  Departing from a Moufang set related to a polarity in an exceptional Moufang
quadrangle of type F_4, we construct a rank three geometry. The main property
of this new geometry is that its automorphism group is identical to the one of
the underlying Moufang set, providing a tool to study this Moufang set in a
geometrical way. As a corollary we obtain that every automorphism of an
exceptional Moufang quadrangle of type F_4 stabilizing the absolute points of a
polarity, also centralizes the polarity. This handles the final case of a
similar result for all polarities of Moufang n-gons.
