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1. You are at a point A on the shore of a circular lake with radius R. You want to get to the point B which is diametrically opposite from A. There is a boat at A. You could row in a straight line from Ato B. You could also run around the lake all the way from A to B. Or you could row the boat from A to some point C on the coast somewhere in between A and B, abandon the boat, and then run to B. Assume that you can run with velocity v₁ and that you can row with velocity v2. Assume v2 < v1(otherwise, the problem is very easy, can you see why?) Where should the point C be located in order to get from A to B as fast as possible?

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