Question 5
(FRA) Let $ABC$ be a triangle, $H$ its orthocenter, $O$ its circumcenter, and $R$ its circumradius. Let $D$ be the reflection of $A$ across $BC$, $E$ that of $B$ across $CA$, and $F$ that of $C$ across $AB$. Prove that $D,E$, and $F$ are collinear if and only if $OH=2R$.