X2496

RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, 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) { 513, 676 }: Central Line L(513, 676) { 522, 2490 }: Central Line L(522, 2490) { 2487, 2505 }: Central Line L(2487, 2505) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_676 = CROSSDIFFERENCE OF X(3) AND X(101) (1.2449, 0.5665) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_2490 = RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, SPIEKER CIRCLE} (-5.7092, 3.2243) X_2487 = RADICAL CENTER OF {INCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (-3.9847, 4.4241) X_2505 = RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, SPIEKER CIRCLE} (0.5051, -0.1583) X_2496 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, SPIEKER CIRCLE} (-1.8622, 2.2579) A B C X513 X676 X522 X2490 X2487 X2505 X2496 (a, b, c) = (5, 6, 7) | AB = 1

X2496 (RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, 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 \(f(a,b,c) = bc(b - c)[7a^{3} - 4a^{2}(b + c) - 2(b + c)(b - c)^{2} + a(3b^{2} - 2bc + 3c^{2})]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.234193514842\)
▸ Incident Central Lines3 lines

{513, 676}, {522, 2490}, {2487, 2505}