6. A circle of radius 4 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 $F A$, and point $D$ is on ray $B F$ such that $A C = B D = 5$. Find the length of the median of triangle $C A D$ drawn from vertex $A$.
Answer: $\quad m_{A}=\frac{5 \sqrt{3}}{2}-2$.

## On-site Selection Round of the "Rosatom" Olympiad in Regions, Autumn

2019

11th grade, set 1

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