17・199 Given four points on a plane, with no three points being collinear. They can form four triangles. The maximum number of acute triangles among them is
(A) 4.
(B) 3.
(C) 2.
(D) 1.
(China Jiangsu Province Suzhou Junior High School Mathematics Competition, 1987)
[Solution] If one of the points lies inside the triangle formed by the other three points, as shown in Figure (1), it can be seen that among the four triangles formed by the four points, at least one is not an acute triangle.

If the four points are exactly the four vertices of a convex quadrilateral as shown in Figure (2), then the quadrilateral has at least one interior angle that is not acute (otherwise, the sum of its four interior angles would be less than $360^{\circ}$), so among the four triangles formed by the four points, at least one is not an acute triangle.
In other words, among the triangles formed by the four points, there can be at most 3 acute triangles.
Therefore, the answer is $(B)$.