Circle A has a radius of #2 # and a center of #(8 ,2 )#. Circle B has a radius of #4 # and a center of #(2 ,3 )#. If circle B is translated by #<-1 ,5 >#, 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 ≈ 3.22
Explanation:
A translation does not change the shape of a figure , only it's position.
Under a translation of
# ((-1),(5))# centre of B (2,3) → (2-1 , 3+5) → (1,8)
We 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)=(8,2)" and " (x_2,y_2)=(1,8)#
# d = sqrt((1-8)^2 + (8-2)^2) = sqrt(49+36) = sqrt85 ≈ 9.22 # now: radius of A + radius of B = 2 + 4 = 6
since sum of radii < distance between centres , no overlap
and distance between them = 9.22 - 6 = 3.22
