Circle A has a center at #(3 ,2 )# and an area of #32 pi#. Circle B has a center at #(9 ,2 )# and an area of #24 pi#. Do the circles overlap?

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Answer 1 · 2018-01-08T10:14:45

As sum of the radii is greater than the distance between the circle centers, the circles overlap .

Circle A center (3,2), area #A_A = 32pi#

Circle B center (9,2), area #A_B = 24pi#

#r_A = sqrt((32pi)/pi) = 5.6569#

#r_B = sqrt((24pi) / pi) = 4.899#

Distance between the two centers

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

As #r_A + r_B = color (red)(10.5548)# is greater than the distance between the centers #d =color (red)( 6)#, the circles overlap.