An exact method to find a circle passing through two points and minimizing the maximal weighted distance to a set of points

This paper proposes an optimal algorithm to solve a circuit design problem. We consider the constrained minimax problem to find a circle which minimizes the maximal weighted distance to a set of points passing through two given points. The problem is reformulated to a minimization problem in one dimension. We propose an algorithm to find an exact solution to the problem, using Cardano's formula. The algorithm is of computational complexity O(n3). The stability of the algorithm comes from the exact formula. Several numerical results are also shown.