IMO 1986 Problem 4

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 $X$ .