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If O is the center of the circle, what is the area of the shaded regio

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GMATSkilled
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If O is the center of the circle, what is the area of the shaded regio [#permalink] New post   28 May 2018, 18:23
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If O is the center of the circle, what is the area of the shaded region?

A. OB = 5cm

B. \(\angle BCO\) = \(\angle ACO\) = \(30^{\circ}\)
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chetan2u
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Re: If O is the center of the circle, what is the area of the shaded regio [#permalink] New post   28 May 2018, 18:42
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GMATSkilled wrote:
If O is the center of the circle, what is the area of the shaded region?

A. OB = 5cm

B. \(\angle BCO\) = \(\angle ACO\) = \(30^{\circ}\)



Clearly ..
Just the side or just the angle will not give us the answer..

A. OB=5..
So we know the radius but nothing about the shaded portion..
Insufficient

B. \(\angle BCO\) = \(\angle ACO\) = \(30^{\circ}\)
This tells us that BCO and ACO are 30-30-120 triangles
Nothing about sides.

Combined..
Unique triangles can be made as all angles and two sides are known. So the area can be measured.
Sufficient

C
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Re: If O is the center of the circle, what is the area of the shaded regio [#permalink] New post   29 May 2018, 20:45
chetan2u
Hi Chetan,
Could you please clarify my doubt,
since we know ob is radius = 5 . OA and OC will also be equal to 5 as these are radius as well. Now, we know OB, OA and OC , we can find BC and AC. Hence the area of triangle ABC can be found. What am I doing incorrect here ?
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Re: If O is the center of the circle, what is the area of the shaded regio [#permalink] New post   29 May 2018, 22:25
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vishuvashishth wrote:
chetan2u
Hi Chetan,
Could you please clarify my doubt,
since we know ob is radius = 5 . OA and OC will also be equal to 5 as these are radius as well. Now, we know OB, OA and OC , we can find BC and AC. Hence the area of triangle ABC can be found. What am I doing incorrect here ?



Hi you just know two sides of any triangle..
OA and OB in OAB...
But since we don't know any angle or the third side AB, we cannot draw a unique triangle.
Angle between OAand OB can be just 1°, thus area will be almost nil, but on other hand say angle is 90°, the area will be 1/2 *5*5=12.5
So not sufficient
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Re: If O is the center of the circle, what is the area of the shaded regio [#permalink] New post   29 Jun 2019, 04:54
chetan2u wrote:
GMATSkilled wrote:
If O is the center of the circle, what is the area of the shaded region?

A. OB = 5cm

B. \(\angle BCO\) = \(\angle ACO\) = \(30^{\circ}\)



Clearly ..
Just the side or just the angle will not give us the answer..

A. OB=5..
So we know the radius but nothing about the shaded portion..
Insufficient

B. \(\angle BCO\) = \(\angle ACO\) = \(30^{\circ}\)
This tells us that BCO and ACO are 30-30-120 triangles
Nothing about sides.

Combined..
Unique triangles can be made as all angles and two sides are known. So the area can be measured.
Sufficient

C

I know that it is not necessary to do the actual calculation. Nevertheless, I would like to know it for this one. You say that we know two sides. I assume those are BO and CO as this is the radius. But how do I know now the other length as the pythagorean theorem cannot be used. Further, the area of a triangle is 1/2*b*h. Here we don't know both, correct?

Thanks for clarification
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Re: If O is the center of the circle, what is the area of the shaded regio [#permalink] New post   11 Apr 2022, 05:58
Bunuel can you give solution on this question with explanation how can we find the area of shaded region.

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Re: If O is the center of the circle, what is the area of the shaded regio [#permalink]
11 Apr 2022, 05:58
Moderator:
Bunuel
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