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# In the figure above, AB, which has length z cm, is tangent to the

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Joined: 01 Sep 2010
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In the figure above, AB, which has length z cm, is tangent to the [#permalink]

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26 Jul 2017, 07:58
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79% (01:47) correct 21% (01:37) wrong based on 201 sessions

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In the figure above, AB, which has length z cm, is tangent to the circle at point A, and BD, which has length y cm, intersects the circle at point C. If BC = x cm and $$z = \sqrt{xy}$$, what is the value of x ?

(1) CD = x cm

(2) $$z = 5 \sqrt{2}$$

[Reveal] Spoiler:
Attachment:

circle.jpg [ 18.64 KiB | Viewed 1311 times ]
[Reveal] Spoiler: OA

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Last edited by Bunuel on 26 Jul 2017, 08:00, edited 1 time in total.
Formatted the question.
Intern
Joined: 28 Apr 2017
Posts: 41
In the figure above, AB, which has length z cm, is tangent to the [#permalink]

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26 Jul 2017, 13:51
Sol- we are given and also by second theorem that z^2=xy
1- this gives y=2x--> z^2=2x^2
2-$$z=5\sqrt{2}$$...not given x or y

Combining we know
$$5\sqrt{2}^2=2x^2$$
Intern
Joined: 27 Dec 2017
Posts: 25
Re: In the figure above, AB, which has length z cm, is tangent to the [#permalink]

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18 Jan 2018, 23:14
From 1 statement we know y = 2x
And then z = x√3 but to calculate z we need it's value
From 2 statement we know will get z
So it's together sufficient

study mode
Intern
Joined: 25 Jan 2016
Posts: 18
Location: India
GPA: 3.9
WE: Engineering (Consulting)
Re: In the figure above, AB, which has length z cm, is tangent to the [#permalink]

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19 Jan 2018, 00:33
carcass , Can you please let us know . How this question can be solved.

Thanks.
Intern
Joined: 01 Nov 2017
Posts: 11
Re: In the figure above, AB, which has length z cm, is tangent to the [#permalink]

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19 Jan 2018, 03:08
Given: z = Root(X*Y) -> to answer question we need to have information about z and y

1) y = 2x -> z=Root(x*2x) = Root (2x^2) = x*root(2) -> however INSUFF. as we have no information about x
2) z=5*root(2) clearly Insuff as we don't have any details about x or y

However combining (1) + (2) you get x*root(2) = 5*root(2) => x=5 , therefor SUFFICIENT
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Re: In the figure above, AB, which has length z cm, is tangent to the [#permalink]

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19 Jan 2018, 05:53
prashant0099 wrote:
carcass , Can you please let us know . How this question can be solved.

Thanks.

Hi

You can go through the solutions posted in this thread.

https://gmatclub.com/forum/math-circles-87957.html
Re: In the figure above, AB, which has length z cm, is tangent to the   [#permalink] 19 Jan 2018, 05:53
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