every two circles touch each other
Source: Vietnam TST 1992 for the 33nd IMO, problem 4
June 25, 2005
geometry unsolvedgeometry
Problem Statement
In the plane let a finite family of circles be given satisfying the condition: every two circles, either are outside each other, either touch each other from outside and each circle touch at most 6 other circles. Suppose that every circle which does not touch 6 other circles be assigned a real number. Show that there exist at most one assignment to each remaining circle a real number equal to arithmetic mean of 6 numbers assigned to 6 circles which touch it.