How to get the radius of a circle that has an inscribed regular polygon.

The radius of a regular polygon is the distance from the center to any vertex. It will be the same for any vertex. The radius of the polygon's circumcircle, which is the circle that passes through every vertex.

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!