# Circle A has a radius of #2 # and a center of #(6 ,2 )#. Circle B has a radius of #3 # and a center of #(5 ,7 )#. If circle B is translated by #<-1 ,2 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

##### 1 Answer

Apr 9, 2016

no overlap , d ≈ 2.28

#### Explanation:

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

Under a translation of

# ((-1),(2))# Centre of B (5 , 7) → (5-1 , 7 + 2 ) → (4 , 9)

Now require to 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)=(6,2)" and " (x_2,y_2)=(4,9) # d

#= sqrt((4-6)^2 + (9-2)^2) = sqrt(4 + 49) = sqrt53 ≈ 7.28 # now, radius of A + radius of B = 2 + 3 = 5

Since sum of radii < distance between centres , no overlap

and distance between circles (d) = 7.28 - 5 = 2.28