Question

Circle A has a center at `(-4 ,-1 )` and a radius of `3`. 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

smallest distance = `1.40312`

Explanation:

Circle `A` center is located at `c_A=(-4,-1)`
Circle `B` center is located at `c_B=(1,3)`
Their distance is `d_{AB} = norm(c_A-c_B) = 6.40312`. If they were tangents their center distance will be `r_A+r_B`. Where `r_A,r_B` are their respective radius. In the present case we have
`d_{AB} > r_A+r_B` so their smallest distance is given by `d_{AB} -( r_A+r_B) = 1.40312`