# Circle A has a center at (-2 ,-4 ) and a radius of 2 . Circle B has a center at (-3 ,2 ) and a radius of 5 . Do the circles overlap? If not, what is the smallest distance between them?

Jun 24, 2016

The circles overlap

#### Explanation:

Circle A's center: $\left(- 2. - 4\right)$
Circle B's center: $\left(- 3 , 2\right)$
Distance between centers: $\sqrt{{\left(- 3 - \left(- 2\right)\right)}^{2} + {\left(2 - \left(- 4\right)\right)}^{2}} = \sqrt{37} \approx 6.08$

Along the line segment joining the two centers:
circle A covers 2 units and
circle B covers 5 units

for a total of 7 units covered by the circles.

But the line segment joining the two circles only has a length of $6.08$ units.

So the circles must overlap (by about $0.92$ units)