3 points are drawn on a plane, and inside their triangular region, more points are added such that no 3 are collinear, such that there are n points in total. What is the maximum possible number of line segments one could draw connecting two of these points such that none intersect other than at their endpoints?

(In reply to

re: How Leonhard would solve it by Charlie)

"It's just that I did not know if merely being a triangulation would guarantee the maximum number of lines."

Yes, it suffices. If you have a full triangulation of all n points,
there is no way to connect two points in such a way that the edge does
not cross other line segments.