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Area of the triangle - TT 2009 Senior-A5

Source:

September 3, 2010
geometry

Problem Statement

Let XYZXY Z be a triangle. The convex hexagon ABCDEFABCDEF is such that AB;CDAB; CD and EFEF are parallel and equal to XY;YZXY; Y Z and ZXZX, respectively. Prove that area of triangle with vertices at the midpoints of BC;DEBC; DE and FAFA is no less than area of triangle XYZ.XY Z.
(8 points)
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