Quadrilateral ABCD is a parallelogram. The midpoints of AB and AD are M and N, respectively. Let P be the intersection of DB and CM and let Q be the intersection of DB and CN. Compute PQ/DB.
From similar triangles PCD and MBP, PB:PD = 1:3, so PB = BD/4. From the other pair of similar triangles, DQ = BD/4. Therefore, PQ/BD = (BD - PB - DQ)/BD = 1/2.