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by jainrahul1985 » Mon Dec 05, 2011 9:23 am
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) There is no finite maximum value
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by VivianKerr » Mon Dec 05, 2011 9:31 am
We have no idea WHERE on the circle these points lie. They could be across from each other, and thus the distance between them could be the diameter, or they could be very close to each other on the outside of the circle, in which case the radius could be much larger.

The answer is E.
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by Anurag@Gurome » Mon Dec 05, 2011 8:25 pm
jainrahul1985 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) There is no finite maximum value
The distance between two given points (4, 0) and (-4, 0) is √(4 + 4)² = 8, but it is not necessary that it will be the diameter of the circle.
The minimum length of the diameter is 8, which means minimum value of radius = 4, but if 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 fixed, it can vary.

The correct answer is E.
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by gunjan1208 » Mon Dec 05, 2011 10:39 pm
Shouldn't ans be 4 as Question is asking for maximumh
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by Anurag@Gurome » Mon Dec 05, 2011 10:40 pm
gunjan1208 wrote:Shouldn't ans be 4 as Question is asking for maximumh
But 4 is the minimum value of radius.
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by gunjan1208 » Mon Dec 05, 2011 11:39 pm
Hi Anurag,

I am bold on this one. Actaully 4 is what we can have; Either minimum or maximum. Am I right or missing something? What do you understand by maximum here. Please elaborate.

Thank you in advance.
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by Anurag@Gurome » Tue Dec 06, 2011 12:05 am
gunjan1208 wrote:Hi Anurag,

I am bold on this one. Actaully 4 is what we can have; Either minimum or maximum. Am I right or missing something? What do you understand by maximum here. Please elaborate.

Thank you in advance.
The trap in this question is to assume that (4, 0) and (-4, 0) are the coordinates of the diameter of the circle. But it is not so, they can be the end points of a chord also. Any point equidistant from both the points can be the center of the circle, so there can be infinite points.
Last edited by Anurag@Gurome on Tue Dec 06, 2011 12:13 am, edited 1 time in total.
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by gunjan1208 » Tue Dec 06, 2011 12:08 am
Oh, I see this now. Thanks a lot.

Regards
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by Anurag@Gurome » Tue Dec 06, 2011 12:13 am
gunjan1208 wrote:Oh, I see this now. Thanks a lot.

Regards
You are welcome.
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by lunarpower » Sat Dec 10, 2011 6:09 am
here's a picture that shows two possibilities. the small circle has diameter 8; that's the SMALLEST (not the biggest!) circle that can contain the two specified points.
the bigger circle -- which is so big that you can only see a small arc of it -- has a diameter much, much greater than 8. looking at this circle, you should be able to tell that you can make the circle as big as you want.

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