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# The interior of a circle is inscribed in a rectangle of side

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The interior of a circle is inscribed in a rectangle of side [#permalink]  03 Mar 2008, 13:27
The interior of a circle is inscribed in a rectangle of side 10 and 8 cms. What is the area of the greatest possible circle ?
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Re: inscribed circle [#permalink]  03 Mar 2008, 13:31
What is the concept being tested? is it the maximization of the inscribed square, resulting in the maximization of the circle?
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Re: inscribed circle [#permalink]  03 Mar 2008, 13:48
2*r <= 8 -> r <= 4 -> pi*r^2 <= 16*pi
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Re: inscribed circle [#permalink]  03 Mar 2008, 14:10
why are we choosing 8 as the diameter?
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Re: inscribed circle [#permalink]  03 Mar 2008, 14:29
bmwhype2 wrote:
why are we choosing 8 as the diameter?

2*r <= min(8,10) = 8 //just think about inscribing a circle in a rectangle - drawing a picture might help.
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Re: inscribed circle [#permalink]  03 Mar 2008, 14:34
Expert's post
Hi, maraticus! How is your preparation? Do you have progress in Verbal?

Hi, bmwhype2! Really thank you for your posts in Verbal part, they are vary helpful!
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Re: inscribed circle [#permalink]  03 Mar 2008, 23:07
can someone post the figure? i am still lost
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Re: inscribed circle [#permalink]  03 Mar 2008, 23:21
1
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figure
Attachments

t60830.gif [ 7.6 KiB | Viewed 807 times ]

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Re: inscribed circle [#permalink]  03 Mar 2008, 23:25
i was confused by the wording of the question since it said INTERIOR of a circle. thought it was a square inscribed in a circle.

thanks walker, the answer makes sense now.
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Re: inscribed circle [#permalink]  04 Mar 2008, 06:01
walker wrote:
Hi, maraticus! How is your preparation? Do you have progress in Verbal?

Hi, bmwhype2! Really thank you for your posts in Verbal part, they are vary helpful!

hi walker, I haven't really started studying yet. I just got a GMAT book and I'm hoping to start studying some time next week. I'm a little intimidated by verbal section.
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Re: inscribed circle [#permalink]  04 Mar 2008, 09:11
Expert's post
maratikus wrote:
hi walker, I haven't really started studying yet. I just got a GMAT book and I'm hoping to start studying some time next week. I'm a little intimidated by verbal section.

When I tried OG diagnostic test after 2 month preparation I was shocked with 23% in SC!
Therefore, I decided to put Quant to the back burner
I would like to recommend you to try Verbal as soon as possible and to concentrate on weaknesses. It is more efficient to do so than to perfect your excellent math skills (I unfortunately know that on my own experience )
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Re: inscribed circle [#permalink]  05 Mar 2008, 11:23
i still dont get it. The area of a circle is give by pi*r^2.

in order to get the max area possible for the circle, dont we consider the max radius it can have ? And in this case, we can have a radius of 4 or 5. i chose the radius of 5 and got max area to be 25*pi.
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Re: inscribed circle [#permalink]  05 Mar 2008, 11:32
pmenon wrote:
i still dont get it. The area of a circle is give by pi*r^2.

in order to get the max area possible for the circle, dont we consider the max radius it can have ? And in this case, we can have a radius of 4 or 5. i chose the radius of 5 and got max area to be 25*pi.

the max radisu is not 5. u are confusing a inscribed circle with an inscribed oval.

the circle is inside the rectangle. it touches the rectangle at 2 points. the max radius possible is 4.
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Re: inscribed circle [#permalink]  05 Mar 2008, 11:38
is there a definition of inscribed circle that im missing somewhere ? i thought an inscribe circle inside a polygon meant that the circle is tangential to each side of the polygon
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Re: inscribed circle [#permalink]  05 Mar 2008, 11:46
pmenon wrote:
is there a definition of inscribed circle that im missing somewhere ? i thought an inscribe circle inside a polygon meant that the circle is tangential to each side of the polygon

technically an inscribed figure touches all sides of the larger figure.

i think the question itself is VERY faulty in its wording...
the circle could touch the rect in 2 or 3 points.
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Re: inscribed circle   [#permalink] 05 Mar 2008, 11:46
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# The interior of a circle is inscribed in a rectangle of side

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