Let $ABCD$ be a rectangle of center $O$ in the plane $\alpha$, and let $V \notin\alpha$ be a point in space such that $V O \perp \alpha$. Let $A' \in (V A)$, $B'\in (V B)$, $C'\in (V C)$, $D'\in (V D)$ be four points, and let $M$ and $N$ be the midpoints of the segments $A'C'$ and $B'D'$. .Prove that $MN \parallel \alpha$ if and only if $V , A', B', C', D'$ all lie on a sphere.