X2627

TRILINEAR POLE OF PU(73)

X2627 = isogonal conjugate of X2626
< 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) { 110, 1296 }: Central Line L(110, 1296) { 1, 2621 }: Central Line L(1, 2621) { 1101, 2618 }: Central Line L(1101, 2618) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2626 = CROSSDIFFERENCE OF PU(73) (0.2607, 0.5635) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_1296 = COLLINGS TRANSFORM OF X(126) (0.0115, 0.2498) X_1 = INCENTER (0.5714, 0.2333) X_2621 = TRILINEAR POLE OF PU(72) (0.5444, 0.2429) X_1101 = TRILINEAR SQUARE OF X(110) (0.5344, 0.4306) X_2618 = DIFFERENCE OF PU(72) (-4.5086, 2.1795) X_2627 = TRILINEAR POLE OF PU(73) (-19.0922, 7.2371) A B C X2626 X110 X1296 X1 X2621 X1101 X2618 X2627 (a, b, c) = (5, 6, 7) | AB = 1

X2627 (TRILINEAR POLE OF PU(73)) 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 \(f(A,B,C) = 1/[\cot(A - B) \cot(A - C) + \cot^{2}(B - C)]\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(4.456815289990\)
▸ Incident Central Lines3 lines

{1, 2621}, {110, 1296}, {1101, 2618}

▸ Functional Relations1 relation