X1440

X309-BETH CONJUGATE OF X309

X1440 = cevapoint of X84 and X1422
< 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) { 2, 77 }: Central Line L(2, 77) { 7, 84 }: Central Line L(7, 84) { 75, 280 }: Central Line L(75, 280) { 86, 285 }: Central Line L(86, 285) { 273, 279 }: Central Line L(273, 279) { 271, 307 }: Central Line L(271, 307) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_309 = ISOTOMIC CONJUGATE OF X(40) (0.6237, 0.7391) X_2 = CENTROID (0.5374, 0.2000) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_7 = GERGONNE POINT (0.5903, 0.2769) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_280 = -CROSS CONJUGATE OF X(8) (0.6379, 0.8041) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_285 = -CROSS CONJUGATE OF X(21) (0.6147, 0.7300) X_273 = ISOGONAL CONJUGATE OF X(212) (0.6191, 0.4329) X_279 = ISOGONAL CONJUGATE OF X(220) (0.6236, 0.3540) X_271 = ISOGONAL CONJUGATE OF X(208) (1.1546, 2.8606) X_307 = ISOTOMIC CONJUGATE OF X(29) (0.4659, 0.0959) X_1440 = -BETH CONJUGATE OF X(309) (0.6062, 0.6592) A B C X309 X2 X77 X7 X84 X75 X280 X86 X285 X273 X279 X271 X307 X1440 (a, b, c) = (5, 6, 7) | AB = 1

X1440 (X309-BETH CONJUGATE OF X309) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (1 - \cos A)u(a,b,c)\), where \(u : v : w\) = X309
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.001688556994\)
▸ Incident Central Lines9 lines

{2, 77}, {7, 84}, {27, 1014}, {75, 280}, {86, 285}, {269, 1256}, {271, 307}, {273, 279}, {673, 1436}

▸ Functional Relations5 relations