Circle A has a radius of #2 # and a center of #(2 ,7 )#. Circle B has a radius of #1 # and a center of #(3 ,1 )#. If circle B is translated by #<1 ,3 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Answer 1 · 2016-12-06T20:14:14

#"1- no overlap"#
#"2-minimum distance is "0.12#

#"1-draw circles given"#

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#"2-Translate circle B by (1,3)"#

enter image source here

#"the new position of circle B is shown in figure below"#

enter image source here

#"now find distance between "O_1" and "O_T#

#O_1O_T=sqrt((2-1)^2+(7-3)^2)#

#O_1O_T=sqrt(1^2+4^2)=sqrt(1+16)=sqrt(17)=4.12#

#"radius "r_1=2#

#"radius "r_2=1#

#r_1+r_2=2+1=3#

#O_1O_T>r_1+r_2" ; no overlap"#

#"minimum distance is AB line segment(colored blue)"#

#AB=O_1O_T-r_1+r_2#

#AB=4.12-3#

#AB=0.12#