# Circle A has a center at (5 ,4 ) and a radius of 4 . Circle B has a center at (6 ,-8 ) and a radius of 2 . Do the circles overlap? If not, what is the smallest distance between them?

The circles do not overlap.
Smallest distance$= d - S = 12.04159 - 6 = 6.04159 \text{ }$units

#### Explanation:

From the given data:
Circle A has a center at (5,4) and a radius of 4. Circle B has a center at (6,−8) and a radius of 2. Do the circles overlap? If not, what is the smallest distance between them?

Compute the sum of the radius:
Sum $S = {r}_{a} + {r}_{b} = 4 + 2 = 6 \text{ }$units

Compute the distance from center of circle A to center of circle B:

$d = \sqrt{{\left({x}_{a} - {x}_{b}\right)}^{2} + {\left({y}_{a} - {y}_{b}\right)}^{2}}$

$d = \sqrt{{\left(5 - 6\right)}^{2} + {\left(4 - - 8\right)}^{2}}$

$d = \sqrt{{\left(- 1\right)}^{2} + {\left(12\right)}^{2}}$

$d = \sqrt{145} = 12.04159$

Smallest distance$= d - S = 12.04159 - 6 = 6.04159$

God bless....I hope the explanation is useful..