# Circle A has a center at (-4 ,-2 ) and a radius of 2 . Circle B has a center at (1 ,3 ) and a radius of 2 . Do the circles overlap? If not what is the smallest distance between them?

##### 1 Answer
Jul 6, 2017

The circles do not overlap and the shortest distanceis $= 3.07$

#### Explanation:

The distance between the centers is

${O}_{A} {O}_{B} = \sqrt{{\left(1 - \left(- 4\right)\right)}^{2} + {\left(3 - \left(- 2\right)\right)}^{2}}$

$= \sqrt{25 + 25}$

$= \sqrt{50} = 7.07$

The sum of the radii is

${r}_{A} + {r}_{B} = 2 + 2 = 4$

As,

${O}_{A} {O}_{B} > \left({r}_{A} + {r}_{B}\right)$

The circles do not overlap.

The smallest distance is

$d = 7.07 - 4 = 3.07$

graph{((x+4)^2+(y+2)^2-4)((x-1)^2+(y-3)^2-4)(y-3-x+1)=0 [-10, 10, -5, 5]}