10.7

Part of 2022 Sharygin Geometry Olympiad

Problems(1)

4 marked points inside each circle and 4 marked points outside each circle

Source: Sharygin Finals 2022 10.7

Several circles are drawn on the plane and all points of their meeting or touching are marked. May be that each circle contains exactly four marked points and exactly four marked points lie on each circle?

geometrycombinatoricscombinatorial geometry