KöMaL 2009 B4215

The points $A$ and $B$ lie on one side of line $e$ in the plane. Let $M$ be the point on the line for which the sum $AM +MB$ is a minimum, and let $N$ be the point of the line with $AN = BN$ . Prove that the points $A$ , $B$ , $M$ , $N$ lie on a circle.