  Transiting exoplanets provide access to data to study the mass-radius
relation and internal structure of extrasolar planets. Long-period transiting
planets allow insight into planetary environments similar to the Solar System
where, in contrast to hot Jupiters, planets are not constantly exposed to the
intense radiation of their parent stars. Observations of secondary eclipses
additionally permit studies of exoplanet temperatures and large-scale
exo-atmospheric properties. We show how transit and eclipse probabilities are
related to planet-star system geometries, particularly for long-period,
eccentric orbits. The resulting target selection and observational strategies
represent the principal ingredients of our photometric survey of known
radial-velocity planets with the aim of detecting transit signatures (TERMS).
