DE-MO 2010 Problem 1

Given two circles $k$ and $l$ which intersect at two points. One of their common tangents touches $k$ at point $K$ , while the other common tangent touches $l$ at $L.$ Let $A$ and $B$ be the intersections of the line $KL$ with the circles $k$ and $l$ , respectively. Prove that $\overline{AK} = \overline{BL}.$