GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 18 Jan 2020, 16:27 ### 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

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.  # A circle in a coordinate plane has a center at point A and a diameter

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 60480
A circle in a coordinate plane has a center at point A and a diameter  [#permalink]

### Show Tags 00:00

Difficulty:   35% (medium)

Question Stats: 73% (01:21) correct 27% (01:24) wrong based on 119 sessions

### HideShow timer Statistics

A circle in a coordinate plane has a center at point A and a diameter of 6. If points B and C also lie in the same coordinate plane, is point B inside the circle?

(1) The distance between point A and point C equals 2.
(2) The distance between point B and point C equals 2.

Kudos for a correct solution.

_________________
CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2981
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: A circle in a coordinate plane has a center at point A and a diameter  [#permalink]

### Show Tags

1
Bunuel wrote:
A circle in a coordinate plane has a center at point A and a diameter of 6. If points B and C also lie in the same coordinate plane, is point B inside the circle?

(1) The distance between point A and point C equals 2.
(2) The distance between point B and point C equals 2.

Kudos for a correct solution.

Question : Is point B inside the circle?

Diameter = 6

CONCEPT: Point B will be inside the circle if The distance AB is less than Radius

Statement 1: The distance between point A and point C equals 2.

i.e. AC= 2

i.e. Point C is in the Circle but the relation of Point C with Point B is still unknown

Hence, NOT SUFFICIENT

Statement 2: The distance between point B and point C equals 2.

But the relation of Point C or Point B with Point A is still unknown

Hence, NOT SUFFICIENT

Combining the two statement

AC = 2 and BC =2 i.e. Distance AB can vary from 0 to 4

Hence, NOT SUFFICIENT

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Math Expert V
Joined: 02 Aug 2009
Posts: 8341
Re: A circle in a coordinate plane has a center at point A and a diameter  [#permalink]

### Show Tags

2
Bunuel wrote:
A circle in a coordinate plane has a center at point A and a diameter of 6. If points B and C also lie in the same coordinate plane, is point B inside the circle?

(1) The distance between point A and point C equals 2.
(2) The distance between point B and point C equals 2.

Kudos for a correct solution.

We have a circle of radius 3 here..
1) statement one tells us the distance of C from A and that A is in circle but nothing about B.. insuff
2) statement one tells us the distance of C from B but nothing about the circle.. insuff

Combined it gives us distance between A and C and also between B and C..
but we can still not say anything about relation of A and B as B could lie on any side of C , basically on any circumference of a circle with center C and radius 2..
insuff
_________________ Joined: 24 Oct 2012
Posts: 163
Re: A circle in a coordinate plane has a center at point A and a diameter  [#permalink]

### Show Tags

1
Bunuel wrote:
A circle in a coordinate plane has a center at point A and a diameter of 6. If points B and C also lie in the same coordinate plane, is point B inside the circle?

(1) The distance between point A and point C equals 2.
(2) The distance between point B and point C equals 2.

Kudos for a correct solution.

My attempt :

Radius of circle is 3. A is center of circle. So any point which is at distance less than 3 will be inside circle. So basically to answer the question " is point B inside the circle?" We must know what is distance between A (center of circle) and point B.

Statement 1 :
It gives distance between A and C, not distance between A and B. Hence not sufficient.

Statement 2 :
It gives distance between B and C, not distance between A and B. Hence not sufficient.

Statement 1 and 2 combine.
d(A,C) = 2
d(B,C) = 2

point B can be anywhere in the Co-ordinate plane and hence we will not know if B is inside circle.

Say for example.
B is same line, and C is between A and B, then d(A,B) = 4 and B will lie outside of circle

B is in same line and A and B coincides. B lie inside the circle.

