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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
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B
No
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C
Sometime
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D
Data not sufficient
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Solution

The correct option is B No
Let ABCD be the quadrilateral in which AC and BD are the diagonals that intersect at O.
Now,
AOOC=12
We know that diagonals of a parallelogram bisect eah other.
So, for ABCD to be a parallelogram,
AOOC=11
But here
AOOC=12
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.

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