ILL 1971 Problem 7

In a triangle $ABC$ , let $H$ be its orthocenter, $O$ its circumcenter, and $R$ its circumradius. Prove that:(a) $|OH| = R \sqrt{1-8 \cos \alpha \cdot \cos \beta \cdot \cos \gamma}$ where $\alpha, \beta, \gamma$ are angles of the triangle $ABC;$ (b) $O \equiv H$ if and only if $ABC$ is equilateral.