X2140

EIGENTRANSFORM OF X101

X2140 = X101-Ceva conjugate of X514
< 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, 116 }: Central Line L(5, 116) { 3, 142 }: Central Line L(3, 142) { 218, 226 }: Central Line L(218, 226) { 85, 514 }: Central Line L(85, 514) { 39, 1086 }: Central Line L(39, 1086) { 170, 1699 }: Central Line L(170, 1699) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_116 = MIDPOINT OF X(4) AND X(103) (0.6990, 0.0375) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_218 = -CEVA CONJUGATE OF X(55) (0.6557, 0.3333) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_1086 = CENTER OF HYPERBOLA {{A,B,C,X(2),X(7)|} (0.7687, 0.1000) X_170 = -ALEPH CONJUGATE OF X(9) (0.4465, -0.0557) X_1699 = EXSIMILICENTER(BEVAN CIRCLE, NINE-POINT CIRCLE) (0.5986, 0.3416) X_2140 = EIGENTRANSFORM OF X(101) (0.5606, 0.2423) A B C X101 X514 X5 X116 X3 X142 X218 X226 X85 X39 X1086 X170 X1699 X2140 (a, b, c) = (5, 6, 7) | AB = 1

X2140 (EIGENTRANSFORM OF X101) 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 \(u : v : w\) = X101
Barycentrics: \(af(u,v,w) : bf(v,w,u) : cf(w,u,v)\)
Search Value (6, 9, 13): \(1.468044730980\)

X2140 lies on the cubic K258.

▸ Incident Central Lines8 lines

{3, 142}, {5, 116}, {39, 1086}, {85, 514}, {101, 2141}, {170, 1699}, {218, 226}, {244, 2085}

▸ Functional Relations2 relations