Show that of all the rectangles inscribed in a given fixed circle, the square has the maximum area.

Explanation

`text(The diagonal of the rectangle will be diameter of the circle, since the rectangle has all four co-ordinates inscribed on the circumference of the circle.
Hence let the sides of the rectangle be x and y.
Now applying Pythagoras theorem gives us, )`



`x^2 + y^2=4r^2 text( where r is the radius.)`



...