Circle A has a center at #(2 ,-2 )# and a radius of #2 #. Circle B has a center at #(1 ,-4 )# and a radius of #4 #. Do the circles overlap? If not, what is the smallest distance between them?

1 Answer
Roella W.
Feb 2, 2016

There is no overlap.

Explanation:

We can find the coordinates of the endpoints of the horizontal and vertical diameters of the circles by adding and subtracting the radius from the coordinates of the circles' centres.

Circle A has a horizontal diameter that runs from #(0,-2)# to #(4,-2)# and a vertical diameter that runs from #(2,-4)# to #(2,0)#.

Circle A therefore has the domain #{0,4}# and range #{-4,0}#

Circle B has a horizontal diameter that runs from #(-3,-4)# to #(5,-4)# and a vertical diameter that runs from #(1,-8)# to #(1,0)#

Circle B has domain #{-3,5}# and range #{-8,0}#

The domain of circle A is completely within the domain of circle B, and likewise the range of circle A is completely within the range of circle B, so circle A falls completely within circle B.
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