The distance between any two of six given points in the plane is at least $1$. Prove that the distance between some two points is at least $\sqrt{\frac{5+\sqrt5}{2}}$
Source: Romania IMO TST 1990 p9
Tags: geometry, distance, combinatorial geometry
The distance between any two of six given points in the plane is at least $1$. Prove that the distance between some two points is at least $\sqrt{\frac{5+\sqrt5}{2}}$