Four Points on a Sphere

The four vertices of a (not necessarily planar) quadrilateral $ABCD$ lie on a sphere $O$. Let $E, F$ be the midpoints of $AB$ and $CD$, with $EF \perp AB$ and $EF \perp CD$. If $AB = EF = 4$ and $CD = 8$, find the radius of the sphere $O$.