Circle A has a center at #(3 ,7 )# and an area of #56 pi#. Circle B has a center at #(9 ,6 )# and an area of #28 pi#. Do the circles overlap?

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Answer 1 · 2016-03-15T05:20:15

the circles will overlap.

the circles will overlap if the distance between the centers is smaller than the sum of the radius.

the distance between the radius is,

#d=sqrt((9-3)^2+(7-6)^2)#

#=sqrt(6^2+1^2)#

#=sqrt(36+1)#

#=6.08#

here,

#pir_1^2=56pi#

#or,r_1^2=56#

#or,r_1=7.48#

again,

#pir_2^2=28pi#

#or,r_2^2=28#

#or,r_2=5.29#

so,
#r_1+r_2=7.48+5.29#

#=12.77#

so, the circles will overlap.