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In the given figure, AD is a median of t...

In the given figure, AD is a median of `triangleABC` and E is the midpoint of AD. If BE is joined and produced to meet AC in F then AF = ?

A

`(1)/(2)AC`

B

`(1)/(3)AC`

C

`(2)/(3)AC`

D

`(3)/(4)AC`

Text Solution

Verified by Experts

The correct Answer is:
B

Let G be the midpoint of FC. Join DG.
In `triangle BCF, D` is the midpoint of BC and G is the midpoint of FC.
`therefore "DG||BF" rArr `DG||EF.
In `triangle ADG, E` is the midpoint of AD and EF||DG.
So, F is the midpoint of AG.
`therefore AF= FG=GC " "[because " G is the midpoint of FC"]`.
`therefore AF=(1)/(3)AC.`
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