Question 1
Given a circle with two chords $AB$, $CD$ that meet at $E$, let $M$ be a point of chord $AB$ other than $E$. Draw the circle through $D$, $E$, and $M$. The tangent line to the circle $DEM$ at $E$ meets the lines $BC$, $AC$ at $F$, $G$, respectively. Given $\frac{AM}{AB}=\lambda$, find $\frac{GE}{EF}$.