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

1 Answer
Oct 1, 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 the 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),(-3))#

#(4,7)to(4+2,7-3)to(6,4)larrcolor(red)" new centre of B"#

#"since the centres have the same y-coordinate then"#
#"d is the difference in the x-coordinates"#

#rArrd=6-2=4#

#"sum of radii "=3+2=5#

#"since sum of radii">d" then circles overlap"#
graph{((x-2)^2+(y-4)^2-9)((x-6)^2+(y-4)^2-4)=0 [-10, 10, -5, 5]}