# Given that the radius of the circumcircle (large circle) is #r#, evaluate the ratio of the area of A regions to B regions - #(sumA_i)/(sumB_i)#?

##### 1 Answer

Nov 9, 2016

Radius of the large circumcircle

Area of this large circle

The length of each side of the square at the center is equal to the radius of the large circumcircle.

So area of the square

Radius of each of four small circle

So its area

From the figure it is obvious that

Each of the petal of flower at the center is composed of **two** similar segments of small circle and 8 such segments form the complete flower.

Area of each such segment

So

So the asked ratio