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

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Answer 1 · 2017-07-23T13:09:40

The circles do not overlap and the distance is $= 1.07$ $=1.07$

The coordinates of the center of circle $B'$ after translation is

$C_B'=(2,3)+<-1,2> = (1,5)$

The distance between the centers is

$C_AC_B'=sqrt((1-8)^2+(5-6)^2)=sqrt(49+1)=sqrt50=7.07$

The sum of the radii is

$r_A+r_B=2+4=6$

As

$C_AC_B' > (r_A+r_B)$ , the circles do not overlap

The shortest distance is $=7.07-6=1.07$

graph{((x-8)^2+(y-6)^2-4)((x-1)^2+(y-5)^2-16)=0 [-8.66, 16.65, -2.97, 9.69]}

Circle A has a radius of 2 22 and a center of (8 ,6 )(8,6)(8 ,6 ). Circle B has a radius of 4 44 and a center of (2 ,3 )(2,3)(2 ,3 ). If circle B is translated by <-1 ,2 ><−1,2><-1 ,2 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?