Two spiders, Alex and Ben, participate in a friendly chase. They draw a large circle of radius R on the floor. Alex starts out on the circle and Ben—at the center of the circle. They begin to run simultaneously. At all times, Alex runs along the circle at a speed v while Ben runs directly toward Alex at a speed u (u < v). After a while, Ben notices that the distance between them is no longer changing. What is that constant distance?
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