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.