We present a general approach to solving the minimizing disagreement problem for geometric hypotheses with finite VC-dimension. These results also imply efficient agnostic-PAC learning of these hypotheses classes. In particular we give an O(n^{min{alpha + ½ , 2k-1}} log n) algorithm that solves the m.d.p. for two-dimensional convex k-gon hypotheses (where alpha is the VC dimension of the implied set system, k is constant), and an O(n^3k-1log n) algorithm for convex k-hedra hypotheses in three dimensions. We extend these results to handle unions of k-gons and give an approach to approximation algorithms.