Question

Question No 6
MATHEMATICS]
[MCQ]
Question
If the diagonals AC and BD of a trapezium ABCD intersect at o such that DO:OB=1:2 then
a) AB=2CD b) CD=2AB C)AC=2BD d) BD=2AC
Question File
Answer
CAOBOCOD​

Answer 1

Given:

ABCD is a trapezium with AB ║ CD.

DO : OB = 1 : 2

To Find:

Ratio of AB is to CD.

Solution:

It is given that, AB ║ CD

In triangle ABO and triangle CDO

∠ABO = ∠CDO  ∵ ( Vertically opposite angles )

∠DCO = ∠BAO  ∵ ( Alternate interior angles )

=> triangle ABO is similar to triangle CDO   ∵ ( AA Similarity rule )

=> $\frac{DO}{OB} = \frac{CD}{AB}$  ∵ ( CPST )

also, DO : OB = 1 : 2

=> CD : AB = 1 : 2

=> AB = 2 CD

Hence, option (a) is correct answer.