X2207

X2-ISOCONJUGATE OF X326

X2207 = X393-Ceva conjugate of X25
< 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) { 4, 6 }: Van Aubel Line { 25, 32 }: Central Line L(25, 32) { 24, 112 }: Central Line L(24, 112) { 3, 232 }: Central Line L(3, 232) { 83, 458 }: Central Line L(83, 458) { 297, 315 }: Central Line L(297, 315) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_393 = -CROSS CONJUGATE OF X(4) (0.6247, 0.5263) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_4 = ORTHOCENTER (0.6122, 0.3958) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_24 = PERSPECTOR OF ABC AND ORTHIC-OF-ORTHIC TRIANGLE (0.6627, 0.5278) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_232 = -CEVA CONJUGATE OF X(132) (0.6919, 0.7779) X_83 = CEVAPOINT OF CENTROID AND SYMMEDIAN POINT (0.5651, 0.2360) X_458 = EULER LINE INTERCEPT OF LINE X(76)X(275) (0.5800, 0.3115) X_297 = -HIRST INVERSE OF X(4) (0.8440, 1.0022) X_315 = ISOTOMIC CONJUGATE OF X(66) (0.3323, -0.0666) X_2207 = -ISOCONJUGATE OF X(326) (0.6268, 0.5485) A B C X393 X25 X4 X6 X32 X24 X112 X3 X232 X83 X458 X297 X315 X2207 (a, b, c) = (5, 6, 7) | AB = 1

X2207 (X2-ISOCONJUGATE OF X326) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X326
Barycentrics: \(a^{2}/f(a,b,c) : b^{2}/f(b,c,a): c^{2}/f(c,a,b)\)
Search Value (6, 9, 13): \(0.090451261496\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A, B, C) = \sin A \tan^{2} A\)

▸ Incident Central Lines21 lines

{3, 232}, {4, 6}, {19, 2281}, {24, 112}, {25, 32}, {39, 1593}, {76, 683}, {83, 458}, {107, 729}, {155, 1625}, {213, 607}, {235, 2138}, {297, 315}, {459, 1611}, {608, 1426}, {800, 1033}, {981, 1896}, {1015, 1398}, {1572, 1829}, {1918, 2212}, {2271, 2332}

▸ Functional Relations9 relations

Notes

X2207 is the vertex conjugate of the foci of the inellipse that is the barycentric square of the orthic axis. This inellipse has center X3767 and perspector X393. (Randy Hutson, October 15, 2018)