X679

ISOGONAL CONJUGATE OF X678

X679 is the isogonal conjugate of X678.
< 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) { 44, 88 }: Central Line L(44, 88) { 320, 519 }: Central Line L(320, 519) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_678 = CROSSPOINT OF X(1) AND X(44) (0.3571, 0.3499) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_320 = ISOTOMIC CONJUGATE OF X(80) (-2.6735, -3.5993) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_679 = ISOGONAL CONJUGATE OF X(678) (1.0000, 0.0000) A B C X678 X44 X88 X320 X519 X679 (a, b, c) = (5, 6, 7) | AB = 1

X679 (ISOGONAL CONJUGATE OF X678) 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 \(f(a,b,c) = 1/(b + c - 2a)^{2}\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(0.051626897482\)
▸ Incident Central Lines2 lines

{44, 88}, {320, 519}

▸ Functional Relations5 relations