Question 29
Unit segments $A B$ and $C D$ are given such that $A B \nparallel C D$. If $M$ is the midpoint of $A C$, $N$ the midpoint of $B D$, and $X$ the intersection of lines $A B$ and $C D$, given $M \neq N$ and $A \neq X \neq C$, show that the angle bisector of $\angle A X C$ is either parallel or perpendicular to $M N$.