X2608

TRILINEAR POLE OF PU(70)

X2608 = point of intersection, other than A, B, C, of 1st and 2nd bicentrics of the Kiepert hyperbola
< 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, 2614 }: Central Line L(1, 2614) { 2606, 2611 }: Central Line L(2606, 2611) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2607 = CROSSDIFFERENCE OF PU(70) (0.5584, 0.2383) X_1 = INCENTER (0.5714, 0.2333) X_2614 = TRILINEAR POLE OF PU(71) (9.1392, -3.1427) X_2606 = CROSSSUM OF PU(70) (1.2843, -0.4943) X_2611 = DIFFERENCE OF PU(71) (0.7448, 0.0628) X_2608 = TRILINEAR POLE OF PU(70) (0.5847, 0.2280) A B C X2607 X1 X2614 X2606 X2611 X2608 (a, b, c) = (5, 6, 7) | AB = 1

X2608 (TRILINEAR POLE OF PU(70)) 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 \(f(A,B,C) = 1/[\sin(A - B) \sin(A - C) + \sin^{2}(B - C)]\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(1.335802251094\)
▸ Incident Central Lines2 lines

{1, 2614}, {2606, 2611}

▸ Functional Relations2 relations