GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Feb 2019, 08:31

Close

GMAT 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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT RC Webinar

     February 23, 2019

     February 23, 2019

     07:00 AM PST

     09:00 AM PST

    Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
  • FREE Quant Workshop by e-GMAT!

     February 24, 2019

     February 24, 2019

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

Two Tangent circles A and B have radii r1 and r2, respectively. What

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53067
Two Tangent circles A and B have radii r1 and r2, respectively. What  [#permalink]

Show Tags

New post 21 Jan 2015, 01:46
6
8
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

43% (00:49) correct 57% (00:53) wrong based on 313 sessions

HideShow timer Statistics

Two Tangent circles A and B have radii r1 and r2, respectively. What is the distance between their centers?

(1) r1 = 3 inches
(2) r2 = 5 inches

Kudos for a correct solution.

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7334
Premium Member Reviews Badge
Two Tangent circles A and B have radii r1 and r2, respectively. What  [#permalink]

Show Tags

New post 21 Jan 2015, 06:58
2
E....
even when two radiis are given ,the two circles can be tangential on the exterior or one inside the other and thus interior, a situation on which ans will depend
Attachments

tangents...png
tangents...png [ 7.3 KiB | Viewed 4510 times ]


_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


GMAT Expert

Manager
Manager
User avatar
Joined: 27 Jun 2014
Posts: 67
Location: New Zealand
Concentration: Strategy, General Management
GMAT 1: 710 Q43 V45
GRE 1: Q161 V163

GRE 2: Q159 V166
GPA: 3.6
WE: Editorial and Writing (Computer Software)
Premium Member
Re: Two Tangent circles A and B have radii r1 and r2, respectively. What  [#permalink]

Show Tags

New post 23 Jan 2015, 17:26
1
3
Bunuel wrote:
Two Tangent circles A and B have radii r1 and r2, respectively. What is the distance between their centers?

(1) r1 = 3 inches
(2) r2 = 5 inches

Kudos for a correct solution.


A great question that leads us to believe that the answer would be C (with the two radii lengths; however the tangent circles could be tangent on the exterior or the smaller one could be inside the larger one and therefore tangent on the interior. We get an answer of 8 in the first scenario and 2 in the second. Therefore, answer choice is E.
_________________

"Hardwork is the easiest way to success." - Aviram

One more shot at the GMAT...aiming for a more balanced score.

VP
VP
User avatar
P
Joined: 05 Mar 2015
Posts: 1001
Re: Two Tangent circles A and B have radii r1 and r2, respectively. What  [#permalink]

Show Tags

New post 24 Jul 2016, 09:44
2
Bunuel wrote:
Two Tangent circles A and B have radii r1 and r2, respectively. What is the distance between their centers?

(1) r1 = 3 inches
(2) r2 = 5 inches

Kudos for a correct solution.


consider two cases as per fig below

One has difference of 2 units
And another has 8 units
Neither suff..

Ans E
Attachments

111.png
111.png [ 9.33 KiB | Viewed 6840 times ]

Intern
Intern
avatar
Joined: 17 Jul 2017
Posts: 15
Re: Two Tangent circles A and B have radii r1 and r2, respectively. What  [#permalink]

Show Tags

New post 03 Aug 2017, 12:30
rohit8865 wrote:
Bunuel wrote:
Two Tangent circles A and B have radii r1 and r2, respectively. What is the distance between their centers?

(1) r1 = 3 inches
(2) r2 = 5 inches

Kudos for a correct solution.


consider two cases as per fig below

One has difference of 2 units
And another has 8 units
Neither suff..

Ans E


Hmm thanks but is this wrong? I don't understand why they have to be tangent like the way you showed and not like this
Attachments

tangent question.png
tangent question.png [ 7.18 KiB | Viewed 5984 times ]

Manager
Manager
avatar
B
Joined: 31 Dec 2016
Posts: 73
Two Tangent circles A and B have radii r1 and r2, respectively. What  [#permalink]

Show Tags

New post 07 Aug 2017, 07:40
Samuelboyle96 wrote:
rohit8865 wrote:
Bunuel wrote:
Two Tangent circles A and B have radii r1 and r2, respectively. What is the distance between their centers?

(1) r1 = 3 inches
(2) r2 = 5 inches

Kudos for a correct solution.


consider two cases as per fig below

One has difference of 2 units
And another has 8 units
Neither suff..

