Question

In a right-angled triangle ABC, $\angle B={90}^o,BC=12cm$ and $AB=5cm$.The radius of the circle inscribed in the triangle (in cm) is

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

Answer: (C)

$2$

We know in $△ABC,AB=5cm,BC=12cm$.
So, by pythagoras theorem we can find the length of side $AC$
$A{C}^2=A{B}^2+B{C}^2=5^2+{12}^2$
$\therefore AC=13cm$
Circle is inscribed in a triangle. This type of circle is called as Incircle.
So, radius of incircle $=\frac{2△}{a+b+c}$
where $△$ is the area of $△ABC$ and $a,b,c$ are the sides of the triangle.
Area of $△ABC=\frac{1}{2}AB\times BC=\frac{1}{2}\times 5\times 12=30sq.cm$
$\therefore$ radius of incircle $=\frac{2\times 30}{5+12+13}=\frac{60}{30}=2cm$