Question

In$\Delta ABC,\left(r_2+r_3\right)\cot \left(\frac{B+C}{2}\right)=$

• A. $a+b+c$
• B. a
• C. b
• D. c

Answer 1

Answer: (B)

Given, in $\Delta ABC$
$\left(r_2+r_3\right)\cot \left(\frac{B+c}{2}\right)=\left(\frac{\Delta }{s-b}+\frac{\Delta }{s-c}\right)\tan \frac{A}{2}$
$=\frac{\Delta (s-c+s-b)}{(s-b)(s-c)}\frac{\Delta }{s(s-a)}$
$=2s-b-c=a$