  Geminga was first detected as a gamma-ray point source by the SAS-2 gamma-ray
satellite observatory and the COS-B X-ray satellite observatory. Subsequent
observations have identified Geminga as a heavily obscured radio-quiet pulsar
associated with a nearby (250 pc) late Sedov phase (300,000 year) supernova
remnant. The Geminga pulsar is the second brightest source detected by the
Large Area Telescope aboard the Fermi gamma-ray satellite (Fermi-LAT) and has
been frequently advanced as a source of the anomalous excess of cosmic ray
positrons reported by PAMELA, Fermi-LAT, and AMS-2. It is surrounded by a
compact X-ray pulsar wind nebula. Observations above 10 TeV by the water
Cherenkov observatory Milagro have also revealed a diffuse gamma-ray halo
around Geminga extending over several square degrees. Since 2007 the VERITAS
IACT observatory has performed observations of Geminga and the surrounding halo
region. However, the standard methods of source detection in VERITAS data have
insufficient sensitivity to angularly extended sources (>0.5 degrees) to reveal
a source on the scale of the Milagro detection. In this talk, we describe two
approaches being developed to search for angularly extended very high energy
gamma-ray emission surrounding the Geminga pulsar.
