The incircle of $ \triangle A_{0}B_{0}C_{0}$, meets legs $B_{0}C_{0}$, $C_{0}A_{0}$, $A_{0}B_{0}$, respectively on points $A$, $B$, $C$, and the incircle of $ \triangle ABC$, with center $I$, meets legs $BC$, $CA$, $AB$, on points $A_{1}$, $B_{1}$, $C_{1}$, respectively. We write with $ \sigma (ABC)$, and $ \sigma (A_{1}B_{1}C_{1})$ the areas of $ \triangle ABC$, and $ \triangle A_{1}B_{1}C_{1}$ respectively. Prove that if $ \sigma (ABC)=2 \sigma (A_{1}B_{1}C_{1})$, then lines $AA_{0}$, $BB_{0}$, $CC_{0}$ are concurrent.