IMO 1976 LL GDR22

A regular pentagon A1A2A3A4A5 with side length s is given.

imolonglistmathematicsolympiad

IMO 1976 LL GDR22

Origin: GDR

Problem

A regular pentagon A1A2A3A4A5 with side length s is given. At each point Ai a sphere Ki of radius s/2 is constructed. There are two spheres K1′ and K2′ eah of radius s/2 touching all the five spheres Ki. Decide whether K1′ and K2′ intersect each other, touch each other, or have no common points.