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Found problems: 1

1997 Portugal MO, 5
Tags: geometry , line segment
A square region of side $12$ contains a water source that supplies an irrigation system constituted by several straight channels forming polygonal lines. Considers the source as a point and each channel as a line segment. Knowing that a point is irrigated if it is not more than $1$ distance from any channel and that the system was designed so that the entire region is irrigated, proves that the total length of irrigation channels exceeds $70$.