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Inscribed Square - Geometry Question Bank

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debmalya.dutta
 Post subject: Inscribed Square - Geometry Question Bank
 Post Posted: Tue Jul 27, 2010 3:03 pm 
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Students


Posts: 47
This question is from the from Manhattan GMAT Geometry question bank

I am confused here . The correct answer per the answer key is C.

Ron/Stacey / Manhattan Gmat Tutors,
Question :
can you please provide a clarification
Rectangle ABCD is inscribed in circle P. What is the area of circle P?
(1) The area of rectangle ABCD is 100.
(2) Rectangle ABCD is a square.

Statement 1
suppose the sides of rectangle are x & y
so ...xy = 100

now in triangle adc ,
ad = x = 2r sin 45 where r is the radius of the circle
cd = y= 2r cos 45 where r is the radius of the circle

xy = 4 r^2 sine 45 cos 45

since we know xy = 100 and sin 45=cos 45 = 1/ root of 2
we can determine the value of r

and hence find the area of the circle.

Please let me know where I went wrong on this one.. Must be missing some fine point
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loving.achin
 Post subject: Re: Inscribed Square - Geometry Question Bank
 Post Posted: Wed Jul 28, 2010 12:07 pm 
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Students


Posts: 7
Hello debmaiya.dutta,
The logic you applied is perfectly valid (__only__ if you take that rectangle to be a square. i.e. the angle you took 45 degree in 2rsin45 and 2rcos45 is only valid if that rectangle is a square).

To illustrate the above, draw two rectangles with the same area 100. For eg: draw a rectangle with sides (50 and 2) and (20 and 5) and see if you can prove 45 degree concept. Surely you won't.

Hence you need statement (2) as well and hence the solution should be 'C'

Thanks
Achin
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debmalya.dutta
 Post subject: Re: Inscribed Square - Geometry Question Bank
 Post Posted: Wed Jul 28, 2010 9:48 pm 
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Posts: 4
Right.. thanks .. forgot that aspect... thanks again
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mschwrtz
 Post subject: Re: Inscribed Square - Geometry Question Bank
 Post Posted: Sun Aug 22, 2010 12:09 pm 
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ManhattanGMAT Staff


Posts: 506
ty loving.achin

another excellent post
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mschwrtz
 Post subject: Re: Inscribed Square - Geometry Question Bank
 Post Posted: Sun Aug 22, 2010 12:12 pm 
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ManhattanGMAT Staff


Posts: 506
Oh, by the way, you'll never need trig on the GMAT. You have to work pretty hard to find a question where it's even helpful.

And, of course, if the rectangle were a square, you could solve this more easily without trig.
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