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Re: Quantitative Section 9 Question 4 of 20 ID: Q02-82 [#permalink]
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IlCreatore wrote:
In the following figure, two circles with center A and B touch a larger circle with center O internally. The ratio of the radii of circle A to circle B is 7:9.


Quantity A

OA
Quantity B

OB


The explanation provided on the test is not very informative. It says "Solve"
Any hint?


Given
\(\frac{RA}{RB}\)=\(\frac{7}{9}\)⇒RB>RA


This works only if the centre A is tangent to the centre O, then
OA=RO−RA

Similarly If the circle with center B is tangent to the circle with center in O we would have:

OB=RO−RB

Therefore we would have RB>RA and OA>OB.


I think some point is missing in the ques.
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Re: Quantitative Section 9 Question 4 of 20 ID: Q02-82 [#permalink]
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Please guys format the question as it should be.

Back to the question, I checked it out .......and you are right either the stem missing something and the explanation misses totally.

Fixin a while. Thank you
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Re: Quantitative Section 9 Question 4 of 20 ID: Q02-82 [#permalink]
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Carcass wrote:
Please guys format the question as it should be.

Back to the question, I checked it out .......and you are right either the stem missing something and the explanation misses totally.

Fixin a while. Thank you


Sorry for the posting I was in a rush.

Thanks for checking!
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Re: GRE Math Challenge #12- Geometry Three Circles [#permalink]
I thought it should be B. I was wrongg.
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Re: GRE Math Challenge #12- Geometry Three Circles [#permalink]
A
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In the figure, two circles with centers A and B touch a lar [#permalink]
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Attachment:
#GREpracticequestion In the figure, two circles with centers A and B .jpg
#GREpracticequestion In the figure, two circles with centers A and B .jpg [ 22.24 KiB | Viewed 10236 times ]


In the figure, two circles with centers A and B touch a larger circle with center O internally. The ratio of the radii of Circle A to Circle B is 7 : 9.


Quantity A
Quantity B
\(OA\)
\(OB\)


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
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Re: In the figure, two circles with centers A and B touch a lar [#permalink]
Solutions please? Thanks so much
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Re: In the figure, two circles with centers A and B touch a lar [#permalink]
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Since the circle with center O and the circle with center A touch each other internally, the distance between their centers equals (Radius of larger circle) – (Radius of circle with center A) = Column A

Similarly, since the circle with center O and the circle with center B touch each other internally, the distance between their centers equals (Radius of larger circle) – (Radius of circle with center B) = Column B

Since the ratio of the radii of the circles with center A and center B is given to be 7 : 9 and since 7 < 9, (Radius of circle with center A) < (Radius of circle with center B).

Multiplying the inequality by –1 and flipping direction yields –(Radius of circle with center A) > –(Radius of circle with center B) Adding “Radius of larger circle” to both sides yields

(Radius of larger circle) – (Radius of circle with center A) > (Radius of larger circle) – (Radius of circle with center B)

Ask for further assistance if you do need.

regards
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Re: In the figure, two circles with centers A and B touch a lar [#permalink]
1
Lets assume radius of the smaller circle with centre A is 7 unit and radius of the other smaller circle with centre B is 9 unit.

since , O is the centre of the bigger circle , we can have this equation below,

OA+7(radius of bigger circle)=OB+9 (radius of bigger circle)
=> OA - OB = 2 (+ve)

Hence , we can say that OA > OB
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Re: GRE Math Challenge #12- Geometry Three Circles [#permalink]
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Bump for further discussion
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In the figure, two circles with centers A and B touch a lar [#permalink]
This was explained before, but I thought I'd present it more clearly.



Ok, let's first draw the radius of the larger circle extending from the it's center, passing through the centers of the two smaller circles, and terminating at the place where the smaller circles touch the larger one.

Image

Observe the radii of the smaller circles below. While we cannot be certain of their exact size, given that x must positive number, 7x > 9x

Image


So now we can set up a simple equation to help us solve the problem:

OA = r - 7x

OB = r - 9x


Subtract r from both sides, and divide the positive number x.

-7 > -9 and thus OA > OB
Attachments

#greprepclub In the following figure, two circles with.jpg
#greprepclub In the following figure, two circles with.jpg [ 32.18 KiB | Viewed 4702 times ]

#GREpracticequestion In the figure, two circles with centers A and B -1.jpg
#GREpracticequestion In the figure, two circles with centers A and B -1.jpg [ 28.61 KiB | Viewed 4687 times ]


Originally posted by r1smith on 19 Dec 2021, 21:54.
Last edited by r1smith on 20 Dec 2021, 06:19, edited 3 times in total.
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Re: In the figure, two circles with centers A and B touch a lar [#permalink]
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The images are missing
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Re: In the figure, two circles with centers A and B touch a lar [#permalink]
Carcass wrote:
The images are missing


Oops, hopefully I fixed it. They were the most important part.
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Re: In the figure, two circles with centers A and B touch a lar [#permalink]
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