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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: Maximum value of the radius [#permalink]
11 Nov 2009, 14:08

Bunuel wrote:

In the rectangular coordinate system, points (4, 0) and (– 4, 0) both lie on circle C. What is the maximum possible value of the radius of C ?

(A) 2 (B) 4 (C) 8 (D) 16 (E) None of the above

I'm getting E

It can be B, but the points mentioned can be a chord and that would make the radius larger. I'm getting other calculations but none are available or can't be determined.

Re: Maximum value of the radius [#permalink]
11 Nov 2009, 15:04

4

This post received KUDOS

1

This post was BOOKMARKED

The answer is E.

It takes 3 distinct points to define a circle. Only 2 are given here.

The two points essentially identify a single chord of the circle C. Since no other information is provided, however, the radius of the circle can essentially be anything. All this information tell us is that the radius is greater than 4. It does not give us an upper limit.

Re: Maximum value of the radius [#permalink]
11 Nov 2009, 16:48

Agree with E.

Another way to look at it is that the two points, lets call them A and B, are equidistant to the centre of the circle, lets call that O. i.e. OA = OB Hence the centre will lie on the Y axis (anywhere where x = 0). So not enough information to determine.

Yet another way to look at it is: Radius^2 = (Difference of X of O to A)^2 + (Difference of Y of O to A)^2 From the question stem we know that A is (4,0). Using the above logic we also know that the centre lies on x=0. Using B would yield the same result as we are after distance it will always end up being positive anyway. This formula reduces to (4-0)^2 + (y-0)^2 = R^2 Depending on the value of y, the length of the radius will keep growing.

Re: Maximum value of the radius [#permalink]
12 Nov 2009, 08:00

1

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

The OA is E.

The only thing we can conclude from the question that center lies on the Y-axis. But it could be ANY point on it, hence we can not determine maximum value of r. _________________

Re: Maximum value of the radius [#permalink]
19 Sep 2010, 00:43

The question is more like a DS question. Rephrase it and you will get "If two points given are enough to define the maximum possible radius of the circle?" The answer is no, cause the radius could be as low as 4 if the points are at the maximum distance from the center and the line between them is the diameter or the radius could be infinitely large if the line between the points is the chord.

Re: Maximum value of the radius [#permalink]
29 Nov 2010, 01:06

Bunuel wrote:

The OA is E.

The only thing we can conclude from the question that center lies on the Y-axis. But it could be ANY point on it, hence we can not determine maximum value of r.

Can we also conclude that the points (4,0) and (-4,0) lie in first and 2nd quadrant so with that we cannot calculate the distance between two points ( which will be radius of circle ) ; because in order to calculate distance we need points in opposite direction. So if the points were in Ist and 3rd quadrant we could have calculated the distance

Re: Maximum value of the radius [#permalink]
29 Nov 2010, 01:22

Expert's post

rite2deepti wrote:

Bunuel wrote:

The OA is E.

The only thing we can conclude from the question that center lies on the Y-axis. But it could be ANY point on it, hence we can not determine maximum value of r.

Can we also conclude that the points (4,0) and (-4,0) lie in first and 2nd quadrant so with that we cannot calculate the distance between two points ( which will be radius of circle ) ; because in order to calculate distance we need points in opposite direction. So if the points were in Ist and 3rd quadrant we could have calculated the distance

I think you are a little bit confused here.

You CAN calculate the distance between any two points with given coordinates on a plane (no matter in which quadrants they are). For example the distance between two points (4,0) and (-4,0) is simply 8.

Generally the formula to calculate the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\).

Next, the distance between (4,0) and (-4,0) won't necessarily be the DIAMETER of a circle. The minimum length of a diameter is indeed 8 (so min r=4) but as ANY point on the y-axis will be equidistant from the given points then any point on it can be the center of the circle thus the maximum length of the radius is not limited at all.

Re: Maximum value of the radius [#permalink]
06 Jan 2011, 15:33

if we join the line connecting the the points (-4,0) and (4,0) to the center of the circle say (0,y), radius will be maximum at the point where the area formed by the above triangle is min. The area will be 0 if the height is 0, which means the center is in the line connecting two pnts (-4,0) and (4,0). Isn't?

Re: Maximum value of the radius [#permalink]
06 Jan 2011, 17:17

Expert's post

praveenvino wrote:

if we join the line connecting the the points (-4,0) and (4,0) to the center of the circle say (0,y), radius will be maximum at the point where the area formed by the above triangle is min. The area will be 0 if the height is 0, which means the center is in the line connecting two pnts (-4,0) and (4,0). Isn't?

The red part is not correct.

