BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Another one with circles , distance , radii

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Senior | Next Rank: 100 Posts
Posts: 67
Joined: Thu Jul 17, 2014 11:04 am
Thanked: 3 times
Followed by:2 members

Another one with circles , distance , radii

by sapuna » Sun Aug 03, 2014 12:43 am
Three circles with radii 1, 2 , 3, respectively, lie on the same plane. Do any of these circles intersect or lie completely within each other ?

1) IF you connect the centers of the circles, an equaliteral triangle is formed with a height of 2 square root of 3.

2) The distance between any two centers is less than 6.

Now, sorry for asking this, I thought I got the last question you guys explained and here I am again :D From statement 1 we can find the side of the trianagle. What does this give us ?
Top
Source: — Data Sufficiency |
User avatar
Legendary Member
Posts: 1100
Joined: Sat May 10, 2014 11:34 pm
Location: New Delhi, India
Thanked: 205 times
Followed by:24 members

by GMATinsight » Sun Aug 03, 2014 1:15 am
sapuna wrote:Three circles with radii 1, 2 , 3, respectively, lie on the same plane. Do any of these circles intersect or lie completely within each other ?

1) IF you connect the centers of the circles, an equaliteral triangle is formed with a height of 2 square root of 3.

2) The distance between any two centers is less than 6.

Now, sorry for asking this, I thought I got the last question you guys explained and here I am again :D From statement 1 we can find the side of the trianagle. What does this give us ?
Question : Three circles with radii 1, 2 , 3, respectively, lie on the same plane. Do any of these circles intersect or lie completely within each other ?

Statement 1) IF you connect the centers of the circles, an equaliteral triangle is formed with a height of 2 square root of 3.

Since (Sqrt3)xSide/2 = Height of Equilateral Triangle

therefore, (Sqrt3)xSide/2 = 2(Sqrt3)

i.e. Side of equilateral Triangle = 4

From Statement 1 we know that side of the Equilateral triangle is 4
Side of Traingle 4 (Distance between centers) is possible only when two Circles with radii 3 and 1 are Tangant

As well as when two Circles with radii 3 and 2 are intersecting at two points
SUFFICIENT

Statement 2) The distance between any two centers is less than 6.
INSUFFICIENT

Answer: Option A
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Top
User avatar
Senior | Next Rank: 100 Posts
Posts: 67
Joined: Thu Jul 17, 2014 11:04 am
Thanked: 3 times
Followed by:2 members

by sapuna » Sun Aug 03, 2014 1:58 am
Ah , you misunderstood what I was asking I think. I already knew the side of the triangle was 4. I was asking why is this true :

Side of Traingle 4 (Distance between centers) is possible only when two Circles with radii 3 and 1 are Tangant

As well as when two Circles with radii 3 and 2 are intersecting at two points
SUFFICIENT

Statement 2) The distance between any two centers is less than 6 - in the answers I have it`s said that the distance has to be less than 5 for the statement to hold
Top
User avatar
Legendary Member
Posts: 1100
Joined: Sat May 10, 2014 11:34 pm
Location: New Delhi, India
Thanked: 205 times
Followed by:24 members

by GMATinsight » Sun Aug 03, 2014 3:26 am
sapuna wrote:Ah , you misunderstood what I was asking I think. I already knew the side of the triangle was 4. I was asking why is this true :

Side of Traingle 4 (Distance between centers) is possible only when two Circles with radii 3 and 1 are Tangant

As well as when two Circles with radii 3 and 2 are intersecting at two points
SUFFICIENT

Statement 2) The distance between any two centers is less than 6 - in the answers I have it`s said that the distance has to be less than 5 for the statement to hold
We have to check this first

R1 + R2 = 1+2 = 3
R2 + R3 = 2+3 = 5
R1 + R3 = 1+3 = 4

i.e. If Circles with R1 and R2 touch each other at just 1 point (i.e. they are Tangent) then the distance between their centers will be 3 units

i.e. the increase in distance between their centers will cause them to go away and they will not touch.

For two circles to intersect (or move completely in the other circles) the distance between their centers must lesser than or equal to Sum of their Radii
Distance between centers < R1+R2 [The figure is as attached]

Since the maximum sum of radii of any two circles out of given is 5 therefore if the equilateral triangle is drawn by joining their centers then the three will NOT intersect only if the length of the side of Equilateral Triangle is greater than 5 units
Attachments
Solution 48.jpg
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sun Aug 03, 2014 3:41 am
sapuna wrote:Three circles with radii 1, 2 , 3, respectively, lie on the same plane. Do any of these circles intersect or lie completely within each other ?

1) IF you connect the centers of the circles, an equaliteral triangle is formed with a height of 2 square root of 3.

2) The distance between any two centers is less than 6.
Figure 1:
Image
In the figure above, x, y and z represent the distances between circles A, B and C.
∆ABC is formed by joining the 3 centers.

Statement 1: If you connect the centers of the circles, an equaliteral triangle is formed with a height of 2 square root of 3.
Figure 2:
Image
Thus, each side of ∆ABC = 4.
In figure 1, BC=4 only if z<0, implying that circles B and C intersect.
SUFFICIENT.

Statement 2: The distance between any two centers is less than 6.
It's possible that x=y=z=0, in which all 3 circles intersect.
It's possible that x=y=z=1/2, in which case none of the circles intersect.
INSUFFICIENT.

The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Post new topic Post Reply
• Page 1 of 1