I was recently tutoring geometry at a university. The students knew how to construct different polygons. Therefore I wanted to know how to prove the construction.
One task was constructing a pentadecagon with a given side length. The steps for the construction are in the following article: https://en.wikipedia.org/wiki/Pentadecagon
I don't get how the circumcircle radius is deducted by the construction of the smaller pentagon. What relations exist for the circumcircle radius that are used here? Why is the construction done the way it is?