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

1 Answer
Sep 13, 2017

#"circles overlap"#

Explanation:

What we have to do here is #color(blue)"compare"# the distance ( d) between the centres of the circles to the #color(blue)"sum of radii"#

#• " if sum of radii ">d" then circles overlap"#

#• " if sum of radii " < d" then no overlap"#

Before calculating d we require to find the 'new ' centre of B under the given translation which does not change the shape of the circle only it's position.

#"under a translation "((2),(-1))#

#(1,4)to(3,3)larrcolor(red)" new centre of B"#

#"since "(5,3)" and "(3,3)" have the same y-coordinate then"#
#"d is the difference of the x-coordinates"#

#rArrd=5-3=2#

#"sum of radii "=4+3=7#

#"since sum of radii ">d" then circles overlap"#
graph{((x-5)^2+(y-3)^2-16)((x-3)^2+(y-3)^2-9)=0 [-20, 20, -10, 10]}