What your demo indicates is actually the location of the CENTER of small circle, which is causing illusion. How about the tip of the red arrow, which is tangential point of the two circles. Suppose you put a small ant at the tangential point (assuming ant not moving by itself). How many time this ant will be in contact with the large circle? Appearantly, the answer is 4, not 5. We are not interested in the movement of the center of small circle at all...