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Cono Sur Olympiad 2013, Problem 6

Source:

August 23, 2014
geometry

Problem Statement

Let ABCDABCD be a convex quadrilateral. Let n≥2n \geq 2 be a whole number. Prove that there are nn triangles with the same area that satisfy all of the following properties:
a) Their interiors are disjoint, that is, the triangles do not overlap. b) Each triangle lies either in ABCDABCD or inside of it. c) The sum of the areas of all of these triangles is at least 4n4n+1\frac{4n}{4n+1} the area of ABCDABCD.
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