X342

ISOTOMIC CONJUGATE OF X271

X342 is the isotomic conjugate of X271.
< 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) { 4, 7 }: Central Line L(4, 7) { 92, 226 }: Central Line L(92, 226) { 85, 264 }: Central Line L(85, 264) { 196, 329 }: Central Line L(196, 329) { 253, 318 }: Central Line L(253, 318) { 9, 653 }: Central Line L(9, 653) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_271 = ISOGONAL CONJUGATE OF X(208) (1.1546, 2.8606) X_4 = ORTHOCENTER (0.6122, 0.3958) X_7 = GERGONNE POINT (0.5903, 0.2769) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_264 = ISOTOMIC CONJUGATE OF CIRCUMCENTER (0.5720, 0.3293) X_196 = -CEVA CONJUGATE OF X(4) (0.5649, -0.1989) X_329 = ISOTOMIC CONJUGATE OF X(189) (0.3847, -0.0222) X_253 = -CROSS CONJUGATE OF X(2) (3.5087, 32.5688) X_318 = ISOTOMIC CONJUGATE OF X(77) (0.5514, 0.2839) X_9 = MITTENPUNKT (0.5110, 0.1615) X_653 = TRILINEAR POLE OF LINE X(1)X(4) (0.5097, 0.6030) X_342 = ISOTOMIC CONJUGATE OF X(271) (0.5119, -0.1470) A B C X271 X4 X7 X92 X226 X85 X264 X196 X329 X253 X318 X9 X653 X342 (a, b, c) = (5, 6, 7) | AB = 1

X342 (ISOTOMIC CONJUGATE OF X271) 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 \(f(A,B,C) = (\csc 2A \tan A/2)(1 + \cos A - \cos B - \cos C)\)
Barycentrics: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = (\sec A \tan A/2)(1 + \cos A - \cos B - \cos C)\)
Search Value (6, 9, 13): \(0.568818365298\)
▸ Incident Central Lines8 lines

{4, 7}, {9, 653}, {85, 264}, {92, 226}, {108, 1005}, {196, 329}, {253, 318}, {393, 948}

▸ Functional Relations5 relations