Question 115
The figure shows a semicircle, where $B$ is a point on its diameter $AC$ so that $AB = 6$ and $BC = 12$. The line perpendicular to this diameter meets the semicircle at $D$. The semicircles with diameters $AB$ and $BC$, drawn as shown, meet $AD$ and $CD$ at $E$ and $F$, respectively. Find the distance between $E$ and $F$.
