Question

Circle A has a center at `(5 ,4 )` and a radius of `9`. Circle B has a center at `(1 ,-2 )` and a radius of `6`. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

Circles do overlap.

Explanation:

Distance between center of Circle A at `(5,4)` and center of Circle Bat `(1,-2)` is given by

`sqrt((5-1)^2+(4-(-2))^2)` i.e. `sqrt(4^2+6^2)` i.e. `sqrt52=7.2111`

As sum of the radii of the two circles at `15` is more than distance between their centers which is `7.2111`, circles do overlap,