Circle A has a radius of #3 # and a center at #(1 ,2 )#. Circle B has a radius of #5 # and a center at #(3 ,7 )#. If circle B is translated by ##, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Question

Circle A has a radius of #3 # and a center at #(1 ,2 )#.  Circle B has a radius of #5 # and a center at #(3 ,7 )#.  If circle B is translated by #<2 ,4 >#, does it overlap circle A?  If not, what is the minimum distance between points on both circles?

Aaliyah Anderson · Accepted Answer

#"no overlap "~~2.82# #"what we have to do here is compare the distance (d)"# #"between the centres to the 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"# #"under the translation "<2,4># #(3,7)to(3+2,7+4)to(5,11)larrcolor(red)"new centre of B"# #"to calculate d use 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)=(1,2)" and "(x_2,y_2)=(5,11)# #d=sqrt((5-1)^2+(11-2)^2)=sqrt(16+81)=sqrt117~~10.82# #"sum of radii "=3+5=8# #"since sum of radii"< d" then no overlap"# #"minimum distance "=d-" sum of radii"# #color(white)(xxxxxxxxxxxxx)=10.82-8=2.82# graph{((x-1)^2+(y-2)^2-9)((x-5)^2+(y-11)^2-25)=0 [-20, 20, -10, 10]}

Circle A has a radius of #3 # and a center at #(1 ,2 )#. Circle B has a radius of #5 # and a center at #(3 ,7 )#. If circle B is translated by #&lt;2 ,4 &gt;#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Circle A has a radius of #3 # and a center at #(1 ,2 )#. Circle B has a radius of #5 # and a center at #(3 ,7 )#. If circle B is translated by #<2 ,4 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?