Given 300 points in R2R2, prove that there exists a point pp such that each closed halfplane determined by each line through pp contains at least 100 of the given points. [Hint: Let DD be a large closed disk containing all the points. For each closed halfplane HH containing at least 200 points, consider HDHD. This gives an infinite collection of closed and bounded convex sets. Show that each three of them intersect. Also note that if a line through a point pp has fewer than 100 points on one side, then a slight perturbation of can be made to yield a halfplane not containing pp and containing at least 200 points of the given set.]