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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # The figure above shows Line L, Circle 1 with center at C1, and Circle

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Math Expert V
Joined: 02 Sep 2009
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The figure above shows Line L, Circle 1 with center at C1, and Circle  [#permalink]

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33 00:00

Difficulty:   55% (hard)

Question Stats: 64% (01:54) correct 36% (02:08) wrong based on 690 sessions

### HideShow timer Statistics The figure above shows Line L, Circle 1 with center at C1, and Circle 2 with center at C2. Line L intersects Circle 1 at points A and B, Line L intersects Circle 2 at points D and E, and points C1 and C2 are equidistant from line L. Is the area of ΔABC1 less than the area of ΔDEC2 ?

(1) The radius of Circle 1 is less than the radius of Circle 2.
(2) The length of chord AB is less than the length of chord DE.

NEW question from GMAT® Quantitative Review 2019

(DS18386)

Attachment: shot20.jpg [ 22.06 KiB | Viewed 6393 times ]

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Director  D
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The figure above shows Line L, Circle 1 with center at C1, and Circle  [#permalink]

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Bunuel wrote: The figure above shows Line L, Circle 1 with center at C1, and Circle 2 with center at C2. Line L intersects Circle 1 at points A and B, Line L intersects Circle 2 at points D and E, and points C1 and C2 are equidistant from line L. Is the area of ΔABC1 less than the area of ΔDEC2 ?

(1) The radius of Circle 1 is less than the radius of Circle 2.
(2) The length of chord AB is less than the length of chord DE.

Question stem:- Is the area of ΔABC1 less than the area of ΔDEC2 ?
Or, Is $$\frac{1}{2}*AB*h<\frac{1}{2}*DE*h$$ ? (points C1 and C2 are equidistant from line L)
Or, Is AB<DE ?

St1:- $$(C_{1}A=C_{1}B)< (C_{2}D=C_{2}E)$$
As points C1 and C2 are equidistant from line L; $$C_{1}H_{1}=C_{2}H_{2}$$
So AB<DE (3rd side of the triangle) (Figure enclosed)
Sufficient

St2:- AB<DE
Sufficient.

Ans. (D)
Attachments Area triangle.JPG [ 27.67 KiB | Viewed 6031 times ]

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##### General Discussion
Director  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 995
WE: Supply Chain Management (Energy and Utilities)
Re: The figure above shows Line L, Circle 1 with center at C1, and Circle  [#permalink]

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Hi Bunuel,
I would request to change the question source tag from power prep to official guide.

Thanking you.
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PKN

Rise above the storm, you will find the sunshine
Math Expert V
Joined: 02 Sep 2009
Posts: 59182
Re: The figure above shows Line L, Circle 1 with center at C1, and Circle  [#permalink]

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PKN wrote:
Hi Bunuel,
I would request to change the question source tag from power prep to official guide.

Thanking you.

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Done. Thank you.
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Intern  B
Joined: 19 Oct 2016
Posts: 4
The figure above shows Line L, Circle 1 with center at C1, and Circle  [#permalink]

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Can anyone please explain why D is the right choice. I am not sure why the second statement is true. Even though the length of the chord AB is smaller than the second circle, can the part where the two points intersect the line can differ, hence, can the radius of Circle with center C1 be bigger?
Director  D
Status: Learning stage
Joined: 01 Oct 2017
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WE: Supply Chain Management (Energy and Utilities)
The figure above shows Line L, Circle 1 with center at C1, and Circle  [#permalink]

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shyamhp wrote:
Can anyone please explain why D is the right choice. I am not sure why the second statement is true. Even though the length of the chord AB is smaller than the second circle, can the part where the two points intersect the line can differ, hence, can the radius of Circle with center C1 be bigger?

Hi shyamhp

Please refer the two triangles under discussion in the two circles, height of the two triangles are equal.(Given in question)

So, while calculating area(1/2 base*height), the only parameter which is the key for comparing the areas of two triangles is the measure of base.

Hence, the triangle with larger measure of base would have larger area and vice-versa.
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Intern  B
Joined: 01 Nov 2018
Posts: 5
Re: The figure above shows Line L, Circle 1 with center at C1, and Circle  [#permalink]

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how do you know that the height of the two triangles is equal? is it from the statement 'points C1 and C2 are equidistant from line L'?

Thanks
Director  D
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Re: The figure above shows Line L, Circle 1 with center at C1, and Circle  [#permalink]

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Skn1608 wrote:
how do you know that the height of the two triangles is equal? is it from the statement 'points C1 and C2 are equidistant from line L'?

Thanks

Hi Skn1608,

Exactly.
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PKN

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Intern  B
Joined: 16 Jul 2019
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Re: The figure above shows Line L, Circle 1 with center at C1, and Circle  [#permalink]

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Hi,

Can someone please explain why statement 1 is sufficient?

My rationale is that the legs of the triangle with radius of 8 will stretch to a greater extent than the legs of the triangle, which has radius of let's say 6.

Thanks!

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Re: The figure above shows Line L, Circle 1 with center at C1, and Circle  [#permalink]

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Might be a stupid question but regarding to (1)

How do I know that A-B is the radius? Couldn't it be the case that it looks like a radius but isn't exactly the radius, hence we need a statement that says "AB is the radius"?

I am confused because I've seen a similar DS question a few days ago and it was only sufficient with statement number (2) that said that a given chord is indeed the diameter / radius.
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Go kick in the door. Re: The figure above shows Line L, Circle 1 with center at C1, and Circle   [#permalink] 18 Oct 2019, 01:16
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