Hence Option E
Manager  Joined: 18 Mar 2014
Posts: 226
Location: India
Concentration: Operations, Strategy
GMAT 1: 670 Q48 V35
GPA: 3.19
WE: Information Technology (Computer Software)
Re: A circle in a coordinate plane has a center at point A and a diameter  [#permalink]

### Show Tags

1
using statement 1 alone , we can see C is inside circle . but no info about B ------ insufficient

Using statement 2 alone , no info about any of B and C location with respect to centre A ------ insufficient

Combining both ,
points can be on radius .. as A-C-B in this case B goes outside circle
or Point A and C on radious and B can be anywhere inside circle at distance of 2 from C.

So even now we can not find B's position uniquely.

Math Expert V
Joined: 02 Sep 2009
Posts: 60480
Re: A circle in a coordinate plane has a center at point A and a diameter  [#permalink]

### Show Tags

Bunuel wrote:
A circle in a coordinate plane has a center at point A and a diameter of 6. If points B and C also lie in the same coordinate plane, is point B inside the circle?

(1) The distance between point A and point C equals 2.
(2) The distance between point B and point C equals 2.

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

Is B inside the circle? Using Rubber Band Geometry concepts, we know from the problem that the exact locations of points A, B, and C do not matter—only the relative locations of the points matter. Therefore, we can arbitrarily assign point A to a specific location (in this case, we should choose the origin of the coordinate plane), and draw a circle with a radius of 3 units around it.

(1) The distance between A and C is 2. Statement (1) does not tell us anything about point B, so it is not sufficient. However, it does tell us that A and C are 2 units apart, so Statement (1) enables us to place point C anywhere along the grey circle.

(1) The distance between B and C is 2. Statement (2) does not tell us anything about point B relative to point A, so it is not sufficient. However, it does constrain point B to be exactly 2 units away from wherever point C is. Thus we can imagine point C at the center of a circle of size 2, with point B somewhere on the circle around it.

(1) and (2) combined Finally, we can combine these two statements to see that depending upon where we draw point C, and then draw point B relative to point C, point B may be inside the dotted circle, and it may not be.

Notice that we never proved the insufficiency of Statements (1) and (2) combined using algebra or any computation—but then again we didn't need to! Rather, we deduced it by drawing the information that was given to us. We reasoned visually that under the constraints, we could draw a scenario in which point B was inside the circle. We could also draw another scenario in which point B was outside of the circle. Done! We achieved a visual proof of the answer.

That's what Rubber Band Geometry is all about: testing scenarios for Geometry problems without the need to plug in numbers or use algebra. All we need is a visual environment that can be manipulated—one that preserves all key constraints and freedoms in the problem, and allows us to see them and test them. Rubber Band Geometry provides that environment for us.

Attachment: 2015-06-22_1601.png [ 34.08 KiB | Viewed 1863 times ]

Attachment: 2015-06-22_1604.png [ 38.73 KiB | Viewed 1861 times ]

Attachment: 2015-06-22_1605.png [ 32.61 KiB | Viewed 1858 times ]

Attachment: 2015-06-22_1607.png [ 42.89 KiB | Viewed 1858 times ]

_________________
Board of Directors P
Joined: 17 Jul 2014
Posts: 2483
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30 GPA: 3.92
WE: General Management (Transportation)
Re: A circle in a coordinate plane has a center at point A and a diameter  [#permalink]

### Show Tags

Bunuel wrote:
A circle in a coordinate plane has a center at point A and a diameter of 6. If points B and C also lie in the same coordinate plane, is point B inside the circle?

(1) The distance between point A and point C equals 2.
(2) The distance between point B and point C equals 2.

Kudos for a correct solution.

2. nothing about the relationship between these two points and the origin (point A).

1+2.
B can be inside or B can be outside.

E
Non-Human User Joined: 09 Sep 2013
Posts: 13978
Re: A circle in a coordinate plane has a center at point A and a diameter  [#permalink]

### Show Tags

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.
_________________ Re: A circle in a coordinate plane has a center at point A and a diameter   [#permalink] 10 Dec 2019, 23:46
Display posts from previous: Sort by

# A circle in a coordinate plane has a center at point A and a diameter  