X2572

INSIMILICENTER(BEVAN, 2nd BROCARD CIRCLE)

X2572 is the insimilicenter(Bevan, 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) { 9, 2569 }: Central Line L(9, 2569) { 1342, 1705 }: Central Line L(1342, 1705) { 1343, 1704 }: Central Line L(1343, 1704) { 1700, 2559 }: Central Line L(1700, 2559) { 1701, 2558 }: Central Line L(1701, 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_9 = MITTENPUNKT (0.5110, 0.1615) X_2569 = EXSIMILICENTER(SPIEKER CIRCLE, 2nd BROCARD CIRCLE) (0.5648, 0.3600) X_1342 = INSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.5319, 0.1548) X_1705 = EXSIMILICENTER(BEVAN CIRCLE, BROCARD CIRCLE) (0.5627, 0.2070) X_1343 = EXSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.6155, 0.2927) X_1704 = INSIMILICENTER(BEVAN CIRCLE, BROCARD CIRCLE) (0.5395, 0.1662) X_1700 = INSIMILICENTER(BEVAN CIRCLE, 1st LEMOINE CIRCLE) (0.5232, 0.1374) X_2559 = EXSIMILICENTER(1st LEMOINE CIRCLE, 2nd BROCARD CIRCLE) (0.4285, -0.0161) X_1701 = EXSIMILICENTER(BEVAN CIRCLE, 1st LEMOINE CIRCLE) (0.5980, 0.2692) X_2558 = INSIMILICENTER(1st LEMOINE CIRCLE, 2nd BROCARD CIRCLE) (0.5185, 0.1327) X_2572 = INSIMILICENTER(BEVAN, 2nd BROCARD CIRCLE) (0.4898, 0.0833) A B C X1 X3 X9 X2569 X1342 X1705 X1343 X1704 X1700 X2559 X1701 X2558 X2572 (a, b, c) = (5, 6, 7) | AB = 1

X2572 (INSIMILICENTER(BEVAN, 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 \(f(a,b,c) = 1 - \cos B - \cos C + (1 + 2/e)\cos A\), where \(e = (1 - 4 \sin^{2}\omega )^{1/2}\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(8.208271072659\)
▸ Incident Central Lines13 lines

{1, 3}, {9, 2569}, {1342, 1705}, {1343, 1704}, {1698, 2567}, {1699, 2566}, {1700, 2559}, {1701, 2558}, {1702, 2561}, {1703, 2560}, {1706, 2568}, {2017, 2563}, {2018, 2562}