X2132

EIGENTRANSFORM OF X30

X2132 is the tangential of X74 on the Neuberg cubic (K001).
< 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, 1138 }: Central Line L(4, 1138) { 30, 2133 }: Central Line L(30, 2133) { 3065, 3466 }: Central Line L(3065, 3466) { 3440, 3441 }: Central Line L(3440, 3441) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_4 = ORTHOCENTER (0.6122, 0.3958) X_1138 = ISOGONAL CONJUGATE OF X(399) (-0.2714, 0.2752) X_2133 = ISOGONAL CONJUGATE OF X(2132) (1.3009, 0.5656) X_3065 = ISOGONAL CONJUGATE OF X(484) (0.8717, -0.1686) X_3466 = ISOGONAL CONJUGATE OF X(3465) (0.6227, -0.5773) X_3440 = -VERTEX CONJUGATE OF X(15) (0.6192, 0.5141) X_3441 = -VERTEX CONJUGATE OF X(16) (-0.3191, 0.5552) X_2132 = EIGENTRANSFORM OF X(30) (1.2703, 0.4856) A B C X30 X74 X4 X1138 X2133 X3065 X3466 X3440 X3441 X2132 (a, b, c) = (5, 6, 7) | AB = 1

X2132 (EIGENTRANSFORM OF X30) 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 \(u : v : w\) = X30
Barycentrics: \(af(u,v,w) : bf(v,w,u) : cf(w,u,v)\)
Search Value (6, 9, 13): \(-12.727448876647\)

X2132 lies on the Neuberg cubic.

▸ Incident Central Lines4 lines

{4, 1138}, {30, 2133}, {3065, 3466}, {3440, 3441}

▸ Functional Relations3 relations