Find $n$ points on a circle with integer distances. 
Let $n$ be a positive integer, prove that it is possible to put $n$ points on a circle so that the distances among them are all integers.

For $n \leq 3$ this is trivial. I have shown it for $n=4$ by considering a rectangle.
I don't know how to do it for larger numbers though.

This is with radius 5 and edge length 6. It appears that the final edge (not drawn in) also has rational length  since it is vertical and both endpoints have rational coordinates 

