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

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

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New post 01 Mar 2017, 04:30
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A
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Difficulty:

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Question Stats:

58% (02:44) correct 42% (02:46) wrong based on 112 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

Attachment:
CD_.PNG
CD_.PNG [ 12 KiB | Viewed 2359 times ]

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

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New post 01 Mar 2017, 07:59
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Bunuel wrote:
Image
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

Attachment:
The attachment CD_.PNG is no longer available



Please follow below fig.

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
CD_.PNG [ 12.36 KiB | Viewed 1887 times ]

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Re: In the figure above, CD is tangent to the circle with center A. If the  [#permalink]

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New post 01 Mar 2017, 09:59
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Re: In the figure above, CD is tangent to the circle with center A. If the  [#permalink]

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New post 04 Feb 2018, 03:31
rohit8865 wrote:
Bunuel wrote:
Image
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

Attachment:
CD_.PNG



Please follow below fig.

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
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Re: In the figure above, CD is tangent to the circle with center A. If the  [#permalink]

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New post 04 Feb 2018, 23:59
Bunuel wrote:
Image
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

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 &nbs [#permalink] 04 Feb 2018, 23:59
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