Circle A has a center at #(1 ,5 )# and an area of #12 pi#. Circle B has a center at #(7 ,2 )# and an area of #8 pi#. Do the circles overlap? If not, what is the shortest distance between them?
1 Answer
We can find the radii of the circles from their areas. If the distance between their centers is less than the sum of the two radii, the circles overlap. If not (as in this case), the distance between the centers minus the sum of the radii equals the distance between the closest points:
Explanation:
We can find the radius of a circle from its area:
Rearranging:
The radius of the circle with area
The distance between the centers of the two circles is given by:
The sum of the two radii is
The distance between their closest points is