Circle A has a center at (2 ,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?

Feb 2, 2016

The circles do overlap.

Explanation:

The distance between the centers is
$\textcolor{w h i t e}{\text{XXX}} \sqrt{{4}^{2} + {3}^{2}} = 5$

The total lengths of the radii is $3 + 4 = 7$
which when measured along the line segment joining the centers is greater than the length of that line segment.

Therefore the circles must overlap.