Circle A has a center at (8 ,3 ) and a radius of 3 . Circle B has a center at (-1 ,-2 ) and a radius of 4 . Do the circles overlap? If not, what is the smallest distance between them?

Nov 8, 2016

They do not overlap. The closest distance between them is:

$\sqrt{106} - 7 \approx 3.3$

Explanation:

The distance, d, between the centers is:

$d = \sqrt{{\left(8 - - 1\right)}^{2} + {\left(3 - - 2\right)}^{2}}$

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

$d = \sqrt{106}$

This distance between the centers is greater than the sum of the radii, therefore, the circles do not overlap.

Here is a plot of the two circles:

The closest distance between them is:

$\sqrt{106} - 7 \approx 3.3$