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

Question

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}

chetan2u · Answer

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

vishuvashishth · Answer

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 ?

chetan2u · Answer

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

Luca1111111111111 · Answer

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

Ghostrider3147 · Answer

Bunuel  can you give solution on this question with explanation how can we find the area of shaded region.

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

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