HG102 Rolling Circle within a Circle

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2002 UK Senior Mathematical Challenge, question 14:

A circular disc of diameter d rolls without slipping around the inside of a ring of internal diameter 3d, as shown in the diagram. By the time that the centre of the inner disc returns to its original position for the first time, how many times will the inner disc have turned about its centre?

A: 1
B: pi
C: 3
D: 2pi
E: 2

This dynamic construction helps students appreciate why the answer is NOT response C: 3, which is the intuitively correct answer!

Have a play and conclude for yourself what the right response is!