X2517

RADICAL CENTER OF {CIRCUMCIRCLE, FUHRMANN CIRCLE, (X4,2R)}

X2517 = isotomic conjugate of X1310
< 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) { 240, 522 }: Central Line L(240, 522) { 325, 523 }: Central Line L(325, 523) { 513, 2533 }: Central Line L(513, 2533) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1310 = COLLINGS TRANSFORM OF X(940) (0.1699, 0.4912) X_240 = -LINE CONJUGATE OF X(48) (0.7457, 0.8594) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_325 = -HIRST INVERSE OF X(69) (-0.3370, -0.7398) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_2533 = RADICAL CENTER OF {BEVAN, FUHRMANN, (X(4),2R)} CIRCLES (-32.5544, 14.4803) X_2517 = RADICAL CENTER OF {CIRCUMCIRCLE, FUHRMANN CIRCLE, (X(4),2R)} (-14.6259, 4.7212) A B C X1310 X240 X522 X325 X523 X513 X2533 X2517 (a, b, c) = (5, 6, 7) | AB = 1

X2517 (RADICAL CENTER OF {CIRCUMCIRCLE, FUHRMANN CIRCLE, (X4,2R)}) 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 \(f(a,b,c) = b^{2}c^{2}(b - c)[a^{2} + (b + c)^{2}]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(29.149197765126\)
▸ Incident Central Lines3 lines

{240, 522}, {325, 523}, {513, 2533}

▸ Functional Relations1 relation