IMO 1962 - Problem 6

Problem: Let $ABC$ be an isosceles triangle with circumradius $r$ and inradius $p$. Prove that the distance $d$ between the circumcenter and incenter is given by $d=\sqrt{r(r-2p)}$.
Solution: This problem is a special case, when the triangle is isosceles, of Euler's formula, which holds for all triangles.