Guarding a line segment

A line segment on the plane, equipped with the maximum norm, is guarded by the defender D. The invader I wants to reach the line segment but he has to keep the distance from the defender no less than a given constant ϱ > 0 . The defender and the invader can move on the whole plane with maximal speed of r D and r I respectively, where r I > r D . No further kinematic or dynamic constrains are imposed on the defender and the invader motions. The maximal length of the line segment which can be guarded by the defender is established in this paper.