X3262

ISOTOMIC CONJUGATE OF X104

X3262 is the isotomic conjugate of X104.
< 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, 8 }: Gergonne–Nagel Line { 92, 345 }: Central Line L(92, 345) { 311, 313 }: Central Line L(311, 313) { 325, 523 }: Central Line L(325, 523) { 314, 1389 }: Central Line L(314, 1389) { 286, 1792 }: Central Line L(286, 1792) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_7 = GERGONNE POINT (0.5903, 0.2769) X_8 = NAGEL POINT (0.4694, 0.1333) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_345 = ISOTOMIC CONJUGATE OF X(278) (0.3405, 0.0381) X_311 = ISOTOMIC CONJUGATE OF X(54) (0.4818, 0.1803) X_313 = ISOTOMIC CONJUGATE OF X(58) (0.4368, 0.1249) X_325 = -HIRST INVERSE OF X(69) (-0.3370, -0.7398) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_314 = ISOTOMIC CONJUGATE OF X(65) (0.4457, 0.1206) X_1389 = ISOGONAL CONJUGATE OF X(1385) (0.5985, 0.3054) X_286 = -CROSS CONJUGATE OF X(27) (0.6033, 0.3810) X_1792 = INVERSE MIMOSA TRANSFORM OF X(20) (0.3324, 0.0321) X_3262 = ISOTOMIC CONJUGATE OF X(104) (-0.2831, -0.7604) A B C X104 X7 X8 X92 X345 X311 X313 X325 X523 X314 X1389 X286 X1792 X3262 (a, b, c) = (5, 6, 7) | AB = 1

X3262 (ISOTOMIC CONJUGATE OF X104) 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 \(f(A,B,C) = (\csc^{2} A)(-1 + \cos B + \cos C)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(7.347171919711\)
▸ Incident Central Lines13 lines

{7, 8}, {92, 345}, {99, 2687}, {100, 2861}, {105, 2865}, {264, 1969}, {286, 1792}, {311, 313}, {314, 1389}, {325, 523}, {1111, 1266}, {1232, 1269}, {1332, 1944}

▸ Functional Relations7 relations