The incircle of the triangle
touches the sides
,
, and
in the points
,
and
, respectively. Let
be the point symmetric to
with respect to the incenter. The lines
and
intersect at
. Prove that
is parallel to
.
%V0
The incircle of the triangle $ABC$ touches the sides $BC$, $CA$, and $AB$ in the points $D$, $E$ and $F$, respectively. Let $K$ be the point symmetric to $D$ with respect to the incenter. The lines $DE$ and $FK$ intersect at $S$. Prove that $AS$ is parallel to $BC$.
Školjka