$16 \cdot 6$ Find a point on the side of a rectangle such that the lines connecting this point to the endpoints of the opposite side divide the rectangle into three mutually similar triangles. The number of such points:
(A) Does not exist.
(B) There are definitely 2.
(C) There are definitely 4.
(D) The number cannot be determined.
(China Guangzhou, Wuhan, Fuzhou, and other five cities junior high school mathematics league, 1987)