IMO 2019 Shortlist G8
Let L be the set of all lines in the plane and let f be a function that assigns to each line ℓ P L a point fpℓq on ℓ. Su...
Category: Geometry
Problem
Let L be the set of all lines in the plane and let f be a function that assigns to each line ℓ P L a point fpℓq on ℓ. Suppose that for any point X, and for any three lines ℓ1, ℓ2, ℓ3 passing through X, the points fpℓ1q, fpℓ2q, fpℓ3q and X lie on a circle. Prove that there is a unique point P such that fpℓq “ P for any line ℓ passing through P. (Australia) Shortlisted problems 9