Circle A has a radius of $2$ $2$ and a center of $(1, 7)$ $(1 ,7 )$ . Circle B has a radius of $2$ $2$ and a center of $(8, 1)$ $(8 ,1 )$ . If circle B is translated by $< - 4, 3 >$ $<-4 ,3 >$ , 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 of $(1, 7)$ $(1 ,7 )$ . Circle B has a radius of $2$ $2$ and a center of $(8, 1)$ $(8 ,1 )$ . If circle B is translated by $< - 4, 3 >$ $<-4 ,3 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Answer 1 · 2016-09-03T01:37:22

Circle A has a radius of 2 and a center of (1,7)
Circle B has a radius of 2 and a center of (8,1)
if circle B is translated by <-4,3>, the center will be (4,4)

Explanation:

distance bewteen circle A (1,7) and circle B (4,4) from center to center is
$= \sqrt{{(4 - 1)}^{2} + {(4 - 7)}^{2}} = \sqrt{3^{2} + 3^{2}}$ $=sqrt((4-1)^2+(4-7)^2) = sqrt(3^2+3^2)$
$= \sqrt{9 + 9} = \sqrt{18} = \sqrt{9 \times 2}$ $=sqrt(9+9) = sqrt18 =sqrt(9xx2)$
$= 3 \sqrt{2} = 4.24$ $=3sqrt2 =4.24$
As circle A and Circle B each has a radius of 2, they do not overlap each other because 4.24 is greater than 2+2 =4 (the sum of the two radii)
the minimum distance between circle A and circle B is
$= 4.24 - 2 - 2 = 0.24$ $=4.24 -2 -2 = 0.24$

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Circle A has a radius of $2$ $2$ and a center of $(1, 7)$ $(1 ,7 )$ . Circle B has a radius of $2$ $2$ and a center of $(8, 1)$ $(8 ,1 )$ . If circle B is translated by $< - 4, 3 >$ $<-4 ,3 >$ , 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 of (1,7)(1 ,7 ). Circle B has a radius of 22 and a center of (8,1)(8 ,1 ). If circle B is translated by <−4,3><-4 ,3 >, 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 $2$ $2$ and a center of $(1, 7)$ $(1 ,7 )$ . Circle B has a radius of $2$ $2$ and a center of $(8, 1)$ $(8 ,1 )$ . If circle B is translated by $< - 4, 3 >$ $<-4 ,3 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?