Middle European Mathematical Olympiad 2021 Problem T-4

Let $n$ be a positive integer. Prove that in a regular $6n$-gon, we can draw $3n$ diagonals with pairwise distinct ends and partition the drawn diagonals into $n$ triplets so that:

• the diagonals in each triplet intersect in one interior point of the polygon and
• all these $n$ intersection points are distinct.