If the Radius of the circle with centre "O" is R, and as per given condition Radius of circle A = 7x & Radius of circle B = 9x.
Then, OA = R-7x
OB = R-9x => OA>OB
Corect answer would be (A)

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	Quantity B
OA	OB

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


Quantitative Section 9 Question 4 of 20 ID: Q02-82

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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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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Sorry for the posting I was in a rush.

Thanks for checking!

I thought it should be B. I was wrongg.

A

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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Solutions please? Thanks so much

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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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

Bump for further discussion
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