X2474

RADICAL CENTER OF {BROCARD, 2nd LEMOINE, (X4,2R)} CIRCLES

The titular notation (X4,2R) means the circle with center X4 and radius 2R, where R denotes the circumradius of triangle ABC.
< 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) { 512, 1570 }: Central Line L(512, 1570) { 525, 2514 }: Central Line L(525, 2514) { 826, 2518 }: Central Line L(826, 2518) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_1570 = MOSES-CIRCLE INVERSE OF X(3) (0.4005, -0.0623) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0468, 0.2556) X_2514 = RADICAL CENTER OF {CIRCUMCIRCLE, 2nd LEMOINE CIRCLE, (X(4),2R)} (8.7303, -4.2052) X_826 = ODD (0, 4) INFINITY POINT (1.1003, 0.0340) X_2518 = RADICAL CENTER OF {BROCARD, MOSES, (X(4),2R)} CIRCLES (6.6758, -3.9518) X_2474 = RADICAL CENTER OF {BROCARD, 2nd LEMOINE, (X(4),2R)} CIRCLES (6.9649, -4.0371) A B C X512 X1570 X525 X2514 X826 X2518 X2474 (a, b, c) = (5, 6, 7) | AB = 1

X2474 (RADICAL CENTER OF {BROCARD, 2nd LEMOINE, (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 \(f(a,b,c) = a(b^{4} - c^{4})(a^{4} + b^{4} + c^{4} + 2a^{2}b^{2} + 2a^{2}c^{2} - 2b^{2}c^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-3.921260859984\)
▸ Incident Central Lines3 lines

{512, 1570}, {525, 2514}, {826, 2518}