constructions in plane geometry

Explorations of circles, triangles and other polygons, especially tangency and relations among measured parts of figure. Discussion: how does the definition of an object relate to its construction process, using compass and straightedge? And what does that tell us about the image it builds, and about the generalizability of the construction process? The definition is tightly linked to the construction process. Several alternative definitions may give us the same product, a general figure, but they will all generate different ways of constructing that same figure.