X247

X4-LINE CONJUGATE OF X110

X247 = X4-line conjugate of X110
< 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) { 4, 110 }: Central Line L(4, 110) { 115, 125 }: Central Line L(115, 125) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_247 = -LINE CONJUGATE OF X(110) (0.9546, 0.2514) A B C X4 X110 X115 X125 X247 (a, b, c) = (5, 6, 7) | AB = 1

X247 (X4-LINE CONJUGATE OF X110) 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 \(f(A,B,C) = \csc(B-A)[\sec A \csc(B - A) + \sec C \csc(B - C)] + \csc(C - A) u(A,B,C)\), \(u(A,B,C) = [\sec A \csc(C - A) + \sec B \csc(C - B)]\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(5.103210291151\)
▸ Incident Central Lines2 lines

{4, 110}, {115, 125}

▸ Functional Relations2 relations