Circle A has a radius of $3$ $3$ and a center of $(2, 4)$ $(2 ,4 )$ . Circle B has a radius of $2$ $2$ and a center of $(4, 7)$ $(4 ,7 )$ . If circle B is translated by $< 2, - 4 >$ $<2 ,-4 >$ , 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 $3$ $3$ and a center of $(2, 4)$ $(2 ,4 )$ . Circle B has a radius of $2$ $2$ and a center of $(4, 7)$ $(4 ,7 )$ . If circle B is translated by $< 2, - 4 >$ $<2 ,-4 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Answer 1 · 2018-02-08T09:13:36

$circles overlap$ $"circles overlap"$

Explanation:

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

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

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

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

$(4, 7) \to (4 + 2, 7 - 4) \to (6, 3) \leftarrow new centre of B$ $(4,7)to(4+2,7-4)to(6,3)larrcolor(red)"new centre of B"$

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

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

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

$d = \sqrt{{(6 - 2)}^{2} + {(3 - 4)}^{2}} = \sqrt{16 + 1} = \sqrt{17} \approx 4.123$ $d=sqrt((6-2)^2+(3-4)^2)=sqrt(16+1)=sqrt17~~4.123$

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

$since sum of radii > d then circles overlap$ $"since sum of radii">d" then circles overlap"$
graph{((x-2)^2+(y-4)^2-9)((x-6)^2+(y-3)^2-4)=0 [-20, 20, -10, 10]}

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Circle A has a radius of $3$ $3$ and a center of $(2, 4)$ $(2 ,4 )$ . Circle B has a radius of $2$ $2$ and a center of $(4, 7)$ $(4 ,7 )$ . If circle B is translated by $< 2, - 4 >$ $<2 ,-4 >$ , 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 33 and a center of (2,4)(2 ,4 ). Circle B has a radius of 22 and a center of (4,7)(4 ,7 ). If circle B is translated by <2,−4><2 ,-4 >, 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 $3$ $3$ and a center of $(2, 4)$ $(2 ,4 )$ . Circle B has a radius of $2$ $2$ and a center of $(4, 7)$ $(4 ,7 )$ . If circle B is translated by $< 2, - 4 >$ $<2 ,-4 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?