Circle A has a radius of #3 # and a center of #(5 ,4 )#. Circle B has a radius of #4 # and a center of #(7 ,2 )#. If circle B is translated by #<3 ,2 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Question

1275 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-06T14:08:38

The circles overlap

Let the center of the circle #A# be #O_A=(5,4)#

and the center of the circle #B# be #O_B=(7,2)#

The center after translation is

#O_B'=(7,2)+ <3,2> =(10,4)#

The distance between the centers is

#O_AO_B'=sqrt((10-5)^2+(4-4)^2)#

#=5#

The sum of the radii is

#r_A+r_B=3+4=7#

As ,

#O_AO_B'<(r_A+r_B)#

The circles overlap

graph{((x-5)^2+(y-4)^2-9)((x-7)^2+(y-2)^2-16)((x-10)^2+(y-4)^2-16)=0 [-6, 16.5, -2.185, 9.065]}