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AG/AC= _ .

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

AG
AC
= ___ .

(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,...