Circle A has a radius of #4 # and a center of #(8 ,5 )#. Circle B has a radius of #2 # and a center of #(6 ,1 )#. If circle B is translated by #<2 ,7 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

1 Answer
Jun 18, 2017

#"circles overlap"#

Explanation:

#"what we have to do here is " color(blue)"compare "" the"#
#"distance (d) between the centres 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' coordinates"#
#"of centre B under the given translation which does not change"#
#" the shape of the circle only it's position"#

#"under a translation" ((2),(7))#

#(6,1)to(6+2,7+1)to(8,8)larr" new centre of B"#

#"to calculate d note the centres are " (8,5)" and " (8,8)#

#"the x-coordinates are equal so centres lie on a "#
#"vertical line and "#

#d=8-5=3#

#"sum of radii "=4+2=6#

#"since sum of radii ">d" then circles overlap"#
graph{(y^2-16y+x^2-16x+124)(y^2-10y+x^2-16x+73)=0 [-20, 20, -10, 10]}