Overlapping
Source: Chinese TST
April 9, 2008
algorithminductiongeometry proposedgeometry
Problem Statement
Prove that in a plane, arbitrary points can be overlapped by discs that the sum of all the diameters is less than , and the distances between arbitrary two are greater than . (where the distances between two discs that have no common points are defined as that the distances between its centers subtract the sum of its radii; the distances between two discs that have common points are zero)