Circle & rectangular coordinate system

crackgmat007 wrote:Q: 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.

How to arrive at 16?

Well, if you do arrive at 16, you're not getting the correct answer. The radius here can be as large as you want. For example, take the point (0,100) as the center of the circle. The two points (4,0) and (-4,0) are the same distance from (0,100), so we can certainly draw a circle with center (0,100) that passes through those two points. The radius of that circle is going to be a bit more than 100 (you can find it exactly by solving for r in r^2 = 100^2 + 4^2, though we don't need to do that here). So the answer is E.