Question

If ABCD is a parallelogram and E, F the centroids of triangles ADD and BCD respectively, then EF equals

• A. AE
• B. BE
• C. CE
• D. DE

Answer 1

The correct option is A AE

We know centroid of the triangles divides the medians in the ratio $2:1$

So we get $\frac{AE}{OE}=\frac{2}{1}$ and $\frac{CF}{OF}=\frac{2}{1}$

$\Rightarrow AE=2OE........\left(i\right)$ and $CF=2OF.........\left(ii\right)$

We know diagonals of parallelogram bisect each other

$\therefore AO=OC$

$AE+EO=OF+FC$

$2OE+OE=OF+OF$

$3OE=3OF$

$OE=OF.......\left(iii\right)$

Similarly $AE=CF........\left(iv\right)$

Using $\left(i\right),\left(ii\right),\left(iii\right)$ and $\left(iv\right)$

$AE=2OE=2OF=CF$

$EF=2OE$

$EF=AE$

So option $A$ is correct