Question 68
Let $H$ be the orthocenter of $\triangle ABC$, $M$ be the midpoint of $AB$ and $H_1$ and $H_2$ be the feet of the perpendiculars from $H$ to the inner and the outer bisector of $\measuredangle ACB$, respectively. Prove that the points $H_1$, $H_2$ and $M$ are colinear.