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 $(3, 5)$ $(3 ,5 )$ . 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?

Question

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 $(3, 5)$ $(3 ,5 )$ . 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

Impact of this question

1395 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-26T19:27:12

$no overlap, \approx 4.22$ $"no overlap ",~~4.22$

Explanation:

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

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

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

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

$under the translation < - 2, 4 >$ $"under the translation "< -2,4>$

$(3, 5) \to (3 - 2, 5 + 4) \to (1, 9) \leftarrow new centre of B$ $(3,5)to(3-2,5+4)to(1,9)larrcolor(red)"new centre of B"$

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

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

$let (x_{1}, y_{1}) = (8, 3) and (x_{2}, y_{2}) = (1, 9)$ $"let "(x_1,y_1)=(8,3)" and "(x_2,y_2)=(1,9)$

$d = \sqrt{{(1 - 8)}^{2} + {(9 - 3)}^{2}} = \sqrt{49 + 36} = \sqrt{85} \approx 9.22$ $d=sqrt((1-8)^2+(9-3)^2)=sqrt(49+36)=sqrt85~~9.22$

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

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

$min. distance = d - sum of radii$ $"min. distance "=d-" sum of radii"$

$\times \times \times \times \times = 9.22 - 5 = 4.22$ $color(white)(xxxxxxxxxx)=9.22-5=4.22$
graph{((x-8)^2+(y-3)^2-4)((x-1)^2+(y-9)^2-9)=0 [-40, 40, -20, 20]}

Science

Math

Humanities

... and beyond

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 $(3, 5)$ $(3 ,5 )$ . 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:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

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 (3,5)(3 ,5 ). 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:

Related questions

Impact of this question

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 $(3, 5)$ $(3 ,5 )$ . 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?