MathDB
8th ibmo - mexico 1993/q5.

Source: Spanish Communities

May 7, 2006
pigeonhole principlegeometrycircumcirclerhombusperpendicular bisectorcombinatorics proposedcombinatorics

Problem Statement

Let PP and QQ be two distinct points in the plane. Let us denote by m(PQ)m(PQ) the segment bisector of PQPQ. Let SS be a finite subset of the plane, with more than one element, that satisfies the following properties: (i) If PP and QQ are in SS, then m(PQ)m(PQ) intersects SS. (ii) If P1Q1,P2Q2,P3Q3P_1Q_1, P_2Q_2, P_3Q_3 are three diferent segments such that its endpoints are points of SS, then, there is non point in SS such that it intersects the three lines m(P1Q1)m(P_1Q_1), m(P2Q2)m(P_2Q_2), and m(P3Q3)m(P_3Q_3). Find the number of points that SS may contain.
Back to ProblemsView on AoPS