RU-ORAL-GEOMETRY 2018 Problem 2

Bisectors of angle $C$ and externalangle $A$ of trapezoid $ABCD$ with bases $BC$ and $AD$ intersect at point $M$ , and the bisector of angle $B$ and external angle $D$ intersect at point $N$ . Prove that the midpoint of the segment $MN$ is equidistant from the lines $AB$ and $CD$ .