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Question

# In the given figure, A, B and C are three points on a circle with centre O such that ∠BOC=30∘ and ∠AOB=60∘. If D is a point on the circle other than the arc ABC, find ∠ADC.

A
(902)
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B
45
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C
(602)
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D
30
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Solution

## The correct options are A (902)∘ B 45∘It can be observed that ∠AOC=∠AOB+∠BOC=60∘+30∘=90 We know that angle subtended by an arc at the center is double the angle subtended by it any point on the remaining part of the circle. So,∠ADC=12∠AOC =12×90∘=45∘ ⇒∠ADC=45∘.

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