Let sharp triangle ABC inscribed circle $(O;R)$ and $H$ is orthocenter of triangle ABC. circle $(E;r)$ tangent to $HB$, $HC$ and tangent to in circle $(O;R)$.
Prove that: midpoint of $HE$ is center of the circle inscribed the triangle $HBC$
Let sharp triangle ABC inscribed circle $(O;R)$ and $H$ is orthocenter of triangle ABC. circle $(E;r)$ tangent to $HB$, $HC$ and tangent to in circle $(O;R)$.
Prove that: midpoint of $HE$ is center of the circle inscribed the triangle $HBC$