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Circles with centers A and B have radii 3 and 8, respectively. A commo

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Circles with centers A and B have radii 3 and 8, respectively. A commo  [#permalink]

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New post 26 Mar 2019, 05:08
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

58% (03:21) correct 42% (03:37) wrong based on 26 sessions

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Circles with centers A and B have radii 3 and 8, respectively. A common internal tangent intersects the circles at C and D, respectively. Lines AB and CD intersect at E, and $AE=5$. What is CD?

(A) 13

(B) 44/3

(C) \(\sqrt{221}\)

(D) \(\sqrt{255}\)

(E) 55/3


Attachment:
2006_AMC12A-16.png
2006_AMC12A-16.png [ 14.82 KiB | Viewed 393 times ]

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Re: Circles with centers A and B have radii 3 and 8, respectively. A commo  [#permalink]

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New post 26 Mar 2019, 06:34
1
Bunuel wrote:
Image
Circles with centers A and B have radii 3 and 8, respectively. A common internal tangent intersects the circles at C and D, respectively. Lines AB and CD intersect at E, and $AE=5$. What is CD?

(A) 13

(B) 44/3

(C) \(\sqrt{221}\)

(D) \(\sqrt{255}\)

(E) 55/3


Attachment:
The attachment 2006_AMC12A-16.png is no longer available

Join Ad and BC, then ADE and BCE are similar triangles....
Triangle ABE is 3:4:5 triangle..
As per similarity AD:BC=3:8=DE:CE=4:CE..
so CE = \(4*\frac{8}{3}=\frac{32}{3}\)
CD=DE+CE=4+\(\frac{32}{3}=\frac{44}{3}\)

B
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2006_AMC12A-16.png
2006_AMC12A-16.png [ 18.05 KiB | Viewed 301 times ]


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Re: Circles with centers A and B have radii 3 and 8, respectively. A commo  [#permalink]

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New post 22 Apr 2019, 07:20
chetan2u wrote:
Bunuel wrote:
Image
Circles with centers A and B have radii 3 and 8, respectively. A common internal tangent intersects the circles at C and D, respectively. Lines AB and CD intersect at E, and $AE=5$. What is CD?

(A) 13

(B) 44/3

(C) \(\sqrt{221}\)

(D) \(\sqrt{255}\)

(E) 55/3


Attachment:
2006_AMC12A-16.png

Join Ad and BC, then ADE and BCE are similar triangles....
Triangle ABE is 3:4:5 triangle..
As per similarity AD:BC=3:8=DE:CE=4:CE..
so CE = \(4*\frac{8}{3}=\frac{32}{3}\)
CD=DE+CE=4+\(\frac{32}{3}=\frac{44}{3}\)

B



Please how did you get to know that both triangles are similar triangles? I can see only one angle equal in both triangles and that is the angle formed by the radii of both circles.
Kindly assist.

Thank you.
GMAT Club Bot
Re: Circles with centers A and B have radii 3 and 8, respectively. A commo   [#permalink] 22 Apr 2019, 07:20
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Circles with centers A and B have radii 3 and 8, respectively. A commo

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