Question

A regular polygon of nine sides, each of length $2$, is inscribed in a circle. The radius of the circle is?

• A. $\sec \left(\pi /9\right)$
• B. $\sin \left(\pi /9\right)$
• C. $cosec\left(\pi /9\right)$
• D. $\tan \left(\pi /9\right)$

Answer 1

The correct option is C $cosec\left(\pi /9\right)$

$\begin{array}{c}Weknowthat,\\ \sin \frac{\pi }{9}=\frac{1}{r}\\ r=\frac{1}{\sin \frac{\pi }{9}}\\ =cosec\frac{\pi }{9}\end{array}$.