X1434

X274-BETH CONJUGATE OF X274

X1434 = isogonal conjugate of X1334
< 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) { 7, 21 }: Central Line L(7, 21) { 57, 85 }: Central Line L(57, 85) { 81, 279 }: Central Line L(81, 279) { 310, 349 }: Central Line L(310, 349) { 65, 664 }: Central Line L(65, 664) { 270, 757 }: Central Line L(270, 757) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_274 = ISOGONAL CONJUGATE OF X(213) (0.5168, 0.1843) X_7 = GERGONNE POINT (0.5903, 0.2769) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_279 = ISOGONAL CONJUGATE OF X(220) (0.6236, 0.3540) X_310 = ISOTOMIC CONJUGATE OF X(42) (0.4762, 0.1536) X_349 = ISOTOMIC CONJUGATE OF X(284) (0.5089, 0.1906) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_664 = TRILINEAR POLE OF LINE X(2)X(7) (0.2391, 0.5142) X_270 = ISOGONAL CONJUGATE OF X(201) (0.6168, 0.3881) X_757 = ISOGONAL CONJUGATE OF X(756) (0.5971, 0.2688) X_1434 = -BETH CONJUGATE OF X(274) (0.6014, 0.2949) A B C X274 X7 X21 X57 X85 X81 X279 X310 X349 X65 X664 X270 X757 X1434 (a, b, c) = (5, 6, 7) | AB = 1

X1434 (X274-BETH CONJUGATE OF X274) 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 \(u : v : w\) = X274
Barycentrics: \(1/((b + c) (a - b - c)) : :\)
Search Value (6, 9, 13): \(0.540801134852\)
▸ Incident Central Lines13 lines

{7, 21}, {27, 1088}, {57, 85}, {58, 1414}, {65, 664}, {81, 279}, {99, 1477}, {270, 757}, {310, 349}, {332, 951}, {552, 553}, {658, 1446}, {576, 1475}

▸ Functional Relations7 relations