X1094

TRILINEAR SQUARE OF X15

< 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) { 15, 36 }: Central Line L(15, 36) { 48, 163 }: Central Line L(48, 163) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_15 = 1st ISODYNAMIC POINT (0.5519, 0.1878) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_163 = TRILINEAR PRODUCT X(6)*X(110) (0.3174, 0.5883) X_1094 = TRILINEAR SQUARE OF X(15) (0.5301, 0.1475) A B C X15 X36 X48 X163 X1094 (a, b, c) = (5, 6, 7) | AB = 1

X1094 (TRILINEAR SQUARE OF X15) 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 \(f(A,B,C) = \sin^{2}(A + \pi /3)\)
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): \(3.163513213689\)
▸ Incident Central Lines2 lines

{15, 36}, {48, 163}