# Circle A has a center at (5 ,2 ) and a radius of 2 . Circle B has a center at (1 ,-2 ) and a radius of 1 . Do the circles overlap? If not, what is the smallest distance between them?

Dec 20, 2017

Smallest distance between the two circles is 2.6569

#### Explanation:

Given
Circle A radius ${r}_{1} = 2$
Circle B radius ${r}_{2} = 1$
${r}_{1} + {r}_{2} = 2 + 1 = 3$

Distance between the centers $d = \sqrt{{\left(5 - 1\right)}^{2} + {\left(2 - \left(- 2\right)\right)}^{2}} = \sqrt{32} = 5.6569$

${r}_{1} + {r}_{2} = 3 i s < d = 5.6569$

Since d > (r_1 + r_2),
both the circles do not overlap.

Smallest distance between the circles is
$d - \left({r}_{1} + {r}_{2}\right) = 5.6569 - 3 = 2.6569$