X2467

INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, SPIEKER CIRCLE)

X2467 is the insimilicenter(orthocentroidal circle, Spieker 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) { 10, 381 }: Central Line L(10, 381) { 2, 2464 }: Central Line L(2, 2464) { 8, 2463 }: Central Line L(8, 2463) { 1377, 2466 }: Central Line L(1377, 2466) { 1378, 2465 }: Central Line L(1378, 2465) { 1678, 2470 }: Central Line L(1678, 2470) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_2 = CENTROID (0.5374, 0.2000) X_2464 = EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, INCIRCLE) (0.5776, 0.3505) X_8 = NAGEL POINT (0.4694, 0.1333) X_2463 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, INCIRCLE) (0.5738, 0.2778) X_1377 = INSIMILICENTER(2nd LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5443, 0.2084) X_2466 = EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, 2nd LEMOINE CIRCLE) (0.5591, 0.3170) X_1378 = EXSIMILICENTER(2nd LEMOINE CIRCLE, SPIEKER CIRCLE) (0.4609, 0.1206) X_2465 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, 2nd LEMOINE CIRCLE) (0.5818, 0.2893) X_1678 = INSIMILICENTER(BROCARD CIRCLE, SPIEKER CIRCLE) (0.5366, 0.1840) X_2470 = EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, BROCARD CIRCLE) (0.2601, -1.1373) X_2467 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, SPIEKER CIRCLE) (0.5491, 0.2436) A B C X10 X381 X2 X2464 X8 X2463 X1377 X2466 X1378 X2465 X1678 X2470 X2467 (a, b, c) = (5, 6, 7) | AB = 1

X2467 (INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, SPIEKER 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 \(f(a,b,c) = bc(a \cos A + 4a \cos B \cos C + (b + c)J\), J as at X1113
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.409166192817\)
▸ Incident Central Lines11 lines

{2, 2464}, {8, 2463}, {10, 381}, {1377, 2466}, {1378, 2465}, {1678, 2470}, {1679, 2469}, {1680, 2472}, {1681, 2471}, {2550, 2553}, {2551, 2551}