Question

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

Answer 1

the circles will overlap

Explanation:

The radius of circle A is `r_A=8` unit
The radius of circle B is `r_B=4` unit
The distance between their centers `d_(AB)=sqrt((-8+3)^2+(8-3)^2)=5sqrt2`unit
It is obvious that
`r_A+r_B>d_(AB)`
Hence the circles will overlap
Further
If `r_A+r_B=d_(AB)` then they would touch
AND
`r_A+r_B< d_(AB)` then they would not touch or overlap
In that case the would have minimum distance
`d_(min)=d_(AB)-(r_A+r_B)`

Is it OK?