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

1 Answer
Feb 9, 2018

Answer:

Two circles DO NOT OVERLAP

Minimum distance between both circles #= 5.83 - 3 = color(brown)(2.83#

Explanation:

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#O_A ((2),(4)), R_A = 1, O_B ((4),(5)), R_B = 2#

Circle B translated by #((1),(4))#

Sum of Radii #R_A + R_B = 1 + 2 = color(green)(3#

New coordinates of #O_B = ((4+1),(5+4)) => ((5),(9))#

Distance d = #vec(O_AO_B) = sqrt((5-2)^2 + (9-4)^2) = sqrt34 ~~ color(blue)(5.83#

#R_a + R_B < vec(O_AO_B) #. Hence the Two circles DO NOT OVERLAP

Minimum distance between both circles #= 5.83 - 3 = color(brown)(2.83#