In triangle ABC AD is the median through A and E is the midpoint of AD.BE is produced to meet AC in F.Prove that AF=1/3AC.

pls its urgent tmrw is my test.....................

Given: AD is the median of triangle. ABC. E is the mid point of AD.
  BE produced meets AD at F
To prove : AF = 1/3 AC

Construction = Through D, draw DG parallel to BF
Proof : In triangle ADG
  E is the midpoint of AD and EF parallel DG
  According to Reverse of Midpoint theorem
  F becomes midpoint of AG and AF = FG-- ( i )
  In triangle BCF
  D is the midpoint of BC and DG parallel to BF   
  According to Reverse of Midpoint theorem
  G becomes midpoint of CF and FG = GC -- ( ii )
  From equation ( i ) & ( ii ),
  AF = FG= GC = AC
  Now, AF + FG + GC = AC
  AF + AF+ AF = AC ( since AF = FG= GC )
  3 AF = AC
  AF = 1/3 AC