## Quadrilateral Parallelogram

#### Problem

Three points, A, B, and C, are chosen at random such that OABC forms a quadrilateral. The midpoints of each edge, P, Q, R, and S, are joined.

Prove that the quadrilateral PQRS will always be a parallelogram.

Problem ID: 250 (02 Dec 2005) Difficulty: 3 Star