Circle A has a center at #(5 ,9 )# and an area of #96 pi#. Circle B has a center at #(7 ,2 )# and an area of #45 pi#. Do the circles overlap?

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Answer 1 · 2018-01-12T17:31:11

Since the sum of radii 16.5062 is greater than the distance
between the two centers, the two circles overlap

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Distance between the two centers

#AB = D = sqrt((7-5)^2 + (2-9)^2) = 7.28#

Radius of circle A #r_a =sqrt(( 96pi )/ pi )= 9.798#

Radius of circle B #r_b = sqrt((45pi)/pi) = 6.7082#

Sum of the two radii = 9.798 + 6.7082 = 16.5062#

Since the sum of radii 16.5062 is greater than the distance
between the two centers, the two circles overlap