Putnam 1977 B2

Problem B-2 Given a convex quadrilateral $A B C D$ and a point $O$ not in the plane of $A B C D$, locate point $A^{\prime}$ on line $O A$, point $B^{\prime}$ on line $O B$, point $C^{\prime}$ on line $O C$, and point $D^{\prime}$ on line $O D$ so that $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ is a parallelogram.