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) $\frac{1}{2}AC$
(b) $\frac{1}{3}AC$
(3) $\frac{2}{3}AC$
(4) $\frac{3}{4}AC$

Answer 1

(b) ⅓ AC

Explanation:

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

​In ∆ ADG, E 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]
∴ AF =⅓ AC​
4AC