Question 104
The incircle of the triangle $ABC$ touches the sides $AC$ and $BC$ at points $P$ and $Q$, respectively, $N$ and $M$ are the midpoints of $AC$ and $BC$, respectively. Let $X = AM \cap BP$, $Y = BN \cap AQ$.
Given $C, X, Y$ are collinear prove that $CX$ is the angle bisector of the angle $ACB$.
Given $C, X, Y$ are collinear prove that $CX$ is the angle bisector of the angle $ACB$.