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.
Sketch

Related questions
See all questions in Distance between Points
Impact of this question
1445 views around the world
You can reuse this answer
Creative Commons License