Regional Olympiad - FBH 2018 Grade 11 Problem 5
Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2018
September 18, 2018
Planecombinatorial geometrycombinatoricscovering
Problem Statement
It is given points in plane. Prove that it is possible to cover them with circles such that:
sum of lengths of all diameters of all circles is not greater than
distance between any two circles is greater than