Question 133
Two points $A$ and $B$ are marked on the right branch of the hyperbola $y = 1/x$ ($x \gt 0$). The straight line $\ell$ passing through the origin $O$ is perpendicular to the line $AB$ and meets $AB$ and the given branch of the hyperbola at points $D$ and $C$, respectively. The circle $S$ passes through the points $A, B, C$ and meets $\ell$ at $F$.
Find all possible values of the ratio $OD:CF$.
Find all possible values of the ratio $OD:CF$.