10.1

Part of 2006 Sharygin Geometry Olympiad

Problems(1)

existence of a closed polygonal line

Source: Sharygin 2006 finals 10.1

Five lines go through one point. Prove that there exists a closed five-segment polygonal line, the vertices and the middle of the segments of which lie on these lines, and each line has exactly one vertex.

geometrybroken line