A family L 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 l1∈L is bounding the line l2∈L,if all intersection points
of the line l2 with other lines from L lie on the one side of the line l1.
Prove that in the family L there are two lines l and l′ such that the following
2 conditions are satisfied simultaneously:
1) The line l is bounding the line l′;
2) the line l′ is not bounding the line l. inductiongeometry unsolvedgeometry