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

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

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New post 03 Aug 2018, 10:38
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A
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C
D
E

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71% (01:31) correct 29% (01:21) wrong based on 110 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.


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

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New post 03 Aug 2018, 12:39
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Bunuel wrote:
Image
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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Re: The figure above shows Line L, Circle 1 with center at C1, and Circle  [#permalink]

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

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New post 06 Aug 2018, 22:49
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The figure above shows Line L, Circle 1 with center at C1, and Circle  [#permalink]

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New post 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?
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The figure above shows Line L, Circle 1 with center at C1, and Circle  [#permalink]

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New post 09 Aug 2018, 05:40
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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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The figure above shows Line L, Circle 1 with center at C1, and Circle &nbs [#permalink] 09 Aug 2018, 05:40
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