IMO Shortlist 1968 problem 17


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2. travnja 2012.
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Given a point O and lengths x, y, z, prove that there exists an equilateral triangle ABC for which OA = x, OB = y, OC = z, if and only if x+y \geq  z, y+z \geq x, z+x \geq y (the points O,A,B,C are coplanar).
Izvor: Međunarodna matematička olimpijada, shortlist 1968