  The SU(2) Yang-Mills-Higgs theory supports the existence of monopoles,
antimonopoles, and vortex rings. In this paper, we would like to present new
exact static antimonopole-monopole-antimonopole (A-M-A) configurations. The net
magnetic charge of these configurations is always negative one, whilst the net
magnetic charge at the origin is always positive one for all positive integer
values of the solution's parameter $m$. However, when $m$ increases beyond one,
vortex rings appear coexisting with these A-M-A configurations. The number of
vortex rings increases proportionally with the value of $m$. They are located
in space where the Higgs field vanishes along rings. We also show that a single
point singularity in the Higgs field does not necessarily corresponds to a
structureless 1-monopole at the origin but to a zero size
monopole-antimonopole-monopole (\textcolor{blue}{MAM}) structure when the
solution's parameter $m$ is odd. This monopole is the Wu-Yang type monopole and
it possesses the Dirac string potential in the Abelian gauge. These exact
solutions are a different kind of BPS solutions as they satisfy the first order
Bogomol'nyi equation but possess infinite energy due to a point singularity at
the origin of the coordinate axes. They are all axially symmetrical about the
z-axis.
