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15 Jun 2020, 09:38
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
70% (02:58) correct
30%
(02:32)
wrong
based on 96
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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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15 Jun 2020, 14:11
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Please refer to the pic uploaded
IMO ans is A
Posted from my mobile device
IMO ans is A
Posted from my mobile device
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General Discussion
15 Jun 2020, 10:14
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Bunuel
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:)
