Question

In an triangle ABC, AD is a median and E is the mid point of AD. If BE is produced to meet AC at F. Show that AE=⅓AC.

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 proved.......

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