The second Brocard circle is the circle having center at the circumcenter O of the reference triangle and radius R_B | = | sqrt(1 - 4sin^2 ω)R | = | a b csqrt((a^4 + b^4 + c^4 - a^2 b^2 - a^2 c^2 - b^2 c^2)/((-a + b + c)(a - b + c)(a + b - c)(a + b + c)(a^2 b^2 + a^2 c^2 + b^2 + c^2))), where R is the circumradius. It has circle function l = - (a^2 b c)/(a^2 b^2 + a^2 c^2 + b^2 c^2) which corresponds to the symmedian point K. The (first) Brocard circle and second Brocard circle meet in the first and second Brocard points.

Brocard circle | cosine circle