Question

The point of intersection of the diagonals of a quadrilateral divides one diagonal in the ratio $1:2.$ Can it be a parallelogram?

• A. Yes
• B. No
• C. Sometime
• D. Data not sufficient

Answer 1

The correct option is B No

Let $ABCD$ be the quadrilateral in which $AC$ and $BD$ are the diagonals that intersect at $O$.

Now,

$\frac{AO}{OC}=\frac{1}{2}$

We know that diagonals of a parallelogram bisect eah other.

So, for $ABCD$ to be a parallelogram,

$\frac{AO}{OC}=\frac{1}{1}$

But here

$\frac{AO}{OC}=\frac{1}{2}$

So, the quadrilateral can't be a parallelogram in which the point of intersection of the diagonals divide one diagonal in the ratio of $1:2$.