Circle A has a center at #(9 ,4 )# and a radius of #3 #. Circle B has a center at #(-1 ,6 )# and a radius of #5 #. Do the circles overlap? If not, what is the smallest distance between them?

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Answer 1 · 2017-12-07T12:34:07

They do not overlap - min distance is about 2.2

If the distance between the two centers is less than the sum of their radii, then they overlap.

We find the distance between the centers with the Pythagorean theorem:

#d = sqrt((9 - (-1))^2 + (4-6)^2) #

#= sqrt(100 + 4)#

= 10.2 (rounding)

the two circles' radii add up to 8.

...so they do NOT overlap. Minimum distance between the circles is
#10.2 - 8 = 2.2# (rounding)

GOOD LUCK