Question 7
Diagonals of the convex quadrilateral $ABCD$ inscribed in a circle intersect at point $E$. The line passing $E$ perpendicular to the side $AD$ intersects the side $BC$ at point $N$. The line passing $E$ perpendicular to the side $BC$ intersects the side $AD$ at point $M$. Prove that $2MN = AB + CD$ implies that $ABCD$ is a trapezoid.
(proposed by N. Argilsan)
(proposed by N. Argilsan)