Question : E is the midpoint of the median AD of $\triangle ABC. BE$ is joined and produced to meet AC at F. F divides AC in ratio:
Option 1: 2 : 3
Option 2: 2 : 1
Option 3: 1 : 3
Option 4: 3 : 2
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Correct Answer: 2 : 1
Solution :
AD is the median.
E is the midpoint of AD.
DG || BF
In $\triangle$BCF,
D is the midpoint of BC and DG || BF.
$\therefore$ G is the midpoint of CF.
$\therefore$ FG = GC
In $\triangle$ADG,
EF || DG and E is the midpoint of AD.
$\therefore$ AF = FG
⇒ AF = FG = GC
⇒ AF = $\frac{1}{3}$AC
⇒ FC = $\frac{2}{3}$AC
So, FC : AF = 2 : 1
Hence, the correct answer is 2 : 1.
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