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1998 Putnam A6

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April 19, 2013
Putnamgeometrycollege contests

Problem Statement

Let A,B,CA,B,C denote distinct points with integer coefficients in R2\mathbb{R}^2. Prove that if (∣AB∣+∣BC∣)2<8⋅[ABC]+1(|AB|+|BC|)^2<8\cdot[ABC]+1 then A,B,CA,B,C are three vertices of a square. Here ∣XY∣|XY| is the length of segment XYXY and [ABC][ABC] is the area of triangle ABCABC.
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