Comment by tomcur

Optimization can work well for interactive CAD usage, because geometric sketches tend to be close to the intended solution, and it's fast. It also has the nice property of stability (i.e., with optimization, small changes in parameters tend not to cause large perturbations in the solution). Doing more gets into what you mentioned, and is called chirality or root identification in the literature. That's much more intense computationally, but could be useful especially if cheaper approaches like optimization failed.