In triangle ABC, AD is a median and E is a midpoint of median AD

In triangle ABC, AD is a median and E is a midpoint of median AD. A line through B and E meets AC at point F. Prove that AC=3AF

The required figure is shown below
image
For helpwe drawa line DG//BF
Now from triangle ADG. DG// DF and E is the midpoint of AD
Therefoce F is the midpoint of AG.ie AF=GF (1)
From triangle BCF, DG//DF and D is the midpoint of BC
Therefore G is the midpoint of CF,ie GF=CF …(2)
AC=AF+GF+CF
AC=3AF(From (1) and (2))
Hence proved