This paper presents the design and implementation of a geometric-object-oriented language Gool for constructing, representing, manipulating, and visualizing symbolic geometric objects and relations and performing symbolic geometric computation and formal reasoning. The language uses case distinction to formalize symbolic geometric objects and relations, reducing the problem of dealing with uncertainty and degeneracy to that of handling geometric constraints. We describe the capabilities, features, and main components of Gool, propose several techniques for geometric constraint handling, and discuss some of the implementation issues.