X2121

ISOGONAL CONJUGATE OF X2120

X2121 is the isogonal conjugate of X2120.
< 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) { 5, 2120 }: Central Line L(5, 2120) { 195, 3462 }: Central Line L(195, 3462) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_54 = KOSNITA POINT (0.5880, 0.2176) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_2120 = EIGENTRANSFORM OF X(5) (0.5135, 0.2811) X_195 = -CEVA CONJUGATE OF X(3) (0.6761, 0.3331) X_3462 = -CEVA CONJUGATE OF X(4) (0.4603, -0.7229) X_2121 = ISOGONAL CONJUGATE OF X(2120) (0.6451, 0.1816) A B C X54 X5 X2120 X195 X3462 X2121 (a, b, c) = (5, 6, 7) | AB = 1

X2121 (ISOGONAL CONJUGATE OF X2120) 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 \(u : v : w\) = X5
Barycentrics: \(a/f(u,v,w) : b/f(v,w,u) : c/f(w,u,v)\)
Search Value (6, 9, 13): \(0.865885750531\)

X2121 lies on the Napoleon cubic.

▸ Incident Central Lines2 lines

{5, 2120}, {195, 3462}

▸ Functional Relations2 relations