# Circle A has a radius of 4  and a center of (5 ,3 ). Circle B has a radius of 3  and a center of (1 ,4 ). If circle B is translated by <2 ,5 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Oct 10, 2016

The distance between the centers, $d \approx 6.3$, is less than the sum of their radii, $4 + 3 = 7$, therefore, the circles overlap.

#### Explanation:

The translation moves the center of the circle to the point $\left(3 , 9\right)$.

Compute the distance between the centers:

$d = \sqrt{{\left(5 - 3\right)}^{2} + {\left(3 - 9\right)}^{2}}$

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

$d = \sqrt{4 + 36}$

$d = \sqrt{40}$

$d \approx 6.3$

The distance between the centers, $d \approx 6.3$, is less than the sum of their radii, $4 + 3 = 7$, therefore, the circles overlap.