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Is the circumference of the largest circle above that can contain all four circles in the figure above equivalent to \(16 + 16\sqrt{2}*\pi\)?

I'm curious about this question, because it might be an interesting problem, but I can't even begin to guess what it means. It asks about a circle "above", and tells us that circle "can contain all four circles ... above", which would mean the circle the question is talking about can contain itself. That doesn't make any sense.
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Re: Is the circumference of the largest circle above that can contain all [#permalink]

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03 Aug 2017, 11:44

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For a circle to encompass all 4 smaller circles, it has to be either tangent to those 4 or simply contain them. The question stem does not provide any info on this so I guess the answer is E?

Re: Is the circumference of the largest circle above that can contain all [#permalink]

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03 Aug 2017, 12:43

IanStewart wrote:

Bunuel wrote:

Is the circumference of the largest circle above that can contain all four circles in the figure above equivalent to \(16 + 16\sqrt{2}*\pi\)?

I'm curious about this question, because it might be an interesting problem, but I can't even begin to guess what it means. It asks about a circle "above", and tells us that circle "can contain all four circles ... above", which would mean the circle the question is talking about can contain itself. That doesn't make any sense.

Same reaction here. Question is not clear. I dont see the "largest" circle"

Re: Is the circumference of the largest circle above that can contain all [#permalink]

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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.

Re: Is the circumference of the largest circle above that can contain all [#permalink]

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03 Aug 2017, 14:39

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The answer should be B.

It doesn't say anywhere that all 4 circles have the same radius, so in statement I, we could have 1 circle at the provided radius and the other 3 at another. Statement II provides you with the area which you can calculate the required circumference.

Re: Is the circumference of the largest circle above that can contain all [#permalink]

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03 Aug 2017, 14:55

nrxbra001 wrote:

The answer should be B.

It doesn't say anywhere that all 4 circles have the same radius, so in statement I, we could have 1 circle at the provided radius and the other 3 at another. Statement II provides you with the area which you can calculate the required circumference.

How would you calculate the circumference of the bigger circle with the sum of areas of smaller circles? The radii of each circle might differ,in that case you would not be able to find the radii of the bigger circle.

If the circles are not of the same size, then the answer would be E.

Re: Is the circumference of the largest circle above that can contain all [#permalink]

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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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Is the circumference of the largest circle above that can contain all four circles in the figure above

I suspect sharmili has correctly guessed the intentions of the question designer, and if so, the question should be asking about the smallest circle that is not depicted above (the 'largest circle' that could contain all the other circles is infinitely big, so asking for the largest circle doesn't make sense), and there seems to be a π missing in the number at the end of the question. We do need information about whether the small circles are identical to solve anything here.
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