18.46 In rectangle $A B C D$, points $E, F, G, H$ are taken on sides $A B, B C, C D, D A$ respectively, such that $E F G H$ is a rectangle. Then the number of such rectangles is
(A) only one.
(B) four.
(C) generally not possible.
(D) infinitely many.
(China Hebei Province Junior High School Mathematics Competition, 1993)
[Solution] A quadrilateral with equal diagonals that bisect each other is a rectangle.
Let $O$ be the intersection point of the diagonals of rectangle $A B C D$. Draw any line $E G$ through $O$ intersecting sides $A B$ and $C D$ of the rectangle at points $E$ and $G$, respectively.
Among the line segments $H F$ passing through $O$ and intersecting sides $A D$ and $B C$ of the rectangle, at least one is equal to $E G$.
In this case, quadrilateral $E F G H$ is a rectangle.
Due to the arbitrariness of $E G$, it is known that infinitely many such rectangles can be formed.
Therefore, the answer is $(D)$.