X315

ISOTOMIC CONJUGATE OF X66

X315 is the isotomic conjugate of X66.
< 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) { 637, 638 }: Central Line L(637, 638) { 2, 32 }: Central Line L(2, 32) { 4, 69 }: Central Line L(4, 69) { 20, 99 }: Central Line L(20, 99) { 5, 183 }: Central Line L(5, 183) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_637 = ANTICOMPLEMENT OF X(371) (0.4819, 0.1805) X_638 = ANTICOMPLEMENT OF X(372) (0.1827, -0.3137) X_2 = CENTROID (0.5374, 0.2000) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_4 = ORTHOCENTER (0.6122, 0.3958) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_99 = STEINER POINT (0.1109, 0.4322) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_183 = TRILINEAR PRODUCT X(75)X(182) (0.4700, 0.1275) X_315 = ISOTOMIC CONJUGATE OF X(66) (0.3323, -0.0666) A B C X637 X638 X2 X32 X4 X69 X20 X99 X5 X183 X315 (a, b, c) = (5, 6, 7) | AB = 1

X315 (ISOTOMIC CONJUGATE OF X66) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(bc(b^{4} + c^{4} - a^{4}) : ca(c^{4} + a^{4} - b^{4}) : ab(a^{4} + b^{4} - c^{4})\)
Barycentrics: \(b^{4} + c^{4} - a^{4} : c^{4} + a^{4} - b^{4} : a^{4} + b^{4} - c^{4}\)
Search Value (6, 9, 13): \(7.326681485094\)
▸ Incident Central Lines15 lines

{2, 32}, {3, 325}, {4, 69}, {5, 183}, {8, 760}, {20, 99}, {68, 290}, {192, 746}, {194, 736}, {274, 377}, {297, 394}, {343, 458}, {371, 491}, {372, 492}, {631, 1007}

▸ Functional Relations7 relations