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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