X829

ISOGONAL CONJUGATE OF X828

X829 is the isogonal conjugate of X828.
< 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) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_158 = -CROSS CONJUGATE OF X(92) (0.6215, 0.5117) X_829 = ISOGONAL CONJUGATE OF X(828) (0.6096, 0.4630) A B C X6 X158 X829 (a, b, c) = (5, 6, 7) | AB = 1

X829 (ISOGONAL CONJUGATE OF X828) 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 \(f(A,B,C) = 1/(\sin C \sec^{2} B + \sin B \sec^{2} C)\)
Barycentrics: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = (\sin A)f(A,B,C)\)
Search Value (6, 9, 13): \(0.829989229099\)
▸ Functional Relations2 relations