Another problem which is [solved in 'one step'][1] (if one assumes proving the existence of a Delaunay triangulation of a finite point set in the Euclidean plane as 'one step') is Thue's Theorem on optimal circle (disk) packing.

(I know that there was already an answer involving Delaunay triangulation, but I still wanted to mention this one).


  [1]: https://arxiv.org/abs/1009.4322