The radical circle of the Lucas circles is the circumcircle of the Lucas tangents triangle. Its center has trilinear center function α_1151 = 2cos A + sin A corresponding to Kimberling center X_1151, and its radius is R_L | = | (a b c)/(a^2 + b^2 + c^2 + 8Δ) | = | R/(cot ω + 2), where Δ is the area of the reference triangle, R is the circumradius of the reference triangle, and ω is the Brocard angle.

Lucas circles | Lucas tangents triangle | radical circle