IMO Shortlist 1986 problem 1


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2. travnja 2012.
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Let A,B be adjacent vertices of a regular n-gon (n\ge5) with center O. A triangle XYZ, which is congruent to and initially coincides with OAB, moves in the plane in such a way that Y and Z each trace out the whole boundary of the polygon, with X remaining inside the polygon. Find the locus of X.
Izvor: Međunarodna matematička olimpijada, shortlist 1986