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maximum ratio in triangle with lattice points as vertices

Source: Czech and Slovak Match 1995 P3

October 1, 2017
lattice pointsratiogeometrymaximization

Problem Statement

Consider all triangles ABCABC in the cartesian plane whose vertices are at lattice points (i.e. with integer coordinates) and which contain exactly one lattice point (to be denoted PP) in its interior. Let the line APAP meet BCBC at EE. Determine the maximum possible value of the ratio APPE\frac{AP}{PE}.
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