Circle A has a radius of #3 # and a center of #(2 ,7 )#. Circle B has a radius of #4 # and a center of #(7 ,5 )#. If circle B is translated by #<-1 ,1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

1 Answer
Feb 9, 2018

Answer:

Circles overlap .

Minimum distance between the circles is

Explanation:

Given : #A(2,7), R_A = 3#, #B (7,5), R_B = 4# B translated by (-1, 1)

Therefore, new coordinates of #B( (7-1), (5+1)) = B((6),(6))#

Distance between A and new B

#d = sqrt((2-6)^2 + (7-6)^2) = sqrt17 ~~ 4.123#

Circles overlap if# d < R_A + R_B# and NOT if #d> R_a + R_B#

#R_A + R_B = 3 + 4 = 7#

Since #d < R_A + R_B#, circles overlap