X2139

ISOGONAL CONJUGATE OF X2138

X2139 is the isogonal conjugate of X2138.
< 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) { 20, 159 }: Central Line L(20, 159) { 69, 2138 }: Central Line L(69, 2138) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_159 = -OF-TANGENTIAL-TRIANGLE (0.4211, -0.7266) X_2138 = EIGENTRANSFORM OF X(69) (0.5787, 0.9388) X_2139 = ISOGONAL CONJUGATE OF X(2138) (0.3817, -0.0947) A B C X25 X69 X20 X159 X2138 X2139 (a, b, c) = (5, 6, 7) | AB = 1

X2139 (ISOGONAL CONJUGATE OF X2138) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/f(u,v,w) : 1/f(v,w,u) : 1/f(w,u,v)\), where f is as given just before X2120 and \(u : v : w\) = X69
Barycentrics: \(a/f(u,v,w) : b/f(v,w,u) : c/f(w,u,v)\)
Search Value (6, 9, 13): \(4.030079922750\)

X2139 lies on the cubic, K169.

▸ Incident Central Lines2 lines

{20, 159}, {69, 2138}

▸ Functional Relations2 relations