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# Area of a rectangle inscribed in a circle of radius r

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Intern
Joined: 29 Mar 2013
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Area of a rectangle inscribed in a circle of radius r [#permalink]

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16 Apr 2013, 16:49
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80% (01:31) correct 20% (01:12) wrong based on 8 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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1.jpg [ 8.46 KiB | Viewed 5494 times ]

Manager
Joined: 27 Jul 2011
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Re: Area of a rectangle inscribed in a circle of radius r [#permalink]

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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

IMO: E
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Re: Area of a rectangle inscribed in a circle of radius r [#permalink]

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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
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Re: Area of a rectangle inscribed in a circle of radius r [#permalink]

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17 Apr 2013, 09:53
Expert's post
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]

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