IMO Shortlist 1962 problem 3

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Dodao/la: arhiva
2. travnja 2012.
Consider the cube ABCDA'B'C'D' (ABCD and A'B'C'D' are the upper and lower bases, repsectively, and edges AA', BB', CC', DD' are parallel). The point X moves at a constant speed along the perimeter of the square ABCD in the direction ABCDA, and the point Y moves at the same rate along the perimiter of the square B'C'CB in the direction B'C'CBB'. Points X and Y begin their motion at the same instant from the starting positions A and B', respectively. Determine and draw the locus of the midpionts of the segments XY.
Izvor: Međunarodna matematička olimpijada, shortlist 1962