E is the mid-point of the median AD of ∆ABC. BE is

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E is the mid-point of the median AD of ∆ABC. BE is joined and produced to meet AC at F. F divides AC in the ratio :

1. 2 : 3
2. 2 : 1
3. 1 : 3
4. 3 : 2

Correct Option: B

We draw a figure whose E is the mid-point of the median AD of ∆ABC ,

AD is the median.
E is the mid–point of AD.
DG || BF
In ∆BCF,
D is the mid–point of BC and DG || BF.
∴ G is the mid–point of CF.
∴ FG = GC
In ∆ADG,
EF || DG
E is the mid–point of AD.
∴ AF = FG
∴ AF = FG = GC

AF =	1	AC
	3

FC =	2	AC
	3

∴ FC : AF = 2 : 1