for any 3 of 6 lines, exists a 4th such that they are tangent to a circle
Source: 2005 Oral Moscow Geometry Olympiad grades 10-11 p6
October 21, 2020
combinatorial geometrygeometryTangents
Problem Statement
Six straight lines are drawn on the plane. It is known that for any three of them there is a fourth of the same set of lines, such that all four will touch some circle. Do all six lines necessarily touch the same circle? (I. Bogdanov)