X2469

INSIMILICENTER(ORTHOCENTROIDALCIRCLE, BROCARD CIRCLE)

X2469 is the insimilicenter(orthocentroidalcircle, 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, 2465 }: Central Line L(1668, 2465) { 1669, 2466 }: Central Line L(1669, 2466) { 1674, 2464 }: Central Line L(1674, 2464) { 1675, 2463 }: Central Line L(1675, 2463) { 1678, 2468 }: Central Line L(1678, 2468) 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_2465 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, 2nd LEMOINE CIRCLE) (0.5818, 0.2893) X_1669 = INSIMILICENTER(BROCARD CIRCLE, 2nd LEMOINE CIRCLE) (0.5631, 0.2062) X_2466 = EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, 2nd LEMOINE CIRCLE) (0.5591, 0.3170) X_1674 = INSIMILICENTER(INCIRCLE, BROCARD CIRCLE) (0.5563, 0.1989) X_2464 = EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, INCIRCLE) (0.5776, 0.3505) X_1675 = EXSIMILICENTER(INCIRCLE, BROCARD CIRCLE) (0.5349, 0.1503) X_2463 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, INCIRCLE) (0.5738, 0.2778) X_1678 = INSIMILICENTER(BROCARD CIRCLE, SPIEKER CIRCLE) (0.5366, 0.1840) X_2468 = EXSIMILICENTER(ORTHOCENTROIDALCIRCLE, SPIEKER CIRCLE) (1.0566, 1.3119) X_2469 = INSIMILICENTER(ORTHOCENTROIDALCIRCLE, BROCARD CIRCLE) (0.5619, 0.2389) A B C X182 X381 X1668 X2465 X1669 X2466 X1674 X2464 X1675 X2463 X1678 X2468 X2469 (a, b, c) = (5, 6, 7) | AB = 1

X2469 (INSIMILICENTER(ORTHOCENTROIDALCIRCLE, 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): \(1.795162361638\)
▸ Incident Central Lines9 lines

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