1.6 (IMO 27) For a regular $n$-sided polygon $(n \geqslant 5)$ centered at point $O$, two adjacent vertices are denoted as $A$ and $B$, and $\triangle X Y Z$ is congruent to $\triangle A B C$. Initially, let $\triangle X Y Z$ overlap with $\triangle O A B$, then move $\triangle X Y Z$ on the plane so that points $Y$ and $Z$ both move along the perimeter of the polygon for one complete round, while point $X$ remains moving inside the polygon. Find the locus of point $X$.
1. 6 Mathematical Experiment: First, let $Y$ move on side $AB$. Apart from point $O$, find two other possible positions for point $X$. Observations show that for these three points, $B X \leqslant \frac{1}{\cos \frac{\pi}{n}}$. Therefore, the trajectory consists of $n$ line segments $O O_{j}(j=1,2, \cdots, n)$ on $AO, BO, \cdots, QO$, with $O O,=\frac{1}{\cos \frac{\pi}{n}} - 1$, and each line segment is traversed twice.