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There are many ways to triangulate a simple n-gon; for certain optimization criteria such as maximization of the smallest internal angle it is known how to efficiently compute the best triangulation with respect to this criterion. In this paper we consider a natural extension of this problem: Given a simple polygon P and one Steiner point p in its interior, determine the optimal location of p and a triangulation of P and p which is best amongst all triangulations and placements of p. We present a polynomial-time algorithm for this problem when the optimization criterion is maximization of the minimum angle. Furthermore, we also provide a more general polynomial-time algorithm for finding the optimal placement of a constant number of Steiner points under the same optimization criterion.