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MSC: 00A08, 97D50
The first example deals with the following question: In how many nonintersecting triangles whose vertices are in the vertices of convex $n$-gon and in $m$ given points inside the $n$-gon is the $n$-gon cut? In the second the set of all points $X$ with the following property is found: If you go from $X$ to given point $B$ in a straight line, the distance to another given point $A$ increases.
[1] Bušek, I., Kubínová, M., Novotná, J.: Matematika pro 9. ročník základní školy. Prometheus, Praha, 1994.
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