X1087

TRILINEAR SQUARE OF X5

X1087 = {X1,X564}-harmonic conjugate of X1109
< 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, 564 }: Central Line L(1, 564) { 31, 91 }: Central Line L(31, 91) { 92, 255 }: Central Line L(92, 255) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1109 = TRILINEAR SQUARE OF X(523) (0.7246, 0.0705) 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_31 = 2nd POWER POINT (0.6228, 0.3008) X_91 = ISOGONAL CONJUGATE OF X(47) (-0.0865, -0.0205) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_1087 = TRILINEAR SQUARE OF X(5) (0.5422, 0.2643) A B C X1109 X1 X564 X31 X91 X92 X255 X1087 (a, b, c) = (5, 6, 7) | AB = 1

X1087 (TRILINEAR SQUARE OF X5) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1 + \cos(2B - 2C) : :\)
Search Value (6, 9, 13): \(0.084226593682\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\cos^{2}(B - C) : :\)

▸ Incident Central Lines5 lines

{1, 564}, {5, 2599}, {31, 91}, {54, 2595}, {92, 255}

▸ Functional Relations2 relations