The incircle of a triangle $ABC$ with $AB\ne BC$ touches $BC$ at $A_1$ and $AC$ at $B_1$. The segments $AA_1$ and $BB_1$ meet the incircle at $A_2$ and $B_2$, respectively. Prove that the lines $AB,A_1B_1,A_2B_2$ are concurrent.
Source: Mongolian MO 2002 Grade 10 P3
Tags: geometry
The incircle of a triangle $ABC$ with $AB\ne BC$ touches $BC$ at $A_1$ and $AC$ at $B_1$. The segments $AA_1$ and $BB_1$ meet the incircle at $A_2$ and $B_2$, respectively. Prove that the lines $AB,A_1B_1,A_2B_2$ are concurrent.