The figure below shows two concentric circles with centre O. PQRS is a square inscribed in the outer circle. It also circumscribes the inner circle, touching it at points B, C, D and A. What is the ratio of the perimeter of the outer circle to that of polygon ABCD?
inner circle perimeter 2⊼x
then length of PQ is 2x
perimeter of PQRS =4x
then SQ= √((2x)^2 +(2x)^2) =2√2x
perimeter of outer circle = 2 ⊼ (√2x ) =2√2 ⊼ x
perimeter of ABCD=√2x *4 =4√2x
ratio of perimeter of outer circle : perimeter of ABCD = ⊼ / 2