In the triangle $ABC$, the cevians $AA_1$, $BB_1$ and $CC_1$ intersect at the point $O$. It turned out that $AA_1$ is the bisector, and the point $O$ is closer to the straight line $AB$ than to the straight lines $A_1C_1$ and $B_1A_1$. Prove that $\angle{BAC} > 120^{\circ}$.