# Circle A has a radius of 5  and a center of (8 ,2 ). Circle B has a radius of 3  and a center of (3 ,7 ). If circle B is translated by <2 ,-1 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Sep 30, 2016

The distance between the two centers is equal to the radius of the larger circle, therefore, the circles overlap

#### Explanation:

The new center of circle B is (5, 6)

The distance between the two centers is:

$d = \sqrt{{\left(8 - 5\right)}^{2} + {\left(2 - 6\right)}^{2}}$

$d = \sqrt{{3}^{2} + {\left(- 4\right)}^{2}}$

$d = \sqrt{9 + 16}$

$d = 5$

The distance between the two centers is equal to the radius of the larger circle, therefore, the circles overlap