  Polar varieties have in recent years been used by Bank, Giusti, Heintz,
Mbakop, and Pardo, and by Safey El Din and Schost, to find efficient procedures
for determining points on all real components of a given non-singular algebraic
variety. In this note we review the classical notion of polars and polar
varieties, as well as the construction of what we here call reciprocal polar
varieties. In particular we consider the case of real affine plane curves, and
we give conditions for when the polar varieties of singular curves contain
points on all real components.
