X2996

CD(X25)

X2996 = cevapoint of X115 and X525
< 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) { 20, 98 }: Central Line L(20, 98) { 4, 193 }: Central Line L(4, 193) { 194, 262 }: Central Line L(194, 262) { 230, 439 }: Central Line L(230, 439) { 485, 487 }: Central Line L(485, 487) { 486, 488 }: Central Line L(486, 488) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3053 = INTERSECTION X(3)X(6)∩X(4)X(230) (0.7332, 0.4873) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_98 = TARRY POINT (0.8891, -0.2281) X_4 = ORTHOCENTER (0.6122, 0.3958) X_193 = -CEVA CONJUGATE OF X(2) (0.7878, 0.4690) X_194 = -CEVA CONJUGATE OF X(2) (0.6989, 0.3222) X_262 = ISOGONAL CONJUGATE OF X(182) (0.5893, 0.2856) X_230 = -CEVA CONJUGATE OF X(114) (0.9746, 0.6698) X_439 = EULER X(193)-9th-SUBSTITUTION POINT (0.6570, 0.5128) X_485 = VECTEN POINT (0.5773, 0.2578) X_487 = ANTICOMPLEMENT OF X(486) (1.7742, 0.6338) X_486 = INNER VECTEN POINT (-0.0810, -0.0170) X_488 = ANTICOMPLEMENT OF X(485) (0.4576, 0.0844) X_2996 = CD(X(25)) (-0.6196, -0.1183) A B C X3053 X20 X98 X4 X193 X194 X262 X230 X439 X485 X487 X486 X488 X2996 (a, b, c) = (5, 6, 7) | AB = 1

X2996 (CD(X25)) 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 \(f(a,b,c) = bc/(3a^{2} - b^{2} - c^{2})\) (M. Iliev, 5/13/07)
Search Value (6, 9, 13): \(-2.543775274481\)
▸ Incident Central Lines8 lines

{2, 1975}, {4, 193}, {20, 98}, {194, 262}, {230, 439}, {315, 671}, {485, 487}, {486, 488}

▸ Functional Relations8 relations

Notes

X2996 is the trilinear pole of the line X523X4885, this line being the complement of orthic axis; the line is also the polar of X20 wrt {circumcircle, nine-point circle}-inverter). Also, let \(R_{a}\) be the radical trace of the A-McCay circle and A-Neuberg circle, and define \(R_{b}\) and \(R_{c}\) cyclically. Then the triangle RaRbRc is perspective to ABC at X2996. (Randy Hutson, October 13, 2015)