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Three circles with their centers on line segment PQ are tang [#permalink]
24 Feb 2017, 02:34
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Question Stats:
78% (00:57) correct
21% (00:52) wrong based on 183 sessions
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#GREpracticequestion Three circles with their centers on line segment PQ.jpg [ 12.07 KiB  Viewed 20133 times ]
Three circles with their centers on line segment PQ are tangent at points P, R, and Q, where point R lies on line segment PQ
Quantity A 
Quantity B 
The circumference of the largest circle 
The sum of the circumferences of the two smaller circles 
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.
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Re: Three circles with their centers on line segment PQ are tang [#permalink]
28 Feb 2017, 16:40
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ExplanationWe know that circumference of a circle = \(\pi \times d\). Here D is diameter of circle. One smaller circle has diameter PR and other is QR. Diameter of the largest circle is PQ. Now PQR lie on the same line. PR + QR = PQ multiplying \(\pi\) both side \(\pi \times PR + \pi \times QR = \pi \times PQ\). Circumference of smaller circle with diameter PR + Circumference of smaller circle with diameter QR = Circumference of larger circle with diameter PQ. Quantity B = Quantity A. Hence C is correct option.
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Re: Three circles with their centers on line segment PQ are tang [#permalink]
15 Jun 2018, 03:49
sandy wrote: Explanation
We know that circumference of a circle = \(\pi \times d\). Here D is diameter of circle.
One smaller circle has diameter PR and other is QR.
Diameter of the largest circle is PQ. Now PQR lie on the same line.
PR + QR = PQ
multiplying \(\pi\) both side
\(\pi \times PR + \pi \times QR = \pi \times PQ\).
Circumference of smaller circle with diameter PR + Circumference of smaller circle with diameter QR = Circumference of larger circle with diameter PQ.
Quantity B = Quantity A.
Hence C is correct option. Even though your explanation is still not clear, I will trust your reasoning on this one. Anytime I see a similar question, even if it has 5 circles inside the major circle and they are tangent, I will assume the circumference is equal to that of the major circle.



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Re: Three circles with their centers on line segment PQ are tang [#permalink]
29 Aug 2018, 02:38
sandy wrote: Explanation
We know that circumference of a circle = \(\pi \times d\). Here D is diameter of circle.
One smaller circle has diameter PR and other is QR.
Diameter of the largest circle is PQ. Now PQR lie on the same line.
PR + QR = PQ
multiplying \(\pi\) both side
\(\pi \times PR + \pi \times QR = \pi \times PQ\).
Circumference of smaller circle with diameter PR + Circumference of smaller circle with diameter QR = Circumference of larger circle with diameter PQ.
"it is said in the question that R lies on a segment", I dont think it is safe to assume that the line segment shown and described in the circle is a diameter. in which case answer should be D...Please correct me if I am wrong.
Quantity B = Quantity A.
Hence C is correct option.



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Re: Three circles with their centers on line segment PQ are tang [#permalink]
18 Jan 2019, 19:13
They are equal as two smaller diameters are equal to large



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Re: Three circles with their centers on line segment PQ are tang [#permalink]
18 Jan 2019, 19:21
Emike56 wrote: sandy wrote: Hence C is correct option.
Even though your explanation is still not clear, I will trust your reasoning on this one. Anytime I see a similar question, even if it has 5 circles inside the major circle and they are tangent, I will assume the circumference is equal to that of the major circle. Even in this case also ha ha ha Attachment:
Circle.jpg [ 29.88 KiB  Viewed 19761 times ]



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Re: Three circles with their centers on line segment PQ are tang [#permalink]
15 Sep 2019, 06:51
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I might not have done this efficiently but I tried plugging in numbers
For example the total distance is 8 and the 2 circles are equal
Big circle Circumference = 2pi*4=8pi Small Circles Circumference = 2pi(2) +2pi(2) = 8pi
Not Equal  one has a diameter of 6 and the other 2 Big Circle = 2pi*4 = 8pi Small Circles = 2pi(3) + 2pi(1) = 8pi
C



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Re: Three circles with their centers on line segment PQ are tang [#permalink]
29 Jun 2020, 23:33
It is more clear now. Since the two small circles share the diameter with the big one, they have equal circumference.
Thanks



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Re: Three circles with their centers on line segment PQ are tang [#permalink]
23 Jul 2020, 05:01
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Emike56 wrote: sandy wrote: Explanation
We know that circumference of a circle = \(\pi \times d\). Here D is diameter of circle.
One smaller circle has diameter PR and other is QR.
Diameter of the largest circle is PQ. Now PQR lie on the same line.
PR + QR = PQ
multiplying \(\pi\) both side
\(\pi \times PR + \pi \times QR = \pi \times PQ\).
Circumference of smaller circle with diameter PR + Circumference of smaller circle with diameter QR = Circumference of larger circle with diameter PQ.
Quantity B = Quantity A.
Hence C is correct option. Even though your explanation is still not clear, I will trust your reasoning on this one. Anytime I see a similar question, even if it has 5 circles inside the major circle and they are tangent, I will assume the circumference is equal to that of the major circle. Fair bit of advice. Never assume anything unless it's given. I learned that the hard way. Moreover, it's stated here that 'three circles with their centers on line segment PQ are tangent at points P, R, and Q where point R lies on segment PQ.' If centers are lying on PQ then we can say PQ is diameter of the biggest circle and thus solve as given.




Re: Three circles with their centers on line segment PQ are tang
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23 Jul 2020, 05:01





