**When a rectangle is inscribed in a circle, then**

**Diagonal of the Rectangle = Diameter of the Circle**

(1) If the radius of the circle is given as ‘r’, then relation
between area and perimeter of the rectangle can be determined as given below:

Diagonal of rectangle = Diameter of circle = 2r

=> √(a

^{2}+b^{2}) = 2r => a^{2}+b^{2}= 4r^{2}=> (a+b)^{2}-2ab = 4r^{2}
=> (½ Perimeter of rectangle)

^{2}– 2(Area of rectangle) = 4r^{2}
(2) If the length and
breadth of the rectangle are given as ‘a’ and ‘b’, then area/perimeter of the circle
can be determined as given below:

Diameter of circle = Diagonal of rectangle = √(a

^{2}+b^{2})
=> Radius of circle = ½ √(a

^{2}+b^{2})
=> Area of circle = π{½ √(a

^{2}+b^{2})}^{2}= π(a^{2}+b^{2})/4
Perimeter of circle = 2π (½ √(a

^{2}+b^{2})) = π √(a^{2}+b^{2})
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