Question

Circle A has a center at `(2 ,-1 )` and a radius of `2`. Circle B has a center at `(-3 ,6 )` and a radius of `1`. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

Circles do not overlap and smallest distance between them is `5.6023`

Explanation:

Distance between `(2,-1)` and `(-3,6)` is given by

`sqrt((2-(-3))^2+((-1)-6)^2)` i.e. `sqrt(5^2+7^2)` i.e. `sqrt74=8.6023`

As radius of circle A is `2` and of circle B is `1` and

sum of radii i.e. `3` is less than distance (`8.6023`) between them they do not overlap and smallest distance between them is `8.6023-3=5.6023`

As sum of the radius of the two circles at `8.4495` is more than distance of `6.3246` between them, circles do overlap,