z

X(72395) = X(30)X(5972)∩X(382)X(15454)

Barycentrics    (4*a^8 + a^6*b^2 - 10*a^4*b^4 + a^2*b^6 + 4*b^8 - 9*a^6*c^2 + 11*a^4*b^2*c^2 + 11*a^2*b^4*c^2 - 9*b^6*c^2 + 3*a^4*c^4 - 17*a^2*b^2*c^4 + 3*b^4*c^4 + 5*a^2*c^6 + 5*b^2*c^6 - 3*c^8)*(4*a^8 - 9*a^6*b^2 + 3*a^4*b^4 + 5*a^2*b^6 - 3*b^8 + a^6*c^2 + 11*a^4*b^2*c^2 - 17*a^2*b^4*c^2 + 5*b^6*c^2 - 10*a^4*c^4 + 11*a^2*b^2*c^4 + 3*b^4*c^4 + a^2*c^6 - 9*b^2*c^6 + 4*c^8) : :
X(72395) = X[477] - 3 X[52219], 3 X[1138] - 7 X[46045], 3 X[5627] + 5 X[10721], 5 X[14536] + 11 X[14989], 5 X[17578] - X[71150]

Antreas Hatzipolakis and Peter Moses, euclid 9440.

X(72395) lies on these lines: {30, 5972}, {382, 15454}, {477, 52219}, {523, 13202}, {1138, 46045}, {2452, 61721}, {3146, 3233}, {3154, 58350}, {3260, 62288}, {3471, 62026}, {3543, 9214}, {3627, 14254}, {5627, 10721}, {5641, 46988}, {9154, 46982}, {13473, 47147}, {14536, 14989}, {17578, 71150}, {36298, 43401}, {36299, 43402}, {41522, 64510}, {44267, 45821}, {44992, 52464}, {51349, 52056}, {52661, 57584}, {53159, 68050}

X(72395) = midpoint of X(3146) and X(3233)
X(72395) = isogonal conjugate of X(15055)
X(72395) = isogonal conjugate of the anticomplement of X(36518)
X(72395) = X(i)-cross conjugate of X(j) for these (i,j): {3154, 523}, {58350, 1990}
X(72395) = X(1)-isoconjugate of X(15055)
X(72395) = X(3)-Dao conjugate of X(15055)
X(72395) = barycentric quotient X(6)/X(15055)

---

X(72396) = X(30)X(125)∩X(115)X(1990)

Barycentrics    (2*a^8 - a^6*b^2 - 2*a^4*b^4 - a^2*b^6 + 2*b^8 - 3*a^6*c^2 + 7*a^4*b^2*c^2 + 7*a^2*b^4*c^2 - 3*b^6*c^2 - 3*a^4*c^4 - 13*a^2*b^2*c^4 - 3*b^4*c^4 + 7*a^2*c^6 + 7*b^2*c^6 - 3*c^8)*(2*a^8 - 3*a^6*b^2 - 3*a^4*b^4 + 7*a^2*b^6 - 3*b^8 - a^6*c^2 + 7*a^4*b^2*c^2 - 13*a^2*b^4*c^2 + 7*b^6*c^2 - 2*a^4*c^4 + 7*a^2*b^2*c^4 - 3*b^4*c^4 - a^2*c^6 - 3*b^2*c^6 + 2*c^8) : :
X(72396) = 3 X[10113] + X[38609], 3 X[13851] + X[47327], X[476] + 7 X[15044], X[477] - 3 X[3154], X[477] - 9 X[14644], X[477] + 3 X[34150], X[3154] - 3 X[14644], 3 X[14644] + X[34150], 5 X[3091] - X[14611], 3 X[5066] - X[33505], 3 X[5627] + X[46045], 3 X[7471] - 7 X[66815], X[10721] + 3 X[40630], 11 X[15025] - 3 X[38701], 5 X[15081] - X[36164], 35 X[15081] - 3 X[60740], 7 X[36164] - 3 X[60740], 3 X[23515] - X[47084], 3 X[36184] + X[38580]

Antreas Hatzipolakis and Peter Moses, euclid 9440.

X(72396) lies on these lines: {4, 12079}, {5, 15454}, {30, 125}, {115, 1990}, {265, 36169}, {339, 3260}, {381, 2452}, {403, 8901}, {476, 15044}, {477, 3154}, {523, 7687}, {546, 14254}, {2970, 10151}, {3091, 14611}, {3258, 41522}, {3471, 3850}, {5066, 33505}, {5627, 46045}, {5641, 16076}, {6070, 52219}, {7471, 66815}, {10721, 40630}, {11438, 46255}, {12052, 15465}, {12068, 17702}, {13479, 17986}, {14120, 53866}, {15025, 38701}, {15081, 36164}, {15738, 68070}, {18907, 35906}, {21046, 69545}, {23515, 47084}, {30786, 36170}, {32230, 68642}, {32815, 36891}, {34209, 51349}, {34978, 43917}, {36184, 38580}, {36253, 68308}, {36298, 43416}, {36299, 43417}, {39533, 67863}, {46988, 70054}, {53159, 62350}, {57603, 65729}

X(72396) = midpoint of X(i) and X(j) for these {i,j}: {4, 12079}, {265, 36169}, {3154, 34150}, {6070, 52219}, {11801, 21316}, {15738, 68070}, {36253, 68308}
X(72396) = reflection of X(i) in X(j) for these {i,j}: {{12052, 15465}, {31945, 5}, {41522, 3258}
X(72396) = isogonal conjugate of X(15035)
X(72396) = antigonal image of X(41522)
X(72396) = isogonal conjugate of the anticomplement of X(23515)
X(72396) = X(i)-cross conjugate of X(j) for these (i,j): {6070, 523}, {11251, 43917}, {52219, 30}
X(72396) = X(i)-isoconjugate of X(j) for these (i,j): {{1, 15035}, {1101, 3154}
X(72396) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 15035}, {523, 3154}
X(72396) = cevapoint of X(125) and X(62350)
X(72396) = crosssum of X(32162) and X(47084)
X(72396) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 15035}, {115, 3154}
X(72396) = {X(14644),X(34150)}-harmonic conjugate of X(3154)

---

X(72397) = X(115)X(468)∩X(125)X(524)

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

Antreas Hatzipolakis and Peter Moses, euclid 9440.

X(72397) lies on these lines: {2, 47293}, {30, 51541}, {115, 468}, {125, 524}, {126, 36953}, {265, 36170}, {339, 3266}, {427, 51823}, {858, 52898}, {1640, 34763}, {2452, 5094}, {2770, 14120}, {2970, 37778}, {3154, 36825}, {3906, 22264}, {4062, 21046}, {4590, 30786}, {5914, 47240}, {5967, 41939}, {8371, 50942}, {13479, 16092}, {14061, 44182}, {16103, 47155}, {30739, 66165}, {30745, 31068}, {37454, 43084}, {39602, 47238}, {53136, 57539}, {57496, 62958}, {57607, 65729}

X(72397) = isogonal conjugate of X(52699)
X(72397) = X(i)-isoconjugate of X(j) for these (i,j): {1, 52699}, {1101, 14120}
X(72397) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 52699}, {523, 14120}
X(72397) = trilinear pole of line {690, 44915}
X(72397) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 52699}, {115, 14120}

---