The intersection of circles frequently appears as a subproblem in the domains of computational kinematics and geometry. For this reason, the computation method for its solution needs to be simple and stable. This paper surveys the solution method for circle intersection given by the approach of distance geometry via Cayley-Menger bideterminants. In particular, the equivalence of the squared-quantity solution to its linear-quantity counterpart is shown and interconnections to related concepts of Non-Euclidean geometry are worked out.