annmary wrote:

ABCD is a rectangle inscribed in a circle.

Rectangle \(ABCD\) can be broken down into 2 congruent triangles, \(\triangle\)\(ABC\) & \(\triangle\)\(CDA\).

area of rectangle \(ABCD\) = 2 * area of \(\triangle\)\(ABC\)

Let's draw a perpendicular from B to AC and denote the length by h.

Also, \(AC = 2r = 2\)

Now, area of \(\triangle\)\(ABC\) \(= (1/2)*(2)*(h) = h\)

area of rectangle \(ABCD = 2h\)

Now maximum value of h can be r and minimum can be tending towards 0.

So, area of rectangle will vary between \(0\) and \(2\).

\(Answer D\)