Question

In figure, $ABC$ is a right triangle right angled at $B$ such that $BC=6cm$ and $AB=8cm$. Find the radius of its incircle

Answer 1

Let O be the centre of the circle and radius be r

Using pythagoras theorem

$A{C}^2=B{C}^2+A{B}^2$

$A{C}^2=6^2+8^2$

$AC=10cm$

Now

Area of $△ABC=$ Area of $△OAB+$ Area of $△OBC+$ Area of $△OCA$

$\Rightarrow \frac{1}{2}\times BC\times AB=\frac{1}{2}\times r\times AB+\frac{1}{2}\times AC\times r+\frac{1}{2}\times BC\times r$

$\Rightarrow \frac{1}{2}\times 6\times 8=\frac{1}{2}\times r\times 8+\frac{1}{2}\times 10\times r+\frac{1}{2}\times 6\times r$

$\Rightarrow 48=24r$

$\Rightarrow r=2cm$