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?

Question

1785 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-06T20:14:14

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

#"1-draw circles given"#

enter image source here

#"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#