CONO-SUR 1993 Problem 2

Consider a circle with centre $O$ , and $3$ points on it, $A,B$ and $C$ , such that $\angle {AOB}< \angle {BOC}$ . Let $D$ be the midpoint on the arc $AC$ that contains the point $B$ . Consider a point $K$ on $BC$ such that $DK \perp BC$ . Prove that $AB+BK=KC$ .