Problem

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Tags: inequalities, analytic geometry, email, combinatorics proposed, combinatorics



Let $K$ be the set of all sides and diagonals of a convex $2010-gon$ in the plane. For a subset $A$ of $K,$ if every pair of line segments belonging to $A$ intersect, then we call $A$ as an intersecting set. Find the maximum possible number of elements of union of two intersecting sets.