), X(52290)}}, {{A, B, C, X(13623), X(15688)}}, {{A, B, C, X(14860), X(15022)}}, {{A, B, C, X(15684), X(18850)}}, {{A, B, C, X(15692), X(36889)}}, {{A, B, C, X(15721), X(57822)}}, {{A, B, C, X(16837), X(44803)}}, {{A, B, C, X(31846), X(55861)}}, {{A, B, C, X(35482), X(54498)}}, {{A, B, C, X(50688), X(54923)}}, {{A, B, C, X(52281), X(60632)}}, {{A, B, C, X(52283), X(60239)}}, {{A, B, C, X(52284), X(60336)}}, {{A, B, C, X(52285), X(54519)}}, {{A, B, C, X(55569), X(60295)}}, {{A, B, C, X(55573), X(60296)}}
X(61936) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10304, 10303}, {2, 15022, 5055}, {2, 15705, 140}, {2, 15717, 15709}, {2, 16402, 16052}, {2, 20, 15708}, {2, 30, 3523}, {2, 3091, 3839}, {2, 3522, 5054}, {2, 3543, 15692}, {2, 3545, 3091}, {2, 376, 15721}, {2, 381, 3543}, {2, 3832, 30}, {2, 3845, 15697}, {2, 5055, 7486}, {2, 5068, 3545}, {3, 381, 14893}, {3, 3856, 4}, {4, 15709, 3534}, {4, 3090, 3526}, {4, 3545, 5066}, {4, 376, 15684}, {4, 5, 15022}, {5, 12811, 1656}, {5, 3091, 5056}, {5, 3544, 5068}, {5, 381, 5071}, {5, 3850, 5079}, {5, 3851, 3090}, {5, 6990, 5154}, {30, 15701, 3528}, {30, 15703, 15702}, {30, 3526, 15698}, {30, 5066, 3857}, {140, 11001, 15705}, {140, 14269, 11001}, {376, 15702, 15700}, {376, 3524, 15714}, {376, 5071, 547}, {381, 14093, 14269}, {381, 15694, 15687}, {381, 15723, 3830}, {381, 1656, 15681}, {381, 5079, 15723}, {382, 15718, 15691}, {546, 5054, 15682}, {547, 15687, 15694}, {632, 12101, 15688}, {946, 53620, 50872}, {1352, 5032, 51215}, {1656, 12811, 3855}, {1656, 15681, 10124}, {1656, 3855, 3146}, {1657, 11812, 15710}, {1699, 3828, 34632}, {3090, 15702, 15703}, {3090, 3851, 3832}, {3091, 3543, 381}, {3091, 5055, 15640}, {3524, 3855, 3845}, {3525, 3843, 5059}, {3526, 5072, 3851}, {3534, 5055, 3628}, {3543, 10304, 15683}, {3545, 10109, 3854}, {3830, 15706, 15704}, {3830, 5079, 15699}, {3853, 15713, 15689}, {3858, 5070, 3529}, {3860, 11539, 382}, {3860, 12812, 11539}, {5054, 15686, 15715}, {5054, 17800, 15759}, {5055, 15759, 5067}, {5480, 21356, 51028}, {8227, 50796, 38314}, {8703, 15708, 4220}, {9779, 10175, 59417}, {10124, 11737, 12811}, {10124, 15681, 3524}, {10303, 15640, 10304}, {10303, 15692, 549}, {10304, 15640, 20}, {10304, 15697, 548}, {11001, 14269, 17578}, {11539, 15691, 15718}, {11540, 15704, 15706}, {11540, 15706, 631}, {14561, 25561, 11180}, {14784, 14785, 16239}, {15681, 15714, 376}, {15682, 15715, 15686}, {15683, 17678, 15717}, {15686, 15715, 3522}, {15689, 15713, 10299}, {15699, 15704, 11540}, {15702, 15703, 2}, {15765, 18585, 5073}, {16267, 41120, 42999}, {16268, 41119, 42998}, {16962, 42159, 49827}, {16963, 42162, 49826}, {18586, 18587, 632}, {19875, 50802, 962}, {19883, 50803, 5691}, {19925, 25055, 50864}, {20582, 53023, 54170}, {21358, 50959, 51212}, {38098, 51075, 11531}, {41951, 41952, 6}, {42146, 42975, 43542}, {42149, 42973, 49875}, {42152, 42972, 49876}, {47354, 59373, 5921}, {48310, 50960, 36990}, {51709, 61261, 38074}

X(61937) = X(2)X(3)∩X(17)X(42125)

Barycentrics    a^4-10*(b^2-c^2)^2+9*a^2*(b^2+c^2) : :
X(61937) = -30*X[2]+11*X[3], X[145]+18*X[61260], 18*X[373]+X[18439], -5*X[399]+24*X[38792], -3*X[568]+22*X[27355], 16*X[576]+3*X[51175], -2*X[1385]+21*X[61265], 11*X[1482]+8*X[4701], -5*X[3616]+24*X[61267], 15*X[3653]+4*X[50868], -25*X[3763]+6*X[55603], 10*X[3818]+9*X[55703] and many others

X(61937) lies on these lines: {2, 3}, {17, 42125}, {18, 42128}, {145, 61260}, {373, 18439}, {397, 42111}, {398, 42114}, {399, 38792}, {568, 27355}, {576, 51175}, {1327, 6448}, {1328, 6447}, {1385, 61265}, {1482, 4701}, {3053, 12815}, {3616, 61267}, {3653, 50868}, {3763, 55603}, {3818, 55703}, {4857, 31479}, {5041, 39601}, {5097, 10516}, {5102, 34507}, {5318, 42951}, {5321, 42950}, {5339, 34754}, {5340, 34755}, {5349, 42116}, {5350, 42115}, {5365, 42124}, {5366, 42121}, {5790, 11278}, {5882, 61268}, {5890, 11017}, {6221, 10195}, {6398, 10194}, {6431, 8960}, {6432, 13665}, {6435, 42578}, {6436, 42579}, {6437, 10576}, {6438, 10577}, {6445, 23263}, {6446, 23253}, {6480, 23261}, {6481, 23251}, {6482, 43885}, {6483, 43886}, {6484, 8253}, {6485, 8252}, {6486, 35787}, {6487, 35786}, {6564, 13961}, {6565, 13903}, {7755, 15484}, {7988, 18525}, {7989, 16200}, {8227, 18526}, {9589, 38083}, {9624, 50871}, {9693, 10143}, {9703, 43614}, {9955, 11531}, {10110, 54048}, {10187, 42158}, {10188, 42157}, {10248, 61614}, {10605, 33539}, {10620, 38725}, {10895, 37587}, {11258, 38802}, {11362, 50806}, {11444, 13421}, {11451, 45959}, {11459, 18874}, {11485, 42920}, {11486, 42921}, {11542, 42495}, {11543, 42494}, {11648, 31470}, {12002, 37484}, {12046, 15028}, {12188, 38735}, {12307, 17810}, {12331, 38758}, {12355, 20399}, {12645, 13464}, {13188, 38746}, {13340, 44863}, {13364, 15056}, {13886, 43377}, {13939, 43376}, {14845, 18436}, {14862, 34780}, {15024, 45958}, {15038, 17814}, {15046, 16534}, {15047, 18451}, {15088, 38789}, {15092, 38743}, {15305, 32205}, {16241, 42890}, {16242, 42891}, {16644, 41973}, {16645, 41974}, {16964, 43199}, {16965, 43200}, {18440, 25555}, {18480, 30392}, {18510, 35771}, {18512, 35770}, {18553, 39561}, {18584, 39565}, {19130, 55722}, {19925, 61266}, {20582, 55595}, {20584, 55039}, {23302, 42970}, {23303, 42971}, {23514, 52090}, {24206, 55582}, {25561, 51027}, {25565, 53093}, {31412, 45385}, {31492, 39563}, {32824, 32891}, {32825, 32890}, {33541, 37475}, {34748, 61255}, {36967, 42610}, {36968, 42611}, {36987, 44871}, {36990, 55691}, {37624, 61269}, {37727, 38076}, {37832, 42995}, {37835, 42994}, {38064, 51025}, {38066, 51120}, {38068, 51119}, {38072, 51172}, {38317, 55699}, {38572, 38770}, {38573, 38782}, {41107, 43422}, {41108, 43423}, {41963, 42268}, {41964, 42269}, {42085, 42794}, {42086, 42793}, {42093, 42936}, {42094, 42937}, {42095, 42815}, {42098, 42816}, {42103, 42945}, {42106, 42944}, {42107, 42152}, {42110, 42149}, {42126, 42915}, {42127, 42914}, {42143, 42472}, {42146, 42473}, {42153, 42992}, {42156, 42993}, {42159, 43104}, {42162, 43101}, {42178, 50245}, {42431, 43028}, {42432, 43029}, {42474, 42488}, {42475, 42489}, {42492, 52079}, {42493, 52080}, {42561, 45384}, {42775, 42924}, {42776, 42925}, {42779, 43206}, {42780, 43205}, {42813, 42978}, {42814, 42979}, {42908, 43194}, {42909, 43193}, {42922, 43556}, {42923, 43557}, {43211, 43413}, {43212, 43414}, {43240, 43776}, {43241, 43775}, {43312, 43787}, {43313, 43788}, {43409, 53516}, {43410, 53513}, {43426, 49907}, {43427, 49908}, {43584, 52055}, {47354, 53092}, {47355, 55688}, {48661, 54447}, {48672, 61735}, {48872, 55645}, {48889, 55685}, {48895, 55640}, {48901, 55618}, {48905, 55680}, {48910, 55633}, {51128, 55643}, {51173, 55724}, {51186, 55583}, {51537, 55697}, {53023, 55594}, {54917, 60182}

X(61937) = reflection of X(i) in X(j) for these {i,j}: {15022, 5}
X(61937) = inverse of X(33923) in orthocentroidal circle
X(61937) = inverse of X(33923) in Yff hyperbola
X(61937) = complement of X(62066)
X(61937) = pole of line {523, 33923} with respect to the orthocentroidal circle
X(61937) = pole of line {185, 49133} with respect to the Jerabek hyperbola
X(61937) = pole of line {6, 33923} with respect to the Kiepert hyperbola
X(61937) = pole of line {523, 33923} with respect to the Yff hyperbola
X(61937) = pole of line {69, 55698} with respect to the Wallace hyperbola
X(61937) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(264), X(33923)}}, {{A, B, C, X(265), X(15022)}}, {{A, B, C, X(1105), X(49133)}}, {{A, B, C, X(3519), X(10303)}}, {{A, B, C, X(3521), X(49140)}}, {{A, B, C, X(3526), X(14841)}}, {{A, B, C, X(3544), X(15749)}}, {{A, B, C, X(3857), X(21400)}}, {{A, B, C, X(6662), X(45759)}}, {{A, B, C, X(12100), X(13599)}}, {{A, B, C, X(14861), X(50693)}}, {{A, B, C, X(15685), X(60121)}}, {{A, B, C, X(15694), X(60171)}}, {{A, B, C, X(15697), X(31363)}}, {{A, B, C, X(15717), X(26861)}}, {{A, B, C, X(31846), X(41985)}}, {{A, B, C, X(34567), X(44879)}}, {{A, B, C, X(35479), X(43908)}}
X(61937) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3858, 5073}, {3, 16239, 5054}, {3, 17800, 15690}, {3, 3843, 3543}, {3, 3851, 3850}, {3, 5055, 5067}, {3, 5067, 15723}, {3, 5070, 11539}, {4, 1656, 15720}, {5, 12811, 2}, {5, 14892, 3544}, {5, 30, 15022}, {5, 3091, 5055}, {5, 381, 5079}, {5, 3850, 5056}, {5, 3857, 10109}, {5, 5066, 3090}, {5, 546, 5071}, {20, 12812, 15703}, {140, 12102, 550}, {140, 3845, 5059}, {140, 3850, 3845}, {140, 5055, 1656}, {140, 550, 15717}, {376, 3091, 3856}, {381, 15720, 4}, {381, 1656, 1657}, {381, 3526, 5076}, {381, 5055, 15693}, {546, 5070, 3534}, {547, 3845, 15708}, {550, 5066, 3854}, {631, 3857, 14269}, {632, 17800, 15700}, {632, 3839, 17800}, {1656, 1657, 3526}, {1656, 3851, 381}, {1656, 3858, 15696}, {1656, 5072, 3851}, {2045, 2046, 15699}, {3090, 14891, 5070}, {3090, 3091, 12102}, {3090, 3543, 16239}, {3090, 5066, 3843}, {3091, 15708, 3832}, {3525, 3861, 15681}, {3526, 5076, 15688}, {3533, 15708, 140}, {3533, 5056, 547}, {3534, 5054, 14891}, {3543, 3545, 5066}, {3627, 7486, 15694}, {3628, 3855, 3830}, {3832, 5056, 3533}, {3845, 11737, 3545}, {3845, 15704, 3853}, {3850, 3853, 3858}, {3851, 5068, 5072}, {3857, 10109, 631}, {3859, 15699, 3146}, {3860, 14869, 17578}, {4221, 5071, 6975}, {5067, 11541, 15702}, {6957, 15720, 6866}, {6985, 12103, 15704}, {12101, 13742, 3}, {12102, 15685, 382}, {12102, 15717, 15685}, {12811, 15704, 3091}, {12812, 15694, 6881}, {14813, 14814, 10303}, {14869, 17578, 15689}, {42129, 42919, 42962}, {42132, 42918, 42963}

X(61938) = X(2)X(3)∩X(13)X(49859)

Barycentrics    5*a^4-31*(b^2-c^2)^2+26*a^2*(b^2+c^2) : :
X(61938) = -31*X[2]+12*X[3], 3*X[165]+16*X[51076], 12*X[946]+7*X[51068], 3*X[962]+16*X[51069], 15*X[1699]+4*X[50814], 5*X[3241]+14*X[61256], 25*X[3623]+32*X[61253], 18*X[3817]+X[4677], -2*X[4669]+21*X[7989], 4*X[4745]+15*X[30308], 3*X[5032]+16*X[25561], -20*X[5476]+X[51178] and many others

X(61938) lies on these lines: {2, 3}, {13, 49859}, {14, 49860}, {165, 51076}, {485, 42609}, {486, 42608}, {946, 51068}, {962, 51069}, {1699, 50814}, {3070, 42607}, {3071, 42606}, {3241, 61256}, {3623, 61253}, {3817, 4677}, {4669, 7989}, {4745, 30308}, {5032, 25561}, {5304, 39601}, {5334, 42532}, {5335, 42533}, {5365, 41978}, {5366, 41977}, {5476, 51178}, {5480, 50994}, {5731, 50803}, {7988, 50864}, {8584, 51215}, {9541, 43567}, {9779, 38127}, {10248, 38068}, {11148, 18546}, {11485, 33603}, {11486, 33602}, {11488, 42803}, {11489, 42804}, {13846, 53520}, {13847, 53517}, {14226, 18538}, {14241, 18762}, {14484, 60286}, {16644, 42692}, {16645, 42693}, {16772, 43202}, {16773, 43201}, {16808, 49875}, {16809, 49876}, {16962, 42967}, {16963, 42966}, {18493, 20049}, {18581, 49874}, {18582, 49873}, {19053, 42572}, {19054, 42573}, {19925, 51110}, {23249, 42557}, {23259, 42558}, {23302, 42589}, {23303, 42588}, {25406, 50960}, {31145, 61261}, {31415, 39593}, {31884, 51131}, {32785, 41961}, {32786, 41962}, {34627, 61277}, {35749, 36765}, {36319, 59402}, {36344, 59401}, {37712, 51071}, {37714, 51091}, {37832, 49827}, {37835, 49826}, {38072, 50992}, {38075, 60971}, {38076, 51093}, {41100, 43540}, {41101, 43541}, {41107, 42111}, {41108, 42114}, {41112, 42919}, {41113, 42918}, {41119, 42507}, {41120, 42506}, {41121, 43404}, {41122, 43403}, {41947, 42523}, {41948, 42522}, {42085, 43370}, {42086, 43371}, {42090, 43476}, {42091, 43475}, {42095, 49812}, {42098, 49813}, {42107, 49905}, {42110, 49906}, {42119, 42474}, {42120, 42475}, {42139, 49947}, {42142, 49948}, {42159, 42976}, {42162, 42977}, {42215, 42526}, {42216, 42527}, {42262, 42570}, {42265, 42571}, {42472, 42502}, {42473, 42503}, {42500, 43002}, {42501, 43003}, {42631, 54581}, {42632, 54580}, {42974, 43247}, {42975, 43246}, {42998, 49810}, {42999, 49811}, {43428, 49862}, {43429, 49861}, {49824, 49907}, {49825, 49908}, {50796, 61275}, {50800, 61269}, {50801, 51094}, {50802, 59417}, {50805, 61260}, {50817, 51072}, {50818, 61280}, {50863, 51080}, {50959, 51186}, {50970, 51211}, {50973, 50990}, {50991, 51028}, {51074, 54447}, {51082, 51105}, {51092, 51709}, {51107, 61289}, {51135, 51216}, {51136, 51185}, {51143, 51212}, {51705, 61265}, {54448, 61287}, {54520, 60279}

X(61938) = inverse of X(62094) in orthocentroidal circle
X(61938) = inverse of X(62094) in Yff hyperbola
X(61938) = complement of X(62072)
X(61938) = anticomplement of X(61838)
X(61938) = pole of line {523, 62094} with respect to the orthocentroidal circle
X(61938) = pole of line {6, 62094} with respect to the Kiepert hyperbola
X(61938) = pole of line {523, 62094} with respect to the Yff hyperbola
X(61938) = intersection, other than A, B, C, of circumconics {{A, B, C, X(253), X(12100)}}, {{A, B, C, X(376), X(46455)}}, {{A, B, C, X(1217), X(58203)}}, {{A, B, C, X(11541), X(54838)}}, {{A, B, C, X(18855), X(55863)}}, {{A, B, C, X(52288), X(60286)}}
X(61938) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15682, 15692}, {2, 3146, 12100}, {2, 3534, 15708}, {2, 3832, 15682}, {2, 3845, 20}, {4, 5055, 17678}, {5, 14893, 5055}, {5, 3146, 5056}, {5, 3855, 13735}, {5, 5066, 3830}, {20, 3851, 3091}, {20, 5056, 3628}, {376, 12108, 15705}, {376, 3854, 3839}, {381, 11539, 4}, {381, 15695, 3845}, {381, 5055, 550}, {381, 5056, 10304}, {1656, 12101, 15719}, {1656, 15719, 2}, {1657, 13735, 10303}, {3091, 10304, 381}, {3523, 3530, 6986}, {3523, 3839, 3543}, {3545, 11737, 5068}, {3545, 5071, 3851}, {3628, 3853, 15712}, {3830, 11001, 3146}, {3830, 12100, 11001}, {3830, 15703, 15693}, {3851, 14892, 5071}, {3860, 10109, 12108}, {5055, 14893, 3525}, {5072, 11737, 3545}, {6940, 6954, 5094}, {10124, 15712, 5054}, {10304, 11001, 15697}, {11001, 15698, 15695}, {11812, 12811, 5066}, {12101, 15719, 15683}, {12102, 15699, 15718}, {15692, 17678, 15721}, {15705, 15721, 3523}

X(61939) = X(2)X(3)∩X(302)X(33608)

Barycentrics    4*a^4-23*(b^2-c^2)^2+19*a^2*(b^2+c^2) : :
X(61939) = -23*X[2]+9*X[3], 9*X[355]+5*X[51097], 4*X[946]+3*X[38081], -9*X[1483]+16*X[51107], -X[3654]+15*X[61264], 4*X[3656]+3*X[59400], -15*X[3817]+X[51077], X[4669]+6*X[9955], -X[4677]+15*X[61261], 4*X[4745]+3*X[22791], -9*X[5476]+2*X[41149], 9*X[5480]+5*X[51142] and many others

X(61939) lies on these lines: {2, 3}, {302, 33608}, {303, 33609}, {355, 51097}, {397, 49904}, {398, 49903}, {516, 50826}, {524, 42785}, {946, 38081}, {1483, 51107}, {1503, 51181}, {3654, 61264}, {3656, 59400}, {3817, 51077}, {4669, 9955}, {4677, 61261}, {4745, 22791}, {5306, 39601}, {5476, 41149}, {5480, 51142}, {5587, 50804}, {6441, 51849}, {6442, 51850}, {6445, 43522}, {6446, 43521}, {7988, 50799}, {8584, 25561}, {10172, 50825}, {10283, 50796}, {10516, 50961}, {10576, 42417}, {10577, 42418}, {11230, 50803}, {11542, 41120}, {11543, 41119}, {12571, 38083}, {12816, 23303}, {12817, 23302}, {14831, 18874}, {14853, 51174}, {14929, 48913}, {15060, 58470}, {15534, 18358}, {16226, 45958}, {18357, 51093}, {18480, 51108}, {19130, 22165}, {19925, 38022}, {20112, 51123}, {20252, 36363}, {20253, 36362}, {20423, 50989}, {21850, 50991}, {25565, 48906}, {28158, 51088}, {28160, 51078}, {28164, 50833}, {28174, 50807}, {28186, 61265}, {28204, 51106}, {28224, 50800}, {29012, 51133}, {29181, 50981}, {30308, 61263}, {33602, 42962}, {33603, 42963}, {34773, 51109}, {36523, 51872}, {37705, 51071}, {37832, 42916}, {37835, 42917}, {38034, 38176}, {38042, 50802}, {38072, 51188}, {38076, 47745}, {38136, 41152}, {38138, 50801}, {38140, 41150}, {38317, 50960}, {41100, 42138}, {41101, 42135}, {41107, 42110}, {41108, 42107}, {41112, 42095}, {41113, 42098}, {41148, 49102}, {41153, 50979}, {42101, 42632}, {42102, 42631}, {42103, 42474}, {42106, 42475}, {42111, 43416}, {42114, 43417}, {42125, 49813}, {42128, 49812}, {42129, 49875}, {42132, 49876}, {42136, 43296}, {42137, 43297}, {42139, 42496}, {42142, 42497}, {42143, 49948}, {42146, 49947}, {42225, 42525}, {42226, 42524}, {42263, 43563}, {42264, 43562}, {42268, 43211}, {42269, 43212}, {42274, 42640}, {42277, 42639}, {42431, 42505}, {42432, 42504}, {42472, 42975}, {42473, 42974}, {42500, 43227}, {42501, 43226}, {42503, 61719}, {42532, 43776}, {42533, 43775}, {42598, 42976}, {42599, 42977}, {42791, 43630}, {42792, 43631}, {42918, 49907}, {42919, 49908}, {42950, 43482}, {42951, 43481}, {43228, 43246}, {43229, 43247}, {43771, 49826}, {43772, 49827}, {47354, 51180}, {50811, 61266}, {50871, 61280}, {50959, 51184}, {50980, 51131}, {51029, 55643}, {51094, 61256}, {51105, 61272}, {51110, 61268}, {51132, 51183}, {54448, 61293}

X(61939) = midpoint of X(i) and X(j) for these {i,j}: {4, 15700}, {381, 3090}, {3832, 15703}
X(61939) = reflection of X(i) in X(j) for these {i,j}: {14869, 15703}, {15686, 3528}, {3526, 547}, {8703, 15701}
X(61939) = inverse of X(15695) in orthocentroidal circle
X(61939) = inverse of X(15695) in Yff hyperbola
X(61939) = complement of X(62073)
X(61939) = pole of line {523, 15695} with respect to the orthocentroidal circle
X(61939) = pole of line {6, 15695} with respect to the Kiepert hyperbola
X(61939) = pole of line {523, 15695} with respect to the Yff hyperbola
X(61939) = intersection, other than A, B, C, of circumconics {{A, B, C, X(264), X(15695)}}, {{A, B, C, X(1494), X(19711)}}, {{A, B, C, X(12101), X(55958)}}, {{A, B, C, X(12102), X(54924)}}, {{A, B, C, X(12108), X(15319)}}, {{A, B, C, X(15694), X(46168)}}
X(61939) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11001, 15722}, {2, 15682, 15716}, {2, 15695, 11812}, {2, 15716, 140}, {2, 15759, 15713}, {2, 381, 12101}, {2, 3830, 15759}, {2, 4, 15695}, {2, 6959, 3857}, {4, 13735, 3}, {5, 11539, 5071}, {5, 15687, 5055}, {5, 15704, 5056}, {5, 15712, 5079}, {5, 381, 15699}, {5, 3850, 632}, {5, 8703, 10109}, {20, 3524, 14093}, {20, 5068, 3544}, {30, 15703, 14869}, {30, 3528, 15686}, {30, 547, 3526}, {140, 15682, 8703}, {381, 15721, 14893}, {381, 3090, 30}, {381, 3524, 3861}, {381, 3545, 12811}, {381, 5055, 20}, {381, 5071, 14891}, {381, 5073, 3839}, {381, 8703, 3845}, {547, 3861, 3524}, {550, 3845, 3830}, {1656, 11001, 11540}, {3090, 3523, 5070}, {3090, 3857, 3627}, {3526, 3851, 3091}, {3544, 3850, 5}, {3545, 5072, 11737}, {3627, 15699, 549}, {3830, 15713, 550}, {3850, 5055, 15687}, {3856, 5079, 15712}, {3859, 10124, 14269}, {5056, 14269, 10124}, {5066, 12100, 3850}, {5070, 14891, 11539}, {6926, 11001, 15690}, {6952, 15693, 3860}, {10109, 12101, 2}, {10109, 12811, 5066}, {10124, 14269, 15704}, {11001, 11540, 17504}, {11540, 14893, 11001}, {11737, 12811, 14892}, {11737, 14892, 5068}, {12811, 14892, 381}, {15702, 15710, 3523}

X(61940) = X(2)X(3)∩X(15)X(43873)

Barycentrics    2*a^4-11*(b^2-c^2)^2+9*a^2*(b^2+c^2) : :
X(61940) = -33*X[2]+13*X[3], -11*X[141]+X[55581], X[389]+4*X[11017], -X[1385]+6*X[61267], X[1482]+9*X[61260], -11*X[3589]+6*X[55700], 3*X[3817]+2*X[61259], 11*X[3818]+9*X[55707], 2*X[4746]+13*X[9955], -11*X[5480]+X[55723], X[5876]+9*X[14845], X[5882]+9*X[38140] and many others

X(61940) lies on these lines: {2, 3}, {15, 43873}, {16, 43874}, {17, 42107}, {18, 42110}, {141, 55581}, {389, 11017}, {397, 16961}, {398, 16960}, {1385, 61267}, {1482, 61260}, {1503, 55702}, {1698, 28216}, {3068, 6494}, {3069, 6495}, {3564, 55714}, {3589, 55700}, {3590, 23273}, {3591, 23267}, {3614, 4857}, {3817, 61259}, {3818, 55707}, {4746, 9955}, {4816, 5844}, {5270, 7173}, {5305, 34571}, {5318, 43198}, {5321, 43197}, {5339, 42114}, {5340, 42111}, {5343, 42132}, {5344, 42129}, {5346, 14075}, {5349, 16966}, {5350, 16967}, {5480, 55723}, {5876, 14845}, {5882, 38140}, {5892, 12046}, {5901, 28236}, {5907, 18874}, {5943, 45958}, {5965, 11803}, {6102, 27355}, {6417, 43377}, {6418, 43376}, {6419, 43409}, {6420, 43410}, {6431, 43341}, {6432, 43340}, {6433, 43516}, {6434, 43515}, {6435, 18538}, {6436, 18762}, {6498, 19117}, {6499, 19116}, {6564, 13993}, {6565, 13925}, {6688, 46852}, {7755, 39601}, {7781, 20112}, {7989, 38034}, {8227, 28224}, {8550, 55712}, {8960, 42270}, {9589, 50807}, {9956, 28228}, {10095, 31834}, {10110, 13421}, {10113, 22250}, {10187, 42137}, {10188, 42136}, {10194, 23251}, {10195, 23261}, {10222, 38076}, {10627, 44863}, {10990, 40685}, {10993, 38141}, {11485, 42776}, {11486, 42775}, {11488, 43649}, {11489, 43644}, {11544, 15079}, {11591, 13451}, {11623, 15092}, {11695, 32137}, {11793, 12002}, {11801, 16534}, {12571, 28232}, {12699, 30315}, {12815, 39590}, {13348, 44871}, {13363, 44870}, {13382, 45959}, {13431, 30531}, {13464, 18357}, {14128, 14449}, {14487, 26861}, {15003, 15067}, {15024, 45957}, {15060, 16881}, {15088, 20417}, {16241, 42908}, {16242, 42909}, {16808, 42628}, {16809, 42627}, {18383, 61606}, {18481, 61265}, {18492, 61266}, {18525, 61270}, {18553, 18583}, {18584, 31406}, {19106, 42948}, {19107, 42949}, {19130, 55719}, {19862, 28190}, {19925, 61269}, {20304, 61598}, {20584, 22051}, {22236, 42512}, {22238, 42513}, {23325, 44762}, {24206, 55586}, {25555, 55709}, {28154, 31253}, {28212, 61264}, {29181, 55619}, {34507, 55717}, {36969, 43635}, {36970, 43634}, {38077, 51525}, {38229, 52090}, {40273, 43174}, {41366, 50718}, {41959, 41963}, {41960, 41964}, {41973, 42581}, {41974, 42580}, {42089, 42889}, {42092, 42888}, {42095, 42921}, {42098, 42920}, {42103, 43238}, {42104, 42773}, {42105, 42774}, {42106, 43239}, {42122, 42794}, {42123, 42793}, {42135, 42152}, {42138, 42149}, {42139, 42988}, {42142, 42989}, {42147, 42979}, {42148, 42978}, {42157, 42682}, {42158, 42683}, {42163, 42777}, {42166, 42778}, {42273, 58866}, {42472, 42999}, {42473, 42998}, {42520, 43426}, {42521, 43427}, {42590, 42942}, {42591, 42943}, {42598, 43417}, {42599, 43416}, {42684, 43196}, {42685, 43195}, {42694, 43245}, {42695, 43244}, {42779, 43774}, {42780, 43773}, {42813, 43101}, {42814, 43104}, {42964, 43199}, {42965, 43200}, {43030, 43206}, {43031, 43205}, {43374, 43520}, {43375, 43519}, {43446, 43465}, {43447, 43466}, {45184, 61607}, {48901, 55613}, {50796, 61278}, {50956, 53093}, {50981, 55620}, {51022, 55681}, {51143, 55588}, {51700, 61268}, {51709, 61255}, {54448, 61295}, {60759, 61605}, {61575, 61600}, {61576, 61599}, {61577, 61604}, {61579, 61602}, {61580, 61601}, {61585, 61603}

X(61940) = midpoint of X(i) and X(j) for these {i,j}: {4, 15712}, {5, 3091}, {632, 3843}, {1656, 3858}, {3627, 15696}, {3845, 15694}, {3859, 12812}
X(61940) = reflection of X(i) in X(j) for these {i,j}: {140, 1656}, {12812, 5}, {14093, 11812}, {15690, 15692}, {15697, 14891}, {15711, 10124}, {3858, 3850}, {3859, 3091}, {546, 3859}, {5076, 3861}, {631, 3628}
X(61940) = inverse of X(62100) in orthocentroidal circle
X(61940) = inverse of X(62100) in Yff hyperbola
X(61940) = complement of X(46853)
X(61940) = X(i)-complementary conjugate of X(j) for these {i, j}: {46851, 10}
X(61940) = pole of line {523, 62100} with respect to the orthocentroidal circle
X(61940) = pole of line {185, 62047} with respect to the Jerabek hyperbola
X(61940) = pole of line {6, 33751} with respect to the Kiepert hyperbola
X(61940) = pole of line {523, 62100} with respect to the Yff hyperbola
X(61940) = pole of line {69, 55694} with respect to the Wallace hyperbola
X(61940) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(265), X(12812)}}, {{A, B, C, X(3519), X(14869)}}, {{A, B, C, X(3522), X(46455)}}, {{A, B, C, X(6662), X(10304)}}, {{A, B, C, X(10109), X(40448)}}, {{A, B, C, X(11539), X(60171)}}, {{A, B, C, X(12100), X(26861)}}, {{A, B, C, X(13599), X(15693)}}, {{A, B, C, X(14487), X(26863)}}, {{A, B, C, X(14536), X(35489)}}, {{A, B, C, X(14841), X(15694)}}, {{A, B, C, X(14860), X(35018)}}, {{A, B, C, X(14861), X(44245)}}, {{A, B, C, X(14938), X(44904)}}, {{A, B, C, X(19710), X(60121)}}
X(61940) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3857, 3861}, {2, 3861, 12103}, {2, 6834, 15716}, {3, 3856, 14893}, {3, 5, 10109}, {4, 1656, 15712}, {5, 15699, 15022}, {5, 30, 12812}, {5, 3545, 12811}, {5, 3627, 5055}, {5, 381, 3628}, {5, 3845, 3090}, {5, 3857, 2}, {5, 5072, 11737}, {5, 546, 547}, {5, 549, 5079}, {5, 550, 5056}, {5, 632, 5071}, {30, 10124, 15711}, {30, 11812, 14093}, {30, 14891, 15697}, {30, 15692, 15690}, {30, 1656, 140}, {30, 3091, 3859}, {30, 3628, 631}, {30, 3861, 5076}, {140, 12812, 1656}, {140, 3850, 546}, {140, 3853, 550}, {140, 5066, 3850}, {140, 5068, 14892}, {140, 550, 12100}, {381, 10304, 3845}, {381, 3628, 3853}, {381, 5055, 11001}, {381, 5071, 15714}, {382, 15022, 15699}, {382, 15699, 12108}, {546, 547, 548}, {546, 548, 12101}, {549, 3832, 12102}, {631, 3091, 381}, {631, 3146, 15695}, {1012, 5067, 376}, {1656, 1657, 15694}, {1656, 3091, 3858}, {1656, 3522, 632}, {1656, 3843, 3522}, {1656, 3851, 3091}, {1656, 3858, 30}, {2045, 2046, 15703}, {3090, 3845, 3530}, {3091, 5071, 3843}, {3091, 5076, 3857}, {3545, 11737, 5066}, {3545, 5068, 3851}, {3627, 15713, 15696}, {3627, 3855, 3860}, {3627, 5055, 16239}, {3832, 5079, 549}, {3839, 5070, 15704}, {3850, 3856, 3854}, {3851, 5072, 5068}, {3855, 5055, 3627}, {3856, 10109, 3}, {3858, 15712, 4}, {5056, 5068, 3544}, {5067, 12103, 6989}, {5070, 15704, 11812}, {5876, 14845, 58531}, {9955, 61262, 61510}, {11737, 12811, 5}, {12100, 15691, 10304}, {14813, 14814, 14869}, {18586, 18587, 15709}

X(61941) = X(2)X(3)∩X(114)X(41147)

Barycentrics    5*a^4-22*(b^2-c^2)^2+17*a^2*(b^2+c^2) : :
X(61941) = -22*X[2]+9*X[3], 9*X[114]+4*X[41147], 11*X[599]+2*X[55723], 9*X[946]+4*X[51070], 9*X[1352]+4*X[41149], X[1482]+12*X[38076], 5*X[3241]+8*X[61253], -55*X[3763]+16*X[55609], 12*X[3817]+X[50798], -2*X[4669]+15*X[61261], X[4677]+12*X[9955], 3*X[5050]+10*X[50956] and many others

X(61941) lies on circumconic {{A, B, C, X(264), X(15690)}} and on these lines: {2, 3}, {114, 41147}, {371, 42526}, {372, 42527}, {395, 42962}, {396, 42963}, {397, 49859}, {398, 49860}, {597, 49945}, {599, 55723}, {946, 51070}, {1352, 41149}, {1482, 38076}, {3241, 61253}, {3763, 55609}, {3817, 50798}, {4669, 61261}, {4677, 9955}, {5050, 50956}, {5093, 51178}, {5339, 42976}, {5340, 42977}, {5476, 50954}, {5480, 41152}, {5587, 50805}, {5790, 30308}, {5886, 50800}, {6417, 42571}, {6418, 42570}, {6427, 41952}, {6428, 41951}, {6435, 13785}, {6436, 13665}, {7989, 34718}, {8148, 51072}, {10171, 51078}, {10175, 50807}, {10246, 50799}, {10516, 50962}, {11178, 50989}, {11542, 49873}, {11543, 49874}, {11648, 18584}, {11898, 38072}, {12331, 38077}, {12355, 36519}, {12645, 38021}, {12702, 51069}, {12816, 42951}, {12817, 42950}, {14075, 15484}, {14561, 50957}, {14848, 55714}, {14853, 51175}, {14926, 33586}, {15533, 19130}, {15534, 25561}, {16808, 49906}, {16809, 49905}, {18440, 51185}, {18480, 51110}, {18493, 51093}, {18510, 42573}, {18512, 42572}, {18525, 51105}, {18526, 51103}, {19925, 41150}, {20112, 51122}, {20252, 36344}, {20253, 36319}, {21850, 50994}, {22791, 51068}, {23267, 42640}, {23273, 42639}, {26446, 51074}, {31467, 39563}, {32789, 43504}, {32790, 43503}, {33416, 54480}, {33417, 54479}, {33878, 51143}, {34627, 61281}, {34748, 61246}, {35786, 42569}, {35787, 42568}, {37640, 43246}, {37641, 43247}, {37712, 50797}, {38075, 60922}, {38079, 48662}, {38083, 48661}, {38084, 38756}, {38127, 50802}, {41100, 42129}, {41101, 42132}, {41107, 42095}, {41108, 42098}, {41112, 42110}, {41113, 42107}, {41121, 42918}, {41122, 42919}, {41943, 42509}, {41944, 42508}, {42093, 43645}, {42094, 43646}, {42096, 43476}, {42097, 43475}, {42111, 42693}, {42114, 42692}, {42121, 42588}, {42124, 42589}, {42125, 49947}, {42128, 49948}, {42135, 49876}, {42138, 49875}, {42143, 42420}, {42146, 42419}, {42163, 42502}, {42166, 42503}, {42268, 42417}, {42269, 42418}, {42274, 53517}, {42277, 53520}, {42510, 43101}, {42511, 43104}, {42566, 43563}, {42567, 43562}, {42627, 43541}, {42628, 43540}, {42631, 43028}, {42632, 43029}, {42694, 42947}, {42695, 42946}, {42815, 43229}, {42816, 43228}, {42817, 49907}, {42818, 49908}, {42910, 43874}, {42911, 43873}, {42914, 46334}, {42915, 46335}, {43273, 55700}, {43416, 49861}, {43417, 49862}, {44456, 50990}, {47352, 55702}, {50796, 51107}, {50806, 51067}, {50821, 61264}, {50864, 61269}, {50963, 51142}, {50964, 50970}, {50973, 51173}, {51022, 55682}, {51071, 61244}, {51104, 61277}, {51108, 61268}, {51133, 51135}, {51186, 55586}, {51705, 61266}, {53023, 55589}, {54131, 55581}, {58230, 61267}

X(61941) = midpoint of X(i) and X(j) for these {i,j}: {381, 5079}
X(61941) = inverse of X(15690) in orthocentroidal circle
X(61941) = inverse of X(15690) in Yff hyperbola
X(61941) = complement of X(62077)
X(61941) = pole of line {523, 15690} with respect to the orthocentroidal circle
X(61941) = pole of line {6, 15690} with respect to the Kiepert hyperbola
X(61941) = pole of line {523, 15690} with respect to the Yff hyperbola
X(61941) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12101, 15695}, {2, 15682, 15711}, {2, 15690, 15701}, {2, 3845, 15685}, {2, 3860, 3830}, {2, 4, 15690}, {3, 11540, 13632}, {5, 12108, 5056}, {5, 3839, 15703}, {5, 3854, 3}, {5, 3860, 2}, {140, 3845, 15640}, {376, 3839, 12102}, {381, 15688, 3843}, {381, 15693, 3845}, {381, 1657, 3839}, {381, 3526, 14269}, {381, 3545, 5072}, {381, 5079, 30}, {382, 15693, 3534}, {382, 5055, 15723}, {547, 3843, 15688}, {1657, 12102, 382}, {1657, 15703, 5054}, {3091, 11737, 5055}, {3091, 3544, 15704}, {3091, 3545, 11737}, {3091, 5055, 381}, {3091, 5059, 3855}, {3091, 5068, 5067}, {3146, 15708, 376}, {3543, 16417, 3524}, {3543, 5070, 15706}, {3830, 12100, 1657}, {3830, 15703, 12100}, {3832, 15699, 15684}, {3845, 5066, 3091}, {3859, 15022, 5073}, {5054, 15716, 15722}, {5055, 14269, 15708}, {5055, 15723, 1656}, {5071, 14269, 3526}, {5072, 14093, 14892}, {10124, 14892, 5}, {14269, 15718, 3146}, {15684, 15699, 15720}, {15693, 15759, 15716}, {15695, 15701, 6908}, {15701, 17504, 15693}, {49945, 49946, 597}

X(61942) = X(2)X(3)∩X(13)X(42778)

Barycentrics    4*a^4-17*(b^2-c^2)^2+13*a^2*(b^2+c^2) : :
X(61942) = -17*X[2]+7*X[3], X[182]+4*X[50960], 4*X[355]+X[50831], -4*X[551]+9*X[61270], 4*X[946]+X[50823], 4*X[1351]+X[51183], 4*X[1352]+X[50986], X[1353]+4*X[47354], X[1385]+4*X[50803], X[1483]+4*X[50796], 2*X[3241]+3*X[61251], X[3625]+14*X[9955] and many others

X(61942) lies on these lines: {2, 3}, {13, 42778}, {14, 42777}, {182, 50960}, {355, 50831}, {395, 42922}, {396, 42923}, {397, 42521}, {398, 42520}, {551, 61270}, {946, 50823}, {1351, 51183}, {1352, 50986}, {1353, 47354}, {1385, 50803}, {1483, 50796}, {3241, 61251}, {3625, 9955}, {3630, 19130}, {3633, 18357}, {3655, 61269}, {3656, 61259}, {3679, 61262}, {3817, 38138}, {3818, 38079}, {3828, 28232}, {4668, 30308}, {5318, 43241}, {5321, 43240}, {5346, 18362}, {5476, 32455}, {5480, 50978}, {5587, 16191}, {5690, 50802}, {5818, 50806}, {5876, 58470}, {5965, 25561}, {6144, 18358}, {6684, 51076}, {8227, 50799}, {9779, 34718}, {10283, 28236}, {10575, 12046}, {10595, 50797}, {10653, 42917}, {10654, 42916}, {11178, 38136}, {11645, 50987}, {12571, 50821}, {12816, 16773}, {12817, 16772}, {13364, 14831}, {13570, 54042}, {14128, 21969}, {16226, 45959}, {16241, 43630}, {16242, 43631}, {16267, 43246}, {16268, 43247}, {16960, 42107}, {16961, 42110}, {16966, 42682}, {16967, 42683}, {18480, 38022}, {18482, 38082}, {18483, 38083}, {18907, 39601}, {19106, 42493}, {19107, 42492}, {19875, 40273}, {19883, 51078}, {19924, 51129}, {19925, 50824}, {20053, 38074}, {21358, 50964}, {22235, 43207}, {22237, 43208}, {22566, 38229}, {22681, 44562}, {23251, 43212}, {23261, 43211}, {25565, 38110}, {27355, 45958}, {28174, 61264}, {28186, 61266}, {28198, 51074}, {28208, 50832}, {28228, 38042}, {28234, 38034}, {31162, 38112}, {34627, 61283}, {34628, 61265}, {34648, 38028}, {34747, 61257}, {34748, 54448}, {35822, 41951}, {35823, 41952}, {37832, 42135}, {37835, 42138}, {38073, 60976}, {38075, 60977}, {38077, 61580}, {38080, 60901}, {38314, 50800}, {40330, 50963}, {41107, 42436}, {41108, 42435}, {41112, 42519}, {41113, 42518}, {41121, 42163}, {41122, 42166}, {41152, 55721}, {41943, 41971}, {41944, 41972}, {41945, 41967}, {41946, 41968}, {41969, 42582}, {41970, 42583}, {42085, 42474}, {42086, 42475}, {42087, 43472}, {42088, 43471}, {42095, 43416}, {42098, 43417}, {42111, 42513}, {42114, 42512}, {42125, 42496}, {42126, 43639}, {42127, 43640}, {42128, 42497}, {42143, 42634}, {42144, 42929}, {42145, 42928}, {42146, 42633}, {42262, 43434}, {42265, 43435}, {42268, 52047}, {42269, 52048}, {42494, 49873}, {42495, 49874}, {42580, 43550}, {42581, 43551}, {42598, 42802}, {42599, 42801}, {42727, 43628}, {42728, 43629}, {42914, 42941}, {42915, 42940}, {42919, 61719}, {42920, 49947}, {42921, 49948}, {42988, 49824}, {42989, 49825}, {43105, 43483}, {43106, 43484}, {46267, 48906}, {47352, 51181}, {47617, 51123}, {48310, 48889}, {48874, 50981}, {48876, 50959}, {48898, 50988}, {48904, 50984}, {50864, 51700}, {50871, 61281}, {50957, 59373}, {51022, 58445}, {51023, 51732}, {51041, 51046}, {51093, 61255}, {51097, 61248}, {54890, 60279}, {56567, 61574}, {59387, 61273}, {60286, 60329}

X(61942) = midpoint of X(i) and X(j) for these {i,j}: {2, 3843}, {4, 15693}, {381, 5071}, {632, 3845}, {3522, 3830}, {5818, 50806}, {8227, 50799}, {10595, 50797}, {15687, 15714}, {15695, 17578}, {30308, 61261}, {40330, 50963}, {51097, 61248}
X(61942) = reflection of X(i) in X(j) for these {i,j}: {15686, 14093}, {15694, 547}, {15696, 12100}, {15704, 15697}, {15711, 632}, {15712, 2}, {15713, 1656}, {15714, 15694}, {2, 12812}, {3091, 5066}, {3845, 3858}, {550, 15711}, {8703, 631}
X(61942) = inverse of X(15689) in orthocentroidal circle
X(61942) = inverse of X(15689) in Yff hyperbola
X(61942) = complement of X(14093)
X(61942) = pole of line {523, 15689} with respect to the orthocentroidal circle
X(61942) = pole of line {6, 15689} with respect to the Kiepert hyperbola
X(61942) = pole of line {523, 15689} with respect to the Yff hyperbola
X(61942) = pole of line {69, 51141} with respect to the Wallace hyperbola
X(61942) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(95), X(14890)}}, {{A, B, C, X(264), X(15689)}}, {{A, B, C, X(1494), X(15712)}}, {{A, B, C, X(12103), X(60121)}}, {{A, B, C, X(14893), X(55958)}}, {{A, B, C, X(45759), X(57896)}}
X(61942) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12108, 11539}, {2, 15689, 12108}, {2, 15706, 140}, {2, 3, 14890}, {2, 30, 15712}, {2, 3545, 5072}, {2, 381, 14893}, {2, 4, 15689}, {2, 5072, 14892}, {5, 11539, 10109}, {5, 14869, 5056}, {5, 15687, 547}, {5, 3845, 15699}, {5, 8703, 5055}, {30, 12100, 15696}, {30, 15697, 15704}, {30, 15711, 550}, {30, 1656, 15713}, {30, 3858, 3845}, {30, 5066, 3091}, {30, 547, 15694}, {30, 631, 8703}, {30, 632, 15711}, {140, 3544, 5}, {381, 15681, 3839}, {381, 15703, 4}, {381, 15723, 14269}, {381, 3543, 546}, {381, 3545, 11737}, {381, 5055, 3543}, {546, 10109, 15705}, {546, 3628, 11541}, {631, 11541, 3522}, {631, 15705, 15693}, {632, 3091, 3857}, {1656, 3091, 3859}, {1656, 3843, 17538}, {1657, 5055, 2}, {3090, 15683, 15723}, {3091, 3522, 3855}, {3091, 3544, 5076}, {3091, 3843, 3850}, {3091, 5071, 381}, {3091, 5072, 12812}, {3523, 7486, 16863}, {3545, 3851, 5066}, {3627, 3858, 3843}, {3628, 15691, 15702}, {3830, 15685, 13633}, {3830, 15702, 15691}, {3832, 5054, 12101}, {3850, 14890, 3860}, {3850, 15712, 3858}, {3854, 5079, 3853}, {3861, 5056, 14869}, {5066, 12811, 3545}, {5067, 15688, 11540}, {5071, 15692, 1656}, {5079, 15681, 17528}, {10124, 14893, 1657}, {14093, 14891, 15714}, {14269, 15723, 15683}, {14891, 14893, 15684}, {14891, 15684, 15686}, {14893, 15684, 15687}, {14893, 15686, 3627}, {15683, 15723, 12100}, {15684, 15694, 14093}, {15687, 15714, 30}, {15689, 15721, 14891}, {15691, 15702, 17504}, {15692, 15713, 549}, {15693, 15694, 15721}, {15694, 15700, 631}, {15699, 15711, 632}, {15703, 15705, 10124}, {18586, 18587, 10303}, {19875, 50807, 40273}, {38034, 61260, 59400}, {48310, 51133, 48889}

X(61943) = X(2)X(3)∩X(13)X(49810)

Barycentrics    7*a^4-29*(b^2-c^2)^2+22*a^2*(b^2+c^2) : :
X(61943) = -29*X[2]+12*X[3], X[193]+16*X[25561], 12*X[355]+5*X[51092], 12*X[946]+5*X[51072], 9*X[1699]+8*X[51069], 7*X[3241]+10*X[61250], 12*X[3576]+5*X[50863], 15*X[3817]+2*X[50801], 2*X[4669]+15*X[30308], -X[4677]+18*X[38076], -4*X[4745]+21*X[7989], 3*X[5085]+14*X[51133] and many others

X(61943) lies on these lines: {2, 3}, {13, 49810}, {14, 49811}, {193, 25561}, {355, 51092}, {946, 51072}, {1327, 13941}, {1328, 8972}, {1699, 51069}, {3241, 61250}, {3424, 60287}, {3576, 50863}, {3817, 50801}, {4669, 30308}, {4677, 38076}, {4745, 7989}, {5085, 51133}, {5304, 18362}, {5334, 49907}, {5335, 49908}, {5365, 41943}, {5366, 41944}, {5476, 51215}, {5480, 50990}, {5587, 51077}, {5603, 50804}, {5657, 50807}, {6451, 54543}, {6452, 54542}, {7752, 32896}, {7773, 32893}, {7917, 46951}, {7967, 50800}, {7988, 50803}, {8596, 61575}, {9779, 50872}, {9812, 51074}, {9955, 31145}, {10164, 50873}, {10516, 50992}, {10519, 50964}, {11148, 20112}, {11160, 19130}, {12571, 34632}, {12816, 42910}, {12817, 42911}, {14484, 60638}, {14853, 50961}, {14912, 50957}, {15031, 32837}, {15534, 50958}, {15589, 48913}, {16808, 42977}, {16809, 42976}, {18357, 20049}, {18581, 43233}, {18582, 43232}, {19925, 51105}, {21167, 51029}, {22165, 51130}, {22237, 61719}, {28198, 46932}, {33416, 43475}, {33417, 43476}, {33604, 43306}, {33605, 43307}, {33748, 47353}, {34627, 61284}, {34631, 61259}, {35255, 43522}, {35256, 43521}, {35750, 36765}, {36318, 59401}, {36320, 59402}, {37689, 39601}, {37712, 51095}, {37714, 51096}, {37832, 43541}, {37835, 43540}, {38021, 47745}, {38140, 61279}, {38150, 60971}, {41100, 42111}, {41101, 42114}, {41112, 49904}, {41113, 49903}, {41119, 42919}, {41120, 42918}, {41121, 49873}, {41122, 49874}, {42085, 42932}, {42086, 42933}, {42089, 54581}, {42092, 54580}, {42095, 43771}, {42098, 43772}, {42107, 49947}, {42110, 49948}, {42119, 42957}, {42120, 42956}, {42129, 43777}, {42132, 43778}, {42139, 43228}, {42142, 43229}, {42159, 42532}, {42160, 43311}, {42161, 43310}, {42162, 42533}, {42472, 49813}, {42473, 49812}, {42494, 42502}, {42495, 42503}, {42506, 42999}, {42507, 42998}, {42512, 44016}, {42513, 44015}, {42920, 49860}, {42921, 49859}, {42950, 43493}, {42951, 43494}, {42984, 43630}, {42985, 43631}, {43100, 43769}, {43101, 43304}, {43104, 43305}, {43107, 43770}, {43246, 43542}, {43247, 43543}, {43364, 43373}, {43365, 43372}, {43507, 53131}, {43508, 53130}, {43566, 60298}, {43567, 60297}, {50796, 61291}, {50802, 51066}, {50806, 61262}, {50810, 61263}, {50828, 61265}, {50864, 51110}, {50959, 50993}, {50994, 51028}, {51129, 51538}, {51143, 53023}, {51186, 51212}, {51709, 54448}, {54519, 60645}, {54520, 60131}

X(61943) = inverse of X(15697) in orthocentroidal circle
X(61943) = inverse of X(15697) in Yff hyperbola
X(61943) = anticomplement of X(61833)
X(61943) = pole of line {523, 15697} with respect to the orthocentroidal circle
X(61943) = pole of line {6, 15697} with respect to the Kiepert hyperbola
X(61943) = pole of line {523, 15697} with respect to the Yff hyperbola
X(61943) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(68), X(45760)}}, {{A, B, C, X(253), X(15698)}}, {{A, B, C, X(264), X(15697)}}, {{A, B, C, X(15715), X(46455)}}, {{A, B, C, X(16837), X(44962)}}, {{A, B, C, X(31363), X(33923)}}, {{A, B, C, X(49138), X(54838)}}, {{A, B, C, X(52283), X(60287)}}, {{A, B, C, X(52288), X(60638)}}
X(61943) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11001, 3523}, {2, 15640, 15692}, {2, 15683, 15693}, {2, 15697, 15708}, {2, 3146, 15698}, {2, 3522, 11812}, {2, 3830, 10304}, {2, 3832, 3830}, {2, 3839, 15640}, {2, 4, 15697}, {2, 5066, 3091}, {2, 8703, 15721}, {4, 14890, 15683}, {4, 3545, 11737}, {5, 10303, 5056}, {5, 381, 3524}, {5, 3850, 5076}, {20, 381, 3839}, {140, 3627, 15696}, {381, 12811, 3545}, {381, 14892, 3090}, {381, 15699, 4}, {381, 15701, 3845}, {381, 3545, 5068}, {381, 5055, 3627}, {3091, 3523, 3855}, {3091, 7486, 3854}, {3522, 14269, 3543}, {3524, 15682, 3534}, {3533, 3544, 5}, {3534, 12101, 15682}, {3534, 15694, 12100}, {3543, 10304, 3529}, {3543, 8703, 6890}, {3544, 3854, 7486}, {3545, 5071, 5072}, {3627, 15716, 11001}, {3845, 10109, 15701}, {3855, 11001, 3860}, {3855, 15696, 3832}, {5067, 15687, 15705}, {5079, 14893, 15709}, {8703, 12101, 5073}, {10109, 12100, 15699}, {10109, 15682, 2}, {12100, 16239, 15713}, {14893, 15709, 5059}, {15685, 15697, 20}, {15686, 15699, 140}, {15694, 15708, 10303}

X(61944) = X(2)X(3)∩X(8)X(30308)

Barycentrics    5*a^4-19*(b^2-c^2)^2+14*a^2*(b^2+c^2) : :
X(61944) = -19*X[2]+8*X[3], X[8]+10*X[30308], X[40]+10*X[51074], -X[144]+12*X[38075], -X[145]+12*X[38021], -X[149]+12*X[38077], -X[193]+12*X[38072], -10*X[551]+21*X[61271], X[944]+10*X[50799], 10*X[946]+X[50817], X[1350]+10*X[51129], 10*X[1352]+X[51178] and many others

X(61944) lies on these lines: {2, 3}, {8, 30308}, {17, 49827}, {18, 49826}, {40, 51074}, {61, 43557}, {62, 43556}, {144, 38075}, {145, 38021}, {149, 38077}, {193, 38072}, {262, 60635}, {395, 42473}, {396, 42472}, {551, 61271}, {598, 54921}, {944, 50799}, {946, 50817}, {1131, 32788}, {1132, 32787}, {1327, 60312}, {1328, 60311}, {1350, 51129}, {1352, 51178}, {2996, 54522}, {3068, 53520}, {3069, 53517}, {3241, 3817}, {3424, 60648}, {3614, 10385}, {3621, 9955}, {3623, 51709}, {3679, 9779}, {3828, 9812}, {4301, 51068}, {5032, 47354}, {5309, 14930}, {5334, 43032}, {5335, 43033}, {5339, 49862}, {5340, 49861}, {5343, 16962}, {5344, 16963}, {5365, 42511}, {5366, 42510}, {5476, 51170}, {5480, 50973}, {5587, 31145}, {5603, 20049}, {5818, 50872}, {5891, 16981}, {5901, 50800}, {5984, 9166}, {6361, 38083}, {6459, 6492}, {6460, 6493}, {6490, 41945}, {6491, 41946}, {6564, 42605}, {6565, 42604}, {6776, 50956}, {7583, 14226}, {7584, 14241}, {7773, 32872}, {7809, 32834}, {7871, 32836}, {7988, 34648}, {7989, 50802}, {7998, 13570}, {8227, 50864}, {8252, 43507}, {8253, 43508}, {8591, 36519}, {8596, 14639}, {9143, 36518}, {9466, 44434}, {9543, 23263}, {9692, 10195}, {9778, 19876}, {9956, 50807}, {10171, 34628}, {10175, 34632}, {10248, 50808}, {10513, 46951}, {10516, 11160}, {10595, 61246}, {11177, 23514}, {11465, 46852}, {11488, 42692}, {11489, 42693}, {11668, 54476}, {12245, 50806}, {12248, 38084}, {12571, 19875}, {12818, 43525}, {12819, 43526}, {13464, 51092}, {14484, 60628}, {14644, 56567}, {14853, 25561}, {14927, 48310}, {15031, 32831}, {15056, 21849}, {16192, 50869}, {16267, 42920}, {16268, 42921}, {16772, 42589}, {16773, 42588}, {16808, 42800}, {16809, 42799}, {16966, 43645}, {16967, 43646}, {18357, 20014}, {18483, 46932}, {18492, 46934}, {18493, 61253}, {18583, 50957}, {18845, 54644}, {19053, 41951}, {19054, 41952}, {19116, 43386}, {19117, 43387}, {19130, 20080}, {19883, 51080}, {19925, 38314}, {20059, 38073}, {20060, 38078}, {20094, 23234}, {20582, 51538}, {21356, 50959}, {21358, 50970}, {22235, 42163}, {22237, 42166}, {23249, 42603}, {23259, 42602}, {24206, 50964}, {25055, 50803}, {28194, 46933}, {31162, 38127}, {31400, 39563}, {31412, 42572}, {31417, 39593}, {32767, 54211}, {32816, 32874}, {32819, 32873}, {32823, 32882}, {32828, 48913}, {34627, 38140}, {34631, 38034}, {34718, 61262}, {35369, 61575}, {35786, 43256}, {35787, 43257}, {37640, 42107}, {37641, 42110}, {37832, 44016}, {37835, 44015}, {38079, 39874}, {38092, 42356}, {38150, 60984}, {38259, 54645}, {39663, 44367}, {40330, 51028}, {40693, 49873}, {40694, 49874}, {41121, 42999}, {41122, 42998}, {41869, 46930}, {42093, 43421}, {42094, 43420}, {42099, 43469}, {42100, 43470}, {42125, 43542}, {42128, 43543}, {42133, 42911}, {42134, 42910}, {42139, 42898}, {42142, 42899}, {42147, 43202}, {42148, 43201}, {42154, 43365}, {42155, 43364}, {42159, 43009}, {42162, 43008}, {42263, 42566}, {42264, 42567}, {42474, 42940}, {42475, 42941}, {42490, 54580}, {42491, 54581}, {42494, 43228}, {42495, 43229}, {42561, 42573}, {42568, 43385}, {42569, 43384}, {42633, 42963}, {42634, 42962}, {42775, 49812}, {42776, 49813}, {42813, 49875}, {42814, 49876}, {42900, 43310}, {42901, 43311}, {42918, 43011}, {42919, 43010}, {42982, 43329}, {42983, 43328}, {42988, 43246}, {42989, 43247}, {42990, 49859}, {42991, 49860}, {43248, 43331}, {43249, 43330}, {43250, 43334}, {43251, 43335}, {43254, 43408}, {43255, 43407}, {43440, 54579}, {43441, 54578}, {43473, 43490}, {43474, 43489}, {43477, 43870}, {43478, 43869}, {43548, 43553}, {43549, 43552}, {43681, 54734}, {43951, 60277}, {47352, 50960}, {47353, 51171}, {47586, 60283}, {48873, 51213}, {48889, 51216}, {50796, 61296}, {50818, 61281}, {50975, 58445}, {51026, 55651}, {51067, 58245}, {51091, 61252}, {51136, 59373}, {51173, 61545}, {51176, 51732}, {53108, 60113}, {54445, 61265}, {54815, 60644}, {54851, 60145}, {54920, 60625}, {59387, 61275}, {59417, 61263}, {60118, 60216}, {60147, 60238}, {60328, 60641}, {60331, 60626}, {60335, 60650}

X(61944) = midpoint of X(i) and X(j) for these {i,j}: {4, 15719}
X(61944) = reflection of X(i) in X(j) for these {i,j}: {15715, 15723}, {15717, 2}, {15719, 5070}, {2, 5056}, {376, 15718}
X(61944) = inverse of X(62120) in orthocentroidal circle
X(61944) = inverse of X(62120) in Yff hyperbola
X(61944) = complement of X(62081)
X(61944) = anticomplement of X(15721)
X(61944) = pole of line {523, 62120} with respect to the orthocentroidal circle
X(61944) = pole of line {6, 50971} with respect to the Kiepert hyperbola
X(61944) = pole of line {523, 62120} with respect to the Yff hyperbola
X(61944) = pole of line {69, 50984} with respect to the Wallace hyperbola
X(61944) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(253), X(15705)}}, {{A, B, C, X(458), X(60635)}}, {{A, B, C, X(1217), X(49137)}}, {{A, B, C, X(1494), X(15717)}}, {{A, B, C, X(3524), X(35510)}}, {{A, B, C, X(3530), X(18855)}}, {{A, B, C, X(3627), X(54923)}}, {{A, B, C, X(3843), X(54552)}}, {{A, B, C, X(4846), X(15691)}}, {{A, B, C, X(5094), X(54921)}}, {{A, B, C, X(6353), X(54522)}}, {{A, B, C, X(12100), X(46455)}}, {{A, B, C, X(14860), X(46936)}}, {{A, B, C, X(17538), X(60121)}}, {{A, B, C, X(18850), X(35404)}}, {{A, B, C, X(21735), X(31363)}}, {{A, B, C, X(32533), X(41989)}}, {{A, B, C, X(38282), X(54645)}}, {{A, B, C, X(52283), X(60648)}}, {{A, B, C, X(52288), X(60628)}}, {{A, B, C, X(52299), X(54644)}}, {{A, B, C, X(54763), X(61138)}}
X(61944) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17578, 10304}, {2, 30, 15717}, {2, 3146, 15705}, {2, 3545, 5068}, {2, 3854, 3839}, {4, 15719, 30}, {4, 3090, 3530}, {5, 12100, 5055}, {5, 12102, 1656}, {5, 1657, 3090}, {5, 3091, 3854}, {5, 3858, 12108}, {20, 3091, 3850}, {30, 15723, 15715}, {376, 14893, 3543}, {376, 15702, 12100}, {376, 3146, 15683}, {376, 3525, 15718}, {376, 5054, 15692}, {376, 5071, 15703}, {381, 11737, 5071}, {381, 15684, 546}, {381, 15694, 3845}, {381, 15700, 3843}, {381, 5055, 15687}, {381, 547, 4}, {546, 7486, 5059}, {547, 12103, 10124}, {631, 14269, 15640}, {1656, 15682, 15708}, {1657, 17578, 3146}, {3091, 5056, 3855}, {3091, 5068, 3832}, {3146, 13735, 3523}, {3523, 3839, 3830}, {3543, 15692, 15681}, {3543, 17678, 3522}, {3543, 3839, 14893}, {3545, 5066, 3091}, {3545, 5071, 11737}, {3628, 5072, 6950}, {3830, 5054, 12103}, {3832, 5068, 15022}, {3843, 15699, 11001}, {3843, 6939, 3525}, {3845, 10304, 17578}, {3850, 15687, 381}, {3851, 5066, 3545}, {3855, 5072, 5056}, {3857, 10109, 14269}, {5055, 15687, 15702}, {5070, 15720, 632}, {10109, 14269, 631}, {10109, 15640, 2}, {11001, 15699, 10303}, {11540, 15696, 3524}, {11737, 14893, 5}, {14093, 15723, 15720}, {14893, 15703, 376}, {15681, 15703, 5054}, {15687, 15702, 20}, {15692, 15721, 15719}, {15702, 15720, 15721}, {15703, 15705, 17678}, {15703, 15718, 15723}, {16267, 42920, 49824}, {16268, 42921, 49825}, {18586, 18587, 14869}, {47352, 50960, 51537}

X(61945) = X(2)X(3)∩X(11)X(31410)

Barycentrics    3*a^4-11*(b^2-c^2)^2+8*a^2*(b^2+c^2) : :
X(61945) = -33*X[2]+14*X[3], 11*X[69]+8*X[55719], 3*X[145]+16*X[61255], 3*X[146]+16*X[20396], 18*X[373]+X[12290], 3*X[568]+16*X[11017], 4*X[575]+15*X[50956], 14*X[946]+5*X[4668], X[962]+18*X[61263], 5*X[1352]+14*X[42785], 9*X[1699]+10*X[31399], 3*X[2979]+16*X[44863] and many others

