Question 40
Let $ABCD$ be a parallelogram. Let $E$ and $F$ denote such points on the sides $AB$ and $BC$ that satisfy $|AE| = |CF|$. Let $G$ be obtained by reflection of the point $E$ through the point $A$. Denote by $M$ the point of intersection of the lines $AF$ and $EC$, and denote by $N$ the point of intersection of the lines $AF$ and $GC$. Prove that $\angle NDM = 90^\circ$.
