X1956

TRILINEAR POLE OF PU(21)

X1956 = X240-cross conjugate of X1
< 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) { 293, 1755 }: Central Line L(293, 1755) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_240 = -LINE CONJUGATE OF X(48) (0.7457, 0.8594) X_1 = INCENTER (0.5714, 0.2333) X_293 = ISOGONAL CONJUGATE OF X(240) (0.7839, -0.0636) X_1755 = MIMOSA TRANSFORM OF X(287) (1.5943, 2.3982) X_1956 = TRILINEAR POLE OF PU(21) (0.6554, -0.4540) A B C X240 X1 X293 X1755 X1956 (a, b, c) = (5, 6, 7) | AB = 1

X1956 (TRILINEAR POLE OF PU(21)) 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 \(f(a,b,c) = 1/(\sin 2B \sin 2C - \sin^{2} 2A)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.003704212948\)
▸ Incident Central Lines1 line

{293, 1755}

▸ Functional Relations2 relations