All common tangents of all circle pairs
Source: Problem 7 of Russian Regional Olympiad 2011, grade 11
September 1, 2011
combinatorics proposedcombinatorics
Problem Statement
Basil drew several circles on the plane and drew all common tangent lines for all pairs of circles. It turned out that the lines contain all sides of a regular polygon with 2011 vertices. What is the smallest possible number of circles?
(Author: N. Agahanov)