# Circle A has a center at #(2 ,4 )# and a radius of #5 #. Circle B has a center at #(9 ,3 )# and a radius of #1 #. Do the circles overlap? If not what is the smallest distance between them?

##### 1 Answer

Dec 8, 2017

#### Explanation:

What we have to do here is

#color(blue)"compare"# the distance (d) between the centres of the circles to the#color(blue)"sum of the radii"#

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

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

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

#color(red)(bar(ul(|color(white)(2/2)color(black)(d=sqrt((x_2-x_1)^2+(y_2-y_1)^2))color(white)(2/2)|)))#

#"let "(x_1,y_1)=(2,4)" and "(x_2,y_2)=(9,3)#

#d=sqrt((9-2)^2+(3-4)^2)=sqrt(49+1)=sqrt50~~7.07#

#"sum of radii "=5+1=6#

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

#"smallest distance "=d-" sum of radii"#

#color(white)(xxxxxxxxxxxx)=7.07-6=1.07#

graph{((x-2)^2+(y-4)^2-25)((x-9)^2+(y-3)^2-1)=0 [-20, 20, -10, 10]}