PL-OM 1994 Problem 2

Let be given two parallel lines $k$ and $l$ , and a circle not intersecting $k$ . Consider a variable point $A$ on the line $k$ . The two tangents from this point $A$ to the circle intersect the line $l$ at $B$ and $C$ . Let $m$ be the line through the point $A$ and the midpoint of the segment $BC$ . Prove that all the lines $m$ (as $A$ varies) have a common point.