Circle A has a center at #(2 ,8 )# and an area of #8 pi#. Circle B has a center at #(3 ,2 )# and an area of #27 pi#. Do the circles overlap?
Checking to see if the sum of the radii of the circles is greater than the distance between the circles' centers, we find that yes, they do overlap.
The distance between two points
Applying that in this case, we get the distance between the centers of the circle to be
Then, the circles only overlap if the sum of their radii is greater than
The area of a circle with radius
As a matter of estimation, we can tell that
meaning we should expect
If we actually calculate the values, we get
meaning the estimation was correct, and the circles do overlap.