A problem by Charles Lien

Level pending

Two points are in a plane at a distance of 2 units from each other. At time t=0, they start moving at velocity v = 1 (unit per second) in random directions with uniform probability distributions. Let P be the probability that there is a point in time in which the distance between the two points is less than or equal to 1. What is the greatest integer that is less than or equal to 1000*P?

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