Room For One More?

Let's assume OF=y where O is the centre of the given circle of radius=R.Now, EF² = 9 -(R+y)² = R²- y² which yields y=(9-2R²)/(2R). If r =radius of C1 then we can further write: (R-r)² = r² + [(9-2R²)/(2R)+ r]². On simplification, for +ve r & R, we get, 2rR + 9 =6R. In other words, r =(6R-9)/(2R). Finally, AL = R + (9-2R²)/(2R) + (6R-9)/(2R). . On simplification, we obtain, AL = 3

I figured, well if the answer is correct for all values of $AF$ , then it must hold for $AF \rightarrow AB$ . In that case $AL=AE = \boxed{3}$