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# Point O is the center of the circle. If the area of the circle is 36π

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Math Expert
Joined: 02 Sep 2009
Posts: 58427
Point O is the center of the circle. If the area of the circle is 36π  [#permalink]

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21 Dec 2018, 02:39
00:00

Difficulty:

25% (medium)

Question Stats:

83% (00:54) correct 17% (00:52) wrong based on 31 sessions

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Point O is the center of the circle. If the area of the circle is 36π and the area of the rectangle is 72, what is the length of DC?

A. 4
B. 6
C. 8
D. 10
E. 12

Attachment:

Capture (7).JPG [ 28.15 KiB | Viewed 373 times ]

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Re: Point O is the center of the circle. If the area of the circle is 36π  [#permalink]

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21 Dec 2018, 03:21
area of circle = 36 pi

OD and OA = 6

rectanle we can say 6*x= 72
x= 12

so since OD= 6 ; DC = 12-6 = 6 IMO B

Bunuel wrote:

Point O is the center of the circle. If the area of the circle is 36π and the area of the rectangle is 72, what is the length of DC?

A. 4
B. 6
C. 8
D. 10
E. 12

Attachment:
Capture (7).JPG
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3074
Point O is the center of the circle. If the area of the circle is 36π  [#permalink]

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21 Dec 2018, 05:49

Solution

Given:
• O is the center of the circle
• Area of the circle = 36ᴨ
• Area of the rectangle = 72

To find:
• The length of DC

Approach and Working:
Area of the circle = $$ᴨr^2 = 36 ᴨ$$
• Thus, r = 6

Breadth of the rectangle = OA, which is the radius of the circle = 6
• We know, l * b = 72
• Thus, $$l = \frac{72}{6} = 12 = OC$$

OC = OD + DC = 6 + DC

Therefore, DC= 12 – 6 = 6

Hence, the correct answer is Option B

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Point O is the center of the circle. If the area of the circle is 36π   [#permalink] 21 Dec 2018, 05:49
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