Question 42
Let $ABC$ be a triangle. Let $P$ be the point on the extension of $BC$ beyond $B$ such that $BP = BA$. Let $Q$ be the point on the extension of $BC$ beyond $C$ such that $CQ = CA$. Prove that the circumcenter $O$ of the triangle $APQ$ lies on the angle bisector of the angle $\angle BAC$.
Figure 3: Problem 10
Figure 3: Problem 10