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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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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.
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Re: Three circles with their centers on line segment PQ are tang [#permalink] New post 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] New post 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

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Re: Three circles with their centers on line segment PQ are tang [#permalink] New post 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] New post 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.

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Re: Three circles with their centers on line segment PQ are tang [#permalink] New post 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   [#permalink] 23 Jul 2020, 05:01
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