Question

Circle A has a center at `(2 ,3 )` and an area of `8 pi`. Circle B has a center at `(7 ,2 )` and an area of `64 pi`. Do the circles overlap?

Answer 1

Circles overlap each other.

Explanation:

Distance between centers of two circles at `(2,3)` and `7,2)` is `sqrt((7-2)^2+(2-3)^2)=sqrt(25+1)=sqrt26=5.1`.

Radius of a circle is given by `sqrt((Area)/pi)`, hence

area of A circle is `sqrt((8pi)/pi)=sqrt8=2.828` and

area of B circle is `sqrt((64pi)/pi)=sqrt64=8`.

As the distance between two circles at `5.1` is less than the sum of their radii `8+2.828=10.828`, circles overlap each other.