Inside the circle $w$ of radius $1$ there are $n$ line segments with total length $2\sqrt{n}$. Prove that there exists a circle such that its center coincides with a center of $w$ and it intersects at least two of line segments.
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Tags: combinatorics, geometry
Inside the circle $w$ of radius $1$ there are $n$ line segments with total length $2\sqrt{n}$. Prove that there exists a circle such that its center coincides with a center of $w$ and it intersects at least two of line segments.