Warren, you are correct, but this is far easier said than done. See a good summary here: Yap, Chee, and Dube, Thomas. "The Exact Computation Paradigm". 1994? (Chapter in "Computing in Euclidean Geometry", by Du and Hwang, 1994.) Available in pdf on the Internet. At 03:04 PM 7/19/2013, Warren D Smith wrote:

a good solution to the geometry consistency problem is to use exact arithmetic. More precisely, you use ordinary lo-precision arithmetic except when it gets dicey, then you go for more precision... the net effect is, hi-precision calculations are rarely needed, so it is efficient.

This is a pain, but it solves everything.