X285

X58-CROSS CONJUGATE OF X21

X285 = isogonal conjugate of X227
< 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) { 21, 84 }: Central Line L(21, 84) { 29, 81 }: Central Line L(29, 81) { 271, 282 }: Central Line L(271, 282) { 280, 1043 }: Central Line L(280, 1043) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_271 = ISOGONAL CONJUGATE OF X(208) (1.1546, 2.8606) X_282 = -CROSS CONJUGATE OF X(9) (0.6199, 0.7507) X_280 = -CROSS CONJUGATE OF X(8) (0.6379, 0.8041) X_1043 = CEVAPOINT OF X(1) AND X(20) (0.4149, 0.0930) X_285 = -CROSS CONJUGATE OF X(21) (0.6147, 0.7300) A B C X58 X21 X84 X29 X81 X271 X282 X280 X1043 X285 (a, b, c) = (5, 6, 7) | AB = 1

X285 (X58-CROSS CONJUGATE OF X21) 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 \(f(A,B,C) = 1/[(\cos B + \cos C)(-1 - \cos A + \cos B + \cos C)]\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(4.527607627783\)
▸ Incident Central Lines4 lines

{21, 84}, {29, 81}, {271, 282}, {280, 1043}

▸ Functional Relations3 relations