MathNet 2025 — Part 01 (100 complete bilingual questions) Question 77

Let $ABCD$ be a parallelogram and let $O$ be the intersection point of the diagonals. Prove that for any point $M \in (AB)$, there exist unique points $N \in (OC)$ and $P \in (OD)$ such that $O$ is the centroid of triangle $MNP$.
Nelu Chichirim