Circle A has a radius of $2$ $2$ and a center at $(3, 6)$ $(3 ,6 )$ . Circle B has a radius of $4$ $4$ and a center at $(2, 3)$ $(2 ,3 )$ . If circle B is translated by $< - 2, 1 >$ $<-2 ,1 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Circle A has a radius of $2$ $2$ and a center at $(3, 6)$ $(3 ,6 )$ . Circle B has a radius of $4$ $4$ and a center at $(2, 3)$ $(2 ,3 )$ . If circle B is translated by $< - 2, 1 >$ $<-2 ,1 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Answer 1 · 2018-07-15T12:31:45

$circles overlap$ $"circles overlap"$

Explanation:

$What we have to do here is compare the distance (d)$ $"What we have to do here is compare the distance (d)"$
$between the centres to the sum of the radii$ $"between the centres to the sum of the radii"$

$∙ if sum of radii > d then circles overlap$ $• " if sum of radii">d" then circles overlap"$

$∙ if sum of radii < d then no overlap$ $• " if sum of radii"< d" then no overlap"$

$Before calculating d we require to find the new$ $"Before calculating d we require to find the new"$
$centre of B under the given translation$ $"centre of B under the given translation"$

$under the translation < - 2, 1 >$ $"under the translation "< -2,1 >$

$B (2, 3) \to (2 - 2, 3 + 1) \to (0, 4) \leftarrow new centre of B$ $B(2,3)to(2-2,3+1)to(0,4)larrcolor(red)"new centre of B"$

$to calculate d use the distance formula$ $"to calculate d use the "color(blue)"distance formula"$

$∙ x d = \sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2}}$ $•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)$

$let (x_{1}, y_{1}) = (3, 6) and (x_{2}, y_{2}) = (0, 4)$ $"let "(x_1,y_1)=(3,6)" and "(x_2,y_2)=(0,4)$

$d = \sqrt{{(0 - 3)}^{2} + {(4 - 6)}^{2}} = \sqrt{9 + 4} = \sqrt{13} \approx 3.61$ $d=sqrt((0-3)^2+(4-6)^2)=sqrt(9+4)=sqrt13~~3.61$

$sum of radii = 2 + 4 = 6$ $"sum of radii "=2+4=6$

$since sum of radii > d then circles overlap$ $"Since sum of radii"> d" then circles overlap"$
graph{((x-3)^2+(y-6)^2-4)((x-0)^2+(y-4)^2-16)=0 [-20, 20, -10, 10]}

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Circle A has a radius of $2$ $2$ and a center at $(3, 6)$ $(3 ,6 )$ . Circle B has a radius of $4$ $4$ and a center at $(2, 3)$ $(2 ,3 )$ . If circle B is translated by $< - 2, 1 >$ $<-2 ,1 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Explanation:

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Circle A has a radius of 22 and a center at (3,6)(3 ,6 ). Circle B has a radius of 44 and a center at (2,3)(2 ,3 ). If circle B is translated by <−2,1><-2 ,1 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?

1 Answer

Explanation:

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Circle A has a radius of $2$ $2$ and a center at $(3, 6)$ $(3 ,6 )$ . Circle B has a radius of $4$ $4$ and a center at $(2, 3)$ $(2 ,3 )$ . If circle B is translated by $< - 2, 1 >$ $<-2 ,1 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?