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In figure, if angleOAB=40^(@),"then"angl...

In figure, if `angleOAB=40^(@),"then"angleACB " is equal to "`

A

`50^(@)`

B

`40^(@)`

C

`60^(@)`

D

`70^(@)`

Text Solution

Verified by Experts

The correct Answer is:
A
`"In "DeltaOAB, OA=OB ["both are the radius of a circle"]`
`:.angleOAB=angleOBArArrangleOBA=40^(@)`
[angle opposite to equal sides are equal]
Also, `angleAOB+angleOBA+angleBAO=180^(@)`
[by angle sum property of a triangle]
`:.angleAOB+40^(@)+40^(@)=180^(@)`
`rArr angleAOB=180^(@)-80^(@)=100^(@)`
We know that, in a circle, the angle subtended by an arc at the centre is twice the angle subtended by it at the remaining part of the circle.
`:. angle AOB=2angleACB`
`rArr 100^(@)=2angleACB`
`:. angleACB=100^(@)/2=50^(@)`
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