OMCC 2003 Problem 2

$S$ is a circle with $AB$ a diameter and $t$ is the tangent line to $S$ at $B$ . Consider the two points $C$ and $D$ on $t$ such that $B$ is between $C$ and $D$ . Suppose $E$ and $F$ are the intersections of $S$ with $AC$ and $AD$ and $G$ and $H$ are the intersections of $S$ with $CF$ and $DE$ . Show that $AH=AG$ .