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655-705 (Hard)|   Geometry|      
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Bunuel
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Four circles of equal size are inscribed in a square as shown in the d 15 Jun 2020, 09:38
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70% (02:58) correct 30% (02:32) wrong based on 96 sessions

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Four circles of equal size are inscribed in a square as shown in the diagram above. Inside of the four circles is a smaller square tangent to each of the four circles. If the large square has a side length equal to 4, what is the area of the small square?


A. \(12 -8\sqrt{2}\)

B. \(12 -6\sqrt{2}\)

C. \(12 -4\sqrt{2}\)

D. \(12 -2\sqrt{2}\)

E. \(12 -\sqrt{2}\)


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Babineaux
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Four circles of equal size are inscribed in a square as shown in the d 15 Jun 2020, 14:11
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Please refer to the pic uploaded

IMO ans is A

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satya2029
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Four circles of equal size are inscribed in a square as shown in the d 15 Jun 2020, 10:14
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Bunuel

Four circles of equal size are inscribed in a square as shown in the diagram above. Inside of the four circles is a smaller square tangent to each of the four circles. If the large square has a side length equal to 4, what is the area of the small square?


A. \(12 -8\sqrt{2}\)

B. \(12 -6\sqrt{2}\)

C. \(12 -4\sqrt{2}\)

D. \(12 -2\sqrt{2}\)

E. \(12 -\sqrt{2}\)


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Radius of big circle is 1
at 4 corners, take any one
\(1^2+1^2=P^2\)
\(P=\sqrt{2}\)
P is the distance from center of the circle to the corner of bigger square
So diagonal of the bigger square=
=\(P+1+side of the small square+1+P=4\sqrt{2}\)
since \(P=\sqrt{2}\)
Side of the small square=\(2(\sqrt{2-1})\)
Area=\( 12-8\sqrt{2}\)
A:)
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sambitspm
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Four circles of equal size are inscribed in a square as shown in the d 16 Jun 2020, 06:44
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Kindly see the attachment.

Option A
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ajinkyajadhav
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Four circles of equal size are inscribed in a square as shown in the d 07 May 2022, 03:29
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A mere cutting the graph into four pieces would give the side of the red square to be [2x(root)2 -2]
just squaring it gives us option A
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Four circles of equal size are inscribed in a square as shown in the d 13 Dec 2024, 05:16
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