Two circles have the following equations #(x -1 )^2+(y -6 )^2= 64 # and #(x +7 )^2+(y +2 )^2= 9 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?

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Answer 1 · 2016-10-16T22:26:52

One does not contain the other.
The greatest distance possible is #8sqrt(2) + 11#

The radius of the first circle is 8
The radius of second circle is 3

The center of the first circle is #(1, 6)#
The center of the second circle is #(-7, -2)#
The distance, d, between their centers is:

#d = sqrt((1 - -7)^2 + (6 - -2)^2#

#d = 8sqrt(2)#

This is greater than the sum of their radii so they do not touch.