IT-CESENATICO 2007 Problem 3

Let ABC be a triangle, G its centroid, M the midpoint of AB, D the point on the line $AG$ such that $AG = GD, A \neq D$ , E the point on the line $BG$ such that $BG = GE, B \neq E$ . Show that the quadrilateral BDCM is cyclic if and only if $AD = BE$ .