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# If the shape inside the circle centered at O is a square, what is the

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Math Expert
Joined: 02 Sep 2009
Posts: 52288
If the shape inside the circle centered at O is a square, what is the  [#permalink]

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17 Sep 2018, 21:05
00:00

Difficulty:

55% (hard)

Question Stats:

50% (01:28) correct 50% (01:20) wrong based on 22 sessions

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If the shape inside the circle centered at O is a square, what is the area of the shaded region?

(1) The radius of the circle is 2.
(2) The portion of the circumference that touches the shaded region has length π.

Attachment:

image015.jpg [ 22.19 KiB | Viewed 253 times ]

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examPAL Representative
Joined: 07 Dec 2017
Posts: 868
Re: If the shape inside the circle centered at O is a square, what is the  [#permalink]

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18 Sep 2018, 11:01
Bunuel wrote:

If the shape inside the circle centered at O is a square, what is the area of the shaded region?

(1) The radius of the circle is 2.
(2) The portion of the circumference that touches the shaded region has length π.

Attachment:
image015.jpg

Since the corner of a square has a 90 degree angle, the sector including the square is a quarter circle. So the area of the sector is (pi*r^2)/4. Additionally, since the diagonal of the square equals the radius, its area is r^2/2. So, if we know the radius of the circle, we can calculate our area.
We'll look for statements that give us this information, a Logical approach.
(1) this is exactly what we need!
Sufficient.
(2) then a fourth of the circumference equals pi and we 2pi*r = 4pi meaning we can calculate the radius.
Sufficient.

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Re: If the shape inside the circle centered at O is a square, what is the &nbs [#permalink] 18 Sep 2018, 11:01
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