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

In $\triangle A B C,\left(r_2+r_3\right) \cot \left(\frac{B+C}{2}\right)=$
  1. a+b+c
  2. a
  3. b
  4. c

Solution

Given, in $\triangle A B C$ $ \begin{aligned} & \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)} \end{aligned} $ $ =2 s-b-c=a $ Hence, option (b) is correct

Asked in: AP EAMCET 2019 (20 Apr Shift 2)

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