There is a set of 39 distinct points on a plane with the following…

There is a set of 39 distinct points on a plane with the following characteristics:

There is a subset A consisting of eight collinear points.

Any subset of three or more collinear points from the 39 is a subset of A.

How many distinct triangles with the positive area can be formed with each of its vertices being one of the 39 points? (Two triangles are said to be distinct if at least one of the vertices is different)