5. (Average) The figure shows a semicircle, where $B$ is a point on its diameter $A C$ so that $A B=6$ and $B C=12$. The line perpendicular to this diameter meets the semicircle at $D$. The semicircles with diameters $A B$ and $B C$, drawn as shown, meet $A D$ and $C D$ at $E$ and $F$, respectively. Find the distance between $E$ and $F$.
Answer: $6 \sqrt{2}$
Solution: Observe that $D E F B$ is a rectangle so $E F=D B$. However, $D B^{2}=A B \times B C=72$. Thus, $E F=6 \sqrt{2}$.