Circle A has a center at #(1 ,7 )# and a radius of #1 #. Circle B has a center at #(-3 ,-2 )# and a radius of #2 #. Do the circles overlap? If not, what is the smallest distance between them?
1 Answer
Aug 10, 2017
Explanation:
what we have to do here is
#color(blue)"compare "# the distance between the centres of the circles to the#color(blue)"sum of 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)|)))#
#(x_1,y_1)=(1,7)" and "(x_2,y_2)=(-3,-2)#
#d=sqrt((-3-1)^2+(-2-7)^2)=sqrt(16+81)~~ 9.849#
#"sum of radii "=1+2=3#
#"since sum of radii"< d" then no overlap"#
#"smallest distance "=d-" sum of radii"#
#color(white)(smallest distance)=9.849-3=6.849#
graph{((x-1)^2+(y-7)^2-1)((x+3)^2+(y+2)^2-4)=0 [-20, 20, -10, 10]}
