Circle A has a center at #(5 ,-2 )# and a radius of #2 #. Circle B has a center at #(4 ,6 )# and a radius of #3 #. Do the circles overlap? If not what is the smallest distance between them?
They do not overlap; there is a minimum distance between them of
Given circles with centers
the distance between the centers can be calculated using the Pythagorean Theorem:
Using a calculator
Measuring along a line joining the two centers:
one circle's radius takes up 2 units and
the other circle's radius takes up 3 units.
Since the sum of the two radii do not make up the distance between the centers, the circles do not overlap,
and the minimum distance between them is (approximately)