GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Circles I, II, and III are mutually tangent with centers O, P, and Q,
[#permalink]
04 Jan 2023, 09:29
04 Jan 2023, 09:29
Expert Reply
00:00
Question Stats:
78% (01:22) correct
21% (01:12) wrong based on 23 sessions
Hide Show timer Statistics
Attachment:
GRE Circles I, II, and III are mutually .jpg [ 37.68 KiB | Viewed 1357 times ]
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,
[#permalink]
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
Moderators:
