Answer:
Three non-co-linear points determine a circle. Three non-co-linear points determine a triangle only if you assume that each pair of these points determines a line which is a side of the triangle. Then, the three points will be the vertices of the triangle.
If you do not have this constraint, so that each line that forms a side of the triangle need pass through only one of the three points, then the three points will not determine a particular triangle
