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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
In the figure above, a square is inscribed in a circle. If the area of
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07 Jan 2023, 09:42
07 Jan 2023, 09:42
Expert Reply
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Question Stats:
50% (03:04) correct
50% (03:29) wrong based on 4 sessions
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In the figure above, a square is inscribed in a circle. If the area of the shaded region is 4π - 8, what is the value of the radius?
(A) 1
(B) 2
(C) 2π
(D) 2√2
(E) 4
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Attachment:
circle_inscribed_square.png [ 1.09 KiB | Viewed 1021 times ]
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Re: In the figure above, a square is inscribed in a circle. If the area of
[#permalink]
08 Jan 2023, 10:37
08 Jan 2023, 10:37
Expert Reply
Let d be the length of a diameter of the circle, which is also the diagonal of the square.
The area of the circle is \(\pi*(\frac{diameter}{2})^2=\pi*\frac{d^2}{4}\).
The area of the square is \(\frac{diagonal^2}{2}=\frac{d^2}{2}\).
The area of the shaded region is \(\pi*\frac{d^2}{4}-\frac{d^2}{2}=4\pi-8\);
\(d^2(\frac{\pi - 2}{4})=4(\pi-2)\);
\(d^2=16\);
\(d = 4\);
\(radius=\frac{d}{2}=2\).
Answer: B
The area of the circle is \(\pi*(\frac{diameter}{2})^2=\pi*\frac{d^2}{4}\).
The area of the square is \(\frac{diagonal^2}{2}=\frac{d^2}{2}\).
The area of the shaded region is \(\pi*\frac{d^2}{4}-\frac{d^2}{2}=4\pi-8\);
\(d^2(\frac{\pi - 2}{4})=4(\pi-2)\);
\(d^2=16\);
\(d = 4\);
\(radius=\frac{d}{2}=2\).
Answer: B
gmatclubot
Re: In the figure above, a square is inscribed in a circle. If the area of [#permalink]
08 Jan 2023, 10:37
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