X(61945) lies on these lines: {2, 3}, {11, 31410}, {13, 42495}, {14, 42494}, {61, 42776}, {62, 42775}, {69, 55719}, {115, 31417}, {145, 61255}, {146, 20396}, {325, 32877}, {373, 12290}, {397, 43543}, {398, 43542}, {485, 6435}, {486, 6436}, {568, 11017}, {575, 50956}, {946, 4668}, {962, 61263}, {1007, 15031}, {1056, 37720}, {1058, 37719}, {1131, 18762}, {1132, 18538}, {1285, 39601}, {1329, 31420}, {1352, 42785}, {1699, 31399}, {2979, 44863}, {3085, 9671}, {3086, 9656}, {3316, 23259}, {3317, 23249}, {3411, 42162}, {3412, 42159}, {3614, 9670}, {3617, 61262}, {3618, 55707}, {3619, 55598}, {3625, 5587}, {3630, 10516}, {3633, 5603}, {3635, 3817}, {3767, 14075}, {3818, 55709}, {4114, 9612}, {4297, 61265}, {4301, 4691}, {4309, 10588}, {4317, 10589}, {5225, 31452}, {5254, 31407}, {5318, 43777}, {5319, 34571}, {5321, 43778}, {5343, 42598}, {5344, 42599}, {5349, 43447}, {5350, 43446}, {5365, 16644}, {5366, 16645}, {5550, 61266}, {5657, 12571}, {5734, 9955}, {5735, 61000}, {5817, 60977}, {5890, 27355}, {6053, 14644}, {6144, 14853}, {6409, 43505}, {6410, 43506}, {6427, 43377}, {6428, 43376}, {6449, 43508}, {6450, 43507}, {6470, 43798}, {6471, 43797}, {6484, 43516}, {6485, 43515}, {6494, 31487}, {6561, 9693}, {6564, 13939}, {6565, 13886}, {6704, 55757}, {7173, 9657}, {7581, 42273}, {7582, 42270}, {7603, 31450}, {7612, 18844}, {7689, 10545}, {7738, 18424}, {7765, 31415}, {7796, 52713}, {7967, 9624}, {7982, 38076}, {7989, 11362}, {8148, 61260}, {8164, 10896}, {8166, 10894}, {8797, 54105}, {9588, 18483}, {9589, 10175}, {9606, 43448}, {9607, 31404}, {9681, 32785}, {9711, 31418}, {9741, 47617}, {9779, 12245}, {9781, 14531}, {10155, 53106}, {10187, 46334}, {10188, 46335}, {10248, 11231}, {10590, 37722}, {10591, 15888}, {10653, 42801}, {10654, 42802}, {10895, 47743}, {11381, 11465}, {11439, 61136}, {11455, 11695}, {11477, 51130}, {11488, 42814}, {11489, 42813}, {11522, 38074}, {12111, 14845}, {12816, 42978}, {12817, 42979}, {13172, 52886}, {13464, 61252}, {14226, 60303}, {14241, 60304}, {14561, 33749}, {15024, 44870}, {15028, 16194}, {15057, 46686}, {15063, 15081}, {15069, 32455}, {15072, 46852}, {15178, 50799}, {15480, 39663}, {16772, 42133}, {16773, 42134}, {16808, 42436}, {16809, 42435}, {16964, 42114}, {16965, 42111}, {18435, 18874}, {18436, 58533}, {18489, 45014}, {18493, 54448}, {18553, 50974}, {18581, 42990}, {18582, 42991}, {18584, 31400}, {18841, 60325}, {19130, 55717}, {19877, 31447}, {20050, 61257}, {20125, 36518}, {22235, 42975}, {22237, 42974}, {23253, 42583}, {23263, 42582}, {23267, 42262}, {23273, 42265}, {24206, 55589}, {24817, 52885}, {25555, 51023}, {25561, 50961}, {30308, 34631}, {31425, 51118}, {31492, 53419}, {31670, 55592}, {32786, 35786}, {32815, 32889}, {32816, 32888}, {32817, 32876}, {32818, 32875}, {32823, 32878}, {33604, 41120}, {33605, 41119}, {34089, 35821}, {34091, 35820}, {34627, 61288}, {35770, 42570}, {35771, 42571}, {35812, 42268}, {35813, 42269}, {37640, 42920}, {37641, 42921}, {37727, 38140}, {38021, 50801}, {38072, 50958}, {38077, 38665}, {38079, 51176}, {38083, 50809}, {38150, 60962}, {40107, 55581}, {40273, 46933}, {40693, 42139}, {40694, 42142}, {41943, 43202}, {41944, 43201}, {41963, 43258}, {41964, 43259}, {42087, 42610}, {42088, 42611}, {42093, 43463}, {42094, 43464}, {42101, 42490}, {42102, 42491}, {42107, 42156}, {42110, 42153}, {42119, 42488}, {42120, 42489}, {42121, 43364}, {42124, 43365}, {42125, 42986}, {42128, 42987}, {42140, 42915}, {42141, 42914}, {42149, 43550}, {42152, 43551}, {42163, 43403}, {42166, 43404}, {42283, 43374}, {42284, 43375}, {42532, 43425}, {42533, 43424}, {42910, 43491}, {42911, 43492}, {42924, 43540}, {42925, 43541}, {42928, 43471}, {42929, 43472}, {42938, 44015}, {42939, 44016}, {42946, 43244}, {42947, 43245}, {43101, 43481}, {43104, 43482}, {43386, 53513}, {43387, 53516}, {43444, 54591}, {43445, 54592}, {43485, 43545}, {43486, 43544}, {43517, 52666}, {43518, 52667}, {46932, 48661}, {48901, 55609}, {50818, 61282}, {50990, 55721}, {51177, 55687}, {51212, 55586}, {51537, 55702}, {51538, 55599}, {53103, 53107}, {54523, 60209}, {54616, 54857}, {54707, 60640}, {54890, 60183}, {59386, 60976}, {60143, 60329}, {60146, 60185}, {60322, 60649}

X(61945) = inverse of X(17538) in orthocentroidal circle
X(61945) = inverse of X(17538) in Yff hyperbola
X(61945) = complement of X(62083)
X(61945) = anticomplement of X(61832)
X(61945) = pole of line {523, 17538} with respect to the orthocentroidal circle
X(61945) = pole of line {185, 62042} with respect to the Jerabek hyperbola
X(61945) = pole of line {6, 17538} with respect to the Kiepert hyperbola
X(61945) = pole of line {523, 17538} with respect to the Yff hyperbola
X(61945) = pole of line {69, 55692} with respect to the Wallace hyperbola
X(61945) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(68), X(15694)}}, {{A, B, C, X(264), X(17538)}}, {{A, B, C, X(1217), X(49138)}}, {{A, B, C, X(1585), X(60290)}}, {{A, B, C, X(1586), X(60289)}}, {{A, B, C, X(1597), X(46851)}}, {{A, B, C, X(3521), X(15685)}}, {{A, B, C, X(3523), X(15319)}}, {{A, B, C, X(3524), X(18855)}}, {{A, B, C, X(3528), X(18854)}}, {{A, B, C, X(5067), X(14860)}}, {{A, B, C, X(7378), X(60325)}}, {{A, B, C, X(7408), X(54890)}}, {{A, B, C, X(7409), X(60326)}}, {{A, B, C, X(10155), X(52297)}}, {{A, B, C, X(10304), X(15318)}}, {{A, B, C, X(11001), X(18853)}}, {{A, B, C, X(11541), X(18852)}}, {{A, B, C, X(15077), X(55857)}}, {{A, B, C, X(15688), X(15740)}}, {{A, B, C, X(15692), X(54763)}}, {{A, B, C, X(16837), X(44960)}}, {{A, B, C, X(18844), X(37174)}}, {{A, B, C, X(21734), X(31363)}}, {{A, B, C, X(21735), X(57896)}}, {{A, B, C, X(36889), X(45759)}}, {{A, B, C, X(47598), X(60007)}}, {{A, B, C, X(52298), X(53103)}}, {{A, B, C, X(52301), X(60329)}}, {{A, B, C, X(55569), X(60309)}}, {{A, B, C, X(55573), X(60310)}}
X(61945) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15718, 15709}, {2, 3091, 3850}, {2, 3839, 15684}, {2, 4, 17538}, {2, 548, 631}, {4, 3090, 3524}, {4, 3525, 11001}, {4, 3544, 5071}, {4, 3545, 3544}, {5, 3091, 3855}, {5, 3526, 5056}, {5, 3530, 5055}, {5, 382, 7486}, {5, 3850, 3843}, {5, 3856, 3}, {5, 3858, 3530}, {5, 3861, 5070}, {5, 546, 3526}, {20, 15717, 8703}, {20, 17578, 5073}, {20, 3524, 3528}, {20, 3832, 3861}, {20, 5068, 5}, {140, 3627, 15689}, {381, 3851, 12811}, {381, 3861, 3832}, {381, 5055, 12101}, {381, 5073, 546}, {632, 14269, 5059}, {632, 5059, 15698}, {1656, 12108, 2}, {1656, 15684, 12108}, {1656, 3529, 15702}, {1656, 3839, 3529}, {1656, 3853, 15717}, {1656, 3857, 3839}, {2041, 2042, 10304}, {3090, 11541, 3525}, {3090, 15682, 140}, {3090, 3545, 5068}, {3091, 12811, 3090}, {3091, 3545, 4}, {3091, 3851, 3545}, {3091, 5068, 381}, {3146, 5055, 3533}, {3526, 17578, 376}, {3528, 11541, 20}, {3528, 5071, 5067}, {3543, 3628, 10299}, {3627, 12811, 5072}, {3627, 14891, 1657}, {3627, 15699, 15712}, {3627, 17538, 11541}, {3832, 13735, 17578}, {3832, 7486, 382}, {3839, 15717, 3853}, {3843, 15713, 7406}, {3845, 5079, 3523}, {3850, 12811, 14892}, {3850, 14892, 3627}, {3851, 15723, 6911}, {3851, 5066, 3091}, {3857, 11737, 1656}, {3858, 5055, 3146}, {5055, 12101, 15721}, {5070, 15699, 13735}, {5734, 61258, 59388}, {9779, 61261, 12245}, {9955, 61258, 5734}, {12102, 15720, 15683}, {12108, 15712, 15707}, {14782, 14783, 3858}, {14784, 14785, 15694}, {14892, 14893, 10109}, {18586, 18587, 11812}, {23253, 42583, 43510}

X(61946) = X(2)X(3)∩X(61)X(43332)

Barycentrics    3*a^4-10*(b^2-c^2)^2+7*a^2*(b^2+c^2) : :
X(61946) = -30*X[2]+13*X[3], 5*X[265]+12*X[38792], 9*X[373]+8*X[46852], 13*X[946]+4*X[4746], 5*X[1482]+12*X[38155], 3*X[3653]+14*X[51078], -25*X[3763]+8*X[55612], -18*X[3817]+X[37727], 10*X[3818]+7*X[55711], 8*X[4301]+9*X[59503], -5*X[4816]+39*X[5587], 12*X[5097]+5*X[15069] and many others

X(61946) lies on these lines: {2, 3}, {61, 43332}, {62, 43333}, {265, 38792}, {373, 46852}, {946, 4746}, {1482, 38155}, {1506, 31470}, {3411, 16808}, {3412, 16809}, {3614, 4309}, {3653, 51078}, {3763, 55612}, {3817, 37727}, {3818, 55711}, {4301, 59503}, {4317, 7173}, {4816, 5587}, {5008, 13881}, {5097, 15069}, {5102, 11898}, {5237, 43490}, {5238, 43489}, {5339, 42799}, {5340, 42800}, {5349, 42911}, {5350, 42910}, {5351, 43330}, {5352, 43331}, {5603, 61255}, {5640, 45958}, {5691, 31662}, {5734, 18357}, {5790, 11531}, {5881, 18493}, {5882, 50799}, {5889, 11017}, {5907, 13321}, {6033, 38735}, {6321, 38746}, {6407, 23263}, {6408, 23253}, {6418, 31414}, {6429, 10576}, {6430, 10577}, {6431, 6565}, {6432, 6564}, {6433, 35821}, {6434, 35820}, {6437, 35812}, {6438, 35813}, {6447, 42602}, {6448, 42603}, {6480, 35787}, {6481, 35786}, {6486, 8253}, {6487, 8252}, {6496, 53519}, {6497, 53518}, {6519, 10195}, {6522, 10194}, {6560, 41966}, {6561, 41965}, {7373, 31410}, {7603, 31492}, {7687, 15046}, {7728, 38725}, {7741, 9656}, {7951, 9671}, {8148, 9779}, {8550, 50956}, {9588, 48661}, {9605, 31417}, {9607, 31415}, {9624, 18525}, {9642, 19372}, {9654, 37720}, {9657, 37587}, {9669, 37719}, {9670, 31479}, {9680, 42283}, {9681, 42582}, {9698, 18424}, {9955, 12645}, {10247, 61249}, {10516, 37517}, {10541, 25565}, {10738, 38758}, {10739, 38770}, {10740, 38782}, {10748, 38802}, {11425, 15752}, {11439, 13363}, {11477, 51173}, {11482, 47354}, {11522, 50805}, {11935, 18350}, {12006, 16261}, {12111, 18874}, {12245, 61260}, {12290, 32205}, {12316, 20584}, {12571, 12702}, {13364, 15058}, {13464, 61248}, {13598, 54047}, {13624, 61265}, {13665, 35770}, {13785, 35771}, {13903, 42277}, {13961, 42274}, {14530, 23324}, {14845, 34783}, {14848, 18553}, {15028, 32137}, {15057, 15088}, {15060, 58533}, {15092, 38744}, {15484, 39565}, {15749, 44731}, {16644, 41971}, {16645, 41972}, {16772, 42103}, {16773, 42106}, {16964, 42132}, {16965, 42129}, {16966, 42890}, {16967, 42891}, {18440, 39561}, {18492, 30392}, {18510, 41953}, {18512, 41954}, {18526, 19925}, {18581, 42962}, {18582, 42963}, {18584, 31467}, {19872, 28154}, {20379, 38789}, {20582, 55602}, {22793, 61264}, {23236, 36518}, {24206, 55591}, {25561, 50962}, {25639, 31494}, {27355, 37481}, {28198, 30315}, {28216, 46932}, {31412, 43316}, {31447, 54447}, {31450, 53419}, {31454, 42268}, {31487, 42265}, {31673, 61266}, {32767, 48672}, {33749, 47353}, {34627, 61290}, {34754, 42098}, {34755, 42095}, {36836, 43245}, {36843, 43244}, {36990, 55695}, {37484, 44863}, {38021, 50797}, {38064, 51133}, {38066, 50807}, {38072, 50954}, {38076, 50806}, {38176, 58244}, {40107, 55582}, {40280, 46849}, {40693, 42107}, {40694, 42110}, {40920, 43604}, {41967, 43887}, {41968, 43888}, {42093, 42488}, {42094, 42489}, {42111, 42148}, {42114, 42147}, {42125, 42156}, {42126, 42950}, {42127, 42951}, {42128, 42153}, {42130, 42490}, {42131, 42491}, {42135, 42472}, {42138, 42473}, {42139, 43328}, {42142, 43329}, {42157, 43421}, {42158, 43420}, {42160, 43104}, {42161, 43101}, {42258, 43314}, {42259, 43315}, {42433, 42611}, {42434, 42610}, {42474, 42936}, {42475, 42937}, {42561, 43317}, {42592, 46335}, {42593, 46334}, {42694, 43497}, {42695, 43498}, {42960, 42993}, {42961, 42992}, {42968, 43775}, {42969, 43776}, {42988, 42991}, {42989, 42990}, {43028, 43633}, {43029, 43632}, {43174, 51074}, {43430, 53520}, {43431, 53517}, {47355, 55685}, {48872, 55642}, {48884, 55680}, {48889, 55691}, {48895, 55633}, {48901, 55607}, {48904, 55645}, {48905, 55683}, {48910, 55627}, {50871, 61288}, {51128, 55648}, {51166, 55580}, {51186, 55588}, {51537, 55705}, {53023, 55587}, {58237, 61256}, {59387, 61278}

X(61946) = midpoint of X(i) and X(j) for these {i,j}: {3544, 3854}
X(61946) = reflection of X(i) in X(j) for these {i,j}: {3, 3533}, {7486, 5}
X(61946) = inverse of X(12103) in orthocentroidal circle
X(61946) = inverse of X(12103) in Yff hyperbola
X(61946) = complement of X(62084)
X(61946) = pole of line {523, 12103} with respect to the orthocentroidal circle
X(61946) = pole of line {185, 62040} with respect to the Jerabek hyperbola
X(61946) = pole of line {6, 12103} with respect to the Kiepert hyperbola
X(61946) = pole of line {523, 12103} with respect to the Yff hyperbola
X(61946) = pole of line {69, 55690} with respect to the Wallace hyperbola
X(61946) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(6), X(44880)}}, {{A, B, C, X(68), X(15709)}}, {{A, B, C, X(264), X(12103)}}, {{A, B, C, X(265), X(7486)}}, {{A, B, C, X(3521), X(15683)}}, {{A, B, C, X(5066), X(21400)}}, {{A, B, C, X(5070), X(14860)}}, {{A, B, C, X(5071), X(15749)}}, {{A, B, C, X(12108), X(13599)}}, {{A, B, C, X(15318), X(33923)}}, {{A, B, C, X(15689), X(60121)}}, {{A, B, C, X(15692), X(18855)}}, {{A, B, C, X(15723), X(60007)}}, {{A, B, C, X(15750), X(44731)}}, {{A, B, C, X(31363), X(58188)}}
X(61946) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3861, 17800}, {2, 4, 12103}, {3, 11539, 15720}, {3, 1656, 15723}, {3, 3543, 1657}, {3, 3830, 5059}, {3, 3843, 3853}, {3, 3850, 381}, {3, 3851, 3545}, {3, 5067, 3526}, {3, 5073, 15686}, {4, 15022, 11540}, {4, 15710, 3146}, {4, 16371, 12100}, {4, 3090, 15692}, {4, 5, 5070}, {4, 632, 15681}, {5, 12102, 13735}, {5, 16239, 5056}, {5, 17533, 15973}, {5, 30, 7486}, {5, 3845, 16239}, {5, 3856, 20}, {5, 3857, 3861}, {5, 3858, 548}, {5, 3861, 2}, {5, 5070, 5079}, {5, 546, 631}, {5, 631, 5055}, {20, 3855, 3856}, {20, 3856, 3843}, {140, 11001, 3}, {381, 14892, 15716}, {381, 15693, 3839}, {381, 1657, 546}, {381, 3851, 5072}, {381, 5079, 4}, {382, 5054, 15696}, {550, 14892, 15022}, {550, 15022, 15703}, {3090, 3525, 16417}, {3090, 3858, 3830}, {3090, 5059, 11539}, {3091, 10303, 13587}, {3091, 3545, 3850}, {3091, 5066, 3851}, {3526, 15696, 3530}, {3526, 3530, 5054}, {3526, 3843, 382}, {3533, 3545, 3544}, {3533, 5067, 13742}, {3543, 15705, 11001}, {3544, 3854, 30}, {3544, 7486, 5}, {3545, 15708, 14892}, {3545, 3855, 5067}, {3628, 3839, 5073}, {3628, 5073, 15693}, {3850, 12811, 547}, {3855, 5067, 3832}, {3858, 11737, 3090}, {3861, 17800, 5076}, {5054, 8703, 15700}, {5055, 14269, 15705}, {6903, 10303, 14891}, {7951, 9671, 31480}, {8703, 12811, 5068}, {12571, 61263, 12702}, {14784, 14785, 15709}, {15022, 15716, 1656}, {18586, 18587, 15701}

X(61947) = X(2)X(3)∩X(962)X(50807)

Barycentrics    7*a^4-23*(b^2-c^2)^2+16*a^2*(b^2+c^2) : :
X(61947) = -23*X[2]+10*X[3], -X[962]+14*X[50807], X[3241]+12*X[38140], -2*X[3244]+15*X[38021], -2*X[3626]+15*X[38076], -2*X[3629]+15*X[38072], 8*X[3631]+5*X[54132], X[3632]+25*X[30308], 12*X[3817]+X[34627], 12*X[5587]+X[34631], -15*X[5603]+2*X[34747], -X[5691]+14*X[51078] and many others

X(61947) lies on these lines: {2, 3}, {962, 50807}, {1151, 43522}, {1152, 43521}, {1285, 43457}, {3241, 38140}, {3244, 38021}, {3626, 38076}, {3629, 38072}, {3631, 54132}, {3632, 30308}, {3817, 34627}, {5343, 49905}, {5344, 49906}, {5587, 34631}, {5603, 34747}, {5691, 51078}, {5818, 38098}, {5881, 51095}, {5921, 50957}, {6329, 47353}, {6431, 43381}, {6432, 43380}, {7773, 32886}, {7788, 32868}, {7967, 61274}, {7989, 50810}, {8227, 50803}, {9770, 53144}, {9955, 20050}, {10155, 54720}, {10576, 12819}, {10577, 12818}, {10595, 50796}, {10653, 42473}, {10654, 42472}, {11008, 19130}, {11160, 38136}, {11180, 20583}, {12816, 43485}, {12817, 43486}, {12820, 42086}, {12821, 42085}, {13464, 51094}, {13846, 23275}, {13847, 23269}, {14226, 42270}, {14241, 42273}, {14488, 60629}, {14494, 60631}, {14810, 51029}, {15058, 58470}, {15808, 18492}, {16241, 43196}, {16242, 43195}, {18357, 20054}, {18581, 43418}, {18582, 43419}, {18842, 60322}, {18843, 60185}, {19875, 51074}, {19877, 28202}, {20049, 38138}, {20057, 51709}, {21358, 51129}, {22793, 50809}, {23253, 42641}, {23263, 42642}, {25406, 25565}, {31145, 38034}, {31412, 43386}, {31663, 50873}, {32000, 57823}, {32819, 32887}, {33604, 42163}, {33605, 42166}, {35019, 41042}, {35020, 41043}, {36990, 51133}, {37640, 42919}, {37641, 42918}, {38073, 60933}, {38075, 60942}, {38139, 60984}, {38314, 50799}, {39884, 51176}, {40330, 50959}, {41112, 42775}, {41113, 42776}, {41119, 42779}, {41120, 42780}, {41121, 42920}, {41122, 42921}, {41943, 42114}, {41944, 42111}, {42101, 42474}, {42102, 42475}, {42107, 43403}, {42110, 43404}, {42125, 43110}, {42128, 43111}, {42130, 43478}, {42131, 43477}, {42133, 43104}, {42134, 43101}, {42142, 61719}, {42153, 49825}, {42154, 43488}, {42155, 43487}, {42156, 49824}, {42159, 49813}, {42162, 49812}, {42262, 54597}, {42265, 43536}, {42271, 43505}, {42272, 43506}, {42478, 42895}, {42479, 42894}, {42496, 42963}, {42497, 42962}, {42510, 43201}, {42511, 43202}, {42522, 42639}, {42523, 42640}, {42561, 43387}, {42582, 43257}, {42583, 43256}, {42598, 49876}, {42599, 49875}, {42635, 43547}, {42636, 43546}, {42637, 43503}, {42638, 43504}, {42813, 43023}, {42814, 43022}, {42898, 42999}, {42899, 42998}, {42932, 43630}, {42933, 43631}, {42972, 49862}, {42973, 49861}, {48901, 50966}, {50806, 61259}, {50818, 61284}, {50956, 59373}, {50964, 51212}, {51092, 61249}, {52519, 60143}, {54523, 60219}, {54595, 60316}, {54596, 60315}, {54616, 54845}, {54637, 60330}, {59387, 61279}, {60127, 60636}, {60132, 60616}, {60142, 60627}, {60284, 60337}

X(61947) = reflection of X(i) in X(j) for these {i,j}: {10299, 2}, {2, 5079}
X(61947) = inverse of X(62130) in orthocentroidal circle
X(61947) = inverse of X(62130) in Yff hyperbola
X(61947) = anticomplement of X(61829)
X(61947) = pole of line {523, 62130} with respect to the orthocentroidal circle
X(61947) = pole of line {6, 50975} with respect to the Kiepert hyperbola
X(61947) = pole of line {523, 62130} with respect to the Yff hyperbola
X(61947) = pole of line {69, 15707} with respect to the Wallace hyperbola
X(61947) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(15707)}}, {{A, B, C, X(1494), X(10299)}}, {{A, B, C, X(3524), X(57823)}}, {{A, B, C, X(8797), X(38071)}}, {{A, B, C, X(15022), X(54660)}}, {{A, B, C, X(15683), X(54838)}}, {{A, B, C, X(15710), X(57897)}}, {{A, B, C, X(15717), X(54763)}}, {{A, B, C, X(18855), X(61138)}}, {{A, B, C, X(34200), X(36889)}}, {{A, B, C, X(50693), X(60121)}}, {{A, B, C, X(52284), X(60322)}}, {{A, B, C, X(52301), X(52519)}}
X(61947) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10304, 14869}, {2, 14269, 3529}, {2, 15715, 15702}, {2, 20, 15707}, {2, 30, 10299}, {2, 3529, 3524}, {2, 3530, 15709}, {2, 3545, 3544}, {2, 382, 15710}, {2, 3839, 382}, {2, 3851, 3545}, {3, 19238, 6875}, {5, 11812, 5055}, {5, 3522, 3090}, {5, 381, 3543}, {5, 546, 15720}, {30, 5079, 2}, {376, 631, 14891}, {381, 14893, 3832}, {381, 15681, 546}, {381, 15703, 3845}, {381, 15723, 3843}, {381, 3544, 15715}, {381, 3545, 5071}, {381, 3851, 11737}, {381, 5055, 14893}, {381, 5072, 15703}, {381, 549, 3839}, {547, 15684, 15721}, {547, 15687, 15700}, {549, 3850, 381}, {3090, 3839, 11001}, {3091, 3851, 3855}, {3146, 15699, 15719}, {3522, 3839, 12101}, {3523, 6871, 4205}, {3524, 11001, 3522}, {3525, 3832, 4}, {3529, 15720, 3528}, {3534, 6908, 8703}, {3543, 15683, 5073}, {3545, 15709, 14892}, {3830, 14892, 5056}, {3830, 15709, 17538}, {3843, 10109, 10304}, {3845, 15703, 15683}, {3845, 6959, 5066}, {3857, 14892, 3830}, {5055, 14893, 15692}, {5055, 15682, 3525}, {5068, 10303, 5}, {5079, 10299, 5067}, {13633, 15699, 3523}, {14891, 15683, 376}, {14893, 15692, 15682}, {15683, 15703, 631}, {15692, 17678, 11812}, {18586, 18587, 12108}, {43546, 49908, 42636}, {43547, 49907, 42635}

X(61948) = X(1)X(50800)∩X(2)X(3)

Barycentrics    5*a^4-16*(b^2-c^2)^2+11*a^2*(b^2+c^2) : :
X(61948) = 2*X[1]+7*X[50800], -16*X[2]+7*X[3], 2*X[6]+7*X[50957], 2*X[10]+7*X[50807], 2*X[69]+7*X[51173], 2*X[141]+7*X[50964], 8*X[597]+X[48662], 2*X[1125]+7*X[51078], X[1351]+8*X[25561], -X[1482]+10*X[30308], 2*X[1699]+X[38066], 5*X[3241]+4*X[61246] and many others

X(61948) lies on these lines: {1, 50800}, {2, 3}, {6, 50957}, {10, 50807}, {13, 42897}, {14, 42896}, {69, 51173}, {115, 22246}, {141, 50964}, {519, 58238}, {597, 48662}, {1125, 51078}, {1327, 13951}, {1328, 8976}, {1351, 25561}, {1384, 39601}, {1482, 30308}, {1699, 38066}, {3241, 61246}, {3589, 51133}, {3617, 58250}, {3625, 3656}, {3630, 20423}, {3633, 9955}, {3654, 12571}, {3655, 50803}, {3817, 61287}, {3828, 48661}, {4668, 8148}, {4718, 51040}, {4726, 51038}, {4764, 51039}, {5024, 39563}, {5093, 38072}, {5339, 42435}, {5340, 42436}, {5418, 60297}, {5420, 60298}, {5461, 38744}, {5790, 38076}, {6144, 19130}, {6221, 42558}, {6398, 42557}, {6407, 35787}, {6408, 35786}, {6472, 41945}, {6473, 41946}, {6500, 35823}, {6501, 35822}, {6560, 17851}, {7583, 42571}, {7584, 42570}, {7988, 28208}, {9691, 10576}, {10246, 61271}, {10247, 37712}, {10575, 40284}, {10653, 42693}, {10654, 42692}, {11178, 44456}, {11179, 50960}, {11485, 42972}, {11486, 42973}, {11645, 55697}, {12355, 61575}, {12699, 50814}, {12816, 42580}, {12817, 42581}, {13340, 13570}, {14226, 19117}, {14241, 19116}, {16267, 42902}, {16268, 42903}, {16644, 43305}, {16645, 43304}, {16962, 42098}, {16963, 42095}, {16966, 42997}, {16967, 42996}, {18357, 20053}, {18358, 50962}, {18362, 30435}, {18440, 50956}, {18524, 61159}, {18525, 50799}, {19106, 54591}, {19107, 54592}, {19878, 58222}, {19883, 61266}, {19925, 61277}, {21358, 55593}, {22515, 52886}, {24827, 52885}, {25565, 36990}, {28164, 58226}, {28194, 61263}, {28202, 54447}, {28204, 61275}, {31454, 42526}, {31670, 50970}, {31673, 51080}, {32455, 47354}, {34595, 58224}, {34627, 61292}, {34648, 61268}, {36967, 42474}, {36968, 42475}, {36969, 43373}, {36970, 43372}, {38065, 59389}, {38073, 38139}, {38075, 51516}, {38077, 51517}, {38078, 51518}, {38083, 61264}, {38756, 45310}, {38790, 45311}, {39565, 43136}, {41100, 43550}, {41101, 43551}, {41112, 42989}, {41113, 42988}, {41119, 42163}, {41120, 42166}, {42085, 43107}, {42086, 43100}, {42103, 43104}, {42106, 43101}, {42107, 42975}, {42110, 42974}, {42115, 43646}, {42116, 43645}, {42117, 43202}, {42118, 43201}, {42126, 42911}, {42127, 42910}, {42270, 42573}, {42273, 42572}, {42494, 49824}, {42495, 49825}, {42625, 43226}, {42626, 43227}, {42801, 42813}, {42802, 42814}, {42815, 43404}, {42816, 43403}, {42817, 43417}, {42818, 43416}, {42920, 43228}, {42921, 43229}, {42928, 43028}, {42929, 43029}, {43150, 51174}, {43211, 43321}, {43212, 43320}, {43240, 43500}, {43241, 43499}, {43477, 52080}, {43478, 52079}, {45384, 53520}, {45385, 53517}, {46931, 50826}, {47353, 53091}, {47617, 51122}, {48889, 55692}, {48895, 55632}, {48943, 51141}, {50797, 61253}, {50864, 61272}, {50954, 51178}, {50993, 55580}, {51024, 55604}, {51091, 61248}, {51131, 54169}, {51189, 55721}, {51709, 61296}, {53620, 61262}, {54105, 57822}, {54857, 60287}, {54890, 60131}, {59387, 61280}, {60326, 60645}, {60329, 60638}, {60884, 61020}

X(61948) = midpoint of X(i) and X(j) for these {i,j}: {4, 15708}
X(61948) = reflection of X(i) in X(j) for these {i,j}: {15688, 15708}, {15689, 15706}, {15706, 2}, {15708, 15699}, {15710, 11539}, {3534, 15710}
X(61948) = inverse of X(15686) in orthocentroidal circle
X(61948) = inverse of X(15686) in Yff hyperbola
X(61948) = complement of X(62086)
X(61948) = pole of line {523, 15686} with respect to the orthocentroidal circle
X(61948) = pole of line {6, 15686} with respect to the Kiepert hyperbola
X(61948) = pole of line {523, 15686} with respect to the Yff hyperbola
X(61948) = intersection, other than A, B, C, of circumconics {{A, B, C, X(264), X(15686)}}, {{A, B, C, X(1494), X(15706)}}, {{A, B, C, X(3843), X(55958)}}, {{A, B, C, X(12108), X(57822)}}, {{A, B, C, X(12811), X(60122)}}, {{A, B, C, X(14093), X(57896)}}, {{A, B, C, X(14860), X(55857)}}, {{A, B, C, X(15696), X(60121)}}, {{A, B, C, X(21735), X(36889)}}, {{A, B, C, X(35404), X(54585)}}
X(61948) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14893, 1657}, {2, 17538, 549}, {2, 30, 15706}, {2, 3545, 14892}, {2, 3627, 14093}, {2, 376, 12108}, {2, 381, 3843}, {2, 3850, 381}, {2, 4, 15686}, {4, 15708, 30}, {5, 3830, 15703}, {5, 3845, 10124}, {5, 3853, 13735}, {5, 3858, 12103}, {5, 3860, 376}, {5, 546, 3523}, {30, 11539, 15710}, {30, 15699, 15708}, {30, 15708, 15688}, {30, 15710, 3534}, {376, 3854, 3860}, {381, 1656, 3845}, {381, 3534, 546}, {381, 3545, 5055}, {381, 5054, 3839}, {381, 5055, 14269}, {381, 5066, 3851}, {381, 5068, 15701}, {548, 15686, 15697}, {631, 11359, 11540}, {632, 15683, 15716}, {1656, 3845, 15681}, {1657, 14893, 3830}, {2043, 2044, 12811}, {3090, 15687, 15693}, {3523, 11539, 5054}, {3526, 3543, 15695}, {3534, 5071, 5070}, {3543, 10109, 3526}, {3543, 3544, 10109}, {3545, 14892, 5072}, {3545, 3855, 3524}, {3628, 15682, 15700}, {3830, 12100, 15685}, {3830, 15681, 3146}, {3830, 3843, 14893}, {3832, 5079, 5073}, {3850, 12811, 548}, {3851, 5055, 3545}, {3855, 12811, 1656}, {3856, 5056, 5076}, {3857, 5068, 382}, {3858, 10109, 3543}, {3860, 6939, 15683}, {5054, 15705, 15707}, {10124, 12100, 14869}, {11178, 50963, 44456}, {11737, 12100, 5}, {12108, 15718, 15722}, {12812, 14890, 15699}, {12812, 14893, 12100}, {12812, 15686, 2}, {14893, 15718, 15684}, {15684, 15703, 15718}, {15685, 15694, 3}, {15686, 15688, 15689}, {15686, 15699, 14890}, {15687, 15693, 17800}, {15688, 15699, 15694}, {15765, 18585, 17578}, {18493, 50796, 34748}, {18586, 18587, 15720}, {50802, 61261, 34718}

X(61949) = X(2)X(3)∩X(13)X(42899)

Barycentrics    8*a^4-25*(b^2-c^2)^2+17*a^2*(b^2+c^2) : :
X(61949) = -25*X[2]+11*X[3], 5*X[182]+2*X[51025], -25*X[551]+18*X[58234], 2*X[962]+5*X[50822], 5*X[1353]+2*X[51027], 5*X[1385]+2*X[50868], 5*X[1483]+2*X[50871], -2*X[3655]+9*X[61270], -2*X[3679]+9*X[61260], -8*X[3817]+X[61283], 10*X[4701]+11*X[11278], 2*X[5097]+5*X[47354] and many others

X(61949) lies on these lines: {2, 3}, {13, 42899}, {14, 42898}, {61, 43246}, {62, 43247}, {182, 51025}, {551, 58234}, {962, 50822}, {1353, 51027}, {1385, 50868}, {1483, 50871}, {3070, 42640}, {3071, 42639}, {3655, 61270}, {3679, 61260}, {3817, 61283}, {4701, 11278}, {5097, 47354}, {5587, 58241}, {5690, 51120}, {5691, 50832}, {5901, 50799}, {5921, 51180}, {6429, 43211}, {6430, 43212}, {6437, 42602}, {6438, 42603}, {6684, 51119}, {7989, 50807}, {9779, 59400}, {9955, 58237}, {9956, 51074}, {10139, 43258}, {10140, 43259}, {10141, 10195}, {10142, 10194}, {10576, 43887}, {10577, 43888}, {10645, 43204}, {10646, 43203}, {11531, 50823}, {11645, 51133}, {11698, 38077}, {16200, 38138}, {16808, 42634}, {16809, 42633}, {18357, 30308}, {18583, 50956}, {19876, 28178}, {20582, 55603}, {22791, 38076}, {22793, 51076}, {23302, 43245}, {23303, 43244}, {24206, 51129}, {25561, 38136}, {25565, 55695}, {27355, 45957}, {28190, 61265}, {28208, 51078}, {30392, 61269}, {31162, 61262}, {33179, 50796}, {34627, 61293}, {34628, 58227}, {36969, 43638}, {36970, 43639}, {36990, 50987}, {37705, 38021}, {38034, 38155}, {38079, 50664}, {38081, 58248}, {38140, 61251}, {38141, 38758}, {39884, 50960}, {41943, 42906}, {41944, 42907}, {42110, 61719}, {42472, 42916}, {42473, 42917}, {42641, 43525}, {42642, 43526}, {42813, 42953}, {42814, 42952}, {42890, 42980}, {42891, 42981}, {42962, 43543}, {42963, 43542}, {43101, 43200}, {43104, 43199}, {48310, 55688}, {48876, 51166}, {48901, 51131}, {50797, 61597}, {50806, 61510}, {50825, 51118}, {50954, 61624}, {50963, 61545}, {50978, 55722}, {50980, 51163}, {51184, 51212}, {51709, 61295}, {58231, 61268}

X(61949) = midpoint of X(i) and X(j) for these {i,j}: {4, 15701}, {3528, 3830}, {7989, 50807}
X(61949) = reflection of X(i) in X(j) for these {i,j}: {15702, 547}, {3845, 3832}, {3851, 5066}, {549, 15703}, {550, 15698}, {8703, 14869}
X(61949) = inverse of X(62137) in orthocentroidal circle
X(61949) = inverse of X(62137) in Yff hyperbola
X(61949) = complement of X(62088)
X(61949) = pole of line {523, 62137} with respect to the orthocentroidal circle
X(61949) = pole of line {6, 43645} with respect to the Kiepert hyperbola
X(61949) = pole of line {523, 62137} with respect to the Yff hyperbola
X(61949) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1494), X(44682)}}, {{A, B, C, X(14860), X(55861)}}, {{A, B, C, X(44245), X(60121)}}
X(61949) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 15713, 5055}, {5, 3858, 15704}, {5, 546, 15712}, {30, 14869, 8703}, {30, 15698, 550}, {30, 3832, 3845}, {30, 5066, 3851}, {30, 547, 15702}, {376, 381, 546}, {381, 15694, 3839}, {381, 3545, 547}, {381, 5068, 14891}, {381, 5071, 14893}, {381, 5072, 15694}, {547, 15690, 10124}, {547, 3850, 381}, {549, 14093, 17504}, {549, 15691, 15714}, {549, 3845, 3543}, {1657, 5070, 5187}, {3526, 15712, 14869}, {3528, 3830, 30}, {3543, 5071, 15723}, {3545, 3845, 5}, {3545, 3855, 11001}, {3627, 15699, 15716}, {3627, 5055, 15713}, {3832, 3850, 3857}, {3839, 5072, 10109}, {3845, 15686, 15687}, {3850, 12811, 3853}, {3850, 5066, 3545}, {3853, 16239, 15696}, {3855, 5055, 3860}, {3856, 5068, 632}, {3860, 5055, 3627}, {5055, 11001, 16239}, {5055, 15696, 2}, {5056, 11812, 15699}, {10124, 14093, 549}, {11539, 15687, 15686}, {11539, 15712, 11812}, {11737, 14893, 5071}, {15684, 17528, 12100}, {15713, 16239, 11539}

X(61950) = X(2)X(3)∩X(13)X(43011)

Barycentrics    7*a^4-20*(b^2-c^2)^2+13*a^2*(b^2+c^2) : :
X(61950) = -20*X[2]+9*X[3], 9*X[355]+2*X[51096], 9*X[1351]+2*X[51188], X[3654]+10*X[51074], 5*X[3656]+6*X[38155], 6*X[3817]+5*X[50799], 6*X[3818]+5*X[51185], 8*X[4669]+3*X[8148], 5*X[4677]+6*X[11278], -4*X[4745]+15*X[61261], -27*X[5093]+16*X[41149], -4*X[5097]+15*X[38072] and many others

X(61950) lies on these lines: {2, 3}, {13, 43011}, {14, 43010}, {355, 51096}, {397, 49810}, {398, 49811}, {1327, 6395}, {1328, 6199}, {1351, 51188}, {1587, 43434}, {1588, 43435}, {3311, 42578}, {3312, 42579}, {3654, 51074}, {3656, 38155}, {3817, 50799}, {3818, 51185}, {4669, 8148}, {4677, 11278}, {4745, 61261}, {5008, 18362}, {5093, 41149}, {5097, 38072}, {5102, 50955}, {5334, 42419}, {5335, 42420}, {5339, 42532}, {5340, 42533}, {5476, 50957}, {5587, 50806}, {5603, 50797}, {5790, 50802}, {5886, 41150}, {6429, 35787}, {6430, 35786}, {6560, 43882}, {6561, 43881}, {7703, 44747}, {7988, 31662}, {7989, 38066}, {8176, 51122}, {8252, 42524}, {8253, 42525}, {9690, 43257}, {9691, 23263}, {9880, 38746}, {9955, 51093}, {10175, 51076}, {10247, 50796}, {10516, 50963}, {10645, 43476}, {10646, 43475}, {11178, 51189}, {11480, 42984}, {11481, 42985}, {11485, 43428}, {11486, 43429}, {11542, 49824}, {11543, 49825}, {11645, 55699}, {12017, 25565}, {12699, 51069}, {12816, 16645}, {12817, 16644}, {13690, 18509}, {13811, 18511}, {14492, 60286}, {14561, 41153}, {14853, 50954}, {15533, 25561}, {15534, 19130}, {16200, 30308}, {16808, 43033}, {16809, 43032}, {18358, 50992}, {18435, 58470}, {18480, 51105}, {18492, 51110}, {18493, 51071}, {18525, 51103}, {19106, 42475}, {19107, 42474}, {19925, 51107}, {20252, 36318}, {20253, 36320}, {20582, 55604}, {21358, 55594}, {21850, 50990}, {22165, 44456}, {22791, 51072}, {23253, 43212}, {23514, 41148}, {31670, 51143}, {33179, 34748}, {33878, 51186}, {34718, 38076}, {34747, 58237}, {34754, 42952}, {34755, 42953}, {36521, 38733}, {36523, 48657}, {36967, 43370}, {36968, 43371}, {37624, 51106}, {37640, 42963}, {37641, 42962}, {37705, 51092}, {38034, 50805}, {38079, 51537}, {38136, 50962}, {38138, 58238}, {38224, 41151}, {38636, 59390}, {38732, 41147}, {39561, 47353}, {41100, 42095}, {41101, 42098}, {41107, 42918}, {41108, 42919}, {41119, 42110}, {41120, 42107}, {41121, 44018}, {41122, 44017}, {41152, 50959}, {42093, 43245}, {42094, 43244}, {42125, 43228}, {42126, 43104}, {42127, 43101}, {42128, 43229}, {42129, 42510}, {42132, 42511}, {42133, 43108}, {42134, 43109}, {42135, 49827}, {42138, 49826}, {42139, 49874}, {42142, 49873}, {42143, 49861}, {42146, 49862}, {42154, 43199}, {42155, 43200}, {42159, 49860}, {42162, 49859}, {42417, 42602}, {42418, 42603}, {42472, 42912}, {42473, 42913}, {42631, 42914}, {42632, 42915}, {42647, 54635}, {42648, 54634}, {42813, 42966}, {42814, 42967}, {42890, 43238}, {42891, 43239}, {42904, 43021}, {42905, 43020}, {43226, 43326}, {43227, 43327}, {43246, 43417}, {43247, 43416}, {43256, 43415}, {43509, 43567}, {43510, 43566}, {48662, 55711}, {49855, 49911}, {49858, 49914}, {50800, 50871}, {50807, 51120}, {50810, 61262}, {50828, 61266}, {50868, 51078}, {50964, 51166}, {50993, 55582}, {51024, 55603}, {51025, 51133}, {51077, 61257}, {51095, 61244}, {51109, 61268}, {51129, 54173}, {51165, 55624}, {51173, 51214}, {54582, 60279}

X(61950) = midpoint of X(i) and X(j) for these {i,j}: {4, 15721}, {381, 5072}
X(61950) = reflection of X(i) in X(j) for these {i,j}: {15716, 2}, {15718, 5070}, {15723, 5056}, {3, 15723}, {381, 3855}
X(61950) = inverse of X(19710) in orthocentroidal circle
X(61950) = inverse of X(19710) in Yff hyperbola
X(61950) = complement of X(62090)
X(61950) = pole of line {523, 19710} with respect to the orthocentroidal circle
X(61950) = pole of line {6, 19710} with respect to the Kiepert hyperbola
X(61950) = pole of line {523, 19710} with respect to the Yff hyperbola
X(61950) = intersection, other than A, B, C, of circumconics {{A, B, C, X(264), X(19710)}}, {{A, B, C, X(1494), X(15716)}}, {{A, B, C, X(5076), X(54924)}}, {{A, B, C, X(14860), X(55858)}}, {{A, B, C, X(15640), X(18550)}}, {{A, B, C, X(18855), X(58188)}}, {{A, B, C, X(52289), X(60286)}}
X(61950) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12101, 3534}, {2, 15682, 15759}, {2, 15695, 15701}, {2, 15722, 15694}, {2, 15759, 5054}, {2, 30, 15716}, {2, 3534, 15722}, {2, 3830, 15695}, {3, 14269, 3543}, {3, 15685, 15690}, {3, 15703, 11539}, {3, 3845, 3830}, {3, 5056, 5070}, {4, 10109, 15693}, {5, 381, 14269}, {5, 3845, 11812}, {5, 546, 3522}, {30, 3855, 381}, {30, 5056, 15723}, {376, 14892, 5079}, {381, 1656, 3839}, {381, 3851, 5055}, {381, 5054, 546}, {381, 5055, 3843}, {381, 5072, 30}, {547, 3845, 11001}, {1656, 15684, 15707}, {1656, 3839, 15684}, {1656, 3853, 3}, {3090, 15640, 15713}, {3091, 13587, 3090}, {3543, 3545, 5}, {3544, 3856, 1657}, {3545, 3832, 547}, {3627, 11540, 15697}, {3830, 15701, 15681}, {3830, 17800, 15682}, {3832, 11001, 3845}, {3839, 11737, 1656}, {3839, 15702, 3853}, {3845, 5066, 3545}, {3850, 3853, 3857}, {3851, 15707, 11737}, {3851, 5070, 5072}, {3854, 12811, 382}, {3858, 14892, 376}, {3861, 13635, 5076}, {3861, 6964, 2}, {5066, 12100, 12811}, {5070, 15689, 15721}, {6803, 6850, 6923}, {10109, 15693, 15703}, {11539, 12108, 15702}, {11540, 15697, 15700}, {11812, 15690, 15711}, {11812, 15719, 15720}, {12108, 15684, 15689}, {14269, 15694, 5073}, {14893, 15713, 15640}, {15640, 15713, 15688}, {15707, 15717, 15718}, {30308, 38140, 50798}, {34754, 42952, 49905}, {34755, 42953, 49906}, {43246, 43417, 49813}

X(61951) = X(2)X(3)∩X(13)X(42478)

Barycentrics    11*a^4-31*(b^2-c^2)^2+20*a^2*(b^2+c^2) : :
X(61951) = -31*X[2]+14*X[3], X[40]+16*X[51076], X[944]+16*X[50803], X[1350]+16*X[51131], -4*X[3625]+21*X[38074], -X[3633]+35*X[30308], 3*X[5032]+14*X[50957], 16*X[5480]+X[51179], -25*X[5818]+8*X[50827], X[6776]+16*X[50960], 7*X[7989]+10*X[51074], -25*X[8227]+8*X[51085] and many others

X(61951) lies on these lines: {2, 3}, {13, 42478}, {14, 42479}, {40, 51076}, {61, 33603}, {62, 33602}, {944, 50803}, {1327, 35814}, {1328, 35815}, {1350, 51131}, {1587, 41951}, {1588, 41952}, {3625, 38074}, {3633, 30308}, {5032, 50957}, {5480, 51179}, {5818, 50827}, {6776, 50960}, {7583, 60290}, {7584, 60289}, {7788, 32888}, {7989, 51074}, {8227, 51085}, {9779, 34631}, {10576, 43526}, {10577, 43525}, {10595, 51087}, {10653, 42905}, {10654, 42904}, {11057, 52718}, {12245, 50802}, {12571, 50810}, {14226, 31412}, {14241, 42561}, {14494, 60630}, {14692, 41135}, {16808, 43006}, {16809, 43007}, {18841, 54852}, {18842, 60323}, {18844, 60175}, {19053, 43342}, {19054, 43343}, {19925, 50818}, {21356, 50964}, {25055, 51078}, {31414, 60304}, {32455, 38072}, {32889, 59634}, {33606, 42775}, {33607, 42776}, {34627, 61294}, {34632, 61263}, {38073, 60962}, {38075, 61000}, {39601, 46453}, {40330, 50982}, {41112, 42495}, {41113, 42494}, {41943, 42103}, {41944, 42106}, {42089, 43471}, {42092, 43472}, {42111, 43545}, {42114, 43544}, {42117, 43554}, {42118, 43555}, {42119, 43483}, {42120, 43484}, {42126, 43493}, {42127, 43494}, {42139, 61719}, {42143, 43540}, {42146, 43541}, {42149, 43201}, {42152, 43202}, {42163, 49874}, {42166, 49873}, {42268, 43568}, {42269, 43569}, {42435, 42972}, {42436, 42973}, {42476, 43402}, {42477, 43401}, {42510, 42965}, {42511, 42964}, {42580, 42695}, {42581, 42694}, {42633, 42969}, {42634, 42968}, {42637, 43559}, {42638, 43558}, {42641, 43888}, {42642, 43887}, {42795, 42915}, {42796, 42914}, {42805, 43550}, {42806, 43551}, {42813, 49861}, {42814, 49862}, {42898, 43403}, {42899, 43404}, {42934, 49907}, {42935, 49908}, {42954, 54591}, {42955, 54592}, {43018, 49813}, {43019, 49812}, {43374, 43508}, {43375, 43507}, {47352, 51133}, {48310, 51177}, {50807, 53620}, {50872, 61259}, {51213, 55629}, {54890, 60643}, {60127, 60250}, {60150, 60649}, {60239, 60325}, {60303, 60314}, {60326, 60646}, {60329, 60637}

X(61951) = inverse of X(46333) in orthocentroidal circle
X(61951) = inverse of X(46333) in Yff hyperbola
X(61951) = pole of line {523, 46333} with respect to the orthocentroidal circle
X(61951) = pole of line {6, 46333} with respect to the Kiepert hyperbola
X(61951) = pole of line {523, 46333} with respect to the Yff hyperbola
X(61951) = pole of line {69, 41983} with respect to the Wallace hyperbola
X(61951) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(41983)}}, {{A, B, C, X(253), X(58184)}}, {{A, B, C, X(264), X(46333)}}, {{A, B, C, X(1494), X(61138)}}, {{A, B, C, X(3530), X(54763)}}, {{A, B, C, X(5079), X(54660)}}, {{A, B, C, X(7378), X(54852)}}, {{A, B, C, X(14093), X(36889)}}, {{A, B, C, X(15077), X(41992)}}, {{A, B, C, X(15640), X(18852)}}, {{A, B, C, X(15681), X(54838)}}, {{A, B, C, X(17800), X(18853)}}, {{A, B, C, X(18854), X(50693)}}, {{A, B, C, X(38071), X(54667)}}, {{A, B, C, X(52284), X(60323)}}
X(61951) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14891, 15702}, {2, 1657, 3524}, {2, 3543, 14093}, {2, 3839, 3627}, {4, 10304, 15682}, {4, 15022, 631}, {4, 3524, 15640}, {4, 3525, 17800}, {4, 3526, 3529}, {4, 3544, 7486}, {4, 5055, 15698}, {4, 5066, 3545}, {5, 10299, 3090}, {376, 15702, 10299}, {376, 3855, 381}, {381, 12811, 15721}, {381, 15687, 3832}, {381, 15694, 546}, {381, 3851, 547}, {381, 5072, 15684}, {547, 3627, 15718}, {548, 15684, 15683}, {548, 3850, 3857}, {549, 15681, 10304}, {549, 3628, 15723}, {3534, 3839, 4}, {3534, 3856, 3839}, {3543, 11737, 5071}, {3543, 15703, 15715}, {3545, 15682, 5}, {3627, 5072, 15022}, {3830, 5067, 15710}, {3845, 12812, 15689}, {3855, 5066, 15709}, {3857, 5066, 5055}, {5055, 15759, 13741}, {5071, 15715, 15703}, {5079, 12101, 15708}, {10304, 17678, 549}, {12812, 15689, 2}, {14093, 14893, 3543}, {15682, 15702, 376}, {15684, 15706, 15686}, {15684, 15718, 3534}, {15702, 17538, 14891}

X(61952) = X(2)X(3)∩X(15)X(43311)

Barycentrics    13*a^4-35*(b^2-c^2)^2+22*a^2*(b^2+c^2) : :
X(61952) = -35*X[2]+16*X[3], -X[145]+20*X[30308], -X[962]+20*X[51074], -5*X[3617]+24*X[38076], -5*X[3623]+24*X[38021], 15*X[5032]+4*X[51027], -20*X[5480]+X[51214], 5*X[5818]+14*X[50807], -X[5921]+20*X[50956], 5*X[8227]+14*X[51078], -5*X[8591]+24*X[38746], -5*X[9143]+24*X[38792] and many others

X(61952) lies on these lines: {2, 3}, {15, 43311}, {16, 43310}, {145, 30308}, {590, 42575}, {615, 42574}, {962, 51074}, {3617, 38076}, {3623, 38021}, {5032, 51027}, {5343, 49907}, {5344, 49908}, {5480, 51214}, {5818, 50807}, {5921, 50956}, {7585, 41952}, {7586, 41951}, {7788, 32894}, {8227, 51078}, {8591, 38746}, {9143, 38792}, {9779, 11224}, {10248, 51119}, {10595, 50800}, {11177, 38735}, {11180, 15520}, {11278, 20052}, {11480, 43478}, {11481, 43477}, {11531, 50802}, {12571, 51120}, {13570, 33884}, {15031, 32840}, {16200, 20049}, {16644, 43365}, {16645, 43364}, {16808, 43233}, {16809, 43232}, {19053, 51850}, {19054, 51849}, {19875, 51076}, {19925, 50871}, {20053, 58239}, {21356, 51166}, {21358, 51131}, {22235, 42898}, {22237, 42899}, {25055, 50868}, {25565, 55693}, {30392, 34648}, {31423, 50873}, {32827, 32893}, {32834, 48913}, {32895, 59634}, {34641, 58241}, {35822, 43323}, {35823, 43322}, {38072, 51170}, {38075, 61006}, {38314, 50803}, {40330, 50964}, {41119, 42481}, {41120, 42480}, {41943, 42133}, {41944, 42134}, {42085, 42997}, {42086, 42996}, {42111, 43200}, {42114, 43199}, {42153, 43556}, {42156, 43557}, {42602, 43796}, {42603, 43795}, {42775, 43229}, {42776, 43228}, {42791, 54580}, {42792, 54581}, {42910, 43244}, {42911, 43245}, {42952, 49876}, {42953, 49875}, {43101, 43552}, {43104, 43553}, {43209, 54542}, {43210, 54543}, {43292, 43330}, {43293, 43331}, {43511, 43888}, {43512, 43887}, {43519, 43566}, {43520, 43567}, {47352, 51025}, {50959, 55722}, {50960, 59373}, {50975, 55683}, {51023, 55711}, {51129, 51212}, {51165, 55622}, {54706, 60131}, {59387, 61285}, {60287, 60324}, {60327, 60645}, {60328, 60638}

X(61952) = reflection of X(i) in X(j) for these {i,j}: {2, 15022}
X(61952) = inverse of X(62148) in orthocentroidal circle
X(61952) = inverse of X(62148) in Yff hyperbola
X(61952) = anticomplement of X(61825)
X(61952) = pole of line {523, 62148} with respect to the orthocentroidal circle
X(61952) = pole of line {6, 51135} with respect to the Kiepert hyperbola
X(61952) = pole of line {523, 62148} with respect to the Yff hyperbola
X(61952) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(15705), X(52443)}}, {{A, B, C, X(18855), X(46853)}}
X(61952) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15688, 17533}, {2, 15715, 17556}, {2, 3530, 11113}, {2, 3839, 17578}, {3, 17578, 5059}, {3, 3850, 3855}, {3, 5066, 3545}, {4, 15699, 15697}, {30, 15022, 2}, {381, 11737, 4}, {381, 15703, 546}, {381, 3545, 3543}, {381, 3851, 549}, {381, 5066, 5071}, {381, 5071, 3839}, {547, 15686, 15694}, {547, 3853, 14891}, {3091, 3839, 5066}, {3091, 3850, 3832}, {3091, 3855, 5068}, {3543, 15692, 11001}, {3543, 15708, 15686}, {3543, 5056, 15702}, {3545, 11001, 5}, {3545, 3845, 5056}, {3839, 15721, 15687}, {3839, 7486, 15682}, {3853, 5055, 15719}, {3855, 5071, 381}, {3860, 5072, 3524}, {3861, 15699, 15685}, {5071, 10124, 7486}, {5071, 15682, 10124}, {5071, 15687, 15721}, {11001, 15709, 3}, {11001, 15723, 15692}, {14869, 15719, 15708}, {15684, 15694, 15688}, {15687, 15691, 15684}, {15687, 15721, 15683}, {15688, 15699, 15709}

X(61953) = X(2)X(3)∩X(6)X(42690)

Barycentrics    3*a^4-8*(b^2-c^2)^2+5*a^2*(b^2+c^2) : :
X(61953) = -24*X[2]+11*X[3], 9*X[373]+4*X[46849], 11*X[946]+2*X[4701], X[962]+12*X[61262], 5*X[1351]+8*X[43150], 3*X[1482]+10*X[37714], 6*X[1539]+7*X[15057], 5*X[3567]+8*X[45958], -2*X[3579]+15*X[61264], -5*X[3617]+18*X[61260], -20*X[3763]+7*X[55616], -15*X[3817]+2*X[13607] and many others

X(61953) lies on these lines: {2, 3}, {6, 42690}, {15, 42688}, {16, 42689}, {373, 46849}, {485, 43792}, {486, 43791}, {496, 31410}, {946, 4701}, {962, 61262}, {999, 9656}, {1007, 32891}, {1159, 10826}, {1327, 43880}, {1328, 43879}, {1351, 43150}, {1384, 39590}, {1479, 31480}, {1482, 37714}, {1539, 15057}, {2548, 22246}, {2549, 31470}, {3053, 39601}, {3070, 43431}, {3071, 31487}, {3172, 50718}, {3295, 9671}, {3411, 5340}, {3412, 5339}, {3531, 34483}, {3567, 45958}, {3579, 61264}, {3614, 9668}, {3617, 61260}, {3763, 55616}, {3817, 13607}, {3818, 33749}, {3820, 31420}, {3947, 18530}, {4297, 61266}, {4301, 5790}, {4309, 31479}, {4338, 17606}, {5093, 15069}, {5254, 31417}, {5319, 15484}, {5365, 42912}, {5366, 42913}, {5368, 5475}, {5550, 58228}, {5587, 8148}, {5603, 61249}, {5640, 45959}, {5691, 58230}, {5734, 12645}, {5735, 51516}, {5876, 13321}, {5881, 9955}, {5882, 50803}, {5885, 61740}, {5889, 58533}, {5890, 18874}, {5943, 18439}, {6199, 35815}, {6221, 35787}, {6395, 35814}, {6398, 35786}, {6407, 10576}, {6408, 10577}, {6417, 6565}, {6418, 6564}, {6429, 42558}, {6430, 42557}, {6445, 35821}, {6446, 35820}, {6472, 23263}, {6473, 23253}, {6500, 13785}, {6501, 13665}, {6561, 9691}, {6767, 10896}, {7173, 9655}, {7373, 10895}, {7583, 43341}, {7584, 31414}, {7687, 23236}, {7741, 9657}, {7748, 18584}, {7759, 40727}, {7765, 18424}, {7814, 15031}, {7951, 9670}, {7982, 50806}, {7989, 12702}, {8550, 50960}, {8976, 42268}, {9540, 43881}, {9588, 22793}, {9589, 9956}, {9606, 31415}, {9624, 18480}, {9644, 19372}, {9654, 37722}, {9669, 15888}, {9680, 42582}, {9681, 9690}, {9692, 43383}, {9698, 44518}, {9779, 18357}, {9781, 15060}, {10095, 15058}, {10113, 15046}, {10175, 48661}, {10222, 30308}, {10246, 18492}, {10516, 44456}, {10545, 43613}, {10546, 43394}, {10595, 61297}, {10620, 20396}, {10625, 13570}, {10645, 42610}, {10646, 42611}, {10721, 38633}, {10722, 38634}, {10723, 38635}, {10724, 38636}, {10728, 38637}, {10733, 38638}, {10735, 38639}, {10982, 50461}, {11002, 31834}, {11017, 11459}, {11178, 55724}, {11362, 12571}, {11439, 12006}, {11441, 15038}, {11451, 13491}, {11456, 15047}, {11472, 43807}, {11477, 25561}, {11482, 18553}, {11485, 42814}, {11486, 42813}, {11522, 50798}, {11542, 42963}, {11543, 42962}, {11898, 38136}, {12007, 18440}, {12017, 48889}, {12111, 13364}, {12290, 13363}, {12308, 14644}, {12315, 23325}, {12331, 38141}, {12699, 31399}, {12902, 36518}, {13378, 47591}, {13464, 34748}, {13474, 40280}, {13566, 33539}, {13623, 52103}, {13630, 16261}, {13881, 21309}, {13886, 43798}, {13903, 23259}, {13925, 23275}, {13935, 17851}, {13939, 43797}, {13951, 42269}, {13961, 23249}, {13993, 23269}, {14128, 54048}, {14530, 18383}, {14561, 48662}, {14692, 38743}, {14845, 37481}, {14848, 50956}, {14981, 38732}, {15026, 15305}, {15041, 15088}, {15045, 32137}, {15048, 31407}, {15063, 38724}, {15072, 32205}, {15851, 36412}, {16003, 38789}, {16772, 42114}, {16773, 42111}, {16808, 42153}, {16809, 42156}, {16964, 42098}, {16965, 42095}, {16966, 43194}, {16967, 43193}, {17605, 37721}, {18394, 26864}, {18483, 61263}, {18493, 19925}, {18510, 31412}, {18512, 42561}, {18526, 61278}, {18550, 44763}, {19106, 42491}, {19107, 42490}, {19877, 28178}, {21358, 55595}, {22332, 39563}, {23251, 35813}, {23261, 35812}, {23332, 48672}, {23513, 38756}, {23514, 38744}, {23515, 38790}, {24206, 55593}, {28146, 31425}, {28168, 34595}, {30435, 39565}, {31447, 41869}, {31454, 42277}, {31457, 44526}, {31467, 53419}, {32767, 35450}, {32789, 43337}, {32790, 43336}, {34469, 43599}, {36519, 38733}, {36748, 61340}, {36836, 43483}, {36843, 43484}, {36990, 55697}, {37725, 51517}, {37726, 38755}, {37832, 42964}, {37835, 42965}, {38021, 50800}, {38074, 50830}, {38076, 50807}, {38139, 60922}, {38150, 60884}, {38161, 48667}, {38317, 55692}, {38640, 44976}, {40107, 53023}, {40693, 42110}, {40694, 42107}, {41973, 49905}, {41974, 49906}, {42101, 42687}, {42102, 42686}, {42103, 42132}, {42106, 42129}, {42115, 42489}, {42116, 42488}, {42117, 42472}, {42118, 42473}, {42119, 42950}, {42120, 42951}, {42130, 42684}, {42131, 42685}, {42135, 42817}, {42138, 42818}, {42139, 42815}, {42142, 42816}, {42150, 43104}, {42151, 43101}, {42154, 42581}, {42155, 42580}, {42159, 42988}, {42162, 42989}, {42163, 42921}, {42164, 42911}, {42165, 42910}, {42166, 42920}, {42260, 43513}, {42261, 43514}, {42284, 43415}, {42433, 43028}, {42434, 43029}, {42474, 42795}, {42475, 42796}, {42775, 43404}, {42776, 43403}, {42786, 48872}, {42914, 43633}, {42915, 43632}, {42968, 43416}, {42969, 43417}, {42980, 43238}, {42981, 43239}, {43016, 43233}, {43017, 43232}, {43174, 51076}, {43409, 43433}, {43410, 43432}, {47353, 53092}, {48884, 55682}, {48895, 55629}, {48901, 55604}, {48904, 55643}, {48910, 55624}, {48942, 55673}, {48943, 55654}, {50796, 61248}, {50799, 61282}, {50964, 50982}, {50985, 51173}, {50993, 55583}, {51024, 55602}, {51078, 51085}, {51093, 58236}, {51133, 51138}, {51709, 61288}, {54917, 60100}, {58233, 61272}, {58247, 59503}, {59387, 61286}

X(61953) = midpoint of X(i) and X(j) for these {i,j}: {4, 10303}
X(61953) = reflection of X(i) in X(j) for these {i,j}: {5067, 5}, {5079, 5068}
X(61953) = inverse of X(15704) in orthocentroidal circle
X(61953) = inverse of X(15704) in Yff hyperbola
X(61953) = complement of X(62092)
X(61953) = anticomplement of X(61824)
X(61953) = pole of line {523, 15704} with respect to the orthocentroidal circle
X(61953) = pole of line {185, 15684} with respect to the Jerabek hyperbola
X(61953) = pole of line {6, 15704} with respect to the Kiepert hyperbola
X(61953) = pole of line {523, 15704} with respect to the Yff hyperbola
X(61953) = pole of line {69, 55688} with respect to the Wallace hyperbola
X(61953) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(68), X(15702)}}, {{A, B, C, X(264), X(15704)}}, {{A, B, C, X(265), X(5067)}}, {{A, B, C, X(1105), X(15684)}}, {{A, B, C, X(1217), X(50692)}}, {{A, B, C, X(3521), X(11001)}}, {{A, B, C, X(3524), X(34483)}}, {{A, B, C, X(3526), X(14860)}}, {{A, B, C, X(3527), X(47485)}}, {{A, B, C, X(3528), X(13623)}}, {{A, B, C, X(3531), X(34484)}}, {{A, B, C, X(3545), X(21400)}}, {{A, B, C, X(3613), X(44959)}}, {{A, B, C, X(8703), X(15318)}}, {{A, B, C, X(10304), X(18855)}}, {{A, B, C, X(11737), X(60122)}}, {{A, B, C, X(13599), X(14869)}}, {{A, B, C, X(15688), X(60121)}}, {{A, B, C, X(18550), X(33703)}}, {{A, B, C, X(23040), X(43713)}}, {{A, B, C, X(35473), X(44763)}}, {{A, B, C, X(52285), X(54917)}}
X(61953) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15714, 5054}, {2, 3853, 15696}, {2, 4, 15704}, {3, 140, 15722}, {3, 4, 15684}, {4, 10303, 30}, {4, 15683, 3627}, {4, 15698, 3146}, {4, 3090, 10304}, {4, 3091, 5066}, {4, 3545, 15022}, {4, 3628, 3534}, {5, 30, 5067}, {5, 3530, 3090}, {5, 3850, 3855}, {5, 3857, 3856}, {5, 3858, 3853}, {5, 546, 20}, {5, 548, 7486}, {20, 13735, 631}, {20, 3528, 15690}, {20, 3545, 5}, {30, 5068, 5079}, {140, 15681, 3}, {140, 3839, 5076}, {140, 5076, 15681}, {376, 3528, 7397}, {381, 12811, 5073}, {381, 3091, 3851}, {381, 3545, 3830}, {381, 382, 3832}, {381, 5072, 4}, {382, 3526, 548}, {382, 548, 17800}, {547, 3146, 15720}, {549, 10304, 15716}, {631, 3832, 3861}, {1656, 15022, 5055}, {1656, 15688, 3525}, {1656, 16239, 5070}, {1657, 3090, 15694}, {2041, 2042, 8703}, {2043, 2044, 11737}, {3090, 17578, 3530}, {3090, 3845, 1657}, {3091, 3850, 381}, {3091, 3854, 3545}, {3091, 3857, 5072}, {3146, 15720, 15689}, {3526, 3534, 15717}, {3526, 3856, 3843}, {3530, 3845, 17578}, {3533, 12103, 15700}, {3544, 3839, 140}, {3545, 3832, 16239}, {3545, 3854, 546}, {3627, 11737, 5056}, {3628, 15717, 3526}, {3830, 12812, 6923}, {3832, 3855, 3859}, {3843, 5070, 382}, {3850, 5066, 3857}, {3851, 15681, 3544}, {3858, 12811, 2}, {3861, 6892, 17538}, {5059, 14869, 14093}, {5734, 61255, 12645}, {10299, 10303, 549}, {11482, 50957, 18553}, {12101, 14869, 5059}, {12102, 15699, 3522}, {12812, 15687, 3523}, {13727, 15713, 1656}, {14269, 15703, 15685}, {14782, 14783, 3854}, {14784, 14785, 15702}, {16868, 18386, 3517}, {18553, 38072, 11482}, {18586, 18587, 15693}, {38034, 61255, 5734}, {42163, 42921, 42974}, {42690, 42691, 6}

