The Miquel point is the point of concurrence of the Miquel circles. It is therefore the radical center of these circles. Let the points defining the Miquel circles be fractional distances k_a, k_b, and k_c along the sides B C, C A, and A B, respectively, and let k_i^, = 1 - k_i. Then the Miquel point has trilinear coordinates α:β:γ, where α | = | a(-a^2 k_a k_a^, + b^2 k_a k_b + c^2 k_a^, k_c^, ) β | = | b(a^2 k_a^, k_b^, - b^2 k_b k_b^, + c^2 k_b k_c) γ | = | c(a^2 k_a k_c + b^2 k_b^, k_c^, - c^2 k_c k_c^, ). In the special case k_a = k_b = k_c = 1/2, the Miquel point becomes the circumcenter.

Miquel circles | Miquel's theorem | Miquel triangle