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In the figure above, line segment CZ = 6. What is the length of line

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In the figure above, line segment CZ = 6. What is the length of line [#permalink]

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In the figure above, line segment CZ = 6. What is the length of line segment AB?

(1) Line segment XY = 4

(2) Line segment AZ > Line segment AY


[Reveal] Spoiler:
Attachment:
Yaz.png
Yaz.png [ 10.51 KiB | Viewed 1926 times ]
[Reveal] Spoiler: OA

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In the figure above, line segment CZ = 6. What is the length of line [#permalink]

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New post 06 Jun 2017, 23:50
Bunuel wrote:
Image
In the figure above, line segment CZ = 6. What is the length of line segment AB?

(1) Line segment XY = 4

(2) Line segment AZ > Line segment AY


[Reveal] Spoiler:
Attachment:
Yaz.png


Using similar triangle approach


Answer Option A
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Last edited by GMATinsight on 11 Jun 2017, 11:00, edited 1 time in total.

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Re: In the figure above, line segment CZ = 6. What is the length of line [#permalink]

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GMATinsight can u explain the answer

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Re: In the figure above, line segment CZ = 6. What is the length of line [#permalink]

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IMHO - Its A
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Re: In the figure above, line segment CZ = 6. What is the length of line [#permalink]

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New post 11 Jun 2017, 05:53
AB/XY =AZ/AZ+YA.
AB/CZ =AY/AZ+YA
Add both equations
AB=2.4
А is enough to get the answer


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Re: In the figure above, line segment CZ = 6. What is the length of line [#permalink]

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In any such question we can use the following trick
1/xy +1/cz = 1/AB, if it is right angled triangle as here
so, here cz=6
i.e. 1/xy + 1/6 = 1/AB.
ST1- XY=4 SO WE CAN GET AB.- SUFFICIENT ANS IS(A)

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Re: In the figure above, line segment CZ = 6. What is the length of line [#permalink]

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New post 17 Sep 2017, 05:56
Leo8 wrote:
Attachment:
FullSizeRender-2.jpg


IMHO - Its A


How are you proving the big triangles similar to the small triangles? One big and one small is possible but how about the other two?

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Re: In the figure above, line segment CZ = 6. What is the length of line [#permalink]

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sinhap07 wrote:
Leo8 wrote:
Attachment:
FullSizeRender-2.jpg


IMHO - Its A


How are you proving the big triangles similar to the small triangles? One big and one small is possible but how about the other two?


Responding to a pm:

We are using the AA property of similarity of triangles. When two angles are the same, the third angle would be the same too since the sum of all three angles of each triangle is 180 degrees. And hence the AAA property of similar triangles is satisfied.

In triangles XYZ and BAZ, angles XYZ and BAZ are 90 degrees each.
Also, angle BZA and angle XZY are the same angle so they will be equal.
So these two triangles are similar by AA.

It is the same logic for triangles CZY and BAY.
Angles CZY and BAY are 90 degrees each.
Also angles CYZ and BYA are the same angles so they will be equal.
So these two triangles are similar by AA.
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In the figure above, line segment CZ = 6. What is the length of line [#permalink]

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New post 19 Sep 2017, 08:00
VeritasPrepKarishma wrote:
sinhap07 wrote:
Leo8 wrote:
Attachment:
FullSizeRender-2.jpg


IMHO - Its A


How are you proving the big triangles similar to the small triangles? One big and one small is possible but how about the other two?


Responding to a pm:

We are using the AA property of similarity of triangles. When two angles are the same, the third angle would be the same too since the sum of all three angles of each triangle is 180 degrees. And hence the AAA property of similar triangles is satisfied.

In triangles XYZ and BAZ, angles XYZ and BAZ are 90 degrees each.
Also, angle BZA and angle XZY are the same angle so they will be equal.
So these two triangles are similar by AA.

It is the same logic for triangles CZY and BAY.
Angles CZY and BAY are 90 degrees each.
Also angles CYZ and BYA are the same angles so they will be equal.
So these two triangles are similar by AA.


Hi

I get that. But how do we prove the similarity between triangle XYZ and CYZ? Can you pls give the complete solution? How do we even arrive at AB

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Re: In the figure above, line segment CZ = 6. What is the length of line [#permalink]

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New post 20 Sep 2017, 02:41
Why do you think they will be similar? Think about it - one of them could be 30-60-90 triangle while another could be 45-45-90.

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Re: In the figure above, line segment CZ = 6. What is the length of line   [#permalink] 20 Sep 2017, 02:41
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