Circle A has a center at #(5 ,4 )# and an area of #16 pi#. Circle B has a center at #(12 ,8 )# and an area of #25 pi#. Do the circles overlap? If not, what is the shortest distance between them?

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Answer 1 · 2017-10-14T07:27:03

The given circles intersect

Since the area of a circle is #pi*r^2#

we get

#16cancelpi=cancelpi*r^2# (circle A)

then #r_A=4#

and

#25cancelpi=cancelpi*r^2# (circle B)

then

#r_B=5#

The distance between the centers is:

#C_AC_B=sqrt((x_B-x_A)^2+(y_B-y_A)^2)#

#=sqrt((12-5)^2+(8-4)^2)=sqrt(49+16)=sqrt65#

that's less than the sum of the radiuses

#C_AC_B=sqrt65<4+5#

We conclude that the circles intersect:

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