Question

In the following figure, $AC\parallel BD$ and $CE\parallel DF$. If $OA=12cm,AB=9cm,OC=8cm$ and $EF=4.5cm$, find $OE$.

Answer 1

Given that:

$AC\parallel BD,CE\parallel DF,OA=12cm,AB=9cm,OC=8cm,EF=4.5cm$

To find:

$OE=?$

Solution:

In $△OBD$

$AC\parallel BD$

$\therefore \frac{OA}{OB}=\frac{OC}{OD}⟹\frac{OA}{AB}=\frac{OC}{CD}$

or,$\frac{12cm}{9cm}=\frac{8cm}{CD}$

or, $CD=\frac{8\times 9}{12}cm$

or, $CD=6cm$

In $△ODF$

$CE\parallel DF$

$\therefore \frac{OC}{OD}=\frac{OE}{OF}⟹\frac{OC}{CD}=\frac{OE}{EF}$

or,$\frac{8cm}{6cm}=\frac{OE}{4.5cm}$

or, $OE=\frac{8\times 4.5}{6}cm$

or, $OE=6cm$