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In the figure above, what is the circumference of the circle with cent

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In the figure above, what is the circumference of the circle with cent [#permalink]

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New post 18 Dec 2017, 20:47
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In the figure above, what is the circumference of the circle with center C?

(A) 2π
(B) 4π
(C) 5π
(D) 8π
(E) 10π

[Reveal] Spoiler:
Attachment:
2017-12-19_0837_003.png
2017-12-19_0837_003.png [ 7.42 KiB | Viewed 640 times ]
[Reveal] Spoiler: OA

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Re: In the figure above, what is the circumference of the circle with cent [#permalink]

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New post 18 Dec 2017, 21:54
Bunuel wrote:
Image
In the figure above, what is the circumference of the circle with center C?

(A) 2π
(B) 4π
(C) 5π
(D) 8π
(E) 10π

[Reveal] Spoiler:
Attachment:
2017-12-19_0837_003.png


The circumference of the circle with center C = 2π r (radius)

But what is r? It is distance between (5, 4) and (5,8)=4

Hence circumference of the circle with center C = 2*4*π = 8π

Hence D
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Re: In the figure above, what is the circumference of the circle with cent [#permalink]

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New post 19 Dec 2017, 06:26
Bunuel wrote:
Image
In the figure above, what is the circumference of the circle with center C?

(A) 2π
(B) 4π
(C) 5π
(D) 8π
(E) 10π

[Reveal] Spoiler:
Attachment:
2017-12-19_0837_003.png


Distance between two points: \(\sqrt{(x2-x1)^2+(y2-y1)^2} = \sqrt{(5-5)^2+(8-4)^2}=√16=4\)

Diameter: \(radius*2=(4)*2=8\)

Circumference: \(diameter*π=(8)π\)

(D) is the answer.
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Re: In the figure above, what is the circumference of the circle with cent [#permalink]

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New post 10 Jan 2018, 05:54
We don't need to find a distance between two points since both points is on x=5 and "moves" along y coordinate. Just finding the difference between y coordinates is enough to find the radius.

8-4=4 so r equals 4,thus circumference is 2{\pi}*r=2*pi*4=8*pi

Answer (D)
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Re: In the figure above, what is the circumference of the circle with cent [#permalink]

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New post 10 Jan 2018, 16:15
Since there is a straight line through the circle because the two coordinates are (5, 8) and (5, 4), calculate the distance between the two y coordinates: 8 - 4 = 4. Hence 4 is the radius.

The equation for circumference of a circle is 2*pi*radius. Thus 2*pi*4 = 8*pi (Option D).
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Re: In the figure above, what is the circumference of the circle with cent [#permalink]

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New post 16 Jan 2018, 16:36
Bunuel wrote:
Image
In the figure above, what is the circumference of the circle with center C?

(A) 2π
(B) 4π
(C) 5π
(D) 8π
(E) 10π

[Reveal] Spoiler:
Attachment:
2017-12-19_0837_003.png


From the diagram, we see that the radius of circle C is 8 - 4 = 4; thus, the circumference is 2π x 4 = 8π.

Answer: D
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Re: In the figure above, what is the circumference of the circle with cent   [#permalink] 16 Jan 2018, 16:36
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