Question

In a $\Delta ABC$, if $a=13,b=14,c=15$ then the radius of the in circle is

• A. $(16\pi$) sq units
• B. $(25\pi$) sq units
• C. $(36\pi$) sq units
• D. None of these

Answer 1

The correct option is A $(16\pi$) sq units

$s=\frac{1}{2}(13+14+15)=21,(s-a)=8,(s-b)=7,(s-c)=6$$\therefore \Delta =\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{21\times 8\times 7\times 6}=\sqrt{21\times 21\times 16}=(21\times 4)=84$ sq units

$\therefore r=\frac{\Delta }{s}=\frac{84}{21}=4$.

Area of the incircle =$\pi r^2=(\pi \times 4\times 4)=\left(16\pi \right)$ sq units.