Question 26
Let $H$ be the orthocenter of an acute triangle $ABC$. Let $M$ be the midpoint of $BC$. Let $A'$ and $H'$ be the reflections of the points $A$ and $H$ across the point $M$. Prove that the points $B$ and $C$ and the reflections of $A'$ over the lines $BH'$ and $CH'$ are concyclic.