X245

X1-LINE CONJUGATE OF X110

X245 = X1-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) { 1, 60 }: Central Line L(1, 60) { 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_1 = INCENTER (0.5714, 0.2333) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_60 = ISOGONAL CONJUGATE OF X(12) (0.5790, 0.2258) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_245 = -LINE CONJUGATE OF X(110) (0.7358, 0.0716) A B C X1 X110 X60 X115 X125 X245 (a, b, c) = (5, 6, 7) | AB = 1

X245 (X1-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 \(f(A,B,C) = \csc^{2}(C - A) + \csc(C - B) [\csc(C - A) -\csc(B - A)] + \csc^{2}(A - B)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(2.204587745588\)
▸ Incident Central Lines2 lines

{1, 60}, {115, 125}

▸ Functional Relations1 relation