Circles A and B have the following equations #(x -4 )^2+(y +3 )^2= 25 # and #(x +4 )^2+(y -1 )^2= 49 #. What is the greatest possible distance between a point on circle A and another point on circle B?

1 Answer
Cesareo R.
May 21, 2016

#d = 20.9443#

Explanation:

Circles #C_1# and #C_2# have respectively centers at
#p_1=(4,-3), p_2=(-1,1)# and radius #r_1=5, r_2=7#
Their distance concerning centers is given by
#d_{12} = norm (p_1-p_2) = 8.94427#.

As we can observe is verified that
#r_1 < r_2 + norm (p_1-p_2) #
#r_2 < r_1 + norm (p_1-p_2)#
#norm (p_1-p_2) < r_1 + r_2#
so the circles intersect in two points.
In this case the maximum distance between #C_1# and #C_2# is given by
#norm (p_1-p_2) +r_1+r_2 = 20.9443#

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