Question

In a parallelogram $ABCD,E$ is mid-point of side $AB$ and $CE$ meets the diagonal $BD$ at point $O$.
If area of $\Delta EOB=80c{m}^2$. Calculate $OE:OC$

• A. $2:1$
• B. $1:2$
• C. $1:3$
• D. $3:1$

Answer 1

The correct option is B $1:2$

gives:

ar ($EOB$) = $80c{m}^2$

In $△$EOB and $△$DOC,

$\angle$$EOB$ $=\angle$$DOC$ (vertically opposite angles are equal)

$\angle$$BEO$ $=\angle$$OCD$ (alternate interior angles are equal)

$\angle$$EBO$ $=\angle$$ODC$ (alternate interior angles are equal)

$\therefore$ $△$EBO $\sim$ $△$CDO

$\therefore$ $\frac{OE}{OC}$ $=\frac{BE}{DC}$ $=\frac{1}{2}$ (since,$E$ is mid point of $AB$)

$\therefore$ Ans: B)$1:2$.