IMO 2007 Shortlist G6
Determine the smallest positive real number k with the following property. Let ABCD be a convex quadrilateral, and let p...
Category: Geometry
Problem
Determine the smallest positive real number k with the following property. Let ABCD be a convex quadrilateral, and let points A1, B1, C1 and D1 lie on sides AB, BC, CD and DA, respectively. Consider the areas of triangles AA1D1, BB1A1, CC1B1, and DD1C1; let S be the sum of the two smallest ones, and let S1 be the area of quadrilateral A1B1C1D1. Then we always have kS1 ≥ S. (U.S.A.)