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

1 Answer
Sep 28, 2016

The circles overlap.

Explanation:

If circle #B# with center #(3,4)# is translated by #<-2,1># its new center will be at #(3-2,4+1)=(1,5)#
The distance between the center of #A# at #(5,6)# and the new center of #B# is given by the Pythagorean Theorem as:
#color(white)("XXX")d=sqrt((5-1)^2+(6-5)^2)=sqrt(17)~~4.123#

We are told that circle #A# has a radius of #2# and circle #B# has a radius of #2# and circle #B# has a radius of #5#.

Considering the line segment joining the centers of the two circles,
we can see that #A# covers #2# units of that line segment and #B# covers #5# units (actually more than the length of the line segment.

Since there is only #4.123# units between the two centers, the circles must overlap.
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