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26 Mar 2019, 05:08
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
66% (03:16) correct
34%
(03:09)
wrong
based on 56
sessions
History
Date
Time
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Not Attempted Yet
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 6513 times ]
26 Mar 2019, 06:34
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Bunuel
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
Attachments
2006_AMC12A-16.png [ 18.05 KiB | Viewed 5870 times ]
oyin26
Joined: 17 Feb 2018
Last visit: 16 Jan 2020
Posts: 3
Own Kudos:
Given Kudos: 8
Location: Nigeria
Schools: Stanford '21 Wharton '21 HBS '21
GRE 1: Q157 V156
GPA: 3.52
WE:Analyst (Accounting)
22 Apr 2019, 07:20
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chetan2u
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.
