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# The figure above shows Line L, Circle 1 with center at C1, and Circle

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Math Expert
Joined: 02 Sep 2009
Posts: 55623
The figure above shows Line L, Circle 1 with center at C1, and Circle  [#permalink]

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03 Aug 2018, 10:38
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55% (hard)

Question Stats:

63% (01:51) correct 37% (02:01) wrong based on 616 sessions

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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)

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##### Most Helpful Community Reply
VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1009
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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03 Aug 2018, 12:39
6
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)
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Area triangle.JPG [ 27.67 KiB | Viewed 3961 times ]

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PKN

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##### General Discussion
VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1009
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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06 Aug 2018, 07:01
Hi Bunuel,
I would request to change the question source tag from power prep to official guide.

Thanking you.
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Regards,

PKN

Rise above the storm, you will find the sunshine
Math Expert
Joined: 02 Sep 2009
Posts: 55623
Re: The figure above shows Line L, Circle 1 with center at C1, and Circle  [#permalink]

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06 Aug 2018, 22:49
PKN wrote:
Hi Bunuel,
I would request to change the question source tag from power prep to official guide.

Thanking you.

___________________
Done. Thank you.
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Intern
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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09 Aug 2018, 05:11
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?
VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1009
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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09 Aug 2018, 05:40
2
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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Regards,

PKN

Rise above the storm, you will find the sunshine
Intern
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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19 Dec 2018, 21:57
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
VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1009
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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19 Dec 2018, 21:59
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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Regards,

PKN

Rise above the storm, you will find the sunshine
Re: The figure above shows Line L, Circle 1 with center at C1, and Circle   [#permalink] 19 Dec 2018, 21:59
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# The figure above shows Line L, Circle 1 with center at C1, and Circle

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