HMMT 2013 G4

Let $\omega_{1}$ and $\omega_{2}$ be circles with centers $O_{1}$ and $O_{2}$, respectively, and radii $r_{1}$ and $r_{2}$, respectively. Suppose that $O_{2}$ is on $\omega_{1}$. Let $A$ be one of the intersections of $\omega_{1}$ and $\omega_{2}$, and $B$ be one of the two intersections of line $O_{1} O_{2}$ with $\omega_{2}$. If $A B=O_{1} A$, find all possible values of $\frac{r_{1}}{r_{2}}$.