Let be adjacent vertices of a regular -gon () with center . A triangle , which is congruent to and initially coincides with , moves in the plane in such a way that and each trace out the whole boundary of the polygon, with remaining inside the polygon. Find the locus of .
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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 $X$.
Izvor: Međunarodna matematička olimpijada, shortlist 1986
Školjka 
be adjacent vertices of a regular 
-gon (
) with center 
. A triangle 
, which is congruent to and initially coincides with 
, moves in the plane in such a way that 
and 
each trace out the whole boundary of the polygon, with 
remaining inside the polygon. Find the locus of