X3118

ISOGONAL CONJUGATE OF GtX(32)

X3118 is the isogonal conjugate of gtx(32).
< 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) { 32, 184 }: Central Line L(32, 184) { 76, 141 }: Central Line L(76, 141) { 83, 694 }: Central Line L(83, 694) { 99, 695 }: Central Line L(99, 695) { 2076, 2916 }: Central Line L(2076, 2916) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3115 = GtX(32) (0.5421, 0.2455) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_83 = CEVAPOINT OF CENTROID AND SYMMEDIAN POINT (0.5651, 0.2360) X_694 = ISOGONAL CONJUGATE OF X(385) (1.0179, 0.0378) X_99 = STEINER POINT (0.1109, 0.4322) X_695 = ISOGONAL CONJUGATE OF X(384) (0.5903, 0.2249) X_2076 = INVERSE-IN-CIRCUMCIRCLE OF X(39) (1.3982, 1.5854) X_2916 = TANGENTIAL-ISOGONAL CONJUGATE OF X(2) (0.4656, -0.0146) X_3118 = ISOGONAL CONJUGATE OF GtX(32) (0.6022, 0.2198) A B C X3115 X32 X184 X76 X141 X83 X694 X99 X695 X2076 X2916 X3118 (a, b, c) = (5, 6, 7) | AB = 1

X3118 (ISOGONAL CONJUGATE OF GtX(32)) 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 \(f(a,b,c) = a^{3}(b^{8} - c^{8})/(b^{2} - c^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.153875119581\)
▸ Incident Central Lines5 lines

{32, 184}, {76, 141}, {83, 694}, {99, 695}, {2076, 2916}

▸ Functional Relations1 relation