X2858

SM(X98, X111)

X2858 = isogonal conjugate of X2872
< 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) { 111, 325 }: Central Line L(111, 325) { 323, 729 }: Central Line L(323, 729) { 691, 2396 }: Central Line L(691, 2396) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2872 = ISOGONAL CONJUGATE OF X(2858) (0.5640, -0.3863) X_111 = PARRY POINT (0.9885, -0.0457) X_325 = -HIRST INVERSE OF X(69) (-0.3370, -0.7398) X_323 = ISOTOMIC CONJUGATE OF X(94) (-0.8839, -1.3275) X_729 = EVEN (- 2, 0) CIRCUMCIRCLE POINT (1.0096, 0.1290) X_691 = TRILINEAR POLE OF LINE X(6)X(110) (1.0101, 0.0886) X_2396 = GIBERT-SIMSON TRANSFORM OF X(99) (-8.5185, -6.6572) X_2858 = SM(X(98), X(111)) (0.3432, -0.3836) A B C X2872 X111 X325 X323 X729 X691 X2396 X2858 (a, b, c) = (5, 6, 7) | AB = 1

X2858 (SM(X98, X111)) 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 \(f(a,b,c) = bc/[(b^{2} - c^{2})(a^{4} + b^{4} + c^{4} - 3b^{2}c^{2})]\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(9.382063584855\)

X2858 lies on the circumcircle.

▸ Incident Central Lines3 lines

{111, 325}, {323, 729}, {691, 2396}

▸ Functional Relations1 relation