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In the figure above, if the square inscribed in the circle h [#permalink]
04 Jun 2016, 07:12
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#GREpracticequestion In the figure above, if the square inscribed in the circle.jpg [ 11.95 KiB  Viewed 8636 times ]
In the figure above, if the square inscribed in the circle has an area of 16, what is the area of the shaded region? A. \(2\pi – 1\) B. \(2\pi – 4\) C. \(4\pi – 2\) D. \(4\pi – 4\) E. \(8\pi – 4\) Practice Questions Question: 9 Page: 102
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Re: In the figure above, if the square inscribed in the circle h [#permalink]
04 Jun 2016, 07:21
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ExplanationAttachment:
#GREpracticequestion In the figure above, if the square inscribed in the circle.jpg [ 16.38 KiB  Viewed 6634 times ]
If the area of the square is 16, that means each side is 4 Now we do have an isosceles triangle with two equal side \(x:x:x\sqrt{2}\) \(4 : 4 : 4 \sqrt{2}\) So the side of the triangle which is also the circumference. Therefore, the radius is half that \(\frac{4 \sqrt{2}}{2} = 2 \sqrt{2}\) and the area of the circle is \(\pi r^2=\pi(2 \sqrt{2} )^2 = 8 \pi\) The area we are looking for is \(\frac{8\pi  16}{4} = 2\pi  4\) B is correct
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Re: In the figure above, if the square inscribed in the circle h [#permalink]
05 Aug 2019, 08:16
Can you explain further detail for the steps after finding 8π? I understand the values but I don't understand why.



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Re: In the figure above, if the square inscribed in the circle h [#permalink]
05 Aug 2019, 08:56
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ehilario wrote: Can you explain further detail for the steps after finding 8π? I understand the values but I don't understand why. 8π is the area of the circle Since the area of the square (that's inside the circle) is 16, then 8π  16 represents the area of ALL 4 tiny circle pieces. Since we just want the area of ONE tiny circle piece, we need to divide 8π  16 by 4 Does that help? Cheers, Brent
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Re: In the figure above, if the square inscribed in the circle h [#permalink]
05 Aug 2019, 09:43
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Yes it does, thank you! GreenlightTestPrep wrote: ehilario wrote: Can you explain further detail for the steps after finding 8π? I understand the values but I don't understand why. 8π is the area of the circle Since the area of the square (that's inside the circle) is 16, then 8π  16 represents the area of ALL 4 tiny circle pieces. Since we just want the area of ONE tiny circle piece, we need to divide 8π  16 by 4 Does that help? Cheers, Brent



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Re: In the figure above, if the square inscribed in the circle h [#permalink]
07 Oct 2020, 00:09
sandy wrote: ExplanationAttachment: #GREpracticequestion In the figure above, if the square inscribed in the circle.jpg If the area of the square is 16, that means each side is 4 Now we do have an isosceles triangle with two equal side \(x:x:x\sqrt{2}\) \(4 : 4 : 4 \sqrt{2}\) So the side of the triangle which is also the circumference. Therefore, the radius is half that \(\frac{4 \sqrt{2}}{2} = 2 \sqrt{2}\) and the area of the circle is \(\pi r^2=\pi(2 \sqrt{2} )^2 = 8 \pi\) The area we are looking for is \(\frac{8\pi  16}{4} = 2\pi  4\) B is correct can you explain why you divide 8π  16 with 4?



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Re: In the figure above, if the square inscribed in the circle h [#permalink]
07 Oct 2020, 05:24
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sleepyowl wrote: sandy wrote: ExplanationAttachment: #GREpracticequestion In the figure above, if the square inscribed in the circle.jpg If the area of the square is 16, that means each side is 4 Now we do have an isosceles triangle with two equal side \(x:x:x\sqrt{2}\) \(4 : 4 : 4 \sqrt{2}\) So the side of the triangle which is also the circumference. Therefore, the radius is half that \(\frac{4 \sqrt{2}}{2} = 2 \sqrt{2}\) and the area of the circle is \(\pi r^2=\pi(2 \sqrt{2} )^2 = 8 \pi\) The area we are looking for is \(\frac{8\pi  16}{4} = 2\pi  4\) B is correct can you explain why you divide 8π  16 with 4? The area of the circle is 8π The area of the inscribed Square is 16 So, 8π  16 = the area of the FOUR partial circles (one of which is shaded) So to find the area of the ONE shaded partial circle, we must divide by 4
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Re: In the figure above, if the square inscribed in the circle h
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