X(61954) = X(1)X(50803)∩X(2)X(3)

Barycentrics    7*a^4-17*(b^2-c^2)^2+10*a^2*(b^2+c^2) : :
X(61954) = X[1]+8*X[50803], -17*X[2]+8*X[3], X[6]+8*X[50960], X[10]+8*X[51076], X[69]+8*X[50959], 8*X[114]+X[8596], X[141]+8*X[51131], X[145]+8*X[50796], X[192]+8*X[51041], X[193]+8*X[47354], 8*X[355]+X[20049], 4*X[597]+5*X[51537] and many others

X(61954) lies on these lines: {1, 50803}, {2, 3}, {6, 50960}, {10, 51076}, {13, 43303}, {14, 43302}, {17, 49876}, {18, 49875}, {69, 50959}, {98, 60650}, {114, 8596}, {115, 14930}, {141, 51131}, {145, 50796}, {192, 51041}, {193, 47354}, {262, 60625}, {315, 32893}, {316, 32885}, {317, 55958}, {355, 20049}, {371, 43561}, {372, 43560}, {395, 43540}, {396, 43541}, {485, 60296}, {486, 60295}, {519, 9779}, {597, 51537}, {598, 60336}, {671, 60331}, {946, 31145}, {1131, 19053}, {1132, 19054}, {1278, 51038}, {1327, 43431}, {1328, 43430}, {1699, 38076}, {2979, 13570}, {2996, 54521}, {3068, 42604}, {3069, 42605}, {3241, 19925}, {3316, 52047}, {3317, 52048}, {3424, 54639}, {3616, 34648}, {3617, 31162}, {3618, 51138}, {3619, 51024}, {3620, 50982}, {3621, 3656}, {3622, 18492}, {3623, 9955}, {3624, 50862}, {3632, 51075}, {3679, 12571}, {3817, 38314}, {4301, 51072}, {4678, 50807}, {4772, 51064}, {4788, 51040}, {5032, 38072}, {5261, 11238}, {5274, 11237}, {5318, 43298}, {5321, 43299}, {5334, 16267}, {5335, 16268}, {5339, 49813}, {5340, 49812}, {5343, 42934}, {5344, 42935}, {5349, 42589}, {5350, 42588}, {5365, 41101}, {5366, 41100}, {5395, 54866}, {5476, 5921}, {5480, 11160}, {5550, 34628}, {5603, 61247}, {5881, 51092}, {6447, 60308}, {6448, 60307}, {6470, 60622}, {6471, 60623}, {6564, 43342}, {6565, 43343}, {7581, 43340}, {7582, 43341}, {7687, 9143}, {7739, 18424}, {7776, 32894}, {7809, 10513}, {7814, 32896}, {7840, 14484}, {7850, 32827}, {7989, 20070}, {8724, 35369}, {9540, 43520}, {9542, 43211}, {9543, 10576}, {9589, 51069}, {9778, 61264}, {9780, 50865}, {9812, 19875}, {9880, 20094}, {10302, 43951}, {10577, 43256}, {11008, 50958}, {11057, 32838}, {11178, 50964}, {11180, 19130}, {11439, 27355}, {11451, 46847}, {11488, 43202}, {11489, 43201}, {11648, 31404}, {11669, 60113}, {12007, 47353}, {12111, 58470}, {12816, 42149}, {12817, 42152}, {13846, 41948}, {13847, 41947}, {13935, 43519}, {14492, 60639}, {14692, 22566}, {14845, 16261}, {15024, 46852}, {15031, 32830}, {15056, 21969}, {15305, 16226}, {15808, 50868}, {16644, 42472}, {16645, 42473}, {16808, 43252}, {16809, 43253}, {16962, 42919}, {16963, 42918}, {18357, 20052}, {18358, 50963}, {18481, 50863}, {18483, 34632}, {18489, 37779}, {18493, 50818}, {18529, 29817}, {18581, 42973}, {18582, 42972}, {18845, 60175}, {19876, 51118}, {19877, 50808}, {20014, 50798}, {20050, 50801}, {20054, 51077}, {20057, 50871}, {20080, 20423}, {20081, 44422}, {21356, 53023}, {21358, 51538}, {22235, 43228}, {22237, 43229}, {25561, 54132}, {27268, 51065}, {27525, 49719}, {28198, 61263}, {28204, 61279}, {31188, 51790}, {31415, 39563}, {31730, 50873}, {32785, 43508}, {32786, 43507}, {32816, 32869}, {32822, 32881}, {32823, 32880}, {32872, 37671}, {33606, 41112}, {33607, 41113}, {33697, 50819}, {33878, 51211}, {34595, 50815}, {35786, 42603}, {35787, 42602}, {35814, 42269}, {35815, 42268}, {36519, 52695}, {36969, 43545}, {36970, 43544}, {37640, 42110}, {37641, 42107}, {37832, 42133}, {37835, 42134}, {38021, 59387}, {38066, 61262}, {38074, 38140}, {38075, 59385}, {38150, 59375}, {38259, 60192}, {40330, 54174}, {40341, 51130}, {40693, 49824}, {40694, 49825}, {41119, 42999}, {41120, 42998}, {41121, 42159}, {41122, 42162}, {41869, 46931}, {41895, 60333}, {41961, 41965}, {41962, 41966}, {42087, 42474}, {42088, 42475}, {42089, 42796}, {42090, 43467}, {42091, 43468}, {42092, 42795}, {42095, 43364}, {42098, 43365}, {42101, 43107}, {42102, 43100}, {42119, 43104}, {42120, 43101}, {42122, 42932}, {42123, 42933}, {42129, 43481}, {42132, 43482}, {42140, 42687}, {42141, 42686}, {42160, 42694}, {42161, 42695}, {42163, 42775}, {42164, 43479}, {42165, 43480}, {42166, 42776}, {42215, 42539}, {42216, 42540}, {42433, 43475}, {42434, 43476}, {42494, 49947}, {42495, 49948}, {42496, 42969}, {42497, 42968}, {42582, 43339}, {42583, 43338}, {42688, 43243}, {42689, 43242}, {42690, 42974}, {42691, 42975}, {42783, 54635}, {42784, 54634}, {42813, 49826}, {42814, 49827}, {42910, 43473}, {42911, 43474}, {42920, 49873}, {42921, 49874}, {42970, 43305}, {42971, 43304}, {42990, 49810}, {42991, 49811}, {43193, 54581}, {43194, 54580}, {43399, 43642}, {43400, 43641}, {43407, 43503}, {43408, 43504}, {43416, 43543}, {43417, 43542}, {43442, 54579}, {43443, 54578}, {43511, 43566}, {43512, 43567}, {43558, 54543}, {43559, 54542}, {43681, 54643}, {46264, 51216}, {46934, 50811}, {46951, 48913}, {47355, 51022}, {47586, 60282}, {48881, 51029}, {48884, 50975}, {48895, 51213}, {50810, 61261}, {50869, 51073}, {50954, 51182}, {50957, 51215}, {51023, 51133}, {51026, 51128}, {51070, 58245}, {51081, 58217}, {51096, 61252}, {51164, 55656}, {51709, 61284}, {52045, 52666}, {52046, 52667}, {53099, 60632}, {53101, 60102}, {53104, 54476}, {54608, 60145}, {54706, 60643}, {54815, 60100}, {59374, 59389}, {60118, 60228}, {60147, 60239}, {60291, 60314}, {60292, 60313}, {60327, 60646}, {60328, 60637}

X(61954) = midpoint of X(i) and X(j) for these {i,j}: {4, 15709}
X(61954) = reflection of X(i) in X(j) for these {i,j}: {10304, 15709}, {15705, 2}, {15707, 15699}, {15709, 5055}, {376, 15707}
X(61954) = inverse of X(15683) in orthocentroidal circle
X(61954) = inverse of X(15683) in Yff hyperbola
X(61954) = complement of X(62095)
X(61954) = anticomplement of X(15708)
X(61954) = pole of line {523, 15683} with respect to the orthocentroidal circle
X(61954) = pole of line {6, 15683} with respect to the Kiepert hyperbola
X(61954) = pole of line {523, 15683} with respect to the Yff hyperbola
X(61954) = pole of line {69, 61806} with respect to the Wallace hyperbola
X(61954) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(264), X(15683)}}, {{A, B, C, X(382), X(54923)}}, {{A, B, C, X(458), X(60625)}}, {{A, B, C, X(468), X(60331)}}, {{A, B, C, X(546), X(54552)}}, {{A, B, C, X(548), X(18855)}}, {{A, B, C, X(1217), X(49136)}}, {{A, B, C, X(1494), X(15705)}}, {{A, B, C, X(1585), X(60296)}}, {{A, B, C, X(1586), X(60295)}}, {{A, B, C, X(3346), X(44245)}}, {{A, B, C, X(3522), X(36889)}}, {{A, B, C, X(3528), X(60121)}}, {{A, B, C, X(3535), X(60300)}}, {{A, B, C, X(3536), X(60299)}}, {{A, B, C, X(3544), X(60122)}}, {{A, B, C, X(3832), X(55958)}}, {{A, B, C, X(4846), X(15690)}}, {{A, B, C, X(5094), X(60336)}}, {{A, B, C, X(6353), X(54521)}}, {{A, B, C, X(8889), X(54866)}}, {{A, B, C, X(10299), X(31363)}}, {{A, B, C, X(10301), X(43951)}}, {{A, B, C, X(10303), X(14860)}}, {{A, B, C, X(11539), X(46455)}}, {{A, B, C, X(13623), X(14093)}}, {{A, B, C, X(14863), X(21735)}}, {{A, B, C, X(15685), X(16251)}}, {{A, B, C, X(15692), X(35510)}}, {{A, B, C, X(18550), X(35400)}}, {{A, B, C, X(18850), X(33699)}}, {{A, B, C, X(33232), X(54682)}}, {{A, B, C, X(33263), X(57857)}}, {{A, B, C, X(33292), X(54551)}}, {{A, B, C, X(38282), X(60192)}}, {{A, B, C, X(52283), X(54639)}}, {{A, B, C, X(52285), X(54815)}}, {{A, B, C, X(52288), X(60200)}}, {{A, B, C, X(52289), X(60639)}}, {{A, B, C, X(52290), X(60333)}}, {{A, B, C, X(52299), X(60175)}}
X(61954) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10303, 17678}, {2, 15683, 15717}, {2, 17578, 376}, {2, 30, 15705}, {2, 3543, 3522}, {2, 381, 3832}, {2, 3854, 381}, {2, 4, 15683}, {2, 5059, 15692}, {3, 381, 3860}, {4, 15709, 30}, {4, 3090, 548}, {4, 3545, 5055}, {4, 3855, 3857}, {4, 5, 10303}, {4, 5072, 7486}, {4, 549, 15640}, {5, 12101, 15694}, {5, 14893, 15722}, {5, 5059, 16417}, {5, 546, 5073}, {20, 3091, 3851}, {30, 15699, 15707}, {30, 15709, 10304}, {30, 5055, 15709}, {381, 3545, 3839}, {381, 3830, 3858}, {381, 3851, 3845}, {381, 5066, 4}, {382, 10109, 15702}, {382, 15702, 15697}, {547, 3843, 15682}, {548, 5066, 11737}, {549, 5066, 5072}, {632, 15685, 15715}, {1656, 11001, 15721}, {1656, 14893, 11001}, {2043, 2044, 3544}, {3091, 3832, 5068}, {3091, 3839, 3545}, {3091, 3855, 3854}, {3522, 15683, 3534}, {3524, 14269, 3543}, {3524, 3533, 5054}, {3524, 3545, 5}, {3525, 5056, 11346}, {3526, 5055, 15699}, {3534, 5076, 15684}, {3543, 3839, 14269}, {3543, 5056, 11812}, {3544, 15682, 547}, {3544, 3843, 3523}, {3545, 5071, 14892}, {3628, 10303, 17542}, {3628, 15684, 15698}, {3830, 15692, 5059}, {3832, 5068, 3146}, {3839, 15699, 17578}, {3845, 3851, 5071}, {3850, 3855, 3091}, {3856, 5066, 549}, {3858, 11737, 3830}, {5054, 5055, 3628}, {5068, 15717, 15022}, {5071, 15721, 17532}, {6927, 15698, 15681}, {7809, 32874, 10513}, {9955, 50799, 34627}, {10109, 15697, 2}, {10303, 10304, 3524}, {10304, 15708, 15706}, {12101, 15694, 3529}, {13735, 15717, 3526}, {13741, 15022, 3090}, {14269, 14892, 3533}, {15684, 15698, 20}, {15706, 15709, 15708}, {18357, 50806, 34631}, {18586, 18587, 15712}, {19130, 50956, 11180}, {42920, 61719, 49873}

X(61955) = X(2)X(3)∩X(485)X(53520)

Barycentrics    5*a^4-12*(b^2-c^2)^2+7*a^2*(b^2+c^2) : :
X(61955) = -36*X[2]+17*X[3], 16*X[575]+3*X[48662], 16*X[946]+3*X[51515], 5*X[1482]+14*X[61256], 3*X[3060]+16*X[11017], -30*X[3763]+11*X[55620], -24*X[3817]+5*X[37624], 12*X[3818]+7*X[53092], 3*X[3917]+16*X[44871], -2*X[4301]+21*X[50807], 15*X[5603]+4*X[61246], 3*X[5790]+16*X[12571] and many others

X(61955) lies on these lines: {2, 3}, {485, 53520}, {486, 53517}, {575, 48662}, {946, 51515}, {1328, 31487}, {1482, 61256}, {3060, 11017}, {3411, 54594}, {3412, 54593}, {3592, 45384}, {3594, 45385}, {3763, 55620}, {3817, 37624}, {3818, 53092}, {3917, 44871}, {4301, 50807}, {5339, 43009}, {5340, 43008}, {5603, 61246}, {5790, 12571}, {5881, 50800}, {6199, 42268}, {6243, 40247}, {6395, 42269}, {6407, 42283}, {6408, 42284}, {6417, 42273}, {6418, 42270}, {6425, 35787}, {6426, 35786}, {6427, 6565}, {6428, 6564}, {6445, 42582}, {6446, 42583}, {6447, 23261}, {6448, 23251}, {6453, 42558}, {6454, 42557}, {6500, 31412}, {6501, 42561}, {6519, 10576}, {6522, 10577}, {7687, 11426}, {7758, 20112}, {7871, 15031}, {7982, 38140}, {9605, 18424}, {9692, 43522}, {9779, 12645}, {9955, 61296}, {10113, 15029}, {10222, 37712}, {10247, 19925}, {10516, 55724}, {10541, 48889}, {10545, 32138}, {10620, 15025}, {11451, 32137}, {11455, 32205}, {11480, 42592}, {11481, 42593}, {11482, 19130}, {11485, 44016}, {11486, 44015}, {12308, 36253}, {13321, 15058}, {13464, 50799}, {13665, 53516}, {13785, 53513}, {14226, 43376}, {14241, 43377}, {14845, 15012}, {14848, 50960}, {15021, 15088}, {15026, 16261}, {15027, 38789}, {15044, 61574}, {15069, 50957}, {15178, 18492}, {15305, 18874}, {15851, 61315}, {16189, 50798}, {16808, 43015}, {16809, 43014}, {18480, 61275}, {18493, 61287}, {18510, 42571}, {18512, 42570}, {18525, 61277}, {18526, 61280}, {18553, 53858}, {18581, 42693}, {18582, 42692}, {20397, 38790}, {20398, 38744}, {20399, 38733}, {20400, 48680}, {21358, 55597}, {22234, 47353}, {22236, 42919}, {22238, 42918}, {22330, 38072}, {22331, 39590}, {22615, 43314}, {22644, 43315}, {23039, 44863}, {23325, 58795}, {24206, 55595}, {25561, 50973}, {27355, 46852}, {30308, 34748}, {30435, 43457}, {31399, 50814}, {32533, 44731}, {34507, 50963}, {34718, 58249}, {35820, 42569}, {35821, 42568}, {37714, 58240}, {38021, 61289}, {38034, 61253}, {38127, 61261}, {38141, 38665}, {40280, 40284}, {42093, 42581}, {42094, 42580}, {42103, 42598}, {42106, 42599}, {42107, 42162}, {42110, 42159}, {42111, 42165}, {42114, 42164}, {42125, 42166}, {42128, 42163}, {42129, 42161}, {42132, 42160}, {42136, 42950}, {42137, 42951}, {42139, 42962}, {42142, 42963}, {42271, 42566}, {42272, 42567}, {42431, 43490}, {42432, 43489}, {42494, 43417}, {42495, 43416}, {42627, 43365}, {42628, 43364}, {42694, 43486}, {42695, 43485}, {42786, 55643}, {42799, 42814}, {42800, 42813}, {42920, 42974}, {42921, 42975}, {42930, 43029}, {42931, 43028}, {42936, 43331}, {42937, 43330}, {43238, 43548}, {43239, 43549}, {43240, 43497}, {43241, 43498}, {43420, 43646}, {43421, 43645}, {48661, 61263}, {48895, 55626}, {48901, 55602}, {50802, 61258}, {51024, 55600}, {51082, 61276}, {51163, 55632}, {53023, 55580}, {58230, 61268}, {59387, 61292}

X(61955) = inverse of X(62155) in orthocentroidal circle
X(61955) = inverse of X(62155) in Yff hyperbola
X(61955) = complement of X(62096)
X(61955) = pole of line {523, 62155} with respect to the orthocentroidal circle
X(61955) = pole of line {185, 62035} with respect to the Jerabek hyperbola
X(61955) = pole of line {6, 62155} with respect to the Kiepert hyperbola
X(61955) = pole of line {523, 62155} with respect to the Yff hyperbola
X(61955) = pole of line {69, 55686} with respect to the Wallace hyperbola
X(61955) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(3527), X(47486)}}, {{A, B, C, X(3855), X(17505)}}, {{A, B, C, X(5054), X(14860)}}, {{A, B, C, X(5068), X(21400)}}, {{A, B, C, X(5071), X(32533)}}, {{A, B, C, X(14093), X(60121)}}, {{A, B, C, X(14892), X(60122)}}, {{A, B, C, X(15319), X(15716)}}, {{A, B, C, X(18550), X(49135)}}, {{A, B, C, X(32534), X(44731)}}, {{A, B, C, X(46853), X(52441)}}
X(61955) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 14269, 3627}, {3, 15703, 3525}, {3, 3091, 3851}, {3, 3529, 15689}, {3, 3628, 15694}, {3, 5079, 5070}, {4, 3091, 12811}, {4, 5, 5054}, {4, 547, 15696}, {5, 12108, 3090}, {5, 14893, 3523}, {5, 1657, 15703}, {5, 3858, 14893}, {5, 546, 3146}, {140, 5076, 6978}, {376, 14269, 3830}, {381, 1656, 3832}, {381, 382, 3858}, {381, 3851, 3843}, {381, 5054, 3860}, {381, 5072, 546}, {382, 1656, 15706}, {546, 12811, 632}, {546, 3090, 5076}, {631, 17678, 140}, {632, 3530, 10303}, {1656, 14269, 17800}, {1656, 3627, 3}, {1656, 3832, 14269}, {2043, 2044, 14892}, {3090, 3146, 12108}, {3091, 16418, 6977}, {3091, 3544, 5066}, {3091, 3832, 3544}, {3091, 3855, 3857}, {3091, 3857, 381}, {3146, 10303, 376}, {3146, 3523, 17538}, {3523, 14893, 382}, {3525, 12102, 1657}, {3525, 3839, 12102}, {3529, 12812, 3526}, {3529, 5068, 12812}, {3530, 3544, 5079}, {3544, 3627, 1656}, {3830, 5054, 15681}, {3830, 5055, 15718}, {3843, 15681, 4}, {3843, 3851, 5055}, {3843, 5055, 5073}, {3845, 12812, 3529}, {3850, 3857, 3091}, {3853, 15720, 15685}, {3853, 5071, 15720}, {3856, 15704, 6956}, {3860, 12811, 12103}, {3861, 5056, 3534}, {5054, 15692, 15722}, {5066, 10303, 5072}, {5070, 17800, 3530}, {5339, 43332, 43009}, {5340, 43333, 43008}, {10113, 15029, 15039}, {12103, 12811, 5}, {15694, 15706, 15701}, {18586, 18587, 15700}

X(61956) = X(2)X(3)∩X(13)X(43307)

Barycentrics    8*a^4-19*(b^2-c^2)^2+11*a^2*(b^2+c^2) : :
X(61956) = -19*X[2]+9*X[3], 9*X[1352]+X[51187], -X[1353]+6*X[38072], -X[1483]+6*X[38021], -X[1484]+6*X[38077], 2*X[1699]+3*X[61260], -X[3654]+6*X[61262], 2*X[3656]+3*X[38138], -6*X[3817]+X[50824], 2*X[4669]+3*X[22791], -X[4677]+6*X[18357], -6*X[5102]+X[51182] and many others

X(61956) lies on these lines: {2, 3}, {13, 43307}, {14, 43306}, {395, 43247}, {396, 43246}, {397, 42507}, {398, 42506}, {511, 51129}, {517, 51067}, {523, 39489}, {952, 30308}, {1327, 18762}, {1328, 18538}, {1352, 51187}, {1353, 38072}, {1483, 38021}, {1484, 38077}, {1699, 61260}, {3564, 50956}, {3654, 61262}, {3656, 38138}, {3817, 50824}, {4669, 22791}, {4677, 18357}, {5102, 51182}, {5306, 43457}, {5318, 49908}, {5321, 49907}, {5349, 41943}, {5350, 41944}, {5461, 41151}, {5476, 50960}, {5587, 50807}, {5603, 50800}, {5690, 38076}, {5844, 50806}, {5965, 38136}, {6490, 6561}, {6491, 6560}, {6492, 42602}, {6493, 42603}, {8176, 51123}, {8252, 43503}, {8253, 43504}, {8584, 19130}, {8981, 42417}, {9300, 18424}, {9779, 50798}, {9955, 51071}, {10516, 50964}, {11178, 41152}, {11542, 41113}, {11543, 41112}, {12571, 51070}, {12816, 42118}, {12817, 42117}, {13570, 15067}, {13966, 42418}, {14226, 18512}, {14241, 18510}, {14458, 60287}, {14492, 60638}, {14831, 45958}, {14845, 45956}, {14853, 50957}, {15060, 21849}, {15300, 61575}, {15533, 18358}, {15605, 54157}, {16226, 18874}, {16644, 43108}, {16645, 43109}, {16808, 43229}, {16809, 43228}, {16960, 41108}, {16961, 41107}, {16966, 42791}, {16967, 42792}, {18362, 18907}, {18480, 51103}, {18483, 51069}, {18492, 51105}, {18581, 42519}, {18582, 42518}, {19116, 43323}, {19117, 43322}, {19925, 51091}, {20252, 36383}, {20253, 36382}, {20423, 51188}, {20583, 42785}, {21850, 22165}, {22505, 41148}, {22515, 36521}, {22566, 36523}, {24827, 36522}, {28146, 50825}, {28172, 51084}, {28178, 61264}, {28186, 50832}, {28190, 61266}, {28204, 51104}, {28212, 50822}, {28228, 38112}, {28232, 50821}, {28234, 38140}, {28236, 50803}, {29317, 50980}, {31162, 38081}, {31406, 39563}, {31670, 51186}, {34380, 50963}, {34648, 38022}, {34747, 61253}, {34773, 51108}, {36967, 43293}, {36968, 43292}, {37705, 51093}, {38034, 50796}, {38155, 50830}, {39884, 41153}, {41100, 42918}, {41101, 42919}, {41121, 42110}, {41122, 42107}, {41135, 61599}, {41858, 61580}, {41971, 42970}, {41972, 42971}, {42087, 54479}, {42088, 54480}, {42095, 42510}, {42098, 42511}, {42101, 46335}, {42102, 46334}, {42103, 42912}, {42106, 42913}, {42121, 42683}, {42124, 42682}, {42136, 42911}, {42137, 42910}, {42139, 49825}, {42142, 49824}, {42143, 49906}, {42144, 42632}, {42145, 42631}, {42146, 49905}, {42149, 42508}, {42152, 42509}, {42159, 49811}, {42162, 49810}, {42215, 42639}, {42216, 42640}, {42274, 52048}, {42277, 52047}, {42419, 43417}, {42420, 43416}, {42431, 43100}, {42432, 43107}, {42472, 42589}, {42473, 42588}, {42474, 43103}, {42475, 43102}, {42496, 42923}, {42497, 42922}, {42516, 49827}, {42517, 49826}, {42532, 42814}, {42533, 42813}, {42557, 43888}, {42558, 43887}, {42586, 42611}, {42587, 42610}, {42817, 43541}, {42818, 43540}, {42914, 43295}, {42915, 43294}, {42940, 42997}, {42941, 42996}, {42942, 42957}, {42943, 42956}, {42962, 43208}, {42963, 43207}, {42972, 49903}, {42973, 49904}, {42974, 49873}, {42975, 49874}, {43101, 43373}, {43104, 43372}, {43105, 43199}, {43106, 43200}, {43197, 43482}, {43198, 43481}, {43312, 53518}, {43313, 53519}, {43562, 53131}, {43563, 53130}, {47353, 59399}, {50805, 54448}, {50811, 61269}, {50865, 61263}, {50979, 51133}, {51026, 55649}, {51066, 61261}, {51094, 61244}, {51110, 61272}, {51173, 51183}, {54477, 60645}, {54582, 60131}, {59387, 61293}

X(61956) = midpoint of X(i) and X(j) for these {i,j}: {4, 15694}, {381, 3091}, {3543, 15696}, {3843, 5071}, {5076, 15692}, {14093, 17578}, {15687, 15712}, {30308, 50799}
X(61956) = reflection of X(i) in X(j) for these {i,j}: {12812, 11737}, {14093, 140}, {15694, 12812}, {15697, 12100}, {15711, 2}, {15714, 632}, {381, 3859}, {3858, 381}, {549, 1656}, {550, 15692}, {5076, 14893}, {631, 547}, {632, 5071}, {8703, 15713}
X(61956) = inverse of X(15685) in orthocentroidal circle
X(61956) = inverse of X(15685) in Yff hyperbola
X(61956) = complement of X(15695)
X(61956) = anticomplement of X(61823)
X(61956) = pole of line {523, 15685} with respect to the orthocentroidal circle
X(61956) = pole of line {6, 15685} with respect to the Kiepert hyperbola
X(61956) = pole of line {523, 15685} with respect to the Yff hyperbola
X(61956) = pole of line {69, 33612} with respect to the Wallace hyperbola
X(61956) = intersection, other than A, B, C, of circumconics {{A, B, C, X(264), X(15685)}}, {{A, B, C, X(1494), X(15711)}}, {{A, B, C, X(3613), X(45007)}}, {{A, B, C, X(3853), X(54924)}}, {{A, B, C, X(3858), X(54512)}}, {{A, B, C, X(3860), X(55958)}}, {{A, B, C, X(5073), X(54585)}}, {{A, B, C, X(11331), X(60287)}}, {{A, B, C, X(14860), X(14869)}}, {{A, B, C, X(33293), X(54551)}}, {{A, B, C, X(33923), X(60121)}}, {{A, B, C, X(52289), X(60638)}}
X(61956) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 30, 15711}, {2, 381, 3860}, {2, 3830, 15690}, {2, 3860, 3845}, {2, 4, 15685}, {5, 15687, 11539}, {30, 11737, 12812}, {30, 12100, 15697}, {30, 140, 14093}, {30, 14893, 5076}, {30, 381, 3858}, {30, 3859, 381}, {30, 5071, 632}, {30, 547, 631}, {30, 632, 15714}, {140, 15705, 549}, {381, 3545, 546}, {381, 3839, 3856}, {381, 3851, 3839}, {381, 5055, 3832}, {546, 10109, 3830}, {546, 11737, 15688}, {546, 12811, 3525}, {546, 16239, 4}, {547, 3627, 17504}, {549, 15699, 16239}, {631, 15694, 14890}, {631, 3091, 3851}, {632, 3858, 3843}, {1656, 15688, 15694}, {3091, 5076, 12811}, {3146, 5059, 6966}, {3545, 3830, 10109}, {3627, 14890, 15686}, {3832, 5055, 14893}, {3839, 3851, 547}, {3845, 8703, 15687}, {3850, 3855, 3857}, {3850, 3859, 3091}, {3851, 3856, 3627}, {3856, 5066, 3534}, {3857, 3858, 3859}, {5055, 15682, 11812}, {5055, 5076, 15692}, {5066, 10109, 3545}, {5066, 11540, 5072}, {5066, 12100, 11737}, {8703, 15713, 15712}, {10109, 12101, 15716}, {10109, 15690, 2}, {11539, 15687, 15704}, {11737, 15699, 5}, {11812, 14893, 15682}, {11812, 15682, 550}, {12100, 15686, 8703}, {12811, 14893, 5055}, {12812, 15694, 15699}, {12812, 16239, 1656}, {14093, 14269, 17578}, {14093, 17578, 30}, {15686, 15699, 14869}, {15694, 15697, 12100}, {15697, 15699, 15713}, {15713, 15714, 15693}, {15765, 18585, 12102}, {18586, 18587, 15717}, {30308, 50799, 952}, {41121, 42520, 42777}, {41122, 42521, 42778}, {42682, 43240, 42124}, {42683, 43241, 42121}

X(61957) = X(2)X(3)∩X(395)X(44015)

Barycentrics    10*a^4-23*(b^2-c^2)^2+13*a^2*(b^2+c^2) : :
X(61957) = -23*X[2]+11*X[3], 5*X[3656]+7*X[61256], -X[3818]+7*X[51133], -2*X[4701]+11*X[18357], X[9955]+2*X[50803], -5*X[10168]+2*X[51135], X[10627]+8*X[44871], 8*X[11017]+X[14449], X[11178]+5*X[51129], 8*X[12571]+X[61510], X[18358]+2*X[50959], -X[18480]+7*X[51078] and many others

X(61957) lies on these lines: {2, 3}, {395, 44015}, {396, 44016}, {3656, 61256}, {3818, 51133}, {4701, 18357}, {5349, 43108}, {5350, 43109}, {5844, 61257}, {6407, 43522}, {6408, 43521}, {7583, 43435}, {7584, 43434}, {9955, 50803}, {10168, 51135}, {10627, 44871}, {10653, 43429}, {10654, 43428}, {11017, 14449}, {11178, 51129}, {12571, 61510}, {12816, 42599}, {12817, 42598}, {12820, 43484}, {12821, 43483}, {16267, 42110}, {16268, 42107}, {16962, 42146}, {16963, 42143}, {18358, 50959}, {18480, 51078}, {18483, 50814}, {18492, 50824}, {19130, 50960}, {19883, 61267}, {19925, 61246}, {21849, 31834}, {21850, 50964}, {22791, 50807}, {23302, 43645}, {23303, 43646}, {25561, 61545}, {28194, 61262}, {28204, 61280}, {28208, 61269}, {28216, 61263}, {30308, 61296}, {34648, 61272}, {35770, 43380}, {35771, 43381}, {35786, 52048}, {35787, 52047}, {35822, 42573}, {35823, 42572}, {36430, 59649}, {37705, 50800}, {37712, 38034}, {37832, 43197}, {37835, 43198}, {38021, 61287}, {38022, 61271}, {38076, 38127}, {42104, 42474}, {42105, 42475}, {42122, 43107}, {42123, 43100}, {42126, 43649}, {42127, 43644}, {42135, 42496}, {42136, 43104}, {42137, 43101}, {42138, 42497}, {42283, 42558}, {42284, 42557}, {42415, 42906}, {42416, 42907}, {42488, 42980}, {42489, 42981}, {42502, 42991}, {42503, 42990}, {42627, 42970}, {42628, 42971}, {42692, 42972}, {42693, 42973}, {42775, 49873}, {42776, 49874}, {42853, 61532}, {42912, 42919}, {42913, 42918}, {42922, 43543}, {42923, 43542}, {42924, 49908}, {42925, 49907}, {42984, 52079}, {42985, 52080}, {43102, 43401}, {43103, 43402}, {43105, 43544}, {43106, 43545}, {43150, 51130}, {43207, 49824}, {43208, 49825}, {43240, 43245}, {43241, 43244}, {43548, 43643}, {43549, 43638}, {45959, 58470}, {50796, 61253}, {50799, 61244}, {50957, 51178}, {51029, 55639}, {51709, 61281}, {53620, 61260}

X(61957) = midpoint of X(i) and X(j) for these {i,j}: {4, 11539}, {5, 3839}, {546, 14892}, {3524, 15687}, {3627, 15688}, {3845, 5055}, {14269, 15699}
X(61957) = reflection of X(i) in X(j) for these {i,j}: {140, 5055}, {11539, 10109}, {14892, 5066}, {14893, 3839}, {15688, 11812}, {15690, 3524}, {19883, 61267}, {3524, 3628}, {3839, 3860}, {547, 14892}, {5055, 11737}, {8703, 14890}
X(61957) = inverse of X(62158) in orthocentroidal circle
X(61957) = inverse of X(62158) in Yff hyperbola
X(61957) = complement of X(62098)
X(61957) = pole of line {523, 62158} with respect to the orthocentroidal circle
X(61957) = pole of line {6, 42429} with respect to the Kiepert hyperbola
X(61957) = pole of line {523, 62158} with respect to the Yff hyperbola
X(61957) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(265), X(47599)}}, {{A, B, C, X(3858), X(55958)}}, {{A, B, C, X(12108), X(14860)}}, {{A, B, C, X(46853), X(60121)}}
X(61957) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15696, 549}, {2, 381, 3858}, {2, 3853, 15691}, {2, 5073, 15714}, {3, 5079, 17697}, {5, 15703, 10109}, {5, 1657, 3628}, {5, 381, 3860}, {5, 3830, 10124}, {5, 3845, 376}, {5, 3857, 3854}, {20, 17530, 631}, {30, 11737, 5055}, {30, 11812, 15688}, {30, 14890, 8703}, {30, 14892, 547}, {30, 3524, 15690}, {30, 3628, 3524}, {30, 3839, 14893}, {30, 3860, 3839}, {30, 5055, 140}, {30, 5066, 14892}, {140, 12812, 5067}, {140, 3853, 15704}, {140, 3856, 546}, {140, 5066, 11737}, {376, 15640, 1657}, {376, 3146, 15685}, {376, 3845, 12102}, {376, 5054, 17504}, {381, 3091, 3845}, {381, 3845, 3856}, {382, 5055, 15708}, {546, 547, 12101}, {547, 12101, 548}, {3090, 15686, 11540}, {3091, 11737, 5066}, {3091, 15704, 12811}, {3091, 5067, 3851}, {3146, 3851, 5}, {3545, 14269, 15699}, {3627, 5071, 11812}, {3830, 10124, 12103}, {3839, 15705, 4}, {3850, 3856, 3091}, {3850, 3857, 3859}, {3855, 3857, 3850}, {3858, 12811, 3853}, {3859, 5066, 381}, {5054, 15689, 15705}, {5056, 15684, 15713}, {5056, 16401, 6832}, {10109, 12108, 15703}, {10124, 12103, 12100}, {11539, 15705, 12108}, {11737, 15685, 12812}, {12103, 14893, 3830}, {14269, 15699, 30}, {15689, 15703, 5054}, {15703, 15705, 11539}, {18586, 18587, 10299}

X(61958) = X(2)X(3)∩X(13)X(42983)

Barycentrics    11*a^4-25*(b^2-c^2)^2+14*a^2*(b^2+c^2) : :
X(61958) = -25*X[2]+12*X[3], -25*X[145]+64*X[58237], X[153]+12*X[38077], X[962]+12*X[38076], 9*X[1699]+4*X[4745], 4*X[3656]+9*X[54448], 25*X[3679]+X[58248], 12*X[3817]+X[50864], 10*X[4669]+3*X[11531], -5*X[4677]+18*X[38155], -3*X[5032]+16*X[19130], 8*X[5097]+5*X[11180] and many others

X(61958) lies on these lines: {2, 3}, {13, 42983}, {14, 42982}, {145, 58237}, {153, 38077}, {671, 54522}, {962, 38076}, {1131, 35770}, {1132, 35771}, {1327, 60623}, {1328, 60622}, {1699, 4745}, {2996, 54734}, {3424, 60283}, {3656, 54448}, {3679, 58248}, {3817, 50864}, {4669, 11531}, {4677, 38155}, {5032, 19130}, {5097, 11180}, {5102, 47354}, {5304, 43457}, {5318, 49861}, {5321, 49862}, {5334, 41121}, {5335, 41122}, {5365, 16962}, {5366, 16963}, {5395, 54851}, {5418, 43563}, {5420, 43562}, {5478, 35750}, {5479, 36331}, {5480, 50992}, {5587, 50872}, {5603, 50799}, {5691, 51109}, {5886, 58234}, {5921, 38072}, {6199, 42539}, {6395, 42540}, {6411, 42537}, {6412, 42538}, {6427, 60291}, {6428, 60292}, {6433, 52666}, {6434, 52667}, {6437, 42417}, {6438, 42418}, {6480, 43257}, {6481, 43256}, {6560, 43566}, {6561, 43567}, {6564, 43889}, {6565, 43890}, {7773, 32874}, {7989, 34632}, {7999, 44871}, {8584, 50960}, {8976, 43561}, {9542, 42283}, {9779, 16200}, {10516, 50990}, {10991, 41148}, {11160, 37517}, {11185, 32896}, {11278, 31145}, {11485, 43246}, {11486, 43247}, {11522, 51096}, {11668, 54642}, {12816, 42918}, {12817, 42919}, {13665, 14226}, {13785, 14241}, {13951, 43560}, {14458, 60648}, {14484, 60216}, {14492, 60628}, {14537, 37689}, {14853, 50956}, {15031, 32836}, {15300, 38746}, {15533, 50959}, {16626, 36326}, {16627, 36324}, {16644, 42589}, {16645, 42588}, {16808, 41120}, {16809, 41119}, {18424, 37665}, {18489, 45794}, {18492, 38314}, {18510, 43386}, {18512, 43387}, {18581, 42533}, {18582, 42532}, {19925, 51093}, {20582, 55607}, {21356, 55582}, {22165, 55722}, {22236, 43202}, {22238, 43201}, {22615, 42525}, {22644, 42524}, {22796, 36318}, {22797, 36320}, {22831, 33624}, {22832, 33622}, {23253, 42603}, {23263, 42602}, {23302, 43421}, {23303, 43420}, {25055, 58231}, {25565, 55691}, {28208, 46934}, {30308, 50803}, {30392, 50868}, {31162, 51068}, {31404, 39563}, {32892, 37668}, {33179, 34627}, {33606, 43418}, {33607, 43419}, {33748, 51023}, {34648, 51110}, {34754, 49876}, {34755, 49875}, {36768, 59393}, {37640, 42502}, {37641, 42503}, {37832, 43466}, {37835, 43465}, {38034, 50800}, {38136, 50957}, {38140, 50807}, {38664, 41154}, {41100, 42106}, {41101, 42103}, {41107, 49859}, {41108, 49860}, {41112, 42507}, {41113, 42506}, {41895, 54645}, {42107, 49948}, {42110, 49947}, {42126, 43553}, {42127, 43552}, {42129, 43109}, {42132, 43108}, {42133, 42511}, {42134, 42510}, {42135, 43542}, {42138, 43543}, {42139, 43229}, {42140, 42791}, {42141, 42792}, {42142, 43228}, {42154, 42472}, {42155, 42473}, {42268, 42522}, {42269, 42523}, {42284, 43888}, {42419, 42988}, {42420, 42989}, {42476, 42626}, {42477, 42625}, {42504, 43331}, {42505, 43330}, {42526, 52047}, {42527, 52048}, {42557, 43525}, {42558, 43526}, {42584, 54579}, {42585, 54578}, {42631, 43226}, {42632, 43227}, {42813, 49904}, {42814, 49903}, {42906, 42912}, {42907, 42913}, {42932, 43478}, {42933, 43477}, {42972, 43009}, {42973, 43008}, {43314, 43504}, {43315, 43503}, {43332, 49813}, {43333, 49812}, {43548, 54580}, {43549, 54581}, {43951, 60641}, {47353, 51133}, {50806, 59388}, {50808, 61264}, {50862, 54445}, {50863, 51705}, {50874, 59420}, {50964, 54132}, {50969, 55645}, {50991, 51131}, {50993, 51212}, {50994, 54131}, {51025, 55703}, {51085, 61271}, {51143, 54170}, {51186, 55591}, {51211, 54173}, {51216, 51737}, {51217, 59411}, {51537, 55711}, {53101, 54644}, {53108, 54896}, {54519, 60238}, {54520, 60277}, {54521, 60626}, {54639, 54934}, {54920, 60632}, {54921, 60281}, {60127, 60635}, {60307, 60312}, {60308, 60311}

X(61958) = inverse of X(62160) in orthocentroidal circle
X(61958) = inverse of X(62160) in Yff hyperbola
X(61958) = complement of X(62099)
X(61958) = anticomplement of X(61822)
X(61958) = pole of line {523, 62160} with respect to the orthocentroidal circle
X(61958) = pole of line {6, 41957} with respect to the Kiepert hyperbola
X(61958) = pole of line {523, 62160} with respect to the Yff hyperbola
X(61958) = pole of line {69, 61805} with respect to the Wallace hyperbola
X(61958) = intersection, other than A, B, C, of circumconics {{A, B, C, X(253), X(19708)}}, {{A, B, C, X(468), X(54522)}}, {{A, B, C, X(6353), X(54734)}}, {{A, B, C, X(7486), X(15749)}}, {{A, B, C, X(8889), X(54851)}}, {{A, B, C, X(11331), X(60648)}}, {{A, B, C, X(15696), X(18855)}}, {{A, B, C, X(15712), X(31363)}}, {{A, B, C, X(17538), X(54838)}}, {{A, B, C, X(21735), X(60121)}}, {{A, B, C, X(33703), X(54585)}}, {{A, B, C, X(50691), X(54923)}}, {{A, B, C, X(52288), X(60216)}}, {{A, B, C, X(52289), X(60628)}}, {{A, B, C, X(52290), X(54645)}}
X(61958) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15682, 10304}, {2, 15683, 12100}, {2, 15705, 15713}, {2, 3522, 15701}, {2, 3830, 15697}, {2, 3832, 3845}, {2, 3845, 3543}, {4, 3090, 15696}, {4, 3530, 3146}, {4, 3545, 547}, {4, 5071, 15710}, {140, 4188, 7486}, {381, 14269, 3856}, {381, 3545, 3832}, {381, 5055, 3858}, {547, 15681, 15702}, {547, 15690, 11540}, {549, 15701, 6967}, {549, 6863, 15719}, {3090, 12100, 2}, {3090, 14269, 15683}, {3091, 3543, 3545}, {3091, 3832, 5056}, {3091, 7486, 3851}, {3146, 5055, 15721}, {3523, 10304, 14891}, {3523, 15710, 15692}, {3524, 11737, 15022}, {3543, 11001, 15640}, {3543, 15708, 20}, {3543, 15721, 15686}, {3543, 3832, 3839}, {3543, 5056, 15708}, {3544, 14269, 17556}, {3545, 15702, 5}, {3830, 11812, 11001}, {3832, 3850, 3091}, {3839, 15692, 4}, {3843, 11737, 3524}, {3845, 11812, 3830}, {3845, 15686, 12101}, {3855, 3857, 3854}, {4223, 13735, 1656}, {5055, 15686, 3533}, {5056, 10303, 5067}, {5071, 15710, 5070}, {7486, 10304, 17678}, {8703, 11540, 15693}, {11001, 15719, 8703}, {15682, 15690, 5059}, {15682, 15702, 15690}, {15704, 17580, 3523}, {16808, 41120, 49825}, {30308, 50803, 59387}, {42539, 42604, 6199}, {42540, 42605, 6395}

X(61959) = X(1)X(51078)∩X(2)X(3)

Barycentrics    13*a^4-29*(b^2-c^2)^2+16*a^2*(b^2+c^2) : :
X(61959) = X[1]+14*X[51078], -29*X[2]+14*X[3], X[6]+14*X[51133], X[8]+14*X[50807], X[69]+14*X[50964], X[145]+14*X[50800], X[193]+14*X[50957], 8*X[3625]+7*X[34631], X[3630]+14*X[50959], X[3633]+14*X[50796], 14*X[3656]+X[20053], X[4668]+14*X[51074] and many others

X(61959) lies on these lines: {1, 51078}, {2, 3}, {6, 51133}, {8, 50807}, {69, 50964}, {145, 50800}, {193, 50957}, {1327, 13939}, {1328, 13886}, {3625, 34631}, {3630, 50959}, {3633, 50796}, {3656, 20053}, {4668, 51074}, {4718, 51041}, {4764, 51038}, {5334, 42777}, {5335, 42778}, {5365, 49905}, {5366, 49906}, {6144, 47354}, {6431, 60306}, {6432, 60305}, {7581, 51850}, {7582, 51849}, {7773, 32888}, {9540, 43522}, {9955, 50818}, {10595, 30308}, {11180, 32455}, {12017, 51216}, {13935, 43521}, {14226, 60289}, {14241, 60290}, {14927, 25565}, {16226, 16261}, {16960, 42972}, {16961, 42973}, {16962, 42103}, {16963, 42106}, {16966, 54592}, {16967, 54591}, {18358, 51179}, {18581, 42517}, {18582, 42516}, {18844, 60185}, {19130, 50974}, {19875, 28232}, {20080, 51173}, {28228, 38076}, {28234, 38074}, {28236, 38021}, {32819, 32889}, {32823, 32877}, {33604, 42166}, {33605, 42163}, {34089, 43408}, {34091, 43407}, {35822, 43387}, {35823, 43386}, {36889, 57896}, {36967, 43472}, {36968, 43471}, {36969, 42473}, {36970, 42472}, {41107, 42495}, {41108, 42494}, {41112, 43016}, {41113, 43017}, {42095, 43481}, {42098, 43482}, {42107, 43543}, {42110, 43542}, {42119, 43240}, {42120, 43241}, {42122, 43478}, {42123, 43477}, {42139, 43015}, {42142, 43014}, {42263, 43517}, {42264, 43518}, {42274, 42574}, {42277, 42575}, {42518, 49827}, {42519, 49826}, {42586, 42948}, {42587, 42949}, {42588, 43491}, {42589, 43492}, {42635, 44016}, {42636, 44015}, {42682, 43493}, {42683, 43494}, {42775, 61719}, {42801, 49908}, {42802, 49907}, {42813, 49812}, {42814, 49813}, {42912, 43365}, {42913, 43364}, {42926, 54581}, {42927, 54580}, {42940, 43463}, {42941, 43464}, {42986, 43417}, {42987, 43416}, {43374, 52666}, {43375, 52667}, {43446, 43501}, {43447, 43502}, {43536, 60310}, {51075, 61256}, {51131, 54131}, {54597, 60309}, {54616, 60325}, {54890, 60629}, {60301, 60304}, {60302, 60303}, {60326, 60616}, {60329, 60627}

X(61959) = midpoint of X(i) and X(j) for these {i,j}: {1656, 14269}, {10304, 17578}
X(61959) = reflection of X(i) in X(j) for these {i,j}: {10304, 15694}, {15689, 15712}, {15693, 15699}, {3522, 5054}, {3545, 3091}, {5071, 3545}
X(61959) = inverse of X(62161) in orthocentroidal circle
X(61959) = inverse of X(62161) in Yff hyperbola
X(61959) = pole of line {523, 62161} with respect to the orthocentroidal circle
X(61959) = pole of line {6, 62161} with respect to the Kiepert hyperbola
X(61959) = pole of line {523, 62161} with respect to the Yff hyperbola
X(61959) = pole of line {69, 15718} with respect to the Wallace hyperbola
X(61959) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(15718)}}, {{A, B, C, X(376), X(57896)}}, {{A, B, C, X(548), X(36889)}}, {{A, B, C, X(15740), X(58192)}}, {{A, B, C, X(21734), X(60121)}}
X(61959) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14093, 631}, {2, 20, 15718}, {2, 3543, 548}, {2, 3627, 376}, {3, 1010, 10303}, {4, 15715, 15682}, {5, 3845, 15691}, {30, 15694, 10304}, {30, 15699, 15693}, {30, 15712, 15689}, {30, 3091, 3545}, {30, 3545, 5071}, {30, 5054, 3522}, {376, 15682, 17800}, {376, 5066, 3544}, {376, 631, 15711}, {381, 3830, 3856}, {381, 3851, 3860}, {381, 5066, 3832}, {632, 3522, 13634}, {3091, 3832, 1656}, {3091, 3854, 3859}, {3091, 6979, 15721}, {3522, 15692, 15759}, {3524, 11001, 15688}, {3524, 3839, 4}, {3530, 3627, 1657}, {3543, 15699, 15710}, {3545, 15709, 5}, {3843, 3850, 3091}, {3843, 5072, 15712}, {3845, 15694, 17578}, {3845, 6964, 8703}, {3851, 3860, 3543}, {3854, 3857, 3855}, {3855, 5067, 6938}, {3858, 12812, 3843}, {3861, 15703, 15640}, {5056, 15687, 15698}, {5067, 15682, 15715}, {5079, 17578, 6947}, {10109, 15683, 3533}, {10304, 17578, 30}, {12812, 14093, 2}, {14269, 15706, 3627}, {14892, 14893, 14890}, {15640, 15703, 10299}, {15682, 15759, 11001}, {15687, 15698, 11541}, {15688, 15709, 3524}, {15691, 15694, 15692}, {15699, 15710, 3525}, {16962, 42103, 43202}, {16963, 42106, 43201}, {42098, 43482, 43554}

X(61960) = X(2)X(3)∩X(511)X(51131)

Barycentrics    14*a^4-31*(b^2-c^2)^2+17*a^2*(b^2+c^2) : :
X(61960) = -31*X[2]+15*X[3], -X[3631]+5*X[25561], 7*X[3656]+9*X[61254], -X[4669]+9*X[38140], -X[4745]+3*X[61259], X[5476]+7*X[51133], 9*X[9779]+7*X[50800], -4*X[15003]+X[16982], -X[15534]+9*X[38136], -5*X[18357]+X[34641], 3*X[18553]+X[41149], -5*X[19130]+X[20583] and many others

X(61960) lies on these lines: {2, 3}, {511, 51131}, {517, 51076}, {952, 50803}, {3564, 50960}, {3631, 25561}, {3656, 61254}, {4669, 38140}, {4745, 61259}, {5318, 42977}, {5321, 42976}, {5339, 49860}, {5340, 49859}, {5476, 51133}, {5844, 50802}, {6459, 42526}, {6460, 42527}, {8981, 12819}, {9779, 50800}, {10653, 43247}, {10654, 43246}, {11542, 43419}, {11543, 43418}, {12816, 42416}, {12817, 42415}, {12818, 13966}, {12820, 42137}, {12821, 42136}, {13846, 42643}, {13847, 42644}, {15003, 16982}, {15534, 38136}, {16267, 42419}, {16268, 42420}, {18357, 34641}, {18553, 41149}, {19130, 20583}, {22165, 51129}, {23249, 42640}, {23259, 42639}, {28174, 51069}, {28224, 51103}, {30308, 61291}, {34380, 50959}, {34648, 51700}, {34747, 61250}, {35786, 42418}, {35787, 42417}, {37832, 43108}, {37835, 43109}, {38021, 61284}, {38034, 50799}, {38076, 40273}, {38137, 60971}, {38138, 50806}, {39884, 51185}, {41100, 42143}, {41101, 42146}, {41107, 42107}, {41108, 42110}, {41119, 43207}, {41120, 43208}, {41121, 43417}, {41122, 43416}, {42087, 43476}, {42088, 43475}, {42093, 43649}, {42094, 43644}, {42099, 54576}, {42100, 54577}, {42103, 49905}, {42106, 49906}, {42125, 49874}, {42128, 49873}, {42129, 42588}, {42132, 42589}, {42135, 49947}, {42138, 49948}, {42510, 42628}, {42511, 42627}, {42530, 42892}, {42531, 42893}, {42682, 43199}, {42683, 43200}, {42888, 46335}, {42889, 46334}, {42942, 43196}, {42943, 43195}, {43110, 43228}, {43111, 43229}, {50810, 61260}, {50824, 61274}, {50828, 61267}, {50830, 61257}, {50963, 50992}, {51078, 51709}, {51092, 61245}, {51096, 61249}, {51109, 61269}, {51123, 53143}, {51213, 55624}

X(61960) = midpoint of X(i) and X(j) for these {i,j}: {4, 10124}, {381, 3850}, {546, 11737}, {547, 3861}, {549, 12102}, {3530, 15687}, {3628, 14893}, {3830, 15759}, {3845, 10109}, {3853, 14891}, {3860, 5066}, {11812, 12101}, {34648, 51700}
X(61960) = reflection of X(i) in X(j) for these {i,j}: {11540, 10109}, {12108, 547}, {3856, 381}
X(61960) = inverse of X(62163) in orthocentroidal circle
X(61960) = inverse of X(62163) in Yff hyperbola
X(61960) = complement of X(62101)
X(61960) = pole of line {523, 62163} with respect to the orthocentroidal circle
X(61960) = pole of line {6, 62163} with respect to the Kiepert hyperbola
X(61960) = pole of line {523, 62163} with respect to the Yff hyperbola
X(61960) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3856), X(54512)}}, {{A, B, C, X(8703), X(57897)}}, {{A, B, C, X(15702), X(46168)}}, {{A, B, C, X(18317), X(41981)}}, {{A, B, C, X(49136), X(54585)}}
X(61960) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11001, 15700}, {2, 15640, 15710}, {2, 382, 8703}, {2, 3830, 550}, {2, 5066, 11737}, {4, 14892, 10124}, {5, 3524, 547}, {5, 3627, 3533}, {5, 3845, 3534}, {5, 5076, 140}, {30, 10109, 11540}, {30, 381, 3856}, {30, 547, 12108}, {140, 15722, 11812}, {381, 3545, 3858}, {381, 5066, 3860}, {382, 3858, 546}, {546, 3851, 3530}, {546, 5066, 2}, {546, 5079, 12102}, {546, 550, 3861}, {547, 14893, 15683}, {547, 3830, 15759}, {550, 17504, 14093}, {1656, 15691, 14890}, {3091, 12108, 12811}, {3091, 15683, 3545}, {3529, 14269, 15687}, {3529, 3851, 5}, {3534, 3845, 12101}, {3544, 3839, 15681}, {3545, 14893, 3628}, {3545, 3839, 15706}, {3545, 3858, 14893}, {3628, 12102, 17538}, {3845, 15713, 3830}, {3845, 15719, 3853}, {3850, 3860, 5066}, {3850, 3861, 3091}, {3853, 5055, 14891}, {3854, 3857, 3859}, {3857, 3859, 3850}, {3860, 10109, 3845}, {5066, 15690, 14892}, {11540, 12108, 15713}, {11812, 12101, 30}, {11812, 15759, 3524}, {14269, 15681, 5076}, {14269, 15694, 382}, {14269, 15720, 3543}, {14892, 15701, 10109}

X(61961) = X(2)X(3)∩X(1285)X(18362)

Barycentrics    19*a^4-35*(b^2-c^2)^2+16*a^2*(b^2+c^2) : :
X(61961) = -35*X[2]+18*X[3], 3*X[1699]+14*X[51078], 15*X[3817]+2*X[50868], -3*X[5102]+20*X[50959], -18*X[5480]+X[51187], -27*X[5587]+10*X[51067], 15*X[5603]+2*X[50871], 9*X[6054]+8*X[41147], -3*X[7967]+20*X[30308], -18*X[9779]+X[50818], -24*X[10172]+7*X[50813], -27*X[10516]+10*X[51142] and many others

X(61961) lies on these lines: {2, 3}, {590, 43522}, {615, 43521}, {1285, 18362}, {1699, 51078}, {1992, 49855}, {3817, 50868}, {5102, 50959}, {5339, 42502}, {5340, 42503}, {5349, 42509}, {5350, 42508}, {5480, 51187}, {5485, 54707}, {5587, 51067}, {5603, 50871}, {6054, 41147}, {6419, 42608}, {6420, 42609}, {6425, 42606}, {6426, 42607}, {6468, 43257}, {6469, 43256}, {6470, 23275}, {6471, 23269}, {6564, 43386}, {6565, 43387}, {7773, 32892}, {7967, 30308}, {9540, 43258}, {9779, 50818}, {10155, 54647}, {10172, 50813}, {10516, 51142}, {10645, 43369}, {10646, 43368}, {11180, 41149}, {11224, 50796}, {11231, 50873}, {11488, 42901}, {11489, 42900}, {11531, 38074}, {12571, 34627}, {12816, 34755}, {12817, 34754}, {13665, 43890}, {13785, 43889}, {13935, 43259}, {14226, 60301}, {14241, 60302}, {14492, 60627}, {14853, 51027}, {15516, 51537}, {15520, 50974}, {16241, 54479}, {16242, 54480}, {16261, 58470}, {18483, 51066}, {18492, 51071}, {18581, 43020}, {18582, 43021}, {18842, 54612}, {19925, 34631}, {21356, 55585}, {22806, 49017}, {22807, 49016}, {23253, 42418}, {23263, 42417}, {25561, 50994}, {25565, 55689}, {31162, 51070}, {32532, 54523}, {32785, 43504}, {32786, 43503}, {33602, 33605}, {33603, 33604}, {34648, 41150}, {37517, 50992}, {38021, 51104}, {38028, 50863}, {38110, 51216}, {38155, 50803}, {38317, 51177}, {39561, 51023}, {39874, 51185}, {41107, 42139}, {41108, 42142}, {41121, 42103}, {41122, 42106}, {41152, 54131}, {41153, 55711}, {42099, 43002}, {42100, 43003}, {42111, 46334}, {42114, 46335}, {42115, 43477}, {42116, 43478}, {42119, 43199}, {42120, 43200}, {42133, 49905}, {42134, 49906}, {42154, 43554}, {42155, 43555}, {42494, 49903}, {42495, 49904}, {42506, 42921}, {42507, 42920}, {42510, 42893}, {42511, 42892}, {42918, 43244}, {42919, 43245}, {42972, 49811}, {42973, 49810}, {42986, 43541}, {42987, 43540}, {43374, 53130}, {43375, 53131}, {43493, 43502}, {43494, 43501}, {43536, 60308}, {43542, 49827}, {43543, 49826}, {43566, 52048}, {43567, 52047}, {44019, 49813}, {44020, 49812}, {47353, 51131}, {47354, 51188}, {48913, 52713}, {50807, 59387}, {50815, 61265}, {50956, 51214}, {50960, 54132}, {50989, 55722}, {50991, 55582}, {51076, 51107}, {51133, 51189}, {51165, 55618}, {54477, 60616}, {54582, 60629}, {54597, 60307}, {54637, 60127}, {54710, 54838}, {54785, 54827}, {60150, 60284}, {60185, 60281}

X(61961) = reflection of X(i) in X(j) for these {i,j}: {3854, 381}
X(61961) = inverse of X(62049) in orthocentroidal circle
X(61961) = inverse of X(62049) in Yff hyperbola
X(61961) = anticomplement of X(15722)
X(61961) = pole of line {523, 62049} with respect to the orthocentroidal circle
X(61961) = pole of line {6, 62049} with respect to the Kiepert hyperbola
X(61961) = pole of line {523, 62049} with respect to the Yff hyperbola
X(61961) = pole of line {69, 61797} with respect to the Wallace hyperbola
X(61961) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3522), X(54838)}}, {{A, B, C, X(3854), X(54512)}}, {{A, B, C, X(4232), X(54707)}}, {{A, B, C, X(5055), X(43699)}}, {{A, B, C, X(5059), X(54585)}}, {{A, B, C, X(5068), X(54667)}}, {{A, B, C, X(5070), X(15749)}}, {{A, B, C, X(13603), X(35501)}}, {{A, B, C, X(14491), X(55572)}}, {{A, B, C, X(15690), X(36889)}}, {{A, B, C, X(17578), X(54924)}}, {{A, B, C, X(52284), X(54612)}}, {{A, B, C, X(52289), X(60627)}}, {{A, B, C, X(53857), X(54523)}}
X(61961) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15685, 15698}, {2, 15690, 15719}, {2, 3543, 15690}, {3, 10124, 15708}, {3, 15682, 11001}, {3, 3545, 5071}, {3, 3858, 3832}, {3, 7486, 3533}, {4, 15704, 1532}, {4, 3545, 15702}, {4, 6906, 3856}, {4, 6938, 5072}, {30, 381, 3854}, {376, 3526, 3524}, {376, 3545, 5056}, {381, 14269, 3857}, {381, 3839, 3855}, {381, 3858, 3839}, {381, 3860, 2}, {381, 5055, 3859}, {546, 11812, 3845}, {3091, 3839, 15683}, {3525, 3843, 4}, {3526, 14093, 15707}, {3526, 3861, 17578}, {3543, 3545, 5067}, {3543, 3850, 3545}, {3832, 5056, 546}, {3839, 15683, 3861}, {3839, 5068, 15687}, {3845, 5066, 3}, {3855, 15682, 5066}, {3861, 15713, 3830}, {3861, 5066, 15713}, {5068, 15687, 15709}, {10109, 14269, 15640}, {10109, 15640, 631}, {15682, 15709, 15697}, {15683, 15721, 14093}, {15687, 15697, 15682}, {15699, 15712, 10124}, {15699, 17578, 376}, {49855, 49858, 1992}

X(61962) = X(1)X(51076)∩X(2)X(3)

Barycentrics    17*a^4-31*(b^2-c^2)^2+14*a^2*(b^2+c^2) : :
X(61962) = -X[1]+16*X[51076], -31*X[2]+16*X[3], -X[6]+16*X[51131], -X[8]+16*X[50803], -X[69]+16*X[50960], -X[145]+16*X[50802], -X[193]+16*X[50959], -16*X[946]+X[20049], -X[1278]+16*X[51041], 8*X[3098]+7*X[51213], -X[3241]+16*X[12571], -X[3621]+16*X[50796] and many others

X(61962) lies on these lines: {1, 51076}, {2, 3}, {6, 51131}, {8, 50803}, {13, 42902}, {14, 42903}, {69, 50960}, {145, 50802}, {193, 50959}, {395, 43201}, {396, 43202}, {946, 20049}, {1278, 51041}, {3098, 51213}, {3241, 12571}, {3621, 50796}, {3622, 34648}, {3623, 18492}, {3656, 20014}, {3828, 10248}, {4678, 31162}, {4788, 51038}, {5318, 42517}, {5321, 42516}, {5343, 41121}, {5344, 41122}, {5550, 50862}, {6459, 43567}, {6460, 43566}, {7773, 32882}, {9543, 41967}, {9779, 28236}, {9812, 38076}, {9880, 35369}, {11008, 51130}, {11057, 32870}, {11180, 50964}, {11522, 51092}, {14484, 60635}, {16267, 42103}, {16268, 42106}, {16644, 42682}, {16645, 42683}, {16960, 42799}, {16961, 42800}, {16962, 42133}, {16963, 42134}, {16966, 43331}, {16967, 43330}, {19106, 43490}, {19107, 43489}, {19925, 31145}, {20050, 51075}, {20052, 50799}, {20054, 50801}, {20080, 47354}, {20105, 44422}, {25561, 54174}, {28228, 53620}, {28234, 54448}, {32827, 32874}, {32869, 48913}, {34627, 50807}, {34631, 50800}, {36969, 42513}, {36970, 42512}, {38259, 54522}, {41945, 43520}, {41946, 43519}, {41968, 43384}, {42095, 43473}, {42098, 43474}, {42139, 42778}, {42142, 42777}, {42159, 49874}, {42162, 49873}, {42472, 42940}, {42473, 42941}, {42520, 42814}, {42521, 42813}, {42582, 54543}, {42583, 54542}, {42588, 42599}, {42589, 42598}, {42690, 43111}, {42691, 43110}, {42775, 43228}, {42776, 43229}, {42803, 42817}, {42804, 42818}, {42942, 43478}, {42943, 43477}, {42972, 43403}, {42973, 43404}, {43328, 43417}, {43329, 43416}, {43401, 43870}, {43402, 43869}, {43465, 43552}, {43466, 43553}, {43479, 54580}, {43480, 54581}, {43497, 43544}, {43498, 43545}, {43560, 60623}, {43561, 60622}, {43783, 49825}, {43784, 49824}, {43951, 60628}, {46931, 50808}, {46933, 50865}, {51129, 51170}, {51133, 54131}, {53101, 54921}, {54706, 60277}, {59375, 59389}, {60147, 60648}, {60216, 60328}, {60238, 60327}, {60283, 60324}

X(61962) = midpoint of X(i) and X(j) for these {i,j}: {3091, 3839}
X(61962) = reflection of X(i) in X(j) for these {i,j}: {14093, 11539}, {15688, 15713}, {15697, 3524}, {3524, 1656}, {631, 5055}
X(61962) = inverse of X(62048) in orthocentroidal circle
X(61962) = inverse of X(62048) in Yff hyperbola
X(61962) = anticomplement of X(61812)
X(61962) = pole of line {523, 62048} with respect to the orthocentroidal circle
X(61962) = pole of line {6, 62048} with respect to the Kiepert hyperbola
X(61962) = pole of line {523, 62048} with respect to the Yff hyperbola
X(61962) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(3854), X(55958)}}, {{A, B, C, X(33703), X(54923)}}, {{A, B, C, X(36889), X(50693)}}, {{A, B, C, X(38282), X(54522)}}, {{A, B, C, X(52288), X(60635)}}, {{A, B, C, X(60121), X(61138)}}
X(61962) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15723, 17542}, {2, 381, 3854}, {4, 3545, 5054}, {4, 3855, 12811}, {4, 5079, 20}, {4, 8703, 3543}, {30, 11539, 14093}, {30, 15713, 15688}, {30, 1656, 3524}, {30, 3524, 15697}, {30, 5055, 631}, {381, 3830, 3857}, {381, 3845, 3855}, {381, 3860, 4}, {546, 10124, 3845}, {631, 3091, 5068}, {631, 8703, 15692}, {1656, 3855, 3091}, {3090, 14893, 15640}, {3091, 3525, 7402}, {3091, 3839, 30}, {3091, 3858, 3832}, {3091, 5076, 15022}, {3146, 15022, 14869}, {3522, 5071, 2}, {3543, 15700, 15683}, {3543, 5055, 15705}, {3545, 14269, 10304}, {3830, 14892, 15709}, {3832, 5068, 546}, {3839, 10304, 14269}, {3845, 12811, 15681}, {5054, 17504, 15719}, {5055, 11541, 15708}, {5068, 15705, 5055}, {5072, 12101, 15702}, {11001, 11737, 7486}, {12812, 15687, 15695}, {14892, 15709, 5056}, {15697, 15714, 3522}

