X2471

INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, 1st LEMOINE CIRCLE)

X2471 is the insimilicenter(orthocentroidal circle, 1st Lemoine 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) { 1672, 2464 }: Central Line L(1672, 2464) { 1673, 2463 }: Central Line L(1673, 2463) { 1680, 2468 }: Central Line L(1680, 2468) { 1681, 2467 }: Central Line L(1681, 2467) { 1687, 2466 }: Central Line L(1687, 2466) 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_1672 = INSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.5619, 0.2116) X_2464 = EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, INCIRCLE) (0.5776, 0.3505) X_1673 = EXSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.6607, 0.4358) X_2463 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, INCIRCLE) (0.5738, 0.2778) X_1680 = INSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5289, 0.1837) X_2468 = EXSIMILICENTER(ORTHOCENTROIDALCIRCLE, SPIEKER CIRCLE) (1.0566, 1.3119) X_1681 = EXSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5004, 0.1824) X_2467 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, SPIEKER CIRCLE) (0.5491, 0.2436) X_1687 = INSIMILICENTER(1st LEMOINE CIRCLE, 2nd LEMOINE CIRCLE) (0.5757, 0.2271) X_2466 = EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, 2nd LEMOINE CIRCLE) (0.5591, 0.3170) X_2471 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, 1st LEMOINE CIRCLE) (0.5682, 0.2677) A B C X182 X381 X1672 X2464 X1673 X2463 X1680 X2468 X1681 X2467 X1687 X2466 X2471 (a, b, c) = (5, 6, 7) | AB = 1

X2471 (INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, 1st LEMOINE 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 \(f(A,B,C) = \cos A + 4 \cos B \cos C + J \cos(A - \omega )\), 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): \(1.465147736742\)
▸ Incident Central Lines9 lines

{182, 381}, {1672, 2464}, {1673, 2463}, {1680, 2468}, {1681, 2467}, {1687, 2466}, {1688, 2465}, {2546, 2553}, {2547, 2552}