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Area of a rectangle inscribed in a circle of radius r

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iwantto
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Area of a rectangle inscribed in a circle of radius r [#permalink] New post   16 Apr 2013, 16:49
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A
B
C
D
E

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80% (00:31) correct 20% (01:12) wrong based on 17 sessions
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Area of a rectangle inscribed in a circle of radius r

A 2r
B 2r^2
C 3r^2
D 4r
E none of these

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Re: Area of a rectangle inscribed in a circle of radius r [#permalink] New post   16 Apr 2013, 20:24
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Interesting question!!!!!!!

For me i will assume this rectangle to be a square then Area diagonal = 2*r
=> side = \(\sqrt{2* r}\)
area = \(2*r^2\)

so my rectangle has a area less than \(2*r^2\)
it can't be A) 2r (diagonal is itself 2r so area must be greater than this)
B) is out
C) is out : greater than B value
D) is out :is side will be some value*r => area should be in terms of \(r^2\)
E) Last option- so correct :done

IMO: E
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Zarrolou
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Re: Area of a rectangle inscribed in a circle of radius r [#permalink] New post   17 Apr 2013, 00:03
If a rectangle is inscribed in a circle its diagonal= 2*radius

To calculate tha area of an iscribed rectangle the diagonal is not sufficient however
Look at the image
IMO E
Attachments

1.jpg
1.jpg [ 26.68 KiB | Viewed 12023 times ]

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Re: Area of a rectangle inscribed in a circle of radius r [#permalink] New post   17 Apr 2013, 09:53
iwantto wrote:
Area of a rectangle inscribed in a circle of radius r

A 2r
B 2r^2
C 3r^2
D 4r
E none of these


The maximum area of a rectangle inscribed in a circle is for a square and that is \(2r^2\). From the given options, 2r and 4r are just lengths, not area. And as \(3r^2\) is more than \(2r^2\), the answer is E.
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Re: Area of a rectangle inscribed in a circle of radius r [#permalink] New post   17 Apr 2013, 13:37
I misread the problem. I assumed that the rectangle inside the circle was a square so I got an area of 2r^2, which is B. Looking at the Zarrolou's drawings, it is clear you cannot find the area with the information given. I agree now that E should be the answer.

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Re: Area of a rectangle inscribed in a circle of radius r [#permalink]
17 Apr 2013, 13:37
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