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

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

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