The intersections of two circles
determine a common chord.
A Delaunay triangulation for a set P of points in the plane is a triangulation such that no point in P is inside the circumcircle of any triangle in the triangulation. It can be shown that for all possible triangulations of P, a Delaunay triangulation maximizes the minimum angle of all angles of the triangles in the triangulation.
Thus, a Delaunay triangulation tends to avoid skinny triangles.
Delaunay triangulation is a good application of the
(circle which passes through the
three vertices of a triangle).