A) \[a\cot \left( \frac{\pi }{n} \right)\]
B) \[\frac{a}{2}\cot \left( \frac{\pi }{2n} \right)\]
C) \[a\cot \left( \frac{\pi }{2n} \right)\]
D) \[\frac{a}{2}\cot \left( \frac{\pi }{2n} \right)\]
Correct Answer: B
Solution :
\[\tan \left( \frac{\pi }{n} \right)=\frac{a}{2r}\] and \[\sin \left( \frac{\pi }{n} \right)=\frac{a}{2R}\] Þ \[r+R=\frac{a}{2}\left[ \cot \frac{\pi }{n}+\text{cosec}\frac{\pi }{n} \right]\] \[=\frac{a}{2}\cot \left( \frac{\pi }{2n} \right)\].
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