ETC

X(72420) = X(2)X(9291)∩X(4)X(290)

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

Antreas Hatzipolakis and Ercole Suppa, euclid 9541.

X(72420) lies on these lines: {2, 9291}, {4, 290}, {20, 16089}, {69, 57677}, {76, 1093}, {107, 37465}, {194, 47739}, {253, 264}, {276, 3090}, {311, 59139}, {317, 42355}, {381, 42368}, {393, 2998}, {683, 6524}, {1235, 52661}, {1975, 15143}, {2052, 2996}, {5071, 55079}, {6331, 6337}, {6530, 44144}, {8795, 15077}, {11185, 62274}, {13450, 44146}, {14618, 53173}, {16081, 64983}, {18817, 59428}, {22456, 53783}, {27376, 42359}, {40680, 68535}, {52448, 62949}

X(72420) = polar conjugate of X(51336)
X(72420) = lies on all circumconics with perspector on the line {30476, 40887}
X(72420) = intersection, other than A, B, C, of the circumconics: {{A,B,C,X(4),X(1968)}, {A,B,C,X(69),X(59527)}, {A,B,C,X(253),X(290)}, {A,B,C,X(263),X(40951)}, {A,B,C,X(6526),X(57677)}}
X(72420) = pole of tripolar of X(51336) with respect to polar circle
X(72420) = pole of the line {16229, 62521} with respect to Steiner circumellipse
X(72420) = pole of the line {417, 10607} with respect to Wallace hyperbola
X(72420) = trilinear pole of line {X(30476), X(40887)}
X(72420) = barycentric product X(i)*X(j) for these (i, j): {264, 9308}, {290, 40887}, {823, 17893}, {1957, 1969}, {1958, 57806}, {1968, 18022}, {1975, 2052}, {6331, 16229}, {6528, 30476}, {9306, 18027}, {15143, 60199}, {17478, 57973}
X(72420) = barycentric quotient X(i)/X(j) for these (i, j): {4, 51336}, {92, 9255}, {158, 9258}, {264, 9289}, {393, 9292}, {1957, 48}, {1958, 255}, {1968, 184}, {1975, 394}, {2052, 9307}, {2451, 39201}, {2996, 60834}, {6528, 43188}, {9306, 577}, {9308, 3}, {15143, 3289}, {15352, 65837}, {16229, 647}, {17215, 4091}, {17478, 822}, {17893, 24018}, {22089, 32320}, {30476, 520}, {37199, 3167}, {40887, 511}, {59527, 6509}, {59561, 22401}, {60841, 60833}, {64983, 43727}
X(72420) = trilinear product X(i)*X(j) for these (i, j): {92, 9308}, {107, 17893}, {158, 1975}, {264, 1957}, {811, 16229}, {821, 59527}, {823, 30476}, {1821, 40887}, {1958, 2052}, {1968, 1969}, {2451, 57973}, {6528, 17478}, {9306, 57806}
X(72420) = trilinear quotient X(i)/X(j) for these (i, j): {48, 9308}, {92, 51336}, {158, 9292}, {184, 1957}, {255, 1975}, {264, 9255}, {520, 17893}, {577, 1958}, {810, 16229}, {820, 59527}, {822, 30476}, {1755, 40887}, {1968, 9247}, {1969, 9289}, {2052, 9258}, {9306, 52430}, {9307, 57806}, {17215, 23224}, {17478, 39201}, {43188, 57973}
X(72420) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6528, 18027, 4}, {9291, 62576, 2}

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