The molecular basis of life rests on the activity of biological macro-molecules, mostly nucleic acids and proteins. A perhaps surprising finding that crystallized over the last handful of decades is that geometric reasoning plays a major role in our attempt to understand these activities. In my presentations, I will explore the connection between the biological activities of proteins and geometry, using a representation of molecules as a union of balls. I will cover three topics: (1) the geometry of biomolecular solvation, (2) understanding electrostatics using implicit solvent models, and (3), designing protein shape descriptors. Part 1: Hydrophobicity. The structure of a biomolecule is greatly influenced by its environment in the cell, which mainly consists of water. Explicit representation of the solvent that includes individual water molecules are costly and cumbersome. It is therefore highly desirable to develop implicit solvent models that are nevertheless accurate. In such models, hydrophobicity is expressed as a weighted sum of atomic accessible surface areas. I will show how these surface areas can be computed from the dual complex, a filtering of the weighted Delaunay triangulation of the centers of the atoms.