X1432

X257-BETH CONJUGATE OF X257

X1432 = X893-cross conjugate of X256
< 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) { 1, 256 }: Central Line L(1, 256) { 2, 257 }: Central Line L(2, 257) { 7, 330 }: Central Line L(7, 330) { 65, 291 }: Central Line L(65, 291) { 57, 893 }: Central Line L(57, 893) { 105, 904 }: Central Line L(105, 904) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_257 = ISOGONAL CONJUGATE OF X(172) (0.5240, 0.1822) X_1 = INCENTER (0.5714, 0.2333) X_256 = 1st SHARYGIN POINT (0.5601, 0.2146) X_2 = CENTROID (0.5374, 0.2000) X_7 = GERGONNE POINT (0.5903, 0.2769) X_330 = ISOTOMIC CONJUGATE OF X(192) (0.4364, 0.1391) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_291 = 2nd SHARYGIN POINT (1.0249, 0.0364) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_893 = -CROSS CONJUGATE OF X(292) (0.5910, 0.2480) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_904 = -HIRST INVERSE OF X(256) (0.6163, 0.2816) X_1432 = -BETH CONJUGATE OF X(257) (0.6068, 0.2916) A B C X257 X1 X256 X2 X7 X330 X65 X291 X57 X893 X105 X904 X1432 (a, b, c) = (5, 6, 7) | AB = 1

X1432 (X257-BETH CONJUGATE OF X257) 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 \(u : v : w\) = X257
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.518892555779\)
▸ Incident Central Lines11 lines

{1, 256}, {2, 257}, {7, 330}, {28, 1178}, {56, 985}, {57, 893}, {65, 291}, {81, 1429}, {105, 904}, {961, 1042}, {1258, 1400}

▸ Functional Relations4 relations