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 $X$.
Školjka