# Circle A has a radius of #3 # and a center of #(3 ,2 )#. Circle B has a radius of #5 # and a center of #(1 ,7 )#. 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

Jan 12, 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 there is 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),(-1))#

#(1,7)to(1+2,7-1)to(3,6)# Note that the centres (3 ,2) and (3 ,6) have the same x-coordinate and so d is just the difference in the y-coordinates.

#rArrd=6-2=4# sum of radii = radius of A + radius of B = 3 + 5 = 8

Since sum of radii > d , then circles overlap

graph{(y^2-4y+x^2-6x+4)(y^2-12y+x^2-6x+20)=0 [-40, 40, -20, 20]}