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Inscribed Semicircle

Age 14 to 16 ShortChallenge Level

The diagram below shows a right angled triangle with sides of length $5\text{cm}$, $12\text{cm}$ and $13\text{cm}$. What is the radius of the inscribed semicircle whose base lies on the side of length $12\text{cm}$? 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.