MathNet 2024-part-04 — 168 problems (EN–VI) Question 113

Consider a parallelogram $ABCD$ and the points $M$ on the side $DC$ and $E$ and $N$ on the diagonal $AC$, such that $BE \perp AC$ and $\frac{CM}{CD} = \frac{EN}{EA}$.
Prove that if $MN$ and $NB$ are perpendicular, then $ABCD$ is a rectangle.