Question

Circle A has a center at `(1 ,-8 )` and a radius of `3`. Circle B has a center at `(-2 ,-5 )` and a radius of `2`. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

The sum of the radii of the circles is `5` `units`. If the distance between their centres is less than this they will overlap. If it is more, the distance between their closest points is the distance between the centres minus 5.

Explanation:

Distance between the centres of the circles:

`r=sqrt((x_2-x_1)^2+(y_2-y_1)^2)=sqrt((-2-1)^2+(-5--8)^2)`
`=sqrt((-3)^2+(3)^2)=sqrt(9+9)=sqrt18~~4.2`

Since this is less than `5` `units`, the circles will overlap.