X1431

X256-BETH CONJUGATE OF X256

X1431 = X904-cross conjugate of X893
< 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) { 57, 87 }: Central Line L(57, 87) { 1, 256 }: Central Line L(1, 256) { 65, 257 }: Central Line L(65, 257) { 7, 870 }: Central Line L(7, 870) { 6, 893 }: Central Line L(6, 893) { 56, 904 }: Central Line L(56, 904) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_256 = 1st SHARYGIN POINT (0.5601, 0.2146) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_87 = -CROSS CONJUGATE OF X(1) (0.4794, 0.1691) X_1 = INCENTER (0.5714, 0.2333) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_257 = ISOGONAL CONJUGATE OF X(172) (0.5240, 0.1822) X_7 = GERGONNE POINT (0.5903, 0.2769) X_870 = ISOGONAL CONJUGATE OF X(869) (0.5328, 0.2015) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_893 = -CROSS CONJUGATE OF X(292) (0.5910, 0.2480) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_904 = -HIRST INVERSE OF X(256) (0.6163, 0.2816) X_1431 = -BETH CONJUGATE OF X(256) (0.6270, 0.3250) A B C X256 X57 X87 X1 X65 X257 X7 X870 X6 X893 X56 X904 X1431 (a, b, c) = (5, 6, 7) | AB = 1

X1431 (X256-BETH CONJUGATE OF X256) 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 \(u : v : w\) = X256
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.260928019762\)
▸ Incident Central Lines12 lines

{1, 256}, {6, 893}, {7, 870}, {56, 904}, {57, 87}, {58, 1178}, {65, 257}, {86, 1447}, {292, 694}, {518, 1222}, {758, 996}, {979, 1046}

▸ Functional Relations1 relation