5. In triangle $A B C$, the perpendicular bisectors of sides $A B$ and $A C$ intersect lines $A C$ and $A B$ at points $N$ and $M$ respectively. The length of segment $N M$ is equal to the length of side $B C$ of the triangle. The angle at vertex $C$ of the triangle is $40^{\circ}$. Find the angle at vertex $B$ of the triangle.
Answer: $80^{\circ}$ or $20^{\circ}$.

## Final round of the "Rosatom" Olympiad, 9th grade, CIS, February 2020

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