Question

If $R$ is the radius of circumscribing circle of a regular polygon of $n$ sides, then $R=?$

• A. $\frac{a}{2}sin\left(\frac{\pi }{n}\right)$
• B. $\frac{a}{2}cos\left(\frac{\pi }{n}\right)$
• C. $\frac{a}{2}cosec\left(\frac{\pi }{n}\right)$
• D. $\frac{a}{2}cosec\left(\frac{\pi }{2n}\right)$

Answer 1

The correct option is C $\frac{a}{2}cosec\left(\frac{\pi }{n}\right)$

since, it is a regular polygon so its interior angle will be equal

Hence, $nA=\pi \Rightarrow A=\frac{\pi }{n}$

and we know that

$\frac{a}{sinA}=2R\Rightarrow R=\frac{a}{2}cosec\left(\frac{\pi }{n}\right)$

therefore,Answer is $C$