6. A circle of radius 3 touches line $P$ at point $A$ and line $Q$ at point $B$ such that the chord $A B$ subtends an arc of $60^{\circ}$. Lines $P$ and $Q$ intersect at point $F$. Point $C$ is located on ray $A F$, and point $D$ is on ray $F B$ such that $A C=B D=4$. Find the length of the median of triangle $C A D$, drawn from vertex $A$.
Answer: $\quad m_{A}=2 \sqrt{3}+\frac{3}{2}$.