  We study dynamical systems that switch between two different vector fields
depending on a discrete variable and with a delay. When the delay reaches a
problem-dependent critical value so-called event collisions occur. This paper
classifies and analyzes event collisions, a special type of discontinuity
induced bifurcations, for periodic orbits. Our focus is on event collisions of
symmetric periodic orbits in systems with full reflection symmetry, a symmetry
that is prevalent in applications. We derive an implicit expression for the
Poincare map near the colliding periodic orbit. The Poincare map is piecewise
smooth, finite-dimensional, and changes the dimension of its image at the
collision. In the second part of the paper we apply this general result to the
class of unstable linear single-degree-of-freedom oscillators where we detect
and continue numerically collisions of invariant tori. Moreover, we observe
that attracting closed invariant polygons emerge at the torus collision.
