Question

In Δ ABC,AD is the median through A & E is the mid point of AD.BE is produced to meet AC in F.Prove that AF=1/3AC.

Answer 1

Given:AD is the median of triangle ABC.E is the mid point of AD.BE produced meet ad at F.
to prove:AF=1/3AC.
Construction:From point D draw DG parallel to BF.
Proof: so by Convere of mid point theorum we get F as the mid point of AG
⇒AF=AG(1)
similarly we have G as the mid point of CF
⇒FG=GC(2)
from 1 and 2 we get 
AF=FG=GC  (3)
now AF + FG + GC =AC
From (3) we get 
AF+AF+AF=AC
3(AF)=AC
AF=1/3AC
hence prove .
Hope this helps

Answer 2

Given:
AD is the median of triangle ABC.
E is the mid point of AD.BE produced meet ad at F.
RTP ::AF=1/3AC.
Construction:From point D draw DG parallel to BF.
solution : 
By mid point theorem we got  F as the mid point of AG
-> AF=AG --------1
 G as the mid point of CF
-> FG=GC--------------2
by one and two
AF = FG= GC  ---------- 3

now ,   AF + FG + GC =AC
by the 3 rd equation
AF+AF+AF=AC
3×AF =AC
 so  1/3 ac = af

hope this helped u dear ...!!!!!