Question 108
In the scalene triangle $ABC$ the points $A_1$ and $B_1$ are the bisector feet, drawn from the vertices $A$ and $B$ respectively. The straight line $A_1B_1$ intersects the line $AB$ at the point $D$. Prove that one of the angles $\angle ACD$ or $\angle BCD$ is obtuse and $m(\angle ACD) + m(\angle BCD) = 180^\circ$.