Problem #PRU-34875

Problems Geometry Plane geometry Geometrical inequalities Inequalities in a triangle A segment inside the triangle is smaller than the largest side ,Problems Polygons Hexagons Methods Pigeonhole principle Pigeonhole principle (angles and lengths) Regular polygons
 12–14  2.0

Problem

There are 7 points placed inside a regular hexagon of side length 1 unit. Prove that among the points there are two which are less than 1 unit apart.