X2565

EXSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE)

X2565 is the exsimilicenter(incircle, 2nd 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) { 1, 3 }: OI Line (Incenter–Circumcenter Line) { 1342, 1674 }: Central Line L(1342, 1674) { 1343, 1675 }: Central Line L(1343, 1675) { 1124, 2560 }: Central Line L(1124, 2560) { 1335, 2561 }: Central Line L(1335, 2561) { 1672, 2558 }: Central Line L(1672, 2558) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1342 = INSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.5319, 0.1548) X_1674 = INSIMILICENTER(INCIRCLE, BROCARD CIRCLE) (0.5563, 0.1989) X_1343 = EXSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.6155, 0.2927) X_1675 = EXSIMILICENTER(INCIRCLE, BROCARD CIRCLE) (0.5349, 0.1503) X_1124 = ISOGONAL CONJUGATE OF X(1123) (0.5846, 0.2489) X_2560 = INSIMILICENTER(2nd LEMOINE CIRCLE, 2nd BROCARD CIRCLE) (0.5384, 0.1655) X_1335 = {X(1),X(6)}-HARMONIC CONJUGATE OF X(1124) (0.4024, 0.0326) X_2561 = EXSIMILICENTER(2nd LEMOINE CIRCLE, 2nd BROCARD CIRCLE) (0.3338, -0.1724) X_1672 = INSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.5619, 0.2116) X_2558 = INSIMILICENTER(1st LEMOINE CIRCLE, 2nd BROCARD CIRCLE) (0.5185, 0.1327) X_2565 = EXSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE) (0.3070, -0.2526) A B C X1 X3 X1342 X1674 X1343 X1675 X1124 X2560 X1335 X2561 X1672 X2558 X2565 (a, b, c) = (5, 6, 7) | AB = 1

X2565 (EXSIMILICENTER(INCIRCLE, 2nd 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 \(f(A,B,C) = e - \cos A\), where \(e = (1 - 4 \sin^{2}\omega )^{1/2}\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-0.420000997373\)
▸ Incident Central Lines13 lines

{1, 3}, {2, 2568}, {8, 2569}, {11, 2567}, {12, 2566}, {1124, 2560}, {1335, 2561}, {1342, 1674}, {1343, 1675}, {1672, 2558}, {1673, 2559}, {2007, 2562}, {2008, 2563}