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

Question

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