NO-ABEL 2004 Problem 3

In a quadrilateral $ABCD$ with $\angle A = 60^o, \angle B = 90^o, \angle C = 120^o$ , the point $M$ of intersection of the diagonals satisfies $BM = 1$ and $MD = 2$ . (a) Prove that the vertices of $ABCD$ lie on a circle and find the radius of that circle. (b) Find the area of quadrilateral $ABCD$ .