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A problem of guarding line segment

Two games of guarding a line segment on the plane are considered. In the first one the line segment is guarded by one defender. One invader wants to pass through the line segment but he has to keep away from a capture region moving together with the defender. In the second game the line segment is guarded by n defenders and the invader has to keep the distance from each defender no less than a given constant. All defenders can move along a straight line only with maximal speed 1. Invader can move on the whole plane with maximal speed greater than 1. Other than this, no kinematic nor dynamic constraints are imposed on the defenders and the invader motions. The maximal length of the line segment which can be guarded by defenders is established in this paper.