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?

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Answer 1 · 2016-07-13T23:39:09

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

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:
$d=sqrt65-3~~5.06$

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