Concyclic points on a regular polygon So if you have two distinct concyclic points, what is the criterion that they are vertices (I find that this is a more interesting problem) of a regular n-gon? Three points? Four points? 5 points? k points?
This was all the information I got on the problem, I can try to clarify if needed.

If the points are vertices of a regular n-gon, then that n-gon's center is the same as that of the circle.  So you just need to check if the angles between the points are all multiples of $2\pi/n$.
