Question

In the given figure, AD is a median of ABC and E is the midpoint of AD. If BE is joined and produced to meet AC in F then AF = ? (a) 2AC (b) A.AC (c) 3 AC (d) 4 AC

Answer 1

ANSWER:
(b) 1⁄3 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]
∴ AC
AF =1⁄3 AC