M'Cay circle

The three circumcircles through the triangle centroid G of a given triangle Δ A_1 A_2 A_3 and the pairs of the vertices of the second Brocard triangle are called the McCay circles. The circumcircle of their centers (i.e., of the second Brocard triangle) is therefore the Brocard circle. The A-McCay circle has center function α:β:γ = 2b c cos A:a b:a c. and radius, R_A = 1/6 a sqrt(cot^2 ω - 3), 1/3 that of the Neuberg circle, where ω is the Brocard angle.

Brocard circle | circle | concurrent | McCay circles radical circle | Neuberg circles | second Brocard triangle | triangle centroid