Question

In a right triangle ABC, right angled at B, $BC=15cm$, and $AB=8cm$. A circle is inscribed in triangle ABC. The radius of the circle is :

• A. 1cm
• B. 2cm
• C. 3cm
• D. 4cm

Answer 1

Answer: (C)

3cm

Using Pythagoras theorem in $△ABC$

${\left(AB\right)}^2+{\left(BC\right)}^2={\left(AC\right)}^2{\left(15\right)}^2+{\left(8\right)}^2={\left(AC\right)}^2\Rightarrow {\left(AC\right)}^2=225+64=289\Rightarrow AC=17cm$

Now inradius $r=\frac{\Delta }{s}$

where $\Delta$ is the area of triangle and $s$ is semi perimeter.

$\Delta =\frac{1}{2}\times 8\times 15=60$

$s=\frac{8+15+17}{2}=\frac{40}{2}=20\Rightarrow r=\frac{\Delta }{s}=\frac{60}{20}=3cm$