X683

ISOGONAL CONJUGATE OF X682

X683 is the isogonal conjugate of X682.
< 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) { 25, 305 }: Central Line L(25, 305) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_682 = POINT ARNEB (0.6397, 0.1604) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_305 = ISOTOMIC CONJUGATE OF X(25) (0.3258, 0.0397) X_683 = ISOGONAL CONJUGATE OF X(682) (0.5272, 0.3086) A B C X682 X25 X305 X683 (a, b, c) = (5, 6, 7) | AB = 1

X683 (ISOGONAL CONJUGATE OF X682) 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 \(f(A,B,C) = 1/[\sec B \csc^{3} C + \sec C \csc^{3} B]\)
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): \(11.250952046156\)
▸ Incident Central Lines1 line

{25, 305}

▸ Functional Relations3 relations