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Question

Assertion: The measure of AOC=60 

Reason:  Angle subtended by an arc of a circle at the center of the circle is double the angle subtended by the arc on the circumference.

Which of the following is correct?




 



A

Both Assertion and Reason are true and Reason is the correct explanation of Assertion

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B

Both Assertion and Reason are true but Reason is not the correct explanation of Assertion

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C

Assertion is true but Reason is false

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D

Assertion is false but Reason is true

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Solution

The correct option is D

Assertion is false but Reason is true


Join BO.
In ΔAOB, we have
OA = OB [radius]
OBA=OAB [Angle opposite to equal sides of a triangle are equal]
OBA=30(1)
Similarly, in ΔBOC, we get OB = OC
OCB=OBC [Angle opposite to equal sides of a triangle are equal]
OBC=40(2)
ABC=OBA+OBC=30+40=70 [Using (1) and (2)]
Since angle subtended by an arc of a circle at the centre of the circle is double the angle subtended by the arc on the circumference.
AOC=2×ABC=2×70=140
As the Assertion states that AOC=60, it is false.


Mathematics

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