The sum of the radii of the inscribed and cir | vedclass

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(B) For a regular $n$-sided polygon with side length $a$,the inradius $r$ and circumradius $R$ are given by:$r = \frac{a}{2} \cot \left( \frac{\pi}{n}

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) For a regular $n$-sided polygon with side length $a$,the inradius $r$ and circumradius $R$ are given by:$r = \frac{a}{2} \cot \left( \frac{\pi}{n} ight)$$R = \frac{a}{2} \csc \left( \frac{\pi}{n} ight)$Sum $= r + R = \frac{a}{2} \left( \cot \frac{\pi}{n} + \csc \frac{\pi}{n} ight)$Using the identity $\cot 	heta + \csc 	heta = \cot \left( \frac{	heta}{2} ight)$:Sum $= \frac{a}{2} \cot \left( \frac{\pi}{2n} ight)$.

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

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