IMO Shortlist 1973 problem 7
Dodao/la:
arhiva2. travnja 2012. Given a tetrahedron
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
, let
![x = AB \cdot CD](/media/m/c/3/7/c37d34e762cbcc6f21a8b9cb7583e832.png)
,
![y = AC \cdot BD](/media/m/5/d/7/5d71e01e1c1d23ba51a389689376e3eb.png)
, and
![z = AD \cdot BC](/media/m/7/9/6/796a4fbc36b60d281fed32e0c466330c.png)
. Prove that there exists a triangle with edges
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Given a tetrahedron $ABCD$, let $x = AB \cdot CD$, $y = AC \cdot BD$, and $z = AD \cdot BC$. Prove that there exists a triangle with edges $x, y, z.$
Izvor: Međunarodna matematička olimpijada, shortlist 1973