## Problem of the Week

**The Locus of X...**

*(Very Difficult!)*-------1/22/07-------

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.

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__IMO 1986__)