Question 93
Let $P$, $Q$ be points on the side $AB$ and $AC$, respectively, of a triangle $\triangle ABC$, which satisfy $BP + CQ = PQ$. Let $R$ be the point of intersection, other than $A$, of the bisector of the angle $\angle BAC$ and the circum-circle of the triangle $\triangle ABC$. If $\angle BAC = \alpha$, express $\angle PRQ$ in terms of $\alpha$. Here we denote by $XY$ the length of the line segment $XY$.