OPM 2010 Problem 2

On a circumference, points $A$ and $B$ are on opposite arcs of diameter $CD$ . Line segments $CE$ and $DF$ are perpendicular to $AB$ such that $A-E-F-B$ (i.e., $A$ , $E$ , $F$ and $B$ are collinear on this order). Knowing $AE=1$ , find the length of $BF$ .