Circle $S$ with center $O$ and circle $S'$ intersect at points $A$ and $B$. Point $C$ is taken on the arc of a circle $S$ lying inside $S'$. Denote the intersection points of $AC$ and $BC$ with $S'$, other than $A$ and $B$, as $E$ and $D$, respectively. Prove that lines $DE$ and $OC$ are perpendicular.