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you [Music] the radius of circle a is one-third the radius of circle B circle a rules around the circle b1 trip back to its initial position how many times will circle a revolve Tillich docHubes back to the initial position these are your options pause for a while and think logically you this question comes from nine the examination and there were only five options and all the candidates answered it incorrectly reason being that the correct answer was not included in the options later three students claimed to the college board that the actual answer is four and thats true thats why I purposely added the sixth option for you as none of these so without further ado lets move to the solution Im going to show you the two methods I solve this problem mathematical and logical starting with a mathematical solution first when circle a rolls around circle B its actual distance traveled can be represented as an imaginary circle three whose radius will be the addition of the red eye of circle