Question

The $\Delta$$abc$ is a right angled triangle with $\angle b={90}^o,bc=3cm$ and $ab=4cm$. A circle with radius $rcm$ has been inscribed in $\Delta abc$. Find radius of the incircle.

Answer 1

$ab=4cm$ and $bc=3cm$

So, by Pythagoras theorem

$a{c}^2=a{b}^2+b{c}^2$

$\Rightarrow a{c}^2=4^2+3^2$

$\Rightarrow a{c}^2=16+9=25$

$\Rightarrow ac=\sqrt{2}5=5$

Radius of incircle=

$\frac{Areaoftriangle}{Semi-perimeter}=\frac{\frac{1}{2}\times 3\times 4}{\frac{3+4+5}{2}}=\frac{6}{\frac{12}{2}}=1$

Radius $=1cm$