  High-magnification microlensing events provide an important channel to detect
planets. Perturbations near the peak of a high-magnification event can be
produced either by a planet or a binary companion. It is known that central
perturbations induced by both types of companions can be generally
distinguished due to the basically different magnification pattern around
caustics. In this paper, we present a case of central perturbations for which
it is difficult to distinguish the planetary and binary interpretations. The
peak of a lensing light curve affected by this perturbation appears to be blunt
and flat. For a planetary case, this perturbation occurs when the source
trajectory passes the negative perturbation region behind the back end of an
arrowhead-shaped central caustic. For a binary case, a similar perturbation
occurs for a source trajectory passing through the negative perturbation region
between two cusps of an astroid-shaped caustic. We demonstrate the degeneracy
for 2 high-magnification events of OGLE-2011-BLG-0526 and
OGLE-2011-BLG-0950/MOA-2011-BLG-336. For OGLE-2011-BLG-0526, the $\chi^2$
difference between the planetary and binary model is $\sim$ 3, implying that
the degeneracy is very severe. For OGLE-2011-BLG-0950/MOA-2011-BLG-336, the
stellar binary model is formally excluded with $\Delta \chi^2 \sim$ 105 and the
planetary model is preferred. However, it is difficult to claim a planet
discovery because systematic residuals of data from the planetary model are
larger than the difference between the planetary and binary models. Considering
that 2 events observed during a single season suffer from such a degeneracy, it
is expected that central perturbations experiencing this type of degeneracy is
common.