Again: The minimum length of a diameter is indeed 8 (so min r=4) but as ANY point on the y-axis will be equidistant from the given points then any point on it can be the center of the circle thus the maximum length of the radius is not limited at all.

Check 2 possible circles: Circle with min radius of 4 (equation x^2+y^2=4^2):

Attachment:

radius 4.gif [ 3.22 KiB | Viewed 9632 times ]

Circle with radius of 5 (equation x^2+(y-3)^2=5^2):

Attachment:

radius 5.gif [ 2.78 KiB | Viewed 9631 times ]

Generally circle passing through the points (4, 0) and (– 4, 0) will have an equation \(x^2+(y-a)^2=4^2+a^2\) and will have a radius of \(r=\sqrt{4^2+a^2}\). As you can see min radius will be for \(a=0\), so \(r_{min}=4\) and max radius is not limited at all (as \(a\) can go to +infinity as well to -infinity).

Re: Maximum value of the radius [#permalink]
26 Apr 2011, 23:42

[quote="Mongolia2HBS"]Only 2 points are given, so E.[/quo

suppose the question says that what is the maximum possible radius of the among the given choices then we can try out the highest choices and foind out whether the the given choice satisfies the pythagoras eqn. so that way D is best.

The only thing we know is that Points A(4,0) and B(-4,0) are on circumference. But that does not necessarily mean that they are opposite ends of diameter.

If they are opposite ends of diameter, Radius will be 4, but if they are opposite ends of circle's smallest chord then Radius would be far more greater then the values mentioned in Options. Hence Choice E is correct. _________________

The Brand New 2015 GMAT Club MBA Application Guide is Out!

Re: Maximum value of the radius [#permalink]
25 Oct 2013, 07:45

Bunuel wrote:

rite2deepti wrote:

Bunuel wrote:

The OA is E.

The only thing we can conclude from the question that center lies on the Y-axis. But it could be ANY point on it, hence we can not determine maximum value of r.

Can we also conclude that the points (4,0) and (-4,0) lie in first and 2nd quadrant so with that we cannot calculate the distance between two points ( which will be radius of circle ) ; because in order to calculate distance we need points in opposite direction. So if the points were in Ist and 3rd quadrant we could have calculated the distance

I think you are a little bit confused here.

You CAN calculate the distance between any two points with given coordinates on a plane (no matter in which quadrants they are). For example the distance between two points (4,0) and (-4,0) is simply 8.

Generally the formula to calculate the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\).

Next, the distance between (4,0) and (-4,0) won't necessarily be the DIAMETER of a circle. The minimum length of a diameter is indeed 8 (so min r=4) but as ANY point on the y-axis will be equidistant from the given points then any point on it can be the center of the circle thus the maximum length of the radius is not limited at all.

Can you please explain on what basis it is concluded that centre lies on Y axis. Secondly which part in Gmat math book the concept is given, I have gone through the book but I didn't find it. Third can you please explain what is the concept which clarifies minimum point to make a circle & maximum radius concept. Please Help

Re: Maximum value of the radius [#permalink]
25 Oct 2013, 07:54

Expert's post

anu1706 wrote:

Bunuel wrote:

rite2deepti wrote:

Can we also conclude that the points (4,0) and (-4,0) lie in first and 2nd quadrant so with that we cannot calculate the distance between two points ( which will be radius of circle ) ; because in order to calculate distance we need points in opposite direction. So if the points were in Ist and 3rd quadrant we could have calculated the distance

I think you are a little bit confused here.

You CAN calculate the distance between any two points with given coordinates on a plane (no matter in which quadrants they are). For example the distance between two points (4,0) and (-4,0) is simply 8.

Generally the formula to calculate the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\).

Next, the distance between (4,0) and (-4,0) won't necessarily be the DIAMETER of a circle. The minimum length of a diameter is indeed 8 (so min r=4) but as ANY point on the y-axis will be equidistant from the given points then any point on it can be the center of the circle thus the maximum length of the radius is not limited at all.

Can you please explain on what basis it is concluded that centre lies on Y axis. Secondly which part in Gmat math book the concept is given, I have gone through the book but I didn't find it. Third can you please explain what is the concept which clarifies minimum point to make a circle & maximum radius concept. Please Help

Re: In the rectangular coordinate system, points (4, 0) and [#permalink]
23 Feb 2015, 11:18

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. _________________

Low GPA MBA Acceptance Rate Analysis Many applicants worry about applying to business school if they have a low GPA. I analyzed the low GPA MBA acceptance rate at...

In out-of-the-way places of the heart, Where your thoughts never think to wander, This beginning has been quietly forming, Waiting until you were ready to emerge. For a long...