Circle A has a center at #(3 ,7 )# and a radius of #2 #. Circle B has a center at #(4 ,-2 )# and a radius of #6 #. Do the circles overlap? If not, what is the smallest distance between them?
1 Answer
Dec 20, 2017
Explanation:
What we have to do here is
#color(blue)"compare"# the distance between the centres (d) with 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)=(3,7)" and "(x_2,y_2)=(4,-2)#
#d=sqrt((4-3)^2+(-2-7)^2)=sqrt(82)~~9.055#
#"sum of radii "=2+6=8#
#"since sum of radii"< d" then no overlap"#
#"smallest distance "=d-" sum of radii"#
#color(white)("smallest distance")=9.055-8=1.055#
graph{((x-3)^2+(y-7)^2-4)((x-4)^2+(y+2)^2-36)=0 [-20, 20, -10, 10]}