X(61963) = X(2)X(3)∩X(511)X(51133)

Barycentrics    16*a^4-29*(b^2-c^2)^2+13*a^2*(b^2+c^2) : :
X(61963) = -29*X[2]+15*X[3], 6*X[1699]+X[50823], -2*X[3654]+9*X[61260], 4*X[3656]+3*X[61251], 5*X[3818]+2*X[20583], -2*X[4677]+9*X[38138], -2*X[4745]+9*X[38140], -X[5476]+8*X[51131], -2*X[8584]+9*X[38136], -3*X[10283]+10*X[30308], -15*X[12571]+X[51095], -X[15533]+15*X[50956] and many others

X(61963) lies on these lines: {2, 3}, {511, 51133}, {517, 51078}, {952, 50807}, {1699, 50823}, {3564, 50964}, {3654, 61260}, {3656, 61251}, {3818, 20583}, {4677, 38138}, {4745, 38140}, {5318, 42533}, {5321, 42532}, {5339, 42419}, {5340, 42420}, {5349, 42939}, {5350, 42938}, {5476, 51131}, {5844, 50800}, {6417, 60306}, {6418, 60305}, {8584, 38136}, {10137, 60293}, {10138, 60294}, {10283, 30308}, {12571, 51095}, {12820, 37835}, {12821, 37832}, {13664, 22807}, {13784, 22806}, {14488, 60286}, {15533, 50956}, {15808, 28208}, {16241, 43643}, {16242, 43638}, {16966, 43476}, {16967, 43475}, {18492, 61295}, {18581, 43429}, {18582, 43428}, {22791, 34641}, {22793, 51069}, {28168, 50833}, {28178, 50826}, {29323, 50988}, {33602, 43208}, {33603, 43207}, {34380, 50957}, {34747, 37705}, {35255, 43504}, {35256, 43503}, {38079, 48889}, {38081, 40273}, {38137, 60963}, {39593, 43457}, {41100, 42107}, {41101, 42110}, {41107, 42503}, {41108, 42502}, {41112, 43111}, {41113, 43110}, {41119, 43417}, {41120, 43416}, {41121, 42633}, {41122, 42634}, {41949, 41956}, {41950, 41955}, {42093, 43108}, {42094, 43109}, {42103, 49947}, {42106, 49948}, {42108, 54576}, {42109, 54577}, {42117, 49907}, {42118, 49908}, {42121, 43195}, {42124, 43196}, {42125, 49825}, {42128, 49824}, {42135, 43228}, {42136, 43639}, {42137, 43640}, {42138, 43229}, {42143, 42510}, {42146, 42511}, {42163, 43546}, {42166, 43547}, {42268, 42608}, {42269, 42609}, {42283, 42606}, {42284, 42607}, {42415, 42916}, {42416, 42917}, {42474, 42492}, {42475, 42493}, {42496, 49827}, {42497, 49826}, {42508, 42913}, {42509, 42912}, {42524, 42583}, {42525, 42582}, {42602, 43516}, {42603, 43515}, {42625, 43648}, {42626, 43647}, {42635, 42967}, {42636, 42966}, {42647, 42728}, {42648, 42727}, {42910, 43631}, {42911, 43630}, {42922, 43404}, {42923, 43403}, {43101, 46334}, {43104, 46335}, {43316, 43792}, {43317, 43791}, {43370, 43402}, {43371, 43401}, {48901, 51143}, {50811, 61270}, {50831, 59387}, {50832, 61269}, {50863, 58230}, {50865, 61262}, {50978, 53023}, {51066, 61259}, {51076, 51709}, {51093, 61245}, {51097, 61297}, {51105, 61273}, {51216, 55697}, {54717, 60279}

X(61963) = midpoint of X(i) and X(j) for these {i,j}: {4, 15703}, {381, 3832}, {3830, 15698}, {14869, 15687}
X(61963) = reflection of X(i) in X(j) for these {i,j}: {3523, 547}, {3857, 381}, {549, 3090}, {550, 15700}
X(61963) = inverse of X(62046) in orthocentroidal circle
X(61963) = inverse of X(62046) in Yff hyperbola
X(61963) = complement of X(62109)
X(61963) = pole of line {523, 62046} with respect to the orthocentroidal circle
X(61963) = pole of line {6, 62046} with respect to the Kiepert hyperbola
X(61963) = pole of line {523, 62046} with respect to the Yff hyperbola
X(61963) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3857), X(54512)}}, {{A, B, C, X(17800), X(54585)}}
X(61963) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15681, 12100}, {2, 15682, 15688}, {2, 15720, 11540}, {2, 17504, 15713}, {2, 3528, 15701}, {2, 3534, 3530}, {2, 3845, 15687}, {2, 546, 3845}, {4, 3545, 15721}, {30, 3090, 549}, {30, 381, 3857}, {30, 547, 3523}, {381, 14269, 3855}, {381, 3545, 3859}, {381, 3839, 3850}, {381, 5055, 3854}, {382, 3851, 3090}, {546, 3850, 382}, {546, 3857, 14869}, {547, 15682, 15711}, {549, 3845, 12101}, {549, 550, 15710}, {1657, 3851, 17566}, {3090, 3522, 3526}, {3091, 14893, 15699}, {3522, 15640, 11001}, {3530, 15714, 17504}, {3543, 14892, 632}, {3544, 15682, 2}, {3544, 15688, 547}, {3832, 3851, 546}, {3839, 15710, 14269}, {3845, 3858, 3860}, {3845, 5066, 8703}, {3851, 14269, 15700}, {3851, 14869, 5}, {3853, 11540, 15685}, {3855, 14269, 11737}, {3857, 3858, 3832}, {5339, 49811, 42419}, {5340, 49810, 42420}, {8703, 11539, 15693}, {10109, 12101, 15689}, {11737, 14269, 550}, {12820, 37835, 43106}, {12821, 37832, 43105}, {14869, 15687, 30}, {15682, 15711, 15704}, {15699, 15705, 11539}, {41100, 42107, 43247}, {41101, 42110, 43246}

X(61964) = X(2)X(3)∩X(8)X(61257)

Barycentrics    5*a^4-9*(b^2-c^2)^2+4*a^2*(b^2+c^2) : :
X(61964) = -27*X[2]+14*X[3], -5*X[8]+18*X[61257], 6*X[113]+7*X[15044], 5*X[145]+8*X[61246], 3*X[146]+10*X[15027], X[153]+12*X[38141], X[194]+12*X[22681], 9*X[265]+4*X[38632], -14*X[355]+X[20053], -45*X[373]+32*X[40284], 4*X[389]+9*X[16261], -X[599]+14*X[51133] and many others

X(61964) lies on these lines: {2, 3}, {8, 61257}, {54, 18296}, {61, 42103}, {62, 42106}, {69, 15031}, {83, 60325}, {98, 18844}, {113, 15044}, {145, 61246}, {146, 15027}, {153, 38141}, {194, 22681}, {265, 38632}, {325, 32875}, {355, 20053}, {373, 40284}, {389, 16261}, {395, 5366}, {396, 5365}, {485, 23275}, {486, 23269}, {575, 19123}, {599, 51133}, {944, 61275}, {946, 3633}, {962, 38140}, {1056, 10896}, {1058, 10895}, {1131, 13785}, {1132, 13665}, {1173, 15077}, {1249, 15860}, {1285, 13881}, {1327, 60304}, {1328, 60303}, {1352, 55718}, {1482, 61253}, {1587, 53516}, {1588, 53513}, {1699, 4668}, {1975, 32876}, {1992, 50964}, {2548, 14482}, {3060, 44863}, {3068, 35787}, {3069, 35786}, {3241, 50807}, {3292, 44872}, {3303, 10590}, {3304, 10591}, {3316, 6561}, {3317, 6560}, {3527, 14843}, {3567, 44870}, {3592, 13886}, {3594, 13939}, {3616, 58232}, {3617, 40273}, {3618, 48889}, {3619, 55606}, {3620, 55580}, {3625, 7982}, {3630, 11477}, {3635, 5603}, {3679, 51078}, {3746, 5225}, {3818, 22330}, {3972, 39143}, {4301, 38074}, {4677, 58242}, {4691, 5587}, {5007, 18424}, {5218, 18514}, {5229, 5563}, {5237, 42111}, {5238, 42114}, {5334, 42166}, {5335, 42163}, {5339, 43403}, {5340, 43404}, {5343, 42156}, {5344, 42153}, {5351, 42105}, {5352, 42104}, {5462, 11439}, {5475, 41940}, {5480, 6144}, {5485, 7758}, {5550, 31666}, {5562, 13570}, {5691, 61271}, {5714, 11518}, {5805, 60976}, {5817, 61000}, {5818, 7991}, {5876, 11002}, {5881, 50802}, {5882, 30308}, {5921, 11482}, {5943, 12290}, {6033, 38627}, {6225, 23325}, {6241, 15012}, {6321, 38628}, {6361, 7989}, {6409, 42566}, {6410, 42567}, {6419, 23273}, {6420, 23267}, {6425, 42283}, {6426, 42284}, {6447, 8972}, {6448, 13941}, {6449, 43374}, {6450, 43375}, {6453, 42277}, {6454, 42274}, {6488, 42258}, {6489, 42259}, {6564, 7582}, {6565, 7581}, {7288, 18513}, {7319, 50194}, {7612, 53107}, {7615, 7843}, {7687, 14094}, {7728, 38626}, {7735, 39590}, {7747, 46453}, {7752, 32822}, {7772, 43457}, {7773, 32878}, {7871, 11185}, {7967, 9955}, {8797, 52712}, {8799, 56303}, {8976, 43883}, {9540, 41961}, {9541, 10147}, {9588, 50809}, {9624, 34648}, {9692, 43211}, {9693, 43257}, {9779, 10595}, {9781, 15030}, {9862, 20398}, {10110, 15058}, {10113, 20125}, {10148, 42569}, {10187, 42631}, {10188, 42632}, {10194, 43503}, {10195, 43504}, {10222, 59387}, {10248, 26446}, {10574, 14845}, {10575, 11451}, {10576, 52666}, {10577, 52667}, {10596, 45631}, {10597, 45630}, {10653, 42436}, {10654, 42435}, {10721, 38729}, {10722, 38740}, {10723, 38751}, {10724, 38763}, {10725, 38775}, {10726, 38787}, {10733, 38795}, {10734, 38807}, {10738, 38629}, {10739, 38630}, {10742, 38631}, {11017, 23039}, {11160, 50957}, {11238, 31410}, {11381, 15024}, {11412, 40247}, {11465, 46850}, {11485, 43365}, {11486, 43364}, {11488, 42160}, {11489, 42161}, {11491, 61159}, {11496, 61154}, {11522, 34627}, {11648, 31417}, {12112, 36752}, {12244, 20397}, {12251, 22682}, {12295, 15020}, {12317, 36253}, {13172, 20399}, {13199, 20400}, {13364, 18439}, {13464, 50818}, {13472, 32533}, {13474, 15045}, {13935, 17852}, {13951, 43884}, {14494, 53106}, {14561, 55708}, {14639, 38745}, {14644, 38791}, {14853, 32455}, {14907, 52718}, {14912, 19130}, {14915, 15028}, {14927, 20190}, {14929, 32872}, {15021, 23515}, {15029, 17702}, {15034, 36518}, {15043, 16194}, {15052, 36749}, {15054, 15081}, {15056, 44871}, {15060, 16982}, {15069, 50959}, {15305, 46852}, {15740, 46848}, {16808, 42159}, {16809, 42162}, {16835, 31371}, {16964, 42802}, {16965, 42801}, {16966, 52079}, {16967, 52080}, {18358, 55724}, {18376, 50414}, {18418, 43844}, {18493, 61280}, {18525, 61281}, {18840, 54890}, {18841, 60326}, {18842, 54857}, {18843, 60323}, {18918, 43831}, {19877, 28146}, {20014, 61251}, {20585, 48675}, {22236, 42110}, {22238, 42107}, {22331, 53418}, {22332, 31404}, {22615, 32785}, {22644, 32786}, {22791, 54448}, {23251, 43880}, {23253, 41947}, {23261, 43879}, {23263, 41948}, {23324, 34781}, {23698, 52886}, {24206, 55600}, {25406, 55698}, {25415, 43734}, {26937, 34563}, {28172, 34595}, {28186, 46934}, {29243, 52885}, {30389, 31673}, {31145, 50800}, {31414, 35823}, {31415, 53096}, {31670, 55588}, {31730, 61264}, {31870, 61740}, {32767, 54050}, {32816, 32877}, {32826, 32889}, {32827, 32888}, {33697, 54445}, {34507, 50956}, {34573, 55641}, {34754, 43778}, {34755, 43777}, {34786, 35260}, {35007, 43620}, {35820, 42557}, {35821, 42558}, {36412, 40065}, {36836, 42101}, {36843, 42102}, {36996, 59389}, {37498, 54434}, {37640, 42814}, {37641, 42813}, {37832, 41978}, {37835, 41977}, {38021, 51076}, {38034, 61292}, {38072, 51131}, {38076, 50814}, {38757, 59391}, {39884, 53092}, {40330, 53097}, {40693, 42775}, {40694, 42776}, {41112, 42993}, {41113, 42992}, {41119, 42991}, {41120, 42990}, {41597, 53860}, {42085, 42472}, {42086, 42473}, {42089, 42928}, {42092, 42929}, {42093, 42598}, {42094, 42599}, {42095, 42165}, {42098, 42164}, {42119, 42919}, {42120, 42918}, {42143, 43465}, {42144, 42590}, {42145, 42591}, {42146, 43466}, {42149, 43481}, {42152, 43482}, {42431, 42910}, {42432, 42911}, {42474, 42949}, {42475, 42948}, {42490, 43402}, {42491, 43401}, {42516, 42934}, {42517, 42935}, {42522, 43561}, {42523, 43560}, {42582, 43408}, {42583, 43407}, {42627, 43243}, {42628, 43242}, {42786, 55647}, {42890, 43483}, {42891, 43484}, {42894, 43235}, {42895, 43234}, {42950, 43630}, {42951, 43631}, {42962, 42982}, {42963, 42983}, {43101, 43193}, {43104, 43194}, {43376, 43386}, {43377, 43387}, {43446, 54591}, {43447, 54592}, {43487, 43499}, {43488, 43500}, {43542, 43551}, {43543, 43550}, {43621, 55637}, {43645, 43770}, {43646, 43769}, {44801, 58378}, {46264, 55694}, {46933, 48661}, {48873, 55628}, {48895, 55617}, {48901, 55597}, {50864, 61276}, {50960, 50973}, {50974, 51129}, {51163, 55626}, {51212, 55583}, {51538, 52987}, {52519, 60250}, {53098, 54493}, {54646, 60123}, {54845, 60649}, {59386, 60962}, {59417, 61259}, {60127, 60209}, {60146, 60150}, {60330, 60630}

X(61964) = midpoint of X(i) and X(j) for these {i,j}: {4, 5067}
X(61964) = reflection of X(i) in X(j) for these {i,j}: {10299, 5067}, {10303, 5079}, {5067, 5068}
X(61964) = inverse of X(33703) in orthocentroidal circle
X(61964) = inverse of X(33703) in Yff hyperbola
X(61964) = complement of X(62110)
X(61964) = anticomplement of X(61811)
X(61964) = pole of line {523, 33703} with respect to the orthocentroidal circle
X(61964) = pole of line {185, 62028} with respect to the Jerabek hyperbola
X(61964) = pole of line {6, 33703} with respect to the Kiepert hyperbola
X(61964) = pole of line {523, 33703} with respect to the Yff hyperbola
X(61964) = pole of line {69, 15712} with respect to the Wallace hyperbola
X(61964) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(5), X(18296)}}, {{A, B, C, X(6), X(55574)}}, {{A, B, C, X(30), X(18854)}}, {{A, B, C, X(68), X(15720)}}, {{A, B, C, X(69), X(15712)}}, {{A, B, C, X(140), X(15077)}}, {{A, B, C, X(264), X(33703)}}, {{A, B, C, X(265), X(46219)}}, {{A, B, C, X(297), X(18844)}}, {{A, B, C, X(376), X(14860)}}, {{A, B, C, X(382), X(18852)}}, {{A, B, C, X(427), X(60325)}}, {{A, B, C, X(547), X(54660)}}, {{A, B, C, X(550), X(31371)}}, {{A, B, C, X(631), X(14843)}}, {{A, B, C, X(1173), X(3515)}}, {{A, B, C, X(1217), X(15682)}}, {{A, B, C, X(1585), X(60310)}}, {{A, B, C, X(1586), X(60309)}}, {{A, B, C, X(1593), X(46848)}}, {{A, B, C, X(1656), X(32533)}}, {{A, B, C, X(3146), X(18853)}}, {{A, B, C, X(3346), X(15697)}}, {{A, B, C, X(3516), X(16835)}}, {{A, B, C, X(3517), X(52518)}}, {{A, B, C, X(3522), X(14863)}}, {{A, B, C, X(3528), X(52441)}}, {{A, B, C, X(3529), X(18855)}}, {{A, B, C, X(3535), X(60290)}}, {{A, B, C, X(3536), X(60289)}}, {{A, B, C, X(3543), X(18851)}}, {{A, B, C, X(3627), X(18849)}}, {{A, B, C, X(3851), X(17505)}}, {{A, B, C, X(4232), X(60329)}}, {{A, B, C, X(5054), X(54763)}}, {{A, B, C, X(5072), X(8797)}}, {{A, B, C, X(6995), X(54890)}}, {{A, B, C, X(7378), X(60326)}}, {{A, B, C, X(7612), X(52298)}}, {{A, B, C, X(8703), X(54838)}}, {{A, B, C, X(13452), X(35477)}}, {{A, B, C, X(13472), X(32534)}}, {{A, B, C, X(13599), X(55864)}}, {{A, B, C, X(14494), X(52297)}}, {{A, B, C, X(15689), X(36889)}}, {{A, B, C, X(15692), X(60121)}}, {{A, B, C, X(15713), X(22270)}}, {{A, B, C, X(15740), X(33923)}}, {{A, B, C, X(15749), X(55856)}}, {{A, B, C, X(17538), X(57896)}}, {{A, B, C, X(17578), X(18847)}}, {{A, B, C, X(18550), X(49139)}}, {{A, B, C, X(19709), X(54667)}}, {{A, B, C, X(22334), X(55571)}}, {{A, B, C, X(35018), X(43699)}}, {{A, B, C, X(37174), X(53107)}}, {{A, B, C, X(40448), X(46936)}}, {{A, B, C, X(44580), X(46412)}}, {{A, B, C, X(44957), X(61133)}}, {{A, B, C, X(52284), X(54857)}}
X(61964) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12108, 3525}, {2, 14892, 5071}, {2, 15686, 3524}, {2, 15692, 14890}, {2, 15706, 15702}, {2, 20, 15712}, {2, 3091, 5072}, {2, 3543, 15689}, {2, 3627, 17538}, {3, 12811, 15022}, {3, 381, 3857}, {3, 3857, 3091}, {3, 3859, 13587}, {3, 5072, 12812}, {4, 3524, 382}, {4, 381, 3855}, {4, 5067, 30}, {4, 631, 15682}, {4, 6896, 6951}, {4, 6939, 6903}, {5, 12100, 1656}, {5, 3627, 12108}, {5, 381, 3854}, {5, 3830, 3523}, {5, 3858, 3860}, {20, 3533, 15698}, {20, 5071, 3533}, {30, 5067, 10299}, {30, 5068, 5067}, {30, 5079, 10303}, {140, 1010, 632}, {140, 14269, 17578}, {140, 17578, 11001}, {376, 15709, 12100}, {381, 3843, 3850}, {381, 3851, 3859}, {381, 3858, 3832}, {381, 3860, 3839}, {546, 3627, 3843}, {546, 3628, 3845}, {547, 5073, 15717}, {632, 3627, 15686}, {1012, 3544, 3543}, {1656, 3528, 15709}, {1656, 3543, 3528}, {1657, 15718, 548}, {1657, 3627, 3146}, {1657, 3843, 14893}, {2050, 5072, 15706}, {3090, 3091, 3545}, {3090, 3529, 631}, {3090, 3533, 3628}, {3091, 10303, 5068}, {3091, 15022, 12811}, {3091, 3146, 5}, {3091, 3832, 546}, {3146, 3523, 12103}, {3523, 13735, 10124}, {3526, 15687, 5059}, {3533, 5076, 3529}, {3544, 11539, 6946}, {3544, 6905, 16239}, {3627, 12108, 1657}, {3628, 3845, 5076}, {3839, 15705, 14269}, {3843, 3851, 15684}, {3845, 3859, 3851}, {3845, 5066, 15695}, {3853, 5055, 3522}, {3856, 3858, 381}, {5068, 10303, 5079}, {5073, 6948, 3534}, {9779, 18480, 10595}, {10019, 18386, 3089}, {11001, 15705, 376}, {11381, 15024, 61136}, {11541, 12811, 3090}, {12108, 14893, 3627}, {12571, 18492, 5603}, {12811, 15022, 3544}, {14269, 17578, 4}, {14782, 14783, 5066}, {14784, 14785, 15720}, {14892, 15684, 2}, {15022, 16371, 5056}, {15640, 15699, 15715}, {15640, 16417, 3}, {15684, 15712, 20}, {15695, 15703, 5054}, {16041, 16044, 16045}, {19130, 51537, 14912}, {23249, 42270, 13939}, {23259, 42273, 13886}, {42111, 43226, 42141}, {42114, 42140, 43463}, {42114, 43227, 42140}, {42269, 42561, 23267}, {42813, 42920, 37641}, {42814, 42921, 37640}

X(61965) = X(2)X(3)∩X(1327)X(6432)

Barycentrics    14*a^4-25*(b^2-c^2)^2+11*a^2*(b^2+c^2) : :
X(61965) = -25*X[2]+13*X[3], 7*X[3656]+5*X[61250], X[3818]+5*X[51129], -4*X[4746]+13*X[18357], 5*X[4816]+13*X[22791], -25*X[7988]+9*X[58227], -X[9955]+4*X[51076], -X[11178]+7*X[51133], X[11278]+5*X[50796], X[11591]+8*X[44871], -10*X[12571]+X[33179], 7*X[16200]+5*X[61247] and many others

X(61965) lies on these lines: {2, 3}, {515, 58234}, {590, 43321}, {615, 43320}, {1327, 6432}, {1328, 6431}, {3656, 61250}, {3818, 51129}, {4746, 18357}, {4816, 22791}, {5349, 49907}, {5350, 49908}, {5844, 58241}, {6429, 42602}, {6430, 42603}, {6480, 43211}, {6481, 43212}, {6496, 42537}, {6497, 42538}, {6749, 61306}, {7988, 58227}, {9955, 51076}, {11178, 51133}, {11278, 50796}, {11485, 43202}, {11486, 43201}, {11542, 42972}, {11543, 42973}, {11591, 44871}, {12571, 33179}, {12816, 42924}, {12817, 42925}, {16200, 61247}, {16962, 42110}, {16963, 42107}, {18358, 50960}, {18480, 51074}, {18492, 50807}, {18510, 43889}, {18512, 43890}, {18581, 42907}, {18582, 42906}, {19106, 43100}, {19107, 43107}, {19130, 51131}, {19875, 28216}, {19883, 28190}, {20582, 55612}, {21849, 45958}, {21850, 50956}, {22236, 43246}, {22238, 43247}, {22566, 61600}, {25565, 55688}, {28174, 38076}, {28178, 38083}, {28182, 38068}, {28198, 61262}, {30392, 38022}, {31162, 58248}, {31662, 61269}, {31834, 44863}, {32424, 38802}, {36969, 42628}, {36970, 42627}, {37517, 47354}, {37705, 50806}, {38066, 61260}, {38079, 55703}, {38627, 41154}, {41008, 55958}, {42136, 43245}, {42137, 43244}, {42154, 43197}, {42155, 43198}, {42500, 43400}, {42501, 43399}, {42598, 43108}, {42599, 43109}, {42777, 44016}, {42778, 44015}, {42785, 51136}, {42793, 54480}, {42794, 54479}, {42918, 43200}, {42919, 43199}, {42940, 43372}, {42941, 43373}, {42956, 42996}, {42957, 42997}, {42960, 42991}, {42961, 42990}, {43195, 43545}, {43196, 43544}, {43621, 50980}, {46852, 58470}, {48310, 55685}, {48895, 51165}, {50664, 51025}, {50802, 58237}, {50811, 58231}, {50830, 61256}, {50957, 51214}, {50964, 51027}, {51077, 61253}, {51078, 51120}

X(61965) = midpoint of X(i) and X(j) for these {i,j}: {4, 15699}, {5, 14269}, {3545, 3845}, {3627, 10304}, {3830, 17504}, {5054, 15687}
X(61965) = reflection of X(i) in X(j) for these {i,j}: {10304, 10124}, {12100, 15699}, {12101, 14269}, {15688, 14890}, {15689, 3530}, {15691, 17504}, {15699, 11737}, {17504, 3628}, {3545, 3850}, {547, 3545}, {548, 5054}, {5054, 10109}
X(61965) = inverse of X(62045) in orthocentroidal circle
X(61965) = inverse of X(62045) in Yff hyperbola
X(61965) = complement of X(62111)
X(61965) = pole of line {523, 62045} with respect to the orthocentroidal circle
X(61965) = pole of line {6, 43310} with respect to the Kiepert hyperbola
X(61965) = pole of line {523, 62045} with respect to the Yff hyperbola
X(61965) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(265), X(47598)}}, {{A, B, C, X(1294), X(58199)}}, {{A, B, C, X(1494), X(58187)}}, {{A, B, C, X(3857), X(55958)}}, {{A, B, C, X(14860), X(44245)}}, {{A, B, C, X(44682), X(60121)}}, {{A, B, C, X(44962), X(61133)}}
X(61965) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 381, 3857}, {5, 15687, 15711}, {5, 3522, 3628}, {5, 3627, 15720}, {5, 3845, 3543}, {30, 10109, 5054}, {30, 10124, 10304}, {30, 11737, 15699}, {30, 14269, 12101}, {30, 14890, 15688}, {30, 17504, 15691}, {30, 3530, 15689}, {30, 3628, 17504}, {30, 3850, 3545}, {381, 3830, 3855}, {381, 3832, 3845}, {381, 3845, 3850}, {381, 3858, 3860}, {381, 3860, 546}, {381, 5066, 3859}, {381, 546, 5066}, {546, 3857, 12103}, {547, 15691, 15702}, {3091, 15687, 10109}, {3091, 5073, 5}, {3524, 11539, 11812}, {3524, 3839, 14269}, {3533, 3543, 3534}, {3543, 15694, 15686}, {3545, 3845, 30}, {3845, 15686, 4}, {3845, 15723, 12102}, {3845, 3853, 14893}, {3845, 5066, 15690}, {3856, 3860, 381}, {5066, 12812, 11737}, {5066, 14893, 140}, {5070, 15640, 15714}, {5076, 11737, 6989}, {7397, 15697, 376}, {10109, 15687, 548}, {11539, 15708, 14890}, {11737, 12100, 12812}, {11737, 15686, 547}, {11812, 16239, 15694}, {12101, 14892, 3524}, {14890, 15688, 12100}, {14890, 16239, 11539}, {14893, 15690, 3853}, {15686, 15699, 15708}, {15687, 15711, 5073}, {15699, 15708, 16239}

X(61966) = X(2)X(3)∩X(6)X(43380)

Barycentrics    13*a^4-23*(b^2-c^2)^2+10*a^2*(b^2+c^2) : :
X(61966) = -23*X[2]+12*X[3], 3*X[147]+8*X[36523], 6*X[165]+5*X[50873], 3*X[962]+8*X[4745], 9*X[1699]+2*X[4669], X[3241]+10*X[18492], -5*X[3620]+16*X[25561], -15*X[3817]+4*X[51085], 8*X[3818]+3*X[5032], -X[4677]+12*X[19925], -15*X[5587]+4*X[50827], -3*X[5603]+14*X[50807] and many others

X(61966) lies on these lines: {2, 3}, {6, 43380}, {13, 42481}, {14, 42480}, {147, 36523}, {165, 50873}, {262, 60632}, {395, 42804}, {396, 42803}, {598, 54866}, {671, 54521}, {962, 4745}, {1131, 35823}, {1132, 35822}, {1327, 7586}, {1328, 7585}, {1699, 4669}, {2996, 54643}, {3241, 18492}, {3316, 43520}, {3317, 43519}, {3424, 60282}, {3592, 56618}, {3594, 56619}, {3620, 25561}, {3817, 51085}, {3818, 5032}, {4677, 19925}, {5304, 18424}, {5318, 49812}, {5321, 49813}, {5334, 41119}, {5335, 41120}, {5343, 16267}, {5344, 16268}, {5395, 54608}, {5478, 35749}, {5479, 36327}, {5587, 50827}, {5603, 50807}, {5731, 50863}, {5734, 51096}, {5921, 8584}, {6221, 43522}, {6398, 43521}, {6564, 43792}, {6565, 43791}, {7773, 32869}, {7809, 32892}, {7988, 50862}, {8972, 43567}, {9541, 43504}, {9542, 42277}, {9543, 43211}, {9779, 51074}, {10033, 61304}, {10302, 54520}, {10516, 50982}, {10653, 43364}, {10654, 43365}, {11160, 43150}, {11412, 44871}, {11439, 16226}, {11522, 51091}, {11669, 54896}, {12007, 38072}, {12571, 51071}, {12816, 18581}, {12817, 18582}, {13570, 21969}, {13607, 38021}, {13886, 43561}, {13939, 43560}, {13941, 43566}, {14226, 60295}, {14241, 60296}, {14458, 54639}, {14484, 60228}, {14492, 60200}, {14853, 50964}, {15031, 46951}, {15060, 16981}, {15305, 58470}, {15534, 50959}, {16241, 43476}, {16242, 43475}, {16626, 36352}, {16627, 36346}, {16808, 41113}, {16809, 41112}, {16962, 42964}, {16963, 42965}, {17503, 60333}, {18362, 37689}, {18483, 53620}, {19116, 60301}, {19117, 60302}, {22165, 50960}, {22235, 42506}, {22237, 42507}, {22796, 36344}, {22797, 36319}, {22831, 33627}, {22832, 33626}, {25406, 51216}, {28198, 46933}, {30308, 50864}, {31162, 51072}, {31884, 51029}, {32006, 32893}, {32532, 60331}, {32787, 43790}, {32788, 43789}, {33602, 42138}, {33603, 42135}, {33606, 41107}, {33607, 41108}, {34627, 51092}, {34632, 38076}, {34648, 51105}, {35786, 43431}, {35787, 43430}, {35820, 43562}, {35821, 43563}, {36362, 59396}, {36363, 59394}, {36427, 61327}, {36769, 59393}, {36969, 43242}, {36970, 43243}, {37665, 43457}, {37668, 48913}, {37712, 51075}, {38136, 50974}, {38140, 50810}, {41100, 42134}, {41101, 42133}, {41121, 49827}, {41122, 49826}, {41398, 44106}, {41895, 60192}, {42085, 43293}, {42086, 43292}, {42093, 42589}, {42094, 42588}, {42104, 42632}, {42105, 42631}, {42107, 49906}, {42108, 42474}, {42109, 42475}, {42110, 49905}, {42129, 43473}, {42132, 43474}, {42136, 43502}, {42137, 43501}, {42139, 49948}, {42140, 43104}, {42141, 43101}, {42142, 49947}, {42143, 42689}, {42146, 42688}, {42262, 42418}, {42265, 42417}, {42266, 43558}, {42267, 43559}, {42270, 42523}, {42273, 42522}, {42274, 43256}, {42283, 42575}, {42284, 42574}, {42472, 42942}, {42473, 42943}, {42494, 43202}, {42495, 43201}, {42504, 43632}, {42505, 43633}, {42510, 43465}, {42511, 43466}, {42524, 43407}, {42525, 43408}, {42528, 43468}, {42529, 43467}, {42532, 42934}, {42533, 42935}, {42602, 43512}, {42603, 43511}, {42604, 42639}, {42605, 42640}, {42777, 43299}, {42778, 43298}, {42791, 42932}, {42792, 42933}, {42795, 43869}, {42796, 43870}, {42904, 43232}, {42905, 43233}, {42910, 43226}, {42911, 43227}, {42918, 43545}, {42919, 43544}, {42920, 42973}, {42921, 42972}, {43195, 43200}, {43196, 43199}, {43248, 43369}, {43249, 43368}, {43330, 43638}, {43331, 43643}, {43951, 60637}, {45103, 60102}, {47354, 50992}, {47867, 59395}, {50799, 54448}, {50800, 50830}, {50802, 51093}, {50865, 51069}, {50871, 51095}, {50956, 54132}, {50957, 50985}, {50991, 51212}, {50993, 51211}, {51023, 51131}, {51024, 51143}, {51066, 59417}, {51173, 51182}, {51186, 54170}, {53101, 60175}, {53104, 54642}, {54519, 60239}, {54522, 60630}, {54815, 60646}, {54852, 60648}, {60127, 60625}, {60150, 60650}, {60281, 60336}

X(61966) = midpoint of X(i) and X(j) for these {i,j}: {3830, 15716}
X(61966) = reflection of X(i) in X(j) for these {i,j}: {15715, 5070}, {15721, 5056}, {15723, 5}, {376, 15720}, {3855, 381}
X(61966) = inverse of X(15640) in orthocentroidal circle
X(61966) = inverse of X(15640) in Yff hyperbola
X(61966) = anticomplement of X(15719)
X(61966) = pole of line {523, 15640} with respect to the orthocentroidal circle
X(61966) = pole of line {6, 15640} with respect to the Kiepert hyperbola
X(61966) = pole of line {523, 15640} with respect to the Yff hyperbola
X(61966) = pole of line {69, 61796} with respect to the Wallace hyperbola
X(61966) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(253), X(8703)}}, {{A, B, C, X(264), X(15640)}}, {{A, B, C, X(265), X(15723)}}, {{A, B, C, X(458), X(60632)}}, {{A, B, C, X(468), X(54521)}}, {{A, B, C, X(3528), X(54838)}}, {{A, B, C, X(3529), X(54585)}}, {{A, B, C, X(3535), X(60314)}}, {{A, B, C, X(3536), X(60313)}}, {{A, B, C, X(3544), X(54667)}}, {{A, B, C, X(3855), X(54512)}}, {{A, B, C, X(5094), X(54866)}}, {{A, B, C, X(6353), X(54643)}}, {{A, B, C, X(8889), X(54608)}}, {{A, B, C, X(10299), X(60121)}}, {{A, B, C, X(10301), X(54520)}}, {{A, B, C, X(11331), X(54639)}}, {{A, B, C, X(14860), X(50693)}}, {{A, B, C, X(15697), X(36889)}}, {{A, B, C, X(15720), X(31363)}}, {{A, B, C, X(17800), X(18855)}}, {{A, B, C, X(31361), X(49137)}}, {{A, B, C, X(35018), X(60618)}}, {{A, B, C, X(35482), X(54942)}}, {{A, B, C, X(44999), X(61133)}}, {{A, B, C, X(49135), X(54923)}}, {{A, B, C, X(52288), X(60228)}}, {{A, B, C, X(52289), X(60200)}}, {{A, B, C, X(52290), X(60192)}}, {{A, B, C, X(52292), X(60333)}}, {{A, B, C, X(52293), X(60102)}}, {{A, B, C, X(53857), X(60331)}}
X(61966) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11001, 15692}, {2, 15683, 15698}, {2, 15697, 3523}, {2, 15698, 10303}, {2, 3146, 8703}, {2, 3543, 15697}, {2, 4, 15640}, {2, 8703, 15708}, {4, 15709, 15684}, {4, 3090, 17800}, {4, 3091, 7486}, {4, 3526, 3146}, {4, 3545, 549}, {4, 3855, 5072}, {4, 5055, 15683}, {5, 15684, 15709}, {5, 30, 15723}, {20, 15692, 15688}, {20, 3854, 3091}, {20, 5056, 3525}, {30, 15720, 376}, {30, 381, 3855}, {30, 5070, 15715}, {381, 14269, 3850}, {381, 3545, 3854}, {381, 3832, 3839}, {381, 5055, 3857}, {381, 546, 3545}, {546, 10109, 3845}, {1656, 3090, 6921}, {1656, 3525, 13742}, {1656, 3830, 15690}, {3090, 15693, 2}, {3091, 3839, 3543}, {3524, 14893, 17578}, {3525, 5072, 15022}, {3534, 3845, 4}, {3534, 5055, 11540}, {3544, 3861, 5059}, {3545, 10299, 5071}, {3830, 15716, 30}, {3832, 3854, 546}, {3839, 15708, 14269}, {3845, 10109, 3830}, {3845, 15713, 12101}, {3851, 14893, 3524}, {3856, 3860, 5066}, {5066, 12101, 3628}, {5066, 15759, 5}, {5068, 15720, 5056}, {10303, 15683, 10304}, {10304, 15721, 15717}, {11001, 15709, 15759}, {12816, 18581, 49875}, {12817, 18582, 49876}, {14892, 15681, 5067}, {15684, 15701, 3534}, {15684, 15759, 11001}, {15692, 15723, 15721}, {15723, 15973, 15699}, {16239, 17578, 20}, {16808, 41113, 49874}, {16809, 41112, 49873}, {42103, 43403, 43541}, {42106, 43404, 43540}, {42277, 43508, 9542}, {43256, 43525, 43382}, {43257, 43526, 43383}, {43380, 43381, 6}

X(61967) = X(1)X(51074)∩X(2)X(3)

Barycentrics    11*a^4-19*(b^2-c^2)^2+8*a^2*(b^2+c^2) : :
X(61967) = -X[1]+10*X[51074], -19*X[2]+10*X[3], -X[6]+10*X[51129], -X[8]+10*X[50799], -X[69]+10*X[50956], -X[145]+10*X[50806], -X[193]+10*X[50963], -X[944]+10*X[30308], -10*X[946]+X[34747], 2*X[1699]+X[38074], 2*X[3244]+25*X[18492], -14*X[3619]+5*X[50966] and many others

X(61967) lies on these lines: {1, 51074}, {2, 3}, {6, 51129}, {8, 50799}, {13, 42479}, {14, 42478}, {15, 12821}, {16, 12820}, {69, 50956}, {145, 50806}, {193, 50963}, {262, 60631}, {397, 33602}, {398, 33603}, {590, 6490}, {598, 60322}, {615, 6491}, {944, 30308}, {946, 34747}, {1327, 42561}, {1328, 31412}, {1587, 14226}, {1588, 14241}, {1699, 38074}, {3068, 43796}, {3069, 43795}, {3244, 18492}, {3316, 41945}, {3317, 41946}, {3619, 50966}, {3621, 50797}, {3624, 50819}, {3626, 31162}, {3629, 11180}, {3631, 50960}, {3632, 34631}, {3636, 34648}, {3644, 51038}, {3656, 20050}, {3818, 50964}, {4686, 51041}, {5032, 38136}, {5318, 43543}, {5321, 43542}, {5343, 49947}, {5344, 49948}, {5349, 49905}, {5350, 49906}, {5476, 51537}, {5485, 52519}, {5587, 38098}, {5603, 61294}, {5657, 38076}, {6329, 39874}, {6748, 36427}, {7581, 43387}, {7582, 43386}, {7736, 39563}, {7739, 43457}, {7809, 52713}, {7967, 38021}, {9681, 43563}, {9741, 53143}, {9778, 38083}, {9779, 28204}, {9780, 50809}, {9955, 50864}, {10155, 33698}, {10168, 51177}, {10576, 43504}, {10577, 43503}, {10595, 12571}, {10653, 42636}, {10654, 42635}, {10733, 11693}, {11008, 20423}, {11459, 13570}, {11522, 51094}, {11542, 43541}, {11543, 43540}, {12818, 54597}, {12819, 43536}, {13846, 23263}, {13847, 23253}, {13886, 35787}, {13939, 35786}, {14488, 31173}, {14492, 60636}, {14494, 54720}, {14845, 61136}, {14912, 38072}, {15044, 56567}, {15058, 21849}, {15808, 50811}, {16226, 46847}, {16267, 42142}, {16268, 42139}, {16644, 43105}, {16645, 43106}, {16808, 43419}, {16809, 43418}, {16964, 49862}, {16965, 49861}, {18357, 50872}, {18358, 51028}, {18480, 20057}, {18482, 60983}, {18483, 50810}, {18842, 54845}, {18843, 60150}, {19053, 42269}, {19054, 42268}, {19130, 51023}, {19877, 50873}, {19925, 34641}, {20054, 50798}, {20080, 50954}, {20583, 47353}, {21168, 38075}, {21850, 50957}, {22791, 50800}, {23269, 32788}, {23275, 32787}, {25561, 51212}, {28202, 61263}, {32532, 60330}, {32886, 37671}, {33604, 40693}, {33605, 40694}, {33606, 43775}, {33607, 43776}, {34089, 54596}, {34091, 54595}, {34595, 50866}, {34632, 61261}, {35242, 50869}, {36412, 61306}, {36889, 57897}, {37640, 42103}, {37641, 42106}, {37832, 42630}, {37835, 42629}, {38068, 61264}, {38073, 59389}, {38140, 53620}, {40341, 47354}, {41107, 42920}, {41108, 42921}, {41119, 42775}, {41120, 42776}, {41121, 43018}, {41122, 43019}, {42093, 43482}, {42094, 43481}, {42107, 43779}, {42110, 43780}, {42119, 43196}, {42120, 43195}, {42135, 43110}, {42138, 43111}, {42140, 42911}, {42141, 42910}, {42149, 42588}, {42152, 42589}, {42153, 49826}, {42156, 49827}, {42159, 42779}, {42160, 42939}, {42161, 42938}, {42162, 42780}, {42283, 42642}, {42284, 42641}, {42472, 43227}, {42473, 43226}, {42474, 42476}, {42475, 42477}, {42510, 43485}, {42511, 43486}, {42946, 46334}, {42947, 46335}, {42962, 43253}, {42963, 43252}, {43101, 43464}, {43104, 43463}, {43150, 51214}, {43374, 52045}, {43375, 52046}, {43444, 54577}, {43445, 54576}, {43570, 60302}, {43571, 60301}, {43676, 54707}, {46930, 50825}, {46934, 50863}, {47355, 50975}, {50812, 51073}, {50967, 51133}, {50968, 51128}, {51026, 55646}, {51072, 61258}, {51171, 51176}, {53100, 60284}, {53102, 54612}, {53103, 54494}, {53105, 54523}, {53109, 60185}, {54616, 60132}, {54637, 60142}, {54717, 60183}, {60127, 60219}, {60281, 60337}

X(61967) = midpoint of X(i) and X(j) for these {i,j}: {3830, 15706}
X(61967) = reflection of X(i) in X(j) for these {i,j}: {15706, 15699}, {15708, 5055}, {15710, 2}, {376, 15708}
X(61967) = inverse of X(62042) in orthocentroidal circle
X(61967) = inverse of X(62042) in Yff hyperbola
X(61967) = complement of X(62112)
X(61967) = anticomplement of X(15707)
X(61967) = pole of line {523, 62042} with respect to the orthocentroidal circle
X(61967) = pole of line {6, 43797} with respect to the Kiepert hyperbola
X(61967) = pole of line {523, 62042} with respect to the Yff hyperbola
X(61967) = pole of line {69, 15700} with respect to the Wallace hyperbola
X(61967) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(15700)}}, {{A, B, C, X(376), X(57897)}}, {{A, B, C, X(458), X(60631)}}, {{A, B, C, X(550), X(36889)}}, {{A, B, C, X(1494), X(15710)}}, {{A, B, C, X(3855), X(55958)}}, {{A, B, C, X(4232), X(52519)}}, {{A, B, C, X(4846), X(15695)}}, {{A, B, C, X(5094), X(60322)}}, {{A, B, C, X(5627), X(37934)}}, {{A, B, C, X(7408), X(54717)}}, {{A, B, C, X(7486), X(54660)}}, {{A, B, C, X(8797), X(11737)}}, {{A, B, C, X(10303), X(54763)}}, {{A, B, C, X(10304), X(54838)}}, {{A, B, C, X(11541), X(18854)}}, {{A, B, C, X(14488), X(52301)}}, {{A, B, C, X(14860), X(17538)}}, {{A, B, C, X(15022), X(60122)}}, {{A, B, C, X(15683), X(54585)}}, {{A, B, C, X(15715), X(57823)}}, {{A, B, C, X(15717), X(60121)}}, {{A, B, C, X(18855), X(49138)}}, {{A, B, C, X(33287), X(54551)}}, {{A, B, C, X(37453), X(54523)}}, {{A, B, C, X(44998), X(61133)}}, {{A, B, C, X(50692), X(54923)}}, {{A, B, C, X(52284), X(54845)}}, {{A, B, C, X(52289), X(60636)}}, {{A, B, C, X(53857), X(60330)}}
X(61967) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10299, 15702}, {2, 15681, 10299}, {2, 15687, 3529}, {2, 15707, 15709}, {2, 20, 15700}, {2, 30, 15710}, {2, 3091, 11737}, {2, 3529, 15715}, {2, 3543, 550}, {2, 3544, 5071}, {2, 381, 3855}, {2, 3839, 14269}, {4, 15702, 15682}, {4, 3091, 5067}, {4, 3855, 3544}, {4, 5067, 11541}, {30, 15699, 15706}, {30, 5055, 15708}, {140, 15640, 376}, {376, 11541, 11001}, {376, 15682, 5059}, {381, 3830, 3850}, {381, 3845, 3091}, {381, 3860, 3832}, {381, 5066, 3854}, {382, 5055, 17504}, {546, 11737, 3845}, {546, 14269, 3839}, {546, 550, 3843}, {547, 3146, 15698}, {1656, 12101, 15683}, {1656, 15683, 15719}, {2043, 2044, 15022}, {3090, 15682, 14891}, {3090, 3843, 4}, {3091, 12102, 3090}, {3091, 5055, 3545}, {3091, 5059, 5}, {3146, 5068, 13742}, {3317, 43521, 41946}, {3524, 17538, 10304}, {3529, 3855, 3851}, {3543, 15717, 15685}, {3543, 3854, 5066}, {3830, 15706, 30}, {3830, 15723, 15704}, {3839, 3854, 5054}, {3845, 11737, 382}, {3845, 3850, 15723}, {3845, 3856, 381}, {3851, 14269, 15688}, {5055, 15723, 15699}, {5071, 11001, 3525}, {5072, 17578, 3533}, {5079, 15681, 11540}, {10109, 15684, 3523}, {10299, 15682, 15681}, {10299, 17538, 3528}, {10304, 15702, 3524}, {11359, 17582, 2}, {11737, 17504, 5055}, {12102, 15685, 3543}, {14269, 15688, 15687}, {14891, 15693, 15717}, {15682, 15702, 17538}, {15709, 15710, 15707}, {15717, 17563, 16418}, {18492, 50802, 34627}

X(61968) = X(2)X(3)∩X(6)X(42902)

Barycentrics    7*a^4-12*(b^2-c^2)^2+5*a^2*(b^2+c^2) : :
X(61968) = -36*X[2]+19*X[3], 3*X[399]+14*X[15044], 14*X[946]+3*X[61247], 7*X[1482]+10*X[61250], 6*X[1539]+11*X[15025], 12*X[3818]+5*X[11482], 2*X[4301]+15*X[50799], X[5562]+16*X[44871], 2*X[5881]+15*X[50806], 8*X[7843]+9*X[40727], 8*X[7982]+9*X[51515], -27*X[7988]+10*X[31666] and many others

X(61968) lies on these lines: {2, 3}, {6, 42902}, {399, 15044}, {946, 61247}, {1151, 43881}, {1152, 43882}, {1482, 61250}, {1539, 15025}, {3592, 35787}, {3594, 35786}, {3818, 11482}, {4301, 50799}, {5562, 44871}, {5881, 50806}, {6199, 42273}, {6395, 42270}, {6407, 42277}, {6408, 42274}, {6417, 42268}, {6418, 42269}, {6427, 6564}, {6428, 6565}, {6445, 22615}, {6446, 22644}, {6447, 42265}, {6448, 42262}, {6482, 42558}, {6483, 42557}, {6519, 35821}, {6522, 35820}, {7687, 11432}, {7843, 40727}, {7850, 15031}, {7982, 51515}, {7988, 31666}, {7991, 38140}, {8148, 19925}, {9605, 43457}, {9779, 18526}, {10095, 16261}, {10222, 18492}, {10516, 55580}, {10576, 43339}, {10577, 43338}, {11439, 13364}, {11459, 16982}, {11477, 43150}, {11522, 34748}, {12290, 18874}, {12295, 38638}, {12355, 38628}, {12571, 18525}, {13202, 38633}, {13321, 45959}, {13464, 50807}, {13607, 18493}, {13903, 23263}, {13961, 23253}, {14023, 20112}, {14530, 18376}, {14692, 38732}, {14848, 51129}, {15012, 16194}, {15027, 46686}, {15029, 32609}, {15034, 15046}, {15039, 61574}, {15069, 50963}, {15178, 61274}, {16625, 18435}, {16808, 42691}, {16809, 42690}, {16964, 43022}, {16965, 43023}, {17851, 43382}, {18405, 50414}, {18424, 30435}, {18436, 44863}, {18480, 61291}, {18510, 43341}, {18512, 43340}, {18550, 43691}, {19130, 48662}, {20070, 61260}, {21358, 55600}, {22234, 38072}, {22236, 42964}, {22238, 42965}, {22330, 47353}, {22331, 39565}, {23251, 35814}, {23261, 35815}, {24206, 55602}, {25561, 55583}, {28202, 30315}, {31454, 43568}, {31673, 58230}, {34507, 50957}, {34783, 46852}, {36253, 38789}, {36836, 42919}, {36843, 42918}, {36990, 55701}, {37481, 46847}, {37640, 42969}, {37641, 42968}, {37705, 58238}, {38141, 38669}, {38634, 39838}, {38635, 39809}, {38637, 52836}, {38724, 38791}, {38734, 38743}, {38757, 51517}, {42093, 42688}, {42094, 42689}, {42103, 42166}, {42106, 42163}, {42107, 42161}, {42110, 42160}, {42115, 42580}, {42116, 42581}, {42125, 42162}, {42126, 42598}, {42127, 42599}, {42128, 42159}, {42129, 42165}, {42130, 42687}, {42131, 42686}, {42132, 42164}, {42135, 42962}, {42138, 42963}, {42140, 42950}, {42141, 42951}, {42157, 43544}, {42158, 43545}, {42490, 42795}, {42491, 42796}, {42528, 43442}, {42529, 43443}, {42592, 43632}, {42593, 43633}, {42786, 55648}, {42934, 43013}, {42935, 43012}, {42946, 43241}, {42947, 43240}, {43008, 43550}, {43009, 43551}, {43298, 44015}, {43299, 44016}, {43342, 43381}, {43343, 43380}, {43366, 43637}, {43367, 43636}, {43509, 60293}, {43510, 60294}, {43513, 53519}, {43514, 53518}, {44872, 50461}, {48675, 61659}, {48884, 55684}, {48889, 53093}, {48895, 55614}, {48901, 55595}, {48904, 55641}, {48910, 55620}, {48942, 55675}, {48943, 55652}, {50798, 58240}, {50802, 58236}, {50803, 58249}, {50830, 61255}, {50955, 55718}, {51024, 55597}, {51076, 58235}, {51140, 53858}, {51163, 55624}, {53023, 55724}, {58247, 61510}

X(61968) = midpoint of X(i) and X(j) for these {i,j}: {4, 7486}
X(61968) = reflection of X(i) in X(j) for these {i,j}: {3533, 5}
X(61968) = inverse of X(62041) in orthocentroidal circle
X(61968) = inverse of X(62041) in Yff hyperbola
X(61968) = pole of line {523, 62041} with respect to the orthocentroidal circle
X(61968) = pole of line {185, 62024} with respect to the Jerabek hyperbola
X(61968) = pole of line {6, 62041} with respect to the Kiepert hyperbola
X(61968) = pole of line {523, 62041} with respect to the Yff hyperbola
X(61968) = pole of line {69, 55680} with respect to the Wallace hyperbola
X(61968) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(253), X(58193)}}, {{A, B, C, X(265), X(3533)}}, {{A, B, C, X(3426), X(35478)}}, {{A, B, C, X(3534), X(14860)}}, {{A, B, C, X(3545), X(17505)}}, {{A, B, C, X(5056), X(21400)}}, {{A, B, C, X(5059), X(18550)}}, {{A, B, C, X(5067), X(32533)}}, {{A, B, C, X(10299), X(34483)}}, {{A, B, C, X(13623), X(21735)}}, {{A, B, C, X(15077), X(15702)}}, {{A, B, C, X(15700), X(60121)}}, {{A, B, C, X(18855), X(49140)}}, {{A, B, C, X(31361), X(58205)}}, {{A, B, C, X(35473), X(43691)}}, {{A, B, C, X(47478), X(60122)}}, {{A, B, C, X(47485), X(52518)}}
X(61968) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 14269, 5076}, {3, 15684, 15704}, {3, 3146, 15681}, {3, 5072, 5055}, {3, 5076, 5073}, {3, 546, 3843}, {3, 632, 15701}, {4, 15640, 3853}, {4, 3091, 3628}, {4, 3526, 15684}, {4, 3545, 15717}, {4, 5, 3534}, {4, 7486, 30}, {5, 12101, 3522}, {5, 30, 3533}, {5, 3543, 15720}, {381, 1656, 3855}, {381, 382, 3850}, {381, 3843, 3851}, {381, 5072, 3857}, {546, 12811, 3845}, {546, 3859, 12102}, {548, 3628, 14869}, {3091, 3529, 5}, {3091, 3627, 5079}, {3091, 3628, 5072}, {3146, 12811, 1656}, {3146, 3855, 12811}, {3522, 12101, 382}, {3522, 3529, 12103}, {3526, 5072, 15022}, {3534, 5055, 15694}, {3534, 5073, 17800}, {3544, 5076, 15722}, {3545, 3861, 1657}, {3628, 12103, 549}, {3628, 3857, 3091}, {3830, 3851, 5070}, {3832, 3858, 381}, {3843, 3850, 15689}, {3843, 5055, 4}, {3843, 5073, 14269}, {3845, 12811, 3146}, {3853, 5068, 5054}, {3857, 15704, 5066}, {3858, 3860, 3832}, {5056, 11541, 12108}, {5072, 15706, 12812}, {11541, 12108, 15696}, {11812, 15714, 3524}, {12108, 15687, 11541}, {12108, 15696, 3}, {13735, 15710, 140}, {14269, 15694, 3830}, {15022, 15704, 3526}, {15717, 17542, 10303}, {18586, 18587, 14093}, {42902, 42903, 6}

X(61969) = X(2)X(3)∩X(17)X(42509)

Barycentrics    17*a^4-28*(b^2-c^2)^2+11*a^2*(b^2+c^2) : :
X(61969) = -28*X[2]+15*X[3], 6*X[1699]+7*X[50800], -X[3654]+14*X[51078], 35*X[4668]+4*X[58246], -2*X[4669]+15*X[50799], -3*X[5093]+16*X[50959], -3*X[5790]+16*X[50803], -3*X[5886]+16*X[51076], 5*X[8148]+8*X[34641], -3*X[10247]+16*X[50802], 6*X[11224]+7*X[50798], -3*X[14561]+16*X[51131] and many others

X(61969) lies on these lines: {2, 3}, {17, 42509}, {18, 42508}, {1699, 50800}, {3066, 33887}, {3654, 51078}, {4668, 58246}, {4669, 50799}, {5093, 50959}, {5339, 42506}, {5340, 42507}, {5790, 50803}, {5886, 51076}, {6470, 35787}, {6471, 35786}, {8148, 34641}, {8976, 42417}, {10247, 50802}, {11224, 50798}, {11485, 12817}, {11486, 12816}, {12818, 42270}, {12819, 42273}, {12820, 42155}, {12821, 42154}, {13886, 60308}, {13939, 60307}, {13951, 42418}, {14488, 60638}, {14561, 51131}, {15516, 38072}, {15520, 47353}, {15533, 55720}, {15534, 50963}, {16644, 42630}, {16645, 42629}, {18440, 20583}, {18483, 38098}, {18492, 34747}, {18553, 51187}, {21358, 55601}, {22165, 50956}, {25561, 55585}, {33602, 43307}, {33603, 43306}, {34648, 37624}, {34748, 51094}, {37832, 43196}, {37835, 43195}, {38076, 48661}, {38077, 38756}, {38140, 51066}, {41107, 43233}, {41108, 43232}, {41112, 42125}, {41113, 42128}, {41945, 42526}, {41946, 42527}, {42093, 43305}, {42094, 43304}, {42096, 43294}, {42097, 43295}, {42103, 42781}, {42106, 42782}, {42107, 42510}, {42110, 42511}, {42111, 42792}, {42114, 42791}, {42262, 42641}, {42265, 42642}, {42268, 43322}, {42269, 43323}, {42502, 42921}, {42503, 42920}, {42520, 44016}, {42521, 44015}, {42602, 43563}, {42603, 43562}, {42625, 54577}, {42626, 54576}, {42633, 43365}, {42634, 43364}, {42639, 42643}, {42640, 42644}, {42817, 49876}, {42818, 49875}, {42910, 42956}, {42911, 42957}, {42914, 43366}, {42915, 43367}, {42918, 43373}, {42919, 43372}, {42962, 43417}, {42963, 43416}, {43238, 54479}, {43239, 54480}, {43503, 43882}, {43504, 43881}, {48901, 51186}, {50796, 51515}, {50866, 61265}, {50954, 50992}, {50957, 53023}, {50989, 55724}, {50991, 55584}, {51024, 55596}, {51070, 61258}, {51074, 51103}, {51109, 58230}, {51133, 54173}, {54595, 60298}, {54596, 60297}, {54717, 60131}, {60132, 60287}

X(61969) = inverse of X(62039) in orthocentroidal circle
X(61969) = inverse of X(62039) in Yff hyperbola
X(61969) = pole of line {523, 62039} with respect to the orthocentroidal circle
X(61969) = pole of line {6, 62039} with respect to the Kiepert hyperbola
X(61969) = pole of line {523, 62039} with respect to the Yff hyperbola
X(61969) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(15693), X(57894)}}, {{A, B, C, X(15704), X(54585)}}, {{A, B, C, X(44904), X(60122)}}
X(61969) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11001, 17504}, {2, 15640, 3528}, {2, 15710, 11812}, {2, 3830, 15681}, {2, 3855, 5066}, {2, 550, 15693}, {2, 8703, 15720}, {3, 14269, 15687}, {3, 15683, 15689}, {3, 15685, 15697}, {3, 15699, 15694}, {3, 15703, 15709}, {3, 3855, 3851}, {4, 11737, 15688}, {4, 14869, 382}, {4, 3091, 16239}, {381, 3843, 5055}, {381, 5054, 3850}, {381, 546, 14269}, {382, 5079, 10299}, {546, 15687, 3839}, {546, 3851, 3843}, {546, 3856, 550}, {546, 3858, 3855}, {547, 15640, 15716}, {1656, 11001, 15722}, {3146, 14892, 15723}, {3534, 15713, 3}, {3545, 15684, 5070}, {3545, 17578, 10124}, {3545, 3856, 381}, {3830, 15694, 15685}, {3830, 15695, 5073}, {3830, 3851, 2}, {3830, 5055, 15695}, {3839, 15682, 3845}, {3839, 5071, 3861}, {3845, 12100, 4}, {3845, 5066, 15682}, {3860, 5066, 3858}, {5055, 5073, 15718}, {5068, 17578, 10303}, {5076, 15716, 15640}, {7486, 15691, 5054}, {10124, 12812, 15699}, {12100, 15694, 15701}, {12101, 15684, 3830}, {12101, 15693, 15684}, {15682, 15713, 3534}, {15694, 15707, 14869}

X(61970) = X(2)X(3)∩X(6)X(43783)

Barycentrics    5*a^4-8*(b^2-c^2)^2+3*a^2*(b^2+c^2) : :
X(61970) = -24*X[2]+13*X[3], 3*X[51]+8*X[46852], -X[52]+12*X[13570], 3*X[568]+8*X[44870], -4*X[576]+15*X[50963], 10*X[946]+X[61244], 3*X[1351]+8*X[18553], -10*X[1385]+21*X[61271], X[1482]+10*X[18492], 39*X[1699]+5*X[4816], 3*X[3060]+8*X[45958], -6*X[3579]+17*X[30315] and many others

X(61970) lies on these lines: {2, 3}, {6, 43783}, {13, 43032}, {14, 43033}, {15, 42908}, {16, 42909}, {17, 42093}, {18, 42094}, {51, 46852}, {52, 13570}, {115, 43136}, {397, 42106}, {398, 42103}, {568, 44870}, {576, 50963}, {590, 9691}, {946, 61244}, {1151, 42558}, {1152, 42557}, {1327, 53516}, {1328, 53513}, {1351, 18553}, {1384, 39565}, {1385, 61271}, {1482, 18492}, {1498, 15037}, {1587, 42571}, {1588, 42570}, {1699, 4816}, {3060, 45958}, {3311, 35787}, {3312, 35786}, {3316, 43508}, {3317, 43507}, {3411, 12816}, {3412, 12817}, {3519, 3531}, {3579, 30315}, {3763, 55624}, {3818, 5093}, {4746, 19925}, {4857, 6767}, {5023, 39601}, {5050, 48889}, {5254, 22246}, {5270, 7373}, {5318, 42920}, {5321, 42921}, {5334, 42962}, {5335, 42963}, {5339, 16808}, {5340, 16809}, {5343, 11542}, {5344, 11543}, {5349, 18582}, {5350, 18581}, {5365, 42142}, {5366, 42139}, {5550, 28190}, {5562, 12002}, {5603, 61292}, {5644, 11550}, {5790, 18483}, {5882, 12571}, {5946, 11439}, {6102, 16261}, {6199, 8960}, {6241, 13364}, {6279, 18509}, {6280, 18511}, {6288, 13431}, {6361, 61262}, {6395, 23251}, {6407, 35821}, {6408, 35820}, {6417, 6564}, {6418, 6565}, {6445, 10576}, {6446, 10577}, {6472, 43413}, {6473, 43414}, {6500, 13665}, {6501, 13785}, {6748, 33636}, {7687, 38789}, {7755, 18424}, {7756, 18584}, {7860, 15031}, {7861, 14535}, {7988, 33697}, {8227, 58230}, {8550, 48662}, {8778, 50718}, {8976, 42283}, {9540, 10145}, {9589, 38066}, {9690, 41963}, {9703, 11424}, {9704, 46261}, {9779, 61280}, {9781, 45959}, {9812, 61259}, {9955, 37624}, {10095, 15305}, {10110, 18435}, {10143, 43887}, {10144, 43888}, {10146, 13935}, {10187, 42491}, {10188, 42490}, {10194, 42259}, {10195, 42258}, {10222, 50806}, {10247, 11522}, {10248, 61524}, {10516, 55584}, {10574, 18874}, {10733, 15046}, {11017, 11444}, {11178, 55580}, {11362, 50803}, {11455, 12006}, {11482, 47353}, {11485, 41973}, {11486, 41974}, {11623, 38744}, {11645, 55701}, {12000, 45631}, {12001, 45630}, {12111, 13321}, {12160, 36852}, {12242, 48675}, {12279, 13363}, {12290, 15026}, {12315, 14864}, {12645, 61253}, {12699, 38127}, {12702, 38140}, {12773, 38141}, {12818, 43431}, {12819, 43430}, {12902, 16534}, {13093, 23325}, {13108, 22681}, {13382, 18439}, {13421, 15060}, {13432, 20424}, {13464, 18525}, {13474, 14845}, {13851, 19347}, {13951, 42284}, {14061, 38634}, {14530, 18405}, {14627, 18451}, {14841, 52518}, {14848, 50964}, {14915, 27355}, {14978, 47392}, {15030, 44863}, {15038, 32139}, {15043, 32137}, {15056, 54048}, {15059, 38633}, {15178, 30308}, {15603, 44535}, {15905, 61327}, {16194, 37481}, {16267, 42995}, {16268, 42994}, {18357, 58247}, {18362, 22331}, {18376, 45185}, {18383, 32063}, {18436, 44871}, {18482, 51516}, {18510, 43412}, {18512, 43411}, {18526, 38034}, {18538, 23263}, {18550, 43719}, {18762, 23253}, {19106, 43239}, {19107, 43238}, {19116, 43377}, {19117, 43376}, {19130, 53091}, {20417, 38790}, {20418, 38756}, {21358, 55602}, {21400, 43908}, {21766, 33542}, {22682, 48673}, {22791, 51515}, {22804, 55039}, {23324, 34780}, {24206, 55604}, {25555, 36990}, {25561, 53097}, {28216, 46933}, {29012, 55692}, {29317, 55632}, {29323, 55678}, {30435, 39590}, {31272, 38637}, {31663, 61264}, {31872, 45924}, {32767, 61721}, {33537, 37494}, {34507, 44456}, {34648, 61276}, {34718, 61258}, {36412, 38292}, {36836, 42979}, {36843, 42978}, {37714, 50800}, {37727, 50802}, {38072, 53092}, {38136, 39899}, {38228, 39656}, {38724, 46686}, {38732, 52090}, {38734, 48657}, {40273, 59503}, {40284, 46850}, {41955, 42273}, {41956, 42270}, {41964, 42274}, {42021, 61137}, {42090, 42949}, {42091, 42948}, {42095, 42158}, {42098, 42157}, {42099, 42773}, {42100, 42774}, {42101, 42132}, {42102, 42129}, {42107, 42127}, {42110, 42126}, {42111, 42131}, {42114, 42130}, {42115, 42431}, {42116, 42432}, {42121, 43769}, {42122, 42472}, {42123, 42473}, {42124, 43770}, {42133, 42494}, {42134, 42495}, {42135, 42815}, {42138, 42816}, {42153, 43427}, {42156, 43426}, {42159, 42974}, {42162, 42975}, {42225, 43881}, {42226, 43882}, {42275, 42566}, {42276, 42567}, {42435, 43332}, {42436, 43333}, {42572, 43433}, {42573, 43432}, {42580, 43193}, {42581, 43194}, {42592, 42632}, {42593, 42631}, {42625, 43249}, {42626, 43248}, {42688, 43486}, {42689, 43485}, {42779, 43251}, {42780, 43250}, {42797, 42954}, {42798, 42955}, {42813, 42993}, {42814, 42992}, {42904, 43014}, {42905, 43015}, {42914, 43637}, {42915, 43636}, {43174, 48661}, {43457, 44518}, {44750, 52101}, {48680, 59390}, {48895, 55610}, {48901, 55593}, {48904, 55639}, {48910, 55616}, {48942, 55676}, {48943, 55651}, {50805, 61249}, {50807, 51082}, {50814, 51078}, {50864, 61278}, {50957, 50973}, {50970, 51133}, {50993, 55588}, {51024, 55595}, {51105, 58235}, {51118, 61263}, {51173, 51178}, {51514, 60901}, {53102, 54891}, {58238, 59387}, {58240, 61252}, {59389, 60884}

