Question 2
Let $\mathcal C_1$ and $\mathcal C_2$ be concentric circles, with $\mathcal C_2$ inside $\mathcal C_1$. From $A\in\mathcal C_1$, draw the tangent $AB$ to $\mathcal C_2$, with $B\in\mathcal C_2$. Let $C$ be the second intersection of ray $AB$ with $\mathcal C_1$, and let $D$ be the midpoint of $AB$. A line through $A$ meets $\mathcal C_2$ at $E,F$ so that the perpendicular bisectors of $DE$ and $CF$ intersect at a point $M$ on line $AB$. Find, with proof, $AM/MC$.