X2465

INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, 2nd LEMOINE CIRCLE)

X2465 is the insimilicenter(orthocentroidal circle, 2nd 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) { 6, 13 }: Central Line L(6, 13) { 1124, 2464 }: Central Line L(1124, 2464) { 1335, 2463 }: Central Line L(1335, 2463) { 1377, 2468 }: Central Line L(1377, 2468) { 1378, 2467 }: Central Line L(1378, 2467) { 1668, 2469 }: Central Line L(1668, 2469) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_1124 = ISOGONAL CONJUGATE OF X(1123) (0.5846, 0.2489) X_2464 = EXSIMILICENTER(ORTHOCENTROIDAL CIRCLE, INCIRCLE) (0.5776, 0.3505) X_1335 = {X(1),X(6)}-HARMONIC CONJUGATE OF X(1124) (0.4024, 0.0326) X_2463 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, INCIRCLE) (0.5738, 0.2778) X_1377 = INSIMILICENTER(2nd LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5443, 0.2084) X_2468 = EXSIMILICENTER(ORTHOCENTROIDALCIRCLE, SPIEKER CIRCLE) (1.0566, 1.3119) X_1378 = EXSIMILICENTER(2nd LEMOINE CIRCLE, SPIEKER CIRCLE) (0.4609, 0.1206) X_2467 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, SPIEKER CIRCLE) (0.5491, 0.2436) X_1668 = EXSIMILICENTER(BROCARD CIRCLE, 2nd LEMOINE CIRCLE) (0.5226, 0.1394) X_2469 = INSIMILICENTER(ORTHOCENTROIDALCIRCLE, BROCARD CIRCLE) (0.5619, 0.2389) X_2465 = INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, 2nd LEMOINE CIRCLE) (0.5818, 0.2893) A B C X6 X13 X1124 X2464 X1335 X2463 X1377 X2468 X1378 X2467 X1668 X2469 X2465 (a, b, c) = (5, 6, 7) | AB = 1

X2465 (INSIMILICENTER(ORTHOCENTROIDAL CIRCLE, 2nd 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 \(f(A,B,C) = \cos A + 4 \cos B \cos C + J \sin A\), 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): \(0.143672756275\)
▸ Incident Central Lines11 lines

{6, 13}, {1124, 2464}, {1335, 2463}, {1377, 2468}, {1378, 2467}, {1587, 2553}, {1588, 2552}, {1668, 2469}, {1669, 2470}, {1687, 2472}, {1688, 2471}

▸ Functional Relations1 relation