Question 28
In $\triangle ABC$ ($AB \neq AC$) the incircle, with center $I$, touches the side $BC$ at $D$. Let $M$ be the midpoint of segment $BC$. Prove that the perpendiculars from $M$ to $AI$ and from $D$ to $MI$, respectively, meet on the line containing the altitude of $\triangle ABC$ from vertex $A$.
(Dusan Djukic)
(Dusan Djukic)