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Six Circles

Age 11 to 14 Short
Challenge Level


In the diagram, six circles of equal size touch adjacent circles and the sides of the large rectangle.

Each of the corners of the small rectangle is the centre of one of the large circles.

The perimeter of the small rectangle is $60\text{cm}$.

What is the perimeter of the large rectangle?





If you liked this problem, here is an NRICH task which 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.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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