X1099

TRILINEAR SQUARE OF X30

< 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) { 162, 255 }: Central Line L(162, 255) { 1, 564 }: Central Line L(1, 564) { 75, 811 }: Central Line L(75, 811) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_162 = CEVAPOINT OF X(108) AND X(109) (0.4897, 0.6018) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_1 = INCENTER (0.5714, 0.2333) X_564 = INTERSECTION OF LINES X(1)X(1048) AND X(47,91) (0.4993, 0.3100) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_811 = ISOGONAL CONJUGATE OF X(810) (0.4151, 0.5616) X_1099 = TRILINEAR SQUARE OF X(30) (0.4597, 0.3520) A B C X162 X255 X1 X564 X75 X811 X1099 (a, b, c) = (5, 6, 7) | AB = 1

X1099 (TRILINEAR SQUARE OF X30) 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 \(f(A,B,C) = (\cos A - 2 \cos B \cos C)^{2}\)
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): \(1.469581371510\)

X1099 lies on the inellipse centered at X10.

▸ Incident Central Lines3 lines

{1, 564}, {75, 811}, {162, 255}