X2796

ISOGONAL CONJUGATE OF X2712

X2796 is the isogonal conjugate of X2712.
< 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) { 86, 99 }: Central Line L(86, 99) { 10, 190 }: Central Line L(10, 190) { 115, 121 }: Central Line L(115, 121) { 30, 511 }: Central Line L(30, 511) { 2, 846 }: Central Line L(2, 846) { 98, 1293 }: Central Line L(98, 1293) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2712 = SR(X(99), X(106)) (0.1778, 0.4978) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_99 = STEINER POINT (0.1109, 0.4322) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_121 = -OF-MEDIAL-TRIANGLE (0.3061, 0.2999) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_2 = CENTROID (0.5374, 0.2000) X_846 = 4th SHARYGIN POINT (0.5437, 0.1969) X_98 = TARRY POINT (0.8891, -0.2281) X_1293 = COLLINGS TRANSFORM OF X(121) (0.0000, 0.2041) X_2796 = ISOGONAL CONJUGATE OF X(2712) (1.0652, -0.0566) A B C X2712 X86 X99 X10 X190 X115 X121 X30 X511 X2 X846 X98 X1293 X2796 (a, b, c) = (5, 6, 7) | AB = 1

X2796 (ISOGONAL CONJUGATE OF X2712) 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 \(f(a,b,c) = bc(-2a^{3} + b^{3} + c^{3} + a^{2}b + a^{2}c + ab^{2} + ac^{2} - 2b^{2}c - 2bc^{2})\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
▸ Incident Central Lines10 lines

{2, 846}, {10, 190}, {30, 511}, {86, 99}, {98, 1293}, {115, 121}, {148, 1654}, {553, 1357}, {1086, 1125}, {3029, 3030}

▸ Functional Relations5 relations