X272

ISOGONAL CONJUGATE OF X209

X272 is the isogonal conjugate of X209.
< 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) { 7, 58 }: Central Line L(7, 58) { 21, 75 }: Central Line L(21, 75) { 60, 86 }: Central Line L(60, 86) { 2, 284 }: Central Line L(2, 284) { 28, 273 }: Central Line L(28, 273) { 261, 310 }: Central Line L(261, 310) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_7 = GERGONNE POINT (0.5903, 0.2769) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_60 = ISOGONAL CONJUGATE OF X(12) (0.5790, 0.2258) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_2 = CENTROID (0.5374, 0.2000) X_284 = -CROSS CONJUGATE OF X(21) (0.5646, 0.2088) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_273 = ISOGONAL CONJUGATE OF X(212) (0.6191, 0.4329) X_261 = ISOTOMIC CONJUGATE OF X(12) (0.5072, 0.1625) X_310 = ISOTOMIC CONJUGATE OF X(42) (0.4762, 0.1536) X_272 = ISOGONAL CONJUGATE OF X(209) (-0.2458, -0.0534) A B C X3 X81 X7 X58 X21 X75 X60 X86 X2 X284 X28 X273 X261 X310 X272 (a, b, c) = (5, 6, 7) | AB = 1

X272 (ISOGONAL CONJUGATE OF X209) 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 \(f(A,B,C) = 1/[(\sin A + \sin(A - B) + \sin(A - C))(\sin B + \sin C)]\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(0.811216421884\)
▸ Incident Central Lines7 lines

{2, 284}, {7, 58}, {21, 75}, {28, 273}, {60, 86}, {261, 310}, {1014, 1088}

▸ Functional Relations2 relations