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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, 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 image 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 image 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