Circle A has a radius of $2$ $2$ and a center of $(3, 1)$ $(3 ,1 )$ . Circle B has a radius of $6$ $6$ and a center of $(8, 5)$ $(8 ,5 )$ . 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 $(3, 1)$ $(3 ,1 )$ . Circle B has a radius of $6$ $6$ and a center of $(8, 5)$ $(8 ,5 )$ . 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 · 2018-02-09T10:27:46

Since $R_{A} + R_{B} (8) > - --- \to O_{A} O_{B} (5.83)$ $color(blue)(R_A + R_B (8)) color(green)(>) color(red)(vec(O_AO_B) (5.83)$ circles A & B overlap

Explanation:

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$O_A ((3),(1)), R_A = 2$ , $O_B ((8), (5)), R_B = 6$

$O_B$ translated by (-4,3)

New $O_B = ((3-5),(1+3)) => ((-2),(4))$

$vec(O_AO_B) = sqr((-2-3)^2 + (4-1)^2) = sqrt34 ~~ 5.83$

Sum of radii $R_A + R_B = 2 + 8 = 8$

Since $R_A + R_B (8) > vec(O_AO_B) (5.83)$ the circles overlap

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Circle A has a radius of $2$ $2$ and a center of $(3, 1)$ $(3 ,1 )$ . Circle B has a radius of $6$ $6$ and a center of $(8, 5)$ $(8 ,5 )$ . 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 22 and a center of (3 ,1 )(3,1)(3 ,1 ). Circle B has a radius of 6 66 and a center of (8 ,5 )(8,5)(8 ,5 ). 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?

1 Answer

Explanation:

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Circle A has a radius of $2$ $2$ and a center of $(3, 1)$ $(3 ,1 )$ . Circle B has a radius of $6$ $6$ and a center of $(8, 5)$ $(8 ,5 )$ . 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?