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2019 IGO Elementary P3

Source: 6th Iranian Geometry Olympiad (Elementary) P3

September 20, 2019
IGOIrangeometrycombinatorics

Problem Statement

There are n>2n>2 lines on the plane in general position; Meaning any two of them meet, but no three are concurrent. All their intersection points are marked, and then all the lines are removed, but the marked points are remained. It is not known which marked point belongs to which two lines. Is it possible to know which line belongs where, and restore them all?
Proposed by Boris Frenkin - Russia