Circles?

As I was doing some last minute practice problems before tomorrows CCC I thought of a possible mathematical paradox involving a simple geometric problem with circles. The problem itself is not the interesting part but the thought is:

As everyone knows, a circle is defined as the locus of all points equidistant from a center. Furthermore, a circle has both a diameter(d) and a circumference (c), and the relationship between the two is:

However, one must realize that pi is an irrational number (some of you might know where i'm going with this), which means we can never say with absolute certainty what the value is. Therefore, even if we know the diameter with absolute certainty, we can never know the circumference, and if we know the circumference with absolute certainty, then the diameter is in doubt. Therefore, we can say that one can never know both the diameter and circumference of a circle. Since a circle has to have both a definable diameter and circumference. We run into a mathematical paradox.

Then I began to think, "Ok, so what does this mean? What's the resolution to this paradox" and soon enough I compiled a list of possible outcomes:

1) There are no such things as circles or any other geometric figure that's dependent on pi.

2) String Theory is to blame as higher dimensions account for the uncertainty in circle geometry (ie. 2D Euclidean Geometry is a simplification even in the flattest worlds).

3) Pi is not a constant but somehow we say it is. Kind of like a mathematical illusion.

4) Pi is in fact a rational number.

5) Because Chuck Norris said so ..

Another thing to consider after this realization: Is circle uncertainty the mechanism behind Heisenberg Indeterminacy? If so, how does it effect observation?

... Worth a thought? At least this distracted me for a while so that I don't fall asleep before the competition.