Circle A has a center at #(4 ,-8 )# and a radius of #3 #. Circle B has a center at #(-2 ,-2 )# and a radius of #5 #. Do the circles overlap? If not, what is the smallest distance between them?
No, since the distance of the centers is greater than the sum of the radii.
You can calculate the distance between the centers. If that distance is less than the sum of the radii, the circles do overlap. If not, they don't.
So, lets calculate the distance between
First we calculate the distance in x (called
You can see this as a triangle, with base
This shows us that the distance between the centers of the circles is approximately
Now we have a distance greater than