MathDB
Combinatorics of family of lines in the plane

Source: Romania TST 4 (All Geometry) 2010, Problem 3

August 25, 2012
geometry proposedgeometry

Problem Statement

Let L\mathcal{L} be a finite collection of lines in the plane in general position (no two lines in L\mathcal{L} are parallel and no three are concurrent). Consider the open circular discs inscribed in the triangles enclosed by each triple of lines in L\mathcal{L}. Determine the number of such discs intersected by no line in L\mathcal{L}, in terms of ∣L∣|\mathcal{L}|.
B. Aronov et al.
Back to ProblemsView on AoPS