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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},