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In figure, AB is a chord of the circle a...

In figure, AB is a chord of the circle and AOC is its diameter such that `angleACB=50^(@)`. If AT is the tangent to the circle at the point A, then `angleBAT` is equal to

A

`45^(@)`

B

`60^(@)`

C

`50^(@)`

D

`55^(@)`

Text Solution

Verified by Experts

The correct Answer is:
C
In figure, AOC is a diameter of the circle. We know that, diameter subtends `90^(@)` at the circle.
So, `angleABC=90^(@)`
In `DeltaACB, angleA+angleB+angleC=180^(@)`
[since, sum of all angles of a triangle is `180^(@)`
`rArrangleA+90^(@)+50^(@)=180^(@)`
`rArrangleA+140=180`
`rArrangle=180^(@)-140^(@)=40^(@)`
`angleAorangleOAB=40^(@)`
Now, AT is the tengent to the circle at point A. So, OA is perpendicular to AT.
`:.angleOAT=90^(@)` [from figure]
`rArrangleOAB+angleBAT=90^(@)`
On putting `angleOAB=40^(@),` we get
`rArrangleOAB+angleBAT=90^(@)`
Hence, the value of `angleBAT` is `50^(@)`
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In figure, AB is a chord of the circle and AOC is the diameter such that angleACB=50^(@) . If AT is the tangent to the circle at the point A, then angleBAT is equal to : (a) 45^(@) , (b) 60^(@) , (c) 50^(@) , (d) 55^(@)

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Knowledge Check

  • In the figure shown , AB is a diameter of the circle and O is the center of the circle If A = (3,4) , then what is the circumference of the circle?

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