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In the given figure, If O is the centre ...

In the given figure, If O is the centre of the circle BC be any diameter of it then the value of x is

A

60

B

50

C

100

D

80

Text Solution

Verified by Experts

The correct Answer is:
B
In the given firgure `angle OAQ=50^(@),angleADC=x^(@)`
Now, `OA=OB( :.` radii of same circle)
`:. angle OAB= angleOBA=50^(@)[ :. angleOPAB=50^(@)]`
`:. angleAOC` = internally opposite `(angle OAB+anglePBA)=50^(@)+50^(@)=100^(@)`
Again, the angle in circle produced by the ciruclar are `overset (frown)(AC)= angleADC=x^(@)`
and central angle `=angleAOC=100^(@)`
`:. angleADC=(1)/(2)angleAOC` [ by theorem -34]
`or, angleADC=(1)/(2)xx100^(@), [ :. angleAOC=100^(@)]`
`or x^(@), =50^(@), :. x=50`
`:. (b)` is correct
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