3-4-5 circle

Can you find the radius of the circle inscribed inside a '3-4-5 triangle'?

Problem



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.

Image
3-4-5 circle
 

This problem is adapted from the World Mathematics Championships