Question

a circle with radius 2 , has a square inscribed in it. At the edges of square,circles are drawn taking sides as a diameter. Find the area of outer circles

Answer 1

What is the answer if square is inscribed in the circle then the ratio of there area will give what?

Let side of square be 'a'

Area of square is a²

Diagonal of sqare is √{a²+a²}

Or √2a

So diameter of circle is equal to diagonal of sqare.

Then diameter=√2a

Radius(r)=√2a/2

=a/√2

Area of circle=πr²

=π{a/√2}²

=πa²/2

Ratio of area of square and area of circle =

a²:πa²/2

=1:π/2

=2:π