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Age 14 to 16 Short Challenge Level:

A wire in the shape of an equilateral triangle with sides of length 9 cm is placed on a flat piece of paper.

Imagine rolling a circular disc of radius 1cm around the inside of the wire.
What path would the centre of the disc trace out?

What if you rolled the disc around the outside of the wire?
 

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.