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The ant and the circle

Imagine there is a circle, an ant is in the circunference. The ant move ahead 1centimetre per second, and the circle wides 1 metre per second. Will the ant take a full turn to the circunference??and, if it could, how many time will it last?? The answer of the riddle of the last week is :  The nail would be at the same height since trees grow at their tops.