Enumerating different box
geometries (table editors)

Rectangles with
adjacencies forming the graph W5

Realizable geometries: planar and rectangular

Five different ways that lines can be tangent to circles

Showing ephemal points in the construction of lines tangent to two circles

Or view demonstration: draw two circles and turn on "ephemera."

Circles of Apollonius

Arrangements of Lines

Lines tangent to two ellipses? (extra credit for doing it in SVG and JavaScript)

Graph theory of line arrangments, of tangential line arrangments, and Voronoi diagrams?? (extra extra credit)