X2490

RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, SPIEKER 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) { 230, 231 }: Central Line L(230, 231) { 661, 1213 }: Central Line L(661, 1213) { 649, 1639 }: Central Line L(649, 1639) { 918, 2487 }: Central Line L(918, 2487) { 513, 2505 }: Central Line L(513, 2505) { 522, 2496 }: Central Line L(522, 2496) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_230 = -CEVA CONJUGATE OF X(114) (0.9746, 0.6698) X_231 = -CEVA CONJUGATE OF X(128) (1.0375, 0.6458) X_661 = CROSSDIFFERENCE OF X(1) AND X(21) (48.4286, -23.0952) X_1213 = ISOGONAL CONJUGATE OF X(1171) (0.5294, 0.1914) X_649 = CROSSDIFFERENCE OF X(1) and X(2) (-21.0000, 14.6969) X_1639 = TRIPOLAR CENTROID OF X(8) (-0.6122, -0.5999) X_918 = ISOTOMIC CONJUGATE OF X(666) (1.0192, 0.5351) X_2487 = RADICAL CENTER OF {INCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (-3.9847, 4.4241) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_2505 = RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, SPIEKER CIRCLE} (0.5051, -0.1583) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_2496 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, SPIEKER CIRCLE} (-1.8622, 2.2579) X_2490 = RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, SPIEKER CIRCLE} (-5.7092, 3.2243) A B C X230 X231 X661 X1213 X649 X1639 X918 X2487 X513 X2505 X522 X2496 X2490 (a, b, c) = (5, 6, 7) | AB = 1

X2490 (RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, SPIEKER 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 \(f(a,b,c) = bc(b - c)(4a^{2} - 3ab - 3ac + (b + c)^{2})\)
Search Value (6, 9, 13): \(10.893099283168\)
▸ Incident Central Lines6 lines

{230, 231}, {513, 2505}, {522, 2496}, {649, 1639}, {661, 1213}, {918, 2487}