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?

1 Answer
Mar 6, 2016

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)=5sqrt2unit
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?