Question 25
Circle $\omega$ with center $O$ and circle $\alpha$ with center $A$ intersect at two distinct points $C$ and $D$, whereas $\angle OCA = 90^\circ$. A point $E$ is chosen on circle $\omega$ inside circle $\alpha$. Let $F$ be the reflection of point $E$ over the point $O$, and $G$ the intersection of line $CE$ with circle $\alpha$ ($G \neq C$). Prove that points $G$, $D$, and $F$ are collinear.