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A6

Part of 2018 Putnam

Problems(1)

Putnam 2018 A6

Source:

12/2/2018
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.
PutnamPutnam 2018