<p>The Douglas–Rachford algorithm was introduced nearly sixty years ago to solve the feasibility problem involving two or more convex closed sets in a Hilbert space. Here, we apply Douglas–Rachford algorithm on nonconvex feasibility problems involving a unit sphere and a singleton in a Hilbert space. We study the behaviour of the Douglas-Rachford method in both the consistent and inconsistent settings. In the consistent case, the Douglas–Rachford sequence converges, and the shadow sequence converges to a common point of the sets. However, the Douglas–Rachford sequence diverges, and the shadow sequence is weakly convergent, provided the intersection of the sets is empty.</p>