X2523

RADICAL CENTER OF {NINE-POINT,BROCARD, BEVAN} CIRCLES

< 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) { 441, 525 }: Central Line L(441, 525) { 649, 2521 }: Central Line L(649, 2521) { 650, 2527 }: Central Line L(650, 2527) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_441 = COMPLEMENT OF X(297) (0.3841, -0.2011) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0468, 0.2556) X_649 = CROSSDIFFERENCE OF X(1) and X(2) (-21.0000, 14.6969) X_2521 = RADICAL CENTER OF {BROCARD, BEVAN,MOSES} CIRCLES (-71.3829, 43.3121) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (13.7143, -4.1991) X_2527 = RADICAL CENTER OF {NINE-POINT, SPIEKER, BEVAN} CIRCLES (-23.0663, 12.6724) X_2523 = RADICAL CENTER OF {NINE-POINT,BROCARD, BEVAN} CIRCLES (6.2080, -0.7560) A B C X441 X525 X649 X2521 X650 X2527 X2523 (a, b, c) = (5, 6, 7) | AB = 1

X2523 (RADICAL CENTER OF {NINE-POINT,BROCARD, BEVAN} CIRCLES) 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 \(f(a,b,c) = (b - c)[b^{2} + c^{2} - a^{2})(a^{2} + a(b + c) + (b + c)^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-10.026160171216\)
▸ Incident Central Lines3 lines

{441, 525}, {649, 2521}, {650, 2527}