X1705

EXSIMILICENTER(BEVAN CIRCLE, BROCARD CIRCLE)

X1705 is the exsimilicenter(Bevan circle, 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) { 40, 182 }: Central Line L(40, 182) { 1, 1341 }: Central Line L(1, 1341) { 165, 1340 }: Central Line L(165, 1340) { 9, 1678 }: Central Line L(9, 1678) { 57, 1675 }: Central Line L(57, 1675) { 43, 1694 }: Central Line L(43, 1694) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_40 = BEVAN POINT (0.4286, -0.0292) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_1 = INCENTER (0.5714, 0.2333) X_1341 = EXSIMILICENTER(CIRCUMCIRCLE, BROCARD CIRCLE) (0.5617, 0.2039) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_1340 = INSIMILICENTER(CIRCUMCIRCLE, BROCARD CIRCLE) (0.5420, 0.1715) X_9 = MITTENPUNKT (0.5110, 0.1615) X_1678 = INSIMILICENTER(BROCARD CIRCLE, SPIEKER CIRCLE) (0.5366, 0.1840) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_1675 = EXSIMILICENTER(INCIRCLE, BROCARD CIRCLE) (0.5349, 0.1503) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_1694 = EXSIMILICENTER(BROCARD CIRCLE,APOLLONIUS CIRCLE) (0.5659, 0.2109) X_1705 = EXSIMILICENTER(BEVAN CIRCLE, BROCARD CIRCLE) (0.5627, 0.2070) A B C X40 X182 X1 X1341 X165 X1340 X9 X1678 X57 X1675 X43 X1694 X1705 (a, b, c) = (5, 6, 7) | AB = 1

X1705 (EXSIMILICENTER(BEVAN CIRCLE, 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 \(f(A,B,C) = 2 \cos(A - \omega ) - e(1 + \cos A - \cos B - \cos C)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(1.830121042684\)
▸ Incident Central Lines17 lines

{1, 1341}, {9, 1678}, {40, 182}, {43, 1694}, {57, 1675}, {165, 1340}, {1348, 1698}, {1349, 1699}, {1571, 2033}, {1572, 2034}, {1668, 1703}, {1669, 1702}, {1674, 1697}, {1679, 1706}, {1693, 1695}, {2011, 2017}, {2012, 2018}