Question

In the figure $AD$ and $BE$ are medians of $△ABC$ and $BE\parallel DF,$ then $CF=$

• A. $\frac{1}{4}AC$
• B. $\frac{1}{3}AC$
• C. $\frac{1}{2}AC$
• D. None

Answer 1

The correct option is A $\frac{1}{4}AC$

Given :

$AD$ and $BE$ are medians

$BE\parallel DF$

$EC=1/2AC$ ($\because$ $E$ is the midpoint of $AC$) $⟶\left(1\right)$

and $D$ is the midpoint of $BC$

Also, $BE\parallel DF$, hence $F$ is the midpoint of $EC$

(this follows from the converse midpoint theorem)

$CF=1/2EC$

$=1/2\left(1/2AC\right)$ (from $\left(1\right)$)

$=1/4AC$

Correct answer : option A.