interesting geometry
A circle of radius unity is centered at origin. two particles start moving at the same time from point (1,0) and move around the circle in opposite direction. one of the particle moves counterclockwise with constant speed v and the other moves clockwise with with constant speed 3v . After leaving (1,0), the two particles meet first at a point P, and continue until they meet next at point Q. The coordinates of the point Q are
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1 solution
Let the particle moving clockwise is C, and particle moving anti clockwise is A. Both the particle reaches point P at the same time. It means C moves thrice the distance as A moves. There are 4 quarter of a circle. So C should have moved 3 quarter in the time as A moves 1 quarter. So the point P is (0,1). Similarly doing it one more time we will get that both the particle meet again at Q = (-1,0).