In the diagram, two rectangles intersect at exactly two points, $A$ and $B$. The maximum possible finite number of points of intersection of any two rectangles is
(A) 3
(B) 4
(C) 12
(D) 8
(E) 6

![](https://cdn.mathpix.com/cropped/2024_04_20_ac36362783317e0251fdg-105.jpg?height=303&width=653&top_left_y=366&top_left_x=1099)

Part B: Each correct answer is worth 6.
Consider rectangles $W X Y Z$ and $P Q R S$.

Each of the four sides of $P Q R S$ can intersect at most 2 of the sides of $W X Y Z$, as any straight line can intersect at most two sides of a rectangle.

Therefore, the maximum possible number of points of intersection between the two rectangles is 8 .

8 points of intersection is possible, as we can see in the diagram:

![](https://cdn.mathpix.com/cropped/2024_04_20_33a8a6559d675f59baa2g-206.jpg?height=401&width=480&top_left_y=510&top_left_x=882)

So the maximum possible number of points of intersection is 8 .

ANSWER: (D)