In a right triangle ABC, $AB=9$ cm, $BC=12$ cm and $AC$ is the hypotenuse. A circle is inscribed in this triangle. Find the radius of the circle.

Step-by-step solution

1. Use Pythagoras to find the hypotenuse: $AC=\sqrt{9^2+12^2}=15$ cm.
2. Compute area of triangle: $A=\frac{1}{2}\times 9\times 12=54$ cm².
3. Compute semiperimeter: $s=\frac{9+12+15}{2}=18$ cm.
4. Use formula for inradius $r=A/s$: $r=54/18=3$ cm.

Concept tested: Inradius of right triangle

Published 10 October 2026 · How this solution was prepared and checked