Question

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

Answer 1

The circles overlap.

Explanation:

To answer your question, let's compute the distance between the two centers `(3,1)` and `(-2,1)`.

The distance can be computed due to Pythagorean theorem as follows:

`d = sqrt((3 - (-2))^2 + (1-1)^2) = sqrt(25 + 0) = 5`

As the first circle has a radius of `6` which is bigger than the distance between the two centers, you know that the two circles overlap.

graph{((x-3)^2 + (y - 1)^2 - 36) * ((x+2)^2 + (y-1)^2 - 9) = 0 [-13.17, 15.31, -6.21, 8.03]}