Let ABCD be a rectangle of center O in the plane α, and let V∈/α be a point in space such that VO⊥α. Let A′∈(VA), B′∈(VB), C′∈(VC), D′∈(VD) be four points, and let M and N be the midpoints of the segments A′C′ and B′D′. .Prove that MN∥α if and only if V,A′,B′,C′,D′ all lie on a sphere. geometry3D geometrysphererectangle6th edition