IMO Shortlist 1995 problem G7


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2. travnja 2012.
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Let ABCD be a convex quadrilateral and O a point inside it. Let the parallels to the lines BC, AB, DA, CD through the point O meet the sides AB, BC, CD, DA of the quadrilateral ABCD at the points E, F, G, H, respectively. Then, prove that \sqrt {\left|AHOE\right|} + \sqrt {\left|CFOG\right|}\leq\sqrt {\left|ABCD\right|}, where \left|P_1P_2...P_n\right| is an abbreviation for the non-directed area of an arbitrary polygon P_1P_2...P_n.
Izvor: Međunarodna matematička olimpijada, shortlist 1995