Ans E


Hmm thanks but is this wrong? I don't understand why they have to be tangent like the way you showed and not like this


I guess no one is going to answer because obviously the GMAT makes up their definition of tangent circles. http://mathworld.wolfram.com/TangentCircles.html I have yet to find anywhere on the internet besides the GMAT define tangent circles as 2 circles where their centers line up perfectly.

See it is a little weird the GMAT mentions tangent circles lining up horizontally here but not in other places https://gmatclub.com/forum/the-figure-a ... 91244.html
Attachments

tangent circles.png
tangent circles.png [ 15.28 KiB | Viewed 5863 times ]

GMAT Tutor
avatar
S
Joined: 24 Jun 2008
Posts: 1350
Re: Two Tangent circles A and B have radii r1 and r2, respectively. What  [#permalink]

Show Tags

New post 07 Aug 2017, 07:59
SamBoyle wrote:

See it is a little weird the GMAT mentions tangent circles lining up horizontally here but not in other places


Two distinct circles are tangent to each other if they touch in exactly one point. You posted a diagram two posts above of two circles that do not touch anywhere, but which share a tangent line. Those circles are not tangent circles. The concept of tangency has nothing to do with whether things 'line up horizontally', so if the diagrams you've seen have displayed tangent circles with centers along a horizontal line, that's likely only because it's easier to draw diagrams that way.

SamBoyle wrote:

I guess no one is going to answer because obviously the GMAT makes up their definition of tangent circles.


All of the math on the GMAT is the same as the math you'd learn anywhere else, so there is no math on the test that the GMAT "makes up".
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2629
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Two Tangent circles A and B have radii r1 and r2, respectively. What  [#permalink]

Show Tags

New post 07 Aug 2017, 08:09
SamBoyle wrote:
Samuelboyle96 wrote:
rohit8865 wrote:

consider two cases as per fig below

One has difference of 2 units
And another has 8 units
Neither suff..

Ans E


Hmm thanks but is this wrong? I don't understand why they have to be tangent like the way you showed and not like this


I guess no one is going to answer because obviously the GMAT makes up their definition of tangent circles. http://mathworld.wolfram.com/TangentCircles.html I have yet to find anywhere on the internet besides the GMAT define tangent circles as 2 circles where their centers line up perfectly.

See it is a little weird the GMAT mentions tangent circles lining up horizontally here but not in other places https://gmatclub.com/forum/the-figure-a ... 91244.html


I agree with what IanStewart has mentioned above. Additionally, there is no need to discuss this further as GMAT or any math book will define tangency as 1 point of contact. But do understand that GMAT is a timed exam and hence, you should stop working on a DS question as soon as you find 2 contradictory scenarios; you are not getting extra points for coming with 100 different scenarios to answer the same set of DS statements. Additionally, it is easier to visualize 'horizontal scenarios' out of many scenarios that negate the statements mentioned in this DS question. Not seeing something on the internet does not mean GMAT 'makes up' math concepts.

Hope this helps.
Manager
Manager
avatar
B
Joined: 31 Dec 2016
Posts: 73
Two Tangent circles A and B have radii r1 and r2, respectively. What  [#permalink]

Show Tags

New post 08 Aug 2017, 08:22
IanStewart wrote:
SamBoyle wrote:

See it is a little weird the GMAT mentions tangent circles lining up horizontally here but not in other places


Two distinct circles are tangent to each other if they touch in exactly one point. You posted a diagram two posts above of two circles that do not touch anywhere, but which share a tangent line. Those circles are not tangent circles. The concept of tangency has nothing to do with whether things 'line up horizontally', so if the diagrams you've seen have displayed tangent circles with centers along a horizontal line, that's likely only because it's easier to draw diagrams that way.

SamBoyle wrote:

I guess no one is going to answer because obviously the GMAT makes up their definition of tangent circles.


All of the math on the GMAT is the same as the math you'd learn anywhere else, so there is no math on the test that the GMAT "makes up".


You just made a bald face lie or are perhaps blind if you think my circles aren't touching.

