Circle A has a center at #(7 ,-5 )# and a radius of #1 #. Circle B has a center at #(4 ,2 )# and a radius of #4 #. Do the circles overlap? If not, what is the smallest distance between them?

1 Answer
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Feb 2, 2016

The circles don't overlap, and the smallest distance between them = 2.62

Explanation:

  • First: using the formula :
    #d=sqrt((x_1-x_2)^2+(y_1-y_2)^2)#

the distance between the two centers#=d=sqrt((7-4)^2+(-5-2)^2)=sqrt(9+49)#
#=sqrt(58)=7.62#

  • Second:
    The distance between the two centers > the sum of the two radii.
    Meaning the circles don't overlap.

  • Third: The smallest distance between them is the portion of the line connecting the two centers that doesn't fall in either circle. Or #s# in the image below.
    kwiznet.com

#s=bar(PO)-"sum of the two radii"#
#s=sqrt(58)-5#
#s=2.62#

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