Question

A circle is inscribed in a right-angled triangle ABC, right-angled at B. If BC = 7 cm and AB = 24 cm, find the radius of the circle

Answer 1

The radius $r$ of the incircle of a right-angled triangle is given by:
\[r = \frac{a + b - c}{2},\]
where $a$ and $b$ are the perpendicular sides, and $c$ is the hypotenuse.
Step 1: Calculate the hypotenuse
\[c = \sqrt{AB^2 + BC^2} = \sqrt{24^2 + 7^2} = \sqrt{576 + 49} = \sqrt{625} = 25 \, \text{cm}.\]
Step 2: Find the radius
\[r = \frac{24 + 7 - 25}{2} = \frac{6}{2} = 3 \, \text{cm}.\]
Correct Answer: $3 \, \text{cm}$.