X309

ISOTOMIC CONJUGATE OF X40

X309 is the isotomic conjugate of X40.
< 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) { 69, 189 }: Central Line L(69, 189) { 85, 264 }: Central Line L(85, 264) { 75, 280 }: Central Line L(75, 280) { 77, 318 }: Central Line L(77, 318) { 84, 314 }: Central Line L(84, 314) { 304, 322 }: Central Line L(304, 322) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_40 = BEVAN POINT (0.4286, -0.0292) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_189 = CYCLOCEVIAN CONJUGATE OF X(8) (0.6131, 0.7055) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_264 = ISOTOMIC CONJUGATE OF CIRCUMCENTER (0.5720, 0.3293) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_280 = -CROSS CONJUGATE OF X(8) (0.6379, 0.8041) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_318 = ISOTOMIC CONJUGATE OF X(77) (0.5514, 0.2839) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_314 = ISOTOMIC CONJUGATE OF X(65) (0.4457, 0.1206) X_304 = ISOTOMIC CONJUGATE OF X(19) (0.3683, 0.0513) X_322 = ISOTOMIC CONJUGATE OF X(84) (0.3430, -0.0168) X_309 = ISOTOMIC CONJUGATE OF X(40) (0.6237, 0.7391) A B C X40 X69 X189 X85 X264 X75 X280 X77 X318 X84 X314 X304 X322 X309 (a, b, c) = (5, 6, 7) | AB = 1

X309 (ISOTOMIC CONJUGATE OF X40) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((\csc^{2} A)/(-1 - \cos A + \cos B + \cos C) : :\)
Search Value (6, 9, 13): \(6.780894052493\)
▸ Alternate Coordinates1 form

  • Trilinears: \(b^{2} c^{2} (a^{2} (a^{2} - (b - c)^{2})^{2} - (b - c)^{2} (a^{2} - (b + c)^{2})^{2}) : :\)

▸ Incident Central Lines6 lines

{69, 189}, {75, 280}, {77, 318}, {84, 314}, {85, 264}, {304, 322}

▸ Functional Relations5 relations