X(61970) = midpoint of X(i) and X(j) for these {i,j}: {4, 5056}, {3830, 15718}
X(61970) = reflection of X(i) in X(j) for these {i,j}: {15720, 5056}, {3, 5070}, {3525, 5}, {3534, 15715}, {5070, 5072}, {5072, 3855}
X(61970) = inverse of X(62036) in orthocentroidal circle
X(61970) = inverse of X(62036) in Yff hyperbola
X(61970) = complement of X(62113)
X(61970) = anticomplement of X(61808)
X(61970) = pole of line {523, 62036} with respect to the orthocentroidal circle
X(61970) = pole of line {185, 12002} with respect to the Jerabek hyperbola
X(61970) = pole of line {6, 62036} with respect to the Kiepert hyperbola
X(61970) = pole of line {523, 62036} with respect to the Yff hyperbola
X(61970) = pole of line {69, 55679} with respect to the Wallace hyperbola
X(61970) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(265), X(3525)}}, {{A, B, C, X(1217), X(50690)}}, {{A, B, C, X(1657), X(14860)}}, {{A, B, C, X(3090), X(21400)}}, {{A, B, C, X(3426), X(35475)}}, {{A, B, C, X(3518), X(3531)}}, {{A, B, C, X(3519), X(3524)}}, {{A, B, C, X(3521), X(17538)}}, {{A, B, C, X(3523), X(14841)}}, {{A, B, C, X(3527), X(44879)}}, {{A, B, C, X(3528), X(14861)}}, {{A, B, C, X(3529), X(18550)}}, {{A, B, C, X(3532), X(23040)}}, {{A, B, C, X(3544), X(17505)}}, {{A, B, C, X(6662), X(15686)}}, {{A, B, C, X(8703), X(52441)}}, {{A, B, C, X(10109), X(60122)}}, {{A, B, C, X(10594), X(61137)}}, {{A, B, C, X(11539), X(13599)}}, {{A, B, C, X(14863), X(15695)}}, {{A, B, C, X(15693), X(60121)}}, {{A, B, C, X(15703), X(40448)}}, {{A, B, C, X(15721), X(31363)}}, {{A, B, C, X(18855), X(49135)}}, {{A, B, C, X(19710), X(54585)}}, {{A, B, C, X(21844), X(43908)}}, {{A, B, C, X(35473), X(43719)}}, {{A, B, C, X(42021), X(61138)}}, {{A, B, C, X(45004), X(61133)}}, {{A, B, C, X(55858), X(60171)}}
X(61970) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3861, 5076}, {2, 5076, 17800}, {3, 15686, 6961}, {3, 382, 15685}, {3, 3843, 14269}, {3, 5, 15703}, {4, 10299, 3543}, {4, 3522, 3627}, {4, 3545, 3522}, {4, 3832, 3858}, {4, 3855, 5056}, {4, 5, 1657}, {4, 5068, 550}, {5, 10124, 3090}, {5, 14893, 3146}, {5, 30, 3525}, {5, 3146, 5054}, {5, 3627, 12100}, {5, 3845, 12102}, {5, 546, 3839}, {20, 5066, 5079}, {20, 5079, 15694}, {20, 7486, 17533}, {30, 15715, 3534}, {30, 3855, 5072}, {30, 5072, 5070}, {140, 15712, 15708}, {140, 15717, 15720}, {140, 3845, 4}, {376, 15723, 15718}, {376, 3091, 5}, {376, 3525, 15717}, {376, 3839, 3845}, {381, 1656, 3850}, {381, 382, 3091}, {381, 5072, 3855}, {381, 546, 3843}, {382, 15693, 15704}, {382, 5059, 5073}, {382, 5072, 15723}, {382, 5079, 17504}, {404, 5067, 15699}, {550, 3850, 5068}, {1656, 1657, 3523}, {1656, 3850, 3851}, {2043, 2044, 10109}, {3091, 3845, 382}, {3091, 3856, 381}, {3091, 5067, 11737}, {3523, 5059, 376}, {3526, 3627, 15681}, {3529, 7402, 3628}, {3533, 5071, 17563}, {3543, 3628, 15696}, {3544, 17578, 549}, {3545, 3627, 3526}, {3627, 3859, 3545}, {3628, 15696, 15701}, {3830, 15718, 30}, {3843, 17800, 3861}, {3845, 3850, 5059}, {3851, 5073, 1656}, {3857, 3861, 2}, {3860, 12102, 3856}, {5067, 15704, 15693}, {5318, 42920, 42989}, {5321, 42921, 42988}, {5343, 42775, 11542}, {11737, 15693, 5055}, {11737, 15704, 5067}, {12811, 15687, 631}, {14269, 15703, 3830}, {14813, 14814, 3524}, {14892, 15704, 4234}, {15022, 15682, 3530}, {15686, 16402, 15716}, {15696, 15701, 3}, {15720, 15723, 140}, {16239, 17538, 15700}, {18586, 18587, 15688}, {42122, 42472, 42950}, {42123, 42473, 42951}, {42134, 42495, 42924}, {42494, 42925, 42817}, {42495, 42924, 42818}, {43783, 43784, 6}

X(61971) = X(2)X(3)∩X(1327)X(6418)

Barycentrics    13*a^4-20*(b^2-c^2)^2+7*a^2*(b^2+c^2) : :
X(61971) = -20*X[2]+11*X[3], 8*X[1699]+X[51515], 5*X[3655]+4*X[50868], 4*X[3818]+5*X[50963], 16*X[4701]+11*X[8148], 4*X[5097]+5*X[47353], 8*X[5476]+X[48662], -10*X[11178]+X[55582], 5*X[11179]+4*X[51025], 2*X[11180]+7*X[51173], 2*X[11278]+25*X[18492], -32*X[12571]+5*X[37624] and many others

X(61971) lies on these lines: {2, 3}, {1327, 6418}, {1328, 6417}, {1699, 51515}, {3316, 6472}, {3317, 6473}, {3655, 50868}, {3818, 50963}, {4701, 8148}, {5097, 47353}, {5237, 43475}, {5238, 43476}, {5476, 48662}, {6407, 42602}, {6408, 42603}, {6431, 35787}, {6432, 35786}, {9690, 43211}, {9691, 43257}, {10137, 43504}, {10138, 43503}, {11178, 55582}, {11179, 51025}, {11180, 51173}, {11278, 18492}, {11480, 43331}, {11481, 43330}, {11485, 43332}, {11486, 43333}, {11645, 55703}, {12571, 37624}, {12699, 50803}, {12816, 42153}, {12817, 42156}, {13321, 16261}, {13570, 18435}, {14831, 46852}, {16267, 42799}, {16268, 42800}, {16644, 43227}, {16645, 43226}, {16962, 42093}, {16963, 42094}, {16964, 54593}, {16965, 54594}, {18439, 58470}, {18440, 50959}, {18480, 34748}, {18483, 34718}, {18493, 34648}, {18525, 50802}, {18581, 42971}, {18582, 42970}, {20582, 55616}, {21358, 55603}, {21850, 50954}, {22791, 50797}, {25561, 55587}, {28204, 61285}, {28208, 30392}, {31162, 50800}, {31670, 50960}, {31673, 51076}, {33887, 44747}, {35820, 43384}, {35821, 43385}, {35822, 51850}, {35823, 51849}, {36967, 43548}, {36968, 43549}, {37517, 50955}, {37640, 43328}, {37641, 43329}, {38066, 38140}, {38072, 39561}, {41949, 41958}, {41950, 41957}, {42095, 43200}, {42098, 43199}, {42099, 42474}, {42100, 42475}, {42103, 42974}, {42106, 42975}, {42111, 43100}, {42114, 43107}, {42130, 43104}, {42131, 43101}, {42481, 61719}, {42512, 43105}, {42513, 43106}, {42528, 43324}, {42529, 43325}, {42625, 42931}, {42626, 42930}, {42690, 44015}, {42691, 44016}, {42775, 49827}, {42776, 49826}, {42980, 43194}, {42981, 43193}, {42984, 43204}, {42985, 43203}, {43008, 49948}, {43009, 49947}, {43110, 43772}, {43111, 43771}, {43201, 43404}, {43202, 43403}, {43212, 43415}, {43254, 53519}, {43255, 53518}, {44456, 47354}, {48889, 55711}, {48892, 51167}, {48895, 55607}, {48943, 50968}, {50815, 58224}, {50817, 58244}, {50823, 58247}, {50862, 61268}, {50956, 51166}, {50957, 54131}, {51024, 55594}, {51075, 61244}, {51078, 61261}, {51091, 58236}, {51165, 54169}, {51186, 55595}, {51514, 59389}, {54917, 60238}

X(61971) = midpoint of X(i) and X(j) for these {i,j}: {3830, 15707}
X(61971) = reflection of X(i) in X(j) for these {i,j}: {15688, 15709}, {15689, 15707}, {15705, 15699}, {15707, 5055}, {15709, 5}, {3534, 15705}
X(61971) = inverse of X(35404) in orthocentroidal circle
X(61971) = inverse of X(35404) in Yff hyperbola
X(61971) = pole of line {523, 35404} with respect to the orthocentroidal circle
X(61971) = pole of line {6, 35404} with respect to the Kiepert hyperbola
X(61971) = pole of line {523, 35404} with respect to the Yff hyperbola
X(61971) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(264), X(35404)}}, {{A, B, C, X(265), X(15709)}}, {{A, B, C, X(3527), X(44880)}}, {{A, B, C, X(7486), X(21400)}}, {{A, B, C, X(12812), X(60122)}}, {{A, B, C, X(14860), X(49137)}}, {{A, B, C, X(15683), X(18550)}}, {{A, B, C, X(15686), X(54585)}}, {{A, B, C, X(35472), X(44731)}}
X(61971) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3858, 381}, {3, 15684, 11001}, {3, 15686, 15695}, {3, 15723, 15701}, {3, 3545, 5055}, {3, 3853, 5073}, {4, 12811, 15696}, {4, 3091, 3530}, {4, 3859, 5079}, {4, 632, 382}, {5, 11001, 15723}, {5, 15691, 2}, {5, 30, 15709}, {30, 15699, 15705}, {30, 15705, 3534}, {30, 15707, 15689}, {30, 15709, 15688}, {30, 5055, 15707}, {381, 3534, 3091}, {381, 382, 5066}, {381, 3830, 3851}, {381, 3839, 14269}, {381, 3843, 3830}, {382, 5066, 15703}, {547, 12103, 11812}, {547, 3845, 4}, {1656, 15685, 15718}, {1656, 15687, 15685}, {2043, 2044, 12812}, {3090, 16418, 3628}, {3146, 10109, 15700}, {3524, 3545, 5056}, {3543, 3545, 11539}, {3543, 5067, 15690}, {3544, 15640, 10124}, {3545, 3839, 3845}, {3830, 15694, 17800}, {3830, 15707, 30}, {3830, 3851, 15694}, {3832, 3839, 3545}, {3839, 14269, 3843}, {3845, 3850, 3543}, {3854, 15682, 11737}, {3857, 12101, 5071}, {5054, 15688, 15692}, {5054, 5055, 5070}, {5071, 12101, 1657}, {5073, 15701, 15691}, {10304, 14892, 1656}, {11001, 15723, 3}, {11539, 15719, 5054}, {11737, 15682, 3526}, {12103, 15685, 15681}, {12108, 15699, 17561}, {14892, 15687, 10304}, {15719, 15723, 6980}, {34648, 50807, 18493}, {43330, 43490, 11481}, {43331, 43489, 11480}

X(61972) = X(2)X(3)∩X(40)X(51078)

Barycentrics    19*a^4-29*(b^2-c^2)^2+10*a^2*(b^2+c^2) : :
X(61972) = -29*X[2]+16*X[3], -X[40]+14*X[51078], 8*X[182]+5*X[51216], -X[944]+14*X[50807], 5*X[962]+8*X[50827], -X[1350]+14*X[51133], 8*X[1385]+5*X[50863], 12*X[1699]+X[31145], -X[3621]+40*X[18492], -7*X[3622]+20*X[30308], 7*X[4678]+32*X[18483], -3*X[5032]+16*X[50959] and many others

X(61972) lies on these lines: {2, 3}, {40, 51078}, {182, 51216}, {316, 32893}, {590, 43383}, {615, 43382}, {944, 50807}, {962, 50827}, {1131, 60296}, {1132, 60295}, {1151, 54543}, {1152, 54542}, {1350, 51133}, {1385, 50863}, {1699, 31145}, {3068, 43800}, {3069, 43799}, {3424, 60650}, {3621, 18492}, {3622, 30308}, {4678, 18483}, {5032, 50959}, {5343, 41119}, {5344, 41120}, {5365, 16267}, {5366, 16268}, {5691, 51085}, {5921, 51140}, {6684, 50873}, {6776, 50964}, {7585, 42539}, {7586, 42540}, {7773, 32880}, {7788, 32882}, {7850, 46951}, {8981, 43522}, {9540, 43504}, {9779, 34648}, {10248, 19875}, {10302, 54706}, {10653, 43005}, {10654, 43004}, {11002, 13570}, {11160, 53023}, {11439, 58470}, {12007, 51023}, {12245, 50800}, {12571, 38314}, {12816, 42920}, {12817, 42921}, {13607, 50864}, {13935, 43503}, {13966, 43521}, {14484, 60625}, {15031, 32872}, {18845, 54866}, {20049, 59387}, {21356, 50960}, {23251, 41951}, {23253, 35814}, {23261, 41952}, {23263, 35815}, {25055, 51076}, {31162, 54448}, {31412, 43561}, {32819, 32881}, {32827, 32869}, {32830, 48913}, {33606, 49826}, {33607, 49827}, {34638, 61264}, {35820, 43525}, {35821, 43526}, {36990, 51138}, {37640, 43365}, {37641, 43364}, {38076, 46933}, {38259, 54521}, {41895, 60331}, {41943, 43227}, {41944, 43226}, {41945, 43508}, {41946, 43507}, {42085, 43544}, {42086, 43545}, {42103, 61719}, {42119, 43478}, {42120, 43477}, {42130, 42932}, {42131, 42933}, {42154, 43474}, {42155, 43473}, {42159, 49825}, {42162, 49824}, {42262, 43519}, {42265, 43520}, {42268, 43342}, {42269, 43343}, {42417, 43883}, {42418, 43884}, {42512, 42630}, {42513, 42629}, {42561, 43560}, {42580, 43475}, {42581, 43476}, {42598, 54580}, {42599, 54581}, {42688, 42912}, {42689, 42913}, {42727, 46476}, {42728, 46473}, {42775, 43202}, {42776, 43201}, {42898, 43541}, {42899, 43540}, {42962, 42969}, {42963, 42968}, {42972, 49874}, {42973, 49873}, {42982, 43417}, {42983, 43416}, {43150, 54132}, {43302, 43419}, {43303, 43418}, {43312, 43375}, {43313, 43374}, {43368, 43633}, {43369, 43632}, {43951, 60200}, {47352, 51131}, {47353, 51170}, {48876, 51211}, {50803, 53620}, {50982, 51212}, {53101, 60336}, {54476, 60102}, {54520, 60639}, {54639, 60147}, {59389, 60984}, {60113, 60333}, {60118, 60632}, {60228, 60328}, {60239, 60327}, {60282, 60324}

X(61972) = reflection of X(i) in X(j) for these {i,j}: {2, 5068}
X(61972) = inverse of X(62032) in orthocentroidal circle
X(61972) = inverse of X(62032) in Yff hyperbola
X(61972) = anticomplement of X(61806)
X(61972) = pole of line {523, 62032} with respect to the orthocentroidal circle
X(61972) = pole of line {6, 51026} with respect to the Kiepert hyperbola
X(61972) = pole of line {523, 62032} with respect to the Yff hyperbola
X(61972) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1494), X(21734)}}, {{A, B, C, X(3529), X(54923)}}, {{A, B, C, X(3535), X(60296)}}, {{A, B, C, X(3536), X(60295)}}, {{A, B, C, X(3855), X(54552)}}, {{A, B, C, X(10301), X(54706)}}, {{A, B, C, X(10304), X(52443)}}, {{A, B, C, X(14860), X(49140)}}, {{A, B, C, X(15715), X(54838)}}, {{A, B, C, X(16251), X(44903)}}, {{A, B, C, X(35482), X(54844)}}, {{A, B, C, X(38282), X(54521)}}, {{A, B, C, X(52288), X(60625)}}, {{A, B, C, X(52290), X(60331)}}, {{A, B, C, X(52299), X(54866)}}
X(61972) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5079, 11112}, {4, 3545, 3534}, {4, 3855, 3628}, {4, 5066, 10304}, {4, 5072, 20}, {4, 549, 3543}, {140, 376, 15692}, {140, 3856, 3857}, {140, 5079, 5067}, {140, 7486, 13741}, {376, 15702, 17504}, {376, 381, 3091}, {376, 5071, 15723}, {381, 14269, 547}, {381, 15684, 5066}, {381, 3843, 15687}, {382, 5055, 15759}, {549, 14093, 15698}, {1657, 6865, 550}, {3091, 15640, 5055}, {3091, 15704, 15022}, {3091, 3839, 3845}, {3091, 5067, 5068}, {3534, 3545, 7486}, {3534, 3857, 3545}, {3830, 17504, 11541}, {3832, 15717, 3856}, {3843, 3857, 4}, {3845, 12102, 14269}, {3860, 15687, 381}, {5056, 15682, 15705}, {5066, 14890, 5}, {10304, 15022, 2}, {10304, 15640, 15704}, {10304, 15684, 15683}, {11541, 15702, 376}, {11737, 15723, 5071}, {12102, 15709, 15640}, {13741, 15717, 140}, {14269, 15693, 12102}, {15687, 15692, 3146}, {15692, 15721, 15707}, {15700, 16842, 17556}, {15708, 15759, 15717}, {15709, 15715, 549}, {42775, 43202, 49947}, {42776, 43201, 49948}, {50959, 51537, 5032}

X(61973) = X(2)X(3)∩X(8)X(58244)

Barycentrics    17*a^4-25*(b^2-c^2)^2+8*a^2*(b^2+c^2) : :
X(61973) = -25*X[2]+14*X[3], 25*X[8]+8*X[58244], 10*X[946]+X[50871], X[962]+10*X[50799], 10*X[1352]+X[51214], -12*X[1699]+X[34631], -2*X[3625]+35*X[18492], 4*X[3630]+7*X[54132], -25*X[3655]+36*X[58234], 5*X[4668]+28*X[18483], -16*X[5097]+5*X[50974], 6*X[5102]+5*X[11180] and many others

X(61973) lies on these lines: {2, 3}, {8, 58244}, {17, 42589}, {18, 42588}, {61, 43202}, {62, 43201}, {371, 43536}, {372, 54597}, {946, 50871}, {962, 50799}, {1285, 18424}, {1327, 35770}, {1328, 35771}, {1352, 51214}, {1587, 43387}, {1588, 43386}, {1699, 34631}, {3070, 14226}, {3071, 14241}, {3316, 6429}, {3317, 6430}, {3625, 18492}, {3630, 54132}, {3655, 58234}, {4668, 18483}, {5097, 50974}, {5102, 11180}, {5339, 42898}, {5340, 42899}, {5349, 49876}, {5350, 49875}, {5365, 49947}, {5366, 49948}, {5480, 51027}, {5691, 51074}, {5818, 50803}, {5921, 50963}, {6361, 38076}, {6431, 23275}, {6432, 23269}, {6480, 42602}, {6481, 42603}, {7773, 32877}, {7788, 32878}, {7818, 54890}, {7855, 60636}, {7967, 34648}, {8227, 51076}, {9956, 50809}, {10137, 54543}, {10138, 54542}, {10139, 43887}, {10140, 43888}, {10155, 54493}, {10248, 50821}, {10595, 50802}, {10645, 43248}, {10646, 43249}, {11278, 20053}, {11531, 50796}, {12111, 44871}, {12248, 38077}, {12571, 50868}, {13570, 14831}, {16200, 34627}, {16267, 42775}, {16268, 42776}, {18480, 58237}, {18583, 51176}, {18842, 60325}, {18844, 60150}, {19053, 35786}, {19054, 35787}, {19875, 51078}, {19925, 51120}, {20582, 55618}, {21356, 55587}, {21358, 51133}, {23253, 42579}, {23263, 42578}, {24206, 50966}, {25561, 51538}, {25565, 55685}, {31162, 38155}, {31423, 50869}, {31673, 58231}, {32455, 47353}, {32822, 32876}, {32823, 32875}, {33179, 50818}, {33602, 42998}, {33603, 42999}, {33604, 41108}, {33605, 41107}, {34089, 42260}, {34091, 42261}, {34632, 38140}, {36967, 42472}, {36968, 42473}, {36990, 51129}, {37640, 43010}, {37641, 43011}, {37832, 43472}, {37835, 43471}, {38072, 39874}, {38073, 61020}, {38314, 50807}, {40273, 50800}, {40330, 50960}, {41100, 42495}, {41101, 42494}, {41121, 42435}, {41122, 42436}, {41943, 43245}, {41944, 43244}, {41965, 43509}, {41966, 43510}, {41973, 49860}, {41974, 49859}, {42085, 43199}, {42086, 43200}, {42103, 43033}, {42106, 43032}, {42125, 43540}, {42128, 43541}, {42133, 43542}, {42134, 43543}, {42149, 42953}, {42152, 42952}, {42160, 42802}, {42161, 42801}, {42163, 49826}, {42166, 49827}, {42263, 43374}, {42264, 43375}, {42413, 43254}, {42414, 43255}, {42478, 43031}, {42479, 43030}, {42725, 42728}, {42726, 42727}, {42906, 42986}, {42907, 42987}, {42920, 49812}, {42921, 49813}, {43250, 43771}, {43251, 43772}, {43401, 52080}, {43402, 52079}, {43444, 54575}, {43445, 54574}, {43515, 43569}, {43516, 43568}, {47354, 55722}, {48874, 51213}, {48889, 50964}, {48898, 51217}, {50280, 54637}, {50956, 51212}, {51025, 55711}, {53103, 54646}, {53106, 54523}, {53107, 60185}, {54612, 60146}, {54616, 60326}, {54707, 60209}, {54857, 60284}, {60303, 60308}, {60304, 60307}

X(61973) = midpoint of X(i) and X(j) for these {i,j}: {3830, 15720}
X(61973) = reflection of X(i) in X(j) for these {i,j}: {15719, 5056}, {2, 5072}, {376, 15721}
X(61973) = inverse of X(62029) in orthocentroidal circle
X(61973) = inverse of X(62029) in Yff hyperbola
X(61973) = anticomplement of X(15718)
X(61973) = pole of line {523, 62029} with respect to the orthocentroidal circle
X(61973) = pole of line {6, 51164} with respect to the Kiepert hyperbola
X(61973) = pole of line {523, 62029} with respect to the Yff hyperbola
X(61973) = pole of line {69, 15706} with respect to the Wallace hyperbola
X(61973) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(15706)}}, {{A, B, C, X(1494), X(21735)}}, {{A, B, C, X(3526), X(15749)}}, {{A, B, C, X(8797), X(14892)}}, {{A, B, C, X(11410), X(11738)}}, {{A, B, C, X(11541), X(14860)}}, {{A, B, C, X(14483), X(55572)}}, {{A, B, C, X(14490), X(35501)}}, {{A, B, C, X(15319), X(58193)}}, {{A, B, C, X(15686), X(36889)}}, {{A, B, C, X(15692), X(54838)}}, {{A, B, C, X(18550), X(58202)}}, {{A, B, C, X(46333), X(57896)}}, {{A, B, C, X(46936), X(54660)}}, {{A, B, C, X(52284), X(60325)}}, {{A, B, C, X(52297), X(54523)}}, {{A, B, C, X(52298), X(60185)}}, {{A, B, C, X(52301), X(54890)}}, {{A, B, C, X(54763), X(55864)}}, {{A, B, C, X(55575), X(57715)}}
X(61973) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10304, 12108}, {2, 17538, 3524}, {2, 20, 15706}, {2, 3091, 14892}, {2, 3543, 15686}, {2, 3839, 3843}, {2, 3850, 3545}, {4, 3091, 3528}, {4, 5, 11541}, {376, 15721, 15715}, {376, 3545, 547}, {381, 14269, 549}, {381, 15681, 5066}, {381, 3830, 11737}, {381, 3843, 14893}, {381, 3845, 3543}, {381, 549, 3091}, {382, 11737, 17556}, {1656, 15640, 15710}, {1657, 3528, 17538}, {1657, 5072, 5070}, {3091, 14269, 15682}, {3091, 3853, 3533}, {3522, 15022, 17527}, {3525, 5056, 5067}, {3543, 15692, 5059}, {3543, 15702, 11001}, {3543, 15708, 15683}, {3543, 3832, 381}, {3545, 15702, 5071}, {3545, 15719, 5056}, {3830, 11737, 15692}, {3830, 15720, 30}, {3832, 3839, 3845}, {3845, 3853, 14269}, {3845, 3858, 11539}, {3851, 12101, 10304}, {3854, 3861, 3529}, {5056, 5059, 15720}, {11301, 11302, 5177}, {11737, 15692, 3090}, {12812, 15706, 2}, {14269, 15682, 4}, {14891, 14893, 15687}, {14891, 15687, 15684}, {15683, 15700, 376}, {15702, 15715, 15719}, {15702, 15723, 3525}, {15719, 15723, 15702}

X(61974) = X(2)X(3)∩X(13)X(42904)

Barycentrics    11*a^4-16*(b^2-c^2)^2+5*a^2*(b^2+c^2) : :
X(61974) = -16*X[2]+9*X[3], -32*X[551]+25*X[58233], -X[568]+8*X[13570], -8*X[946]+X[34748], -9*X[1351]+2*X[51187], 6*X[1699]+X[50798], -X[3654]+8*X[50803], -X[3655]+8*X[12571], -9*X[3656]+2*X[51096], 6*X[3818]+X[15534], X[4669]+6*X[18483], 4*X[4677]+3*X[8148] and many others

X(61974) lies on these lines: {2, 3}, {13, 42904}, {14, 42905}, {61, 42694}, {62, 42695}, {511, 50957}, {515, 50807}, {516, 51078}, {517, 50800}, {551, 58233}, {568, 13570}, {590, 43504}, {598, 54608}, {615, 17851}, {671, 54643}, {946, 34748}, {1327, 13785}, {1328, 13665}, {1351, 51187}, {1384, 18362}, {1503, 50964}, {1587, 43341}, {1588, 43340}, {1699, 50798}, {3564, 51173}, {3654, 50803}, {3655, 12571}, {3656, 51096}, {3818, 15534}, {4669, 18483}, {4677, 8148}, {4745, 12699}, {5093, 47353}, {5318, 41120}, {5321, 41119}, {5475, 22246}, {5478, 36363}, {5479, 36362}, {5480, 41149}, {5790, 50799}, {5886, 51074}, {6033, 36523}, {6055, 41148}, {6417, 35787}, {6418, 35786}, {6472, 42526}, {6473, 42527}, {6474, 41945}, {6475, 41946}, {6500, 35822}, {6501, 35823}, {6560, 43562}, {6561, 43563}, {7949, 60250}, {7989, 28202}, {8584, 18440}, {8972, 43522}, {9541, 43881}, {9605, 39563}, {9691, 35821}, {9777, 12308}, {9779, 50824}, {9880, 38743}, {9955, 51105}, {10145, 42602}, {10146, 42603}, {10246, 30308}, {10247, 50806}, {10302, 54582}, {11178, 55584}, {11179, 41153}, {11485, 41121}, {11486, 41122}, {11488, 43108}, {11489, 43109}, {11542, 49827}, {11543, 49826}, {11632, 41154}, {11645, 55705}, {11669, 54478}, {12007, 14848}, {12156, 22803}, {12702, 51066}, {12816, 16809}, {12817, 16808}, {13607, 34648}, {13941, 43521}, {14458, 60282}, {14492, 60228}, {14537, 21309}, {14561, 51129}, {14692, 41147}, {14711, 48673}, {14830, 41151}, {14831, 44863}, {15300, 38733}, {15533, 43150}, {15655, 39601}, {15851, 18487}, {16194, 58470}, {16226, 46849}, {16267, 42934}, {16268, 42935}, {16962, 42509}, {16963, 42508}, {16964, 49903}, {16965, 49904}, {16966, 42795}, {16967, 42796}, {17503, 60192}, {18357, 51072}, {18358, 50990}, {18435, 21849}, {18480, 51093}, {18481, 51109}, {18493, 51103}, {18525, 51071}, {19130, 51185}, {19924, 51186}, {19925, 34718}, {20112, 44678}, {21358, 48895}, {21850, 50992}, {22484, 22596}, {22485, 22625}, {22793, 38066}, {22794, 36368}, {22795, 36366}, {22796, 35752}, {22797, 36330}, {25561, 33878}, {25565, 48905}, {28208, 51110}, {29181, 51133}, {31487, 41952}, {31670, 50991}, {31673, 51108}, {32532, 54521}, {33636, 36412}, {34483, 61137}, {34632, 61259}, {36967, 43369}, {36968, 43368}, {36969, 42689}, {36970, 42688}, {37624, 38021}, {37640, 42419}, {37641, 42420}, {38034, 50864}, {38072, 48889}, {38074, 40273}, {38136, 51023}, {38138, 50872}, {38140, 50865}, {39590, 43136}, {41100, 42094}, {41101, 42093}, {41107, 42690}, {41108, 42691}, {41112, 42103}, {41113, 42106}, {42095, 43545}, {42096, 42955}, {42097, 42954}, {42098, 43544}, {42099, 42476}, {42100, 42477}, {42104, 42687}, {42105, 42686}, {42111, 42685}, {42114, 42684}, {42115, 43475}, {42116, 43476}, {42117, 49862}, {42118, 49861}, {42125, 43229}, {42126, 42511}, {42127, 42510}, {42128, 43228}, {42129, 42941}, {42130, 42791}, {42131, 42792}, {42132, 42940}, {42133, 49813}, {42134, 49812}, {42135, 42478}, {42138, 42479}, {42139, 49875}, {42142, 49876}, {42153, 42533}, {42154, 43227}, {42155, 43226}, {42156, 42532}, {42163, 49810}, {42166, 49811}, {42263, 42525}, {42264, 42524}, {42268, 43343}, {42269, 43342}, {42270, 42418}, {42273, 42417}, {42283, 45384}, {42284, 45385}, {42474, 42529}, {42475, 42528}, {42502, 42988}, {42503, 42989}, {42514, 43003}, {42515, 43002}, {42588, 42913}, {42589, 42912}, {42815, 43417}, {42816, 43416}, {42914, 43399}, {42915, 43400}, {42920, 49859}, {42921, 49860}, {42932, 54578}, {42933, 54579}, {42964, 42976}, {42965, 42977}, {42968, 49873}, {42969, 49874}, {43030, 43032}, {43031, 43033}, {43336, 53518}, {43337, 53519}, {43501, 54581}, {43502, 54580}, {44422, 48663}, {45103, 60175}, {47865, 48655}, {47866, 48656}, {49941, 49942}, {50797, 50830}, {50802, 51107}, {50805, 59387}, {50808, 61263}, {50823, 54448}, {50954, 50985}, {50955, 51188}, {50956, 50982}, {50960, 54173}, {50989, 54131}, {51024, 55593}, {51069, 61261}, {51076, 51705}, {51131, 51737}, {51172, 51182}, {54477, 60239}, {54520, 60637}, {54612, 60650}, {54647, 60333}, {54707, 60625}, {54734, 60630}, {54813, 60278}, {54852, 60283}, {54866, 60281}, {58228, 61268}, {60127, 60632}, {60295, 60302}, {60296, 60301}, {60299, 60308}, {60300, 60307}, {60884, 60963}, {60901, 60971}

X(61974) = midpoint of X(i) and X(j) for these {i,j}: {3528, 3543}, {3830, 15701}
X(61974) = reflection of X(i) in X(j) for these {i,j}: {15700, 3090}, {15702, 5}, {15703, 3851}, {3, 15703}, {376, 14869}, {381, 3832}, {3534, 15698}, {3851, 381}
X(61974) = inverse of X(33699) in orthocentroidal circle
X(61974) = inverse of X(33699) in Yff hyperbola
X(61974) = complement of X(62115)
X(61974) = anticomplement of X(19711)
X(61974) = pole of line {523, 33699} with respect to the orthocentroidal circle
X(61974) = pole of line {6, 33699} with respect to the Kiepert hyperbola
X(61974) = pole of line {523, 33699} with respect to the Yff hyperbola
X(61974) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(264), X(33699)}}, {{A, B, C, X(265), X(15702)}}, {{A, B, C, X(382), X(54924)}}, {{A, B, C, X(468), X(54643)}}, {{A, B, C, X(550), X(54585)}}, {{A, B, C, X(3531), X(47485)}}, {{A, B, C, X(3851), X(54512)}}, {{A, B, C, X(5067), X(21400)}}, {{A, B, C, X(5094), X(54608)}}, {{A, B, C, X(10299), X(54838)}}, {{A, B, C, X(10301), X(54582)}}, {{A, B, C, X(11001), X(18550)}}, {{A, B, C, X(13623), X(19708)}}, {{A, B, C, X(14860), X(49136)}}, {{A, B, C, X(15720), X(60121)}}, {{A, B, C, X(18317), X(50693)}}, {{A, B, C, X(23040), X(44763)}}, {{A, B, C, X(34483), X(61138)}}, {{A, B, C, X(34484), X(61137)}}, {{A, B, C, X(35018), X(60122)}}, {{A, B, C, X(44580), X(57822)}}, {{A, B, C, X(52289), X(60228)}}, {{A, B, C, X(52292), X(60192)}}, {{A, B, C, X(52293), X(60175)}}, {{A, B, C, X(53857), X(54521)}}
X(61974) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11001, 15711}, {2, 15682, 15690}, {2, 15695, 15722}, {2, 3830, 15685}, {2, 3860, 381}, {4, 15709, 3543}, {4, 15717, 3627}, {4, 3091, 548}, {4, 3832, 3857}, {4, 3855, 10303}, {4, 3856, 5072}, {5, 30, 15702}, {30, 14869, 376}, {30, 3090, 15700}, {30, 381, 3851}, {30, 3851, 15703}, {381, 3534, 5066}, {381, 382, 3545}, {381, 3839, 3843}, {381, 3843, 14269}, {381, 3845, 3830}, {381, 5054, 3091}, {382, 15706, 15683}, {547, 1657, 15707}, {1656, 3543, 15689}, {3091, 10299, 5}, {3091, 11001, 10109}, {3146, 15699, 14093}, {3523, 3628, 3526}, {3526, 3534, 15698}, {3528, 3543, 30}, {3534, 15640, 17800}, {3534, 15693, 10304}, {3534, 15706, 8703}, {3534, 3830, 15684}, {3534, 5066, 5055}, {3543, 15709, 15704}, {3545, 14893, 382}, {3545, 15683, 3628}, {3627, 5071, 15688}, {3628, 15683, 15706}, {3628, 15706, 15694}, {3830, 15681, 15682}, {3830, 3843, 3845}, {3845, 3856, 15640}, {3845, 8703, 14893}, {3850, 5076, 5070}, {3851, 12101, 6891}, {3853, 3854, 5079}, {5054, 15687, 5073}, {5055, 15689, 15709}, {5055, 17800, 549}, {5066, 12101, 15759}, {10109, 11001, 5054}, {10109, 15687, 11001}, {10109, 15711, 2}, {10304, 11540, 15693}, {10304, 15683, 17538}, {11540, 15682, 3534}, {12811, 17578, 15720}, {12816, 16809, 49948}, {12817, 16808, 49947}, {14269, 15684, 4}, {14269, 15722, 12101}, {15681, 15699, 6948}, {15682, 15693, 15681}, {15685, 15722, 15695}, {15693, 15702, 15701}, {15695, 15722, 3}, {18586, 18587, 15696}, {43108, 43246, 11488}, {47353, 50963, 5093}

X(61975) = X(2)X(3)∩X(17)X(42126)

Barycentrics    7*a^4-10*(b^2-c^2)^2+3*a^2*(b^2+c^2) : :
X(61975) = -30*X[2]+17*X[3], -3*X[51]+16*X[44871], 4*X[143]+9*X[16261], -3*X[568]+16*X[44863], 10*X[576]+3*X[51027], 7*X[1482]+6*X[61247], -15*X[1699]+2*X[11278], -3*X[2979]+16*X[11017], -3*X[3653]+16*X[51076], -25*X[3763]+12*X[55627], 10*X[3818]+3*X[5102], 3*X[5093]+10*X[51537] and many others

X(61975) lies on these lines: {2, 3}, {17, 42126}, {18, 42127}, {51, 44871}, {61, 42960}, {62, 42961}, {143, 16261}, {397, 42103}, {398, 42106}, {399, 10982}, {568, 44863}, {576, 51027}, {1131, 6500}, {1132, 6501}, {1204, 52055}, {1327, 6428}, {1328, 6427}, {1482, 61247}, {1699, 11278}, {2979, 11017}, {3311, 43796}, {3312, 43795}, {3316, 9691}, {3653, 51076}, {3763, 55627}, {3818, 5102}, {4857, 9654}, {5023, 12815}, {5041, 15484}, {5093, 51537}, {5097, 18440}, {5270, 9669}, {5318, 42963}, {5321, 42962}, {5339, 42128}, {5340, 42125}, {5349, 11485}, {5350, 11486}, {5365, 11542}, {5366, 11543}, {5493, 61261}, {5640, 32137}, {5882, 61279}, {6199, 23263}, {6243, 12002}, {6288, 13432}, {6395, 23253}, {6407, 52666}, {6408, 52667}, {6429, 35821}, {6430, 35820}, {6431, 6564}, {6432, 6565}, {6433, 10576}, {6434, 10577}, {6437, 8976}, {6438, 13951}, {6449, 10195}, {6450, 10194}, {6455, 53519}, {6456, 53518}, {6486, 42263}, {6487, 42264}, {6519, 42602}, {6522, 42603}, {7581, 43890}, {7582, 43889}, {7926, 43676}, {8227, 31662}, {9540, 10137}, {9655, 37587}, {9681, 43887}, {9779, 37624}, {9955, 61274}, {10095, 11439}, {10138, 13935}, {10187, 42433}, {10188, 42434}, {10222, 50871}, {10246, 12571}, {10248, 38042}, {10516, 55587}, {10539, 11935}, {10990, 38725}, {10991, 38735}, {10992, 38746}, {10993, 38758}, {11362, 50799}, {11438, 11999}, {11455, 15026}, {11459, 13421}, {11522, 18525}, {11531, 18492}, {11898, 18553}, {12162, 13321}, {12290, 13364}, {12295, 15046}, {12315, 23324}, {12331, 59390}, {12953, 51817}, {13108, 22682}, {13382, 16194}, {13464, 18526}, {13665, 35771}, {13785, 35770}, {13903, 42273}, {13961, 42270}, {14490, 14861}, {14862, 18376}, {15072, 18874}, {15602, 18584}, {16200, 18480}, {16808, 42988}, {16809, 42989}, {16964, 43021}, {16965, 43020}, {18405, 45185}, {18435, 46852}, {18483, 38155}, {18510, 42268}, {18512, 42269}, {18514, 31479}, {19130, 55711}, {19877, 28182}, {19925, 59503}, {20582, 55620}, {21400, 34567}, {22615, 41963}, {22644, 41964}, {22681, 48673}, {22804, 55038}, {23267, 43377}, {23273, 43376}, {23325, 48672}, {24206, 55607}, {25555, 55703}, {25565, 55684}, {27355, 40280}, {30714, 38792}, {33520, 38770}, {34507, 55722}, {34754, 42093}, {34755, 42094}, {34783, 46847}, {36836, 42890}, {36843, 42891}, {36990, 50664}, {37481, 46849}, {37514, 52100}, {37727, 50806}, {38064, 51131}, {38066, 50803}, {38136, 48662}, {38140, 48661}, {38141, 38756}, {39561, 48889}, {41973, 42156}, {41974, 42153}, {42095, 42431}, {42096, 42936}, {42097, 42937}, {42098, 42432}, {42101, 42152}, {42102, 42149}, {42104, 42945}, {42105, 42944}, {42107, 42151}, {42110, 42150}, {42117, 42494}, {42118, 42495}, {42129, 42158}, {42130, 42919}, {42131, 42918}, {42132, 42157}, {42133, 42775}, {42134, 42776}, {42135, 42998}, {42138, 42999}, {42139, 42924}, {42142, 42925}, {42144, 42472}, {42145, 42473}, {42154, 42892}, {42155, 42893}, {42528, 42611}, {42529, 42610}, {42557, 43338}, {42558, 43339}, {42625, 42958}, {42626, 42959}, {42639, 43883}, {42640, 43884}, {42690, 43774}, {42691, 43773}, {42773, 42915}, {42774, 42914}, {42793, 43101}, {42794, 43104}, {42813, 42975}, {42814, 42974}, {42894, 42905}, {42895, 42904}, {42926, 43644}, {42927, 43649}, {42994, 49948}, {42995, 49947}, {43256, 43414}, {43257, 43413}, {43312, 43882}, {43313, 43881}, {47354, 55724}, {47355, 55683}, {48872, 55640}, {48884, 55688}, {48895, 55603}, {48901, 55591}, {48904, 55636}, {48905, 55685}, {48910, 55612}, {50800, 51120}, {50807, 50868}, {50957, 51166}, {50964, 51025}, {51078, 51119}, {51133, 51165}, {51186, 55597}, {58238, 61245}, {58244, 61256}, {58247, 59400}, {59389, 60922}

X(61975) = midpoint of X(i) and X(j) for these {i,j}: {4, 5068}
X(61975) = reflection of X(i) in X(j) for these {i,j}: {10303, 5}, {3, 5067}
X(61975) = inverse of X(62026) in orthocentroidal circle
X(61975) = inverse of X(62026) in Yff hyperbola
X(61975) = complement of X(62117)
X(61975) = anticomplement of X(61802)
X(61975) = pole of line {523, 62026} with respect to the orthocentroidal circle
X(61975) = pole of line {185, 62016} with respect to the Jerabek hyperbola
X(61975) = pole of line {6, 42888} with respect to the Kiepert hyperbola
X(61975) = pole of line {523, 62026} with respect to the Yff hyperbola
X(61975) = pole of line {69, 55677} with respect to the Wallace hyperbola
X(61975) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(265), X(10303)}}, {{A, B, C, X(3519), X(15717)}}, {{A, B, C, X(3521), X(50693)}}, {{A, B, C, X(3525), X(15749)}}, {{A, B, C, X(3527), X(35479)}}, {{A, B, C, X(3531), X(55578)}}, {{A, B, C, X(3628), X(21400)}}, {{A, B, C, X(5073), X(14860)}}, {{A, B, C, X(6662), X(19710)}}, {{A, B, C, X(10124), X(13599)}}, {{A, B, C, X(10304), X(14861)}}, {{A, B, C, X(14483), X(44879)}}, {{A, B, C, X(14490), X(14865)}}, {{A, B, C, X(14869), X(46168)}}, {{A, B, C, X(15022), X(17505)}}, {{A, B, C, X(15690), X(54585)}}, {{A, B, C, X(15698), X(42021)}}, {{A, B, C, X(15701), X(60121)}}, {{A, B, C, X(15704), X(18550)}}, {{A, B, C, X(18855), X(50691)}}, {{A, B, C, X(21844), X(34567)}}, {{A, B, C, X(35472), X(43908)}}, {{A, B, C, X(35475), X(57715)}}, {{A, B, C, X(55866), X(60171)}}
X(61975) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 11001, 15696}, {3, 3832, 381}, {3, 3843, 3845}, {3, 3851, 5056}, {3, 5055, 16239}, {3, 5070, 15702}, {3, 547, 3526}, {4, 10019, 3517}, {4, 3091, 550}, {4, 3523, 3627}, {4, 3533, 3543}, {4, 3545, 5059}, {4, 3832, 3850}, {4, 3854, 140}, {4, 3855, 3523}, {4, 5, 5073}, {4, 5059, 3853}, {4, 5068, 30}, {4, 5073, 5076}, {5, 12101, 3529}, {5, 14891, 16417}, {5, 15711, 3628}, {5, 30, 10303}, {5, 3146, 15722}, {5, 3529, 15694}, {140, 3854, 3851}, {140, 3858, 3854}, {381, 14893, 15700}, {381, 15688, 5066}, {381, 3526, 3091}, {381, 382, 5072}, {382, 5072, 5054}, {546, 3839, 3843}, {546, 3845, 3832}, {547, 15759, 11539}, {631, 12102, 15684}, {631, 7486, 4205}, {1656, 3534, 15720}, {1657, 15720, 3522}, {1657, 3522, 3534}, {1657, 3851, 1656}, {2050, 5071, 382}, {3090, 15687, 17800}, {3090, 17800, 15693}, {3091, 3524, 5}, {3091, 3861, 3830}, {3146, 5066, 5070}, {3146, 5070, 15688}, {3146, 6885, 15703}, {3522, 10303, 10299}, {3522, 5056, 3533}, {3522, 5073, 1657}, {3524, 3534, 14093}, {3543, 3545, 11812}, {3543, 3845, 14269}, {3627, 16239, 11001}, {3627, 3855, 5055}, {3627, 3860, 3855}, {3628, 17578, 15681}, {3845, 11539, 14893}, {3845, 3850, 4}, {3851, 10299, 5079}, {3857, 14893, 20}, {3859, 15687, 3090}, {5349, 42921, 11485}, {5350, 42920, 11486}, {7486, 12103, 15701}, {11001, 16239, 3}, {14269, 15694, 12101}, {14813, 14814, 15717}, {15685, 17564, 15706}, {18586, 18587, 15689}, {42130, 42919, 42950}, {42131, 42918, 42951}, {42891, 43200, 36843}

X(61976) = X(2)X(3)∩X(6)X(43422)

Barycentrics    8*a^4-11*(b^2-c^2)^2+3*a^2*(b^2+c^2) : :
X(61976) = -33*X[2]+19*X[3], -2*X[40]+9*X[61260], -11*X[141]+4*X[55592], 3*X[146]+4*X[13393], -X[389]+8*X[44871], -5*X[576]+12*X[51130], -8*X[946]+X[61295], -3*X[1483]+10*X[11522], 6*X[1699]+X[37705], 11*X[3818]+3*X[55717], -11*X[5480]+4*X[55715], -2*X[5493]+9*X[38042] and many others

X(61976) lies on these lines: {2, 3}, {6, 43422}, {17, 42101}, {18, 42102}, {40, 61260}, {141, 55592}, {146, 13393}, {371, 41957}, {372, 41958}, {389, 44871}, {397, 42135}, {398, 42138}, {576, 51130}, {946, 61295}, {1483, 11522}, {1503, 42785}, {1587, 43412}, {1588, 43411}, {1699, 37705}, {3070, 6436}, {3071, 6435}, {3519, 14487}, {3818, 55717}, {5318, 43774}, {5321, 43773}, {5339, 42106}, {5340, 42103}, {5343, 42128}, {5344, 42125}, {5349, 16808}, {5350, 16809}, {5355, 34571}, {5480, 55715}, {5493, 38042}, {5734, 50831}, {5876, 46852}, {5882, 38034}, {5907, 12002}, {5946, 46849}, {6053, 10113}, {6102, 44863}, {6241, 58531}, {6417, 43376}, {6418, 43377}, {6437, 43516}, {6438, 43515}, {6494, 31412}, {6495, 42561}, {7745, 14075}, {7755, 53418}, {7780, 20112}, {7987, 61267}, {7989, 28178}, {7991, 38081}, {8550, 38136}, {8960, 42283}, {9624, 50807}, {9955, 61273}, {10095, 16194}, {10194, 42264}, {10195, 42263}, {10222, 51075}, {10575, 18874}, {10592, 18514}, {10593, 18513}, {10625, 11017}, {10991, 38229}, {11381, 13364}, {11485, 42775}, {11486, 42776}, {11694, 15029}, {11698, 59390}, {12006, 32062}, {12111, 13451}, {12433, 51792}, {12571, 34773}, {13421, 45958}, {13431, 20424}, {13464, 61283}, {13474, 15026}, {14449, 15058}, {14861, 46851}, {14862, 41362}, {14864, 23324}, {15305, 16881}, {15873, 44872}, {18383, 44762}, {18480, 61245}, {18481, 61270}, {18492, 38138}, {18525, 61293}, {18553, 21850}, {18555, 31802}, {19106, 43874}, {19107, 43873}, {19116, 42268}, {19117, 42269}, {19130, 55709}, {19925, 38176}, {20190, 51022}, {20418, 38141}, {22235, 42962}, {22237, 42963}, {22251, 36518}, {22791, 47745}, {22793, 38112}, {24206, 55609}, {25555, 55702}, {28190, 61268}, {28202, 51078}, {29181, 55605}, {31162, 61255}, {31406, 43457}, {32137, 45956}, {34507, 55723}, {34598, 35721}, {35770, 43341}, {35771, 43340}, {37714, 50823}, {38022, 51074}, {38079, 51129}, {38140, 43174}, {39884, 55714}, {41869, 61262}, {41963, 42225}, {41964, 42226}, {42093, 42921}, {42094, 42920}, {42095, 43631}, {42098, 43630}, {42099, 42949}, {42100, 42948}, {42104, 43238}, {42105, 43239}, {42107, 42158}, {42110, 42157}, {42112, 42773}, {42113, 42774}, {42117, 43227}, {42118, 43226}, {42121, 42431}, {42124, 42432}, {42126, 42916}, {42127, 42917}, {42129, 42889}, {42132, 42888}, {42133, 42988}, {42134, 42989}, {42136, 42152}, {42137, 42149}, {42143, 42151}, {42144, 42919}, {42145, 42918}, {42146, 42150}, {42159, 43416}, {42162, 43417}, {42163, 42634}, {42166, 42633}, {42284, 58866}, {42488, 42794}, {42489, 42793}, {42686, 43241}, {42687, 43240}, {42777, 42934}, {42778, 42935}, {42779, 44016}, {42780, 44015}, {42797, 43366}, {42798, 43367}, {42815, 43365}, {42816, 43364}, {42936, 43643}, {42937, 43638}, {42940, 43639}, {42941, 43640}, {42942, 42979}, {42943, 42978}, {42998, 43771}, {42999, 43772}, {43012, 43020}, {43013, 43021}, {43016, 43030}, {43017, 43031}, {43101, 43633}, {43104, 43632}, {48874, 55613}, {48876, 55586}, {48895, 55599}, {48901, 55589}, {48906, 55707}, {48942, 51126}, {50804, 61249}, {50956, 53097}, {50981, 55626}, {51143, 55600}, {51163, 55619}

X(61976) = midpoint of X(i) and X(j) for these {i,j}: {4, 3851}, {3830, 15702}
X(61976) = reflection of X(i) in X(j) for these {i,j}: {14869, 5}, {15698, 547}, {15703, 5066}, {3832, 546}, {3857, 3832}, {5, 3857}, {550, 3523}
X(61976) = inverse of X(62023) in orthocentroidal circle
X(61976) = inverse of X(62023) in Yff hyperbola
X(61976) = complement of X(62121)
X(61976) = anticomplement of X(61801)
X(61976) = pole of line {523, 62023} with respect to the orthocentroidal circle
X(61976) = pole of line {185, 62013} with respect to the Jerabek hyperbola
X(61976) = pole of line {6, 48942} with respect to the Kiepert hyperbola
X(61976) = pole of line {523, 62023} with respect to the Yff hyperbola
X(61976) = pole of line {69, 55675} with respect to the Wallace hyperbola
X(61976) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(265), X(14869)}}, {{A, B, C, X(548), X(15319)}}, {{A, B, C, X(3518), X(14487)}}, {{A, B, C, X(3519), X(12100)}}, {{A, B, C, X(3521), X(44245)}}, {{A, B, C, X(6662), X(15681)}}, {{A, B, C, X(11812), X(60121)}}, {{A, B, C, X(12812), X(17505)}}, {{A, B, C, X(14861), X(46853)}}, {{A, B, C, X(14865), X(46851)}}, {{A, B, C, X(15695), X(54585)}}, {{A, B, C, X(18855), X(50690)}}, {{A, B, C, X(21400), X(55857)}}, {{A, B, C, X(55862), X(60171)}}
X(61976) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 10299, 17578}, {4, 3091, 1657}, {4, 3522, 3830}, {4, 381, 140}, {4, 3832, 3851}, {4, 3855, 3522}, {4, 5056, 382}, {4, 5068, 5073}, {4, 546, 3858}, {5, 15687, 15704}, {5, 15704, 11539}, {5, 30, 14869}, {20, 12101, 3627}, {20, 12811, 15699}, {20, 3090, 15701}, {20, 381, 12811}, {30, 3832, 3857}, {30, 5066, 15703}, {30, 546, 3832}, {30, 547, 15698}, {140, 3850, 5068}, {140, 3861, 4}, {140, 5073, 550}, {140, 8703, 15712}, {381, 14269, 15682}, {381, 15685, 3545}, {381, 3524, 5066}, {381, 5068, 3850}, {381, 5070, 3091}, {382, 5066, 632}, {382, 632, 15686}, {546, 14893, 3856}, {546, 3843, 3845}, {546, 3853, 3860}, {549, 3845, 14269}, {3090, 15682, 3528}, {3090, 3832, 381}, {3091, 14269, 3853}, {3091, 15682, 5070}, {3091, 5070, 14892}, {3523, 5068, 3090}, {3528, 3533, 3523}, {3543, 5072, 3530}, {3545, 5076, 548}, {3627, 3845, 3861}, {3830, 15702, 30}, {3830, 3855, 3628}, {3839, 3843, 546}, {3850, 3853, 3533}, {3856, 14893, 3}, {3859, 12102, 2}, {3861, 12811, 12101}, {5055, 17578, 12103}, {5071, 17800, 12108}, {5318, 43774, 43775}, {10095, 16194, 45957}, {12101, 12811, 20}, {12811, 15699, 5}, {14813, 14814, 12100}, {14892, 15682, 549}, {15022, 15696, 10124}, {15685, 15713, 8703}, {18492, 40273, 38138}, {42094, 42920, 42924}, {43422, 43423, 6}

X(61977) = X(2)X(3)∩X(6)X(43032)

Barycentrics    19*a^4-26*(b^2-c^2)^2+7*a^2*(b^2+c^2) : :
X(61977) = -26*X[2]+15*X[3], -15*X[946]+4*X[51095], -12*X[1699]+X[50805], -4*X[4677]+15*X[50797], -4*X[4745]+15*X[50799], -3*X[5050]+14*X[50964], -4*X[8584]+15*X[50963], -3*X[10246]+14*X[50807], 2*X[11055]+9*X[48663], 5*X[12699]+6*X[38098], 3*X[13321]+8*X[46847], 3*X[14848]+8*X[48889] and many others

X(61977) lies on these lines: {2, 3}, {6, 43032}, {371, 42642}, {372, 42641}, {598, 54934}, {946, 51095}, {1327, 18510}, {1328, 18512}, {1699, 50805}, {3311, 12819}, {3312, 12818}, {4677, 50797}, {4745, 50799}, {5050, 50964}, {6200, 42577}, {6221, 43504}, {6396, 42576}, {6398, 43503}, {6441, 6564}, {6442, 6565}, {6474, 60311}, {6475, 60312}, {6476, 42526}, {6477, 42527}, {6478, 42265}, {6479, 42262}, {8584, 50963}, {9690, 43313}, {10246, 50807}, {10653, 42503}, {10654, 42502}, {11055, 48663}, {11480, 43548}, {11481, 43549}, {11485, 49860}, {11486, 49859}, {12699, 38098}, {12816, 42507}, {12817, 42506}, {12820, 41100}, {12821, 41101}, {13321, 46847}, {13903, 43563}, {13961, 43562}, {14488, 60216}, {14492, 60626}, {14848, 48889}, {15484, 39593}, {15533, 50954}, {16808, 42532}, {16809, 42533}, {17502, 50866}, {17503, 54920}, {17508, 51167}, {18439, 44871}, {18480, 34747}, {18483, 34641}, {18553, 51188}, {19053, 43317}, {19054, 43316}, {19106, 43368}, {19107, 43369}, {20583, 39899}, {22793, 51066}, {26446, 51078}, {32787, 42608}, {32788, 42609}, {33698, 54645}, {34682, 53109}, {34754, 42518}, {34755, 42519}, {36967, 42950}, {36968, 42951}, {36969, 42508}, {36970, 42509}, {37832, 43476}, {37835, 43475}, {41107, 42125}, {41108, 42128}, {41119, 42962}, {41120, 42963}, {41121, 42093}, {41122, 42094}, {41147, 52090}, {42095, 46334}, {42096, 43367}, {42097, 43366}, {42098, 46335}, {42101, 42511}, {42102, 42510}, {42103, 43229}, {42104, 42791}, {42105, 42792}, {42106, 43228}, {42126, 49905}, {42127, 49906}, {42135, 43111}, {42136, 43246}, {42137, 43247}, {42138, 43110}, {42153, 42636}, {42154, 43196}, {42155, 43195}, {42156, 42635}, {42157, 54479}, {42158, 54480}, {42270, 43515}, {42273, 43516}, {42586, 42937}, {42587, 42936}, {42629, 49908}, {42630, 49907}, {42779, 42972}, {42780, 42973}, {42799, 49947}, {42800, 49948}, {42918, 43330}, {42919, 43331}, {42922, 43208}, {42923, 43207}, {42974, 43251}, {42975, 43250}, {43028, 43399}, {43029, 43400}, {43312, 43415}, {43328, 49827}, {43329, 49826}, {43416, 49824}, {43417, 49825}, {43547, 61719}, {43554, 43639}, {43555, 43640}, {45103, 60335}, {47353, 51173}, {48901, 50993}, {50800, 59503}, {50806, 51071}, {50815, 61266}, {50956, 50991}, {50962, 53023}, {50994, 55584}, {51067, 61258}, {51074, 51108}, {51084, 61265}, {51120, 61257}, {51122, 53143}, {53105, 54734}, {54494, 54644}, {54522, 54720}, {54582, 60210}, {54717, 60277}, {60132, 60283}

X(61977) = reflection of X(i) in X(j) for these {i,j}: {15718, 5056}, {15721, 5}, {15723, 5072}, {3534, 15716}, {5072, 381}
X(61977) = inverse of X(62022) in orthocentroidal circle
X(61977) = inverse of X(62022) in Yff hyperbola
X(61977) = anticomplement of X(61800)
X(61977) = pole of line {523, 62022} with respect to the orthocentroidal circle
X(61977) = pole of line {6, 62022} with respect to the Kiepert hyperbola
X(61977) = pole of line {523, 62022} with respect to the Yff hyperbola
X(61977) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(265), X(15721)}}, {{A, B, C, X(548), X(54585)}}, {{A, B, C, X(3534), X(57897)}}, {{A, B, C, X(5072), X(54512)}}, {{A, B, C, X(5094), X(54934)}}, {{A, B, C, X(15684), X(54924)}}, {{A, B, C, X(18550), X(19710)}}, {{A, B, C, X(21400), X(48154)}}, {{A, B, C, X(37453), X(54734)}}, {{A, B, C, X(52289), X(60626)}}, {{A, B, C, X(52292), X(54920)}}, {{A, B, C, X(52293), X(60335)}}
X(61977) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10299, 15713}, {2, 15682, 550}, {2, 3534, 15700}, {2, 3544, 10109}, {2, 3845, 14269}, {3, 3830, 15640}, {4, 3832, 12811}, {4, 3859, 3}, {5, 30, 15721}, {30, 381, 5072}, {30, 5056, 15718}, {30, 5072, 15723}, {381, 15688, 3851}, {381, 15693, 5066}, {381, 1657, 3545}, {382, 5054, 15681}, {546, 550, 3832}, {1657, 14890, 14093}, {2049, 15715, 5054}, {3529, 17564, 17504}, {3530, 15681, 15688}, {3530, 3851, 5079}, {3534, 15723, 15716}, {3543, 10109, 15695}, {3830, 5066, 15693}, {3832, 5055, 381}, {3851, 14269, 15687}, {3859, 12101, 11540}, {3860, 11540, 3859}, {5054, 15716, 15719}, {5055, 14893, 5076}, {5071, 5073, 15706}, {5079, 15720, 5070}, {8703, 11812, 15692}, {10109, 15695, 3526}, {10109, 17504, 2}, {11540, 13633, 3534}, {12101, 15640, 3830}, {12811, 15692, 5055}, {14269, 15681, 4}, {15681, 15710, 15696}, {15687, 15688, 382}, {15688, 15720, 15715}, {15707, 15721, 15720}, {43032, 43033, 6}

X(61978) = X(2)X(3)∩X(17)X(43108)

Barycentrics    14*a^4-19*(b^2-c^2)^2+5*a^2*(b^2+c^2) : :
X(61978) = -19*X[2]+11*X[3], -X[182]+5*X[51129], -5*X[355]+X[50830], -5*X[946]+X[51087], X[962]+7*X[50800], -5*X[1351]+X[51182], -5*X[1352]+X[50985], -X[1353]+5*X[50963], -X[1385]+5*X[51074], -X[1483]+5*X[50806], 7*X[1699]+X[61247], -7*X[3655]+15*X[61274] and many others

X(61978) lies on these lines: {2, 3}, {17, 43108}, {18, 43109}, {182, 51129}, {355, 50830}, {395, 42971}, {396, 42970}, {946, 51087}, {962, 50800}, {1327, 43343}, {1328, 43342}, {1351, 51182}, {1352, 50985}, {1353, 50963}, {1385, 51074}, {1483, 50806}, {1699, 61247}, {3070, 43381}, {3071, 43380}, {3655, 61274}, {3828, 28178}, {4701, 18483}, {5349, 16267}, {5350, 16268}, {5480, 51140}, {5663, 13570}, {5690, 50799}, {5691, 50807}, {5921, 51173}, {6459, 42639}, {6460, 42640}, {6492, 8981}, {6493, 13966}, {8252, 43336}, {8253, 43337}, {10095, 44871}, {10113, 56567}, {11645, 51138}, {11694, 12295}, {12007, 48889}, {12571, 28208}, {12820, 34755}, {12821, 34754}, {13451, 14831}, {13607, 50802}, {14692, 61600}, {14810, 51026}, {14927, 50987}, {16808, 42496}, {16809, 42497}, {16881, 44863}, {19106, 43484}, {19107, 43483}, {19924, 50960}, {19925, 50827}, {20070, 50822}, {21849, 45959}, {21969, 31834}, {22791, 61250}, {22806, 22820}, {22807, 22819}, {28168, 61267}, {28198, 50803}, {28216, 38140}, {28224, 34648}, {30308, 34773}, {31162, 61254}, {31663, 50869}, {32137, 58531}, {33416, 43642}, {33417, 43641}, {33606, 42163}, {33607, 42166}, {34631, 61251}, {34638, 61614}, {36990, 50964}, {37640, 42691}, {37641, 42690}, {38034, 61279}, {38076, 61524}, {38077, 61566}, {40273, 50796}, {41107, 42695}, {41108, 42694}, {41121, 42925}, {41122, 42924}, {41943, 42146}, {41944, 42143}, {41951, 41956}, {41952, 41955}, {42101, 42912}, {42102, 42913}, {42107, 42889}, {42110, 42888}, {42122, 43649}, {42123, 43644}, {42133, 42633}, {42134, 42634}, {42144, 42911}, {42145, 42910}, {42149, 43247}, {42152, 43246}, {42164, 49907}, {42165, 49908}, {42225, 42602}, {42226, 42603}, {42262, 43503}, {42265, 43504}, {42268, 43341}, {42269, 43340}, {42270, 52048}, {42273, 52047}, {42520, 43773}, {42521, 43774}, {42580, 42792}, {42581, 42791}, {42684, 43104}, {42685, 43101}, {42686, 42918}, {42687, 42919}, {42775, 49876}, {42776, 49875}, {42795, 43204}, {42796, 43203}, {42799, 43000}, {42800, 43001}, {42815, 43541}, {42816, 43540}, {42916, 43482}, {42917, 43481}, {42926, 54579}, {42927, 54578}, {42942, 43544}, {42943, 43545}, {43100, 43633}, {43107, 43632}, {43201, 49873}, {43202, 49874}, {43417, 61719}, {43622, 43627}, {43623, 43626}, {46849, 58470}, {48872, 50980}, {48876, 50956}, {48942, 50971}, {50826, 50873}, {50833, 50866}, {50957, 51212}, {50981, 51029}, {50988, 51167}, {51077, 61246}, {51078, 51118}, {51133, 51163}, {51142, 55583}, {51181, 51216}, {51184, 61044}, {51537, 61624}, {54917, 60239}

X(61978) = midpoint of X(i) and X(j) for these {i,j}: {2, 3853}, {4, 5066}, {5, 12101}, {140, 3830}, {381, 14893}, {382, 15690}, {546, 3845}, {547, 15687}, {3627, 12100}, {3860, 3861}, {10109, 12102}, {11694, 12295}, {12103, 15682}, {14810, 51026}, {21849, 45959}, {21969, 31834}, {31663, 50869}, {40273, 50796}, {46849, 58470}, {48889, 50959}, {48942, 50971}, {51077, 61246}
X(61978) = reflection of X(i) in X(j) for these {i,j}: {10109, 3850}, {10124, 11737}, {11737, 381}, {11812, 5}, {14891, 547}, {15690, 12108}, {15759, 3628}, {2, 12811}, {3530, 10109}, {3628, 5066}, {3850, 3860}, {3860, 546}, {3861, 3845}, {548, 11540}, {5066, 3856}, {61259, 50803}, {8703, 16239}
X(61978) = inverse of X(62020) in orthocentroidal circle
X(61978) = inverse of X(62020) in Yff hyperbola
X(61978) = complement of X(15691)
X(61978) = pole of line {523, 62020} with respect to the orthocentroidal circle
X(61978) = pole of line {6, 62020} with respect to the Kiepert hyperbola
X(61978) = pole of line {523, 62020} with respect to the Yff hyperbola
X(61978) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(265), X(11812)}}, {{A, B, C, X(1494), X(33923)}}, {{A, B, C, X(11737), X(54512)}}, {{A, B, C, X(13623), X(45759)}}, {{A, B, C, X(14869), X(60121)}}, {{A, B, C, X(15688), X(54585)}}
X(61978) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 10304, 3830}, {4, 15022, 382}, {4, 15684, 15687}, {4, 15704, 3853}, {4, 3091, 17800}, {4, 3526, 3627}, {4, 3545, 15640}, {4, 3832, 5072}, {4, 546, 3856}, {5, 14269, 12101}, {5, 30, 11812}, {5, 3529, 140}, {5, 3627, 3522}, {5, 3845, 14269}, {30, 11540, 548}, {30, 11737, 10124}, {30, 12108, 15690}, {30, 12811, 2}, {30, 3628, 15759}, {30, 381, 11737}, {30, 3845, 3861}, {30, 3856, 5066}, {30, 3860, 3850}, {30, 546, 3860}, {30, 547, 14891}, {140, 546, 3832}, {381, 14093, 3851}, {381, 14269, 3543}, {381, 15681, 3545}, {381, 15691, 12811}, {381, 15703, 3091}, {381, 3830, 5071}, {381, 3845, 14893}, {546, 3853, 3858}, {548, 5055, 11540}, {548, 5066, 5055}, {549, 15687, 15684}, {3091, 15720, 5}, {3534, 14269, 4}, {3534, 5055, 10303}, {3543, 10303, 15683}, {3545, 15640, 3526}, {3545, 3627, 12100}, {3628, 15759, 14890}, {3830, 5071, 15686}, {3830, 5072, 10304}, {3832, 14269, 15711}, {3832, 5071, 381}, {3839, 3843, 3845}, {3839, 3845, 546}, {3851, 15682, 11539}, {5073, 15696, 3529}, {10109, 12102, 30}, {10109, 14890, 3628}, {10124, 11737, 10109}, {10124, 14893, 12102}, {10124, 15759, 549}, {11539, 15682, 12103}, {11737, 14891, 547}, {14890, 15759, 3530}, {15684, 15694, 3534}, {15686, 15696, 15691}, {15690, 15699, 12108}, {15709, 17800, 8703}, {18586, 18587, 17538}, {28198, 50803, 61259}

