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Three circles with their centers on line segment PQ are tang [#permalink]
Expert's post 00:00

Question Stats: 79% (00:59) correct 20% (00:34) wrong based on 73 sessions

Attachment: #GREpracticequestion Three circles with their centers on line segment PQ.jpg [ 12.07 KiB | Viewed 2638 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.
[Reveal] Spoiler: OA

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Re: Three circles with their centers on line segment PQ are tang [#permalink]
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Expert's post
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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Sandy
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Re: Three circles with their centers on line segment PQ are tang [#permalink]
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]
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]
They are equal as two smaller diameters are equal to large
Director Joined: 09 Nov 2018
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Re: Three circles with their centers on line segment PQ are tang [#permalink]
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 2362 times ] Re: Three circles with their centers on line segment PQ are tang   [#permalink] 18 Jan 2019, 19:21
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