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 are laid out on the vertices of a square lattice of edge 5 meters. The trees are circular with equal radius, and do not grow where there is a fence. At the very center, instead of a tree, there stands a man.

What is the minimum radius for the trees (in meters) such that the man cannot see the fence?

Hint: think at Minkowski's theorem.

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