Question 1
Let $\Gamma$ and $\omega$ be two circles, intersecting at points $C$ and $D$. The center of circle $\omega$ is denoted as $P$, and it lies on circle $\Gamma$. A line passing through point $D$ intersects circle $\Gamma$ at point $A$ and circle $\omega$ at point $B$, with $D$ being located between points $A$ and $B$. Line $PB$ intersects circle $\Gamma$ at a point $E$ (distinct from $P$). Prove that $AE = AB$.