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# Rectangle ABCD is inscribed in circle P. What is the area of

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Manager
Joined: 26 Sep 2013
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Rectangle ABCD is inscribed in circle P. What is the area of [#permalink]

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21 Oct 2013, 07:36
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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.
[Reveal] Spoiler: OA

Last edited by Bunuel on 21 Oct 2013, 07:50, edited 1 time in total.
Edited the question.
Manager
Joined: 26 Sep 2013
Posts: 217
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Re: Rectangle ABCD is inscribed in circle P. What is the area of [#permalink]

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21 Oct 2013, 07:42
AccipiterQ wrote:
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.

1. area of rectangle ABCD is 100. If the rectangle is also a square, then you can solve. It doesn't say that though, so the rectangle could have a number of different side lengths. insufficient.

2. rectangle ABCD is a square. No values are given. Insufficient.

1&2 combined. the rectangle is also a square, meaning that all sides are length of 10. you can draw a line from a to c (which would be the cirlce's diameter), and form a right triangle, with two sides of 10, and AC (the hypothaneuse (sp??) being unknown).

10^2+10^2=X^2
200=X^2
X=$$\sqrt{200}$$
X=10*$$\sqrt{2}$$
so the diameter is 10*$$\sqrt{2}$$

since the radius is half the diamter you get 5*$$\sqrt{2}$$

area of a cirlce is pi*r^2, so pi*(5*$$\sqrt{2}$$)^2
=pi*25*2
=50*pi

so 1&2 are sufficient.
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Posts: 43381
Re: Rectangle ABCD is inscribed in circle P. What is the area of [#permalink]

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21 Oct 2013, 08:14
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Expert's post
AccipiterQ wrote:
AccipiterQ wrote:

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.

1. area of rectangle ABCD is 100. If the rectangle is also a square, then you can solve. It doesn't say that though, so the rectangle could have a number of different side lengths. insufficient.

2. rectangle ABCD is a square. No values are given. Insufficient.

1&2 combined. the rectangle is also a square, meaning that all sides are length of 10. you can draw a line from a to c (which would be the cirlce's diameter), and form a right triangle, with two sides of 10, and AC (the hypothaneuse (sp??) being unknown).

10^2+10^2=X^2
200=X^2
X=$$\sqrt{200}$$
X=10*$$\sqrt{2}$$
so the diameter is 10*$$\sqrt{2}$$

since the radius is half the diamter you get 5*$$\sqrt{2}$$

area of a cirlce is pi*r^2, so pi*(5*$$\sqrt{2}$$)^2
=pi*25*2
=50*pi

so 1&2 are sufficient.

When combined: the area of a square is (diagonal)^2/2, so we are given that (diagonal)^2/2=100 --> $$d=10\sqrt{2}$$.
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Re: Rectangle ABCD is inscribed in circle P. What is the area of [#permalink]

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28 Oct 2014, 07:50
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Rectangle ABCD is inscribed in circle P. What is the area of [#permalink]

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15 Sep 2015, 23:36
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.

Ans is C right for this question ....

as 1 is not sufficient
and 2 alone is also not

But 1 and 2 we get ... square with area 100 so lenght is 10 and we get the diagonal ...half of which is radius of the circle .
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Re: Rectangle ABCD is inscribed in circle P. What is the area of [#permalink]

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10 Jan 2017, 00:44
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Rectangle ABCD is inscribed in circle P. What is the area of [#permalink]

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05 Sep 2017, 15:25
AccipiterQ wrote:
Attachment:
inscribedsquare.jpg
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.

Ok so Bunuel gave us another trick we can use to attack square within circle problems and circle within square problems-

If you multiply both the diagonals of a square and then divide the product by 2 then you have the area of the square. For example, the area of a 4 x 4 square is 16. The diagonal of the square would then be 4\sqrt{2} - if we square this and divide it by 2 this also results in 16.

Statement 1

What kind of rectangle is this? We cannot use the formula above unless we know that the shape is precisely a square.

Statement 2

We can establish the formula above but with no side lengths we cannot calculate anything.

Statement 1 and 2

Simply do
(x)^2/2= 100
x^2= 50

C
Re: Rectangle ABCD is inscribed in circle P. What is the area of   [#permalink] 05 Sep 2017, 15:25
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