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

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

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Answer 1 · 2016-02-17T08:10:46

Circles do not overlap and smallest distance between them is $5.6023$ $5.6023$

Explanation:

Distance between $(2, - 1)$ $(2,-1)$ and $(- 3, 6)$ $(-3,6)$ is given by

$\sqrt{{(2 - (- 3))}^{2} + {((- 1) - 6)}^{2}}$ $sqrt((2-(-3))^2+((-1)-6)^2)$ i.e. $\sqrt{5^{2} + 7^{2}}$ $sqrt(5^2+7^2)$ i.e. $\sqrt{74} = 8.6023$ $sqrt74=8.6023$

As radius of circle A is $2$ $2$ and of circle B is $1$ $1$ and

sum of radii i.e. $3$ $3$ is less than distance ( $8.6023$ $8.6023$ ) between them they do not overlap and smallest distance between them is $8.6023 - 3 = 5.6023$ $8.6023-3=5.6023$

As sum of the radius of the two circles at $8.4495$ $8.4495$ is more than distance of $6.3246$ $6.3246$ between them, circles do overlap,

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Circle A has a center at $(2, - 1)$ $(2 ,-1 )$ and a radius of $2$ $2$ . Circle B has a center at $(- 3, 6)$ $(-3 ,6 )$ and a radius of $1$ $1$ . 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 (2,−1)(2 ,-1 ) and a radius of 22 . Circle B has a center at (−3,6)(-3 ,6 ) and a radius of 11 . 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 $(2, - 1)$ $(2 ,-1 )$ and a radius of $2$ $2$ . Circle B has a center at $(- 3, 6)$ $(-3 ,6 )$ and a radius of $1$ $1$ . Do the circles overlap? If not, what is the smallest distance between them?