MathNet 2024-part-04 — 168 problems (EN–VI) Question 90

Let $ABCD$ be a convex quadrilateral in which the diagonals intersect at $O$. Given that $\overrightarrow{AB} + \overrightarrow{AD} + \overrightarrow{AO} = \overrightarrow{BC} + \overrightarrow{DC} + \overrightarrow{OC}$, prove that $ABCD$ is a parallelogram.

Marius Dolcan