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Circles I, II, and III are mutually tangent with centers O, P, and Q,
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04 Jan 2023, 09:29
04 Jan 2023, 09:29
Expert Reply
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Question Stats:
78% (01:22) correct
21% (01:12) wrong based on 23 sessions
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Circles I, II, and III are mutually tangent with centers O, P, and Q, respectively. Points O, P, and Q lie on line segment AB.
Quantity A |
Quantity B |
The sum ofthe circumferences of circle I and II |
The circumference of circle III |
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.
Re: Circles I, II, and III are mutually tangent with centers O, P, and Q,
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30 Jan 2023, 06:17
30 Jan 2023, 06:17
1
Expert Reply
OE
Because O, P, and Q all lie on line segment AB, the diameter of circle I (call it DI) plus the diameter of circle II (DII) must equal the diameter of circle III (DIII): DI+DII=DIII. Because the circumference of a circle equals the diameter times \(\pi\) you can write \(\pi (DI+DII)= \pi DIII\) or (letting C denote circumference), (CI + C II ) = C III. Therefore, the two quantities are equal.
Because O, P, and Q all lie on line segment AB, the diameter of circle I (call it DI) plus the diameter of circle II (DII) must equal the diameter of circle III (DIII): DI+DII=DIII. Because the circumference of a circle equals the diameter times \(\pi\) you can write \(\pi (DI+DII)= \pi DIII\) or (letting C denote circumference), (CI + C II ) = C III. Therefore, the two quantities are equal.
gmatclubot
Re: Circles I, II, and III are mutually tangent with centers O, P, and Q, [#permalink]
30 Jan 2023, 06:17
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