Question 149
Let $C_1$ and $C_2$ be two concentric circles, with $C_2$ inside $C_1$. From a point $A$ on $C_1$ draw a tangent $AB$ to $C_2$, with $B$ on $C_2$. Let $C$ be the second intersection of ray $AB$ with $C_1$, and let $D$ be the midpoint of $\overline{AB}$. A line through $A$ meets $C_2$ at $E, F$ such that the perpendicular bisector of $DE$ and the perpendicular bisector of $CF$ meet at a point $M$ on $AB$. Find all possible values of $AM/MC$.