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

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

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New post Updated on: 26 Jul 2017, 09:00
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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) \(z = 5 \sqrt{2}\)


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Originally posted by carcass on 26 Jul 2017, 08:58.
Last edited by Bunuel on 26 Jul 2017, 09:00, edited 1 time in total.
Formatted the question.
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In the figure above, AB, which has length z cm, is tangent to the [#permalink]

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New post 26 Jul 2017, 14:51
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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
\(5\sqrt{2}^2=2x^2\)
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Re: In the figure above, AB, which has length z cm, is tangent to the [#permalink]

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New post 19 Jan 2018, 00:14
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

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Re: In the figure above, AB, which has length z cm, is tangent to the [#permalink]

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New post 19 Jan 2018, 01:33
carcass , Can you please let us know . How this question can be solved.

Thanks.
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Re: In the figure above, AB, which has length z cm, is tangent to the [#permalink]

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New post 19 Jan 2018, 04:08
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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New post 19 Jan 2018, 06:53
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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.
You can also read about circles theory here:

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

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New post 17 May 2018, 08:24
Bunuel, chetan2u could you please share your approach here? Thanks.
Re: In the figure above, AB, which has length z cm, is tangent to the   [#permalink] 17 May 2018, 08:24
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