IMO 2008 Shortlist G5
Let k and n be integers with 0 ≤ k ≤ n−2. Consider a set L of n lines in the plane such that no two of them are parallel...
Category: Geometry
Problem
Let k and n be integers with 0 ≤ k ≤ n−2. Consider a set L of n lines in the plane such that no two of them are parallel and no three have a common point. Denote by I the set of intersection points of lines in L. Let O be a point in the plane not lying on any line of L. A point X ∈ I is colored red if the open line segment OX intersects at most k lines in L. Prove that I contains at least 1 (k + 1)(k + 2) red points.