A family l of 2006 lines
Source: 5 th Silk Road Mathematical Competition(SRMC 2006)
April 18, 2006
inductiongeometry unsolvedgeometry
Problem Statement
A family of 2006 lines on the plane is given in such a way that it doesn't contain
parallel lines and it doesn't contain three lines with a common point.We say that
the line is bounding the line ,if all intersection points
of the line with other lines from lie on the one side of the line .
Prove that in the family there are two lines and such that the following
2 conditions are satisfied simultaneously:
1) The line is bounding the line ;
2) the line is not bounding the line .