X2031

RADICAL TRACE OF MOSES AND BROCARD CIRCLES

< 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) { 3, 6 }: Brocard Axis { 230, 625 }: Central Line L(230, 625) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_230 = -CEVA CONJUGATE OF X(114) (0.9746, 0.6698) X_625 = MIDPOINT OF X(623) AND X(624) (0.2068, -0.3280) X_2031 = RADICAL TRACE OF MOSES AND BROCARD CIRCLES (0.3607, -0.1281) A B C X3 X6 X230 X625 X2031 (a, b, c) = (5, 6, 7) | AB = 1

X2031 (RADICAL TRACE OF MOSES AND BROCARD CIRCLES) 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 \(f(A,B,C) = 2 \sin(A - 3\omega ) + (\sin \omega )[5 \cos A + \cos(A + 2\omega )]\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(1.341510538075\)
▸ Alternate Coordinates1 form

  • Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(4a^{6} + b^{6} + c^{6} - 5a^{4}b^{2} - 5a^{4}c^{2} + 4a^{2}b^{4} + 4a^{2}c^{4} - 6a^{2}b^{2}c^{2} + b^{2}c^{4} + b^{4}c^{2})\) (M. Iliev, 5/13/07)

▸ Incident Central Lines2 lines

{3, 6}, {230, 625}