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2013 China IMO Team Selection Test 3 Day 2 Q3

Source: 25 Mar 2013

April 1, 2013
analytic geometrygeometrycombinatorics proposedcombinatorics

Problem Statement

A point (x,y)(x,y) is a lattice point if x,y∈Zx,y\in\Bbb Z. Let E={(x,y):x,y∈Z}E=\{(x,y):x,y\in\Bbb Z\}. In the coordinate plane, PP and QQ are both sets of points in and on the boundary of a convex polygon with vertices on lattice points. Let T=P∩QT=P\cap Q. Prove that if T≠∅T\ne\emptyset and T∩E=∅T\cap E=\emptyset, then TT is a non-degenerate convex quadrilateral region.
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