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

Explanation

Let `{ABCD}` be a rectangle inscribed in a circle of radius `r`. Let `{AB}={x}` and `{BC}={y}`.


Then `x^{2}+y^{2}=4 r^{2}`


Area of rectangle `=x y`



`=x sqrt{4 r^{2}-x^{2}} quad text {...[By (1)] }`



Let `f(x)=x^{2}(4 t^{2}-x^{2})`



...