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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