Question

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

Answer 1

Given

$BC=6cm$

$AB=8cm$

We know that in right angle triangle is

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

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

$A{C}^2=64+36$

$A{C}^2=100$

$AC=10cm$

Now

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

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

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

$\Rightarrow 24r=48$

$\Rightarrow 24r=48$

$\Rightarrow r=2cm$

Thus the radius of the circle is $2cm$