Two Spheres Through a Pyramid

A regular quadrilateral pyramid $O\text{-}ABCD$ has base edge length $\sqrt 6$ and height $3$. The sphere centered at $O$ with radius $\sqrt 2$ intersects the sphere $O_1$ passing through $A,B,C,D$, and the circle of intersection has area $\pi$. Find all possible values of the radius of the sphere $O_1$.