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C is the center of the circle below. The length of segment CB is 7 uni

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C is the center of the circle below. The length of segment CB is 7 uni  [#permalink]

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New post 15 Jul 2018, 07:53
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

67% (02:07) correct 33% (01:48) wrong based on 15 sessions

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C is the center of the circle below. The length of segment CB is 7 units. The length of segment BD is 4 units. Find the length of diagonal AB in the rectangle.
Attachment:
Capture.PNG
Capture.PNG [ 20.46 KiB | Viewed 463 times ]


A. 11
B. 12
C. 13
D. 14
E. \(\sqrt{65}\)
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Re: C is the center of the circle below. The length of segment CB is 7 uni  [#permalink]

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New post 15 Jul 2018, 12:26
1
Man, you killed my 9 minutes and the answer is so simple.

You have just to be smart enough to see that the other diagonal of the rectangle from the vertex C is just a radius of the circle

IMO
Ans: A
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C is the center of the circle below. The length of segment CB is 7 uni  [#permalink]

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New post 15 Jul 2018, 17:03
From the values given in the question stem, Radius(CD) = CB + BD = 7+4 = 11

Attachment:
Capture.PNG
Capture.PNG [ 21.78 KiB | Viewed 374 times ]


Concept used: In a rectangle, the length of the diagonals is equal.

Since one of the diagonals of the rectangle(CE) of the rectangle AEBC, marked in red is the
radius of the circle, the other diagonal, AB will also be equal to the radius of the circle.

Therefore, the length of the diagonal AB is 11(Option A)
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C is the center of the circle below. The length of segment CB is 7 uni &nbs [#permalink] 15 Jul 2018, 17:03
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C is the center of the circle below. The length of segment CB is 7 uni

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