In the given figure, AD is a median of ∆ABC and E is the mid-point of AD.
Question:

In the given figure, AD is a median of ABC and E is the mid-point of AD. If BE is joined and produced to meet AC in F, then AF = ?

(a) $\frac{1}{2} A C$

(b) $\frac{\overline{1}}{3} A C$

(3) $\frac{2}{3} A C$

(4) $\frac{3}{4} A C$

 

Solution:

(b) $1 / 3 A C$

Explanation:

Let G be the mid point of FC. Join DG.
​In BCFD is the mid point of BC and G is the mid point of FC.
∴ DG || BF 
⇒ DG || EF

​In ∆ ADGE is the mid point of AD and EF || DG.
i.e., 
F is the mid point of AG.
Now
AF = FG = GC       [∵ G is the mid point of FC] 

$\therefore A F=1 / 3 A C$

 

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