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

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Math Expert
Joined: 02 Sep 2009
Posts: 61544
C is the center of the circle below. The length of segment CB is 7 uni  [#permalink]

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20 Jan 2020, 02:25
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Difficulty:

55% (hard)

Question Stats:

66% (02:20) correct 34% (02:51) wrong based on 35 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.

A. √65
B. 11
C. 12
D. 13
E. 14

Attachment:

Capture.PNG [ 11.12 KiB | Viewed 394 times ]

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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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20 Jan 2020, 03:47
Bunuel wrote:

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.

A. √65
B. 11
C. 12
D. 13
E. 14

Attachment:
The attachment Capture.PNG is no longer available

Check the solution as attached.

The length of CE = Length of AB (Both are diagonals of same rectangle

Also, CE = CD (Both are radius of circle) = 7+4 = 11

Attachments

Screenshot 2020-01-20 at 5.17.20 PM.png [ 432.31 KiB | Viewed 330 times ]

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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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20 Jan 2020, 04:02
Bunuel wrote:

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.

A. √65
B. 11
C. 12
D. 13
E. 14

Given, CB = 7 units & BD = 4 units
--> Radius of the circle, r = CB + BD = 7 + 4 = 11 units

We know that, length of the diagonals AB & CF are equal
--> Length of AB = CF = radius = 11

Option B
Attachments

1.png [ 19.99 KiB | Viewed 451 times ]

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Joined: 03 Jan 2018
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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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28 Jan 2020, 18:44
Hi Bunuel,

Quick question - I tried to do it using Pythagorean’s theorem, assuming the diagonal bisects the rectangle into 2 x 90:45:45 triangle in which case doesn’t AC = CB = 7?
Therefore the hypotenuse will be sqr root of 98 = ~9.9?

If not then that would mean the diagonals bisecting rectangles are not always angle bisector?

Thanks ?
Lasya
Re: C is the center of the circle below. The length of segment CB is 7 uni   [#permalink] 28 Jan 2020, 18:44
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