X1291

COLLINGS TRANSFORM OF X50

X1291 = cevapoint of X50 and X512
< 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) { 477, 550 }: Central Line L(477, 550) { 30, 1141 }: Central Line L(30, 1141) { 74, 1154 }: Central Line L(74, 1154) { 523, 930 }: Central Line L(523, 930) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_50 = -CEVA CONJUGATE OF X(184) (2.1559, 2.8368) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_477 = TIXIER ANTIPODE (0.0176, -0.0644) X_550 = MIDPOINT OF X(3) AND X(20) (0.4439, -0.0448) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_1141 = GIBERT POINT (-0.0724, -0.2027) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_1154 = ISOGONAL CONJUGATE OF X(1141) (0.8932, 0.6667) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_930 = ANTICOMPLEMENT OF X(137) (0.0497, 0.3422) X_1291 = COLLINGS TRANSFORM OF X(50) (0.9957, -0.0194) A B C X50 X512 X477 X550 X30 X1141 X74 X1154 X523 X930 X1291 (a, b, c) = (5, 6, 7) | AB = 1

X1291 (COLLINGS TRANSFORM OF X50) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X1286)
Barycentrics: \(a^{2}/((b^{2} - c^{2}) (a^{12} - 4 a^{10} (b^{2} + c^{2}) + 5 a^{8} (b^{4} + b^{2} c^{2} + c^{4}) + a^{6} b^{2} c^{2} (b^{2} + c^{2}) - a^{4} (5 b^{8} - b^{6} c^{2} + 2 b^{4} c^{4} - b^{2} c^{6} + 5 c^{8}) + a^{2} (b^{2} - c^{2})^{2} (4 b^{6} + 3 b^{4} c^{2} + 3 b^{2} c^{4} + 4 c^{6}) - (b^{2} - c^{2})^{4} (b^{2} + c^{2})^{2})) : :\)
Search Value (6, 9, 13): \(11.169667043161\)

X1291 lies on the circumcircle.

▸ Incident Central Lines4 lines

{30, 1141}, {74, 1154}, {477, 550}, {523, 930}

▸ Functional Relations1 relation