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Semicircle in a Triangle

Age 14 to 16 Short Challenge Level:

A semicircle is drawn to fit tightly inside a right-angled triangle with sides of length 3, 4 and 5 centimetres, as shown in the diagram.

Find the length marked in red.

This problem is taken from 1000 Problems to Enjoy
You can find more short problems, arranged by curriculum topic, in our short problems collection.