Maybe well known as Sylvester Gallai result
Source:
January 25, 2011
searchcombinatorics unsolvedcombinatorics
Problem Statement
A finite set of points in the plane has the following property: Every line through two points in contains at least one more point belonging to . Prove that all points in lie on a straight line.[hide="Remark."]This may be a well known theorem called "Sylvester Gallai", but I didn't find this problem (I mean, exactly this one) using search function. So please discuss about the problem here, in this topic. Thanks :)