# Circle A has a center at #(1 ,5 )# and a radius of #3 #. Circle B has a center at #(2 ,-3 )# and a radius of #5 #. Do the circles overlap? If not, what is the smallest distance between them?

##### 1 Answer

Feb 23, 2016

They do not overlap.

#### Explanation:

To overlap the distance between centres has to be less than the sum of their radii.

Let the sum of radii be

Let the distance between radii be

Sum of radii

Using Pythagoras

As we are comparing sizes the

As