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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. _________________

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.

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.

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.

Graphical Illustration [#permalink]
26 Nov 2004, 02:13

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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