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

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Math Expert
Joined: 02 Sep 2009
Posts: 58396
Circles with centers A and B have radii 3 and 8, respectively. A commo  [#permalink]

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26 Mar 2019, 05:08
00:00

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 [ 14.82 KiB | Viewed 393 times ]

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Joined: 02 Aug 2009
Posts: 8004
Re: Circles with centers A and B have radii 3 and 8, respectively. A commo  [#permalink]

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26 Mar 2019, 06:34
1
Bunuel wrote:

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

Triangle ABE is 3:4:5 triangle..
so CE = $$4*\frac{8}{3}=\frac{32}{3}$$
CD=DE+CE=4+$$\frac{32}{3}=\frac{44}{3}$$

B
Attachments

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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22 Apr 2019, 07:20
chetan2u wrote:
Bunuel wrote:

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

Triangle ABE is 3:4:5 triangle..
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.
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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