Rectangles, Circles and Tangents
Archimedes,  Apollonius, Voronoi, Kuratowski and the gang
Enumearting different box geometries
Enumerating different box geometries (table editors)
Rectangles with adjacencies forming the graph W5
Rectangles with adjacencies forming the graph W5

division of plane by either voronoi diagrams or tangential line arrangements
division of plane by either voronoi diagrams or tangential line arrangements
Realizable geometries: planar and rectangular
Realizable geometries: planar and rectangular
Five different ways that lines can be tangent to circles
Five different ways that lines can be tangent to circles

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