Circle A has a center at #(1 ,3 )# and an area of #24 pi#. Circle B has a center at #(8 ,2 )# and an area of #66 pi#. Do the circles overlap?

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Answer 1 · 2017-03-01T19:49:01

Yes

#A_1 = 24pi = pi r_1^2#
#r_1^2 = 24# therefore #r_1 = sqrt(24) = sqrt(6*4) = 2sqrt(6) ~~ 4.9#

#A_2 = 66pi = pi r_2^2#
#r_2^2 = 66# therefore #r_2 = sqrt(66) ~~8.12#

From #(1,3)# add #r_1# to the #x# gives #(5.9, 3)#

From #(8,2)# subtract #r_2# from the #x# gives #(-.12, 2)#

Since #-.12 < 5.9# the circles overlap.

Graph of first circle: #(x-1)^2 + (y-3)^2 = 24#:
graph{(x-1)^2 + (y-3)^2 = 24 [-11.66, 13.65, -3.34, 9.32]}

Graph of second circle: #(x-8)^2 + (y-2)^2 = 66#:
graph{(x-8)^2 + (y-2)^2 = 66 [-15.68, 20.35, -6.93, 11.09]}