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Given that AB is tangent to the circle with center C, what is the leng

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Given that AB is tangent to the circle with center C, what is the leng [#permalink]

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New post 24 Jan 2016, 05:27
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Given that AB is tangent to the circle with center C, what is the length of the circle’s radius?

(1) AD = 4
(2) AC = 10

[Reveal] Spoiler:
Attachment:
2016-01-24_1725.png
2016-01-24_1725.png [ 4.72 KiB | Viewed 1485 times ]
[Reveal] Spoiler: OA

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Kudos [?]: 135833 [0], given: 12715

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Re: Given that AB is tangent to the circle with center C, what is the leng [#permalink]

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New post 24 Jan 2016, 07:28
Bunuel wrote:
Image
Given that AB is tangent to the circle with center C, what is the length of the circle’s radius?

(1) AD = 4
(2) AC = 10

[Reveal] Spoiler:
Attachment:
2016-01-24_1725.png


two ways to do it..
1) if we extend the radius DC to intersect at circumference say at E..
then AB^2=AD*AE..
8^2=AD(2r+AD)..
there are two unknowns, value of AD or the radius is suff to answer..

2) Join BC..
ABC becomes a right angle triangle, whose sides are..
AB=8, BC=r, AC=r+AD..
so AC^2=AB^2+BC^2..
if we know r or AD we can again answer,,..

lets see the choices.

(1) AD = 4..
Suff
(2) AC = 10
Suff
ans D
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Re: Given that AB is tangent to the circle with center C, what is the leng [#permalink]

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New post 24 Jan 2016, 10:39
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Bunuel wrote:
Image
Given that AB is tangent to the circle with center C, what is the length of the circle’s radius?

(1) AD = 4
(2) AC = 10

[Reveal] Spoiler:
Attachment:
2016-01-24_1725.png


Since AB is tangent, <ABC is right angle.
In the Right angle triangle ABC, AB^2 + BC^2 = AC^2; we need to find BC^2

(1) AD = 4 => Given AD, we can certainly find BC, as (AD+DC)^2 + BC^2 = 8^2 & BC = DC;
(2) AC = 10 => Clearly , BC^2 = 10^2 + 8^2
Ans is D.

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Re: Given that AB is tangent to the circle with center C, what is the leng [#permalink]

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New post 24 Jan 2016, 11:11
Any of these option is sufficient to answer the given question

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Re: Given that AB is tangent to the circle with center C, what is the leng [#permalink]

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New post 14 Sep 2017, 10:34
chetan2u wrote:
Bunuel wrote:
Image
Given that AB is tangent to the circle with center C, what is the length of the circle’s radius?

(1) AD = 4
(2) AC = 10

[Reveal] Spoiler:
Attachment:
2016-01-24_1725.png


two ways to do it..
1) if we extend the radius DC to intersect at circumference say at E..
then AB^2=AD*AE..
8^2=AD(2r+AD)..
there are two unknowns, value of AD or the radius is suff to answer..

2) Join BC..
ABC becomes a right angle triangle, whose sides are..
AB=8, BC=r, AC=r+AD..
so AC^2=AB^2+BC^2..
if we know r or AD we can again answer,,..

lets see the choices.

(1) AD = 4..
Suff
(2) AC = 10
Suff
ans D


In the above solutions, I understood your second approach, but can you please explain how is the equation AB^2=AD*AE arrived at in your first approach?

Kudos [?]: 76 [0], given: 124

Re: Given that AB is tangent to the circle with center C, what is the leng   [#permalink] 14 Sep 2017, 10:34
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