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Soviet Union 7

Source: IMO LongList 1959-1966 Problem 50

September 2, 2004
geometryinequalitiestrigonometrygeometry proposed

Problem Statement

For any quadrilateral with the side lengths a,a, b,b, c,c, dd and the area S,S, prove the inequalityS≤a+c2⋅b+d2.S\leq \frac{a+c}{2}\cdot \frac{b+d}{2}.
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