Question

ABC is a triangle right angled at point B with $BC=6cmandAB=8cm$. A circle with centre O and radius x cm has been inscribed in $△$ABC as shown in the figure. The value of x is :

• A. 2cm
• B. 3cm
• C. 4cm
• D. 5cm

Answer 1

The correct option is A 2cm

Using Pythagoras theorem in $△ABC$

${\left(AB\right)}^2+{\left(BC\right)}^2={\left(AC\right)}^2{\left(8\right)}^2+{\left(6\right)}^2={\left(AC\right)}^2\Rightarrow {\left(AC\right)}^2=64+36=100\Rightarrow AC=10cm$

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

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

$\Delta =\frac{1}{2}\times 8\times 6=24$

$s=\frac{8+6+10}{2}=\frac{24}{2}=12\Rightarrow x=r=\frac{\Delta }{s}=\frac{24}{12}=2cm$