This problem was suggested by Gokul43201, based on this year's Putnam A2.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose that [tex]K[/tex] is a convex set in [tex]\mathbb{R}^2[/tex] which is contained in the region bounded by the graphs of the hyperbolas [tex]xy=1, xy=-1[/tex] (so the set is in the inner + shaped region which contains the origin also). What is the maximum possible area of [tex]K[/tex]?

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# Maximal area of a convex region bounded by hyperbolas

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