Counting Regions
Source: 2013 Greek TST,Pr.4
May 24, 2016
combinatoricscountingcircleslines
Problem Statement
Given are different concentric circles on the plane.Inside the disk with the smallest radius (strictly inside it),we consider two distinct points .We consider distinct lines passing through and distinct lines passing through .There is no line passing through both and and all the lines passing through intersect with all the lines passing through .The intersections do not lie on some of the circles.Determine the maximum and the minimum number of regions formed by the lines and the circles and are inside the circles.