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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