X322

ISOTOMIC CONJUGATE OF X84

X322 is the isotomic conjugate of X84.
< 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 { 78, 273 }: Central Line L(78, 273) { 92, 264 }: Central Line L(92, 264) { 304, 309 }: Central Line L(304, 309) { 227, 347 }: Central Line L(227, 347) { 253, 341 }: Central Line L(253, 341) 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_7 = GERGONNE POINT (0.5903, 0.2769) X_8 = NAGEL POINT (0.4694, 0.1333) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_273 = ISOGONAL CONJUGATE OF X(212) (0.6191, 0.4329) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_264 = ISOTOMIC CONJUGATE OF CIRCUMCENTER (0.5720, 0.3293) X_304 = ISOTOMIC CONJUGATE OF X(19) (0.3683, 0.0513) X_309 = ISOTOMIC CONJUGATE OF X(40) (0.6237, 0.7391) X_227 = -CEVA CONJUGATE OF X(65) (0.4792, -0.0460) X_347 = ISOTOMIC CONJUGATE OF X(280) (0.4531, -0.0404) X_253 = -CROSS CONJUGATE OF X(2) (3.5087, 32.5688) X_341 = ISOTOMIC CONJUGATE OF X(269) (0.3509, 0.0650) X_322 = ISOTOMIC CONJUGATE OF X(84) (0.3430, -0.0168) A B C X84 X7 X8 X78 X273 X92 X264 X304 X309 X227 X347 X253 X341 X322 (a, b, c) = (5, 6, 7) | AB = 1

X322 (ISOTOMIC 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 \(f(A,B,C) = (-1 - \cos A + \cos B + \cos C)\csc^{2} A\)
Barycentrics: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = (-1 - \cos A + \cos B + \cos C)\csc A\)
Search Value (6, 9, 13): \(6.445884556756\)
▸ Incident Central Lines9 lines

{2, 1108}, {7, 8}, {78, 273}, {92, 264}, {227, 347}, {253, 341}, {286, 1043}, {304, 309}, {326, 664}

▸ Functional Relations7 relations