Circle A has a radius of $2$ $2$ and a center of $(1, 7)$ $(1 ,7 )$ . Circle B has a radius of $6$ $6$ 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 · 2018-02-09T12:23:50

Circles Overlap

Given :
$O_A ((1), (7)), R_A =m 2, O_B ((8),(1)), R_B = 6$

Circle B translated by $((-4),(3))$

Sum of Radii $R_A + R_B = 2 + 6 = color(purple)(8$

New coordinates of $O_B -> ((8-4),(1+3)) => ((4),(4))$

$vec(O_AO_B) = sqrt((4-1)^2 + (4-7)^2) = sqrt18 ~~ color(green)(4.24$

Since sum of radii greater than the distance between the two circle

centers, Circles Overlap

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Circle A has a radius of 2 22 and a center of (1 ,7 )(1,7)(1 ,7 ). Circle B has a radius of 6 66 and a center of (8 ,1 )(8,1)(8 ,1 ). If circle B is translated by <-4 ,3 ><−4,3><-4 ,3 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?