# Circle A has a center at (3 ,1 ) and a radius of 1 . 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?

Mar 5, 2016

no overlap. distance = 1 unit.

#### Explanation:

The first step is to calculate the distance between the centres.

Here both centres have a y-coord = 1 , hence the line joining the centres is parallel to the x-axis

and it's length = 3 - (-2) = 3+ 2 = 5

now radius of A + radius of B = 1 + 3 = 4 which is < 5

hence there is no overlap.

distance between them = 5 - 4 = 1