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3-4-5 Circle

Age 14 to 16 Short
Challenge Level

A circle is drawn inside a right-angled triangle so that each side of the triangle is a tangent to the circle, as shown in the diagram.

The sides of the triangle are 3, 4 and 5 units long, as shown.

Find the radius of the circle.


This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.