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Problem of the Week

The Locus of X... (Very Difficult!)

Let A, B be adjacent verticies of a regular n-gon (n is greater than or equal to 5) in the plane having center O. A triangle XYZ, which is congruent to and initially coincided with OAB, moves rigidly in the plane in such a way that Y and Z each trace out the whole boundary of the polygon, X remaining inside the polygon. Find the locus of X.

(IMO 1986)

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