Hard and nice combinatorial geometry
Source: 239MO-2021
April 29, 2021
geometrycombinatorial geometry
Problem Statement
Given lines on the plane, they divide the plane onto several
bounded or bounded polygonal regions. Define the rank of a region as
the number of vertices on its boundary (a vertex is a point which
belongs to at least two lines). Prove that the sum of squares of
ranks of all regions does not exceed .
(D. Fomin)