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Putnam 2018 A6

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December 2, 2018
PutnamPutnam 2018

Problem Statement

Suppose that AA, BB, CC, and DD are distinct points, no three of which lie on a line, in the Euclidean plane. Show that if the squares of the lengths of the line segments ABAB, ACAC, ADAD, BCBC, BDBD, and CDCD are rational numbers, then the quotient area(△ABC)area(△ABD)\frac{\mathrm{area}(\triangle ABC)}{\mathrm{area}(\triangle ABD)} is a rational number.
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