I figured out my answer. The way I drew the diagram my answer is correct. However you can draw the radius to the center of the circle anyway you want. So I could have drawn it by a shorter route. Hence my distance is correct but not the shortest possible distance
Attachments

debate.png
debate.png [ 11.25 KiB | Viewed 5753 times ]

Manager
Manager
avatar
B
Joined: 31 Dec 2016
Posts: 73
Two Tangent circles A and B have radii r1 and r2, respectively. What  [#permalink]

Show Tags

New post 08 Aug 2017, 08:27
Engr2012 wrote:
SamBoyle wrote:

I agree with what IanStewart has mentioned above. Additionally, there is no need to discuss this further as GMAT or any math book will define tangency as 1 point of contact. But do understand that GMAT is a timed exam and hence, you should stop working on a DS question as soon as you find 2 contradictory scenarios; you are not getting extra points for coming with 100 different scenarios to answer the same set of DS statements. Additionally, it is easier to visualize 'horizontal scenarios' out of many scenarios that negate the statements mentioned in this DS question. Not seeing something on the internet does not mean GMAT 'makes up' math concepts.

Hope this helps.


No that does the opposite of helping anyone and is the worst possible advice. That response makes very little sense. You think on the test, I would come up with 100 different scenarios on a single question. or do you think it's important to understand how tangency works before the test? Very unproductive advice.

We are here to learn. Learning and knowledge leads to speed. Speed without knowledge is pointless. It would just be guessing
GMAT Tutor
avatar
S
Joined: 24 Jun 2008
Posts: 1350
Re: Two Tangent circles A and B have radii r1 and r2, respectively. What  [#permalink]

Show Tags

New post 08 Aug 2017, 10:15
2
SamBoyle wrote:
You just made a bald face lie or are perhaps blind if you think my circles aren't touching.

I figured out my answer. The way I drew the diagram my answer is correct. However you can draw the radius to the center of the circle anyway you want. So I could have drawn it by a shorter route. Hence my distance is correct but not the shortest possible distance


You drew a diagram of one circle with radius 5, and one circle with radius 3, where the distance between the centers of the two circles was √68. It is mathematically impossible for those two circles to touch; they're too far apart. If you diagram that situation, and in your diagram the circles appear to touch, then you've drawn the diagram incorrectly.

The rest of your reply is not correct, because you are not using the correct definition of the word "distance". Absent any qualifications, the "distance" between two points is always the straight line distance between them, which is the shortest possible distance. Your distance cannot be correct and not be the shortest possible distance.

If you continue to reply to people the way you have here, I think you'll discover that eventually other members will become disinclined to try to help you.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Intern
Intern
avatar
Joined: 17 Jul 2017
Posts: 15
Two Tangent circles A and B have radii r1 and r2, respectively. What  [#permalink]

Show Tags

New post 09 Aug 2017, 07:58
IanStewart wrote:
SamBoyle wrote:
You just made a bald face lie or are perhaps blind if you think my circles aren't touching.

I figured out my answer. The way I drew the diagram my answer is correct. However you can draw the radius to the center of the circle anyway you want. So I could have drawn it by a shorter route. Hence my distance is correct but not the shortest possible distance


You drew a diagram of one circle with radius 5, and one circle with radius 3, where the distance between the centers of the two circles was √68. It is mathematically impossible for those two circles to touch; they're too far apart. If you diagram that situation, and in your diagram the circles appear to touch, then you've drawn the diagram incorrectly.

The rest of your reply is not correct, because you are not using the correct definition of the word "distance". Absent any qualifications, the "distance" between two points is always the straight line distance between them, which is the shortest possible distance. Your distance cannot be correct and not be the shortest possible distance.

If you continue to reply to people the way you have here, I think you'll discover that eventually other members will become disinclined to try to help you.


Thanks, ironically the best response I have gotten here though I don't ask many questions. I mostly just provide solutions to help other people out--I find the solutions here are often lacking--and assume you know things like external angle theorem and just list it and don't explain how it works. That's fine but I try to explain things like that when I solve. I do like to understand the nuances of the problem, so that I can get another different question more easily
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2629
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Re: Two Tangent circles A and B have radii r1 and r2, respectively. What  [#permalink]

Show Tags

New post 09 Aug 2017, 08:20
Samuelboyle96 wrote:
IanStewart wrote:
SamBoyle wrote:
You just made a bald face lie or are perhaps blind if you think my circles aren't touching.

