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China Mathematical Olympiad 1994 problem1

Source: China Mathematical Olympiad 1994 problem1

September 17, 2013
geometrytrapezoidgeometry unsolved

Problem Statement

Let ABCDABCD be a trapezoid with AB∥CDAB\parallel CD. Points E,FE,F lie on segments AB,CDAB,CD respectively. Segments CE,BFCE,BF meet at HH, and segments ED,AFED,AF meet at GG. Show that SEHFG≤14SABCDS_{EHFG}\le \dfrac{1}{4}S_{ABCD}. Determine, with proof, if the conclusion still holds when ABCDABCD is just any convex quadrilateral.
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