  We provide an explicit geometric algorithm involving only ruler and compass
constructions in order to specify the specular reflection point on the surface
of a reflecting sphere of radius $r$ given two focal points $A$ and $B$ lying
outside of it. By numerically implementing the algorithm we compute the point
in question for a number of cases. We conclude by discussing how the first
iteration of the algorithm constitutes a first order approximation to the real
solution by providing a closed expression for it as well as the error involved
in doing so, as a function of the distances of the two focal points from the
origin and the angle formed between them.
