Question

ad is a median of triangle ABC and E is midpoint of AD, BE is produced meet AC in F prove that AF is equals to one third AC

Answer 1

Through D draw a line parallel to BF to meet AC at G.
In triangle ADG, Eis the mid point of side AD and DG parallel to BF i.e. DG parallel to EF , therefore , by converse of mid point theorem , G is mid- point of AG i.e. AF=FG-------ep1
In triangle BCF , D is mud- point of side BC andDG parallel to BF , therefore, by converse of mid point theorem , G is the mid point of CF i.e. FG = GC ------- ep2
From ep 1 and ep 2 , we get
AF = FG= GC --------- ep3
Now AC =AF+FG+GC=AF + AF + AF (using ep 3 )
AC = 3 AF
AF = 1/3AC

Answer 2

here is your answer

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