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Diagonals are concurrent triplewise

Source: 2021 MEMO T-4

September 5, 2021
regular polygoncombinatoricsmemoMEMO 2021

Problem Statement

Let nn be a positive integer. Prove that in a regular 6n6n-gon, we can draw 3n3n diagonals with pairwise distinct ends and partition the drawn diagonals into nn triplets so that:
[*] the diagonals in each triplet intersect in one interior point of the polygon and [*] all these nn intersection points are distinct.
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