Question

Circle A has a center at `(8 ,3 )` and a radius of `4`. Circle B has a center at `(4 ,4 )` and a radius of `3`. Do the circles overlap? If not what is the smallest distance between them?

Answer 1

Center of 1st Circle `(8,3)`
Radius of 1st Circle `(r_1=4)`
Center of 2nd Circle `(4,4)`
Radius of 2nd Circle `(r_2=3)`
Distance between their centers
`d=sqrt((8-4)^2+(3-4)^2)=sqrt17~~4.12`
again sum of their radius `=r_1+r_2=4+3=7`

Since `r_1+r_2>d` the circles will not overlap
Their smallest distance `d_(sm)=r_1+r_2-d=7-4.12=2.88`