<p>Regular polygons with <img alt="$5,6,7,$" height="16" src="https://latex.artofproblemsolving.com/1/5/c/15cf9c5ca516b05bd21084f414edb7a9ee01642b.png" width="47" /> and <img alt="$8$" height="14" src="https://latex.artofproblemsolving.com/8/4/5/8455f3b5cb3b4880b8c9d782a5c1f0334db819eb.png" width="11" /> sides are inscribed in the same circle. No two of the polygons share a vertex, and no three of their sides intersect at a common point. At how many points inside the circle do two of their sides intersect?</p>

Question No: 436

Regular polygons with $5,6,7,$ and $8$ sides are inscribed in the same circle. No two of the polygons share a vertex, and no three of their sides intersect at a common point. At how many points inside the circle do two of their sides intersect?

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Tags: Combinatorics

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