In triangle ABC, AD is the median through A. E is mid-point of AD. BE produced to AC at F. Prove that AF=1/3 AC

Asked by Farhad Nawaz | 2nd Nov, 2010, 09:56: PM

Expert Answer:

Dear Student,
 
Draw a line DG, parallel to BF, cutting AC at G.
 
 
Now, in triangle ADG:
EF || DG
and
AE = ED
So by mid point theorem, AF = FG.............(1)
Similarly, in triangle FBC:
BF || DG
and
BD = DC
So by mid point theorem, FG = GC...................(2)
From (1) and (2),
AF = FG = GC
=> AF = 1/3 AC
Hence Proved
 
Regards Topperlearning.

Answered by  | 5th Nov, 2010, 01:04: PM

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