Consider $n>9$ lines on the plane such that no two lines are parallel. Show that there exist at least $n/9$ lines such that the angle between any two of the lines is at most $20^\circ$.
Source: KAMO 2022 Grade 9 P4
Tags: combinatorics, geometry
Consider $n>9$ lines on the plane such that no two lines are parallel. Show that there exist at least $n/9$ lines such that the angle between any two of the lines is at most $20^\circ$.