Question

In a triangle, $a=26,b=30$ and $\cos C=\frac{63}{65}$. Then
$r_2=$

• A. $3$
• B. $4$
• C. $16$
• D. $48$

Answer 1

The correct option is D $48$

REF.Image.

Given a = 26, b = 30, cos c = 63/65

Applying cosine rule : $C=\sqrt{a^2+b^2-2abcosc}=8$

$\Rightarrow S=\frac{a+b+c}{2}=22$

$\Rightarrow △=\sqrt{S(S-a)(S-b)(S-c)}=96$

$\Rightarrow r_2=\frac{△}{S-b}=\frac{96}{32-30}=48$