X1413

X84-BETH CONJUGATE OF X84

X1413 = crosspoint of X84 and X1256
< 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, 84 }: Central Line L(1, 84) { 86, 285 }: Central Line L(86, 285) { 6, 603 }: Central Line L(6, 603) { 57, 937 }: Central Line L(57, 937) { 73, 939 }: Central Line L(73, 939) { 3, 1167 }: Central Line L(3, 1167) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_1 = INCENTER (0.5714, 0.2333) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_285 = -CROSS CONJUGATE OF X(21) (0.6147, 0.7300) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_603 = -CEVA CONJUGATE OF X(56) (0.5992, 0.1851) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_937 = ISOGONAL CONJUGATE OF X(936) (0.6143, 0.2920) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_939 = ISOGONAL CONJUGATE OF X(938) (0.5573, 0.2204) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1167 = 1st SARAGOSSA POINT OF X(34) (0.5172, 0.1910) X_1413 = -BETH CONJUGATE OF X(84) (0.6037, 0.6378) A B C X84 X1 X86 X285 X6 X603 X57 X937 X73 X939 X3 X1167 X1413 (a, b, c) = (5, 6, 7) | AB = 1

X1413 (X84-BETH CONJUGATE OF X84) 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 \(u : v : w\) = X84
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.174281509856\)
▸ Incident Central Lines13 lines

{1, 84}, {3, 1167}, {6, 603}, {34, 1407}, {57, 937}, {64, 1364}, {73, 939}, {86, 285}, {189, 1220}, {280, 1222}, {998, 1448}, {1406, 1411}, {1408, 1474}

▸ Functional Relations5 relations