A counterexample to a dynamic algorithm for convex hulls of line arrangements

An algorithm was recently published to maintain dynamically the convex hull of the set I of intersection points of a set L of n lines in the plane (Boreddy 1990). In other words, given the convex hull of I it is desired to update the convex hull when a new line is added to L (the insertion problem) and it is desired to update the convex hull when an old line is deleted from L (the deletion problem). No proofs of correctness are given in (Boreddy 1990). In fact, we show in this note that the deletion algorithm proposed is incorrect.