MathDB

1

Part of 1994 China National Olympiad

Problems(1)

China Mathematical Olympiad 1994 problem1

Source: China Mathematical Olympiad 1994 problem1

9/17/2013
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.
geometrytrapezoidgeometry unsolved