Points M,N,P,Q are taken on the sides AB,BC,CD,DA respectively of a square ABCD such that AM=BN=CP=DQ=1nAB. Find the ratio of the area of the square determined by the lines MN,NP,PQ,QM to the ratio of ABCD.
Source: Slovenia 1997 2nd Grade P2
Tags: geometry
Points M,N,P,Q are taken on the sides AB,BC,CD,DA respectively of a square ABCD such that AM=BN=CP=DQ=1nAB. Find the ratio of the area of the square determined by the lines MN,NP,PQ,QM to the ratio of ABCD.