X2871

ISOGONAL CONJUGATE OF X2857

X2871 is the isogonal conjugate of X2857.
< 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) { 6, 157 }: Central Line L(6, 157) { 30, 511 }: Central Line L(30, 511) { 53, 1843 }: Central Line L(53, 1843) { 287, 1632 }: Central Line L(287, 1632) { 263, 1989 }: Central Line L(263, 1989) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2857 = SM(X(98), X(110)) (0.0004, -0.0018) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_157 = -OF-TANGENTIAL-TRIANGLE (0.5266, 0.3812) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_53 = SYMMEDIAN POINT OF ORTHIC TRIANGLE (0.6164, 0.4390) X_1843 = ZOSMA TRANSFORM OF X(75) (0.6278, 0.4214) X_287 = -HIRST INVERSE OF X(98) (0.7437, -0.0511) X_1632 = TCC-PERSPECTOR OF X(648) (0.2937, 0.6477) X_263 = ISOGONAL CONJUGATE OF X(183) (0.6298, 0.3525) X_1989 = ISOGONAL CONJUGATE OF X(323) (0.9916, -0.2095) X_2871 = ISOGONAL CONJUGATE OF X(2857) (0.2197, 0.6934) A B C X2857 X6 X157 X30 X511 X53 X1843 X287 X1632 X263 X1989 X2871 (a, b, c) = (5, 6, 7) | AB = 1

X2871 (ISOGONAL CONJUGATE OF X2857) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/f(a,b,c) : 1/f(b,c,a) : 1/f(c,a,b)\), where f(a,b,c) is as at X2857
Barycentrics: \(a^{2} (a^{6} (b^{2} + c^{2}) - a^{4} (b^{2} + c^{2})^{2} + a^{2} (b^{6} + c^{6}) - (b^{2} - c^{2})^{2} (b^{2} - b c + c^{2}) (b^{2} + b c + c^{2})) / (a^{6} (b^{2} + c^{2}) - 2 a^{4} (b^{4} + c^{4}) + a^{2} (b^{6} + c^{6}) + b^{2} c^{2} (b^{2} - c^{2})^{2}) : :\)
▸ Incident Central Lines5 lines

{6, 157}, {30, 511}, {53, 1843}, {263, 1989}, {287, 1632}

▸ Functional Relations2 relations