Question

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

Answer 1

After the translation `C_B=(4-3,5+4)=(1,9)`

Explanation:

The distance between `C_AandC_B` can be calculated by the good old Pythagoras:
`(C_AC_B)^2=(5-1)^2+(2-9)^2=16+49=65`
`->C_AC_B=sqrt65~~8.06`

Since the radii of the circles add up to `3`, they don't overlap, and the minimum distance between points on the circles will be:
`d=sqrt65-3~~5.06`