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Is the circumference of the largest circle above that can contain all

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Bunuel
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Is the circumference of the largest circle above that can contain all [#permalink] New post   01 Aug 2017, 12:44
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Is the circumference of the smallest circle that is not depicted above that can contain all four identical circles in the given figure equal to \(16 + 16\sqrt{2}*\pi\)?

(1) The radius of one of the small circles is 8

(2) The area of all four circles is \(256\pi\)


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sharmili
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Re: Is the circumference of the largest circle above that can contain all [#permalink] New post   03 Aug 2017, 14:28
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The answer is D.

If all the four centres of the four circles are joined , it will form a square, we will have a square of length 16 units, from this the diagonal would be 16 √2 , the diameter of the bigger circle would be 16+16 √2 (adding the addtional radii to formulate the diameter). (Please refer the attached figure). This would give us the circumference of the bigger circle as (16+16 √2) π.

Since both 1 and 2 give the same data, each statement alone is sufficient as we have the radii of each circle and by forming a square we can find the diameter of the larger circle, thereby finding out the circumference of the circle.
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Re: Is the circumference of the largest circle above that can contain all [#permalink] New post   03 Aug 2017, 19:36
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Statements I and II basically give you the same information:

The area of all four circles is 256π: 4π\(r^{2}\)= 256π -> \(r^{2}\) = 64 -> r = 8

The distance X from the center of the imaginary bigger circle to the center of any smaller circle can be calculated using the Pythagorean theorem:
\(16^{2}\) = \(x^{2}\) + \(x^{2}\) -> 2\(x^{2}\) = 256 -> \(x^{2}\) = 128

The circumference of the larger circle therefore is:
2π*(x + r) -> 2π (8\(\sqrt{2}\) + 8) -> 16\(\sqrt{2}\)π + 16

Therefore, the correct answer is D.
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Re: Is the circumference of the largest circle above that can contain all [#permalink] New post   01 Aug 2017, 20:11
\(16 + 16\sqrt{2}*\pi\)?

Well (1) and (2) gives the same information. So answer must be D or E.

Working out, I got the diameter of larger circle as \(16 + 16\sqrt{2}\)

Circumference of the circle will be 2*pi*r or pi*d
= \(16\pi + 16\sqrt{2}*\pi\)

Which is not equal to one given in prompt.

Hence D.

Am I correct?
I will elaborate once I get to know this is correct :P
Bunuel: Your questions with suspense answers kill me :(
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Re: Is the circumference of the largest circle above that can contain all [#permalink] New post   28 Oct 2022, 06:53
The question doesn't specifically state whether the four circles are tangent to each other/where do they touch each other.
Despite this, should the answer be 'D'?

Experts, please guide.
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Re: Is the circumference of the largest circle above that can contain all [#permalink]
28 Oct 2022, 06:53
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Bunuel
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