Squares, Circles, and Rectangles!

The circle and square gives the radius of the circle.

Square Area is 18, so square side is sqrt(18) = 3*sqrt(2)
Square diagonal is sqrt(2)*square side = 3*(sqrt(2))^2 = 6
Half square diagonal = circle radius = 3

Diagonal of Rectangle = diameter of circle = 6
Looking at one corner (¼) of the rectangle, it has diagonal = 3.
Call the short piece 'a'
Call the long piece 'b'.

Then a^2 + b^2 = 3 and (2a)*(2b) = 12 ==> a*b = 3
 
thank you so much for your help!

Know how I can put it into a picture?
 
I started with the square.

The circle was next, hitting each vertex from the square.

Suash the square, keeping the vertices on the circle, and you've an inscribed rectangle.
 
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