Circle A has a center at #(1 ,8 )# and an area of #15 pi#. Circle B has a center at #(5 ,3 )# and an area of #24 pi#. Do the circles overlap?

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Answer 1 · 2016-10-03T07:27:37

The distance between the centers is less than the sum of their radii, therefore, the circles overlap.

The area of a circle is #A = pir²#. This allows us to observe that the radius of circle A is:

#r_a= sqrt15#

And the radius of circle B is:

#r_b = sqrt24#.

The distance, d, between the centers is:

#d = sqrt((1 - 5)² + (8 - 3)²)#

#d = sqrt((-4)² + (5)²)#

#d = sqrt(16 + 25)#

#d = sqrt41#

#d < (r_a + r_b)# by 2.369, therefore, the circles overlap