Question

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?

Answer 1

The circles do not overlap.
Smallest distance`=d-S=12.04159-6=6.04159 " "`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" "`units

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

`d=sqrt((x_a-x_b)^2+(y_a-y_b)^2)`

`d=sqrt((5-6)^2+(4--8)^2)`

`d=sqrt((-1)^2+(12)^2)`

`d=sqrt145=12.04159`

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

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