Question 116
Let $O$ be the circumcenter of an acute triangle $ABC$. A circle passing through points $A, O$ intersects lines $AB$ and $AC$ at points $P, Q$ distinct from $A$, respectively. If the lengths of the line segments $PQ$ and $BC$ are equal, what is the magnitude of the angle formed by the lines $PQ$ and $BC$ and less than $90^\circ$?