Click to place a point, drag to move it, and shift-click to remove it. The stage panel switches between convex hull, Delaunay, and Voronoi, and each stage stays visible under the next one.
Pick a triangle to see its circumcircle. No other point ever falls inside it, which is the empty circle property that defines a Delaunay triangulation. Pick an edge instead and the Voronoi edge that crosses it at a right angle appears: the two diagrams are the same information seen from opposite sides.
Among all possible triangulations, Delaunay is the one that makes the thinnest triangle as fat as it can be, so it maximises the smallest angle. The shortest tree joining the points, the minimum spanning tree, is also built only from Delaunay edges.
Two of the point layouts are degenerate on purpose. On a circle every point is cocircular, so the circumcircle test comes out as a tie. On a line no triangle forms at all and the cells become strips. Relaxing moves each point toward the centroid of its own cell, and repeating it pushes the cells toward hexagons.