X879

ISOTOMIC CONJUGATE OF X877

X879 is the isotomic conjugate of X877.
< 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) { 74, 98 }: Central Line L(74, 98) { 4, 512 }: Central Line L(4, 512) { 3, 525 }: Central Line L(3, 525) { 6, 523 }: Central Line L(6, 523) { 69, 520 }: Central Line L(69, 520) { 67, 526 }: Central Line L(67, 526) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_877 = INTERSECTION OF LINES X(4)X(69) AND X(99)X(112) (0.8267, 0.7499) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_98 = TARRY POINT (0.8891, -0.2281) X_4 = ORTHOCENTER (0.6122, 0.3958) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0468, 0.2556) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_520 = ISOGONAL CONJUGATE OF X(107) (-0.0490, 0.2227) X_67 = ISOGONAL CONJUGATE OF X(23) (0.7606, -0.2152) X_526 = ISOGONAL CONJUGATE OF X(476) (1.0501, 0.4856) X_879 = ISOTOMIC CONJUGATE OF X(877) (1.2088, 0.0345) A B C X877 X74 X98 X4 X512 X3 X525 X6 X523 X69 X520 X67 X526 X879 (a, b, c) = (5, 6, 7) | AB = 1

X879 (ISOTOMIC CONJUGATE OF X877) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(u(bv - cw)/(a^{2}u^{2} - bcvw) : :\), where \(u : v : w\) = X4
Barycentrics: \((b^{2} - c^{2}) (b^{2} + c^{2} - a^{2})/(b^{4} + c^{4} - a^{2} b^{2} - a^{2} c^{2}) : :\)
Search Value (6, 9, 13): \(-17.380419573092\)

X879 lies on the Jerabek hyperbola.

▸ Incident Central Lines10 lines

{3, 525}, {4, 512}, {6, 523}, {54, 826}, {66, 924}, {67, 526}, {69, 520}, {74, 98}, {287, 895}, {2966, 4266}

▸ Functional Relations9 relations