  We recall the definition of classical polar varieties, as well as those of
affine and projective reciprocal polar varieties. The latter are defined with
respect to a non-degenerate quadric, which gives us a notion of orthogonality.
In particular we relate the reciprocal polar varieties to the "Euclidean
geometry" in projective space. The Euclidean distance degree and the degree of
the focal loci can be expressed in terms of the ranks, i.e., the degrees of the
classical polar varieties, and hence these characters can be found also for
singular varieties, when one can express the ranks in terms of the
singularities.
