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

##### 2 Answers

The circle B does not overlap circle A.

The minimum distance between points on both circles is 3 units

#### Explanation:

Circle A:

radius

center

Circle B:

radius

center

translation of B

new center

Distance between center of A and new center of B' is

radius of A

radius of B

Sum of the radii

Sum of the radii

Hence, they do d

not overlap.

The difference between

the distance between the centers'an

the sum of the radii

represents the shortest distance between the two circles

separation

The two circles are separated by 3 units

#### Explanation:

#"what we have to do here is "color(blue)"compare ""the distance (d)"#

#"between the centres to the "color(blue)"sum of radii"#

#• " if sum of radii">d" then circles overlap"#

#• " if sum of radii"< d" then no overlap"#

#"before calculating d we require to find the centre of"#

#"B under the given translation"#

#"under the translation "<-2,6>#

#(3,2)to(3-2,2+6)to(1,8)larrcolor(red)"new centre of B"#

#"to calculate d use the "color(blue)"distance formula"#

#•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#"let "(x_1,y_1)=(5,1)" and "(x_2,y_2)=(1,8)#

#d=sqrt((1-5)^2+(8-1)^2)=sqrt(16+49)=sqrt65~~8.062#

#"sum of radii "=2+1=3#

#"since sum of radii"< d" then no overlap"#

#"min. distance "=d-" sum of radii"#

#color(white)(xxxxxxxxxx)=8.062-3=5.062#

graph{((x-5)^2+(y-1)^2-4)((x-1)^2+(y-8)^2-1)=0 [-20, 20, -10, 10]}