6. On the sides $A B$ and $A C$ of an acute-angled triangle $A B C$, two equal rectangles $A M N B$ and $A P Q C$ are constructed outside. Find the distance between the vertices $N$ and $Q$ of the rectangles, if the lengths of the sides $A B$ and $A C$ are 5 and $\sqrt{11}$, respectively, and the angle at vertex $A$ of the triangle is $\arccos \frac{1}{3}$.
Answer: $\sqrt{72+48 \sqrt{2}}$.

## Final round of the "Rosatom" Olympiad, 11th grade, CIS, February 2020

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