Question 114
Let $\Gamma$ be the circum-circle of a triangle $\triangle ABC$. Suppose a circle with its center at a point $O$ is tangent to the line segment $BC$ at a point $P$, and is tangent to the arc $BC$ (not containing $A$) at a point $Q$. If $\angle BAO = \angle CAO$, show that $\angle PAO = \angle QAO$ must be satisfied.