# Circle A has a center at (-5 ,7 ) and a radius of 4 . Circle B has a center at (-3 ,2 ) and a radius of 3 . Do the circles overlap? If not, what is the smallest distance between them?

Feb 9, 2016

Draw a diagram to represent the situation.

#### Explanation:

The diagram shows that the two circles do overlap. you could have also determined this algebraically by adding and subtracting the radius from your points.

$\left(- 3 - 3 , 2\right) - \to \left(- 6 , 2\right)$

As you can see, this point would be inside the other circle and so the two circles do overlap.

Hopefully you understand now!