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Question

In the given figure, M is the mid-point of the side CD of the parallelogram ABCD. What is ON:OB?

283178_9cfddf30dc2e49c6b3462d20b0d2bf39.png

A
3:2
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B
2:1
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C
3:1
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D
5:2
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Solution

The correct option is B 2:1
In s AOB and COM
AOB=COM (vertically opposite angles)
OAB=OCM (Alternate angles)
Thus, AOBCOM (AA rule)
ABMC=AOOC=OBOM21=AOOC=OBOM (Since, M is the mid point of CD and AB = CD)
Now In s AON and COB
AON=COB (Vertically opposite angles)
ANO=OBC (Alternate angles)
Thus, AONCOB (AA rule)
Hence, AOOC=ONOBONOB=2ON:OB=2:1.

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