Question 70
Given $\triangle ABC$ with $CA \gt BC \gt AB$, let $O$ and $H$ be the circumcentre and orthocentre of $\triangle ABC$ respectively. Denote by $D$ and $E$ the midpoints of arcs $\widehat{AB}$ and $\widehat{AC}$ of the circumcircle of $\triangle ABC$ not containing the opposite vertices. Let $D'$ be the reflection of $D$ in side $AB$ and $E'$ be the reflection of $E$ in side $AC$. Prove that $O, H, D', E'$ are concyclic if and only if $A, D', E'$ are collinear.
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