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# A circle passes thru the coordinates (4,0) (-4,0). What is

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A circle passes thru the coordinates (4,0) (-4,0). What is [#permalink]

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23 Nov 2004, 13:19
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A circle passes thru the coordinates (4,0) (-4,0). What is the biggest possible radius?

A) 2
B) 4
C) 6
D) 8
E) infinite
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23 Nov 2004, 13:32
B) 4

if it is a true circle and passes through both of those points (which form a line with length of 8)- then diameter would be 8, therefore radius of 4
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23 Nov 2004, 14:19
I pick E too

You will always find a bigger circle with required conditions (the 2 points in the stem are not on the diameter as Dookie emphasized...)
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23 Nov 2004, 14:27
indeed. E it is. could simply be the top or the bottom of a circle... grrr
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24 Nov 2004, 01:04
Thanks guys. I thot it's E too but the OA is D, 8. Can't figure why...
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24 Nov 2004, 03:20
I thought it was (E) too.

Would be great if you could jot down the explaination for it to be 8

Thanks.
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24 Nov 2004, 13:42
Biggest possible radius is only possible if its the diameter that is passing through the two points. Try and think about it. Since the co=ordinates of the two points are given, we cant have "infinite" number of largest radius.

Im getting the diameter as8, hence radius as 4. But I dont think this question is good, because the diameter is the "largest chord". There is nothing like the "largest radius". A circle can have only a single length for its radius.
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Let's get it right!!!!

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25 Nov 2004, 16:51
I think the ans would be E.
Consider the line joining the 2 points (part of X axis in this case) as a very small chord of a circle which has radius equal to say 50.
Then such a circle can be drawn with coordinates of center as (0, sqrt(2500-16)).
Hence the ans is infiite, because we can chose any value for the radius (in place of 50 above).

Also, its a known genoetric truth that infinite no. of circles can be drawn through any 2 points but only one circle can be drawn through 3 given points.

Maybe theres a typo n the original question.
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25 Nov 2004, 17:46
ruhi160184 wrote:
Biggest possible radius is only possible if its the diameter that is passing through the two points.

No. Smallest possible radius is only possible if it is the diameter that is passing through the two points. If the two specified points are on anything but the diameter, the radius will be larger.

E
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26 Nov 2004, 02:06
mbahope wrote:
I think the ans would be E.
Consider the line joining the 2 points (part of X axis in this case) as a very small chord of a circle which has radius equal to say 50.
Then such a circle can be drawn with coordinates of center as (0, sqrt(2500-16)).
Hence the ans is infiite, because we can chose any value for the radius (in place of 50 above).

Also, its a known genoetric truth that infinite no. of circles can be drawn through any 2 points but only one circle can be drawn through 3 given points.

Maybe theres a typo n the original question.

I agree that we can pick many possible numbers to solve this question.
However, how about we think this way:
points (4,0) (-4,0) make a line in a circle. The line divide the circle into two parts, which has smaller chord and bigger chord.
If the circle is big enough, the smaller chord will close enough to the "(4,0) (-4,0)" line.
If we say the biggest possible radius is infinite, the smaller chord will lie on the "(4,0) (-4,0)" line. It won't be circle any more. Therefore, (E) is wrong.
(B), (C) and (D) except (A) are all possible radii, so the biggest possible is (D) 8.

Personally, I do not like this kind of question, getting rid of the impossible answer and picking the biggest answer.
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26 Nov 2004, 03:13
Hello folks,

By definition, the maximum radius of a circle cannot be determined if only 2 coordinates, which are NOT diametrically opposite, are specified. The coordinated (-4,0) and (4,0) have not been specified to be diametrically opposite, hence the maximum radius of the circle would be tending to infinity.

For the purpose of clarity, I've attached a slide. Any feedback is welcome
Attachments

File comment: Graphical illustration of proposed solution
PS_Circle.ppt [32 KiB]

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27 Nov 2004, 17:35
Yes, Infinite is the answer. The two points dont tell us anything about the MAXIMUM possible radius.

27 Nov 2004, 17:35
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# A circle passes thru the coordinates (4,0) (-4,0). What is

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