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a tough geometry question

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by chatekar » Sat Aug 04, 2007 9:56 am
Is there a standard method to solve this problem?

What is the greatest possible area of a triangular region with one vertex at the centre of the circle of radius 1 and other two vertices on the circle

1. sqrt(3)/4
2. ½
3. pi/4
4. 1
5. sqrt(2)


Thanks
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by devesh » Sat Aug 04, 2007 10:54 am
is it 1/2.
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by chatekar » Sat Aug 04, 2007 12:33 pm
Thats correct.

Could you please explain how to solve that?

thanks
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Re: a tough geometry question

by jayhawk2001 » Sat Aug 04, 2007 3:01 pm
chatekar wrote:Is there a standard method to solve this problem?

What is the greatest possible area of a triangular region with one vertex at the centre of the circle of radius 1 and other two vertices on the circle

1. sqrt(3)/4
2. ½
3. pi/4
4. 1
5. sqrt(2)


Thanks
The area of a triangle given 2 sides a and b is
1/2 * ab * sin (angle between a and b). The max of this value is when
sin (angle) is 1. Hence 1/2 * 1 * 1 = 1/2

I think for purposes of GMAT, you can just remember that the largest
area of a triangle given 2 sides a & b = 1/2 * a * b
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