Question 95
Let $AA_0$, $BB_0$ and $CC_0$ be angular bisectors of $\triangle ABC$. Let $A_0A_1 \parallel BB_0$ and $A_0A_2 \parallel CC_0$, where $A_1$ and $A_2$ lie on $AC$ and $AB$, respectively, and let line $A_1A_2$ intersect $BC$ at $A_3$. The points $B_3$ and $C_3$ are obtained similarly. Prove that points $A_3$, $B_3$, $C_3$ are collinear. (posed by Tao Pingsheng)