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UKMT Senior Mathematical Challenge, 2016

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

The diagram shows a circle with radius 1 that rolls without slipping around the inside of a square with sides of length 5. The circle rolls once around the square, returning to its starting point. What distance does the centre of the circle travel?

(A) $16 - 2\pi$ (B) $12$ (C) $6 + \pi$ (D) $20 - 2\pi$ (E) $20$

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