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

##### 1 Answer

Apr 6, 2016

no overlap , d ≈ 2.81

#### Explanation:

A translation does not change the shape of a figure , only it's position.

Under a translation of

# ((-3),(2))# centre B (4,5) → (4-3 , 5+2) → (1 , 7)

Calculate the distance between the centres of A and B using the

#color(blue)" distance formula " #

# d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2) # 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)=(1,7) # d

#=sqrt((1-6)^2 + (7-1)^2) = sqrt(25+36) = sqrt61 ≈ 7.81# radius of A + radius of B = 4 + 1 = 5

since sum of radii < distance between centres , no overlap.

and distance between them = 7.81 - 5 = 2.81