A) \[r+R\]
B) \[r-R\]
C) \[2(r+R)\]
D) \[2(r-R)\]
Correct Answer: C
Solution :
\[a\cot A+b\cot B+c\cot C\] = \[2R(\sin A\cot A+\sin B\cot B+\sin C\cot C)\] = \[2R(\cos A+\cos B+\cos C)\] =\[2R\left( 1+4\sin \frac{A}{2}\sin \frac{B}{2}\sin \frac{C}{2} \right)=2R\left( 1+\frac{r}{R} \right)=2\,(R+r)\].
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