Is the Midpoint of HE the Center of the Inscribed Circle in Triangle HBC?

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The discussion centers on the geometric properties of triangle HBC, specifically regarding the relationship between the midpoint of segment HE and the center of the inscribed circle of triangle HBC. It establishes that in a sharp triangle ABC with orthocenter H and incircle (O;R), the circle (E;r) is tangent to sides HB and HC, as well as to the incircle (O;R). The conclusion drawn is that the midpoint of HE serves as the center of the incircle of triangle HBC.

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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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max said:
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 $HBC$

Hi max, :)

I am not understanding your question correctly. What is a "sharp triangle"? And what is circle $(E;r)$ ?
 

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