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

1 Answer

Answer:

circle B do not overlap.
Shortest distance is #3.764-2=1.764#

Explanation:

Circle A
Center #(2,7)#
radius #2#

Equation of circle A
#(x-2)^2+(y-7)^2=2^2#

Circle B
Center #(7,5)#
radius #6#

Equation of circle B
#(x-7)^2+(y-5)^2=6^2#

ranslation of B
<-1,1>
Center of B after translation #((7-1),(5+1))#
Center of B after translation #(6,6)#

Equation of circle B after translation
#(x-6)^2+(y-6)^2=6^2#

Intersection of the circles
#(x-2)^2+(y-7)^2=2^2#
and
#(x-6)^2+(y-6)^2=6^2#
can be found out

Distance from center of Circle A to
center of Circle B is
#(2,7) ---- (6,6)#
#=sqrt((6-7)^2+(6-2)^2#
#=sqrt((1+4)#
#=sqrt(5)#
#=2.236#

Radius of circle A is #2#
point on the Perimeter of the circle B is away from its center by 6
point on the Perimeter of the circle B is away from (2,7) is#6-2.236#
#=3.764#
Hence, the two circles donot overlap.
Shortest distance is #3.764-2=1.764#