CGMO 2008 Problem 4

Equilateral triangles $ABQ$ , $BCR$ , $CDS$ , $DAP$ are erected outside of the convex quadrilateral $ABCD$ . Let $X$ , $Y$ , $Z$ , $W$ be the midpoints of the segments $PQ$ , $QR$ , $RS$ , $SP$ , respectively. Determine the maximum value of $$\frac {XZ+YW}{AC + BD}.$$