Q67 / 160 · AP EAMCET 2024 (20 May Shift 2) · Mathematics

In $\triangle A B C, r r_1 \cot \frac{A}{2}+r r_2 \cot \frac{B}{2}+r r_3 \cot \frac{C}{2}=$

  • Correct answer
    A
    $3 \Delta$
  • B
    3 S
  • C
    $\frac{\mathrm{S}}{\Delta}$
  • D
    $\Delta$

Solution

$r_1 \cot \frac{\mathrm{~A}}{2}+r r_2 \cot \frac{\mathrm{~B}}{2}+r r_3 \cot \frac{\mathrm{C}}{2}$ $\begin{aligned} & =\frac{\Delta}{s} \times \frac{\Delta}{s-a} \times \frac{s(s-a)}{\Delta}+\frac{\Delta}{s} \times \frac{\Delta}{s-b} \times \frac{s(s-b)}{\Delta}+\frac{\Delta}{s} \times \\ & \frac{\Delta}{s-c} \times \frac{s(s-c)}{\Delta} \\ & \Delta+\Delta+\Delta=3 \Delta\end{aligned}$

Hence, the correct answer is option: 'A'.

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