# Circle A has a radius of #2 # and a center of #(6 ,5 )#. Circle B has a radius of #3 # and a center of #(2 ,4 )#. 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?

##### 2 Answers

#### Explanation:

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

#"between the centres to the sum of the 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 new centre"#

#"of B after the given translation"#

#"under the translation "< 1,1>#

#(2,4)to(2+1,4+1)to(3,5)larrcolor(red)"new centre of B"#

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

#d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#"let "(x_1,y_1)=(6,5)" and "(x_2,y_2)=(3,5)#

#d=sqrt((3-6)^2+(5-5)^2)=sqrt9=3#

#"sum of radii "=2+3=5#

#"since sum of radii">d" then circles overlap"#

graph{((x-6)^2+(y-5)^2-4)((x-3)^2+(y-5)^2-9)=0 [-20, 20, -10, 10]}

The distance between the centers is

#### Explanation:

I thought I did this one already.

A is

B's new center is

Distance between centers,

Since the distance between the centers is less than the sum of the two radii, we have overlapping circles.