In triangle ABC,find the value of r r_1 cot f | vedclass

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(A) We know that $r = \frac{\Delta}{s}$,$r_1 = \frac{\Delta}{s-a}$,$r_2 = \frac{\Delta}{s-b}$,$r_3 = \frac{\Delta}{s-c}$,and $\cot \frac{A}{2} = \sqrt

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$3 \Delta$

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(A) We know that $r = \frac{\Delta}{s}$,$r_1 = \frac{\Delta}{s-a}$,$r_2 = \frac{\Delta}{s-b}$,$r_3 = \frac{\Delta}{s-c}$,and $\cot \frac{A}{2} = \sqrt{\frac{s(s-a)}{(s-b)(s-c)}} = \frac{s(s-a)}{\Delta}$.Substituting these values into the expression:$r r_1 \cot \frac{A}{2} = \left(\frac{\Delta}{s}\right) \left(\frac{\Delta}{s-a}\right) \left(\frac{s(s-a)}{\Delta}\right) = \Delta$.Similarly,$r r_2 \cot \frac{B}{2} = \Delta$ and $r r_3 \cot \frac{C}{2} = \Delta$.Therefore,the sum is $\Delta + \Delta + \Delta = 3 \Delta$.

In $\triangle ABC$,find the value of $r r_1 \cot \frac{A}{2} + r r_2 \cot \frac{B}{2} + r r_3 \cot \frac{C}{2}$.

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