Circle A has a radius of #1 # and a center of #(5 ,4 )#. Circle B has a radius of #2 # and a center of #(4 ,5 )#. If circle B is translated by #<-3 ,4 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
1 Answer
no overlap , ≈ 3.4
Explanation:
Here, we have to calculate the distance (d) between the centres and compare this with the sum of the radii.
• If sum of radii > d , then circles overlap.
• If sum of radii < d , then no overlap.
Now a translation does not change the shape of a figure , only it's position.
Under a translation of
#((-3),(4))# centre of B(4 , 5) → (4-3 , 5+4) → (1 , 9)
To calculate the distance between the centres , use 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 points."# let
# (x_1,y_1)=(5,4)" and " (x_2,y_2)=(1,9)#
# d =sqrt((1-5)^2+(9-4)^2)=sqrt(16+25)=sqrt41 ≈ 6.4# radius of A + radius of B = 1+2 = 3
Since sum of radii < d , then no overlap
and minimum distance = d -sum of radii = 6.4 - 3 = 3.4
