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

B

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

C

Assertion is true but Reason is false

D

Assertion is false but Reason is true

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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