Question

Circle A has a center at `(8 ,-4 )` and a radius of `2`. Circle B has a center at `(4 ,3 )` and a radius of `4`. Do the circles overlap? If not what is the smallest distance between them?

Answer 1

The circles do not overlap.
The smallest distance is `=2.1`

Explanation:

The distance between the centre is `d_c`

`sqrt((8-4)^2+(-4-3)^2)`

`=sqrt(16+49)=sqrt65`

The sum of the radii is `r_A+r_B`

`=4+2=6`

As `d_c>(r_A+r_B)`, the circles do not overlap.

The smallest distance between the cicles is

`=sqrt65-6=8.1-6=2.1`

graph{((x-8)^2+(y+4)^2-4)((x-4)^2+(y-3)^2-16)(y-3+7/4(x-4))=0 [-14.24, 14.24, -7.12, 7.12]}