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the number of sides approaches infinity, the xth shortest diagonal approaches the length . Additionally, the formula for the shortest diagonal simplifies in the case of x = 1:

:

If the number of sides is even, the longest diagonal will be equivalent to the diameter of the polygon's circumcircle because the long diagonals all intersect each other at the polygon's center.

Special cases include:

A square has two diagonals of equal length, which

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