X1091

TRILINEAR SQUARE OF X12

< 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) { 5, 1090 }: Central Line L(5, 1090) { 12, 1109 }: Central Line L(12, 1109) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_1090 = TRILINEAR SQUARE OF X(11) (0.8768, 0.0123) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_1109 = TRILINEAR SQUARE OF X(523) (0.7246, 0.0705) X_1091 = TRILINEAR SQUARE OF X(12) (0.5571, 0.2482) A B C X5 X1090 X12 X1109 X1091 (a, b, c) = (5, 6, 7) | AB = 1

X1091 (TRILINEAR SQUARE OF X12) 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 \(f(A,B,C) = [1 + \cos(B - C)]^{2}\)
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): \(0.946610690797\)
▸ Incident Central Lines2 lines

{5, 1090}, {12, 1109}