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Question

# In the given figure if 'O' is the centre of the circle then ∠ AOB =___

A

260

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B

100

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C

50

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D

None of the above

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Solution

## The correct option is B 100∘ Give ∠ OAC=20∘ and ∠ OBC=30∘ Let us draw aa line joining 'O' and 'C' Now in Δ OAC OA = OC ∴ ∠ OCA=∠ OAC ∴ ∠ OCA=20∘ Similarly in Δ BOC OB = OC ∴ ∠ OCB=∠ OBC ⇒ ∠ OCB=30∘ ∴ ∠ ACB=∠ OCA+∠ OCB =20∘+30∘ =50∘ Now ∠ AOB=2×∠ ACB (because The angle subtends by arc at centre is twice that it subtends at any point on the remaining part of circumference) ∴ ∠ AOB=2×50∘ =100∘

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