I figured out my answer. The way I drew the diagram my answer is correct. However you can draw the radius to the center of the circle anyway you want. So I could have drawn it by a shorter route. Hence my distance is correct but not the shortest possible distance


You drew a diagram of one circle with radius 5, and one circle with radius 3, where the distance between the centers of the two circles was √68. It is mathematically impossible for those two circles to touch; they're too far apart. If you diagram that situation, and in your diagram the circles appear to touch, then you've drawn the diagram incorrectly.

The rest of your reply is not correct, because you are not using the correct definition of the word "distance". Absent any qualifications, the "distance" between two points is always the straight line distance between them, which is the shortest possible distance. Your distance cannot be correct and not be the shortest possible distance.

If you continue to reply to people the way you have here, I think you'll discover that eventually other members will become disinclined to try to help you.


Thanks, ironically the best response I have gotten here though I don't ask many questions. I mostly just provide solutions to help other people out--I find the solutions here are often lacking--and assume you know things like external angle theorem and just list it and don't explain how it works. That's fine but I try to explain things like that when I solve. I do like to understand the nuances of the problem, so that I can get another different question more easily


You cant expect answers complete in 'all' respects as there are n different things that need to be captured every single time. Experts on this forum are more than happy to answer your questions but only if you ask them properly. If you have an issue with some explanation; dont be condescending to the OP but add to the discussion by asking "hey you know what, I think you are assuming that people would know xyz. So, if you could explain how you came about determining the angle measure, that would be great". If you ask a question in this manner, there will be tons of experts who would be more than happy to help you out.

Another aspect to covering all possible concepts is that some questions are already at a slightly higher level of usual comprehension, e.g. probability questions with multiple issues to keep a track of. So without the OP mentioning what he has/has not done; no one would know where to start with their explanation and everyone will take the path of least resistance and mention the solution directly.

If you dont ask 'many questions', good for you. Either you know your concepts or are too afraid to get answers by posting your queries online.

TL;DR: there is a proper way of engaging in these forums. Stick to that method and there will be a lot of people willing to help you out. Stay humble and eager to learn.
Intern
Intern
avatar
Joined: 17 Jul 2017
Posts: 15
Two Tangent circles A and B have radii r1 and r2, respectively. What  [#permalink]

Show Tags

New post 09 Aug 2017, 11:50
Engr2012 wrote:

You cant expect answers complete in 'all' respects as there are n different things that need to be captured every single time. Experts on this forum are more than happy to answer your questions but only if you ask them properly. If you have an issue with some explanation; dont be condescending to the OP but add to the discussion by asking "hey you know what, I think you are assuming that people would know xyz. So, if you could explain how you came about determining the angle measure, that would be great". If you ask a question in this manner, there will be tons of experts who would be more than happy to help you out.

Another aspect to covering all possible concepts is that some questions are already at a slightly higher level of usual comprehension, e.g. probability questions with multiple issues to keep a track of. So without the OP mentioning what he has/has not done; no one would know where to start with their explanation and everyone will take the path of least resistance and mention the solution directly.

If you dont ask 'many questions', good for you. Either you know your concepts or are too afraid to get answers by posting your queries online.

TL;DR: there is a proper way of engaging in these forums. Stick to that method and there will be a lot of people willing to help you out. Stay humble and eager to learn.



I think, I did highlight a very important concept. That circle can be tangent and not be touching horizontally. My point is while this seems so obvious to me now but I couldn't find anything on the internet showing 2 tangent circles and distance. Everyone else calculated 2 tangent circles on a line and the distance between.

I think my exploration of the concept should help more people better picture why the distance between 2 tangent circles on the outside is just their radius.
Attachments

radius tangent circles.png
radius tangent circles.png [ 92.21 KiB | Viewed 5554 times ]

CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2629
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Two Tangent circles A and B have radii r1 and r2, respectively. What  [#permalink]

Show Tags

New post 09 Aug 2017, 12:08
Samuelboyle96 wrote:
I think, I did highlight a very important concept. That circle can be tangent and not be touching horizontally. My point is while this seems so obvious to me now but I couldn't find anything on the internet showing 2 tangent circles and distance. Everyone else calculated 2 tangent circles on a line and the distance between.

I think my exploration of the concept should help more people better picture why the distance between 2 tangent circles on the outside is just their radius.


