X2123

ISOGONAL CONJUGATE OF X2122

X2123 is the isogonal conjugate of X2122.
< 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) { 8, 2122 }: Central Line L(8, 2122) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_89 = ISOGONAL CONJUGATE OF X(45) (0.5963, 0.2697) X_8 = NAGEL POINT (0.4694, 0.1333) X_2122 = EIGENTRANSFORM OF X(8) (0.3815, -2.1505) X_2123 = ISOGONAL CONJUGATE OF X(2122) (0.4395, -0.6430) A B C X56 X89 X8 X2122 X2123 (a, b, c) = (5, 6, 7) | AB = 1

X2123 (ISOGONAL CONJUGATE OF X2122) 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 \(u : v : w\) = X8
Barycentrics: \(a/f(u,v,w) : b/f(v,w,u) : c/f(w,u,v)\)
Search Value (6, 9, 13): \(5.205916338988\)

X2123 lies on the cubic K692.

▸ Incident Central Lines1 line

{8, 2122}

▸ Functional Relations2 relations