X(61979) = X(2)X(3)∩X(6)X(33602)

Barycentrics    23*a^4-31*(b^2-c^2)^2+8*a^2*(b^2+c^2) : :
X(61979) = -31*X[2]+18*X[3], -18*X[946]+5*X[51097], -15*X[1699]+2*X[51077], -3*X[3576]+16*X[51076], -2*X[4669]+15*X[18492], X[4677]+12*X[18483], -3*X[5085]+16*X[51131], -3*X[5657]+16*X[50803], -3*X[6361]+16*X[51069], -3*X[7967]+16*X[50802], -18*X[7988]+5*X[50819], 3*X[9812]+10*X[50799] and many others

X(61979) lies on these lines: {2, 3}, {6, 33602}, {598, 54612}, {671, 54707}, {946, 51097}, {1327, 43792}, {1328, 43791}, {1699, 51077}, {3576, 51076}, {4669, 18492}, {4677, 18483}, {5085, 51131}, {5318, 49873}, {5321, 49874}, {5349, 42502}, {5350, 42503}, {5478, 36344}, {5479, 36319}, {5657, 50803}, {6361, 51069}, {7967, 50802}, {7988, 50819}, {9812, 50799}, {10155, 54478}, {10519, 50960}, {10595, 34648}, {12699, 51068}, {12816, 33605}, {12817, 33604}, {13846, 41950}, {13847, 41949}, {14226, 23249}, {14241, 23259}, {14458, 60284}, {14492, 54637}, {14494, 54647}, {14912, 50959}, {16261, 21849}, {16808, 49813}, {16809, 49812}, {16964, 49860}, {16965, 49859}, {17503, 54523}, {18581, 42588}, {18582, 42589}, {19925, 51067}, {22794, 33627}, {22795, 33626}, {22796, 35749}, {22797, 36327}, {23267, 43387}, {23273, 43386}, {31670, 50994}, {31673, 51110}, {32532, 60127}, {32785, 42525}, {32786, 42524}, {32823, 32896}, {33608, 33613}, {33609, 33612}, {34627, 51096}, {34631, 47745}, {36969, 43292}, {36970, 43293}, {38021, 51106}, {38253, 54924}, {40693, 43202}, {40694, 43201}, {41100, 42139}, {41101, 42142}, {41107, 42103}, {41108, 42106}, {41112, 43771}, {41113, 43772}, {41121, 43227}, {41122, 43226}, {41149, 47353}, {42085, 43476}, {42086, 43475}, {42093, 43542}, {42094, 43543}, {42101, 43482}, {42102, 43481}, {42111, 42631}, {42114, 42632}, {42119, 43554}, {42120, 43555}, {42133, 49947}, {42134, 49948}, {42135, 43540}, {42138, 43541}, {42160, 42976}, {42161, 42977}, {42215, 43567}, {42216, 43566}, {42727, 54635}, {42728, 54634}, {42785, 59373}, {42791, 43463}, {42792, 43464}, {42920, 49904}, {42921, 49903}, {42932, 42950}, {42933, 42951}, {42974, 43365}, {42975, 43364}, {43016, 61719}, {43101, 52080}, {43104, 52079}, {43246, 43478}, {43247, 43477}, {43368, 46334}, {43369, 46335}, {43507, 52048}, {43508, 52047}, {43536, 43563}, {43562, 54597}, {45103, 60185}, {47354, 50989}, {50804, 59387}, {50868, 61275}, {50869, 54447}, {50956, 51538}, {50957, 54174}, {50958, 54132}, {51075, 51091}, {51132, 51187}, {51213, 55610}, {54477, 54616}, {54520, 60627}, {54531, 54667}, {54582, 60143}, {54585, 54710}, {54643, 60631}, {54759, 54947}, {54761, 54827}, {54797, 54942}, {54813, 60183}, {54838, 54867}, {60150, 60281}

X(61979) = reflection of X(i) in X(j) for these {i,j}: {376, 10303}, {5068, 381}
X(61979) = inverse of X(62019) in orthocentroidal circle
X(61979) = inverse of X(62019) in Yff hyperbola
X(61979) = anticomplement of X(61797)
X(61979) = pole of line {523, 62019} with respect to the orthocentroidal circle
X(61979) = pole of line {6, 43521} with respect to the Kiepert hyperbola
X(61979) = pole of line {523, 62019} with respect to the Yff hyperbola
X(61979) = pole of line {69, 15716} with respect to the Wallace hyperbola
X(61979) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(15716)}}, {{A, B, C, X(468), X(54707)}}, {{A, B, C, X(3146), X(54924)}}, {{A, B, C, X(3522), X(54585)}}, {{A, B, C, X(3523), X(54838)}}, {{A, B, C, X(5056), X(54667)}}, {{A, B, C, X(5068), X(54512)}}, {{A, B, C, X(5094), X(54612)}}, {{A, B, C, X(7408), X(54813)}}, {{A, B, C, X(19710), X(36889)}}, {{A, B, C, X(37460), X(54809)}}, {{A, B, C, X(46935), X(54660)}}, {{A, B, C, X(52289), X(54637)}}, {{A, B, C, X(52292), X(54523)}}, {{A, B, C, X(52293), X(60185)}}, {{A, B, C, X(52301), X(54582)}}, {{A, B, C, X(53857), X(60127)}}
X(61979) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12101, 15682}, {2, 15640, 15695}, {2, 15695, 15719}, {2, 15722, 15709}, {2, 15759, 631}, {2, 20, 15716}, {4, 381, 3524}, {4, 3832, 3544}, {4, 3855, 17538}, {20, 381, 3545}, {30, 10303, 376}, {30, 381, 5068}, {140, 3627, 17800}, {376, 3545, 1656}, {381, 14269, 3627}, {381, 15689, 12811}, {381, 15699, 3091}, {381, 15701, 5066}, {381, 3830, 10109}, {381, 5073, 14892}, {546, 15690, 3860}, {546, 1656, 3832}, {546, 3845, 3830}, {3090, 15682, 8703}, {3090, 3861, 4}, {3146, 3529, 6942}, {3146, 6974, 15720}, {3524, 15682, 11001}, {3525, 3545, 5071}, {3543, 15022, 15688}, {3627, 5066, 15701}, {3832, 17800, 3855}, {3845, 5066, 14269}, {3845, 8703, 3861}, {4200, 5070, 6852}, {5056, 15684, 15710}, {5073, 14892, 15721}, {10109, 15716, 2}, {11001, 15682, 11541}, {12811, 15687, 15689}, {14892, 15721, 3090}, {15022, 17538, 3525}, {15685, 15690, 20}, {15685, 15716, 15690}, {15699, 15714, 140}, {33602, 33603, 6}

X(61980) = X(2)X(3)∩X(40)X(50803)

Barycentrics    13*a^4-17*(b^2-c^2)^2+4*a^2*(b^2+c^2) : :
X(61980) = -17*X[2]+10*X[3], -X[40]+8*X[50803], -X[944]+8*X[50802], -8*X[946]+X[50818], -X[1350]+8*X[50960], -8*X[1352]+X[51179], -17*X[1699]+3*X[16191], -4*X[3626]+25*X[18492], 2*X[3629]+5*X[47353], X[3632]+20*X[18483], -8*X[3636]+15*X[38021], -2*X[3655]+9*X[9779] and many others

X(61980) lies on these lines: {2, 3}, {40, 50803}, {262, 54720}, {397, 49824}, {398, 49825}, {598, 54845}, {671, 52519}, {944, 50802}, {946, 50818}, {1131, 43386}, {1132, 43387}, {1327, 7581}, {1328, 7582}, {1350, 50960}, {1352, 51179}, {1699, 16191}, {3070, 51849}, {3071, 51850}, {3163, 40065}, {3316, 22615}, {3317, 22644}, {3626, 18492}, {3629, 47353}, {3632, 18483}, {3636, 38021}, {3655, 9779}, {3818, 11008}, {4297, 51076}, {5032, 39884}, {5318, 42782}, {5321, 42781}, {5343, 43228}, {5344, 43229}, {5349, 49947}, {5350, 49948}, {5365, 49874}, {5366, 49873}, {5475, 14482}, {5476, 39874}, {5480, 50974}, {5485, 14488}, {5603, 34648}, {5818, 50865}, {5890, 13570}, {6241, 58470}, {6329, 38072}, {6417, 43561}, {6418, 43560}, {6419, 43570}, {6420, 43571}, {6455, 34089}, {6456, 34091}, {6459, 43516}, {6460, 43515}, {6560, 42574}, {6561, 42575}, {6776, 50959}, {7612, 54494}, {7989, 51078}, {8227, 50862}, {8596, 38743}, {9166, 35021}, {9770, 53143}, {9780, 28202}, {10194, 42524}, {10195, 42525}, {10248, 28198}, {10595, 50864}, {10653, 42987}, {10654, 42986}, {10711, 59390}, {10728, 38077}, {11178, 51538}, {11180, 53023}, {11439, 44863}, {11488, 42630}, {11489, 42629}, {11645, 50964}, {11693, 15029}, {12245, 50796}, {12290, 16226}, {12571, 50811}, {12816, 40694}, {12817, 40693}, {12818, 14226}, {12819, 14241}, {12820, 16809}, {12821, 16808}, {13886, 41952}, {13903, 43520}, {13939, 41951}, {13961, 43519}, {14458, 18843}, {14484, 60631}, {14492, 60219}, {14494, 33698}, {14831, 46847}, {14853, 20583}, {15058, 21969}, {16192, 50874}, {16241, 42472}, {16242, 42473}, {16960, 43778}, {16961, 43777}, {16962, 42494}, {16963, 42495}, {16964, 42635}, {16965, 42636}, {17503, 60330}, {18358, 54174}, {18480, 20050}, {18482, 60957}, {18538, 43508}, {18553, 50992}, {18581, 43195}, {18582, 43196}, {18762, 43507}, {18840, 54717}, {18842, 60132}, {18844, 54934}, {19053, 23269}, {19054, 23275}, {19875, 50809}, {19876, 28150}, {19883, 50819}, {19925, 38098}, {20054, 22791}, {20057, 28204}, {20423, 51537}, {21356, 48901}, {21358, 50966}, {22505, 41135}, {22793, 50799}, {23234, 35022}, {23253, 32788}, {23263, 32787}, {23267, 35823}, {23273, 35822}, {25055, 51074}, {25406, 46267}, {25561, 54170}, {28208, 50807}, {30308, 31673}, {31162, 34641}, {31423, 50813}, {32062, 61136}, {32532, 60142}, {32823, 48913}, {33602, 41113}, {33603, 41112}, {34631, 59387}, {34638, 54447}, {34718, 54448}, {36889, 42853}, {36967, 43463}, {36968, 43464}, {36969, 42139}, {36970, 42142}, {37640, 42106}, {37641, 42103}, {37832, 42140}, {37835, 42141}, {38073, 60980}, {38076, 41869}, {40273, 50872}, {40330, 51024}, {40341, 54132}, {41100, 42920}, {41101, 42921}, {41107, 43201}, {41108, 43202}, {41121, 42160}, {41122, 42161}, {41943, 42119}, {41944, 42120}, {42089, 43638}, {42090, 43400}, {42091, 43399}, {42092, 43643}, {42093, 43403}, {42094, 43404}, {42111, 43366}, {42114, 43367}, {42129, 43494}, {42132, 43493}, {42136, 43478}, {42137, 43477}, {42143, 43555}, {42146, 43554}, {42153, 49875}, {42156, 49876}, {42157, 43476}, {42158, 43475}, {42159, 42973}, {42162, 42972}, {42262, 43256}, {42265, 43257}, {42415, 42817}, {42416, 42818}, {42510, 42938}, {42511, 42939}, {42602, 43509}, {42603, 43510}, {42633, 42962}, {42634, 42963}, {42643, 45384}, {42644, 45385}, {42645, 42726}, {42646, 42725}, {42904, 43033}, {42905, 43032}, {42918, 52080}, {42919, 52079}, {42946, 43446}, {42947, 43447}, {42974, 43110}, {42975, 43111}, {43364, 43416}, {43365, 43417}, {43419, 61719}, {43566, 60621}, {43567, 60620}, {44882, 51131}, {45103, 60337}, {47352, 51129}, {48310, 50975}, {48873, 51029}, {48889, 51023}, {51068, 61258}, {51075, 61296}, {51164, 55651}, {51176, 59373}, {51211, 55584}, {53100, 60281}, {53101, 60322}, {53105, 60127}, {53109, 60150}, {54520, 60636}, {54647, 60332}

X(61980) = midpoint of X(i) and X(j) for these {i,j}: {3526, 3830}, {16192, 50874}, {51164, 55651}
X(61980) = reflection of X(i) in X(j) for these {i,j}: {15698, 3090}, {15701, 5}, {2, 3851}, {376, 15702}, {3528, 2}, {5070, 6959}, {50813, 31423}, {51068, 61258}, {7989, 51078}
X(61980) = inverse of X(62017) in orthocentroidal circle
X(61980) = inverse of X(62017) in Yff hyperbola
X(61980) = complement of X(62122)
X(61980) = anticomplement of X(15700)
X(61980) = pole of line {523, 62017} with respect to the orthocentroidal circle
X(61980) = pole of line {6, 42641} with respect to the Kiepert hyperbola
X(61980) = pole of line {523, 62017} with respect to the Yff hyperbola
X(61980) = pole of line {69, 17504} with respect to the Wallace hyperbola
X(61980) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(17504)}}, {{A, B, C, X(265), X(15701)}}, {{A, B, C, X(458), X(54720)}}, {{A, B, C, X(468), X(52519)}}, {{A, B, C, X(549), X(54838)}}, {{A, B, C, X(1494), X(3528)}}, {{A, B, C, X(3524), X(57894)}}, {{A, B, C, X(3526), X(54763)}}, {{A, B, C, X(3627), X(18854)}}, {{A, B, C, X(3628), X(54660)}}, {{A, B, C, X(3830), X(18852)}}, {{A, B, C, X(3853), X(18849)}}, {{A, B, C, X(4232), X(14488)}}, {{A, B, C, X(4846), X(14093)}}, {{A, B, C, X(5055), X(54667)}}, {{A, B, C, X(5094), X(54845)}}, {{A, B, C, X(6995), X(54717)}}, {{A, B, C, X(7486), X(60122)}}, {{A, B, C, X(10124), X(43699)}}, {{A, B, C, X(10303), X(60121)}}, {{A, B, C, X(10304), X(54585)}}, {{A, B, C, X(11331), X(18843)}}, {{A, B, C, X(11812), X(46168)}}, {{A, B, C, X(13623), X(58189)}}, {{A, B, C, X(15640), X(54924)}}, {{A, B, C, X(15681), X(36889)}}, {{A, B, C, X(15710), X(57823)}}, {{A, B, C, X(15740), X(58190)}}, {{A, B, C, X(17578), X(18853)}}, {{A, B, C, X(18296), X(55861)}}, {{A, B, C, X(18847), X(50687)}}, {{A, B, C, X(18851), X(50688)}}, {{A, B, C, X(21400), X(55866)}}, {{A, B, C, X(37174), X(54494)}}, {{A, B, C, X(37453), X(60127)}}, {{A, B, C, X(50693), X(54923)}}, {{A, B, C, X(52284), X(60132)}}, {{A, B, C, X(52288), X(60631)}}, {{A, B, C, X(52289), X(60219)}}, {{A, B, C, X(52292), X(60330)}}, {{A, B, C, X(52293), X(60337)}}, {{A, B, C, X(53857), X(60142)}}, {{A, B, C, X(54595), X(55569)}}, {{A, B, C, X(54596), X(55573)}}
X(61980) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10304, 15720}, {2, 11737, 5071}, {2, 14269, 4}, {2, 15681, 15715}, {2, 15700, 15702}, {2, 15710, 631}, {2, 20, 17504}, {2, 30, 3528}, {2, 3529, 15710}, {2, 3839, 546}, {2, 3855, 3545}, {2, 550, 3524}, {4, 17538, 3853}, {4, 3524, 3830}, {4, 3525, 17578}, {4, 3544, 382}, {4, 3545, 15682}, {4, 3858, 3533}, {4, 5067, 3627}, {5, 11001, 15709}, {5, 30, 15701}, {30, 3090, 15698}, {30, 6959, 5070}, {381, 12101, 15721}, {381, 15681, 11737}, {381, 15684, 5}, {381, 15694, 5066}, {381, 547, 3091}, {382, 3851, 14869}, {546, 15687, 381}, {546, 3530, 3858}, {546, 3845, 14269}, {546, 3851, 3832}, {550, 15759, 15688}, {1657, 10109, 15708}, {3090, 3855, 3851}, {3091, 15683, 547}, {3146, 15721, 15686}, {3523, 3832, 3857}, {3524, 12108, 15719}, {3525, 6848, 30}, {3528, 14869, 10299}, {3528, 3832, 3855}, {3528, 3851, 3090}, {3627, 3854, 5067}, {3628, 15685, 15705}, {3843, 3845, 3839}, {3850, 17578, 3525}, {3851, 15681, 15703}, {3853, 5054, 15640}, {3853, 5068, 17538}, {3854, 17578, 17697}, {3855, 10299, 3544}, {3856, 5076, 5056}, {3858, 12101, 5055}, {3859, 5073, 15022}, {5055, 12101, 3146}, {5066, 10109, 6944}, {5066, 17504, 5079}, {5068, 15640, 5054}, {5073, 11539, 15697}, {11001, 15692, 376}, {11113, 15640, 550}, {11737, 14893, 15687}, {11737, 15681, 2}, {11737, 15687, 15681}, {14892, 15693, 7486}, {15022, 15697, 11539}, {15681, 15687, 3543}, {15681, 15688, 15691}, {15681, 15703, 15700}, {15682, 15710, 3529}, {15684, 15692, 11001}, {15684, 15759, 15683}, {15691, 15723, 15692}, {15701, 15703, 15723}, {17542, 17578, 5059}, {18586, 18587, 12103}, {39884, 50963, 5032}, {42494, 42589, 16962}, {42495, 42588, 16963}

X(61981) = X(2)X(3)∩X(13)X(42969)

Barycentrics    17*a^4-22*(b^2-c^2)^2+5*a^2*(b^2+c^2) : :
X(61981) = -22*X[2]+13*X[3], -11*X[599]+2*X[55581], 8*X[3818]+X[50962], -4*X[4746]+13*X[50796], 5*X[4816]+13*X[31162], 5*X[8148]+4*X[50830], -11*X[10516]+2*X[55589], -11*X[11178]+2*X[55586], 4*X[11180]+5*X[51172], 11*X[11898]+16*X[55719], 5*X[12017]+4*X[51022], 2*X[12699]+7*X[50800] and many others

X(61981) lies on these lines: {2, 3}, {13, 42969}, {14, 42968}, {598, 54891}, {599, 55581}, {1327, 6499}, {1328, 6498}, {3818, 50962}, {4746, 50796}, {4816, 31162}, {5339, 42694}, {5340, 42695}, {5349, 41119}, {5350, 41120}, {6417, 43340}, {6418, 43341}, {6435, 13665}, {6436, 13785}, {6451, 43513}, {6452, 43514}, {6453, 42526}, {6454, 42527}, {6494, 32787}, {6495, 32788}, {8148, 50830}, {10516, 55589}, {10653, 42963}, {10654, 42962}, {11178, 55586}, {11180, 51172}, {11645, 55707}, {11898, 55719}, {12017, 51022}, {12699, 50800}, {12702, 50799}, {12820, 16961}, {12821, 16960}, {14848, 55713}, {15484, 39563}, {16267, 42093}, {16268, 42094}, {16808, 43293}, {16809, 43292}, {16962, 42126}, {16963, 42127}, {18440, 51140}, {18480, 50805}, {18481, 51074}, {18483, 50798}, {18492, 34718}, {18510, 43343}, {18512, 43342}, {18525, 51087}, {18526, 34648}, {19106, 43545}, {19107, 43544}, {21850, 51175}, {21969, 46852}, {22615, 43526}, {22644, 43525}, {25561, 55592}, {31670, 50957}, {31673, 50807}, {33606, 42989}, {33607, 42988}, {33878, 50956}, {36969, 42818}, {36970, 42817}, {36990, 55709}, {37481, 44871}, {39899, 50963}, {41943, 43476}, {41944, 43475}, {41945, 43568}, {41946, 43569}, {42095, 43484}, {42098, 43483}, {42101, 42688}, {42102, 42689}, {42103, 42690}, {42106, 42691}, {42153, 42965}, {42156, 42964}, {42268, 43381}, {42269, 43380}, {42270, 43503}, {42273, 43504}, {42684, 43107}, {42685, 43100}, {42686, 42910}, {42687, 42911}, {42786, 50968}, {42934, 49947}, {42935, 49948}, {42972, 42974}, {42973, 42975}, {43150, 50954}, {43273, 55702}, {44456, 50985}, {46264, 51129}, {47352, 55700}, {48879, 51164}, {48889, 55714}, {48895, 55598}, {48910, 55609}, {50964, 51138}, {51076, 61268}, {51143, 55602}, {53023, 55717}

X(61981) = midpoint of X(i) and X(j) for these {i,j}: {3543, 15710}
X(61981) = reflection of X(i) in X(j) for these {i,j}: {15689, 15708}, {15706, 5055}, {15708, 5}, {15710, 15699}, {3534, 15706}
X(61981) = inverse of X(62015) in orthocentroidal circle
X(61981) = inverse of X(62015) in Yff hyperbola
X(61981) = pole of line {523, 62015} with respect to the orthocentroidal circle
X(61981) = pole of line {6, 62015} with respect to the Kiepert hyperbola
X(61981) = pole of line {523, 62015} with respect to the Yff hyperbola
X(61981) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(265), X(15708)}}, {{A, B, C, X(5094), X(54891)}}, {{A, B, C, X(14487), X(47485)}}, {{A, B, C, X(15686), X(18550)}}, {{A, B, C, X(16239), X(21400)}}, {{A, B, C, X(34200), X(54585)}}, {{A, B, C, X(55863), X(60121)}}
X(61981) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 17800, 5076}, {4, 3832, 3628}, {4, 3856, 3}, {4, 3857, 17800}, {4, 5066, 15684}, {4, 5072, 382}, {4, 7486, 3627}, {5, 30, 15708}, {30, 15699, 15710}, {30, 15706, 3534}, {30, 15708, 15689}, {30, 5055, 15706}, {381, 15687, 15723}, {381, 15688, 3545}, {381, 3526, 5066}, {381, 3534, 5072}, {381, 5076, 2}, {546, 14893, 10109}, {546, 16239, 3858}, {547, 11001, 6948}, {549, 15759, 10299}, {549, 5066, 15022}, {1656, 15688, 5054}, {2050, 3534, 15687}, {3091, 12101, 15681}, {3146, 11737, 15701}, {3522, 5068, 377}, {3522, 6895, 5059}, {3523, 5056, 17582}, {3526, 15022, 1656}, {3543, 15710, 30}, {3543, 3851, 15693}, {3543, 3860, 3851}, {3545, 3830, 15688}, {3545, 3839, 546}, {3628, 15687, 15640}, {3839, 14269, 381}, {3839, 3845, 14269}, {3843, 14269, 3839}, {3850, 15682, 15703}, {3853, 5071, 15685}, {3854, 14893, 3830}, {3857, 3861, 4}, {5054, 15688, 15716}, {5054, 5072, 5055}, {5055, 10304, 3526}, {5067, 15691, 15722}, {5071, 15685, 15720}, {7486, 15759, 15694}, {14890, 15704, 10304}, {14892, 15711, 17537}, {15682, 15703, 15696}, {15705, 15709, 549}

X(61982) = X(2)X(3)∩X(13)X(5365)

Barycentrics    9*a^4-11*(b^2-c^2)^2+2*a^2*(b^2+c^2) : :
X(61982) = -33*X[2]+20*X[3], X[153]+12*X[59390], -11*X[193]+24*X[55717], -18*X[373]+5*X[52093], 8*X[551]+5*X[50863], 8*X[597]+5*X[51216], 8*X[599]+5*X[51211], -20*X[946]+7*X[20057], 5*X[962]+8*X[3626], 11*X[1352]+2*X[55723], -15*X[1699]+2*X[3244], 12*X[1853]+X[54211] and many others

X(61982) lies on these lines: {2, 3}, {6, 52707}, {13, 5365}, {14, 5366}, {68, 14487}, {153, 59390}, {193, 55717}, {253, 57897}, {264, 52711}, {315, 32868}, {371, 43508}, {372, 43507}, {373, 52093}, {388, 9671}, {390, 37719}, {497, 9656}, {551, 50863}, {590, 9692}, {597, 51216}, {599, 51211}, {938, 3982}, {946, 20057}, {962, 3626}, {1131, 6435}, {1132, 6436}, {1151, 41965}, {1152, 41966}, {1352, 55723}, {1479, 31410}, {1699, 3244}, {1853, 54211}, {2549, 31407}, {2996, 14488}, {3071, 31414}, {3087, 45245}, {3316, 9543}, {3317, 42226}, {3411, 42161}, {3412, 42160}, {3424, 53109}, {3567, 46849}, {3583, 5261}, {3585, 5274}, {3590, 54596}, {3591, 54595}, {3600, 37720}, {3617, 22793}, {3620, 48901}, {3621, 61249}, {3623, 61290}, {3629, 5921}, {3631, 51212}, {3632, 4301}, {3636, 5691}, {3818, 55719}, {3828, 50873}, {3876, 31822}, {4031, 9581}, {4309, 10590}, {4317, 10591}, {4325, 5265}, {4330, 5281}, {4739, 51063}, {4846, 46851}, {5225, 15888}, {5229, 37722}, {5318, 42983}, {5319, 14075}, {5321, 42982}, {5334, 42813}, {5335, 42814}, {5343, 42162}, {5344, 42159}, {5349, 37640}, {5350, 37641}, {5395, 6249}, {5446, 16261}, {5587, 10248}, {5603, 32900}, {5640, 13474}, {5731, 12571}, {5735, 60957}, {5881, 18483}, {5889, 46847}, {5890, 44863}, {6225, 23324}, {6329, 36990}, {6419, 43376}, {6420, 43377}, {6431, 42570}, {6432, 42571}, {6494, 42215}, {6495, 42216}, {6496, 43505}, {6497, 43506}, {6498, 7582}, {6499, 7581}, {6776, 55713}, {7585, 23263}, {7586, 23253}, {7620, 7759}, {7747, 37689}, {7748, 31417}, {7751, 23334}, {7765, 37665}, {7775, 11148}, {7796, 32827}, {7814, 32815}, {7991, 38098}, {8972, 35821}, {9542, 9681}, {9588, 51118}, {9589, 19925}, {9624, 9779}, {9657, 14986}, {9680, 43408}, {9705, 46261}, {9706, 11424}, {9730, 44871}, {9740, 47617}, {9781, 16194}, {9812, 11362}, {10110, 11439}, {10519, 55598}, {10541, 51022}, {10653, 12820}, {10654, 12821}, {10722, 35021}, {10723, 35022}, {10724, 35023}, {10725, 35024}, {11002, 12162}, {11008, 15069}, {11017, 13340}, {11036, 37723}, {11160, 18553}, {11271, 22804}, {11381, 13570}, {11431, 18390}, {11459, 46852}, {11465, 14641}, {11488, 43105}, {11489, 43106}, {11522, 50864}, {11745, 34796}, {12244, 20396}, {12245, 61255}, {12699, 54448}, {13202, 15057}, {13941, 35820}, {14484, 53105}, {14531, 44870}, {14561, 55702}, {14853, 55714}, {15043, 32062}, {15056, 15606}, {15062, 34417}, {15431, 61506}, {15589, 32886}, {16772, 42140}, {16773, 42141}, {16808, 43196}, {16809, 43195}, {16964, 42106}, {16965, 42103}, {16981, 18436}, {18376, 34781}, {18480, 20054}, {18510, 42540}, {18512, 42539}, {18581, 42629}, {18582, 42630}, {18843, 60147}, {18845, 54845}, {19130, 55707}, {19877, 28150}, {20105, 48663}, {20582, 51029}, {20583, 51023}, {20791, 27355}, {22236, 42775}, {22238, 42776}, {22615, 35812}, {22644, 35813}, {22682, 32450}, {23267, 43560}, {23273, 43561}, {24206, 55613}, {25555, 50964}, {28160, 46934}, {30389, 50862}, {31399, 41869}, {31400, 43457}, {31412, 41955}, {31457, 43619}, {31663, 46930}, {31670, 55581}, {32789, 43406}, {32790, 43405}, {32825, 48913}, {33698, 53099}, {33748, 55712}, {34641, 50872}, {34783, 58533}, {35019, 36961}, {35020, 36962}, {35369, 38743}, {36412, 61301}, {36967, 42947}, {36968, 42946}, {36991, 60980}, {37832, 43479}, {37835, 43480}, {38140, 46933}, {38259, 52519}, {39590, 43448}, {39884, 51170}, {40107, 55589}, {40330, 48895}, {40693, 42133}, {40694, 42134}, {41119, 41973}, {41120, 41974}, {41895, 60142}, {41956, 42523}, {42095, 43874}, {42096, 42472}, {42097, 42473}, {42098, 43873}, {42101, 42156}, {42102, 42153}, {42107, 43193}, {42108, 42490}, {42109, 42491}, {42110, 43194}, {42111, 42433}, {42114, 42434}, {42117, 43474}, {42118, 43473}, {42139, 42148}, {42142, 42147}, {42154, 42494}, {42155, 42495}, {42163, 42804}, {42166, 42803}, {42270, 52667}, {42273, 52666}, {42413, 42582}, {42414, 42583}, {42598, 43770}, {42599, 43769}, {42613, 61719}, {42635, 49876}, {42636, 49875}, {42643, 43313}, {42644, 43312}, {42912, 43496}, {42913, 43495}, {42920, 43477}, {42921, 43478}, {42930, 43643}, {42931, 43638}, {42932, 43238}, {42933, 43239}, {42974, 43556}, {42975, 43557}, {42980, 43372}, {42981, 43373}, {42998, 43418}, {42999, 43419}, {43008, 43292}, {43009, 43293}, {43030, 43251}, {43031, 43250}, {43316, 43798}, {43317, 43797}, {43366, 43633}, {43367, 43632}, {43503, 43884}, {43504, 43883}, {43521, 54542}, {43522, 54543}, {43537, 54494}, {43566, 43571}, {43567, 43570}, {43676, 54520}, {43951, 60219}, {46264, 55700}, {46931, 61263}, {48873, 55621}, {48889, 55715}, {50867, 51076}, {50956, 52987}, {50960, 51213}, {51131, 51217}, {51171, 55709}, {53100, 53101}, {53102, 54519}, {54476, 60337}, {54642, 60334}, {54706, 60636}, {54717, 60285}, {54720, 60118}, {54896, 60332}, {59385, 60933}, {59389, 60942}, {60113, 60330}, {60328, 60631}

X(61982) = reflection of X(i) in X(j) for these {i,j}: {10299, 5079}, {10303, 5068}
X(61982) = inverse of X(50688) in orthocentroidal circle
X(61982) = inverse of X(50688) in Yff hyperbola
X(61982) = complement of X(62125)
X(61982) = anticomplement of X(10299)
X(61982) = pole of line {523, 50688} with respect to the orthocentroidal circle
X(61982) = pole of line {185, 50687} with respect to the Jerabek hyperbola
X(61982) = pole of line {6, 43405} with respect to the Kiepert hyperbola
X(61982) = pole of line {523, 50688} with respect to the Yff hyperbola
X(61982) = pole of line {69, 55671} with respect to the Wallace hyperbola
X(61982) = intersection, other than A, B, C, of circumconics {{A, B, C, X(20), X(57897)}}, {{A, B, C, X(24), X(14487)}}, {{A, B, C, X(68), X(12100)}}, {{A, B, C, X(253), X(550)}}, {{A, B, C, X(264), X(50688)}}, {{A, B, C, X(378), X(46851)}}, {{A, B, C, X(1105), X(50687)}}, {{A, B, C, X(1217), X(3853)}}, {{A, B, C, X(1657), X(31361)}}, {{A, B, C, X(3090), X(46455)}}, {{A, B, C, X(3521), X(15688)}}, {{A, B, C, X(3526), X(31363)}}, {{A, B, C, X(3628), X(60618)}}, {{A, B, C, X(3830), X(18855)}}, {{A, B, C, X(4846), X(46853)}}, {{A, B, C, X(5076), X(18850)}}, {{A, B, C, X(6353), X(14488)}}, {{A, B, C, X(6662), X(58203)}}, {{A, B, C, X(7714), X(54717)}}, {{A, B, C, X(8889), X(60132)}}, {{A, B, C, X(10304), X(54923)}}, {{A, B, C, X(14484), X(37453)}}, {{A, B, C, X(14860), X(17578)}}, {{A, B, C, X(14869), X(32533)}}, {{A, B, C, X(15318), X(17538)}}, {{A, B, C, X(15687), X(18846)}}, {{A, B, C, X(15694), X(21400)}}, {{A, B, C, X(15698), X(54585)}}, {{A, B, C, X(15708), X(15749)}}, {{A, B, C, X(15709), X(60121)}}, {{A, B, C, X(17505), X(55857)}}, {{A, B, C, X(38282), X(52519)}}, {{A, B, C, X(52283), X(53109)}}, {{A, B, C, X(52288), X(53105)}}, {{A, B, C, X(52290), X(60142)}}, {{A, B, C, X(52299), X(54845)}}
X(61982) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10299, 10303}, {2, 15683, 15710}, {2, 3146, 550}, {2, 3544, 5056}, {2, 382, 20}, {2, 3832, 3855}, {2, 4190, 11346}, {2, 4234, 13742}, {2, 5068, 5079}, {2, 6904, 4234}, {3, 14893, 4}, {4, 15682, 12102}, {4, 3090, 3830}, {4, 3091, 3543}, {4, 3529, 15687}, {4, 3545, 3627}, {4, 376, 5076}, {4, 381, 3146}, {4, 5, 17578}, {4, 631, 3853}, {5, 3853, 17800}, {20, 15692, 548}, {20, 3091, 7486}, {20, 3832, 3091}, {20, 3839, 3832}, {20, 5056, 631}, {20, 631, 10304}, {20, 7486, 3523}, {30, 5079, 10299}, {376, 3850, 15022}, {381, 15687, 15715}, {381, 3830, 11539}, {381, 550, 3544}, {382, 3526, 15681}, {382, 3530, 3529}, {382, 3843, 546}, {382, 3851, 3530}, {546, 11737, 3858}, {546, 15687, 3851}, {546, 550, 381}, {550, 3628, 15707}, {550, 6944, 1010}, {1656, 12102, 15682}, {1657, 3545, 17542}, {1657, 3857, 5071}, {2041, 2042, 17538}, {3090, 3830, 5059}, {3090, 5059, 15692}, {3522, 3627, 15640}, {3526, 3859, 3545}, {3528, 14869, 5154}, {3528, 3855, 5}, {3530, 15687, 382}, {3534, 3544, 6675}, {3534, 6825, 8703}, {3544, 15714, 377}, {3545, 15640, 15721}, {3545, 3627, 3522}, {3627, 3859, 3526}, {3832, 3843, 3839}, {3832, 3854, 3856}, {3845, 3861, 3843}, {3850, 5076, 376}, {3851, 15685, 2049}, {3851, 15710, 17568}, {3856, 3861, 14893}, {3857, 12101, 1657}, {4193, 15683, 3528}, {5066, 5073, 3525}, {10304, 15721, 12100}, {11737, 15720, 3090}, {16052, 16408, 2}, {23249, 35787, 1132}, {23253, 42268, 7586}, {23259, 35786, 1131}, {23263, 42269, 7585}

X(61983) = X(2)X(3)∩X(17)X(43476)

Barycentrics    19*a^4-23*(b^2-c^2)^2+4*a^2*(b^2+c^2) : :
X(61983) = -23*X[2]+14*X[3], -5*X[1698]+14*X[51078], X[1992]+8*X[48889], 4*X[3098]+5*X[51029], 4*X[3579]+5*X[50873], -16*X[3589]+7*X[51177], -5*X[3616]+14*X[50807], -5*X[3617]+14*X[50800], -5*X[3618]+14*X[50964], -5*X[3620]+14*X[50957], 2*X[3625]+7*X[31162], -5*X[3630]+14*X[50958] and many others

X(61983) lies on these lines: {2, 3}, {17, 43476}, {18, 43475}, {371, 43522}, {372, 43521}, {598, 60325}, {1151, 41967}, {1152, 41968}, {1249, 36430}, {1327, 7582}, {1328, 7581}, {1698, 51078}, {1992, 48889}, {3098, 51029}, {3579, 50873}, {3589, 51177}, {3616, 50807}, {3617, 50800}, {3618, 50964}, {3620, 50957}, {3625, 31162}, {3630, 50958}, {3633, 18483}, {3634, 50813}, {3654, 10248}, {3763, 51133}, {3818, 50961}, {4668, 50796}, {4691, 18492}, {5339, 49825}, {5340, 49824}, {5349, 49827}, {5350, 49826}, {5365, 43228}, {5366, 43229}, {5485, 54890}, {5550, 50867}, {6144, 11180}, {6431, 43380}, {6432, 43381}, {6459, 43504}, {6460, 43503}, {7612, 54646}, {7773, 32875}, {9779, 28208}, {9812, 38176}, {10385, 18514}, {10574, 44871}, {11179, 42785}, {11455, 13570}, {12290, 58470}, {12816, 42159}, {12817, 42162}, {14226, 42268}, {14241, 42269}, {14458, 18844}, {14482, 53419}, {14494, 54493}, {16267, 42106}, {16268, 42103}, {16962, 41971}, {16963, 41972}, {18424, 46453}, {18480, 20053}, {18482, 60976}, {18842, 60326}, {18843, 54852}, {19053, 35787}, {19054, 35786}, {19878, 50820}, {21850, 51174}, {23269, 35823}, {23275, 35822}, {31145, 40273}, {31414, 60308}, {32455, 50974}, {32532, 60329}, {32818, 48913}, {32819, 32876}, {33602, 43551}, {33603, 43550}, {34573, 50969}, {34628, 51074}, {34632, 50799}, {34773, 50863}, {36969, 43543}, {36970, 43542}, {39809, 52886}, {41100, 43491}, {41101, 43492}, {41869, 50803}, {41943, 43770}, {41944, 43769}, {41953, 42284}, {41954, 42283}, {41969, 42265}, {41970, 42262}, {41973, 49811}, {41974, 49810}, {42089, 43399}, {42092, 43400}, {42101, 43403}, {42102, 43404}, {42111, 42928}, {42114, 42929}, {42126, 43478}, {42127, 43477}, {42147, 42806}, {42148, 42805}, {42160, 42435}, {42161, 42436}, {42163, 49875}, {42166, 49876}, {42270, 43256}, {42273, 43257}, {42494, 42511}, {42495, 42510}, {42588, 42776}, {42589, 42775}, {42645, 54635}, {42646, 54634}, {42694, 43546}, {42695, 43547}, {42904, 43235}, {42905, 43234}, {42910, 52080}, {42911, 52079}, {42920, 49861}, {42921, 49862}, {42972, 43227}, {42973, 43226}, {42974, 43364}, {42975, 43365}, {42990, 56615}, {42991, 56614}, {43201, 43781}, {43202, 43782}, {43416, 43541}, {43417, 43540}, {43446, 54575}, {43447, 54574}, {43562, 60304}, {43563, 60303}, {43566, 60290}, {43567, 60289}, {43773, 49874}, {43774, 49873}, {48895, 50956}, {48906, 51216}, {48910, 50960}, {50819, 51076}, {50959, 51176}, {50975, 51131}, {50976, 51127}, {51120, 61256}, {51170, 51173}, {52519, 60630}, {53106, 60127}, {53107, 60150}, {54857, 60281}

X(61983) = midpoint of X(i) and X(j) for these {i,j}: {3543, 15705}
X(61983) = reflection of X(i) in X(j) for these {i,j}: {15705, 5055}, {15707, 5}, {15709, 3545}, {376, 15709}
X(61983) = inverse of X(62011) in orthocentroidal circle
X(61983) = inverse of X(62011) in Yff hyperbola
X(61983) = anticomplement of X(15706)
X(61983) = pole of line {523, 62011} with respect to the orthocentroidal circle
X(61983) = pole of line {6, 62011} with respect to the Kiepert hyperbola
X(61983) = pole of line {523, 62011} with respect to the Yff hyperbola
X(61983) = pole of line {69, 14891} with respect to the Wallace hyperbola
X(61983) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(14891)}}, {{A, B, C, X(265), X(15707)}}, {{A, B, C, X(547), X(54667)}}, {{A, B, C, X(632), X(54763)}}, {{A, B, C, X(1657), X(36889)}}, {{A, B, C, X(3853), X(18853)}}, {{A, B, C, X(4232), X(54890)}}, {{A, B, C, X(5054), X(54838)}}, {{A, B, C, X(5070), X(54660)}}, {{A, B, C, X(5076), X(18851)}}, {{A, B, C, X(5094), X(60325)}}, {{A, B, C, X(11331), X(18844)}}, {{A, B, C, X(15319), X(50693)}}, {{A, B, C, X(15687), X(18847)}}, {{A, B, C, X(15692), X(54585)}}, {{A, B, C, X(15713), X(43699)}}, {{A, B, C, X(18852), X(50687)}}, {{A, B, C, X(18854), X(50688)}}, {{A, B, C, X(21734), X(54923)}}, {{A, B, C, X(37174), X(54646)}}, {{A, B, C, X(46936), X(60122)}}, {{A, B, C, X(52284), X(60326)}}, {{A, B, C, X(52297), X(60127)}}, {{A, B, C, X(52298), X(60150)}}, {{A, B, C, X(53857), X(60329)}}, {{A, B, C, X(55864), X(60121)}}
X(61983) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14893, 4}, {2, 15684, 17538}, {2, 15712, 15702}, {2, 20, 14891}, {2, 3543, 1657}, {2, 5072, 5071}, {4, 11001, 15687}, {4, 3525, 3853}, {4, 3528, 5076}, {4, 3544, 17578}, {4, 5071, 3830}, {5, 15685, 15721}, {5, 30, 15707}, {30, 3545, 15709}, {30, 5055, 15705}, {140, 10304, 3524}, {140, 8703, 15700}, {381, 10109, 3091}, {381, 12101, 20}, {381, 15685, 5}, {381, 15689, 14892}, {381, 15701, 12811}, {381, 3524, 3545}, {381, 3830, 140}, {381, 5070, 5066}, {381, 5073, 10109}, {381, 5076, 15716}, {381, 8703, 5068}, {411, 19238, 3}, {547, 5076, 15640}, {631, 3545, 5055}, {1657, 3843, 546}, {3091, 15687, 11001}, {3524, 3545, 3090}, {3529, 5071, 15719}, {3543, 11541, 15682}, {3543, 15705, 30}, {3543, 5068, 8703}, {3543, 8703, 11541}, {3627, 14892, 15689}, {3830, 5071, 3529}, {3830, 5072, 15686}, {3839, 10304, 3832}, {3845, 14269, 3839}, {3845, 14893, 3843}, {3845, 3861, 381}, {3854, 15640, 547}, {3854, 5076, 3528}, {10109, 15687, 5073}, {10299, 11001, 376}, {12101, 14891, 3627}, {12812, 15718, 2}, {14891, 14892, 15699}, {15682, 15698, 15685}, {15686, 15711, 548}, {15702, 15722, 631}

X(61984) = X(2)X(3)∩X(6)X(17505)

Barycentrics    5*a^4-6*(b^2-c^2)^2+a^2*(b^2+c^2) : :
X(61984) = -18*X[2]+11*X[3], 6*X[51]+X[18439], X[52]+6*X[46847], -12*X[141]+5*X[55595], 4*X[143]+3*X[15305], -X[185]+8*X[44863], 3*X[265]+4*X[38791], -11*X[355]+4*X[4701], -9*X[373]+2*X[14641], 4*X[575]+3*X[36990], 4*X[576]+3*X[18440], -9*X[599]+2*X[55583] and many others

X(61984) lies on these lines: {2, 3}, {6, 17505}, {51, 18439}, {52, 46847}, {61, 42093}, {62, 42094}, {83, 54917}, {141, 55595}, {143, 15305}, {185, 44863}, {195, 18451}, {265, 38791}, {355, 4701}, {373, 14641}, {399, 36749}, {515, 61277}, {517, 61256}, {542, 51173}, {567, 26883}, {575, 36990}, {576, 18440}, {590, 6519}, {599, 55583}, {615, 6522}, {942, 51792}, {944, 61280}, {946, 18526}, {1173, 21400}, {1181, 15038}, {1352, 55724}, {1482, 18483}, {1493, 48675}, {1498, 18376}, {1503, 53092}, {1511, 15029}, {1539, 15054}, {1699, 10222}, {1853, 48672}, {3053, 18424}, {3060, 45959}, {3070, 6428}, {3071, 6427}, {3087, 59655}, {3241, 58236}, {3303, 3583}, {3304, 3585}, {3311, 42269}, {3312, 42268}, {3521, 22334}, {3527, 32533}, {3531, 15077}, {3592, 6564}, {3594, 6565}, {3619, 55616}, {3624, 28168}, {3653, 51074}, {3746, 9668}, {3763, 48904}, {3818, 11477}, {3933, 32890}, {4301, 50798}, {4857, 9656}, {5013, 43457}, {5093, 39884}, {5225, 6767}, {5229, 7373}, {5237, 42095}, {5238, 42098}, {5270, 9671}, {5290, 18530}, {5318, 42159}, {5321, 42162}, {5339, 42813}, {5340, 42814}, {5349, 40693}, {5350, 40694}, {5351, 42097}, {5352, 42096}, {5418, 53519}, {5420, 53518}, {5446, 18435}, {5462, 32062}, {5480, 11482}, {5562, 46852}, {5563, 9655}, {5603, 61281}, {5609, 12902}, {5640, 13491}, {5663, 9781}, {5691, 15178}, {5694, 61740}, {5734, 34748}, {5790, 7991}, {5876, 16261}, {5878, 23324}, {5881, 50805}, {5890, 32137}, {5893, 12315}, {5895, 23325}, {5925, 32767}, {5946, 12290}, {6033, 38734}, {6102, 11439}, {6199, 31412}, {6221, 22615}, {6241, 10095}, {6243, 15030}, {6248, 22728}, {6279, 26336}, {6280, 26346}, {6321, 38745}, {6361, 61259}, {6390, 32891}, {6395, 42561}, {6398, 22644}, {6407, 42225}, {6408, 42226}, {6417, 23259}, {6418, 23249}, {6419, 13665}, {6420, 13785}, {6425, 8976}, {6426, 13951}, {6445, 43408}, {6446, 43407}, {6447, 6561}, {6448, 6560}, {6449, 42271}, {6450, 42272}, {6451, 42566}, {6452, 42567}, {6453, 42265}, {6454, 42262}, {6455, 42275}, {6456, 42276}, {6459, 45384}, {6460, 45385}, {6496, 32789}, {6497, 32790}, {6500, 23273}, {6501, 23267}, {6748, 61315}, {7583, 23263}, {7584, 23253}, {7603, 44519}, {7687, 9786}, {7728, 36253}, {7747, 22331}, {7748, 22332}, {7772, 15484}, {7773, 7871}, {7823, 50570}, {7843, 34505}, {7982, 12645}, {7989, 28146}, {8148, 40273}, {8227, 33697}, {8981, 52666}, {9581, 18541}, {9588, 28202}, {9605, 53419}, {9624, 28208}, {9641, 37697}, {9704, 15033}, {9779, 34773}, {9780, 28178}, {9812, 18357}, {9880, 52090}, {10110, 13321}, {10113, 14094}, {10246, 31673}, {10247, 61292}, {10248, 28174}, {10263, 15058}, {10516, 48895}, {10540, 11424}, {10541, 29012}, {10574, 13364}, {10605, 33541}, {10645, 43636}, {10646, 43637}, {10721, 15025}, {10728, 38141}, {10738, 38757}, {10739, 38769}, {10740, 38781}, {10742, 59390}, {10748, 38801}, {10894, 24042}, {10982, 15087}, {11178, 55588}, {11381, 37481}, {11412, 45958}, {11438, 15432}, {11455, 13630}, {11472, 37490}, {11480, 42581}, {11481, 42580}, {11485, 42101}, {11486, 42102}, {11550, 43821}, {11565, 40241}, {11645, 55708}, {11793, 54047}, {11935, 37472}, {12002, 14531}, {12006, 12279}, {12121, 15046}, {12162, 16625}, {12289, 15807}, {12293, 41597}, {12295, 32609}, {12307, 33586}, {12355, 14981}, {12429, 15083}, {12571, 18481}, {12699, 59503}, {12702, 19925}, {12816, 42990}, {12817, 42991}, {12953, 31479}, {13111, 41755}, {13202, 15041}, {13391, 15056}, {13464, 50806}, {13474, 13570}, {13598, 23039}, {13881, 35007}, {13886, 43313}, {13925, 43883}, {13939, 43312}, {13966, 52667}, {13993, 43884}, {14023, 40727}, {14561, 55701}, {14627, 32139}, {14639, 38744}, {14644, 38790}, {14845, 46850}, {14848, 22234}, {14853, 48662}, {14881, 32520}, {14927, 55697}, {15019, 18394}, {15021, 20304}, {15026, 15072}, {15034, 61574}, {15039, 17702}, {15040, 36518}, {15045, 18874}, {15069, 50962}, {15170, 31410}, {15801, 22804}, {16001, 48655}, {16002, 48656}, {16241, 43204}, {16242, 43203}, {16644, 42432}, {16645, 42431}, {16808, 22236}, {16809, 22238}, {16835, 18550}, {16962, 43369}, {16963, 43368}, {16964, 42988}, {16965, 42989}, {18358, 51538}, {18381, 58795}, {18383, 34780}, {18436, 44870}, {18482, 60922}, {18542, 37622}, {18543, 26332}, {18545, 26333}, {18553, 54131}, {18576, 56407}, {18581, 42165}, {18582, 42164}, {18584, 37512}, {19106, 36843}, {19107, 36836}, {19116, 23269}, {19117, 23275}, {19130, 53093}, {19160, 38689}, {19163, 38676}, {20127, 38729}, {20190, 48884}, {20299, 61721}, {20398, 39838}, {20399, 39809}, {20415, 36961}, {20416, 36962}, {20585, 61715}, {20791, 32205}, {21401, 36992}, {21402, 36994}, {21850, 51537}, {22235, 42633}, {22237, 42634}, {22505, 38664}, {22515, 23235}, {22566, 38628}, {22682, 32519}, {22791, 61246}, {22799, 38669}, {22819, 45439}, {22820, 45438}, {22938, 38665}, {24206, 55614}, {24387, 34739}, {25561, 55597}, {28154, 31423}, {28160, 30389}, {28164, 61268}, {28194, 50800}, {28204, 61289}, {29181, 55602}, {29317, 55626}, {29323, 47355}, {30315, 31447}, {30435, 53418}, {30531, 55039}, {31399, 50803}, {31467, 31652}, {31670, 55580}, {31671, 59389}, {31672, 59380}, {31730, 61263}, {32063, 41362}, {32821, 48913}, {34507, 50954}, {34573, 55643}, {34648, 37727}, {34718, 37714}, {34754, 43196}, {34755, 43195}, {34786, 50414}, {35450, 51491}, {36969, 42153}, {36970, 42156}, {37582, 51790}, {37624, 38034}, {37832, 43194}, {37835, 43193}, {38064, 51129}, {38066, 50799}, {38136, 53091}, {38140, 41869}, {38317, 55684}, {38633, 40685}, {38666, 38767}, {38667, 38779}, {38672, 49117}, {38675, 38799}, {38730, 38751}, {38733, 51524}, {38740, 38741}, {38756, 51529}, {38768, 51528}, {38780, 51534}, {39563, 41940}, {39601, 44535}, {40107, 51024}, {40330, 55593}, {40647, 44871}, {41121, 42908}, {41122, 42909}, {41973, 49947}, {41974, 49948}, {42085, 42598}, {42086, 42599}, {42104, 42110}, {42105, 42107}, {42108, 42114}, {42109, 42111}, {42133, 42138}, {42134, 42135}, {42136, 42142}, {42137, 42139}, {42140, 42146}, {42141, 42143}, {42147, 42921}, {42148, 42920}, {42149, 42941}, {42152, 42940}, {42263, 42558}, {42264, 42557}, {42350, 42854}, {42490, 42592}, {42491, 42593}, {42494, 42912}, {42495, 42913}, {42625, 42937}, {42626, 42936}, {42682, 42688}, {42683, 42689}, {42694, 43419}, {42695, 43418}, {42779, 42969}, {42780, 42968}, {42785, 55711}, {42786, 55651}, {42904, 43031}, {42905, 43030}, {42916, 43243}, {42917, 43242}, {42922, 42983}, {42923, 42982}, {42924, 43404}, {42925, 43403}, {42946, 43366}, {42947, 43367}, {42998, 43417}, {42999, 43416}, {43201, 49824}, {43202, 49825}, {43238, 43632}, {43239, 43633}, {43273, 55704}, {43298, 43782}, {43299, 43781}, {43332, 43492}, {43333, 43491}, {43376, 43567}, {43377, 43566}, {43380, 43570}, {43381, 43571}, {43621, 55629}, {45186, 54048}, {46933, 61260}, {47352, 55698}, {47392, 60828}, {48680, 51525}, {48681, 51536}, {48872, 55637}, {48879, 55650}, {48896, 55677}, {48901, 53097}, {48905, 55687}, {48910, 55606}, {48942, 55679}, {48943, 55647}, {50797, 50817}, {50802, 61276}, {50811, 58232}, {50864, 61286}, {50956, 50970}, {50963, 51136}, {51118, 61261}, {51163, 55610}, {51172, 51178}, {58230, 61272}, {58249, 61255}, {59385, 60884}

X(61984) = midpoint of X(i) and X(j) for these {i,j}: {4, 3832}, {3543, 15698}, {3627, 14869}, {3830, 15703}
X(61984) = reflection of X(i) in X(j) for these {i,j}: {3, 3090}, {3090, 3857}, {3523, 5}, {3526, 3851}, {3534, 15700}, {3851, 3832}, {3857, 546}, {55616, 3619}, {55651, 42786}, {55711, 42785}
X(61984) = inverse of X(3853) in orthocentroidal circle
X(61984) = inverse of X(3853) in Yff hyperbola
X(61984) = complement of X(62127)
X(61984) = anticomplement of X(44682)
X(61984) = pole of line {523, 3853} with respect to the orthocentroidal circle
X(61984) = pole of line {185, 5076} with respect to the Jerabek hyperbola
X(61984) = pole of line {6, 3853} with respect to the Kiepert hyperbola
X(61984) = pole of line {523, 3853} with respect to the Yff hyperbola
X(61984) = pole of line {69, 55670} with respect to the Wallace hyperbola
X(61984) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(17505)}}, {{A, B, C, X(6), X(17506)}}, {{A, B, C, X(68), X(10299)}}, {{A, B, C, X(140), X(21400)}}, {{A, B, C, X(186), X(52518)}}, {{A, B, C, X(264), X(3853)}}, {{A, B, C, X(265), X(3523)}}, {{A, B, C, X(427), X(54917)}}, {{A, B, C, X(548), X(52441)}}, {{A, B, C, X(550), X(18550)}}, {{A, B, C, X(631), X(32533)}}, {{A, B, C, X(1105), X(5076)}}, {{A, B, C, X(1173), X(21844)}}, {{A, B, C, X(1217), X(50687)}}, {{A, B, C, X(3426), X(35477)}}, {{A, B, C, X(3515), X(3531)}}, {{A, B, C, X(3517), X(61137)}}, {{A, B, C, X(3520), X(22334)}}, {{A, B, C, X(3521), X(3522)}}, {{A, B, C, X(3524), X(15077)}}, {{A, B, C, X(3525), X(18296)}}, {{A, B, C, X(3527), X(32534)}}, {{A, B, C, X(3528), X(31371)}}, {{A, B, C, X(3830), X(14860)}}, {{A, B, C, X(4846), X(21735)}}, {{A, B, C, X(10018), X(61127)}}, {{A, B, C, X(12100), X(54585)}}, {{A, B, C, X(13452), X(23040)}}, {{A, B, C, X(13599), X(16239)}}, {{A, B, C, X(14490), X(35478)}}, {{A, B, C, X(15319), X(15689)}}, {{A, B, C, X(15685), X(54924)}}, {{A, B, C, X(15687), X(18848)}}, {{A, B, C, X(15694), X(60121)}}, {{A, B, C, X(15699), X(60122)}}, {{A, B, C, X(16835), X(35473)}}, {{A, B, C, X(18855), X(50688)}}, {{A, B, C, X(35475), X(46848)}}, {{A, B, C, X(40448), X(55857)}}, {{A, B, C, X(43970), X(44580)}}
X(61984) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3853, 5073}, {2, 4, 3853}, {2, 5073, 15696}, {3, 10303, 15693}, {3, 17800, 17538}, {3, 3091, 5079}, {3, 3146, 1657}, {3, 381, 5072}, {3, 3830, 3146}, {3, 3843, 546}, {3, 3851, 3090}, {3, 4, 5076}, {3, 5070, 10303}, {3, 5072, 1656}, {3, 5073, 15704}, {3, 546, 381}, {4, 10151, 1598}, {4, 17578, 12101}, {4, 20, 15687}, {4, 3146, 12102}, {4, 3541, 13473}, {4, 3545, 17578}, {4, 3845, 3843}, {4, 3855, 3543}, {4, 3861, 14269}, {5, 30, 3523}, {5, 3530, 13735}, {5, 3860, 3854}, {5, 550, 10124}, {20, 15720, 14093}, {20, 3544, 632}, {20, 3850, 5055}, {20, 5055, 15720}, {30, 15700, 3534}, {30, 3832, 3851}, {30, 546, 3857}, {51, 46849, 18439}, {140, 17800, 15688}, {140, 3543, 17800}, {376, 3839, 3860}, {381, 15693, 3545}, {381, 5079, 3091}, {546, 12811, 3858}, {546, 12812, 3856}, {546, 15687, 3544}, {547, 15685, 15706}, {548, 5056, 15694}, {549, 3859, 5068}, {1656, 15700, 3526}, {2043, 2044, 15699}, {3091, 3146, 3525}, {3091, 3525, 5}, {3091, 3529, 3628}, {3146, 12102, 3830}, {3146, 3525, 12103}, {3146, 3544, 12100}, {3146, 3857, 15703}, {3523, 3525, 14869}, {3523, 3839, 3832}, {3526, 15720, 15702}, {3530, 5059, 15689}, {3533, 3854, 6917}, {3543, 15698, 30}, {3545, 10303, 12812}, {3545, 12101, 15684}, {3627, 3628, 3529}, {3830, 14269, 14893}, {3832, 15702, 3850}, {3843, 14269, 4}, {3845, 14893, 3839}, {3850, 15687, 20}, {3855, 17538, 15022}, {3858, 15704, 12811}, {3860, 12102, 12108}, {5056, 15682, 548}, {5059, 5071, 3530}, {5339, 42813, 42974}, {6447, 43879, 13903}, {6560, 43880, 6448}, {6561, 43879, 6447}, {6891, 15701, 15698}, {7486, 11001, 15712}, {7887, 14042, 11159}, {10109, 15683, 15707}, {10110, 16194, 34783}, {10110, 34783, 13321}, {10124, 15693, 5054}, {10303, 11541, 550}, {10303, 12812, 5070}, {10303, 17578, 11541}, {10895, 18514, 9668}, {10896, 18513, 9655}, {11485, 42106, 42962}, {11486, 42103, 42963}, {11541, 12812, 3}, {11737, 15712, 7486}, {12102, 12103, 3627}, {12811, 15704, 2}, {14093, 15702, 15700}, {14784, 14785, 10299}, {15022, 17538, 140}, {15687, 15720, 382}, {16808, 42126, 42817}, {16809, 42127, 42818}, {17538, 17548, 15759}, {18358, 51538, 55584}, {18492, 22793, 5790}, {18586, 18587, 15681}, {23261, 35786, 13665}, {39590, 44518, 15484}, {40273, 59387, 8148}, {42101, 42106, 11485}, {42101, 42166, 42160}, {42102, 42103, 11486}, {42102, 42163, 42161}, {42103, 42161, 42163}, {42106, 42160, 42166}, {42268, 42284, 3312}, {42269, 42283, 3311}, {42272, 42274, 6450}, {42276, 42583, 6456}, {43226, 43227, 6}

X(61985) = X(2)X(3)∩X(6)X(42478)

Barycentrics    11*a^4-13*(b^2-c^2)^2+2*a^2*(b^2+c^2) : :
X(61985) = -13*X[2]+8*X[3], -X[145]+16*X[18483], X[147]+4*X[9880], -2*X[182]+7*X[50964], X[193]+4*X[47353], 4*X[355]+X[50872], -4*X[551]+9*X[9779], 2*X[599]+3*X[51538], 4*X[946]+X[50864], X[962]+4*X[50796], 4*X[1351]+X[51215], 4*X[1352]+X[51028] and many others

X(61985) lies on these lines: {2, 3}, {6, 42478}, {7, 51792}, {13, 42133}, {14, 42134}, {17, 54578}, {18, 54579}, {61, 49874}, {62, 49873}, {83, 54815}, {98, 54476}, {145, 18483}, {147, 9880}, {182, 50964}, {193, 47353}, {262, 60113}, {275, 54552}, {315, 32874}, {316, 46951}, {355, 50872}, {371, 43504}, {372, 43503}, {395, 42683}, {396, 42682}, {485, 54543}, {486, 54542}, {524, 51537}, {542, 51170}, {551, 9779}, {590, 6439}, {598, 60147}, {599, 51538}, {615, 6440}, {671, 43951}, {946, 50864}, {962, 50796}, {1029, 54726}, {1131, 19054}, {1132, 19053}, {1327, 1588}, {1328, 1587}, {1351, 51215}, {1352, 51028}, {1353, 51173}, {1385, 50807}, {1699, 3241}, {1992, 53023}, {2052, 54923}, {2996, 7837}, {3058, 5261}, {3060, 46847}, {3068, 41952}, {3069, 41951}, {3087, 3163}, {3311, 14241}, {3312, 14226}, {3424, 53017}, {3590, 6425}, {3591, 6426}, {3616, 30308}, {3617, 18492}, {3621, 18480}, {3622, 31673}, {3623, 28204}, {3653, 33697}, {3679, 9812}, {3817, 34628}, {3818, 20080}, {3828, 9778}, {3926, 48913}, {3935, 18529}, {4678, 12699}, {4745, 9589}, {5032, 5480}, {5225, 11237}, {5229, 11238}, {5274, 5434}, {5286, 39563}, {5304, 53418}, {5318, 43365}, {5321, 43364}, {5334, 42905}, {5335, 42904}, {5339, 43202}, {5340, 43201}, {5343, 12817}, {5344, 12816}, {5346, 14537}, {5349, 42898}, {5350, 42899}, {5365, 41108}, {5366, 41107}, {5395, 54519}, {5435, 51790}, {5485, 54706}, {5587, 28232}, {5640, 13570}, {5656, 18376}, {5690, 50800}, {5691, 38314}, {5734, 51092}, {5818, 28198}, {5921, 18392}, {5965, 11180}, {5984, 41135}, {6054, 8596}, {6172, 59389}, {6199, 43313}, {6241, 44863}, {6395, 43312}, {6417, 43386}, {6418, 43387}, {6431, 42572}, {6432, 42573}, {6435, 43322}, {6436, 43323}, {6441, 7585}, {6442, 7586}, {6478, 22615}, {6479, 22644}, {6684, 51078}, {7739, 39590}, {7753, 14930}, {7757, 22682}, {7773, 32840}, {7776, 32880}, {7799, 32826}, {7802, 32870}, {7809, 32830}, {7811, 32893}, {7987, 50866}, {7989, 50808}, {7991, 51068}, {8165, 49732}, {8227, 51074}, {8972, 41945}, {9166, 39838}, {9541, 42602}, {9542, 42225}, {9612, 15933}, {9748, 11177}, {9780, 38076}, {9781, 46849}, {9802, 50906}, {9809, 50889}, {10056, 18514}, {10072, 18513}, {10248, 19925}, {10385, 10895}, {10513, 11185}, {10516, 54170}, {10519, 25561}, {10539, 13482}, {10575, 44871}, {10595, 50806}, {10707, 59390}, {10723, 52695}, {11002, 14831}, {11004, 18451}, {11057, 32885}, {11160, 54131}, {11381, 58470}, {11412, 46852}, {11454, 44106}, {11469, 51996}, {11488, 42940}, {11489, 42941}, {11531, 50801}, {11645, 51216}, {12111, 21849}, {12243, 22505}, {12571, 25055}, {12818, 35770}, {12819, 35771}, {13364, 61136}, {13474, 16226}, {13665, 43798}, {13785, 43797}, {13903, 43536}, {13941, 41946}, {13961, 54597}, {14458, 18845}, {14484, 41895}, {14488, 60625}, {14492, 38259}, {14683, 46686}, {14848, 39874}, {14881, 20105}, {14927, 47352}, {15052, 44413}, {16001, 36344}, {16002, 36319}, {16241, 43240}, {16242, 43241}, {16261, 16981}, {16267, 42160}, {16268, 42161}, {16644, 42140}, {16645, 42141}, {16960, 36970}, {16961, 36969}, {16962, 42921}, {16963, 42920}, {16964, 41119}, {16965, 41120}, {16966, 43400}, {16967, 43399}, {17037, 42854}, {17503, 60118}, {18482, 20059}, {18842, 60327}, {19875, 50803}, {19876, 34638}, {19883, 51076}, {19924, 40330}, {20014, 22791}, {20049, 34627}, {20085, 50908}, {20192, 61721}, {21356, 51024}, {21358, 50960}, {21969, 44870}, {22235, 49947}, {22236, 42518}, {22237, 49948}, {22238, 42519}, {22515, 35369}, {22793, 50810}, {23234, 39809}, {23249, 35823}, {23253, 35787}, {23259, 35822}, {23263, 35786}, {23267, 42540}, {23273, 42539}, {28158, 61264}, {28202, 61261}, {28208, 50863}, {28234, 31145}, {31363, 54893}, {31670, 54174}, {31672, 38073}, {31730, 46931}, {32532, 60328}, {32785, 53519}, {32786, 53518}, {32819, 32841}, {32823, 32879}, {32827, 32833}, {32907, 59394}, {32909, 59396}, {33698, 60331}, {33748, 38136}, {34781, 43838}, {35814, 43515}, {35815, 43516}, {36430, 40138}, {36961, 59378}, {36962, 59379}, {36990, 50959}, {36991, 59375}, {37640, 42093}, {37641, 42094}, {37665, 53419}, {37714, 51072}, {37832, 42104}, {37835, 42105}, {38064, 48884}, {38068, 46930}, {38072, 51171}, {39358, 43981}, {39884, 50974}, {40273, 50798}, {40693, 42520}, {40694, 42521}, {41036, 51484}, {41037, 51485}, {41112, 42972}, {41113, 42973}, {41121, 43369}, {41122, 43368}, {41869, 46933}, {41943, 42085}, {41944, 42086}, {42095, 43401}, {42096, 43104}, {42097, 43101}, {42098, 43402}, {42101, 42516}, {42102, 42517}, {42108, 42472}, {42109, 42473}, {42117, 43542}, {42118, 43543}, {42136, 43482}, {42137, 43481}, {42139, 42155}, {42142, 42154}, {42147, 42775}, {42148, 42776}, {42150, 49907}, {42151, 49908}, {42163, 49812}, {42164, 42494}, {42165, 42495}, {42166, 49813}, {42270, 43511}, {42273, 43512}, {42496, 42962}, {42497, 42963}, {42510, 43475}, {42511, 43476}, {42570, 43380}, {42571, 43381}, {42773, 43002}, {42774, 43003}, {42801, 54594}, {42802, 54593}, {42908, 42976}, {42909, 42977}, {42912, 43243}, {42913, 43242}, {42932, 43463}, {42933, 43464}, {43193, 43480}, {43194, 43479}, {43418, 44016}, {43419, 44015}, {43537, 54642}, {43562, 60292}, {43563, 60291}, {43681, 54582}, {43889, 53517}, {43890, 53520}, {44678, 47617}, {45103, 47586}, {46264, 46267}, {46934, 51705}, {47354, 51212}, {48310, 51131}, {48872, 51026}, {48876, 50957}, {48895, 54173}, {48901, 50967}, {50828, 50867}, {50829, 50874}, {50958, 55722}, {50977, 51213}, {50983, 51217}, {50984, 51164}, {50994, 53097}, {51041, 51063}, {51167, 53094}, {51176, 53091}, {51482, 59393}, {51483, 59395}, {51488, 52852}, {52835, 61023}, {52836, 59377}, {53015, 61304}, {53099, 54896}, {53513, 56618}, {53516, 56619}, {54477, 60145}, {54494, 60336}, {54601, 60162}, {54623, 60167}, {54646, 54921}, {54688, 55027}, {54717, 60639}, {54762, 60174}, {54765, 60166}, {54794, 60158}, {54856, 60105}, {54890, 60635}, {54892, 60618}, {59385, 60984}, {60132, 60650}, {60281, 60324}

