X2987

DC(X98)

X2987 = cevapoint of X6 and X511
< 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) { 25, 110 }: Central Line L(25, 110) { 111, 323 }: Central Line L(111, 323) { 193, 317 }: Central Line L(193, 317) { 263, 576 }: Central Line L(263, 576) { 37, 1332 }: Central Line L(37, 1332) { 42, 1331 }: Central Line L(42, 1331) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_230 = -CEVA CONJUGATE OF X(114) (0.9746, 0.6698) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_111 = PARRY POINT (0.9885, -0.0457) X_323 = ISOTOMIC CONJUGATE OF X(94) (-0.8839, -1.3275) X_193 = -CEVA CONJUGATE OF X(2) (0.7878, 0.4690) X_317 = ISOTOMIC CONJUGATE OF X(68) (0.6796, 0.5070) X_263 = ISOGONAL CONJUGATE OF X(183) (0.6298, 0.3525) X_576 = ORTHOHARMONIC OF X(187) (0.6500, 0.3498) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_1332 = ORTHOCORRESPONDENT OF X(100) (-0.2317, 0.1866) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_1331 = ORTHOCORRESPONDENT OF X(101) (-0.2308, 0.2512) X_2987 = DC(X(98)) (1.4170, 0.2477) A B C X230 X25 X110 X111 X323 X193 X317 X263 X576 X37 X1332 X42 X1331 X2987 (a, b, c) = (5, 6, 7) | AB = 1

X2987 (DC(X98)) 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) is as given just before X2979, using U = X98
Barycentrics: \(a^{2}/(a^{2} (2 a^{2} - b^{2} - c^{2}) + (b^{2} - c^{2})^{2}) : :\)
Search Value (6, 9, 13): \(5.754012178437\)

X2987 lies on the MacBeath circumconic.

▸ Incident Central Lines15 lines

{25, 110}, {37, 1332}, {42, 1331}, {69, 2165}, {111, 323}, {141, 2963}, {193, 317}, {251, 1994}, {263, 576}, {287, 2395}, {511, 1976}, {524, 1989}, {526, 895}, {651, 1880}, {1400, 1813}

▸ Functional Relations8 relations