Consider two circles which intersect at the points $B$ and $C$. From a point $A$ on one circle, the rays from $A$ through the points $B$ and $C$ intersect the second circle in the points $D$ and $E$. Prove that the tangent at $A$ is parallel to the line segment $DE$.
Thanks for the help.
In the figure, $AF$ is a tangent of circle $ABC$
\begin{align*} \angle CAF &= \angle ABC \tag{$\angle$ in alt. segment} \\ \angle ABC &= \angle CED \tag{ext. $\angle$, cyclic quad.} \\ \angle CAF &= \angle CED \\ \therefore \quad AF \; & /\!/ \; DE \tag{alt. $\angle$s equal} \end{align*}
