MathDB

2

Part of 1982 IMO Shortlist

Problems(1)

Area and convex polygon

Source: IMO LongList 1982 - P57 (Last problem! Yay!)

9/10/2010
Let KK be a convex polygon in the plane and suppose that KK is positioned in the coordinate system in such a way that area (K∩Qi)=14area K (i=1,2,3,4,),\text{area } (K \cap Q_i) =\frac 14 \text{area } K \ (i = 1, 2, 3, 4, ), where the QiQ_i denote the quadrants of the plane. Prove that if KK contains no nonzero lattice point, then the area of KK is less than 4.4.
geometryanalytic geometryIMO LonglistIMO Shortlistconvex polygonareageometric inequality