Problem
COM-B1-M05-P017 Five Points in a Triangle
#17
★★★☆☆ Level 3 of 5
In an equilateral triangle of side \(2\), \(5\) points are chosen. Prove that two are at distance at most \(1\).
Divide the triangle into \(4\) equilateral triangles of side \(1\).
Join the midpoints of the sides to obtain \(4\) small equilateral triangles of side \(1\). Five points force two into one small triangle. The distance between any two points in such a triangle is at most \(1\).
Geometric box with small diameter.