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IMO ShortList 2002, geometry problem 5

Source: IMO ShortList 2002, geometry problem 5

September 28, 2004

geometryratioareaIMO ShortlistTrianglepentagon

Problem Statement

For any set

S

of five points in the plane, no three of which are collinear, let

M(S)

and

m(S)

denote the greatest and smallest areas, respectively, of triangles determined by three points from

S

. What is the minimum possible value of

M(S)/m(S)