The Distances to the Incenter and Excenters from the Circumcenter
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 +++=12.
R
2
OI
2
OA'
2
OB'
2
OC'
2
R