Circle A has a center at #(5 ,1 )# and an area of #4 pi#. Circle B has a center at #(2 ,8 )# and an area of #16 pi#. Do the circles overlap? If not, what is the shortest distance between them?

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Answer 1 · 2016-11-11T18:37:25

They do not overlap. The closest distance is #d = sqrt(58) - 6 ~~ 1.6#

The radius of circle A is: 2
The radius of circle B is: 4

The distance, d, between the centers is:

#d = sqrt((5 - 2)^2 + (1 - 8)^2)#

#d = sqrt((3)^2 + (-7)^2)#

#d = sqrt(58)#

This is greater than the sum of the radii, thefore, the circles do not overlap.

Here is a graph of the two circles:

enter image source here

The closest distance is #d = sqrt(58) - 6 ~~ 1.6#