Question

Circle A has a center at `(-5 ,7 )` and a radius of `4`. Circle B has a center at `(7 ,2 )` and a radius of `3`. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

The circles do not overlap and the shortest distance between them is `6` units.

Explanation:

Using Pythagoras Theorem, you can find the distance between the center of the 2 circles.

`sqrt{(-5-7)^2 + (7-2)^2} = 13 > 7 = 3 + 4`

The distance between the center of the 2 circles is larger than the sum of the 2 radii of the circles, hence the circles do not overlap, and the shortest distance between them is `13-7=6` units.