OPM 1997 Problem 5
- Final day 2
A square region of side 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 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 .
Dataset text AI-MO AoPS. Quoted with source.
Official text: Portuguese Mathematical Olympiad 1997 official paper, page 1.
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.