Circle A has a center at #(2 ,1 )# and a radius of #4 #. Circle B has a center at #(4 ,7 )# and a radius of #3 #. Do the circles overlap? If not what is the smallest distance between them?

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Answer 1 · 2016-02-04T10:23:06

The circles overlap because both the domains and the ranges overlap.

Work out the domain and range of each of the circles. If those overlap then the circles overlap.

The #x# values of circle #A# run from #2-4# to #2+4# so the domain is #{-2,6}#

The #x# values of circle #B# run from #4-3# to #4+3# so the domain is #{1,7}#

The #y# values of circle #A# run from #1-4# to #1+4# so the range is #{-3,5}#

The #y# values for circle #B# run from #7-3# to #7+3# so the range is #{4,10}#

The circles overlap because both the domains and the ranges overlap.

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