Rolling Rolling

Two circles of equal radii touch at the point say at P. One circle is fixed[br] whilst the other moves, rolling without slipping, all the way round.[br][br]How many times does the moving circle revolve before returning to P?
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What happens if the radius of the moving circle is half that of the fixed circle?
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Can you generalise it?[br][br]Key question: How far does the centre of the rolling disk travel?
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Information: Rolling Rolling