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?

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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?

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Answer 1 · 2016-04-07T08:57:05

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

Explanation:

Center to center distance $= \sqrt{{(x_{a} - x_{b})}_{a}^{2} + {(y_{a} - y_{b})}_{a}^{2}}$ $=sqrt((x_a-x_b)^2+(y_a-y_b)^2)$
$= \sqrt{{(0)}^{2} + {(- 5)}^{2}} = 5$ $=sqrt((0)^2+(-5)^2)=5$

Sum of radii $= r_{a} + r_{b} = 3 + 2 = 5$ $=r_a+r_b=3+2=5$

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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?

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Circle A has a center at (-1 ,-4 )(−1,−4)(-1 ,-4 ) and a radius of 3 33 . Circle B has a center at (-1 ,1 )(−1,1)(-1 ,1 ) and a radius of 2 22 . Do the circles overlap? If not, what is the smallest distance between them?

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Explanation:

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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?