Question

In a triangle ABC, $C={90}^o$ . If r is the in radius and R is the circum radius of the triangle, then $2(r+R)$ is equal to

• A. $a+c$
• B. $a+b+c$
• C. $b+c$
• D. $a+b$

Answer 1

Answer: (D)

We know that $\frac{c}{\sin C}=2R$ $(\because \angle C={90}^o)$
$\Rightarrow$ $c=2R$ ..(i) and $\tan \frac{C}{2}=\frac{r}{s-c}$
$\Rightarrow$ $\tan {45}^o=\frac{r}{s-c}$
$\Rightarrow$ $r=s-c$
$\Rightarrow$ $r=\frac{a+b+c}{2}-c$
$\Rightarrow$ $2r=a+b-c$
On adding Eqs. (i) and (ii), we get $2(r+R)=a+b$