X2785

ISOGONAL CONJUGATE OF X2701

X2785 is the isogonal conjugate of X2701.
< 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) { 98, 102 }: Central Line L(98, 102) { 99, 109 }: Central Line L(99, 109) { 114, 117 }: Central Line L(114, 117) { 115, 124 }: Central Line L(115, 124) { 147, 151 }: Central Line L(147, 151) { 30, 511 }: Central Line L(30, 511) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2701 = SR(X(98), X(102)) (0.9990, 0.2091) X_98 = TARRY POINT (0.8891, -0.2281) X_102 = Λ(INCENTER, ORTHOCENTER) (0.6364, -0.3897) X_99 = STEINER POINT (0.1109, 0.4322) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_114 = KIEPERT ANTIPODE (0.3616, 0.4140) X_117 = MIDPOINT OF X(4) AND X(109) (0.4879, 0.4948) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_124 = -OF-MEDIAL-TRIANGLE (0.6243, 0.0030) X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE (-0.1660, 1.0561) X_151 = REFLECTION OF X(20) IN X(109) (0.3395, 1.3793) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_2785 = ISOGONAL CONJUGATE OF X(2701) (1.0319, 0.5161) A B C X2701 X98 X102 X99 X109 X114 X117 X115 X124 X147 X151 X30 X511 X2785 (a, b, c) = (5, 6, 7) | AB = 1

X2785 (ISOGONAL CONJUGATE OF X2701) 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 \(f(a,b,c) = bc(b - c)(a^{3} + b^{3} + c^{3} - 2a^{2}b - 2a^{2}c + abc)\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
▸ Incident Central Lines7 lines

{30, 511}, {98, 102}, {99, 109}, {114, 117}, {115, 124}, {147, 151}, {671, 1121}

▸ Functional Relations7 relations