Question

The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon of side a, is

• A. $a \cot \left( \frac { \pi } { n } \right)$
• B. $\frac { a } { 2 } \cot \left( \frac { \pi } { 2 n } \right)$
• C. $a \cot \left( \frac { \pi } { 2 n } \right)$
• D. $\frac { a } { 4 } \cot \left( \frac { \pi } { 2 n } \right)$

Answer 1

Answer: (C)

$a \cot \left( \frac { \pi } { 2 n } \right)$

Answer 2

$\tan \left( \frac { \pi } { n } \right) = \frac { a } { 2 r }$ and $\sin \left( \frac { \pi } { n } \right) = \frac { a } { 2 R }$

⇒ $r + R = \frac { a } { 2 } \left[ \cot \frac { \pi } { n } + \operatorname { cosec } \frac { \pi } { n } \right] = \frac { a } { 2 } \cot \left( \frac { \pi } { 2 n } \right)$ .