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

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Manager
Joined: 18 Jun 2018
Posts: 154
C is the center of the circle below. The length of segment CB is 7 uni  [#permalink]

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15 Jul 2018, 08:53
1
00:00

Difficulty:

35% (medium)

Question Stats:

71% (02:07) correct 29% (01:51) wrong based on 14 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 [ 20.46 KiB | Viewed 354 times ]

A. 11
B. 12
C. 13
D. 14
E. $$\sqrt{65}$$
Manager
Joined: 13 Feb 2018
Posts: 131
Re: C is the center of the circle below. The length of segment CB is 7 uni  [#permalink]

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15 Jul 2018, 13:26
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
BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 3131
Location: India
GPA: 3.12
C is the center of the circle below. The length of segment CB is 7 uni  [#permalink]

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15 Jul 2018, 18:03
From the values given in the question stem, Radius(CD) = CB + BD = 7+4 = 11

Attachment:

Capture.PNG [ 21.78 KiB | Viewed 266 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, 18:03
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