  Parapolar spaces are point-line geometries introduced as a geometric approach
to (exceptional) algebraic groups. We characterize a wide class of Lie
geometries as parapolar spaces satisfying a simple intersection property. In
particular many of the exceptional Lie incidence geometries occur. {In an
appendix, we extend our result to the locally disconnected case and discuss the
locally disconnected case of some other well known characterizations.
