X680

CROSSDIFFERENCE OF X6 AND X158

As the isogonal conjugate of a point on the circumcircle, X680 lies on the line at infinity.
< 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) { 30, 511 }: Central Line L(30, 511) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_681 = TRILINEAR POLE OF LINE X(6)X(158) (0.5783, 0.6063) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_680 = CROSSDIFFERENCE OF X(6) AND X(158) (-0.0491, 0.2198) A B C X681 X30 X511 X680 (a, b, c) = (5, 6, 7) | AB = 1

X680 (CROSSDIFFERENCE OF X6 AND X158) 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 \(f(A,B,C) = \cos^{2} A (\sin B \cos^{2} B - \sin C \cos^{2} C)\)
Barycentrics: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = \sin A f(A,B,C)\)
▸ Incident Central Lines1 line

{30, 511}

▸ Functional Relations4 relations