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MathNet 2014 Question 75

Math Olympiad Vault · MathNet 2014

Question 75

There are $n$ line segments in the plane such that no two of them intersect with each other and among the $2n$ endpoints of these line segments no three are collinear. Is it always possible to find a simple $2n$-gon such that its vertices are the endpoints of these line segments and also each of these line segments is completely inside or on the perimeter of this $2n$-gon?

Question illustration