Circle A has a center at #(11 ,2 )# and an area of #100 pi#. Circle B has a center at #(7 ,9 )# and an area of #36 pi#. Do the circles overlap? If not, what is the shortest distance between them?

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Answer 1 · 2017-06-11T17:22:56

The circles overlap.

The radius of circle #A# is

#r_A=sqrt(100pi/pi)=10#

The radius of circle #B# is

#r_B=sqrt(36pi/pi)=6#

The distance between the center of circle #A# and the center of circle #B# is

#d=sqrt((11-7)^2+(2-9)^2)#

#=sqrt(4^2+7^2)#

#sqrt(16+49)=sqrt65#

#=8.06#

The sum of the radii is

#r_A+R_B=10+6=16#

Therefore,

As #r_A+r_B > d#

the circles overlap

graph{((x-11)^2+(y-2)^2-100)((x-7)^2+(y-9)^2-36)=0 [-20.64, 30.66, -8, 17.66]}