Circle A has a radius of #4 # and a center of #(6 ,1 )#. Circle B has a radius of #1 # and a center of #(5 ,3 )#. 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 #4 # and a center of #(6 ,1 )#.  Circle B has a radius of #1 # and a center of #(5 ,3 )#.  If circle B is translated by #<-2 ,2 >#, does it overlap circle A?  If not, what is the minimum distance between points on both circles?

James Atkins · Accepted Answer

circles have a single point of contact.

A translation does not change the shape of a figure , only it's position. Under a translation of # ((-2),(2))# centre of B (5 , 3 ) → (5 -2 , 3+2) → (3 , 5) Now require to calculate the distance between the centres of A and B using the #color(blue)" distance formula "# #color(red)(|bar(ul(color(white)(a/a)color(black)(d = sqrt((x_2 - x_1)^2 + (y_2-y_1)^2))color(white)(a/a)|)))# where # (x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points " # let # (x_1,y_1)=(6,1)" and " (x_2,y_2)=(3,5) # d # = sqrt((3-6)^2 + (5-1)^2) = sqrt(9 + 16) = sqrt25 = 5# now: radius of A + radius of B = 4 + 1 = 5 Since sum of radii = distance between centres , then the circles will have a single point of contact.

Caroline Aucoin · Answer

undefined The minimum distance between points on both circles is 3 units.

Circle A has a radius of #4 # and a center of #(6 ,1 )#. Circle B has a radius of #1 # and a center of #(5 ,3 )#. If circle B is translated by #&lt;-2 ,2 &gt;#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Circle A has a radius of #4 # and a center of #(6 ,1 )#. Circle B has a radius of #1 # and a center of #(5 ,3 )#. If circle B is translated by #<-2 ,2 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?