We show the following two results on a set on "n" points in the plane, tus answering questions posed by Erdős and Purdy (1971). 1\. The maximum number of triangles of maximum area (or of maximum perimeter) in a set of "n" points in the plane is exactly "n". 2\. The maximum possible number of triangles of minimum positive area in a set of "n" points in the plane is (-)(n²).
