X2120

EIGENTRANSFORM OF X5

X2120 = X5-Ceva conjugate of X54
< 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) { 4, 1157 }: Central Line L(4, 1157) { 5, 2121 }: Central Line L(5, 2121) { 1, 3461 }: Central Line L(1, 3461) { 3, 3463 }: Central Line L(3, 3463) { 3467, 3469 }: Central Line L(3467, 3469) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_54 = KOSNITA POINT (0.5880, 0.2176) X_4 = ORTHOCENTER (0.6122, 0.3958) X_1157 = INVERSE-IN-CIRCUMCIRCLE OF X(54) (1.5871, 1.5280) X_2121 = ISOGONAL CONJUGATE OF X(2120) (0.6451, 0.1816) X_1 = INCENTER (0.5714, 0.2333) X_3461 = ISOGONAL CONJUGATE OF X(3460) (0.6102, 0.2013) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_3463 = ISOGONAL CONJUGATE OF X(3462) (0.3625, -1.7161) X_3467 = ISOGONAL CONJUGATE OF X(3336) (0.4625, 0.1294) X_3469 = ISOGONAL CONJUGATE OF X(3468) (0.6104, 0.5687) X_2120 = EIGENTRANSFORM OF X(5) (0.5135, 0.2811) A B C X5 X54 X4 X1157 X2121 X1 X3461 X3 X3463 X3467 X3469 X2120 (a, b, c) = (5, 6, 7) | AB = 1

X2120 (EIGENTRANSFORM OF X5) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(u,v,w) : f(v,w,u) : f(w,u,v)\), where f is as given just before X2120 and \(u : v : w\) = X5
Barycentrics: \(af(u,v,w) : bf(v,w,u) : cf(w,u,v)\)
Search Value (6, 9, 13): \(1.879615690302\)

X2120 lies on the Napoleon cubic.

▸ Incident Central Lines5 lines

{1, 3461}, {3, 3463}, {4, 1157}, {5, 2121}, {3467, 3469}

▸ Functional Relations2 relations