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Given two points "A" and "B" outside of a given circle of center "O". Where is the point X on the circle, such that AX + XB is the shortest possible?
For the problem "Given two points "A" and "B" on the same side of a given line. Where is the point X on the line, such that AX + XB is the shortest possible", there is that trick of reflecting one of the points about the given line, let's say the point A, and then the point X is the intersection of the line A'B with the given line. But I did not find a way of using that trick to this variation that changes the line for a circle...
Is there a way of solving the problem without long calculations? Something like the trick for the points and a straight line?