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]}
