X2543

EXSIMILICENTER(BROCARD CIRCLE, (X4,2R))

The circle (X4,2R) is identified at X2474.
< 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) { 4, 83 }: Central Line L(4, 83) { 2, 1340 }: Central Line L(2, 1340) { 20, 1341 }: Central Line L(20, 1341) { 10, 1704 }: Central Line L(10, 1704) { 388, 1674 }: Central Line L(388, 1674) { 497, 1675 }: Central Line L(497, 1675) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_83 = CEVAPOINT OF CENTROID AND SYMMEDIAN POINT (0.5651, 0.2360) X_2 = CENTROID (0.5374, 0.2000) X_1340 = INSIMILICENTER(CIRCUMCIRCLE, BROCARD CIRCLE) (0.5420, 0.1715) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_1341 = EXSIMILICENTER(CIRCUMCIRCLE, BROCARD CIRCLE) (0.5617, 0.2039) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_1704 = INSIMILICENTER(BEVAN CIRCLE, BROCARD CIRCLE) (0.5395, 0.1662) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_1674 = INSIMILICENTER(INCIRCLE, BROCARD CIRCLE) (0.5563, 0.1989) X_497 = CROSSPOINT OF GERGONNE POINT AND NAGEL POINT (0.5593, 0.1851) X_1675 = EXSIMILICENTER(INCIRCLE, BROCARD CIRCLE) (0.5349, 0.1503) X_2543 = EXSIMILICENTER(BROCARD CIRCLE, (X(4),2R)) (0.5435, 0.1626) A B C X4 X83 X2 X1340 X20 X1341 X10 X1704 X388 X1674 X497 X1675 X2543 (a, b, c) = (5, 6, 7) | AB = 1

X2543 (EXSIMILICENTER(BROCARD CIRCLE, (X4,2R))) 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 \(f(A,B,C) = e \cos B \cos C - \cos(A - \omega ) e = (1 - 4 \sin^{2} \omega )^{1/2}\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(6.351531170791\)
▸ Incident Central Lines17 lines

{2, 1340}, {4, 83}, {10, 1704}, {20, 1341}, {388, 1674}, {497, 1675}, {516, 1705}, {1587, 1669}, {1588, 1668}, {1678, 2550}, {1679, 2551}, {2011, 2544}, {2012, 2545}, {2033, 2548}, {2034, 2549}, {2469, 2552}, {2470, 2553}