MathDB
Jbmo 2011 Problem 4

Source: Jbmo 2011

June 21, 2011
geometryrectangleinequalitiestrigonometryvectortriangle inequalitygeometry unsolved

Problem Statement

Let ABCDABCD be a convex quadrilateral and points EE and FF on sides AB,CDAB,CD such that ABAE=CDDF=n\tfrac{AB}{AE}=\tfrac{CD}{DF}=n
If SS is the area of AEFDAEFD show that S≤AB⋅CD+n(n−1)AD2+n2DA⋅BC2n2{S\leq\frac{AB\cdot CD+n(n-1)AD^2+n^2DA\cdot BC}{2n^2}}
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