X(61985) = midpoint of X(i) and X(j) for these {i,j}: {2, 17578}, {382, 15695}, {1656, 3830}, {3543, 15692}, {3627, 15713}, {3859, 12101}, {7987, 50866}, {15682, 17538}, {51167, 53094}
X(61985) = reflection of X(i) in X(j) for these {i,j}: {10595, 50806}, {11001, 15696}, {15692, 5071}, {15693, 5}, {15695, 632}, {15696, 15713}, {15697, 631}, {15711, 12812}, {15714, 547}, {17538, 15693}, {2, 3091}, {376, 15694}, {3522, 2}, {3534, 15712}, {3616, 30308}, {3843, 3845}, {40330, 50956}, {5071, 381}, {5818, 50799}, {51072, 37714}, {51092, 5734}, {51176, 53091}, {632, 5066}, {8227, 51074}
X(61985) = inverse of X(50687) in orthocentroidal circle
X(61985) = inverse of X(50687) in Yff hyperbola
X(61985) = complement of X(62129)
X(61985) = anticomplement of X(15692)
X(61985) = pole of line {523, 50687} with respect to the orthocentroidal circle
X(61985) = pole of line {6, 43507} with respect to the Kiepert hyperbola
X(61985) = pole of line {525, 44568} with respect to the Steiner circumellipse
X(61985) = pole of line {523, 50687} with respect to the Yff hyperbola
X(61985) = pole of line {69, 15705} with respect to the Wallace hyperbola
X(61985) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(54923)}}, {{A, B, C, X(5), X(54552)}}, {{A, B, C, X(68), X(44682)}}, {{A, B, C, X(69), X(15705)}}, {{A, B, C, X(264), X(50687)}}, {{A, B, C, X(265), X(15693)}}, {{A, B, C, X(297), X(54476)}}, {{A, B, C, X(427), X(54815)}}, {{A, B, C, X(451), X(54726)}}, {{A, B, C, X(458), X(60113)}}, {{A, B, C, X(468), X(43951)}}, {{A, B, C, X(472), X(54579)}}, {{A, B, C, X(473), X(54578)}}, {{A, B, C, X(1217), X(5076)}}, {{A, B, C, X(1494), X(3522)}}, {{A, B, C, X(1585), X(54543)}}, {{A, B, C, X(1586), X(54542)}}, {{A, B, C, X(3346), X(12103)}}, {{A, B, C, X(3524), X(54585)}}, {{A, B, C, X(3525), X(60121)}}, {{A, B, C, X(3533), X(31363)}}, {{A, B, C, X(3535), X(43567)}}, {{A, B, C, X(3536), X(43566)}}, {{A, B, C, X(3541), X(54886)}}, {{A, B, C, X(3853), X(18855)}}, {{A, B, C, X(4232), X(54706)}}, {{A, B, C, X(4846), X(34200)}}, {{A, B, C, X(5067), X(60122)}}, {{A, B, C, X(5071), X(54512)}}, {{A, B, C, X(5084), X(54932)}}, {{A, B, C, X(5094), X(60147)}}, {{A, B, C, X(6353), X(54520)}}, {{A, B, C, X(6819), X(54762)}}, {{A, B, C, X(6820), X(54765)}}, {{A, B, C, X(7392), X(54704)}}, {{A, B, C, X(8801), X(13473)}}, {{A, B, C, X(8889), X(54519)}}, {{A, B, C, X(10304), X(35510)}}, {{A, B, C, X(11001), X(54924)}}, {{A, B, C, X(11331), X(18845)}}, {{A, B, C, X(12108), X(32533)}}, {{A, B, C, X(14069), X(54828)}}, {{A, B, C, X(14458), X(52299)}}, {{A, B, C, X(14484), X(52290)}}, {{A, B, C, X(14492), X(38282)}}, {{A, B, C, X(14860), X(50688)}}, {{A, B, C, X(15681), X(16251)}}, {{A, B, C, X(15683), X(36889)}}, {{A, B, C, X(15687), X(18850)}}, {{A, B, C, X(15689), X(18550)}}, {{A, B, C, X(15702), X(54838)}}, {{A, B, C, X(15721), X(43699)}}, {{A, B, C, X(15740), X(58188)}}, {{A, B, C, X(17505), X(55858)}}, {{A, B, C, X(21400), X(55863)}}, {{A, B, C, X(32951), X(54551)}}, {{A, B, C, X(33278), X(57857)}}, {{A, B, C, X(37119), X(54844)}}, {{A, B, C, X(37276), X(54766)}}, {{A, B, C, X(38259), X(52289)}}, {{A, B, C, X(41895), X(52288)}}, {{A, B, C, X(47586), X(52293)}}, {{A, B, C, X(52252), X(54688)}}, {{A, B, C, X(52283), X(53101)}}, {{A, B, C, X(52284), X(60327)}}, {{A, B, C, X(52292), X(60118)}}, {{A, B, C, X(53857), X(60328)}}
X(61985) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15702, 17678}, {2, 20, 15705}, {2, 30, 3522}, {2, 3543, 15683}, {2, 3545, 15022}, {2, 3839, 3832}, {2, 3854, 3545}, {3, 381, 11737}, {4, 10151, 6995}, {4, 18386, 7378}, {4, 3090, 3853}, {4, 3091, 17578}, {4, 3545, 3830}, {4, 376, 15687}, {4, 3845, 3839}, {4, 3855, 3627}, {4, 631, 5076}, {4, 8889, 13473}, {5, 15681, 15702}, {5, 30, 15693}, {20, 10304, 15690}, {20, 13735, 15717}, {20, 3091, 1656}, {20, 546, 3854}, {30, 12812, 15711}, {30, 15693, 17538}, {30, 15696, 11001}, {30, 15712, 3534}, {30, 15713, 15696}, {30, 381, 5071}, {30, 3845, 3843}, {30, 5066, 632}, {30, 547, 15714}, {30, 631, 15697}, {30, 632, 15695}, {376, 15687, 3543}, {376, 15702, 14891}, {376, 5071, 15694}, {376, 547, 15721}, {381, 14269, 14893}, {381, 14893, 4}, {381, 15681, 5}, {381, 15684, 547}, {381, 15703, 5066}, {381, 15723, 3851}, {381, 382, 15703}, {547, 15687, 15684}, {1656, 3843, 546}, {1657, 15699, 15698}, {1657, 3856, 3544}, {1699, 34648, 3241}, {2043, 2044, 5067}, {3090, 15715, 10124}, {3146, 3832, 5068}, {3146, 3854, 13735}, {3522, 17578, 3146}, {3522, 3832, 3091}, {3523, 3839, 3860}, {3524, 5066, 5056}, {3525, 3545, 10109}, {3529, 3850, 7486}, {3534, 10124, 15715}, {3543, 3839, 381}, {3543, 5056, 15686}, {3544, 15698, 15699}, {3545, 11001, 16239}, {3545, 15682, 10299}, {3545, 3830, 20}, {3627, 3855, 3523}, {3627, 3860, 5055}, {3628, 15689, 15719}, {3628, 6867, 5079}, {3830, 15690, 15682}, {3839, 15697, 3858}, {3845, 3861, 14269}, {3858, 5076, 631}, {3860, 5055, 3855}, {5055, 15696, 15713}, {5072, 15685, 11539}, {5480, 51023, 5032}, {10109, 15688, 3525}, {10124, 15715, 15708}, {10248, 19925, 20070}, {10248, 53620, 50865}, {10299, 15690, 10304}, {10299, 15702, 549}, {10304, 15682, 5059}, {11539, 15685, 3528}, {12811, 17800, 3533}, {13570, 32062, 5640}, {14891, 15681, 376}, {15022, 15705, 2}, {15640, 16857, 15689}, {15682, 15702, 15681}, {15682, 17538, 30}, {15686, 15703, 3524}, {15692, 15697, 14093}, {15712, 15715, 15692}, {16268, 42161, 49875}, {16371, 16866, 16417}, {16417, 16861, 16408}, {18586, 18587, 15704}, {19924, 50956, 40330}, {21356, 51024, 61044}, {28198, 50799, 5818}, {36970, 42106, 43403}, {36990, 50959, 59373}, {41112, 42972, 42999}, {41113, 42973, 42998}, {42109, 42473, 43870}, {42478, 42479, 6}, {47352, 51022, 14927}

X(61986) = X(2)X(3)∩X(395)X(42689)

Barycentrics    29*a^4-34*(b^2-c^2)^2+5*a^2*(b^2+c^2) : :
X(61986) = -34*X[2]+21*X[3], -15*X[1699]+2*X[51087], -8*X[4745]+21*X[50800], -8*X[8584]+21*X[51173], 4*X[14711]+9*X[22728], X[15534]+12*X[48889], -16*X[41152]+3*X[55580], 8*X[47353]+5*X[51172], 3*X[48661]+10*X[51066], -21*X[50807]+8*X[51108], -5*X[50809]+18*X[61260], -2*X[50830]+15*X[59387] and many others

X(61986) lies on these lines: {2, 3}, {395, 42689}, {396, 42688}, {598, 54852}, {1699, 51087}, {4745, 50800}, {5318, 42968}, {5321, 42969}, {6221, 43568}, {6398, 43569}, {6500, 60308}, {6501, 60307}, {8584, 51173}, {10653, 42690}, {10654, 42691}, {11485, 42502}, {11486, 42503}, {12816, 42975}, {12817, 42974}, {14492, 60630}, {14711, 22728}, {15534, 48889}, {33606, 42533}, {33607, 42532}, {36969, 42963}, {36970, 42962}, {41100, 43368}, {41101, 43369}, {41107, 42816}, {41108, 42815}, {41119, 42101}, {41120, 42102}, {41121, 42126}, {41122, 42127}, {41152, 55580}, {42103, 49859}, {42106, 49860}, {42119, 43246}, {42120, 43247}, {42125, 42507}, {42128, 42506}, {42129, 46334}, {42132, 46335}, {42135, 49826}, {42136, 49862}, {42137, 49861}, {42138, 49827}, {42139, 43109}, {42142, 43108}, {42153, 43491}, {42154, 43476}, {42155, 43475}, {42156, 43492}, {42268, 43562}, {42269, 43563}, {42283, 43380}, {42284, 43381}, {42417, 43504}, {42418, 43503}, {42474, 43467}, {42475, 43468}, {42504, 42795}, {42505, 42796}, {42518, 43301}, {42519, 43300}, {42684, 42950}, {42685, 42951}, {42694, 42973}, {42695, 42972}, {42964, 42988}, {42965, 42989}, {42976, 43013}, {42977, 43012}, {43022, 49903}, {43023, 49904}, {43110, 43771}, {43111, 43772}, {43312, 60300}, {43313, 60299}, {43544, 54574}, {43545, 54575}, {45103, 60323}, {47353, 51172}, {48661, 51066}, {50807, 51108}, {50809, 61260}, {50830, 59387}, {50869, 61263}, {50957, 50991}, {50960, 55610}, {51140, 53023}, {51164, 55649}, {53106, 54643}, {53107, 54608}, {54477, 60649}, {54493, 60192}, {54582, 60250}, {54646, 60175}, {54890, 60228}, {60282, 60326}

X(61986) = midpoint of X(i) and X(j) for these {i,j}: {3543, 10299}
X(61986) = reflection of X(i) in X(j) for these {i,j}: {5079, 381}
X(61986) = inverse of X(62010) in orthocentroidal circle
X(61986) = inverse of X(62010) in Yff hyperbola
X(61986) = pole of line {523, 62010} with respect to the orthocentroidal circle
X(61986) = pole of line {6, 62010} with respect to the Kiepert hyperbola
X(61986) = pole of line {523, 62010} with respect to the Yff hyperbola
X(61986) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3530), X(54585)}}, {{A, B, C, X(5079), X(54512)}}, {{A, B, C, X(5094), X(54852)}}, {{A, B, C, X(15681), X(54924)}}, {{A, B, C, X(15690), X(18550)}}, {{A, B, C, X(52289), X(60630)}}, {{A, B, C, X(52293), X(60323)}}, {{A, B, C, X(52297), X(54643)}}, {{A, B, C, X(52298), X(54608)}}
X(61986) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15682, 15686}, {2, 17538, 12100}, {2, 3534, 15706}, {2, 3845, 3843}, {4, 10304, 15687}, {4, 15022, 3853}, {4, 3526, 5076}, {4, 3839, 549}, {30, 381, 5079}, {381, 15706, 5072}, {381, 15720, 3545}, {381, 3830, 15693}, {381, 5076, 15688}, {382, 1656, 12103}, {382, 3839, 381}, {547, 5054, 2049}, {550, 6893, 140}, {1657, 5072, 3526}, {3522, 12103, 6882}, {3522, 15686, 15689}, {3534, 5054, 15759}, {3543, 10299, 30}, {3830, 11001, 382}, {3843, 14269, 14893}, {3845, 12101, 3839}, {3856, 11812, 5066}, {3856, 15687, 10304}, {3857, 15683, 5055}, {5055, 14893, 2050}, {5055, 15684, 548}, {10109, 15712, 2}, {10304, 15685, 3534}, {11001, 12101, 3830}, {11001, 15710, 15697}, {14892, 15718, 1656}, {15682, 15759, 17800}, {15684, 15706, 1657}

X(61987) = X(2)X(3)∩X(165)X(51078)

Barycentrics    25*a^4-29*(b^2-c^2)^2+4*a^2*(b^2+c^2) : :
X(61987) = -29*X[2]+18*X[3], -3*X[165]+14*X[51078], -9*X[944]+20*X[51104], -12*X[1699]+X[50818], -15*X[3817]+4*X[51080], -12*X[3818]+X[50992], -10*X[4669]+21*X[61256], -4*X[4745]+15*X[18492], 6*X[5050]+5*X[51216], -16*X[5476]+5*X[51176], -15*X[5587]+4*X[50814], -15*X[5603]+4*X[51082] and many others

X(61987) lies on these lines: {2, 3}, {165, 51078}, {262, 54647}, {459, 54924}, {944, 51104}, {1327, 23273}, {1328, 23267}, {1699, 50818}, {3068, 43504}, {3069, 43503}, {3817, 51080}, {3818, 50992}, {4669, 61256}, {4745, 18492}, {5050, 51216}, {5318, 49824}, {5321, 49825}, {5476, 51176}, {5478, 36318}, {5479, 36320}, {5485, 54582}, {5587, 50814}, {5603, 51082}, {5702, 36430}, {5731, 50807}, {6199, 54543}, {6395, 54542}, {7773, 32896}, {7838, 60219}, {9166, 41151}, {9812, 61257}, {10165, 50866}, {10246, 50863}, {10516, 50970}, {10653, 43011}, {10654, 43010}, {11180, 51187}, {11455, 58470}, {11648, 14482}, {12699, 51072}, {12816, 33603}, {12817, 33602}, {12820, 42521}, {12821, 42520}, {14226, 43562}, {14241, 43563}, {14458, 60281}, {14492, 32532}, {14494, 54478}, {14639, 41154}, {14853, 51136}, {16261, 21969}, {16808, 43476}, {16809, 43475}, {16960, 43488}, {16961, 43487}, {16962, 42775}, {16963, 42776}, {16964, 49811}, {16965, 49810}, {17503, 60127}, {18362, 46453}, {18482, 60971}, {18483, 51093}, {18525, 51092}, {18840, 54813}, {18842, 54477}, {21356, 48895}, {22794, 33624}, {22795, 33622}, {22796, 35750}, {22797, 36331}, {23249, 53520}, {23259, 53517}, {25406, 50964}, {26446, 50873}, {31145, 61253}, {31670, 50990}, {31673, 51105}, {31884, 51133}, {32817, 48913}, {33604, 42128}, {33605, 42125}, {34648, 51091}, {35770, 60306}, {35771, 60305}, {35786, 42570}, {35787, 42571}, {36969, 43368}, {36970, 43369}, {38021, 41150}, {38072, 41153}, {38074, 51070}, {38127, 50865}, {39284, 54838}, {41100, 42103}, {41101, 42106}, {41107, 43227}, {41108, 43226}, {41112, 44015}, {41113, 44016}, {41119, 42986}, {41120, 42987}, {41121, 42589}, {41122, 42588}, {41869, 51069}, {41895, 54707}, {42093, 49827}, {42094, 49826}, {42099, 42515}, {42100, 42514}, {42101, 49947}, {42102, 49948}, {42111, 43399}, {42114, 43400}, {42117, 43478}, {42118, 43477}, {42119, 49907}, {42120, 49908}, {42133, 42693}, {42134, 42692}, {42139, 42510}, {42140, 43645}, {42141, 43646}, {42142, 42511}, {42143, 43494}, {42146, 43493}, {42160, 42532}, {42161, 42533}, {42274, 42524}, {42277, 42525}, {42283, 42572}, {42284, 42573}, {42417, 42578}, {42418, 42579}, {42516, 43778}, {42517, 43777}, {42557, 53131}, {42558, 53130}, {42576, 52046}, {42577, 52045}, {42982, 43553}, {42983, 43552}, {43202, 61719}, {43242, 54579}, {43243, 54578}, {43366, 43484}, {43367, 43483}, {43386, 43567}, {43387, 43566}, {43446, 43633}, {43447, 43632}, {43536, 52047}, {45103, 60150}, {47353, 51178}, {47354, 51189}, {48910, 51143}, {50800, 59417}, {50802, 51106}, {50810, 51067}, {50813, 54447}, {50817, 59388}, {50864, 61287}, {50874, 61264}, {50967, 51142}, {50974, 53023}, {51188, 54132}, {51705, 61271}, {52048, 54597}, {53101, 54612}, {54512, 54531}, {54519, 60284}, {54520, 54637}, {54523, 54896}, {54585, 54867}, {54642, 60185}, {54643, 54720}, {54660, 54791}, {54667, 60120}, {54717, 60637}, {54759, 54789}, {54762, 54827}, {54764, 54942}, {54766, 54947}, {54772, 54879}, {54778, 54809}

X(61987) = midpoint of X(i) and X(j) for these {i,j}: {3543, 15717}
X(61987) = reflection of X(i) in X(j) for these {i,j}: {15715, 5056}, {15718, 5}, {15721, 5072}, {376, 3525}, {5056, 381}
X(61987) = inverse of X(62009) in orthocentroidal circle
X(61987) = inverse of X(62009) in Yff hyperbola
X(61987) = anticomplement of X(15716)
X(61987) = pole of line {523, 62009} with respect to the orthocentroidal circle
X(61987) = pole of line {6, 62009} with respect to the Kiepert hyperbola
X(61987) = pole of line {523, 62009} with respect to the Yff hyperbola
X(61987) = pole of line {69, 15711} with respect to the Wallace hyperbola
X(61987) = intersection, other than A, B, C, of circumconics {{A, B, C, X(20), X(54924)}}, {{A, B, C, X(69), X(15711)}}, {{A, B, C, X(140), X(54838)}}, {{A, B, C, X(265), X(15718)}}, {{A, B, C, X(458), X(54647)}}, {{A, B, C, X(1656), X(54667)}}, {{A, B, C, X(3521), X(58192)}}, {{A, B, C, X(3523), X(54585)}}, {{A, B, C, X(4232), X(54582)}}, {{A, B, C, X(5056), X(54512)}}, {{A, B, C, X(5076), X(18854)}}, {{A, B, C, X(6995), X(54813)}}, {{A, B, C, X(14492), X(53857)}}, {{A, B, C, X(15685), X(36889)}}, {{A, B, C, X(15687), X(18852)}}, {{A, B, C, X(32532), X(52289)}}, {{A, B, C, X(35486), X(54809)}}, {{A, B, C, X(46219), X(54763)}}, {{A, B, C, X(46935), X(60122)}}, {{A, B, C, X(52284), X(54477)}}, {{A, B, C, X(52290), X(54707)}}, {{A, B, C, X(52292), X(60127)}}, {{A, B, C, X(52293), X(60150)}}, {{A, B, C, X(54660), X(55856)}}
X(61987) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15640, 15690}, {2, 15690, 3524}, {2, 20, 15711}, {2, 3543, 15685}, {2, 3839, 3860}, {2, 5076, 6834}, {4, 3524, 15687}, {4, 3544, 3853}, {4, 3843, 3090}, {4, 5067, 5076}, {5, 30, 15718}, {30, 381, 5056}, {30, 5056, 15715}, {30, 5072, 15721}, {376, 3523, 15710}, {376, 3830, 15682}, {381, 10304, 3544}, {381, 3830, 12100}, {381, 3853, 10304}, {381, 631, 3545}, {382, 10109, 15697}, {382, 17578, 6934}, {550, 11539, 14891}, {550, 3090, 631}, {1010, 15704, 3}, {3068, 43504, 43522}, {3069, 43503, 43521}, {3146, 12100, 11001}, {3146, 3839, 381}, {3523, 5070, 3525}, {3543, 15717, 30}, {3543, 3839, 3854}, {3543, 3854, 5054}, {3545, 15682, 15698}, {3830, 12100, 3146}, {3830, 3845, 3839}, {3830, 3860, 2}, {3839, 14893, 4}, {3845, 14893, 3830}, {3845, 5066, 3843}, {5054, 12102, 3543}, {5054, 14891, 3523}, {5054, 15703, 16239}, {5056, 11001, 15719}, {6891, 15716, 15759}, {8226, 17578, 15696}, {10109, 15697, 15702}, {11001, 12100, 376}, {15682, 15698, 3529}, {17578, 17579, 15683}

X(61988) = X(2)X(3)∩X(53)X(15860)

Barycentrics    8*a^4-9*(b^2-c^2)^2+a^2*(b^2+c^2) : :
X(61988) = -27*X[2]+17*X[3], 3*X[51]+2*X[32137], -9*X[141]+4*X[55597], 2*X[143]+3*X[16194], 9*X[355]+X[58245], -4*X[575]+9*X[38136], 2*X[576]+3*X[39884], -7*X[946]+2*X[32900], 2*X[962]+3*X[59400], -X[1353]+6*X[53023], -X[1483]+6*X[1699], -9*X[1484]+4*X[38631] and many others

X(61988) lies on these lines: {2, 3}, {51, 32137}, {53, 15860}, {61, 42101}, {62, 42102}, {141, 55597}, {143, 16194}, {355, 58245}, {395, 43012}, {396, 43013}, {495, 18514}, {496, 18513}, {517, 4537}, {575, 38136}, {576, 39884}, {946, 32900}, {952, 16189}, {962, 59400}, {1173, 17505}, {1353, 53023}, {1483, 1699}, {1484, 38631}, {1503, 22234}, {1539, 36253}, {1698, 28182}, {3411, 42909}, {3412, 42908}, {3521, 46848}, {3527, 18296}, {3592, 42269}, {3594, 42268}, {3619, 55620}, {3656, 61297}, {3818, 55721}, {3917, 11017}, {5007, 53418}, {5237, 42107}, {5238, 42110}, {5254, 41940}, {5339, 43416}, {5340, 43417}, {5346, 18907}, {5349, 42813}, {5350, 42814}, {5351, 42109}, {5352, 42108}, {5365, 42974}, {5366, 42975}, {5480, 22330}, {5609, 46686}, {5691, 10283}, {5790, 10248}, {5818, 28216}, {5876, 46847}, {5893, 18376}, {5943, 44871}, {5946, 13474}, {5965, 21850}, {6101, 40247}, {6102, 46849}, {6243, 16261}, {6419, 42283}, {6420, 42284}, {6425, 18538}, {6426, 18762}, {6427, 23259}, {6428, 23249}, {6447, 13925}, {6448, 13993}, {6451, 43406}, {6452, 43405}, {6453, 42225}, {6454, 42226}, {6488, 35255}, {6489, 35256}, {6749, 61314}, {7687, 51522}, {7728, 15044}, {7772, 53419}, {7982, 37705}, {7991, 18357}, {8227, 28190}, {8718, 46865}, {9612, 15935}, {9656, 15170}, {9779, 51700}, {9812, 61510}, {9955, 58232}, {10095, 11381}, {10113, 38791}, {10147, 42263}, {10148, 42264}, {10222, 18483}, {10263, 44870}, {10264, 38626}, {10386, 10895}, {10575, 13364}, {11488, 42888}, {11489, 42889}, {11531, 61253}, {11542, 42160}, {11543, 42161}, {11698, 38629}, {11801, 15054}, {12121, 15029}, {12245, 58249}, {12571, 33697}, {12699, 38138}, {13451, 34783}, {13491, 15012}, {13570, 40647}, {13598, 15060}, {13630, 32062}, {14449, 18435}, {14677, 20397}, {14843, 61137}, {14855, 32205}, {14915, 15026}, {15025, 61548}, {15048, 39590}, {15178, 31673}, {15619, 20414}, {15807, 61139}, {16657, 45731}, {16659, 43575}, {16808, 42164}, {16809, 42165}, {16881, 18439}, {16960, 42117}, {16961, 42118}, {16964, 42633}, {16965, 42634}, {16982, 45187}, {17852, 42262}, {18358, 53097}, {18480, 28234}, {18492, 28174}, {19106, 42599}, {19107, 42598}, {19116, 23251}, {19117, 23261}, {19130, 55704}, {19925, 28232}, {21167, 48943}, {22236, 42106}, {22238, 42103}, {22251, 38795}, {22331, 43291}, {22505, 38734}, {22515, 38745}, {22660, 45184}, {22681, 32521}, {22682, 32448}, {22791, 58240}, {22793, 28228}, {22938, 38757}, {24206, 55617}, {28164, 31666}, {28178, 61261}, {28202, 31399}, {29012, 55698}, {29181, 55600}, {29317, 55623}, {30389, 61272}, {30531, 36966}, {31162, 61249}, {31454, 42639}, {31652, 43457}, {31672, 38137}, {32138, 34417}, {32365, 32367}, {32533, 52518}, {32536, 35728}, {34380, 51537}, {34573, 55644}, {34584, 38729}, {34773, 61273}, {35786, 42215}, {35787, 42216}, {35820, 43880}, {35821, 43879}, {36836, 42104}, {36843, 42105}, {36969, 42778}, {36970, 42777}, {36990, 59399}, {38022, 50862}, {38042, 51118}, {38079, 51022}, {38081, 50865}, {38083, 50869}, {38110, 48884}, {38229, 39838}, {38628, 51872}, {40330, 55595}, {41869, 61259}, {42087, 42581}, {42088, 42580}, {42093, 42162}, {42094, 42159}, {42111, 42584}, {42112, 43103}, {42113, 43102}, {42114, 42585}, {42133, 42923}, {42134, 42922}, {42139, 42917}, {42140, 42627}, {42141, 42628}, {42142, 42916}, {42157, 43639}, {42158, 43640}, {42415, 42688}, {42416, 42689}, {42433, 43101}, {42434, 43104}, {42516, 42988}, {42517, 42989}, {42520, 42992}, {42521, 42993}, {42635, 42960}, {42636, 42961}, {42694, 43547}, {42695, 43546}, {42786, 55652}, {42894, 43206}, {42895, 43205}, {42900, 43011}, {42901, 43010}, {42906, 44015}, {42907, 44016}, {42912, 42921}, {42913, 42920}, {42954, 43637}, {42955, 43636}, {42962, 43466}, {42963, 43465}, {42986, 43474}, {42987, 43473}, {43008, 54591}, {43009, 54592}, {43207, 54580}, {43208, 54581}, {43463, 43649}, {43464, 43644}, {43621, 55626}, {43883, 45384}, {43884, 45385}, {45186, 45958}, {48874, 55611}, {48876, 48895}, {48901, 55583}, {48904, 55628}, {48906, 55708}, {48920, 51128}, {50823, 61255}, {51126, 55677}, {51163, 55606}, {51538, 55580}, {58242, 61248}, {59657, 61315}, {61260, 61524}, {61540, 61721}

X(61988) = midpoint of X(i) and X(j) for these {i,j}: {4, 3843}, {382, 3522}, {632, 3627}, {1656, 17578}, {3091, 5076}, {3543, 15693}, {3830, 5071}
X(61988) = reflection of X(i) in X(j) for these {i,j}: {1656, 3859}, {15686, 15711}, {15694, 5066}, {15696, 140}, {15711, 5071}, {15712, 5}, {3, 12812}, {3091, 546}, {3627, 5076}, {3858, 3843}, {5, 3858}, {550, 631}, {632, 3091}
X(61988) = inverse of X(62008) in orthocentroidal circle
X(61988) = inverse of X(62008) in Yff hyperbola
X(61988) = complement of X(62131)
X(61988) = anticomplement of X(61790)
X(61988) = pole of line {523, 62008} with respect to the orthocentroidal circle
X(61988) = pole of line {185, 12102} with respect to the Jerabek hyperbola
X(61988) = pole of line {6, 62008} with respect to the Kiepert hyperbola
X(61988) = pole of line {523, 62008} with respect to the Yff hyperbola
X(61988) = pole of line {69, 55667} with respect to the Wallace hyperbola
X(61988) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(140), X(17505)}}, {{A, B, C, X(265), X(15712)}}, {{A, B, C, X(631), X(18296)}}, {{A, B, C, X(1105), X(12102)}}, {{A, B, C, X(1173), X(17506)}}, {{A, B, C, X(3520), X(46848)}}, {{A, B, C, X(3521), X(33923)}}, {{A, B, C, X(3523), X(32533)}}, {{A, B, C, X(3531), X(55574)}}, {{A, B, C, X(6662), X(17800)}}, {{A, B, C, X(10124), X(60121)}}, {{A, B, C, X(10299), X(15077)}}, {{A, B, C, X(13599), X(55866)}}, {{A, B, C, X(14843), X(61138)}}, {{A, B, C, X(14860), X(15687)}}, {{A, B, C, X(15319), X(15691)}}, {{A, B, C, X(15690), X(54924)}}, {{A, B, C, X(15701), X(54585)}}, {{A, B, C, X(15720), X(21400)}}, {{A, B, C, X(18848), X(38335)}}, {{A, B, C, X(21735), X(31371)}}, {{A, B, C, X(22334), X(35477)}}, {{A, B, C, X(32534), X(52518)}}, {{A, B, C, X(40448), X(55861)}}, {{A, B, C, X(41983), X(43970)}}
X(61988) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 12812, 632}, {3, 3091, 12812}, {3, 3544, 3628}, {3, 381, 3544}, {3, 3857, 5}, {3, 4, 12102}, {3, 546, 3857}, {4, 14269, 3861}, {4, 18386, 13488}, {4, 3091, 5076}, {4, 381, 3853}, {4, 382, 12101}, {4, 3832, 3830}, {4, 5, 15687}, {4, 7547, 13473}, {5, 15704, 14869}, {5, 30, 15712}, {5, 550, 11539}, {20, 5079, 12108}, {30, 140, 15696}, {30, 15711, 15686}, {30, 3843, 3858}, {30, 3859, 1656}, {30, 5066, 15694}, {30, 546, 3091}, {51, 32137, 45957}, {140, 15696, 15711}, {381, 17504, 6944}, {381, 17800, 5056}, {381, 3830, 10304}, {382, 3090, 12103}, {382, 3839, 3850}, {382, 3851, 15710}, {547, 3857, 6911}, {548, 3860, 3851}, {549, 3845, 3839}, {631, 11001, 3522}, {1656, 17578, 30}, {1657, 3855, 547}, {3090, 12103, 549}, {3090, 15710, 3525}, {3091, 17578, 17538}, {3091, 3522, 3090}, {3091, 3843, 546}, {3091, 5071, 5072}, {3146, 10304, 3529}, {3523, 6857, 15702}, {3526, 3854, 11737}, {3529, 15686, 15704}, {3529, 5072, 140}, {3534, 5068, 16239}, {3543, 3851, 548}, {3543, 3860, 15699}, {3545, 5073, 3530}, {3628, 3853, 3146}, {3839, 11001, 381}, {3843, 15696, 3832}, {3843, 17578, 3859}, {3845, 3858, 3843}, {3850, 12101, 382}, {3850, 3853, 11001}, {3854, 15682, 3526}, {3857, 5059, 6914}, {3858, 17578, 15713}, {3861, 14893, 4}, {5056, 17800, 12100}, {5066, 12108, 5079}, {6887, 14093, 5054}, {6899, 15698, 3528}, {10095, 11381, 45956}, {10304, 15711, 15714}, {11539, 15712, 631}, {11541, 15022, 3}, {12100, 17800, 550}, {13596, 13621, 10226}, {13598, 46852, 15060}, {14269, 14893, 3845}, {14869, 15704, 8703}, {15687, 15704, 3627}, {15765, 18585, 3860}, {16960, 42682, 42117}, {16961, 42683, 42118}, {16982, 45959, 45187}, {18586, 18587, 15683}, {42101, 43226, 42138}, {42102, 43227, 42135}, {42104, 42146, 43630}, {42105, 42143, 43631}, {43012, 43023, 395}, {43013, 43022, 396}

X(61989) = X(2)X(3)∩X(13)X(43364)

Barycentrics    17*a^4-19*(b^2-c^2)^2+2*a^2*(b^2+c^2) : :
X(61989) = -19*X[2]+12*X[3], 3*X[165]+4*X[50869], 3*X[962]+4*X[4669], 6*X[1699]+X[50864], -X[3241]+8*X[18483], -3*X[3576]+10*X[51074], 5*X[3620]+16*X[48895], -12*X[3656]+5*X[51092], -8*X[3818]+X[11160], -5*X[4677]+12*X[50801], 4*X[4745]+3*X[50865], -3*X[5085]+10*X[51129] and many others

X(61989) lies on these lines: {2, 3}, {13, 43364}, {14, 43365}, {98, 54642}, {165, 50869}, {262, 54896}, {395, 42508}, {396, 42509}, {397, 43201}, {398, 43202}, {485, 54599}, {486, 54598}, {553, 51792}, {598, 54519}, {671, 54520}, {962, 4669}, {1131, 43563}, {1132, 43562}, {1327, 23259}, {1328, 23249}, {1699, 50864}, {2996, 54582}, {3068, 42417}, {3069, 42418}, {3241, 18483}, {3424, 45103}, {3576, 51074}, {3620, 48895}, {3622, 28208}, {3656, 51092}, {3818, 11160}, {4677, 50801}, {4745, 50865}, {5085, 51129}, {5261, 18514}, {5274, 18513}, {5304, 14537}, {5318, 43772}, {5321, 43771}, {5334, 12817}, {5335, 12816}, {5343, 61719}, {5395, 54477}, {5476, 33748}, {5657, 50799}, {5691, 51103}, {5731, 30308}, {5734, 51091}, {5921, 15534}, {6201, 13687}, {6202, 13807}, {6492, 41945}, {6493, 41946}, {6564, 42608}, {6565, 42609}, {6748, 45245}, {7581, 43561}, {7582, 43560}, {7917, 32836}, {7920, 18845}, {7921, 38259}, {7967, 50806}, {7988, 50866}, {7991, 51067}, {8584, 51023}, {8596, 22515}, {8796, 54585}, {8972, 43257}, {9143, 46686}, {9740, 44678}, {9779, 50811}, {9812, 50796}, {10033, 19569}, {10172, 50812}, {10248, 28194}, {10519, 50956}, {10653, 42507}, {10654, 42506}, {10723, 36521}, {11002, 16194}, {11178, 61044}, {11180, 48889}, {11185, 32892}, {11230, 50819}, {11439, 14831}, {11522, 51107}, {11538, 54942}, {11542, 43474}, {11543, 43473}, {11645, 42785}, {11648, 37665}, {12571, 34628}, {13482, 46261}, {13570, 15072}, {13639, 33457}, {13759, 33456}, {13846, 52666}, {13847, 52667}, {13886, 43520}, {13939, 43519}, {13941, 43256}, {14226, 42216}, {14241, 42215}, {14458, 53101}, {14484, 17503}, {14488, 60632}, {14492, 41895}, {14912, 50963}, {15024, 44871}, {15031, 32885}, {15052, 37672}, {15305, 21849}, {15533, 50958}, {16808, 42511}, {16809, 42510}, {16981, 18435}, {18480, 31145}, {18482, 60984}, {18492, 53620}, {18546, 23334}, {18842, 54815}, {19053, 42284}, {19054, 42283}, {19925, 34632}, {20049, 22791}, {20094, 22566}, {21969, 46847}, {22165, 51212}, {22235, 42160}, {22237, 42161}, {22240, 33880}, {22793, 38074}, {23253, 35823}, {23263, 35822}, {23302, 42932}, {23303, 42933}, {25154, 36344}, {25164, 36319}, {25406, 51022}, {28150, 51078}, {28154, 50813}, {28158, 50874}, {28160, 50807}, {28164, 50867}, {28174, 50800}, {28236, 51094}, {29012, 50964}, {29181, 51186}, {31162, 47745}, {31672, 59375}, {31673, 38314}, {31884, 51026}, {32006, 32874}, {32062, 58470}, {32532, 43951}, {32785, 43210}, {32786, 43209}, {32815, 48913}, {32827, 32896}, {33602, 42974}, {33603, 42975}, {33697, 46934}, {33698, 54521}, {34631, 40273}, {34648, 51093}, {35749, 41042}, {36327, 41043}, {36382, 59396}, {36383, 59394}, {36430, 52707}, {36969, 41120}, {36970, 41119}, {37640, 42101}, {37641, 42102}, {37714, 51070}, {38042, 50809}, {38176, 50810}, {38317, 50975}, {39593, 43448}, {39809, 52695}, {41100, 43005}, {41101, 43004}, {41107, 42134}, {41108, 42133}, {41121, 42106}, {41122, 42103}, {42085, 49907}, {42086, 49908}, {42093, 42982}, {42094, 42983}, {42095, 42792}, {42098, 42791}, {42099, 43643}, {42100, 43638}, {42104, 46335}, {42105, 46334}, {42126, 43542}, {42127, 43543}, {42139, 42941}, {42142, 42940}, {42154, 49862}, {42155, 49861}, {42159, 43775}, {42162, 43776}, {42262, 42607}, {42265, 42606}, {42502, 49813}, {42503, 49812}, {42504, 43400}, {42505, 43399}, {42512, 43645}, {42513, 43646}, {42576, 53518}, {42577, 53519}, {42602, 43408}, {42603, 43407}, {42631, 42910}, {42632, 42911}, {42795, 43240}, {42796, 43241}, {42854, 60874}, {42906, 43110}, {42907, 43111}, {42972, 42998}, {42973, 42999}, {43022, 43311}, {43023, 43310}, {43312, 43387}, {43313, 43386}, {43382, 43569}, {43383, 43568}, {47353, 51132}, {47354, 50990}, {47865, 59393}, {47866, 59395}, {50802, 50863}, {50803, 50873}, {50820, 61265}, {50829, 61264}, {50959, 51185}, {50960, 51029}, {50961, 54132}, {50991, 51024}, {50992, 51537}, {50993, 54170}, {51069, 51118}, {51131, 51167}, {51142, 53097}, {51143, 51163}, {51176, 59399}, {53099, 54478}, {54476, 60150}, {54493, 54522}, {54494, 54866}, {54512, 60161}, {54517, 54622}, {54531, 54552}, {54539, 54565}, {54595, 60300}, {54596, 60299}, {54623, 60172}, {54637, 54706}, {54647, 60118}, {54663, 54943}, {54688, 54766}, {54713, 54889}, {54717, 60200}, {54726, 54756}, {54758, 54794}, {54764, 54844}, {54789, 55027}, {54791, 60618}, {54795, 54862}, {54797, 54886}, {54813, 60285}, {54864, 54941}, {54867, 54923}, {54892, 60122}, {54893, 60121}, {54924, 56270}, {59385, 60963}, {60113, 60127}, {60147, 60281}, {60284, 60327}

X(61989) = midpoint of X(i) and X(j) for these {i,j}: {3523, 3543}, {3857, 15687}
X(61989) = reflection of X(i) in X(j) for these {i,j}: {15700, 5}, {15702, 3851}, {15703, 3857}, {376, 3526}, {3090, 381}, {3528, 15703}
X(61989) = inverse of X(62007) in orthocentroidal circle
X(61989) = inverse of X(62007) in Yff hyperbola
X(61989) = complement of X(62132)
X(61989) = anticomplement of X(15698)
X(61989) = pole of line {523, 62007} with respect to the orthocentroidal circle
X(61989) = pole of line {6, 62007} with respect to the Kiepert hyperbola
X(61989) = pole of line {523, 62007} with respect to the Yff hyperbola
X(61989) = pole of line {69, 61781} with respect to the Wallace hyperbola
X(61989) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(253), X(3534)}}, {{A, B, C, X(265), X(15700)}}, {{A, B, C, X(297), X(54642)}}, {{A, B, C, X(376), X(54924)}}, {{A, B, C, X(458), X(54896)}}, {{A, B, C, X(468), X(54520)}}, {{A, B, C, X(470), X(54580)}}, {{A, B, C, X(471), X(54581)}}, {{A, B, C, X(631), X(54585)}}, {{A, B, C, X(1217), X(12102)}}, {{A, B, C, X(1585), X(54599)}}, {{A, B, C, X(1586), X(54598)}}, {{A, B, C, X(3090), X(54512)}}, {{A, B, C, X(3424), X(52293)}}, {{A, B, C, X(3523), X(54923)}}, {{A, B, C, X(3525), X(54838)}}, {{A, B, C, X(3533), X(60121)}}, {{A, B, C, X(4846), X(45759)}}, {{A, B, C, X(5056), X(54552)}}, {{A, B, C, X(5067), X(54667)}}, {{A, B, C, X(5094), X(54519)}}, {{A, B, C, X(6143), X(54942)}}, {{A, B, C, X(6353), X(54582)}}, {{A, B, C, X(7714), X(54813)}}, {{A, B, C, X(8889), X(54477)}}, {{A, B, C, X(11331), X(53101)}}, {{A, B, C, X(14484), X(52292)}}, {{A, B, C, X(14492), X(52290)}}, {{A, B, C, X(15319), X(17538)}}, {{A, B, C, X(15695), X(18550)}}, {{A, B, C, X(15704), X(31361)}}, {{A, B, C, X(16045), X(54897)}}, {{A, B, C, X(16251), X(46333)}}, {{A, B, C, X(17503), X(52288)}}, {{A, B, C, X(18850), X(38335)}}, {{A, B, C, X(31363), X(46219)}}, {{A, B, C, X(37118), X(54941)}}, {{A, B, C, X(41895), X(52289)}}, {{A, B, C, X(43951), X(53857)}}, {{A, B, C, X(45103), X(52283)}}, {{A, B, C, X(52252), X(54789)}}, {{A, B, C, X(52284), X(54815)}}, {{A, B, C, X(52296), X(54870)}}, {{A, B, C, X(55856), X(60618)}}
X(61989) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12100, 10303}, {2, 15640, 15697}, {2, 15717, 15713}, {2, 3146, 3534}, {2, 3522, 15719}, {2, 3534, 15692}, {2, 3845, 3839}, {2, 5068, 10109}, {3, 381, 14892}, {4, 15682, 12101}, {4, 3545, 15687}, {4, 3855, 5076}, {4, 546, 17578}, {4, 631, 12102}, {5, 30, 15700}, {20, 15721, 10304}, {20, 3839, 381}, {30, 15703, 3528}, {30, 3526, 376}, {30, 381, 3090}, {30, 3851, 15702}, {30, 3857, 15703}, {140, 3146, 20}, {140, 381, 3545}, {381, 14269, 3861}, {381, 15689, 5}, {381, 3524, 5068}, {381, 3543, 15721}, {381, 3830, 8703}, {381, 5073, 15699}, {382, 3855, 17533}, {546, 15687, 15707}, {546, 17578, 5056}, {547, 3529, 15705}, {1657, 11737, 15709}, {3090, 15701, 2}, {3090, 3528, 140}, {3146, 10109, 6960}, {3523, 3543, 30}, {3523, 3832, 3091}, {3524, 15682, 15685}, {3526, 15716, 15701}, {3528, 3843, 3832}, {3534, 3843, 3860}, {3545, 15687, 3146}, {3545, 15692, 7486}, {3627, 15685, 15682}, {3830, 5066, 11001}, {3845, 3860, 3843}, {3855, 5076, 5059}, {3861, 12101, 3845}, {8703, 11812, 15716}, {8703, 12101, 3830}, {8703, 15699, 11812}, {8703, 15701, 15698}, {10109, 12101, 3627}, {10109, 15685, 3524}, {11108, 15714, 15708}, {11541, 15689, 15683}, {11812, 17578, 15640}, {12816, 41113, 5335}, {14269, 14893, 4}, {15687, 15692, 3543}, {15700, 15708, 3523}, {15703, 15707, 3526}, {30308, 50862, 5731}, {36969, 41120, 49875}, {36970, 41119, 49876}, {42134, 49824, 41107}, {43365, 54581, 49826}, {47354, 51538, 54174}, {51538, 54174, 51211}

X(61990) = X(2)X(3)∩X(6)X(43292)

Barycentrics    9*a^4-10*(b^2-c^2)^2+a^2*(b^2+c^2) : :
X(61990) = -30*X[2]+19*X[3], 3*X[568]+8*X[46849], -18*X[946]+7*X[61282], 3*X[962]+8*X[61255], -12*X[1699]+X[18526], -25*X[3763]+14*X[55633], 10*X[3818]+X[55722], 8*X[4301]+3*X[12645], -16*X[5097]+5*X[39899], 6*X[5102]+5*X[18440], 9*X[5790]+2*X[9589], 5*X[5881]+6*X[11278] and many others

X(61990) lies on these lines: {2, 3}, {6, 43292}, {17, 43245}, {18, 43244}, {371, 42578}, {372, 42579}, {568, 46849}, {946, 61282}, {962, 61255}, {1327, 6427}, {1328, 6428}, {1498, 15038}, {1699, 18526}, {3070, 43790}, {3071, 43789}, {3316, 9690}, {3317, 43415}, {3521, 14490}, {3531, 15749}, {3583, 9656}, {3585, 9671}, {3763, 55633}, {3818, 55722}, {4301, 12645}, {4330, 31479}, {5024, 31417}, {5041, 44518}, {5097, 39899}, {5102, 18440}, {5319, 53418}, {5334, 42906}, {5335, 42907}, {5343, 43416}, {5344, 43417}, {5351, 43399}, {5352, 43400}, {5790, 9589}, {5881, 11278}, {5882, 50806}, {6417, 23263}, {6418, 23253}, {6429, 35812}, {6430, 35813}, {6431, 13665}, {6432, 13785}, {6437, 13903}, {6438, 13961}, {6449, 53519}, {6450, 53518}, {6480, 42265}, {6481, 42262}, {6484, 42263}, {6485, 42264}, {6500, 23275}, {6501, 23269}, {6519, 43887}, {6522, 43888}, {6564, 31487}, {6748, 59655}, {6767, 31410}, {7765, 15484}, {7989, 31447}, {8148, 61249}, {8550, 50963}, {9588, 38140}, {9654, 9670}, {9655, 37720}, {9657, 9669}, {9668, 37719}, {9680, 42271}, {9681, 42273}, {9705, 11935}, {9781, 32137}, {9786, 15752}, {9955, 30392}, {10095, 11455}, {10194, 43209}, {10195, 43210}, {10247, 61290}, {10248, 18357}, {10263, 16261}, {10516, 55594}, {10575, 13570}, {10721, 20396}, {10895, 31480}, {10896, 37587}, {11477, 51175}, {11482, 51173}, {11531, 18480}, {11999, 38848}, {12279, 13364}, {12295, 38792}, {12355, 38745}, {12699, 38155}, {12702, 61258}, {12773, 59390}, {13093, 23324}, {13202, 38725}, {13321, 18439}, {13598, 54048}, {14483, 21400}, {14531, 18435}, {14848, 33749}, {15069, 37517}, {15602, 44519}, {15605, 15800}, {16200, 18525}, {16267, 42908}, {16268, 42909}, {16772, 42104}, {16773, 42105}, {16964, 42128}, {16965, 42125}, {18376, 34780}, {18436, 46847}, {18483, 37727}, {18492, 48661}, {18509, 22819}, {18510, 23251}, {18511, 22820}, {18512, 23261}, {18550, 57715}, {19106, 42891}, {19107, 42890}, {19116, 43312}, {19117, 43313}, {19130, 55703}, {20379, 38790}, {22615, 31454}, {22793, 37714}, {23236, 46686}, {23241, 61592}, {24206, 55618}, {29012, 55699}, {29317, 55622}, {29323, 55683}, {31467, 43457}, {31662, 33697}, {31673, 61276}, {32062, 37481}, {32205, 52093}, {34754, 42126}, {34755, 42127}, {36969, 42989}, {36970, 42988}, {36990, 39561}, {38735, 39838}, {38746, 39809}, {40107, 55591}, {40693, 42101}, {40694, 42102}, {42087, 42950}, {42088, 42951}, {42093, 42813}, {42094, 42814}, {42095, 43633}, {42096, 42488}, {42097, 42489}, {42098, 43632}, {42103, 42148}, {42106, 42147}, {42129, 43193}, {42132, 43194}, {42283, 43791}, {42284, 43792}, {42472, 42585}, {42473, 42584}, {42490, 42919}, {42491, 42918}, {42602, 43794}, {42603, 43793}, {42775, 42912}, {42776, 42913}, {42920, 42941}, {42921, 42940}, {42974, 42991}, {42975, 42990}, {43102, 43397}, {43103, 43398}, {43174, 50799}, {44456, 51537}, {47354, 55580}, {47355, 48942}, {48672, 52102}, {48675, 55038}, {48872, 55636}, {48884, 55695}, {48895, 55587}, {48901, 55582}, {48904, 55627}, {48905, 55688}, {48910, 55603}, {48943, 55645}, {50797, 51120}, {50954, 51166}, {50956, 51165}, {51027, 51172}, {51186, 55600}, {58233, 61273}, {58237, 61296}

X(61990) = midpoint of X(i) and X(j) for these {i,j}: {3543, 15719}
X(61990) = reflection of X(i) in X(j) for these {i,j}: {15717, 5}, {15720, 5072}, {3, 5056}, {3534, 15718}, {5070, 3855}
X(61990) = inverse of X(12102) in orthocentroidal circle
X(61990) = inverse of X(12102) in Yff hyperbola
X(61990) = complement of X(62133)
X(61990) = anticomplement of X(61789)
X(61990) = pole of line {523, 12102} with respect to the orthocentroidal circle
X(61990) = pole of line {185, 38335} with respect to the Jerabek hyperbola
X(61990) = pole of line {6, 12102} with respect to the Kiepert hyperbola
X(61990) = pole of line {523, 12102} with respect to the Yff hyperbola
X(61990) = pole of line {69, 55666} with respect to the Wallace hyperbola
X(61990) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(68), X(15698)}}, {{A, B, C, X(264), X(12102)}}, {{A, B, C, X(265), X(15717)}}, {{A, B, C, X(548), X(18550)}}, {{A, B, C, X(549), X(21400)}}, {{A, B, C, X(1105), X(38335)}}, {{A, B, C, X(3520), X(14490)}}, {{A, B, C, X(3521), X(10304)}}, {{A, B, C, X(3524), X(15749)}}, {{A, B, C, X(3527), X(35472)}}, {{A, B, C, X(3531), X(15750)}}, {{A, B, C, X(10303), X(17505)}}, {{A, B, C, X(11738), X(23040)}}, {{A, B, C, X(11812), X(54585)}}, {{A, B, C, X(12103), X(15318)}}, {{A, B, C, X(13599), X(55862)}}, {{A, B, C, X(13623), X(58186)}}, {{A, B, C, X(14483), X(21844)}}, {{A, B, C, X(15695), X(54924)}}, {{A, B, C, X(35473), X(57715)}}, {{A, B, C, X(55572), X(61137)}}
X(61990) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 12102}, {3, 15723, 15720}, {3, 3545, 1656}, {3, 3843, 3832}, {3, 3851, 547}, {3, 5055, 3533}, {3, 5056, 15723}, {3, 5059, 3534}, {3, 5073, 11001}, {4, 3091, 15687}, {4, 3146, 12101}, {4, 381, 5076}, {4, 3832, 3853}, {4, 3839, 3627}, {4, 546, 3830}, {5, 17578, 17800}, {5, 30, 15717}, {5, 382, 15696}, {20, 10299, 548}, {20, 13735, 10299}, {20, 15022, 631}, {20, 16239, 3}, {20, 3091, 13735}, {20, 3545, 16239}, {20, 3832, 3545}, {20, 5070, 15716}, {30, 3855, 5070}, {381, 15696, 5}, {381, 15720, 5072}, {381, 1657, 5079}, {381, 382, 3526}, {381, 3830, 15688}, {381, 5076, 1657}, {382, 1656, 20}, {546, 3627, 15022}, {546, 549, 3854}, {547, 3627, 5059}, {547, 3845, 3839}, {631, 3839, 3856}, {1656, 15716, 3525}, {1657, 5079, 15693}, {2041, 2042, 12103}, {3091, 10299, 10109}, {3091, 15687, 5073}, {3091, 5073, 5054}, {3146, 3533, 15686}, {3146, 3858, 5055}, {3522, 12811, 15703}, {3525, 3545, 5056}, {3525, 6950, 3090}, {3534, 3839, 381}, {3543, 15719, 30}, {3543, 3545, 15690}, {3543, 3832, 5067}, {3627, 3839, 3851}, {3832, 3845, 3843}, {3832, 5056, 3855}, {3832, 5067, 3850}, {3843, 14269, 3861}, {3853, 3861, 3845}, {3858, 12101, 3146}, {3860, 15704, 5068}, {5068, 15704, 15694}, {11317, 14062, 7866}, {14784, 14785, 15698}, {17578, 17800, 382}, {18586, 18587, 15685}, {43292, 43293, 6}

X(61991) = X(2)X(3)∩X(6)X(43781)

Barycentrics    11*a^4-12*(b^2-c^2)^2+a^2*(b^2+c^2) : :
X(61991) = -36*X[2]+23*X[3], 6*X[1539]+7*X[15044], -36*X[3655]+49*X[58235], 12*X[3818]+X[55724], 10*X[4301]+3*X[50804], -15*X[5050]+28*X[42785], -2*X[5493]+15*X[50799], 8*X[6053]+5*X[12902], X[6243]+12*X[46847], -5*X[7991]+18*X[38176], 5*X[8148]+8*X[47745], -22*X[10222]+9*X[61294] and many others

X(61991) lies on these lines: {2, 3}, {6, 43781}, {1539, 15044}, {3303, 18514}, {3304, 18513}, {3527, 17505}, {3531, 32533}, {3592, 35786}, {3594, 35787}, {3655, 58235}, {3818, 55724}, {4301, 50804}, {5050, 42785}, {5349, 42974}, {5350, 42975}, {5365, 43416}, {5366, 43417}, {5493, 50799}, {5708, 51792}, {6053, 12902}, {6199, 42269}, {6243, 46847}, {6395, 42268}, {6407, 42273}, {6408, 42270}, {6417, 42283}, {6418, 42284}, {6427, 23261}, {6428, 23251}, {6445, 42271}, {6446, 42272}, {6447, 35821}, {6448, 35820}, {6449, 43881}, {6450, 43882}, {6474, 8972}, {6475, 13941}, {6500, 23259}, {6501, 23249}, {6519, 42265}, {6522, 42262}, {7991, 38176}, {8148, 47745}, {9691, 42225}, {10222, 61294}, {10516, 55595}, {10541, 48884}, {10653, 43774}, {10654, 43773}, {10733, 15039}, {11477, 48889}, {11482, 48662}, {11485, 43226}, {11486, 43227}, {12308, 37493}, {12315, 18376}, {13903, 52666}, {13961, 52667}, {15020, 15046}, {15025, 15041}, {15027, 38790}, {15069, 51174}, {15077, 61137}, {16194, 16625}, {16960, 42688}, {16961, 42689}, {18383, 58795}, {18480, 51515}, {18482, 51514}, {18510, 23253}, {18512, 23263}, {18550, 22334}, {19130, 55701}, {21358, 55611}, {21400, 52518}, {22615, 43879}, {22644, 43880}, {23039, 46852}, {23267, 43312}, {23273, 43313}, {23324, 48672}, {24206, 55620}, {25561, 55600}, {25565, 51167}, {30389, 33697}, {31673, 37624}, {36969, 43019}, {36970, 43018}, {36990, 53092}, {37484, 40247}, {37545, 51790}, {37727, 58236}, {38072, 55708}, {38292, 61315}, {38633, 38729}, {38634, 38740}, {38635, 38751}, {38636, 38763}, {38638, 38795}, {38756, 59390}, {40107, 50957}, {42093, 42905}, {42094, 42904}, {42096, 42581}, {42097, 42580}, {42101, 42162}, {42102, 42159}, {42103, 42165}, {42104, 42598}, {42105, 42599}, {42106, 42164}, {42125, 42161}, {42126, 42166}, {42127, 42163}, {42128, 42160}, {42133, 43771}, {42134, 43772}, {42136, 42962}, {42137, 42963}, {42472, 42590}, {42473, 42591}, {42478, 42999}, {42479, 42998}, {42488, 43400}, {42489, 43399}, {42592, 42919}, {42593, 42918}, {42633, 43478}, {42634, 43477}, {42813, 43007}, {42814, 43006}, {42908, 43476}, {42909, 43475}, {42964, 43196}, {42965, 43195}, {43136, 53418}, {43369, 61719}, {43621, 55624}, {45958, 54048}, {47353, 55718}, {48895, 53097}, {48901, 55580}, {48904, 55626}, {48910, 55602}, {48942, 55681}, {48943, 55644}, {50955, 55721}, {51024, 55588}, {51163, 55604}, {58247, 59388}

X(61991) = reflection of X(i) in X(j) for these {i,j}: {10299, 5}, {3, 5079}
X(61991) = inverse of X(62006) in orthocentroidal circle
X(61991) = inverse of X(62006) in Yff hyperbola
X(61991) = anticomplement of X(61785)
X(61991) = pole of line {523, 62006} with respect to the orthocentroidal circle
X(61991) = pole of line {185, 62004} with respect to the Jerabek hyperbola
X(61991) = pole of line {6, 62006} with respect to the Kiepert hyperbola
X(61991) = pole of line {523, 62006} with respect to the Yff hyperbola
X(61991) = pole of line {69, 55664} with respect to the Wallace hyperbola
X(61991) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(265), X(10299)}}, {{A, B, C, X(631), X(17505)}}, {{A, B, C, X(3515), X(61137)}}, {{A, B, C, X(3521), X(21735)}}, {{A, B, C, X(3522), X(18550)}}, {{A, B, C, X(3523), X(21400)}}, {{A, B, C, X(3524), X(32533)}}, {{A, B, C, X(3527), X(17506)}}, {{A, B, C, X(3531), X(32534)}}, {{A, B, C, X(3534), X(15319)}}, {{A, B, C, X(12101), X(18848)}}, {{A, B, C, X(14860), X(38335)}}, {{A, B, C, X(15077), X(61138)}}, {{A, B, C, X(15713), X(54585)}}, {{A, B, C, X(15723), X(60121)}}, {{A, B, C, X(16835), X(23040)}}, {{A, B, C, X(19708), X(31371)}}, {{A, B, C, X(21844), X(52518)}}, {{A, B, C, X(22334), X(35473)}}, {{A, B, C, X(47599), X(60122)}}
X(61991) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 12103, 15695}, {3, 14869, 15718}, {3, 15684, 3529}, {3, 3091, 5055}, {3, 3627, 5073}, {4, 14269, 3843}, {4, 20, 12101}, {4, 3091, 12102}, {4, 3832, 15687}, {4, 3839, 3853}, {4, 546, 5076}, {5, 30, 10299}, {5, 5059, 15693}, {5, 550, 11540}, {140, 3627, 11541}, {140, 382, 15685}, {140, 3861, 3845}, {140, 5055, 5070}, {140, 8703, 15717}, {381, 15716, 14892}, {381, 3830, 15689}, {381, 5070, 3851}, {382, 15693, 5059}, {382, 15723, 1657}, {382, 1657, 15640}, {546, 3146, 5072}, {546, 3853, 12108}, {631, 11346, 16239}, {1656, 3853, 15684}, {3090, 15682, 17538}, {3090, 3525, 17697}, {3091, 11541, 140}, {3091, 12102, 382}, {3091, 15708, 15022}, {3529, 3839, 3857}, {3529, 4188, 3530}, {3543, 3544, 12103}, {3543, 3858, 3526}, {3627, 12811, 20}, {3627, 3857, 8703}, {3830, 3851, 17800}, {3839, 8703, 381}, {3843, 15695, 3858}, {3845, 11737, 3839}, {3845, 12102, 3091}, {3845, 15704, 546}, {3850, 17578, 3534}, {3851, 17800, 15694}, {3858, 12103, 3544}, {5059, 17538, 15704}, {5068, 10303, 3090}, {5072, 5076, 3146}, {11737, 15717, 1656}, {12101, 12811, 3627}, {12101, 15701, 3830}, {14869, 15696, 3}, {14892, 15716, 15703}, {15684, 15702, 15681}, {43781, 43782, 6}

X(61992) = X(1)X(50868)∩X(2)X(3)

Barycentrics    23*a^4-25*(b^2-c^2)^2+2*a^2*(b^2+c^2) : :
X(61992) = 5*X[1]+4*X[50868], -25*X[2]+16*X[3], 5*X[8]+4*X[51120], 5*X[10]+4*X[51119], 5*X[69]+4*X[51166], 5*X[141]+4*X[51165], X[145]+8*X[34648], 5*X[193]+4*X[51027], 5*X[1698]+4*X[50869], 5*X[3616]+4*X[50862], 5*X[3617]+4*X[50865], 5*X[3618]+4*X[51022] and many others

X(61992) lies on these lines: {1, 50868}, {2, 3}, {6, 42539}, {8, 51120}, {10, 51119}, {69, 51166}, {141, 51165}, {145, 34648}, {193, 51027}, {316, 32874}, {519, 58241}, {598, 60327}, {671, 54706}, {1131, 6431}, {1132, 6432}, {1327, 23263}, {1328, 23253}, {1698, 50869}, {3070, 43561}, {3071, 43560}, {3087, 36430}, {3424, 54476}, {3592, 54599}, {3594, 54598}, {3616, 50862}, {3617, 50865}, {3618, 51022}, {3619, 50960}, {3620, 51024}, {3621, 31162}, {3622, 50802}, {3623, 18483}, {3624, 51076}, {3655, 50863}, {3656, 58237}, {3679, 10248}, {3763, 51026}, {3818, 51028}, {4678, 50796}, {4704, 51065}, {4772, 51041}, {4821, 51064}, {5032, 53023}, {5318, 43541}, {5321, 43540}, {5334, 42973}, {5335, 42972}, {5343, 41112}, {5344, 41113}, {5365, 61719}, {5395, 54815}, {6054, 35369}, {6201, 13807}, {6202, 13687}, {6221, 42604}, {6361, 50799}, {6398, 42605}, {6409, 42537}, {6410, 42538}, {6433, 53519}, {6434, 53518}, {6437, 52666}, {6438, 52667}, {6484, 42602}, {6485, 42603}, {7773, 32879}, {7811, 32872}, {8796, 54923}, {9543, 10139}, {9589, 51068}, {9778, 38076}, {9779, 30392}, {9780, 50803}, {9812, 38155}, {10140, 42270}, {10653, 42900}, {10654, 42901}, {11160, 51537}, {11179, 51216}, {11180, 37517}, {11278, 20014}, {11439, 21849}, {11531, 31145}, {11538, 54844}, {12816, 42998}, {12817, 42999}, {14484, 60113}, {14930, 53419}, {15431, 44569}, {16267, 43021}, {16268, 43020}, {16962, 42106}, {16963, 42103}, {16964, 49874}, {16965, 49873}, {17503, 60328}, {18480, 20052}, {18492, 34632}, {18581, 42893}, {18582, 42892}, {18845, 54519}, {19862, 50870}, {19872, 50816}, {19877, 34638}, {20057, 51075}, {20080, 51214}, {20582, 55622}, {21356, 55591}, {21454, 51792}, {21850, 51215}, {22235, 54578}, {22237, 54579}, {25565, 55683}, {28164, 58227}, {28194, 54448}, {28208, 58234}, {31412, 43520}, {32006, 32894}, {32826, 48913}, {34628, 46934}, {34754, 43403}, {34755, 43404}, {35786, 43504}, {35787, 43503}, {36889, 52443}, {37640, 43364}, {37641, 43365}, {38259, 54520}, {38746, 52695}, {39874, 50963}, {41895, 43951}, {41943, 42890}, {41944, 42891}, {42090, 43398}, {42091, 43397}, {42096, 43107}, {42097, 43100}, {42136, 43542}, {42137, 43543}, {42153, 42588}, {42156, 42589}, {42159, 49826}, {42162, 49827}, {42164, 49862}, {42165, 49861}, {42262, 43888}, {42265, 43887}, {42283, 43889}, {42284, 43890}, {42431, 42953}, {42432, 42952}, {42472, 42626}, {42473, 42625}, {42532, 42908}, {42533, 42909}, {42561, 43519}, {42690, 43777}, {42691, 43778}, {42775, 49905}, {42776, 49906}, {42803, 42986}, {42804, 42987}, {42910, 43399}, {42911, 43400}, {43101, 43870}, {43104, 43869}, {43366, 43646}, {43367, 43645}, {43473, 43477}, {43474, 43478}, {43475, 49875}, {43476, 49876}, {43493, 43630}, {43494, 43631}, {43556, 54580}, {43557, 54581}, {45103, 60324}, {46932, 50808}, {47354, 55582}, {47355, 51131}, {47586, 54642}, {48884, 50964}, {48889, 54132}, {48895, 50967}, {48901, 54174}, {48905, 51129}, {50819, 61268}, {50867, 51074}, {50956, 51213}, {50959, 51171}, {50969, 55642}, {51023, 51170}, {51029, 54169}, {53101, 60147}, {54552, 60161}, {54601, 60174}, {54894, 54901}, {54896, 60118}

