X246

X3-LINE CONJUGATE OF X110

X246 = X3-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) { 3, 74 }: Central Line L(3, 74) { 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_3 = CIRCUMCENTER (0.5000, 0.1021) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_246 = -LINE CONJUGATE OF X(110) (0.5857, -0.0517) A B C X3 X110 X74 X115 X125 X246 (a, b, c) = (5, 6, 7) | AB = 1

X246 (X3-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 \(f(A,B,C) = \csc(B-A)[\cos A \csc(B - A) + \cos C \csc(B - C)] + \csc(C - A) u(A,B,C)\), \(u(A,B,C) = [\cos A \csc(C - A) + \cos B \csc(C - B)]\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(4.199423192172\)
▸ Incident Central Lines2 lines

{3, 74}, {115, 125}

▸ Functional Relations1 relation