  In applications such as wireless communication, it is important to study the
statistical properties of $L_{2}$, the minimal arc distance between a random
point (e.g., a cellphone user) uniformly distributed on a sphere to a set of
pre-defined seeds (e.g., wireless towers) on that sphere. In this study, we
first derive the distribution (CDF) and density (PDF) functions of the arc
distance between a selected vertex of a spherical triangle to a random point
uniformly distributed within this triangle. Next, using computational
techniques based on spherical Voronoi diagram and triangular partition of
Voronoi cells, we derive moments of $L_{2}$ and $\cos L_{2}$. These results are
verified by extensive Monte Carlo simulations.
