X2621

TRILINEAR POLE OF PU(72)

X2621 = isogonal conjugate of X2620
< 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) { 1109, 2619 }: Central Line L(1109, 2619) { 1, 2627 }: Central Line L(1, 2627) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2620 = CROSSDIFFERENCE OF PU(72) (0.5994, 0.2226) X_1109 = TRILINEAR SQUARE OF X(523) (0.7246, 0.0705) X_2619 = CROSSSUM OF PU(72) (1.3247, -0.5036) X_1 = INCENTER (0.5714, 0.2333) X_2627 = TRILINEAR POLE OF PU(73) (-19.0922, 7.2371) X_2621 = TRILINEAR POLE OF PU(72) (0.5444, 0.2429) A B C X2620 X1109 X2619 X1 X2627 X2621 (a, b, c) = (5, 6, 7) | AB = 1

X2621 (TRILINEAR POLE OF PU(72)) 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 \(f(A,B,C) = 1/[\tan(A - B) \tan(A - C) + \tan^{2}(B - C)]\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(25.957250298624\)
▸ Incident Central Lines2 lines

{1, 2627}, {1109, 2619}

▸ Functional Relations1 relation