Let $\omega$ be the incircle of a triangle $ABC$. The line passing though the incenter $I$ and parallel to $BC$ meets $\omega$ at $A_b$ and $A_c$ ($A_b$ lies in the same semi plane with respect to $AI$ as $B$). The lines $BA_b$ and $CA_c$ meet at $A_1$. The points $B_1$ and $C_1$ are defined similarly. prove that $AA_1,BB_1,CC_1$ concur.