In or Out?

'In or Out?' printed from https://nrich.maths.org/

The shaded region shown in the diagram is bounded by four arcs, each of the same radius as that of the surrounding circle.

What fraction of the surrounding circle is shaded?

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.