There is a shape

Question

first a regular triangle inscribed in a circle, and inscribed in a square, inscribed in a circle, inscribed in a pentagon, etc.
so polygon circle polygon circle, etc. the radius of the first circle is 1, find an equation for radius n.
number 2:give an argument that lim as x-infinity of r subscript n has an upper bound, or if you think it doesn't, why.
I'm not sure where to start and how to do this problem
Thanks.

Answer 1

You could start here:

http://www.mathopenref.com/polygonincircle.html