You raise a very small but important concept for complete understanding of when multiple circles that are tangent to each other or touch each other at 1 and only 1 point. I understood your question the first time around and so did IanStewart .

For the sake of this question and for similar questions:

r1, r2 = radii of the 2 circles; where r2 > r1

For 2 circles touching each other:
a) If tangency is on the outside: distance between the centers = r1 + r2
b) If tangency is on the inside: distance between the centers = r2-r1

This relatively straightforward concept has much broader application:

a) If you are given that distance between the centers of any 2 circles = r1+r2 --> Circles are tangent on the outside.
b) If you are given that distance between the centers of any 2 circles = r2-r1 --> Circles are tangent on the inside.
c) If you are given that distance between the centers of any 2 circles > r2+r1 --> Circles are such that one is NOT inside the other and that they are NOT touching each other.
d) If you are given that distance between the centers of any 2 circles < r2+r1 --> Circles are intersect each other at 2 points
e) If you are given that distance between the centers of any 2 circles < r2-r1 --> One circle is inside the other and not touching.

Again, think about these intuitively instead of memorizing these observations. Important point is that these 'observations' have been derived from your understanding of how the distance between the centers of 2 circle varies with certain combinations of respective radii.

Finally, to your point of tangent circles might not be horizontal, that is a completely correct statement. It just so happens that there can be infinite points of tangency between 2 circles and if I give you a choice of showing this tangency, you will always/instinctly choose the horizontal scenario as it is more straightforward to visualize.

Hope this helps.
Intern
Intern
avatar
Joined: 17 Jul 2017
Posts: 15
Re: Two Tangent circles A and B have radii r1 and r2, respectively. What  [#permalink]

Show Tags

New post 09 Aug 2017, 13:19
Engr2012 wrote:
Samuelboyle96 wrote:
I think, I did highlight a very important concept. That circle can be tangent and not be touching horizontally. My point is while this seems so obvious to me now but I couldn't find anything on the internet showing 2 tangent circles and distance. Everyone else calculated 2 tangent circles on a line and the distance between.

I think my exploration of the concept should help more people better picture why the distance between 2 tangent circles on the outside is just their radius.


You raise a very small but important concept for complete understanding of when multiple circles that are tangent to each other or touch each other at 1 and only 1 point. I understood your question the first time around and so did IanStewart .

For the sake of this question and for similar questions:

r1, r2 = radii of the 2 circles; where r2 > r1

For 2 circles touching each other:
a) If tangency is on the outside: distance between the centers = r1 + r2
b) If tangency is on the inside: distance between the centers = r2-r1

This relatively straightforward concept has much broader application:

a) If you are given that distance between the centers of any 2 circles = r1+r2 --> Circles are tangent on the outside.
b) If you are given that distance between the centers of any 2 circles = r2-r1 --> Circles are tangent on the inside.
c) If you are given that distance between the centers of any 2 circles > r2+r1 --> Circles are such that one is NOT inside the other and that they are NOT touching each other.
d) If you are given that distance between the centers of any 2 circles < r2+r1 --> Circles are intersect each other at 2 points
e) If you are given that distance between the centers of any 2 circles < r2-r1 --> One circle is inside the other and not touching.

Again, think about these intuitively instead of memorizing these observations. Important point is that these 'observations' have been derived from your understanding of how the distance between the centers of 2 circle varies with certain combinations of respective radii.

Finally, to your point of tangent circles might not be horizontal, that is a completely correct statement. It just so happens that there can be infinite points of tangency between 2 circles and if I give you a choice of showing this tangency, you will always/instinctly choose the horizontal scenario as it is more straightforward to visualize.

Hope this helps.


Sure thanks. The reason, I like to show one other example besides horizontal is to show that this isn't something special which occurred because the lines were 100% horizontal it's something true in 100% of scenarios. So I usually like to show a couple of examples. One the obvious one and another the less obvious way.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9894
Premium Member
Re: Two Tangent circles A and B have radii r1 and r2, respectively. What  [#permalink]

Show Tags

New post 19 Jan 2019, 03:49
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: Two Tangent circles A and B have radii r1 and r2, respectively. What   [#permalink] 19 Jan 2019, 03:49
Display posts from previous: Sort by

Two Tangent circles A and B have radii r1 and r2, respectively. What

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.