CR-MO 2003 Problem 2

Let $AB$ be a diameter of circle $\omega$ . $\ell$ is the tangent line to $\omega$ at $B$ . Take two points $C$ , $D$ on $\ell$ such that $B$ is between $C$ and $D$ . $E$ , $F$ are the intersections of $\omega$ and $AC$ , $AD$ , respectively, and $G$ , $H$ are the intersections of $\omega$ and $CF$ , $DE$ , respectively. Prove that $AH=AG$ .