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In ∆ABC AD is the median E is the midpoint of AD . If BE produce to meet AC then show that AE=1/³ AC?
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In ∆ABC AD is the median E is the midpoint of AD . If BE produce to me...
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 .
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In ∆ABC AD is the median E is the midpoint of AD . If BE produce to meet AC then show that AE=1/³ AC?
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