Circle A has a radius of #3 # and a center of #(5 ,9 )#. Circle B has a radius of #4 # and a center of #(1 ,2 )#. If circle B is translated by #<3 ,-1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Question

1357 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-09T12:15:31

circles do not overlap

Minimum distance between circles A & B is #8.06 - 7 = color(red)(1.06)#

enter image source here

#R_A = 3, O_A ((5),(9)), R_B = 4, O_B ((1),(2))#.

Center of circle B translated by #((3),(-1))#

Sum of radii #R_A + R_B = 3 + 4 = color(purple)(7)#

New coordinates of #O_B -> ((1+3),(2-1)) => ((4),(1))#

#vec(O_AO_B) = sqrt((5-4)^2 + (9-1)^2) = sqrt65 ~~ color(green)(8.06)#

#vec(O_AO_B) > R_A + R_B#

Hence the circles do not overlap

Minimum distance between circles A & B is #8.06 - 7 = color(red)(1.06)#