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Question

In the following figure, O is centre of the circle,  AOB=60 and  BDC=100, Find  OBC

 

 



Correct Answer
A

 OBC=50

Your Answer
B

 OBC=90

Your Answer
C

 OBC=10

Your Answer
D

 OBC=120


Solution

The correct option is A

 OBC=50


Arc AB subtends  AOB at the centre and  ACB at the remaining part of circle,

   AOB=2  ACB
Or     ACB=12  AOB=12×60=30

Now in Δ DBC

 DBC+ ACB+ BDC=180

    DBC+30+100=180

    DBC=180130=50

Or    OBC=50

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