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Question No 6MATHEMATICS][MCQ]QuestionIf the diagonals AC and BD of a trapezium ABCD intersect at o such that DO:OB=1:2 thena) AB=2CD b) CD=2AB C)AC=2BD d) BD=2ACQuestion FileAnswerCAOBOCOD​

Answer»

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.


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