Let
be a triangle, and
its incenter. Consider a circle which lies inside the circumcircle of triangle
and touches it, and which also touches the sides
and
of triangle
at the points
and
, respectively. Show that the point
is the midpoint of the segment
.
%V0
Let $ABC$ be a triangle, and $I$ its incenter. Consider a circle which lies inside the circumcircle of triangle $ABC$ and touches it, and which also touches the sides $CA$ and $BC$ of triangle $ABC$ at the points $D$ and $E$, respectively. Show that the point $I$ is the midpoint of the segment $DE$.
Školjka