Question

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

• A. $\operatorname { cosec } \frac { \pi } { 9 }$
• B. $\operatorname { cosec } \frac { \pi } { 3 }$
• C. $\cot \frac { \pi } { 9 }$
• D. $\tan \frac { \pi } { 9 }$

Answer 1

Answer: (A)

$\operatorname { cosec } \frac { \pi } { 9 }$

Answer 2

We know that radius of the circumcircle is given by

$R = \frac { a } { 2 } \operatorname { cosec } \left( \frac { \pi } { n } \right)$; Here, $a = 2 , n = 9$

$\therefore$Required radius = $\frac { 2 } { 2 } \operatorname { cosec } \frac { \pi } { 9 } = \operatorname { cosec } \frac { \pi } { 9 }$.