Problem #PRU-116301

Problems Geometry Plane geometry Geometrical inequalities Area inequalities Methods Pigeonhole principle Pigeonhole principle (finite number of poits, lines etc.) Area
 13–14  4.0

Problem

101 random points are chosen inside a unit square, including on the edges of the square, so that no three points lie on the same straight line. Prove that there exist some triangles with vertices on these points, whose area does not exceed 0.01.