Before revision:  SODA95}. By applying the new technique proposed in Jin's recent work for the dual problem of computing the maximum area triangle inside a convex polygon, we solve the problem at hand in O(n) time, thus justify Jin's claim that his technique may find applications in other polygon inclusion problems. Our algorithm actually computes all the local minimal area circumscribing triangles touching edge-to-edge.
After revision:  SODA95}. Our algorithm computes all the local minimal area circumscribing triangles touching edge-to-edge.