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If O is the center of the circle and radius of the circle is 5, what i

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If O is the center of the circle and radius of the circle is 5, what i  [#permalink]

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If O is the center of the circle and radius of the circle is 5, what is the area of \(\triangle{ AOB}\)?


(1) \(\angle{ ACB}=30\)

(2) \(AB=OA\)

New question!!!..


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4.png
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Originally posted by chetan2u on 27 Jul 2018, 22:56.
Last edited by Bunuel on 28 Jul 2018, 01:05, edited 1 time in total.
EDITED.
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Re: If O is the center of the circle and radius of the circle is 5, what i  [#permalink]

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New post 27 Jul 2018, 23:10
chetan2u wrote:
Attachment:
4.png
If O is the center of the circle and radius of the circle is 5, what is the area of \(\triangle{ AOB}\)?
(1) \(\angle{ ACB}=30\)
(2) \(AB=OA\)

New question!!!..

Given radius of circle =OA=OB=5 unit
Question stem:- Area of \(\triangle{ AOB}\)=?

St1:-
The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
Given \(\angle{ ACB}=30\),
We have \(\angle{ AOB}=60\)
Now \(\triangle{ AOB}\) has measure of each of the three angles 60 degree. (Since OA=OB)
Or, \(\triangle{AOB}\) is an equilateral triangle with side 5 unit.
Area can be determined, though exact computation isn't required.
Sufficient.

St2:- \(AB=OA\)
Already we have OA=OB. Therefore, OA=OB=AB.
Or, \(\triangle{ AOB}\) is an equilateral triangle with side 5 unit.
Area can be determined, though exact computation isn't required.
Sufficient.

Ans. (D)
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Re: If O is the center of the circle and radius of the circle is 5, what i &nbs [#permalink] 27 Jul 2018, 23:10
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