Suppose a regular $m$-gon is inscribed inside a unit circle. And suppose a regular $n$-gon is inscribed in another unit circle. What's the relation between sides of $m$ and $n$?
I know $$l_{2n}=\sqrt{2R^2 - R\sqrt{4R^2-l_{n}^2}}$$
where $l_n$ is the side of a regular $n$-sided polygon inscribed in a circle with $R$ radius.
But how can I use this equation to derive a relation between $m$ and $n$?