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Three circles with their centers on line segment PQ are tang

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Three circles with their centers on line segment PQ are tang [#permalink] New post 24 Feb 2017, 02:34
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Question Stats:

75% (01:00) correct 25% (00:39) wrong based on 52 sessions


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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.
[Reveal] Spoiler: OA

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Re: Three circles with their centers on line segment PQ are tang [#permalink] New post 28 Feb 2017, 16:40
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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.
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Re: Three circles with their centers on line segment PQ are tang [#permalink] New post 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] New post 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.
Re: Three circles with their centers on line segment PQ are tang   [#permalink] 29 Aug 2018, 02:38
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Three circles with their centers on line segment PQ are tang

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