9

Part of 1990 Romania Team Selection Test

Problems(1)

distance of two points is >= \sqrt{(5+\sqrt5)/2}

Source: Romania IMO TST 1990 p9

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}}

geometrydistancecombinatorial geometry