# Can't See The Forest From The Trees

Geometry Level 5

There is a circular fence of radius $$R=25\text{ m}$$ that encloses an orchard. The trees in the orchard have the distance $$d=5 \text{ m}$$ between them and they are arranged in a square lattice. Th​ere is no tree and there stands a man in the middle point of the plantation. What is the minimum radius for the trees in meters such that the man can't see outside the fence (a straight line between the center and the fence cannot be drawn without intersecting a tree)?

Assume the trees are circular and they have no gap. Trees cannot grow where the fence is.

Hint: think at Minkowski's theorem.

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