Circle A has a radius of #5 # and a center of #(3 ,2 )#. Circle B has a radius of #2 # 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
Aug 6, 2018

#"circle B inside circle A"#

Explanation:

#"What we have to do here is compare the distance (d)"#
#"to the sum/difference of radii"#

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

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

#• " if difference of radii"> d" one circle inside other"#

#"Before calculating d we require to find the new centre"#
#"of B under the given translation"#

#"under the translation "< 2,-1>#

#(1,4)to(1+2,4-1)to(3,3)larrcolor(red)"new centre of B"#

#"calculate d using the "color(blue)"distance formula"#

#•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#"let "(x_1,y_1)=(3,3)" and "(x_2,y_2)=(3,2)#

#d=sqrt((3-3)^2+(3-2)^2)=sqrt1=1#

#"sum of radii "=5+2=7#

#"difference of radii "=5-2=3#

#"since difference of radii">d" circle B inside circle A"#
graph{((x-3)^2+(y-2)^2-25)((x-3)^2+(y-3)^2-4)=0 [-40, 40, -20, 20]}