X(61992) = midpoint of X(i) and X(j) for these {i,j}: {3543, 15708}
X(61992) = reflection of X(i) in X(j) for these {i,j}: {15706, 5}, {15708, 3545}, {15710, 5055}, {20, 15710}
X(61992) = inverse of X(62005) in orthocentroidal circle
X(61992) = inverse of X(62005) in Yff hyperbola
X(61992) = anticomplement of X(15705)
X(61992) = pole of line {523, 62005} with respect to the orthocentroidal circle
X(61992) = pole of line {6, 62005} with respect to the Kiepert hyperbola
X(61992) = pole of line {523, 62005} with respect to the Yff hyperbola
X(61992) = pole of line {69, 61778} with respect to the Wallace hyperbola
X(61992) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(265), X(15706)}}, {{A, B, C, X(376), X(52443)}}, {{A, B, C, X(468), X(54706)}}, {{A, B, C, X(631), X(54923)}}, {{A, B, C, X(3090), X(54552)}}, {{A, B, C, X(3535), X(54543)}}, {{A, B, C, X(3536), X(54542)}}, {{A, B, C, X(4846), X(15759)}}, {{A, B, C, X(5055), X(46455)}}, {{A, B, C, X(5059), X(36889)}}, {{A, B, C, X(5094), X(60327)}}, {{A, B, C, X(6143), X(54844)}}, {{A, B, C, X(6819), X(54601)}}, {{A, B, C, X(8889), X(54815)}}, {{A, B, C, X(11410), X(14490)}}, {{A, B, C, X(12101), X(18850)}}, {{A, B, C, X(14483), X(35472)}}, {{A, B, C, X(15702), X(54585)}}, {{A, B, C, X(15717), X(15749)}}, {{A, B, C, X(15740), X(58186)}}, {{A, B, C, X(16251), X(19710)}}, {{A, B, C, X(17559), X(54932)}}, {{A, B, C, X(19708), X(54924)}}, {{A, B, C, X(32952), X(54828)}}, {{A, B, C, X(32953), X(54551)}}, {{A, B, C, X(37119), X(54886)}}, {{A, B, C, X(37276), X(54794)}}, {{A, B, C, X(38282), X(54520)}}, {{A, B, C, X(43951), X(52290)}}, {{A, B, C, X(52283), X(54476)}}, {{A, B, C, X(52288), X(60113)}}, {{A, B, C, X(52292), X(60328)}}, {{A, B, C, X(52293), X(60324)}}, {{A, B, C, X(52299), X(54519)}}
X(61992) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3543, 5059}, {4, 376, 12101}, {4, 3855, 12102}, {4, 3861, 3091}, {5, 30, 15706}, {30, 15710, 20}, {30, 3545, 15708}, {30, 5055, 15710}, {381, 12100, 3544}, {381, 15695, 5}, {381, 3830, 550}, {547, 15690, 12108}, {547, 3861, 3845}, {550, 12100, 14093}, {3090, 15684, 15697}, {3091, 12108, 15022}, {3091, 3830, 15683}, {3146, 3832, 5056}, {3524, 3545, 547}, {3533, 15690, 15692}, {3543, 11001, 3146}, {3543, 15708, 30}, {3543, 3839, 3545}, {3543, 3845, 3832}, {3544, 11001, 15702}, {3545, 11001, 11539}, {3545, 15702, 5055}, {3545, 3845, 3839}, {3830, 15759, 15682}, {3839, 10304, 381}, {3843, 12101, 376}, {3845, 15686, 546}, {3845, 15687, 3850}, {3860, 15684, 3090}, {5054, 15759, 3524}, {5067, 11001, 15715}, {5067, 15682, 15686}, {5068, 15683, 15713}, {5073, 11737, 15698}, {6825, 11812, 15719}, {10304, 15707, 15705}, {11001, 11539, 10304}, {11001, 15719, 15695}, {12101, 15713, 3830}, {15022, 15692, 2}, {15682, 15715, 17800}, {15686, 17800, 11001}, {15687, 15702, 3543}, {42539, 42540, 6}

X(61993) = X(2)X(3)∩X(6)X(12816)

Barycentrics    13*a^4-14*(b^2-c^2)^2+a^2*(b^2+c^2) : :
X(61993) = -14*X[2]+9*X[3], X[599]+4*X[48895], -9*X[946]+4*X[51107], X[1482]+4*X[34648], -13*X[1699]+3*X[61285], -3*X[3653]+8*X[12571], -9*X[3655]+14*X[51106], -7*X[3763]+4*X[55634], -6*X[3818]+X[15533], 2*X[4669]+3*X[12699], -X[4677]+6*X[18480], -8*X[4745]+3*X[12702] and many others

X(61993) lies on these lines: {2, 3}, {6, 12816}, {13, 42520}, {14, 42521}, {76, 54813}, {262, 54478}, {395, 42963}, {396, 42962}, {485, 42417}, {486, 42418}, {511, 50954}, {515, 50806}, {516, 50799}, {517, 50797}, {598, 54477}, {599, 48895}, {671, 54582}, {946, 51107}, {1327, 18512}, {1328, 18510}, {1482, 34648}, {1503, 50963}, {1699, 61285}, {2052, 54924}, {3531, 43699}, {3564, 51172}, {3583, 8162}, {3653, 12571}, {3654, 28232}, {3655, 51106}, {3656, 28236}, {3763, 55634}, {3818, 15533}, {4669, 12699}, {4677, 18480}, {4745, 12702}, {5050, 41153}, {5093, 51023}, {5318, 41113}, {5321, 41112}, {5339, 42973}, {5340, 42972}, {5351, 42586}, {5352, 42587}, {5478, 36383}, {5479, 36382}, {5790, 50865}, {5886, 50862}, {5965, 47353}, {6519, 42606}, {6522, 42607}, {8584, 39899}, {8596, 61599}, {9703, 13482}, {9880, 41147}, {9955, 51110}, {10165, 51076}, {10171, 50870}, {10175, 50869}, {10246, 41150}, {10247, 50864}, {10248, 38074}, {10516, 55596}, {10620, 17810}, {11055, 14881}, {11178, 55590}, {11224, 50805}, {11237, 18514}, {11238, 18513}, {11485, 41119}, {11486, 41120}, {11542, 42516}, {11543, 42517}, {11645, 51185}, {11648, 15484}, {11898, 48889}, {12156, 48674}, {12188, 36523}, {12645, 31162}, {12820, 42968}, {12821, 42969}, {13102, 36362}, {13103, 36363}, {13603, 18550}, {13665, 51850}, {13687, 45441}, {13785, 51849}, {13807, 45440}, {13903, 22615}, {13961, 22644}, {14226, 54598}, {14241, 54599}, {14458, 45103}, {14484, 54647}, {14492, 17503}, {14561, 51022}, {14831, 46849}, {14848, 15516}, {14927, 38079}, {15520, 51173}, {15534, 18440}, {15811, 43845}, {16194, 21849}, {16226, 44863}, {16644, 46335}, {16645, 46334}, {16808, 49905}, {16809, 49906}, {16960, 41101}, {16961, 41100}, {16964, 42506}, {16965, 42507}, {17834, 33539}, {18357, 51068}, {18358, 50994}, {18435, 21969}, {18481, 51108}, {18482, 60963}, {18483, 18526}, {18492, 28198}, {18493, 28208}, {18503, 47617}, {18525, 51093}, {18538, 43257}, {18541, 51792}, {18762, 43256}, {19106, 49908}, {19107, 49907}, {19924, 50993}, {19925, 38066}, {20070, 38081}, {20112, 47102}, {20423, 41149}, {20582, 43621}, {22165, 31670}, {22236, 49903}, {22238, 49904}, {22484, 48659}, {22485, 48660}, {22515, 48657}, {22566, 38733}, {22681, 33706}, {22793, 34718}, {22794, 36388}, {22795, 36386}, {22796, 35751}, {22797, 36329}, {23267, 43313}, {23273, 43312}, {25055, 33697}, {25561, 48910}, {26446, 50803}, {28160, 30308}, {28164, 51074}, {28168, 50866}, {28178, 50873}, {28194, 51067}, {28204, 51097}, {28228, 50796}, {28234, 50798}, {29181, 50956}, {29323, 51167}, {31673, 51103}, {32519, 44422}, {32532, 54520}, {32787, 41954}, {32788, 41953}, {33602, 54580}, {33603, 54581}, {33604, 54578}, {33605, 54579}, {33606, 54577}, {33607, 54576}, {33614, 33621}, {33615, 33620}, {33698, 54643}, {33878, 50991}, {34417, 52055}, {34627, 40273}, {35752, 48655}, {36330, 48656}, {36366, 48666}, {36368, 48665}, {36521, 39809}, {36969, 42125}, {36970, 42128}, {37484, 46852}, {37832, 42130}, {37835, 42131}, {38077, 38753}, {38224, 41148}, {39284, 54585}, {39593, 44518}, {40727, 44678}, {41107, 42094}, {41108, 42093}, {41121, 41971}, {41122, 41972}, {41152, 47354}, {41967, 42258}, {41968, 42259}, {42096, 42632}, {42097, 42631}, {42101, 42815}, {42102, 42816}, {42103, 42510}, {42104, 42512}, {42105, 42513}, {42106, 42511}, {42107, 42792}, {42108, 42911}, {42109, 42910}, {42110, 42791}, {42115, 43401}, {42116, 43402}, {42117, 49813}, {42118, 49812}, {42133, 43416}, {42134, 43417}, {42135, 49873}, {42136, 42589}, {42137, 42588}, {42138, 49874}, {42153, 42508}, {42156, 42509}, {42163, 49859}, {42166, 49860}, {42262, 42527}, {42265, 42526}, {42271, 42602}, {42272, 42603}, {42274, 43209}, {42277, 43210}, {42419, 49827}, {42420, 49826}, {42433, 42505}, {42434, 42504}, {42496, 43466}, {42497, 43465}, {42532, 42988}, {42533, 42989}, {42537, 43406}, {42538, 43405}, {42572, 54596}, {42573, 54595}, {42574, 45385}, {42575, 45384}, {42594, 51915}, {42595, 51916}, {42625, 42918}, {42626, 42919}, {42694, 42780}, {42695, 42779}, {42952, 43367}, {42953, 43366}, {42984, 43398}, {42985, 43397}, {42998, 43202}, {42999, 43201}, {43006, 43206}, {43007, 43205}, {43108, 49862}, {43109, 49861}, {43211, 43408}, {43212, 43407}, {43273, 55706}, {43477, 43501}, {43478, 43502}, {44456, 50992}, {47352, 48884}, {48872, 55635}, {48901, 51189}, {48904, 55625}, {48905, 55689}, {49802, 49941}, {49803, 49942}, {50807, 51705}, {50812, 61264}, {50813, 61614}, {50827, 61257}, {50831, 58238}, {50833, 61267}, {50872, 51515}, {50957, 54173}, {50964, 51737}, {51075, 61287}, {51078, 61263}, {51175, 54132}, {52099, 59777}, {53130, 53519}, {53131, 53518}, {54476, 54612}, {54493, 54734}, {54494, 54608}, {54512, 60120}, {54519, 60281}, {54539, 54584}, {54540, 54583}, {54542, 60302}, {54543, 60301}, {54574, 54593}, {54575, 54594}, {54601, 54827}, {54642, 60150}, {54646, 54851}, {54667, 54892}, {54707, 60113}, {54717, 60228}, {54765, 54942}, {54766, 54789}, {54791, 60122}, {54794, 54947}, {54809, 54927}, {54815, 60284}, {54838, 54893}, {54896, 60127}, {60884, 60971}

X(61993) = midpoint of X(i) and X(j) for these {i,j}: {381, 5076}, {382, 14093}, {631, 3543}, {3858, 15687}, {5071, 17578}, {15682, 15697}
X(61993) = reflection of X(i) in X(j) for these {i,j}: {1656, 381}, {14093, 1656}, {15681, 3522}, {15692, 5}, {15694, 3091}, {15695, 2}, {15696, 15694}, {15697, 15713}, {15713, 5066}, {15714, 12812}, {17538, 549}, {17578, 15687}, {20, 15714}, {3, 5071}, {376, 632}, {381, 3843}, {3534, 15693}, {5071, 3858}
X(61993) = inverse of X(12101) in orthocentroidal circle
X(61993) = inverse of X(12101) in Yff hyperbola
X(61993) = complement of X(62135)
X(61993) = anticomplement of X(15711)
X(61993) = pole of line {523, 12101} with respect to the orthocentroidal circle
X(61993) = pole of line {6, 12101} with respect to the Kiepert hyperbola
X(61993) = pole of line {523, 12101} with respect to the Yff hyperbola
X(61993) = pole of line {69, 61777} with respect to the Wallace hyperbola
X(61993) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(54924)}}, {{A, B, C, X(25), X(54813)}}, {{A, B, C, X(140), X(54585)}}, {{A, B, C, X(264), X(12101)}}, {{A, B, C, X(265), X(15692)}}, {{A, B, C, X(458), X(54478)}}, {{A, B, C, X(468), X(54582)}}, {{A, B, C, X(470), X(54479)}}, {{A, B, C, X(471), X(54480)}}, {{A, B, C, X(1494), X(15695)}}, {{A, B, C, X(1656), X(54512)}}, {{A, B, C, X(3521), X(21734)}}, {{A, B, C, X(3524), X(43699)}}, {{A, B, C, X(3530), X(21400)}}, {{A, B, C, X(3531), X(55576)}}, {{A, B, C, X(3533), X(54838)}}, {{A, B, C, X(4846), X(15710)}}, {{A, B, C, X(5094), X(54477)}}, {{A, B, C, X(8703), X(18550)}}, {{A, B, C, X(11331), X(45103)}}, {{A, B, C, X(13603), X(35473)}}, {{A, B, C, X(14458), X(52293)}}, {{A, B, C, X(14492), X(52292)}}, {{A, B, C, X(17503), X(52289)}}, {{A, B, C, X(17538), X(18317)}}, {{A, B, C, X(19711), X(57822)}}, {{A, B, C, X(46219), X(60121)}}, {{A, B, C, X(52288), X(54647)}}, {{A, B, C, X(52296), X(54879)}}, {{A, B, C, X(53857), X(54520)}}, {{A, B, C, X(55570), X(61137)}}, {{A, B, C, X(55856), X(60122)}}
X(61993) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11001, 15759}, {2, 12103, 6908}, {2, 15759, 15701}, {2, 30, 15695}, {2, 3534, 15716}, {2, 4, 12101}, {2, 8703, 15722}, {3, 3839, 381}, {3, 3843, 3858}, {3, 3851, 7486}, {3, 5055, 10124}, {4, 14893, 14269}, {4, 3832, 12102}, {4, 3839, 15687}, {4, 3843, 5076}, {5, 15691, 15709}, {5, 30, 15692}, {20, 15703, 15706}, {30, 12812, 15714}, {30, 15687, 17578}, {30, 15694, 15696}, {30, 15713, 15697}, {30, 15714, 20}, {30, 1656, 14093}, {30, 3091, 15694}, {30, 381, 1656}, {30, 3858, 5071}, {30, 5066, 15713}, {30, 549, 17538}, {30, 632, 376}, {381, 15684, 15723}, {381, 15688, 5}, {381, 1657, 5055}, {381, 3526, 3545}, {381, 5054, 5072}, {547, 15689, 15720}, {547, 3146, 15689}, {1656, 14093, 5054}, {1656, 5076, 382}, {1657, 5055, 15700}, {3090, 15686, 15707}, {3534, 15700, 8703}, {3543, 15705, 11541}, {3543, 3839, 5068}, {3543, 5055, 1657}, {3545, 15640, 12100}, {3545, 15681, 3526}, {3627, 12100, 15640}, {3627, 3859, 3522}, {3830, 14269, 3845}, {3830, 15701, 15684}, {3832, 12102, 5073}, {3832, 5073, 5079}, {3839, 15682, 5066}, {3839, 15683, 3855}, {3845, 12101, 2}, {3845, 5066, 3839}, {3845, 8703, 546}, {3854, 15702, 14892}, {3855, 15683, 15699}, {3860, 15699, 6952}, {3861, 17578, 3843}, {3861, 6846, 6847}, {5073, 6961, 3529}, {10124, 15687, 3543}, {10304, 11737, 5070}, {11001, 15688, 3534}, {11001, 15701, 15688}, {12100, 15640, 15681}, {12816, 12817, 6}, {14892, 15704, 15702}, {15682, 15687, 3830}, {15682, 15697, 30}, {15682, 15709, 11001}, {15683, 15699, 3}, {15692, 15701, 15693}, {15697, 17578, 15682}, {18586, 18587, 17800}, {42153, 42508, 42977}, {42156, 42509, 42976}

X(61994) = X(2)X(3)∩X(397)X(43202)

Barycentrics    29*a^4-31*(b^2-c^2)^2+2*a^2*(b^2+c^2) : :
X(61994) = -31*X[2]+20*X[3], 4*X[1350]+7*X[51213], -16*X[3631]+5*X[54174], 4*X[4297]+7*X[50867], -25*X[5734]+14*X[51094], -5*X[7987]+16*X[51076], 7*X[7989]+4*X[50869], -5*X[9740]+16*X[53144], 7*X[10248]+4*X[50796], X[11008]+10*X[47353], 4*X[12512]+7*X[50874], -14*X[15808]+25*X[30308] and many others

X(61994) lies on these lines: {2, 3}, {397, 43202}, {398, 43201}, {1131, 54596}, {1132, 54595}, {1350, 51213}, {1587, 12819}, {1588, 12818}, {2996, 54717}, {3424, 54494}, {3631, 54174}, {4031, 51792}, {4297, 50867}, {5334, 43251}, {5335, 43250}, {5343, 42973}, {5344, 42972}, {5365, 41112}, {5366, 41113}, {5734, 51094}, {6459, 41952}, {6460, 41951}, {7987, 51076}, {7989, 50869}, {8252, 43405}, {8253, 43406}, {9740, 53144}, {10248, 50796}, {10653, 43195}, {10654, 43196}, {11008, 47353}, {11542, 42803}, {11543, 42804}, {12512, 50874}, {12816, 42999}, {12817, 42998}, {12820, 42134}, {12821, 42133}, {14484, 33698}, {14488, 41895}, {15808, 30308}, {16966, 43398}, {16967, 43397}, {18483, 20057}, {18843, 54815}, {19875, 50873}, {19883, 50866}, {20583, 53023}, {21358, 51029}, {22235, 49876}, {22237, 49875}, {28202, 46933}, {32787, 42642}, {32788, 42641}, {34641, 59387}, {34648, 34747}, {35786, 42522}, {35787, 42523}, {36969, 43011}, {36970, 43010}, {38098, 50865}, {38314, 50863}, {41107, 43547}, {41108, 43546}, {41119, 42635}, {41120, 42636}, {41943, 42104}, {41944, 42105}, {42085, 43367}, {42086, 43366}, {42160, 43476}, {42161, 43475}, {42163, 42588}, {42166, 42589}, {42779, 49825}, {42780, 49824}, {42813, 49827}, {42814, 49826}, {42940, 43243}, {42941, 43242}, {42948, 43003}, {42949, 43002}, {43004, 43311}, {43005, 43310}, {43110, 43553}, {43111, 43552}, {43226, 43403}, {43227, 43404}, {43501, 54579}, {43502, 54578}, {43570, 54599}, {43571, 54598}, {43951, 54720}, {44882, 51217}, {48310, 51167}, {48901, 51211}, {50809, 61259}, {51028, 51537}, {51131, 53094}, {51216, 59373}, {52519, 60113}, {53100, 54642}, {53101, 60132}, {53105, 54520}, {53109, 54519}, {54476, 54845}, {54542, 60306}, {54543, 60305}, {54706, 60631}, {54896, 60142}

X(61994) = midpoint of X(i) and X(j) for these {i,j}: {3543, 15721}, {3830, 5072}
X(61994) = reflection of X(i) in X(j) for these {i,j}: {15716, 5}, {15719, 5072}, {2, 3855}, {376, 15723}
X(61994) = inverse of X(62003) in orthocentroidal circle
X(61994) = inverse of X(62003) in Yff hyperbola
X(61994) = anticomplement of X(15715)
X(61994) = pole of line {523, 62003} with respect to the orthocentroidal circle
X(61994) = pole of line {6, 51216} with respect to the Kiepert hyperbola
X(61994) = pole of line {523, 62003} with respect to the Yff hyperbola
X(61994) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(265), X(15716)}}, {{A, B, C, X(3535), X(54596)}}, {{A, B, C, X(3536), X(54595)}}, {{A, B, C, X(4846), X(15714)}}, {{A, B, C, X(6353), X(54717)}}, {{A, B, C, X(7486), X(54552)}}, {{A, B, C, X(10303), X(54923)}}, {{A, B, C, X(10304), X(57823)}}, {{A, B, C, X(14488), X(52290)}}, {{A, B, C, X(15698), X(54924)}}, {{A, B, C, X(15709), X(54585)}}, {{A, B, C, X(18850), X(35403)}}, {{A, B, C, X(31363), X(55859)}}, {{A, B, C, X(33698), X(52288)}}, {{A, B, C, X(37453), X(54520)}}, {{A, B, C, X(52283), X(54494)}}, {{A, B, C, X(55860), X(60618)}}
X(61994) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15688, 3523}, {2, 15705, 14869}, {2, 3522, 15707}, {2, 3529, 10304}, {4, 3545, 12101}, {4, 3861, 3146}, {5, 30, 15716}, {30, 3855, 2}, {30, 5072, 15719}, {140, 382, 3529}, {140, 3832, 3091}, {376, 15723, 15717}, {376, 3543, 15640}, {376, 5067, 549}, {376, 5071, 140}, {381, 10124, 3545}, {381, 15684, 10124}, {381, 15686, 5071}, {381, 3543, 15692}, {381, 3830, 15686}, {382, 14269, 3845}, {382, 550, 11541}, {546, 15687, 15681}, {546, 15720, 3855}, {3091, 11541, 10303}, {3091, 15717, 5056}, {3091, 3845, 3839}, {3523, 10304, 15711}, {3543, 15721, 30}, {3544, 15682, 15688}, {3545, 11541, 15693}, {3545, 12101, 17578}, {3627, 5076, 3149}, {3830, 15711, 15682}, {3839, 15692, 381}, {3845, 12102, 5055}, {3845, 15687, 11737}, {3845, 17504, 546}, {3855, 16371, 13729}, {5056, 10303, 5070}, {5067, 11106, 16863}, {6904, 17566, 17568}, {10303, 15693, 15708}, {11737, 15687, 382}, {13635, 15705, 15697}, {14893, 15687, 14269}, {15640, 15708, 20}, {15681, 17504, 376}, {15684, 17578, 3543}, {15715, 15719, 15700}, {15717, 15723, 15721}, {43365, 43477, 10653}

X(61995) = X(2)X(3)∩X(397)X(12817)

Barycentrics    16*a^4-17*(b^2-c^2)^2+a^2*(b^2+c^2) : :
X(61995) = -17*X[2]+11*X[3], -4*X[1699]+X[61283], -X[3098]+4*X[50960], -X[3579]+4*X[50803], -4*X[3656]+X[61295], -5*X[3818]+2*X[50958], -2*X[4701]+11*X[18480], 2*X[9812]+X[59400], 2*X[9955]+X[50862], -2*X[10168]+5*X[51129], 7*X[10248]+2*X[61510], 5*X[11180]+X[51174] and many others

X(61995) lies on these lines: {2, 3}, {395, 43227}, {396, 43226}, {397, 12817}, {398, 12816}, {598, 54917}, {952, 16191}, {1327, 19117}, {1328, 19116}, {1699, 61283}, {3098, 50960}, {3579, 50803}, {3653, 28190}, {3656, 61295}, {3818, 50958}, {4701, 18480}, {5318, 42972}, {5321, 42973}, {5334, 43201}, {5335, 43202}, {5349, 43368}, {5350, 43369}, {5355, 39563}, {5368, 14537}, {6429, 43568}, {6430, 43569}, {6500, 43560}, {6501, 43561}, {6748, 36430}, {7581, 43566}, {7582, 43567}, {7776, 32890}, {9812, 59400}, {9955, 50862}, {10168, 51129}, {10248, 61510}, {11180, 51174}, {11645, 38136}, {11693, 61574}, {12355, 61599}, {12699, 50823}, {13491, 58470}, {13687, 45863}, {13807, 45862}, {16267, 42117}, {16268, 42118}, {16644, 43630}, {16645, 43631}, {16962, 42940}, {16963, 42941}, {16964, 43476}, {16965, 43475}, {18357, 50865}, {18358, 51024}, {18440, 50986}, {18483, 51075}, {18525, 50831}, {19130, 51022}, {19875, 28178}, {19883, 28168}, {20193, 43607}, {20582, 48904}, {21849, 46849}, {21850, 51132}, {21969, 45959}, {22615, 52047}, {22644, 52048}, {22791, 34648}, {25561, 51163}, {25565, 48942}, {28146, 38076}, {28150, 38083}, {28154, 38068}, {28160, 38022}, {28174, 38081}, {28186, 38021}, {28194, 38176}, {28198, 38112}, {28202, 38042}, {28204, 61293}, {28208, 38034}, {28212, 38074}, {28216, 38066}, {29012, 38079}, {29323, 48310}, {31162, 37705}, {31670, 50978}, {31673, 50824}, {32062, 45956}, {34628, 50807}, {34632, 50800}, {34638, 50825}, {34773, 50802}, {35242, 50874}, {36969, 42135}, {36970, 42138}, {37832, 42144}, {37835, 42145}, {40273, 61245}, {41119, 42925}, {41120, 42924}, {41121, 42164}, {41122, 42165}, {41152, 55583}, {41869, 50799}, {41943, 43246}, {41944, 43247}, {41945, 42639}, {41946, 42640}, {42085, 43639}, {42086, 43640}, {42087, 43204}, {42088, 43203}, {42093, 43416}, {42094, 43417}, {42101, 43292}, {42102, 43293}, {42103, 42913}, {42106, 42912}, {42108, 43107}, {42109, 43100}, {42121, 43401}, {42124, 43402}, {42126, 42496}, {42127, 42497}, {42263, 43211}, {42264, 43212}, {42283, 43312}, {42284, 43313}, {42472, 43398}, {42473, 43397}, {42598, 46335}, {42599, 46334}, {42635, 42777}, {42636, 42778}, {42785, 48906}, {42799, 43472}, {42800, 43471}, {42888, 42916}, {42889, 42917}, {42910, 43648}, {42911, 43647}, {42922, 42975}, {42923, 42974}, {43150, 51166}, {43228, 43776}, {43229, 43775}, {43418, 43781}, {43419, 43782}, {43644, 52080}, {43649, 52079}, {44456, 51183}, {47354, 48895}, {48879, 50984}, {48892, 50988}, {48910, 50956}, {50957, 51184}, {50961, 54131}, {50964, 50987}, {50980, 51133}, {51164, 55646}, {51173, 51180}

X(61995) = midpoint of X(i) and X(j) for these {i,j}: {4, 14269}, {382, 10304}, {3543, 5054}, {3545, 3830}, {3627, 15699}, {15682, 15689}
X(61995) = reflection of X(i) in X(j) for these {i,j}: {10304, 547}, {11693, 61574}, {14269, 14893}, {15686, 17504}, {15689, 140}, {15699, 381}, {17504, 5}, {3524, 14892}, {3545, 546}, {3845, 14269}, {549, 3545}, {550, 5054}, {5054, 5066}, {8703, 15699}
X(61995) = inverse of X(35403) in orthocentroidal circle
X(61995) = inverse of X(35403) in Yff hyperbola
X(61995) = complement of X(62137)
X(61995) = anticomplement of X(61782)
X(61995) = pole of line {523, 35403} with respect to the orthocentroidal circle
X(61995) = pole of line {6, 35403} with respect to the Kiepert hyperbola
X(61995) = pole of line {523, 35403} with respect to the Yff hyperbola
X(61995) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(264), X(35403)}}, {{A, B, C, X(265), X(17504)}}, {{A, B, C, X(3521), X(58190)}}, {{A, B, C, X(5094), X(54917)}}, {{A, B, C, X(6662), X(49139)}}, {{A, B, C, X(12100), X(54924)}}, {{A, B, C, X(12103), X(15319)}}, {{A, B, C, X(12811), X(55958)}}, {{A, B, C, X(14093), X(18550)}}, {{A, B, C, X(15694), X(54585)}}, {{A, B, C, X(15699), X(54512)}}, {{A, B, C, X(16239), X(60121)}}, {{A, B, C, X(36889), X(49138)}}, {{A, B, C, X(55857), X(60122)}}
X(61995) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15704, 15714}, {2, 381, 12811}, {2, 5073, 15691}, {4, 381, 12101}, {4, 3843, 12102}, {5, 15686, 15713}, {5, 30, 17504}, {20, 3524, 15688}, {20, 381, 10109}, {20, 3854, 3090}, {20, 5068, 3525}, {20, 549, 8703}, {30, 140, 15689}, {30, 14269, 3845}, {30, 14892, 3524}, {30, 14893, 14269}, {30, 17504, 15686}, {30, 381, 15699}, {30, 5066, 5054}, {30, 546, 3545}, {30, 547, 10304}, {140, 15716, 549}, {381, 15682, 140}, {381, 15701, 5068}, {381, 3524, 14892}, {381, 382, 15701}, {381, 8703, 5}, {382, 3857, 15712}, {546, 16239, 3854}, {546, 3525, 3857}, {550, 3832, 6981}, {632, 3627, 11541}, {1656, 13742, 3628}, {1657, 6868, 17538}, {2050, 17800, 4}, {3090, 12102, 3627}, {3090, 15685, 14891}, {3090, 3543, 15685}, {3091, 15684, 12100}, {3524, 15699, 11539}, {3524, 3839, 381}, {3529, 15703, 15759}, {3534, 11737, 632}, {3534, 3832, 11737}, {3543, 3843, 5066}, {3544, 15697, 15723}, {3545, 15705, 1656}, {3627, 12101, 15687}, {3627, 12811, 15704}, {3628, 15681, 15711}, {3830, 15716, 15682}, {3843, 3854, 546}, {3851, 11001, 10124}, {3853, 12811, 5073}, {3855, 15640, 15694}, {5056, 14093, 11540}, {5066, 12102, 3543}, {5068, 15701, 547}, {10109, 12101, 3830}, {10109, 14891, 16239}, {10299, 11541, 20}, {11541, 15721, 3534}, {12101, 14893, 3861}, {12101, 15691, 3853}, {12811, 15691, 2}, {14093, 17530, 11812}, {14891, 15685, 550}, {15640, 15694, 12103}, {15682, 15689, 30}, {15683, 17577, 15692}, {15765, 18585, 3856}, {18586, 18587, 5059}, {34628, 50807, 61272}, {36969, 42135, 42634}, {36970, 42138, 42633}

X(61996) = X(2)X(3)∩X(61)X(43476)

Barycentrics    19*a^4-20*(b^2-c^2)^2+a^2*(b^2+c^2) : :
X(61996) = -20*X[2]+13*X[3], 5*X[355]+2*X[51120], 5*X[946]+2*X[50868], 2*X[962]+5*X[50797], 5*X[1351]+2*X[51027], 5*X[1352]+2*X[51166], 5*X[1482]+2*X[50871], 8*X[4746]+13*X[12699], -5*X[4816]+26*X[18480], 16*X[5097]+5*X[48662], -16*X[5461]+9*X[38634], 5*X[5480]+2*X[51025] and many others

X(61996) lies on these lines: {2, 3}, {61, 43476}, {62, 43475}, {355, 51120}, {946, 50868}, {962, 50797}, {1327, 6417}, {1328, 6418}, {1351, 51027}, {1352, 51166}, {1482, 50871}, {4746, 12699}, {4816, 18480}, {5097, 48662}, {5334, 42907}, {5335, 42906}, {5339, 12816}, {5340, 12817}, {5343, 43201}, {5344, 43202}, {5349, 41112}, {5350, 41113}, {5461, 38634}, {5480, 51025}, {5691, 50806}, {5921, 51172}, {6437, 45384}, {6438, 45385}, {6445, 42602}, {6446, 42603}, {6500, 23263}, {6501, 23253}, {6560, 41951}, {6561, 41952}, {7581, 43567}, {7582, 43566}, {10137, 42273}, {10138, 42270}, {10605, 33887}, {10645, 42984}, {10646, 42985}, {11178, 55591}, {11480, 43400}, {11481, 43399}, {11531, 50798}, {11645, 55711}, {11898, 51214}, {12902, 56567}, {14490, 18550}, {14666, 38802}, {14830, 38735}, {15749, 61137}, {16200, 34748}, {16241, 42587}, {16242, 42586}, {16808, 43245}, {16809, 43244}, {18492, 38066}, {19876, 28154}, {19924, 50957}, {19925, 51119}, {20582, 55624}, {21358, 55612}, {22236, 43013}, {22238, 43012}, {25561, 55603}, {25565, 55682}, {28198, 50800}, {30308, 33697}, {31423, 50874}, {31662, 34628}, {32907, 59393}, {32909, 59395}, {34638, 61263}, {34718, 38155}, {36990, 50963}, {37517, 47353}, {38072, 50664}, {38633, 45311}, {38637, 45310}, {40273, 50805}, {42093, 61719}, {42101, 42974}, {42102, 42975}, {42115, 43200}, {42116, 43199}, {42129, 43401}, {42132, 43402}, {42153, 43023}, {42154, 43226}, {42155, 43227}, {42156, 43022}, {42159, 42899}, {42162, 42898}, {42890, 49907}, {42891, 49908}, {42900, 43233}, {42901, 43232}, {43312, 43889}, {43313, 43890}, {46267, 48884}, {47354, 55584}, {48873, 50960}, {48874, 51029}, {48889, 50955}, {48895, 55582}, {48898, 51167}, {48904, 55622}, {48942, 55683}, {48943, 55642}, {50799, 51118}, {50954, 51212}, {50956, 51163}, {51024, 55587}, {51106, 58235}, {51186, 55602}, {54494, 54891}

X(61996) = midpoint of X(i) and X(j) for these {i,j}: {3543, 15702}, {3830, 3851}, {31423, 50874}
X(61996) = reflection of X(i) in X(j) for these {i,j}: {14869, 5066}, {15698, 5}, {15701, 3851}, {15703, 381}, {2, 3857}, {3534, 3523}, {3832, 3845}, {55602, 51186}
X(61996) = inverse of X(62001) in orthocentroidal circle
X(61996) = inverse of X(62001) in Yff hyperbola
X(61996) = pole of line {523, 62001} with respect to the orthocentroidal circle
X(61996) = pole of line {6, 62001} with respect to the Kiepert hyperbola
X(61996) = pole of line {523, 62001} with respect to the Yff hyperbola
X(61996) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(265), X(15698)}}, {{A, B, C, X(3531), X(35472)}}, {{A, B, C, X(10304), X(18550)}}, {{A, B, C, X(11539), X(54585)}}, {{A, B, C, X(14490), X(35473)}}, {{A, B, C, X(15693), X(54924)}}, {{A, B, C, X(15703), X(54512)}}, {{A, B, C, X(15717), X(21400)}}, {{A, B, C, X(15749), X(61138)}}, {{A, B, C, X(15750), X(61137)}}, {{A, B, C, X(23040), X(57715)}}, {{A, B, C, X(48154), X(60122)}}, {{A, B, C, X(55858), X(60121)}}
X(61996) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6952, 6964}, {2, 6958, 6908}, {3, 11001, 15689}, {3, 14269, 3845}, {3, 15703, 15702}, {3, 3832, 3851}, {4, 3839, 12101}, {4, 3861, 5076}, {5, 15685, 15707}, {5, 30, 15698}, {30, 3523, 3534}, {30, 381, 15703}, {30, 3845, 3832}, {30, 3857, 2}, {30, 5066, 14869}, {381, 14093, 5}, {381, 14893, 14269}, {381, 15681, 5055}, {381, 15687, 15684}, {381, 15723, 3545}, {381, 3534, 5071}, {381, 382, 549}, {381, 5054, 11737}, {547, 14891, 11539}, {632, 3628, 16863}, {1006, 3525, 10303}, {3090, 3525, 474}, {3090, 3832, 3850}, {3090, 6906, 3091}, {3091, 10303, 4188}, {3523, 14891, 15700}, {3529, 10109, 15706}, {3543, 15702, 30}, {3543, 3545, 15686}, {3543, 3845, 381}, {3543, 5056, 15683}, {3545, 15686, 15723}, {3545, 5059, 11812}, {3628, 6913, 3090}, {3830, 14269, 3843}, {3830, 15689, 382}, {3830, 5055, 5073}, {3845, 11539, 546}, {3845, 12101, 11001}, {3845, 12102, 15708}, {3845, 15687, 547}, {3845, 3850, 3839}, {3853, 15686, 3543}, {5055, 15681, 15718}, {11737, 15683, 5054}, {15640, 15699, 15696}, {15681, 15718, 15695}, {15684, 15687, 3830}, {15684, 15694, 15681}, {15686, 15723, 3}, {15687, 15714, 3627}, {15694, 15700, 15701}, {15694, 15707, 15721}, {15696, 15699, 15722}, {15700, 15703, 15694}

X(61997) = X(2)X(3)∩X(13)X(42781)

Barycentrics    22*a^4-23*(b^2-c^2)^2+a^2*(b^2+c^2) : :
X(61997) = -23*X[2]+15*X[3], X[3631]+5*X[48895], -15*X[3656]+7*X[51094], X[4669]+3*X[22793], 5*X[9766]+3*X[53143], 3*X[9812]+X[50823], 7*X[10248]+X[34718], -3*X[11231]+7*X[51078], X[15534]+3*X[39884], 7*X[15808]+5*X[33697], 2*X[16656]+X[43575], -5*X[18357]+3*X[38098] and many others

X(61997) lies on these lines: {2, 3}, {13, 42781}, {14, 42782}, {395, 42629}, {396, 42630}, {671, 54717}, {1327, 54596}, {1328, 54595}, {3631, 48895}, {3636, 28208}, {3656, 51094}, {4669, 22793}, {4745, 28174}, {5318, 12817}, {5321, 12816}, {5334, 42478}, {5335, 42479}, {5349, 42973}, {5350, 42972}, {5365, 43201}, {5366, 43202}, {6199, 43522}, {6329, 11645}, {6395, 43521}, {6441, 51850}, {6442, 51849}, {6560, 42644}, {6561, 42643}, {6564, 42417}, {6565, 42418}, {9766, 53143}, {9812, 50823}, {10248, 34718}, {11231, 51078}, {11542, 42532}, {11543, 42533}, {12818, 23261}, {12819, 23251}, {14226, 43507}, {14241, 43508}, {14458, 54494}, {14488, 17503}, {14492, 33698}, {15170, 18514}, {15534, 39884}, {15808, 33697}, {16656, 43575}, {16808, 43367}, {16809, 43366}, {18357, 38098}, {18480, 34641}, {18483, 32900}, {19053, 43313}, {19054, 43312}, {22165, 48901}, {22791, 34747}, {23267, 43567}, {23273, 43566}, {23302, 43400}, {23303, 43399}, {28146, 50803}, {28160, 51108}, {28172, 51076}, {28182, 50869}, {28186, 50802}, {28202, 51069}, {28204, 51095}, {28212, 50796}, {28224, 51071}, {29317, 50960}, {34648, 40273}, {36382, 59395}, {36383, 59393}, {36969, 42507}, {36970, 42506}, {38028, 50807}, {38034, 51105}, {38081, 48661}, {38110, 50964}, {38112, 50800}, {38136, 51185}, {38138, 51072}, {39593, 53419}, {41100, 42137}, {41101, 42136}, {41107, 42102}, {41108, 42101}, {41112, 42093}, {41113, 42094}, {41119, 42117}, {41120, 42118}, {41121, 42940}, {41122, 42941}, {42087, 43649}, {42088, 43644}, {42103, 49906}, {42106, 49905}, {42108, 42632}, {42109, 42631}, {42125, 49875}, {42126, 49813}, {42127, 49812}, {42128, 49876}, {42135, 49948}, {42138, 49947}, {42143, 43401}, {42146, 43402}, {42147, 49903}, {42148, 49904}, {42163, 42977}, {42166, 42976}, {42215, 43504}, {42216, 43503}, {42268, 42609}, {42269, 42608}, {42270, 42607}, {42271, 43211}, {42272, 43212}, {42273, 42606}, {42500, 43231}, {42501, 43230}, {42508, 49859}, {42509, 49860}, {42516, 42691}, {42517, 42690}, {42576, 53131}, {42577, 53130}, {42584, 43101}, {42585, 43104}, {42627, 43246}, {42628, 43247}, {42633, 49874}, {42634, 49873}, {42635, 42925}, {42636, 42924}, {42639, 43257}, {42640, 43256}, {42888, 42912}, {42889, 42913}, {42904, 43006}, {42905, 43007}, {42962, 43482}, {42963, 43481}, {42982, 54578}, {42983, 54579}, {43546, 54479}, {43547, 54480}, {43676, 54813}, {45103, 60132}, {50808, 61262}, {50825, 61263}, {50870, 61267}, {50872, 61251}, {50874, 54447}, {50956, 51186}, {50978, 51538}, {51029, 55610}, {51074, 61269}, {52519, 54896}, {53105, 54582}, {53109, 54477}, {54478, 60142}, {54520, 54720}, {54598, 60306}, {54599, 60305}, {54642, 54845}, {54646, 54934}

X(61997) = midpoint of X(i) and X(j) for these {i,j}: {4, 14893}, {140, 3543}, {381, 3853}, {546, 15687}, {547, 3627}, {3830, 5066}, {3845, 12101}, {12103, 15684}, {15682, 15690}, {34648, 40273}
X(61997) = reflection of X(i) in X(j) for these {i,j}: {10109, 3860}, {10124, 3850}, {11737, 546}, {11812, 5066}, {14891, 5}, {15690, 11540}, {15691, 12108}, {15759, 10109}, {376, 16239}, {3530, 11737}, {3628, 381}, {3860, 3845}, {3861, 14893}, {547, 3856}, {549, 12811}
X(61997) = inverse of X(62000) in orthocentroidal circle
X(61997) = inverse of X(62000) in Yff hyperbola
X(61997) = complement of X(62138)
X(61997) = anticomplement of X(61779)
X(61997) = pole of line {523, 62000} with respect to the orthocentroidal circle
X(61997) = pole of line {6, 62000} with respect to the Kiepert hyperbola
X(61997) = pole of line {523, 62000} with respect to the Yff hyperbola
X(61997) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(265), X(14891)}}, {{A, B, C, X(468), X(54717)}}, {{A, B, C, X(470), X(54576)}}, {{A, B, C, X(471), X(54577)}}, {{A, B, C, X(549), X(54924)}}, {{A, B, C, X(3526), X(54585)}}, {{A, B, C, X(3628), X(54512)}}, {{A, B, C, X(11331), X(54494)}}, {{A, B, C, X(12100), X(57894)}}, {{A, B, C, X(14488), X(52292)}}, {{A, B, C, X(33698), X(52289)}}, {{A, B, C, X(37453), X(54582)}}, {{A, B, C, X(52293), X(60132)}}, {{A, B, C, X(55859), X(60121)}}, {{A, B, C, X(55860), X(60122)}}
X(61997) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11737, 10109}, {2, 15682, 15681}, {2, 15700, 15713}, {2, 15710, 15701}, {2, 3534, 17504}, {4, 14269, 15687}, {4, 3845, 12101}, {4, 3861, 12102}, {5, 15690, 11540}, {5, 17538, 140}, {5, 3627, 5059}, {30, 10109, 15759}, {30, 11540, 15690}, {30, 11737, 3530}, {30, 12108, 15691}, {30, 12811, 549}, {30, 14893, 3861}, {30, 16239, 376}, {30, 381, 3628}, {30, 3845, 3860}, {30, 3856, 547}, {30, 546, 11737}, {140, 546, 3855}, {376, 14892, 16239}, {376, 3858, 14892}, {381, 10304, 5}, {381, 15707, 3544}, {381, 3146, 11539}, {381, 3543, 15714}, {381, 382, 15707}, {381, 3830, 11001}, {546, 14893, 14269}, {546, 3529, 12811}, {546, 3851, 3856}, {550, 11539, 15715}, {631, 3839, 381}, {3530, 10109, 2}, {3543, 3839, 15022}, {3543, 3855, 15688}, {3830, 15693, 15682}, {3830, 3845, 5066}, {3832, 15684, 15699}, {3855, 15022, 3851}, {3859, 15691, 5055}, {3860, 10109, 3850}, {5055, 15691, 12108}, {5066, 12101, 3830}, {5318, 43419, 43111}, {5321, 43418, 43110}, {10109, 15759, 10124}, {10304, 15681, 550}, {11539, 15695, 12100}, {11540, 15690, 14891}, {11540, 15693, 11812}, {11812, 14891, 15693}, {12100, 12101, 3853}, {12100, 15690, 10304}, {12101, 14893, 3845}, {12103, 15684, 30}, {12820, 43419, 5318}, {12821, 43418, 5321}, {14269, 15687, 546}, {15681, 15688, 17538}, {15684, 15699, 12103}, {15685, 15713, 548}, {15687, 17504, 3627}, {41122, 42941, 43109}

X(61998) = X(2)X(3)∩X(13)X(42682)

Barycentrics    32*a^4-31*(b^2-c^2)^2-a^2*(b^2+c^2) : :
X(61998) = -31*X[2]+21*X[3], X[3630]+14*X[48895], -8*X[3656]+3*X[61293], -4*X[4677]+9*X[61251], -3*X[17502]+8*X[51076], -3*X[17508]+8*X[51131], -X[22165]+6*X[48889], 4*X[31162]+X[61245], 3*X[38034]+2*X[50862], 3*X[38136]+2*X[51022], 3*X[38138]+2*X[50865], 3*X[38140]+2*X[50869] and many others

X(61998) lies on these lines: {2, 3}, {13, 42682}, {14, 42683}, {395, 44020}, {396, 44019}, {3630, 48895}, {3656, 61293}, {4677, 61251}, {4745, 28232}, {5318, 43472}, {5321, 43471}, {6560, 42609}, {6561, 42608}, {6564, 43312}, {6565, 43313}, {9541, 42526}, {12816, 54591}, {12817, 54592}, {12820, 42907}, {12821, 42906}, {14458, 54493}, {14492, 54646}, {16960, 42502}, {16961, 42503}, {17502, 51076}, {17503, 60326}, {17508, 51131}, {18510, 43567}, {18512, 43566}, {18581, 43640}, {18582, 43639}, {19116, 43563}, {19117, 43562}, {22165, 48889}, {28154, 50825}, {28168, 51074}, {28178, 50799}, {28186, 51105}, {28190, 30308}, {28212, 51072}, {28216, 50822}, {29323, 51129}, {31162, 61245}, {33698, 54852}, {36969, 42521}, {36970, 42520}, {38034, 50862}, {38136, 51022}, {38138, 50865}, {38140, 50869}, {39593, 53418}, {40273, 51093}, {41100, 42135}, {41101, 42138}, {41107, 42101}, {41108, 42102}, {41119, 42509}, {41120, 42508}, {41121, 43368}, {41122, 43369}, {42095, 43648}, {42098, 43647}, {42104, 49905}, {42105, 49906}, {42107, 42631}, {42110, 42632}, {42117, 42532}, {42118, 42533}, {42125, 42588}, {42126, 42516}, {42127, 42517}, {42128, 42589}, {42136, 49947}, {42137, 49948}, {42144, 43024}, {42145, 43025}, {42154, 49860}, {42155, 49859}, {42164, 42976}, {42165, 42977}, {42225, 42639}, {42226, 42640}, {42258, 42606}, {42259, 42607}, {42504, 42929}, {42505, 42928}, {42506, 42633}, {42507, 42634}, {42510, 42519}, {42511, 42518}, {42801, 49904}, {42802, 49903}, {42888, 43403}, {42889, 43404}, {42900, 43032}, {42901, 43033}, {42924, 49810}, {42925, 49811}, {42942, 43246}, {42943, 43247}, {42970, 43232}, {42971, 43233}, {43226, 46335}, {43227, 46334}, {43401, 49908}, {43402, 49907}, {43501, 54580}, {43502, 54581}, {43550, 54480}, {43551, 54479}, {45103, 54890}, {48661, 51068}, {48874, 51143}, {50807, 61270}, {50811, 61273}, {50826, 61262}, {51213, 55593}, {53106, 54477}, {53107, 54582}, {54478, 54857}, {54598, 60309}, {54599, 60310}, {54813, 60146}, {54896, 60325}

X(61998) = midpoint of X(i) and X(j) for these {i,j}: {381, 17578}, {382, 15692}, {1656, 3543}, {15682, 15695}, {15684, 17538}
X(61998) = reflection of X(i) in X(j) for these {i,j}: {14093, 12812}, {15686, 15712}, {15693, 5066}, {15694, 3859}, {15714, 5}, {3522, 547}, {3843, 14893}, {549, 3091}, {550, 15694}, {5071, 546}, {50832, 30308}, {632, 381}
X(61998) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(265), X(15714)}}, {{A, B, C, X(470), X(54575)}}, {{A, B, C, X(471), X(54574)}}, {{A, B, C, X(547), X(54924)}}, {{A, B, C, X(632), X(54512)}}, {{A, B, C, X(5070), X(54585)}}, {{A, B, C, X(11331), X(54493)}}, {{A, B, C, X(15716), X(18550)}}, {{A, B, C, X(52289), X(54646)}}, {{A, B, C, X(52292), X(60326)}}, {{A, B, C, X(52293), X(54890)}}, {{A, B, C, X(52297), X(54477)}}, {{A, B, C, X(52298), X(54582)}}
X(61998) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14893, 3845}, {2, 15682, 1657}, {2, 15689, 12100}, {2, 15712, 15713}, {2, 3534, 14891}, {2, 5072, 10109}, {5, 30, 15714}, {30, 12812, 14093}, {30, 14893, 3843}, {30, 15694, 550}, {30, 381, 632}, {30, 3859, 15694}, {30, 5066, 15693}, {30, 546, 5071}, {30, 547, 3522}, {381, 15640, 11812}, {381, 17504, 5}, {381, 3830, 15640}, {549, 15699, 3533}, {549, 5070, 11539}, {1657, 14892, 549}, {1657, 3843, 3091}, {1657, 3853, 3627}, {3091, 15682, 15695}, {3091, 3528, 1656}, {3627, 3843, 15712}, {3627, 3845, 2}, {3839, 15694, 3859}, {3839, 5067, 381}, {3843, 12812, 3858}, {3843, 17538, 3850}, {3845, 12101, 15687}, {3853, 14893, 14892}, {3853, 3860, 15682}, {3853, 3861, 3528}, {5059, 6940, 15696}, {8703, 11812, 17504}, {8703, 15687, 3830}, {14269, 15682, 3860}, {14891, 14892, 5070}, {14893, 15687, 15686}, {15682, 15695, 30}, {15686, 17504, 548}, {15697, 15711, 8703}

X(61999) = X(2)X(3)∩X(61)X(43207)

Barycentrics    26*a^4-25*(b^2-c^2)^2-a^2*(b^2+c^2) : :
X(61999) = -25*X[2]+17*X[3], 7*X[10248]+X[50798], -25*X[12699]+X[58248], -25*X[18481]+49*X[58231], -5*X[20582]+3*X[55627], -5*X[22793]+X[51120], -5*X[25565]+3*X[55680], -25*X[31162]+9*X[58241], -15*X[38079]+11*X[55699], -5*X[39884]+X[51027], -5*X[47354]+X[55587], -15*X[48310]+11*X[55683]

X(61999) lies on these lines: {2, 3}, {61, 43207}, {62, 43208}, {395, 42889}, {396, 42888}, {397, 42480}, {398, 42481}, {1327, 6431}, {1328, 6432}, {3828, 28182}, {5097, 51025}, {5349, 43476}, {5350, 43475}, {5368, 39563}, {5844, 34648}, {5901, 50862}, {6433, 42602}, {6434, 42603}, {6455, 42537}, {6456, 42538}, {6480, 53519}, {6481, 53518}, {6484, 43211}, {6485, 43212}, {6486, 43210}, {6487, 43209}, {9956, 50869}, {10248, 50798}, {12699, 58248}, {13451, 32062}, {15170, 18513}, {16964, 42898}, {16965, 42899}, {17851, 42605}, {18481, 58231}, {18510, 43797}, {18512, 43798}, {18583, 51022}, {19924, 51165}, {20582, 55627}, {21849, 32137}, {22793, 51120}, {24206, 51026}, {25565, 55680}, {28186, 58234}, {28190, 31662}, {28198, 51119}, {28204, 58237}, {28212, 38155}, {31162, 58241}, {33179, 50868}, {33606, 43485}, {33607, 43486}, {34754, 42496}, {34755, 42497}, {35786, 41952}, {35787, 41951}, {35822, 43789}, {35823, 43790}, {36836, 43246}, {36843, 43247}, {36969, 43015}, {36970, 43014}, {38079, 55699}, {39884, 51027}, {41943, 42530}, {41944, 42531}, {42102, 61719}, {42130, 43398}, {42131, 43397}, {42143, 43200}, {42146, 43199}, {42163, 43109}, {42166, 43108}, {42215, 43791}, {42216, 43792}, {42271, 43887}, {42272, 43888}, {42516, 42688}, {42517, 42689}, {42574, 43313}, {42575, 43312}, {42629, 42778}, {42630, 42777}, {42694, 43774}, {42695, 43773}, {42912, 43245}, {42913, 43244}, {42920, 43635}, {42921, 43634}, {42934, 54577}, {42935, 54576}, {42960, 42976}, {42961, 42977}, {43342, 54595}, {43343, 54596}, {47354, 55587}, {48310, 55683}, {48874, 50956}, {48898, 51129}, {48901, 51166}, {48942, 50983}, {50802, 51700}, {50825, 50874}, {50832, 50867}, {50864, 61597}, {50865, 61510}, {50959, 51732}, {50978, 51537}, {50980, 51164}, {50987, 51217}, {51023, 61624}, {51024, 61545}, {51065, 61623}, {51075, 61281}, {51131, 58445}, {51184, 51213}

X(61999) = midpoint of X(i) and X(j) for these {i,j}: {4, 12101}, {382, 12100}, {546, 3830}, {547, 3543}, {548, 15682}, {3627, 5066}, {3845, 3853}, {5097, 51025}, {5901, 50862}, {9956, 50869}, {13451, 32062}, {14893, 15687}, {15684, 15691}, {18583, 51022}, {21849, 32137}, {24206, 51026}, {33179, 50868}, {48942, 50983}, {50864, 61597}, {50865, 61510}, {51023, 61624}, {51024, 61545}, {51065, 61623}
X(61999) = reflection of X(i) in X(j) for these {i,j}: {10109, 546}, {10124, 381}, {11812, 3850}, {12100, 12811}, {12102, 12101}, {14891, 11737}, {15690, 16239}, {15759, 5}, {2, 3856}, {3530, 5066}, {3534, 12108}, {3628, 3860}, {3850, 3845}, {3860, 3861}, {550, 11540}, {51700, 50802}, {51732, 50959}, {58445, 51131}, {61281, 51075}
X(61999) = complement of X(62139)
X(61999) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(68), X(58186)}}, {{A, B, C, X(265), X(15759)}}, {{A, B, C, X(1494), X(44245)}}, {{A, B, C, X(10124), X(54512)}}, {{A, B, C, X(14490), X(35472)}}, {{A, B, C, X(15706), X(18550)}}, {{A, B, C, X(55861), X(60121)}}, {{A, B, C, X(55866), X(60122)}}
X(61999) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 12102, 3861}, {4, 15687, 14893}, {5, 15684, 15691}, {5, 30, 15759}, {20, 13727, 3523}, {30, 11540, 550}, {30, 11737, 14891}, {30, 12101, 12102}, {30, 12108, 3534}, {30, 12811, 12100}, {30, 16239, 15690}, {30, 381, 10124}, {30, 3845, 3850}, {30, 3856, 2}, {30, 3861, 3860}, {30, 5066, 3530}, {30, 546, 10109}, {376, 5071, 10303}, {381, 10124, 11737}, {381, 15684, 15692}, {381, 15692, 5}, {381, 3543, 15686}, {549, 15687, 3830}, {549, 15714, 10299}, {550, 14892, 11540}, {1656, 15688, 15701}, {3543, 11001, 15684}, {3543, 15687, 3853}, {3544, 5076, 3627}, {3545, 15690, 16239}, {3545, 3845, 546}, {3627, 14269, 5066}, {3627, 3845, 11539}, {3830, 14269, 1656}, {3832, 14269, 3845}, {3845, 11539, 3832}, {3845, 15686, 381}, {3845, 15687, 3543}, {3850, 10109, 3545}, {10109, 15690, 11812}, {11737, 11812, 547}, {11737, 14891, 3628}, {12101, 14893, 15687}, {14269, 15706, 3839}, {14893, 15687, 30}, {15681, 15706, 376}, {15684, 15723, 11001}, {15694, 15705, 549}, {18586, 18587, 11541}

X(62000) = X(2)X(3)∩X(13)X(54577)

Barycentrics    23*a^4-22*(b^2-c^2)^2-a^2*(b^2+c^2) : :
X(62000) = -22*X[2]+15*X[3], -11*X[599]+4*X[55586], -15*X[3656]+8*X[51095], -8*X[4669]+15*X[50797], X[4677]+6*X[22793], 3*X[5050]+4*X[51022], -5*X[8667]+12*X[53144], 3*X[10165]+4*X[50870], 3*X[10246]+4*X[50862], -11*X[10516]+4*X[55599], -11*X[11178]+4*X[55592], -X[12645]+8*X[34648] and many others

X(62000) lies on these lines: {2, 3}, {13, 54577}, {14, 54576}, {516, 50800}, {598, 54717}, {599, 55586}, {1151, 42526}, {1152, 42527}, {1327, 54595}, {1328, 54596}, {1503, 51173}, {3070, 6498}, {3071, 6499}, {3311, 43516}, {3312, 43515}, {3656, 51095}, {4669, 50797}, {4677, 22793}, {5050, 51022}, {5334, 43111}, {5335, 43110}, {6435, 18512}, {6436, 18510}, {6447, 41952}, {6448, 41951}, {8667, 53144}, {10165, 50870}, {10246, 50862}, {10516, 55599}, {11178, 55592}, {11485, 49811}, {11486, 49810}, {11542, 42589}, {11543, 42588}, {11645, 55712}, {11935, 13482}, {12156, 17503}, {12645, 34648}, {12699, 34641}, {12702, 38098}, {12816, 12820}, {12817, 12821}, {12818, 43562}, {12819, 43563}, {13321, 32062}, {14075, 14537}, {14458, 33698}, {14487, 18550}, {14488, 45103}, {14492, 54494}, {15533, 48901}, {15534, 51172}, {16267, 42509}, {16268, 42508}, {16644, 43400}, {16645, 43399}, {18525, 34747}, {18553, 50989}, {19106, 43369}, {19107, 43368}, {21400, 46851}, {22165, 50954}, {22615, 42417}, {22644, 42418}, {25561, 55609}, {26446, 50869}, {28154, 50874}, {28158, 51078}, {28160, 51110}, {28164, 50807}, {28174, 51068}, {28190, 50867}, {28204, 51094}, {29181, 50957}, {34571, 44518}, {34748, 40273}, {36969, 42816}, {36970, 42815}, {36990, 55714}, {38066, 51118}, {38127, 51119}, {39899, 55715}, {40341, 48895}, {41100, 42125}, {41101, 42128}, {41107, 42093}, {41108, 42094}, {41112, 42102}, {41113, 42101}, {41119, 42940}, {41120, 42941}, {41121, 42962}, {41122, 42963}, {42095, 42631}, {42098, 42632}, {42108, 43873}, {42109, 43874}, {42117, 49874}, {42118, 49873}, {42126, 49947}, {42127, 49948}, {42135, 49812}, {42136, 49876}, {42137, 49875}, {42138, 49813}, {42147, 49860}, {42148, 49859}, {42154, 42976}, {42155, 42977}, {42164, 42502}, {42165, 42503}, {42262, 42576}, {42265, 42577}, {42283, 43503}, {42284, 43504}, {42472, 42984}, {42473, 42985}, {42496, 43364}, {42497, 43365}, {42504, 42581}, {42505, 42580}, {42510, 42818}, {42511, 42817}, {42635, 42988}, {42636, 42989}, {42682, 42781}, {42683, 42782}, {42688, 42693}, {42689, 42692}, {43108, 43403}, {43109, 43404}, {43226, 49907}, {43227, 49908}, {43256, 45385}, {43257, 45384}, {43273, 55707}, {43386, 54542}, {43387, 54543}, {43416, 49827}, {43417, 49826}, {43546, 54480}, {43547, 54479}, {46847, 54048}, {47353, 51175}, {48884, 55702}, {48889, 55581}, {48904, 55619}, {48910, 55598}, {50799, 51069}, {50806, 51103}, {50819, 61269}, {50865, 59503}, {50868, 61287}, {50956, 51143}, {50990, 55584}, {51185, 55709}, {51186, 55605}, {52519, 54642}, {53023, 55713}, {53100, 54478}, {53102, 54813}, {53105, 54477}, {53109, 54582}, {54131, 55719}, {54493, 54934}, {54519, 54720}, {54598, 60305}, {54599, 60306}, {54815, 60631}, {54845, 54896}

X(62000) = midpoint of X(i) and X(j) for these {i,j}: {382, 15700}, {3090, 3543}
X(62000) = reflection of X(i) in X(j) for these {i,j}: {15681, 3528}, {15700, 3851}, {15702, 3857}, {15703, 3832}, {3526, 381}, {3534, 15701}
X(62000) = inverse of X(61997) in orthocentroidal circle
X(62000) = inverse of X(61997) in Yff hyperbola
X(62000) = anticomplement of X(62057)
X(62000) = pole of line {523, 61997} with respect to the orthocentroidal circle
X(62000) = pole of line {6, 61997} with respect to the Kiepert hyperbola
X(62000) = pole of line {523, 61997} with respect to the Yff hyperbola
X(62000) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(470), X(54577)}}, {{A, B, C, X(471), X(54576)}}, {{A, B, C, X(3526), X(54512)}}, {{A, B, C, X(3628), X(54585)}}, {{A, B, C, X(5055), X(54924)}}, {{A, B, C, X(5094), X(54717)}}, {{A, B, C, X(8703), X(57823)}}, {{A, B, C, X(11331), X(33698)}}, {{A, B, C, X(12100), X(18550)}}, {{A, B, C, X(14487), X(35473)}}, {{A, B, C, X(14488), X(52293)}}, {{A, B, C, X(21400), X(46853)}}, {{A, B, C, X(21844), X(46851)}}, {{A, B, C, X(37453), X(54477)}}, {{A, B, C, X(52289), X(54494)}}, {{A, B, C, X(52292), X(60132)}}, {{A, B, C, X(55859), X(60122)}}, {{A, B, C, X(55860), X(60121)}}
X(62000) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15687, 3830}, {2, 15688, 15693}, {2, 15697, 10299}, {2, 15698, 14869}, {2, 15715, 11812}, {2, 3529, 8703}, {2, 8703, 15707}, {3, 3843, 3854}, {4, 12102, 3843}, {4, 15687, 14269}, {5, 11541, 6827}, {5, 15640, 15695}, {30, 15701, 3534}, {30, 3528, 15681}, {30, 381, 3526}, {30, 3832, 15703}, {30, 3851, 15700}, {30, 3857, 15702}, {381, 15696, 5055}, {381, 15706, 5}, {382, 5079, 1657}, {382, 546, 15720}, {547, 15697, 15722}, {1656, 3839, 381}, {3090, 3523, 16239}, {3090, 3543, 30}, {3523, 15713, 15701}, {3526, 3851, 5079}, {3529, 15717, 550}, {3529, 3839, 11737}, {3534, 5072, 11540}, {3543, 3839, 15717}, {3543, 3843, 5054}, {3543, 5066, 15685}, {3545, 5073, 14093}, {3627, 3845, 15713}, {3627, 3860, 11001}, {3830, 14269, 2}, {3830, 15685, 3543}, {3832, 14869, 3851}, {3839, 15702, 3857}, {3839, 3853, 15684}, {3843, 15685, 5066}, {3845, 15713, 3860}, {5055, 11001, 15716}, {5066, 12101, 12102}, {10109, 14893, 3845}, {11001, 15716, 15696}, {11737, 15707, 1656}, {14269, 15681, 546}, {14269, 15687, 382}, {14269, 15707, 3839}, {15681, 15720, 15688}, {15684, 15707, 3529}, {15697, 16434, 15690}, {15722, 17800, 15697}, {41107, 43476, 42093}, {41108, 43475, 42094}

(Higher numbered parts will be started in the future.)

This is the end of PART 31: Centers X(60001) - X(62000)

PART 1: Introduction and Centers X(1) - X(1000) PART 2: Centers X(1001) - X(3000) PART 3: Centers X(3001) - X(5000)
PART 4: Centers X(5001) - X(7000) PART 5: Centers X(7001) - X(10000) PART 6: Centers X(10001) - X(12000)
PART 7: Centers X(12001) - X(14000) PART 8: Centers X(14001) - X(16000) PART 9: Centers X(16001) - X(18000)
PART 10: Centers X(18001) - X(20000) PART 11: Centers X(20001) - X(22000) PART 12: Centers X(22001) - X(24000)
PART 13: Centers X(24001) - X(26000) PART 14: Centers X(26001) - X(28000) PART 15: Centers X(28001) - X(30000)
PART 16: Centers X(30001) - X(32000) PART 17: Centers X(32001) - X(34000) PART 18: Centers X(34001) - X(36000)
PART 19: Centers X(36001) - X(38000) PART 20: Centers X(38001) - X(40000) PART 21: Centers X(40001) - X(42000)
PART 22: Centers X(42001) - X(44000) PART 23: Centers X(44001) - X(46000) PART 24: Centers X(46001) - X(48000)
PART 25: Centers X(48001) - X(50000) PART 26: Centers X(50001) - X(52000) PART 27: Centers X(52001) - X(54000)
PART 28: Centers X(54001) - X(56000) PART 29: Centers X(56001) - X(58000) PART 30: Centers X(58001) - X(60000)
PART 31: Centers X(60001) - X(62000) PART 32: Centers X(62001) - X(64000) PART 33: Centers X(64001) - X(66000)
PART 34: Centers X(66001) - X(68000) PART 35: Centers X(68001) - X(70000) PART 36: Centers X(70001) - X(72000)