Question

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

Answer 1

The circles overlap.

Explanation:

The new center of circle `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]}