109877 – We Solve Problem

#### Equilateral triangle , Hexagons , Pigeonhole principle (finite number of poits, lines etc.) , Polygons and polyhedra with vertices in lattice points , Regular polygons

A regular hexagon with sides of length 5 is divided by straight lines, that are parallel to its sides, to form regular triangles with sides of length 1 $($see the figure$)$.

We call the vertices of all such triangles, nodes. It is known that more than half of the nodes are marked. Prove that there are five marked nodes lying on one circumference.

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