P11

Part of 2017 Sharygin Geometry Olympiad

Problems(1)

Set with circumcenters of each triangle in set

Source: Sharygin Geometry Olympiad Correspondence Round 2017 P-11 (Grade-8-11)

A finite number of points is marked on the plane. Each three of them are not collinear. A circle is circumscribed around each triangle with marked vertices. Is it possible that all centers of these circles are also marked? Proposed by A.Tolesnikov

geometrycircumcircle