Circle A has a center at #(5 ,1 )# and an area of #4 pi#. Circle B has a center at #(2 ,8 )# and an area of #9 pi#. Do the circles overlap? If not, what is the shortest distance between them?

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Answer 1 · 2016-03-11T12:11:11

The circles do not overlap
Shortest distance#=d-r_a-r_b=sqrt58-5=2.615#

Compute first the distance between the centers

#d=sqrt((5-2)^2+(1-8)^2)#

#d=sqrt((3^2+(-7)^2)#

#d=sqrt((9+49)#
#d=sqrt58=7.615#

Compute the sum of the radius

#r_a+r_b=sqrt4+sqrt9=5#

God bless....I hope the explanation is useful.