The circumcenter is the center O of a triangle's circumcircle. It can be found as the intersection of the perpendicular bisectors. The trilinear coordinates of the circumcenter are cos A:cos B:cos C, and the exact trilinear coordinates are therefore R cos A:R cos B:R cos C, where R is the circumradius, or equivalently (1/2 a cot A, 1/2 b cot B, 1/2 c cot C). The circumcenter is Kimberling center X_3.

Brocard diameter | Carnot's theorem | circle | circumcenter of mass | circumcircle | Euler line | Euler's inequality | Euler triangle formula | incenter | Lester circle | orthocenter | triangle centroid