CGMO 2014 Problem 1

In the figure of http://www.artofproblemsolving.com/Forum/download/file.php?id=50643&mode=view $\odot O_1$ and $\odot O_2$ intersect at two points $A$ , $B$ . The extension of $O_1A$ meets $\odot O_2$ at $C$ , and the extension of $O_2A$ meets $\odot O_1$ at $D$ , and through $B$ draw $BE \parallel O_2A$ intersecting $\odot O_1$ again at $E$ . If $DE \parallel O_1A$ , prove that $DC \perp CO_2$ .