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Putnam 1981 A6

Source: Putnam 1981

March 31, 2022
Putnamgeometrylattice points

Problem Statement

Suppose that each of the vertices of ABCABC is a lattice point in the xyxy-plane and that there is exactly one lattice point PP in the interior of the triangle. The line APAP is extended to meet BCBC at EE. Determine the largest possible value for the ratio of lengths of segments ∣AP∣∣PE∣.\frac{|AP|}{|PE|}.
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