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Putnam 2015 A1

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December 6, 2015
PutnamPutnam 2015Putnam calculus

Problem Statement

Let AA and BB be points on the same branch of the hyperbola xy=1.xy=1. Suppose that PP is a point lying between AA and BB on this hyperbola, such that the area of the triangle APBAPB is as large as possible. Show that the region bounded by the hyperbola and the chord APAP has the same area as the region bounded by the hyperbola and the chord PB.PB.
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