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# In the figure above, CD is tangent to the circle with center A. If the

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Math Expert
Joined: 02 Sep 2009
Posts: 44351
In the figure above, CD is tangent to the circle with center A. If the [#permalink]

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01 Mar 2017, 05:30
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Difficulty:

95% (hard)

Question Stats:

53% (02:54) correct 47% (01:59) wrong based on 95 sessions

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In the figure above, CD is tangent to the circle with center A. If the length of BE is 10 and the length of CE is 2, what is the length of CD?

A. 2
B. 8/3
C. 3
D. 10/3
E. 4

[Reveal] Spoiler:
Attachment:

CD_.PNG [ 12 KiB | Viewed 1415 times ]
[Reveal] Spoiler: OA

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Director
Joined: 05 Mar 2015
Posts: 961
In the figure above, CD is tangent to the circle with center A. If the [#permalink]

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01 Mar 2017, 08:59
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Bunuel wrote:

In the figure above, CD is tangent to the circle with center A. If the length of BE is 10 and the length of CE is 2, what is the length of CD?

A. 2
B. 8/3
C. 3
D. 10/3
E. 4

[Reveal] Spoiler:
Attachment:
The attachment CD_.PNG is no longer available

Since AB = AC = radius
thus from pythagorian triplet , in triangle ABE AB=8 and AE =6 (as AC=6+2=8=radius AB)
Now both triangles are AAA similar (since tangent to circle makes 90 deg with circle)
we can write AB/ CD = AE/EC
putting values
8/CD= 6/2
thus CD= 8/3

Ans B
Attachments

CD_.PNG [ 12.36 KiB | Viewed 1144 times ]

Intern
Joined: 07 Sep 2012
Posts: 8
GMAT 1: 650 Q50 V28
GPA: 2.8
WE: Operations (Retail)
Re: In the figure above, CD is tangent to the circle with center A. If the [#permalink]

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01 Mar 2017, 10:59

Sent from my iPhone using GMAT Club Forum mobile app
Intern
Joined: 20 Dec 2014
Posts: 10
Re: In the figure above, CD is tangent to the circle with center A. If the [#permalink]

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04 Feb 2018, 04:31
rohit8865 wrote:
Bunuel wrote:

In the figure above, CD is tangent to the circle with center A. If the length of BE is 10 and the length of CE is 2, what is the length of CD?

A. 2
B. 8/3
C. 3
D. 10/3
E. 4

[Reveal] Spoiler:
Attachment:
CD_.PNG

Since AB = AC = radius
thus from pythagorian triplet , in triangle ABE AB=8 and AE =6 (as AC=6+2=8=radius AB)
Now both triangles are AAA similar (since tangent to circle makes 90 deg with circle)
we can write AB/ CD = AE/EC
putting values
8/CD= 6/2
thus CD= 8/3

Ans B

the insight on the Pythagoras triplet would save a lot of time.. i got it correct but took about twice the time to complete the question that the average,
Would have finished in 2 mins if realized the triplet in play...
noted it as one of the things to do for Geometry questions
Senior Manager
Joined: 31 Jul 2017
Posts: 322
Location: Malaysia
WE: Consulting (Energy and Utilities)
Re: In the figure above, CD is tangent to the circle with center A. If the [#permalink]

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05 Feb 2018, 00:59
Bunuel wrote:

In the figure above, CD is tangent to the circle with center A. If the length of BE is 10 and the length of CE is 2, what is the length of CD?

A. 2
B. 8/3
C. 3
D. 10/3
E. 4

[Reveal] Spoiler:
Attachment:
CD_.PNG

Given,

$$r^2 + (r-2)^2 = 100$$
$$r = 8.$$

Triangle ABE is Similar to Triangle CDE.

$$\frac{8}{CD} = \frac{6}{2}$$
$$CD = \frac{8}{3}$$
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Re: In the figure above, CD is tangent to the circle with center A. If the   [#permalink] 05 Feb 2018, 00:59
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