The adjacent figure shows two squaresABCD and PQRS inscribed in two concentric circles. The sides of ABCD are tangents to the circumcircle of PQRS.

find the ratio of the area of pqrs to the area of abcd.

in the solution it is given

that diameter of the inner circle is equal to the side of the outer square.why?

Given figure,

 

 

 

 

 

 

 

Lets divide the figure into 2 parts:

→Lets take the 1st outer square and inner circle,

 

As you can see from the figure, diameter of the inner circle = side of outer square

Let us take radius of this inner circle = 2 cm

Therefore diameter = 4cm, Hence, side of outer square = 4cm,

Area of Outer square = 4×4=16..................................(1)

→Now take inner circle and square

now by pythagorous theorem, 

Area of Inner Square =

 ........................(2)

From 1 and 2 

 

 


 

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