Geometry Concepts -1

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

=> √(a²+b²) = 2r => a²+b² = 4r² => (a+b)²-2ab = 4r²

=> (½ Perimeter of rectangle)² – 2(Area of rectangle) = 4r²

(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 = √(a²+b²)

=> Radius of circle = ½ √(a²+b²)

=> Area of circle = π{½ √(a²+b²)}² = π(a²+b²)/4

Perimeter of circle = 2π (½ √(a²+b²)) = π √(a²+b²)