



 
Hi Levan, I am unclear as to what you want to do. It looks to me that you want to inscribe a regular polygon with side length $c$ into a circle of radius $r$ and your problem is to determine the number of sides, $n$ of the resulting polygon. On our page that you quote Stephen developed the expression \[c^2 = r^2 \left( 2  2 \cos \left( \frac{360^o}{n}\right) \right)\] which he then solved for $c.$ You want to solve this expression for $n.$ Is this what you want? The difficulty I am having is that for $n$ to be a whole number only certain values of $c$ and $r$ are possible. Penny  


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