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The diagram shows four equal discs and a square. Each disc touches its two neighbouring discs. Each corner of the square is positioned at the centre of a disc. The side length of the square is $\frac{2}{\pi}$. What is the length of the perimeter of the figure?






If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

 
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.