17-201 On a plane, there are 5 points, none of which are collinear. Then the minimum number of obtuse triangles formed with these points as vertices is
(A) 4.
(B) 3.
(C) 2.
(D) 1.
(Anhui Province Hefei City Junior High School Mathematics Competition, 1986)
[Solution] If the 5 points do not form the vertices of a convex pentagon, then the number of obtuse triangles formed by them is more than 2 (note that no three points are collinear).

If the 5 points are exactly the vertices of a convex pentagon, since a convex pentagon has at least 2 obtuse angles, the number of obtuse triangles with these 5 points as vertices is at least 2.
Therefore, the answer is $(C)$.