Τρίτη, 10 Οκτωβρίου 2017

2008 JBMO Shortlist G8

The side lengths of a parallelogram are $a, b$ and diagonals have lengths $x$ and $y$. Knowing that $ab = \frac{xy}{2}$, show that $\left( a,b \right)=\left( \frac{x}{\sqrt{2}},\frac{y}{\sqrt{2}} \right)$  or $\left( a,b \right)=\left( \frac{y}{\sqrt{2}},\frac{x}{\sqrt{2}} \right)$.

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