Question 4
Let $ABC$ be a scalene triangle. The midpoints of the sides $AB$, $BC$ and $CA$ are denoted $C_0$, $A_0$ and $B_0$ respectively. Let $l_A$, $l_B$ and $l_C$ denote the bisectors of the interior angles of $A$, $B$ and $C$ respectively. If $M$ is the intersection of the perpendicular from $C_0$ to $l_C$ and the perpendicular from $A_0$ to $l_A$, then show that $MB_0$ is parallel to $l_B$.