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 $HBC$

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- March 4th 2013, 06:44 AMleezangqeGeometry interested
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 $HBC$