X341

ISOTOMIC CONJUGATE OF X269

X341 is the isotomic conjugate of X269.
< 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) { 10, 75 }: Central Line L(10, 75) { 8, 210 }: Central Line L(8, 210) { 40, 190 }: Central Line L(40, 190) { 253, 322 }: Central Line L(253, 322) { 280, 345 }: Central Line L(280, 345) { 304, 668 }: Central Line L(304, 668) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_269 = ISOGONAL CONJUGATE OF X(200) (0.6369, 0.3847) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_8 = NAGEL POINT (0.4694, 0.1333) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_40 = BEVAN POINT (0.4286, -0.0292) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_253 = -CROSS CONJUGATE OF X(2) (3.5087, 32.5688) X_322 = ISOTOMIC CONJUGATE OF X(84) (0.3430, -0.0168) X_280 = -CROSS CONJUGATE OF X(8) (0.6379, 0.8041) X_345 = ISOTOMIC CONJUGATE OF X(278) (0.3405, 0.0381) X_304 = ISOTOMIC CONJUGATE OF X(19) (0.3683, 0.0513) X_668 = TRILINEAR POLE OF LINE X(2)X(37) (0.0159, 0.3302) X_341 = ISOTOMIC CONJUGATE OF X(269) (0.3509, 0.0650) A B C X269 X10 X75 X8 X210 X40 X190 X253 X322 X280 X345 X304 X668 X341 (a, b, c) = (5, 6, 7) | AB = 1

X341 (ISOTOMIC CONJUGATE OF X269) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(b^{2}c^{2}(b + c - a)^{2} : c^{2}a^{2}(c + a - b)^{2} : a^{2}b^{2}(a + b - c)^{2}\)
Barycentrics: \(bc(b + c - a)^{2} : ca(c + a - b)^{2} : ab(a + b - c)^{2}\)
Search Value (6, 9, 13): \(6.222728671983\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\csc^{4} A/2 : \csc^{4} B/2 : \csc^{4} C/2\)

▸ Incident Central Lines9 lines

{1, 1050}, {8, 210}, {10, 75}, {40, 190}, {200, 1043}, {253, 322}, {280, 345}, {304, 668}, {305, 1088}

▸ Functional Relations7 relations