X1302

COLLINGS TRANSFORM OF X381

X1302 = cevapoint of X381 and X523
< 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) { 2, 74 }: Central Line L(2, 74) { 23, 477 }: Central Line L(23, 477) { 30, 841 }: Central Line L(30, 841) { 22, 1294 }: Central Line L(22, 1294) { 25, 1300 }: Central Line L(25, 1300) { 459, 1299 }: Central Line L(459, 1299) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_2 = CENTROID (0.5374, 0.2000) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_23 = FAR-OUT POINT (1.3871, 2.4232) X_477 = TIXIER ANTIPODE (0.0176, -0.0644) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_841 = ISOGONAL CONJUGATE OF X(541) (0.0813, -0.1897) X_22 = EXETER POINT (0.4143, -0.1221) X_1294 = COLLINGS TRANSFORM OF X(122) (0.4267, -0.4030) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_1300 = COLLINGS TRANSFORM OF X(136) (0.9926, 0.2353) X_459 = -CEVA CONJUGATE OF X(4) (0.5934, 0.8103) X_1299 = COLLINGS TRANSFORM OF X(135) (0.7905, 0.5216) X_1302 = COLLINGS TRANSFORM OF X(381) (0.3827, 0.5987) A B C X381 X523 X2 X74 X23 X477 X30 X841 X22 X1294 X25 X1300 X459 X1299 X1302 (a, b, c) = (5, 6, 7) | AB = 1

X1302 (COLLINGS TRANSFORM OF X381) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/((\cos A) (\sin 2B - \sin 2C) + \cos B \sin C - \sin B \cos C) : :\)
Barycentrics: \(1/((b^{2} - c^{2}) (a^{4} + b^{4} + c^{4} - 2 a^{2} b^{2} - 2 a^{2} c^{2} + 4 b^{2} c^{2})) : :\)
Search Value (6, 9, 13): \(0.492820671664\)

X1302 lies on the circumcircle.

▸ Incident Central Lines7 lines

{2, 74}, {22, 1294}, {23, 477}, {25, 1300}, {30, 841}, {459, 1299}, {648, 1304}

▸ Functional Relations7 relations