问题描述: 已知:平行四边形ABCD中,点E是AB的中点,在直线AD上截取AF=2FD,EF交AC于G,则AGAC 1个回答 分类:数学 2014-10-30 问题解答: 我来补答 (1)点F在线段AD上时,设EF与CD的延长线交于H,∵AB∥CD,∴△EAF∽△HDF,∴HD:AE=DF:AF=1:2,即HD=12AE,∵AB∥CD,∴△CHG∽△AEG,∴AG:CG=AE:CH∵AB=CD=2AE,∴CH=CD+DH=2AE+12AE=52AE,∴AG:CG=2:5,∴AG:(AG+CG)=2:(2+5),即AG:AC=2:7;(2)点F在线段AD的延长线上时,设EF与CD交于H,∵AB∥CD,∴△EAF∽△HDF,∴HD:AE=DF:AF=1:2,即HD=12AE,∵AB∥CD,∴△CHG∽△AEG,∴AG:CG=AE:CH∵AB=CD=2AE,∴CH=CD-DH=2AE-12AE=32AE,∴AG:CG=2:3,∴AG:(AG+CG)=2:(2+3),即AG:AC=2:5.故答案为:25或27. 展开全文阅读