Question

A circle is inscribed in a triangle whose sides are $8cm,15cm$ and $17cm$ then the radius of the circle is

• A. $3cm$
• B. $4cm$
• C. $5cm$
• D. none of these

Answer 1

The correct option is A $3cm$

Consider given the a circle is inscribed in a triangle whose sides are $8cm$, $15$ cm and $17cm$,

Let, $ABC$ be the triangle with$AB=8cm,BC=15cm$ and$AC=17cm$.
Consider,$8^2+{15}^2=64+225=289$

that is $8^2+{15}^2={17}^2$

Hence, $ABC$ is a right angled triangle
Therefore area of $\Delta ABC$ =$=\frac{1}{2}\times 8\times 15=60cm$

Let $r$ be the radius of the incircle whose centre is I.

Now consider,

$ar(\Delta AIB+\Delta BIC+\Delta CIA)=(\frac{1}{2}\times AB\times r)+(\frac{1}{2}\times BC\times r)+(\frac{1}{2}\times AC\times r)$

$(\frac{1}{2}\times r\times (8+15+17)=\frac{1}{2}\times r\times 40=20r$

But, $ar(\Delta AIB+\Delta BIC+\Delta CIA)=ar\left(\Delta ABC\right)=60sq.cm$

$20r=60$

Hence, $r=3cm$

Hence, this is the answer.