Question 151
Let $A$ be a point outside the circle $\mathcal{C}$. The tangents from $A$ touch the circle at $B$ and $C$. Let $P$ be an arbitrary point on $AC$ produced, $Q$ the projection of $C$ onto $PB$ and $E$ the second intersection point of the circumcircle of $ABP$ with the circle $\mathcal{C}$. Prove that $\angle PEQ = 2\angle APB$.
Cuban Olympiad, 2003
Cuban Olympiad, 2003