International Mathematical Olympiad 1986 Problem 4

Let $A$, $B$ be adjacent vertices of a regular $n$-gon ($n \geq 5$) in the plane having center at $O$. 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, $X$ remaining inside the polygon. Find the locus of $X$.