Circle A has a radius of $2$ $2$ and a center at $(8, 3)$ $(8 ,3 )$ . Circle B has a radius of $3$ $3$ and a center at $(3, 2)$ $(3 ,2 )$ . If circle B is translated by $< - 2, 6 >$ $<-2 ,6 >$ , 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 $(8, 3)$ $(8 ,3 )$ . Circle B has a radius of $3$ $3$ and a center at $(3, 2)$ $(3 ,2 )$ . If circle B is translated by $< - 2, 6 >$ $<-2 ,6 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Answer 1 · 2018-06-15T09:38:34

$no overlap, \approx 3.6$ $"no overlap ",~~3.6$

Explanation:

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

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

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

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

$under the translation < - 2, 6 >$ $"under the translation "< -2,6>$

$(3, 2) \to (3 - 2, 2 + 6) \to (1, 8) \leftarrow new centre of B$ $(3,2)to(3-2,2+6)to(1,8)larrcolor(red)"new centre of B"$

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

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

$let (x_{1}, y_{1}) = (8, 3) and (x_{2}, y_{2}) = (1, 8)$ $"let "(x_1,y_1)=(8,3)" and "(x_2,y_2)=(1,8)$

$d = \sqrt{{(1 - 8)}^{2} + {(8 - 3)}^{2}}$ $d=sqrt((1-8)^2+(8-3)^2)$

$d = \sqrt{49 + 25} = \sqrt{74} \approx 8.60$ $color(white)(d)=sqrt(49+25)=sqrt74~~8.60$

$sum of radii = 2 + 3 = 5$ $"sum of radii "=2+3=5$

$since sum of radii < d then no overlap$ $"since sum of radii"< d" then no overlap"$

$minimum distance = d - sum of radii$ $"minimum distance "=d-" sum of radii"$

$\times \times \times \times \times \times \times = 8.6 - 5 = 3.6$ $color(white)(xxxxxxxxxxxxxx)=8.6-5=3.6$
graph{((x-8)^2+(y-3)^2-4)((x-1)^2+(y-8)^2-9)=0 [-20, 20, -10, 10]}

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Circle A has a radius of $2$ $2$ and a center at $(8, 3)$ $(8 ,3 )$ . Circle B has a radius of $3$ $3$ and a center at $(3, 2)$ $(3 ,2 )$ . If circle B is translated by $< - 2, 6 >$ $<-2 ,6 >$ , 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 (8,3)(8 ,3 ). Circle B has a radius of 33 and a center at (3,2)(3 ,2 ). If circle B is translated by <−2,6><-2 ,6 >, 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 $(8, 3)$ $(8 ,3 )$ . Circle B has a radius of $3$ $3$ and a center at $(3, 2)$ $(3 ,2 )$ . If circle B is translated by $< - 2, 6 >$ $<-2 ,6 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?