Question

Circle A has a center at `(-4 ,-2 )` and a radius of `4`. 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?

Answer 1

`"The circles do not overlap."`
`"The smallest distance between them is "sqrt(50)-6" ."`

Explanation:

`"The distance between the two centers is "`
`sqrt((-4 - 1)^2 + (-2-3)^2) = sqrt(50) .`
`"The sum of the two radius is 6."`
`"As "sqrt(50) > 6" the circles do not overlap."`
`"The smallest distance between them is "sqrt(50) - 6" ."`