X681

TRILINEAR POLE OF LINE X6X_158

X681 = isogonal conjugate of X680
< 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, 823 }: Central Line L(110, 823) { 1612, 1924 }: Central Line L(1612, 1924) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_680 = CROSSDIFFERENCE OF X(6) AND X(158) (-0.0491, 0.2198) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_823 = ISOGONAL CONJUGATE OF X(822) (0.5623, 0.6035) X_1612 = TCC-PERSPECTOR OF X(28) (0.7985, 0.5318) X_1924 = BICENTRIC DIFFERENCE OF PU(13) (-1.8888, 2.8526) X_681 = TRILINEAR POLE OF LINE X(6)X(158) (0.5783, 0.6063) A B C X680 X110 X823 X1612 X1924 X681 (a, b, c) = (5, 6, 7) | AB = 1

X681 (TRILINEAR POLE OF LINE X6X_158) 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 \(f(A,B,C) = (\sec^{2} A)/(\sin B \cos^{2} B - \sin C \cos^{2} C)\)
Barycentrics: \((\sin A)f(A,B,C): (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-0.239664061994\)

X681 lies on the circumcircle.

▸ Incident Central Lines2 lines

{110, 823}, {1612, 1924}

▸ Functional Relations4 relations