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# If the circle passes through the origin and has a perimeter of kπ, wha

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Math Expert
Joined: 02 Sep 2009
Posts: 50627
If the circle passes through the origin and has a perimeter of kπ, wha  [#permalink]

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30 Aug 2018, 03:54
00:00

Difficulty:

25% (medium)

Question Stats:

82% (00:51) correct 18% (00:42) wrong based on 17 sessions

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If the circle passes through the origin and has a perimeter of kπ, what is the value of k?

(1) The center has coordinates (4,4).
(2) Area of the circle is 32π.

Attachment:

image020.gif [ 1.63 KiB | Viewed 264 times ]

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Re: If the circle passes through the origin and has a perimeter of kπ, wha  [#permalink]

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30 Aug 2018, 05:21
Bunuel wrote:

If the circle passes through the origin and has a perimeter of kπ, what is the value of k?

(1) The center has coordinates (4,4).
(2) Area of the circle is 32π.

Attachment:
image020.gif

Question : If the circle passes through the origin and has a perimeter of kπ, what is the value of k?

Perimeter of circle = πD = kπ
i.e. Diameter of circle = k = ?

Statement 1:The center has coordinates (4,4).

Now we know that circle has circumference passing through origin hence distance between origin and centre is teh radius

hence radius = 4√2 i.e. Diameter = k = 8√2

SUFFICIENT

Statement 2: Area of the circle is 32π.

i.e. πr^2 = 32π

SUFFICIENT

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Re: If the circle passes through the origin and has a perimeter of kπ, wha  [#permalink]

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30 Aug 2018, 07:43
Bunuel wrote:

If the circle passes through the origin and has a perimeter of kπ, what is the value of k?

(1) The center has coordinates (4,4).
(2) Area of the circle is 32π.

Perimeter of circle, 2πr=kπ or, r=$$\frac{k}{2}$$

Question stem:- k=?

St1:- The center has coordinates (4,4).
Radius , k/2 is the distance between center of circle (4,4) and origin(0,0)
So, k can be determined.
Sufficient

St2:- Area of the circle is 32π.
Radius of circle can be determined.
So, k can be determined.
Sufficient

Ans. (D)
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Re: If the circle passes through the origin and has a perimeter of kπ, wha &nbs [#permalink] 30 Aug 2018, 07:43
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