I know that that the Delaunay triangulation maximizes the minimum angle of triangulation. And it does not minimize the maximum angle. If we consider the set of points in general position(no four points are co-circular). Can someone please give a simple example where the Delaunay triangulation does not minimize the maximum angle.
This animation from the wikipedia article on delaunay triangulations shows you an example of where the delaunay triangulation will switch from having a horizontal interior edge to a vertical interior edge:
The moment this configuration switches to a horizontal interior edge, it is showing that the delaunay triangulation prefers a triangulation with a smallest maximum angle of 88-ish degrees to one that has a smallest maximum of 66-ish degrees.