X2526

RADICAL CENTER OF {NINE-POINT, APOLLONIUS, (X4,2R)} CIRCLES

X2526 = reflection of X650 in X1491
< 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) { 650, 1491 }: Central Line L(650, 1491) { 44, 513 }: Central Line L(44, 513) { 830, 905 }: Central Line L(830, 905) { 523, 2525 }: Central Line L(523, 2525) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (13.7143, -4.1991) X_1491 = CROSSDIFFERENCE OF X(1) AND X(32) (25.5000, -10.6145) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_830 = ODD (1, 3) INFINITY POINT (1.0590, -0.0690) X_905 = POINT ACHERNAR (5.6190, -0.6999) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_2525 = RADICAL CENTER OF {NINE-POINT, BROCARD, (X(4),2R)} CIRCLES (-9.1140, 0.7037) X_2526 = RADICAL CENTER OF {NINE-POINT, APOLLONIUS, (X(4),2R)} CIRCLES (37.2857, -17.0298) A B C X650 X1491 X44 X513 X830 X905 X523 X2525 X2526 (a, b, c) = (5, 6, 7) | AB = 1

X2526 (RADICAL CENTER OF {NINE-POINT, APOLLONIUS, (X4,2R)} 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 \(f(a,b,c) = (b - c)(a^{2} + 3b^{2} + 2bc + 3c^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-41.050349515385\)
▸ Incident Central Lines3 lines

{44, 513}, {523, 2525}, {830, 905}

▸ Functional Relations2 relations