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Show that the triangle contains a nontrivial lattice point

Source: Kürschák 1988, problem 3

July 20, 2014
geometry unsolvedgeometry

Problem Statement

Consider the convex lattice quadrilateral PQRSPQRS whose diagonals intersect at EE. Prove that if ∠P+∠Q<180∘\angle P+\angle Q<180^\circ, then the △PQE\triangle PQE contains inside it or on one of its sides a lattice point other than PP and QQ.
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