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Australian AMC 2019 - Intermediate Question 25

AMC AUSTRALIA · Australian AMC 2019 - Intermediate

Question 25

A circular coin of radius 1 cm rolls around the inside of a square without slipping, always touching the boundary of the square.
When it returns to where it started, the coin has performed exactly one whole revolution.
In centimetres, what is the side length of the square?

Question illustration
  1. $\pi$
  2. 3.5
  3. $1+\pi$
  4. 4
  5. $2+\frac\pi2$