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

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Answer 1 · 2016-04-07T08:57:05

They do not overlap
Smallest distance $=0$ , they are tangent to each other.

Center to center distance $=sqrt((x_a-x_b)^2+(y_a-y_b)^2)$
$=sqrt((0)^2+(-5)^2)=5$

Sum of radii $=r_a+r_b=3+2=5$

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