X2473
RADICAL CENTER OF {BROCARD CIRCLE, BEVAN CIRCLE, INCIRCLE}
X(2473 lies on these lines: 513,2487 649,2521 2488,2504
5, 6, 7
3, 4, 5
Kepler
Kimberling
< 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)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2473 = RADICAL CENTER OF {BROCARD CIRCLE, BEVAN CIRCLE, INCIRCLE} (21.7939, -9.6080)
A
B
C
X2473
(a, b, c) = (5, 6, 7) | AB = 1
< 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)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_2473 = RADICAL CENTER OF {BROCARD CIRCLE, BEVAN CIRCLE, INCIRCLE} (9.6000, -3.3500)
A
B
C
X2473
(a, b, c) = (3, 4, 5) | AB = 1
< 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)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_2473 = RADICAL CENTER OF {BROCARD CIRCLE, BEVAN CIRCLE, INCIRCLE} (11.3469, -3.3252)
A
B
C
X2473
Kepler (1, √φ, φ) | AB = 1
< 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)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_2473 = RADICAL CENTER OF {BROCARD CIRCLE, BEVAN CIRCLE, INCIRCLE} (4.6725, -0.6706)
A
B
C
X2473
Kimberling (6, 9, 13) | AB = 1
X2473 (RADICAL CENTER OF {BROCARD CIRCLE, BEVAN CIRCLE, INCIRCLE} ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) , where \(f(a,b,c) = (b - c)[a^{4} - (b + c)a^{3} + 2bca^{2} - a(b + c)^{3} + (b^{2} + c^{2})(b - c)^{2}]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-22.039825104316\)
