X2799

ISOGONAL CONJUGATE OF X2715

X2799 is the isogonal conjugate of X2715.
< 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) { 99, 112 }: Central Line L(99, 112) { 115, 127 }: Central Line L(115, 127) { 114, 132 }: Central Line L(114, 132) { 30, 511 }: Central Line L(30, 511) { 98, 1297 }: Central Line L(98, 1297) { 2, 1637 }: Central Line L(2, 1637) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2715 = SR(X(99), X(112)) (0.9444, 0.3528) X_99 = STEINER POINT (0.1109, 0.4322) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_127 = -OF-MEDIAL-TRIANGLE (0.5480, -0.0061) X_114 = KIEPERT ANTIPODE (0.3616, 0.4140) X_132 = ∩X(4)X(32) (0.5642, 0.5039) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_98 = TARRY POINT (0.8891, -0.2281) X_1297 = COLLINGS TRANSFORM OF X(127) (0.4838, -0.4080) X_2 = CENTROID (0.5374, 0.2000) X_1637 = TRIPOLAR CENTROID OF X(4) (1.3086, 0.5422) X_2799 = ISOGONAL CONJUGATE OF X(2715) (1.0738, 0.4380) A B C X2715 X99 X112 X115 X127 X114 X132 X30 X511 X98 X1297 X2 X1637 X2799 (a, b, c) = (5, 6, 7) | AB = 1

X2799 (ISOGONAL CONJUGATE OF X2715) 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 \(f(a,b,c) = bc(b^{2} - c^{2})(b^{4} + c^{4} - a^{2}b^{2} - a^{2}c^{2})\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
▸ Incident Central Lines12 lines

{2, 1637}, {30, 511}, {39, 2507}, {98, 1297}, {99, 112}, {114, 132}, {115, 127}, {287, 2395}, {620, 2492}, {671, 1494}, {850, 2525}, {2514, 2531}

▸ Functional Relations10 relations