X2872

ISOGONAL CONJUGATE OF X2858

X2872 is the isogonal conjugate of X2858.
< 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) { 30, 511 }: Central Line L(30, 511) { 1976, 2422 }: Central Line L(1976, 2422) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2858 = SM(X(98), X(111)) (0.3432, -0.3836) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_1976 = TRILINEAR POLE OF PU(39) (1.0272, -0.3962) X_2422 = ISOGONAL CONJUGATE OF X(2396) (1.0041, 0.1128) X_2872 = ISOGONAL CONJUGATE OF X(2858) (0.5640, -0.3863) A B C X2858 X30 X511 X1976 X2422 X2872 (a, b, c) = (5, 6, 7) | AB = 1

X2872 (ISOGONAL CONJUGATE OF X2858) 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 \(f(a,b,c) = a(b^{2} - c^{2})(a^{4} + b^{4} + c^{4} - 3b^{2}c^{2})\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
▸ Incident Central Lines2 lines

{30, 511}, {1976, 2422}

▸ Functional Relations1 relation