In a right angled triangle ABC, the lengths of the sides containing the right angle are 5 cm and 12 cm respectively. A circle is inscribed in the triangle ABC. What is the radius of the circle (in cm)?

2

By Pythagoras's theorem

BC² = AC² + AB²

= BC² = (5)² + (12)²

= BC² = (25 + 144)

= BC² = 169

= BC = 13 cm

Radius of circle = \(\frac{(AC + AB - BC)}{2}\) = \(\frac{(12 + 5 - 13)}{2}\) = \(\frac{4}{2}\) = 2 cm