X2470

EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, BROCARD CIRCLE)

X2470 is the exsimilicenter(orthocentroidal 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) { 182, 381 }: Central Line L(182, 381) { 1668, 2466 }: Central Line L(1668, 2466) { 1669, 2465 }: Central Line L(1669, 2465) { 1674, 2463 }: Central Line L(1674, 2463) { 1675, 2464 }: Central Line L(1675, 2464) { 1678, 2467 }: Central Line L(1678, 2467) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_1668 = EXSIMILICENTER(BROCARD CIRCLE, 2nd LEMOINE CIRCLE) (0.5226, 0.1394) X_2466 = EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, 2nd LEMOINE CIRCLE) (0.5591, 0.3170) X_1669 = INSIMILICENTER(BROCARD CIRCLE, 2nd LEMOINE CIRCLE) (0.5631, 0.2062) X_2465 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, 2nd LEMOINE CIRCLE) (0.5818, 0.2893) X_1674 = INSIMILICENTER(INCIRCLE, BROCARD CIRCLE) (0.5563, 0.1989) X_2463 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, INCIRCLE) (0.5738, 0.2778) X_1675 = EXSIMILICENTER(INCIRCLE, BROCARD CIRCLE) (0.5349, 0.1503) X_2464 = EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, INCIRCLE) (0.5776, 0.3505) X_1678 = INSIMILICENTER(BROCARD CIRCLE, SPIEKER CIRCLE) (0.5366, 0.1840) X_2467 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, SPIEKER CIRCLE) (0.5491, 0.2436) X_2470 = EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, BROCARD CIRCLE) (0.2601, -1.1373) A B C X182 X381 X1668 X2466 X1669 X2465 X1674 X2463 X1675 X2464 X1678 X2467 X2470 (a, b, c) = (5, 6, 7) | AB = 1

X2470 (EXSIMILICENTER(ORTHOCENTROIDAL 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 \(f(A,B,C) = e(\cos A + 4 \cos B \cos C) - J \cos(A - \omega )\), \(e = (1 - 4 \sin^{2} \omega )^{1/2}\), J as at X1113
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(13.120928496333\)
▸ Incident Central Lines9 lines

{182, 381}, {1668, 2466}, {1669, 2465}, {1674, 2463}, {1675, 2464}, {1678, 2467}, {1679, 2468}, {2542, 2552}, {2543, 2553}