UPDATE 2014-01-15: The attached .zip file now contains a Mathcad Prime 3.0 worksheet (.mcdx) and—for those of you who are still using earlier verisions of Mathcad—an Adobe Acrobat printout (.pdf) of the worksheet so can see how it is put together.
This worksheet finds the center and radius of the unique circle that passes through three known points P1, P2, and P3, which have the surveyed coordinates (N1,E1), (N2,E2), and (N3,E3). From this result, the original design intent for the circle or arc defined by these three points can be estimated. Although this solution can be easily accomplished graphically in Autocad (or similar), the purpose of this worksheet it to show one of the mathematical solutions to this problem. I created the original version of this worksheet to answer a question posed by a surveyor.