X2793

ISOGONAL CONJUGATE OF X2709

X2793 is the isogonal conjugate of X2709.
< 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, 111 }: Central Line L(98, 111) { 114, 126 }: Central Line L(114, 126) { 30, 511 }: Central Line L(30, 511) { 99, 1296 }: Central Line L(99, 1296) { 671, 2408 }: Central Line L(671, 2408) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2709 = SR(X(98), X(111)) (0.8573, -0.2623) X_98 = TARRY POINT (0.8891, -0.2281) X_111 = PARRY POINT (0.9885, -0.0457) X_114 = KIEPERT ANTIPODE (0.3616, 0.4140) X_126 = -OF-MEDIAL-TRIANGLE (0.3119, 0.3228) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_99 = STEINER POINT (0.1109, 0.4322) X_1296 = COLLINGS TRANSFORM OF X(126) (0.0115, 0.2498) X_671 = TRILINEAR POLE OF LINE X(2)X(523) (0.9639, -0.0323) X_2408 = GIBERT-SIMSON TRANSFORM OF X(111) (0.9952, 0.0250) X_2793 = ISOGONAL CONJUGATE OF X(2709) (0.2567, -0.3154) A B C X2709 X98 X111 X114 X126 X30 X511 X99 X1296 X671 X2408 X2793 (a, b, c) = (5, 6, 7) | AB = 1

X2793 (ISOGONAL CONJUGATE OF X2709) 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 \(f(a,b,c) = bc(b^{2} - c^{2})(4a^{4} + b^{4} + c^{4} - 4b^{2}c^{2} - a^{2}b^{2} - a^{2}c^{2})\) (M. Iliev, 5/13/07)
▸ Incident Central Lines5 lines

{30, 511}, {98, 111}, {99, 1296}, {114, 126}, {671, 2408}

▸ Functional Relations4 relations