X687

TRILINEAR POLE OF LINE X4X_110

X687 = isogonal conjugate of X686
< 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) { 107, 250 }: Central Line L(107, 250) { 249, 648 }: Central Line L(249, 648) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_686 = CROSSDIFFERENCE OF X(4) AND X(110) (0.1521, -0.4080) X_107 = Ψ(SYMMEDIAN POINT, ORTHOCENTER) (0.5733, 0.6071) X_250 = ISOGONAL CONJUGATE OF X(125) (0.5892, 0.5347) X_249 = ISOGONAL CONJUGATE OF X(115) (0.5045, 0.3948) X_648 = TRILINEAR POLE OF EULER LINE (0.4563, 0.5855) X_687 = TRILINEAR POLE OF LINE X(4)X(110) (1.3956, -3.1383) A B C X686 X107 X250 X249 X648 X687 (a, b, c) = (5, 6, 7) | AB = 1

X687 (TRILINEAR POLE OF LINE X4X_110) 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 \(f(A,B,C) = 1/[\sec B \csc(A - B) + \sec C \csc(A - C)]\)
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): \(-2.864702884868\)
▸ Incident Central Lines2 lines

{107, 250}, {249, 648}

▸ Functional Relations2 relations