X1097

TRILINEAR SQUARE OF X20

< 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) { 1, 75 }: Central Line L(1, 75) { 31, 775 }: Central Line L(31, 775) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_775 = ISOGONAL CONJUGATE OF X(774) (0.4699, 0.1510) X_1097 = TRILINEAR SQUARE OF X(20) (0.3653, 0.0487) A B C X1 X75 X31 X775 X1097 (a, b, c) = (5, 6, 7) | AB = 1

X1097 (TRILINEAR SQUARE OF X20) 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 \(f(A,B,C) = (\cos A - \cos B \cos C)^{2}\)
Barycentrics: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = (\sin A) f(A,B,C)\)
Search Value (6, 9, 13): \(1.860383709253\)
▸ Incident Central Lines2 lines

{1, 75}, {31, 775}