X2130

EIGENTRANSFORM OF X20

X2130 = X20-Ceva conjugate of X64
< 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) { 3348, 3 }: Central Line L(3348, 3) { 4, 1073 }: Central Line L(4, 1073) { 20, 2131 }: Central Line L(20, 2131) { 1, 3347 }: Central Line L(1, 3347) { 40, 3354 }: Central Line L(40, 3354) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3348 = ISOGONAL CONJUGATE OF X(3183) (0.4000, -0.1150) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_4 = ORTHOCENTER (0.6122, 0.3958) X_1073 = -CROSS CONJUGATE OF X(3) (0.4792, -0.4343) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_2131 = ISOGONAL CONJUGATE OF X(2130) (0.5325, 0.1568) X_1 = INCENTER (0.5714, 0.2333) X_3347 = ISOGONAL CONJUGATE OF X(3182) (0.3848, -0.3283) X_40 = BEVAN POINT (0.4286, -0.0292) X_3354 = ISOGONAL CONJUGATE OF X(3353) (0.4568, 0.0283) X_2130 = EIGENTRANSFORM OF X(20) (0.6000, 0.3192) A B C X3348 X3 X4 X1073 X20 X2131 X1 X3347 X40 X3354 X2130 (a, b, c) = (5, 6, 7) | AB = 1

X2130 (EIGENTRANSFORM OF X20) 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 \(u : v : w\) = X20
Barycentrics: \(af(u,v,w) : bf(v,w,u) : cf(w,u,v)\)
Search Value (6, 9, 13): \(14.193656041041\)

X2130 lies on the Darboux cubic (K004).

▸ Incident Central Lines7 lines

{1, 3347}, {3, 3348}, {4, 1073}, {20, 2131}, {40, 3354}, {84, 3345}, {1490, 3473}

▸ Functional Relations3 relations