AT-OEMO-BEG 2009 Problem 4

The center $M$ of the square $ABCD$ is reflected wrt $C$ . This gives point $E$ . The intersection of the circumcircle of the triangle $BDE$ with the line $AM$ is denoted by $S$ . Show that $S$ bisects the distance $AM$ .

(W. Janous, WRG Ursulinen, Innsbruck)