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The sum of the radii of inscribed and circumscribed circles for an $\mathrm{n}$ sided regular polygon of side a, is
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$\operatorname{acot}\left(\frac{\pi}{2 n}\right)$
$\operatorname{acot}\left(\frac{\pi}{2 n}\right)$
$\tan \left(\frac{\pi}{n}\right)=\frac{a}{2 r} ; \sin \left(\frac{\pi}{n}\right)=\frac{a}{2 R}$
$r+R=\frac{a}{2}\left[\cot \frac{\pi}{n}+\operatorname{cosec} \frac{\pi}{n}\right] \Rightarrow r+R=\frac{a}{2} \cdot \cot \left(\frac{\pi}{2 n}\right)$
$r+R=\frac{a}{2}\left[\cot \frac{\pi}{n}+\operatorname{cosec} \frac{\pi}{n}\right] \Rightarrow r+R=\frac{a}{2} \cdot \cot \left(\frac{\pi}{2 n}\right)$
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