The Distances to the Incenter and Excenters from the Circumcenter
Let ABC be a triangle with circumradius , circumcenter O, and incenter I. Let A', B', and C' be the radii of the excircles opposite A, B, and C, respectively. Then .
The statement of the theorem is in Problem 159. Distances from the Circumcenter to the Incenter and the Excenters.