X2033

INSIMILICENTER(MOSES CIRCLE, BROCARD CIRCLE)

X2033 is the insimilicenter(moses circle, Brocard circle).
< 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 { 115, 1348 }: Central Line L(115, 1348) { 1349, 1506 }: Central Line L(1349, 1506) 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_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_1348 = INSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.5517, 0.2023) X_1349 = EXSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.5463, 0.1455) X_1506 = INSIMILICENTER OF MOSES AND NINE-POINT CIRCLES (0.5676, 0.2392) X_2033 = INSIMILICENTER(MOSES CIRCLE, BROCARD CIRCLE) (0.5583, 0.1983) A B C X3 X6 X115 X1348 X1349 X1506 X2033 (a, b, c) = (5, 6, 7) | AB = 1

X2033 (INSIMILICENTER(MOSES CIRCLE, BROCARD CIRCLE)) 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 \(f(A,B,C) = \sin A + e \sin(A + \omega ) - \sin(A - 2\omega )\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(2.320009643051\)
▸ Alternate Coordinates1 form

  • Trilinears: \(2 \sin \omega \cos(A - \omega ) + e \sin(A + \omega )\)

▸ Incident Central Lines3 lines

{3, 6}, {115, 1348}, {1349, 1506}