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A, B, C are the centers of the three circles, each of which touches th
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15 Nov 2023, 01:00
15 Nov 2023, 01:00
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28% (01:47) correct
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GRE A, B, C are the centers of the three circles,.jpg [ 15.73 KiB | Viewed 1145 times ]
A, B, C are the centers of the three circles, each of which touches the other. The radius of circle with center C is 10 units.
Quantity A |
Quantity B |
Perimeter of triangle ABC |
20 |
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.
Part of the project: The Butler-GRE Daily New Quant and Verbal Questions to Practice (2023) - Gain 20 Kudos & Get FREE Access to GRE Prep Club TESTS
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Free Materials for the GRE General Exam - Where to get it!!
GRE Geometry Formulas
GRE - Math Book
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Free Materials for the GRE General Exam - Where to get it!!
GRE Geometry Formulas
GRE - Math Book
Re: A, B, C are the centers of the three circles, each of which touches th
[#permalink]
17 Nov 2023, 18:36
17 Nov 2023, 18:36
2
A, B, C are the centers of the three circles, each of which touches the other. The radius of circle with center C is 10 units.
Extend the line CA to make the radius of the circle C as CD , and extend the line CB to make another radius of the circle C as CE , Please see image attached.
So we know the line CD is the radius of the circle C i.e. CD = 10 , thus if we consider the value of DA =r1 (which is same as radius of the Circle A) , then CA=10-r1
Similarly we know the line CE is the radius of the circle C i.e. CE = 10, thus if we consider the value of BE = r2 (which is same as the radius of the circle B), then CB = 10-r2
now we know the point A and B are the centers of circle A and B , thus the line segment AB = r1 + r2
Thus perimeter of triangle ABC = CA+AB+CB = 10-r1 + r1+r2 + 10-r2 = 20
answer C .
PS. Sorry for my bad drawing
Extend the line CA to make the radius of the circle C as CD , and extend the line CB to make another radius of the circle C as CE , Please see image attached.
So we know the line CD is the radius of the circle C i.e. CD = 10 , thus if we consider the value of DA =r1 (which is same as radius of the Circle A) , then CA=10-r1
Similarly we know the line CE is the radius of the circle C i.e. CE = 10, thus if we consider the value of BE = r2 (which is same as the radius of the circle B), then CB = 10-r2
now we know the point A and B are the centers of circle A and B , thus the line segment AB = r1 + r2
Thus perimeter of triangle ABC = CA+AB+CB = 10-r1 + r1+r2 + 10-r2 = 20
answer C .
PS. Sorry for my bad drawing
Attachments
GRE A, B, C are the centers of the three circles,.jpg [ 11.01 KiB | Viewed 1042 times ]
gmatclubot
Re: A, B, C are the centers of the three circles, each of which touches th [#permalink]
17 Nov 2023, 18:36
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