Question

In $△ABC,$ right angled at $B$, what is the value of $2(r+R)$?

• A. $a+b$
• B. $b+c$
• C. $a+c$
• D. $\frac{a+b+c}{2}$

Answer 1

The correct option is C $a+c$

$2R=\frac{b}{\sin B}⟹2R=b$

$r=(s-b)\tan \frac{B}{2}⟹r=\frac{a+b+c}{2}-b⟹2r=a+c-b$

$\therefore 2(R+r)=b+a+c-b=a+c$