X1997

ORTHOCORRESPONDENT OF X8

< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 37 }: Central Line L(2, 37) { 1210, 1265 }: Central Line L(1210, 1265) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_1210 = ISOGONAL CONJUGATE OF X(1167) (0.6144, 0.2754) X_1265 = ISOTOMIC CONJUGATE OF X(1119) (0.2751, 0.0213) X_1997 = ORTHOCORRESPONDENT OF X(8) (0.7807, 0.3999) A B C X2 X37 X1210 X1265 X1997 (a, b, c) = (5, 6, 7) | AB = 1

X1997 (ORTHOCORRESPONDENT OF X8) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = yz + (-x \cos A + y \cos B + z \cos C)x\), where \(x : y : z\) = X8
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-5.096430869392\)
▸ Incident Central Lines2 lines

{2, 37}, {1210, 1265}