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 Geometry Plane geometry Polygons Hexagons Methods Pigeonhole principle Pigeonhole principle (angles and lengths) Polygons 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.