Circle A has a radius of $5$ $5$ and a center of $(2, 6)$ $(2 ,6 )$ . Circle B has a radius of $2$ $2$ and a center of $(4, 3)$ $(4 ,3 )$ . If circle B is translated by $< - 3, 1 >$ $<-3 ,1 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Answer 1 · 2017-07-15T05:44:59

The circles overlap.

The new center of circle $B$ $B$ is

$C'_B=(4,3)+<-3,1> =(1,4)$

The distance between the centers of the circles after translation is

$C_AC'_B=sqrt((1-2)^2+(4-6)^2)=sqrt(1+4)=sqrt5$

The sum of the radii is

$=r_A+r_B'=5+2=7$

As $C_AC_B'< r_A+r_B$ , the circles overlap

graph{((x-2)^2+(y-6)^2-25)((x-1)^2+(y-4)^2-4)=0 [-10, 10, -5, 5]}

Circle A has a radius of 5 55 and a center of (2 ,6 )(2,6)(2 ,6 ). Circle B has a radius of 2 22 and a center of (4 ,3 )(4,3)(4 ,3 ). If circle B is translated by <-3 ,1 ><−3,1><-3 ,1 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?