Question 102
Let $M$ be the midpoint of the side $AB$ of the acute-angled non-isosceles triangle $ABC$, $H$ be the orthocenter of $ABC$, and $I$ be the incenter of $ABC$.
Prove that if $M$, $I$, and $H$ are collinear, then the length of the segment $CH$ is equal to the length of the radius of the incircle of the triangle $ABC$.
(Folklore)
Prove that if $M$, $I$, and $H$ are collinear, then the length of the segment $CH$ is equal to the length of the radius of the incircle of the triangle $ABC$.
(Folklore)