Question

Circle A has a center at `(6 ,4 )` and a radius of `3`. Circle B has a center at `(-1 ,6 )` and a radius of `5`. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

The circles overlap.

Explanation:

If circle A has a center at `(6,4)`
and circle B has a center at `(-1,6)`

The distance between the centers is
`color(white)("XXX")d=sqrt((6-(-1))^2+(4-6)^2)`
`color(white)("XXXX")=sqrt(49+4)`
`color(white)("XXXX")=sqrt(53)`
`color(white)("XXXX")~~7.28`

Along the line segment joining the centers of the two circles
A takes up 3 units
and B takes up 5 units.

Since `3+5=8` is greater that the distance between the two centers (`7.28`) the circles overlap (by approximately `8-7.28=0.72` units).