Delaunay triangulation: Finding all triangles with empty circumcircle

Question

I have a set of points and I want to find all possible triangles which have empty circumcircle. I want to use Delaunay Triangulation.

I have read some papers on the subject but I am not sure whether Delaunay Triangulation finds all possible triangles or not. If yes, then how can I mathematically prove that?

Answer 1

To find all possible triangles you can make all the faces the same length:https://stackoverflow.com/questions/20695680/i-found-an-algorithm-for-computing-multiple-msts-in-oe-v-is-this-publishable.