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Circle Inscribed in a Regular Polygon

TOP/Collection of Mathematical Formulas/Inscribed and circumscribed
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Calculates a table of radii and areas of circles inscribed in regular n-gons.
Side length a
Regular Polygon n
〜
sides(Up to 200 times)
\(\normalsize Incircle\ of\ regular\ polygons\\ \hspace{20px} n:\ number\ of\ sides\\ (1)\ inradius:\hspace{40px} r={\large\frac{a}{2tan{\large\frac{\pi}{n}}}}\\ (2)\ incircle\ area:\hspace{10px} S_c=\pi r^2={\large\frac{\pi a^2}{4tan^2({\large\frac{\pi}{n}})}}\\ (3)\ polygon\ area:\hspace{10px} S_p={\large\frac{1}{2}}nar={\large\frac{na^2}{4tan{\large\frac{\pi}{n}}}}\\\)

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