Circle A has a center at #(2 ,3 )# and an area of #18 pi#. Circle B has a center at #(7 ,2 )# and an area of #64 pi#. Do the circles overlap?

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Answer 1 · 2018-03-02T11:40:49

#d# lies between #(R_B-R_A) and (R_B+R_A)#, so circles
will overlap.

Circle "A" area is #A_A=pi*R_A^2=18 pi :. R_A^2=18#

#:.R_A=sqrt(18) ~~ 4.24 # Centre :# (x_1=2,y_1=3)#

Circle "B" area is #A_B=pi*R_B^2=64 pi :. R_B^2=64#

#:.R_B=sqrt(64) =8.0 # Centre :# (x_2=7,y_2=2)#

Distance between centres #d= sqrt((x_1-x_2)^2+(y_1-y_2)^2#

#d= sqrt((2-7)^2+(3-2)^2)=sqrt 26 ~~ 5.1#

#R_B+R_A=8+4.24 ~~12.24# and

#R_B-R_A=8-4.24 ~~3.76 :. 3.76 < 5.1 < 12.24#

If #d# lies in between #(R_B-R_A) and (R_B+R_A)# then circles

will intersect or overlap and have one common chord. [Ans]