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Question

# In the given diagram O is the center of the circle and CD is a tangent. ∠CAB and ∠ACD are supplementary to each other ∠OAC = 30∘. Find the value of ∠OCB:

A

30

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B

20

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C

60

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D

50

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Solution

## The correct option is A 30∘ Since, OA = OC (Radii) ∠OAC = ∠OCA = 30∘ Therefore ∠AOC = 180∘ - ∠OAC - ∠OCA = 180∘ – 30∘ – 30∘ = 120∘ ∠ ABC = 12 ∠AOC [The angle at the centre is twice the angle at the circumference.] = 12×120∘ = 60∘ ∠CAB and ∠ACD are supplementary ⇒ AB is parallel to CD ∠ABC = ∠BCD (Alternate interior angle) ∠BCD=60∘ From the figure, ∠ACB=∠ACO+∠OCB⇒60°=30°+∠OCB⇒∠OCB=60°−30°=30°

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