Circle A has a center at #(3 ,4 )# and an area of #18 pi#. Circle B has a center at #(8 ,1 )# and an area of #40 pi#. Do the circles overlap?

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Answer 1 · 2018-02-10T09:37:34

Circles Overlap

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Distance between the centers of the circles using distance formula

#vec(O_AO_B) = sqrt((8-3)^2 + (1-4)^2) ~~ 5.83#

#A_A = pi (R_A)^2#

#R_A = sqrt((18pi) / pi ) ~~ 4.24#

Similarly #R_B = sqrt((40pi)/pi) ~~ 6.32#

Sum of the radii #R_A + R_B = 4.24 + 6.32 = 10.56#

Since #R_A + R_B > vec(O_AO_B)#, two circles overlap.