Question 91
Let $ABC$ be an acute, non-isosceles triangle inscribed in $(O)$ and $BB'$, $CC'$ are altitudes. Denote $E$, $F$ as the intersections of $BB'$, $CC'$ with $(O)$ and $D$, $P$, $Q$ are projections of $A$ on $BC$, $CE$, $BF$. Prove that the perpendicular bisector of $PQ$ bisects two segments $AO$, $BC$.