VTMO 2015 — Grade 8 — semifinal Question 5

Question 5

$ABCD$ is a parallelogram, $O$ the intersection of its diagonals, $E$ on $OD$, and $F$ the reflection of $C$ over $E$. Where must $E$ lie for $AFDE$ to be a parallelogram?

Question illustration

$DE = DO$
$DE = \left(\frac{2}{3}\right) DO$
$DE = \frac{OE}{2}$
$DE = \frac{DO}{2}$
$DE = \frac{DO}{3}$