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Question

In the given figure, AOB and COD are two diameters of a circle with centre O. If OAC = 60o then ABD is
243031_4103e9d73b7747f0bdf44180d481a065.png

A
40o
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B
80o
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C
50o
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D
60o
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Solution

The correct option is B 60o


Angle subtended by chord BC at the centre will be double than that of angle
subtended by it at circumference.
therefore BOC=2CAB=2(60)=120
and CAB=CDB=60 {chord substend equal angle on circumference.}
COD=180.
Hence, COB+BOD=180
Hence, BOD=180120=60
In triangle BOD, BOD+ODB+DBO=180 (Angle sum property of a triangle)
Thus, 60+60+ODB=180
Thus, ODB=60. Thus, ADB=60
So, option D is the answer.

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