On this page we will state a few very basic properties of a regular polygon with $n$ sides. We assume that each side is of length $a$. The next figure shows a typical example, in this case a heptagon, a seven-sided regular polygon.
The blue circle is called the circumcircle of radius $r_u$, passing through all the vertices. In analogy, there is a unique incircle of radius $r_i$ touching all sides from within, here drawn in red.