# Circle A has a center at (1 ,-2 ) and a radius of 3 . Circle B has a center at (-4 ,6 ) and a radius of 2 . Do the circles overlap? If not, what is the smallest distance between them?

Nov 4, 2016

The circles do not overlap. The smallest distance between the circles is about 4.434 units.

#### Explanation:

I know that the circles do not overlap after graphing both circles.

The smallest distance between the circles can be found by finding the distance between their centers, and subtracting out the radii.
${d}_{r} = \sqrt{{5}^{2} + {8}^{2}} = \sqrt{89}$
The distance between the edges of the circles is ${d}_{r} - 2 - 3$

${d}_{r} - 2 - 3 = \sqrt{89} - 5$
This is approximately 4.434 units between the edges of the 2 circles.